As many readers know, there was quite a hullaballo over the Kaya Identity last week, two posts by Willis Eschenbach here and here created sides seemingly equally split on whether the equation is useful or not.
One of the most strident critics was Dr. Roger Pielke Jr., and in the spirit of keeping an open mind on the issue, I offered him space on WUWT. Here is my email and his response, reprinted with his explicit permission.
On Mon, Jul 14, 2014 at 9:52 AM, Anthony xxxxxxx@xxxx.com wrote:
Hello, Roger Jr.,
I’d like to direct you to a comment on WUWT that challenges your calculations using the Kaya Identity.
http://wattsupwiththat.com/2014/07/12/the-beer-identity/#comment-1685623
I provide it only for your information.
I know both of you have issues with the current state of discussion on WUWT regarding that equation/identity/relationship, and I’m certainly OK with that.
I think that much of the dissent over it has to do with the difference in viewpoints between science and engineering. I and many others look at the Kaya identity equation more from the engineering perspective, and expect it to perform as many other calcs do, but it seems that it doesn’t act as a hard equation, but more like a soft one, that generally defines the relationships of terms. A number of commenters have approached it from the engineering viewpoint, and find themselves puzzled as to why the numbers they get don’t seem sensible.
I puzzle over that also.
To that end, and because you’ve been highly critical, agreeing with such statements as “breathtakingly ignorant”, therefore, given the critical comment above, I’d like to offer this, first raised in another comment:
http://wattsupwiththat.com/2014/07/12/the-beer-identity/#comment-1684325
Perhaps Anthony could give equal time to Pielke in defense of the Kaya identity?
I’m more than happy to do so should you be so inclined; not just for my own education on the topic, but for the hundreds, if not thousands of others that suffer from the same doubts that the equation isn’t as well thought out as some claim it to be. Or, if it was never intended to produce real world numbers accurately, but serves only to illustrate the relationship of the variables, explain that clearly so that the engineering types understand it better.
If you wish to make a submission, MS Word with embedded images works best. Any equations you might want to use in MS word’s equation editor don’t translate to WordPress well, so they will be converted to images. Or, you can optionally use LaTex, which is supported directly in WordPress.
I would appreciate an answer, no matter if it is a yes or a no. Thank you for your consideration.
Anthony Watts
=========================================================
Roger’s response Tuesday, July 15, 2014 6:59 AM (published with permission)
Hi Anthony-
Thanks for your email. Apologies for the delay in responding, as have been off email while traveling.
If you’d like to help your readers better understand the use of the Kaya identity, which I think is the most important tool for analyzing actual and proposed carbon policies, then I would recommend that you introduce them to this paper (open access);
http://iopscience.iop.org/1748-9326/4/2/024010
The mathematics are simple. Of course, there is a more in depth discussion in my book, The Climate Fix.
Finally, for those who’d prefer a lecture format, here is me at Columbia Univ last summer explaining the significance of the Kaya Identity for climate policy analysis:
Thanks, and all the best,
Roger (Jr.)
==============================================================
I agree with Roger that: “The mathematics are simple.”
In fact I think it is that simplicity that lends itself to being criticized as not being fully representative of a complex system. Willis described the Kaya Identity as being “trivially true” while Roger in his book and video treats its with the same respect as some physical law equation. My take is that the truth is somewhere in the middle between those viewpoints.
Whether it is best used as a political tool or as a physical science tool is still an open question in my mind, though I tend to think it leans more towards political usefulness. Whatever your viewpoint is, let’s thank Roger Pielke Jr. for taking the time to respond and to offer his view here.
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Total CO2 Emissions = Sum of all CO2 Emissions
The Kaya and Beer CO2 emissions are not exclusive, they are overlapping subsets of total CO2 emissions. The number of arbitrarilary definable subsets is is very large. The left side of the Kaya Identy represents total CO2 emissions related to population, per capita GDP, and energy per GDP. The product of these factors is only useful for describing changes in this subset of CO2 emissions as arbitrarily defined. Other factors could be included to describe a different subset.
The arrangement of units in an equation to define an identity is called dimensional analysis.
Tim Hammond says: July 19, 2014 at 8:11 am
Not sure what all the fuss is about.
It keeps us off the streets. Our wives like that.
Johan says: July 19, 2014 at 8:29 am
I have never known a physicist to call F = ma an identity.
No argument. However, if it walks like a duck and quacks like a ……
This semantic discussion does not impact the relevance of Kaya to real world policy making.
Johan says: July 19, 2014 at 8:37 am It keeps us off the streets. Our wives like that.”
+1
Dr Pielke at 56 minutes in talks about average human lifespan. In 100 years we have substantially increased human lifespan, without any global treaty to increase lifespans.
What would have happened if we placed a tax on death? What would have happened if we used cap and trade to reduce death? Would this have reduced death? According to economic theory, this should have the effect of reducing death.
The problem not accounted for in economic theory is that there is no alternative to death. Price sensitivity, supply and demand simply do not apply when there is a monopoly. CO2 is a similar problem. CO2 has a de facto monopoly as far as energy production is concerned.
I started this thread in 1989 when it was simple global warming. Premises: 1) earth is warming at an alarming rate (seems subjective and lately not so) 2) the sole cause is rising levels of atmospheric CO2 concentrations (Keeling) 3) mankind’s industrial activity is solely responsible for this increasing CO2 concentration (only because no one has bothered to locate other sources such as ocean floor volcanic vents. IPCC AR5 admits it has no knowledge of the bottom half of the oceans.) After twenty five years not one of these points has been conclusively demonstrated.
I don’t understand why this old divide by zero example is supposed to have anything to do with Dr. Roger Pielke Jr. and the matter in question today. Obviously if a = b then (a – b) = 0 and you can not divide both sides of the equation by zero. But so what? Why is that part of this Kaya Identity discussion?
Someone enlighten me?
The Kaya “identity” is too simplistic to be of any scientific use. It simply lends scientific credibility to the political opinion that we developed people are too destructive, and too numerous, to be allowed to continue our way of life.
Carlos Slim has a solution – destroy the per-capita contribution to GDP. What he is suggesting is the elitist notion of reducing the quality of life. That is behind all schemes that regulate consumption.
http://www.ft.com/cms/s/0/4899aaf8-0e9f-11e4-ae0e-00144feabdc0.html
Next: a well-regulated caste system.
Michael 2 says:
July 18, 2014 at 8:11 pm
Ian says:”and that effect is close to, if not at, saturation.”
Saturation would be 1 million parts per million. We have a long, long way to go.
Michael, Ian is addressing the absorption spectrum of CO2, that is how that molecule absorbs selective wavelengths of infra red radiation, which does follow a logarithmic curve. You are referring to concentration which relates to the gas mixture. Ian is entirely correct that the atmosphere is already absorbing most of the IR it is sensitive to in the system so increasing CO2 will only have a diminishing effect on heat content. This is the great flaw of the alarmist community argument. They assume that the CO2 / heat relationship is linear. It is not.
Mark Stoval (@MarkStoval) says: July 19, 2014 at 9:00 am
Someone enlighten me?
Hello? It was a joke, in response to RobertInAz who claimed that “Maybe there are some equations that are not identities. Have not thought that notion through.”
If you can prove that y = x is true regardless of what values are substituted for y and x, than clearly y = x is an identity. If not, it’s an equation but not an identity.
RobertInAz:
At July 19, 2014 at 8:41 am you say
YES!
As I have repeatedly said, the Kaya Identity is a useful propaganda tool but has no other use.
Richard
You make the case best. While the equation/identity is true, and appears useful, it only applies to statistical averages, and none of the terms on the right, other than population, can be determined directly.
The equation does not sum over individual contributions. We are not calculation the GDP contributed by John Doe, only the average per person, which comes from the total GDP divided by the population. So the product “total GDP per person” x “population” is no more meaningful than just one term, “total GDP.” Likewise, CO2 per unit GDP is not a known quantity, nor is GDP per unit energy.
The known quantities are Total CO2, Total GDP, Total energy, Total population. The ratios in Kaya are not known.
To be useful, an equation/identity should be based on quantities that are directly measurable. When Total CO2 is needed to find one of the terms on the right hand side, the whole thing is trivial, as Willis has stated.
It would’ve been real nice if Pielke Jr. had at least admitted that the equation is *not* an identity, and is not justified through algebraic construction.
It would be even nicer if he and others would write the equation properly, with the required variables included, rather than using the exact same text to refer to both a variable *and* a unit.
The confusion and controversy have, as their root cause, imprecision in expression.
richardscourtney says: July 19, 2014 at 9:12 am “YES!
As I have repeatedly said, the Kaya Identity is a useful propaganda tool but has no other use.”
On the contrary, Kaya reflects real world data (see Ruth Dixon: http://mygardenpond.wordpress.com/2014/07/13/a-graphical-look-at-the-kaya-identity/#more-706 )
It is relevant to policy making because it quantifies the economic and engineering impossibility of the mitigation approaches most loved by the alarmists.
I am still not getting the joke here. In the case of a function y = x we see that the value of y is dependent upon our choice of x. If I pick x = 1 then y = 1.
Consider f(x) = 2x +2 when x = 4. We get 2(4) + 2 = 10 and that is it. So, f(4)=10 and nothing else. Y = 10. You don’t get to just pick both x and y independently of each other then claim it satisfies the given relationship for god’s sake. If that were true it sure would make grading math tests a whole lot easier! (no child left behind indeed!)
Consider F=MA. Where F is expressed as KG * M/SEC**2, M is KG and A is expressed as M/SEC**2.
Rewritten as the “Kaya Identity” is presented, with only units, we would teach our physicists:
KG*M/SEC**2 = (KG)(M/SEC**2)
The “Kaya Identity”, presented in the same way we present F = ma would read:
F = P*g*e*f
The people who write the “Kaya Identity” with units only, instead of including variables, are wrong.
Mark Stoval (@MarkStoval) says: July 19, 2014 at 9:21 am
I am still not getting the joke here
My word! All I had to do to prove that y = x is not an identity, is to provide a counter-example. Which is exactly what I did. What if y = 2 and x = 1. Clearly, 2 does not equal 1, hence we conclude y = x cannot be an identity.
(drum roll). Enters the joke. Oh, but wait, what if we can prove that 2 = 1 … !!!
I cannot believe I even have to explain such a silly joke. This whole thread on KAYA is more absurd than any Monthy Python sketch I’ve ever seen.
scarletmacaw says: July 19, 2014 at 9:13 am
To be useful, an equation/identity should be based on quantities that are directly measurable. When Total CO2 is needed to find one of the terms on the right hand side, the whole thing is trivial, as Willis has stated.
It would be nice. I would replace “To be useful” with “To be most useful.”
Total CO2 is not needed to determine any of the terms on the right. I don’t know where that notion originates. In fact, total CO2 from energy production is probably derived from adding up all sources of energy and then calculating the CO2 emitted by each. We can eliminate the population and GDP terms of Kaya and just focus on energy terms to get total CO2.
The point of the first two terms is to illustrate Pielke’s Iron Law: politicians are not going to reduce population and they are not going to reduce GDP. Therefore, they have to either increase the GDP efficiency of energy or decrease the CO2 emitted by energy. Kaya illustrates in a quantitative way the magnitude of GDP efficiency increases required or the magnitude of CO2 reductions required. The results of applying Kaya to the alarmist desired CO2 scenarios shows they are not obtainable.
Johan says: July 19, 2014 at 9:29 am “My word! All I had to do to prove that y = x is not an identity, is to provide a counter-example. Which is exactly what I did. What if y = 2 and x = 1.”
Oh my oh my. You have a physics degree and are currently an economist? I guess as an economist, you can provide counter-example to all of the trigonometric identities listed here. Mathematicians do use the term identity – a lot.
http://en.wikipedia.org/wiki/Trigonometric_identity
In fact, you can invalidate all of modern mathematics with similarly framed counter-examples. Start here:
http://en.wikipedia.org/wiki/List_of_mathematical_identities
Sorry, but you can’t divide by zero, nor can you just pick any value you want for x and y if y is the dependent variable and x is the independent variable. I think they might have named the variables in that manner for that reason you see. What I really did not get is why the non-proof (error in logic) of 1=2 has anything at all to do with the topic under discussion.
I first saw your “proof” in an undergrad number theory course in ’72 if memory serves me. It was presented to demonstrate that subtle errors in logic will creep into your work (divide by zero in this case) if you are not rigorous. I still find no reason to equate Dr. Pielke’s work with that “proof”.
“I think that much of the dissent over it has to do with the difference in viewpoints between science and engineering.”
The viewpoints of science and engineering? How about the viewpoint of Jr High Math.
The Kaya Identity is a fancy pants version of The Multiplicative Identity Property:
x = (1)x
The Kaya Identity does not show the relationship between population, GDP, energy consuption and CO2. I think what would be needed would not be an identity but and equation along the lines of Ohm’s Law. A “Kaya equation” that shows the relationship of population, wealth (I would use income per capita not GDP) and CO2 emissions.
How this formula is used politically becomes ugly very quickly. Poverty and population control = good…….wealth and babies = bad.
I propose a procedure that would once and for all make our leaders aware of the cost and implications on life style and comfort of every law or regulation.
The approach is that any new government proposal such as de-carbonization should first be implementation on the governing class first as a trial, in this case the Administration, all congressional representatives and their staff including all the cabinet members and their staff. Since their activities do not appear in any significant way contribute to the GDP, it would lower the emissions per GDP of the country without affecting the economy. More importantly it would make them fully aware of the consequences of their actions, since they appear to be oblivious to the effect of new laws/regulations. If there are no negative consequences after a 5 year trial, then the proposal could be gradually extended to other areas starting with cities. Does anyone think that if the “Affordable Care Act” was implemented under these rules there would have had so many problems and issues if it directly impacted them? Remember Congress sought and received an executive exemption, although they were supposed to also comply with the ACA.
Think about it. Who has the largest footprint in the world? Surprising, it is those individuals who are concerned about your carbon footprint. How much would the US carbon footprint be reduce if the every government agency including the White House cut it’s carbon emissions 20% near term. Besides the cost of our energy use would fall and fossil imports would decline.
Scott Wilmot Bennett says:
July 19, 2014 at 4:17 am
“You can put any values you like into any variables and “c” will equal the value you gave it.
Just do the Math yourself, as Dr Rodger Pielke Jr recommended, over and over.”
There’s nothing wrong with your math – it just describes an *unrealistic* situation. Neither you nor anyone can find a real world example that is consistent with your hypothetical.
RobertInAz says: July 19, 2014 at 9:41 am
Mathematicians do use the term identity – a lot.
Where and when did I say there is no such thing as “identity” in mathematics? I even gave the formal definition of identity – so many times already I am getting tired of it.
In fact, there IS a KAYA identity, namely CO2 = P * (GDP/P) * (E/GDP) * (CO2/E), where CO2, P, GDP and E are just numbers (not variables). It’s the kind of identity where one says 24 = 4*3*2*1 (because an identity does not need to contain variables).
Now, before you continue insulting me, by asserting that “Maybe there are some equations that are not identities. Have not thought that notion through.”, you already made a laughing stock of yourself. But maybe you can show us some formal proof that ALL equations, without any exception, are identities. I am sure mathematicians would be very interested in that.