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 that Willis’ Beer example could have been more powerful if, instead of substituting GBP for GDP, he had added in the term into the product, leaving GDP in place. The question is not whether Kaya is mathematically correct, but whether it is adequate, sufficient, and necessary…
Consider this: CO2 = population x (CO2/population).
We all agree that this reduces to CO2 = CO2, but we could also argue that CO2 emission per head of population could vary, even if population remains constant (through changed behaviour). We could argue that this identity does not contain sufficient terms to be useful.
But does Kaya include ALL the terms that are required in order to understand the economic impact of human CO2 emission (assuming all the while that this fractional portion of TOTAL CO2 emission is even worth considering – separate topic!). Population, GDP, and energy seems a conveniently simplistic triumvirate. Can’t disprove; just distrust our ability to fully understand such a complex scenario!
The Kaya Identity, is an identity it is not a formula or an equation!
It is described by the IPCC as a “The Kaya multiplicative identity” *.
Strictly, an equation contains unknown quantities (eg. 3x+2=11) and can be solved to determine x.
A formula links one quantity to one or more quantities (eg. f=ma) and can be used to determine f for any given value m, a.
As has been argued by many here, a multiplicative identity is “an identity that when used to multiply a given element in a specified set leaves that element unchanged, (such) as the number 1 for the real-number system” **.
An identity is usually indicated by the equivalence symbol “≡” rather than equals “=” symbol.
Many have noted as the original post did that the variables are not independent.
And the IPCC admit this important caveat:
But this is an odd confession and in my opinion deliberately confusing.
In a formula the result requires that the terms on the right-hand side, should be independent but contingent. In an equation the unknown quantity, the result, is dependant on the other terms.
What is actually being said by the IPCC, is that in the real world, the terms are not independent. To confuse matters further, working through the Kaya identity with real numbers, quickly demonstrates that the terms are truly independent! Change what ever you like and CO2 remains the same. Changing any value does not change the relationship between terms because the ratios cancel across the identity.
Yes, the Kaya Identity is an identity.
An identity will be true for any values of its terms and the Kaya is shown to be an identity when tested:
If
c= 2, g=20, p=4, e=8.
Then
LHS = c = 2
RHS = p x (g/p) x (e/g) x (c/e) = 4 x (20/4) x (8/20) x (2/8)= 4 x 5 x 0.4 x 0.25 = 2
Therefore LHS of K = RHS of K if c= 2, g=20, p=4, e=8.
* http://www.grida.no/publications/other/ipcc_sr/?src=/climate/ipcc/emission/050.htm
** http://dictionary.reference.com/browse/multiplicative+identity
I meant to say: “Change what ever you like and CO2 remains the same (Independently of the other terms).”
Regardless of whether the Kaya Identity is correctly including all the factors in man-made CO2 or not there remains significant confusion on the difference between unit cancellation (dimensional check) and variable cancellation. They are not the same!
An example of unit cancellation (dimensional check) would be checking the units in the following equation (velocity = distance/time) to make sure they make sense. The units of velocity could be expressed as miles/hour. Thus the unit of distance must be expressed in miles and the unit of time must be expressed in hours. Thus miles/hour = miles/hour and we can be sure that we have a correct calculation. If distance was in meters and the time expressed in seconds we would get a velocity expressed in meters/second — not the same as miles/hour! This is a dimensional check.
Variable cancellation simply reduces an equation to a simpler format — it has nothing to do with the units that the variable is expressed in! For example in the equation:
A = (x*y + d*y)/(y + c*y)
the variable y may be cancelled to obtain
A = (x + d)/(1+ c)
which has nothing to do with whatever the units of y were. y could be any number in this formula and it would not change what the final value of A was. To see this let y = 3 in case #1:
thus A = (3x + 3d)/(3 + 3c) = [3*(x + d)]/[3*(1 + c)] = ( x + d)/(1 + c)
in case #2 let y = 100
thus A = (100x + 100d)/(100 + 100c) = [100*(x+ d)]/[100*(1 + c)] = (x+d)/(1+c)
in other words the value of y does not change the value of A.
The Kaya Identity as written allows the variables to cancelled out until you are left with:
CO2_emissions = CO2_emissions
which means that whatever you change in the other variables (GDP, population, energy) doesn’t matter. In other words it is saying that in order to know CO2_emissions you have to know CO2_emissions!! This is what Willis was trying to point out in his original article.
If what people are saying the Kaya Identity is trying to show is correct, the correct formulation would be:
CO2_emissions = f (population, energy, GDP)
which is saying that CO2 emissions are a function of population, energy and GDP (left to be determined for the moment is exactly what that function is!). However CO2 emissions cannot be a function of CO2 emissions which is what the Kaya Identity as written is saying. That would be like writing an equation with the variables (NOT the units of the variables) like so:
C = P * (G/P) * (E/G) * (C / E)
In this case the variables cancel until we are left with C = C which is telling us that in order to know the quantity C we have to know the quantity C!! P, G, and E don’t matter…
Disciple: Master, what is a tree?
Confucius: That’s a good question, my son.
Disciple: Yes, but…
Confucius: A tree is a leaf, but a tree is not a leaf. A tree is a house, but a tree is not a house. A tree is a mountain, but a tree is not a mountain. A tree is the Chinese Gross National Product, but it is not.
Disciple: Master, that makes no sense.
Confucius: A tree is not everything which is not a tree. Therefore, a tree is a tree.
Disciple: That doesn’t really help, Master.
Confucius: You are not enlightened yet. Go meditate upon your breathing and wash the dishes. When you reach simplification, the true identity of all things will be revealed to you.
In my opinion, it is deliberately misleading to use the equals symbol rather than the equivalence symbol as the IPCC have done with the Kaya Identity. Particularly for such a famous, far reaching and important document as their report is!
Writing “M = G * M/G.” is not helpful as the M on the RHS is not the same as M on LHS.
More helpful would be a formula that worked:
TotalFuelUsed = distance/consumption
where:
TotalFuelUsed is your favorite liquid measure
Distance is your distance traveled in your favorite measure Miles or K’s
Consumption is your miles per gallon or litres per k to suit the above.
We can even put in values to try it out:
120 miles / 40 miles per gallon = 3 gallons.
As this is a regular equation it can be transposed using the normal rules of algebra for us to find either distance or consumption.
note: if I had written
M = M/(M/G)
we would have the same nonsense arguments as we are having about Kaya.
PS it is my firm understanding that a mathematical identity is an equation that has proven equality for all of its unknown values.
As such the Kaya equation is not an identity, because it is demonstrably false.
Re: Josualdo: July 13, 2014 at 2:31 am
Disciple: Master, I have meditated and I see now that the very life of a tree is dependant on CO2
Confucius: Yes you see now the cycle of life, the identity of all living things, from carbon they come and to carbon they go, earth to earth, ash to ash, dust to dust.
The IPCC itself says about the Kaya Identity: “While the Kaya identity…can be used to organize discussion of the primary driving forces of CO2 emissions and, by extension, emissions of other GHGs, there are important caveats. Most important, the four terms on the right-hand side of [the] equation should be considered neither as fundamental driving forces in themselves, nor as generally independent from each other. Global analysis is often not instructive and even misleading, because of the great heterogeneity among populations with respect to GHG emissions. The ratios of per capita emissions of the world’s richest countries to those of its poorest countries approach several hundred (Parikh et al., 1991; Engelman, 1994).”
Which seems to invalidate the Kaya Identity before even using it!! Or as richardscourtney says in his comment on July 12, 2014 at 11:40 pm “I have repeatedly argued that the equation is useless and misleading nonsense except as a propaganda tool: the ratios are arguments propagandists want to promote, and a claim that a ratio is “meaningful” is a statement that there is a desire to promote it.”
richardscourtney says: July 13, 2014 at 2:01 am
“Can anybody provide a definition of “meaningful” which determines what should and what should not be used as “factors” in the Kaya identity?”
Yes. Let’s do it recursively, to show how identities should be used.
Willis said originally that all the terms could be cancelled, leaving CO2=CO2. Not useful.
Let’s start there, but make one split:
CO2 emitted = Population x (CO2 emitted/population)
Already we’re making progress. We do have population projections, and we can say something about the second term. If you look at a plot like this, you can see that CO2 emissions in advanced economies are likely to be in the range of 10-20 tons/capita. That isn’t very precise, but already we have two factors each better known than CO2 emission.
Can we refine? Try (CO2 emitted/population)=(GDP/Population)x(CO2/GDP). Yes, CO2 is correlated with GDP, so we can get a better estimate there. And again GDP/population is something people think a lot about. So probably that split has helped.
And so it goes. The test isn’t whether each term is known perfectly. It’s just whether breaking up into extra terms helps or hinders.
As presented, the Kaya identity is not an identity.
If it were in a maths book of identities, it would be reduced to its simplest form:
CO2 = CO2
I know of no mathematical identity which is published and shown in its none simplest form.
There is a challenge!
If someone had stood up and said CO2 = CO2, they would be laughed out of the room, but here people use it as written.
From the paper linked above and here:
http://www.pnas.org/content/104/24/10288.full.pdf+html
“The full formula is used where each variable is named
where P is global population, G is world GDP or gross world
product, E is global primary energy consumption”
Stating the obvious, if E=E, P=P and G=G, then the do cancel out and you are left with CO2=CO2.
No point in saying you do not use it as a regular equation when that is how it is used in peer reviewed papers (see above).
An identity is a regular equation that has a useful meaning, proven equality, hold true for all values and shown in its simplest form.
It seems to me that the confusion mainly lies in the unstable definition of “CO2 emission” on the left side of the equation. In Kaya Identity and Beer Identity, “CO2 emission” — although written the same,— has effectively different meaning. You can produce all the “Identity” in the world, the “CO2 emission” presented would be CO2 emission of a specific realm.
In my opinion, it is deliberately misleading to call the Kaya Identity an equation as the IPCC have done, particularly as equations, formulas and identities, have distinct meaning in Mathematics. For such an important document, as their report surely is, it is not a small oversight (To put it very kindly).
What an incredible blog post. Just scanned through comments.
“steverichards1984 says: July 13, 2014 at 2:37 am”
Nails it completely for me.
It makes perfect sense that if we start with the said equation we end up with CO2=CO2 and I fail to see any of arguments that makes this remotely useful.
I agree that it is not an identity but it is a formula. The issue is simply whether it is useful because each right-hand term can be independently computed or measured without knowing the left-hand value. And whether this is the most direct way to calculate the left hand value.
I am by profession an energy and environmental economist. I do not like the KAYA identity for a whole slew of reasons. But rest assured, none of those have anything to do with the utter nonsense in this guest post. Although I did not have the courage to read all the 262 comments (at the time of writing), it seems others have already thoroughly debunked the main “arguments”. I will therefore only say this. Someone ought to teach the author the “Expenditures Approach” to calculating GDP, including the fact that (exports – imports) is one of the four main components of the consumption expenditures by households. This is Economics 101.
This guest post should never have been allowed, as it only serves to provide ammunition to those who use the KAYA identity for all the wrong reasons.
Mike M. Why only scratch problem solving semantics, when CACA goes all the way? E.g. fossil fuel = coal = carbon = carbon dioxide = human caused carbon dioxide = human caused global warming = global warming = climate change = climate disruption = weather event.
It’s puzzling to witness CACA rushing into anthropocalypse from such poems while keeping Kaya identity immune to logic – irrespectively of Δt(CO2 emissions) explanations. Appeal to authority makes the situation worse, especially if the derivatives are used to filter out populations (über/unter).
For those seeking humor here, the following clip connects witchcraft to buoyancy in a familiar manner: http://www.youtube.com/watch?v=yp_l5ntikaU&feature=kp. Skip to 2:00.
Geez, another post of this nonsense? It really is just an identity, how ever you look at it. Before starting to laugh at this identity, one should really first look into how it is applied.
Willis Eschenbach says:
July 13, 2014 at 12:22 am
Steve Keohane says:
July 12, 2014 at 12:29 pm
You’re right wrt only human caused emissions. I stopped by quickly and made my ill-thought out comment while in being in the middle of cooking dinner.
This a perfect identity for a World Government bureaucrat, who can give the “market” flexibility to all countries, as long as she controls the co2 per pop. The developed countries can respond by becoming austere. (GDP per pop) or efficient (energy per GDP) or advance technology (energy per co2). Meanwhile allowing the third world to continue using the contemporaneous technology, since their GDP per pop is lower. This perpetual machine will then continue, driving everyone towards the “nirvana” of similar GDP per pop. Or a least perish while trying to attain it.
Arthur 12:03pm said: “For anyone not following what this Kaya formula actually does, put numbers in for Energy, Population, GDP and CO2. Any numbers will work, 10, 24, 36, 40 – whatever. See what happens. The end result will always be CO2 = CO2. Then explain how this is useful – in any real world situation.”
You can use it in two ways. 1. You decide what level of CO2 emissions you want to achieve and then use the Kaya Identity to look at how that could come about. 2. You project trends in population, GDP and energy consumption into the future and see what CO2 emissions might do.
I agree that it falls down in applying it directly to the real world. In that respect it is no different from unverifiable climate models which even climate modelers admit are projections not predictions. The climate models and the Kaya Identiy are not saying what *will* happen, just what *might* happen so long as all the assumptions made within them hold true for the length of the projection. What the Kaya Identity is is a model for making ‘evidence’ to fit a predetermined policy.
Daniel G. 3:02pm said: “Of course, if it is per unit of energy, then the co2 on the rhs (only for a unit) differs from the co2 on the lhs.”
CO2 per unit of energy on the right hand side is calculated by dividing total CO2 by total energy consumption. It plainly says this in the Kaya Identity. It is the same ‘total CO2’ variable on both sides. You either say CO2 per unit of energy (a ratio) or total CO2 / total energy (the variables). You don’t say CO2 per unit of energy per unit of energy.
So, a dumb question: Why would anyone create an identity like this, unless they have an agenda about carbon dioxide emissions? Root-cause-analysis would say that this is just a political tool being used to make some point about how evil carbon dioxide is. This is a political statement, and not scientific or mathematical, and therefore can never make sense in a real-world way.
When the GDP of Somalia is comprised of the same factors as Germany or the US, I’ll buy into the equation.
As far as I can see the Kayla relationship is mathematically sound whether it is regarded as an identity or as an equation. But in spite of its mathematical correctness it still appears utterly useless to me from the point of view of practical environmental science and economics. You cannot apply it to the calculation of anything in the real world and I think this fact makes it an item of pseudo-science or pseudo-economics as the case may be.
As I said before (see above 12/7/2014 5:58pm) the reason that I see for its practical uselessness is the fact that you cannot calculate or measure any of the fractions involved without first measuring their primary components and these all cancel one another out ultimately so that the measuring of them in the first place is a pointless, uninformative exercise that leaves us ultimately none the wiser about global CO2 emissions. This point is so glaringly obvious to me that I am finding it hard to understand why so many people appear unable to see it. Perhaps I should explain it in more detail.
The equation/identity states (using my abbreviations of terms):
CO2 = Pop’n x (GDP/Pop’n) x (Energy/GDP) x (CO2/Energy)
In order to calculate global CO2 emissions from this formula we would first need to estimate the global population (Pop’n), which the U.N. purports to have done for us already so we can take that as given. No problem exists there unless one wants to argue with the U.N.’s figure, which I don’t propose to do for the purposes of this demonstration.
Next we would need to estimate the value of the fraction (GDP/Pop’n), which we can do by estimating the value of global GDP (i.e. the sum total of the GDPs of all the individual countries in the world) and dividing it by our estimate of the global population already obtained. The pointlessness of this exercise becomes immediately apparent at this second stage of the calculation because it automatically eliminates the global Pop’n as a factor in the calculation. We might as well have ignored global Pop’n from the outset and just estimated global GDP!
But if we look ahead we can also see that global GDP will be eliminated at Stage 3 of the calculation and that global Energy will be eliminated at Stage 4 to leave us ultimately with the uninformative statement CO2 = CO2.
There is only one possible way of avoiding this automatic collapse of the Kayla function and that is to measure or estimate the fractions independently of their defined components. In other words, we need to calculate (GDP/Pop’n) for instance by some other method than by dividing global GDP by global Pop’n.
But we have no such other method! At present there simply is none in existence that does not rely fundamentally on our calculating the primary components GDP and Pop’n first. And the same consideration applies to the other two fractions as well. We have no independent alternative methods of calculating any of these fractions. Therefore the automatic self-elimination of these fractions as factors in the calculation by the cancellation of their primary components is an unavoidable, inescapable, inevitable and inexorable certainty that returns us back to square one at the bottom line with the uninformative tautology: CO2 = CO2.
I can see no other possible conclusion to come to than that the whole exercise is a meaningless mathematical ritual and an empty pantomime.
Willis,
You have a valid point. The Kaya identity only includes measured CO2 emissions. Our personal emissions are not included. But there are more significant emissions that are not included. An example was observed by Paul Homewood at the beginning of June. A biomass recycling center caught fire.
http://notalotofpeopleknowthat.wordpress.com/2014/06/04/biomass-on-fire-in-yorkshire/
I also documented a number of instances where storage depots of recycled material have caught fire. It appears to be a frequent occurrence in England at the moment.
http://notalotofpeopleknowthat.wordpress.com/2014/06/04/biomass-on-fire-in-yorkshire/#comment-24936
What is more important (and pointed out by others) is that measured CO2 emissions are only a small part of total emissions. Natural emissions are far more important than human emissions, and are pretty much offset by natural adsorptions of CO2. Though we can only estimate the amount either way, so could easily be way out on the net impact.