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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Willis Eschenbach says:
July 22, 2014 at 5:13 pm
“I doubled the population, the GDP, and the energy used. The Kaya Identity says if you do that, the “carbon efficiency of energy production” will automatically double, and the CO2 emitted will stay the same.”
Reality check here: let’s assume that we double P, GDP and E but keep the CO2/E ratio constant – what happens to CO2 emitted? What happens to CO2 if we reduce the CO2/E by 10%? What happens if instead of assuming a value for the CO2/E ratio, we *measure* it instead?
Shawnhet: “What happens if instead of assuming a value for the CO2/E ratio, we *measure* it instead?”
Then the tautology disappears and the formula can actually be calculated.
Shawnhet says: “let’s assume that we double P, GDP and E but keep the CO2/E ratio constant”
You don’t actually get to do that. Ratios have no physical existence. It is a word that describes an abstraction that exists only in your mind.
Does the apple know it is being compared to an orange? Probably not.
You decide what actual physical parameters you CAN change and the ratio might change, might not, depending on how clever or forceful you are.
I can hardly believe we are all still here arguing about it as if you or anyone else can just change, or not change “ratios”.
What is changeable are physical things. The ratios of physical things will change as soon as you put your mind to observing the ratio. Until then its like Schroedinger’s Cat, maybe it is a ratio and maybe it isn’t.
Willis, you are clearly misinterpreting the formula. As others have patiently pointed out, the authors include a definition for their formula. Why do you continue to ignore the definition they give? They are practically in the same sentence:
Your entire argument amounts to “the formula as written is misleading”. Well, sure. If you ignore the definition they give you right above it, when they introduce it to you. And if you ignore how they actually use the formula in the study. So yeah, if you take the formula completely out of context, and make up your own interpretation, then I guess you can argue that.
How about:
Does that help? Or are you going to continue to argue that your misinterpretation is the REAL Kaya identity, and keep beating up on that straw man?
JamesNV says “CO 2 emissions can be expressed as the product of four inputs: population, GDP per capita, energy use per unit of GDP, and CO 2 emissions per unit of energy: CO 2 emissions = Population x (GDP/Population) x (Energy/GDP) x (CO 2 /Energy). Your entire argument amounts to ‘the formula as written is misleading’.”
Or you could just read any of half a dozen of my comments where I write that very thing. It makes no difference how many times you re-write the exact same formula — population still cancels, GDP still cancels, energy still cancels and you must enter in the fourth term the thing you are trying to calculate.
But it is still wrong. CO2 emissions come only from CO2 emitters.
JamesNV “As others have patiently pointed out, the authors include a definition for their formula. Why do you continue to ignore the definition they give?”
How about because formulas are not supposed to need “explaining”?
If I wrote
2 = 3
and then explained it by saying “2 * infinity = infinity, but 3 * infinity is also infinity, and since infinity equals infinity (by inspection), therefore, 2 = 3”.
So in the WORDS I explain it, but you don’t NEED the explanation. The math is trivial and as a statement it is “false.”
So long as you follow the ordinary rules of algebra, the Kaya Identity is “CO2 = CO2” and it really doesn’t matter what values you choose for P, G, or E because each of them is both numerator and denominator.
If you are NOT going to follow the rules of algebra, for heaven’s sake don’t make it LOOK like algebra!
Willis Eschenbach says:
July 22, 2014 at 5:01 pm
Hi Willis
As I read how the Kaya is defined you are wrong there.
It says in AR4 WG3 chapter 1.3.1.2 “The Kaya identity (Kaya 1990) is a decomposition that expresses the level of energy related CO2 emissions as the product of four indicators: (1) carbon intensity (CO2 emissions per unit of total primary energy supply (TPES)), (2) energy intensity (TPES per unit per unit of GDP), (3) gross domestic product per capita (GDP/cap) and (4) population”
http://books.google.no/books?id=U_4ltxID60UC&pg=PA107&lpg=PA107&dq=kaya+(1990)+identity&source=bl&ots=AMAzYpI0X4&sig=ZSnfi-sQF9gIccmDgU5zNrC-cp8&hl=no&sa=X&ei=5EjPU-DnNofg4QT6-IH4Dg&ved=0CHAQ6AEwCQ#v=onepage&q=kaya%20(1990)%20identity&f=false
Those four factors are the free variables. It is therefore wrong to say that if you cut the population in half and keep all other factors unchanged the result will be unchanged. The result will be 50% reduction because the “GDP per capita” is the free variable, not the GDP.
/Jan
Jan says: “The result will be 50% reduction because the “GDP per capita” is the free variable, not the GDP. ”
That’s TWO variables, a ratio. GDP is a quantity, Population is a quantitty, GDP per capita is a fraction, a ratio of these two variables.
“It is therefore wrong to say that if you cut the population in half and keep all other factors unchanged the result will be unchanged”
What any person means by “factor” seems somewhat unpredictable and perhaps the term should be avoided or at least explained each time.
Anyway, many or most here see the variables as being the independent variables, such as P, G, E. If you change “P” you have NOT changed “G” or “E”. Since “P” is both numerator and denominator, CO2 is NOT CHANGED just because you changed “P”. Something changes — just not CO2, the thing being calculated. Instead, the ratio changes in the second term – G/2P is half of G/P.
So the correct interpretation of the FORMULA is that doubling P halves (G/P) making it (G/2P).
As a policy consideration that is exactly correct — doubling population without changing the other factors (G, E) will cut everyone’s everything in half.
The implication is clear — reducing population, especially if you reduce the non-productive parts, increases “G” for the remainder. China is pursuing that goal, Pol Pot did so rather abruptly although I doubt it was for the reason of increasing GDP per capita.
Greg Cavanagh says: July 22, 2014 at 8:21 pm
And for my first question to be outside of Roger’s or your own expertise, or the fact that neither of you even considered the questions, makes me think the entire enterprise is playing with only half the information you need.
Hi Greg,
You and I (and I suspect Dr. Pielke) agree here. The short half life of CO2 in the atmosphere makes the alarmist case even more hysterical. Consider the argument:
– CO2 increase leads to changes in the planetary energy budget over the course of a few years
– This energy budget changes will be long lasting irrespective of future CO2 emissions.
– Therefore we must implement the alarmist agenda now!
But since CO2 has a short half life, when we eventually do run out of fossil fuels or invent zero point modules (these being required for deep decarbonization), the energy budget should rapidly return to pre-industrial levels.
Willis Eschenbach described the Kaya Identity as being “trivially true”, his opinion is uncontested by Dr Pielke Jr., whose only retort in its defence was, ‘the math is simple’.
The Kaya is a simple Identity, used as a tautological instrument. To deny this, would be to deny the very heart of its utility. The algebraic cancellation and isolation of its terms is de rigueur for its use. (The “Kaya Identity” as depicted in the lecture by Dr Roger Pielke Jr. : Climate Policy for a High Energy Planet⁴)
I really wanted to understand how the Identity was actually applied, both mathematically and as a “tool” of policy discourse. To that end, I spent several days grappling with Kaya, as demonstrated by Dr Pielke Jr..
When I felt I fully understood its application, I turned to the real world, from whence the model was presumably derived.
It doesn’t take very long to see why the Kaya is being used as an instrument of policy. Examining the real world, makes it abundantly obvious, just what a stake-to-the-heart, reality is, for policy wonks!
The Kaya’s real value is in its use, as a claim to authority. It is a construct, designed to frame the debate and thus isolate and compartmentalise contradiction.
Everywhere I looked, the terms as factors of total emissions where erroneous. But how could this be, I wondered? It seemed reasonable to suppose that the factors as given in the Kaya, according to Dr Pielke Jr., are the ‘only levers available in the tool box’.
I spent some time gathering data and comparing real places. More and more I began to see, that there was a fundamental factor missing. How is it possible that emissions weren’t a direct measure of the energy intensity of GDP and the efficiency of its energy production? Clearly there was a missing factor that was making the proportionality of the Kaya’s terms aberrant. Some hidden input was providing efficiencies that oddly, reduced the size of real world terms, making their ratios, counter intuitive!
But before I reveal what it is, I will tell you why it was left out! It was censored because it exposes the fact that the relationships of the Kaya are not universally applicable (Across the countries of the world). The inclusion of this important term renders the Kaya impotent as a tool of national policy.
Truly, the phrase “one size does not fit all” could never be ascribed more applicably than to the Kaya Identity!
Land area¹, is the missing term and including it makes it very difficult to compare economies directly, and at the same time keep a straight face!
Ratios like, population density and emissions per km, would seem to be, essential aspects of any genuine and realistic analysis. Without this quantity it is irrational to compare national emissions and their individual contribution to the global total.
Singapore, with the world’s highest population density, is 11,000 times smaller than Australia. Australia’s land area represents 5% of the Earth’s surface, while its emissions are just 1% of the global total. The entirety of Europe² fits inside Australia with room to spare.
In relation to the Kaya, I find Dr Pielke’s logic and that of the paper he links to, torturously circular. The assumptions are simplistic and unproven. No attempt is made to demonstrate the validity of the relationships, or the choice of “factors” and his appeals to the authority of this tautological Identity completes the fallaciousness of its citation.
Singapore’s population is 4 times smaller than Australia, its GDP is 5 times smaller, its emissions are 3 times smaller and its total energy usage is 45 times smaller. Yet, using the ratio of Emissions/GDP³, we find that Singapore produces 1.7 times more CO2 emissions for every dollar of GDP than Australia. This isn’t a real mystery, when you realise that not all GDPs are equal, of course!
It is probably safe to say that the resources in Australia’s vast land area, something Singapore lacks, is the missing factor in this case. The numbers are also strongly at odds with the assumptions spruiked by Kaya devotees, because Singapore produces all its electricity from natural gas while Australia is coal fired!
It is also probably not a surprise, that with such a small land area, Singapore produces 3,500 times the CO2 per km compared to Australia’s tiny contribution of just 5.5 kt/km.
This is the weakness of the Kaya. It can’t be universally applied. As soon as you compare figures across countries you discover the logical fallacies inherent in it.
Australia’s ratio of, emissions to GDP, is just double that of France. If emissions per square kilometre are compared however, France emits 12 times that of Australia.
It is clear why governments around the world aren’t rushing to embrace the logic of the Kaya. They understand, that they would be ill advised to do so. The Kaya is a tool of the global minded, useless for national policy, that reveals with perfect clarity, the hubris of groupthink and the latent stupidity of collectivist ambitions.
1. Absolute values are given here, rather than “Real Land Area” which is of less relevance to the geography of climate.
2. Western Eurasia excluding Asia and Russia. The West or Western Europe.
3. This ratio is demonstrated in Dr Pielke’s lecture! The intent here, is to highlight that its “usefulness” also extends to invalidating the relationships between all four terms of the Kaya itself 😉
4. https://www.youtube.com/watch?v=QTUE5Ue6Z38
Scott Wilmot Bennett (4:31 am):
As far as I have seen, no one denies that the values of the ratios in the Kaya Identity may differ for different countries. It is not meant to be ‘universally applied’ in the sense that bothers you. It is not a scientific law with universal constants — and no one claims that it is. Rather, it is a tool to analyze how and why the values of the ratios (including, ultimately, CO2 emissions per unit of GDP or per head of population) vary across time and place, and how these values can be changed.
I’m sure that land area indeed makes a difference, but not only land area. The difference between Australia and Singapore is largely in their economic structures — how they produce their GDP, and thus how energy-intensive their economies are. Also relevant are their sources of energy, which differ in CO2 intensity. These differences are accounted for in different values of the ratios in the Kaya Identity.
Willis:
Willis, perhaps you could help us by practicing what you quite rightly preach: Please quote the exact words from some user or proponent of the Kaya Identity where they say that GDP, energy, or CO2 emissions are independent of other variables. Only when you have done so do you have a case. Otherwise you are arguing simply with your own mental construct, not with anyone who applies the Kaya Identity.
No, the consistent practice, as far as I have seen, is to say that GDP depends on population, energy use depends on GDP, and CO2 emissions depend on energy use. The ratios in the Kaya Identity express those realistic relationships.
I suppose that your real difficulty is that you can’t escape your mental construct about what the identity “ought” to mean, as opposed to how its practitioners apply it. At some point you’ll just have to acknowledge that the Kaya Identity (i) has proven useful and (ii) works as an equation. What more should one expect?
Dr. Doug says “you are attacking a straw man.”
Of course, and so are the warmists. Consider Lewandowsky’s “Fury” paper — exactly how many skeptics believe the earth is flat? We have no idea — the online survey says 11 respondents claiming to be skeptics also claim the earth is flat (which it is in most of Kansas and Nebraska).
And yet the the implication or claim is that these 11 people are representative of skeptics and/or deniers, and on that basis, the warmists attack those 11 people as if representative, when in fact warmists are at least as conspiratorial believing the Koch brothers are behind all “denial”.
But you can see right here today that some skeptics are educated, write well, think clearly and still do not subscribe to the whole kit and caboodle of anthropogenic global warming. It seems reasonable to me to want math formulas to actually *work* like math formulas.
Dr. Doug says:
July 23, 2014 at 7:57 am
I have already done so when I quoted and used the equation from the original paper. Look at the equation. It contains the following variables:
Population
GDP
Energy Uses
CO2 emissions
If you cannot see that those are independent variables, I fear I cannot help you.
However, the ratios (per capita GDP, energy intensity of economy, carbon intensity of energy consumption) are clearly NOT independent, as the independent variables appear in more than one of them.
w.
John Moore says:
July 22, 2014 at 6:37 pm
Thanks for that, John. I see nothing in there that I’d disagree with.
My difficulty with the Kaya Identity is that we don’t learn anything from it. It can’t prove or establish anything about the real world, because you can replace any given value (say GDP) with another given value (say Gross National Product or Total Goods Produced) and it is still an identity.
In general, IF we imagine that CO2 is a problem (which I don’t), there is only one ratio of interest. This is how much carbon we produce for every unit of GDP. We’re not gonna cut the population in half. Nor do we want to cut the GDP in half. That leaves only the question of how much CO2 we produce for each unit of GDP … and for that we don’t need the Kaya Identity.
All the best,
w.
Willis:
Those of us, like yourself, who are paying intention indeed do not learn anything from it. But some subset of the population can learn something useful from this, and I think that’s its real use.
The CO2/gdp-unit is an interesting ratio. But by decomposing it we get other interesting ratios: energy use / unit of GDP and carbon emitted / unit of energy.
Those are useful things to consider. For example, there has been a lot of public discourse about each of those two ratios. “Green energy” usually means less carbon emitted / unit of energy. “Energy conservation” is about reducing energy use / unit of GDP.
Hence the ratios in the KI have been and continue to be in common usage in policy discussions and thus putting them into the KI is useful.
I submit that this rather loose, limited use of KI is what counts. Expecting precision from it doesn’t work. Teaching those who have been paying numerate attention is redundant.
John Moore says:
July 22, 2014 at 6:37 pm
This I do disagree with. For example, the most common trig identity is that
Tangent = Sine / Cosine
Since the sine of a right triangle is the length of the opposite side over the hypotenuse (O / H), and the cosine of the right triangle is the length of the adjacent side over the hypotenuse (A / H), this means that the tangent = O / A, the opposite side over the adjacent side.
This is useful because it gives us a way to calculate the tangent of an angle. But it doesn’t reduce to CO2 = CO2, as the Kaya Identity does, giving us no way to calculate the CO2 emissions.
w.
Willis, to clarify my last point:
You seem hung up on what you think the Kaya Identity “ought” to mean — specifically, that GDP, energy, and CO2 ought to be treated as independent variables.
Practitioners of the Identity instead treat the ratios as independent variables. Do you see that yet? (If not, then you need to do your homework.)
If you see this, then can you give a cogent reason why their usage is invalid? You yourself have amply demonstrated that the equation works out fine. There is nothing wrong with the algebra.
Here’s a challenge: Show that Pielke’s actual use of the Kaya Identity gives wrong or misleading results. If not, then what’s your point?
Willis, I see our posts crossed.
As I said, you need to do your homework. You are not addressing how the Kaya Identity is actually used, and you are attacking a straw man.
Willis Eschenbach says:
July 23, 2014 at 8:31 am
And what is your “original paper”?
I have not found Yoichi Kaya’s original paper from 1990 online anywhere, but anyway, the identity was known to a wider public through the usage in the IPCC reports.
The IPCC 2007 report says that: “The Kaya identity (Kaya 1990) is a decomposition that expresses the level of energy related CO2 emissions as the product of four indicators: (1) carbon intensity (CO2 emissions per unit of total primary energy supply (TPES)), (2) energy intensity (TPES per unit per unit of GDP), (3) gross domestic product per capita (GDP/cap) and (4) population”
http://books.google.no/books?id=U_4ltxID60UC&pg=PA107&lpg=PA107&dq=kaya+(1990)+identity&source=bl&ots=AMAzYpI0X4&sig=ZSnfi-sQF9gIccmDgU5zNrC-cp8&hl=no&sa=X&ei=5EjPU-DnNofg4QT6-IH4Dg&ved=0CHAQ6AEwCQ#v=onepage&q=kaya%20(1990)%20identity&f=false
/Jan
The perseveration of Willis’ silly error is oddly placed in a technical blog. The old saw that insanity is defined as repeating the same thing and expecting a different response comes to mind. It suggests ignorance of some basic mathematical constructions is far more extant than one might have thought. It is damaging to reputations when a person who regularly critiques the math and science of others persists in defending such an obvious error. Given the number of valid proper examples of the Kaya Identity at work, and the presence of interactive tools that clearly identify correct usage, the continued debate has become an embarrassment for the host site.
Michael 2,
Your last comment was a good one.
Michael 2 says:
July 23, 2014 at 7:36 am
Shawnhet says: “(Willis:) ‘In other words, despite the population doubling, and the GDP and energy used to produce the GDP doubling … the Kaya Identity says that the CO2 emissions are UNCHANGED.’ No, the Kaya identity doesn’t say that”
“Indeed it does. All terms except the fourth are null and void in the formula as usually written.”
No, you are making the same mistake Willis is. Look at it this way: this problem as phrased is a way of relating the CO2 in the non-doubled situation to the CO2 in the doubled situation.
As such, CO2(2)=XCO2(1) and you are trying to solve for X.
Using Kaya to expand the CO2 terms we get the following:
2P1*(2GDP1/2P1)*(2E1/2GDP1)*(CO2(2)/2E1)=X*P1*(GDP1/P1)*(E1/GDP1)*(CO2(1)/E1)
which reduces back to
CO2(2)=XCO2(1)
In other words, **without assuming something*,Kaya doesn’t tell us anything about how much CO2 is going to increase when energy, population and GDP double – the question is *what assumptions* make the most sense for the real world.
Willis assumes that X is 1 – that it is impossible for CO2 to vary under any circumstances, ever which is pretty unrealistic in my opinion. Another more plausible assumption is the CO2/E stays constant(and this pretty closely matches our observations of countries over time). I must admit that this is a tricky notion – I missed the fact that I was making an assumption (that CO2/E stays constant) in my first response to Willis in this question.
No one has to make the assumption that CO2/E stays constant necessarily but the one that Willis and you are making is not at all realistic. No matter how many times you do Kaya, you will never be able to prove that X=1 (or any other number). If you think you’ve proven that, respectfully, that’s just because you’ve done the math wrong 😉
Cheers, 🙂
Michael 2 says:
July 23, 2014 at 9:32 am
Michael 2, see the definition quoted from IPCC in my post 9:11 am
The ratios are the free variables, not GDP. And for clarity, there shall be “per capita” in the denominator, not population
By your logic one cannot consider the speed of a car in miles per hour as one free variable chosen by the driver. It is two variables; the miles and the hours. Try that to the police if you get a speed ticket.
/Jan
Jan says “By your logic one cannot consider the speed of a car in miles per hour as one free variable chosen by the driver. It is two variables; the miles and the hours. Try that to the police if you get a speed ticket.”
You have it exactly backwards. By my logic the speed of a car IS a specific independent variable. At any moment it has the single quantity “speed” and it can be measured and you don’t actually need time. Limit t ->0 for ds/dt.
It can be *expressed* as distance-traveled over time to establish the meaning of the measure but the “meaning of the measure” is NOT THE MEASURE.
A speedometer is measuring the magnetic force caused by a spinning magnet inducing electrical current in a spring loaded rotating metal plate. This force is more or less continuous and works against the spring moving the needle.
It doesn’t need to wait an hour to see how far you went.
So it is with Kaya Identity. You are substituting the “meaning of the measure” instead of providing the measures.
Jan “The ratios are the free variables, not GDP. And for clarity, there shall be ‘per capita’ in the denominator, not population”
I don’t accept that. The fraction “GDP/Population” results in a single value whose unit is “GDP per Capita”. But you could arrive at that value other ways, including by fiat or specification. (After all, GDP is already a specification).
The second term OUGHT to be a single variable “GDP per capita” independently measured or calculated or even assumed. Then its factors won’t cancel. None of the terms should be expressed as fractions because it means you don’t know what they are independantly of the other terms.
Is anything measured? Population is measured. The rest of Kaya is a daisy chain of fractions, extremely elegant in its cleverness — no need to measure anything, everything is stated in terms of something else.
That was strange. I posted a URL to YouTube and it actually embedded it. I had no idea WordPress worked this way! I’m not sure that’s useful.
Willis Eschenbach says July 22, 2014 at 3:18 pm
This means, of course, that the Kaya Identity cannot add to our knowledge of what is going on. It is true, no question about that … but it is trivially true. It is certainly instructive, as you point out, to look at the individual factors. But the KI as a whole just leads to meaningless conclusions, like the idea that emissions won’t change if we double the population, the GDP, and the energy needed to produce that GDP.
—
i would say that if it is “instructive to look…at the individual factors” then it is adding to someone’s knowledge of what is going on – altho that target audience will typically not include those of us who are challenging the co2 paradigm
while it’s initially baffling that all quantities reduce to CO2 = CO2 – Kaya isn’t meant to be used in that way – it is meant to be used unfolded where the factors can be seen – and interestingly – that’s when the correct co2(n) value can be seen – Kaya can be said to exist in a subset of math – to call it invalid because it doesn’t follow tradition and show us CO2(n) when reduced might be analogous to calling Finite Mathematics invalid cuz it doesn’t use all the numbers
—
Kaya works cuz the variables aren’t independent of each other – earlier i had called them “cherry picked” – but that isn’t correct – they were chosen because of their real-world relationship in the production of man-made CO2 emissions – sure they’re crude choices – i doubt changes in population or gdp will produce the precise changes in CO2 that Kaya says – and other factors might be defined to make a better Kaya (see Scott Bennett’s July 23 post) – hopefully the people using Kaya are aware of that
Kaya may not be the best way to accomplish what the users want – but to find one requires fresh ideas – not just criticism
—
i’m not here to convert Willis – he’s intelligent and will see the light in time – or i may see the light and recant – but right now – i’m (somewhat) confident in my perception of the Kaya Identity – and that clarification is all i wanted out of this
–john eyon
Michael 2 says:
July 23, 2014 at 10:03 am
Shawnhet says: “let’s assume that we double P, GDP and E but keep the CO2/E ratio constant”
“You don’t actually get to do that. Ratios have no physical existence. It is a word that describes an abstraction that exists only in your mind.”
Oh, come on. This is a perfectly reasonable assumption that reflects a physical reality (that we are only imperfectly good at getting energy using minimal carbon). OTOH, your assumption is that someone who buys their first car (and increases GDP doing so) can’t possibly increase CO2 emissions by driving it.
Michael 2 says:
July 23, 2014 at 10:21 am
“Well then just make it a constant and all this hullabaloo goes away. :-)”
This makes no sense.
Did you read my 9:42 am post?
I showed using *math* how you have to assume (or measure) *something* to calculate the change in CO2 per Kaya. I *assume* that CO2/E is constant because I think that this is a reasonable assumption. Whether it turns out to be a reasonable assumption will depend on later testing. You think it is more reasonable to “make” CO2 itself constant than the ratio of CO2/E but it quite plainly isn’t for any real world situation you would claim to name.
here are environmentals who want to add “economic system” to the Kaya Identity – http://dailycaller.com/2014/07/23/130-environmental-groups-call-for-an-end-to-capitalism/
oops – i should have added a smiley to my last post since Kaya was never mentioned
dp says:July 23, 2014 at 9:13 am the continued debate has become an embarrassment for the host site.
I’m not sure where Willis’s head is. Michael2 has admitted in a couple of comments he understands this is a straw man. I think it is just those two who insist on talking about the beer identity and not Kaya. I wish the host would close this thread. I keep tracking it because I am embarrassed for WUWT.
Michael 2 says:
July 23, 2014 at 10:45 am
The fact that you can make a mechanical device to show the speed does not change the principles. The speed is the ratio of distance divided on time. Instantaneous speed is the derivative of position with respect to time. Average speed is the distance covered divided on time used over a time period.
Similar to that can any of the ratios in the Kaya be defined for both instantaneous and average values. You can for example define instantaneous energy efficiency as the partial derivative of energy used with respect to GDP, and average energy intensity as average energy use divided on a chosen amount of GDP. We have of cause no mechanical tool that show instantaneous energy efficiency, but that does not change the principle.
Why can’t you just see how the IPPC, as I quoted above, explain which the free variables are? That is how the Kaya is used in the scientific community. You are insisting that the Kaya identity is something other than the creator has defined it to be.
/Jan
Jan Kjetil Andersen: “The fact that you can make a mechanical device to show the speed does not change the principles.”
Actually it does. The mechanical device has no concept of either time or distance, only rotational velocity which maps to speed a whole lot better than your odometer and stopwatch.
Your definition cannot follow the limit of t down to zero but speed does not cease to exist at dt = 0.
Consider a cartesian graph with a simple line Y = X. The slope is usually defined as dy/dx but what happens when dx =0? Algebra fails at this point. Calculus steps in and the differential is simply “1”. It can handle dt=0 just fine and you can calculate the slope of a POINT on that line! You cannot do that in algebra, but you CAN in calculus, because the line doesn’t lose slope just because dt = 0.
So it is with speed. Speed is simply the slope of that line at some point on X. It requires no dt, but it does require knowing the function by which it came to exist.
Jan says: “You are insisting that the Kaya identity is something other than the creator has defined it to be.”
There is no insistence. You are free to think of it as anything you wish. I am as free to do likewise. It looks like algebra therefore it is. The attention this is getting puts before thousands, maybe millions of people a thing that looks like algebra and a few dozen people say “No, it’s not algebra” but won’t change it. That’s pride. Take a duck, call it a swan, and insist the whole world calls it a swan. Who is really doing the “insisting” here?
This should have been written as a *function* (IMO).