Diving into the Deeps of Decarbonization

[UPDATE: Comment from Anthony: There has been a tremendous amount of discussion and dissent on this topic, far more than I ever would have imagined. On one hand some people have said in comments that Willis has completely botched this essay, and the Kaya identity holds true, others are in agreement saying that the way the equation is written, the terms cancel and we end up with CO2=CO2. It would seem that the cancellation of terms is the sort of thing that would rate an “F” in a simple algebra test. But, I think there’s room for both views to be right. It seems true that *technically* the terms cancel, but I think the relationship, while maybe not properly technically equated, holds as well. Here is another recent essay that starts with Willis’ premise, where CO2=CO2 and expounds from there. See: What is Kaya’s equation?

Further update (modified 3AM 7/12/14): Willis has posted his response in comments, and due to my own travels, I have not been able to post it into the body of the message until several hours later, see it below. – Anthony]

Guest Post by Willis Eschenbach

pathways to deep decarbonizationAnother day, another new piece of mad garbage put out by the UN. It’s called “pathways to deep decarbonization”, all in lower case (8 Mb PDF). Their proposal is to get CO2 emissions down to zero.  I didn’t get far into it before I cracked up laughing and lost the plot.

It starts with the following definition:

Deep decarbonization requires a very significant transformation of energy systems. The ultimate objective of this transformation is to phase out fossil fuel combustion with uncontrolled CO2 emissions. Only fossil fuels in conjunction with CCS [carbon capture and storage] would remain.

But that wasn’t the funny part. That was just depressing. The funny part came later.

Now, out here in the real world the most charitable way to describe this lunacy of forcing the nations of the world to give up fossil fuels is to … to … well, now that I think about it, there is no way to describe this as anything but a pathetic joke which if implemented will cause untold economic disruption, disaster, and death.

In any case, in order to figure out how to “phase out fossil fuel combustion”, they go on to describe what they call the “principal drivers” of CO2 emissions, viz:

The simplest way to describe the deep decarbonization of energy systems is by the principal drivers of energy-related CO2 emissions—for convenience, since the focus of this chapter is on energy systems, we simply refer to them as CO2 emissions. CO2 emissions can be expressed as the product of four inputs: population, GDP [gross domestic production] per capita, energy use per unit of GDP, and CO2 emissions per unit of energy:

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

That was where I lost it …

Now, at first glance that looks kind of reasonable. I mean, emissions must go up with population and with GDP per capita, and go down with energy efficiency.

Here’s why I laughed. Lets apply the usual rules of math to that equation. We know that if a variable occurs both on the top and bottom of a fraction, we can cancel it out. Starting from the left, Population on the top cancels Population on the bottom. Then GDP on the top cancels GDP on the bottom. Then Energy on the top cancels Energy on the bottom … and we’re left with …

CO2_{emissions} = CO2_{emissions}

Pretty profound, huh? CO2 emissions are equal to CO2 emissions. Who knew?

OK, now let’s build their equation back up again. But instead of using gross domestic production (GDP), we’ll use gross beer production (GBP) instead.

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

Note that this is identical to and equally as valid as their whiz-bang equation, in that it simplifies down to the same thing: CO2 emissions = CO2 emissions.

And as a result, the clear conclusion from my analysis is that the best way to fight the evil menace of CO2 is to figure out a way to make beer using less energy …

Now, there’s a carbon reduction program I could get behind.

Best wishes to all,

w.

The Usual Request: If you disagree with someone, please quote the exact words you disagree with. This prevents misunderstandings, and lets us all understand your objection.

PS—Due to a cancelled flight, I’m stuck here in a hotel in LA on my way back from the Ninth International Climate Change Conference, which I’ll write about another time, and sitting in my hotel room wishing I were home. Not much to do but read boring UN documents … at least this one was funny.

PPS—Although it’s not mentioned in the document, their goofy equation is known as the “Kaya Identity“. Apparently, the number of innumerate people on the planet is larger than I had feared.

==============================================================

Willis Eschenbach says:

Well, yesterday was a long day. Up early to get to the airport, and this time the flight actually flew. Go deal with the rental car. Roll on home.

Then change clothes, I’d spent the night without luggage. Hang out with the gorgeous ex-fiancee and catch up. Put in a load of wash. Put the trash in the trash bin, the recyclables in their bin, the kitchen scraps in the garden waste bin. Roll all three of them up the driveway to the street. Unpack. Pack. Wash the dishes. Make coffee. Scrub the toilet.

Then when I got around to opening up my computer in the afternoon, after waking up from its normal sleep and running for about 15 minutes … it died. Dead. As in when I turned it on, It ran for about 5 seconds, and croaked …

So … that meant another 45 minute drive to the “local” Apple store. It also meant about an hour’s worth of waiting for an appointment. Then another three hours while they worked on the machine before finally getting It to run again. Net result?

It’s now 10 PM, and I’m back where I was last night … on line again. Oh, and a couple hundred bucks lighter.

Anyhow, that was how my day went. I hope Bart had more fun than I did.

Regarding the comments, I’m overjoyed that there is much discussion of the issue. My point, albeit poorly expressed given some of the comments, was that since the Beer Identity Is equally as true and valid as the Kaya Identity, it is obvious that we cannot use the Kaya Identity to “prove” anything.

So yes, the Kaya Identity is true, but trivially so. We cannot depend on it to represent the real world, and it can’t show us anything.

For example, folks upstream said that we can use the Kaya Identity to show what happens if the GDP per capita goes up by say 10%. According to the Kaya Identity, emissions will also go up by 10%.

But according to the Beer Identity, if Gross Beer Production per capita goes up by 10%, then CO2 emissions have to go up by 10% … and we know that’s not true. So clearly, neither identity can serve to establish or demonstrate anything about the real world.

What I tried to say, apparently unsuccessfully, is that by itself, the Kaya Identity cannot demonstrate or show or prove anything about the real world. If there is anythlng true about it, that truth must exist outside of the Kaya Identity. Otherwise the Beer Identity would be a valuable guide to CO2 emissions … but we know that’s not true.

Finally, l hear rumblings that Anthony shouldn’t have published this piece of mine. This totally misunderstands Anthony’s position in the game. The strength of WattsUpWithThat is not that it is always right or that it publishes only the best stuff guaranteed to be true.

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, 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 someone can point out my mistakes, it saves me endless time following a blind alley.

And indeed, there is much value in the public defenestration of some hapless piece of bad science. It is as important to know not only which ideas are wrong but exactly why they are wrong. When Anthony publishes scientific claims from the edges, 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 will 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 scientific comments. Even if Anthony had a week to analyze and dissect each piece, there’s no way that one man’s wisdom can substitute for that of the free marketplace of ideas … which is why it’s not his job. 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/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 wtthstand that test … 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 remember, 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 cards with interesting bouts … and if this post is any example, he is doing it very well.

Best to everyone,

w.

===============================================================

And a final update from Anthony:

While Willis wants to cut me some slack, and I thank him for that, I’m ultimately responsible for all the content on this website, whether I write it or not. While some people would like nothing more than to have content they deem “wrong” removed, such things generally present a catch-22, and cause more problems than they solve. Of course some people would be pleased to have WUWT disappear altogether. Some days, I’m one of them, because it would allow me to get my life back.

The value is being wrong is learning from it. If you don’t learn from it, then being wrong deserves every condemnation thrown at you. I plan on being wrong again, maybe as soon as today, though one never knows exactly when your training and experience will lead you down the wrong path. In this case I was wrong in thinking that this simple terms cancellation argument pretty much made the Kaya identity useless. I’m still unsure how useful it is, or whether its usefulness is mainly scientific or political, but rest assured I now know more than I ever thought I would know about it, and so do many of you. And there’s the value.

I thought this was relevant, and worth sharing:

“For a scientist, this is a good way to live and die, maybe the ideal way for any of us – excitedly finding we were wrong and excitedly waiting for tomorrow to come so we can start over.”  ― Norman Maclean

Thanks for your consideration – Anthony Watts

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Daniel G.
July 11, 2014 5:09 am

The problem is that the four terms that cancel are chosen because the author (Kaya?) wants to talk about those terms:
• Population
• Energy
• GDP
• CO2 emissions
Why choose to limit the discussion to these terms? The author has their reasons but what are they and do we agree with them? And why?

Because we can create meaningful ratios that completely factor out energy-related co2 emissions

Simplest illustration of the silliness of framing the argument in these terms only – there is no technological change.

It is embedded on the ratios.

Imagine a country that produces pig iron for export to generate its GDP. One day it switches to Gold (shiny, shiny gold). But it doesn’t produce as much gold so its GDP is unchanged. Suddenly its energy per GDP has reduced dramatically.
Is this what the Kaya Identity shows us?
No.
Innovation is dependent on education (GDP) and number of brains (population) and luck. The Kaya Identity excludes all other factors (such as random chance) and claims the factors they do include are independent. Innovation means that ain’t so.

If your question is whether switching from iron-exporting economy to gold-exporting one will reduce energy-related CO2 emissions, Kaya might help.

So the problem isn’t that the Kaya Identity is an Identity.
The problem is that the Kaya Identity is a means of limiting thought and debate.

You can bring as much complexity and though as you want, it doesn’t matter. The identity is scalable.

Joseph Murphy
July 11, 2014 5:10 am

Will Nelson says:
July 10, 2014 at 5:52 pm
Louis says:
July 10, 2014 at 5:13 pm
[…]
m = h * m/h.
**********************************
This is a great equation if you know m ahead of time in order back calculate the ‘m/h’ rate, but you do need to know m first. Given m and h you can solve for m. The general and more useful equation is d = r * t.
————–
Now that I have a full education on identities, it is amazing to me that people familiar with them aren’t fully aware and versed in this criticism. They contain no useful information, you need prior information in order to make them useful. And there usefullness is dependant on the accuracy of your prior information rather than the identity. I apreciate all the comments.

Daniel G.
July 11, 2014 5:11 am

Again, everyone has ignored the M&M’s example. The variables don’t cancel to one, I and other have already explained this multiple times.

Edit_XYZ
July 11, 2014 5:15 am

John West
“2) I’ve devised new methods for solving ordinary differential equations and have made a decent living from mathematical competence for 20+ years. Assume much?”
I assume nothing. I know you cannot do simple divisions because you’ve redundantly proven it in this very thread by not being able to simplify a tautology.
“3) You are a troll.”
Really?
You keep saying the kaya tautology doesn’t trivially reduce to CO2=CO2 – despite the blatant obvious to the contrary – and I’m the troll?
John West – All I’ve said here is the truth, as determied by basic mathematics and your posts from this thread. If you don’t like the image appearing when someone puts a mirror in front of you, you should refrain from posting non-sense.
“1) It’s not a real orginazation, it’s a joke. Read much?”
Is it? Well – your posts mostly read like long bad jokes. So I suppose it fits right in.

LanceB
July 11, 2014 5:18 am

For those still discussing the formula in abstract variables only, please see my post
LanceB says:
July 10, 2014 at 9:05 pm
I suspect that this is how the UN report would use the formula. My post showed that the formula is not ‘broken’ because both sides of the equation have CO2 emissions listed. I’m not arguing about the usefulness of the formula or the validity of the ratio relationships, but just showing that using numbers and a future ‘scenario’ will give an output of Total CO2 emissions as expected.

Daniel G.
July 11, 2014 5:27 am

I suspect that this is how the UN report would use the formula.

I’m not entirely sure on whether bureaucrats can do basic arithmetic. /smirk

July 11, 2014 5:47 am

This discussion separates the wheat from the chaff. If it did not reduce to a tautology, it would be wrong.
If I know my average walking speed (v or d/t) and the time I will spent walking (t), I can calculate the distance I will cover.
d = (d/t) *t

Frenchie77
July 11, 2014 5:53 am

A=B*A/B
set B=1 to x
for all x –> A doesn’t change
A=D*C/D*B/C*A/B
set B=1 to x
set C=1 to y
set D=1 to z
for all combinations of x,y,z –> A doesn’t change
Any graph that shows A changing has another undeclared variable involved

Edit_XYZ
July 11, 2014 5:59 am

Edim
“d = (d/t)*t”
This formula is not a tautology.
Why?
Because, after the trivial divisions on each side of the ‘equal’ sign are performed, we have 3 different concepts:
-on one side of ‘equal’ be have ‘d:total distance traversed in a number of hours’;
-on the other side of ‘equal’ we have ‘t: number of hours’ and ‘v: the distance traversed in an hour’. We could NOT put here any concepts (variables) we wanted and have their multiplication still equal d.
In the case of a tatutology (such as the kaya tautology), after the trivial simplificatons are done (and, instead of population, GDP and energy you can put in the tautology ANY variable and it will smplify to 1), we have the same concept (variable) – CO2 – on both sides of the ‘equal’ sign.
And a variable is always equal to itself – which is all that the kaya tautology (any tautology) tells you.

Daniel G.
July 11, 2014 6:19 am

EDit_XYZ can’t do basic division:
d = (d/t)*t = d

CLR II
July 11, 2014 6:25 am

So sad that Anthony seems to be giving some credibility to the seemingly innumerate majority here who agree with Willis that any equation whose units cancel out correctly must be invalid. None of those people would have made it through my first engineering class. I have great respect for Anthony and have appreciated the insight in many of Willis’ posts, but I’m incredibly disappointed that so many closed minds here are unwilling to admit that the Kaya Identity is valid by definition and that the way the factors (population, standard of living, energy efficiency of wealth creation and CO2 efficiency of energy production) are arranged would serve a useful purpose if one were evaluating how to impact total CO2 emissions from energy production.
Is innumeracy the problem here or are people simply blinded by their (valid) “CO2 drives catastrophic warming” skepticism? What if CO2 in the identity were replaced by an actual pollutant like SO2? Would you then be able to see that population, standard of living, energy efficiency of wealth creation and SO2 efficiency of energy production would serve as useful factors for reducing SO2. In that particular case, nearly all of the gains we’ve made have been with the SO2 efficiency term by shifting to lower-sulfur fuels and scrubbing SO2 from emissions before release, but can anyone deny that reducing the demand for energy by reducing standard of living or population could have had similar effects? I’m glad we made the right choice on that one and I don’t believe we have to make a choice on CO2, but the Kaya Identity sure gives us a handle on what the levers if we had to make that choice.
One final option for where people are going wrong. The factors in the identity are not Population, GDP, Energy production and CO2 emissions as most people seem to believe. Those could be viewed as the units of the factors. The factors are Population (in units of population), standard of living (in units of GDP per population), energy efficiency of wealth creation (in units of energy produced per GDP) and CO2 efficiency of energy production (in units of CO2 emissions per energy produced).
Since none of the other explanations such as the M&M identity, velocity or gas mileage seems to have helped, I’m not hopeful that this will help many understand their error, but it makes me sad that so many here are unable to grasp these concepts. I had thought that the skeptic community was above average in grasping abstract concepts. Sadly, it seems that either that not the case or the level of ability in the population as a whole is even lower than I thought. I suppose my hope is that many here are simply blinded by their anti-CAGW bias in the same way that we observe that the CAGW true believers are blinded by their bias. Perhaps we’re not as skeptical as we think we are.

Pete Brown
July 11, 2014 6:28 am

M Courtney says:
July 11, 2014 at 4:58 am
“The problem isn’t that the Kaya Identity is an Identity and so it reduces to CO2 = CO2.
The problem is that the four terms that cancel are chosen because the author (Kaya?) wants to talk about those terms:
• Population
• Energy
• GDP
• CO2 emissions
Why choose to limit the discussion to these terms? The author has their reasons but what are they and do we agree with them? And why?”

You’ve got the four terms not quite right. It’s Population, GDP per population, Energy efficiency of GDP, and CO2 efficiency of energy generation.
Your example of moving from iron to gold production would change the energy efficiency of GDP, so yes, the Kaya identity does account for this. Generally, technological changes would fall under energy efficiency of GDP or CO2 efficiency of energy generation. Luck, I guess, could change any of the terms, depending on what the luck is…

JJ
July 11, 2014 6:30 am

Scott Wilmot Bennett says:
Attempting to solve the formula in the head post, for any of its variables, is meaningless!

Uh, no. The fact that you can algebraically reduce an equation to identity does not prove that the equation is meaningless. It proves that the equation is an equation.
You do realize that every equation in the world can be algebraically reduced to identity, don’t you? The thing that you and Willis and the rest of the “it cancels out” crowd have discovered is not a math error in the Kaya identity. What you have discovered is the meaning of the equal sign.
Congratulations.

Edit_XYZ
July 11, 2014 6:35 am

Daniel G.
“EDit_XYZ can’t do basic division:
d = (d/t)*t = d”
So – v (d/t) and t (2 distinct concepts) equal d (another distinct concept), if multiplied*. As such, this formula tells you that d can be decomposed into t and v.
The kaya tautology tells you only that CO2 equals CO2 multiplied by 1 multiplied by 1 etc – after you do basic division and if you can do basic division, of course (Daniel G., you may not be aware, but, trivially, CO2*1*1*1…=CO2).
*BTW, you should really learn the difference between division and multiplication. In truth, you embarassed yourself long ago, but, as it’s said, ‘It’s never too late’.

Daniel G.
July 11, 2014 6:41 am

*BTW, you should really learn the difference between division and multiplication.

They are equivalent operations, the only difference is that you can’t divide by zero
So – gdp per capita, energy intensity of the economy, co2 intensity of energy, and population (4 distinct concepts) equal co2 (another distinct concept), if multiplied. As such, the Kaya identity tells you that co2 can be decomposed into those four factors.
d = (d/t)*t = d * (t/t) = d * 1
Therefore the distance equation is worthless too, because it is just d multiplied by 1.
(Edit_XYZ, you may not be aware, but, trivially, d * 1 = d)

Björn from Sweden
July 11, 2014 6:48 am

JJ, I think even Einstein would have been questioned had he presented his famous equation of relativity like this: E=(m/F)(c/G)(c/r)(F/s)Grs
It is mathematically correct you know.

Daniel G.
July 11, 2014 6:51 am

I suppose my hope is that many here are simply blinded by their anti-CAGW bias in the same way that we observe that the CAGW true believers are blinded by their bias.

No, the problem is that technical comprehension is complicated. A layman can easily jump on and criticize a paper because he doesn’t understand it. No one is gatekeeping them, but even this stuff can cause problems, imagine more complicated stuff.

Perhaps we’re not as skeptical as we think we are.

Well, we are still humans… I think Brandon Shollenberger said some smart quote about this.

Daniel G.
July 11, 2014 6:55 am

It is mathematically correct you know.

Physicists tend to use differential equations. Ratios are not that useful.

Edit_XYZ
July 11, 2014 6:58 am

Daniel G.
d = (d/t)*t = d * (t/t) = d * 1
Therefore the distance equation is worthless too, because it is just d multiplied by 1.
(Edit_XYZ, you may not be aware, but, trivially, d * 1 = d)”
Daniel G., you can’t even keep the concepts straight in a simple formula such as the above? Let me ‘baby-step’ it for you.
After all possible simplifications are done, on one part of ‘equal’ you have:
v=distance traversed in an hour – dv/tv, if you will.
t=the time (several hours)
On the other part of ‘equal’ you have:
d=total distance traversed (in those several hours) – d total, if you will.
As such, t/tv does NOT equal 1, when you try to simplify it.
And dv does NOT equal d.
Unbelievable. Your lack of mathematical competence is not just for show, is it?

July 11, 2014 7:04 am

Pete Brown says at July 11, 2014 at 6:28 am

You’ve got the four terms not quite right. It’s Population, GDP per population, Energy efficiency of GDP, and CO2 efficiency of energy generation.

Well, yes. You are correct in saying that.
But you miss the point that you are being correct in the only way that the Kaya Identity allows you to be correct. It equates GDP per population as a fixed component when it is actually made from two components and then calculated (or measured, loosely).
That just plays the game by the Kaya Identity rules and so constrains thought. Why do we accept that? It isn’t wrong but there are many other correct answers that are right too.
Luck – random events – that which was not foreseen… these all are ruled inadmissible by accepting the Kaya Identity as a legitimate identity (A Law) and not a piece of rhetoric that is only true as far as it goes.
It isn’t justifiable as true logical identity as there are unknowns and other interactions amongst the knowns that the Kaya Identity does not acknowledge.

Daniel G.
July 11, 2014 7:14 am

Edit_XYZ, you can’t even keep the concepts straight in a simple formula such as the above? Let me ‘baby-step’ it for you.
After all possible simplifications are done, on one part of ‘equal’ you have:
co2_intensity=co2 emissions for a unit of energy – co2_part/energy_part, if you will.
pop=the population (several million people)
On the other part of ‘equal’ you have:
co2=total energy-related co2 emitted (for those several people) – co2 total, if you will.
Kaya Identity:
co2 = pop * (gdp/pop) * (energy/gdp) * (co2_part/energy_part)
As such energy never cancels. BUT THAT IS A POINTLESS GAME, as gdp per capita is ultimately calculated by dividing gdp over population. But the really important variable is gdp per capita, as this represents living standards. The detail is that you do not need the total of energy-related co2 emissions to calculate the co2 intensity of energy. What matters is to plug it in the ratios.
And co2_part does NOT equal co2.
Unbelievable. Your lack of mathematical competence is not just for show, is it?

gnomish
July 11, 2014 7:18 am

it takes a witchdoctorate in numerology to cast effective spells or prophecy.
M = 10 * B/10…. check
M = 20 * B/20….mmk
M = 4000 * B/4000…. so useful
so we’re shipping 8 trucks, each carrying 500 cases with 1/2 a box in each case. splendid.
now i know just who i want running my warehouse, ubet.

Daniel G.
July 11, 2014 7:22 am

M Courtney says:

That just plays the game by the Kaya Identity rules and so constrains thought. Why do we accept that? It isn’t wrong but there are many other correct answers that are right too.

See my comments above.
M Courtney says:

Luck – random events – that which was not foreseen… these all are ruled inadmissible by accepting the Kaya Identity as a legitimate identity (A Law) and not a piece of rhetoric that is only true as far as it goes.

False. For example, if by accident, there is another nuclear meltdown, politicians will be more wary of creating more nuclear plants. This is accounted in the Kaya identity, by stating the reductions in CO2 intensity become more difficult.
M Courtney says:

It isn’t justifiable as true logical identity as there are unknowns and other interactions amongst the knowns that the Kaya Identity does not acknowledge.

Kaya Identity, while having limited usability, is logically scalable. It doesn’t have to “acknowledge” anything.

Daniel G.
July 11, 2014 7:23 am

Gnomish, please be more clear. I don’t quite get your point.

Edit_XYZ
July 11, 2014 7:42 am

Daniel G.
“After all possible simplifications are done, on one part of ‘equal’ you have:
co2_intensity=co2 emissions for a unit of energy – co2_part/energy_part, if you will.
[…]
Kaya Identity:
co2 = pop * (gdp/pop) * (energy/gdp) * (co2_part/energy_part)
[…]
But the really important variable is gdp per capita”
It comes as no surprise that you won’t keep the concepts straight with the kaya tautology – when you didn’t do so with the simple d=v*t.
Now you’ve taken the kaya tautology and replaced the CO2 and one of the energy concepts from one side of ‘equal’ with CO2_part and energy_part.
The kaya tautology does no such thing:
http://en.wikipedia.org/wiki/Kaya_identity (‘Global CO2 emissions’ from one part of ‘equal’ is ‘Global CO2 emissions’ from the other part of equal; and ‘Gross Energy Consumption’ is ‘Gross Energy Consumption’).
Tnis is merely an example of you making a poor attempt to hide your incompetence by blatant data fudging.
And the amusing part? After all possible simplifications are done on your new formula (“co2 = pop * (gdp/pop) * (energy/gdp) * (co2_part/energy_part)”), it reduces to:
CO2=energy*CO2_part/energy_part.
Your valuable gdp per capita (GDP and population) were simplified to 1.
You can’t even blatantly fudge your data correctly, Daniel G.
That said, I like how you try to model the format of your posts on mine. Imitation is the sincerest form of flattery, after all.

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