**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:

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:

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

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.

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.

The Kaya identity is even more useless than the Drake equation. With the Kaya identity,

anythingcan 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 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?

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

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. 😎

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.

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

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.

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

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.

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.

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.

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.

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.

So, I see you’ve quietly backed away from your original mathematical objections and resorted to even more specious objections.. Could you please comment on Pielke’s usage of the Kaya equation, and his findings that it matches real world numbers well? http://rogerpielkejr.blogspot.com/2014/06/clueless-krugman.html

Perhaps Anthony could give equal time to Pielke in defense of the Kaya identity?

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.

Doesn’t the gas you put in your car contribute to GDP?

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.

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

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!”

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.

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.

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.

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.

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.

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

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.

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.

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

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.

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”.)

When in a hole, stop digging.

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.

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. (:

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.

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?

I agree with Arthur it is a meaningless formula as it is a beancounters approach to complex issues.

Perhaps Obama should make “Beano” mandatory?

(OOPS! Wrong emission. Sorry. Carry on.)

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.

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.

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%.

“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.

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.

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.

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.

Hopeless (inutil) thread.

http://wattsupwiththat.com/2014/07/12/the-beer-identity/#comment-1684364

How about auto insurance, motor vehicle fees and property taxes? How do they count towards Kaya

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.

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.

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

UnfrozenCavemanMD says:

July 12, 2014 at 9:09 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.

w.

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.

What happens if we divide both sides with CO2?

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).

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.

I think the Kaya Identity is meaningful.

It’s the recipe for Soylent Green.

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

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.

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…

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.

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.

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.

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.

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.

What about the methane from drinking beer and sending the used grains to the feedlots?

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?

Willis,

Thankfully, you have dropped the mathematically ignorant

look ma, everything cancels so it must be wrong and I must laughassertions. 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:

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 G

BP 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:

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

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.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’).

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.

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.

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.

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.

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.

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.

kabend says:

July 12, 2014 at 10:53 am

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

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?

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.

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

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.

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.

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).

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.

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.

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

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?

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.

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.

Damn typo:

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.

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’.

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.

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.

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?)

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?

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.

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.

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

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.

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

Willis Eschenbach wrote:

Fuel is included in the gdp, duh.

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.

“””””……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.

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.

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.

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.

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

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

You do not have to measure that.

climatereflections says:

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

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

nottotal 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.

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.

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

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?

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!)

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

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.

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 laughassertions. 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:

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 G

BP 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:

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 accuratesub heading:“Willis Eschenbach’s “Beer Identity” carbon equation and criticism of the “Kaya Identity” has been falsified – due to a stupid maths error“.That is not in discussion, read the UN’s paper.

co2 emissions accounting is more complicated, but that has nothing to with Kaya identity.

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

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?

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

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.

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).

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

Read the UN’s paper again:

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.

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.

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.

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.

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

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.

Reply to JJ ==> Exactly so, sir.

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..

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.

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

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.

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.

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.

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.

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!

Scott Scarborough says:

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.

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

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

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

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.

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.

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

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

mathisalwaysto multiply the factors.climatereflections says:

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.

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.

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.

@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.

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?

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

catastrophicwarming 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/

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.

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.

Dr. Doug gets it.

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.

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

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.”

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.

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.

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

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]

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]

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. .

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.

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.

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/

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

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.

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.

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?

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.

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?

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.

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.

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.

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.

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

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

@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.

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.

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.

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.

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.

Willis, have you looked at the talk tab on the Kaya Identity page?

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

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.

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! 😉

I’ve been wondering. What does all this have to do with the price of tea in China?

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!

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.

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.)

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.

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 productionin 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 constantsare mixed up but there is some sense in it, and that is why you are getting all these comments.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.

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.

Dave38:

Sorry to disagree with you but “grue ” is a valid english word oldThanks 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.

pwl – will these help?

http://therefusers.com/refusers-newsroom/90-of-peer-reviewed-clinical-research-is-completely-false-greenmedinfo/#.U8IG27FCx8E

http://www.plosmedicine.org/article/info%3Adoi%2F10.1371%2Fjournal.pmed.0020124

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.

Those are excellent Robert in Calgary. Any for climate science?

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.

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.

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.

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.

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.

pwl @8:43pm:

Yes, I do recall seeing several of those kinds of studies a few years ago. Unfortunately, they have now been falsified. 🙂

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.

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

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.

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.. 😉

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, 🙂

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.

Roger Pielke Jr. has weighed in. He’s one of those scientists who has actually used the Kaya identity correctly. Those who don’t get it are encouraged to read more.

http://rogerpielkejr.blogspot.com/2014/07/common-ground-on-climate.html#comment-form

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).

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.

” 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.

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.

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.

Robert Boyd says:

You don’t get it. An identity is not what you think and does not work the way you think. Read what Plain Bill wrote at http://wattsupwiththat.com/2014/07/12/the-beer-identity/#comment-1684795 because he gets it. Then tell others. If everyone helps just two people per day understand identities and how they work the entire world will get it by the end of next week.

JJ says:

July 12, 2014 at 11:33 am

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.

Falsify This:

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

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

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.

William C. Rostron says:

July 12, 2014 at 9:16 am

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.

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 $).

joshv says:

July 12, 2014 at 9:39 am

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

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.

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.

Al Gore = Couldn’t hack it as an Economist.

Richard:

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

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 explainedwhat they mean by “meaningful”.They have

not explainedhow and why any of the the ratios in the Kaya identity is “meaningful”,and they have

not explainedwhy 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

Hans Erren says:

July 12, 2014 at 9:39 am

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.

I prefer the Climate Science / $ = Bullshit Produced Identity.

Matthew R Marler says:

July 12, 2014 at 10:02 am

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

variables.w.

DH says:

July 12, 2014 at 10:04 am

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?

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.

Don’t let go Willis, Brainwashing is a formidable Foe.

Steven Mosher says:

July 12, 2014 at 10:05 am

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.

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.

Steven, you miss the point entirely. The contribution of energy to GDP is not when you

buythe energy. It is when youburn 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.

Matthew R Marler says:

July 12, 2014 at 10:16 am

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.

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.

Kip Hansen says:

July 12, 2014 at 10:46 am

True. Any mistakes are my own.

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.

JK says:

July 12, 2014 at 11:38 am

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=MC

^{2}. But of course, it’s not. You can put any variables into it you’d like.So while E=MC

^{2}says something true and unchangeable about the real world, we have no such guarantee with the Kaya Identity.w.

granda boris says:

July 12, 2014 at 12:17 pm

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.

Steve Keohane says:

July 12, 2014 at 12:29 pm

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.

Thomas says:

July 12, 2014 at 3:55 pm

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

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.

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?

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.

: )

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.

Dr. Doug says:

July 12, 2014 at 4:42 pm

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.

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.

Willis Eschenbach says:

Willis Eschenbach says:

July 13, 2014 at 12:57 am

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.

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.

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.

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!

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