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.
No, i have just reformed the equation, using a ratio of symbols to represent a ratio variable. I can do the same with Kaya identity:
energy-rel. co2 em. = pop. * (gdp per cap.) * (energy inten. of the econ.) * (co2 inten. of energy)
Willis said: “..something like two-thirds of peer-reviewed science is falsified within a year.”
Where did this claim originate? Any background information on this?
Thanks,
Nigel.
gdp is not term of the identity.
Again look at two terms:
population
gdp/population
If increase population (let’s say double)
Then (fallaciously):
new gdp per capita = dp/(new pop.) = gdp/(2*old pop.) = (1/2)(gdp/old pop.) = (1/2)(old gdp per capita)
Therefore (fallaciously) energy-related co2 emissions stay the same.
But, why is this reasoning wrong? It is wrong because gdp also changes. That will make energy consumption change too. That will ultimately increase co2 emissions.
No, i have just reformed the equation, using a ratio of symbols to represent a ratio variable. I can do the same with Kaya identity:
What does that mean “I have reformed”
I have written the identity in a mathematically equivalent way.
Just slow down, and tell me if that doesn’t apply to M&M’s.
@Daniel G. says: July 13, 2014 at 8:21 am:
The implication of what you are saying is that the Kaya identity does not consist of fractions but just 4 unique terms:
CO2 = Pop * GDP * Energy * CO2
Where the 4 terms interact with each other in a complex manner.
Is this your case?
Is this your case?
Incorrect.
energy-rel. co2 em. = pop. * (gdp per cap.) * (energy inten. of the econ.) * (co2 inten. of energy)
Well, your 8:31 am will not cancel down so it has a possibility of doing something.
What is your definition of each term?
The broadway identity:
Dollars per show = visitors per show x price per ticket
Willis when in a hole, stop digging.
Read JK’s post, please.
JK writes:
I think Willis’s original point is now well accepted.
The passing off of a political construct as a mathematical formula or worse, as a ‘proven identity’ has been shown to be wrong.
I realise that some people will not accept it but you can not go round stating that something is a mathematical identity then trying to stop people from applying the normal rules of maths to it.
I am happy that I now understand Daniel G, when he declares that B/C could, at one hour be B divided by C and latter, a ratio that cannot be so divided or simplified.
This is post normal maths, we have a lot to learn.
What a stupid thing to say. First you attack the validity of algebraic expansion and dimensional analysis, now you attack the validity of conditionals in formal logic. You are rapidly becoming a caricature, Willis.
And when GDP does not keep up with population, what happens? Standard of living (GDP/Pop) goes down. OH LOOK, there is a term for standard of living in the Kaya identity (GDP/Pop), and when GDP doesn’t keep up with population, that term in the Kaya identity drops. Huh. Whattaya know.
As has been pointed out to you, when you make these sort of errors it is because you are equivocating on terms. The “energy use” in the KI is not total energy used by the country for everything, it is energy used by the country for the purposes of economic production.
OH LOOK, there is a term for the CO2 intensity of energy in the Kaya Identity (CO2/Energy), and when that term is decreased, the total energy used for production may increase while CO2 emissions show a drop. Huh. Whattaya know.
Good grief. Do you even realize that you are arguing against yourself?
More energy use may or may not involve more emissions? So you think that the Kaya Identity should account for that, by including a CO2 intensity term. OH LOOK, IT DOES!
Greater GDP may or may not involve greater energy use? So you think that the Kaya Identity should account for that, by including an energy efficiency term. OH LOOK, IT DOES!
Increasing population may or may not increase GDP? So you think that the Kaya Identity should account for that, by including a standard of living term. OH LOOK, IT DOES!
In your original post, you insisted on algebraically reducing those terms out of the Kaya Identity, and pretending that the fact that you could meant something bad. Now you are arguing in favor of the necessary expansion of any such identity to include those terms. You are arguing against the derivation of the Kaya Identity, by deriving the Kaya Identity.
In other words, your argumentation here reduces logically to “Willis does not equal Willis”. NOW you have something to laugh about.
May last attempt:
Daniel G at 08:40…. by referring to JKs post: (GDP / population) and (energy / GDP) you’re putting real numbers into fractions which can the be simplified (if this a mathematical formula)
Your rant does not amuse, I have answered to all your arguments using traditional logic.
Yes, you can simplify, but it is meaningless! But that simplification has nothing to do with the real world. The same argument applies to M&M’s identity.
JK was dealing with the way the identity was presented. But you can substitute the fractions by letters. Then you have variables by themselves. The fact is that population increase is not cancelled by gdp per capita decrease.
Hans Erren says: July 13, 2014 at 8:37 am
The broadway identity: Dollars per show = visitors per show x price per ticket
Willis when in a hole, stop digging.
+1
Now, here is something indisputable: Girls = Evil
Given that Girls = Time x Money and that Time = Money, it follows Girls = (Money)²
Given that Money is the root of all Evil, or Money = sqrt(Evil), it follow Girls = [sqrt(Evil)]², or
Girls = Evil, QED.
Han Erren
You are missing the point, you have written a ‘formula’, not an equation and not an identity. That said, do you mean average dollars per average number of shows x average ticket price per show? I guess you are saying c (Total cash) = t (number of tickets sold) x p (ticket price). Either way, neither are identities, because the variable(s) on the LHS are not represented on the (RHS).
Yes it is pedantic but that is what this whole post is about. 😉
Wow, just wow. I though the post and previous one gave the ultimate absolute proof that the Kaya Identity is despicable postmodern political construct disguised as math.
Anyway, it is possible to make the first-order approximation that people going = tickets.
I am reminded of Lewis Carroll’s Humpty Dumpty:
“When I use a word,’ Humpty Dumpty said in rather a scornful tone, ‘it means just what I choose it to mean — neither more nor less.’
The “Kaya Identity” is an attempt to give a weak argument spurious validity by ‘appeal to maths’. As with Humpty Dumpty above – it can mean just what someone wants it to mean. This is shown by the multiplicity of views in this and the previous thread.
If the terms are not defined – and in this ‘equation’/’identity’ they are not then anything can be claimed from this type of pseudo mathematics.
So for example:
IF
1/2F = 1/2E
Then
F=E
Mathematically correct until the terms are defined:
F<- Full and E <- Empty
(this was borrowed from a similar medieval ‘proof’ of life after death as half dead = half alive)
Hand-waving and bloviating waffle do not make this arts grad attempt at claiming mathematical authority correct. It is a pure PR exercise and any engineer would have thrown it out.
So why resort to some fancy, schmancy equation? Just go to EIA and work with real numbers. CO2 emissions from: Coal – 31.9%, NG – 25.8%, Petroleum – 42.1%. (figure 12_3) What I found surprising is that NG produces 80.8% as much CO2 as coal. I suppose that’s because NG unlike coal is used for more than electricity, i.e. space and water heating. And since petroleum is the biggest source of CO2 how about applying the 1,100 pounds of CO2 per MWh (HPh) to planes, trains, and automobiles?
Daniel G. says:
July 13, 2014 at 8:05 am
“Probably, but the problem is that Eschenbach et al. still maintain the “cancelling” and “i can put any variable” arguments.”
I agree with you and that these arguments are flawed. I was simply attempting to see if we could move the debate forward. Some folks seem to have a hard time admitting when they are wrong …
Cheers, 🙂
Ian W says:
July 13, 2014 at 9:04 am
“1/2F = 1/2E
Then
F=E
Mathematically correct until the terms are defined:
F<- Full and E <- Empty"
Your problem is that given the definition of full and empty your 1/2F=1/2E can't be true (this condition does not apply to Kaya).
Given the definition of full and empty – a correct mathematical description of full and empty would be:
Total volume=full volume + empty volume
Then, when TV=1 and F=0.5, then E must equal 0.5 as well (like your hypothetical).
We could then use measurements of TV and F to calculate/predict E, for instance.
Nothing wrong with that at all but it is the last step(ie making valid predictions) that determines whether or not the expression/identity is science.
Cheers, 🙂
OK, one more time, since Hans Erren has given a useful example:
‘The broadway identity:
Dollars per show = visitors per show x price per ticket’
Scott Wilmot Bennett says ‘variable(s) on the LHS are not represented on the (RHS)’ but since visitors = tickets we get the same thing by writing:
Dollars per show = tickets per show x (dollars per show / tickets per show)
The CO2 = CO2 or ‘other things are not equal’ crowd would point out that if you change the price of a ticket then you will change the number of visitors per show.
That’s quite true.
Does that mean the equation is not true? No.
Does that mean it’s never useful, as an analytical tool? I would say no.
multiplying by shows we get:
Dollars = number of shows * (tickets / show) * (dollars / ticket)
Again, the CO2 = CO2 or ‘other things are not equal’ crowd would point out that if you put on more shows then anything could happen! Quite true. Dollars = Dollars, after all.
The formula suggests that putting on 21 shows instead of 20 would result in 5% more dollars brought in. But that assumes (tickets / show) is constant! Maybe after 20 showings everyone who’s seen the show has seen it and you can’t sell more tickets, or maybe it takes 20 shows before word of mouth spreads and sales take off? Other things are not equal.
At this point you could just say that the identity is just useless. How could we ever hope to guess what might happen to income if we change the number of shows, increase the advertising budget or change the ticket price?
Dollars = Dollars, after all! Who could argue with that?
Or, we could attempt to use the identity to estimate the effects of simultaneous changes in the variables in these different scenarios. It could give us an analytic starting point for trying to understand how many more customers we need to attact to break even if we reduce the ticket price.
The CO2 = CO2 or ‘other things are not equal’ crowd would presumably just say that’s a hopeless exercise. After all, this is just as true:
Dollars = number of shows * (GBP / shows) * (dollars / GBP)
Gross bear production obviously has nothing to do with it – just like CO2 emissions / energy production and energy production / GDP obviously have nothing to do with total CO2 emissions in an economy from energy producion.
So we might as well just say that Dollars = Dollars, that CO2 = CO2 and be done with it.
richardscourtney @2:01am:
“The “ratios” in the Kaya identity are claimed to be “meaningful” so they are included as “factors” which combine to determine anthropogenic CO2 emissions.
Can anybody provide a definition of “meaningful” which determines what should and what should not be used as “factors” in the Kaya identity? ”
Nick Stokes @2:52am:
“CO2=CO2. Not useful.
Let’s start there, but make one split:
CO2 emitted = Population x (CO2 emitted/population)
Already we’re making progress.”
——
The equation, as Willis has written it, is meaningless and is incorrect. Nick, it makes not one whit of difference what we plug in and it isn’t one bit meaningful . . . that is, if the terms fully cancel each other out (as Willis has wrongly written it).
We might as well say:
CO2 = (# of Miley Cyrus fans) * (CO2/# of Miley Cyrus fans).
It is most certainly not meaningful, not helpful, is not making any progress. It is pure nonsense.
The issue here — the reason we have spilled so much ink over this blasted “identity” nonsense that some people feel inclined to defend with silly claims that it is meaningful — is that Willis (and Wikipedia) do *not* write the Kaya equation the way it really works. Check out how Roger Pielke writes the equation to see what the real equation is in practice. It is a straight-forward, multiplication, result-producing equation. Not some silly cancel-identical-parameters-on-the-same-side-of-the-equation business.
So, Richard, let’s stop picking apart an equation that was presented wrongly and that no-one uses anyway. Willis right to laugh at such a notion, but he is laughing at an equation that doesn’t exist in practice. Nick, let’s stop trying to defend an indefensible equation on the idea that it is somehow a magical “identity” that gets to avoid the regular rules of logic and mathematical reason.
Climatereflections says “So, Richard, let’s stop picking apart an equation that was presented wrongly and that no-one uses anyway. Willis right to laugh at such a notion, but he is laughing at an equation that doesn’t exist in practice.”
It’s fun to pick it apart and contrary to your assertion, it is also on display at the world’s leading resource for casual information — Wikipedia!
http://en.wikipedia.org/wiki/Kaya_identity
It really does cancel out.
The page cites IPAT which is “I (bottles per mile) P (capita) A1 (miles driven per capita) A2 (gallons of beer per mile driven) T1 (bottles used per gallon beer) T2 (bottles out the window per bottle used).”
As you can see, IPAT does not self-cancel. What we have here is a clear-cut case of idiotic Wikipedia editing. But whoever it is, he’s not alone.
http://www.manicore.com/anglais/documentation_a/greenhouse/kaya_equation.html
As you can see, many people (including right here) think it’s great to have algebra that cancels out but somehow still has meaning. THAT is entertainment!