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.
dp @11:02am:
“The implication is there is a wrong way to use the identity and there is, of course, but that is easily corrected. The unspoken claim is there is no right way to use the identity and that is evidence of a deep misunderstanding of math.”
The equation as cited by Willis (and some other sources) is useless. Utter, complete garbage. Not worth the electrons it occupies on my screen.
The issue is not that there is some “right” way to use the equation Willis cited. The issue is that Willis cited the wrong equation.
—–
P.S. I apologize if my prior reference was unclear. My prior comment was referring to your comment at 10:11 am, not 10:00 am.
Will @3:24pm:
You are exactly right. Good catch and I should have been more precise.
I was focusing on the M’s as that was the variable under discussion.
In fact all of the denominators must refer to an individual unit (the C, the B, and the P).
That is the way the Kaya identity actually works. Unfortunately, the way Willis wrote it, based on other sources he’s seen, is wrong. It doesn’t distinguish between the aggregate and the individual, thus everything cancels on the same side of the equation and we’re left with meaningless nonsense.
—–
BTW, much of this confusion would have been avoided if the Kaya Identity had never been called an “identity.” Lots of folks on this thread apparently assign some magical properties to this word which the word is incapable of supporting. A lot of confusion would have been avoided if the thing had been called what it really is and how it is intended to be used. When written properly, it is just an equation — a simple run-of-the-mill, multiplication equation.
The breathtaking beauty of this identity is that it is true for all values of Population, GDP, and Energy. Genius.
climatereflections says:
July 13, 2014 at 4:49 pm
In fact all of the denominators must refer to an individual unit (the C, the B, and the P).
—
Exactly! That’s a point I tried to make in several posts, although the people like ghl at July 13, 2014 at 5:00 pm continue to misunderstand.
Ian W says:
July 13, 2014 at 4:26 pm
Shawnhet says:
July 13, 2014 at 10:39 am
Ian W says:
July 13, 2014 at 10:11 am
“You are wrong of course.
Belgium used to claim that they were one of the few countries visible from space as their surplus nuclear power capacity meant that all their autoroutes/motorwegs were lit all night. So Belgium creates far less CO2 for its GDP per head than say Poland or Germany that use lots of coal. Increasing Belgium’s GDP may have no effect on its CO2 emissions whereas increasing Poland’s GDP would do so.”
Pay attention to the point, we’re discussing, please. I said that the Kaya Identity can still be valid because its Kaya-factors changea gradually and that your hypothetical was unrealistic because you can’t go to a non-carbon regime regime at the flick of a switch. You claim I am wrong by pointing to Belgium that 1. changes its KAya factors gradually and 2. has not moved to a non-carbon regime yet. Can you see the problem in your logic?
“If LNER nuclear fusion becomes reality – then the ‘identity’ fails. If GDP rises because of the banking or reinsurance markets, then the identity fails”
Once we move to a non-carbon economy, the identity will be invalid, for sure, but, at this point, this is just a hypothetical and doesn’t mean the identity doesn’t work now. Growth in the financial sector of the economy will affect the predictive value of the Kaya *but only if that growth is at a different rate than that of the “carbonised” economy and it is a large enough difference to be noticed*. Think about it.
“Only someone in PR would think this was a useful exercise. It is the level of logic that said London would be feet deep in horse manure due to the increase in population and transport requirements.”
Your arguments against it working *now* are all based on stuff that hasn’t happened yet or is probably too small to make a significant difference. I’m not sure what the PR guys would say about that 😉
James Gibbons says:
July 13, 2014 at 2:50 pm
The real Kaya Equation is here and is used to model emissions over time:
http://climatemodels.uchicago.edu/kaya/
**********************************
Thanks, James. Yeah should’ve checked myself.
James has dubbed it an ‘equation’ which I would agree with as I don’t consider it an ‘identity’ in the common definition. So if I hurt Kaya’s feelings I apologize for her sensitivity. I haven’t yet found any defenders in this thread not using bogus math however and I think my comments to that will stand sans my commentary on Kaya.
The tautology is broken at the GDP and $(1990) factors.
It does not reduce to CO2 = CO2, instead,
CO2 = GDP/yr * co2/$(1990)
Units: t/yr = $/yr * t/$
climatereflections says:
July 13, 2014 at 4:49 pm
*****************************************
I tend to accept arguments as presented run with it. The crazy M&M thing didn’t help. Thanks for being on the wrong side for the right reason.
ghl says:
July 13, 2014 at 5:00 pm
The breathtaking beauty of this identity is that it is true for all values of Population, GDP, and Energy. Genius.
********************************************
You are absolutely correct in your assessment of the IDENTITY… as given in the post.
I have found none of its defenders to be of any help mathematically (but I can’t claim to have seen all the comments).
In the paper he was reviewing in the original post here: http://wattsupwiththat.com/2014/07/09/diving-into-the-deeps-of-decarbonization/ what equation should he have parsed?
Recall in that post he began laughing when he saw the Kaya Identity, dove off the deep end, and began his spiral downward from there. The Kaya identity he cited is correct – I’m not aware of another version of it though there are many examples of equations built from it. The Kaya Identity was created by Dr. Yoichi Kaya (male) at the Keio University in Japan and co-author of a book on sustainable energy (http://unu.edu/publications/books/environment-energy-and-economy-strategies-for-sustainability.html), a lofty goal if it doesn’t destroy the world order.
The Kaya identity is a piece of garbage that will disappear as fast as when the UNs environment website took down the X number of climate refugees that will occur by X year statement.
dp @6:33pm:
Thanks, dp.
Willis is absolutely correct to laugh at the equation as listed on page 12 of that report. It is a joke, completely nonsense, utterly worthy of scorn. Same goes for Kaya’s Identity as Kaya himself outlined it. He should be forced to endure long and painful public humiliation for willful and wanton abuse of mathematics and made to recite three verses of penitent-related scripture (or similar punishment).
*However,*
The way the Kaya Identity graphic is presented in the report, and the way Kaya himself outlined it in his shorthand formula, *is not the way it is actually implemented.* Every one of the authors who have followed Kaya’s terrible example over the years by writing the equation the way Kaya did should be ashamed of themselves.
What we see in practice, once authors get past this ridiculous genuflection to Kaya’s original mistake, is that they implement the equation the way it should be: namely, on a *per unit* basis.
So, for example, in the paper Willis referred to, on page 12 — notwithstanding their absurd presentation of the equation as Willis rightly critiqued — they actually say in the prose:
“CO2 emissions can be expressed as the product of four inputs: population, GDP *per capita,* energy use *per unit of GDP,* and CO2 emissions *per unit of energy.* (Emphasis added.)
Thus, if Willis had closely read the prose text he would have seen the real equation (rather than the absurdity written elsewhere on the page) and we could have avoided much of the present discussion and the prior thread as well. As I said, I think Willis should come clean and admit that he didn’t carefully read the paper. However, there are multiple papers from multiple authors who have all put forward this abominable “identity” in the same meaningless, mindless fashion, perhaps to give a nod to Kaya. So I can understand Willis getting wrong-footed by it. But the authors in those papers in fact go on to calculate everything on a per unit basis, rather than the way the alleged “identity” was written.
The way the equation actually works in practice is perfectly fine. It is a legitimate, simple, ordinary, every-day multiplication problem. Nothing funny about it.
The climate community should be ashamed for putting the nonsense, meaningless, self-canceling, “identity” version into their papers. Willis should be ashamed for not having seen that the text in the paper didn’t comport with the graphic. Many people on this thread should be ashamed for trying desperately to justify a bogus, nonsensical “identity” that no-one in the real world uses anyway.
And I should be ashamed for spending so much time on this thread, instead of taking care of the chores around the house the Mrs. wants done. 🙂
Johan says (July 13, 2014 at 11:48 am): “Now,now, Gary, and what if one of the deer only has 3 legs ! :)”
Way ahead of you. While I have yet to count a fractional deer (presumably because 3-legged deer are soon removed by predators), I have in reserve a more complex method that includes counting legs, ears, tails, and noses, and dividing by eight. Of course a three-legged deer will still give a fraction, but the more advanced formula should produce a fraction closer to unity, at which point I’ll triumphantly round off! 🙂
Rewording it to this may help you understand your misunderstanding:
“CO2 emissions can be expressed as the product of four inputs: population, GDP *per capita,* energy use *per unit of GDP,* and CO2 emissions *per unit of energy
Which verbosely expressed as an identity is:
Population x (GDP/Population) x (Energy/GDP) x (CO2/Energy) gives us a result expressed in units of CO2 emissions (e.g., = CO2 emissions)
Curious George says:
July 12, 2014 at 10:19 am
“Let’s try a simpler case – a total CO2 generated by cars:
CO2 = (number of cars) * (CO2 per car), or
CO2 = (number of cars) * (CO2 / (number of cars))
True or false – Does it matter if the cars are driven at all? Does it respect the efficiency of car engines?”
Of course what matters is the cars being driven, how much they are driven, how many passengers they carry, their fuel efficiency, …
So formulating the above a different way,for example noting CO2 as a function of CO2/mile (an expression of fuel efficiency) and of passengers/car, gets you thinking of options for managing carbon emissions associated with passenger transport. So for example policies promoting ride sharing, carpooling, high-passenger vehicle lanes could be a policy “lever”. Or providing non-car options – mass transport, bicycling, telecommuting.
Expressing emissions in terms of CO2/mile rather than gasoline/diesel miles-per-gallon would allow electric vehicles to be compared in a more useful way to conventional internal combustion engine vehicles. If electric vehicles are recharged with electricity derived from coal, then their relative virtue in reducing emissions is not so great as if they were charged via nuclear power or hydro.
Thomas says (July 13, 2014 at 11:57 am): “Therefore, Kaya erred when he included factors for GDP and population. Those factors only make the equation less accurate. Constructing a long equation with factors that don’t make the equation more precise is not helpful. Actually it’s harmful.”
If I’m reading you right, then you see the Kaya Identity as the equivalent of a Rube Goldberg device?
http://en.wikipedia.org/wiki/Rube_Goldberg_machine
climatereflections
good summation.
This set of exchanges is an example of the differences between the mathematical (or in this case algebraic) “correctness” of a model, and its utility as an analytical tool. The Kaya Identity is “correct” within the context of its own definitions. But like any model it is a simplified and incomplete depiction of the system it represents.
The question is, does the Kaya Identity provide a useful framework for thinking about anthropogenic carbon emissions and communicating the policy trade-offs to politicians and the community as a whole? I would say “yes.” The Kaya Identity provides a simplified understanding of the connections among emissions, population, energy, and economic development in a similar way to simple energy balance models providing a simplified understanding of climate sensitivity to radiative balances.
The global policy challenge of reducing emissions (assuming we seek to do so) is this:
to “break” the Kaya Identity.
What I mean by that is so far in the post-industrial world the Kaya Identity “works.” Economic development has been largely supported by rapid growth in energy access, and that energy has been overwhelmingly derived from fossil fuels whose combustion has driven carbon dioxide emissions. Combine that coupling of economic development to fossil fuels, with population growth and we have a good overall explanation for the growth in emissions.
So, can we “decouple” population growth from economic development? We could if billions of people were willing to live in abject poverty.
Can we decouple economic development from energy access growth? We could if billions were willing to live in energy poverty.
Can we decouple growth in energy access from carbon emissions? Yes, but there are many “buts” in that “yes.” The technological challenge of developing and *scaling up* reliable, 24/7, cost-effective energy options that do not involve carbon emissions is a huge one. In my view it’s often underestimated.
So each term in the Kaya Identity highlights a set of policy challenges and options. From this perspective it is a useful “rubric” for thinking about the energy/emissions issue. The Kaya Identity is itself simplified and incorporates simplified and incomplete terms such as GDP. If we seek to cut greenhouse gas emissions there are non-CO2 GHGs such as methane and nitrous oxide whose emissions are more associated with land use than energy use, so require different policy mechanisms. This is another way in which the Kaya Identity is an incomplete description of the system.
No – in the context of this post by Willis (keep your eye on the pea) the question is did Willis misunderstand and abuse the Kaya Identity in the article he reviewed and the answer is yes, he did.
In another post a discussion of the value of the Kaya Identity and the analyses based on it can be discussed and it may be worth having. Personally I don’t think this crowd is ready for it.
dp says “Personally I don’t think this crowd is ready for it.”
Thank you for sparing the crowd!
dp @8:32pm:
“Which verbosely expressed as an identity is:
Population x (GDP/Population) x (Energy/GDP) x (CO2/Energy) gives us a result expressed in units of CO2 emissions (e.g., = CO2 emissions)”
No. Which is wrongly and confusingly expressed as you wrote it. Unless, of course, you are falling back to the idea that the Kaya Identity is an utterly useless triviality, in which case, sure, go ahead and write it however you want with whatever self-cancelling parameters you desire; knock yourself out.
On the other hand, if we want to write it properly we can write:
Total CO2 emission = Population x (GDP/Person) x (Energy/GDP Unit) x (CO2/Energy Unit).
Again, I’m not sure why there is so much knee-jerk effort on this thread to defend a silly, useless “identity” when no scientist that I am aware of actually uses it in that form anyway and when it is so easy to just write the equation in a way that makes it useful and meaningful and has the added benefit of being what scientists actually use.
Can we reach a consensus?
Total man-made CO2 emissions are a function of population, total production per head of population, energy consumed per unit of production, and CO2 emissions per unit of energy.
So to reduce CO2 emissions, at a macro level the levers you have are to reduce population, reduce GDP, increase energy efficiency, and switch to low CO2 fuels.
Johan says:
July 13, 2014 at 2:59 pm
That is complete *****, for a whole number of reasons, most of them correctly identified in many of the posts above.
You can’t use an identity like Willis supplied to calculate anything so perhaps this whole discussion is meaningless. That was why I was having so much trouble with the “equation” because it didn’t seem useful for anything. If we use the actual computer code it makes more sense. Here is the equation used to calculate energy use per year:
Energy Used per Year (W) = Population * ($/person/y) * (W*y/$)
The units cancel to Watts so from a physical units viewpoint, it is correct. When you look at the values on the right, Population * ($/person/y) is seen to be total yearly GDP and (W*y/$) is seen to be how may Watts you can buy over a year with a dollar. But it wasn’t until I started plugging numbers into this that I noticed the real problem. This assumes that the whole GDP is spent on energy, so this is clearly wrong.
Let’s take the numbers for the year 2000:
13.79 TW = 6.0E9 * 4890 ($/person/y) * 0.47 (W*y/$)
I looked up global energy use and found in 2006 it was 16 TW so 13.79 for 2000 sounds about right. I looked up global GDP for 2000 and it was $41.016 Trillion. This works out to about $6836 per person, so there appears to be some discounting of the GDP already applied, but I doubt that we spend 72% of every person’s income on energy. Trying to figure a value on energy is a little difficult because it is a mix of oil, gas, coal, electricity and third world combustibles, such as firewood. If you simply use electricity, the 2000 US retail average was 1 KWH for $0.0821 or 12.18 KWH per dollar. Divide by 8760 hours per year and you get 1.39 W*y/$ which shows where the true discount is likely to be. It looks like they did some number adjustments to GDP and energy costs to get the total energy produced to come out correctly.
Once you have total Energy Used per Year, it is easy to multiply by the CO2 tons per Watt year to get the CO2 Emissions per Year.
CO2 Emissions per Year (tons) = (Energy Used per Year) * CO2ton/(Watt*year)
Again, the physical units work and are correct but because this is based on the first equation it is also suspect.
So in summary, it is really hard to calculate actual global yearly energy use because of the strange mix of energy sources in use and we need to multiply the GDP per person by an unknown factor to get the amount the average person spends on energy.
Going into the future not only requires guesses on all these unknowns, but also makes an assumption of a somewhat exponential growth or decline factor in each of population, GDP, energy cost and the ability to sequester CO2 per energy produced.
And no, the Kaya Identity doesn’t hold because it assumes all GDP goes to energy production. But it looks nice on a PowerPoint!
Looks like Willis was right to be worried about this.
Not everyone gets it. BTW, total CO2 emission may not be what the result is. It may be rate of change of CO2 emission, depending on what it is fed.
Think of the identity’s RHS as a black box and you don’t see the constituent parts inside. All you see is the LHS. The input would be data types appropriate to produce that output type, and pragmatically, agreed to by the creator and the customer. You could write this as “USD = f(b)”. In this case USD represents a dimensionless value in US dollars as calculated by the f function of b, the black box. We’ve given it no data but we know the output will be US dollars. We don’t know if USD is dollars per hour, or a tax rate, or an absolute value point on a graph, so we can’t write it as e.g. USD/hour = f(b). When we see what parameters are in the black box that becomes known. The black box doesn’t care if the output is a rate of change or an absolute – so long as the inputs are appropriate it will provide the correct output. For that we move beyond the identity to an implementation of the identity which is an enumerated equation in which the data types are known and appropriate to produce the expected data type in the result. That is what happened in the paper Willis reviewed.
Once we’re beyond the mechanics of the math the worth of the process can be questioned and that is a healthy exercise.
Equations, formulas and identities have distinct meaning in Mathematics.
There is much confusion in this thread caused by mistaking one for another.
An identity is true for all values of the variables. For example:
2(x + y) ≡ 2x + 2y
The above statement is true for all possible values of x and y, so it is called an identity.
An identity is true for any value of the variable, but an equation is not. For example the equation:
3x + 2 = 11
is true only when x = 3, so it is an equation, but not an identity. In fact, to solve it, is to find the single value of x that makes the equation true:
3x = 11 – 2
3x = 9
x = 9 ÷ 3
x = 3
A formula links one quantity to one or more other quantities; for example,
e = mc²
Einstein’s formula can be used to determine the value of E for any given value of the variable M.
An identity is tested by substituting values for its variables.
I have tested the Kaya to prove it is an identity below.
The Kaya multiplicative identity (K) :
Global CO2 Emissions ≡ (Global Population) (Gross World Product/Global Population) (Gross Energy Consumption/Gross World Product) (Global CO2 Emissions/Gross Energy Consumption
Variables of K:
Global CO2 Emissions = c
Global Population = p
Gross World Product = g
Gross Energy Consumption = e
GIVEN
c=2, p=4, g=20, e=8 [Assign values to the variables]
FOR
K c ≡ p x (g/p) x (e/g) x (c/e)
THEN
2 ≡ 4 x (20/4) x (8/20) x (2/8)
2 ≡ 4 x 5 x 0.4 x 0.25
2 ≡ 2
THUS
LHS = 2
RHS = 2
THEREFORE
LHS of K ≡ RHS of K if c= 2, g=20, p=4, e=8.
—————————————————————
This does not prove or disprove the usefulness of the Kaya, or identities in general.
I advise everybody to actually work with the Kaya Identity by putting your own values into it (Real or otherwise).
As soon as you start working with it, you will understand what it is and what it definitely is not!
I particularly advise just changing the CO2 term on the RHS a number of times!
The IPCC version of K uses an equal “=” symbol rather than an equivalence “≡” symbol (Despite calling it the Kaya multiplicative identity*) and it is not clear if “CO2 Emissions” is the same variable as CO2 on the RHS but it makes not difference to the result:
CO2 Emissions = Population × (GDP/Population) × (Energy/GDP) × (CO2/Energy)
CO2 Emissions = ?
Population = p
GDP = g
Energy = e
CO2 = c
If
c= 2, g=20, p=4, e=8.
Then
RHS = p x (g/p) x (e/g) x (c/e) = 4 x (20/4) x (8/20) x (2/8) = 4 x 5 x 0.4 x 0.25 = 2
Therefore CO2 Emissions = 2 if c= 2, g=20, p=4, e=8.
OR
CO2 Emissions = 2 if c= 2, g=20, p=4, e=9.
CO2 Emissions = 2 if c= 2, g=20, p=4, e=765.
OR
CO2 Emissions = 2 if c= 2, g=7, p=9, e=8.
RHS = p x (g/p) x (e/g) x (c/e) = 9 x (7/9) x (8/7) x (2/8) = 9 x 0.777777777777778 x 1.142857142857143 x 0.25 = 2
ETC
CO2 Emissions = 70 if c= 70, g=20, p=4, e=8.
CO2 Emissions = 899 if c= 899, g=20, p=4, e=8.
CO2 Emissions = 2345 if c= 2345, g=20, p=4, e=8.
Try it yourself, it could change your life 😉
* http://www.grida.no/publications/other/ipcc_sr/?src=/climate/ipcc/emission/050.htm
e = mc² mean’t to read as e=mc2. The test page needs cleaning up it is too long now to load on my computer.
climatereflections:
At July 13, 2014 at 10:03 pm you say
So no scientist “actually uses it” but rearranged it is “what scientists actually use”.
Such is the kind of illogical nonsense which advocates of the Kayla identity present: they really do think that anything can mean anything so the undefined Kaya identity is valid.
The Kayla identity is an abomination: it is presented as a method to replace science with propaganda.
Richard