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.
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 not total CO2 emissions. That is true for both the left and right hand sides of the equation. So when you make your efficiency savings the CO2e,b = 0.9*CO2e,b,original, but the TOTAL CO2e is not described or captured in the equation, so the supposed paradox simply doesn’t exist.
D+ for effort but inattention to detail.
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 laugh assertions. It would have been manly of you to have acknowledged the error instead of simply walking away from it, but at least you did walk away from it.
Unfortunately, that means that you’re doubling down on the remainder of your argument. That has two main components. The first is your “Beer Identity”. The second is used to enable the first, and is your use of equivocation, playing on the ambiguity of the vernacular descriptions of the KI terms. Both are fallacious.
Addressing the second first, we have this assertion from you:
That is not exactly correct. It is certainly good enough for people who read the whole paper and understand the KI and who are using it and discussing it in good faith. Unfortunately, that doesn’t describe how you are approaching it.
In the KI, “CO2 emissions” are not “the CO2 emissions of say a given country”. They are more specifically the energy-related CO2 emissions of a given country’s economic production.
Similarly, in the KI “Energy” is not “energy consumed by the country”. It is more specifically the energy consumed by the country for economic production.
You equivocate on these terms, switching back and forth between specifics of your choosing. You then think you have proved something when you point out the bust that you have fabricated by playing with the definition of terms. This is how you hide the fact that your “Beer Identity” is mal formed, when the KI is not. Uncovering your ruse is as simple as putting descriptive subscripts on the terms. The KI thus becomes:
Kaya Identity EQN w/expanded descriptions
And your “Beer Identity” kludged from the KI becomes:
Beer Identity w/expanded descriptions
With the equivocation removed, the reader now easily sees that some things in your “Beer Identity” look a little odd. A couple of your terms express a ratio of one item defined relative to GBP vs another item defined relative to GDP. Those terms don’t seem particularly useful, as (unlike all of the terms in the Kaya Identity) they don’t have any meaning WRT things we commonly talk about in the real world.
More importantly, the reader now easily sees that there are some things in your “Beer Identity” that are very different than you describe them. This is shown in you supposition:
And in your subsequent restatement of the “Beer Identity” with the figure 0.9 thrown in, which allegedly represents an increase in the energy efficiency of beer production.
The problem is, there is no term for the efficiency of producing beer in your “Beer Identity”. That term would look like this:
Energy Efficiency of Beer Production Term
And that term is not to be found anywhere in your “Beer Identity”. So, your claim that your application of the 0.9 factor to your “Beer Identity” represents a 10% increase in beer production energy efficiency is simply false. You did not do the math correctly.
I trust that the website owner will now add to this post the entirely accurate sub heading:
“Willis Eschenbach’s “Beer Identity” carbon equation and criticism of the “Kaya Identity” has been falsified – due to a stupid maths error“.
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.