The Beer Identity

Guest Post by Willis Eschenbach

It’s morning here in Reno, and I thought I’d write a bit more about the Kaya Identity and the Beer Identity. My last post about the Kaya Identity was controversial, and I wanted to see if I could clarify my point. On the last thread, a commenter did a good job of laying out the objections to my work:

Sorry but I think you’ve all entirely misunderstood the point of the identity. The Kaya identity is a means of communicating the factors of which CO2 emissions are comprised, in order to explain the physical levers that are available if one wishes to control an economy’s CO2 emissions.

These are analogous to mathematical factors, for e.g. 6 = 3 x 2. This illustrates that 2 and 3 are factors of 6. This doesn’t prove anything mathematically – it’s just an identity. But it is informative nonetheless. It tells you that 6 can be broken down into factors of 2 and 3. In the same way, CO2 emissions can be broken down into factors of population, GDP per population, energy per population, and CO2 emissions per energy.

That is a very clear and succinct description of what the Kaya Identity is supposed to do. The only problem is … it doesn’t do that.

Let me take another shot at explaining why. To start with, the Kaya Identity states:

CO2_{emissions} = Population * \frac{GDP}{Population} * \frac{Energy}{GDP} * \frac{CO2_{emissions}}{Energy}

where “CO2 emissions” are the CO2 emissions of say a given country; “Population” is the population of that country; “GDP” is gross domestic production of the country, which is the total value of all the goods and services produced; and “Energy” is energy consumed by the country.

The Beer Identity, on the other hand, states the following:

CO2_{emissions} = Population * \frac{GBP}{Population} * \frac{Energy}{GBP} * \frac{CO2_{emissions}}{Energy}

Where all of the other variables have the same value as in the Kaya Identity, and “GBP” is gross beer production by the country.

I think that everyone would agree with those two definitions. They would also agree that both of them are clearly true.

Now, as the commenter said above, when we write

6 = 3 x 2

it tells us that six can be broken into factors of three and two. Not only that, but we can say that for example

(6 * 0.9) = 3 x (2 * 0.9)

That is to say, if we change one of the factors by e.g. multiplying it times 0.9, the total also changes by multiplying it by 0.9.

But is that true of the Beer Identity? Suppose we get more efficient at producing beer, so that it only takes 90& of the energy to make the same amount of beer. Will this decrease our CO2 production by 10%, such that

CO2_{emissions}*.9 = Population * \frac{GBP}{Population} * \frac{Energy}{GBP}*.9 * \frac{CO2_{emissions}}{Energy}

Well … no. It’s obvious that changing our beer production to make it 10% more energy-efficient will NOT reduce CO2 emissions by 10%. In other words, despite it being unquestionably true, we have no guarantee at all that such an identity actually reflects real world conditions. And the reason why it is not true is that it doesn’t include all of the factors that go into the emission of the CO2, it only includes the beer.

Now, I can hear you thinking that, well, it doesn’t work for gross beer production, but it does work for gross domestic production.

And up until yesterday, I was convinced that the Kaya Identity doesn’t work for GDP any more than it works for GBP … but I couldn’t figure out why. Then yesterday, as I was driving along the Lincoln Highway on my holiday with the gorgeous ex-fiancee, I realized the factor that is missing from the Kaya Identity is … me, driving along the Lincoln Highway on my holiday with my gorgeous ex-fiancee.

The problem is … I’m burning energy, and I’m emitting CO2, but I’m not part of the GDP. I’m not producing anything with that energy—no goods, no services, nothing. My CO2 emission is a part of the total, but it is not included in the Kaya Identity anywhere.

So in fact, the Kaya Identity does NOT tell us the “factors of which CO2 emissions are comprised, in order to explain the physical levers that are available if one wishes to control an economy’s CO2 emissions” as the commenter said.

And that to me is the problem with the Kaya Identity. It’s not that it is false. It is that it gives a false sense of security that we’ve included everything, when in fact we haven’t. And because it looks like mathematical truth, we have folks who take it as gospel, and object strongly when it is questioned or laughed at. Steven Mosher thinks I was wrong to laugh at the Kaya Identity, and I do respect his and the other opinions on the matter, his science-fu is strong … but in fact, the Kaya Identity is no more complete than the Beer Identity, which is why I laughed at it.

So that’s my objection. It’s not that the Kaya Identity is false. It can’t be, by definition its true.

It is that it gives the false impression of mathematical certitude, the impression that it represents the real world, the idea that it identifies the “factors of which CO2 emissions are comprised” … but it doesn’t. This false certainty, because people think it’s “mathematically demonstrable”, leads people to not question whether it applies to the real world.

Finally, in closing let me repeat something I said in the comments on the first thread, which likely didn’t get seen because it was somewhere down around the five hundredth comment.

l hear rumblings that people think that Anthony shouldn’t have published this piece of mine, or should disavow it in some fashion. This totally misunderstands both what Watts Up With That (WUWT) does, and Anthony’s position in the game. The strength of WUWT is not that it is always right or that it publishes only the best stuff that’s guaranteed to be valid.

The beauty and value of WUWT that it is the world’s premier location for public peer review of climate science. On a personal level, the public peer review afforded by WUWT is of immense use to me, because my work either gets falsified or not very quickly … or else, as in this case, there’s an interesting ongoing debate. For me, being shown to be wrong is more valuable than being shown to be right. If I’m right, well, I thought so to begin with or I wouldn’t have published it, and it doesn’t change my direction.

But if someone can point out my mistakes, it saves me endless time following blind alleys and wrong paths. And my opinions on the Kaya Identity may indeed be wrong.

There is much value in this public defenestration of some hapless piece of bad science, whether it is mine or someone else’s. It is important to know not only which ideas are wrong, but exactly why they are wrong. When Anthony publishes scientific claims from the edges of the field, generally they are quickly either confirmed or falsified. This is hugely educational for scientists of all kinds, to know how to counter some of the incorrect arguments, as well as giving room for those unusual ideas which tomorrow may be mainstream ideas.

So it is not Anthony’s job to determine whether or not the work of the guest authors will stand the harsh light of public exposure. That’s the job of the peer reviewers, who are you and I and everyone making defensible supported scientific comments. Even if Anthony had a year to analyze and dissect each piece, he couldn’t do that job. There’s no way that one man’s wisdom can substitute for that of the crowd in the free marketplace of scientific ideas. Bear in mind that even with peer review, something like two-thirds of peer-reviewed science is falsified within a year, and Anthony is making judgements, publish or don’t publish, on dozens of papers every week.

So please, dear friends, cut Anthony some slack. He’s just providing the arena wherein in 2014 we practice the blood sport of science, the same sport we’ve had for a few hundred years now, ripping the other guys ideas to bits, also known as trying to scientifically falsify another person’s claims that you think don’t hold water. It is where we can get a good reading on whether the ideas will stand up to detailed hostile examination.

It is not Anthony’s job to decide if mine or any other ideas and expositions and claims will withstand that test of time … and indeed, it is often of value for him to publish things that will not stand the test of time, so that we can understand exactly where they are lacking.

So please don’t fill up the poor man’s email box with outrage simply because you think a post is not scientifically valid enough to be published. Send your emails to the guest author instead, or simply post your objections in a comment on the thread. Anthony is just providing the boxing ring. It is not his job to predict in advance who is going to win the fight. His job is to fill the fight cards with interesting bouts … and given the number of comments on my previous post about the Beer Identity, and the huge popularity of his website, he is doing it very well.

Regards to each and all of you, my best to Mosher and all the folks who have commented, and my great thanks to Anthony for the huge amount of work he does behind the scenes to keep this all going. I’m on the road again, and my highway CO2 emissions are still not included in the Kaya Identity …

w.

As Always: If you disagree with something that someone has said, please have the courtesy to quote their exact words. It avoids much confusion and misunderstanding.

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524 thoughts on “The Beer Identity

  1. I think you need to come up with a better objection than “I’m burning energy, and I’m emitting CO2, but I’m not part of the GDP. “

    If you filled up at a gas station and paid money for your fuel, your CO2 producing activity most certainly is part of the GDP. If you stop and by a sandwich, that activity is also part of the GDP, and if the ingredients of that sandwich were farmed and transported using fossil fuel, then it contains an implicit CO2 production as well.

  2. The Kaya identity is even more useless than the Drake equation. With the Kaya identity, anything can be put on the right-hand side, because they are not factors when they are on both the numerator and denominator. They are all 1.

  3. “The problem is … I’m burning energy, and I’m emitting CO2, but I’m not part of the GDP.”

    Is not the retail purchase of gasoline part of the GDP?

  4. So please, dear friends, cut Anthony some slack. He’s just providing the arena wherein in 2014 we practice the blood sport of science, the same sport we’ve had for a few hundred years now, ripping the other guys ideas to bits, also known as trying to scientifically falsify another person’s claims that you think don’t hold water. It is where we can get a good reading on whether the ideas will stand up to detailed hostile examination.

    It is not Anthony’s job to decide if mine or any other ideas and expositions and claims will withstand that test of time … and indeed, it is often of value for him to publish things that will not stand the test of time, so that we can understand exactly where they are lacking.

    ====================================================================
    Awhile ago the merits of “blog-review” vs “pal-review” was discussed.
    Genuine peer-review is, of course, of great value. “Blog-review” can also be a great augment to that. It opens the paper or post to input from experts in other fields whose input may be of value.
    (If others had seen Mann’s work before it became gospel….)
    The downside is the authors would have to put up with comments from people like me. 8-)

  5. Yes, 6 = 3 x 2 is an identity.

    Yes, 6 = 3 x 2 / 5 * 5 is an identity, just not a useful one.

    Yes, 6 = 3 x 2 / 5 * 5 / 4 * 4 is an identity, just not a useful one.

    The Beer Identity and the Kaya Identity are both *not* useful. Dividing one side of an identity by one, no matter how many times, does not add utility.

  6. Willis,
    I am sure that *you* may not be contributing to the GDP by driving down the road, but your car and everything that supports the operation of that car are providing a service to you. And that service can be part of the GDP, can it not?
    I read somewhere that GDP is actually not a good indicator of useful economic activity because it includes all of the goods and services produced, whether useful or not. Cleanup after a natural disaster is part of the GDP. So is war.
    -BillR

  7. slp says:
    July 12, 2014 at 9:11 am
    The Kaya identity is even more useless than the Drake equation. With the Kaya identity, anything can be put on the right-hand side, because they are not factors when they are on both the numerator and denominator. They are all 1.
    =====
    This is my take on it, especially after reading Anthony Watt’s link on the equation formulation at http://www.manicore.com/anglais/documentation_a/greenhouse/kaya_equation.html. The equation will always be true because it’s not 6=3×2, it’s 6x1x1x1x1x1x1x1 and so forth. If you divide by something and then immediately multiply by it again you have returned to whence you started.

  8. You most certainly are a part of the GDP. You bought the gas and that was registered as part of the GDP when it was manufactured and sold to you. It is a decent assumption that most gas sold will be consumed in internal combustion engines and CO2 thereby released into the atmosphere, so your emissions are lumped in with mine and everyone elses.

    Dave

  9. I guess whoever dreamed up the Kaya identity was trying to appear clever. Claiming it identifies the levers available to control CO2 emissions – meaningless BS.

  10. The same problem of not representing the real world can be seen with climate models and the passionate belief some have in them. In fact many models in many fields.

  11. Long time lurker but a first time commenter. I read both posts. I think Willis has done a good job here of raising valid questions.

    In the previous post both Willis and Anthony displayed what I think is integrity by admitting their first ideas were wrong. That’s something you won’t get from the climate crowd like Michael Mann who still thinks his hockey stick is valid science. McIntyre and McKitterick showed it was flat wrong. He’ll never admit it though.

  12. I confess to not reading through all the comments on the other thread so this point may have already been made.

    I think there is an inherent fallacy in dsimissing this “entity” with the argument that items above and below the line cancel each other out. I don’t know that there is any real world evidence to support the idea that if population increases by 10% that GDP per capita (GDPC) decreases by 10%. My sense is that the new additions to the population will end up contributing to the GDP at roughly the same rate as the overall GDPC, keeping GDPC roughly the same. If so, then an increase in population will not have a null effect on the formula.

  13. The Kaya Identity shows wat happens if you change the contributing parameters, if population goes up, another factor needs to go down if you want to keep the total emission constant. In a world with a continuous global recession and population increase the total emission could remain constant.
    A very useful tool.

  14. I wasn’t very good at math but I think that if you write X= Y*z/y*w/z*x/w
    The ys,zs,and ws all cancel each other, and all you are left with is x=x . You can substitute any terms you want and it doesn’t make any difference. So you have CO2 emissions= CO2 emissions. So what we know that.

  15. My complaint is the evil simplicity inherit in such nonsense. Writing up some silly little line of mathematics, with values attributed to less than a handful of things… this is a reflection? Bollocks. The problem with science and all other analyticals are that they are still much too simple and pedestrian. How do I feel today? Feelings=S (stuff) multiplied by T (things) aggregated by O (others) trumped by W (weather). It’s bright and sunshiny. I feel like crap. But the lake is nearby and I’m gonna have an awesome day! Predict that. I dare you. Come up with an “Al Gore Rhythm” that predicts what sort of day I’m going to have. YOU CAN’T! I’m too complex. The world I live in is too complex. Am I to believe that my own little body, my own little brain is more complex than the entire world’s climate? Before your answer, know this: I’ve already got a big enough ego. No need to feed.

  16. As presented, the Kaya Identity is both useless and not the original formula.

    “it is developed so that the carbon emission calculation becomes easy”

    It does nothing of the sort. All terms cancel out except “global co2 emissions” which you must guess at, enter, and get back what you entered.

    The original thinking was rather a lot like the Drake equation. “It states that total emission level can be expressed as the product of four inputs: population, GDP per capita, energy use per unit of GDP, carbon emissions per unit of energy consumed.”

    http://en.wikipedia.org/wiki/Kaya_identity

    Well that’s pretty simple. CO2(total) = P * G * E * CO2 (per E).

    But that’s not the IDENTITY. The Identity is bogus.

    The Formula is better. Here is a calculator that does NOT use the output as the input, but more correctly expresses carbon-per-unit-of-energy as the last term

    http://forecast.uchicago.edu/kaya.html

    You can plainly see that somewhere along the line the idiots that edited Wikipedia got the formula wrong and so do many other people, like this one, which goes to great lengths to make sure you know that he knows it is wrong and yet right all at the same time:

    http://www.manicore.com/anglais/documentation_a/greenhouse/kaya_equation.html

  17. Gary says “Come up with an ‘Al Gore Rhythm’ that predicts what sort of day I’m going to have.”

    Well, you did cause me to think about Willie Nelson’s “Sunny Side of the Street!”

  18. I think the problem with the Kaya identity is that it states the “bleeding obvious.” All it says is that total CO2 emissions are a function of energy use per capita, the amount of CO2 emitted per unit of energy per capita all multiplied by the population.

    We also don’t know what the amount of CO2 emitted per unit of energy will be in the future only what it is at present and is therefore useless as a policy tool. Look at the US CO2 emissions per capita – they have been going down. Who would have predicted that coal would be replaced by shale gas?

    Somebody mentioned the Drake equation. That was useless because we don’t know (and are unlikely ever to know) some of the terms, and the Kaya identity is useless because the parameters constantly change with time in ways that cannot possibly be predicted.

  19. Willis,

    You REALLY should preface this entire topic by pointing out that:
    1) human CO2 emissions comprise approximately 2% of TOTAL global CO2 production,
    2) therefore this discussion is pretty much like arguing about how many angels dance on the head of a pin.

    Humans always like to think of themselves as important. However, in this case, humans are pretty much as significant as the rounding error. But I agree with you that attempting to model complex systems with a simple equation is bound to fail to predict aspects of that system’s behavior.

  20. Willis, you are correct that the kaya identity is useless.

    There are lots of things in GDP that do not cause carbon emissions. There are lots of carbon emissions not accounted for in GDP. Therefore, there is no linear equation describing a relation between the two. To pretend that such an equation exists is useless.

  21. About that Pielke piece. http://rogerpielkejr.blogspot.com/2014/06/clueless-krugman.html

    “As an identity, it is expressed –> CO2 = P * GDP/P * E/GDP * CO2/E (where P is population and E is energy consumption). The math here is simple. Increases in GDP, all else equal, mean that CO2 emissions go up.”

    Yes, the math is simple, and if you increase GDP it STILL CANCELS.

    I think my PhD buddy calls this “Harvard Stupid”.

    Pielke did what nearly everyone does — Transforms the text into a formula that does not capture the text.

    “population * GDP per capita * energy intensity of the economy * carbon intensity of energy”

    The problem is expressing each term as a ratio of the other terms. That makes it inherently reflexive or self-dependent (circular) and it DOES matter how you actually do this. The carbon intensity of energy is PER UNIT of each.

  22. Willis Eschenbach: despite it being unquestionably true, we have no guarantee at all that such an identity actually reflects real world conditions.

    True. Use of equations requires constant checking of how well the equations fit the reality.

    From the other day: Here’s why I laughed. Lets apply the usual rules of math to that equation. We know that if a variable occurs both on the top and bottom of a fraction, we can cancel it out. Starting from the left, Population on the top cancels Population on the bottom. Then GDP on the top cancels GDP on the bottom. Then Energy on the top cancels Energy on the bottom … and we’re left with …

    CO2_{emissions} = CO2_{emissions}

    Pretty profound, huh? CO2 emissions are equal to CO2 emissions. Who knew?

    Making sure that the unit ratios cancel properly is a reasonable first step on checking the credibility of the equation. You showed that the units cancel properly, so LHS CO2 can be computed from the formula on the RHS.

    So you have an equation that reasonably can be used to predict annual CO2 production from a total count (population) times 3 ratios, and can reasonably be used to predict the effects of changes in the terms on the RHS..

    As you wrote, you could put in any total (area in km^2, say, or area planted in soybeans, or area irrigated — you stayed with population, actually, and I generalized by noting that the total can be changed as well as the ratios), and three ratios (starting with GDP/area, etc), and you would still have a reasonably accurate model for annual CO2 production, assuming that the 4 terms on the RHS can be known with reasonable accuracy. The usefulness of such an equation would depend on how well one could model, estimate, know etc changes on the RHS. Area of a country or region is hard to change, absent war, but area devoted to irrigation could be increased or decreased, as could area devoted to growing soybeans. Energy devoted to irrigation, or whatever, could be analyzed, and improved. Thus, with reasonable care in estimating the terms on the RHS, and reasonable care in estimating possible changes, you can get reasonable estimates of the prospects of reducing, or increasing, annual CO2 emissions.

    However, as you wrote, you could with comical or mocking intent put ridiculous terms on the RHS, which creates a new identity that is totally without any value. Whether you have a useful equation or a ridiculous equation is your choice.

    In like fashion, one can note that the instantaneous acceleration of an interplanetary probe is the vector sum of the instantaneous accelerations due to diverse forces, such as rocket thrust, gravitational pulls from the sun and from Jupiter, and so on. If you put ridiculous entities on the RHS, you get fairly ridiculous equations: knowing the instantaneous acceleration, you could write it as the vector sum of all sorts of stuff, and the equation would still be accurate, at that instant, despite being totally worthless for predicting the trajectory of the interplanetary probe.

    Whether you choose to use a reasonable equation in a reasonable manner or a ridiculous manner is, I repeat, a human choice, not an intrinsic flaw of the equation, or of other people who use it.

  23. And that to me is the problem with the Kaya Identity. It’s not that it is false. It is that it gives a false sense of security that we’ve included everything, when in fact we haven’t.

    That isn’t what the paper said it was doing:

    The simplest way to describe the deep decarbonization of energy systems is by the principal drivers of energy-related CO2 emissions—for convenience, since the focus of this chapter is on energy systems, we simply refer to them as CO2 emissions.

    CO2 emissions can be expressed as the product of four inputs: population, GDP per capita, energy use per unit of GDP, and CO2 emissions per unit of energy:

    CO2 emissions = Population x (GDP/Population) x (Energy/GDP) x (CO2/Energy)

    If we take as given the population trajectory and assume a rising trajectory of GDP per capita in line with a successful economic development program, then CO2 emissions are driven mainly by two factors: Energy/GDP and CO2/Energy. The first term is the energy intensity, meaning the amount of energy per unit of final output. The second term is the carbon intensity of energy.

    Since GDP is defined as the sum total of all economic activity and every unit of economic activity requires some amount of energy to produce there is nothing wrong with the identity.

    There is plenty of room to quibble with how those two values are comprised, and how they should be calculated. Saying the identity was a “basic math error” is simply an error on your part and a misrepresentation of what they were trying to do.

  24. Anyway, it still “feels wrong”. When I play chess I do much better when I heed the “feel”, that non-linguistic part of my brain that calculates in the background fast and parallel, a quick approximation of wrongness or rightness. I really don’t see why GDP is in there. Change the unit of currency and suddenly GDP changes — but what really changed? Nothing.

    This whole thing exists because there is no way to know any of these factors other than the fourth term, the carbon dioxide produced per unit of energy produced for each method of producing energy. Since that isn’t actually specified, your MIX of energy sources makes the fourth term highly variable.

  25. Quote my words
    You laughed because of the cancelling of units.
    As I said
    Not because it didn’t capture everything.
    And when you drive you buy gas.
    If no one bought gas what would happen to gdp

  26. Matthew R Marler says: “LHS CO2 can be computed from the formula on the RHS.”

    Okay, I double dog dare you to actually DO that with THIS equation, using “Global CO2 emissions” as the numerator of the 4th term.

    Duh.

    That’s what you are trying to calculate.

    What you put anywhere else doesn’t make the slightest difference since every numerator has a matching denominator.

    That’s math.

    But I sense your intention — you intend for GDP in the second parmater to NOT be GDP in the third parameter!

    That’s NOT math.

  27. I don’t understand what the argument is about. The “Kaya equation” is mathematically meaningless. Standard mathematical reduction removes “Population”, “Energy” and “GDP” from the equation, leaving “CO2 = CO2″.

    While this is obviously true, it is meaningless.

    (Anyone not understanding “mathematical reduction” it means any expression “A / A” can be removed from an equation without changing the truth of the equation. This also includes such expressions as “(A / B) * (B / A)” – that also equates to “1”.)

  28. Willis Eschenbach: And that to me is the problem with the Kaya Identity. It’s not that it is false. It is that it gives a false sense of security that we’ve included everything, when in fact we haven’t.

    If you could come up with some examples of such false sense of security, you might have a case.

    Note that with the more complex applications of the general circulation models, there have been examples of a false sense that the model outputs are accurate. Much more complicated models, but it could be the case that the models themselves are complete and accurate, but the parameter values (analogous to the ratios in the RHS of the equation under discussion) might be wrong, either a few of them or many of them, by small or large amounts.

    In lots of places it has been shown that correct applications of reasonable rules sometimes produce unreasonable results. By the usual rules of English, “grue” and “bleen” could be words, it just happens that they are not.

    But if someone can point out my mistakes, it saves me endless time following blind alleys and wrong paths. And my opinions on the Kaya Identity may indeed be wrong.

    Where you are wrong is in your inference that, because the Kaya identity may be used ridiculously, it must necessarily be ridiculous. But where you choose ridicule, others may choose utility.

    I think that point doesn’t make sense to you (a guess!) because from the start you see no utility in reducing anthropogenic CO2 (another guess! or perhaps a reasonable inference?). On that I agree with you (or with my guess about you), but the flaw is not in the equation.

  29. Vince Causey says:
    July 12, 2014 at 9:53 am I think the problem with the Kaya identity is that it states the “bleeding obvious.” All it says is that total CO2 emissions are a function of energy use per capita, the amount of CO2 emitted per unit of energy per capita all multiplied by the population.

    The interesting thing about the politicians and progressive scientists making an equation putting me and my family on one side and carbonic acid molecules on the other side is that politicians and progressive scientists are creating an equation with me and my family on one side and carbonic acid molecules on the other side.

    And as far as energy use, we all have energy inputs into our homes in the form of electricity, and we all have sunlight shining on our property. The intelligent use of that energy is going to vary greatly between families, with different results. One family uses the energy largely in spending recreational time together, which has value for them, and the other family may also be producing food, artistic works such as music and illustrations, recreation, and education. So the use of the energy will have widely differing results, and these values are not calculable by government because they have lost the plot. (:

  30. Clearly both identities need a additional factor, (1 + epsilon). And some way of estimating the size of epsilon. And in the case of the Beer identity, lots and lots of field work.

  31. Let’s try a simpler case – a total CO2 generated by cars:

    CO2 = (number of cars) * (CO2 per car), or
    CO2 = (number of cars) * (CO2 / (number of cars))

    True or false – Does it matter if the cars are driven at all? Does it respect the efficiency of car engines?

  32. The gas and the sandwich do not get credited to W. That would be double counting as the cook and big oil already got credit. The only thing added is the joy of travel. Hard to put a number on that. I agree the GDP was not increased.

  33. Michael, Okay, I double dog dare you to actually DO that with THIS equation, using “Global CO2 emissions” as the numerator of the 4th term.

    this is the equation:CO2_{emissions} = Population * \frac{GBP}{Population} * \frac{Energy}{GBP} * \frac{CO2_{emissions}}{Energy}

    What exactly is the problem? If you can reduce the CO2emissions/energy you can reduce total global CO2 emissions. The equation is more useful on a regional or gdp segment view: such as reducing the energy input to agriculture, or the energy cost of transportation, or the CO2 output per energy in Sweden. No particular change can make much difference to total global CO2, but that is not a flaw in the equation.

  34. Again?!?!? Willis really has explicit a mistake which on the last thread I just assumed he knew was not right. I assumed he was making a joke, but apparently he really believes it.

    Willis writes that in the Kaya identity:

    ‘“Energy” is energy consumed by the country.’

    Willis writes that in the Beer identity:

    ‘all of the other variables have the same value as in the Kaya Identity, and “GBP” is gross beer production by the country.’

    To be clear then, “Energy” in the Kaya identity means ALL energy consumed by the country. “Energy” in the Beer identity has, to quote Willis’ words ‘the same value’. That means that “Energy” in the Beer identity means ALL energy consumed by the country.

    Then Willis asks ‘Suppose we get more efficient at producing beer, so that it only takes 90% of the energy to make the same amount of beer?’

    But what does “energy” mean here. Energy means ALL energy consumed by the country.

    That’s one remarkable advance in brewing technology you’re proposing – especially if making beer consumed less than 10% of the country’s energy in the first place. Not one an advance in brewing that reduces the energy used to make beer by 10%, but an advance in brewing that reduces the whole country’s consumption by 10%.

    But IF such a remarkable advance did take place THEN the Beer identity would be entirely realistic.

    Willis writes ‘Well … no. It’s obvious that changing our beer production to make it 10% more energy-efficient will NOT reduce CO2 emissions by 10%.’

    This statement is plain wrong.

    Changing our beer production in such a miraculous way would indeed reduce CO2 emissions (from energy) by 10%.

  35. “such as reducing the energy input to agriculture”

    We already have reduced the energy input into agriculture, reduced the needed land for agriculture, reduced the needed labor hours, and increased the output to 2 to 5 times yields known in the 1940’s.

    You cannot reduce the energy input into agriculture without greatly increasing labor and lowering yields. So you actually did not reduce energy at all but shifted it to manual labor and got much less per acre. It is a hidden shift to hand weeding and greatly increased energy input. That is the truth about organic agriculture and why it provides only 1% of the crops in the US.

  36. Thanks Willis, GDP is an interesting parameter, mass destruction, i.e. riots, wild fire, so on, will cause GDP to rise, if the effected society rebuilds.
    So vandalism is arguably good for GDP.
    The reaction to your earlier post is very interesting, almost an “Ah Ha” moment.
    We see a major communication breakdown.
    Why?
    From my perspective, algebra requires agreed definitions and internal consistency, therefore I too LOL at the self cancelling Identity.
    From others POV apparently the defined terms are flexible, CO2=Not CO2, but some other definition, yet they insist the equation as expressed is valid.
    Either my reasoning processes are completely askew or we are not using the same language.
    Now as a cynic with experience as a govt employee, I lean toward the belief this corruption of language(Algebra in this case) is deliberate.
    Policy meetings are a revelation that should be compulsory viewing for all taxpayers.
    This “Identity” has all the earmarks of bureau speak, as it says nothing of value, while appearing to contain information.

  37. Matthew R Marler says:
    July 12, 2014 at 10:02 am

    I agree Mathew – I too could not believe this piece of nonsense! These “equations” could be wrongly attributed to anything, not just “Beer or Kaya Identity”, whatever they are. CO2 would always = CO2, because all else cancels out!! I think we need to drop this silly subject pronto.

  38. All should know that Willis E. publishes here without prior approval from Anthony or anyone else — in other words, he has authority to put up his own work directly without oversight.

    This is not the first time he has gone off half-cocked and shot himself in the foot with something ill-considered. Nor will it be the last.

  39. To put it more simply:
    I have no pb with the kaya identity unless someone pretends to use it in the real world.
    Doing so, one makes 2 mistakes: One conceptual, and one operational.

    – Conceptual: The fact it is (trivially) true in algebra does not mean it has anything to do with actual physical relationships in the real world. Hence the “gross beer production” joke and alike.
    Someone has demonstrated this very clearly in another thread: Take V (voltage), R (resistance) and I (intensity), we know that V = R * I for good physical and scientific reasons.
    But I can also write a beautiful “kaya-like identity” : V = R * ( I / R ) * ( V / I )
    This unfortunately demonstrates nothing (and even *shows* nothing) with any physical meaning in the real world, even if I suspect some relationship between V, R and I, because it holds true whatever V, R and I, which is not very useful when, say … building electrical circuitry…

    – Operational: One can pretend to “find” some useful relationship between variables only by doing a wrong (illogical) usage of the identity, by voluntarily (but silently) forgetting one term of each pair. Let me explain: In the above V = R * (I / R) * (V / I), I can proudly tell that “V is proportional to (I / R)”, which is NOT true. Doing so, I am only ignoring the remaining R and I factors elsewhere. If I was to use them correctly, it would turn that V is proportional to R * (I / R) / I, or more simply that V is proportional to … 1. Bravo.

    So, unless someone finds some strong physical relationship between CO2 and whatever in the real world, the kaya identity is only a trivial and pretentious algebraic thing.

    My 2 cents.

  40. Well, as the EU has included blow and hookers in its GDP, we can clearly now fix the Global Warming thing by using less blow and hookers because that way we would reduce our GDP. BTW we would get the added advantage of less addiction and STD’s.

  41. The problem is … I’m burning energy, and I’m emitting CO2, but I’m not part of the GDP. I’m not producing anything with that energy—no goods, no services, nothing. My CO2 emission is a part of the total, but it is not included in the Kaya Identity anywhere.

    Since GDP includes government spending, it is even worse than you imagine.

  42. UnfrozenCavemanMD says:
    July 12, 2014 at 9:09 am

    I think you need to come up with a better objection than

    “I’m burning energy, and I’m emitting CO2, but I’m not part of the GDP. “

    If you filled up at a gas station and paid money for your fuel, your CO2 producing activity most certainly is part of the GDP. If you stop and by a sandwich, that activity is also part of the GDP, and if the ingredients of that sandwich were farmed and transported using fossil fuel, then it contains an implicit CO2 production as well.

    Thanks, Caveman, but nope. I’m buying fuel inter alia from Saudi Arabia, where it is counted correctly as part of their GDP, and thus it can’t be part of ours.

    w.

  43. That’s one remarkable advance in brewing technology you’re proposing – especially if making beer consumed less than 10% of the country’s energy in the first place. Not one an advance in brewing that reduces the energy used to make beer by 10%, but an advance in brewing that reduces the whole country’s consumption by 10%.

    It seems that you are being deliberately obtuse.

  44. Willis Eschenbach says:
    July 12, 2014 at 10:57 am

    I’m buying fuel inter alia from Saudi Arabia, where it is counted correctly as part of their GDP, and thus it can’t be part of ours.

    =======
    Well, no, not really. GDP is economic value added during a period. The distributor of the gasoline added value (i.e. made money) by making the gasoline available to you where you needed it (unless you sucked it out of the ground in Saudi Arabia, and refined it yourself, which I don’t think you did).

  45. Also, Caveman, since you asked for a better example, consider things like the flaring of gas from oil wells, or the CO2 coming from underground coal fires in Pennsylvania, India, and China. None of them are in the Kaya identity, but all of them emit copious quantities of CO2.

    w.

  46. I don’t know anything about Kaya’s Identity but shouldn’t it be:
    CO2 emissions = Population * GDP * Energy use
    _______________________
    Energy efficiency

    Where efficiency is based on CO2 generated per unit of energy?
    cn

  47. Willis sez: “I’m buying fuel inter alia from Saudi Arabia, where it is counted correctly as part of their GDP,”

    Consider the concept of “value added” (which in some nations is taxed via the appropriately named “Value Added Tax”. Buy raw ore, crude oil, fresh hides, etc. GDP goes up. Smelt, refine, tan, etc, GDP goes up. Pour ingots, distill gas, cut the leathers… ship a barge load, truck out fuel to the gas station, and sew up a vest. At each stage the value goes up.

    In VAT calculating nations the tax is deferred until the ultimate consumer buys the finished goods, at which point all accumulated values are realized for the goal of extracting the taxable value.

    If Willis buys gas in California, Saudia Arabian sheiks, Liberian oil tanker operators, US coastal refiners, chain gas station retailer management, and the local Exxon (or whatever) franchisees have all contributed to “value added”, getting the product to market. EVERYBODY along the way, Saudi to the local station, has contributed to GDP. (and may be said to be paying taxes on the profits or income of such, even though the US does not have a VAT)

    But not Willis. He bought the gas and produces nothing measured in the GDP. No value is added in moving the consumer from here to there and back.

    The trip may be the most valuable precious memory the pair of them will ever make. But it’s not measured in the GDP.

    http://www.jfklibrary.org/Research/Research-Aids/Ready-Reference/RFK-Speeches/Remarks-of-Robert-F-Kennedy-at-the-University-of-Kansas-March-18-1968.aspx

    ” Gross National Product counts air pollution and cigarette advertising, and ambulances to clear our highways of carnage. It counts special locks for our doors and the jails for the people who break them. It counts the destruction of the redwood and the loss of our natural wonder in chaotic sprawl. It counts napalm and counts nuclear warheads and armored cars for the police to fight the riots in our cities. It counts Whitman’s rifle and Speck’s knife, and the television programs which glorify violence in order to sell toys to our children. Yet the gross national product does not allow for the health of our children, the quality of their education or the joy of their play. It does not include the beauty of our poetry or the strength of our marriages, the intelligence of our public debate or the integrity of our public officials. It measures neither our wit nor our courage, neither our wisdom nor our learning, neither our compassion nor our devotion to our country, it measures everything in short, except that which makes life worthwhile. And it can tell us everything about America except why we are proud that we are Americans.”

    Kennedy was, as far as I can tell, incorrect on the specifics but correct in the general trend. The GNP (now GDP) is a flawed measure. Willis is incorrect as well about where and which nation his purchase is credited, but I think he is correct, like Kennedy, in his general point.

  48. Willis is basically correct. THE major problem is that GDP is a very wobbly concept. The secondary problem is that those number don’t exit globally, only locally. GDP is DOMESTIC product of a country. Every country is different.

    So take, for example, an organic farmer in a 3rd world country. Their energy input is very low. Yet they produce. Compare with USA farming by agribusiness, huge fossil fuel inputs. Next take a look at my garden in the back yard. I often have decent “produce” from my garden, but it is not part of “GDP”. All three of us can grow corn, but with drastic variation in energy / corn. My product is not part of the “money” economy and uncounted. The farmer in 3rd Land may be bartering, or in a cash and not counted market. (For example, what is the contribution of Mexican M.J. to GDP?…) So which of this is in GDP? What energy intensity ought to be used?

    Similar issues exist for doing dishes, working on your car, doing your own home repairs, etc. etc.

    So Willis, driving down the road, is “manufacturing a good or service”. An enjoyable day out. He can make that same “day out” of joy with one gallon, or ten gallons, depending on when and where he goes. That “production” is not captured in GDP. The quantity of fuel used is highly variable per unit of GPP (Gross Personal Product ;-) made). The SALE of the gasoline shows up in GDP, but what if it sits in a can in the garage as part of earthquake / generator prep? Does it enter GDP a second time if used to run the lawn mower? (It does if the lawn mower user is billing you… but not if you do your own mowing…)

    That’s the problem with GDP that Willis is pointing out. Dumping the gas on a bonfire is great fun, and makes little product past the entertainment (that isn’t part of GDP), while that same gas in a Taxi is counted as part of GDP again when the taxi reports the transaction.

    A similar problem is the Broken Window Fallacy. If Willis spends his day breaking windows, then fixing them, that shows up in GDP as an increase, yet no net increase in real net wealth or utility happened. So it works both ways. Some things are GDP but net negative “production”. Others are net positives but not in GDP. It is basically wrong to use GDP in the way used in the formula, and certainly wrong to use it as a global term.

    Basically, I can make lots of nonsense equations that are clearly a valid math identity. Doesn’t give them any meaning our utility.

    Per the question of folks using for shown correct results: Well, it IS the case that CO2=CO2, so I’d expect the results to be right… Calculate something based on CO2 with that equation, it darned well better get the CO2 number right…

  49. progressive grantees who wish to manipulate all activities based on a scary looking scientific mathematical ‘model’. It does not say much about poor Central Americans countries who have low GDPs but use slash and burn agriculture every dry season.

    Nor does it say much about the American economy of which the GDP is mostly printed dollars propping up 5 sacred banks and a balloon stock market.

    You are correct in addressing and calling this out NOW..before the Krugman Progressives weigh out our grocery sacks and tax us accordingly… so they can line the pockets of Central American Despots and buy beach houses next to Charlie Rengels’ place.

  50. You can rearrange the equation in a multitude of ways, since terms cancel out. One way would be to say, ultimately, that co2 emissions = GDP * (dollar-of-GDP-specific co2 emissions).

    Of course, the problem is that the last term, the dollar-of-GDP-specific co2 emissions*, can only be calculated by dividing the total amount of co2 emissions by the GDP. Consequently the rewritten identity predicts nothing.

    The value of an “identity”, at least in accounting, is that you can have a basis to reconcile independently-determined terms in the identity. When you can’t get terms in the identity other than by “begging the question” (i.e. only as a function of other terms in the identity), then the identity is as useful as any other tautology.

    *Why call them “carbon” emissions, when the molecule is represented as CO2, with twice as many oxygen atoms as carbon? Logically, we should call them “oxygen” emissions, in preference to “carbon” emissions, if we want not to call them carbon-dioxide emissions.

  51. Willis writes:

    ‘I’m buying fuel inter alia from Saudi Arabia, where it is counted correctly as part of their GDP, and thus it can’t be part of ours.’

    Although I don’t think your specific point about fuel from Saudi Arabia is all that strong when argued through to the end, this general line of thinking is far more productive.

    As I said on the last thread, I think the Kaya identity (like the beer identity) is true as a matter of arithmetic, but the real question is whether it is useful.

    The Kaya identity will be useful in so far as GDP is a useful measure of economic activity. Of course GDP has all sorts of limitations. As someone said above, it doesn’t capture your enjoyment from driving, and might go up as a result of repairing damage from a riot.

    These criticisms of GDP have been extensively developed – mostly by greens and lefties as it happens, although also by Austrian economists and others.

    But it would be a useful starting point to recognise that GDP does have at least some use as an indicator of overall economic progress – more than GBP, anyway. Many economists in the private sector as well as academics have been working for decades on trying to develop meaningful, reliable figures.

    Notably, the concept of GDP has been developed decades before the climate debate took off.

    It turns out that some thought has gone in to the problem of cross border trade (such as with Saudi Arabia), problems such as the fact that currencies change value (as was raised in the last thread) and adding up GDP of different countries (as raised by E. M. Smith above).

    If you want to try developing a measure of economic progress that is better than GDP, then go ahead, I would be eager to see the results. (Although I would recommend you glance back first and see how economists have thought about concepts such as value added.)

    But if we have an improved economic measure (IEM) we could still get a new identity, just as true as the Kaya or beer idendity:

    CO2 emissions = population * (IEM / population) * (Energy / IEM) * (CO2 / Energy)

    and I would argue that this would be more useful to the extent that IEM was better than GDP.

  52. Steven Mosher says:
    “If no one bought gas what would happen to gdp”

    I do believe it would go down and the equation in question would suggest CO2 emissions would also go down. How about that, an equation that reduces to X=X revealing useful information.

    Kinda like:
    Seconds = Seconds
    Seconds = Minutes X Seconds/Minute
    Seconds = Hours X Minutes/Hour X Seconds/Minute
    Seconds = Days X Hours/Day X Minutes/Hour X Seconds/Minute
    Seconds = Years x Days/Year X Hours/Day X Minutes/Hour X Seconds/Minute
    etc. etc.

    So how many seconds in 3 years? Use the equation above that reduces to X=X without even knowing the answer to begin with but knowing how many seconds are in a minute, minutes in an hour, hours in a day, and days in a year you can calculate it. Amazing!

    BUT: How many hours are in a day? 24 you say? Well, is that exactly 24? What difference does it make? For 3 years not much, but what if you were calculating for a few hundred million years? Hmmm. The accuracy of my equation is dependant upon the accuracy of the factors within it. Surprise surprise.

  53. I didn’t see it at first, but I see now how the Kaya Identity can be useful in showing the relationships of factors that go into the output of human produced CO2 and in estimating how changing one factor can affect that output. I’m not sure how good such estimates are in the real world, but it does seem to give you a rough idea of what goes into raising or lowering human-caused CO2. If you change the CO2 emissions per energy used, for example, by switching from coal to natural gas, it gives you an estimate on how much that change will reduce CO2. That can be useful to those who care about human produced CO2 emissions. Those who don’t care will not find it useful. (It doesn’t tell you about natural CO2 emissions, such as that from the oceans, volcanoes, wild fires, changes in plant growth, insects, or bacteria. But those are pretty much outside our control anyway.)

    As for all identities being “useless”, as many commenters seem to think, that is not the case. For example, consider the problem of determining the number of truck trailers needed to haul a given amount of goods. To keep it simple, let’s say the goods are already boxed and on pallets. You need to ship 96 pallets across country. If the pallets and trailers are all standard size, you can use the following formula to calculate the number of truck trailers you need: t = p/(p/t). You know that you can fit 24 pallets on a trailer, so the pallets per trailer (p/t) = 24. Now we can solve for t by plugging in what we know: t = 96/24 or t = 4. So you need 4 truck trailers to haul 96 pallets. As you can see, the formula is useful even though it can be reduced to an identity of t=t.

    The real world doesn’t come in standard sizes like trailers and pallets, but rough estimates can still be useful.

  54. Following Matthew R Marler at 10:02 am …

    Let “instantaneous acceleration of an interplanetary probe” = A
    We can now say: A = Pop * GDP/Pop * Energy/GDP * A/Energy
    Clearly, we can increase the instantaneous acceleration of an interplanetary probe by increasing our standard of living! It will also increase if the population goes up.

    Why is the Kaya Identity any more meaningful than this?

  55. Willis,

    Thankfully, you have dropped the mathematically ignorant look ma, everything cancels so it must be wrong and I must laugh assertions. It would have been manly of you to have acknowledged the error instead of simply walking away from it, but at least you did walk away from it.

    Unfortunately, that means that you’re doubling down on the remainder of your argument. That has two main components. The first is your “Beer Identity”. The second is used to enable the first, and is your use of equivocation, playing on the ambiguity of the vernacular descriptions of the KI terms. Both are fallacious.

    Addressing the second first, we have this assertion from you:

    “To start with, the Kaya Identity states:

    where “CO2 emissions” are the CO2 emissions of say a given country; “Population” is the population of that country; “GDP” is gross domestic production of the country, which is the total value of all the goods and services produced; and “Energy” is energy consumed by the country.

    That is not exactly correct. It is certainly good enough for people who read the whole paper and understand the KI and who are using it and discussing it in good faith. Unfortunately, that doesn’t describe how you are approaching it.

    In the KI, “CO2 emissions” are not “the CO2 emissions of say a given country”. They are more specifically the energy-related CO2 emissions of a given country’s economic production.

    Similarly, in the KI “Energy” is not “energy consumed by the country”. It is more specifically the energy consumed by the country for economic production.

    You equivocate on these terms, switching back and forth between specifics of your choosing. You then think you have proved something when you point out the bust that you have fabricated by playing with the definition of terms. This is how you hide the fact that your “Beer Identity” is mal formed, when the KI is not. Uncovering your ruse is as simple as putting descriptive subscripts on the terms. The KI thus becomes:

    And your “Beer Identity” kludged from the KI becomes:

    With the equivocation removed, the reader now easily sees that some things in your “Beer Identity” look a little odd. A couple of your terms express a ratio of one item defined relative to GBP vs another item defined relative to GDP. Those terms don’t seem particularly useful, as (unlike all of the terms in the Kaya Identity) they don’t have any meaning WRT things we commonly talk about in the real world.

    More importantly, the reader now easily sees that there are some things in your “Beer Identity” that are very different than you describe them. This is shown in you supposition:

    Suppose we get more efficient at producing beer, so that it only takes 90& of the energy to make the same amount of beer.

    And in your subsequent restatement of the “Beer Identity” with the figure 0.9 thrown in, which allegedly represents an increase in the energy efficiency of beer production.

    The problem is, there is no term for the efficiency of producing beer in your “Beer Identity”. That term would look like this:

    And that term is not to be found anywhere in your “Beer Identity”. So, your claim that your application of the 0.9 factor to your “Beer Identity” represents a 10% increase in beer production energy efficiency is simply false. You did not do the math correctly.

    I trust that the website owner will now add to this post the entirely accurate sub heading:

    “Willis Eschenbach’s “Beer Identity” carbon equation and criticism of the “Kaya Identity” has been falsified – due to a stupid maths error“.

  56. Willis writes:

    ‘consider things like the flaring of gas from oil wells … None of them are in the Kaya identity, but all of them emit copious quantities of CO2.’

    Why could they not be included?

    Take the example of flaring from oil and gas production. The WG III IPCC report chapter 7 writes:

    ‘Overall, fossil fuel extraction and distribution are currently estimated to contribute 5%–10% of total fossil‐fuel related GHG emissions (Alsalam and Ragnauth, 2011; IEA, 2011a; Burnham et al., 2012). Emissions associated with fuel production and transmission can be reduced through higher energy efficiency and the use of lower carbon energy sources in mines, fields, and transportation networks (IPIECA and API, 2007; Hasan et al., 2011), the capture and utilization (UNECE, 2010b), or treatment (US EPA, 2006; IEA, 2009a; Karacan et al., 2011; Karakurt et al., 2011; Su et al., 2011) of methane from coal mining, the reduction of venting and flaring from oil and gas production (IPIECA and API, 2009; Johnson and Coderre, 2011), and leak detection and repair for natural gas systems (Goedbloed, 2011; Wilwerding, 2011).’

    and later

    ‘Whilst growth in GHG emissions is expected as countries build their industrial 
    base and consumption moves beyond meeting basic needs, minimizing this trend will involve 
    exploring new opportunities for scaling up modern energy access where possible by embracing 
    cleaner and more efficient energy options that are consistent with regional and global sustainability 
    goals. One such opportunity is the avoidance of associated natural gas flaring in oil‐ and gas‐
    producing developing countries where venting and flaring amounts to 69% of world total of 
    150 billion cubic metres–representing 1.2% of global CO2 emissions (Farina, 2011; GGFR and World 
    Bank, 2011). For a country such as Nigeria, which flares about 15 billion m3
     of gas–sufficient to meet  its energy needs along with the current needs of many neighbouring countries (Dung et al., 2008, this represents an opportunity towards a low‐carbon pathway (Hassan and Kouhy, 2013).’

    http://report.mitigation2014.org/drafts/final-draft-postplenary/ipcc_wg3_ar5_final-draft_postplenary_chapter7.pdf

    I’m not interested in taking the IPCC’s policy advice – that’s NOT why I quoted the lines here. I’m not saying reducing these emissions is necessarily the way to go (although in some cases it may be a good idea regardless of CO2).

    I also have not read their discussions on flaring in any depth – I’m sure I’ve missed other places where they discuss it.

    I’m quoting the lines only to show that there doesn’t seem to be a technical problem in counting up emissions from flaring as part of emissions from energy production.

    Willis was claiming that they are not (or cannot?) be counted. This looks to me like evidence that they can be (and are?) counted.

  57. Chief, such a great post we will add it to the GDP, just this once. lol

    However, remember this formula: organic=weeding by hand. Please reconsider this statement:
    “So take, for example, an organic farmer in a 3rd world country. Their energy input is very low. Yet they produce.”

    Since the weeds must be controlled by hand, then you cannot say that their energy input is very low, because it will require hundreds of hours to weed that same hectare by hand. These hours of labor and the lesser yield produced cannot be dismissed as “energy input which is very low in organic farming” except by sleight of hand. And perhaps this is a problem with the whole Kaya Identity: by forcing a hand labor economy, with hundreds of hours required to get the same yield in agriculture, the energy appears to be reduced but has been greatly increased.
    *********
    Additional information from pesticideguy:
    There are an avg of 300,ooo weed seeds in every acre of land.
    These weed seeds can remain dormant easily up to 70 years.
    Organic = human drudgery of bending over weeding, usually by women and children.

    This also causes cultivated fields to be left and new fields to be cleared because the weeds get to numerous to be dealt with by hand in C and S American farms, for example. So the energy input is out of this world for organic farmers because you must consider how the weeds were controlled, and that is through hand weeding within the rows, even if a tractor is used between rows. Controlling weeds by hand also permanently limits any farmer in Africa or S America to about one hectare, because hand weeding any more land than that is impossible.

  58. Someone has doubtless pointed this out already, but fuel consumption is part of personal consumption expenditures which is the largest component of GDP=PCE+I+G+E (see basic economics texts). This is actually the way US GDP is calculated. It’s not so obvious when GDP is calculated in terms of production.

    This is not to say that GDP necessarily accounts for all CO2 emissions (as in ‘externalities’).

  59. Correction

    Additional information from pesticideguy:
    There are an avg of 300,ooo weed seeds in every acre of land.

    It should say that there are an avg of 300 million to a billion weed seeds in every acre of land. Ty.

  60. For anyone not following what this Kaya formula actually does, put numbers in for Energy, Population, GDP and CO2. Any numbers will work, 10, 24, 36, 40 – whatever. See what happens. The end result will always be CO2 = CO2. Then explain how this is useful – in any real world situation.

    If you missed the point, no matter what values you put for Energy, Population, GDP and CO2, the answer will always be the value of CO2.

  61. Arthur says:
    July 12, 2014 at 12:03 pm
    =================

    As I mentioned above, it is useful if you have determined the quantities that you plug into the identity independently of each other, otherwise it is not.

    Consider the identity:
    Balance in my bank account = (statement balance) + (deposits made since statement) – (withdrawals made since statement).

    Ultimately, this says “balance in my bank account = balance in my bank account”.

    However, since you can determine each quantity independent of the others, when you go through the motions and find out that it does NOT balance, you look for an error.

    Millions of accountants do this every day, and have done so for a good number of years. They don’t seek to derive new insight from the identity itself, they use the identity as a way of validating independent observations of the factors in the identity.

  62. Both the Kaya Identity and the Beer Identity are tautologies. There is no useful information in either. Put in CO2 in the right side of the equation. Multiply and divide CO2 by numbers evaluating to one. Voila, you get CO2 on the left. Multiplying and dividing CO2 by *any* set of numbers evaluating to one, and you will get CO2 on the left.

  63. Willis is completely missing the point of this identity. The Kaya Identity has 4 terms and shows that an UP or DOWN change in any of those 4 terms will result in a corresponding change, in the same direction, in the CO2 output. It doesn’t include coefficients or non-linearities. It doesn’t communicate the _magnitude_ of change, only its _direction_.

    Willis says:
    “Well … no. It’s obvious that changing our beer production to make it 10% more energy-efficient will NOT reduce CO2 emissions by 10%.”

    You are correct, Willis, It will not reduce CO2 emissions by exactly 10%. But that’s where you are getting lost, You are looking for this identity to predict precisely how large the change will be and it simply doesn’t attempt to do that. The identity only shows you the _direction_ off the affect, not its magnitude.

  64. Willis stated:

    but in fact, the Kaya Identity is no more complete than the Beer Identity, which is why I laughed at it.
    ——————-

    I was thinking the Beer Identity looked incomplete, …. cause it appears to me the equation is missing an important factor, ….. which is, …… *(GBP)(BECO2)

    Wherein GBP is the gross beer production ….. and BECO2 is the …… beer emitted CO2.

    But then all I know for sure is the “beer drinking” part of the equation.

  65. kabend says:
    July 12, 2014 at 10:53 am

    V = R * ( I / R ) * ( V / I )

    To rephrase it and expose the subtlety:

    The equation:

    V = I / R

    Expressed simply as an identity:

    V = R * ( I / R ) * ( V / I )

    Then verbosely expressed as a dimensionless identity,

    units of voltage = units of resistance * (units of current / units of resistance ) * (units of voltage / units of current )

    defines a dimensionless unit (of voltage) on the LHS and nothing else. It does not resolve to a value expressed in this form.

    V = I/R produces a quantity expressed in volts where variable I is a quantity of current, and the variable R is a quantity of resistance

  66. This has been quite the can of worms. If you want to consider the flaring of wells as outside the Kaya identity. then isn’t most, like 96%, of CO2 outside the identity?

  67. Sheesh. Mr. Kaya must be laughing his ^%$* off at how seriously everyone is taking his equation. The thing is nothing more than a political statement masquerading as a scientific formula. It deserves ridicule, not serious thought.

  68. I’m exhausted with this two part Kaya post. I have this strange, surreal feeling that I’m watching a Bill Murray movie. . . I just can’t figure out whether it’s “Groundhog Day” or “What About Bob?”

    Cheers, enjoy the WC consolation match!

    Dan

  69. I may be missing the higher point about the Kaya identity equation, but I agree with Willis it is practically useless. In order determine a value, we must already know so much about energy consumption, GDP, and CO2 emissions and their relationships it would be more direct to just use total fossil fueled power consumption and the rate of CO2 per unit of power consumed (gas, oil, coal)? Also, Kaya implies that for any society or country the rate of non-GDP power consumption will be the same. Comparing for example China and in the U.S., the Kaya calculation of CO2 would skew the numbers favorably to the U.S., because although not included in the GDP, power consumed (and thereby CO2 emitted) for personal auto use, home heating, recreational uses, etc.) per GDP would be much higher in the U.S. than in China. Of course, the power used in producing the energy is included in GDP, but the potential energy in the fuels burned is not. I think that with the huge amount of data already available about the hot-potato issue of CO2, concepts such as the Kaya identity have no practical or scientific value.

  70. Reply to Kate Forney.
    There is a HUGE difference. In your formula none of the items reduce out of the equation. I’m amazed that people don’t get this.
    If you said “bankbalance = myweight * (bankbalance / myweight) you would have an equivalent to the Kaya equation. The equation is certainly true and the result would be bankbalance but – and here is the whole point – the value of myweight does not affect the outcome.
    So it is with the Kaya equation.
    Do it yourself to see. Plug in arbitrary values into the formula. No matter what values you put in, the result can only be the value of CO2.
    No matter what values are put into the equation for Population, Energy and GDP, the result will ALWAYS be CO2.

  71. In order to consume a car, insurance, gas, sandwiches, beer, sunglasses, and the road you’re driving on those goods must first be produced. The total value of goods produced must equal total expenditures. You can calculate GDP by adding up either one (or incomes for that matter).

  72. Willis, your driving around consumes energy and provides you are your ex-fiancé some pleasure sightseeing, but seeing pleasant (or otherwise) sights is not part of the GDP. In other words you have emitted CO2 without changing the GDP. That falsifies the original equation.

    Several people above (lots actually) have said that buying gas means adding to the GDP. Well, the service portion of it does. The raw fuel does not as it originated outside the US, probably. So what? The main point is that 100% of the CO2 from that gasoline is producing nothing of ‘benefit’ and all of the ‘correctors’ admit that it contributes to the GDP a bit at least. Energy consumed, CO2 emitted, disproportionally small GDP increase, no product. You could have purchased the gas and not burned it so the purchased is added to the GDP, but the CO2 may or may not have been emitted, and no productive work was accomplished. More falsification of the concepts behind the Kaya equation.

    These facts demonstrate a couple of things: GDP is not necessarily related to the useful application of energy sources that produce CO2, after all the GDP did not rise ‘efficiently’. One can easily think of ways to emit CO2 without providing any GDP increase such as burning a forest or breaking windows to demonstrate the broken window fallacy. And lastly one can show that an increase in population that wastes more energy driving around for no GDP gain is not working in the formula as mooted..

    CO2 Total = CO2 per something where the number of somethings is finite and countable + CO2 per something else where the number of something elses is finite and countable + CO2 per additional thing where the number of additional things is finite and countable . As you correctly and reasonably point out, putting the CO2 both above and below the line is silly – it don’t add up. Why? Not just because the CO2’s cancel (if the fractions are multiplied) , but because the units are not in agreement.

    Tons of CO2 = Dinosaurs per Tuesday * Tuesdays per Dinosaur * CO2 in tons

    That doesn’t demonstrate anything. It is logically and mathematically true, but examined rationally it is pointless.

  73. Wouldn’t one need to know all of the inclusions that go into calculating GDP before they could exempt their activity from the equation? Likewise, the Kaya equation places value on economies that can create higher GDP with lower CO2 emissions which both presently and unfortunately incentivizes paying more than we should for energy. The US political risk on coal should cause its price to plummet so keep building those coal plants China your ROI can only get better.

  74. Matthew R Marler says:
    July 12, 2014 at 10:16 am

    By the usual rules of English, “grue” and “bleen” could be words, it just happens that they are not.

    Sorry to disagree with you but “grue ” is a valid english word old fashioned but still in the dictionary meaning ” a shiver or shudder; a creeping of the flesh” origin middle english also a part of gruesome

  75. Look carefully at GDP. It is a B/S number. (Google DJIA and GOLD) In the USA, Magically it has increased over the last 5 years. Why has it increased? Because of Quantitative Easing. If you look at GDP for the USA in terms of GOLD or any other hard currency, it is NOT increasing. The fed has been pumping close to a 100 Billion Dollars a Month into the USA, devaluing the Dollar and giving the FALSE impression that the GDP is increasing. Even the DJIA is not worth what it was in ounces of GOLD ten years ago. HOW is this factored in the equation. How does the equation correct for Government Meddling of the inputs to the equation? A valid “Identity” would eliminate inflation from the factors.

    What is going to happen to the USA, in the real world, when the cost of energy “Necessarily Skyrockets” and it becomes to expensive to manufacture anything in the USA (as is beginning in many countries that have pushed this green agenda further than the USA)? Yes, CO2 emissions in the USA may go down, but what about India and China when they start making everything the USA consumes? What is going to happen the GDP of the USA then?

  76. Arthur says:
    July 12, 2014 at 12:54 pm
    ====
    Well, yes, actually they do.

    And, in your example, if indeed I could independently ascertain myweight and the ratio bankbalance/myweight (call it “rho”), where rho could be read directly (i.e. without reference to bankbalance or myweight), instead of indirectly (by dividing bankbalance/myweight), then the identity is useful, because your independently-read rho, when multiplied by your independently-determined myweight, should give your independently-read bankbalance.

    For example, it’s possible to estimate mean density without calculating both mass and volume and dividing, even though “density=mass/volume”. So if I had my estimate of density, then measured mass and volume, and my estimated density did not equal my estimated mass divided by my estimated volume, I would know that I had a problem.

    On the other hand, if you determine rho by dividing bankbalance by myweight, or estimate density by dividing mass by volume, then you are right, you’ve gained nothing by proceeding with the reconciliation.

    Now, NB, I’m not saying that there IS a way to directly read rho, but have just posited such for the purpose of argument.

    Just as in my post above, were it possible, through some hitherto-unknown technology, to read directly (or, compute, via some variables that do not include either GDP or total co2 emissions), the term (co2 emissions/$GDP), which I termed “dollar-of-gdp-specific co2 emissions”, but serves the same illustrative purpose as my “rho”, above) then the identity co2 emissions = GDP * (dollar-of-gdp-specific co2 emissions) would be useful. However, since we must determine dollar-of-gdp-specific co2 emissions by dividing co2 emissions by GDP, we do not achieve anything useful by carrying out the exercise.

    Again, I’m not saying it’s possible to directly come up with the gdp-specific co2 emissions. In fact, the only known way of doing that is to carry out out the division. So, irrespective of any algebraic cancellation, *were it possible* to get independent measures of any (most, actually) of the terms in the Kaya identity, then it would be useful. I leave it as an exercise for the reader to determine if any of the factors can be read without measuring the numerator and denominator and dividing.

    I certainly don’t *believe* per-capita GDP can be determined without separately determining GDP and population, neither do I *believe* energy used per dollar of GDP can be determined without determining total energy used and total GDP. Maybe co2 emissions be unit of energy can be approximated without measuring aggregate co2 emissions and aggregate energy consumption, but I would question how accurately.

    Thus, in my little world, I don’t see how the Kaya identity can be of particularly much benefit as each of the ratios must be determined by division — there is no other means available, and thus the cancelling problem that you describe is manifest.

    I apologize if my previous, rather more brief, explanations were somewhat cryptic.

  77. Arthur says:
    July 12, 2014 at 10:10 am

    I don’t understand what the argument is about. The “Kaya equation” is mathematically meaningless. Standard mathematical reduction removes “Population”, “Energy” and “GDP” from the equation, leaving “CO2 = CO2″.

    Your misunderstanding comes from misreading. It is “Kaya Identity”, not “Kaya equation”. There have been multiple examples given of what identities are and now they differ from a mathematical formula, but this is not being understood by the identity deniers. (I say, that’s a joke, son)

    The Kaya identity if perfectly valid as a mathematical tool when used correctly. Whether it is useful for analyzing the import of CO2 to GDP growth, population growth, and rate of energy consumption is certainly debatable. The difficulty thus far has been the lack of scope of the variables, GDP, population, and energy. Even if scoped there is still the disagreement of the validity of the scope. In the PNAS and Roger Pielke Jr. analyses the scopes have been identified but with no consensus, but that does not prevent discussing the results. As a visualization tool it is perfectly suited to what-if’ing a problem where ranges of reasonable data are tested.

    The calculator here is buggy but does give you a sense of impact the variables impose on the results.

    http://forecast.uchicago.edu/kaya.html

    For example, set the end population to the current population, 6 billion (population does not change over time) the result is just what you expect – a flat line. That is an unrealistic value, though, unless there is a pandemic or catastrophic world war. Reasonable best, and worst case values can be plugged in to see what happens over the period of analysis.

    It may not be obvious, but the analysis is done over the time period 1900 – 2100, and observed is shown by red dots ending at Y2K, and the errors are obvious though the trends are close.

  78. Kabend 10:53 says
    “V is proportional to (I/R),” which is NOT true.

    Being a New Yorker, I felt it incumbent on me to write something obnoxious like, “The proportionality constant is R*R, which is a constant, as those little lines someone drew around the circumference of my resistors tell me.” But then, a light bulb went off in my head: I doubled my thinking intensity, but the flow of ideas increased by only 25%! Sincerely, thanks for a great idea for helping my students understand that V = IR is not a complete statement of Ohm’s Law.

    Now, this brings us to use of Kaya-Beer and the use of GDP as a surrogate for carbon dioxide emissions, or, for that matter, tree rings for temperatures. As noted above, the nonlinearities and excluded variables kill you. I never did like the Chain Rule anyhow. Fortunately (?), the UN realizes that a “carbon” tax based on GDP is a non-starter, as the PRC is still a developing nation, and would never go for it. Unless Kerry was a better diplomat around the time of his Jakarta speech than he was a Climate Scientist.

  79. Matthew R Marler says:

    July 12, 2014 at 10:16 am

    Willis Eschenbach: And that to me is the problem with the Kaya Identity. It’s not that it is false. It is that it gives a false sense of security that we’ve included everything, when in fact we haven’t.

    If you could come up with some examples of such false sense of security, you might have a case.

    OK, so my neighbor and I, both driving the same model new car that we bought last Thursday, go on a 500 mile (each) trip. We each burn close to the same amount of fuel and emit close to the same amount of CO2.

    But, I bought gasoline from an entirely US company, gas that came from US wells and was refined in the US. My neighbor bought gasoline from Citco – oil from Venezuela.

    How, then, could we both be considered having equal impact on the US’s GDP?

    Just wonderin’.

  80. Kate Forney says:
    July 12, 2014 at 1:22 pm
    I certainly don’t *believe* per-capita GDP can be determined without separately determining GDP and population, neither do I *believe* energy used per dollar of GDP can be determined without determining total energy used and total GDP.

    For purposes of understanding the relationships, assumed values of GDP and population can be used. For purposes of policy actual values should be used. If actual values are not available then the process is invalid except as an exercise.

  81. Astonishing. The number of people and comments taking this kaya-thing seriously. And I suspect it was the objective of this tautology: do not think about logical or physical reality of the thing (it has not), just react to the usual keywords as GDP, energy, efficiency, etc… and focus on the agenda they have put straight into the equation. And it works.

  82. Here is another “identity” along the lines of what dp and John West were explaining
    G = M / MPG
    where G is gallons of gasoline consumed
    M miles in trip
    MPG vehicle mileage in miles per gallon of gas consumed
    Which when you look at the terms
    (Gasoline consumed) = (miles traveled) / (miles traveled per gallon consumed)
    Whoopie, we now have
    (Gasoline Consumed) = (Gasoline Consumed)

    So, the “identity” tells us that the gasoline used for a given trip is the gasoline used for a given trip. Big whoop.

    I put “identity” in quotes since this is really a DIMENSIONAL EQUATION that lets me determine how much gasoline I will need for the 230 mile trip from my place in Southern California to Las Vegas. (I know what kind of MPG my car gets.) You can argue all you want about how useful the equation might be if you have no clue as to how you get MPG for your car. I know what MY car gets in fuel economy.

    Anyway, the “Kaya Identity” is NOT an identity but a DIMENSIONAL EQUATION. And the REAL question is: How do you measure CO2 emissions per GDP? (And is that even a worthwhile measurement?)

  83. Are there any factors in this equality from natural CO2 sources or is it assumed that only man’s contributions really count? How would that look? .95 natural components and .05 anthrocentric components?

  84. dp says:
    July 12, 2014 at 1:38 pm

    For purposes of understanding the relationships, assumed values of GDP and population can be used. For purposes of policy actual values should be used. If actual values are not available then the process is invalid except as an exercise.

    ===============

    Why yes, thank you for that, although that is of only tangential bearing on my argument, except to illustrate that there is no way of ascertaining the ratios without first ascertaining the principal quantities and dividing, unlike, say density, mass and volume: It is possible to estimate density without first measuring mass and volume and then dividing. If you do so, then the tautology/identity/definition of density=mass/volume becomes a useful tool for you to check on the correctness of your three estimated quantities.

  85. It’s useful. It’s an analogy to the DuPont identity in finance.

    http://www.investopedia.com/exam-guide/cfa-level-1/financial-ratios/return-equity-dupont-system.asp

    For example one use was exposing Chinese plans to DOUBLE CO2s in their 5YP by rabbiting on about “intensity.” Looking at the factors IS useful.

    In your example, driving increases energy per unit of GDP for the economy as a whole. If there is more “recreational” energy use, that increases energy intensity.

  86. Well MY problem, with granting the “Kaya Identity”, with any credibility at all, is that ANYBODY can simply write his own product of factors; each of which is some ratio, that all conveniently, cancel via the Willis math; and simply concoct an illusion that some factor is a significant issue in climate.

    Take “Energy / GDP ” for example. What evidence is there that this is an important climate phenomenon. ??

    For starters, The USA is a big energy user; but we also have a big GDP; well we used to pre-Obama. We also don’t have that large a population, in World terms. So why is the USA the whipping boy in the pollution sweepstakes. and the USA is a net carbon sink, because of our agriculture and forestry. In fact we are the only large (land) one on the planet. Also, the USA spends vast amounts of its resources, which are energy intensive, on defence. much of that is to provide defence of others, who spend little of their own resources for their own defence; relying on the USA to bail them out.

    How do you compare the GDP and population, and petroleum based US economy, with the GDP. population, and cow dung fuelled economy of some other country.

    If energy consumption per GDP is an important factor to minimize, then PV and wind solar should be abandoned immediately. Natural gas and petroleum, are much more efficient at GDP production.

    No I put the Kaya Identity at about the same place as the Drake Equation (identity), as something to sit up and take notice of; pretty much idle nonsense.

    And that is a personal opinion. No great climate significance should be assigned to my opinion.

    g

  87. This is silly. Every single factor in both equations is cancelled out except for CO2 emmissions. For example you multiply by population, then divide by population. Population divided by population is one. Ever factor in the equation is treated that way except CO2 emmissions, so there is no handle to grab.

  88. I wasn’t very good at math but I think that if you write X= Y*z/y*w/z*x/w
    The ys,zs,and ws all cancel each other, and all you are left with is x=x . You can substitute any terms you want and it doesn’t make any difference. So you have CO2 emissions= CO2 emissions. So what we know that.

    The z/y and w/z and x/w are just representing ratio variables.

    Again, I will invoke the M&M’s example:
    You have crates (C crates), inside those crates there are boxes (B boxes). Inside those boxes, there are M&M’s packages (P packages), and of course, there are M&M’s (M M&M’s) inside of those.
    The number of M&M’s can be found by multiplying the number of crates by three rations: boxes per crate, packages per box, M&M’s per package. Those ratios can be represented by B/C, P/B, M/P

    Then:
    M = C * (B / C) * (P / B) * (M / P)

    Is this identity too trivial? Useless?

    The Kaya identity is even more useless than the Drake equation. With the Kaya identity, anything can be put on the right-hand side, because they are not factors when they are on both the numerator and denominator. They are all 1.

    The factors are population, gdp per capita, energy intensity of the economy and co2 intensity of energy. They are not all 1.

    Willis Eschenbach wrote:

    The problem is … I’m burning energy, and I’m emitting CO2, but I’m not part of the GDP. I’m not producing anything with that energy—no goods, no services, nothing. My CO2 emission is a part of the total, but it is not included in the Kaya Identity anywhere.

    Fuel is included in the gdp, duh.

  89. Curious George says:
    July 12, 2014 at 10:19 am

    Let’s try a simpler case – a total CO2 generated by cars:

    CO2 = (number of cars) * (CO2 per car), or
    CO2 = (number of cars) * (CO2 / (number of cars))

    True or false – Does it matter if the cars are driven at all? Does it respect the efficiency of car engines?
    *****************************************************************8
    Somehow we have all been blinded by the light of the Kaya Identity. I think everyone agrees it is an identity so it should be treated as such, true and worthless. Your case, the George Identity (?), if one knew two things to solve for CO2: (number of cars), and (CO2/(number or cars. I trust we can look up both items in a government publication. Say we want to reduce CO2, so we squint at the formula, scratch our heads, and try increasing the number of cars to see what that will do. It might not work but it is worth a try in the model, especially because it looks like if we get the CO2/car ratio down CO2 will decrease. I think it is working, lets increase the number of cars by a factor of 1000. A million. At this rate even our children won’t know what carbon dioxide gas is.

    The answer to your questions is, probably and Rome wasn’t built in a day.

    Really though, anyone could solve both the George Identity and the Kaya Identity just by knowing, ahead of time, CO2. Really really though you MUST know CO2 ahead of time to solve for CO2.

    Unfortunately the excellent George Identity isn’t going to change minds. It just doesn’t have that Kaya (identity) ring to it.

  90. “””””……dp says:

    July 12, 2014 at 12:21 pm

    kabend says:
    July 12, 2014 at 10:53 am

    V = R * ( I / R ) * ( V / I )

    To rephrase it and expose the subtlety:

    The equation:

    V = I / R ……””””””

    Well I don’t know at what school you studied Electricity, but a simple dimensional check would show you that V most certainly does not, nor cannot, be equal to I/R.

    For that to be true, I would have to have units of volt, instead of amp, and R would have to be a dimensionless number, instead of ohm; or at least R^2 would, since you have, in effect:-
    volt = (volt / ohm) /ohm = volt / ohm^2

    I have no idea what ohm^2 represents in electricity.

  91. Greg Smith says:
    July 12, 2014 at 1:44 pm

    Here is another “identity” along the lines of what dp and John West were explaining
    G = M / MPG
    .
    .
    .
    So, the “identity” tells us that the gasoline used for a given trip is the gasoline used for a given trip. Big whoop.

    Your example isn’t an identity, it is a mathematical formula, but if it were rewritten as an identity it would have told you that the left hand side is data in units of type gallon (vs furlongs, fortnights, parsecs, buckets, Hiroshima bombs), but not how many.

  92. george e. smith says:
    July 12, 2014 at 2:14 pm

    You’re correct – I miss managed a cut/paste from the OP’s post.

  93. Well MY problem, with granting the “Kaya Identity”, with any credibility at all, is that ANYBODY can simply write his own product of factors; each of which is some ratio, that all conveniently, cancel via the Willis math; and simply concoct an illusion that some factor is a significant issue in climate.

    See M&M’s example above, the ratios don’t cancel. This has been adressed multiple times.
    Look, all the ratios have a clear meaning and constitute the factors of energy-related co2 emissions. Find other variables with that characteristic.

  94. Anyway, the “Kaya Identity” is NOT an identity but a DIMENSIONAL EQUATION. And the REAL question is: How do you measure CO2 emissions per GDP? (And is that even a worthwhile measurement?)

    You do not have to measure that.

  95. climatereflections says:

    How would one go about actually *applying* the Kaya Identity?

    I’m struggling to see how it would work in practice.

    See J.K.’s example in the previous post by Willis.

  96. This is just very, very sloppy reasoning and formulation by Willis. And yes I’ll point out exactly where you’re wrong, Willis.

    To begin with:

    Willis Eschenbach says:
    July 12, 2014 at 11:02 am

    Also, Caveman, since you asked for a better example, consider things like the flaring of gas from oil wells, or the CO2 coming from underground coal fires in Pennsylvania, India, and China. None of them are in the Kaya identity, but all of them emit copious quantities of CO2.

    All of those terms, excepting possibly the underground fires as semi-natural causes, impact the carbon intensity term of the Kaya equation (CO2/Energy), so they DO show up in the equation in the average/aggregate. Others have pointed out your misunderstanding of GDP already.

    Now on to the truly sloppy math. Your GBP equation is fundamentally flawed for the simple reason that it captures CO2e,b, i.e. CO2 emissions due to beer and not total CO2 emissions. That is true for both the left and right hand sides of the equation. So when you make your efficiency savings the CO2e,b = 0.9*CO2e,b,original, but the TOTAL CO2e is not described or captured in the equation, so the supposed paradox simply doesn’t exist.

    D+ for effort but inattention to detail.

  97. The Kayla equation leaves out valuable input information. Carbon dioxide emissions come from nature as well as GDP generation activities. Carbon dioxide from burning fossil fuels is 10 billion tonnes per year. Loss of wetlands in just Brazil and Indonesia total 2.5 billion tonnes per year of carbon dioxide emissions. GDP implicitly implies human activities. The Kayla equation would have to be rearranged to a fixed (natural) + variable (human) term to be of any use for climate predictions involving GDP. GDP is not uniformly generated either. The 80-20 rule basically applies to GDP. Twenty percent of the population generate 80% of the GDP while 80% of the population generates 20% of the GDP. Thus, there is no direct 1 to 1 relationship as suggested by the Kayla equation between GDP and population increase. It would take more factors to come up with the proper coefficients to use for the GDPs in the 20% group and in the 80% group relative to energy use.

    I think that Willis wins this one while Mosh loses big time.

  98. This seems relevant:

    “In the space of one hundred and seventy-six years the Mississippi has
    shortened itself two hundred and forty-two miles. Therefore … in the
    Old Silurian Period the Mississippi River was upward of one million
    three hundred thousand miles long … seven hundred and forty-two years
    from now the Mississippi will be only a mile and three-quarters long.
    … There is something fascinating about science. One gets such
    wholesome returns of conjecture out of such a trifling investment of
    fact.”
    — Mark Twain

  99. Daniel G. says:
    July 12, 2014 at 2:06 pm
    Then:
    M = C * (B / C) * (P / B) * (M / P)
    *********************************************
    Why so many terms to prove your case? Why not just M = P * M/P ?
    Lets say M = the grand total final number of M&Ms we are trying to find without knowing ahead of time how many.
    Lets say P = number of packages = 100. (I like M&Ms)
    Lets say M/P = the grand total final number of M&Ms we are trying to find without knowing ahead of time how many DIVIDED BY number of packages = 100. Your know, just to be clear so no one thinks we have a 3 card monty going on here.

    Ah but it is a shell game, the M on the left is not the same M we have on the right is it?

  100. I just can’t see why people are finding this so hard.

    Let’s say we want to understand the number of web page hits.

    We can invent an identity:

    page hits = number of readers * ( page hits / number of readers)

    or we can invent another identity:

    page hits = national baked bean consumption * ( page hits / national baked bean consumption)

    These are both just as true as identities. You can plug the numbers in to either one and the arithmetic will come out correct.

    The first one might be more useful. Why?

    Because hits really are generated by readers, and it really does make sense to think of changing the two terms independently.

    If we want to raise the number of page hits then one way to think about doing it that might sometimes be helpful is to think about different strategies to either raise the number of readers or to raise the number of hits / reader.

    By contrast, I can’t think of any circumstance it would be useful to think about trying to raise the number of hits by having strategies to first increase national baked bean consumption and then to raise page hits / national baked bean consumption.

    What does this tell us about the Kaya identity? In my opinion, the question is whether the terms break down in a useful way.

    Kaya says:

    CO2 = population * (GDP / population) * (energy / GDP) * (CO2 / energy)

    Where CO2 is CO2 emissions from energy and energy is total energy production.

    If you are confused about cross border trade (and I think most objections about this above are just confusions) then just apply all numbers on a world wide basis.

    I would say that these factors are of some interest, whether we are trying to manipulate CO2 emissions or just to understand it.

    In particular:

    – (GDP / population) is a well known proxy for “living standards”. This the wealth produced and consumed per head. I would argue that even though GDP is an imperfect measure of wealth, rising GDP per capita is a fundamental measure of progress.

    – (energy / GDP) is a fundamental ratio for thinking about economic history. If you want to understand the industrial revolution, or pretty much all economic history since, you need to look at how amount of wealth that can be generated from each unit of energy has developed.

    – (CO2 / energy) shows in a basic way the effect of that different energy generation technologies (coal, oil, gas, nuclear, hydro, wind, etc) have on CO2 emissions.

    These are useful basic categories of economics and engineering. They have been known to be useful even before and outside the climate debate (maybe a little less so with CO2 / energy).

    By contrast, in Willis’ identity the basic ratios of

    (Gross Beer Production / population) and (energy / Gross Beer Production)

    are just not useful. (This is aside from his plain error of confusing energy used to make beer with total energy production).

    It’s as if he told people discussing how to get more page hits that their strategy of getting more hits by targeting more readers and more hits / reader must be nonsense, because their formula might just as well have been

    page hits = national baked bean consumption * ( page hits / national baked bean consumption)

    and baked beans plainly have nothing to do with it. (And then for good measure claiming that because the baked bean equation is absurd it must therefore be wrong – when or course it is perfectly true!)

  101. Does it respect the efficiency of car engines?

    Hey, take a look at one of your ratios: (CO2 / (number of cars))

  102. Douglas Adams already answered this question. It is turtles all the way down.

    What I find fascinating is the Rorschach type self identifying occurring because of this meaningless tautology.

    Anyone trying to defend the Kaya identity is either innumerate or has an agenda. The fact the IPCC uses this ‘equation’ to determine the impact humans have on the climate, invalidates everything done by the IPCC.

    I suppose it all comes back to the Rorschach test, people will see what they want to see.

  103. Anthony or Mods – The LaTex encoded formulas in my post above got stripped, leaving a long post that is more or less pointless as the referenced formulas cannot be seen. Could you

    a) replace the post above with the post appended below, which is identical except in that it replaces the stripped LaTeX references with hyperlinks that I have run thru the WWUT test page to ensure function

    b) point toward a couple tips on the best method for posting LaTex to WUWT?

    Thx

    ********

    Willis,

    Thankfully, you have dropped the mathematically ignorant look ma, everything cancels so it must be wrong and I must laugh assertions. It would have been manly of you to have acknowledged the error instead of simply walking away from it, but at least you did walk away from it.

    Unfortunately, that means that you’re doubling down on the remainder of your argument. That has two main components. The first is your “Beer Identity”. The second is used to enable the first, and is your use of equivocation, playing on the ambiguity of the vernacular descriptions of the KI terms. Both are fallacious.

    Addressing the second first, we have this assertion from you:

    “To start with, the Kaya Identity states:

    Kaya Identity EQN

    where “CO2 emissions” are the CO2 emissions of say a given country; “Population” is the population of that country; “GDP” is gross domestic production of the country, which is the total value of all the goods and services produced; and “Energy” is energy consumed by the country.

    That is not exactly correct. It is certainly good enough for people who read the whole paper and understand the KI and who are using it and discussing it in good faith. Unfortunately, that doesn’t describe how you are approaching it.

    In the KI, “CO2 emissions” are not “the CO2 emissions of say a given country”. They are more specifically the energy-related CO2 emissions of a given country’s economic production.

    Similarly, in the KI “Energy” is not “energy consumed by the country”. It is more specifically the energy consumed by the country for economic production.

    You equivocate on these terms, switching back and forth between specifics of your choosing. You then think you have proved something when you point out the bust that you have fabricated by playing with the definition of terms. This is how you hide the fact that your “Beer Identity” is mal formed, when the KI is not. Uncovering your ruse is as simple as putting descriptive subscripts on the terms. The KI thus becomes:

    Kaya Identity EQN w/expanded descriptions

    And your “Beer Identity” kludged from the KI becomes:

    Beer Identity w/expanded descriptions

    With the equivocation removed, the reader now easily sees that some things in your “Beer Identity” look a little odd. A couple of your terms express a ratio of one item defined relative to GBP vs another item defined relative to GDP. Those terms don’t seem particularly useful, as (unlike all of the terms in the Kaya Identity) they don’t have any meaning WRT things we commonly talk about in the real world.

    More importantly, the reader now easily sees that there are some things in your “Beer Identity” that are very different than you describe them. This is shown in you supposition:

    Suppose we get more efficient at producing beer, so that it only takes 90& of the energy to make the same amount of beer.

    And in your subsequent restatement of the “Beer Identity” with the figure 0.9 thrown in, which allegedly represents an increase in the energy efficiency of beer production.

    The problem is, there is no term for the efficiency of producing beer in your “Beer Identity”. That term would look like this:

    Energy Efficiency of Beer Production Term

    And that term is not to be found anywhere in your “Beer Identity”. So, your claim that your application of the 0.9 factor to your “Beer Identity” represents a 10% increase in beer production energy efficiency is simply false. You did not do the math correctly.

    I trust that the website owner will now add to this post the entirely accurate sub heading:

    “Willis Eschenbach’s “Beer Identity” carbon equation and criticism of the “Kaya Identity” has been falsified – due to a stupid maths error“.

  104. The Kayla equation leaves out valuable input information. Carbon dioxide emissions come from nature as well as GDP generation activities. Carbon dioxide from burning fossil fuels is 10 billion tonnes per year. Loss of wetlands in just Brazil and Indonesia total 2.5 billion tonnes per year of carbon dioxide emissions. GDP implicitly implies human activities.

    That is not in discussion, read the UN’s paper.
    co2 emissions accounting is more complicated, but that has nothing to with Kaya identity.

  105. The fact the IPCC uses this ‘equation’ to determine the impact humans have on the climate, invalidates everything done by the IPCC.

    Well, is that true? I didn’t read the AR5 WGII report, but can you find the chapter for me?

  106. Duke C. says:
    July 12, 2014 at 9:15 am
    “The problem is … I’m burning energy, and I’m emitting CO2, but I’m not part of the GDP.”
    Is not the retail purchase of gasoline part of the GDP?
    ———————————————————————————————————————–
    For the one-time purchase of a rake and a match, how much has been added to the GDP compared to the millions of piles of leaves that get burned every fall adding to the CO2 totals?

  107. Ah but it is a shell game, the M on the left is not the same M we have on the right is it?

    Kaya Identity is analogous, because we have been using symbolic a/b to represent a ratio variable.

  108. Daniel G, I understand your point about the M&M’s, but your analogy does not hold to the Kaya Identity situation.

    Specifically, in your M&M example each step of the way is necessary to getting the final answer.

    M = C * (B / C) * (P / B) * (M / P)

    BTW, what you should have written is M(Total) = C * (B/C) * (P/B) * (M(Individual)/P), as the M on the front is not the same as the M on the end.

    In the M&M’s example, we know the number of cartons, boxes, packages, and individual M&M’s per package. So, yes, we can do a simple multiplication equation and use the fractions to track the type of unit through the equation.

    This is *not* what is happening with the Kaya Identity. Specifically, the Global CO2 Emissions, which is our “answer” on the left hand side, is also an input on the right side. So in order to solve the “equation” we would already have to know the answer beforehand. This is very different from your M&M’s example.

    Furthermore, with the Kaya Identity, we could drop out any or all of the factors and it would not change things a bit. But in your M&M’s example, every reducing unit (C, B, P, M) is required, or you get the wrong answer. With the Kaya Identity, we could keep but one factor (just for sake of retaining the formula) and it would be just the same. For example, with just the last factor, we could say Global CO2 = Energy * Global CO2/Energy.

    With due respect, this is trivially true, but not particularly enlightening.

    The bottom line is that the Kaya Identity might be of some minor interest in flagging various global factors one might want to think about, but it is not a “calculation”.

    Your M&M’s example is therefore, respectfully, not relevant.

  109. I agree with JK. Identities are very common in mathematics, and are useful as long as you are better placed to estimate the terms on the right hand side than the term on the left. And as he says, each of the terms on the right is something that has been studied, of which there is historical experience. We have a better idea how they will behave than CO2 emissions. Progress.

    The fallacy with substituting GBP is that you don’t then have that knowledge of all the terms. OK, we know GBP/population, and energy/GBP, taking energy as energy to make beer. But we have no idea about (Total CO2 emissions)/(energy to make beer).

  110. co2(Total) = pop * (gdp/pop) * (energy/gdp) * (co2(for a unit of energy)/energy)

    Read the UN’s paper again:

    CO2 emissions per unit of energy

    Of course, if it is per unit of energy, then the co2 on the rhs (only for a unit) differs from the co2 on the lhs.

  111. climatereflections says in response to Daniel G:

    ‘Specifically, in your M&M example each step of the way is necessary to getting the final answer.

    M = C * (B / C) * (P / B) * (M / P)

    BTW, what you should have written is M(Total) = C * (B/C) * (P/B) * (M(Individual)/P), as the M on the front is not the same as the M on the end.’

    First, M at the beginning is the same as M at the end. M is the total number of M&Ms shipped and P is the total number of packets shipped.

    Second, we can collapse terms and still get a true identity:

    M = C * (P / C) * (M / P)

    or

    M = B * (P / B) * (M / P)

    where B is the total number of boxes and C is total number crates are both true.

    At least it looks like that to me. But probably I’m just innumerate, or seeing what I like in a Rorschach test, or there’s room for both points of view, or there’s no reason to think about this anyway, or I have an agenda. Or all of the above.

  112. Let’s see, Daniel:
    CO2_{emissions} = Population * \frac{GDP}{Population} * \frac{Energy}{GDP} * \frac{CO2_{emissions}}{Energy} from Willis article

    CO2 emissions = Population (varies by country) * GDP/Population (varies by country) * energy/GDP (varies by country) * CO2/energy (varies by country)
    How would you use the Kayla equation to predict the relationship between population and CO2 emissions? It certainly is not 10% growth in population = 10% more CO2 emitted.

  113. How would you use the Kayla equation to predict the relationship between population and CO2 emissions? It certainly is not 10% growth in population = 10% more CO2 emitted.

    Well, that is indeed the case if the ratios stay more or less constant.
    Of course, one could posit that such increase would change the other ratios, but that must be evaluated on a case-by-case basis.

  114. It seems climatereflections and JK are both correct. Cf using the (implied?) equation and JK the identity. Is the difference between “=” and “≡”?

  115. Daniel G:

    Thanks for your comments.

    “co2(Total) = pop * (gdp/pop) * (energy/gdp) * (co2(for a unit of energy)/energy)”

    That is somewhat better, yes. But we can still drop the pop and GDP completely from the above equation and get the same result.

    The following would be a different story:

    co2(Total) = # of persons * (GDP(individual)/person) * (# energy units/GDP(individual) * (co2/energy unit)

    If the latter is the way it is actually done, and if we know the three ratios individually: (i) individual GDP per person, (ii) # energy units per individual GDP, and (iii) amount of co2 per energy unit, then, yes, I agree the Kaya Identity would be a useful calculation. However, I have sometimes seen it described the way Willis described it, including on Wikipedia. So maybe all this disconnect is simply an issue of properly laying out the equation so that people can see the actual units? I am personally rather new to this issue, so if the equation in practice is calculated the way I laid it out in the second example above (and not as Willis and Wikipedia have described it), I’d be grateful to know.

    —–

    Incidentally, my comments thus far have been separate from the question of whether the Kaya Identity gives the right answer. Probably most people would agree that the amount of co2 per energy unit is readily calculable (within some reasonable margin of error). The other two factors: GDP per person, and energy units per individual GDP, are presumably subject to quite a bit more subjectivity. But that is a separate matter.

  116. Man, what a lot of verbage.
    It is really simple:
    When you’re in Kaya during the dry season, you drink beer.
    Flag is good and brewed in Ouagadougou..

  117. If you just reduce GDP by itself – What happens to CO2 emissions – Nothing.

    If you just reduce Population by itself – What happens to CO2 emissions – Nothing.

    If you just reduce Energy by itself – What happens to CO2 emissions – Nothing.

    If you reduce GDP, Population and Energy ALL at the same time – what happens to CO2 emissions – Nothing

    ————————————————–

    That is what is wrong with the equation.

    You cannot reduce CO2 emissions without reducing CO2 emissions.

  118. Let me rephrase my question, Daniel. How would you calculate the Kayla equation the very first time?

  119. Willis! You’re obviously a brilliant guy but you were wrong about this in the first post and you’re wrong about it again. The car you’re driving in, the road you’re driving on, the fuel the car burns, etc. are all components of GDP.

    The equation is valid but the only thing it does is approximate how much plant food we emit. It says nothing about whether that plant food will cause dangerous warming or how long it will remain in the atmosphere or anything else that might inform the debate.

  120. Hard to comprehend why there are hundreds of comments on such a simple thing. It must be this burning desire to see Willis fail, no matter how trivial the point. I haven’t read all the comments – who has? – so there is a slight possibility that the following is duplicated.

    This kind of expansion is similar to a chain rule expansion in calculus. For example we might write Newton’s second law in the following form (rectilinear motion).

    F(x)/m = dv/dt = (dv/dx)(dx/dt) = vdv/dx

    This simplifies the equation that can now be solved for “v” as a function of “x” if you know F(x). The important thing to note is that you can only do this if there is only one independent variable, here time “t”. On the other hand if there is more than one independent variable, application of the chain rule involves partial derivatives and more than one term. It might look like this:

    du/dt = (du/dx)(dx/dt) + (du/dy)(dy/dt)

    where the derivatives on the right hand side are partial. My point in all this math is that the Kaya identity assumes that there is only one independent variable (path) and that Willis is pointing out that there are many paths or variables.

  121. Bill I,

    GDP includes consumption. It even includes government handouts, even if they’re financed by debt. The only American’s who don’t emit CO2 are Luddites who live on self-sufficient farms and don’t use fossil fuel, even for kerosene lights.

    If you add up all the energy consumed in America and divide by all the number people, you get something like the equivalent of a 7.5 horsepower engine, per person, running 24 hours per day. I think we should be proud of that fact.

    American’s emissions went down significantly in the last recession because fewer products were being made and consumed.

    America emits more CO2 than Canada mostly because we have more people.

  122. Kaya Identity. Useless equation. You can always put an infinite number of terms into an equation that all cancel out. F= ((((Ma +C-C)/142)*142)/e**2)* e**2. The CO2 emissions per unit energy consumption of the country times the energy consumption of the country gives you the CO2 emissions. Population and GDP have nothing to do with it. If three people lived in the country and they had the same energy consumption as the United States (with the same energy mix) they would have the same CO2 emissions as the United States.

  123. CO2_{emissions} = Population * \frac{GBP}{Population} * \frac{Energy}{GBP} * \frac{CO2_{emissions}}{Energy}
    So your saying I can do my share to fight Global Waming and stop being a vile Denier by simply drinking less beer and more mead, I can do that!

  124. Scott Scarborough says:

    If three people lived in the country and they had the same energy consumption as the United States (with the same energy mix) they would have the same CO2 emissions as the United States.

    What those three people are doing with all that energy? How do they manage to produce, distribute, consume that energy? Yeah, you have only proved that Kaya identity breaks down in a fantasy scenario.

  125. that Willis is pointing out that there are many paths or variables.

    Willis’ request cuts both ways. Quote the exact words of him saying that.

    [obs: I don’t get what you are saying.]

  126. Population would be a factor if you wanted to count breathing as CO2 pollution.

  127. JFD, the equation is used to calculate HUMAN emissions add to the environment by HUMAN activity. Since virtually all human activity that produces GDP requires burring fossil fuels the equation gives a close approximation.

  128. Looks like a bit of semantic legerdemain.One is taking a semantic construct and mistaking it for a mathematical construct. Let’s take the M&M example. It is taking the phrase “Boxes per Crate” and rewriting it in a mathematical formula as B/C as though we are literally dividing the number of boxes by the number of crates. If the Ms on both sides of the equation are identical then this is patently useless. If the Ms are not identical then it is patently wrong. Let’s do the math. Let C=2, B=3, P=4. Lets use Mp to represent the number of M&Ms per package and Let Mp=5. We can all agree (hopefully there’s no debate :) that the total number of M&Ms in all packages is:
    Mt = C*B*P*Mp = 2*3*4*5 = 120. So far so good. Now let’s apply the M&M formula as written and as the authors apparently intended it to be applied, that is: Mt = C * B/C * P/B * Mp/P where the Ms on either side represent different quantities. So then we have Mt = 2 * 3/2 * 4/3 * 5/4 = 5. Patently wrong. On the other hand if both Ms are the same value then we have
    Mt = 2 * 3/2 * 4/3 * 120/4 = 120. Which is patently useless as we need to know a priori the value of Mt.

    The Mark Twain quote above says it all.

  129. The Kaya Identity reminds me of a joke my college mathematics professor played on us back in the 1960s. He announced in class one day that someone had recently discovered a function f(n) whose value was a prime number for all positive integers, n:
    f(n) = 10 + [sqrt(2)*exp(2*pi*n)+sin(2*pi*n) + etc. + etc.]^0

  130. Let me rephrase my question, Daniel. How would you calculate the Kayla equation the very first time?

    There are many ways. You could go and see how each energy source emits co2, take some samples, make the proper weighted average. There you have: carbon intensity of energy.
    Measure gdp, energy consumption, and population. Calculate the ratios. Put on the Kaya Identity.

    But the most simple way of using the identity is estimating energy-related co2 emissions some other way. And then start hypothesizing on what happens when rhs variables change. The relation between a rhs variable and energy-related co2 emissions might not be linear, but that is due to relationships between the rhs variables. The correct math is always to multiply the factors.

    climatereflections says:

    So maybe all this disconnect is simply an issue of properly laying out the equation so that people can see the actual units?

    It is a technical convention, they are representing a [ratio variable] by a ratio of [variables], if you read the english on the paper, you may become less confused.

  131. thallstd says:
    July 12, 2014 at 9:37 am – re adding 10% to pop not necessarily reducing GDP/capita by 10%.

    There is more to this. Indeed a history of GDP PER CAPITA GROWTH shows that GDP by the nature of its economic mechanics is not independent of population growth. In productive economies growing population causes excess GDP growth over and above the rate of population growth. This is a huge error in the Kaiya formula and demonstrates the level of economics understanding of sinistras. Indeed, one can see that their formula only works for despotic political economies by the fact that many of these have negative per capita growth.

    Moreover, the CO2/energy also has an effect on GDP – the “alternative energies” reduce GDP growth and in the extreme even reduce population through destruction of economic activity, fuel poverty, etc. Ya know, when you are an elite who knows best for the great unwashed, these aspects are undescoverable to them.

    Good call Willis, but its worth than you thought.

  132. We can and do measure how much fossil fuels we burn. We can and do measure how much GDP we produce (which includes consumption). We can and do measure how many people there are. All these factors are knowable so the equation can and does allow one to approximate HUMAN emissions of CO2. Which is all it was trying to do.

    The equation allows us to quickly compute approximately how much plant food we made in a given time period. That might be all it’s good for but it is good for that.

  133. @Daniel G.

    Here it is “And that to me is the problem with the Kaya Identity. It’s not that it is false. It is that it gives a false sense of security that we’ve included everything, when in fact we haven’t.” I paraphrased. Of course I am assuming that you are speaking to me. You didn’t say. :-)

    “I don’t get what you are saying.” To channel Dirac, this is not a question.

  134. Willis and friends,

    First, I take it that the discussion has progressed to the point that you (Willis) and most readers now see that a mathematical identity can be useful if it serves to account for real-world causal relationships that affect the magnitude we’re interested in — in this case, CO2 emissions. The Kaya Identity incorporates multiple hypotheses: that greater population leads to greater GDP (other things equal), that greater GDP leads to more energy use, that more energy use leads to more CO2 emissions, and that each of these causal linkages can be roughly quantified. The fact that the equation reduces algebraically to 1=1 is a red herring, because the ratios are measured directly as separate causal effects; the ratios are NOT measured simply as one empirical grand total divided by another empirical grand total. The Kaya Identity serves simply to account for the hypothesized causal effects and shows how they fit together into a bigger picture. It has no empirical content in itself, and it proves nothing itself — or as you say, “despite it being unquestionably true, we have no guarantee at all that such an identity actually reflects real world conditions.” The real-world conditions need to be tested. Still, the Kaya Identity is useful in providing an analytical framework that clarifies what conditions are to be tested. Agreed?

    What you (Willis) appear to remain unconvinced about is that GDP is sufficiently correlated with energy usage (or that it addresses enough CO2 sources) to make for useful analysis. I believe you are mistaken.

    Let me first join you and others here in acknowledging that GDP is an imperfect measure, especially when it comes to the value of non-marketed ‘household production’ and, for that matter, the enjoyment (or blessing or utility — all loaded words) derived from consumption activities. We economists know this, and we tell it to our students. If your gorgeous ex-fiancee had paid you for your drive (and this were reported to the IRS as self-employment income), or if you had taken the bus, then the trip as such would have counted directly toward GDP. Even so, as several commenters have pointed out, consumption expenses are accounted for anyway within GDP. GDP is (by definition) not only the total value of production, but also (roughly) the total value of income. Greater GDP means greater income, meaning greater household consumption, including consumption of energy.

    Already on this basis, it doesn’t matter whether (quoting Willis), “I’m buying fuel inter alia from Saudi Arabia, where it is counted correctly as part of their GDP, and thus it can’t be part of ours.” Our GDP includes your income that you spend in part on energy consumption, whether from domestic or foreign sources.

    Beyond that, it turns out that, given the ways that international payments have to add up, the value of oil imports still affects the total value of U.S. production. Greater imports lead, via depreciating exchange rates, to greater exports and thus greater U.S. goods production, at least to a first approximation. (A decent macroeconomics textbook will explain why. It’s analogous, by the way, to why we don’t care whether your drive affected the GDP of California or of Nevada. It truly doesn’t matter.)

    Your counterexample does not stand.

    (Willis, 11:02 a.m.): “consider things like the flaring of gas from oil wells, or the CO2 coming from underground coal fires in Pennsylvania, India, and China. None of them are in the Kaya identity, but all of them emit copious quantities of CO2.”

    The Kaya Identity does not purport to account for all CO2, in particular what comes from natural sources (volcanos) or unintended human sources (underground fires, or forest fires for that matter). Those are not the object of proposed “levers”. Gas flaring is a normal part of energy production, so it’s accounted for in the CO2 intensity of energy usage. Furthermore, the reduction of flaring is indeed a potential lever.

    These counterexamples do not stand either.

    Do you have another?

  135. Greg Smith says:
    July 12, 2014 at 1:44 pm
    Here is another “identity” along the lines of what dp and John West were explaining
    G = M / MPG
    where G is gallons of gasoline consumed
    M miles in trip
    MPG vehicle mileage in miles per gallon of gas consumed
    Which when you look at the terms
    (Gasoline consumed) = (miles traveled) / (miles traveled per gallon consumed)
    Whoopie, we now have
    (Gasoline Consumed) = (Gasoline Consumed)

    So, the “identity” tells us that the gasoline used for a given trip is the gasoline used for a given trip. Big whoop.

    I put “identity” in quotes since this is really a DIMENSIONAL EQUATION that lets me determine how much gasoline I will need for the 230 mile trip from my place in Southern California to Las Vegas. (I know what kind of MPG my car gets.) You can argue all you want about how useful the equation might be if you have no clue as to how you get MPG for your car. I know what MY car gets in fuel economy.

    It’s not as simple as that. A car’s MPG varies with highway or city driving, traffic conditions, engine maintenance—and driving style. Two cars in identical condition driven through the same area in identical traffic conditions can have different MPG depending on how they’re driven.

    As for anthropogenic CO2 emissions, doesn’t the Kaya Identity apply to countries? If a country imports and consumes a lot of soft drinks, beer, champagne, and other bubbly (carbonated) drinks, wouldn’t the release of all that CO2 count in the consuming country’s emissions, but the sales would be reflected mainly in the manufacturing country’s GDP?

    But personally, I agree with BioBob when he said, “this discussion is pretty much like arguing about how many angels dance on the head of a pin.” Anthropogenic CO2 is a minuscule percentage of total CO2. And the threat of catastrophic warming from CO2 is only in the models—models that haven’t been validated. In reality, the increase in CO2 has been beneficial in greening the planet. Even if total CO2 were to reach 10 times—or even 20 times—the current level, it would still be within the safe range for human life, so why are we bothering with accounting for it?

    http://wattsupwiththat.com/2012/10/17/claim-co2-makes-you-stupid-as-a-submariner-that-question/

  136. All valid equations have the units cancel out. The question remains whether there is validity to the equation and if it captures most of the important variables related to emissions. It has some validity. After all, humans do emit CO2 in a variety of ways. But this equation leaves out natural emissions.

    I like it because it will be obvious to most people that the goal of the extremists is to lower the number of people and to lower standards of living. I hope Hilary uses it in a commercial or a debate.

  137. Folks, there are two issues at play:

    1. Whether the Kaya Identity is in fact (i) an equation that allows us to perform a calculation, or whether it is (ii) a largely tautological formulation that doesn’t teach us anything on the left side that we didn’t already know on the right side.

    A lot of ink has been spilled on this point in this thread, but it may all be down to a misunderstanding of how the Kaya Identity is described and calculated. See my comment @ 3:47 p.m.

    2. Whether the three factors in the Kaya Identity (individual GDP, energy units per GDP, and CO2 per energy unit) are in fact correct; in other words, do they reflect real-world realities.

    The least contentious of the three seems to be CO2 per energy unit, so the question largely comes down to whether GDP is properly ascertained and whether GDP, in turn, can be meaningfully translated into energy units.

    —-

    But, again, this second issue is separate from the question of whether the Kaya Identity itself is a true equation (as Daniel G and others are arguing) or whether it is a tautological equivalence (as Willis and others seem to think). #2 above never even comes into play unless the Kaya Identity is a true calculable equation.

  138. I don’t have time to read this endless list of comments. Willis’ point is transparently specious. The energy used in beer production is not equal to the energy used in producing the GDP. They are completely different quantities, and do not cancel.

    This should have been obvious to a fifth grader.

    Anthony, this does not help the reputation of your blog.

  139. Dr. Doug @ July 12, 2014 at 4:42 pm

    Thanks for your clear, lucid, and compelling argument. . . truly a welcome voice of reason. Yet after two or three day of WUWT folks decrying that the Kaya Identify is nonsense because the identity balances dimensionally . . . and regrettably this group includes Mr. Eschenbach. To me, identities and equations, such at the Kaya Identity are common in What-If analyses as well as in macroeconomics. But to Mr. Eschenbach and his acolytes this means nothing and they reject any such thoughts on trivial dimensional grounds.

    Thanks again for your clarity of thought. Maybe you’ve made inroads in providing a useful perspective to Willis and company. But I fear that Willis has entrenched and doesn’t seem to want to listen or attempt to understand alternative perspectives. Sad.

    Best

    Dan

  140. noaaprogrammer,

    Cute, but generally speaking, one is not considered a prime number. From Crowdapedia:

    “The fundamental theorem of arithmetic establishes the central role of primes in number theory: any integer greater than 1 can be expressed as a product of primes that is unique up to ordering. The uniqueness in this theorem requires excluding 1 as a prime because one can include arbitrarily many instances of 1 in any factorization, e.g., 3, 1 × 3, 1 × 1 × 3, etc. are all valid factorizations of 3.”

  141. Don’t you see that how many people produce the CO2 has absolutely nothing to do with how much CO2 is produced? If 10 people produce 1 lb of CO2 or 1000 people produce 1 Lb of CO2 it makes no difference at all to the amount of CO2 produced. No “scenarios” involved.

  142. tl;dr – the kaya identity was constructed by asserting we could place whatever we wanted to the right hand of an equation by multiplying by X/X. We start with CO2 = CO2, and can magically add all kinds of things to the right hand side. This is mathematically correct, but completely useless.

    The defenders of the kaya identity assert that it’s not really X/X that is being added to the right hand side, but rather Xz/Yz (where z is units, X is some measured quantity, and Y = 1).

    So, are you allowed to blindly add Xz/Yz to one side of an equation? No. This is possibly useful, but mathematically incorrect.

    The Xz/Yz additions to the Kaya Identity may very well be *proper*, but you can’t justify blindly add those multiplicative terms to the equation and assert they’re true because of algebra – they may be true for other reasons, but that’s a different argument.

  143. Charles the moderator –

    I don’t know whether you’re recent response to noaaprogrammer was the comment at July 12, 2014 at 4:33 pm

    But his/her equation: f(n) = 10 + [sqrt(2)*exp(2*pi*n)+sin(2*pi*n) + etc. + etc.]^0 evaluates to 11 for all n (presuming the etc. etc. don’t exhibit singular lies). You’re correct, it’s simply “cute” and not very informative but 11 is a valid prime number. Correct me if I’m wrong.

    Dan

  144. Charlies the Moderator

    my most recent comment should have been written “don’t exhibit singularities” Sorry.

    Dan

    [But “don’t exhibit singular lies” also works. Sometimes. 8<) .mod]

  145. The equation only makes sense if some of the terms actually are equal to something in particular. That is, what do these terms mean?
    ( GBP / Population )
    ( Energy / GBP )
    ( CO2 emissions / Energy )
    What real-world identities do they correspond to? What units can they be expressed by? If I was asked to do dimensional analysis, to prove this equation, I wouldn’t even know where to start.

    [GBP or GDP? .mod]

  146. Willis Eschenbach says:
    July 12, 2014 at 10:57 am
    ….
    Thanks, Caveman, but nope. I’m buying fuel inter alia from Saudi Arabia, where it is counted correctly as part of their GDP, and thus it can’t be part of ours.”
    /////////////////////////////

    No.

    Someone is buying crude from Saudi Arabia. Someone is arranging the shipment. Someone is arranging the importation, and more significantly, someone is perfoming the refining, distributing it to the gas station whereat it is sold to the customer.

    In this chain, there is value added, and jobs, the workers earn money which they can use to spend on consumer goods, thereby fueling demand and economic activity over a wider area. .

  147. Lots of folks are still not getting it.

    The Kaya Identity is an identity, not an equation. The identity contains only units. The units better cancel out in an identity, or the identity is false. There are no variables in an identity. It’s purpose, useful or not, valid or not, is not about calculating a value. It can’t; it has no placeholders for values.

    An equation has variables in it, and can be used to calculate something.

    If the Kaya identity was altered to be an equation, is would look something like:
    .
    (T Co2 Emissions) = (X Population) * (Y GDP / Z Population) … * (A Co2 Emissions / B energy)

    And X and Z would have different values. X might be something lke 100,000,000, and Z would probably be something like 1. Similarly, A and T would have different values.

    Other people’s discussions about the functional validity of the identity can’t be understood without recognizing the difference between an identity and an equation.

  148. charles the moderator says: July 12, 2014 at 5:11 pm
    “Cute, but generally speaking, one is not considered a prime number.”

    I think the prime number claimed is 11.

    Scott Scarborough says: July 12, 2014 at 4:17 pm
    “Kaya Identity. Useless equation.”

    It’s just like any identity in maths. Universally used. Take the one we all learnt at school
    a²-b²=(a-b)(a+b)
    It doesn’t tell you the value of anything. It just says that if you can work out (a-b) and (a+b), you can get a²-b².

  149. 10 July: Bloomberg: Eric Roston: Fix the Climate Problem? Easy. Cut U.S.
    Emissions to 1901 Levels
    A draft report prepared for the United Nations suggests, out loud, what the
    U.S. needs to do about climate change: Cut emissions to one-tenth of current
    levels, per person, in less than 40 years…
    The report, Pathways to Deep Decarbonization, describes how nations might be
    able mitigate against dangerous climate change.
    ***Two organizations wrote it to provide national leaders and UN agencies with a specific vision of how 15
    leading economies can slash climate pollution.
    The study contains detailed sections on each of a dozen large national
    emitters, including the U.S., China, Russia and the U.K. It suggests to
    national leaders that cutting carbon may be possible, without economic
    compromise and without fear that they’ll have to go it alone. Such analysis
    might help them generate the political support they’ll need to make the UN
    climate negotiations in Paris at the end of 2015 successful…

    http://www.bloomberg.com/news/2014-07-09/fix-the-climate-problem-easy-cut-u-s-emissions-to-1901-levels.html

    ***Bloomberg’s Roston may have provided a link to the following, but it was clear he wasn’t eager to name his “two organizations”!

    UN Sustainable Development Solutions Network: Deep Decarbonization Pathways
    The Sustainable Development Solutions Network (SDSN) and the Institute for
    Sustainable Development and International Relations (IDDRI) co-founded and
    lead the DDPP.
    Currently, the DDPP comprises 15 Country Research Teams composed of leading
    researchers and research institutions from countries representing 70% of
    global GHG emissions and different stages of development: Australia, Brazil,
    Canada, China, France, Germany, India, Indonesia, Japan, Mexico, Russia,
    South Africa, South Korea, the UK, and the USA…
    Several Partner Organizations contribute to the analysis and outreach of the
    DDPP, including the German Development Institute (GDI), the International
    Energy Agency (IEA), the International Institute for Applied Systems
    Analysis (IIASA), and the World Business Council on Sustainable Development
    (WBCSD). We invite other organizations to become DDPP partners and
    contribute to practical problem solving for deep decarbonization.
    Australia:
    Centre of Policy Studies, Victoria University
    ClimateWorks Australia, Monash University
    Commonwealth Scientific and Industrial Research Organisation (CSIRO)
    Crawford School of Public Policy, Australian National University
    United States
    Energy and Environment Economics (E3)

    http://unsdsn.org/what-we-do/deep-decarbonization-pathways/

  150. from the UNSDSN link u can check out the saturation MSM coverage for their nonsense, but these two provided the most laughs:

    my favourite – which i couldn’t read due to subscription required, but which showed the one and only comment to the economic hit man Jeffrey Sachs’ piece:

    8 July: Financial Times: Jeffrey Sachs: How to decarbonise the global
    economy
    ONE COMMENT ONLY: by Richard Gordon: Sadly the lack of comments on this
    important article shows the indifference of the vast majority of the public.
    Climate change is the most critical threat to mankind and the planet…etc

    http://blogs.ft.com/the-a-list/2014/07/08/77872/

    8 July: NYT: Eduardo Porter: Blueprints for Taming the Climate Crisis
    This course, created by a team of energy experts, was unveiled on Tuesday in
    a report for the United Nations that explores the technological paths
    available for the world’s 15 main economies to both maintain reasonable
    rates of growth and cut their carbon emissions enough by 2050 to prevent
    climatic havoc.
    It offers a sobering conclusion. We might be able to pull it off. But it
    will take an overhaul of the way we use energy, and a huge investment in the
    development and deployment of new energy technologies…
    The new assessment also underscores the pointlessness of small, incremental
    emissions cuts…
    For the first time, when we say we can stop the climate from heating we will
    more or less know what we are talking about…

    http://www.nytimes.com/2014/07/09/business/blueprints-for-taming-the-climate-crisis.html?_r=1

  151. It’s worth noting the name, ‘Kaya Identity’. From a branding perspective, it’s an ideal choice of name. It evokes colour, rainforests, peaceful tribes, femininity, compassion and magical force.

    If it had been called the Schmidt* Identity, people would dismiss it more readily as something that comes from a paper-pusher.

    * A Hogan’s Heroes reference.

  152. I am with Willis and the Kaya identity is total mathematical nonsense. I suppose this is to back up the scientific nonsense which is called CAGW.

    All you have to do is plug some values in the equation.
    GDP = 50
    Pop = 10
    Energy = 5

    So Emissions = 10 X 50/10 X 5/50 X Emission/5 and the answer is Emissions = Emissions

    Some of the people here should go back to college for remedial mathematics.

  153. Here’s something to ponder based on Willis’ gasonline / GDP example. The oil used in the gas Willis purchased was from Saudi Arabia. They sold it, it became a part of their GDP, but no carbon was released from that oil to add to the CO2 emissions in Saudia Arabia. The oil was then sold in the us as gasoline and burned, adding to the US GDP and CO2 emissions. You could almost argue that two GDPs combined to create the subsquent CO2 emitted. When I looked at what I think was the original definition of the Kaya Identity, it was global GDP, population, energy and CO2 emissions being described. As such, is the Kaya Identity useful at all when used to analyze individual countries or should it be confined to analysis global in scope?

  154. Oh, and Willis, I forgot to add an observation. I think I’ve found a third way in which the Kaya Identity is useless. Instead of trying to MODEL how much CO2 is or will be produced, would it not be better to MEASURE IT?

    I know that climate science these days is all about models (and ‘adjusted’ data sets) but there is always the hope that measurement will once again be seen as useful.

  155. Rdcii @5:35 p.m.

    Just to be clear, are you saying that the Kaya Identity does not in fact calculate anything, contra to what Daniel G has been arguing, and contra to what Daniel G says the UN paper does?

  156. The Kaya identity would be practically useful if the fractions on the Right Hand Side could be measured as single independent variables in their own right. We could then calculate CO2 emissions as the simple product of these variables. In fact they cannot be measured as single independent variables but each fraction must be calculated from measurements of the primary components that Willis has pointed out cancel each other and are thus redundant. Hence the Kaya identity is indeed practically useless as Willis has said.

  157. Charles the Moderator said:
    “Cute, but 1 is not considered a prime number…”

    You missed the term “10” in front of the equation:
    f(n) = 10 + [sqrt(2)*exp(2*pi*n)+sin(2*pi*n) + etc. + etc.]^0

    10+1 = 11

    which is always prime.

    Side Note: Mathematicians have excluded 1 from the set of primes, as a convenience for stating many theorems in number theory. (It prevents the verbiage of stating many exceptions.) However if a formula for generating consecutive primes is ever discovered (highly unlikely), it most likely would include 1 since there are no positive integers smaller than 1 which would be factors of one.

  158. The Kaya Identity is fundamentally correct. How it is displayed is incorrect and hence the confusion and debate. Dimensionally everything cancels out. So kg CO2 = kg CO2.

    The identity should be shown as –

    Total CO2 Emissions = Population * GDP Intensity * Energy Intensity * CO2 Intensity.

    Where –

    GDP Intensity = GDP per unit population
    Energy Intensity = Energy per unit GDP
    CO2 Intensity = kg CO2 per unit Energy.

    Ultimately everything cancels out and you are left with total kg CO2.

    So if population increases and nothing else changes CO2 goes up. If we produce less CO2 per unit energy and nothing else changes CO2 goes down. etc. etc.

    If you take Australia for example. Our CO2 Intensity is high because we do not use nuclear for power production unlike most other G20 nations. Our Energy Intensity is also high because we are geographicall large, so we use more energy for transportation. Our GDP intensity is high because we are an advanced economy.

  159. Consumption Production – even though putting gas in one’s car contributes to commerce, driving down the road for pleasure is not a productive activity – nothing of value results from it. Contrary to Krugman’s fantasy, a country’s wealth lies in its productivity, not its spending. Since war is destruction, it cannot contribute to our productivity, once the bomb has been used, nothing of value remains, and much of value has been destroyed, just as the hundreds of billions of dollars wasted by the federal government on useless programs and fraud are actually decreasing our national product rather than increasing it, yet both of these examples are included in the current GDP calculation. So I concur with Willis, driving down the road using gasoline is contributing to the CO2 in the atmosphere but not the true GDP.

  160. This is an other important contribution of Mr. Eschenbach to show how science is done.

  161. I have a NEW Equation / Identity! Klimut Science = CO2 = GDP / CO2 = Bullshit produced * $ / CO2 THEREFORE: CO2 * Klimut Science = Bullshit produced * $ AND: Klimut Science / $ = Bullshit Produced

  162. @Rdcii “The Kaya Identity is an identity, not an equation. The identity contains only units. ”

    You can algebraically add X/X to one side of the equation CO2 = CO2, and be mathematically proper.

    If you construct an identity of units, you cannot justify it algebraically – you must use a different argument than “we can add X/X to one side of the equation”.

    The Kaya Identity may in fact be proper, but it cannot be justified via algebra – you need a different argument.

  163. Yes unfortunately GDP is not linked to energy use in any formal sense, though there might be a loose association, such the GC02-e rises at the same time as GDP. The question is one of causality, which is unproven. I think you are making a case for the green argument such that they claim to believe that economies can be uncoupled from carbon energy. Though I don’t think they really know how.

  164. Longtime lurker here. This lively but almost entirely polite and learned exchange prompts me to paraphrase William F. Buckley Jr: I would rather have our state and country managed by the contributors and commenters of WUWT than by our current President, Congress, California Governor & state legislature.

  165. Andrew N @6:15 pm:

    Whether it is “fundamentally correct” depends on whether the variables do what they are claimed to do. Which is another topic. (See #2 of my comment @5:03 pm.)

    That said, I suspect you are right that we are dealing with confusion due to how the Kaya Identity was presented (by Willis, Wikipedia, and who knows who else). The way you have outlined it @6:15 makes sense and is a bona-fide, legitimate calculation.

    Ironically, some here who seem intent on arguing that the “identity” is useful and meaningful are arguing over the wrong thing. The way Willis (and Wikipedia) present the Kaya Identity, it *cannot possibly* be meaningful. Thus, those who want to support the Kaya Identity should be arguing over what the Kaya Identity really is — the proper way to write the equation — not digging in their heels with the indefensible position that if we put an (X/X) on one side of the equation then we have done something meaningful.

    So, on the generous assumption that all the smart and clever people who have been using the Kaya Identity in actual practice for years aren’t clueless, I’m tempted to assume for the time being that you are correct and that what we are dealing with here is an initial failure to properly state what the Kaya Identity actually is.

  166. Hi Willis,

    Once again your post on this subject is eliciting a lot of comments. I will add one more.

    I do not think the purpose of the identity is to capture reality with perfect fidelity; it is just a simplified model of reality. A broad strokes model, if you will. I think it does show reasonably clearly the most important factors which influence CO2 emissions, and more importantly, it points toward the real-world obstacles to reducing CO2 emissions, especially in light of the growing wealth (and rapidly growing energy demand) in developing countries and in mid-income countries. The identity points to the great difficulty (indeed, many would say the near impossibility) of a rapid reduction in global CO2 emissions.

    I think the value of the identity is that it helps to move the political discussion away from non-sensical, wasteful, impractical, and even impossible approaches for large CO2 emissions reduction, and toward a more realistic analysis of global energy production and use. What gets Roger Pielke Jr in hot water with the entire loony-green left (like most of the climate science pooh-bahs and Paul Krugman… and his many mindless sycophants) is that he uses the identity to point out that every ‘green energy’ approach the loony-green left adores is just not going to cut CO2 emissions in a world of rapidly growing wealth (and modestly growing population). It forces the loonies to face reality….. and they hate it.

    It is very funny to see them go ballistic every time Pielke uses the identity to point out the magnitude of the problems they face in implementing their policy fantasies. That is utility enough for me.

  167. climatereflections @6:40pm

    Actually I feel that it is a bona fide equation, not an identity. In other words, if you change any of the variables, Population, GDP intensity, Energy intensity or CO2 intensity then the total CO2 emitted changes. I believe that Population and CO2 Intensity are independent variables. The other two would most likely be reduced to one variable, as freely available energy is the basis of all advanced economies. CO2 intensity could theoretically be reduced to zero if you had 100% nuclear power producing electricity, hydrogen via an Iodine reaction and liquid fuels from the hydrogen and CO2. That of course would leave CO2 emitted by a presumably breathing population.

  168. Dang. I just knew it would sooner or later come down to beer. I have for decades gleefully released CO2 from copious amounts of beer. Brown bottles, clear bottles, cans and kegs. The choice based upon situational impact from supply, cost and demand, flavor not with standing in the matrix.

    Leave my beer alone. Beer is CO2 neutral. No more CO2 goes into it than comes out of it. Kinda like cow flatulence. Attack that on a transportation generated by products basis and I will rabidly counter with the same relative cost applied to wines, liquors, cordials, aperitifs, coffees and bottled water.

    Beer is good. Latte is very bad. Bottled water is horrid.

    Go ahead, econazis, mess with my beer. I can exist on home brew beer or even backyard vodka and tap water if needs be. You will wither and babble even more than now when you see how much carbon tax you have to pay for your elitist tipples.

    Leave beer alone. You have been warned! ;)

  169. Given: CO2(POP,GDP,E,CO2)=POP*(GDP/POP)*(E/GDP)*(CO2/E), an equation of CO2 that is a function of POP, GDP, E and CO2.

    I was taught in Physics that one thing that must be true if an equation is correct: the units must match on both sides of the equal sign. That is true in this case, so we have one thing correct.

    The next thing that I was taught is that to predict things you use calculus. So what happens when we increase population or other factors without changing anything else?

    dCO2/dPOP=0 or CO2 doesn’t increase if POP does and everything else stays the same.
    dCO2/dGDP=0 or CO2 doesn’t increase if GDP does and everything else stays the same.
    dCO2/dE=0 or CO2 doesn’t increase if E does and everything else stays the same.
    dCO2/dCO2=1 or CO2 increases linearly if CO2 does and everything else stays the same.

    Well, that doesn’t tell us much!

  170. Daniel G. says:
    July 12, 2014 at 4:21 pm
    Scott Scarborough says:

    If three people lived in the country and they had the same energy consumption as the United States (with the same energy mix) they would have the same CO2 emissions as the United States.

    What those three people are doing with all that energy? How do they manage to produce, distribute, consume that energy? Yeah, you have only proved that Kaya identity breaks down in a fantasy scenario.

    Scott used an extreme example, but that doesn’t make his argument any less valid. Countries vary greatly in the amount of energy they generate/consume per capita, per unit of GDP, or GDP per capita.

    The Kaya equation assumes that each term is independent of the others. That is an absurd assumption. If you double the population you may quadruple the GDP, so the GDP / person ratio then also doubles.

    Admittedly, simplifying equations such as this can be useful. Consider the simple business equation total income = widgets sold * price per widget.

    In the case of the Kaya equation, it is useless.

  171. Hans Erren says:
    July 12, 2014 at 9:39 am
    The Kaya Identity shows wat happens if you change the contributing parameters, if population goes up, another factor needs to go down if you want to keep the total emission constant. In a world with a continuous global recession and population increase the total emission could remain constant.
    A very useful tool.

    No…its not. In fact, it is a counter productive tool. The counter productivity has nothing to do with its mathematical correctness or its ability to identify the factors of CO2 production. The problem is the assumption that this helps decision makers make good decisions, which is most certainly false. That’s because it is a linear representation of a non-linear world, and the decision makers who use it as the rationale for their decisions will almost certainly make bad ones.

    Let me demonstrate this with an example from history. Consider a Kaya identity for the late 19th century problem of horse manure in New York City. You can develop your own factors, but certainly human population, horse population, GDP and sanitation services would be among them. Decision makers would look at this Kaya identity for horse manure and conclude that they would have to dramatically increase the sanitation effort or reduce the horse population through draconian regulation, or reduce the human population or reduce the GDP. All of these solutions would result in costly, negative impacts that might have exceeded the problem of the manure.

    The invention of mass manufactured automobiles ultimately reduced the number of horses dramatically, but this ‘solution’ was not, and could not have been derived from the Kaya identity for horse manure! Even if some clever city councilman decided that they could reduce the number of horses with some new invention that would make horses less necessary, the result would have been the horse manure equivalent of Solyndra.

    The solution came from left field; it came from someone not even trying to solve the problem, and had a completely positive impact with no draconian regulation required. The Kaya identity does not allow for such solutions. It closes the minds of decision makers to a very small, linear way of thinking, shutting out the infinitely more creative and resourceful non-linear world. Ultimately, it gives decision makers the permission to make bad decisions much more quickly and effortlessly than ever before.

    And there’s the rub. That is the problem that so many of us have sensed when we looked at the Kaya identity. That is what gives us the heebee-jeebees! It may be the correct equation to describe the problem, but when it comes to solutions, it is a recipe for disaster. It is a false map to a positive solution, and as such, will likely cause much more harm than good.

    (I have not read all the other posts, so if someone else has already commented along this line, my apologies for the repetition.)

  172. Willis wrote that something like “… two-thirds of peer-reviewed science is falsified within a year …” above.

    This makes one wonder how many of the remaining third of papers is falsified the second, third and subsequent years… and how much actually survives unscathed from any given year? Are there years where none remain unscathed?

    Is there a site that tracks published papers and their falsification status? That sure would be useful although it might be controversial if people can’t agree that a paper is falsified or not.

    Willis Eschenbach (or anyone else) do you know of any references or sources on the rate of falsification of old and new peer reviewed papers?

    I’m curious about that. It would be revealing to see graphs of those statistics for various science fields as well as the alleged science fields such as “climate science”.

    Are there any papers on this topic that collect such statistics and provide analysis that themselves haven’t been falsified? [;-)]

    Thanks in advance.

  173. Dear Willis, I usually am in agreement with your rants and discussions and presentations.

    Once again, it is a badly symbolized equation, true, but it holds as an algebraic equation if one does not confuse units/dimensions with constant values.

    The last in a row for example is a constant measured in a chemistry lab which tells us how much CO2 is emitted in producing a gram of , in units of grams/joule.

    energy/GBP is a constant . a number, measurement of the total energy spent in producing beer , somebody has to measure it in units of joules per gram.

    GBP/population is also a measured constant in grams/(number of people)

    and finally somebody has to measure the population.

    These are a series of measurable constants and will give different results for different inputs.

    And finally this is a CO2 constant/contribution in grms from beer production in a specific country. This will be reduced by 10% if beer production per unit emits less CO2 by 10%. It will ofcourse become insignificant in the total CO2 sum.

    So it is true that it is a badly expressed algebraic equation where units and constants are mixed up but there is some sense in it, and that is why you are getting all these comments.

  174. The long answer (because even I don’t like my first attempt at explaining what I don’t like about the Kaya Identity).

    Given something simple like CO2(E, CO2perE)=E*CO2perE, or CO2 emitted equals total energy units used times CO2 per unit of energy, we have a working equation. Notice that CO2perE is CO2/E unit wise but the CO2 on the right isn’t the same as CO2 on the left. The CO2 on the right is a constant amount of CO2 emitted per unit of energy.

    We can add more variables to the equation, but they don’t have any effect on the final result because their derivatives are zero:

    CO2(POP, GDP, E, CO2perE)=POP*(GDP/POP)*(E/GDP)*CO2perE

    In other words, population and GDP are useless additions. Now that doesn’t suggest that they don’t have an effect on total E use in the first valid equation. That would be a whole other discussion. It just simply means adding them doesn’t tell us anything useful.

  175. Continued:

    It is also true that the equation does not count all of the CO2 emitted on earth by biological organisms , as we all are, we are not adding to the GDP by existing ( except in some countries where there is a head tax) . But it is also true that the GDP is strongly connected to energy consumption and it must be true as an algebraic relationship to first order. How much GDP has a poor nation in Africa? Isn’t our argument that CO2 reduction hits the poor much more as it does not allow them to expand in energy usages which is important for the enrichment of an economy?

    If we did not burn fuels other than wood we would still be in the stone age. What is the GDP of a stone age economy.

    So the algebraic equation is a first order equation of the multitude of variables that enter such estimates.

  176. Dave38: Sorry to disagree with you but “grue ” is a valid english word old

    Thanks for the update. I had used it colloquially a couple times, but I did not know it was considered valid.

    This discussion makes me think of some analogies with tools:

    a. an axe is still an axe after you chop into a rock pile a couple dozen times; it didn’t stop being an axe just because you buggered the blade.

    b. a cordless drill can be used to drive screws, but not if you have drill bits in it instead of screw bits.

    c. a hatchet can be used to drive tent pegs, but you do want to be careful how you wield it; contrariwise, the blunt edge isn’t good for preparing kindling..

    Don’t blame the tool just because you can, should you choose a particular set of options, render it useless.

  177. By the way, in my posting, I inadvertently substituted GBP for GDP. I blame my cat for the error. However, the reasoning is the same. If population increases, for instance, it won’t change anything, because the population number is going to cancel itself to a one. Same with energy and GDP. Unless these grouped terms can be morphed into some other form (which is what we did in trig identities), this is an equation that is totally meaningless. If you could just turn a few of the terms into a series, or a trig function, or a partial derivative, we might have something to work with.

  178. Our education system is in serious need of a makeover. Based on this thread more than half the people are below average at math. Unprecedented, worse than we thought.

    Sadly, Willis has blown two chances to get it right. Where is the pile-on that Dr. Evans suffered for his notch filter? Hey Leif – show some consistency.

    Yes that is an impossible claim, but humorous and makes a point that many won’t understand because they’re part of the below average majority.

    Someone brought it up earlier but credibility is the victim here.

  179. Willis Eschenbach: consider things like the flaring of gas from oil wells, or the CO2 coming from underground coal fires in Pennsylvania, India, and China. None of them are in the Kaya identity, but all of them emit copious quantities of CO2.

    In common with most mathematical expressions in science, the Kaya equation does not have everything relevant in it. The first mathematical expression for conservation of energy, for example, was way off because entropy had not yet been discovered and included. Later Einstein added in a constant times mass, though the correction is not needed in most analyses of electrical generation from fuel. In pharmacokinetic equations (used for computing dosing regimens) most important factors are omitted and “blended” (aka “confounded”) in just a few rate equations among non-physical concepts such as “apparent volume”. In fact, “apparent volume” is a ratio: total dose in the body divided by concentration in the plasma; for drugs that concentrate in the fat, or bones, etc, the “apparent volume” may greatly exceed the actual volume of the animal, hence the abstract name “apparent volume”. Science is full of incomplete equations of this nature, that are nevertheless useful in planning or other ways.

    GDP is a limited measure of the rate of growth of wealth, but urinary melatonin metabolite is a limited measure of the rate of secretion of melatonin and melatonin metabolism. To a greater or lesser degree, every measurement type has limitations of accuracy; the existence of known limitations of GDP hardly disqualifies every particular use for it.

  180. Has nobody actually put numbers into the equation and watched what happens? Come on people.

    According to the “formula” (it isn’t a formula, of course, it’s an identity), delta CO2 for ANY change in population, GDP, or energy (or any combination of changes) is ZERO. Don’t believe me? Put numbers in and actually try it.

    Its obvious. The only variable which can actually change CO2 is CO2. Otherwise the equal sign in the equation would be broken.

    Please tell me that I’m not the only one to recognize this.

  181. anna v has it right, and I am astounded at the large number of commenters who don’t apparantly understand the first thing about math, and proceed to display their ignorance in spades.
    In the Kaya Identity, the UNITS cancel, but not the VALUES.
    For instance, the population term is in units of people, so the first term is the total population VALUE, but the second term expressing per-capita GDP the population term is in UNITS of 1 person – that’s the definition of per-capita.
    The same goes for the other terms – the denominator is expressed as single units (People, dollars, joules, kegs, whatever) which don’t vary, and the numerator is what’s possible to vary to determine the effect on the output.

    The appropriateness of the selected variables can be argued for certain, as can the unexpressed interdependencies of the variabiles (e.g., if population is halved what really happens to GDP/population? If practical nuclear fusion is achieved, what happens to energy/GDP and co2/energy?) – but as presented the Kaya identity seems to be a reasonable first-order estimation tool.

    The one thing that’s interesting to me about the Kaya Identity is that the way it’s composed, the only way to reduce the output is to reduce one or more of the inputs – a handy policy tool indeed.

  182. Andrew N @7:06 pm:

    “Actually I feel that it is a bona fide equation . . . In other words, if you change any of the variables, Population, GDP intensity, Energy intensity or CO2 intensity then the total CO2 emitted changes.”

    I think that’s the right approach.

  183. Daniel G. says:
    July 12, 2014 at 2:50 pm

    Ah but it is a shell game, the M on the left is not the same M we have on the right is it?

    Kaya Identity is analogous, because we have been using symbolic a/b to represent a ratio variable.
    ******************************************************************
    Daniel, the number 1 is a ratio and that a/b is a ratio as you rightfully say. A ratio is just a rational number. But I repeat myself.

    In order to find a value for a/b you need to know a and b.
    Kaya is a mess because it uses [total CO2 we don’t know what it is before we do the calculation] divided in this case by [total to the last drop energy consumed to produce the GDP] to FIND CO2.

    With respect to the M&M identity. One doesn’t count all the M&Ms ahead of time and divide by the total number of packages to figure out how many M&Ms there are in a package, that is M/P. One picks up one (or 2 or 3 but not P) package and count the M&Ms and divide that by one (or however many) package and now you have a ratio with independent information to use in the formula. This is why I say the M on the left is different from the M on the right, the M on the right is an increment of the total M. Now if one did decide to count all the M&Ms and divide by the total number of packages it would be the same ratio, but they’d now just using the M you are looking for to calculate the M you want.

  184. anna v @8:52pm and
    James Gibbons @9:01pm:

    The issue is that the equation as written by Willis (and the graphic equation in Wikipedia*) is incorrect.
    With the correct equation we could have avoided the great majority of this thread, although the more substantive issue of whether the equation variables in fact capture reality would still be open for discussion.

    —–

    *I note, however, that the text in Wikipedia (at least a couple of hours ago) does not match up with the graphic equation. The text seems more correct.

  185. “The problem is … I’m burning energy, and I’m emitting CO2, but I’m not part of the GDP. I’m not producing anything with that energy—no goods, no services, nothing. My CO2 emission is a part of the total, but it is not included in the Kaya Identity anywhere.”

    Just get pulled over and fined for one of the many imaginary “victimless crimes” and you’ll be part of the GDP – if you pay of course.. ;)

  186. I think it is worth reminding folks that GDP is an *aggregate* measure that typically changes only *gradually*. It is pretty trivial to construct a hypothetical that could make the Kaya identity useless FAPP. For instance, if all the families with one working and one stay at home parent, suddenly forced the working parent to send a cheque for childcare services to the nonworking one, we could have a huge jump in GDP that wouldn’t have any impact on CO2 emissions.

    The first point is, though, that these sorts of things may either be insignificant in terms of the total size of the economy and/or move more or less in tandem with other changes in the economy so the equation may still be useful, for instance, in predicting the effect of a recession on CO2 emissions.

    And this leads to the second point, which is, is Kaya useful? i don’t know the answer to this question (and I suspect it might not be). Can we, for instance, measure the relevant data surrounding the 2008 recession and come up with a reasonably close estimate of the actual CO2 emitted in 2008? If we can, then all the other objections seem moot to me and if we can’t, there isn’t much benefit to Kaya one way or another.

    Cheers, :)

  187. My first article in Communications of the ACM had some major issues. Unlike the academic journals in my field of information systems, CACM publishes letters to the editor and I really got hammered. It was a very painful experience for me, but the problems did get adequately exposed.

    In contrast, there was a seriously flawed publication by a prominent figure in a top academic journal in my field. A colleague saw it, recognized the problems and submitted a rebuttal paper. Although the reviewers acknowledged the problems, it went through a stalling process of multiple review cycles and then was rejected.

    I suspect things work like that in other fields also.

  188. Rdcii says:
    July 12, 2014 at 5:35 pm
    (T Co2 Emissions) = (X Population) * (Y GDP / Z Population) … * (A Co2 Emissions / B energy)
    *************************************************
    The population can’t be different values in the same equation, X = Z. Goes for the CO2 also, CO2 emissions has to be the same on both sides of the equation (T = A).

  189. dp says:
    July 12, 2014 at 9:53 pm

    [snip off topic – not going there again -mod]

    I don’t blame you wanting to avoid that. It is part of the bigger picture, though old news. You guys do a good job.

  190. ” The Kaya identity (CO2_{emissions} = Population * \frac{GDP}{Population} * \frac{Energy}{GDP} * \frac{CO2_{emissions}}{Energy} ) is a means of communicating the factors of which CO2 emissions are comprised, in order to explain the physical levers that are available if one wishes to control an economy’s CO2 emissions.”

    As Willis points out, this is just an identity equation. The fallacy, however, is not just that it is an identity, but that these are levers that are controllable independently.
    If you kill off a sizable portion of the population, GDP per population, energy per unit of GDP, and CO2 emissions per unit of energy will all change (and it likely will depend on who you kill off). On the other side, a growing population will have more intellectual capital and vigor and may come up with much more cost- and energy- efficient means of production. Similarly, a change in energy use per unit of GDP will affect GDP and in the long run have some (unknown) effect on population and a change in the emissions to energy use ratio will affect GDP and population. These are all things you can calculate after the fact, but not things you can control.
    As an example, you may be able to find a more energy-efficient way to make beer. That method may increase or decrease CO2 emissions per beer (may require different processing or farming methods) and depending on the cost effects may increase or decrease GDP (more or less expensive beer will change consumption). If more or less beer is consumed, that may affect the population growth of the country, both directly and as a function of disposable income.
    It is the conceit of the statists and their limited stage 1 thinking that these are levers they can control.

  191. Will @10:21pm:
    There are two different “populations.” One is the aggregate population, the other is a population of 1 person. Specifically, the denominator is per head. Same for all the other variables.

    The problem arose because the equation was written as though the numerator of one fraction were equivalent to the denominator of the next one. They are not equivalent. They are of the same type of unit, yes; but not the same quantity of those units.

    “Goes for the CO2 also, CO2 emissions has to be the same on both sides of the equation.”

    Nope. The left side is CO2(Total). The right side is CO2(per energy unit).

    • climatereflections says “Nope. The left side is CO2(Total). The right side is CO2(per energy unit).”

      That is what it was perhaps meant to be, but it is not what we are discussing.

      http://en.wikipedia.org/wiki/Kaya_identity

      What we are discussing with considerable glee is that it seems some people, maybe many, really have no clue and actually prefer the elegance of a formula that cancels out to itself — namely, an “identity”. If it didn’t, how could you call it an identity? It would then simply be a formula or equation, which are really the same thing except equation names the thing the formula calculates.

      The intended formula is simple, obvious and still not all that meaningful since it is filled with assumptions.

      Here’s an explanation of the “identity” complete with dozens of charts and graphs all given meaning by — nothing!

      http://www.manicore.com/anglais/documentation_a/greenhouse/kaya_equation.html

      But it’s very cool. To the casual observer it would look like this self-canceling formula really is a huge advance in science.

  192. Doug says “that greater GDP leads to more energy use” without any qualification. If this were true Italy would have a greater GDP than France. There is no reason this should be true. It may be true sometimes, but it is not true all of the time. Surely many on this forum can provide counter examples both to this assertion and the unqualified assertion “that more energy use leads to more CO2 emissions.” Neither claim nor the supposed Kaya identity account for substitutions. If the Kaya “identity” says anything at all, which is doubtful, it states the obvious; it’s nothing handed down from a mountain top.

  193. JJ says:
    July 12, 2014 at 11:33 am

    Willis,

    Thankfully, you have dropped the mathematically ignorant look ma, everything cancels so it must be wrong and I must laugh assertions. It would have been manly of you to have acknowledged the error instead of simply walking away from it, but at least you did walk away from it.

    My point has not changed in the slightest, nor have I “walked away” from anything. I never said, however, that “everything cancels so it must be wrong”. That’s just your curious fantasy.

    JJ, point out to me in the Kaya Identity where I can find all of the CO2 from gas flaring all over the US.

    Point out to me where in the Kaya Identity are the megatonnes CO2 from the coal mine fires that have been burning for decades in China.

    Point out to me where in the Kaya Identity I can find the gas I burned today on my vacation. Now, if I had burned that exact same gasoline in a furnace and made a product, it would show up in the GDP part of the Kaya Identity.

    But it doesn’t show up in it anywhere … and there are millions of people driving around the US on their vacations.

    My point regarding the Kaya Identity is the same it has been all along. It is no better than the Beer Identity, because it doesn’t show or demonstrate or prove anything, and it doesn’t represent the real world. If you think it does, point out to me the CO2 I specified above.

    w.

  194. Falsify This:

    Klimut Science = CO2 = GDP / CO2 = Bullshit produced * $ / CO2 THEREFORE: CO2 * Klimut Science = Bullshit produced * $ AND: Klimut Science / $ = Bullshit Produced

  195. climatereflections says:
    *************************************

    Sorry man, I flicked by a response you had to me and now I can’t find it again. I am in a bit of a rush.

    You said P does not equal P. But I say P does equal P.
    Capita means P.
    GDP/1 person is not helpful.
    It is GDP/capita…..
    Thanks for the correspondence. Sorry for the lack of reference to your comment. I wish the comments were numbered.
    Will Nelson

  196. PREDICTION: If it hasn’t happened already, some A-Hole ‘Economist’ will tell us how much each Government-Imported Illegal Alien ‘Contributes’ to GDP and another A-Hole Climate scientist will tell us how each Illegal Alien’s ‘Carbon Footprint’ has been reduced by virtue of relocating to the U.S.

  197. William C. Rostron says:
    July 12, 2014 at 9:16 am

    Willis,
    I am sure that *you* may not be contributing to the GDP by driving down the road, but your car and everything that supports the operation of that car are providing a service to you.

    You guys are missing the point. If I burned that same gasoline to produce something useful, it would be part of our Gross Domestic Production.

    But I didn’t. So the burning of that gas doesn’t show up in the GDP … and it also doesn’t show up in the Kaya Identity.

    w.

  198. THEREFORE (and this is a problem) The more $ spent on climate science, the less Bullshit produced – unless, of course, Climate science becomes more ‘Efficient’, in which case more Bullshit is produced. (per $).

  199. joshv says:
    July 12, 2014 at 9:39 am

    So, I see you’ve quietly backed away from your original mathematical objections and resorted to even more specious objections.

    So, I see that you are unable to read. As I said above,

    As Always: If you disagree with something that someone has said, please have the courtesy to quote their exact words. It avoids much confusion and misunderstanding.

    Go away until you can grasp the subtleties of that paragraph. I am not interested in discussing your fantasies of what I’ve done or not done.

    w.

  200. Willis is right – when I was parking cars for Minimum Wage, I wasn’t producing Jack. And when I’m sitting on my fat arse at 41,000 feet with the Autopilot on burning 300 Gal an hour, I’m not producing Jack.

  201. Richard:

    You begin your post at July 12, 2014 at 10:52 pm saying

    Doug says “that greater GDP leads to more energy use” without any qualification. If this were true Italy would have a greater GDP than France. There is no reason this should be true. It may be true sometimes, but it is not true all of the time.

    Yes! That is an illustration of my objections to the so-called Kaya identity.

    Advocates of the equation presented as an “identity” assert that the “ratios” provided on its RHS are “meaningful”. But that assertion is ‘Alice in Wonderland’ logic.

    The advocates have not explained what they mean by “meaningful”.
    They have not explained how and why any of the the ratios in the Kaya identity is “meaningful”,
    and they have not explained why other components would not be “meaningful”.
    Furthermore, why ratios?

    I have repeatedly argued that the equation is useless and misleading nonsense except as a propaganda tool: the ratios are arguments propagandists want to promote, and a claim that a ratio is “meaningful” is a statement that there is a desire to promote it.

    Importantly, the fallacious Kaya identity needs to be rejected now because otherwise it threatens to become THE propaganda tool used to revive the ailing AGW-scare.

    Richard

  202. Hans Erren says:
    July 12, 2014 at 9:39 am

    The Kaya Identity shows wat happens if you change the contributing parameters, if population goes up, another factor needs to go down if you want to keep the total emission constant. In a world with a continuous global recession and population increase the total emission could remain constant.
    A very useful tool.

    If it is so useful, point out to me where in the Kaya Identity I can find the megatonnes of CO2 emitted over the last decades by the ongoing coal mine fires in China. These fires are estimated to burn between 20,000,000 and 200,000,000 tonnes of coal per year. So lets call it say 50 million tonnes of coal per year to be conservative. A tonne of coal produces about two tonnes of CO2 (because of the added weight of the oxygen). So that’s a hundred million tonnes of CO2 you’re looking for in the Kaya Identity, a huge amount, and that’s just China. Have you ever been to Centralia, Pennsylvania? I wouldn’t recommend it, long-term ongoing underground coal fires have caused the town to be abandoned. Where is that CO2 in the Kaya Identity.

    The answer is … you can’t find it in the Kaya Identity, because it’s not in there anywhere. Which is PROOF that the Kaya Identity doesn’t reflect the real world.

    w.

  203. Matthew R Marler says:
    July 12, 2014 at 10:02 am

    Making sure that the unit ratios cancel properly is a reasonable first step on checking the credibility of the equation. You showed that the units cancel properly, so LHS CO2 can be computed from the formula on the RHS.

    Thanks, Matthew. You’re making the same mistake Mosher did. I’m not canceling the units. I’m canceling the variables.

    w.

  204. DH says:
    July 12, 2014 at 10:04 am

    There is plenty of room to quibble with how those two values are comprised, and how they should be calculated. Saying the identity was a “basic math error” is simply an error on your part and a misrepresentation of what they were trying to do.

    Since I never said it was a “basic math error”, you are either confused or lying. I pick confused … and I’m very tired of accusations that I’ve said things that I haven’t said. Is there something in the following from the head post that was unclear to you?

    As Always: If you disagree with something that someone has said, please have the courtesy to quote their exact words. It avoids much confusion and misunderstanding.

    Read it over and over until you get the message, and THEN come back and start again. I can defend my own words. I cannot defend your misrepresentation of my words.

    w.

  205. Steven Mosher says:
    July 12, 2014 at 10:05 am

    Quote my words
    You laughed because of the cancelling of units.

    There are NO UNITS IN THE KAYA EQUATION AS THE PAPER PRESENTED IT! So how on earth you get the idea that I’m canceling units is beyond me. I am canceling VARIABLES.

    As I said
    Not because it didn’t capture everything.

    Dear heavens, is my writing really that unclear? The whole point of the Beer Identity was to show that there is no guarantee that the Identity captures all of the variables.

    And when you drive you buy gas.
    If no one bought gas what would happen to gdp

    Steven, you miss the point entirely. The contribution of energy to GDP is not when you buy the energy. It is when you burn it to produce something.

    If I burned the exact same gas in a furnace, it would have an effect on the GDP … but that didn’t happen. I burned it to move around the country producing nothing at all.

    w.

  206. Matthew R Marler says:
    July 12, 2014 at 10:16 am

    Willis Eschenbach:

    And that to me is the problem with the Kaya Identity. It’s not that it is false. It is that it gives a false sense of security that we’ve included everything, when in fact we haven’t.

    If you could come up with some examples of such false sense of security, you might have a case.

    Good heavens, Matthew, there are dozens of comments on this and the other thread where people say that they think everything is included. However, as my examples of gas burned on holiday travel, gas flaring, and coal mine fires shows, not everything is included. I’d say that shows a false sense of security …

    w.

  207. In the Bullshit Identity, the more that is spent on Climate ‘Science’, the less Bullshit is produced (per $) – a perverse diminishing return scenario, where they become a victim of their own Bullshit.

  208. Kip Hansen says:
    July 12, 2014 at 10:46 am

    All should know that Willis E. publishes here without prior approval from Anthony or anyone else — in other words, he has authority to put up his own work directly without oversight.

    True. Any mistakes are my own.

    This is not the first time he has gone off half-cocked and shot himself in the foot with something ill-considered. Nor will it be the last.

    Dear heavens, is the inability to read catching? QUOTE MY WORDS, you nasty little man, I said that in the head post because I know there are sleazebags like you out here just waiting to run your mouths.

    Your claims of what I’ve done in the past are just handwaving. You make ugly accusations without the slightest attempt to back them up. Do you think that throwing mud at the wall is the proper way to hold a scientific discussion? QUOTE MY WORDS.

    w.

  209. JK says:
    July 12, 2014 at 11:38 am

    Willis writes:

    ‘consider things like the flaring of gas from oil wells … None of them are in the Kaya identity, but all of them emit copious quantities of CO2.’

    Why could they not be included?

    Certainly, they could be. My point is that people think that the Kaya Identity contains all the variables, but it doesn’t—it’s missing out on megatonnes of CO2.

    I think that it is a problem because people have great faith in math, and they think that the Kaya Identity is an equation like say E=MC2. But of course, it’s not. You can put any variables into it you’d like.

    So while E=MC2 says something true and unchangeable about the real world, we have no such guarantee with the Kaya Identity.

    w.

  210. granda boris says:
    July 12, 2014 at 12:17 pm

    Willis is completely missing the point of this identity. The Kaya Identity has 4 terms and shows that an UP or DOWN change in any of those 4 terms will result in a corresponding change, in the same direction, in the CO2 output.

    Show me where the 100 megatonnes annually of CO2 from the chinese coal mines can be found in the Kaya identity. If you can’t, then obviously the identity is missing at least one variable.

    Then show me where the gas I burned today shows up in the GDP. If I’d burned it to make a product, that would show up in the GDP … but I didn’t produce anything at all. If you can’t, then obviously the identity is missing another variable.

    As a result, your claim is demonstrably false.

    w.

  211. Steve Keohane says:
    July 12, 2014 at 12:29 pm

    This has been quite the can of worms. If you want to consider the flaring of wells as outside the Kaya identity. then isn’t most, like 96%, of CO2 outside the identity?

    No, because we’re looking solely at CO2 that is the result of human actions. Humans flare of the gas, humans set the fires in the coal seams, humans burn gas on vacation and produce nothing with it.

    w.

  212. Thomas says:
    July 12, 2014 at 3:55 pm

    Willis! You’re obviously a brilliant guy but you were wrong about this in the first post and you’re wrong about it again. The car you’re driving in, the road you’re driving on, the fuel the car burns, etc. are all components of GDP.

    If I burned that exact amount of gasoline in a furnace to make a tool, that would add to the GDP.

    But I didn’t. I burned it in an activity that does not add to the GDP.

    So no, the fuel I burned is NOT a component of GDP at all. It would be if I built something by burning it … but I didn’t.

    w.

    PS—In addition, any part of that fuel that was sourced outside the US is a component of that country’s GDP … and thus cannot be a portion of the US GDP, that’s what the “D” stands form

  213. Will, you have made the following comment about the M&M example several times above: “Ah but it is a shell game, the M on the left is not the same M we have on the right is it?”

    Yes it is. Let’s keep it simple with the expression M = P * (M/P), which tells you how many M&Ms you have depending on the number of packets. You don’t have to know M ahead of time to know M/P. Let’s say the package information tells you that there are 100 M&Ms inside each packet. You now know M/P = 100 even before you decide how many packets to buy. Then if you buy 5 packets, you can now determine how many M&Ms you have by plugging in the known values: M = 5 * 100. So 5 packets gives you 500 M&Ms, 6 gives you 600, etc. And, yes, M is the same variable on both sides. Just plug the values for M back in to see that 500 = 5 * 500/5 and 600 = 6 * 600/6. If the packets are uniform, it doesn’t matter what M is because the ratio of M/P always remains 100.

    It’s a similar process when estimating miles you can travel on X gallons of gas using “M = G * M/G.” You don’t have to know M (the total miles you will travel) to know what the ratio M/G (MPG) works out to be on your car under similar conditions. Knowing M/G, you can estimate ahead of time how far you can go on a tank of gas before you need to stop for gasoline. That can be useful information. (The left M is the same variable as the right M in this example, too. Keep in mind that for these examples we are assuming a constant MPG and a constant M&Ms per Packet.)

    There are lots of things where you can know a ratio, like MPG, MPH, or M&Ms per Packet, without knowing the individual variables that make up the ratio. And that knowledge can be very useful as shown in the simple examples above. If you still think it is a “shell game,” please show me an example where the M on the left CANNOT be the same as the M on the right for the M&M formula. Just one such valid example can prove your point. Otherwise, stop repeating it.

  214. Willis. I enjoyed your first article introducing beer into Kaya identity. The second introducing your holidays pleases me even more. But, regrettably, cutting both seem to fit CACA picture so well that your kind and considerate message got blurred.

    Let’s use Mosher et al understanding of Kaya identity on something global, consuming masses of energy, harming GDP and providing citizens no products, services or results to speak of. The IPCC conferences springs into mind. Suggestions anyone?

  215. Willis, Willis, Willis … the gasoline you burn driving around on your vacation IS included in GDP. You have have in mind a non-standad definition of GDP. If you buy the gasoline from Saudi Arabia, then you ought to include the population of Saudi Arabia in the equation.

    Taken in context, the equation expresses HUMAN emission of CO2 for economic purposes. It does not presume to include all sources of CO2, or sources that are beyond human control — volcanoes, underground coal fires, etc.

    It would be better to expressed human emissions of CO2 as energy used by humans times the amount of CO2 emitted per unit of energy used by humans. (Human CO2 emissions = energy used by humans x CO2/energy.) GDP and population are unnecessary factors because we have a pretty good estimate of how much energy we consume in the USA, and in most other countries. The population and GDP factors only add potential for error. Maybe this is what you (and I) find objectionable. Including those terms implies that killing, starving or impoverishing people are all valid ways to reduce our output of plant food.

    Of course, even my simplified (and more accurate) equation implies that we should, or even could, reduce our use of fossil fuels. I also find this objectionable. If you like being able to get cool stuff cheap, or if you like diving around the American West with gorgeous fellow humans (opposite sex in my case, and yours, but who are we to judge?), then emitting more plant food seems like a pretty good idea.

    The equation is, I think, intended to offend thinking skeptics. It’s a bit like writing an equation showing which factors cause perfectly good American children to grow up to be flaming liberals. One could write such an equation but one would have a hard time getting it accepted by Liberal Americans.

    : )

  216. Steven Mosher says:
    July 12, 2014 at 10:05 am

    Quote my words
    You laughed because of the cancelling of units.
    As I said
    Not because it didn’t capture everything.
    And when you drive you buy gas.
    If no one bought gas what would happen to gdp

    So when a French driver of a Fisker does not fill up with gas but plugs in and gets recharged from a nuclear power plant (most of French electrical power generation is nuclear) – what happens to GDP Steven?

    As France has most of its energy nuclear does this ‘identity’ even make valid sense for France or as a comparator between nations?

    There are three illogicalities –
    1. Equating energy use with CO2 output
    2. Assuming linearity of all the variables
    3. Assuming that GDP which can include financial non-industrial product has a direct relationship with emissions of anything.

    This is an example of the level of logic in academia and the reason why if you want anything sensible you need to go to an engineer.

  217. Dr. Doug says:
    July 12, 2014 at 4:42 pm

    Willis and friends,

    First, I take it that the discussion has progressed to the point that you (Willis) and most readers now see that a mathematical identity can be useful if it serves to account for real-world causal relationships that affect the magnitude we’re interested in — in this case, CO2 emissions.

    Thanks, Doc. You claim it “can be useful”. Perhaps you could give a real world example of using it, and exactly what the use of it might be.

    The Kaya Identity incorporates multiple hypotheses: that greater population leads to greater GDP (other things equal), that greater GDP leads to more energy use, that more energy use leads to more CO2 emissions, and that each of these causal linkages can be roughly quantified.

    Suppose for a moment that the US government decreed that all fuel burned on wasteful holidays such as I’m taking must go into actual production. What would be the result?

    Well … the population wouldn’t change. And the energy used wouldn’t change. And the CO2 emitted wouldn’t change.

    But the GDP would increase, because instead of using that gas to carry my sorry okole and a whole lot of other folks around the United States, that same energy would be used to produce say new homes for the poor, or more beer.

    However, the GDP appears in both the numerator and the denominator, so the net result is unchanged. We’ve totally restructured the economy, we’ve converted huge amounts of energy from being “wasted” on holidays to actually producing something … and yet it makes no difference at all to the Kaya Identity. It looks just like when we started.

    So perhaps you could explain, Dr. D, how the Kaya Identity is “useful” in that regard? Because I’m not seeing the utility. What do we know from using the KI that we didn’t know before we made the switch from holidays to production?

    w.

  218. Willis Eschenbach says:

    My point has not changed in the slightest, nor have I “walked away” from anything.

    Your point has changed, now more than once. Your original thesis was that there was something laughably wrong with the Kaya Identity because (like all equations) it can be algebraically reduced to the form X = X. Please don’t pretend otherwise. Your intent was plain enough that not only did the chorus of Willis’ Fanboys parrot their explicitly stated agreement with that same silliness over the span of 600 some-odd excruciating comments, but even poor Anthony was duped by the over confidence of your blustery rant into putting an embarrassingly worded subhead to that effect on your original post. Kaya Identity falsified by stupid maths error … indeed.

    In this post you suddenly aren’t chuckling any more about the fact that equations can be algebraically reduced. Not a peep about it now, though it was the bulk of your first post. You walked away from that point, without manning up and acknowledging your error for having laughed at the fundamentals of algebra. Instead, you decided to double down on the secondary point from your original post – your Beer Identity.

    Problem is, the argument that you constructed from your “Beer Identity” is false, because you got the math wrong. You did not properly identify the terms that you created, because you misunderstood both the original identity and the nature of the effect of your inane alteration of it. Your application of the 0.9 factor was not what you claimed it to be. That error was pointed out to you, and so now you pull a Willis and walk away from it without acting like a man and acknowledging your screw up.

    Instead, you decide to double-double down on your secondary-secondary point, first introduced in this post – your silly complaint that an equation intended to address the relationship between energy-related CO2 emissions and economic production does not (GASP!) appear to incorporate non-economic production related CO2 emissions. Hilarious. You start out this post complaining that the Kaya Identity does not do what it intends to do, and you are now complaining that the Kaya Identity only does what it intends to do.

    Of course the worst bit is that you now pretend that this childish complaint that you have run to in refuge was your point all along though it did not appear at all in your original post.

    Shameful.

    Walk like a man, not like a Mann.

  219. Willis Eschenbach says:
    July 13, 2014 at 12:57 am

    The Kaya Identity incorporates multiple hypotheses: that greater population leads to greater GDP (other things equal), that greater GDP leads to more energy use, that more energy use leads to more CO2 emissions, and that each of these causal linkages can be roughly quantified.

    First, whenever a man says “other things being equal”, I have to point out that in this all-too-real world of ours, other things are never equal … and since your claim depends on that clause, your claim is falsified.

    Next, although the population of the US has grown steadily, at times the GDP has dropped. So obviously, greater population does NOT always lead to greater GDP.

    Next, I don’t understand the claim that greater GDP somehow leads to more energy use. As I pointed out above, increased GDP may only reflect a shift in energy use from non-productive use to actual production of something.

    Nor do I agree that more energy use leads to more CO2 emissions. Energy use in the US is shifting from coal to natural gas … which gives us more energy use with LESS emissions.

    So in fact, your example points out the problem. When we break the Kaya Identity into pieces and look at them individually, none of the hypotheses are true. More energy use may or may not involve more emissions. Greater GDP may or may not involve greater energy use. Increasing population may or may not increase GDP.

    And those problems are not solved by cramming them into an identity.

    Best regards, and thanks for your interesting points.

    w.

  220. Rdcii says:
    July 12, 2014 at 5:35 pm
    (T Co2 Emissions) = (X Population) * (Y GDP / Z Population) … * (A Co2 Emissions / B energy)
    *************************************************
    Well, is that how an increase in Chinese parameters needs to be off-set by corresponding reduction in the US? Which parameters would need to be cut, by whom, where and for what reason? I’m asking this because temperatures have not risen for a couple of decades and I’m having increasingly hard time differentiating Kaya identity from an equally insatiable Lebensraum identity.

  221. This Wikipedia post points to a paper showing how the Kaya Identity is actually used in one study:

    http://www.pnas.org/cgi/reprint/0700609104v1

    It seems that the identity is only the starting point and derivatives are used to look at trends. Units are conveniently balanced in the identity so that the trends can be analyzed according to the assumptions of the identity. The units and math are correct, but are the assumptions or the numbers plugged into the equations right?

    And no, I don’t see where they included “100 megatonnes annually of CO2 from the chinese coal mines” in the analysis. A paper may be literally correct in what it says, but not in what it doesn’t say.

  222. You can take any linear formula and factor out whatever you wish when only the units are being presented. Take X= V*T The terms X, V and T are simply names. if you take away the variable names distance, velocity and time: inches = inches/second * seconds which can be factored down to inches=inches or 1= seconds/seconds etc.

    The only ‘problem’ I see with the Kaya formula is that it has no names for the values GDP/population, Energy/GDP or CO2/energy and simply uses the unit ratios instead. Give them names and the Willis “problem” goes away. Let’s call GDP/population “L”, Energy/GDP “H” and CO2/energy “Q” so now the Kaya formula becomes: CO2 = Population * L * H * Q

    Try the formula for figuring out your gasoline mileage: MPG = miles driven / gallons consumed
    so … miles/gallons = miles/gallon . So yes, miles=miles or gallons=gallons … so what?

    I’m sorry Willis, I don’t think you’ve stumbled on to anything at all here, you have just stumbled. The moment you factor out this or that unit from a formula you have taken information away from it and it is not the same formula anymore and doing so in some cases can become nonsense. For example X= 1/2 * A * T^2 reduced to its units is: inches = 1/2 * (inches / sec^2 ) * sec^2. factoring out inches and sec^2 we are left with: 1= 1/2 Does that invalidate the original formula? Of course not!

  223. Friends:

    OK. I will try to put this as a question in hope somebody will address the basic problem which I have pounded throughout the previous thread and again stated in this thread (at July 12, 2014 at 11:40 pm).

    The “ratios” in the Kaya identity are claimed to be “meaningful” so they are included as “factors” which combine to determine anthropogenic CO2 emissions.
    Can anybody provide a definition of “meaningful” which determines what should and what should not be used as “factors” in the Kaya identity?

    Is anybody able and willing to address this instead of waving red-herrings and providing reams of sophistry as happened in the other thread? I want to know because I am certain I know what “meaningful” means (see my above post at July 12, 2014 at 11:40 pm).

    In the previous thread I pointed out that GDP per capita is a misleading indicator of anthropogenic CO2 emissions and I notice that others have also pointed that out in this thread (including the use of my illustration). Clearly, GDP per capita is asserted to be “meaningful” because it is a factor in the Kaya identity; why?

    Richard

  224. @JK:
    “I just can’t see why people are finding this so hard.
    Let’s say we want to understand the number of web page hits.
    We can invent an identity:
    page hits = number of readers * ( page hits / number of readers)
    …”

    Yes, but we could also invent an identity (among … many many many possibilities):
    pages hits = minimum size of pages in bytes * ( page hits / minimum size of pages in bytes )

    as I’m sure that the size of the pages has *some* influence on each individual reader, don’t you think ?

    But this identity would lead to weird strategies, if you want, say, to maximize the number of hits, either to *increase* the size of your pages (if you consider the 1st term) or *reduce* it (if you consider the last division). And both of them are nonsense, all other things being equal. Besides, the inability to decide if you need to increase or decrease is salient, to say the least.

    The fact is that you have put into the equation a *vaguely plausible relationship that you assume* between terms, then you pretend to *find* it into the terms because of the algebraic formalism which gives you a feeling of scientific legitimacy. If you want to demonstrate something, and define a policy, work on your vaguely plausible hypothesis first, rather than on any identity.

  225. I think that Willis’ Beer example could have been more powerful if, instead of substituting GBP for GDP, he had added in the term into the product, leaving GDP in place. The question is not whether Kaya is mathematically correct, but whether it is adequate, sufficient, and necessary…

    Consider this: CO2 = population x (CO2/population).

    We all agree that this reduces to CO2 = CO2, but we could also argue that CO2 emission per head of population could vary, even if population remains constant (through changed behaviour). We could argue that this identity does not contain sufficient terms to be useful.

    But does Kaya include ALL the terms that are required in order to understand the economic impact of human CO2 emission (assuming all the while that this fractional portion of TOTAL CO2 emission is even worth considering – separate topic!). Population, GDP, and energy seems a conveniently simplistic triumvirate. Can’t disprove; just distrust our ability to fully understand such a complex scenario!

  226. The Kaya Identity, is an identity it is not a formula or an equation!
    It is described by the IPCC as a “The Kaya multiplicative identity” *.

    Strictly, an equation contains unknown quantities (eg. 3x+2=11) and can be solved to determine x.
    A formula links one quantity to one or more quantities (eg. f=ma) and can be used to determine f for any given value m, a.

    As has been argued by many here, a multiplicative identity is “an identity that when used to multiply a given element in a specified set leaves that element unchanged, (such) as the number 1 for the real-number system” **.

    An identity is usually indicated by the equivalence symbol “≡” rather than equals “=” symbol.

    Many have noted as the original post did that the variables are not independent.
    And the IPCC admit this important caveat:

    While the Kaya identity above can be used to organize discussion of the primary driving forces of CO2 emissions and, by extension, emissions of other GHGs, there are important caveats. Most important, the four terms on the right-hand side of equation (3.2) should be considered neither as fundamental driving forces in themselves, nor as generally independent from each other” **.

    But this is an odd confession and in my opinion deliberately confusing.
    In a formula the result requires that the terms on the right-hand side, should be independent but contingent. In an equation the unknown quantity, the result, is dependant on the other terms.

    What is actually being said by the IPCC, is that in the real world, the terms are not independent. To confuse matters further, working through the Kaya identity with real numbers, quickly demonstrates that the terms are truly independent! Change what ever you like and CO2 remains the same. Changing any value does not change the relationship between terms because the ratios cancel across the identity.

    Yes, the Kaya Identity is an identity.

    An identity will be true for any values of its terms and the Kaya is shown to be an identity when tested:

    If
    c= 2, g=20, p=4, e=8.

    Then

    LHS = c = 2
    RHS = p x (g/p) x (e/g) x (c/e) = 4 x (20/4) x (8/20) x (2/8)= 4 x 5 x 0.4 x 0.25 = 2

    Therefore LHS of K = RHS of K if c= 2, g=20, p=4, e=8.

    * http://www.grida.no/publications/other/ipcc_sr/?src=/climate/ipcc/emission/050.htm
    ** http://dictionary.reference.com/browse/multiplicative+identity

  227. Regardless of whether the Kaya Identity is correctly including all the factors in man-made CO2 or not there remains significant confusion on the difference between unit cancellation (dimensional check) and variable cancellation. They are not the same!

    An example of unit cancellation (dimensional check) would be checking the units in the following equation (velocity = distance/time) to make sure they make sense. The units of velocity could be expressed as miles/hour. Thus the unit of distance must be expressed in miles and the unit of time must be expressed in hours. Thus miles/hour = miles/hour and we can be sure that we have a correct calculation. If distance was in meters and the time expressed in seconds we would get a velocity expressed in meters/second — not the same as miles/hour! This is a dimensional check.

    Variable cancellation simply reduces an equation to a simpler format — it has nothing to do with the units that the variable is expressed in! For example in the equation:

    A = (x*y + d*y)/(y + c*y)

    the variable y may be cancelled to obtain

    A = (x + d)/(1+ c)

    which has nothing to do with whatever the units of y were. y could be any number in this formula and it would not change what the final value of A was. To see this let y = 3 in case #1:

    thus A = (3x + 3d)/(3 + 3c) = [3*(x + d)]/[3*(1 + c)] = ( x + d)/(1 + c)

    in case #2 let y = 100

    thus A = (100x + 100d)/(100 + 100c) = [100*(x+ d)]/[100*(1 + c)] = (x+d)/(1+c)

    in other words the value of y does not change the value of A.

    The Kaya Identity as written allows the variables to cancelled out until you are left with:

    CO2_emissions = CO2_emissions

    which means that whatever you change in the other variables (GDP, population, energy) doesn’t matter. In other words it is saying that in order to know CO2_emissions you have to know CO2_emissions!! This is what Willis was trying to point out in his original article.

    If what people are saying the Kaya Identity is trying to show is correct, the correct formulation would be:

    CO2_emissions = f (population, energy, GDP)

    which is saying that CO2 emissions are a function of population, energy and GDP (left to be determined for the moment is exactly what that function is!). However CO2 emissions cannot be a function of CO2 emissions which is what the Kaya Identity as written is saying. That would be like writing an equation with the variables (NOT the units of the variables) like so:

    C = P * (G/P) * (E/G) * (C / E)

    In this case the variables cancel until we are left with C = C which is telling us that in order to know the quantity C we have to know the quantity C!! P, G, and E don’t matter…

  228. Disciple: Master, what is a tree?
    Confucius: That’s a good question, my son.
    Disciple: Yes, but…
    Confucius: A tree is a leaf, but a tree is not a leaf. A tree is a house, but a tree is not a house. A tree is a mountain, but a tree is not a mountain. A tree is the Chinese Gross National Product, but it is not.
    Disciple: Master, that makes no sense.
    Confucius: A tree is not everything which is not a tree. Therefore, a tree is a tree.
    Disciple: That doesn’t really help, Master.
    Confucius: You are not enlightened yet. Go meditate upon your breathing and wash the dishes. When you reach simplification, the true identity of all things will be revealed to you.

  229. In my opinion, it is deliberately misleading to use the equals symbol rather than the equivalence symbol as the IPCC have done with the Kaya Identity. Particularly for such a famous, far reaching and important document as their report is!

  230. Writing “M = G * M/G.” is not helpful as the M on the RHS is not the same as M on LHS.

    More helpful would be a formula that worked:

    TotalFuelUsed = distance/consumption

    where:
    TotalFuelUsed is your favorite liquid measure
    Distance is your distance traveled in your favorite measure Miles or K’s
    Consumption is your miles per gallon or litres per k to suit the above.

    We can even put in values to try it out:
    120 miles / 40 miles per gallon = 3 gallons.

    As this is a regular equation it can be transposed using the normal rules of algebra for us to find either distance or consumption.

    note: if I had written

    M = M/(M/G)

    we would have the same nonsense arguments as we are having about Kaya.

    PS it is my firm understanding that a mathematical identity is an equation that has proven equality for all of its unknown values.
    As such the Kaya equation is not an identity, because it is demonstrably false.

  231. Re: Josualdo: July 13, 2014 at 2:31 am

    Disciple: Master, I have meditated and I see now that the very life of a tree is dependant on CO2
    Confucius: Yes you see now the cycle of life, the identity of all living things, from carbon they come and to carbon they go, earth to earth, ash to ash, dust to dust.

  232. The IPCC itself says about the Kaya Identity: “While the Kaya identity…can be used to organize discussion of the primary driving forces of CO2 emissions and, by extension, emissions of other GHGs, there are important caveats. Most important, the four terms on the right-hand side of [the] equation should be considered neither as fundamental driving forces in themselves, nor as generally independent from each other. Global analysis is often not instructive and even misleading, because of the great heterogeneity among populations with respect to GHG emissions. The ratios of per capita emissions of the world’s richest countries to those of its poorest countries approach several hundred (Parikh et al., 1991; Engelman, 1994).”

    Which seems to invalidate the Kaya Identity before even using it!! Or as richardscourtney says in his comment on July 12, 2014 at 11:40 pm “I have repeatedly argued that the equation is useless and misleading nonsense except as a propaganda tool: the ratios are arguments propagandists want to promote, and a claim that a ratio is “meaningful” is a statement that there is a desire to promote it.”

  233. richardscourtney says: July 13, 2014 at 2:01 am
    “Can anybody provide a definition of “meaningful” which determines what should and what should not be used as “factors” in the Kaya identity?”

    Yes. Let’s do it recursively, to show how identities should be used.

    Willis said originally that all the terms could be cancelled, leaving CO2=CO2. Not useful.

    Let’s start there, but make one split:
    CO2 emitted = Population x (CO2 emitted/population)
    Already we’re making progress. We do have population projections, and we can say something about the second term. If you look at a plot like this, you can see that CO2 emissions in advanced economies are likely to be in the range of 10-20 tons/capita. That isn’t very precise, but already we have two factors each better known than CO2 emission.

    Can we refine? Try (CO2 emitted/population)=(GDP/Population)x(CO2/GDP). Yes, CO2 is correlated with GDP, so we can get a better estimate there. And again GDP/population is something people think a lot about. So probably that split has helped.

    And so it goes. The test isn’t whether each term is known perfectly. It’s just whether breaking up into extra terms helps or hinders.

  234. As presented, the Kaya identity is not an identity.

    If it were in a maths book of identities, it would be reduced to its simplest form:

    CO2 = CO2

    I know of no mathematical identity which is published and shown in its none simplest form.

    There is a challenge!

    If someone had stood up and said CO2 = CO2, they would be laughed out of the room, but here people use it as written.

    From the paper linked above and here:

    http://www.pnas.org/content/104/24/10288.full.pdf+html

    “The full formula is used where each variable is named
    where P is global population, G is world GDP or gross world
    product, E is global primary energy consumption”

    Stating the obvious, if E=E, P=P and G=G, then the do cancel out and you are left with CO2=CO2.

    No point in saying you do not use it as a regular equation when that is how it is used in peer reviewed papers (see above).

    An identity is a regular equation that has a useful meaning, proven equality, hold true for all values and shown in its simplest form.

  235. It seems to me that the confusion mainly lies in the unstable definition of “CO2 emission” on the left side of the equation. In Kaya Identity and Beer Identity, “CO2 emission” — although written the same,— has effectively different meaning. You can produce all the “Identity” in the world, the “CO2 emission” presented would be CO2 emission of a specific realm.

  236. In my opinion, it is deliberately misleading to call the Kaya Identity an equation as the IPCC have done, particularly as equations, formulas and identities, have distinct meaning in Mathematics. For such an important document, as their report surely is, it is not a small oversight (To put it very kindly).

  237. What an incredible blog post. Just scanned through comments.
    “steverichards1984 says: July 13, 2014 at 2:37 am”
    Nails it completely for me.
    It makes perfect sense that if we start with the said equation we end up with CO2=CO2 and I fail to see any of arguments that makes this remotely useful.

  238. I agree that it is not an identity but it is a formula. The issue is simply whether it is useful because each right-hand term can be independently computed or measured without knowing the left-hand value. And whether this is the most direct way to calculate the left hand value.

  239. I am by profession an energy and environmental economist. I do not like the KAYA identity for a whole slew of reasons. But rest assured, none of those have anything to do with the utter nonsense in this guest post. Although I did not have the courage to read all the 262 comments (at the time of writing), it seems others have already thoroughly debunked the main “arguments”. I will therefore only say this. Someone ought to teach the author the “Expenditures Approach” to calculating GDP, including the fact that (exports – imports) is one of the four main components of the consumption expenditures by households. This is Economics 101.
    This guest post should never have been allowed, as it only serves to provide ammunition to those who use the KAYA identity for all the wrong reasons.

  240. Mike M. Why only scratch problem solving semantics, when CACA goes all the way? E.g. fossil fuel = coal = carbon = carbon dioxide = human caused carbon dioxide = human caused global warming = global warming = climate change = climate disruption = weather event.

    It’s puzzling to witness CACA rushing into anthropocalypse from such poems while keeping Kaya identity immune to logic – irrespectively of Δt(CO2 emissions) explanations. Appeal to authority makes the situation worse, especially if the derivatives are used to filter out populations (über/unter).

    For those seeking humor here, the following clip connects witchcraft to buoyancy in a familiar manner: http://www.youtube.com/watch?v=yp_l5ntikaU&feature=kp. Skip to 2:00.

  241. Geez, another post of this nonsense? It really is just an identity, how ever you look at it. Before starting to laugh at this identity, one should really first look into how it is applied.

  242. Willis Eschenbach says:
    July 13, 2014 at 12:22 am

    Steve Keohane says:
    July 12, 2014 at 12:29 pm

    You’re right wrt only human caused emissions. I stopped by quickly and made my ill-thought out comment while in being in the middle of cooking dinner.

  243. This a perfect identity for a World Government bureaucrat, who can give the “market” flexibility to all countries, as long as she controls the co2 per pop. The developed countries can respond by becoming austere. (GDP per pop) or efficient (energy per GDP) or advance technology (energy per co2). Meanwhile allowing the third world to continue using the contemporaneous technology, since their GDP per pop is lower. This perpetual machine will then continue, driving everyone towards the “nirvana” of similar GDP per pop. Or a least perish while trying to attain it.

  244. Arthur 12:03pm said: “For anyone not following what this Kaya formula actually does, put numbers in for Energy, Population, GDP and CO2. Any numbers will work, 10, 24, 36, 40 – whatever. See what happens. The end result will always be CO2 = CO2. Then explain how this is useful – in any real world situation.”

    You can use it in two ways. 1. You decide what level of CO2 emissions you want to achieve and then use the Kaya Identity to look at how that could come about. 2. You project trends in population, GDP and energy consumption into the future and see what CO2 emissions might do.

    I agree that it falls down in applying it directly to the real world. In that respect it is no different from unverifiable climate models which even climate modelers admit are projections not predictions. The climate models and the Kaya Identiy are not saying what *will* happen, just what *might* happen so long as all the assumptions made within them hold true for the length of the projection. What the Kaya Identity is is a model for making ‘evidence’ to fit a predetermined policy.

    Daniel G. 3:02pm said: “Of course, if it is per unit of energy, then the co2 on the rhs (only for a unit) differs from the co2 on the lhs.”

    CO2 per unit of energy on the right hand side is calculated by dividing total CO2 by total energy consumption. It plainly says this in the Kaya Identity. It is the same ‘total CO2′ variable on both sides. You either say CO2 per unit of energy (a ratio) or total CO2 / total energy (the variables). You don’t say CO2 per unit of energy per unit of energy.

  245. So, a dumb question: Why would anyone create an identity like this, unless they have an agenda about carbon dioxide emissions? Root-cause-analysis would say that this is just a political tool being used to make some point about how evil carbon dioxide is. This is a political statement, and not scientific or mathematical, and therefore can never make sense in a real-world way.

  246. When the GDP of Somalia is comprised of the same factors as Germany or the US, I’ll buy into the equation.

  247. As far as I can see the Kayla relationship is mathematically sound whether it is regarded as an identity or as an equation. But in spite of its mathematical correctness it still appears utterly useless to me from the point of view of practical environmental science and economics. You cannot apply it to the calculation of anything in the real world and I think this fact makes it an item of pseudo-science or pseudo-economics as the case may be.

    As I said before (see above 12/7/2014 5:58pm) the reason that I see for its practical uselessness is the fact that you cannot calculate or measure any of the fractions involved without first measuring their primary components and these all cancel one another out ultimately so that the measuring of them in the first place is a pointless, uninformative exercise that leaves us ultimately none the wiser about global CO2 emissions. This point is so glaringly obvious to me that I am finding it hard to understand why so many people appear unable to see it. Perhaps I should explain it in more detail.

    The equation/identity states (using my abbreviations of terms):

    CO2 = Pop’n x (GDP/Pop’n) x (Energy/GDP) x (CO2/Energy)

    In order to calculate global CO2 emissions from this formula we would first need to estimate the global population (Pop’n), which the U.N. purports to have done for us already so we can take that as given. No problem exists there unless one wants to argue with the U.N.’s figure, which I don’t propose to do for the purposes of this demonstration.

    Next we would need to estimate the value of the fraction (GDP/Pop’n), which we can do by estimating the value of global GDP (i.e. the sum total of the GDPs of all the individual countries in the world) and dividing it by our estimate of the global population already obtained. The pointlessness of this exercise becomes immediately apparent at this second stage of the calculation because it automatically eliminates the global Pop’n as a factor in the calculation. We might as well have ignored global Pop’n from the outset and just estimated global GDP!

    But if we look ahead we can also see that global GDP will be eliminated at Stage 3 of the calculation and that global Energy will be eliminated at Stage 4 to leave us ultimately with the uninformative statement CO2 = CO2.

    There is only one possible way of avoiding this automatic collapse of the Kayla function and that is to measure or estimate the fractions independently of their defined components. In other words, we need to calculate (GDP/Pop’n) for instance by some other method than by dividing global GDP by global Pop’n.

    But we have no such other method! At present there simply is none in existence that does not rely fundamentally on our calculating the primary components GDP and Pop’n first. And the same consideration applies to the other two fractions as well. We have no independent alternative methods of calculating any of these fractions. Therefore the automatic self-elimination of these fractions as factors in the calculation by the cancellation of their primary components is an unavoidable, inescapable, inevitable and inexorable certainty that returns us back to square one at the bottom line with the uninformative tautology: CO2 = CO2.

    I can see no other possible conclusion to come to than that the whole exercise is a meaningless mathematical ritual and an empty pantomime.

  248. Willis,

    You have a valid point. The Kaya identity only includes measured CO2 emissions. Our personal emissions are not included. But there are more significant emissions that are not included. An example was observed by Paul Homewood at the beginning of June. A biomass recycling center caught fire.

    http://notalotofpeopleknowthat.wordpress.com/2014/06/04/biomass-on-fire-in-yorkshire/

    I also documented a number of instances where storage depots of recycled material have caught fire. It appears to be a frequent occurrence in England at the moment.

    http://notalotofpeopleknowthat.wordpress.com/2014/06/04/biomass-on-fire-in-yorkshire/#comment-24936

    What is more important (and pointed out by others) is that measured CO2 emissions are only a small part of total emissions. Natural emissions are far more important than human emissions, and are pretty much offset by natural adsorptions of CO2. Though we can only estimate the amount either way, so could easily be way out on the net impact.

  249. Nick Stokes:

    Sincere thanks for your post at July 13, 2014 at 2:52 am which is the first real attempt to answer my question instead of avoiding it.

    Sadly, your attempt fails to answer each of the two parts of my question. Your post says in total

    richardscourtney says: July 13, 2014 at 2:01 am

    Can anybody provide a definition of “meaningful” which determines what should and what should not be used as “factors” in the Kaya identity?


    Yes. Let’s do it recursively, to show how identities should be used.

    Willis said originally that all the terms could be cancelled, leaving CO2=CO2. Not useful.

    Let’s start there, but make one split:
    CO2 emitted = Population x (CO2 emitted/population)
    Already we’re making progress. We do have population projections, and we can say something about the second term. If you look at a plot like this, you can see that CO2 emissions in advanced economies are likely to be in the range of 10-20 tons/capita. That isn’t very precise, but already we have two factors each better known than CO2 emission.

    Can we refine? Try (CO2 emitted/population)=(GDP/Population)x(CO2/GDP). Yes, CO2 is correlated with GDP, so we can get a better estimate there. And again GDP/population is something people think a lot about. So probably that split has helped.

    And so it goes. The test isn’t whether each term is known perfectly. It’s just whether breaking up into extra terms helps or hinders.

    “Helps or hinders” what?
    I did NOT ask for a “test”, and I did not ask “how identities should be used.
    I asked for a definition of “meaningful”.

    The definition should provide two pieces of information; viz.
    (a) What should be used as “factors” in the Kaya identity?
    And
    (b) What should not be used as “factors” in the Kaya identity?

    Your “recursive procedure” does not provide a definition of “meaningful”, and it does not indicate what should and what should not be used as “factors” in the Kaya identity.

    Perhaps an answer to my very basic question can be provided by some other advocate of the propaganda tool known as the Kaya identity?

    Richard

  250. G = M/(M/G)
    we would have the same nonsense arguments as we are having about Kaya.

    The two forms are mathematically equivalent.

  251. I meant to say: “Change what ever you like and CO2 remains the same (Independently of the other terms).”

    Well, that is false. If you change population, gdp will change too. So co2 doesn’t remain the same.

  252. @ Janice,
    No, not a dumb question at all. The intent behind the “equation” was what immediately struck me, which is why I proposed (sarcastically) a “Deep Racial Purity” formula. I find the agenda of “Deep Decarbonization” to be an affront to humanity, and all life itself. Arguing about whether or not the formula means anything has been, I suppose, fun, but it has involved people arguing past one another more than anything. Frankly, it gives me a headache.

  253. Magic Turtle says:July 13, 2014 at 7:02 am You say the Kaya is mathematically sound.

    On what basis can a formula such as A = A be sound?

    Yes LHS = RHS but what is the point of such an equation when its usefulness is limited to demonstrating that LHS = RHS?

    If its alleged use is to find the amount of CO2 somewhere, then it fails miserably because it always gives you whatever answer you want.

    I want 2, I find 2 = 2, gosh I am right again.

    How can that be mathematically sound?

  254. “Daniel G. says:
    July 13, 2014 at 7:27 am
    I meant to say: “Change what ever you like and CO2 remains the same (Independently of the other terms).”

    Well, that is false. If you change population, gdp will change too. So co2 doesn’t remain the same.”

    If you have identical terms in a formula, one above and one below ‘the line’ they always cancel.

    So changing one will change the other leaving no change in output.

    Thats maths.

  255. There are NO UNITS IN THE KAYA EQUATION AS THE PAPER PRESENTED IT! So how on earth you get the idea that I’m canceling units is beyond me. I am canceling VARIABLES.

    “gdp/pop” represents a variable by itself. The relation between gdp and pop is much more simple than the relationship than gdp/pop and pop. Again, read the paragraph directly above the identity.

    Again, the M&M’s example comes to mind again. You can do your cancelling exercise on M&M’s identity, but it doesn’t make the identity invalid.

  256. I’ve changed my mind on the kaya identity. it is not necessarily useless. certainly in routine physics and chemistry problems the units must necessarily cancel each other for the equation to be correct. so in that sense the kaya identity is mathematically correct and may be correct.

    the problem I have with the identity is that it holds true even if you include things that have nothing to do with CO2. so you cannot trust that the identity is correct. because it remains true even if you include garbage factors, so how can you be sure that the identity doesn’t already include garbage factors?

    natural CO2 production is huge as compared to human CO2 production. there is an assumption that natural CO2 production is in equilibrium and it is humans alone that are responsible for the change in CO2. However, we know from the ice cores that CO2 follows temperature, so how do we know that CO2 isn’t increasing as a result of warming from the Little Ice Age, or other factors not yet identified?

    this is the problem in the kaya identity. maybe it can predict CO2, maybe it cannot.

  257. If you have identical terms in a formula, one above and one below ‘the line’ they always cancel.

    So changing one will change the other leaving no change in output.

    Thats maths.

    co2 = pop * (gdp/pop) * (energy/gdp) * (co2/energy)

    Unfortunately, those ratios are not algebraic expressions. They can’t cancel with anything, they are variables.

    If you increase pop, gdp/pop doesn’t decrease proportionally, because there will be an increase of gdp. Result: co2 doesn’t remain the same.

  258. so how can you be sure that the identity doesn’t already include garbage factors?

    Because each factor was throughtly explained.

    there is an assumption that natural CO2 production is in equilibrium and it is humans alone that are responsible for the change in CO2. However, we know from the ice cores that CO2 follows temperature, so how do we know that CO2 isn’t increasing as a result of warming from the Little Ice Age, or other factors not yet identified?

    Well, where is that assumption made?

  259. Furthermore, with the Kaya Identity, we could drop out any or all of the factors and it would not change things a bit. But in your M&M’s example, every reducing unit (C, B, P, M) is required, or you get the wrong answer. With the Kaya Identity, we could keep but one factor (just for sake of retaining the formula) and it would be just the same. For example, with just the last factor, we could say Global CO2 = Energy * Global CO2/Energy

    Bolded is (limitedly) useful, but it is lacking factors, because the energy we’re talking about specifically is the energy consumed in economic activity.

    Anyway, you are wrong about the M&M’s. I can drop factors too:

    M = C * (B/C) * (P/B) * (M/P)
    or
    M = P * (M/P)
    or
    M = C * (M/C)

  260. Moreover, the CO2/energy also has an effect on GDP – the “alternative energies” reduce GDP growth and in the extreme even reduce population through destruction of economic activity, fuel poverty, etc. Ya know, when you are an elite who knows best for the great unwashed, these aspects are undescoverable to them.

    The Kaya Identity doesn’t rule out such relationships. Again, this is not what Willis is talking about.

  261. It makes perfect sense that if we start with the said equation we end up with CO2=CO2 and I fail to see any of arguments that makes this remotely useful.

    The problem is that such argument applies equally to M&M’s. But if a argument is valid and applies to both situtations, then either M&M’s and Kaya identity are both wrong, or they are both false. Which is it?

  262. Willis writes:

    ‘First, whenever a man says “other things being equal”, I have to point out that in this all-too-real world of ours, other things are never equal’

    Which is obviously correct.

    However, many people have found it useful for analytical purposes to consider the effect of changes with other things being equal. There’s even a fancy Latin phrase for it, ceteris paribus, that you can look up on wikipedia.

    Pretty much all economists, most other social scientists (and natural scientists who cannot always control observational conditions), use this assumption repeatedly. None of them believe that in the real world other things really are equal.

    Presumably (correct me if I’m wrong) your claim is not that the whole of economics is wrong, but specifically that the terms of the Kaya identity are too interdependent to make it useful.

    You are quite right that ‘although the population of the US has grown steadily, at times the GDP has dropped’ and to point out that greater GDP does not inevitably lead to more energy use and that more energy use does not inevitably lead to more CO2 emissions.

    In fact, the only use of the Kaya idendity is in understanding changes in exactly these variables. The idea is to get an analytical handle on what happens when one of them changes while the others remain the same, which can then be generalised to the case when they vary simultaneously.

    The ‘other things equal’ assumption is not that these change, but that a base case where one or more of these do not change can be useful for analysis.

    All I can say at this point is, if you don’t find the Kaya identity useful then don’t use it.

    If somebody asked me to estimate what would happen to CO2 emissions IF the shale gas boom resulted in completely eliminating coal generation in favour of gas then I might start by seeing that emissions from gas generation are roughly half that of coal. I could then say that if other things stayed the same, the CO2 emissions previously generated by coal will halve and other emissions remain unchanged.

    Would I be stupid enough to believe that this was some some inevitable truth about the universe? Of course not. I would find it a useful starting point for then investigating the effects of what else might happen under that scenario.

    Commentators here who point out that other things are never equal will point out that my estimate will be wrong. After all, they are quite right that CO2 = CO2! They are not wrong that if other things are not the same, it could do anything.

    I’m sure you will object equally strongly to the idea that we could have any understanding whatever of the effect to of a carbon tax on GDP. $10000 a ton? How can you say that will effect GDP? After all, other things are neve equal and all we can ever say is GDP = GDP!

    Knock yourselves out.

    PS I appreciate that Willis has had a lot of comments to answer, but I will note that all the way back on

    July 12, 2014 at 10:38 am

    I explained that in addition to these more interesting questions of interpretation your OP does contain a plain wrong arithmetic statement, and you haven’t responded to that.

    Anyway, I’ve tried to explain myself so many times on this topic I feel diminishing returns have set in, so doubt I will return to it.

  263. Daniel G.

    You have made many posts in both this and the other thread but you have not answered my basic question. I remind that it is:

    The “ratios” in the Kaya identity are claimed to be “meaningful” so they are included as “factors” which combine to determine anthropogenic CO2 emissions.
    Can anybody provide a definition of “meaningful” which determines what should and what should not be used as “factors” in the Kaya identity?

    I would appreciate your provision of a clear answer to this question because everything you have written about the so-called Kaya identity is meaningless nonsense in the absence of the required clear definition.

    Richard

  264. C=2, B=3, P=4. Lets use Mp to represent the number of M&Ms per package and Let Mp=5. We can all agree (hopefully there’s no debate :) that the total number of M&Ms in all packages is:
    Mt = C*B*P*Mp = 2*3*4*5 = 120. So far so good. Now let’s apply the M&M….

    Basic mistake right there, 4 is the absolute number of packages. 5 is the number of M&M’s per package.
    There are 20 M&M’s.

    I hope you come back to see my reply, you might get embarassed.

  265. Can anybody provide a definition of “meaningful” which determines what should and what should not be used as “factors” in the Kaya identity?

    The ratios have very clear meaning. That is what it means to meaningful.

  266. Willis Eschenbach says:
    July 12, 2014 at 11:25 pm
    “You guys are missing the point. If I burned that same gasoline to produce something useful, it would be part of our Gross Domestic Production.

    But I didn’t. So the burning of that gas doesn’t show up in the GDP … and it also doesn’t show up in the Kaya Identity.”

    It would show up in the GDP when you(or someone) bought the gas regardless of what was done with it. IAC, there are ways to alter the GDP without altering the CO2 emissions and vice versa **but** for the Kaya Identity to be flawed these things would have to be significant in terms of the rest of the total picture and it is pretty doubtful that they are IMO *currently*.

    Respectfully, you’re much better off focussing on whether the Kaya Identity is *useful*. Personally, I doubt that it can be shown to have made a single significant prediction – which is what science is supposed to be about.

    Cheers, :)

  267. Steven, you miss the point entirely. The contribution of energy to GDP is not when you buy the energy. It is when you burn it to produce something.

    False, buying such energy is part of a very complex economic process.

  268. Respectfully, you’re much better off focussing on whether the Kaya Identity is *useful*. Personally,

    Probably, but the problem is that Eschenbach et al. still maintain the “cancelling” and “i can put any variable” arguments.

  269. There is more to this. Indeed a history of GDP PER CAPITA GROWTH shows that GDP by the nature of its economic mechanics is not independent of population growth.

    Mere population growth is mere population growth. The key here is growing use of capital, so that productivity is vastly increased. Increasing GDP per capita can increase population, but that doesn’t invalidated Kaya identity.

  270. Daniel G, the M&M case is not an identity. It is a poorly written formula.

    1) M = C * (B / C) * (P / B) * (M / P) should be written as

    2) M = NumOfCrates * (BoxesPerCrate) * (PktsPerBox) * (MperPkt)

    You had C as your 1st term as the number of crates in your shipment, also in your 2nd term you had B/C implying C is boxes of crates in your shipment.

    But if that were true your B/C ratio changes depending on how many crates there are in your shipment!

    It is best to ensure that unique variables are named so clearly that anyone can see at a glance that your C and B/C are not related or joined in anyway whatsoever.

    My equation 2) works, double any of the terms and you double the answer (correct).

    It is also transposable.

  271. Let “instantaneous acceleration of an interplanetary probe” = A
    We can now say: A = Pop * GDP/Pop * Energy/GDP * A/Energy
    Clearly, we can increase the instantaneous acceleration of an interplanetary probe by increasing our standard of living! It will also increase if the population goes up.

    Why is the Kaya Identity any more meaningful than this?

    Well, if you manage to use that energy to make the probe accelerate, then that is not a bad identity.

    Again, all the factors were explained, there isn’t a big mistery.

  272. Daniel G.:

    At July 13, 2014 at 8:00 am your post replies to my question by saying in total

    Can anybody provide a definition of “meaningful” which determines what should and what should not be used as “factors” in the Kaya identity?

    The ratios have very clear meaning. That is what it means to meaningful.

    OK. I accept that. So I have a few more “factors” that “have very clear meaning” so should be included in the so-called identity.

    For example, ‘the heating and cooling requirements of the sleigh used by Santa Claus to transport presents from the North Pole to around the world’ is a stated “factor” that has a “very clear meaning” and, therefore, according to you a missing factor in the Kaya identity is (Santa’s travel/ sleigh temperature control CO2).

    This “factor” is required but omitted and, therefore, the Kaya identity is incomplete according to your definition.

    Richard

  273. Daniel G. says:
    July 13, 2014 at 7:27 am

    “Well, that is false. If you change population, gdp will change too. So co2 doesn’t remain the same.”

    Daniel G. and others, It does not matter if you use variables or replace them with values.

    However, actually replacing the terms with values (numbers) will reveal much to you.

    I ask you please, test the identity because you will find, that it is an identity, that is what the IPCC say it is and that is what I and many are trying hard to agree with!!

    You don’t even have to write it all out for yourself, I have done it for you in my post above. I added values to the identity as specified by the IPCC.
    I know what an Identity is.
    I know what a formula is.
    I know what an equation is.

    Just slow down and take a moment to put your own values into the Identity.
    Why? Because you will see that I and many others are being a little bit Socratic (Playing the fool in a very nice way!)

    And no, it is not true that if “you change population, gdp will change too. So co2 doesn’t remain the same”. Changing the population does not affect Co2, if it did, it would not be an identity! I know you want it to be an equation or a formula but it is an identity!!

  274. But if that were true your B/C ratio changes depending on how many crates there are in your shipment!

    No, i have just reformed the equation, using a ratio of symbols to represent a ratio variable. I can do the same with Kaya identity:

    energy-rel. co2 em. = pop. * (gdp per cap.) * (energy inten. of the econ.) * (co2 inten. of energy)

  275. Willis said: “..something like two-thirds of peer-reviewed science is falsified within a year.”

    Where did this claim originate? Any background information on this?

    Thanks,
    Nigel.

  276. However, actually replacing the terms with values (numbers) will reveal much to you.

    gdp is not term of the identity.
    Again look at two terms:
    population
    gdp/population

    If increase population (let’s say double)

    Then (fallaciously):

    new gdp per capita = dp/(new pop.) = gdp/(2*old pop.) = (1/2)(gdp/old pop.) = (1/2)(old gdp per capita)

    Therefore (fallaciously) energy-related co2 emissions stay the same.

    But, why is this reasoning wrong? It is wrong because gdp also changes. That will make energy consumption change too. That will ultimately increase co2 emissions.

  277. No, i have just reformed the equation, using a ratio of symbols to represent a ratio variable. I can do the same with Kaya identity:

    What does that mean “I have reformed”

  278. What does that mean “I have reformed”

    I have written the identity in a mathematically equivalent way.

  279. Just slow down and take a moment to put your own values into the Identity.
    Why? Because you will see that I and many others are being a little bit Socratic (Playing the fool in a very nice way!)

    Just slow down, and tell me if that doesn’t apply to M&M’s.

  280. @Daniel G. says: July 13, 2014 at 8:21 am:

    The implication of what you are saying is that the Kaya identity does not consist of fractions but just 4 unique terms:

    CO2 = Pop * GDP * Energy * CO2

    Where the 4 terms interact with each other in a complex manner.

    Is this your case?

  281. Is this your case?

    Incorrect.

    energy-rel. co2 em. = pop. * (gdp per cap.) * (energy inten. of the econ.) * (co2 inten. of energy)

  282. Well, your 8:31 am will not cancel down so it has a possibility of doing something.

    What is your definition of each term?

  283. What is your definition of each term?

    Read JK’s post, please.

    JK writes:

    – (GDP / population) is a well known proxy for “living standards”. This the wealth produced and consumed per head. I would argue that even though GDP is an imperfect measure of wealth, rising GDP per capita is a fundamental measure of progress.

    – (energy / GDP) is a fundamental ratio for thinking about economic history. If you want to understand the industrial revolution, or pretty much all economic history since, you need to look at how amount of wealth that can be generated from each unit of energy has developed.

    – (CO2 / energy) shows in a basic way the effect of that different energy generation technologies (coal, oil, gas, nuclear, hydro, wind, etc) have on CO2 emissions. addendum by me: this includes fuel

  284. I think Willis’s original point is now well accepted.

    The passing off of a political construct as a mathematical formula or worse, as a ‘proven identity’ has been shown to be wrong.

    I realise that some people will not accept it but you can not go round stating that something is a mathematical identity then trying to stop people from applying the normal rules of maths to it.

    I am happy that I now understand Daniel G, when he declares that B/C could, at one hour be B divided by C and latter, a ratio that cannot be so divided or simplified.

    This is post normal maths, we have a lot to learn.

  285. Willis Eschenbach says:

    First, whenever a man says “other things being equal”, I have to point out that in this all-too-real world of ours, other things are never equal … and since your claim depends on that clause, your claim is falsified.

    What a stupid thing to say. First you attack the validity of algebraic expansion and dimensional analysis, now you attack the validity of conditionals in formal logic. You are rapidly becoming a caricature, Willis.

    Next, although the population of the US has grown steadily, at times the GDP has dropped. So obviously, greater population does NOT always lead to greater GDP.

    And when GDP does not keep up with population, what happens? Standard of living (GDP/Pop) goes down. OH LOOK, there is a term for standard of living in the Kaya identity (GDP/Pop), and when GDP doesn’t keep up with population, that term in the Kaya identity drops. Huh. Whattaya know.

    Next, I don’t understand the claim that greater GDP somehow leads to more energy use

    As has been pointed out to you, when you make these sort of errors it is because you are equivocating on terms. The “energy use” in the KI is not total energy used by the country for everything, it is energy used by the country for the purposes of economic production.

    Nor do I agree that more energy use leads to more CO2 emissions. Energy use in the US is shifting from coal to natural gas … which gives us more energy use with LESS emissions.

    OH LOOK, there is a term for the CO2 intensity of energy in the Kaya Identity (CO2/Energy), and when that term is decreased, the total energy used for production may increase while CO2 emissions show a drop. Huh. Whattaya know.

    So in fact, your example points out the problem. When we break the Kaya Identity into pieces and look at them individually, none of the hypotheses are true. More energy use may or may not involve more emissions. Greater GDP may or may not involve greater energy use. Increasing population may or may not increase GDP.

    Good grief. Do you even realize that you are arguing against yourself?

    More energy use may or may not involve more emissions? So you think that the Kaya Identity should account for that, by including a CO2 intensity term. OH LOOK, IT DOES!

    Greater GDP may or may not involve greater energy use? So you think that the Kaya Identity should account for that, by including an energy efficiency term. OH LOOK, IT DOES!

    Increasing population may or may not increase GDP? So you think that the Kaya Identity should account for that, by including a standard of living term. OH LOOK, IT DOES!

    In your original post, you insisted on algebraically reducing those terms out of the Kaya Identity, and pretending that the fact that you could meant something bad. Now you are arguing in favor of the necessary expansion of any such identity to include those terms. You are arguing against the derivation of the Kaya Identity, by deriving the Kaya Identity.

    In other words, your argumentation here reduces logically to “Willis does not equal Willis”. NOW you have something to laugh about.

  286. May last attempt:

    Daniel G at 08:40…. by referring to JKs post: (GDP / population) and (energy / GDP) you’re putting real numbers into fractions which can the be simplified (if this a mathematical formula)

  287. Your rant does not amuse, I have answered to all your arguments using traditional logic.

    Yes, you can simplify, but it is meaningless! But that simplification has nothing to do with the real world. The same argument applies to M&M’s identity.

  288. you’re putting real numbers into fractions which can the be simplified (if this a mathematical formula)

    JK was dealing with the way the identity was presented. But you can substitute the fractions by letters. Then you have variables by themselves. The fact is that population increase is not cancelled by gdp per capita decrease.

  289. Hans Erren says: July 13, 2014 at 8:37 am
    The broadway identity: Dollars per show = visitors per show x price per ticket
    Willis when in a hole, stop digging.

    +1

    Now, here is something indisputable: Girls = Evil
    Given that Girls = Time x Money and that Time = Money, it follows Girls = (Money)²
    Given that Money is the root of all Evil, or Money = sqrt(Evil), it follow Girls = [sqrt(Evil)]², or
    Girls = Evil, QED.

  290. Han Erren
    You are missing the point, you have written a ‘formula’, not an equation and not an identity. That said, do you mean average dollars per average number of shows x average ticket price per show? I guess you are saying c (Total cash) = t (number of tickets sold) x p (ticket price). Either way, neither are identities, because the variable(s) on the LHS are not represented on the (RHS).

    Yes it is pedantic but that is what this whole post is about. ;-)

  291. Yes it is pedantic but that is what this whole post is about. ;-)

    Wow, just wow. I though the post and previous one gave the ultimate absolute proof that the Kaya Identity is despicable postmodern political construct disguised as math.

    Anyway, it is possible to make the first-order approximation that people going = tickets.

  292. I am reminded of Lewis Carroll’s Humpty Dumpty:

    “When I use a word,’ Humpty Dumpty said in rather a scornful tone, ‘it means just what I choose it to mean — neither more nor less.’

    The “Kaya Identity” is an attempt to give a weak argument spurious validity by ‘appeal to maths’. As with Humpty Dumpty above – it can mean just what someone wants it to mean. This is shown by the multiplicity of views in this and the previous thread.

    If the terms are not defined – and in this ‘equation’/’identity’ they are not then anything can be claimed from this type of pseudo mathematics.

    So for example:

    IF
    1/2F = 1/2E
    Then
    F=E

    Mathematically correct until the terms are defined:
    F<- Full and E <- Empty

    (this was borrowed from a similar medieval ‘proof’ of life after death as half dead = half alive)

    Hand-waving and bloviating waffle do not make this arts grad attempt at claiming mathematical authority correct. It is a pure PR exercise and any engineer would have thrown it out.

  293. So why resort to some fancy, schmancy equation? Just go to EIA and work with real numbers. CO2 emissions from: Coal – 31.9%, NG – 25.8%, Petroleum – 42.1%. (figure 12_3) What I found surprising is that NG produces 80.8% as much CO2 as coal. I suppose that’s because NG unlike coal is used for more than electricity, i.e. space and water heating. And since petroleum is the biggest source of CO2 how about applying the 1,100 pounds of CO2 per MWh (HPh) to planes, trains, and automobiles?

  294. Daniel G. says:
    July 13, 2014 at 8:05 am
    “Probably, but the problem is that Eschenbach et al. still maintain the “cancelling” and “i can put any variable” arguments.”

    I agree with you and that these arguments are flawed. I was simply attempting to see if we could move the debate forward. Some folks seem to have a hard time admitting when they are wrong …

    Cheers, :)

  295. Ian W says:
    July 13, 2014 at 9:04 am
    “1/2F = 1/2E
    Then
    F=E

    Mathematically correct until the terms are defined:
    F<- Full and E <- Empty"

    Your problem is that given the definition of full and empty your 1/2F=1/2E can't be true (this condition does not apply to Kaya).

    Given the definition of full and empty – a correct mathematical description of full and empty would be:

    Total volume=full volume + empty volume

    Then, when TV=1 and F=0.5, then E must equal 0.5 as well (like your hypothetical).

    We could then use measurements of TV and F to calculate/predict E, for instance.

    Nothing wrong with that at all but it is the last step(ie making valid predictions) that determines whether or not the expression/identity is science.

    Cheers, :)

  296. OK, one more time, since Hans Erren has given a useful example:

    ‘The broadway identity:
    Dollars per show = visitors per show x price per ticket’

    Scott Wilmot Bennett says ‘variable(s) on the LHS are not represented on the (RHS)’ but since visitors = tickets we get the same thing by writing:

    Dollars per show = tickets per show x (dollars per show / tickets per show)

    The CO2 = CO2 or ‘other things are not equal’ crowd would point out that if you change the price of a ticket then you will change the number of visitors per show.

    That’s quite true.

    Does that mean the equation is not true? No.

    Does that mean it’s never useful, as an analytical tool? I would say no.

    multiplying by shows we get:

    Dollars = number of shows * (tickets / show) * (dollars / ticket)

    Again, the CO2 = CO2 or ‘other things are not equal’ crowd would point out that if you put on more shows then anything could happen! Quite true. Dollars = Dollars, after all.

    The formula suggests that putting on 21 shows instead of 20 would result in 5% more dollars brought in. But that assumes (tickets / show) is constant! Maybe after 20 showings everyone who’s seen the show has seen it and you can’t sell more tickets, or maybe it takes 20 shows before word of mouth spreads and sales take off? Other things are not equal.

    At this point you could just say that the identity is just useless. How could we ever hope to guess what might happen to income if we change the number of shows, increase the advertising budget or change the ticket price?

    Dollars = Dollars, after all! Who could argue with that?

    Or, we could attempt to use the identity to estimate the effects of simultaneous changes in the variables in these different scenarios. It could give us an analytic starting point for trying to understand how many more customers we need to attact to break even if we reduce the ticket price.

    The CO2 = CO2 or ‘other things are not equal’ crowd would presumably just say that’s a hopeless exercise. After all, this is just as true:

    Dollars = number of shows * (GBP / shows) * (dollars / GBP)

    Gross bear production obviously has nothing to do with it – just like CO2 emissions / energy production and energy production / GDP obviously have nothing to do with total CO2 emissions in an economy from energy producion.

    So we might as well just say that Dollars = Dollars, that CO2 = CO2 and be done with it.

  297. richardscourtney @2:01am:

    “The “ratios” in the Kaya identity are claimed to be “meaningful” so they are included as “factors” which combine to determine anthropogenic CO2 emissions.
    Can anybody provide a definition of “meaningful” which determines what should and what should not be used as “factors” in the Kaya identity? ”

    Nick Stokes @2:52am:

    “CO2=CO2. Not useful.

    Let’s start there, but make one split:
    CO2 emitted = Population x (CO2 emitted/population)
    Already we’re making progress.”

    ——

    The equation, as Willis has written it, is meaningless and is incorrect. Nick, it makes not one whit of difference what we plug in and it isn’t one bit meaningful . . . that is, if the terms fully cancel each other out (as Willis has wrongly written it).

    We might as well say:
    CO2 = (# of Miley Cyrus fans) * (CO2/# of Miley Cyrus fans).

    It is most certainly not meaningful, not helpful, is not making any progress. It is pure nonsense.

    The issue here — the reason we have spilled so much ink over this blasted “identity” nonsense that some people feel inclined to defend with silly claims that it is meaningful — is that Willis (and Wikipedia) do *not* write the Kaya equation the way it really works. Check out how Roger Pielke writes the equation to see what the real equation is in practice. It is a straight-forward, multiplication, result-producing equation. Not some silly cancel-identical-parameters-on-the-same-side-of-the-equation business.

    So, Richard, let’s stop picking apart an equation that was presented wrongly and that no-one uses anyway. Willis right to laugh at such a notion, but he is laughing at an equation that doesn’t exist in practice. Nick, let’s stop trying to defend an indefensible equation on the idea that it is somehow a magical “identity” that gets to avoid the regular rules of logic and mathematical reason.

    • Climatereflections says “So, Richard, let’s stop picking apart an equation that was presented wrongly and that no-one uses anyway. Willis right to laugh at such a notion, but he is laughing at an equation that doesn’t exist in practice.”

      It’s fun to pick it apart and contrary to your assertion, it is also on display at the world’s leading resource for casual information — Wikipedia!

      http://en.wikipedia.org/wiki/Kaya_identity

      It really does cancel out.

      The page cites IPAT which is “I (bottles per mile) P (capita) A1 (miles driven per capita) A2 (gallons of beer per mile driven) T1 (bottles used per gallon beer) T2 (bottles out the window per bottle used).”

      As you can see, IPAT does not self-cancel. What we have here is a clear-cut case of idiotic Wikipedia editing. But whoever it is, he’s not alone.

      http://www.manicore.com/anglais/documentation_a/greenhouse/kaya_equation.html

      As you can see, many people (including right here) think it’s great to have algebra that cancels out but somehow still has meaning. THAT is entertainment!

  298. Shawnhet:

    At July 13, 2014 at 9:08 am you say to Daniel G.:

    Some folks seem to have a hard time admitting when they are wrong …

    Yes. And in this thread the prime culprit (by a large margin) is Daniel G..

    For example, the Kayla identity can only be meaningless nonsense unless there is a definition of “meaningful” “factors” which determines what “factors” should and what “factors” should not be included in the so-called “identity”. Eventually, after much effort, I managed to get Daniel G. to provide his definition which he did at July 13, 2014 at 8:00 am. But his definition is ridiculous and I did ridicule it in my reply at July 13, 2014 at 8:13 am which is here.

    As he repeatedly did on the other thread, Daniel G. has conveniently forgotten the matter when shown to be wrong.

    Richard

  299. richardscourtney: Can anybody provide a definition of “meaningful” which determines what should and what should not be used as “factors” in the Kaya identity?

    There is probably not an abstract definition that you would accept. One can list the usual things (which provides an ostensive defintion), or a rough rubric such as “anything that contributes at least 1% to the R^2 value of the equation. The meaningful things that contribute to GDP are not the same in all countries: Germany doesn’t grow coffee or pineapples; Kenya doesn’t manufacture automobiles or lithium batteries.

  300. Shawnhet says:
    July 13, 2014 at 9:23 am

    Sigh

    If a country moves to all Nuclear/Wind/Hydro/wave power as its input is your ‘identity; true?

    The primary hidden assumption (making it mean what you want it to mean) is that all energy generation is equal in creating CO2 as a byproduct. This is false.

    The second assumption is that GDP is driven solely by energy consumption, this is also false.

    It has as much validity as the medieval proof of the afterlife.

    Its fake maths – and Shawnhet – I will have large fries with that. ;-)

    Cheers

  301. Willis is punching above his weight here and has disqualified himself from ever criticizing the mathematical work of anyone else. His wiggling where there is no wiggle room is surely drawing laughter from Anthony’s peers. His errors are the platform upon which other uninformed people chant the same wrong conclusion: CO2 = CO2! There will be no gracious mea culpa, no apologies to math teachers everywhere for confusing their students, no clarification as emergent phenomena of his failure. The hole he’s dug here is deep enough to be considered one of the wonders of the world. The Willis Eschenbach by-line is now junk stock.

    WTFUWT?

    Time to move on – nothing to see here

  302. Ian W says: July 13, 2014 at 10:11 am
    Its fake maths –

    I wouldn’t even call it that – it has absolutely nothing to do with math ! KAYA is just shorthand for 4 true but trivial assertions, namely:
    to halve worldwide anthropogenic CO2 emissions, and all other things being equal or held constant,
    1) cut the worldwide population in half;
    2) cut worldwide consumption in half;
    3) cut energy used in production in half;
    4) cut carbon used to produce that energy in half.

    Pielke in his dispute with Krugman succesfully used KAYA to demonstrate that 1) and 2) are simply not realistic; that 3) offers only limited (and short-term) possibities as it is impossible to produce (or do) anything without using energy; and so that 4) is the only long-term realistic option to drastically cut CO2 emissions.

    Does Pielke not know that those factors are dependent! Of course he does! But even IPCC has known that for some odd 20 years, certainly long before Willis had ever heard of KAYA. But that’s not the point. KAYA is not a “model”, let alone a “mathematical model” ! Again, it has absolutely nothing do with mathematics.

  303. richardscourtney says:
    July 13, 2014 at 9:40 am
    “For example, the Kayla identity can only be meaningless nonsense unless there is a definition of “meaningful” “factors” which determines what “factors” should and what “factors” should not be included in the so-called “identity”. ”

    The scientific method gives a standard for determining what should and should not be included in a hypothesis – namely that you should include things that allow/help you to make meaningful predictions of measurable stuff that happens in the real world and exclude those that do not.

    As i said previously, I strongly doubt one can actually make such meaningful predictions using the Kaya framework but if one can do it, then the objections raised against it in the thread and its predecessor are moot.

    Cheers, :)

  304. Ian W says:
    July 13, 2014 at 10:11 am
    “Sigh

    If a country moves to all Nuclear/Wind/Hydro/wave power as its input is your ‘identity; true?”

    Sign. Not the point at all. Countries can’t just decide to move to non-carbon sources of energy at the flip of a switch. Rather, it has to happen slowly and gradually, which means that something like Kaya could still provide a valuable picture of the world (in other words its math will not be “fake”).

  305. Bertrand Russell wrote: If you can not know something without knowing everything, then it is obvious that you can not know anything.

    People who have been criticizing the Kaya identity (or Kaya equation or Kaya formula) have, I think, established a few things beyond doubt:

    1. the units cancel properly;

    2. neither CO2, GDP, Energy per GDP, nor CO2 per energy can be known with exquisite accuracy for any place and time.

    3. analogies to the Kaya equation can be written that are of no use whatsoever (that is:

    LHS = scale*ratio1*ratio2*ratio3.)

    4. other important contributors to CO2 are not in the equation.

    The history of science is replete with such incompleteness as represented by points 2,3 , and 4. In the early 1800s, three different people showed with statistical analysis that cleaning stuff in hospitals improved the survival rates of patients; no one could explain why, not all deaths were tallied, not all causes of death were well-recorded, and so on. But the knowledge proved useful in the US Civil War even though, is it happened, most of the injured soldiers cared for in clean conditions died anyway.

    In 1998 or 1999, Perlman and Ho showed in an article published in Science magazine, using a dynamical model in which most of the really important factors were not included, that HIV reproduced at a high rate in infected individuals and that anti-retroviral medications reduced that reproductive rate to near 0. This important step in the fight against AIDS contained many of the liabilities highlighted in these two threads: the model could be mimicked by other models of the same structure that were totally useless; the HIV viral burden could not be measured very accurately in blood, and hardly at all in other reservoirs of the body; most of the infectious agents that caused deaths in HIV-infected individuals were not measured at all; the life histories of the patients were not included in the model at all (these life histories were considered “meaningful” by some scientists working on AIDS, not meaningful by others, and there was no a priori definition of “meaningful”); and so forth.

    The integrate-and-fire and quadratic integrate-and-fire models of the neuron likewise omit many important facts of neural science, but they are extremely useful in simulations anyway (see Izhikevich, “Dynamical Systems in Neuroscience”, and Kass, Eden and Brown, “Analysis of Neural Data”, for other examples of modeling complex systems with models that have known liabilities and systems measured with bias and error.)

    If the standards promoted here by Willis Eschenbach had always been followed, nothing would ever have been learned. Since I don’t believe there is any utility in reducing CO2 I don’t think that use of the Kaya equation will prove fruitful. That said, I hope that no one is deterred from working out the details in actual cases merely because of the critiques presented in these 2 threads.

    Next up: can you increase GDP by reducing malaria incidence? By how much? Do the components of GDP and the techniques of reducing malaria incidence have to be the same in each country or region? Is malaria the only problem impeding GDP growth? Is malaria itself equally destructive in all economies? Are there equations that that are potentially useful, yet with comical parallels? Do those equations instill overconfidence in people working to eradicate malaria.

  306. Willis Eschenbach: Thanks, Matthew. You’re making the same mistake Mosher did. I’m not canceling the units. I’m canceling the variables.

    No, Willis, you cancelled the units. The values of the variables are multiplied together.

    “canceling the variables” doesn’t even have a definition.

  307. thallstd says:
    July 12, 2014 at 9:37 am

    Excellent point that an increase in population does not necessarily imply a corresponding decrease in GDP per capita. In fact, GDP per capita could go up, down or stay the same depending on whether the net population change results in more or fewer people in the workforce.

    Tom Trevor says:
    July 12, 2014 at 9:42 am

    The error in your thinking has been thoroughly explained in the other thread. Search for “dimensional analysis”.

    Michael 2 says:
    July 12, 2014 at 9:57 am

    Yet readers still insist on thinking they can look at a ratio, e.g. GDP per capita, and fiddle with the numerators and denominators independently. As long as they think that, they’ll never understand their error.

    Arthur says:
    July 12, 2014 at 10:10 am

    See my comment to Tom Trevor above, and please stop with this silly and incorrect line of thinking.

    Arthur says:
    July 12, 2014 at 12:03 pm

    Please, please, please – when you’re already in a hole, stop digging.

    Bob Sullivan says:
    July 12, 2014 at 12:16 pm

    I’ll say this again to all of you who think this logic is correct…

    You don’t substitute a value for the denominator of any of the ratios. The value of each denominator is always 1.

    “GDP per capita” means “GDP per 1 person”. “Energy per GDP” means “energy per $1 of GDP”. “CO2 emission per energy” means “CO2 emission per 1 Joule of energy”.

    You can substitute a value for the entire ratio, which is, in effect, substituting a value for the numerator. But, leave the denominators alone!

    I’ve only gone about a quarter of the way through the thread, but I’m too fed up to go any farther. If any of you mentioned above have admitted farther down in the thread to the error of your way, I apologize.

  308. “You Keep Using That Word, I Do Not Think It Means What You Think It Means”

    1) useless equation (kaya identity as constructed)
    total distance traveled = total distance traveled/hours traveled * hours traveled

    2) useful equation (kaya identity as intended?)
    total distance traveled = distance traveled/hour * hours traveled

    hours traveled != hour
    total distance traveled != distance traveled

    You cannot justify equation 2 algebraically:

    total distance traveled = total distance traveled
    -> transform total distance traveled into distance traveled algebraically?
    total distance traveled = distance traveled
    -> multiply by hours traveled/hour algebraically?
    total distance traveled = distance traveled/hour * hours traveled

  309. Willis Eschenbach quotes someone else quoting Willis Eschenbach:
    Willis Eschenbach says:
    July 13, 2014 at 12:57 am

    The Kaya Identity incorporates multiple hypotheses: that greater population leads to greater GDP (other things equal), that greater GDP leads to more energy use, that more energy use leads to more CO2 emissions, and that each of these causal linkages can be roughly quantified.

    First, whenever a man says “other things being equal”, I have to point out that in this all-too-real world of ours, other things are never equal … and since your claim depends on that clause, your claim is falsified.

    And those problems are not solved by cramming them into an identity.

    “Other things are never equal” applies to every equation ever applied to anything. Practically, you can only assess whether the omitted variables have changed enough, or will change enough, to add too much to the already present error of approximation.

    Has anybody claimed that those problems have been solved “completely”?

    At this rate, you will soon establish that the Brooklyn Bridge can’t be built, much less stand.

  310. Daniel G. says:
    July 13, 2014 at 8:05 am

    Respectfully, you’re much better off focussing on whether the Kaya Identity is *useful*. Personally,

    Probably, but the problem is that Eschenbach et al. still maintain the “cancelling” and “i can put any variable” arguments.

    The implication is there is a wrong way to use the identity and there is, of course, but that is easily corrected. The unspoken claim is there is no right way to use the identity and that is evidence of a deep misunderstanding of math.

  311. richardscourtney says:
    July 12, 2014 at 11:40 pm

    “I have repeatedly argued that the (Kaya identity) equation is useless and misleading nonsense except as a propaganda tool: the ratios are arguments propagandists want to promote, and a claim that a ratio is “meaningful” is a statement that there is a desire to promote it.

    Importantly, the fallacious Kaya identity needs to be rejected now because otherwise it threatens to become THE propaganda tool used to revive the ailing AGW-scare.”
    ——————

    richardscourtney, I liked and agreed with your above commentary, and if I may, I would like to take the liberty to paraphrase said commentary, with my substitutions of specific verbiage, so that it then states what I have repeatedly argued for years and years, to wit:
    ——————-

    “I have repeatedly argued that the Global Average Surface Temperature calculation is useless and misleading nonsense except as a propaganda tool: the “average changes” are arguments propagandists want to promote, and a claim that an average is “meaningful” is a statement that there is a desire to promote it.

    Importantly, the fallacious Global Average Surface Temperature calculations need to be rejected now because otherwise they will continue to be THE propaganda tool used to exacerbate the fear mongering CAGW scare.”
    —————-

    IMO, …. average temperatures are akin to average football/soccer scores …… which makes for “HOT” arguments between opposing fans of the sport.
    ===============

    richardscourtney says:
    July 13, 2014 at 7:55 am

    Can anybody provide a definition of “meaningful” which determines what should and what should not be used as “factors” in the Kaya identity?
    ————

    I think I can, to wit: …. “meaningful” means “author discretion”.

  312. A similar objection that I have with GCMs, elegant, mathematically rigorous, but not actually modeling the total climate system due to limited spatially collected datasets. One can gain insight into a particular subset of the system, but to claim the larger, overall model represents reality, is fundamentally wrong. Then to use such ‘evidence’ for policy directives is borderline corruption…

  313. This is not as hard as all the discussion makes it seem. Willis is both right and wrong. Here is why — The Kaya Identity and the Beer Identity are both trivially true and seriously misleading. As Steve M says, you have to watch the pea very carefully or you will be tricked very easily.

    The error is in how these things are used. If you want to estimate CO2 emissions, it is reasonable to break it down into pieces more easily estimated (with the proper caveats of course). If you want to predict what-ifs, that is a different story.

    One of the early comments on the first thread said:

    The point of the Kaya Identity (Identity, as in being the same thing) is that it allows us to figure out what effect a 10% growth in population will have, all other things being equal. And how much energy efficiency we would need to cancel out a given GDP growth.

    This is an example falling into the trap. The key words here are “all other things being equal”. They are not. The so-called identities are like a stopped watch. They look like multiplying numbers, static things, constants. If that is what the terms represent, fine. But if they are really functions, you have to ask what they are functions of. Time, f(t), but probably also many other things, f(x,y,z,…) and those terms share those variables. So the “all other things being equal” line does not work, change one term and the other terms will change too. The stopped watch works for one point in time, but not others.

    Talking about change is like taking derivatives. Dig that calculus out of your memory and take the derivative of composed functions.

  314. Matthew R Marler says:
    quote: “The history of science is replete with such incompleteness as represented by points 2,3 , and 4.”

    Nice shot. Your point sounds pretty profound but …

    quote: “In the early 1800s, three different people showed with statistical analysis that cleaning stuff in hospitals improved the survival rates of patients;”

    Well, the Kaya identity is everything but a statistical analysis. It is a tautology. An algebraic tautology.
    It contains *no information* whatsoever, regarding CO2, population, energy or whatever.
    If such identity was used in hospitals, probably nothing would have changed, or worse, the wrong decisions could have been taken, as an identity can be read either way, and contains only the information you wanted to put in (here, for instance: “CO2 is proportional to Population hence we are too many!”)

    quote: “If the standards promoted here by Willis Eschenbach had always been followed, nothing would ever have been learned.”

    You are too harsh with him. As I understand, he only wants this pedantic Kaya formula to have some relationship with reality and physical processes and measures. It has not. If identities were a good scientific tool, we would know nothing by now…
    In fact, if the Kaya identity is a sort of “scientific summum”, the maximum that the warmists and greens can produce after 40 years and billions of dollars, well, … you see my point.

    quote: “Since I don’t believe there is any utility in reducing CO2 I don’t think that use of the Kaya equation will prove fruitful”

    No. It is not fruitful because it is an algebraic tautology, whatever your opinion on reducing CO2. It is, literally, not a scientific tool in any way.

  315. I hesitate to comment because this is the first I’ve heard of the Kaya identity but knowing it came from the IPCC and having read this post and most of the comments I do have a take on it. Kaya is an identity being treated like a linear equation and as such is a brilliant piece of agitprop. Danny Lofo who struggled through fractions in the third grade but didn’t quite make it to algebra in high school would look at that equation, note population, GDP and energy consumption in the numerators of the factors on the right hand side of the equation and say wow, we have to reduce those to reduce CO2. We can’t reduce the population and don’t want to reduce the GDP so that only leaves energy. WE HAVE TO REDUCE ENERGY! This is as intended, you know, just to put the various factors into the proper perspective as has been noted. Well, and it’s a major purpose of the IPCC to take control of energy use (just to save the planet of course).

    I don’t think there’s anything proper about that perspective. It’s not a linear equation, those factors are non linear functions of one another, evidence is that CO2 is more a result of global warming than a cause (rendering the perspective meaningless) and there are extraneous factors that could make nonsense of the whole thing (e.g. we get nuclear fusion going and energy becomes disconnected from CO2). Willis is spot on to treat it lightly, it is not a serious effort to illuminate the subject, it is propaganda.

  316. The Beer Identity:

    1 beer = I should have another
    2 beers = I should have a third
    3 beers = 1 trip to rest room

  317. Deer occasionally wander onto my property. When I want to count the deer in a particular group, I count the number of legs and divide by four.

  318. Gary Hladik says:July 13, 2014 at 11:45 am
    Deer occasionally wander onto my property. When I want to count the deer in a particular group, I count the number of legs and divide by four.

    Now,now, Gary, and what if one of the deer only has 3 legs ! :)

  319. Willis Eschenbach says: July 13, 2014 at 12:34 am

    “If I burned that exact amount of gasoline in a furnace to make a tool, that would add to the GDP. But I didn’t. I burned it in an activity that does not add to the GDP.”

    You are using a definition of GDP that is not the common definition. GDP is the sum of *consumption*, investment, government spending, and net exports (from Wikipedia).

    If you bought the gas in the USA it was counted in US GDP. If you bought the gas in Canada, and smuggled it across the border, then it would not be counted in US GDP but that doesn’t happen often enough to have a significant impact on the answer.

    As I said above, the Kaya equation is politically loaded because it includes population and GDP factors, thereby implying that killing, starving or impoverishing the population would be one way to lower CO2 levels.

    More importantly, it was “silly” for Kaya to include those factors in his equation. We have a good estimation of how much fossil fuels we burn and how much CO2 is produced when we burn the fuel. We measure how much fuel we fuel burn in coal plants, gas plants, automobiles, heating oil, etc., and we have good estimations of the efficiencies of those processes, so we have good estimates of CO2 emissions.

    Therefore, Kaya erred when he included factors for GDP and population. Those factors only make the equation less accurate. Constructing a long equation with factors that don’t make the equation more precise is not helpful. Actually it’s harmful.

    Given the above, the logical and most useful equation is CO2 emitted = CO2 emitted. In other words, if you want to know how much CO2 humans are emitting, LOOK IT UP, and if you want to estimate future emissions of CO2, extrapolate the trend.

    I’ve come full circle. At first I thought equation was useless, then on closer examination I realized it can predict what it is intended to predict. Now I see that it is not the most efficient equation and the factors that make it less efficient, and less accurate, were probably added for to make a political point.

    Silly means ridiculously trivial or frivolous. Adding population and GDP to the equation, to make a political point, is bad science. It makes the identity ridiculously trivial and frivolous.

    Willis got this one right. He seems to not fully understand why his gut reaction was the correct reaction. But right is right so I won’t pick any more nits.

    I’m putting Wills back on his pedestal where he belongs.

  320. kabend says: July 13, 2014 at 11:34 am

    “It is not fruitful because it is an algebraic tautology”

    Please define “algebraic tautology.”

  321. Thomas says: July 13, 2014 at 12:01 pm
    Please define “algebraic tautology.”

    There is no such thing as algebraic tautology. Tautology is a term used in logic.
    The KAYA identity is an identity, of the sort: a = a x 1 x 1 x 1

  322. RH says:
    July 12, 2014 at 12:34 pm
    Sheesh. Mr. Kaya must be laughing his ^%$* off at how seriously everyone is taking his equation. The thing is nothing more than a political statement masquerading as a scientific formula. It deserves ridicule, not serious thought.

    RH,
    Exactly. I am soooo glad I chose to go up to the EAA Fly In and Airshow yesterday in Arlington WA (and camp overnight to enjoy a phenomenal ‘blood moon’ rise over snow capped mountains, a wonderful jazz/swing performance by the big band Mojo, a night pyrotechnic aerobatics airshow and an outdoor viewing of the movie “Gravity”) instead of wasting time on arguments about this drivel of a pseudoscience political statement.

    Now that the truck is unloaded (sans camping gear, cooler, etc), it is time for a good hour long swim in the local lake, before firing up the ‘barbie’ for some hardwood smoke grilled carnivores delight washed down with adult beverages that definitely contributed to CO2 emissions… and I don’t give a damn if my (tasty!) home brewed plum wine from 2009 contributed anything to GDP!

    Regards to you RH,
    Mac

  323. mkelly says:
    July 13, 2014 at 11:41 am

    The Beer Identity:

    1 beer = I should have another
    2 beers = I should have a third
    3 beers = 1 trip to rest room

    4 beers + 1 car = 1 trip to the pokey

  324. Johan says:July 13, 2014 at 12:18 pm
    There is no such thing as algebraic tautology. Tautology is a term used in logic.
    The KAYA identity is an identity, of the sort: a = a x 1 x 1 x 1

    To avoid misunderstandings, the x is a multiplication sign. There are no variables in the Kaya identity.

  325. Toto says: July 13, 2014 at 11:25 am

    “So the “all other things being equal” line does not work, change one term and the other terms will change too.

    This seems wrong. The equation works if you use the same valve for all variable that have the same name. It is to be used for one snap shot of data. At any given time there are fixed and knowable valves for population, energy, GDP, etc.

    “Other things being equal” is a perfectly valid logical tool. You hold all but one variable constant and see what the answer is. It tells you something about the process and it tells you something about which variables you should control to get your desired outcome.

    The Kaya identity is silly only because we don’t need to know the population, or GDP, to know emissions. We track emissions so we can just look up the value. No measurement is exactly precise but the other variables only add to the measurement errors.

  326. Matthew R Marler and Shawnhet:

    Genuine thanks for your replies to me at July 13, 2014 at 9:54 am and July 13, 2014 at 10:30 am, respectively.

    I intend no offence to either of you by this single reply to your posts addressed to me. I understand you to be saying the same thing in different words and, therefore, I am making this one reply.

    I understand each of you to be making an honest admission that there is no clear answer to my question. If my understanding is correct then the Kaya identity can only be an expression of the opinion held by whoever presents it.

    I explain that understanding by addressing Matthew’s post because it was the former. It says

    richardscourtney:

    Can anybody provide a definition of “meaningful” which determines what should and what should not be used as “factors” in the Kaya identity?

    There is probably not an abstract definition that you would accept. One can list the usual things (which provides an ostensive defintion), or a rough rubric such as “anything that contributes at least 1% to the R^2 value of the equation. The meaningful things that contribute to GDP are not the same in all countries: Germany doesn’t grow coffee or pineapples; Kenya doesn’t manufacture automobiles or lithium batteries.

    I am not sure what you mean by an “abstract definition”. All I want is a clear statement such as;
    ‘Factors in the identity are all the known quantifiable effects which X and they are included in the form of Y’.

    The things which contribute to GDP in a country are not relevant. Either GDP fulfills ‘X’ or it does not. And the “rubric” idea is not helpful because it presupposes the outcome of its use in the ‘identity’.

    Hence, I contend that the Kayla identity is not defined unless and until the nature of its components (i.e. the “factors”) are defined. This leaves its definition to anybody who cares to present a version of the ‘identity’ to ‘make it up’ in any way they want.

    And I again thank each of you for your honest and clear presentation of your view.

    Richard

  327. Willis

    Thanks for the quote.

    Firstly, can I just point out that your post is not just a clarification of your original point. Your original point was different and it was just wrong – there was no “stupid maths error”. If you want to be taken seriously as someone who is on a genuine quest for truth and reason, you could do more to acknowledge this.

    Moving on:

    As I said in a previous comment in this saga the very fact that the Kaya equation reduces to CO2 Emissions = CO2 Emissions is precisely because the right hand side is a valid decomposition of the left hand side. It stands to reason that a valid logical decomposition of a concept can be ‘re-composed’ back into the thing that you started with. If it doesn’t then you’ve made a mistake.

    To be clear though, that does not mean that any mathematical expression following a similar form, where the RHS can be reduced to the LHS in a similar way, should be deemed equally meaningful in its application. It certainly does not mean that you can just throw anything into the mix as long as you balance it in the numerator with it’s equivalent in the denominator – and expect to come out with something equally meaningful.

    The Kaya Identify is useful not because the terms cancel, but because the decomposition that it communicates is a correct reflection of macro economic theory and because it is broadly supported by macro economic facts.

    The Kaya Identity is mathematically ‘true’ because the terms on the right hand side do indeed reduce to the term on the left. But for a logical decomposition of this sort to be useful it has be both logically ‘true’ AND correctly reflect the theory and facts that it is intended to represent.

    As your example makes clear, your beer identity passes the first test but not the second. The terms are not true in the context of macro-economic theory or fact. In reality, CO2 emissions are not limited to beer production (although round my place, it is quite a big contributor).

    Certainly if it were not mathematically ‘true’, then it would not be meaningful for that reason. It would be refuted, and that would be a good challenge. But the fact that it is mathematically true isn’t sufficient for it to be meaningful in context. It is necessary but not sufficient, to coin a phrase.

    That’s why the Kaya identity is considered useful whereas the beer identity is not – as other people have pointed out many times previously.

    So the Kaya Identity doesn’t rely on mathematical certitude for its usefulness as you suggest. It isn’t a mathematical proof. And the people that use it in their area of speciality are not generally lulled into a false sense of security about it’s usefulness, as you also suggest. – And if you’re not convinced of that then you could try reading their work…

    But that is not the nub of your current misunderstanding……..

    The real nub of the issue from your current post is that you do not agree that the terms of the Kaya Identity correctly reflect the relevant economic facts and theory. Whilst that is an entirely valid way to challenge the usefulness of the Kaya Identity (finally), there is still a very basic problem in your thinking.

    The problem is twofold:

    Firstly, you are absolutely and categorically wrong to imagine that your purchase of a tank of fuel for your car is not included in GDP figures. The fact that the crude oil was pulled out of the ground somewhere else is entirely beside the point according to the definition of GDP.

    GDP can be defined as the market value of all of the finished goods and services produced within a country’s borders in a specific time period. As soon as you put the fuel in your car and ‘consumed’ it, it counts as a ‘finished product’ and it is most certainly included in the figures.

    If it helps you can think roughly of GDP as being the total value of everything that we do in an economy. But the definition uses ‘finished’ products and services to try to avoid double counting.

    The point is, given the definition of GDP it is very difficult to see that one could do anything that results in human CO2 emissions without it being reflected somewhere in GDP figures – other than breathing, defecating or passing wind, but I’d question whether they count as human emissions in the context of economic policy.

    Secondly though, the theory only requires that your consumption of a tank of fuel is related to GDP. That’s not necessarily the same as requiring that the cost is included in the GDP figures. In other words, you and the other couple of hundred million people in your country like you are more likely to buy a tank of fuel if you can readily afford it than if you cannot. And your ability to afford it, your wealth, is tied to GDP (and population).

    Similarly, as GDP goes up, demand for oil goes up which results in increased “flaring of gas from oil wells” to address one of your comments.

    I’m not sure if the underground coal fires in Pennsylvania, India, and China you refer to are man made or naturally occurring? If the latter then they’re irrelevant anyway for current purposes. If the former then presuambly they’re a by-product of coal mining in which case the same point applies as with flaring oil well gas, and their economic impact is included in the price of coal.

    I hope this helps.

  328. “I am astounded at the large number of commenters who don’t apparantly understand the first thing about math, and proceed to display their ignorance in spades.” — PlainBill

    It’s still bunk and poorly expressed bunk at that, having left itself open to interpretation. As John G observes (and I believe i paraphrase correctly) the Kaya Identity is an effort to describe a non-linear problem with linear model. It’s not even a good first order approximation given the degree of non-linearity. It takes no account of interdependencies, substitutions, unintended consequences–because those are always overlooked–plus other factors that, no doubt, belong in the model. Nor does it account for the vagaries of GDP and how it’s measured. It is the same sort of static analysis the Congressional Budget Office uses to score tax and spending bills. In other words, it is not only wrong, it is harmful. It is the same sort of analysis that led people, some of them very bright with very sophisticated models, to believe housing prices would keep going up and that if there were any pauses in appreciation they would be local and limited in scope. And then 2008 and Lehman Bros. happened. Go figure.

    We’ve seen this movie before. Analyses like the Kaya identity are worse than useless–they are harmful. They lead to bad policy decisions. Even worse is that they let true believers cloak their crummy policy choices in the mantle of science.

  329. algebraic tautology ?
    The term is purely illustrative. I do not pretend to invent some new mathematical notion.
    tautology because it’s a formula of the sort : CO2 = 1 * 1 * 1 * CO2 (of course, the value 1 is not explicit)
    algebraic because the algebraic form obfuscates the obvious, and allows some people to pretend discover or prove interesting findings as the usage of algebra gives the illusion of scientific legitimacy.
    does it answer the question ?

  330. The Kaya identity is silly only because we don’t need to know the population, or GDP, to know emissions. We track emissions so we can just look up the value. No measurement is exactly precise but the other variables only add to the measurement errors.

    Tracking emissions is not predictive. Understanding why emissions grow or shrink as a function of GDP/Population/Energy Usage allows us to inform policy, hopefully to ensure policy is appropriate to the purpose. It can also be used to identify bad policy but nobody in government would pay for such research.

    A problem people here are having with the simple variables is that they view them as simple rather than the complex things they are. There is an acceptable definition of GDP (several, actually), for example, and the formula for calculating that is quite lengthy. But every element of it is implicit in the Kaya identity. Same with emissions – there is an acceptable definition (scope) of what is meant by emissions else we could not have a conversation about emissions. Population is more complex than many might think in determining per-capita GDP. What is the role of children, for example, in the per-capita GDP calculation? Energy consumption is another that needs to be commonly understood when instantiating the Kaya identity. Each of these simple variables has, necessarily, a complex definition and scope and this has to be established and agreed upon by the creators and consumers of Kaya identity-driven analyses. Willis’ view of things does not consider this implied data appropriateness agreement in his criticism. Analyzed as he presents it the creator and customer are working in a void. It can work that way but the result of any such analysis would be of dubious value.

    The nonsense of grabbing numbers out of the air and plugging them into the identity, or suggesting changing one thing necessarily changes another is wrong-headed. The entire purpose is to explore independently the impact of each variable on the outcome even when it is well understood from experience that a change in one parameter will change another because of the linked relationships. Case in point: What becomes of the per-capita GDP if there is another baby boom? What becomes of the per-capita GDP if you allow hundreds of thousands of uneducated people to cross the border into your country to stay permanently? How are border states affected vs opposite border and interior states? What happens to the quality of health care if everyone is guaranteed access to all the care they want? If doing a global analysis vs Willis’ regional analysis there are no international boundaries and regulations to get in the way or obfuscate the problem. An analysis will show that if one significant parameter changes, necessarily another must change, and because this is predictive, we can anticipate the dependent changes needed to accommodate a desired change (policy is informed).

    And we haven’t even addressed how rates of change of each element affect the growth/shrinkage of the units in the output. That is what the Kaya calculator at the U of Chicago site is presenting and it is well worth a visit to see how it works.

  331. Some salute an Identity, Kaya!
    At this blog, it is burning like fire!
    But “1 equals 1”
    Ain’t new under the sun.
    Nor is “zero is zero” much higher.

  332. Richard says: July 13, 2014 at 12:55 pm
    As John G observes (and I believe i paraphrase correctly) the Kaya Identity is an effort to describe a non-linear problem with linear model.

    Both the Ehrlich-Holdren IPAT identity and the KAYA identity emerged out of efforts to investigate the drivers of environmental impact / CO2 emissions.

    But they’re not even very good at that. For example, they do not take explicit account of culture and institutions, so they cannot be used to examine the potential influence of these drivers. Which is what Krugman was kind of saying to Pielke.

  333. Pete Brown says:
    “The Kaya Identify is useful not because the terms cancel, but because the decomposition that it communicates is a correct reflection of macro economic theory and because it is broadly supported by macro economic facts.”

    Well. Seems strong (think about it: the *whole* macro economics are behind the formula !) but in fact contains a weakness:
    As said many times before, and by many: the formula is only a tautology, CO2 = 1 * 1 * 1 * CO2. It contains *no information* at all, and the decomposition of 1 is purely rhetorical, just expressing some common beliefs (we are too many, we need to improve engines efficiency, etc.) .
    Saying it is a correct reflection of macro economic means … that macro economic knows nothing about CO2. And your argument looks like a circular reasoning.

  334. I don’t like this KI because I think it’s incorrect.
    By using “models all the way down” (h/t to w.) it assumes that people and CO2 are evil and must be dealt with.
    I believe that human CO2 is at worse a minor problem.

    To me, I see emissions as a factor of 2 things.
    Fossil Fuel Use and Energy Efficiency of the Fuel.
    More people doesn’t guarantee more CO2.
    More GDP doesn’t guarantee more CO2.

    If more fossil fuels are burned then CO2 goes up no matter who or how many people burned it and no matter what they did to consume the energy from the burned fossil fuel.

    The only Identity the IPCC is pushing is to convince the world that they must identify humans and their CO2 as a problem and force the UN to fix said problem.
    cn

  335. “Willis

    Thanks for the quote.

    Firstly, can I just point out that your post is not just a clarification of your original point. Your original point was different and it was just wrong – there was no “stupid maths error”. If you want to be taken seriously as someone who is on a genuine quest for truth and reason, you could do more to acknowledge this.”

    #########################

    Willis used to be known as someone who would readily admit his errors.

    In this case he wont. Its sad because his Subsequent argument is more cogent.

    So, until he admits his error, HELL he could call it an error of FOCUS, until he does that,
    he is lost. he is like those people who wont call out the climate gate folks for their errors of judgement.

    he screwed that part up. he needs to own it, even in some miminized, inconsequential way.

    he could say ‘I goofed by focusing on the maths error part, and that has obscured the discussing of the more fundamental point I wanted to make”

    Simple. just a flesh wound

    but. he wont. for some strange reason.

  336. As said many times before, and by many: the formula is only a tautology, CO2 = 1 * 1 * 1 * CO2

    This pretty well sums up the complete lack of understanding of what an identity is. Well done.

  337. Willis wrote: “The problem is … I’m burning energy, and I’m emitting CO2, but I’m not part of the GDP. I’m not producing anything with that energy—no goods, no services, nothing. My CO2 emission is a part of the total, but it is not included in the Kaya Identity anywhere.”

    Your purchase of the gasoline you burned is part of GDP. The depreciation of the car you were driving is part of GDP, because someday that car will need to be replaced. Servicing your car every X thousand miles is part of GDP, even if you provide the labor. Sure, there are some activities that don’t get captured by GDP (especially for a DIYer like you), but GDP captures a large fraction of activity that is responsible for our standard of living. Beer consumption doesn’t. Every government wants its per capita GDP to grow, especially underdeveloped countries.

    As for Andy and credibility of WUWT, I find it extremely difficult to read through hundreds of comments and replies (written with little thought) to find the few comments that provide useful information. Nothing is stopping Andy from submitting articles like this one to some sort of peer review process before they are released to the public or asking submitters like you to summarize the limited peer review your posts receive from peer review. Your knowledge may be increased by answering comment, but how much of that reaches the average reader?

  338. Well, I laughed too, when I got to that ridiculous Kaya equation. I mentally crossed off the factors just as you did, and figured out how meaningless it realy was before you explained it.
    All the real details are missing:
    how do people use the energy?
    where else is CO2 coming from besides fuels? (I think its mostly poison-agriculture killing soil lifeforms)

    Not to mention:
    Why do they hate humans so much that they are willing to kill everything else alive? (CO2 is where every land-based living thing comes from)
    How can they imagine that raising the Earth’s temperature from 12C/57F would be a bad thing?

  339. richardscourtney: All I want is a clear statement such as;
    ‘Factors in the identity are all the known quantifiable effects which X and they are included in the form of Y’.

    There is nothing wrong with “Everything that contributes at least 1% of GDP.” It does not satisfy you, but you do not explain or list what is lacking.

    However, you specify “known quantifiable effects” which precludes anything that might be learned, and seems from your previous posts to be “known exactly” instead of “known within a margin of error”; and you require “all” which is not satisfied by any other equation in applied math. “In the form of Y” is satisfied already by (a) a scaling factor and (b) ratios; and of course the units should resolve to CO2..

  340. richardscourtney says:
    July 13, 2014 at 12:49 pm
    “I understand each of you to be making an honest admission that there is no clear answer to my question. If my understanding is correct then the Kaya identity can only be an expression of the opinion held by whoever presents it.”

    That wasn’t really my point. It seems to me that all the components of the Kaya are understandable and at least potentially measurable. The issue I was having was whether we can use the factors presented in the Kaya model to make reasonably accurate predictions about the real world.

    Someone above helpfully pointed us to this link that discusses this particular issue.

    http://rogerpielkejr.blogspot.ca/2014/06/clueless-krugman.html

    “Using the Kaya Identity in crude fashion tells us that China’s CO2 emissions should have increased by ~8.1% in 2011 (that is 11.1 – [0.6+2.4]). Data from EIA shows an increase of just under 9%. So very close.”

    I must admit that this is much better than results than I was expecting (assuming 2011 is not just a fluke) but there is definitely room for improvement. In my book a prediction of 8.1% vs. a reality of 9% is in the right ballpark.

    Cheers, :)

  341. richardscourtney: I understand each of you to be making an honest admission that there is no clear answer to my question. If my understanding is correct then the Kaya identity can only be an expression of the opinion held by whoever presents it.

    Your understanding is not correct. The terms in the Kaya identity can be given operational definitions that can be understood by a group of people. There is no answer that you will accept. You require that the terms in the equation be defined better than “mass” and “electric charge” are defined.

  342. Frank says: July 13, 2014 at 2:08 pm
    Sure, there are some activities that don’t get captured by GDP (especially for a DIYer like you),

    For instance, he could have mentioned that the black market isn’t counted in calculating GDP, which in some countries may be fairly substantial (although one probably shouldn’t exaggerate). The European System of Accounts would require their member countries to add their respective black market when calculating GDP for next year.

    This is the sad thing about the original post. There are so many, many valuable arguments against the use of KAYA, yet Willis with his uninformed ‘analysis’ only makes a fool of himself, and by association, of WUWT.

  343. Shawnhet: Someone above helpfully pointed us to this link that discusses this particular issue.

    http://rogerpielkejr.blogspot.ca/2014/06/clueless-krugman.html

    “Using the Kaya Identity in crude fashion tells us that China’s CO2 emissions should have increased by ~8.1% in 2011 (that is 11.1 – [0.6+2.4]). Data from EIA shows an increase of just under 9%. So very close.”

    I must admit that this is much better than results than I was expecting (assuming 2011 is not just a fluke) but there is definitely room for improvement. In my book a prediction of 8.1% vs. a reality of 9% is in the right ballpark.

    Some or perhaps all of us read some of Pielke’s links. It was good of you to think to quote one.

  344. Every now and then through this thread, a comment pops up, warming that the credibility of WUWT is at stake if this conversation is not deleted or discontinued…
    Why?
    Surely there is something very interesting going on here, we have a clear failure to communicate, this needs explored, not hidden from.
    As for the KAYA IDENTITY, if it is poorly expressed by Willis and Wiki, then express it properly.
    Do not continue to bleat on that we, who snicker,fail to discriminate between two terms both assigned the same definition.
    So CO2total is not CO2 per unit of energy used locally.
    Everyone gets that.
    The comedy is in the constant misrepresentation of this identity as a useful equation.
    Which it is not, as expressed by Willis or Wiki.Nor by the IPCC.
    This pseudo formulae is used as a tool, there are no accidents when information created by Public Relation firms is the dominant source of 30% of UN documents.
    Everything from the CAGW control folks has an agenda, this devious identity is yet another deliberate distortion.
    Only a Policy Wonk or Economist will insist a series of assumptions has a certainty of result.
    Each and every assumption ,if erroneous will sink the entire speculation.
    There fore to me the “identity” is useless, scrying the entrails of a duck has as much scientific or algebraic credibility.
    And if you know how to cook, you can eat the duck.

  345. kabend says: July 13, 2014 at 1:02 pm … Thanks Kabend. I don’t agree that the equation is flawed. It’s “silly” but it can be used for it’s purpose.

    dp says: July 13, 2014 at 1:21 pm “Tracking emissions is not predictive. Understanding why emissions grow or shrink as a function of GDP/Population/Energy Usage allows us to inform policy, hopefully to ensure policy is appropriate to the purpose.”

    Tracking GDP, population and energy is no more predictive than tracking emissions of CO2. We all know where human CO2 emissions come from, they come from humans burning fossil fuels to make useful power.

    Tracking GDP, population and energy production informs CO2 policy only if you’re considering policies which would kill, starve, or impoverish the population in order to reduce CO2 emission. I suppose abortion and birth control could be policy choices but the government already promotes those for other reasons (which I don’t pretend to understand).

    Here are a list of fallacies currently being repeated over and over again on this thread:

    Fallacy: GDP does not include stuff consumed for recreational purposes.
    Truth: By definition, GDP includes everything consumed for recreation purposes or any other purpose. It also includes all imports … unless you smuggle them in.

    Fallacy: The Kaya equation doesn’t include all possible sources of CO2.
    Truth: It doesn’t try to. It’s merely a way of calculating HUMAN CO2 emissions.

    Fallacy: The Kaya equation is mathematically absurd.
    Truth: It’s a valid equation. It shows the relationship of human CO2 emission to human activities that produce CO2 emissions.

    Fallacy: The Kaya equation is a good (or the best) way to predict future human CO2 emissions.
    Truth: It is neither a good way nor the best way. We know current emission and we know the trend. Past performance is no guarantee of future performance but for something as macro and all encompassing as this question, it more reasonable to predict future emission but extrapolating the current trend. Adding factors for population, and energy use, and CO2/energy produced, and GDP does not add to the utility of the equation. All those factors will have uncertainties that add to the uncertainty of the result. For example, the USA has a trillion dollar grey economy that is not included in GDP.

    The Kaya equation has a mild heuristic (teaching) valve in that it shows that changes is population, and/or GPD (consumption), and/or changes in the ratio of CO2 per unit of energy produced, would result in a change in CO2 emissions. However, the answer the equation produces is “human-produce CO2 emissions.” It’s given that humans produce emissions by burning fossil fuels, and that by doing so they increase their standard of living. So it’s a silly equation. It’s better just to recognize the CO2 emissions = CO2 emissions and go look up the value.

    Here’s a better equation with far more heuristic value. We simple replace the term on the left (the answer) with the following factor.

    Human Prosperity Factor = population x GDP/population x Energy/GDP x CO2/energy.

    This equation teaches us that human prosperity is directly linked to CO2 emissions. It can be simplified to:

    Human Prosperity Factor = CO2 emissions.

    We can “prove” this equation with a simple thought experiment. Imagine a year without fossil fuels? CO2 emissions would go to near zero, and the human prosperity factor would plummet. Forests, which have regrown since the dawn of the fossil fuel revolution, would be cut down and burned for heating and cooking. When they were gone, most humans would be gone too.

    My equation will not hold true forever but it is true now and will continue to be true until we find a cheaper source of energy, or develop methods to reduce energy use without reducing GDP.

  346. kabend: Well, the Kaya identity is everything but a statistical analysis. It is a tautology. An algebraic tautology.

    The terms on the RHS are to be determined by statistical analyses of states and regions. If estimated with sufficient accuracy (a practical problem), then the effects of changes in the terms can be calculated. The ratios on the RHS are to be output/input relations in the processes in the production of CO2 (links in the chain of causation.) There are indeed people who wish to lower CO2 by reducing the size of the scaling factor (population); others want to lower CO2 by reducing at least 1 of the ratios (energy/gdp or CO2/energy), but nothing in the presentation of the equation, or in the equation, prescribes an optimal policy. All it says is how much change in the LHS can be effected by changes in the terms on the RHS.

  347. Oh dear dp:

    The nonsense of grabbing numbers out of the air and plugging them into the identity, or suggesting changing one thing necessarily changes another is wrong-headed.

    Part of the definition of an identity is that its equality exists for all possible values of its variables!

    You must be able to put any value into any variable otherwise its not a valid identity.

    For example in:

    a^2 −b^2 = (a+b)(a−b)

    both a and b can be replaced with any value and the equation retains its equality.

    As such totally pointless, unless you are trundling through lines and lines of mathematical calculations, when the line you just wrote contains the pattern like the identity above (either the LHS or the RHS will do. As soon as you spot it, you can replace it with the opposite side:

    If it helps your calculation.

    That is the only reason I would use an identity.

    Pattern matching to save work and intellectual effort.

    If you say you can not perform normal mathematical operations on your KI formula then it is not an identity.

  348. Matthew R Marler:

    At July 13, 2014 at 2:26 pm you write

    richardscourtney: I understand each of you to be making an honest admission that there is no clear answer to my question. If my understanding is correct then the Kaya identity can only be an expression of the opinion held by whoever presents it.

    Your understanding is not correct. The terms in the Kaya identity can be given operational definitions that can be understood by a group of people. There is no answer that you will accept. You require that the terms in the equation be defined better than “mass” and “electric charge” are defined.

    NO!
    I could not care less if “The terms in the Kaya identity can be given operational definitions”.

    I want to know the definition which specifies what terms should be in the Kaya identity and which should not.

    Without that specification the Kaya identity can only be an expression of the opinion held by whoever presents it.

    And I will not be satisfied with excuses for failure to provide a definition which makes the REQUIRED specification. The excuses are a proclamation that the Kaya identity is an expression of the opinion held by whoever presents it; i.e. it is disingenuous propaganda.

    Richard

  349. The real Kaya Equation is here and is used to model emissions over time:

    http://climatemodels.uchicago.edu/kaya/

    There’s even code but not data:

    http://climatemodels.uchicago.edu/kaya/kaya.F

    The units are correct, so from a physical viewpoint, it checks out. Some assumptions are made, such as exponential growth or loss in population, GDP, Energy or CO2 efficiency and there is also a small mistake in the code for exponential population growth, but otherwise it all checks out.

    The main problem here is there are too many sites that simplify this stuff including Wikipedia and Manicore. Give me garbage and I will regurgitate it back at you like I did in previous comments. My sorry.

    There are still assumptions made about the source of all the CO2. The paper I quoted previously only allows for 1% of non-fuel hydrocarbons in total consumption, but the “100 megatonnes” that Willis quotes is actually closer to 10% of China’s output, so there are real problems with how the numbers are used.

  350. richardscourtney: I could not care less if “The terms in the Kaya identity can be given operational definitions”.

    I want to know the definition which specifies what terms should be in the Kaya identity and which should not.

    Without that specification the Kaya identity can only be an expression of the opinion held by whoever presents it.

    And I will not be satisfied with excuses for failure to provide a definition which makes the REQUIRED specification. The excuses are a proclamation that the Kaya identity is an expression of the opinion held by whoever presents it; i.e. it is disingenuous propaganda.

    If you won’t accept rubricks, won’t accept ostensive definitions, and won’t accept operational definitions, is there anything in science that you find to be adequately defined? Dogs and cats? atomic weight? the curvature of space-time?

  351. James Gibbons says: July 13, 2014 at 2:50 pm
    The main problem here is there are too many sites that simplify this stuff including Wikipedia and Manicore.

    No, the main problem with the site you link too is that they use the KAYA identity as a “model”, something that would allow you to somehow “predict” (or as they say “prognosticate”) CO2 emissions.

    That is complete *****, for a whole number of reasons, most of them correctly identified in many of the posts above.

  352. Shawnhet:

    Thanks for your clarification at July 13, 2014 at 2:22 pm.

    I write both to thank you for it and to draw attention to it.

    Richard

  353. Steven Mosher says:
    July 13, 2014 at 2:06 pm

    “Firstly, can I just point out that your post is not just a clarification of your original point. Your original point was different and it was just wrong – there was no “stupid maths error”. If you want to be taken seriously as someone who is on a genuine quest for truth and reason, you could do more to acknowledge this.”

    I agree fully with Steven Mosher and am now in the quandary as to what, if anything,I can reliably accept as reliable that is posted on WUWT by Willis. OK, an overstatement, I only accept what “I think makes sense”. But I’ve had my doubts about Willis for some time. . . now my doubts have been only been accentuated.

    Way to go Willis. . . you know, it’s not all about your immense ego and arrogance! I dare say you have no inkling as to the depth of your ignorance.

    Dan

  354. As my wife would say if you fellows can do this for 380 some comments on this subject, you will live long.

  355. Matthew R Marler:

    I am copying all of your ridiculous post at July 13, 2014 at 2:55 pm because it is so daft it is in the Pete Brown league.

    richardscourtney:

    I could not care less if “The terms in the Kaya identity can be given operational definitions”.

    I want to know the definition which specifies what terms should be in the Kaya identity and which should not.

    Without that specification the Kaya identity can only be an expression of the opinion held by whoever presents it.

    And I will not be satisfied with excuses for failure to provide a definition which makes the REQUIRED specification. The excuses are a proclamation that the Kaya identity is an expression of the opinion held by whoever presents it; i.e. it is disingenuous propaganda.

    If you won’t accept rubricks, won’t accept ostensive definitions, and won’t accept operational definitions, is there anything in science that you find to be adequately defined? Dogs and cats? atomic weight? the curvature of space-time?

    If you cannot give it a unique specification then you cannot conduct a scientific investigation of it.

    That is why taxonomy exists. You mention dogs and cats. A definition which says a dog is an animal with a leg in each corner is not an adequate specification of canines.

    And that is why I will not be satisfied with excuses for failure to provide a definition which makes the REQUIRED specification, and why without that specification the Kaya identity is only a propaganda tool.

    Richard

  356. No time to read all the posts, but consider this scenario:

    For unspecified reasons, the cost of natural gas rises dramatically. Many people in northern areas decide to substitute the burning of wood in stoves or fireplaces for some portion of their winter heating needs. Rather than purchase wood, they spend their summer and fall weekends felling trees and cutting them into logs which are then burned over the winter.

    Net result: the effect on GDP is indeterminate, dependent upon the elasticity of natural gas consumption and other substitution effects. i.e., the total consumption of natural gas would decrease, but any change in the total value of production is indeterminate here. However, the output created by weekend logging is certainly not fully captured by GDP figures outside of purchasing chainsaws, fuel, axes, etc. The most valuable portion — labor — goes unreported. Additionally, since some of that logging labor might be substituting for actual paid labor (e.g., a separate weekend job), it potentially represents additional downward pressure on GDP. Actual reported energy usage measured in BTUs definitely decreases here. However, since wood is a far more carbon intensive fuel per BTU produced, carbon output would almost certainly go up in this scenario.

    The fact that the equation presents the inputs and output as an identity is thus negated. GDP, energy production and carbon output are all uncoupled in this case.

    The bottom line is that there is far more economic activity that occurs than is captured in GDP accounting. (Think of the trade in illegal drugs, arms and prostitution to name obvious examples. Or for that matter, unreported child care income.) The equation smacks of “scientism”: lending a false sense of accuracy through the use of numbers and equations.

    I can accept that one might be able to use the equation as some kind of baseline for the purposes of inter-temporal comparisons, but to pretend it produces some sort of valid absolute number is highly questionable. And its usefulness for the purposes of comparison would be immediately suspect if there were some supply shock as I described in my scenario, wherein the shock results in a radical change in behavior that is not captured by standard measures.

    Cheers!

  357. climatereflections says:
    July 12, 2014 at 2:51 pm
    […]
    BTW, what you should have written is M(Total) = C * (B/C) * (P/B) * (M(Individual)/P), as the M on the front is not the same as the M on the end.
    ***********************************************
    This is good but still just a little bit more: M (Individual) must be the amount of M in one P. So the P’s can’t also be the same value either. Actually the last term should be M (Individual) / P (Individual). A rate that is not dependent on knowing M ahead of time.

  358. His point is valid, let me provide a better example.

    I can go out into the forest, cut down a tree, and build a bonfire. There is no impact on GDP, but an increase in atmospheric CO2. This works, even though I am not utilizing fossil fuels, because I have also reduced the size of the carbon sink.

    Identities are useful tools for performing mathematical operations. But they cannot provide useful information, in this instance because 1=1 (which is known).

  359. Daniel G. says:
    July 12, 2014 at 3:02 pm

    co2(Total) = pop * (gdp/pop) * (energy/gdp) * (co2(for a unit of energy)/energy)
    ***********************************************************
    Units problem.
    ton / year = ton Joules / year

  360. Ruth Dixon says: July 13, 2014 at 3:21

    Hello Ruth,

    The chart you posted,
    (pmhttp://geodata.grid.unep.ch/extras/posters.php#infographics_posters_bubble_charts)
    proves my new and improved Kaya Identity (see 2:42 PM):

    Human Prosperity Factor = population x GDP/pop x Energy/GDP x CO2/energy.

    It simplifies to:

    Human Prosperity Factor = Human CO2 emissions.

    I call it the the Eschenbach Identity.

    : )

  361. Thomas (at 2.42 and 3.42pm), as you say, prosperity is linked to CO2 emissions at the moment, but more fundamentally. Prosperity = Energy, regardless of how it’s generated.

  362. steverichards1984 says:
    July 13, 2014 at 2:43 pm

    Oh dear dp:

    The nonsense of grabbing numbers out of the air and plugging them into the identity, or suggesting changing one thing necessarily changes another is wrong-headed.

    Part of the definition of an identity is that its equality exists for all possible values of its variables!

    You must be able to put any value into any variable otherwise its not a valid identity.

    By grabbing numbers out of the air I mean grabbing numbers that have no relationship to the purpose of the identity. For example (seen above):

    CO2 = 1 * 1 * 1 * CO2

    This is a meaningless but valid instantiation of the Kaya identity and does not represent how it would be used in an analysis. Secondarily, claims that changing one parameter (in nature) forces a response in other parameters. Yes but this is not a dynamic model.

    I agree with your points but apparently made mine badly.

  363. Ruth Dixon 4:02 pm.

    Ruth, prosperity = energy so long as energy is not too expensive. I once calculated that Americans use the energy equivalent of about 300 oxen. Oxen are expensive to feed and require a lot of space. When we most depended on animal power we were mostly not prosperous.

  364. Reply to Willis E. ==> In regards yours above. Your comment violates WUWT commenting policy as it is a personal attack and includes rank name calling — quoting your salacious words: “you nasty little man, I said that in the head post because I know there are sleazebags like you”.

    As for my comment that “This is not the first time he has gone off half-cocked and shot himself in the foot with something ill-considered”, please refer back to your previous post re: Andy Revkin. Readers should review w.’s comments to his own piece for the full effect, it is quite a show–and judge for themselves. I believe my observation not only to be correct, but extremely mild given the cases in hand.

    I freely admit, based on previous personal communication with you, that “Nor will it be the last.” is a prediction resulting from both past performance and privately held information.

  365. Thomas, yes, but the same applies to your equality – it has to be ‘cheap’ CO2. I don’t think you are proposing burning diamonds to generate electricity!

  366. Shawnhet says:
    July 13, 2014 at 10:39 am

    Ian W says:
    July 13, 2014 at 10:11 am
    “Sigh

    If a country moves to all Nuclear/Wind/Hydro/wave power as its input is your ‘identity; true?”

    Sign. Not the point at all. Countries can’t just decide to move to non-carbon sources of energy at the flip of a switch. Rather, it has to happen slowly and gradually, which means that something like Kaya could still provide a valuable picture of the world (in other words its math will not be “fake”).

    You are wrong of course.

    Belgium used to claim that they were one of the few countries visible from space as their surplus nuclear power capacity meant that all their autoroutes/motorwegs were lit all night. So Belgium creates far less CO2 for its GDP per head than say Poland or Germany that use lots of coal. Increasing Belgium’s GDP may have no effect on its CO2 emissions whereas increasing Poland’s GDP would do so.

    If LNER nuclear fusion becomes reality – then the ‘identity’ fails. If GDP rises because of the banking or reinsurance markets, then the identity fails, Only someone in PR would think this was a useful exercise. It is the level of logic that said London would be feet deep in horse manure due to the increase in population and transport requirements.

    The error comes in the definition of the terms and their relationships not in the maths. It is deliberately vague so each reader can get what they want out of it. It would fail validation and verification testing but who cares right? It is PR spin and was not intended to be testable.

  367. richardscourtney: You mention dogs and cats. A definition which says a dog is an animal with a leg in each corner is not an adequate specification of canines.

    You and I agree on that. I think you’d be hard pressed to find a scientific term which is defined to your standards. Most of them have ostensive definitions and operational definitions.

  368. dp @10:00am:

    “Willis is punching above his weight here and has disqualified himself from ever criticizing the mathematical work of anyone else. His wiggling where there is no wiggle room is surely drawing laughter from Anthony’s peers. His errors are the platform upon which other uninformed people chant the same wrong conclusion: CO2 = CO2! There will be no gracious mea culpa, no apologies to math teachers everywhere for confusing their students, no clarification as emergent phenomena of his failure. The hole he’s dug here is deep enough to be considered one of the wonders of the world. The Willis Eschenbach by-line is now junk stock.”

    —–

    You are going a bridge too far. Yes, Willis cited to an incorrect version of the Kaya equation, which got him off on the wrong foot. *However,* there are other sources, including Wikipedia and some published papers I’ve seen which present the Kaya Identity essentially as Willis has written it. In that form, it is a joke, an absurdity, laughable, useless. Willis should sneer at such an equation. So should every other rational individual. (Embarrassingly, there are many people on this thread who think they need to dig in their heels and defend an indefensible equation on the mistaken idea that because it is called an “identity” magic can happen, allowing us to imagine that canceling equivalent terms on the same side of an equation is somehow meaningful . It is not. It is nonsense.)

    In my humble opinion, Willis should admit that he took the Kaya equation (from wherever he got it) without looking at how it is actually used in practice. He should apologize for jumping the gun. I would personally think him a better man for doing so and for providing an update to this thread which got wrong-footed from the outset due to an incorrect description of what the Kaya equation actually is. If he were to post an update to the thread, it might also (mercifully) help us avoid the numerous red-herring comments this thread is generating.

    However, that said, Willis is not the first one to list the Kaya equation the wrong way. In addition, his other questions about whether the Kaya equation in fact captures real-world realities are useful, relevant questions, regardless of one’s assessment on that substantive point. So to say that he has no credibility and is “junk stock” is going a bridge too far.

  369. dp @11:02am:

    “The implication is there is a wrong way to use the identity and there is, of course, but that is easily corrected. The unspoken claim is there is no right way to use the identity and that is evidence of a deep misunderstanding of math.”

    The equation as cited by Willis (and some other sources) is useless. Utter, complete garbage. Not worth the electrons it occupies on my screen.

    The issue is not that there is some “right” way to use the equation Willis cited. The issue is that Willis cited the wrong equation.

    —–

    P.S. I apologize if my prior reference was unclear. My prior comment was referring to your comment at 10:11 am, not 10:00 am.

  370. Will @3:24pm:

    You are exactly right. Good catch and I should have been more precise.

    I was focusing on the M’s as that was the variable under discussion.

    In fact all of the denominators must refer to an individual unit (the C, the B, and the P).

    That is the way the Kaya identity actually works. Unfortunately, the way Willis wrote it, based on other sources he’s seen, is wrong. It doesn’t distinguish between the aggregate and the individual, thus everything cancels on the same side of the equation and we’re left with meaningless nonsense.

    —–

    BTW, much of this confusion would have been avoided if the Kaya Identity had never been called an “identity.” Lots of folks on this thread apparently assign some magical properties to this word which the word is incapable of supporting. A lot of confusion would have been avoided if the thing had been called what it really is and how it is intended to be used. When written properly, it is just an equation — a simple run-of-the-mill, multiplication equation.

  371. The breathtaking beauty of this identity is that it is true for all values of Population, GDP, and Energy. Genius.

  372. climatereflections says:
    July 13, 2014 at 4:49 pm
    In fact all of the denominators must refer to an individual unit (the C, the B, and the P).

    Exactly! That’s a point I tried to make in several posts, although the people like ghl at July 13, 2014 at 5:00 pm continue to misunderstand.

  373. Ian W says:
    July 13, 2014 at 4:26 pm
    Shawnhet says:
    July 13, 2014 at 10:39 am

    Ian W says:
    July 13, 2014 at 10:11 am
    “You are wrong of course.

    Belgium used to claim that they were one of the few countries visible from space as their surplus nuclear power capacity meant that all their autoroutes/motorwegs were lit all night. So Belgium creates far less CO2 for its GDP per head than say Poland or Germany that use lots of coal. Increasing Belgium’s GDP may have no effect on its CO2 emissions whereas increasing Poland’s GDP would do so.”

    Pay attention to the point, we’re discussing, please. I said that the Kaya Identity can still be valid because its Kaya-factors changea gradually and that your hypothetical was unrealistic because you can’t go to a non-carbon regime regime at the flick of a switch. You claim I am wrong by pointing to Belgium that 1. changes its KAya factors gradually and 2. has not moved to a non-carbon regime yet. Can you see the problem in your logic?

    “If LNER nuclear fusion becomes reality – then the ‘identity’ fails. If GDP rises because of the banking or reinsurance markets, then the identity fails”

    Once we move to a non-carbon economy, the identity will be invalid, for sure, but, at this point, this is just a hypothetical and doesn’t mean the identity doesn’t work now. Growth in the financial sector of the economy will affect the predictive value of the Kaya *but only if that growth is at a different rate than that of the “carbonised” economy and it is a large enough difference to be noticed*. Think about it.

    “Only someone in PR would think this was a useful exercise. It is the level of logic that said London would be feet deep in horse manure due to the increase in population and transport requirements.”

    Your arguments against it working *now* are all based on stuff that hasn’t happened yet or is probably too small to make a significant difference. I’m not sure what the PR guys would say about that ;)

  374. James Gibbons says:
    July 13, 2014 at 2:50 pm

    The real Kaya Equation is here and is used to model emissions over time:

    http://climatemodels.uchicago.edu/kaya/

    **********************************
    Thanks, James. Yeah should’ve checked myself.

    James has dubbed it an ‘equation’ which I would agree with as I don’t consider it an ‘identity’ in the common definition. So if I hurt Kaya’s feelings I apologize for her sensitivity. I haven’t yet found any defenders in this thread not using bogus math however and I think my comments to that will stand sans my commentary on Kaya.

    The tautology is broken at the GDP and $(1990) factors.
    It does not reduce to CO2 = CO2, instead,
    CO2 = GDP/yr * co2/$(1990)
    Units: t/yr = $/yr * t/$

  375. climatereflections says:
    July 13, 2014 at 4:49 pm
    *****************************************
    I tend to accept arguments as presented run with it. The crazy M&M thing didn’t help. Thanks for being on the wrong side for the right reason.

  376. ghl says:
    July 13, 2014 at 5:00 pm

    The breathtaking beauty of this identity is that it is true for all values of Population, GDP, and Energy. Genius.
    ********************************************
    You are absolutely correct in your assessment of the IDENTITY… as given in the post.
    I have found none of its defenders to be of any help mathematically (but I can’t claim to have seen all the comments).

  377. climatereflections says:
    July 13, 2014 at 4:36 pm

    You are going a bridge too far. Yes, Willis cited to an incorrect version of the Kaya equation, which got him off on the wrong foot.

    In the paper he was reviewing in the original post here: http://wattsupwiththat.com/2014/07/09/diving-into-the-deeps-of-decarbonization/ what equation should he have parsed?

    Recall in that post he began laughing when he saw the Kaya Identity, dove off the deep end, and began his spiral downward from there. The Kaya identity he cited is correct – I’m not aware of another version of it though there are many examples of equations built from it. The Kaya Identity was created by Dr. Yoichi Kaya (male) at the Keio University in Japan and co-author of a book on sustainable energy (http://unu.edu/publications/books/environment-energy-and-economy-strategies-for-sustainability.html), a lofty goal if it doesn’t destroy the world order.

  378. The Kaya identity is a piece of garbage that will disappear as fast as when the UNs environment website took down the X number of climate refugees that will occur by X year statement.

  379. dp @6:33pm:

    Thanks, dp.

    Willis is absolutely correct to laugh at the equation as listed on page 12 of that report. It is a joke, completely nonsense, utterly worthy of scorn. Same goes for Kaya’s Identity as Kaya himself outlined it. He should be forced to endure long and painful public humiliation for willful and wanton abuse of mathematics and made to recite three verses of penitent-related scripture (or similar punishment).

    *However,*

    The way the Kaya Identity graphic is presented in the report, and the way Kaya himself outlined it in his shorthand formula, *is not the way it is actually implemented.* Every one of the authors who have followed Kaya’s terrible example over the years by writing the equation the way Kaya did should be ashamed of themselves.

    What we see in practice, once authors get past this ridiculous genuflection to Kaya’s original mistake, is that they implement the equation the way it should be: namely, on a *per unit* basis.

    So, for example, in the paper Willis referred to, on page 12 — notwithstanding their absurd presentation of the equation as Willis rightly critiqued — they actually say in the prose:

    “CO2 emissions can be expressed as the product of four inputs: population, GDP *per capita,* energy use *per unit of GDP,* and CO2 emissions *per unit of energy.* (Emphasis added.)

    Thus, if Willis had closely read the prose text he would have seen the real equation (rather than the absurdity written elsewhere on the page) and we could have avoided much of the present discussion and the prior thread as well. As I said, I think Willis should come clean and admit that he didn’t carefully read the paper. However, there are multiple papers from multiple authors who have all put forward this abominable “identity” in the same meaningless, mindless fashion, perhaps to give a nod to Kaya. So I can understand Willis getting wrong-footed by it. But the authors in those papers in fact go on to calculate everything on a per unit basis, rather than the way the alleged “identity” was written.

    The way the equation actually works in practice is perfectly fine. It is a legitimate, simple, ordinary, every-day multiplication problem. Nothing funny about it.

    The climate community should be ashamed for putting the nonsense, meaningless, self-canceling, “identity” version into their papers. Willis should be ashamed for not having seen that the text in the paper didn’t comport with the graphic. Many people on this thread should be ashamed for trying desperately to justify a bogus, nonsensical “identity” that no-one in the real world uses anyway.

    And I should be ashamed for spending so much time on this thread, instead of taking care of the chores around the house the Mrs. wants done. :)

  380. Johan says (July 13, 2014 at 11:48 am): “Now,now, Gary, and what if one of the deer only has 3 legs ! :)”

    Way ahead of you. While I have yet to count a fractional deer (presumably because 3-legged deer are soon removed by predators), I have in reserve a more complex method that includes counting legs, ears, tails, and noses, and dividing by eight. Of course a three-legged deer will still give a fraction, but the more advanced formula should produce a fraction closer to unity, at which point I’ll triumphantly round off! :-)

  381. Rewording it to this may help you understand your misunderstanding:

    “CO2 emissions can be expressed as the product of four inputs: population, GDP *per capita,* energy use *per unit of GDP,* and CO2 emissions *per unit of energy

    Which verbosely expressed as an identity is:
    Population x (GDP/Population) x (Energy/GDP) x (CO2/Energy) gives us a result expressed in units of CO2 emissions (e.g., = CO2 emissions)

  382. Curious George says:
    July 12, 2014 at 10:19 am
    “Let’s try a simpler case – a total CO2 generated by cars:

    CO2 = (number of cars) * (CO2 per car), or
    CO2 = (number of cars) * (CO2 / (number of cars))

    True or false – Does it matter if the cars are driven at all? Does it respect the efficiency of car engines?”

    Of course what matters is the cars being driven, how much they are driven, how many passengers they carry, their fuel efficiency, …

    So formulating the above a different way,for example noting CO2 as a function of CO2/mile (an expression of fuel efficiency) and of passengers/car, gets you thinking of options for managing carbon emissions associated with passenger transport. So for example policies promoting ride sharing, carpooling, high-passenger vehicle lanes could be a policy “lever”. Or providing non-car options – mass transport, bicycling, telecommuting.

    Expressing emissions in terms of CO2/mile rather than gasoline/diesel miles-per-gallon would allow electric vehicles to be compared in a more useful way to conventional internal combustion engine vehicles. If electric vehicles are recharged with electricity derived from coal, then their relative virtue in reducing emissions is not so great as if they were charged via nuclear power or hydro.

  383. Thomas says (July 13, 2014 at 11:57 am): “Therefore, Kaya erred when he included factors for GDP and population. Those factors only make the equation less accurate. Constructing a long equation with factors that don’t make the equation more precise is not helpful. Actually it’s harmful.”

    If I’m reading you right, then you see the Kaya Identity as the equivalent of a Rube Goldberg device?

    http://en.wikipedia.org/wiki/Rube_Goldberg_machine

  384. This set of exchanges is an example of the differences between the mathematical (or in this case algebraic) “correctness” of a model, and its utility as an analytical tool. The Kaya Identity is “correct” within the context of its own definitions. But like any model it is a simplified and incomplete depiction of the system it represents.

    The question is, does the Kaya Identity provide a useful framework for thinking about anthropogenic carbon emissions and communicating the policy trade-offs to politicians and the community as a whole? I would say “yes.” The Kaya Identity provides a simplified understanding of the connections among emissions, population, energy, and economic development in a similar way to simple energy balance models providing a simplified understanding of climate sensitivity to radiative balances.

    The global policy challenge of reducing emissions (assuming we seek to do so) is this:
    to “break” the Kaya Identity.

    What I mean by that is so far in the post-industrial world the Kaya Identity “works.” Economic development has been largely supported by rapid growth in energy access, and that energy has been overwhelmingly derived from fossil fuels whose combustion has driven carbon dioxide emissions. Combine that coupling of economic development to fossil fuels, with population growth and we have a good overall explanation for the growth in emissions.

    So, can we “decouple” population growth from economic development? We could if billions of people were willing to live in abject poverty.

    Can we decouple economic development from energy access growth? We could if billions were willing to live in energy poverty.

    Can we decouple growth in energy access from carbon emissions? Yes, but there are many “buts” in that “yes.” The technological challenge of developing and *scaling up* reliable, 24/7, cost-effective energy options that do not involve carbon emissions is a huge one. In my view it’s often underestimated.

    So each term in the Kaya Identity highlights a set of policy challenges and options. From this perspective it is a useful “rubric” for thinking about the energy/emissions issue. The Kaya Identity is itself simplified and incorporates simplified and incomplete terms such as GDP. If we seek to cut greenhouse gas emissions there are non-CO2 GHGs such as methane and nitrous oxide whose emissions are more associated with land use than energy use, so require different policy mechanisms. This is another way in which the Kaya Identity is an incomplete description of the system.

  385. wrhoward says:
    July 13, 2014 at 8:50 pm

    The question is, does the Kaya Identity provide a useful framework for thinking about anthropogenic carbon emissions and communicating the policy trade-offs to politicians and the community as a whole?

    No – in the context of this post by Willis (keep your eye on the pea) the question is did Willis misunderstand and abuse the Kaya Identity in the article he reviewed and the answer is yes, he did.

    In another post a discussion of the value of the Kaya Identity and the analyses based on it can be discussed and it may be worth having. Personally I don’t think this crowd is ready for it.

    • dp says “Personally I don’t think this crowd is ready for it.”

      Thank you for sparing the crowd!

  386. dp @8:32pm:

    “Which verbosely expressed as an identity is:
    Population x (GDP/Population) x (Energy/GDP) x (CO2/Energy) gives us a result expressed in units of CO2 emissions (e.g., = CO2 emissions)”

    No. Which is wrongly and confusingly expressed as you wrote it. Unless, of course, you are falling back to the idea that the Kaya Identity is an utterly useless triviality, in which case, sure, go ahead and write it however you want with whatever self-cancelling parameters you desire; knock yourself out.

    On the other hand, if we want to write it properly we can write:

    Total CO2 emission = Population x (GDP/Person) x (Energy/GDP Unit) x (CO2/Energy Unit).

    Again, I’m not sure why there is so much knee-jerk effort on this thread to defend a silly, useless “identity” when no scientist that I am aware of actually uses it in that form anyway and when it is so easy to just write the equation in a way that makes it useful and meaningful and has the added benefit of being what scientists actually use.

  387. Can we reach a consensus?
    Total man-made CO2 emissions are a function of population, total production per head of population, energy consumed per unit of production, and CO2 emissions per unit of energy.

    So to reduce CO2 emissions, at a macro level the levers you have are to reduce population, reduce GDP, increase energy efficiency, and switch to low CO2 fuels.

  388. Johan says:
    July 13, 2014 at 2:59 pm

    That is complete *****, for a whole number of reasons, most of them correctly identified in many of the posts above.

    You can’t use an identity like Willis supplied to calculate anything so perhaps this whole discussion is meaningless. That was why I was having so much trouble with the “equation” because it didn’t seem useful for anything. If we use the actual computer code it makes more sense. Here is the equation used to calculate energy use per year:

    Energy Used per Year (W) = Population * ($/person/y) * (W*y/$)

    The units cancel to Watts so from a physical units viewpoint, it is correct. When you look at the values on the right, Population * ($/person/y) is seen to be total yearly GDP and (W*y/$) is seen to be how may Watts you can buy over a year with a dollar. But it wasn’t until I started plugging numbers into this that I noticed the real problem. This assumes that the whole GDP is spent on energy, so this is clearly wrong.

    Let’s take the numbers for the year 2000:

    13.79 TW = 6.0E9 * 4890 ($/person/y) * 0.47 (W*y/$)

    I looked up global energy use and found in 2006 it was 16 TW so 13.79 for 2000 sounds about right. I looked up global GDP for 2000 and it was $41.016 Trillion. This works out to about $6836 per person, so there appears to be some discounting of the GDP already applied, but I doubt that we spend 72% of every person’s income on energy. Trying to figure a value on energy is a little difficult because it is a mix of oil, gas, coal, electricity and third world combustibles, such as firewood. If you simply use electricity, the 2000 US retail average was 1 KWH for $0.0821 or 12.18 KWH per dollar. Divide by 8760 hours per year and you get 1.39 W*y/$ which shows where the true discount is likely to be. It looks like they did some number adjustments to GDP and energy costs to get the total energy produced to come out correctly.

    Once you have total Energy Used per Year, it is easy to multiply by the CO2 tons per Watt year to get the CO2 Emissions per Year.

    CO2 Emissions per Year (tons) = (Energy Used per Year) * CO2ton/(Watt*year)

    Again, the physical units work and are correct but because this is based on the first equation it is also suspect.

    So in summary, it is really hard to calculate actual global yearly energy use because of the strange mix of energy sources in use and we need to multiply the GDP per person by an unknown factor to get the amount the average person spends on energy.

    Going into the future not only requires guesses on all these unknowns, but also makes an assumption of a somewhat exponential growth or decline factor in each of population, GDP, energy cost and the ability to sequester CO2 per energy produced.

    And no, the Kaya Identity doesn’t hold because it assumes all GDP goes to energy production. But it looks nice on a PowerPoint!

    Looks like Willis was right to be worried about this.

  389. No. Which is wrongly and confusingly expressed as you wrote it.

    Not everyone gets it. BTW, total CO2 emission may not be what the result is. It may be rate of change of CO2 emission, depending on what it is fed.

    Think of the identity’s RHS as a black box and you don’t see the constituent parts inside. All you see is the LHS. The input would be data types appropriate to produce that output type, and pragmatically, agreed to by the creator and the customer. You could write this as “USD = f(b)”. In this case USD represents a dimensionless value in US dollars as calculated by the f function of b, the black box. We’ve given it no data but we know the output will be US dollars. We don’t know if USD is dollars per hour, or a tax rate, or an absolute value point on a graph, so we can’t write it as e.g. USD/hour = f(b). When we see what parameters are in the black box that becomes known. The black box doesn’t care if the output is a rate of change or an absolute – so long as the inputs are appropriate it will provide the correct output. For that we move beyond the identity to an implementation of the identity which is an enumerated equation in which the data types are known and appropriate to produce the expected data type in the result. That is what happened in the paper Willis reviewed.

    Once we’re beyond the mechanics of the math the worth of the process can be questioned and that is a healthy exercise.

  390. Equations, formulas and identities have distinct meaning in Mathematics.

    There is much confusion in this thread caused by mistaking one for another.

    An identity is true for all values of the variables. For example:

    2(x + y) ≡ 2x + 2y

    The above statement is true for all possible values of x and y, so it is called an identity.

    An identity is true for any value of the variable, but an equation is not. For example the equation:

    3x + 2 = 11

    is true only when x = 3, so it is an equation, but not an identity. In fact, to solve it, is to find the single value of x that makes the equation true:

    3x = 11 – 2
    3x = 9
    x = 9 ÷ 3
    x = 3

    A formula links one quantity to one or more other quantities; for example,

    e = mc&#178

    Einstein’s formula can be used to determine the value of E for any given value of the variable M.

    An identity is tested by substituting values for its variables.
    I have tested the Kaya to prove it is an identity below.

    The Kaya multiplicative identity (K) :

    Global CO2 Emissions ≡ (Global Population) (Gross World Product/Global Population) (Gross Energy Consumption/Gross World Product) (Global CO2 Emissions/Gross Energy Consumption

    Variables of K:

    Global CO2 Emissions = c
    Global Population = p
    Gross World Product = g
    Gross Energy Consumption = e

    GIVEN

    c=2, p=4, g=20, e=8 [Assign values to the variables]

    FOR

    K c ≡ p x (g/p) x (e/g) x (c/e)

    THEN

    2 ≡ 4 x (20/4) x (8/20) x (2/8)
    2 ≡ 4 x 5 x 0.4 x 0.25
    2 ≡ 2

    THUS

    LHS = 2
    RHS = 2

    THEREFORE

    LHS of K ≡ RHS of K if c= 2, g=20, p=4, e=8.

    —————————————————————

    This does not prove or disprove the usefulness of the Kaya, or identities in general.

    I advise everybody to actually work with the Kaya Identity by putting your own values into it (Real or otherwise).
    As soon as you start working with it, you will understand what it is and what it definitely is not!

    I particularly advise just changing the CO2 term on the RHS a number of times!

    The IPCC version of K uses an equal “=” symbol rather than an equivalence “≡” symbol (Despite calling it the Kaya multiplicative identity*) and it is not clear if “CO2 Emissions” is the same variable as CO2 on the RHS but it makes not difference to the result:

    CO2 Emissions = Population × (GDP/Population) × (Energy/GDP) × (CO2/Energy)

    CO2 Emissions = ?
    Population = p
    GDP = g
    Energy = e
    CO2 = c

    If
    c= 2, g=20, p=4, e=8.

    Then

    RHS = p x (g/p) x (e/g) x (c/e) = 4 x (20/4) x (8/20) x (2/8) = 4 x 5 x 0.4 x 0.25 = 2

    Therefore CO2 Emissions = 2 if c= 2, g=20, p=4, e=8.

    OR

    CO2 Emissions = 2 if c= 2, g=20, p=4, e=9.
    CO2 Emissions = 2 if c= 2, g=20, p=4, e=765.

    OR

    CO2 Emissions = 2 if c= 2, g=7, p=9, e=8.
    RHS = p x (g/p) x (e/g) x (c/e) = 9 x (7/9) x (8/7) x (2/8) = 9 x 0.777777777777778 x 1.142857142857143 x 0.25 = 2

    ETC

    CO2 Emissions = 70 if c= 70, g=20, p=4, e=8.
    CO2 Emissions = 899 if c= 899, g=20, p=4, e=8.
    CO2 Emissions = 2345 if c= 2345, g=20, p=4, e=8.

    Try it yourself, it could change your life ;-)

    * http://www.grida.no/publications/other/ipcc_sr/?src=/climate/ipcc/emission/050.htm

  391. climatereflections:

    At July 13, 2014 at 10:03 pm you say

    Again, I’m not sure why there is so much knee-jerk effort on this thread to defend a silly, useless “identity” when no scientist that I am aware of actually uses it in that form anyway and when it is so easy to just write the equation in a way that makes it useful and meaningful and has the added benefit of being what scientists actually use.

    So no scientist “actually uses it” but rearranged it is “what scientists actually use”.

    Such is the kind of illogical nonsense which advocates of the Kayla identity present: they really do think that anything can mean anything so the undefined Kaya identity is valid.

    The Kayla identity is an abomination: it is presented as a method to replace science with propaganda.

    Richard

  392. Scott Wilmot Bennett says: “An identity is true for all values of the variables.”

    I sit corrected and have learned something new tonight.

  393. If it slides, slithers, swims, scurries, scuttles, slips, creeps, crawls, climbs, dips, dives, hops, hobbles, jumps, jives, walks, wades, waddles, flys, flaps, flounders, flutters, frolics or f**ks – is outside the Kaya thing, unless of course it is on menu in a Chinese restaurant and becomes a part of GDP.

  394. Matthew R Marler says:
    quote: “The terms on the RHS are to be determined by statistical analyses of states and regions. ”

    Well, why not ? But this is *not* what you claimed before. You claimed that *the decomposition of the Kaya identity* was strongly supported by macroeconomic facts. So, where are those facts ? And how your RHS-statistical-analysis could *justify* the decomposition ? Please explain.

    quote: “All it says is how much change in the LHS can be effected by changes in the terms on the RHS.”
    No. The kaya identity itself cannot say that. Whatever your statistical analysis, any change on RHS cannot “affect” LHS because all the terms are, by construction of this tautology, completely interdependent and redundant. It is strictly equivalent to LHS = 1 * 1 * 1 * LHS. Please explain how a change in the decomposition of 1 could provide information on LHS ?

    I agree with you that if by chance you get, maybe by the way of statistical analysis, other (external) physical relationships between some terms, measured separately and reliably, then you could reduce some degrees of freedom. But definitively, this would be *no more* this Kaya-thing. It would become some (more useful) equation. For the moment it is not.

  395. Dan Metal says: “I dare say you have no inkling as to the depth of your ignorance.”

    That’s easy. The upper limit of ignorance is infinity, as ignorance is simply 1/knowledge. As knowledge goes down, the reciprocal of it, ignorance, rises to an asymptote and then becomes undefined.

    The other limit is zero. 1/everything-that-can-be-known is zero or very close to it.

  396. Michael 2 says:
    July 14, 2014 at 12:00 am

    […]

    http://www.manicore.com/anglais/documentation_a/greenhouse/kaya_equation.html

    As you can see, many people (including right here) think it’s great to have algebra that cancels out but somehow still has meaning. THAT is entertainment!
    *********************************************************************
    It would be entertaining if it wasn’t so depressing. That’s some real garbage you dredged up with that link.

    James Gibbons at July 13, 2014 at 2:50 pm
    posted this link: http://climatemodels.uchicago.edu/kaya/
    This is an equation that works (no comment on validity) though it is not very clean as the “watt year” term cancels.

    I have argued against the M&M analogy:
    M = P * M/P

    and the distance analogy:
    d = d/t * t

    I will abandon the quest here. If I have missed any corrections or counter arguments to anything I’ve said I’m sorry about that. The comments are much too many to navigate any longer. I wish everyone well.

  397. Oh brother. Here I was wondering all night what all the fuss is about. Turns out most can’t even grasp the simple fact that (number of a per unit of b) times (number of b) equals (number of a).

    And the main criticism still holds. You can use (number of a per unit of b) as a parameter in an equation; and (number of b) as a variable, in which case you have some sort of (linear) “model”, but to use the KAYA identity in such a fashion is still a travesty. Because it’s an oversimplification: 4 lousy variables, and no inter-dependencies.

    If Willis had said that in the first place, we might have had a fruitful discussion. Now this site has become the laughing stock of everyone who knows elementary algebra.

  398. Sorry Matthew, it seems that the first claim “supported by macroeconomics facts” was made by Pete Brown, not you. But my comments above hold anyway, as you were, as I understand, completing Pete’s views in your comment, and the 2nd claim is from you.

  399. Prof Yoichi Kaya first proposed his relationship (subsequently labeled as an identity) in the 1980s and published it in the mid 1990s. It eventually was utilized by the UN / IPCC.

    As an economic and industrial conception his relationship does not appear to have been made to order for the alarmist ideology of CAGW.

    John

  400. John Whitman says:July 14, 2014 at 12:57 am
    As an economic and industrial conception his relationship does not appear to have been made to order for the alarmist ideology of CAGW.

    Of course not. As sais above (but nobody reads all the posts of course) the identity emerged out of a quest to identify the main driving forces of CO2 emissions. That’s all.
    And others started “abusing” it as if the KAYA identity is some sort of mathematical model.

  401. John Whitman:

    Your post at July 14, 2014 at 12:57 am says in total
    Prof Yoichi Kaya first proposed his relationship (subsequently labeled as an identity) in the 1980s and published it in the mid 1990s. It eventually was utilized by the UN / IPCC.

    As an economic and industrial conception his relationship does not appear to have been made to order for the alarmist ideology of CAGW.
    So what?
    Svante Arrhenius first proposed his proposal that increased atmospheric CO2 concentration would cause global warming in the 1890s and published it in the mid 1890s.
    (ref . Philosophical Magazine and Journal of Science. Series 5, Volume 41, April 1896, pages 237-276.) Margaret Thatcher elevated it to be a political issue in the 1980s. It eventually was utilized by the UN / IPCC.

    As an economic and industrial conception his hypothesis does not appear to have been made to order for the alarmist ideology of CAGW.

    Richard

  402. dp says:

    July 13, 2014 at 2:06 pm
    “As said many times before, and by many: the formula is only a tautology, CO2 = 1 * 1 * 1 * CO2″
    This pretty well sums up the complete lack of understanding of what an identity is. Well done.”

    Thank you. But we are not talking about the abstract definition of what identities should be. We are talking about the usage of this specific “Kaya identity” to define real world policies. I do not try to prove that this Kaya-thing is *not an identity*, I argue that it contains *no information* whatsoever about CO2, population, GDP or whatever.
    If you can find any *non trivial piece of information* in this formula, please share.
    If you are just satisfied by the fact is an identity without contest, well, I have nothing to add.

  403. Johan says:
    July 14, 2014 at 12:50 am

    Oh brother. Here I was wondering all night what all the fuss is about. Turns out most can’t even grasp the simple fact that (number of a per unit of b) times (number of b) equals (number of a).
    ********************************************************
    a = a/b * b is what you are saying?
    I hope not because this is an identity and requires you to know “a” ahead of time.
    Let a = number of grains of sand on the beach,
    Let b = number of cubic cm of sand on the beach,
    Then a/b = (number of grains of sand on the beach) / (number of cubic cm of sand on the beach)
    or Let a1 = number of grains of sand in 3 cubic cm,
    Let b1 = 3 cubic cm.

    I would not attempt a/b. That can only be found if a is known.

    It makes more sense to solve for a useful rate: a1/b1, what say 100 000 gos / 3 cm^3
    a1/b1 = 33 000 or so gos/cm^3

    a = 33 000 gos/cm^3 * b

    this is a heck of a lot better than a = a

  404. Will says: July 14, 2014 at 1:26 am
    a = a/b * b is what you are saying?

    For Pete’s sake, if you can’t grasp that 10.9 kg CO2/gallon x 1.18 gallons = 12.8 kg CO2; then obviously this whole discussion is a complete waste of time.

    Even the ancient Babylonians knew more of algebra than some commenters here.

  405. Johan says:
    July 14, 2014 at 1:40 am

    Will says: July 14, 2014 at 1:26 am
    a = a/b * b is what you are saying?

    For Pete’s sake, if you can’t grasp that 10.9 kg CO2/gallon x 1.18 gallons = 12.8 kg CO2; then obviously this whole discussion is a complete waste of time.

    Even the ancient Babylonians knew more of algebra than some commenters here.
    ********************************************************
    I would not dis the ancient Babylonians.

    But I guess I am missing your point. If you meant a = a/b * b is meaningful then you miss the fact that a on the left is different that a on the right, your example, a on the right = 12.8 and a on the left is 10.9, illogical. Not to mention the value of b is 1 and 1.18 respectively.

    If you didn’t mean that then well, I guess we are in agreement.

  406. Will says: July 14, 2014 at 1:56 am
    But I guess I am missing your point. If you meant a = a/b * b is meaningful then you miss the fact that a on the left is different that a on the right, your example, a on the right = 12.8 and a on the left is 10.9, illogical. Not to mention the value of b is 1 and 1.18 respectively.

    Applying elementary rules of algebra:

    a = a x 1 = a x (b / b) = a x [b x (1/b)] = a x [(1/b) x b] = [a x (1/b)] x b = (a/b) x b

    In my example 12.8 kg CO2 is a; 1.18 gallons is b and 10.9 kg CO2/gallon is (a/b).

    So of course 12.8 doesn’t equal 10.9; for the simple fact that 12.8 = a and 10.9 = (a/b).

    Since when is a = (a/b), if b is not equal to one (and for the sake of convenience one might also assume b is different from zero) ???

  407. The utility of the Kaya identity would be revealed by establishing its universality for a consistent set of parameters. It is a — possibly useful — linearized decomposition of the dependence of the rate of CO_2 production on population.

    So one has to look at the various parameters. CO_2/energy is hardly universal — it is one of the parameters we are supposed to be trying to vary in order to reduce the rate of CO_2 production. CO_2/energy for nuclear power plants or solar cells is essentially zero. For methane-based generation it is one value. For an efficient modern coal plant it is another. For a wood based fire in a fireplace it is another. Different countries have very, very different mixes of energy generation, with first world (redefined as the wealthiest 33%) predominantly “efficient” (comparatively less CO2/joule), with the third world (the poorest 33%) predominantly “inefficient” (burning animal dung and charcoal on open fires to cook), and the second world in between.

    Then one has the next few parameters, although I don’t completely understand why. One could just jump to energy/population and then multiply by population instead of going through energy/gdp, gdp/population as intermediaries. I suppose the point they are trying to make is that some countries are relatively efficient in the energy they consume per unit of “wealth” as measured by gdp, but this is already reflected, as noted, in CO_2/energy. Again, it is hardly a set of universal values. It cannot be. Different parts of the world have different baseline energy requirements just to stay alive, and have very different sources of “wealth” that go into their GDP. Antarctica, for example, has a negative GDP and a huge energy requirement just to have a human population exist there. Parts of the world have no wealth or resources for generating wealth. Other parts have climates suitable for agriculture, or massive collections of natural resources. This all sorts out in the first, second, third world decomposition once again — Kuwait is enormously wealthy with a huge GDP/population, and yet it is almost irrelevant to the average economic profile of the rest of the world — tiny population, small country, and nearly 100% of its wealth derived from a single valuable resource that is present in abundance. On the other end of the spectrum are the tiny island nations of the south pacific — no natural resources of any value, tiny populations, no need for most of the trappings of modern civilization and no way to pay for them if they needed them. There isn’t even homogeneity within countries — India is wealthy and industrialized and dirt poor neighborhood by neighborhood as one wanders about in the country.

    In the end, the lack of universality makes the identity useful primarily as a political oversimplification. Here’s an easy way to show that. Forget CO_2. Suppose we want to relate population to energy consumption directly. That is, after all, the name of the game. We can easily go through all of the countries of the world, tally their populations, and add up all of their sources of energy. What, exactly, is the advantage of adding the the GDP step in that? We learn a bit from GDP/population times energy/GDP that we didn’t already know from energy/population, but not much, and what we do learn isn’t likely to be universal or describable in functional form. It’s gangbusters useful for political argumentation, though…

    rgb

  408. Thomas says:
    July 13, 2014 at 11:57 am

    [Willis quote] “If I burned that exact amount of gasoline in a furnace to make a tool, that would add to the GDP. But I didn’t. I burned it in an activity that does not add to the GDP.”

    You are using a definition of GDP that is not the common definition. GDP is the sum of *consumption*, investment, government spending, and net exports (from Wikipedia).
    —————–

    Your stated “common definition” of GDP does not negate Willis’s above statement simply because you are misunderstanding your stated GDP definition which should read, to wit:

    GDP is the sum of *consumption spending*, investment spending, government spending, and net revenue from exports

    Thus, his purchase of gasoline was “consumption spending” which added to the GDP ….. but he “burned” it without producing anything of value ….. thus NO increase in GDP.

    Whereas, if he had “burned” it to produce a “tool”, … then the sale of said tool would have garnered more “consumption spending” and/or an increase in “net revenue from exports” ….. thus an increase in GDP.

    Willis is “right as rain” ……… so quit picking on him.

    Cheers

  409. Shawnhet says:
    July 13, 2014 at 5:05 pm

    Ian W says:
    July 13, 2014 at 4:26 pm
    Shawnhet says:
    July 13, 2014 at 10:39 am

    Ian W says:
    July 13, 2014 at 10:11 am
    “You are wrong of course.”

    Your arguments against it working *now* are all based on stuff that hasn’t happened yet or is probably too small to make a significant difference. I’m not sure what the PR guys would say about that ;)

    France gets 75% of its power from Nuclear energy – and you say that is ‘stuff that hasn’t happened yet’?

    The base assumption of this ‘identity’ breaks down to the ‘green’ PR battle based on 3 weak points:
    Claim 1 — GDP requires energy generation and
    Claim 2 — Energy generation is equivalent to CO2 generation and
    Claim 3 — CO2 generation is something bad.
    ——- therefore reduce GDP

    Energy generation is NOT equivalent to CO2 generation – see France, and I am sure there are other examples and there will be more in the future. There are also non-industrial inputs to GDP that require no energy source.

    There is also no proof that CO2 does any harm in the real world but considerable evidence that it does good in greening the deserts and increasing crop yields.

    The three level argument does not then support the claim that GDP growth is a ‘bad’ thing.

    This ‘identity’ is just a subtle way of introducing Holdren’s favored de-development and de-industrialization as otherwise there will be more of the demon gas CO2.

  410. rgbatduke:

    You conclude your post at July 14, 2014 at 4:53 am saying

    In the end, the lack of universality makes the identity useful primarily as a political oversimplification. Here’s an easy way to show that. Forget CO_2. Suppose we want to relate population to energy consumption directly. That is, after all, the name of the game. We can easily go through all of the countries of the world, tally their populations, and add up all of their sources of energy. What, exactly, is the advantage of adding the the GDP step in that? We learn a bit from GDP/population times energy/GDP that we didn’t already know from energy/population, but not much, and what we do learn isn’t likely to be universal or describable in functional form. It’s gangbusters useful for political argumentation, though…

    Yes!
    I have been saying that for days. For example, at July 11, 2014 at 7:55 am in one of my posts on the other thread I wrote

    The equation as presented – as you say – pretends and “is intended to illustrate” that reduction of CO2 emissions requires fewer people or poorer people. It is an excuse for Malthusianism. This evil is screened by being accompanied with assertions that similar effects may be achieved by more efficient energy production or more efficient energy use, but those efficiency improvements will happen as a by-product of normal economic activity if no interference is adopted.

    Richard

  411. The equation as presented – as you say – pretends and “is intended to illustrate” that reduction of CO2 emissions requires fewer people or poorer people. It is an excuse for Malthusianism.

    Well, it can be. Or not. It can also be used as a means of pointing out that there is a real difference between Kuwait, India, the United States, China, Ukraine, Viet Nam, and Nigeria. Kuwait has a huge GDP/population because it is a desert country sitting on top of a single valuable resource. That resource requires little energy to produce, and so the energy/GDP reflects a reasonably affluent populace living in a hot dry climate with no particular industrial base. India, on the other hand, has a huge population and hence a comparatively low GDP/population, even though objectively it has far greater “wealth” than Kuwait. It is also very mixed in its economy, with substantial agriculture (sufficient to feed a billion people and export the remainder), a large and growing industrial base, and substantial natural resources. Its energy generation is a very mixed bag, though, and its delivery of both energy produced and the social benefits of that energy (clean water, sewage systems, cheap and universally available electricity) is enormously uneven — so much so that the notion of “energy/GDP” is nearly useless, as is (really) “GDP/population”. India is in some sense two or three countries in one, certainly compared to a Kuwait that would comprise a single smallish state in India.

    The point is that it is all well and good to study the economics of things like CO_2 production if one thinks that it is an important parameter that human civilization might should be worried about. That is, even though I disagree about the evidence supporting CO_2 linked CAGW/CACC, I think that there are enough benefits to tracking down and understanding the global energy ecology/economy to warrant this sort of study. The problem arises when one writes down oversimplified equations like this. This “identity” (decomposition) is too low resolution and two few dimensions to be useful to any actual economist or to anyone seeking to “solve” the hypothesized CO_2 problem. This is overwhelmingly evident in the case of large countries like China, India, Russia, the United States, Canada, and most of the larger, wealthier countries with a highly mixed economic base. Energy/GDP isn’t comparable between wealthy/mixed countries and averages over all of the detail, and it is the DETAIL that matters. In the case of smaller, less economically varied countries, it is downright misleading.

    rgb

  412. kabend says:
    July 14, 2014 at 1:11 am

    dp says:

    July 13, 2014 at 2:06 pm
    “As said many times before, and by many: the formula is only a tautology, CO2 = 1 * 1 * 1 * CO2″
    This pretty well sums up the complete lack of understanding of what an identity is. Well done.”

    Thank you. But we are not talking about the abstract definition of what identities should be.

    No – we are all gathered here because Willis reviewed a paper and misunderstood the math (http://wattsupwiththat.com/2014/07/09/diving-into-the-deeps-of-decarbonization/). He then started this second post to better explain his claim. He shifted slightly from his original misstep but did no better here because he still doesn’t understand the math and as Mosher pointed out, is unrepentant in the matter. The formula in the quote above demonstrates Willis is not alone. So the conversation has been to solve the problem of people not understanding the math. It was the identity, not the application of it that Willis parsed to his great amusement to CO2 emissions = CO2 emissions. The problem is these are two different things which invalidates his mathematical cancellations in the original post. You should find out what they are.

    A second conversation has to do with the value of the Kaya Identity to inform policy. I’m with the majority on that in that I think it is a very course tool with poorly defined parameters. There is too much going on behind the curtain for a proper skeptical inspection. It doesn’t help that Dr. Kaya himself is focused on renewables which is another way of saying the emerging world economies deserve nothing better than expensive mediocrity. Imagine if renewables had been mandated in the Marshal Plan – Europe would still be digging themselves out of WWII.

    Time to move on from here and follow his excellent travelogues which he always gets right.

  413. Roger Pielke jr writes,

    { http://rogerpielkejr.blogspot.ca/2014/06/clueless-krugman.html?m=1 }

    “The Kaya Identity is the centerpiece of the analyses found in The Climate Fix and a lot of my work. It is a very powerful tool for understanding the challenge of emissions reductions. It holds that carbon dioxide emissions are influenced by four factors:
    population
    GDP per capita
    energy intensity of the economy
    carbon intensity of energy
    As an identity, it is expressed –> CO2 = P * GDP/P * E/GDP * CO2/E

    (where P is population and E is energy consumption).

    . . . .

    The math here is simple. Increases in GDP, all else equal, mean that CO2 emissions go up. Improvements in technology (that is decreases in EI or CI) mean (all else equal) that CO2 emissions go down. Thus, we have two big levers with which to affect emissions – (a) GDP and (b) technologies of energy consumption and production.”

    – – – – – – – – –

    This seems conceptually straight forward and not slanted toward any climate tribe ‘sides’.

    That said, I must point out, however, Pielke jr’s position does illogically beg the question of an incorrect premise that fossil fuels are a net climate liability.

    John

  414. Sakoku Village, USA
    Sakoku is a small isolated fictional village in which 100 people live, work, and recreate using only food and electricity for energy consumption where there’s neither surplus production nor unsupplied want/need (a truly magical place). The village is nestled beside a lake which supplies 1,000 kWh of hydroelectric power to the village. The village also has a coal fired plant producing 100,000 kWh. The hydroelectric power produces 0 CO2↑ per kWh of electricity while the coal fired plant produces 1 Ton of CO2↑ per 100 kWh. On average each person in Sakoku uses 500 kWh of electricity every day for personal use. Commerce within the village consists of a brewery using 5,000 kWh, a bakery using 10,000 kWh, a general manufacturing plant/store using 10,000 kWh, farms using 5,000 kWh, and everything else (including the diner) using 20,000 kWh in all producing $1,000,000 worth of goods and services (including the electricity being generated).
    On average the village CO2↑ per kWh = (1000 Tons CO2↑ / 100,000 kWh) 99,000 kWh – (0 tons CO2↑ / 1,000 kWh) 1,000 kWh = 990 Tons CO2↑/kWh

    In 2009 the village elders (Gilligan, Skipper, Professor, Ginger, Mary Ann, Mr. and Mrs. Howell) were visited by three ghosts from 350.org, showing them the 10:10 video. They were so scared of being blown to bits they decided to reduce the village’s CO2↑ by 10% in 2010. The professor immediately went to research the problem and came back with: According to the Kaya “Identity” the village could reduce its CO2↑ by A) reducing the population, B) decreasing standard of living, C) increasing production efficiency, D) reducing the CO2↑ intensity of its energy production, or E) some combination thereof. He continues …

    Current situation:
    Population = 100
    GDP = $1,000,000 (value of goods and services produced)
    GDP/Population = $10,000 per capita (standard of living)
    Energy/GDP = 0.1 kWh/$ (production efficiency)
    CO2↑/ Energy = 990 Tons / kWh (CO2↑ intensity of energy)

    CO2↑ = 100 people x ($10,000 per capita) x (0.1 kWh/$) x (990 Tons CO2↑/kWh)
    = 99,000,000 Tons CO2↑
    10% of CO2↑ = 9,900,000 Tons CO2↑
    2010 Emission Goal = 89,100,000 Tons CO2↑

    Plan A) Reduce population to 90 people:
    CO2↑ = 90 people x ($10,000 per capita) x (0.1 kWh/$) x (990 Tons CO2↑/kWh)
    = 89,100,000 Tons CO2↑

    Plan B) Decrease Standard of living to $9,000 per capita:
    CO2↑ = 100 people x ($9,000 per capita) x (0.1 kWh/$) x (990 Tons CO2↑/kWh)
    = 89,100,000 Tons CO2↑

    Plan C) Increase production efficiency to attain 0.09kWh/$ Energy per GDP:
    CO2↑ = 100 people x ($10,000 per capita) x (0.09 kWh/$) x (990 Tons CO2↑/kWh)
    = 89,100,000 Tons CO2↑

    Plan D) Reduce CO2↑ intensity of Energy production to 891 Tons CO2↑/kWh:
    CO2↑ = 100 people x ($10,000 per capita) x (0.1 kWh/$) x (891 Tons CO2↑/kWh)
    = 89,100,000 Tons CO2↑

    Plan E) Attain 0.095 kWh/$ and 940.5 Tons CO2↑/kWh (5% ↑ in prod. Eff. and Energy ↑ intensity each)
    CO2↑ = 100 people x ($10,000 per capita) x (0.095 kWh/$) x (940.5 Tons CO2↑/kWh)
    89,347,500 Tons CO2↑

    Surprised that a five percent reduction in two factors isn’t equivalent to a 10% reduction in one factor?
    Well it ain’t (not according to the Kaya identity anyway):
    0.95A x 0.95B = 0.95AB NOT 0.9AB

    So what about a 10% reduction in 2 factors:
    CO2↑ = 100 people x ($10,000 per capita) x (0.09 kWh/$) x (891 Tons CO2↑/kWh)
    = 80,190,000 Tons CO2↑ which is equivalent to a 19% reduction from original not a 20% reduction from original.

    So what about a 10% reduction across the board:
    CO2↑ = 90 people x ($9,000 per capita) x (0.09 kWh/$) x (891 Tons CO2↑/kWh)
    = 64,953,900 Tons CO2↑ which is equivalent to a 34% reduction from original not a 40% reduction from original.

    So, according to the kaya identity the village is better off putting all its efforts into one of the factors to get the most bang for the buck. This doesn’t seem to jive with the Law of Diminishing Marginal Returns but what the heck, it’s just Climate “Science”.

    The professor being a level headed sort of person recommends calling the Ghost Busters, exercising their right to keep and bear arms to protect themselves from anyone that might want to blow them to bits for any reason, and not worrying about their insignificant CO2↑.

  415. steverichards1984 (July 13, 2014 at 7:31 am) says:

    You say the Kaya is mathematically sound.

    On what basis can a formula such as A = A be sound?

    I say it is mathematically sound because it is true for all possible values of A by definition. The Kaya expression is also mathematically sound for the same reason because it is derived from the similar statement CO2 = CO2 that is likewise universally true by definition.

    Yes LHS = RHS but what is the point of such an equation when its usefulness is limited to demonstrating that LHS = RHS?

    This is a different question. Just because a mathematical statement is true that does not mean it is necessarily useful or has a point. The statement LHS = RHS may be pointless and useless depending on the situation to which one is applying it, but if it is nevertheless true then it would still be mathematically sound, would it not?

    If its alleged use is to find the amount of CO2 somewhere, then it fails miserably because it always gives you whatever answer you want.

    The Kaya equation appears to have been derived from the fundamental identity CO2 ≡ CO2 by the judicious addition of self-cancelling fractions to the RHS. This is a standard pure mathematical technique in common use. So the Kaya expression is sound from the standpoint of pure mathematics because its inherent mathematical integrity has been preserved at every step of the way.

    Nevertheless, from the standpoint of applied mathematics it still “fails miserably” as you say. As I’ve already explained, I think it does so because the fractional variables that it ultimately derives on the RHS cannot be measured independently of their primary components which have been defined in the pure mathematical derivation and which all cancel one another out. In the end it just reduces back down to the original tautology CO2 ≡ CO2 and so leaves us none the wiser.

    But I think this currently-inescapable dependence on the primary components of its fractional variables is its critical flaw. Ways to measure the fractional variables independently of their primary components need to be found before the Kaya function can become the effectual tool of global environmental science and economics that it is made out to be.

  416. John West,

    You were doing really, really well there until you said:

    0.95A x 0.95B = 0.95AB

    In fact, 0.95A x 0.95B = (0.95x 0.95) AB = 0.9025 AB

    So it’s just short of a 10% reduction.

    To get a 10% reduction you need to use the square root of 0.9 = 0.94868…

    That is, you need to reduce two factors by 5.13% each.

    Then, as you say, diminishing returns may well suggest this route is more effective than a single 10% reduction. (Assuming, of course, you believe reducing CO2 is an effective way of scaring off ghosts.)

  417. I’m not producing anything with that energy—no goods, no services, nothing.

    Wrong, you produced formal GDP when you bought the gasoline, bought the car, changed the oil. serviced the brakes, paid a toll etc. Also, you informally produced utility by moving people somewhere they wanted to be.

    In any case, an equation with cancelling factors is just a dumb equation.

  418. @dp 6:19.
    Check your assumptions.. page 12 of the 8Mb pDF Pathways to deep decarbonization.
    As defined, here, Willis makes no mistake.
    As he stated in first post, a Laugh Out Loud moment.
    The fourth term is poorly written.
    Making an appearance of an algebraic absurdity.
    You could have saved all the typing by, snickering ..pointing out the actual definition of this term and moving on.
    Instead… you sneer at the commenters here,our intelligence is impaired, we do not comprehend higher maths, you also seem to have “Willis Derangement Syndrome”.
    And keep telling us viewers we do not appreciate the texture, warp and weave of the Emperors new Clothes.
    Because we do not see that CO2 emissions does not mean CO2 emissions, as used in the 4th term.
    Do not mistake your blindness for that of others.
    I have seen this behaviour before, it reoccurs in government bureaucrats at an alarming rate.
    Where we taxpayers are assured that what the document states is not what the document means.
    Until we wind up in court being raped by sub clause 3 paragraph 4.

  419. Ian W says:
    July 14, 2014 at 5:38 am
    “France gets 75% of its power from Nuclear energy – and you say that is ‘stuff that hasn’t happened yet’?”

    And your evidence that the Kaya identity doesn’t work for France is?

    “Claim 2 — Energy generation is equivalent to CO2 generation”

    You’re way off base here. The CO2,/Energy term in Kaya explicitly takes account of precisely this factor. If France moved to 100% Carbon sources for its energy, it’s CO2/Energy term would be 4 times as high, which *everything else being equal* would result in its CO2 emissions being 4 times greater.

    Respectfully, your criticisms fail because you don’t understand the *basics* here.

    Cheers, :)

  420. Whatever it is that Roger Pielke Jr is doing, he is not doing it using the Kaya Identity.

    He says:

    “Increases in GDP, all else equal, mean that CO2 emissions go up.”

    However,

    1. If

    c= 2, g=20, p=4, e=8.

    Then

    RHS = p x (g/p) x (e/g) x (c/e) = 4 x (20/4) x (8/20) x (2/8) = 4 x 5 x 0.4 x 0.25 = 2

    Therefore CO2 Emissions = 2 if c= 2, g=20, p=4, e=8.

    2. If

    c= 2, g=2000, p=4, e=8. (Increasing g)

    Then

    RHS = p x (g/p) x (e/g) x (c/e) = 4 x (2000/4) x (8/2000) x (2/8) = 4 x 500 x 0.004 x 0.25 = 2

    Therefore CO2 Emissions = 2 if c= 2, g=2000, p=4, e=8.

    ————————————————————————–

    Again he says:

    “improvements in technology (that is decreases in EI or CI) mean (all else equal) that CO2 emissions go down.”

    From 1. above

    c= 2, g=20, p=4, e=4. (Reducing e)

    Then

    RHS = p x (g/p) x (e/g) x (c/e) = 4 x (20/4) x (4/20) x (2/4) = 4 x 5 x 0.2 x 0.5 = 2

    Therefore CO2 Emissions = 2 if c= 2, g=20, p=4, e=4

    —————————————————————————-

    You get the picture!

    What I actually think he is doing, is using numbers that have not been derived from the ratios of the Kaya but are completely independent and therefore completely arbitrary, such that:

    c= 2, g=20, p=4, e=8.
    c = g*e*c*p
    c =20x8x2x4
    c = 1280

    Or

    c= 2, g=200, p=4, e=8.
    c = g*e*c*p
    c =200x8x2x4
    c = 12800

    If so, the ‘construction’ is no longer an identity but a crude product of meaningless factors (Meaningless because they are mathematically independent).
    It doesn’t matter if they are real world figures. If they aren’t derived from the identity statement then it no longer holds any claim to mathematical rigour of the ‘Kaya statement’.

  421. rgbatduke:

    Thankyou for your reply to me at July 14, 2014 at 6:00 am which includes

    The problem arises when one writes down oversimplified equations like this. This “identity” (decomposition) is too low resolution and two few dimensions to be useful to any actual economist or to anyone seeking to “solve” the hypothesized CO_2 problem.

    Again, I agree and I have been attempting – with no success – to obtain a definition of the “factors” which would specify what should and what should not be included in the “identity”. At present the ONLY use of the Kaya identity is propaganda because – as I have been persistently saying – it is inadequately specified and can be used to suggest anything. Or, as you put it in your first post

    We learn a bit from GDP/population times energy/GDP that we didn’t already know from energy/population, but not much, and what we do learn isn’t likely to be universal or describable in functional form. It’s gangbusters useful for political argumentation, though…

    Richard

  422. Johan says:
    July 14, 2014 at 2:14 am

    Will says: July 14, 2014 at 1:56 am
    But I guess I am missing your point. If you meant a = a/b * b is meaningful then you miss the fact that a on the left is different that a on the right, your example, a on the right = 12.8 and a on the left is 10.9, illogical. Not to mention the value of b is 1 and 1.18 respectively.

    Applying elementary rules of algebra:

    a = a x 1 = a x (b / b) = a x [b x (1/b)] = a x [(1/b) x b] = [a x (1/b)] x b = (a/b) x b

    In my example 12.8 kg CO2 is a; 1.18 gallons is b and 10.9 kg CO2/gallon is (a/b).

    So of course 12.8 doesn’t equal 10.9; for the simple fact that 12.8 = a and 10.9 = (a/b).

    Since when is a = (a/b), if b is not equal to one (and for the sake of convenience one might also assume b is different from zero) ???
    **************************************************************
    You say a = a/b * a, which is absolutely true but doesn’t mean much.
    you say b = 1.18
    solve for a
    a = a / 1.18 * 1.18
    The only way you know a is 12.8 is because you declared it ahead of time.
    But I declare it to be pink elephants
    Pink elephants = pink elephants / 1.18 * 1.18
    Pe = Pe so I’m right too.

  423. Michael 2 @12:00 am:

    “It’s fun to pick it apart and contrary to your assertion, it is also on display at the world’s leading resource for casual information — Wikipedia!”

    It is not contrary to my assertion. I realize there are too many comments here for everyone to read everything, but I have stated several times already in this thread that this abominable “identity” shows up on Wikipedia as well. You are quite right on that front.

    The real point, however, is that *no-one* uses the identity. It cannot be used, by definition.

    Instead, what they do (after showing the silly identity in their papers — or on Wikipedia) is run a straight-forward, every-day, simple, multiplication calculation based on *per unit* numbers. Indeed, even the Wikipedia page shows the calculation taking place on a per unit basis, notwithstanding the large page-width graphic of the useless identity.

    So we have the ironic situation in which this identity shows up everywhere, but no-one actually uses it.

    It isn’t Willis’ fault that so many researchers keep writing the darn thing in their papers. His mistake was simply not reading the papers in more detail to realize that the researchers don’t actually end up using the cited “identity” in any way.

  424. rgbatduke says:
    July 14, 2014 at 4:53 am

    “What, exactly, is the advantage of adding the the GDP step in that? We learn a bit from GDP/population times energy/GDP that we didn’t already know from energy/population, but not much, and what we do learn isn’t likely to be universal or describable in functional form.”

    I’m not sure why you’re having a hard time seeing the value of including GDP – clearly, the level of economic growth is related to energy use (and, hence, CO2 emissions)- GDP measures (amongst other things) the stuff that gets made and moved in an economy. The simplest way to eliminate all carbon emissions would be to destroy all economies – reduce GDP to 0 and no CO2 emissions. Problem solved. No new technology needed or expensive and time consuming efforts to encourage conservation or whatever. The only problem is people like their economies and, generally, want them to be as big as possible.

    As a practical matter, it costs money (or GDP) to affect parts of the Kaya, so one can, in theory, evaluate the cost of various proposals. All other things being equal, dropping CO2 levels by 5% would cost a country 5% of its GDP unless it can find a way to make its energy generation less carbonized. If a CO2 reduction scheme will cost about 2% of GDP but will only reduce the C02/E by 0.5% most people would probably not be a good value. 80% of the CO2 benefit would come from the loss to the economy of (for instance) inflated costs on relevant items.

    Cheers, :)

  425. Will Nelson @9:09am:

    Quite right. The alleged “identity” cannot possibly be meaningful in any substantive sense. Anyone arguing that we somehow have “more information” because we have written self-cancelling variables on the same side of the equals sign doesn’t know what they are talking about.

    Again, it is surprising to see so many people trying to defend the identity as though it teaches us something, when the silly thing is never used in practice anyway.

    —–

    Well, I’ll check back in a time or two, but I think we’ve about exhausted this thread.

  426. Johan says:
    July 14, 2014 at 2:14 am
    […]
    Since when is a = (a/b), if b is not equal to one (and for the sake of convenience one might also assume b is different from zero) ???
    ******************************************
    You confused me. Is your rate 10.9 kg CO2 per (1) gallon OR 10.9 kg CO2 per 1.18 gallons? You might want to answer this one carefully.

  427. John West said:
    July 14, 2014 at 7:19 am

    “Current situation:
    Population = 100
    GDP = $1,000,000 (value of goods and services produced)
    GDP/Population = $10,000 per capita (standard of living)
    Energy/GDP = 0.1 kWh/$ (production efficiency)
    CO2↑/ Energy = 990 Tons / kWh (CO2↑ intensity of energy)

    CO2↑ = 100 people x ($10,000 per capita) x (0.1 kWh/$) x (990 Tons CO2↑/kWh)
    = 99,000,000 Tons CO2↑”

    I was really struggling to work out how to apply the Kaya practically, then I saw you using it with ease! I checked the above and it calculated for me! ;-)

    However, your next line had me stumped:

    “CO2↑ = 90 people x ($10,000 per capita) x (0.1kWh/$) x (990 Tons CO2↑/kWh)
    = 89,100,000 Tons CO2↑”

    How did you do this, I wondered. On careful examination I noticed that you changed
    population but (GDP/Population) had remained the same. This is fine but it means that GDP
    must be changed in the next ratio also (Energy/GDP):

    “CO2↑ = 90 people x ($10,000 per capita) x (0.111111111111111 kWh/$) x (990 Tons CO2↑/kWh)
    = 99,000,000 Tons CO2↑”

    I’d like to know how to use the Kaya Identity as constructed. Let me know what you think.

    It’s very late here, will look at this tomorrow, cheers.

  428. Wikipedia definition of “Flogging a Dead Horse” should include an External Link to this thread.

  429. I’m not sure why you’re having a hard time seeing the value of including GDP – clearly, the level of economic growth is related to energy use (and, hence, CO2 emissions)- GDP measures (amongst other things) the stuff that gets made and moved in an economy. The simplest way to eliminate all carbon emissions would be to destroy all economies – reduce GDP to 0 and no CO2 emissions. Problem solved. No new technology needed or expensive and time consuming efforts to encourage conservation or whatever. The only problem is people like their economies and, generally, want them to be as big as possible.

    Because comparing the GDP of Kuwait to the GDP of Vanuatu to the GDP of the Catholic Church to the GDP of the United States is not, actually a useful exercise. Kuwait makes and exports one thing — oil (plus, doubtless, a small trickle of other stuff). Vanuatu has a tiny handful of exports and has a correspondingly tiny GDP. The Catholic Church doesn’t make anything at all of concrete value, and yet is the 19th wealthiest “country” on Earth. The United States has an enormously complex economy. GDP is also not a measure of “growth” — it is an expression of the value of goods and services produced within an economy. But Vanuatu makes very different “stuff” than Kuwait or the US or world Catholicism, and has a very different standard of living in a very different climate where one has very different fundamental needs.

    Your inability to see this point may be reflected in your suggesting that the “simplest” way to eliminate all carbon emissions would be to reduce the GDP to 0. First of all, that wouldn’t do it because human contributions to global CO_2 levels are one small part of huge gain terms (balanced by huge loss terms) in e.g. the Bern formula. Natural emissions and absorptions would continue. It isn’t even clear that net gain would immediately trend to zero as the solution is non-Markovian with feedbacks, just as there is some reasonably serious argument over how accurately we know the natural vs anthropogenic decomposition in this equation (or, by extension, how much of the additional CO_2 is truly anthropogenic).

    Second, the only way to make a GDP go to zero is to make the population go to zero, because another term for a nation with zero GDP is “extinct”. Humans require food, water, sufficient shelter and other protections from the environment, and an opportunity to reproduce and care for offspring and even a barter economy or hunter-gatherer economy that meets those needs has a “GDP”, even if it isn’t based on a monetary currency. Humans by existing produce CO_2 with every breath, so only by them completely dying can the “carbon emissions” from anthropogenic sources go to zero. If they insist on doing things like cooking their food or living north of the tropics, they start up the CO_2 emissions tree long before there is any meaningful shift in GDP compared to their raw food eating tropical cousins who have yet to discover or “need” fire in order to survive.

    As you note, one can certainly reduce human carbon emissions by killing off populations. That is the most prominent feature of this “identity” — if one makes a small mountain of assumptions — most notably a homogeneity that is virtually nonexistent in the primary world economies — it is easy to reduce carbon consumption by killing people or sterilizing them.

    Of course this isn’t really true, as even in our economy, some people bike to work, live in small communities where one can bike or walk most places, are supplied by nuclear or hydroelectric power, and generally have a small “carbon footprint”. Other people — note that I’m reducing this to the level of individuals — fly all over the place in jets, logging as much as a million miles a year as they work, spending substantial time in cold or air conditioned climates where they burn carbon with the lights and AC and heater that is on all of the time. You could kill any number of the former to equal the “carbon impact” of a single one of the latter (and amusing, people who globe trot to sell the climate catastrophe are like as not in the latter category. Both of these individuals can easily be “American” — or “Indian” or Chinese” or “Kuwaiti” — and the GDP doesn’t really reflect their prevalence on average across multiple countries with very different economic schemes and distributed productivity.

    You’re reminding me of a line from “The Sheep Look Up”, a prophetic novel by Brunner — at the very end of the story a suitably programmed supercomputer spits out The Answer, the way humanity will save itself from extinction. What is it? Kill the 200 million wealthiest individuals on the planet.

    And this, of course, is the all-too-simple political subtext of this equation. According to the Bern formula, we will never be carbon neutral as long as we peskily insist on living. We could drop back to a 16th century economy and we would still increase atmospheric CO_2 at a steady (perhaps slower) rate. The only way to drop it to zero (with anything even vaguely plausible technology even in a pure science fiction novel) is to wipe out not 200 million, but 7 billion, humans, or else drop the standard of living to pre-Holocene levels and wait for nature to take its course.

    This is what the catastrophic climate change folks never seem to grasp. You aren’t balancing a possible future catastrophe against minor inconvenience now. You’re balancing an ongoing, real-time catastrophe that is happening right now because of the measures being taken to prevent it against the possibility of future catastrophe. You are performing the moral (literally) equivalent of sacrificing children to the gods by throwing them into the volcano to prevent it from erupting or ripping the still beating hearts out of captive slaves in order to ensure a good harvest next year. Maybe it works, maybe it doesn’t, but in the meantime its a job and keeps the population down and the wealth under the control of the wealthy and their obedient priesthood.

    rgb

  430. rgbatduke:

    re your post at July 14, 2014 at 11:03 am.

    Yes! Thankyou! Hear, hear!
    That one post collates everything I have been trying to say about this subject for days, and says all of it more clearly and more cogently than I have achieved.

    Hopefully everybody with an interest in the subject will read your excellent summary of the issues.

    Again, thankyou.

    Richard

  431. rgbatduke says:
    July 14, 2014 at 11:03 am
    “Because comparing the GDP of Kuwait to the GDP of Vanuatu to the GDP of the Catholic Church to the GDP of the United States is not, actually a useful exercise. Kuwait makes and exports one thing — oil (plus, doubtless, a small trickle of other stuff). Vanuatu has a tiny handful of exports and has a correspondingly tiny GDP. The Catholic Church doesn’t make anything at all of concrete value, and yet is the 19th wealthiest “country” on Earth. The United States has an enormously complex economy. GDP is also not a measure of “growth” — it is an expression of the value of goods and services produced within an economy. But Vanuatu makes very different “stuff” than Kuwait or the US or world Catholicism, and has a very different standard of living in a very different climate where one has very different fundamental needs.”

    I’m sorry but you are mistaken about this. Comparing GDP levels between countries doesn’t tell you much about the *specifics* of an economy, but does give a decent view of its general size and comparing changes in the growth of GDP between countries. There are many ways to make this point but perhaps the simplest is trade – countries with a lot of GDP can buy a lot of stuff from other countries and trade causes two countries to be more similar to one another. Vanuatu probably doesn’t build any of its own computers but there are probably lots of computers on Vanuatu. Vanuatu may have lots of differences with other countries but it has some similarities to other countries and those similarities are partially the result of the size of its economy.

    Most of the rest of your post seems to be based on the idea that I was actually advocating reducing the GNP to 0 – I was not – I was pointing out that by not paying attention to GNP you would end up choosing outcomes that are suboptimal.

    “And this, of course, is the all-too-simple political subtext of this equation. According to the Bern formula, we will never be carbon neutral as long as we peskily insist on living. We could drop back to a 16th century economy and we would still increase atmospheric CO_2 at a steady (perhaps slower) rate. The only way to drop it to zero (with anything even vaguely plausible technology even in a pure science fiction novel) is to wipe out not 200 million, but 7 billion, humans, or else drop the standard of living to pre-Holocene levels and wait for nature to take its course.”

    Take a look at the graphs posted here:

    http://mygardenpond.wordpress.com/2014/07/13/a-graphical-look-at-the-kaya-identity/

    You’ll see that GDP vs. CO2 shows a pretty direct linear correlation between the two – for a listing of many countries. Respectfully, I think you are paying way too much attention to what you see as the subtext and ignoring the practical reality that GDP and CO2 emissions are directly related to one another and are likely going to remain so for the foreseeable future. You do not have to be in favor of killing lots of people (which I am not) to recognize this. OTOH, recognizing that they are directly related to one another gives you some idea of the real costs associated with different options.

    Cheers, :)

  432. @ Scott Wilmot Bennett

    The Plan letters (A-E) correspond to the letters of the choices originally reported by the professor to the rest of the elders. I just varied the factors one at a time in order of appearance in the kaya identity and then an additional combo. Of course, you are correct it is nearly impossible to imagine varying any of the factors in the real world without changing the others as well and the identity doesn’t deal well with evaluating combinations of changes. That’s the problem with the kaya identity as I see it, no terms all factors, way too simple for evaluating real world scenarios.

  433. silly me – i thought the public argument was about the left side of the equation – shouldn’t that be CO2(man-made emissions)

  434. Samuel C Cogar says: July 14, 2014 at 5:36 am

    “Thus, his purchase of gasoline was “consumption spending” which added to the GDP ….. but he “burned” it without producing anything of value ….. thus NO increase in GDP.”

    Value is determined by what people are willing to pay. Willis paid for the gasoline (added GDP) so he could take a vacation that he though was at least as valuable as the money he paid, otherwise he would not have paid the money. Entertainment is a significant part of the average American’s consumption so it’s a significant part of GDP.

    A thing doesn’t have to have value to be counter as GDP. Consider for example the billions of dollars spent on climate research. I would argue a lot of that expenditure has a negative value because it’s used to justify harmful policies. Nevertheless, in the modern world there is a direct correlation between GDP and CO2 emissions.

    Wills was wrong to accuse the Kaya equation for being algebraically non-sensical and he was wrong when he said his driving trip produced CO2 without adding to GDP. He was also wrong too dismiss an argument based on the fact that someone said “other things being equal.” That’s a logical method to use when evaluating an equation that explains a process.

    Willis’ Beer Identity is funny and it’s actually workable because there is probably a strong correlation beer consumption and CO2 emissions. In fact it might be nearly as accurate as the correlation between population, GDP (prosperity) and CO2. As populations expand and get richer, the produce more CO2 and consume more beer.

    I agree that the Kaya equation is “silly.” It’s silly because it presumes to provide a method for calculating a factor (CO2 emissions) that we already track with a relatively high degree of accuracy. It’s silly to write a long equation with factors than only introduce uncertainty to calculate something that is accurately measured. If you want to know how much CO2 a particular country produces, look it up. The equation is also silly in that it includes population and GDP, as if anyone in their right mind would want to reduce population or prosperity just to control our output of plant food.

    I have a great respect for Wills. I even named an equation after him.

    The Eschenbach Identity: Human Prosperity Factor = CO2 emissions.

    (See my post of July 13, 2014 at 2:42 pm.)

  435. Some compare KI with conversions of seconds to minutes to hours. Well every second is the same. Every minute is the same. Every hour is the same. But KI? None of the terms in KI are standards. Not every person consumes the same products. Not every product took the same energy to produce, ship, store, etc. Not every energy producer emits the same percentage of CO2. And GDP ignores trade.

    Some say KI is useful for seeing what happens if you change one term and keep the others the same. Consider changing from coal to nuclear to reduce the last term. It’s not magic. You need people and machines and materials and a lot of energy and time to construct the new plant to replace the old, so to reduce the term I’ve increased emissions! Meanwhile the coefficients of KI are changing (population, consumer demand, efficiency of mechanization, and fuel costs increasing) so by the time I turn on the nuclear plant and shut down the coal one, I can’t just adjust one term of the KI I was using in the beginning. I would have to discover the new coefficients of each term during the grand opening.

    I don’t even see KI as a way to “tag” CO2 to people. It only looks at domestic products. Considering that the contents of a can of corn could vary from local to foreign from one day to the next depending on the season and commodity prices and more, I’d love to know how you calculate products per energy. People emit CO2 not just in producing products, but consuming them too. People also do stuff that removes CO2 out of the air.

    But are the uses suggested above all straw men? What am I missing?

  436. Willis Eschenbach says (July 13, 2014 at 12:57 am): “However, the GDP appears in both the numerator and the denominator, so the net result is unchanged. We’ve totally restructured the economy, we’ve converted huge amounts of energy from being “wasted” on holidays to actually producing something … and yet it makes no difference at all to the Kaya Identity. It looks just like when we started.”

    Touché!

  437. Tommy, GDP does not ignore trade. Look it up. The Kaya index only works for one snapshot of time and only for the aggregate GDP and population. Some consume more, some less, but there is an average consumption and an average of how much energy went into that consumption.

    Gary, vacations ARE “something of value.” For example, I’d rather have a vacation than another IPCC report.

  438. Mike M says:
    July 13, 2014 at 1:38 am

    You can take any linear formula and factor out whatever you wish when only the units are being presented.

    Mike, as I’ve said many times, there are no units presented in the Kaya Identity …

    w.

  439. Willis Eschenbach says (July 13, 2014 at 12:57 am): “However, the GDP appears in both the numerator and the denominator, so the net result is unchanged.

    Willis, all your posts prior to these two seem so well thought out, I can’t believe you’re making such a mess of this one.

    GDP (the economic output of e.g. a country) does not appear in the equation at all! But, there are two GDP-related quantities. The second term is GDP per capita, which is obviously a much smaller value than total GDP. The third term is energy per unit of GDP, or, in other words, energy per $1 of economic output. THE NUMERIC VALUE OF THE DENOMINATOR IN THE THIRD TERM IS 1.

    You can’t “cancel” the terms. “Cancel’” is not even an arithmetic operation. You can divide the value of the top term by the value of the bottom term, but the bottom term is 1, so the result is still the value of the top term.

    And even that is not the right way to think about it. You insist on performing dimensional analysis and mistaking it for algebraic reduction. KNOCK IT OFF!

    • bk51 says: ” THE NUMERIC VALUE OF THE DENOMINATOR IN THE THIRD TERM IS 1.”

      Well I see “GWP” (in the Wikipedia version of it)

      If you re-write the equation well then of course it comes out differently.

      Canceling terms is the common name for the operation. Nobody is making you cancel terms but I find it a very handy algebraic shortcut.

  440. Here is a video by Roger Pielke, Jr who has a handle on this:

    He actually uses Willis’ canceling operation to demonstrate the validity of the identity. It is a short but three-part speech.

  441. bk51 says:
    July 14, 2014 at 10:18 pm

    bk51,
    The point is, that simplifying this ‘expression’ will save you the time of putting numbers into it.
    It is not an equation and it is not a formula. It is an identity and that is all.
    If you do exactly as you have just said, you get the same result. Why? Because your new terms (“WITH DENOMINATOR 1″) are the reciprocals of one another.

    For example:

    CO2 Emissions = Population × (GDP/Population) × (Energy/GDP) × (CO2/Energy)

    CO2 Emissions = ?
    Population = p
    GDP = g
    Energy = e
    CO2 = c

    If
    c= 2, g=20, p=4, e=8.

    Then

    RHS = p x (g/p) x (e/g) x (c/e) = 4 x (20/4) x (8/20) x (2/8) = 4 x 5 x 0.4 x 0.25 = 2

    Therefore CO2 Emissions = 2 if c= 2, g=20, p=4, e=8.

    OR

    CO2 Emissions = 2 if c= 2, g=7, p=9, e=8.
    RHS = p x (g/p) x (e/g) x (c/e) = 9 x (7/9) x (8/7) x (2/8) = 9 x 0.777777777777778 x 1.142857142857143 x 0.25 = 2

    And etc, etc
    CO2 Emissions = 2 if c= 2, g=20, p=4, e=9.
    CO2 Emissions = 2 if c= 2, g=20, p=4, e=765.

  442. Some people seem to think that you can not transpose ‘identities’!

    Whyever not?

    They are a mathematical construct, produced by using normal ‘rules’ of maths.

    They can be transposed to make any unknown to be the subject (LHS).

    I think we should drop the name ‘identity’ from this discussion.

  443. Reposting this from the original thread, as it has become too long for my old iPad!

    I am in complete agreement with Richard Courtney.

    I am also on record, for pointing out the propaganda value of this silly e-quack-tion (Yes it is an Identity but that is all it is!). Ok, forget the identity, it is useless as a mathematical tool because it is not an equation or formula in any functional way!

    What is apparent, is that nobody who works with it, uses the Identity.
    What they do do, is apply it as a product of factors. Simply multiplying across the variables.

    Straight up, I find the idea of multiplying the factors, unjustifiable and meaningless; except as propaganda.

    Is it true that population and GDP are directly related, or proportional; a product?

    The very first three places in the world I looked at, not only challenge this assertion, they wipe the floor with the stupidity of it!

    Hong Kong has an inverse relationship of GDP to population, because its massive GDP dwarfs its population.

    GDP/ Population : 263.3 Billion / 7.2 million

    Singapore, according to current figures has an even greater inverse relationship of GDP to population, because it has a smaller population.

    GDP/ Population : 274.7 Billion / 5.3 million

    Both are massively inverse in there relationship of GDP to population and both are orders of magnitude above the next place I looked at; Bangladesh.

    Bangladesh has the exact opposite but still inverse relationship of GDP per capita, because of its huge population!!

    GDP/ Population : 115.6 Billion / 154.7 million

    CO2 emission are also in an inverse relationship to GDP for Hong Kong and Singapore and are also inversely proportional to population in Bangladesh.

    cheers,

    Scott

  444. John Whitman says:
    July 14, 2014 at 6:20 am

    Roger Pielke jr writes,

    “The Kaya Identity is the centerpiece of the analyses found in The Climate Fix and a lot of my work. It is a very powerful tool for understanding the challenge of emissions reductions. It holds that carbon dioxide emissions are influenced by four factors:
    population
    GDP per capita
    energy intensity of the economy
    carbon intensity of energy

    ———————-

    I’ll say it again, to wit:

    I compiled the following statistics via reliable sources, to wit:

    Increases in World Population & Atmospheric CO2 by Decade

    year — world popul. – % incr. — Dec CO2 ppm – % incr. — avg increase/year
    1940 – 2,300,000,000 est. ___ ____ 300 ppm
    1950 – 2,556,000,053 – 11.1% ____ 310 ppm – 3.1% —— 1.0 ppm/year
    1960 – 3,039,451,023 – 18.9% ____ 316 ppm – 3.2% —— 0.6 ppm/year
    1970 – 3,706,618,163 – 21.9% ____ 325 ppm – 2.7% —— 0.9 ppm/year
    1980 – 4,453,831,714 – 20.1% ____ 338 ppm – 3.8% —– 1.3 ppm/year
    1990 – 5,278,639,789 – 18.5% ____ 354 ppm – 4.5% —– 1.6 ppm/year
    2000 – 6,082,966,429 – 15.2% ____ 369 ppm – 4.3% —– 1.5 ppm/year
    2010 – 6,809,972,000 – 11.9% ____ 389 ppm – 5.1% —– 2.0 ppm/year
    2012 – 7,057,075,000 – 3.62% ____ 394 ppm – 1.3% —– 2.5 ppm/year

    Source CO2 ppm: ftp://aftp.cmdl.noaa.gov/products/trends/co2/co2_mm_mlo.txt

    Based on the above statistics, to wit:

    Fact #1 – In 70 years – population increased 198% – CO2 increased 29% – Heat Islands increased est. 300/400+%

    Fact #2 – Atmospheric CO2 has been steadily and consistently increasing at a rate of 1 to 2 ppm per year for the past 70 years, …… whereas human generated CO2 releases have been increasing exponentially every year for the past 70 years.

    Fact #3 – Global Temperatures have been steadily and consistently increasing a few hundredths or tenths of a degree for the past 70 years, ……. whereas human created infrastructure, housing, vehicles, etc. (Heat Islands) have been increasing exponentially every year for the past 70 years.

    Conclusions:

    Given the above statistics, it appears to me to be quite obvious that for the past 70 years there is absolutely no direct association or correlation between:

    • Increases in atmospheric CO2 ppm and world population increases.
    • Increases in Average Global Temperature and world population increases.
    • Increases in Average Global Temperature and Heat Islands construction increases.
    • Increases in Average Global Temperature and atmospheric CO2 ppm increases.

    But then of course, …… I am not looking through Rose Colored Glasses.

  445. A slight improvement on the Kaya Identity might be to replace GDP in the GDP/Energy factor with GAP (Gross Activity Product) which I’d define as the same as GDP except adding imports and exports instead of subtracting them.

    GDP = private consumption + gross private investment + government spending + (exports – imports)

    Since exporting and importing requires energy for the purposes of CO2 emissions these should be added instead of subtracted. If a country exports exactly the same value of goods as it imports this term would be 0, yet energy would still be being consumed but not captured in the GDP.

    So, Kaya’ Identity would be:

    CO2↑ = Population x (GDP/Population) x (Energy/GAP) x (CO2↑/Energy)
    Or
    CO2↑ = Population x standard of living x Energy per Economic Activity x CO2↑ intensity of Energy production

    Since GDP and GAP have the same units ($), they still cross out.

    Perhaps a small improvement but I’m still not happy with it. I’m putting way more thought into this than I should. Thanks Willis.

  446. Thomas says:
    July 14, 2014 at 12:36 pm

    Value is determined by what people are willing to pay. ………….. Entertainment is a significant part of the average American’s consumption …………… so it’s a significant part of GDP.
    ——————-

    YES, ….. and YES, ….. and absolutely NO.

    Purchasing the entertainment services provided by prostitutes, ….. purchasing the entertainment products provided by drug dealers, …… purchasing entertainment via donations and contributions to churches, charities, benevolent organizations, …… purchasing political favors provided by politicians, ……… purchasing your entertainment via bets and wagers, …. etc., etc. …. are all, … inclusive of, ….. the average American’s YEARLY “entertainment” consumption spending of hundreds of billions of dollars ….. yet not a penny of said consumption spending is included in the GDP.
    ==============

    A thing doesn’t have to have value to be counted as GDP. Consider for example the billions of dollars spent on climate research.
    ————-

    Don’t be silly, if an entity has no value ….. then there is no way to count it as part of the GDP. And the billions expended by government on climate research is not counted in the GDP, ….. but the expenditures of the recipients of said billions is counted in the GDP, …… that is, minus the afore mentioned entertainment expenditures.

    The GDP is a “fuzzy math” figure that is no more accurate than the “unemployment #” or the number of illegal immigrants residing in the US.

  447. A few brief notes for now:

    Scott Wilmot Bennett says:
    July 15, 2014 at 4:08 am
    “CO2 emission are also in an inverse relationship to GDP for Hong Kong and Singapore and are also inversely proportional to population in Bangladesh.”

    I’m not sure how you come to this conclusion but you are mistaken: all three will show a direct relationship for CO2 to GDP. (You can’t simply look at one pair of data points and claim to have found an inverse relationship).

    Samuel C Cogar says:
    July 15, 2014 at 5:26 am
    “Fact #2 – Atmospheric CO2 has been steadily and consistently increasing at a rate of 1 to 2 ppm per year for the past 70 years”

    This is a bit misleading. Clearly the rate of atmospheric increase has gone up over time.

    Samuel C Cogar says:
    July 15, 2014 at 7:24 am
    “….. yet not a penny of said consumption spending is included in the GDP.”

    Just because not all of the spending on entertainment does not make it into the GDP numbers doesn’t mean that entertainment is not a significant part of American GDP.

    Cheers, :)

  448. I realize I’m a bit late to the party on this post, but there are a couple of points that need to be made;

    1) Any equation that has the variable to be solved for as a numerator on both sides, and where literally all of the other factors cancel out is just mathematical masturbation. I too performed the cancellations in my head immediately upon seeing it, and began to laugh. CO2 emissions = CO2 emissions.

    2) The equation is meaningless, but not for the GDP problem you cite; indeed, your consumption of food and fuel is counted in the GDP. There is no requisite that your consumption of fuel produce something of value. You consumed it and it is assumed that you got value for that, whether it be from driving to work or some non-intrinsic value such as driving through the desert. Indeed, our method of measuring GDP has no way to differentiate such things.

    3) Although the math is entirely different, in looking at the Kaya ID, I get the same feeling I get when I look at the Drake equation. Neither of these is of any value to science.

  449. Shawnhet

    Singapore’s GDP per capita, is 8.5 times that of China, despite having a population (Of 5.3 million.) which is 255 times smaller than China’s 1351 million. And Singapore’s CO2 emissions (Of 13520 kt) are 400 times smaller than China’s (5433057 kt).

    Bangladesh has a GDP per capita 70 times smaller than Singapore, despite having, a population 30 times larger. It also has the tiny CO2 emissions per capita of 0.000227.

    Bangladesh’s CO2 emissions are 4 times larger than Singapore’s despite having a population 30 times larger.

    The alarmist assertion that GDP is proportional to population and CO2 emissions, has no substance in the real world, except perhaps, inversely!

  450. The Kaya is not intended to “calculate” CO2, or any other value at all. All the “factors”, CO2, P, GDP, and E are known ahead of time for input (see Pielke, Jr). Kaya just sets up indexes of ratios between these factors. This is purely arithmetic and has nothing to do with algebra. Kaya is amenable to any arrangement of terms and you CAN cancel terms OR NOT as desired.

    CO2/P = GDP/P * E/GDP * CO2/E
    CO2/GDP = E/GDP * CO2/E (Pielke, Jr.)

    Maybe this is the ultimate arrangement:
    GDP/P = CO2/P * GDP/CO2

    richardscourtney and rgbatduke are right to ignore the math and argue directly to the philosophy.

    I can sleep safer now knowing the “Policy Makers” have it all under control.

  451. Couple more points.

    1. Dr. Kaya’s identity as he wrote it is applied to global data, not regional.
    2. It is an identity, not a working formula.

    Use it to find global CO2 emissions as a function of each contributor, solved independently. Use it to calculate what must be changed in each parameter (independently) to reduce the current emissions to 10%, globally, in 30 years. Or just visit the U of Chicago’s calculator and use that. The link can be found in this thread. That calculator uses simple tabled data for the known era, and your inputs to plot future values INDEPENDENTLY because it is a what-if tool!

  452. Mike M says: July 13, 2014 at 1:38 am ” You can take any linear formula and factor out whatever you wish when only the units are being presented.”

    Willis Eschenbach says: July 14, 2014 at 9:51 pm ” Mike, as I’ve said many times, there are no units presented in the Kaya Identity …”

    I’m using the term “units” loosely, (and I think it’s rather petty telling me “energy” is not a “unit” when everyone knows energy is measured by some form of unit), but if you wish to push this nonsense further let’s convert all the items to your hard units and see what happens going back to my OP…

    “The only ‘problem’ I see with the Kaya formula is that it has no names for the values GDP/population, Energy/GDP or CO2/energy and simply uses the unit ratios instead. ”

    GDP/population “L” – dollars/person
    Energy/GDP “H” – joules/dollar
    CO2/energy “Q” – kg/joule

    The formula becomes kg = persons * (dollars/person) * (joules/dollar) * (kg/joule)

    You can factor any which way to get any nonsensical “result” you want, kg=kg or persons = persons or 1=1.

    Again I challenge you by pointing out other formulas like miles= hours * (miles/hour), in which I’ve intentionally satisfied your “hard units” meme and it’s blatantly clear we can do the same thing to that formula that you did to the Kaya formula also reducing it to 1=1.

    I will point out again, when you factor things OUT of any formula is no longer the same formula. Factoring out units of a formula is only a test that the the formula is dimensionally congruent – nothing else.

  453. Scott Wilmot Bennett says:
    July 15, 2014 at 9:39 am
    “Singapore’s GDP per capita, is 8.5 times that of China, despite having a population (Of 5.3 million.) which is 255 times smaller than China’s 1351 million. And Singapore’s CO2 emissions (Of 13520 kt) are 400 times smaller than China’s (5433057 kt).”

    Your comparing apples to televisions here. Singapore’s per *capita GDP* is higher than China’s and China’s *total* population and *total* CO2 is higher than Singapore but this does not mean CO2 is inversely related to GDP. If you use per capita numbers for both GDP and CO2 you can see this easily – take a look at the fourth graph here:

    http://mygardenpond.wordpress.com/2014/07/13/a-graphical-look-at-the-kaya-identity/

    As you can see, it is pretty much a textbook example of a direct relationship and definitely not an inverse one as you suggest.

    Cheers, :)

  454. Hey Thomas, I agree with your objection to my statement “GDP ignores trade”. Of course, the market price of domestic products is determined during trade, so my statement was flat out wrong.

    What I meant to say was that GDP doesn’t show the effect on value by methods of trade. Examples: Speculation causes value swings completely unrelated to energy. Same product traded in larger units gets an economy-of-scale savings in energy for shipping. Trade with subsidized producers divorces value from energy costs. KI is attempting to relate GDP and CO2, but I wonder if the energy signal in GDP is lost in the noise of non-energy aspects.

  455. Will Nelson says:
    July 15, 2014 at 10:27 am

    “I can sleep safer now knowing the “Policy Makers” have it all under control.”

    I don’t think it is possible to be more Orwellian or proletarian! ;-{

  456. Scott Wilmot Bennett says:
    July 15, 2014 at 10:53 am

    Will Nelson says:
    July 15, 2014 at 10:27 am

    “I can sleep safer now knowing the “Policy Makers” have it all under control.”

    I don’t think it is possible to be more Orwellian or proletarian! ;-{
    ***************************************
    It is nice to end with a hearty laugh. Thanks.

  457. The real intent behind the “Kaya Identity”:

    V CO2 = W Population × X (GDP/Population) × Y(Energy/GDP) × Z(CO2/Energy)

    Note the units properly cancel, so that the result on the RHS is the same units as the LHS.

    Note that there is nothing about this that is an identity – without units, it looks like:

    V = W * X * Y * Z

    V varies for any change in W, X, Y or Z.

    You cannot construct this “identity” algebraically:

    V = V

    V = W * X * Y * Z ???

  458. Well Chasmod, I don’t like arbitrary exclusions.

    I prefer that “Primes have no factors other than one (1) and themselves.” That pretty much limits it to TWO factors only.

    And 1 has only 1 and itself (1) as its two factors.

    So in my book, one (1) IS a prime number, and if I wrote a math book, it would say that.

    Well my original number theory math book, which I did not write, said precisely that.

    The arbitrary exclusion, is juvenile in the extreme.

    g

  459. Some real world examples expressed again, in GDP per capita:

    Singapore’s GDP per capita is 1.5 times that of Hong Kong’s but it produces half the CO2 emissions per capita of Hong Kong!

    Hong Kong’s GDP per capita is 48 times that of Bangladesh but Hong Kong’s CO2 emissions per capita are only 13.5 times larger!

    Singapore’s GDP per capita is 70 times that of Bangladesh but Singapore’s CO2 emissions per capita are just 7 times larger!

    None of these relationships are directly proportional. They demonstrate either inverse or fractional rates of proportion.

    The only way to resolve the impasse is to imagine incredible efficiencies for energy production in the cases that don’t follow the ‘model’.

    This of course, would be absurd but in this post-normal world, who knows, anything is possible!

    It is clear to me, when looking at real examples, that the directly proportional relationships of the “Kaya” are erroneous.

    The the real world is not represented by the model.

  460. krischel says:
    July 15, 2014 at 3:28 pm

    The point krischel, is that an Identity (A mathematical term.) is tested by replacing its variables with values. An Identity is true for all possible values of its variables such that the RHS equals the LHS.

    What you have written (below) is a formula and it is an arbitrary one:

    V = W * X * Y * Z

    As an identity:
    v ≡ w*x*y*z
    v=3, w=4, x=5, y=6, z=7
    3 ≡ 4x5x6x7
    3 ≡ 840
    RHS is not equivalent to LHS

    As an equation:
    v=3, w=4, y=6, z=7
    3 = 4xxx6x7
    3 ÷ 4x6x7 = x
    3 ÷ 168 = x
    x = 0.017857142857143

    As a formula:
    v = w*x*y*z
    w=4, x=5, y=6, z=7
    v = 4x5x6x7
    v = 168

    The propaganda value of the Kaya is in its claim to scientific rigour. However, it is meaningless as a formula or equation and is of dubious value as an Identity.

  461. krischel says: July 15, 2014 at 3:28 pm

    Exactly; better stated than I. If you then include the units they are supposed factor down so that the units remaining on the right are the same as those on the left – as a check. If they do not then the formula would be invalid.

  462. i’ve been mediating on the “identity” for some time now – and i am no longer terrified of it – and only slightly bewildered

    it remains for me a secondary issue – i would rather focus on the degree of threat in increasing co2 – and its corollary – the necessity of reducing man-made co2 emissions – if i’m defeated on that issue – then the implications of the kaya equation could take center stage

    i would first insist on knowing the cost as well as the man-made co2 emissions – it looks like kaya would give a correct picture of the co2 output of an economy based entirely on nuclear energy – as well a entirely on wind turbines – but does it tell me the cost of each – or rather – the efficiency of each – i’m not sure – if so – kudos for kaya yoichi

    in a way – these threads on kaya identity are an example of how the alarmists can control the debate – by drawing attention away from the real issue – into a topic where their assumptions are taken for granted

    that’s not a criticism of these threads – i see that kaya will need to be confronted from time to time – and its best to be prepared – once again – thank you Willis

    –john eyon

  463. Willis,
    Like you I’ve been busy traveling.

    On July 13, 2014 (12:57 am AND 1:08 am) you quoted me as follows:

    … a mathematical identity can be useful if it serves to account for real-world causal relationships that affect the magnitude we’re interested in — in this case, CO2 emissions. …
    The Kaya Identity incorporates multiple hypotheses: that greater population leads to greater GDP (other things equal), that greater GDP leads to more energy use, that more energy use leads to more CO2 emissions, and that each of these causal linkages can be roughly quantified.

    Your responses:

    Thanks, Doc. You claim it “can be useful”. Perhaps you could give a real world example of using it, and exactly what the use of it might be.

    Well, Pielke Jr. is an expert on this, and I’m not, so see his work for stronger examples. For myself, I find the identity useful for thinking about recent rises and declines in U.S. CO2 emissions. When the recession hit in 2008, GDP/pop declined, leading to a decline in energy use and thus emissions as well. And as electricity generation has shifted from coal to natural gas fuel, the value of the energy-CO2 linkage declined, leading to a decline in emissions. In both cases, the identity serves a useful accounting role for understanding the effects of structural shifts.

    Suppose for a moment that the US government decreed that all fuel burned on wasteful holidays such as I’m taking must go into actual production. What would be the result?

    (You go on to say that GDP would increase but other things, notably energy use, would not.)

    The point of your scenario, as you note, is that economic structure affects the value of the linkage between GDP and energy use. (You’ll grant, I presume, that your specific scenario is hopelessly unrealistic. Such a government decree would have numerous unintended consequences; it could never simply achieve its intended objective.)

    I quite agree with your basic point here. (Similar points have been made by rgbatduke and others.) But that does not negate the usefulness of the Kaya identity. As I note above, the identity is frequently useful precisely for the purpose of accounting for the effects of structural changes within one economy — or for that matter, accounting for the effects of structural differences between one economy and another (rgbatduke’s concern).

    I presume that those who use the Kaya identity do so competently — not claiming that the same parameter values apply to all times and places. I’m sure, of course, that the identity can be abused.

    other things are never equal …

    Indeed, they’re often not, which is precisely why I specified ‘other things equal’. Nonetheless, there are regularities that we can count on.

    although the population of the US has grown steadily, at times the GDP has dropped. So obviously, greater population does NOT always lead to greater GDP.

    Quite right. GDP/pop may shift (“exogenously”, as economists say). The rest of the Kaya Identity then suggests how this affects CO2 emissions.

    Nor do I agree that more energy use leads to more CO2 emissions. Energy use in the US is shifting from coal to natural gas … which gives us more energy use with LESS emissions.

    Again, quite right. Here there’s an exogenous shift in energy/GDP. Again, the Kaya Identity accounts for the effects of this, holding other things equal. Note that, both before and after the shift in the value of energy/GDP, it remains the case that more GDP means more energy use. The issue is simply that the parameter value has shifted.

    Best regards, and thanks for your interesting points.

    Likewise!
    d.

  464. Scott Wilmot Bennett says:
    July 16, 2014 at 3:39 am
    The the real world is not represented by the model.

    According to Dr. Kaya the Kaya Identity was conceived as applying to global parameters, not regional, so your example of Hong Kong is not a valid usage.

  465. Scott Wilmot Bennett says:
    July 16, 2014 at 3:39 am
    “Singapore’s GDP per capita is 70 times that of Bangladesh but Singapore’s CO2 emissions per capita are just 7 times larger!”

    I think you have got the total/per capita thing mixed up again – the following page claims that Singapore’s CO2 emissions are ~150 times larger than Bangladesh’s *per capita*.

    http://en.wikipedia.org/wiki/List_of_countries_by_carbon_dioxide_emissions_per_capita

    “None of these relationships are directly proportional. They demonstrate either inverse or fractional rates of proportion.”

    When you use the correct numbers, the relationship is more or less direct.

    “The only way to resolve the impasse is to imagine incredible efficiencies for energy production in the cases that don’t follow the ‘model’.”

    You’ve heard of nuclear power, right?

    Cheers, :)

  466. @Scott Wilmot Bennett: I think you restated my point – I put “Kaya Identity” in scare quotes precisely because I don’t believe it is actually an identity :)

  467. dp says:
    July 16, 2014 at 10:53 am

    Scott Wilmot Bennett says:
    July 16, 2014 at 3:39 am

    The the real world is not represented by the model.

    According to Dr. Kaya the Kaya Identity was conceived as applying to global parameters, not regional, so your example of Hong Kong is not a valid usage.

    Thanks, dp … cite?

    And … why would it be valid for the planet but not for a portion of the planet? The planet both receives and exports energy just like countries do …

    w.

  468. This is a cross post from old thread:

    The problem with the Kaya is that it isn’t an equation or a formula and therefore has no claim to that kind of veracity. Governments might start culling population or attempt to reduce GDP rather than looking at the root cause of inefficient energy production.

    Australia is an odd case, in this context, being resources rich, it is also the worlds biggest supplier of fossil fuels. Australia’s resources stoke the fires of the worlds energy production. So much so, that It has now become more profitable (Or two expensive) for Australia to use its natural gas for power generation.

    I would argue that there needs to be a couple of more terms in that “equation”. The first one, is in my opinion the most import of all. For the wizards of the black art of economics, it is the equivalent of “he who can’t be named”; the Money Supply!

    Is it debt based or credit based? The real reason for growth economies and built in obsolescence, is that money is always chasing money. And I don’t mean simple profit. I mean that the Supply itself, comes into existence, mostly as debt. Thus, the world is chasing the virtual not the actual economy!!

    The other term that I think might be very important to include, is physical extent, the geographic size of a Nation compared with its GDP. Two of the examples I chose are extreme because of the tiny space they take up on the globe. Australia is massive by any standard, so is it even rational to compare its GDP with that of Singapore? And if we did, are we really being aware of just how abstract the idea is!!

  469. Scott Wilmot Bennett says: July 17, 2014 at 2:31 am And I don’t mean simple profit. I mean that the Supply itself, comes into existence, mostly as debt. Thus, the world is chasing the virtual not the actual economy!!

    Not true for what actually counts – tangible goods. Profit creates a surplus, surplus controls the price. No profit= no surplus= scarcity & extremely high prices (=USSR)

    There are plenty of cars unsold, lots of food left uneaten, shelves packed with every imaginable gizmo just sitting there becoming obsolete, etc. That surplus is real not “virtual” and it was created by capitalism in the pursuit of profit within a competitive free market where every producer is locked-in to over-produce in the hope that they will sell more than their competition.

    That is the real US economy, a land of plenty created by Lady Liberty.

    • “That surplus is real … it was created by capitalism in the pursuit of profit within a competitive free market where every producer is locked-in to over-produce in the hope that they will sell more than their competition.”

      Incorrect on all parameters. Profit is maximized when you sell exactly what you make, no more, no less. Making too few is much better than making too much. If you make too few your “capital” is not sitting idle in a warehouse, you simply will not have made as much profit as you could have.

      Your description is of Soviet style central management that decrees how many of a thing is to be made regardless of demand.

      Long term profit does not exist in a free market. It cannot exist. If your company is profitable, making Frisbees for instance, other companies will start making Frisbees. The volume of Frisbees is such that your own factory will reduce its prices so as to AVOID that “surplus” of which you speak. All other factories will do likewise.

      The least efficient factories will close or make something else. Pretty soon the production of Frisbees and the price of Frisbees and the demand for Frisbees will “meet” at some magical price/quantity.

      Because of the existence of patents, the “free market” has never existed in the United States, but it is a bit more free than many European nations, and considerably more free than centrally managed economies.

  470. Mike M says:
    July 17, 2014 at 8:11 am

    “Supply” as in Money Supply! Have a close look at this, you will find that true “Capitalism” and real free markets, have never actually happened. What you will find is the dirty art of central banking with economics as its propaganda wing. A “discipline” that spares no expense, to make sure that it doesn’t have a working theory of Banking or Money-Supply and their role in market creation and destruction.

    I’m not left or right, both are wings of the same bird. I’m a pragmatist. If you genuinely want to understand the problem beyond the cliches, you have to ask why do economies always have to grow, why does you “gizmo” have a limited life span (Planned obsolescence). Yes, how is wasted surplus even possible in a free market, where real demand drives real supply? Yes it is a competitive market but what is it ultimately competing against?

    Ultimately, profit must overcome the cost of Money (The loan you got to buy the resources for your steelworks, the products of which you sell to manufacturers who loaned money to pay you until they can sell their products to the consumers who loaned money to buy the goods; on credit.

    The point is, that the Money Supply today, far exceeds the world’s entire GDP. Making all ‘economic’ activity virtual by comparison. And all this money comes into existence as debt. Because this ‘Supply’ is created out of thin air (No real reserve.) it is decoupled from reality.

    The result of this system is that wealth is concentrated into narrower and narrower elites. Currently 90% of the worlds entire population own less than 15% of its wealth. A tiny 10% of the global population own 85%.

  471. Just to get both feet on the ground : go and try to put the “identity” into Excel. Put in values for each: pop(heads), GDP($),Energy(Watt), and… well not CO2 because that is what you want to solve for. Thats where it breaks down….. But lets continue to excel: Leave it as the C02/Watt Ratio without computing this from inputs. Then you can solve the equation for C02. Only when you change the fixed ratio will the C02 change. so in this case you can only change the C02/Enery ratio. So your energy/GDP and C02/Energy are not linked any more.
    I have no idea how the climate procrastinator works: forecast.uchicago.edu/kaya.html buti assume it just greps output from a “Model”. FAIL.

  472. “Daniel G. says:
    July 13, 2014 at 7:36 am
    […]
    If you increase pop, gdp/pop doesn’t decrease proportionally, because there will be an increase of gdp. Result: co2 doesn’t remain the same.”

    Regrettably, the Kaya thing does not include that gdp-pop tkat makes gdp grow relationship. So, if what you say is true, it is incomplete.

    But it does include GDP both in the numerator and the denominator, cancelling it out (and also population and energy). Unless GDP “above the line” is different from GDP “below the line”. I wonder what sort of game this is, but it is not algebra.

  473. Just to bring forward some discussion from the older thread. Scott W Bennett’s points about Bangladesh, HK and Singapore indicating a negative relationship between CO2 emissions and GDP are misleading – because he had only taken three examples.

    If one plots the data for all the countries in the world – as I have done – see links. The positive linear relationship works ‘just fine’. I have shown Bangladesh, HK and Singapore in pink dots.

    CO2 Emissions vs GDP

    https://www.flickr.com/photos/126112946@N07/14486064739/

    log(CO2 Emissions) vs log(GDP)

    https://www.flickr.com/photos/126112946@N07/14673065305/

    Bangladesh lies far above the trend line – a reflection of its low-tech economy. HK sits pretty-much right on the trend line. Singapore lies a bit below the trend line – and lies might be the best word as their last set of CO2 emissions sound too good to be true.

  474. Sorry – error! The pink spots on my previous graphs contained errors. Revised links below. Now it’s Bangladesh which sits pretty-much on the trend line. HK is slightly below it (possibly due to the Daya Bay Nuclear Power Station). Singapore is well below it (possibly due to a palm-oil* burning power station and some creative accounting).
    * How very green!

    CO2 Emissions vs GDP

    CO2 vs GDP

    log(CO2 Emissions) vs log(GDP)

    logCO2 vs log GDP

    Still, in spite of the earlier mistakes, the graphs show a good positive linear correlation between CO2 emissions and GDP.

    I will also do some graphs of CO2 emissions vs Population.

  475. Willis Eschenbach says:
    July 16, 2014 at 7:08 pm

    dp says:
    July 16, 2014 at 10:53 am

    Scott Wilmot Bennett says:
    July 16, 2014 at 3:39 am

    The the real world is not represented by the model.

    According to Dr. Kaya the Kaya Identity was conceived as applying to global parameters, not regional, so your example of Hong Kong is not a valid usage.

    Thanks, dp … cite?

    And … why would it be valid for the planet but not for a portion of the planet? The planet both receives and exports energy just like countries do …

    w.

    I have to withdraw the statement based on a re-reading of my original source:

    Raupach, M.R.; et al. (May 22, 2007), Global and regional drivers of accelerating CO2 emissions

    In the paper they provide a definition of the Kaya Identity but on re-reading it, they've defined a particular application of the identity, that being, global F. The willipedia compounds this by repeating the definition as specifically applying to global parameters. I've found no solid reference from Kaya himself that requires this limitation.

    Second point – Kaya himself is a pragmatist, investing his interest in global problems. It is, for that purpose, probably not helpful to use his identity to do a full analysis of Tuvalu, Ghana, and Tristan da Cunha in seeking global solutions to decarbonization, but yes, it can be done. It may even solve regional problems of resistance to micromanaging people if the royal family of the Kingdom of Tonga can leverage such analysis for their purposes while ignoring KOT's nearly invisible global footprint. Crazier ideals have been floated. As a tool of skepticism the KI can be used to show how futile it is for Oz to flog their economy with a carbon tax while China and India backfill what ever miserable small hole in the CO2 budget Oz may make. So yes, I concede that point, too. I was not thinking clearly as a climate warrior in the blood sport of climate science.

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