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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Crispin in Waterloo but really in Yogyakarta
July 10, 2014 5:14 am

Astley
>The UN equation deep decarbonization equation is not correct.
>The UN equation assumes a 50% drop in GDP will result in a 50% drop in CO2 emissions. That is not correct. The drop in GDP is not sustainable.
As usual you are correct.
The idea that if we stop burning ‘fossil fuels’ (right now or gradually) has two thing goings against it: first who said all are fossil fuels? I won’t explore that now. Second, if burning coal (which is finite in supply) were to be stopped now, people would burn biomass, not so? How much would be needed? We would strip the planet.
Geothermal power is possible in many places but the return on the investment is pretty poor except in certain places.
In the far future (300 years is reasonable) we may be able to use hydrothermal vents to generate a huge amount of power. There are lots of them and they are total uncontrollable so will vent for ever, we can presume. Why not take the power available?
The ‘need to decarbonize’ has a political and economic goal, and is not really about ‘decarbonization’, which everyone knows is impossible in the foreseeable future. It is a way to tax emissions, plain and simple. As there is no risk created by the emissions (none we can detect anyway) there is no problem charging people to emit. Emissions will continue, just send money. As long as the fear of emissions is sustained, people will keep handing over money.
I am in support of giving a reformed UN more money, no doubt about it, but it has to be representative of the global peoples and it has to be accountable. This means a vote in international elections, something several major powers are dead set against because it would make them accountable to a higher power. That would make prosecution of war virtually impossible. And that, in some circles, is anathema.

Jerry Henson
July 10, 2014 5:20 am

The entire CO2 question is based on fraud. The USEPA doc 430-R-10-001 states that upland soils in the US absorb 30GT of methane from the atmosphere per year. Not true. Methane rises when introduced into the atmosphere. The natural gas in topsoil (not just methane) rises from deep in the earth. The consumption of natural gas by aerobic metnanatropes, which use the hydrogen for energy, excrete the carbon, darkening the soil, is the energy which powers topsoil.
Not all the natural gas upwelling through the topsoil is consumed by the methanatropes, adding methane to the atmosphere, thence after conversion, CO2.
This makes the EPA balance of gasses in the atmosphere off by more than 30 GT that I have identified.
This statement is easy to prove. Dig a hole through any good upland topsoil into the subsoil (not in a flood plain), invert a ss bowl with a copper tube soldered to the now top, extend the tube above the topsoil, attach a closed gas valve, refill the hole using added water to reconsolidate the soil. Wait a couple of days, one day in Kansas quality topsoil, and use a sensitive hydrocarbon sensor with a vacuum pump to test. Amazon sells one which works for about $170.

Editor
July 10, 2014 5:30 am

The “new report” has been produced by IIFs (independent issue fanatics). They were required to add a disclaimer:
“Disclaimer: The Interim 2014 DDPP report was written by a group of independent experts acting in their personal capacities and who have not been nominated by their respecitice governments. Any views expressed in this report do not necessarily reflect the views of any government or organization, agency or programme of the United Nations.”
Even a brief overview shows that it was an exercise in “let’s all pretend that all things are possible” so they could claim to have “found” a solution.
Not even the authors can think that deep decarbonization on that scale is actually doable in the real physical and real political world.
It seems to be yet another of the paper products run up in advance of important climate meetings…this one for the 2014 Climate Summit to be held in New York 23 September 2014, or for Paris 2015.
Its practical value approaches zero

Pete Brown
July 10, 2014 5:34 am

richardscourtney says:
July 10, 2014 at 4:57 am
Richard.
4 questions:
All other things being equal, will CO2 emissions go up or down with each of the following:
1. increasing population?
2. increasing GDP per capita?
3. increasing energy intensity of the economy?
4. increasing carbon intensity of energy?
I’m going to say “up” on each count. That’s all that the Kaya identity is intended to illustrate.
You’re not going to get anywhere by misrepresenting the logic of what is being represented – even if you disagree with it. Nor are you going to get anywhere by using your imagination rather than what I’ve actually said in order to disagree with me.
Maybe wind your neck in a bit, please.

James
July 10, 2014 5:34 am

I think if you add a time index to each quantity and then think of this “kaya identity” as an estimation tool it will make more sense.
For example, suppose we have:
a_0 = b_0*c_0*d_0
and this is an identity.
Now lets suppose that at some future time, time =1, I think I can change the value of c. The usefulness of this “identity” I think is the following assumed approximation:
a_1 approximately equals b_0*c_1*d_0
I have no idea if this approximation is reasonable, but I think this is what is going on…
James

gnomish
July 10, 2014 5:36 am

good find, willis. it seems to have great utility as a diagnostic tool.
it sure made the innumerati shine forth blazingly but it’s beyond schadenfreude. ouch..
now i’m gonna go do something smart to rinse the stain off the brain.

Pete Brown
July 10, 2014 5:37 am

richardscourtney:
Incidentally, if you’re looking for evidence and analysis on point 2, start with Roger Pielke Jr

ferdberple
July 10, 2014 5:39 am

Momentum = mass x velocity. Cancelling out variables we get momentum = momentum.
===========
Not correct. momentum does not appear on the right hand side of the equal sign. Willis is correct. The Kaya identity is mathematically worthless. It can be used to prove anything causes CO2. You could put Al Gore’s weight in place of population, and the Kaya Identity would still be correct, proving that it is Al Gore that is driving CO2 worldwide.

Tom in Florida
July 10, 2014 5:42 am

Perhaps we non math majors would better understand the meaning if it was expressed this way:
CO2 emissions = (a) x (b) x (c) x (d)
Whereas :
(a) is population
(b) is GDP per population
(c) is energy used to create GDP
(d) is CO2 emissions from energy in (c)
First you can throw out (a) because it is already expressed in (b) so is therefore redundant
Next you can throw out (d) because that is the answer you are already looking for on the left side of the equation.
That leaves us with the amount of CO2 emissions being derived by calculating the energy used to create a certain GDP based on a certain population.
Now, population is not needed because GDP is not dependent solely on population; less people can produce a higher GDP and more people can produce a lower GDP.
So we are left with CO2 emissions are equal to the energy used to produce GDP.
Finally, that is nonsense because different types of energy production create different levels of CO2 emissions.
That’s why it is said figures lie and liars figure.

AJ
July 10, 2014 5:42 am

I agree with Jos. It’s a useful identity. As far as people reducing it down to 1=1, I’ll subtract the LHS from the RHS and get 0=0. Doesn’t sound like anything interesting could come of that, right? Except this is more or less the definition of the zero energy universe and I don’t think anyone would argue the the universe is not a useful thing. As per Stephen Hawking: “Bodies such as stars or black holes cannot just appear out of nothing. But a whole universe can.”

Pete Brown
July 10, 2014 5:44 am

richardscourtney
…or you could try thinking about it logically! If an economy consumes a certain amount of energy which produces a certain amount of CO2, and if that economy gets bigger, then all other things being equal, it will produce more CO2! QED. (GDP per head x population = the size of the economy)

ferdberple
July 10, 2014 5:51 am

eg sin(2x)=2.sin(x).cos(x)
It does not add any new information
============
wrong. the sin cos identity adds new information. it tells you the trig relationship when you double an angle.
the kaya identify however tells you absolutely nothing. Replace any of the terms with anything, and the identity still holds, proving that CO2 is caused by anything. Replace population with Al Gore’s belt size and the identity still holds, proving that it is AL Gore’s waist line driving global warming.

Joseph Murphy
July 10, 2014 5:53 am

Oh dear Lord. I expected more out of the WUWT audience. Simple math :facepalm:.
Thanks for the post Willis.
————–
problem on China and they can pay the reparations to Vanatu.
NikFromNYC says:
July 10, 2014 at 5:12 am
Because all other variables cancel out, this equation negates instead of supports the idea that any of those variables affect carbon dioxide levels!
————
Bingo

July 10, 2014 5:59 am

So here’s my Kate Identity:
CO2 emissions = Population * zork/blerk * blerk/population* energy/zork * CO2 emissions/energy
So clearly we can reduce emissions by making the zork/blerk factor very low, for which only I have the technology, and with which I would be willing to part for a mere few fractions of a trillion dollars.

ferdberple
July 10, 2014 6:01 am

That’s all that the Kaya identity is intended to illustrate.
=============
We are not discussing what it is intended to illustrate. We are discussing what it does illustrate.
Intentions are a slippery slope. The road to hell is paved with good intentions.

A Different James
July 10, 2014 6:01 am

Several commenters (but not enough, dear me not enough) have pointed out that this analysis is meaningless and incorrect. This is just going to make everyone look terrible. I don’t advocate deleting it, but a mention or something should be put at the top of the article.
To repeat what the others have said, Willis just did a dimensional analysis. Of course the dimensions must cancel to be equivalent on both sides of the equation. If I do:
miles / hr = feet / sec * sec / min * min / hr * miles/feet
I get the right hand side to cancel down to miles / hr. That doesn’t make the equation invalid. It actually makes it completely correct. But remember, that’s a dimensional analysis. The actual quantities used are whatever they are, and they have the units in the equation.
For the identity that has been erroneously mocked, emissions per unit energy is a single quantity. Someone might say “I averaged a nation’s data, and got 1 ton of CO2 for every kilojoule of energy”. Another person will bring data that says a population uses some number of kilojoules per person per year (or whatever). You can multiply those things together to get tons of CO2 per population per year. Then multiply by a population to get tons of CO2 in a year.
WUWT can do much better than this.

tttt
July 10, 2014 6:02 am

Richard,
quoting you
“You then say the equation can be used “when you now how much CO2 you use for producing unit of energy, i.e., when you have a value for the last term CO2/Energy”.
Yes, and the equation can also be used when you DON’T have that value. I explain this as follows.”
My point was, if that was not clear, that the original equation really has four terms: population, GDP produced by that population, energy intensity of GDP and carbon intensity of energy, and using those you can come up with “Total CO2 emissions”. This is also evident if you read the original source.
And it is really simple stuff, I know. It is not difficult to write identities like this. But that does not invalidate the original equation.
quoting you
“And you try to get around this saying, “You shouldn’t treat CO2 as a “separate variable” in the numerator as then you would from the start already know what the total CO2 emissions would be, and wouldn’t need to calculate anything.”
Frankly, “twaddle” is a mild word for that when the equation has CO2 as the sole parameter on one side of the equation and when the equation does not calculate anything because all its variables except CO2 cancel each other.”
If you really want to treat the equation as representing independent parameters which cancel out then please do. But, as I said, if you already know the total CO2 emissions there is nothing to calculate. The point of the equation, be it political or not, is to show how an example of different factors for CO2 emissions and discuss the effect of these factors and how they could be reduced.

JK
July 10, 2014 6:02 am

This has been explained above by others, but it seems not to have got through, so I will have another go.
If you just swap GBP for GDP you get Willis’ identity:
CO2 = pop * (GBP / pop) * ( All Energy produced in the world / GBP ) * (CO2 / All Energy produced the world)
Willis seems to think that the following line is in some way absurd:
“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”
But what is so absurd here? If the ratio All Energy produced in the world / GBP can be reduced while holding the other terms constant, then of course that would reduce emissions.
The humour seems to come from the ease of misreading Willis’ identify as:
CO2 = pop * (GBP / pop) * ( Energy produced to make beer / GBP ) * (CO2 / All Energy produced the world)
But then it would not be an identity.
We might try rescuing it with
CO2 = pop * (GBP / pop) * ( All Energy produced to make beer / GBP ) * (CO2 / All Energy produced to make beer)
But now what is that last term about? That would be the ratio of all the CO2 produced by humanity to the all energy produced to make beer.
So why is GDP any better than GBP? I would say that there is more insight to be gained from comparing total world energy production (or CO2 emissions) to GDP than to GBP.
That’s because there is an historically variable, but still intimate and profound, connection between total world GDP and energy production. They have risen hand in hand, and they will continue to do so. You cannot understand the history of one without the other. GDP does have many limitations as a summary statistic, but I believe it does capture something useful about human enterprise as a whole. The ratio (All Energy produced in the world / GDP) is a useful one.
But there is no necessary relationship between beer production and total world energy production. The ratio can move arbitrarily without telling us anything of interest.
To me Willis’ post comes across as ridiculing anyone who wants to understand the role of energy production in economics, history or development by implicitly equating any relationship they might study to the arbitrary and bizarre ratio (All Energy produced in the world / GDP).

Robert of Ottawa
July 10, 2014 6:03 am

OK I’ll play this game. Using the Kaya identity, we can cut CO2 emissions by setting Population = 0.

JK
July 10, 2014 6:05 am

Oops, the bizarre ratio in my last sentence should have been (All Energy produced in the world / GBP). The beer ratio is bizarre. The production ratio is sensible.

Mark Bofill
July 10, 2014 6:05 am

Pete Brown says:
July 10, 2014 at 5:34 am

richardscourtney says:
July 10, 2014 at 4:57 am
Richard.
4 questions:
All other things being equal, will CO2 emissions go up or down with each of the following:
1. increasing population?
2. increasing GDP per capita?
3. increasing energy intensity of the economy?
4. increasing carbon intensity of energy?
I’m going to say “up” on each count. That’s all that the Kaya identity is intended to illustrate.

Let’s plug it in and see, shall we?
Co2 emissions = (Pop * 10^6) * (GDP / (Pop * 10^6)) * (Energy / GDP) * (CO2 emissions / Energy)
So, this reduces to:
Co2 emissions = Co2 emissions.
Nope.
Look. No matter what you do to ANY of the terms, no matter what value you assign to ANY of them, the expression is valid. That’s why it reduces. CO2 emissions = CO2 emissions, there is no relationship between CO2 emissions and any of the other variables in that expression.
Let’s check this.
CO2 emissions = 5, population = 6, GDP = 7, energy = 8. then:
5 = 6 * (7/6) * (8/7) * (5/8) -> 5=5 yup.
CO2 emissions = 14, population= 33, GDP = 19, energy = 17, then:
14 = 33 * (19/33) * (17/19) * (14/17) -> 14=14 yup.

To generalize, you have not added any information to the expression:
X=X
by multiplying in and distributing around the factor 1:
X = X * (A/A) * (B/B) * (C/C)
X = A * (B/A) * (C/B) * (X/C)

Hope this helps.

ferdberple
July 10, 2014 6:08 am

The Gory details:
CO2 emissions = Al Gore’s Waistline * GDP/Al Gore’s Waistline * energy/GDP * CO2 emissions/energy

ferdberple
July 10, 2014 6:11 am

OK I’ll play this game. Using the Kaya identity, we can cut CO2 emissions by setting Population = 0.
=========
We can do the same if Gore would go on a serious diet. Once his waistline reaches zero, CO2 emissions will reach zero.

Tom O
July 10, 2014 6:15 am

” Hoser says:
July 9, 2014 at 10:31 pm
Notice how they emphasize Population. Well, would that not indicate what they believe is the biggest problem? And the solution is of course to make the biggest problem smaller. I wonder what their plan is? ”
Simple, Hoser. Turn tilable land into a source of biofuel, and reduce the total energy available when it gets cold. Net result, you starve and freeze the poor to death. What could be easier at getting rid of unwanted, “carbon generating” people?
In reference to the comment “if carbon dioxide equals carbon, then water equals oxygen” – no not really. It would be water equals hydrogen which, when you think of it, makes nuclear fusion the equivalent of “burning our water for energy.” Life on Earth requires two things for an absolute certainty – carbon dioxide and water. So what we can do is burn one to reduce the other and eliminate life on Earth as a bonus.

Bruce Cobb
July 10, 2014 6:19 am

How about “Deep Racial Purity” (DRP)?
Deep Racial Purity can be expressed as the product of four inputs: Population of Non-Whites (PN-W), Gross Domestic Births (GDB) per capita, Birth-Control Use (B-CU) per unit of GDB, and PN-W per unit of B-CU.
It works!
Ain’t math grand?
/sarc

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