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.
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 @ur momisugly 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 @ur momisugly 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.