The Beer Identity

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:

CO2_{emissions} = Population * \frac{GDP}{Population} * \frac{Energy}{GDP} * \frac{CO2_{emissions}}{Energy}

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:

CO2_{emissions} = Population * \frac{GBP}{Population} * \frac{Energy}{GBP} * \frac{CO2_{emissions}}{Energy}

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

CO2_{emissions}*.9 = Population * \frac{GBP}{Population} * \frac{Energy}{GBP}*.9 * \frac{CO2_{emissions}}{Energy}

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.

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richardscourtney
July 13, 2014 7:23 am

Nick Stokes:
Sincere thanks for your post at July 13, 2014 at 2:52 am which is the first real attempt to answer my question instead of avoiding it.
Sadly, your attempt fails to answer each of the two parts of my question. Your post says in total

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.

“Helps or hinders” what?
I did NOT ask for a “test”, and I did not ask “how identities should be used.
I asked for a definition of “meaningful”.
The definition should provide two pieces of information; viz.
(a) What should be used as “factors” in the Kaya identity?
And
(b) What should not be used as “factors” in the Kaya identity?
Your “recursive procedure” does not provide a definition of “meaningful”, and it does not indicate what should and what should not be used as “factors” in the Kaya identity.
Perhaps an answer to my very basic question can be provided by some other advocate of the propaganda tool known as the Kaya identity?

Richard

Daniel G.
July 13, 2014 7:24 am

G = M/(M/G)
we would have the same nonsense arguments as we are having about Kaya.

The two forms are mathematically equivalent.

Daniel G.
July 13, 2014 7:27 am

I meant to say: “Change what ever you like and CO2 remains the same (Independently of the other terms).”

Well, that is false. If you change population, gdp will change too. So co2 doesn’t remain the same.

Bruce Cobb
July 13, 2014 7:28 am

Janice,
No, not a dumb question at all. The intent behind the “equation” was what immediately struck me, which is why I proposed (sarcastically) a “Deep Racial Purity” formula. I find the agenda of “Deep Decarbonization” to be an affront to humanity, and all life itself. Arguing about whether or not the formula means anything has been, I suppose, fun, but it has involved people arguing past one another more than anything. Frankly, it gives me a headache.

steverichards1984
July 13, 2014 7:31 am

Magic Turtle says:July 13, 2014 at 7:02 am You say the Kaya is mathematically sound.
On what basis can a formula such as A = A be sound?
Yes LHS = RHS but what is the point of such an equation when its usefulness is limited to demonstrating that LHS = RHS?
If its alleged use is to find the amount of CO2 somewhere, then it fails miserably because it always gives you whatever answer you want.
I want 2, I find 2 = 2, gosh I am right again.
How can that be mathematically sound?

steverichards1984
July 13, 2014 7:33 am

“Daniel G. says:
July 13, 2014 at 7:27 am
I meant to say: “Change what ever you like and CO2 remains the same (Independently of the other terms).”
Well, that is false. If you change population, gdp will change too. So co2 doesn’t remain the same.”
If you have identical terms in a formula, one above and one below ‘the line’ they always cancel.
So changing one will change the other leaving no change in output.
Thats maths.

Daniel G.
July 13, 2014 7:33 am

There are NO UNITS IN THE KAYA EQUATION AS THE PAPER PRESENTED IT! So how on earth you get the idea that I’m canceling units is beyond me. I am canceling VARIABLES.

“gdp/pop” represents a variable by itself. The relation between gdp and pop is much more simple than the relationship than gdp/pop and pop. Again, read the paragraph directly above the identity.
Again, the M&M’s example comes to mind again. You can do your cancelling exercise on M&M’s identity, but it doesn’t make the identity invalid.

ferdberple
July 13, 2014 7:35 am

I’ve changed my mind on the kaya identity. it is not necessarily useless. certainly in routine physics and chemistry problems the units must necessarily cancel each other for the equation to be correct. so in that sense the kaya identity is mathematically correct and may be correct.
the problem I have with the identity is that it holds true even if you include things that have nothing to do with CO2. so you cannot trust that the identity is correct. because it remains true even if you include garbage factors, so how can you be sure that the identity doesn’t already include garbage factors?
natural CO2 production is huge as compared to human CO2 production. there is an assumption that natural CO2 production is in equilibrium and it is humans alone that are responsible for the change in CO2. However, we know from the ice cores that CO2 follows temperature, so how do we know that CO2 isn’t increasing as a result of warming from the Little Ice Age, or other factors not yet identified?
this is the problem in the kaya identity. maybe it can predict CO2, maybe it cannot.

Daniel G.
July 13, 2014 7:36 am

If you have identical terms in a formula, one above and one below ‘the line’ they always cancel.
So changing one will change the other leaving no change in output.
Thats maths.

co2 = pop * (gdp/pop) * (energy/gdp) * (co2/energy)
Unfortunately, those ratios are not algebraic expressions. They can’t cancel with anything, they are variables.
If you increase pop, gdp/pop doesn’t decrease proportionally, because there will be an increase of gdp. Result: co2 doesn’t remain the same.

Daniel G.
July 13, 2014 7:38 am

so how can you be sure that the identity doesn’t already include garbage factors?

Because each factor was throughtly explained.

there is an assumption that natural CO2 production is in equilibrium and it is humans alone that are responsible for the change in CO2. However, we know from the ice cores that CO2 follows temperature, so how do we know that CO2 isn’t increasing as a result of warming from the Little Ice Age, or other factors not yet identified?

Well, where is that assumption made?

Daniel G.
July 13, 2014 7:45 am

Furthermore, with the Kaya Identity, we could drop out any or all of the factors and it would not change things a bit. But in your M&M’s example, every reducing unit (C, B, P, M) is required, or you get the wrong answer. With the Kaya Identity, we could keep but one factor (just for sake of retaining the formula) and it would be just the same. For example, with just the last factor, we could say Global CO2 = Energy * Global CO2/Energy

Bolded is (limitedly) useful, but it is lacking factors, because the energy we’re talking about specifically is the energy consumed in economic activity.
Anyway, you are wrong about the M&M’s. I can drop factors too:
M = C * (B/C) * (P/B) * (M/P)
or
M = P * (M/P)
or
M = C * (M/C)

Daniel G.
July 13, 2014 7:48 am

Moreover, the CO2/energy also has an effect on GDP – the “alternative energies” reduce GDP growth and in the extreme even reduce population through destruction of economic activity, fuel poverty, etc. Ya know, when you are an elite who knows best for the great unwashed, these aspects are undescoverable to them.

The Kaya Identity doesn’t rule out such relationships. Again, this is not what Willis is talking about.

Daniel G.
July 13, 2014 7:51 am

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.

The problem is that such argument applies equally to M&M’s. But if a argument is valid and applies to both situtations, then either M&M’s and Kaya identity are both wrong, or they are both false. Which is it?

JK
July 13, 2014 7:51 am

Willis writes:
‘First, whenever a man says “other things being equal”, I have to point out that in this all-too-real world of ours, other things are never equal’
Which is obviously correct.
However, many people have found it useful for analytical purposes to consider the effect of changes with other things being equal. There’s even a fancy Latin phrase for it, ceteris paribus, that you can look up on wikipedia.
Pretty much all economists, most other social scientists (and natural scientists who cannot always control observational conditions), use this assumption repeatedly. None of them believe that in the real world other things really are equal.
Presumably (correct me if I’m wrong) your claim is not that the whole of economics is wrong, but specifically that the terms of the Kaya identity are too interdependent to make it useful.
You are quite right that ‘although the population of the US has grown steadily, at times the GDP has dropped’ and to point out that greater GDP does not inevitably lead to more energy use and that more energy use does not inevitably lead to more CO2 emissions.
In fact, the only use of the Kaya idendity is in understanding changes in exactly these variables. The idea is to get an analytical handle on what happens when one of them changes while the others remain the same, which can then be generalised to the case when they vary simultaneously.
The ‘other things equal’ assumption is not that these change, but that a base case where one or more of these do not change can be useful for analysis.
All I can say at this point is, if you don’t find the Kaya identity useful then don’t use it.
If somebody asked me to estimate what would happen to CO2 emissions IF the shale gas boom resulted in completely eliminating coal generation in favour of gas then I might start by seeing that emissions from gas generation are roughly half that of coal. I could then say that if other things stayed the same, the CO2 emissions previously generated by coal will halve and other emissions remain unchanged.
Would I be stupid enough to believe that this was some some inevitable truth about the universe? Of course not. I would find it a useful starting point for then investigating the effects of what else might happen under that scenario.
Commentators here who point out that other things are never equal will point out that my estimate will be wrong. After all, they are quite right that CO2 = CO2! They are not wrong that if other things are not the same, it could do anything.
I’m sure you will object equally strongly to the idea that we could have any understanding whatever of the effect to of a carbon tax on GDP. $10000 a ton? How can you say that will effect GDP? After all, other things are neve equal and all we can ever say is GDP = GDP!
Knock yourselves out.
PS I appreciate that Willis has had a lot of comments to answer, but I will note that all the way back on
July 12, 2014 at 10:38 am
I explained that in addition to these more interesting questions of interpretation your OP does contain a plain wrong arithmetic statement, and you haven’t responded to that.
Anyway, I’ve tried to explain myself so many times on this topic I feel diminishing returns have set in, so doubt I will return to it.

richardscourtney
July 13, 2014 7:55 am

Daniel G.
You have made many posts in both this and the other thread but you have not answered my basic question. I remind that it is:
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?
I would appreciate your provision of a clear answer to this question because everything you have written about the so-called Kaya identity is meaningless nonsense in the absence of the required clear definition.
Richard

Daniel G.
July 13, 2014 7:59 am

C=2, B=3, P=4. Lets use Mp to represent the number of M&Ms per package and Let Mp=5. We can all agree (hopefully there’s no debate 🙂 that the total number of M&Ms in all packages is:
Mt = C*B*P*Mp = 2*3*4*5 = 120. So far so good. Now let’s apply the M&M….

Basic mistake right there, 4 is the absolute number of packages. 5 is the number of M&M’s per package.
There are 20 M&M’s.
I hope you come back to see my reply, you might get embarassed.

Daniel G.
July 13, 2014 8:00 am

Can anybody provide a definition of “meaningful” which determines what should and what should not be used as “factors” in the Kaya identity?

The ratios have very clear meaning. That is what it means to meaningful.

Shawnhet
July 13, 2014 8:03 am

Willis Eschenbach says:
July 12, 2014 at 11:25 pm
“You guys are missing the point. If I burned that same gasoline to produce something useful, it would be part of our Gross Domestic Production.
But I didn’t. So the burning of that gas doesn’t show up in the GDP … and it also doesn’t show up in the Kaya Identity.”
It would show up in the GDP when you(or someone) bought the gas regardless of what was done with it. IAC, there are ways to alter the GDP without altering the CO2 emissions and vice versa **but** for the Kaya Identity to be flawed these things would have to be significant in terms of the rest of the total picture and it is pretty doubtful that they are IMO *currently*.
Respectfully, you’re much better off focussing on whether the Kaya Identity is *useful*. Personally, I doubt that it can be shown to have made a single significant prediction – which is what science is supposed to be about.
Cheers, 🙂

Daniel G.
July 13, 2014 8:03 am

Steven, you miss the point entirely. The contribution of energy to GDP is not when you buy the energy. It is when you burn it to produce something.

False, buying such energy is part of a very complex economic process.

Daniel G.
July 13, 2014 8:05 am

Respectfully, you’re much better off focussing on whether the Kaya Identity is *useful*. Personally,

Probably, but the problem is that Eschenbach et al. still maintain the “cancelling” and “i can put any variable” arguments.

Daniel G.
July 13, 2014 8:08 am

There is more to this. Indeed a history of GDP PER CAPITA GROWTH shows that GDP by the nature of its economic mechanics is not independent of population growth.

Mere population growth is mere population growth. The key here is growing use of capital, so that productivity is vastly increased. Increasing GDP per capita can increase population, but that doesn’t invalidated Kaya identity.

steverichards1984
July 13, 2014 8:11 am

Daniel G, the M&M case is not an identity. It is a poorly written formula.
1) M = C * (B / C) * (P / B) * (M / P) should be written as
2) M = NumOfCrates * (BoxesPerCrate) * (PktsPerBox) * (MperPkt)
You had C as your 1st term as the number of crates in your shipment, also in your 2nd term you had B/C implying C is boxes of crates in your shipment.
But if that were true your B/C ratio changes depending on how many crates there are in your shipment!
It is best to ensure that unique variables are named so clearly that anyone can see at a glance that your C and B/C are not related or joined in anyway whatsoever.
My equation 2) works, double any of the terms and you double the answer (correct).
It is also transposable.

Daniel G.
July 13, 2014 8:13 am

Let “instantaneous acceleration of an interplanetary probe” = A
We can now say: A = Pop * GDP/Pop * Energy/GDP * A/Energy
Clearly, we can increase the instantaneous acceleration of an interplanetary probe by increasing our standard of living! It will also increase if the population goes up.
Why is the Kaya Identity any more meaningful than this?

Well, if you manage to use that energy to make the probe accelerate, then that is not a bad identity.
Again, all the factors were explained, there isn’t a big mistery.

richardscourtney
July 13, 2014 8:13 am

Daniel G.:
At July 13, 2014 at 8:00 am your post replies to my question by saying in total

Can anybody provide a definition of “meaningful” which determines what should and what should not be used as “factors” in the Kaya identity?

The ratios have very clear meaning. That is what it means to meaningful.

OK. I accept that. So I have a few more “factors” that “have very clear meaning” so should be included in the so-called identity.
For example, ‘the heating and cooling requirements of the sleigh used by Santa Claus to transport presents from the North Pole to around the world’ is a stated “factor” that has a “very clear meaning” and, therefore, according to you a missing factor in the Kaya identity is (Santa’s travel/ sleigh temperature control CO2).
This “factor” is required but omitted and, therefore, the Kaya identity is incomplete according to your definition.
Richard

July 13, 2014 8:16 am

Daniel G. says:
July 13, 2014 at 7:27 am

“Well, that is false. If you change population, gdp will change too. So co2 doesn’t remain the same.”

Daniel G. and others, It does not matter if you use variables or replace them with values.
However, actually replacing the terms with values (numbers) will reveal much to you.
I ask you please, test the identity because you will find, that it is an identity, that is what the IPCC say it is and that is what I and many are trying hard to agree with!!
You don’t even have to write it all out for yourself, I have done it for you in my post above. I added values to the identity as specified by the IPCC.
I know what an Identity is.
I know what a formula is.
I know what an equation is.
Just slow down and take a moment to put your own values into the Identity.
Why? Because you will see that I and many others are being a little bit Socratic (Playing the fool in a very nice way!)
And no, it is not true that if “you change population, gdp will change too. So co2 doesn’t remain the same”. Changing the population does not affect Co2, if it did, it would not be an identity! I know you want it to be an equation or a formula but it is an identity!!

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