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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Johnny
July 9, 2014 10:30 pm

Orwellian

Hoser
July 9, 2014 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?

July 9, 2014 10:33 pm

Too funny. The UN and the eco-freaks are gripped by madness. Decarbonization is impossible unless we are prepared to forego air transport and international trade of any kind, to say nothing of modern economies. And for what? To solve a non-existent problem!

4 eyes
July 9, 2014 10:39 pm

Their equation is OK. So is yours Willis but yours will only work out the amount of CO2 emitted from producing beer. The GDP variable is meant to include everything that can possible produce CO2 including beer.
It could be written :
CO2 emissiions = Sum of [CO2 emissions for beer + CO2 emissions for transport + CO2 emissions for growing food + CO2 emissions for everything else]
anf if the equation doesn’t show CO2 emissions = CO2 emissions i.e. the same units then there is a problem

Geoffrey
July 9, 2014 10:39 pm

If carbon dioxide is ‘carbon’ then that makes water ‘oxygen’.

July 9, 2014 10:40 pm

Ask Holdren.

Travis Casey
July 9, 2014 10:43 pm

Nobody ever mentions all the CO2 in beer and soft drinks. There are other example of course. It’s worse than we thought.

4 eyes
July 9, 2014 10:44 pm

I do think the UN’s target is laughable. Maybe in 300 years or so zero CO2 emissions will be achievable butI still don’t understand why they want zero CO2 emissions.

Joe Prins
July 9, 2014 10:45 pm

Now that is, sadly, funny.lol

JPeden
July 9, 2014 10:52 pm

Nice, ye olde math move to see if you’re going to end up with the units you want to end up with.

bobl
July 9, 2014 10:54 pm

Of course if we take Willis’s final equation and divide though by CO2 emissions we of couse get the very useful identity of
1=1
I hear the sounds of millions of heads shaken in disbelief all over the planet.

Niff
July 9, 2014 10:57 pm

I am pretty sure it was Einstein who said ‘everything should be made as simple as possible, but not simpler”. He was referring to reduction of mathematical formalae, but the UN demonstrates its mindset…WE are all ‘population’ and we are the evil doers that need to be ‘reduced’.
The sooner these clowns are de-funded and gone…the better.

Mooloo
July 9, 2014 10:58 pm

The point of equations is that one side equals the other. That’s what an equals sign means.
Momentum = mass x velocity. Cancelling out variables we get momentum = momentum. As we should.
The point of the Kaya Identity (Identity, as in being the same thing) is that it allows us to figure out what effect a 10% growth in population will have, all other things being equal. And how much energy efficiency we would need to cancel out a given GDP growth.
It’s no use in using it in relation to a zero carbon future, of course, since only by getting CO2 emissions per unit of energy equal to zero can we get CO2 emissions down to zero, which is rather obvious. It’s a tool used by those who actually want to rationally look at reducing carbon emissions without ruining the economy. And it shows it is more or less impossible with modern (and foreseeable) technology.

Kevin Schurig
July 9, 2014 11:03 pm

Just when you thought a group couldn’t get any dumber…. I want to know many tax dollars(or whatever currency was used) went into developing this charlie foxtrot of a formula.

david gould
July 9, 2014 11:09 pm

Willis,
sin/cos = tan, because sin = opp/hyp, cos = adj/hyp and tan = opp/adj
You could say that sin/cos = tan is simply an equation showiing that tan is equal to tan. And you would be right – that is what the ‘equals’ sign means, in reality. But the fact that sin/cos = tan is still useful; in fact, the reason it is useful is that tan indeed equals tan.
By the way, I am pretty near to conceding our bet on Arctic sea ice. I do not think that there is any way that extent will fall to less than a million this melt season. If you need to contact me with collection details, you can do so through
davidchegould
@bigpond
.com
(I have line separated the address in an attempt to foil spammers)
David

Thomas
July 9, 2014 11:13 pm

Well done Willis.
An old friend once told me that civilization was invented to make beer. Think about it, you can grow gain to feed people on small plots of land but to grow enough grain to make beer … well that takes organization.

John Law
July 9, 2014 11:15 pm

There are ways of very effective population reduction, requiring only “Jackboots and Thugs”. We had a dry run in the 1930’s/ 1940’s. The plan just needs dusting off and suitable groups identified for the first tranches. We just need an assessment of which ethnic groups are most carbon intensive (or who we don’t particularly like).
It really is difficult to distinguish modern ecoloons from fascists!

AntonyIndia
July 9, 2014 11:36 pm

Another Devious aspect from this report:
Page 21 of the SDNS report: “(5.2.2) Levels of per capita emissions by 2050 as a bench mark, not as a target”.
Page 28 of the report (figure 6.3):
GtCO2….2010….2050
India……….2……… 4
China……. 7……… 5
India gets screwed through fantasy figures from 2050 while China can get away with CO2 “murder”. Real numbers – 2010 – do not count.

Peter Sable
July 9, 2014 11:39 pm

as many have pointed out, the equation is wrong if the units aren’t the same on both side of the equation…this is how I verify all sorts of equations starting with analytical chemistry to name-an-engineering field. (matching units on either side of the equals sign are another “necessary but not sufficient” type of condition for equations).
I’ve caught many an engineering mistake by verifying the units are the same on both sides.
Willis you are chasing the wrong thing here…

July 9, 2014 11:49 pm

The whole UN / Bankster “Environmental” drive is a depopulation project, plain & simple, & the motivation is not sustainability, it’s control.
Google the Georgia Guidestones : carved in 8 languages, both sides of 4 huge granite standing stones is the prime object : “Maintain the Earth’s population under 500 million”
These stones, 110 tons, including a capstone, are precisely aligned with the heavens, & were erected in the 80s & paid for by “A Christian”, in cash. They are the 10 commandments of The New World Order.
Simple maths 500 million remaining from a present population of ~7 billion = do away with 13 out of 14 of us.
& they’ve a fair good start. Get hold of a copy of Michael Crichton’s best seller ‘State of Fear’, dealing with the start of the global warming scam. Page 579 of 717 ( in my paperback edition ) he deals with the banning of DDT. June 1972 Ruckelshaus, new head of the EPA, banned DDT as carcinogenic. It wasn’t. Extensive tests had been done, people had ate it for 2 years, for the Sweeny Commission, which had reported DDT as safe 2 months previously, April 1972.
Ruckelshaus never bothered to read the Sweeny report.
Since the DDT ban, deaths from malaria shot up from ~50,000 pa to ~ 2 million pa. That’s ~ 80 million deaths, mostly children in the third world, more than Hitler killed, more than Mao & Stalin.
Ironically, DDT was never officially banned. Third World leaders were told, “keep ordering DDT, you’ll get no more foreign aid” Foreign aid is bribery to foreign “leaders” to allow the slaughter of their own people, & it works the exact same way here in the UK.
Crichton references Wildavsky, Aaron: But is it True? A Citizen’s Guide to Environmental Health & Safety Issues. Cambridge : Harvard University Press, 1994 (or 95)
25 pages on DDT, with sections on Alar, Love Canal, the ozone hole, global warming & acid rain.
“Environmentalism” is for genocide.

Jerry
July 9, 2014 11:54 pm

Seriously Peter, you’ve never simplified an equation? Obviously the units are the same if CO2=CO2 but it’s still an assnine equation.

richard verney
July 9, 2014 11:54 pm

Nature has already solved the carbon capture issue. It is called trees.
Simply create a new carbon net sink by say foresting an area of scrub land.
IF one is concerned about CO2 and wants to control its emissions, we can continue to use fossil fuels provided that we at rthe same time create new carbon sinks.
Obviously switching from coal to gas would be sensible as can be seen from the US, which is the only developed country that has managed a ‘worthwhile’ reduction in CO2 emissions brought about its exploitation of its shale gas reserves and switching energy production away from coal to the newly sourced gas.
Presently the drive towards renewables has resulted in all but no reduction in CO2 emissions, due to the intermittent nature of renewables, and the need for conventionally powered back up which conventionally powered back up is not used at full capacity. The stop/start ramping up and ramping down of conventionally powered back up generators, creates nearly as much CO2 emissions as would have been the case had these conventional powered back up generators not been used as back up, but instead been used for base load (without any renewable energy involvement)..

phaedo
July 9, 2014 11:56 pm

On the Wikipedia page about the Kaya Identity is a link to an online simulation here
http://climatemodels.uchicago.edu/kaya/
and from there is a link providing an overview and source code for the simulation here http://climatemodels.uchicago.edu/kaya/kaya.doc.html
Might give an insight into how it is intended to work.
The other thing is its an identity, http://en.wikipedia.org/wiki/Identity_(mathematics)
which means you get the same result no matter what values are entered. Sounds like a certain hockey stick.

Matt
July 10, 2014 12:07 am

” Geoffrey says:
July 9, 2014 at 10:39 pm
If carbon dioxide is ‘carbon’ then that makes water ‘oxygen’.”
Oh dear… you had a 50:50 chance – and f*ed it up.
If carbon dioxide is carbon, that would make water hydrogen by that logic.

SAMURAI
July 10, 2014 12:15 am

Good One Willis!
Algebra can be so enlightening!
30 Gigatons = 30 Gigatons…. Oh, the humanity!
A=A… How much more profound can you get!
Why do people still take the UN seriously?

Mick
July 10, 2014 12:18 am

Er Matt, Co2, 2 parts oxygen to 1 part CARBON, H2o, 2 parts hydrogen to 1 part OXYGEN

BuckIV
July 10, 2014 12:19 am

Where do the volcanoes and forest fires fit in the equation?

Jos.
July 10, 2014 12:30 am

This is an “identity, an equation that holds by definition and is always true. I don’t think it is fair to ridicule it. Identities are widely used in economics and econometrics and actually quite useful, like for analyzing economical data.
The Kaya Identity is commonly used in climate/energy economics (just ask Roger Pielke jr.) for analysis purposes. The reason is that the expressions on the right hand side are well known and widely used economic indicators: population, economic growth (= GDP/population), energy efficiency of your economy (energy/GDP), and emissions per unit of energy produced (emissions/energy)
So, based on the identity, possibilities to reduce CO2 emissions could be achieved by reducing population, reduce economic growth, increase energy efficiency or decrease the amount of CO2 emissions per unit of energy produced.
The first one, reduce population, is simply a No-No, in particular if one wants to achieve drastic emission reductions. By the way, by way of the Kaya Identity, China has argued that its one-child policy has thereby helped reducing CO2 emissions.
The second one – reduce economic output/growth – is in a democratic society very unlikely to be achievable, as those who propose it simply will be voted out of office: few people are willing to drastically reduce their welfare and prosperity. It is what Roger Pielke jr calls the Iron Law of Climate Policy.
The third one – increase energy use efficiency – has some merits but there are clear (physical) limits to what can be achieved by more efficient energy use.
Which leaves the fourth one – which is the so-called decarbonization – that is to reduce the amount of emission per unit of energy production. And so “everybody” is looking for ways to decarbonize, for example by “renewable” energy like wind and solar etc., or by capturing and storing the emissions.
In terms of analyzing data, if I recall correctly, Roger Pielke jr once discussed what countries had been able to decarbonize their economies faster than the global average over the last 35 years or so. The global economy has been decarbonizing “naturally” via economic growth (more efficient use of energy can be an advantage over your competitors). He mentioned that only the UK, Ireland, France, Sweden and Belgium had been able to decarbonize their economies faster than the global average since the 1970s or so.
http://thebreakthrough.org/archive/which_nations_have_reduced_car
Why? Well, the UK and Ireland had gotten rid of most of their energy intensive energy (de-industrialization), France had massively switched to nuclear, Sweden had switched to nuclear as well as some renewables (hydro and biomass), in part because there are few Sweeds but lots of water and trees in Sweden. Belgium did both (get rid of energy intensive industry and switch to more nuclear). Note that biomass can only be considered CO2 emission neutral in the long run, as that is when the emitted CO2 can be stored, whereas on the short run it actually increases CO2 emissions as the energy density of biomass is much less than that of fossil fuels.
Surprisingly enough, both Denmark and Germany did not decarbonize much faster than the global average, despite massive subsidies for solar and wind.
So, what does that tell us about the practical sides of decarbonizing your economy? Well, exporting your energy intensive industry elsewhere does not really solve the problem. Stuff still has to be made, so it simply moves your problem elsewhere (sort of a book-keeping thick). Renewables may help a little bit but apparently only under certain conditions, and there are only few countries where these conditions are met. Which leaves only nuclear as a “proven” technology to decarbonize your economy.

In summary, the Kaya Identity helps putting things in perspective.
Lots and lots more has been said and written about this, a Google search will get you plenty of hits and documents.

Another Ian
July 10, 2014 12:36 am

Then there is this find of Hilary’s
“The UN Charter does not specifically mention the environment or sustainable development. However, there has been increased activity in the area over the years.”
More at
http://hro001.wordpress.com/2014/07/06/unep-sails-on-the-unchartered-waters-of-the-un/

ironargonaut
July 10, 2014 12:41 am

Momentum = mass x velocity
@mooloo here is the difference
mass = 2
vel = 2
what is momentum you have an answer correct?
now replace every variable except CO2 emissions with the value 2. Solve for CO2. Answer is 1. Do it again use 7. Answer = 1. Again using any number or combination of numbers answer =1
put 7 into first equation answer is 49.
one equation gives a useful answer one does not.

Greg Goodman
July 10, 2014 12:41 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?
===
Yes, that would seem to be what this is trying to communicate. So “deep decarbonisation” means “deep depopulation”. I assume the greens will be the first to step up to the plate and offer themselves and their children to be sacrificed for the greater good of GAIA.
Or maybe they’ll decide that they, morally and intellectually superior beings, need to stick around to make sure it all works correctly and everyone BUT them and their families needs to die first.
Let’s guess which way they play it.

Dr. Paul Mackey
July 10, 2014 12:41 am

Apparently the Kaya identity is key to working out the IPCC scenarios………

john karajas
July 10, 2014 12:41 am

India and China will pay no attention whatsoever and that is 40% of the world’s population before we consider any other countries that will pour scorn and derision on this, another strange and stupid UN idea.

SAMURAI
July 10, 2014 12:42 am

Running the numbers through UN’s elegant equation looks like this:
30 Gigatons annual CO2 emissions = (7.046 billion folks) x ($72 Trillion GDP/7.046 billion folks) x (144,000 TWH energy production/$72 trillion GDP) x (30 Gigaton annual CO2 emissions/144,000 TWH energy production)
Drum roll please….
30 gigatons = 30 gigatons….
LOL!!

ironargonaut
July 10, 2014 12:42 am

Momentum = mass x velocity
@mooloo here is the difference
mass = 2
vel = 2
what is momentum you have an answer correct?
now replace every variable except CO2 emissions with the value 2. Solve for CO2. Answer is 1. Do it again use 7. Answer = 1. Again using any number or combination of numbers answer =1
put 7 into first equation answer is 49.
one equation gives a useful answer one does not.

phaedo
July 10, 2014 12:42 am

SAMURAI says:
July 10, 2014 at 12:15 am
Why do people still take the UN seriously?
In this instance, CAGW, the UN can best be viewed as a lunatic holding a loaded gun to your head. As such it should be take very seriously. 🙂

4TimesAYear
July 10, 2014 12:43 am

They could save themselves all that nonsense if they would just realize it’s ALL carbon. Every last bit of it creates CO2, in spite of their little man-made rule that emissions from bio-fuels don’t count. They still add to the total volume of CO2. The U.N.=irrelevant

ironargonaut
July 10, 2014 12:45 am

Correction would be to say you get 1=1. Not an answer of one.

sonofametman
July 10, 2014 12:45 am

Baking and brewing were among the first recorded industries. Yeasts produce carbon dioixide. In the brave new ‘de-carbonised’ world, will yeasts have to be genetically modified to release , say, Nitrogen instead? Or will breweries and bakeries need carbon dioxide capture and storage? Oh, some breweries have that already….
More seriously, I tried reading that document. It made my head spin. They really are on a crusade. Just take a good look at the language.

John
July 10, 2014 12:56 am

I was also going to say that this is an equation commonly used in climate economic but Jos has given a much better explanation than I could.

Frank
July 10, 2014 12:58 am

Willis: Your equation (Kaya Identity) is meant to help governments REALISTICALLY evaluate opportunities to reduce carbon emission – should they wish to do so. If the equation didn’t mathematically reduce to CO2 = CO2, it wouldn’t be of any use.
Population: For the next few decades, there is little opportunity to change the number of people in a country. Most of them are already living and family size tends to change slowly. Over the longer term, population growth tends to go down with increasing GDP.
Per capita GDP: No government wants to reduce CO2 emissions by reducing the growth in per capita GDP – which is roughly equivalent to prosperity. All countries have minimum expectations for increasing per capita GDP and will include this factor in their plans.
CO2/energy is something that can be improved. For electricity (roughly 50% of CO2 emissions), one can replace coal with natural gas. Or fossil fuels with nuclear, solar, or wind. Roughly 100 nuclear plants provide about 20% of US electricity. Reality: Another 200 nuclear power plants (plus replacements) probably would handle our base demand for electricity, which accounts for perhaps 25% of current US emissions. If we want to get there in 25 years, we need to start building about 10 new plants per year. If you don’t think current designs are safe enough and you want something like thorium, how long will it be before you can start building 10 plants per year? A decade to develop the new technology and a decade of operating experience? For transportation and heating, there currently aren’t very good replacements for fossil fuels and the ones that exist will demand more electricity.
GDP/energy also is something that can be improved by energy conservation: better insulation, higher mileage vehicles, replacing incandescent light bulbs, etc. We’ve been concerned about energy conservation since the 1970’s, so this is familiar ground.
If you are a developing country whose population will increase 20% by 2050 and you want to emulate China and increase your GDP two to four fold by then, you probably won’t be signing any international agreements to restrict emissions.

Greg Goodman
July 10, 2014 1:06 am

david gould says: “sin/cos = tan, because sin = opp/hyp, cos = adj/hyp and tan = opp/adj
You could say that sin/cos = tan is simply an equation showiing that tan is equal to tan. ”
Mooloo says: “Momentum = mass x velocity. Cancelling out variables we get momentum = momentum. As we should.”
Jeezus H ! What is the matter with you bozos? If you have three DIFFERENT terms in an equation, there is NOTHING to cancel out.
If you have a total lack of understanding of even the most elementary algebra you’d be well advise to remain silent instead of making total fools of yourselves. ( Either that or apply for a job at the U.N. , you’re apparently fully qualified. )
Mooloo says: “The point of the Kaya Identity (Identity, as in being the same thing) is that it allows us to figure out what effect a 10% growth in population will have, all other things being equal. And how much energy efficiency we would need to cancel out a given GDP growth.”
No, it does not “allow” any such thing, it is useless and contains no information at all other then CO2=CO2 . If you increase GDP by 10%, it affects the top and bottom line equally and the rest of the equation stays the same. It tells you nothing.
Does the following “allow” you calculate the how the price of figs depends on population growth?
Price of figs = POPULATION * Price of figs / POPULATION
No. all it says is: Price of figs = Price of figs

DHF
July 10, 2014 1:18 am

Frightening that this document must have been through review by many people without any of them has spotted the flaws in this formula.Reading the text above it seems that it should have been something like:
CO2 emissions (Tonne/year) = Number of persons on earth (capita) * Produced value per person per year ($/capita*year)* Energy use per produced value (J/$) * CO2 emission per used unit of energy (Tonne CO2/J)
Or, with units only:
(Tonne/year) = (capita)*($/capita*year)*(J/$)*(Tonne CO/J)
Then it is still overly simplistic, but at least it is consistent with regards to units:
Theoretically, to reduce CO2 emissions you can reduce:
Number of persons on earth
Value production per person
Energy use per unit produced value (Increase the energy efficiency)
Reduce the carbon emission per produced unit of energy

Björn from Sweden
July 10, 2014 1:24 am

Now! Firstly I would like to make the argument that simplification sometimes hides where the sum comes from. If you are on prescription medication you take 4 pills per day, 2 in the morning and 2 in the afternoon. So there would be a point in not simplyfiing the text on the bottle to just say eat 4 pills/day, but instead let it say eat 2+2 pills/day. Ok that caveat is out of the way.

Here comes what I found missing in the equation, probably on purpose on UN:s part;
I believe the equation should read:
CO2 emissions = population * GDP/population * energy/GDP * CO2/energy * money/CO2
CO2 emissions = money

Which is what they all are drooling over, money.
No doubt the UN would like to see a price of 100$ per metric ton of CO2.
So the emissions are 30 Gtons/year currently.
We pay the UN in 100$ bills, robbers like 100$ bills.
Lets assume one bill is a tenth of a mm thick, that means a stack of ten 100$ amounts to 1 mm, 10 thousand 100$ is one meter, one million$.
3 million meters of 100$ bills? 3000 km? Thats something like 2000 miles I think, I use only metrics normally.
So yes it would seem that CO2=money, lots of money.

July 10, 2014 1:24 am

Oh my god I am a complete mathematics bozo and even I can see this is just dumb. If your equation can reduce to 1=1 then you are not doing anything useful, no matter how much you insist that it’s “necessary” to have your equation reduce to that. The contortions some of you are going through to try and prove that this is anything other than a completely nonsensical waste of time are incredible.

Cheshirered
July 10, 2014 1:28 am

You may think it funny, Willis, but alarmists will consider it an essential action. Look out for ‘deep decarbonisation’ to gain traction amongst all on-message media outlets very soon. It will become the next big objective. It must be ridiculed and obstructed from day one.

bobl
July 10, 2014 1:29 am

Of course if we take Willis’s final equation and divide though by CO2 emissions we of couse get the very useful identity of
1=1
I hear the sounds of millions of heads shaken in disbelief all over the planet.
Mooloo and Jos.
No the equation is absurd, it is independent of all its variables, the equation says literally 1 = 1 .

William Astley
July 10, 2014 1:34 am

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.
It is a fact that the UN and EU carbon taxing and carbon limiting policies is causing a drop in GDP and it is a fact that for small drops in GDP, carbon emissions drops.
The error in the UN equation is the drop in the GDP is not sustainable and cannot therefore be used to achieve the insane, purposeless deep decarbonization goal. If GDP trends to zero (no goods and services produced by a country and no funds to purchase critical input goods and services, such as the volatile food and energy) we starve and in cold countries freeze to death.
Well before GDP drops to zero there will be riots in our cities. The politicians will respond to the riots by stopping the insane deep decarbonization policies.
Comments:
1. Deep decarbonization would require worldwide population reduction and the banning of all air travel for tourism. That type of policy would not have public support.
2. Deep decarbonization would require the banning of the consumption of all meat (agriculture currently is directly or indirectly (due to cutting down forests to grow food to feed to animals which are then eaten and the CH4 emitted by the animals, and so on for 18% of the CO2 emissions.) The 18% of GWG due to the food industry can be reduced by a factor of three if the entire population switches to a vegan diet.

david gould
July 10, 2014 1:35 am

All identities reduce to one equals one.
The trigonometric identities – for example, the one that I discussed above, or the Pythagorean trigonometric identities – can all be reduced to the expression one equals one. They are still incredibly useful.

Robert Christopher
July 10, 2014 1:35 am

Geoffrey on July 9, 2014 at 10:39 pm
“If carbon dioxide is ‘carbon’ then that makes water ‘oxygen’.”
Or hydrogen!
And, if there were no CO2 in the atmosphere, with everyone not being able to breath out, would these Greenies still expect plants, that is, trees, flowers and food crops, to grow?

Greg Goodman
July 10, 2014 1:43 am

Frank says: “Willis: Your equation (Kaya Identity) is meant to help governments REALISTICALLY evaluate opportunities to reduce carbon emission…etc.”
Yes, I think that is what this is about. If it’s called Kaya Identity, that means both sides are not just equal but mathematically identical.
Identities do not contain any new information but may be a useful way of rearranging things, eg.
cos(2x) = 2*cos(x)*sin(x)
This is a similar 1=1 situation if you reduce it but if you have a harmonic and its derivative it may be useful to realise that the result will have twice the frequency.
Willis did not report that it was called Kaya Identity and seems to have missed to point of what an identity is.
So as Frank says, if you know population will grow and you wish to at least maintain per capital wealth, you need to look to reducing energy / GDP (as the Chinese seem to be doing) or improve CO2 footprint of power generation.
The other alternative is to look out of window and realise that for the last 17 years temps have not risen, the computer models are useless, the whole “low carbon” paradigm is huge waste of human effort and throw the whole U.N. document out of said window.

July 10, 2014 1:43 am

david gould says:
July 10, 2014 at 1:35 am
That would be great, but we’re not doing trigonometry. We’re trying to calculate how much CO2 will be produced by taking different actions – and if the equation can reduce to CO2 = CO2, it is meaningless and entirely useless for that purpose.

July 10, 2014 1:44 am

A=A, more than an identity, is a tautology. Like A= (B/C)*(A*C/B). In such a dumb children thing, the values of B and C can change all they want and nothing will change in the result. It is not the same as saying that A=D/F, which actually relates something to something different.
I did those kinds of “complications” of tautologies when I was 10, just to impress friends. I’m sure these still impress politicians and people from the Humanities, like Drake’s equation.

July 10, 2014 1:54 am

Let me clarify what I mean.
Including the same term on both sides of the equation is the problem here. sin/cos = tan is valid because you’re deriving tan from sin/cos. This equation is more equivalent to tan = a*(tan/a). You get the same result (tan = tan) but it serves no purpose, because all your other terms can be simplified out.

Jim Turner
July 10, 2014 1:57 am

I cannot follow the arguments of the various posts that seem to think this ‘Kaya identity’ is somehow useful. The equation as given is exactly as Willis said, all the terms except CO2 emissions cancel, halving or doubling any of them will make no difference. Separating the terms is false logic, of course it is possible to improve Energy per unit GDP for instance, but in doing so you must either reduce the Energy term or increase GDP (or both), and these values appear elsewhere and must also be changed, putting them in this equation is pointless.

Greg Goodman
July 10, 2014 1:59 am

ironargonaut says:
July 10, 2014 at 12:42 am
Momentum = mass x velocity
@mooloo here is the difference
===
The difference is that that is a equation which embodies a natural law which adds new information. There is nothing to cancel out and it is not 1=1. It is not an identity, It has nothing to do with article.

Greg Goodman
July 10, 2014 2:00 am

ironargonaut says:
July 10, 2014 at 12:42 am
Momentum = mass x velocity
@mooloo here is the difference
===
The difference is that that is a equation which embodies a natural law which adds new information. There is nothing to cancel out and it is not 1=1. It is not an identity, It has nothing to do with article.

July 10, 2014 2:04 am

And to think we are carbon based lifeforms that oxidise carbon for our energy.

Coke
July 10, 2014 2:08 am

Is this “Excuse for the Pause #11”? “Plant life is sequestering CO2 faster than humans are emitting it”?

July 10, 2014 2:10 am

Oh dang, I posted that on the wrong article! Mods, delete as you see fit lol

Greg Goodman
July 10, 2014 2:19 am

What Willis failed to state was that this is called the Kata Identity. That is a recognition that both sides are mathematically identical as in 1=1. He presumably did not realise what “identity” means in maths.
eg sin(2x)=2.sin(x).cos(x)
It does not add any new information but can be useful as a means of rearranging what is known.
For example if you have a harmonic variation and its derivative, it may be useful to note that adding them will produce a result with twice the frequency.

steveta_uk
July 10, 2014 2:20 am

It appears the economists and mathemeticians have a different mind set. Several people above have made the point that an “identity” is supposed to balance, but is still useful.
One commenter (mooloo) even says that despite it all balancing, it is still useful as it can be used to see what effect changing a variable will have, for example “it allows us to figure out what effect a 10% growth in population will have”.
Since it’s hard to beleive that mooloo cannot do simple sums, but can use a computer well enough to type in the comment, there’s is clearly some form of disconnect in the reasoning.
Mooloo, I assume you can see that as written, any increase or decrease in population will have absolutely no effect since the term is both above and below the line in the expression. If you don’t see what I mean, try it with real numbers – varying any term whatsoever will have no effect, and the result will always be dependant on CO2 and nothing else.
So please explain to us non-economists how the expression is supposed to be interpreted, because it clearly isn’t maths.

richardscourtney
July 10, 2014 2:31 am

Friends:
I fail to understand those who are arguing that Willis is merely presenting a unit check. I would be grateful if at least one of them were to explain their argument.
As I understand it, the true situation is succinctly illustrated by ironargonaut who wrote saying at July 10, 2014 at 12:42 am

Momentum = mass x velocity
@mooloo here is the difference
mass = 2
vel = 2
what is momentum you have an answer correct?
now replace every variable except CO2 emissions with the value 2. Solve for CO2. Answer is 1. Do it again use 7. Answer = 1. Again using any number or combination of numbers answer =1
put 7 into first equation answer is 49.
one equation gives a useful answer one does not.

{emphasis added: RSC}
However,
the ‘Momentum equation’ is the physically useful one (it says the momentum)
but
the ‘CO2 equation’ is the politically useful one (it says whatever one wants).

Richard

tttt
July 10, 2014 2:44 am

There is nothing wrong with the equation, other that it is obviously a simplification for illustration. You can use the equation 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.
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.

stephan
July 10, 2014 2:48 am

Dear Willis,
I usually like your posts, but this was silly. All you showed was that the units on both sides of the equation are equal. In elementary physics its called “dimensional analysis”, and it is first step in checking a calculation.
Cheers,
SLL

richardscourtney
July 10, 2014 2:52 am

Friends:
Immediately after my post at July 10, 2014 at 2:31 am concluded saying

the ‘CO2 equation’ is the politically useful one (it says whatever one wants).

tttt wrote a post (July 10, 2014 at 2:44 am) which demonstrates that.
The assertion by tttt is twaddle but it explains one way the ‘CO2 equation’ can be used to mislead the public, and an explanation of why the assertion is twaddle would bore most of the public.
Richard

July 10, 2014 2:55 am

Your beer formulae is wrong, because you don’t calculate CO2 . You calculate CO2 from beer production.

tttt
July 10, 2014 2:59 am

Richard, please explain where the twaddle in my assertion is, I’m interested.

Jaakko Kateenkorva
July 10, 2014 3:09 am

It’s somewhat harsh to discover that ‘Being there’ was a documentary.

Patrick
July 10, 2014 3:12 am

May have been mentioned before but, to me, this is a clear indication of UN Agenda 21. Control population through energy poverty. I have a feeling this won’t work without massive concentartion camps…oh wait…we already have one example on the border between Ethiopia and Kenya, ~2million population some of which were born there and have lived there for 20 years or more.

Bloke down the pub
July 10, 2014 3:24 am

First they came for the car users, and as I don’t use my car much I was not concerned.
Then they came for the energy users, and as I don’t use much energy it didn’t worry me.
Then they came for the flyers, and as I rarely fly I didn’t care.
Then they came for theBeer Production, Oh my God can’t someone do something to stop these people?!

Hlaford
July 10, 2014 3:29 am

IMHO the Kaya identity transforms to something entirely different if presented in a differential form with d/dt. In its common static form it is useless, and downright laughable.
Let’s see what happens when a society becomes richer over time:
– GDP/population goes up, that’s obvious
– population stagnates, and eventually goes down – that’s a tricky one as it is counter-Malthusian fact of life
– Energy/GDP is also tricky one as it depends on state of technology and energy price, where efficient technology pushes it down, but price rises it up.
– CO2 emmission/energy is also a stupid one as it relates with state of technology, and in a richer society it goes down
We are bombarded with notions that there is a Malthusian problem of overpopulation that is fuelled by affluence, which is wrong.
Real life verdict … with richer people the falling population growth trend and the rising GDP/population trend cancel each other, and CO2 emission/energy trend goes down. Total emissions go down, provided the energy price does not hinder progress.
Hence the only true factor to observe is a rising energy price trend that hinders technology advancement towards energy efficiency, enrichment of all, and natural decline in population. And decline in CO2 emissions too.

TimC
July 10, 2014 3:33 am

Willis says “Pretty profound, huh? CO2 emissions are equal to CO2 emissions. Who knew”?
Well, if (to keep it simple) A = B * C/B * A/C (as of course it does), where B, C/B and A/C are all meaningful, measurable quantities, isn’t it (at least algebraically) a fair point to say that one can reduce A by reducing any one or more of B, C/B or A/C – so long as the others don’t thereby increase disproportionately?
And, as to “the best way to fight the evil menace of CO2 is to figure out a way to make beer using less energy” are you sure that making beer with less energy (so, dare one assume, more cheaply…) wouldn’t disproportionately increase demand (and perhaps in time, population!), thereby outweighing any saving :-‘)

TinyCO2
July 10, 2014 3:37 am

I’m sorry but I do have a genuine fault in Willis’ maths. When you have Population on top and Population below, they don’t cancel each other out, they multiply 😉
The rate of multiplication is roughly inversely proportional to GDP and may go negative if the population have more fun spending their GDP than multiplying.

Greg
July 10, 2014 3:46 am

Patrick says:
July 10, 2014 at 3:12 am
May have been mentioned before but, to me, this is a clear indication of UN Agenda 21. Control population through energy poverty. I have a feeling this won’t work without massive concentartion camps…oh wait…we already have one example on the border between Ethiopia and Kenya, ~2million population some of which were born there and have lived there for 20 years or more.
====
Another one is called Palestine. Population 1.5 million.

david gould
July 10, 2014 3:49 am

steveta_uk,
Of course simply changing the population will have no effect, as the GDP of the world has been unchanged.
What the GDP/population part of the equation is talking about is per capita wealth. If per capita wealth falls and all other things remain the same, CO2 emissions will fall. If population has fallen, but global GDP has not changed, then per capita wealth must have increased.
You need to look at each ratio presented as one thing to understand what is going on with this identity.
David
archonix,
The trigonometric identity I presented does not ‘derive’ tan from sin and cos. If you break it down, what is shows is this:
opp/hyp / adj/hyp = opp/adj
which is a tautology, as the hypotenuse terms cancel. This is exactly the same thing as the identity presented by Willis.
David

July 10, 2014 3:53 am

Jos. says:
July 10, 2014 at 12:30 am

Why? Well, the UK and Ireland had gotten rid of most of their energy intensive energy (de-industrialization)

==================
Where did it go? Are people doing without those things that those energy-intensive industries once produced? Maybe some are, because of the declining wealth of Great Britain (per capita), but otherwise would you say those industries have perhaps just migrated to, uhhh, China and India?
So they really haven’t reduced their “CO2 emissions”, have they?

Norman Milliard
July 10, 2014 4:00 am

Carbon Dioxide control is about COO, the Control Of Others. It’s not about saving the world, controlling population, saving glaciers, and so on… It is about creating a controlling redistribution system where the controllers gain wealth and power.
There is no realistic chance at real population control, GDP reduction, The goal is to create an organization to tax that population and production.
Always ask “Why?”.

July 10, 2014 4:08 am

Willis – I am all for humour, but having just read through the intro and UK section of this report, I don’t find it remotely funny. It is deathly serious. This report has the backing of the UN Secretary General and will form the basis of the Paris 2015 ‘son of Kyoto’ initiative. It has a huge writing team and massive funding. About $200 million/annum is spent in climate activism at all levels of government, lobbying, NGOs, development agencies, and much of this from philanthropic foundations – not just the EU. This is NOT a bunch of ‘green loonies’ – as one commentators posted.
Already the UK government has legally obliged itself to reach 80% decarbonisation by 2050! It will aim to do this with 30 nuclear reactors (building one per year after 2020); 300% increase in wind turbines; the decommissioning of the domestic gas grid (down to zero gas heating) to replaced by heat pumps/solar; 25 million electric vehicles and a massive increase in biofuels for transport and electricity generation…..now this IS a form of madness, and wilful blindness to the economic realities, let alone the environmental and social impact.
We are a small country – these activist/green/politicians have a vision (if they actually do have any eyesight at all) of an electro-technical landscape, massive exploitation of the ‘developing’ world (for biofuel); complete disregard for community, indigenous people and wildlife; strong government control of the economy, surveillance and accounting…..
part of the blindness is that Germany, with a strong non-indebted export led economy, has already tried this road – its people rejected nuclear expansion and its exchequer recently called a halt to the programme of wind/solar/biomass because at 20% of the ‘turn-around’ to a low-carbon economy, they can’t afford to go further! The UK is broke and fuels its ‘growth’ by investing its newly printed in money in Chinese growth (and India, Indonesia, Russia and Brazil).
No one can face the fact that cheap energy is a thing of the past and the world economy faces a grinding halt int he next decade. The sad thing is that by taking control of the economy – much as happened in Russia and eastern Europe, all manner of stupidities and brutal damage can be inflicted before the edifice crumbles.
I and a few colleagues look report and wonder – is it worth trying to critique it and feed in to the process (they do request feedback) – even though we know we are dealing not with a technical proposition, but a political ideology. We have spent 20 years providing advice to our government on energy policy and its impacts – most of it not listened to, but some got through. Maybe it is important for our children – that they can see that not everyone was gripped by this curious madness. But to do the job requires resources – and who would provide? Not the government agencies concerned with countryside and community, nor wildlife – as used to be the case. Not the Friends of the Earth, Greenpeace, RSPB, Woodland Trust, Wildlife Trust and WWF…they are ALL part of the Climate Coalition, with well-paid activists in their staff.
The situation is deathly serious. I make a plea to get beyond the name-calling and the ridiculous thought that these people want to destroy the economy…..their equations only work if the economy grows. They want to control the economy. And they are NOT closet communists – they know nothing of communism. They have virtually no political education. We desperately need to understand what this ‘movement’ is – in terms of its ideology and structure, if we are to prevent it destroying so much of real value.

richardscourtney
July 10, 2014 4:09 am

tttt:
At July 10, 2014 at 2:59 am ou ask me

Richard, please explain where the twaddle in my assertion is, I’m interested.

Oh dear! I really thought you knew and it was deliberate which is why I used it as illustration in my post at July 10, 2014 at 2:52 am.
However, since you ask and because it demonstrates what I said would “bore most of the public”, I provide the following answer to your question.
Your post was at July 10, 2014 at 2:44 am and said said in total

There is nothing wrong with the equation, other that it is obviously a simplification for illustration. You can use the equation 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.
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.

I will address that by using “CO2” for “CO2 emissions” as you have.
Your post begins with an excuse for the equation being nonsense; i.e. “it is obviously a simplification for illustration”. Not so, it is an equation for use.
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.
The penultimate term is Energy/GDP, so those two terms are
{ (CO2/Energy) * (Energy/GDP) }
and that is exactly the same as {CO2/GDP}
This is because
{ (CO2/Energy) * (Energy/GDP) } = { (CO2 * Energy) / (Energy * GDP) }
and
{ (CO2/Energy) * (Energy/GDP) } = { (CO2/GDP) * (Energy/Energy) }
and
{(Energy/Energy) =1 }
so
{ (CO2/GDP) * (Energy/Energy) } = { (CO2/GDP) * 1 }
which is the same as
(CO2/GDP)
That proves you do not need “a value for the last term CO2/Energy” because Energy has gone and the equation has not altered.
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.
In summary, and as I said, the equation has political value because “it says whatever one wants” and “an explanation of why the assertion is twaddle would bore most of the public”.
I hope this answer is sufficient and demonstrates the points in my summary.
Richard

Olaf Koenders
July 10, 2014 4:13 am

We’re only putting the CO2 back into the atmosphere from where it all once was before nature herself sequestered it in the Carboniferous and various other eras. The more and faster we put it up there, the more and faster the CO2 sinks take it up again. I doubt we’ll ever get it up to the roughly 5000ppm (0.5% – tiny) that was around in the Jurassic.

Editor
July 10, 2014 4:17 am

Willis, thanks for the laugh. I enjoyed that equation immensely.

steveta_uk
July 10, 2014 4:18 am

David Gould, thanks for proving my point for me. Different mindset.

July 10, 2014 4:23 am

Willis:
Yes, you can reduce the left hand side to the right hand side. That’s why it’s called an identity. You have totally missed the point. One should be careful with mockery; those who use it unwisely render themselves eminently mockable.
The point is, you can take one quantity (CO2 emissions) and factor it into a product of several potentially measurable and independently adjustable quantitites.

climatereason
Editor
July 10, 2014 4:26 am

Peter
Good to see you posting here. You said;
‘We are a small country – these activist/green/politicians have a vision (if they actually do have any eyesight at all) of an electro-technical landscape, massive exploitation of the ‘developing’ world (for biofuel); complete disregard for community, indigenous people and wildlife; strong government control of the economy, surveillance and accounting…..’
To me this gets to the heart of the madness and as we both know the UK are world leaders in the climate insanity stakes. Have you written anything which puts some referenced flesh on the bones of your comment? It seems to me to get to the heart of the madness and needs us all to point out that what is being proposed is a dystopian view of the future .
tonyb

steveta_uk
July 10, 2014 4:27 am

Gerard Harbison, please explain. Every other of those “independently adjustable quantitites” appears twice in the expression. If you for example were to double population, then you halve the following expression – this has no effect whatsoever on the result of the expression.
Clearly you and others have something in mind, but it really doesn’t make any sense to most of us.

Pete Brown
July 10, 2014 4:32 am

Sorry but I think you’ve all entirely misunderstood the point of the identity. The Kaya identity is a means of communicating the factors of which CO2 emissions are comprised, in order to explain the physical levers that are available if one wishes to control an economy’s CO2 emissions. These are analogous to mathematical factors, for e.g. 6 = 3 x 2. This illustrates that 2 and 3 are factors of 6. This doesn’t prove anything mathematically – it’s just an identity. But it is informative nonetheless. It tells you that 6 can be broken down into factors of 2 and 3. In the same way, CO2 emissions can be broken down into factors of population, GDP per population, energy per population, and CO2 emissions per energy.
Roger Pielke Jr has a lot to say about this – and doubtless he explains it a lot better than me. Whether you agree with him or not, you need to be slow indeed to dismiss his analysis as trivial twoddle – as you all seem to be here!!
Willis Eschenbach – you might want to do a bit more background reading on this before dismissing it the way you have. (That isn’t to say you shouldn’t dismiss it in other ways…)

July 10, 2014 4:33 am

Hlaford says:
July 10, 2014 at 3:29 am
Excellent point.

Rogueelement451
July 10, 2014 4:50 am

XCO2 —> T
XCO2 x 112% ——-> T?
Can anyone advise me what T? should be ?

Bill Illis
July 10, 2014 4:50 am

The equation is irrelevant since:
–> CO2 EMISSIONS ≠ TEMP RISING ASSUMPTION
they want they “believe” it does.

Pete Brown
July 10, 2014 4:55 am

Moderators – seriously, this entire post is embarrassing. I fear this site will risk serious loss of credibility as long as this post is allowed to stand.
[your opinion is noted, and ignored -mod]

Crispin in Waterloo but really in Yogyakarta
July 10, 2014 4:56 am

“Now, at first glance that looks kind of reasonable.”
At first glance (before you expounded on it silliness) it didn’t look reasonable at all because as soon as there is a calculation that says “GDP” and “Population” with some carbon thrown in, there is no way the output is going to be rational as the GDP is related to energy, one way or another. The idea that photo-voltaic cells or windmills are ‘zero carbon’ products it ridiculous. How were they made? Where is the solar powered aluminum smelter or the high tech industrial park and surrounding city that can make silicon cells or amorphous cells?
There are two existing possibilities for a zero carbon future and they are hydro (which includes wave power) and nuclear power. Proof? Ontario, Canada. So what is all the buzz about? Just do it. People live very well in Ontario (or could) and it is powered by ‘non-carbon’ burning processes. The fact that the power company sponsors thousands of useless, unreliable windmills manufactured with masses of carbon dioxide emissions is proof that lunatics rule the asylum. What had to happened because of that? Installation of (near me) three natural gas plants for covering peak loads. Well, duh. All they needed was the Pickering nuclear power station (CANDU reactors) to be upgraded.

richardscourtney
July 10, 2014 4:57 am

Pete Brown:
You attempt to defend nonsense presented as political spin when you write saying atJuly 10, 2014 at 4:32 am

Sorry but I think you’ve all entirely misunderstood the point of the identity. The Kaya identity is a means of communicating the factors of which CO2 emissions are comprised, in order to explain the physical levers that are available if one wishes to control an economy’s CO2 emissions. These are analogous to mathematical factors, for e.g. 6 = 3 x 2. This illustrates that 2 and 3 are factors of 6. This doesn’t prove anything mathematically – it’s just an identity. But it is informative nonetheless. It tells you that 6 can be broken down into factors of 2 and 3. In the same way, CO2 emissions can be broken down into factors of population, GDP per population, energy per population, and CO2 emissions per energy.

Sorry, but I know you’ve entirely misunderstood the point of the equation.
It is a political tool provided by a political organisation for political purposes.
The equation is nonsense. It links independent variables to form abstract constructs which only indicate political desires. I am astonished that this is not blatantly obvious to everyone.
The abstract constructs are NOT “factors” which combine to be CO2 emissions.
For example, what evidence is there that in any nation a significant factor to CO2 emissions isGDP per capita?
When a country has constant GDP and constant population a change from manufacturing industry to service industries alters its CO2 emissions. Conversely, what evidence is there that when a country’s GDP is constant then changes to its CO2 emissions are significantly and directly related to its immigration or emigration?
Richard

joshv
July 10, 2014 4:59 am

The innumeracy presented by Willis and many readers here is galling. This identity decomposes CO2 emissions into three components. They don’t cancel – they are observables. We can measure the GDP per capita, we can measure the energy required to produce a unit of GDP, and the CO2 produced by the production of a given amount of energy. So for example, if you want to cap CO2 emissions, and Population is increasing, but energy itensivity is not decreasing (energy per unit GDP) and CO2 intensity is not decreasing (CO2 per unit energy) – you know that the only way to hit the CO2 target is to decrease GDP per capita.
See a real world application of this equation on Roger Pielke Jr’s blog: http://rogerpielkejr.blogspot.com/2014/06/clueless-krugman.html

old44
July 10, 2014 5:02 am

Author, author, name the author.

Daniel G.
July 10, 2014 5:06 am

The equation could be written like this:
CO2emissions = p * w * e * c
where p is population, w is GDP per capita, e is energy per unit of GDP and c is co2 emissions per unit of energy.
Now, consider b as GBP per capita and eb as energy per unit of GBP:
Obviously:
w * e =/= b * eb (energy_all/pop =/= energy_beer/pop)
Thus:
p * w * e * c =/= p * b * eb * c (CO2emission_all =/= CO2emissions_beer)
Thus your point is invalid.
Yes, the equation is tautalogical, but what is the matter, so is the pythagorean theorem.
@steveta_uk:
Population doesn’t just grow automatically, it is usually accompanied with economic growth, preserving (or increasing somewhat) GDP per capita.

Duncan
July 10, 2014 5:08 am

I don’t think it’s as dumb as you’re portraying it. I’ve been impressed with Roger Pielke Jr.’s analysis of it in the past.
GDP/Population is a measure of how wealthy a society is.
Energy/GDP is a measure of how efficiently that wealth is produced.
CO2/Energy is a measure of how dependent on fossil fuels that economy is.
The point of that identity is that if your aim is to reduce CO2, your options are:
1. Make everyone poorer
2. Kill off energy-intensive industries
3. Switch energy production to non-fossil sources
If renewables like wind and solar are more expensive, it makes everyone a little poorer and they’ll use less energy. If renewables can’t support industries like aluminum smelting, it’s a triple win!
We can outsource aluminum production to someplace else where the CO2 emissions don’t matter… oops, can’t do that; guess we’d just stop using aluminum. Or if we stop making aluminum in America and Europe, we can blame the CO2 problem on China and they can pay the reparations to Vanatu.

NikFromNYC
July 10, 2014 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! Any change in GDP always cancels out to unity, suggesting GDP has no influence on emissions. So we have here the most maverick climate alarm skeptical equation of all. Trying to attach words of meaning to such a silly equation simply smoke screens this fact of mathematics away.

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

@William 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

Mark Bofill
July 10, 2014 6:19 am

tttt,

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.

But that’s just it. It’s an illusion. You think population, GDP and energy are factor in that expression, but they is not. The factor is (population / population) or 1. Same with the other terms. And there is nothing expressed by it. You can vary any of the terms as you like and it doesn’t have any effect on the result. Whatever you plug in for CO2 emissions is the value you get for CO2 emissions (unless you zero the equation out by zeroing one of the a/a terms, which makes the whole thing invalid anyway since you’re also dividing by zero).

Mark Bofill
July 10, 2014 6:20 am

they is not.
Nice.
What I meant to say is, ‘they is not bein’ factors in that ‘spression homey.’

SanityP
July 10, 2014 6:21 am

Every single correct equation boiles down to “a = a”, that’s why they’re called “equations.
I used to think that you Willis knew what you were doing … now I’m actually in doubt.

ferdberple
July 10, 2014 6:22 am

It is not difficult to write identities like this. But that does not invalidate the original equation.
==========
correct. the equation is mathematically valid. what it demonstrates is that X=X, which is consistent with the meaning of “=”.
What the identity does not tell us is anything meaningful or useful about CO2. It is hocus pocus. Sleight of hand. A mathematical piece of nonsense intended to fool us into thinking it is telling us something profound, while telling us zip, nada, diddly squat.

ferdberple
July 10, 2014 6:23 am

Every single correct equation boiles down to “a = a”
=======
wrong.

July 10, 2014 6:25 am

Reblogged this on Centinel2012 and commented:
Their true colors come out! This logic came out of the UN agenda 21 initiative passed in Rio-de-Janeiro in 1992 which when one reads, along with all the rest of the ‘propaganda,’ one sees that the REAL purpose behind all of this is a major reduction in population. What is really meant by ‘sustainable’ is a world with less than one billion people powered by solar and wind which is the maxim that they think those forms of generating energy will support. Their population estimated are probably off as its more like a lot less than one billion.

ferdberple
July 10, 2014 6:27 am

e=mc2
v= at
d=1/2at2
a2+b2=c2
these equations are useful, because they are not of the form a=a.

tttt
July 10, 2014 6:28 am

Mark,
you said: “You think population, GDP and energy are factor in that expression, but they is not.”
Indeed they all are not. Factors are population, GDP produced by that population, energy intensity of GDP and energy intensity of carbon. This is also the way it is explained in the original source. You can increase or decrease any of these factors without changing the others.

SanityP
July 10, 2014 6:29 am


Explain why or when an equation, is not an equation.

July 10, 2014 6:30 am

They call it the Kaya Identity. Wondering who this Kaya is, I looked her up. In the Urban Dictionary, found her!
“Kaya. a term used to describe someone who is both amazingly beautiful and wonderfully talented, also with a personality fit for an angel.”
Now we know how these do-gooders see themselves. Not really news, though.

earwig42
July 10, 2014 6:36 am

UN now using Common Core math. Their algorithms are working as designed.

ColA
July 10, 2014 6:36 am

Wills,
I see above you have dismissed 4eyes and failed to acknowledged others who have correctly told you that you are wrong – the Kaya Identity is correctly expressed. Did you even bother to check out Roger Pielke Jr.’s analysis with the Kaya Identity? It appears NOT.
Basic maths says one side must ultimately equal the other or don’t you understand the basic laws of maths, physics, chemistry etc??
6 = 3 x 2
F = m x a
E = mC^2
“That was where I lost it …” lost what? your aim? Shot from the hip again …. right through the foot!
Do you have the balls to admit your wrong? any self respecting scientist would!

tttt
July 10, 2014 6:37 am

ferdberdle,
Quoting you:
“What the identity does not tell us is anything meaningful or useful about CO2. It is hocus pocus. Sleight of hand. A mathematical piece of nonsense intended to fool us into thinking it is telling us something profound, while telling us zip, nada, diddly squat.”
The identity in question is in no means a great mathematical discovery, nor profound in any way.
What it says is: if you know how much CO2 is emitted when producing unit of energy, and you know how many units of energy are produced per unit of GDP, and you know the total produced GDP you get total CO2 emissions. What part of this is wrong?

ferdberple
July 10, 2014 6:38 am

a=a
a=b*a/b
a=c*b/c*a/b
a=d*d/c*b/c*a/b
the above equations shows the derivation of the general form of the Kaya Identity. The Kaya Identity tells us ABSOLUTELY NOTHING about the relationship between a,b,c,d. If it did, we would be able to reduce the equation so that “a” is on the left and all the other terms are on the right. Something like this:
a = Xb+Yc+Zd (for demonstration purposes only)
However, no matter what you do, you cannot reduce the Kaya identify to put CO2 by itself on the left hand side of the equation. Which means the Kaya Identity has no solution in terms of CO2. Which means the Kaya Identity tells us nothing about CO2.

Mark Bofill
July 10, 2014 6:41 am

tttt,
Yeah, and without changing the resulting CO2 emissions as well.
If you get that, then why dress the discussion up with a farcical equation? Why not simply say “Let’s talk about GDP, population, energy, and their relationship with CO2 emissions?”
IMO, that backfires. Whatever point someone is trying to make is lost in the wake of the astonishment people like me feel when presented with a tautology that looks at a glance like it’s supposed to convey something more than the fact that 1 * X = X.

July 10, 2014 6:44 am

IMO the zero proposal makes as much sense as any other religious doctrine relating to demanded penance for imaginary sins….ala self-flagellation…I mean really….what’s next? “Father forgive me for I have farted?” As a longtime Monty Python fan I’m truly looking forward to decades of mocking this whole affair, since history has shown time, and time again, that dogmatic extremism eventually leads to extremists being portrayed as the immoral idiots they are…imagine a TV series about rich eco-fascists and their wild and crazy ideas to save the planet, while each episode reveals how their day-to-day evangelistic hypocrisies results in unintended and sometimes fatal consequences for others less fortunate than themselves…you could run it with a laugh track as a sit-com, or without the laugh track as a horror docu-drama.

Rodney
July 10, 2014 6:46 am

I agree that the Kaya is mathematically worthless as it can be used to prove anything. That is why I think you all need to replace the Kaya equation with my much more useful equation: Name it after me and call it the Rodney equation if you like. It goes as follows:
CO2 = BSP * (AGW / BSP) * (BSS / AGW) * (CO2/ BSS)
where
CO2 = Annual global CO2 production in metric tonnes.
BSP = Australia’s annual brussel sprout production in metric tonnes.
AGW = Al Gore’s weight in pounds.
BSS = Number of Britney Spears signals that have charted in the top 100 in Sweden.
So clearly Britney needs to stop singing, Al needs to lose a few pounds and you’ve now got a good reason not to eat your greens. How hard can that be? See controlling the climate is easy.

ferdberple
July 10, 2014 6:47 am

What it says is: … What part of this is wrong?
=========
your understanding of what it says is wrong. This is quite simple to demonstrate. Build an equation of the form:
CO2 = X
That does not have CO2 included in X. In that case, X will tell you something about CO2. But if you cannot eliminate CO2 from X, then X tells you nothing about CO2.
So, in terms of your statement, this is the term that you need to reduce;
“if you know how much CO2 is emitted when producing unit of energy,”
You need to remove CO2 from this term and move it over to the left hand side of the equal sign, so that you can solve for CO2. But when you do this, the left hand side will be reduced to 1, which means you cannot solve for CO2, which means the identity tells you nothing about CO2.

tttt
July 10, 2014 6:49 am

Mark,
You said: “Yeah, and without changing the resulting CO2 emissions as well.”
No, the CO2 emissions would naturally change.
To be fair to the authors of the original text, the equation is expressed a bit differently and also explained in the text which makes its purpose totally clear.

steveta_uk
July 10, 2014 6:50 am

tttt – i’m now confused as to who is being thick here.
Assuming that the expression follows rules of algebra, it makes no sense whatsoever to say “you can increase or decrease any of these factors without changing the others.”
You cannot. If you increase population, you decrease GDP produced by that population. The reduction is precisely in proporton to the increase, so there is no overall effect whatsoever.
Anyone over 13 years of age who has done any trivial algebra can see this.
So clearly the only possible conclusion is that this is not an algebraic expression. An anyone who thinks it is has simply the wrong mind set to understand the soft sciences.
C = P * (G/P) * (E/G) * (C/E) == C = (P/P) * (G/G) * (E/E) * C == C = 1 * 1 * 1 * C == C=C
Q.E.D.

donaldosaurus
July 10, 2014 6:51 am

This post (and accompanying comments) would make a good case study on the Dunning Kruger effect.
Identities (like sin/cos=tan) are *meant* to reduce to 1=1. The point of it isn’t to prove or derive anything, it’s to be used as a tool in other calculations. This just decomposes the single variable of CO2 emissions into other variables, which can in principle be altered.

Mark Bofill
July 10, 2014 6:53 am

tttt,

What it says is: if you know how much CO2 is emitted when producing unit of energy, and you know how many units of energy are produced per unit of GDP, and you know the total produced GDP you get total CO2 emissions. What part of this is wrong?

I don’t know tttt. What part of this is wrong?:
if you know how many bananas per hookers in Vegas, and how many hookers in Vegas per 1952 quarters in circulation, and 1952 quarters in circulation per Vegas hooker, what do you really know?
You know that 1 * X = X. That’s all that tells you.

A Different James
July 10, 2014 6:53 am

There’s still confusion apparently, so let’s do a simple example to clear things up. Let’s suppose that you are managing a warehouse, and want to get a rough idea of how many trucks you will need on a given day. You sit down and, while watching the warehouse, you realize the following steps happen:
1. Items are put in boxes
2. Boxes are put on pallets
3. Pallets are loaded on trucks
Being a good manager, you know how many of those things fit into each other, on average. What you have is the following relationship (purely dimensional):
Trucks = Trucks / Pallets * Pallets / Boxes * Boxes / Items * Items
This obviously reduces to: Trucks = Trucks. That’s the point. Now, let’s say you had the following average amounts for those values (given variable letters):
a = 10 pallets per truck
b = 5 boxes per pallet
c = 4 items per box
d = number of items
e = number of trucks
Now we can write the equation:
e = 1/a * 1/b * 1/c * d
Notice how the units are the exact same, but now we have numbers associated with them.
Using that relationship, you can estimate that if you have 100 items to ship in a day, that you’ll need just a half a truck. What the equation lets you do is estimate what will happen if you need to ship more or less items, if the box size changes, if the truck size changes, etc.
The Identity in question is doing the same thing. It’s a simplified relationship between carbon emitted per unit energy times an estimate of energy used (derived from population and GDP). It’s no more complicated than relating miles traveled to your fuel efficiency to get fuel used.

DanMet'al
July 10, 2014 6:53 am

There appear to be two separate issues being argued in this comment thread:
(1) Some commenters believe that because the Kaya Identity can be reduced to the equation “Amount of CO2” = “Amount of CO2”, it has been falsified (unverified). From my view point, all identities share this property and if the two sides of an equation fail to have identical dimensions, that is a sign of a fatal problem. On this issue I side with Pete Brown’s comments on July 10, 2014 and later.
(2) The second objection(s) relate to George Box’s famous quote that “ all models are wrong; but some are useful. Clearly, the Kaya Identity is a simplistic “zero order model”; but apparently, Roger Pielke Jr. has found it useful for certain analyzes, I believe involving “what-if” analysis. And yet, given my own lack of exposure to Prof. Pielke’s work, it seems reasonable that more knowledgable people might find the application of the Kaya Identify to be problematic and subject to political chicanery. In others they find the model to have no practical value or utility.
So my conclusion is that while the Kaya Identity may be criticized as a non-useful or even an easily abused model, the identity itself can not be falsified on mathematical grounds based on Pete Brown’s arguments (relative to factoring) which I believe to be rational.
Thanks
Dan

Oscar Bajner
July 10, 2014 6:54 am

OK I’ll play this game. Using the Kaya identity, we can cut CO2 emissions by setting Population = 0.
=========
Mind you, all those decaying corpses will push methane emissions through the roof!
Wait, there’s an identity for that!

hunter
July 10, 2014 6:55 am

Ironically, this puts Willis on the same side of n issue with a certain Rabett who posted this at Pielke Jr’s blog:
EliRabettSat Jun 14, 04:00:00 PM MDT
Applying the Kaya identity as a mantra is naive.
CO2 Emissions = Population (GNP/Pop) (Energy/GNP)(CO2/Energy)
since all it says is CO2 EM = CO2 EM.
The circular logic required of the Katya identity does, however, nicely sum up the underlying fundamental fail of CO2 obsession.

tttt
July 10, 2014 6:55 am

ferdberple,
You didn’t explain what part of my textual description was wrong, which is what I asked for.
Anyways, in the left side we have “total” CO2 emissions, on the right side we have how much CO2 is emitted per produced unit of energy.

ferdberple
July 10, 2014 6:55 am

Kaya Identity:
CO2 emissions = population * GDP/population * energy/GDP * CO2 emissions/energy
Berple Challenge: Solve for CO2 in terms of Population, Energy and GDP:
move CO2 over to left hand side:
CO2 emissions/CO2 emissions = population * GDP/population * energy/GDP * 1/energy
simplify:
CO2 emissions/CO2 emissions = 1

steveta_uk
July 10, 2014 6:57 am
David in Cal
July 10, 2014 6:59 am

IMHO that equation is not a joke. Of course it’s an identity: it would have to be in order to be correct. However, the point is to look at specific methods of cutting CO emissions. E.g., we could cut population, or we could cut CO2 emissions/energy, etc.

ferdberple
July 10, 2014 6:59 am

You didn’t explain what part of my textual description was wrong
=========
what was wrong is your understanding of what the equation is showing.
WHat I asked you to do was to use that Kaya Identity to produce an equation for the form
CO2 = F(population, GDP, energy)
Where F is any mathematically valid formula that does not include CO2. Give it a try and report back here with your results. Skip the words, give us a mathematical solution for CO2 and you will quickly discover the problem.

Mark Bofill
July 10, 2014 7:00 am

tttt says:
July 10, 2014 at 6:49 am

Mark,
You said: “Yeah, and without changing the resulting CO2 emissions as well.”
No, the CO2 emissions would naturally change.

The expression doesn’t capture that. See here.
You can put ANY value in you like for population, GDP, and energy, and the expression remains true. That’s why it’s a tautology
CO2 emissions = CO2 emissions
CO2 emissions = CO2 emissions * 1
CO2 emissions = CO2 emissions * (a*b*c / a*b*c)
CO2 emissions = (a*b*c / a*b*c) * CO2 emissions
CO2 emissions = a * (b/a) * (c/b) * CO2 emissions/c
The point is, a * (b/a) * (c/b) * 1/c = 1. It makes no difference what values you assign a b c. How you vary them. There is no impact on CO2 emissions, because a b and c are not factors. a*b*c / a*b*c is the factor, and that’s == 1.

ferdberple
July 10, 2014 7:01 am

the point is to look at specific methods of cutting CO emissions. E.g., we could cut population, or we could cut CO2 emissions/energy, etc.
=============
or we could cut Al Gore’s waistline and thereby reduce CO2, according to this equally valid equation:
CO2 emissions = Al Gore’s Waistline * GDP/Al Gore’s Waistline * energy/GDP * CO2 emissions/energy

Speed
July 10, 2014 7:11 am

Willis excellent mathematical reductio ad absurdum is clearly correct but some are having trouble accepting it. I suggest the following piecewise analysis …
CO2 Emissions = Population * (GDP/Population) reduces to CO2 Emissions = GDP
CO2 Emissions = GDP * (Energy/GDP) reduces to CO2 Emissions = Energy
CO2 Emissions = Energy * (CO2 Emissions/Energy) reduces to CO2 Emissions = CO2 Emissions

Daniel G.
July 10, 2014 7:14 am

@steveta_uk:
You cannot. If you increase population, you decrease GDP produced by that population. The reduction is precisely in proporton to the increase, so there is no overall effect whatsoever.
Bullshit. If you increase population, GDP will also increase. Preserving GDP per capita or increasing it somewhat.

tttt
July 10, 2014 7:16 am

Al Gore’s waistline has nothing to do with GDP, right?
Direct quote from the original source (also in the original post by Willis): “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 per capita, energy use per unit of GDP, and CO2 emissions per unit of energy:
CO2 emissions = Population x (GDP/Population) x (Energy/GDP) x (CO2/Energy) ”
—–
On the right side you have Co2 emissions per produced unit of energy. If you really think that cannot be used to calculate total CO2 emissions then so be it.
Miles driven = Gallons * Miles / gallon. Can this be used or not?

ferdberple
July 10, 2014 7:17 am

ps: in case anyone missed the joke:
CO2 emissions = Al Gore’s Waistline * GDP/Al Gore’s Waistline * energy/GDP * CO2 emissions/energy
it makes no difference what amount you use for Al Gore’s waistline (or world population)
CO2 emissions = 2 * GDP/2 * energy/GDP * CO2 emissions/energy
CO2 emissions = 3 * GDP/3 * energy/GDP * CO2 emissions/energy
CO2 emissions = 4 * GDP/4 * energy/GDP * CO2 emissions/energy
….
CO2 emissions = N * GDP/N * energy/GDP * CO2 emissions/energy
Notice, that no matter what amount we use for population (or Gore’s waistline), according to the Kaya Identity, CO2 emissions will remain unchanged!!
So, the ONLY conclusion that we can derive from the Kaya Identity with regard to CO2 and population, is that world population has NO EFFECT on CO2.

Daniel G.
July 10, 2014 7:21 am

You are thinking too much math if you think increasing population will reduce GDP per capita.
It doesn’t “cancel”.

GDP/Al Gore’s Waistline
Ok, if Al Gore’s Waistline increases, what happens to GDP?

ferdberple
July 10, 2014 7:22 am

Al Gore’s waistline has nothing to do with GDP, right?
=============
The term: “GDP/Al Gore’s Waistline” Is a measure of how much the world’s economy must expand to accommodate Gore’s expanding appetite. How much extra you and I must work to support Gore’s lifestyle.
You have failed to demonstrate a solution for CO2 = F(population, GDP, energy).
As can be seen from this equation:
CO2 emissions = N * GDP/N * energy/GDP * CO2 emissions/energy
The Kaya Identity tells us that no matter what amount you use for N (population), CO2 emissions are unchanged.

Check
July 10, 2014 7:23 am

The equation can be useful as a way to show how modifying anything on the right changes the answer on the left, which is mislabelled and should be something like DeltaCO2. The equation can show clearly what effects large scale changes can have on CO2 emissions. It can be shown, for instance, that a global pandemic killing say 80% of humanity would seriously reduce our CO2 emissions. It makes clear the stark reality of reducing CO2 emissions.

Pete Brown
July 10, 2014 7:27 am

Mark Bofill:
July 10, 2014 at 6:05 am
….
This is ridiculous.
The identity reduces to CO2 emissions = CO2 emissions precisely BECAUSE the terms on the right are a valid decomposition of the term on the left. The identity would be broken if it didn’t reduce to, well, identity!
Consider this:
30 = 5 x 3 x 2
Not a very exciting mathematical statement, certainly. Not at all informative from a mathematical perspective, UNLESS your question is: ‘what are the factors of 30?’ But fortunately in the case of the Kaya identity, that is PRECISELY what the question is.
Now consider this:
in the case of 30 = 5 x 3 x 2, what do you have to do to the value on the left if you change any of the values on the right? Try it with some examples…
It is precisely these simple truisms that Willis Eschenbach and others seem to find so ridiculous, and that is what I find embarrassing, I’m afraid.

Pete Brown
July 10, 2014 7:28 am

P.S. Mods – it can’t be both “noted” and “ignored”. Those are mutual exclusive concepts.

JohnB
July 10, 2014 7:28 am

Oh dear!
All this because Willis (and most commenters here) don’t understand the difference between an *equation* and an *identity*.
It is called the Kaya Identity, not the Kaya Equation. An identity is true for all values. You don’t *solve* an identity, it is always true. So what is the purpose of it? As has been noted above, the purpose is to show CO2 emissions as a product of meaningful terms: population, wealth per person, energy use and CO2 efficiency of energy production. It is *meant* to cancel out. That is what identities do!
http://en.wikipedia.org/wiki/Identity_%28mathematics%29

July 10, 2014 7:31 am

So the objective would be to make a world with the energy intensity of Congo (30.5 toe/M dollars); the per capita annual energy consumption of Afghanistan (3.78 GJ per capita) and the population of the Pitcairn Islands (56).
All numbers from Wikipedia.

Daniel G.
July 10, 2014 7:31 am

Increasing population does not decrease GDP per capita.
More people means more GDP.

The term: “GDP/Al Gore’s Waistline” Is a measure of how much the world’s economy must expand to accommodate Gore’s expanding appetite. How much extra you and I must work to support Gore’s lifestyle.
Indeed, if Gore eats too much, the economy has to grow, emitting more CO2. But if he goes on a diet or not, how does that impact the economy?

DanMet'al
July 10, 2014 7:33 am

Again I agree with Pete Brown. . . to those that attempt to invalidate the Kaya Identity based on mathematical grounds. . . your arguments are embarrassing! If you find the Identity to be overly simplistic (e.g., missing important factors, non-linearities etc.) fine. . . otherwise . . .
Dan

JohnB
July 10, 2014 7:38 am

ferdberple says:
July 10, 2014 at 7:22 am
As can be seen from this equation:
CO2 emissions = N * GDP/N * energy/GDP * CO2 emissions/energy
The Kaya Identity tells us that no matter what amount you use for N (population), CO2 emissions are unchanged.
——————–
No! It tells you that if population changes, but GDP, energy use per GDP, and CO2 emissions per energy unit stay the same, CO2 emissions will be unchanged.Reasonable, but an unlikely scenario.

Daniel G.
July 10, 2014 7:40 am

@JohnB:
GDP per capita, not GDP.

Mark Bofill
July 10, 2014 7:46 am

Pete Brown says:
July 10, 2014 at 7:27 am

This is ridiculous.

I agree.

The identity reduces to CO2 emissions = CO2 emissions precisely BECAUSE the terms on the right are a valid decomposition of the term on the left. The identity would be broken if it didn’t reduce to, well, identity!

Yes.

Consider this:
30 = 5 x 3 x 2
Not a very exciting mathematical statement, certainly. Not at all informative from a mathematical perspective, UNLESS your question is: ‘what are the factors of 30?’ But fortunately in the case of the Kaya identity, that is PRECISELY what the question is.

No.
X = (a/a) * (b/b) * … * (n/n) * X
tells you nothing about the factors of X. The identity is a restatement of the tautology
X = 1 * X.
Mark Bofill:
July 10, 2014 at 6:05 am
….

Now consider this:
in the case of 30 = 5 x 3 x 2, what do you have to do to the value on the left if you change any of the values on the right? Try it with some examples…

As I have stated repeatedly, the identity is true for ALL values of CO2 emissions, population, GDP, and energy, excepting where values cause division by zero. That does not represent the identity.

It is precisely these simple truisms that Willis Eschenbach and others seem to find so ridiculous, and that is what I find embarrassing, I’m afraid.

It is ridiculous. Put it back in context.

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

Now think it through. By accepting the identity, we have assumed without evidence that this expression describes something in the real world, and we’ve assumed a specific relationship. Perhaps the relationship is with the square root of GDP in fact? Perhaps not population but (F(population)? Perhaps there are significant additional variables missing, or perhaps some of these variables are irrelevant?
That’s what makes it outrageous in my book. You can’t just plop down an expression that’s obviously true by virtue of being an identity and expect people to take it seriously merely because it is an identity. You’ve got to demonstrate why and how it describes something in the real world. Otherwise, you might as well be talking about the number of bananas imported, hookers in vegas, and the number of 1952 quarters in circulation. Merely because I can make an identity out of these variables doesn’t mean my identity has any useful application.

JohnB
July 10, 2014 7:46 am

@DanielG
Thanks for the comment, but I did mean GDP.
If population doubles and GDP *per capita* stays the same, CO2 emissions would double. CO2 emissions would stay the same if GDP per capita halved. i.e. *GDP* stayed the same.

george e. smith
July 10, 2014 7:46 am

Sound more like the kaka identity to me.
But this exercise leads me to a tragic mistake we have all been making in our math.
For eons, we have all said:
Garbage in = Garbage out.
Clearly that is incorrect; Garbage in = Garbage in !
But now we can understand why they keep doing it.
George

Joseph Murphy
July 10, 2014 7:49 am

concepts.
JohnB says:
July 10, 2014 at 7:28 am
Oh dear!
All this because Willis (and most commenters here) don’t understand the difference between an *equation* and an *identity*.
It is called the Kaya Identity, not the Kaya Equation. An identity is true for all values. You don’t *solve* an identity, it is always true. So what is the purpose of it? As has been noted above, the purpose is to show CO2 emissions as a product of meaningful terms: population, wealth per person, energy use and CO2 efficiency of energy production. It is *meant* to cancel out. That is what identities do!
http://en.wikipedia.org/wiki/Identity_%28mathematics%29
—————————-
But the equation shows that CO2 is not a product of the other variables, it shows that CO2 is independant of the other variables.

Daniel G.
July 10, 2014 7:53 am

Mark Bofill writes:

That’s what makes it outrageous in my book. You can’t just plop down an expression that’s obviously true by virtue of being an identity and expect people to take it seriously merely because it is an identity. You’ve got to demonstrate why and how it describes something in the real world. Otherwise, you might as well be talking about the number of bananas imported, hookers in vegas, and the number of 1952 quarters in circulation. Merely because I can make an identity out of these variables doesn’t mean my identity has any useful application.

What happens to CO2 emissions in these scenarios (while keeping other variables constant):
1. increasing population? decreasing population?
2. increasing GDP per capita? decreasing GDP per capita?
3. increasing energy intensity of the economy? decreasing energy intensity of the economy?
4. increasing CO2 intensity of energy? decreasing CO2 intensity of energy?

July 10, 2014 7:54 am

An interesting article. Isn’t one of the limitations of the Kaya Equation that it only relates to carbon dioxide emmisioned used to produce energy ? For example wif e chop down trees and burn them, i.e. deforestation, then carbon dioxide is released into the atmosphere, but no one using this energy.
I am unclear how this “Carbon dioxide released into the air by burning” would be reflected in the carbon emissions per unit of energy consumed term .
The Science Geek

Al
July 10, 2014 7:58 am

A funny post indeed. There’s a difference between someone who can do math and someone who actually knows math.

Daniel G.
July 10, 2014 7:58 am

@Joseph Murphy
But the equation shows that CO2 is not a product of the other variables, it shows that CO2 is independant of the other variables.
It is an identity, and it doesn’t show anything. You have to use logic in order to work out results. One might think that increasing population won’t cause increasing CO2 emissions due to the identity. After all, GDP per capita will decrease proportionally. But that is not what happens in real life. When population increases, so does GDP. Therefore math cannot tell whether CO2 emissions will rise or not. If we assume some degree of linearity, GDP will increase proportionally to the population (production, consumption, imports, exports, and gov. spending). Thus GDP per capita is more or less independent of population. Rising population, rising CO2 emissions.

Earline
July 10, 2014 8:00 am

This kind of post gives those who question the ‘consensus’ a bad name and provides fuel for the argument that we don’t understand math. Willis, I’ve enjoyed many of your posts in the past, but this is embarrassing.

Pete Brown
July 10, 2014 8:03 am

JohnB
Yes!
Admittedly your way was quicker…

Joseph Murphy
July 10, 2014 8:04 am

Daniel G. says:
What happens to CO2 emissions in these scenarios (while keeping other variables constant):
1. increasing population? decreasing population?
2. increasing GDP per capita? decreasing GDP per capita?
3. increasing energy intensity of the economy? decreasing energy intensity of the economy?
4. increasing CO2 intensity of energy? decreasing CO2 intensity of energy?
———-
according to the identity, absolutely nothing. You need to use logic to see it.

Mark Bofill
July 10, 2014 8:07 am

Daniel,
If you think there is a relationship between the variables (and in fact I do), use empirical data to work out the relationship. Or use a theoretical relationship, that’s fine too. The tautology does not tell us anything about what the relationship is in reality.
How do I choose between these tautologies?
1) CO2 emissions = sqrt(GDP) * (population^2) / (sqrt(GDP) * energy/(population^2) * co2em / energy
2) CO2 emissions = (GDP^2) * sqrt(population) / (GDP^2) * energy/(sqrt(population) * co2em / energy
3) CO2 emissions = bannas * hookersinVegas / bananas * coinsInCirc/hookersInVegas * co2em / coinsinCirdc
I need to know which describes something in reality that I care about.
Maybe I’m being unreasonable. I think that
F = MA
tells me something useful about reality. I don’t think that
F = X * (Y/X) * (Z/Y) * (F/Z)
gives me any information about anything.

John West
July 10, 2014 8:09 am

TATS Identity
TATS = Trip Around The Sun (in Seconds)
TATS = Seconds/Year = Days/Year X Hours/Day X Minutes/Hour X Seconds/Minute
TATS = Seconds/Year = Seconds/Year
It works for any planet by just putting in the appropriate values.
Just because it reduces to X=X doesn’t make it invalid, on the contrary, it validates it. There’s a bunch that can be accomplished (like unit conversions) with just the concept of anything divided by itself equals one (X/X=1) which also means anything multiplied by one equals itself (X*1=X).

Rodney
July 10, 2014 8:10 am

“As has been noted above, the purpose is to show CO2 emissions as a product of meaningful terms: population, wealth per person, energy use and CO2 efficiency of energy production.”-JohnB
But the point is the Kayla Identity is not “SHOWING” anything (any more than my Rodney equation I posted earlier does). The Kayla equation is merely stating what you assume (i.e. that you think there is a connection between C02 and population etc).
As it happens I for one do think C02 is linked to the terms in the Kayla equation. And that only makes it worse because unlike my Rodney equation which is easy to spot as nonsense albeit true nonsense because the Kayla equation contains connected terms it makes it look like it saying something more meaningful than it really is.
For example lets say I suspect that current (I), Voltage (V) and Resistance (R) are somehow related to each other. So taking my queue from the Kayla equation I write.
V = R * (I/R) * (V/I)
In this equation as it happens I correctly imply that there is a relation between V, I and R. But this equation (which is completely true) hides the fact that it gives no actual useful information about how V, I and R are related to each other. It does not tell me for example that V = IR. It is just a useless tautology stating that V=V and that I’m guessing it might have something to do with I and R (but I am not actually stating anything meaningful about how V relates to I and R if it does).
That all change once I right V = IR.

Tamara
July 10, 2014 8:11 am

Mark Bofill: “1 * X = X.”
Well, stated. I think a lot of people are missing the fact that Willis is not saying the Identity is mathematically incorrect, and he is not merely reducing the units. He is saying that The equation never transforms CO2 emissions. Why measure CO2 emissions for the right side of the equation, then put it through an equation that gives the original measured amount as the answer.
The ONLY thing you can do to reduce CO2 emissions is to reduce CO2 emissions. This is because the terms in the numerator are dependent on the terms in the denominator and vice versa.
If there are 2 people in the world, then Population = 2, and per capita GDP is GDP/2. Hence, you do not need to know the population of the world to calculation CO2 emissions.
ColA, none of your equations are identities. 2 x 3 transforms these two numbers into 6.
E = mc2 transforms a mass and an acceleration into energy.
This is an identity:
elephants = dogs * geese/dogs * mice/geese * elephants/mice
The elephants are not transformed by the equation.

July 10, 2014 8:12 am

You can reduce or raise the population. You can reduce or raise the GDP per capita. You can reduce or raise the energy intensiveness of GDP. You can reduce or raise the carbon intensiveness of energy. These are all independent quantities, susceptible to being changed by appropriate policy.
I can’t believe some of you are having difficulty with this.

July 10, 2014 8:13 am

E = mc2 transforms a mass and an acceleration into energy.
Nah.

Kasuha
July 10, 2014 8:14 am

I don’t think there’s anything to laugh to on that equation. It is reasonable decomposition of the CO2 production. You just reduced it backwards the way how it was originally created.
Of course that equation has little sense if you’re trying to reduce emissions to zero. Because the only way is just that – to reduce CO2 to zero. You don’t solve it e.g. by reducing population, GDP, or energy production to zero because that way you only get CO2 = CO2 * 0 / 0.
But on the other hand this equation does have a lot of sense when talking about CO2 emission reductions. And its factors can often be reasonably forecasted.
Unlike your Gross Beer Production factors.

Mark Bofill
July 10, 2014 8:14 am

Tamara,
Thank you! That’s what I’m trying to say. Merely because I can construct a tautology doesn’t automatically give my tautology any meaning. It may merely mislead the unwary into thinking a relationship exists where none necessarily does exist.

July 10, 2014 8:15 am

The ONLY thing you can do to reduce CO2 emissions is to reduce CO2 emissions.
Really? So (for the state of argument) shooting every living human wouldn’t reduce CO2 emissions?

Jurgen
July 10, 2014 8:16 am

splitting a variable or figure into factors may be useful
but when you have more choices here, say 12=1×12 or 2×6 or 3×4 or 3x2x2 etc the choice you do make depends on the purpose you have for factoring, say constructing a fancy scale for a clock or whatever
co2 production can be split in many many factors, the ones you choose depend on your intended use
now the factoring in the Kaya identity clearly has a political reasoning behind it, so first and foremost is a political tool
to present your political aims in a mathematical formula gives it the appearance of inevitability – the mathematics is right isn’t it? – as right as 1=1
but in the real world maybe not so right, because of the selective political choices made
for me a political wolf dressed up as a mathematical sheep
also there is an immense difference in the mathematical simplicity of the identity, suggesting it is a useful tool, and the real-world situation regarding co2 including what nature does and has always done, suggesting it is a futile tool
so my useful equation without factoring would be:
kaya identity = futile politics

Daniel G.
July 10, 2014 8:19 am

@Tamara:
Prove that there is a relation between dogs and geese, geese and mice, and mice and elephants.
Guess What: There isn’t.
@Rodney:
Note that R is defined to be V/I:
V = I * (V/I)
Bofil:
Sqrt(GDP) is meaningless. Prove there is a relation between co2em and coinsinCirdc.
The point of the ratio quantities is to create independent variables.

UsUrbrain
July 10, 2014 8:20 am

Having graduated with a BS in Mathematics (Suma Cum Laude, National Mathematics Honor Society, Mensa) I strongly suggest that those of you that feel or think, hat the above “equation” is valid to review their first year algebra course. It is a “Tautology,” a trick! Like the game where you were asked to pick a number and then go through various manipulations, give the result of the manipulations and “magically” they tell you the number you picked. It is far different than the I=PAT equation, which, at least has some validity. They should have stuck with I = PAT.

David in Texas
July 10, 2014 8:21 am

There is no math error. You, in fact, proved that there wasn’t an error. When we write Y = f(x), well, f(x) better equal Y. I can’t understand how it could be otherwise.
Maybe your criticism is that the equation is trivial. Here again, I would disagree. The equation tells you that if we reduce population we reduce CO2 emissions. Logical, no? Maybe you consider that trivial. OK. But, it also tells you that if we reduce GDP/population. In other words, if we reduce the average wealth of individuals, we reduce CO2 emissions. Now that, I, for one, consider profound, and a stunning admission.

Daniel G.
July 10, 2014 8:23 am

says:
Why I=PAT is valid and Kaya’s identity isn’t?

July 10, 2014 8:24 am

If this identity (as its supporters call it) is other than a standard mathematical equation (is it?) and its purpose is to calculate and/or display the relationships between population change/GDP change/energy usage changes on one hand and CO2 emission changes on the other, then I think such an effort is best accomplished with data graphs rather than this identity. If this is indeed other than a standard mathematical equation, exactly how is it supposed to work and be understood? Graphs are easier to understand.
This “equation” would have to be other than a standard mathematical equation because it indeed makes no sense as such due to the CO2 emissions variable being on both sides and the remaining variables cancelling themselves out.
The only thing being accomplished by using this identity in the climate debate rather than displayed data in graphic form is to generate controversy.

Daniel G.
July 10, 2014 8:25 am

@David in Texas says:
Apparently, you understand the identity’s meaning. It is the math of totalitarianism.

urederra
July 10, 2014 8:30 am

I am for recarbonization because is the good thing to do for the environment. And since it is good for the environment by helping plants grow faster, it is also good for the people.

steveta_uk
July 10, 2014 8:31 am

Hmmmmm – I think I am beginning to get it.
Lets say I have some crates of M&Ms. In the crate there are many boxes. In the boxes there are many packets. In the packets there are many M&Ms.
So the equations for how many M&Ms I’ve got is
M = C * B/C * P/B * M/P
So if I know how many M&M per packet, and packets per box, and boxes per crate, and the number of crates, I can easily calculate the number of M&Ms. This is the Kaya method.
Alternatively, I can simply count the M&Ms. This is the Willis method.
I’m beginning to see an advantage to the Kaya method ;(

July 10, 2014 8:36 am

>> The equation tells you that if we reduce population we reduce CO2 emissions.
It most definitely DOES NOT tell you this.
Let’s try some high school algebra (even)
Assume these variables
Population = 300 million
GDP = 3 trillion dollars
energy = 500 trillion joules
According to the forumula
CO2 = 300 million people * ($3 trillion / 300 million people) * (500 trillion joules / $3 trillion) * (CO2 emissions/500 trillion joules)
Note that you cannot solve for CO2 (other than the fact that it can be anything – even units don’t matter – it could be “400 bananas” or “5 quadrillion barrels of oil”). But if we use algebra that’s been around for the last, oh, few thousand years, you end up with this after simplifying:
CO2 = CO2
Now let’s say that we halve the population to 150 million. Everything else remains the same.
CO2 = 150 million people * ($3 trillion / 150 million people) * (500 trillion joules / $3 trillion) * (CO2 emissions/500 trillion joules)
That simplifies to (suprise!)
CO2 = CO2
If we had gone with 400 bananas of CO2 or 5 quadrillion barrels of oil, they are unaffected by population.
It’s disheartening to see how many people think this equation is somehow useful.

Daniel G.
July 10, 2014 8:37 am

If this identity (as its supporters call it)…

It is a identity. What do you mean by supporters?

is other than a standard mathematical equation (is it?) and its purpose is to calculate and/or display the relationships between population change/GDP change/energy usage changes on one hand and CO2 emission changes on the other, then I think such an effort is best accomplished with data graphs rather than this identity. If this is indeed other than a standard mathematical equation, exactly how is it supposed to work and be understood? Graphs are easier to understand.

pop. and GDP (I will repeat: production, consumption, exports, imports, gov. spending) are more or less proportional to each other. That Makes GDP per capita independent of population. The point is not to show that relationships, but rather to represent the main factors of energy-related CO2 emissions.
Population
Average Wealth
Energy Intensity of the Economy
CO2 Efficiency for Energy
So how are those variables joined to get energy-related CO2 emissions???

Daniel G.
July 10, 2014 8:39 am

@Jason L says:
Everything else remains the same.
Bullshit, GDP decreases.

July 10, 2014 8:39 am

It tells you, the other three quantitates being equal, if you reduce population, you reduce carbon emissions. In
Now let’s say that we halve the population to 150 million. Everything else remains the same.
CO2 = 150 million people * ($3 trillion / 150 million people) * (500 trillion joules / $3 trillion) * (CO2 emissions/500 trillion joules)

Of course, you halved population, and doubled GOP per capita. All other things weren’t equal.

Mark Bofill
July 10, 2014 8:40 am

Daniel G,

Sqrt(GDP) is meaningless. Prove there is a relation between co2em and coinsinCirdc.

1) You give me the unsupported assertion that sqrt(GDP) is meaningless, and in the next breath demand that I prove a relationship. Why do you get to make unsupported assertions where I have to prove relationships?
2) But this is in fact my point. Prove there is a relationship between these variables (or at least demonstrate it) and show me what it is.

The point of the ratio quantities is to create independent variables.

Yes. And doing so assumes without a scrap of support that there is a specific relationship between the variables. And again, I happen to believe that there is a relationship, but that has not been demonstrated, nor has the specific nature of the relationship been illuminated. It would be much clearer and less misleading to say:
Co2 Emissions = F(Population, GDP, Energy, Misc)
in my book.

Daniel G.
July 10, 2014 8:40 am

@steveta_uk says:
Alternatively, I can simply count the M&Ms. This is the Willis method.
That can be difficult for too many M&Ms. It is way easier to just measure one quantity and do the math.

July 10, 2014 8:41 am

>> Of course, you halved population, and doubled GOP per capita. All other things weren’t equal.
No, I halved population. The formula — as presented — doubled GDP per capita.

July 10, 2014 8:42 am

Every human emits 1/2 ton of CO2 annually by breathing, as a species we emit 3.5 billion tons of CO2 just by breathing.

July 10, 2014 8:43 am

So you think it plausible that if we magically eliminated half the human population, we’d all be twice as productive?

Daniel G.
July 10, 2014 8:47 am

Bofill says:
Co2 Emissions = F(Population, GDP, Energy, Misc)
Read the paper: We are talking about energy-related emissions.
If there are more people, more wealth is being produced, such production requires more energy, so more emissions.
If people start using more energy to produce the same amount of wealth, more energy, more emissions.
If people get wealthier on average, more wealth is being produced, such production requires more energy, so more emissions.
If people start emitting more CO2 for the same ammount of energy, more emissions.
sqrt(GDP) is meaningless, because meaning is something humans create. sqrt(GDP) might cause an real impact to the economy, but no one has proven how.

July 10, 2014 8:47 am

>> Of course, you halved population, and doubled GOP per capita. All other things weren’t equal.
By the way, let’s say halving the population also halves GDP per capita. It doesn’t change anything. The formula still reduces to CO2 = CO2. You can study for ten years the effect that population has on GDP (maybe you find that halving population causes people to be a little more productive, so it only reduces per capita GDP by 40%). Plug in your findings into that formula, and learn exactly nothing about CO2.

Daniel G.
July 10, 2014 8:49 am

Jason L. writes:

The formula — as presented — doubled GDP per capita.

It is your mistake to think GDP stays the same, not the formula’s.

Tamara
July 10, 2014 8:50 am

Gerald Harbison,
Using the Kaya Identity, please predict the CO2 emissions for 0 population. The answer is not 0, either mathematically or in the real world. The result is an indeterminate number, as CO2 could be infinite in that equation.
0 population = 0 GDP = 0 Energy
A whole lotta division by 0.

Nancy C
July 10, 2014 8:51 am

we all know e = mc^2, but here’s what I’m going to call the nancy identity:
e = population * (m/GDP) * (GDP*c) * (c/population)
The UN and half of the people commenting here can clearly see that this allows us to adjust the energy yield of nuclear reactions by adjusting population and GDP! This should be a bonanza for our species.

JJ
July 10, 2014 8:52 am

OYG.
Categories don’t cancel. Units cancel, but even when they do, the quantities they are associated with don’t just disappear. Is there a seventh grader handy – or a Chinese fourth grader – to perform a basic QA/QC on these posts?

Joseph Murphy
July 10, 2014 8:54 am

Jason L says:
July 10, 2014 at 8:36 am
It’s disheartening to see how many people think this equation is somehow useful.
——–
My face and palm are both worn out.
All this ‘identity’ does is needlessly and pointlessly add variables to A=A. It does not assist with any more knowledge than A=A. There is nothing in it beyond that understanding. The variables contained it it are meaningless, changing their values changes nothing else. It is equivalent to a list of variables, the equation is not neccessary. If someone could post a use for this ‘identity’ so that I can somehow understand what I am missing I would be greatfull.

ColA
July 10, 2014 8:54 am

I thought I was wrong once ….. but I was actually mistaken!
Tamara says:
July 10, 2014 at 8:11 am
I agree you are correct, it bugged me a bit until I got into bed and then it annoyed the crap out of me … hence I got up and actually did what I should have done first and what Wills should have also done right at the start … check and research …. don’t go half cocked and shoot from the hip!! Now I limply advise you all to have a look at this delightful bit of analysis on the Kaya Identity >
http://www.manicore.com/anglais/documentation_a/greenhouse/kaya_equation.html

July 10, 2014 8:55 am

c is a constant. You therefore can’t vary c/population independent of c.
I wouldn’t put my name on that.

Mark Bofill
July 10, 2014 8:55 am

Daniel,

If there are more people, more wealth is being produced, such production requires more energy, so more emissions.
If people start using more energy to produce the same amount of wealth, more energy, more emissions.
If people get wealthier on average, more wealth is being produced, such production requires more energy, so more emissions.
If people start emitting more CO2 for the same ammount of energy, more emissions.

Yes. But what are the quantitative relationships? If there are more people, does the wealth produced rise logarithmically? Linearly? As a polynomial function, as an exponential function? Are there no constants involved to scale anything; could it be that the energy part of the expression should weight more than the GDP part?
Without knowing these relationships, I don’t see how we know that the identity describes what’s really going on. We’re just assuming it.

richardscourtney
July 10, 2014 8:56 am

Pete Brown
Your post at July 10, 2014 at 5:34 am says in total

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.

.
Firstly, it would have helped if you had addressed my point because your post stresses its importance.
As I said at July 10, 2014 at 2:31 am and at July 10, 2014 at 2:52 am and again with explanation at July 10, 2014 at 4:57 am in my post addressed to you

Sorry, but I know you’ve entirely misunderstood the point of the equation.
It is a political tool provided by a political organisation for political purposes.
The equation is nonsense. It links independent variables to form abstract constructs which only indicate political desires. I am astonished that this is not blatantly obvious to everyone.

And my explanation of that which you have ignored included

The abstract constructs are NOT “factors” which combine to be CO2 emissions.
For example, what evidence is there that in any nation a significant factor to CO2 emissions is GDP per capita?
When a country has constant GDP and constant population a change from manufacturing industry to service industries alters its CO2 emissions. Conversely, what evidence is there that when a country’s GDP is constant then changes to its CO2 emissions are significantly and directly related to its immigration or emigration?

You have not answered those questions but, instead, have asked me your “4 questions” which are meaningless because they rely on “all other things being equal”, but if one were to change then that would change others.
I am rejecting “the logic of what is being represented”. Please note that I am NOT disagreeing with the equation. I am saying the equation is illogical: it is a naked Emperor and I am refusing to engage in a discussion of the colour of the “logic” used to dress it up.
So, I have no intention of answering meaningless questions which divert from the important fact that
The equation is a political tool provided by a political organisation for political purposes.
Or, to transpose that into your type of language
Maybe face reality a bit, please.
Richard

Daniel G.
July 10, 2014 8:56 am

Jason L. writes:

By the way, let’s say halving the population also halves GDP per capita.

Doomsday Scenerio.

It doesn’t change anything.

In your Doomsday scenario, CO2 decreases.
So in you Doomsday scenario, GDP per capita decreases.
It was $3 trillion / (300 million people) = $10/people
Now it is $5/people. GDP is a quarter of what it was, now it is $750 billion.
But (CO2 emissions/500 trillion joules) remains contant.
So CO2 decreases by a quarter.

July 10, 2014 8:56 am

Jason L: check your math. In your example, you divided the rhs by 4.

July 10, 2014 8:57 am

Anthropogenic CO2 emissions for zero population are obviously zero. This is getting very, very silly.

July 10, 2014 8:58 am

That should have been “You therefore can’t vary c/population independent of population.

steverichards1984
July 10, 2014 8:59 am

Let me try and state it more clearly than ‘Rodney’:
Yes
V = IR
So we could substitute V for anywhere we see IR
So V = V
The above is valid but unproductive, it gets you know where.
If you use V = IR to calculate V when you know both I and R, then you have done something productive.
To transpose a formula from V = IR —> V = V whilst true, is unproductive.
Now, if you have a formula such as the one Willis spoke of, where, after the normal rules of simplification gives you the equivalent of V = V, then your starting formula is rubbish, no more, no less, just rubbish.
I was going to write that it is really sad that some people do not know basic transposition and substitution, but I decided not to.
We all have our own level of knowledge, its just a bit scary at times to find out what everyone understands……..

July 10, 2014 9:04 am

>> It was $3 trillion / (300 million people) = $10/people
>>Now it is $5/people. GDP is a quarter of what it was, now it is $750 billion.
Ok, let’s plug it back into the formula at $750 billion (GDP being a quarter of what it once was)
CO2 = 150 million people * ($750 billion / 150 million people) * (500 trillion joules / $750 billion) * (CO2 emissions/500 trillion joules)
It still simplifies to CO2 = CO2. According to this ‘formula’ CO2 can still be anything.
Look, I’m not arguing that lowered population = lowered CO2. I’m arguing that the formula is incapable of telling you that.

July 10, 2014 9:06 am

No, if your equation reduces to lhs = rhs, it’s not rubbish, it’s an identity. Which is probably why this particular example is called the Kaya identiyy. The quantities on the right: population, per capita GDP, energy intensity of GDP, carbon intensity of energy are all meaningful and largely independent, just as current and resistance are in Ohm’s Law.

Daniel G.
July 10, 2014 9:06 am

Bofil:
Without knowing these relationships, I don’t see how we know that the identity describes what’s really going on. We’re just assuming it.
Linearity is not a bad assumption. And ultimately, the identity describe qualitative relationships.

July 10, 2014 9:07 am

Look, I’m not arguing that lowered population = lowered CO2. I’m arguing that the formula is incapable of telling you that.
The other three variables being held equal, it’s telling you exactly that.

kenw
July 10, 2014 9:08 am

steverichards1984 says:
July 10, 2014 at 8:59 am
Thank you. I was also trying to clarify but you beat me to it. The fact is that if you DO NOT get 1=1 you have a big problem.

Tamara
July 10, 2014 9:08 am

Gerald, let’s try it this way.
Let’s say we are totally awesome, and reduce the CO2 intensity of our energy to zero.
What variable has changed?
What is our GDP?
What is our population?

Daniel G.
July 10, 2014 9:09 am

I’m arguing that the formula is incapable of telling you that.

You are using it incorrectly.
Look at steveta wrote:

Lets say I have some crates of M&Ms. In the crate there are many boxes. In the boxes there are many packets. In the packets there are many M&Ms.
So the equations for how many M&Ms I’ve got is
M = C * B/C * P/B * M/P
So if I know how many M&M per packet, and packets per box, and boxes per crate, and the number of crates, I can easily calculate the number of M&Ms. This is the Kaya method.

Curious George
July 10, 2014 9:10 am

I like the simplicity of the UN CO2 equation – a direct application of accounting rules to the problem at hand. Let’s try the same approach to determine the exact number of intelligent civilizations in our Galaxy:
ICt = ICy + ICb – ICd
where ICt is the number of Intelligent Civilizations today, ICy is the number for yesterday, ICb is a number of civilizations born in one day, and ICd is a number of civilizations disappearing in one day. As a test, we can set all for variables to zero (consistent with observations), and get a perfect agreement.
To keep it simple, I omitted technical details like a relativity of time or a choice of a reference frame.

Dave Wendt
July 10, 2014 9:10 am

I think we really need to embrace this equation. We need to make sure every person on the planet is exposed to it for it demonstrates unequivocally that we have done all that is possible to solve the “problem” of CO2. No matter how we change global population, or per capita GDP, or the economic efficiency of energy, or the emission efficiency of energy production, CO2 emissions remain the same. As our next dictator in waiting Ms. Clinton has said at this point what does it matter? It’s game over! Tell all those leeches at the IPCC, the UN, the NGOs, etc. to hit the bricks! No more jetting about to various garden spots across the globe to plot their extortions of the rest of us, no more six figure salaries to plot the impoverishment of the rest of us. You are all immediately redundant, don’t let the screen door hit you on the way out!

Daniel G.
July 10, 2014 9:12 am

Tamara says:

Let’s say we are totally awesome, and reduce the CO2 intensity of our energy to zero.
What variable has changed?
What is our GDP?
What is our population?

Let me remind you that we are talking about energy-related emissions. (read Willis’ post)
If we manage to capture all CO2 we emit in energy generation, our energy-related emissions drop to zero.
CO2 = p * w * b * 0 = 0
Can you see it?

JK
July 10, 2014 9:13 am

ferdberple says:
“Notice, that no matter what amount we use for population (or Gore’s waistline), according to the Kaya Identity, CO2 emissions will remain unchanged!!
So, the ONLY conclusion that we can derive from the Kaya Identity with regard to CO2 and population, is that world population has NO EFFECT on CO2.”
But what the identity tells us is that
IF the following are held constant:
GDP/population
energy/GDP
CO2 emissions/energy
THEN:
CO2 emissions are proportional to population.
So what? Why is this of any more interest that learning that
IF the following are held constant:
GDP/Al Gore’s waistline
energy/GDP
CO2 emissions/energy
THEN:
CO2 emissions are proportional to Al Gore’s waistline?
The answer is that GDP / population means something, and holding it constant or varying it, whether in reality or in our imagination for analytical purposes, leads to understanding.
GDP / population is perhaps the most important number there is for understanding how the economy works. Sometimes it is described by an innocuous term like ‘living standards’. It reflects the most profound truth about the economy – namely, that all wealth is created by human beings. All economic progress, I would argue, is ultimately measured by this number. How much wealth can be produced by each individual? How can we raise productivity? This is the determinant of all human prosperity. GDP / population does not tell us everything – for example it ignores the question of inequality, since in reality the difference parts of the population do not produce or consumer even amounts of GDP. The GDP / population ratio is only an average. But it is a crucial starting point for understanding.
GDP/Al Gore’s waistline is just an arbitrary number. It’s a joke. Of course you can plug it in to your identity and get and arithmetically correct formula. But if you think the identities are just as significant as one another, I don’t believe you are thinking carefully enough about what the numbers mean.
It makes sense to imagine the population changing while GDP / population stays the same, or vice versa. These are useful thought experiments for understanding the real world. The useful information that the identity is adding to CO2 = CO2 is in understanding how the consequences of those assumptions play out.
If you want to think about the consequences of varying the ratio of GDP / Al Gore’s waistline independently of Al Gore’s waistline then the corresponding identity will help you figure that out.
But if you believe GDP / population is just as important a measure as GDP / Al Gore’s waistline I can’t help you.
The same problem arises with Willis’ original example.
Whether or not you think CO2 is a problem, the fact remains that the ratios GDP / population, Energy / GDP and CO2 / energy are meaningful numbers.
The reason is that in each of these ratios the numerator and the denominator have a a real relationship to each other, not just an arbitrary arithmetic relationship.
You may not think that CO2 is a problem, or even that CO2 causes global warming. But surely it’s riduculous not to see that (world CO2 emissions / world energy production) is a more meaningful number than (world CO2 emissions / energy production to make beer). Just as we could interpret (GDP / population) to mean something, we can see that (CO2 emissions / world energy production) reflects something real, namely the technology used to generate energy (of course it does not reflect this perfectly as not all human emissions come from energy). What in reality does )world CO2 emissions / energy production to make beer) reflect? Nothing.
Of course we could consider a functional form such as GDP squared / population, rather than GDP and get an arithmetic identity that is just as valid as the Kaya idendity. But it would not be so useful because it does not reflect the real relationship between GDP and population in the way that GDP / population does. This is why you find it tabulated by so many economic analysts, and they have been doing so for years before the climate scare.
It’s the same with the NancyC’s proposal:
e = population * (m/GDP) * (GDP*c) * (c/population)
It’s a valid equation. But it’s not useful, because the relationship between mass and GDP is arbitrary.
In focusing on arithmetic, it looks to me that Willis forget to think about what the numbers mean.

richardscourtney
July 10, 2014 9:13 am

tttt:
At July 10, 2014 at 6:02 am you reply to me

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.

YES! That is what I have been saying!
However, you and some others are refusing to see that the factors are not real and can – with equal validity – be claimed to be anything. Substitute bullsh*t for Energy and the equation still works only it now indicates that CO2 emissions are affected by bullsh*t but not Energy.
With that substitution the equation would have unchanged validity but be more honest.
Richard

Daniel G.
July 10, 2014 9:14 am

Dave Wendt says:

No matter how we change global population, or per capita GDP, or the economic efficiency of energy, or the emission efficiency of energy production, CO2 emissions remain the same.

It doesn’t.

Mark Bofill
July 10, 2014 9:16 am

K, this is going nowhere. I’m not going to waste time and space continuing the debate. You want to go ahead and make a bunch of unfounded assumptions, probably including some we haven’t though of, that’s your business. I don’t see the point. For the record, I’m not persuaded, but I’m going to drop it.

Joseph Murphy
July 10, 2014 9:19 am

Daniel G. says:
July 10, 2014 at 9:09 am
I’m arguing that the formula is incapable of telling you that.
You are using it incorrectly.
Look at steveta wrote:
Lets say I have some crates of M&Ms. In the crate there are many boxes. In the boxes there are many packets. In the packets there are many M&Ms.
So the equations for how many M&Ms I’ve got is
M = C * B/C * P/B * M/P
So if I know how many M&M per packet, and packets per box, and boxes per crate, and the number of crates, I can easily calculate the number of M&Ms. This is the Kaya method.
———————-
all you have done here is to use a lot of words to say “I know the number of M&Ms, therefore I know the number of M&M’s” The number of boxes, crates, packets is not relevant and independant of the number of M&Ms. You can plug in any value for them and it changes nothing, especially the number of M&Ms.

bones
July 10, 2014 9:22 am

Willis,
The warmistas will try to use this to discredit the many correct pieces of work that you have posted here. You should retract this one. Identities of this sort are useful for estimating things unknown from things known. I think that ttt expressed this most succinctly with his example. If you know your car’s average gas mileage and you travel somewhere requiring some known amount of gas, you can estimate the miles driven from
Miles driven = Gallons * Miles / gallon.
Maybe not as good as an odometer, but it does yield useful information.

July 10, 2014 9:27 am

>> M = C * B/C * P/B * M/P
Here’s where those using the “M&M examples are in error. The units and quantities are NOT the same.
Let’s spell it out a little further
M&M’s = Crates * Boxes / Crate * Packages / Box * M&M’s / Pacakge.
If I know that I have 5 crates, 10 boxes per crate, 20 packages per box, and 30 M&M’s per package, the result looks like this:
M&Ms = 5 crates * (10 boxes / 1 crate) * (20 packages / 1 box) * (30 M&M’s / 1 pacakge)
PLEASE NOTE: While the units cancel each other out, the quantities still express a relationship. So this formula reduces to
5 * 10 * 20 * 30M&M’s (crates, boxes, and package units all cancel leaving just quanity)
So you have 30,000 M&Ms.
In the formula Willis posted, there is nowhere for quantities to vary between the numerator and denominator, and therefore no relationship that can be expressed. To put it in the M&M analogy, it would be the same as saying that “however many number of crates you use, it holds as many boxes as we shipped” (and so on down the line of containers). It’s logical fallacy.
Silly, yes. Just like the original formula.

Daniel G.
July 10, 2014 9:28 am

@Joseph Murphy says:
You might not know the number of M&Ms. But the producer tells you the number of M&Ms per packet. An co-worker tells you the number of boxes per crate. What do you do?
Best method:
Step 1: Count packets per box.
Step 2: Count crates.
Step 3: Use the tautological identity.
[Everyone, keep in mind we are talking about energy-related emissions, read the UN’s paper.]

Daniel G.
July 10, 2014 9:29 am

In the formula Willis posted, there is nowhere for quantities to vary between the numerator and denominator, and therefore no relationship that can be expressed.

Yes, there is. More population increases GDP. Duh.

Dr. Doug
July 10, 2014 9:31 am

Friends,
Permit a few remarks from an economist who knows something about both both the use — and abuse — of modeling and about the empirical referents here.
First, I think we all agree that a mathematical identity has neither empirical content nor theoretical demonstrative power in itself. It is nothing more nor less than an accounting device. The limited nature of a mathematical identity is not a point in dispute. It would help this discussion greatly if everyone would see that this point is not in dispute.
So, when might such an accounting device, consisting largely of ratios, be useful? When these ratios themselves (1) exhibit some sort of regularity and (2) vary independently of each other, at least to some extent. This is the issue giving rise to disagreement here.
Take GDP/population. This is a useful ratio for multiple reasons: (1) it expresses production per capita as well as income per capita, and thus average standard of living. It’s a highly meaningful ratio in itself, apart from its usefulness in thinking about decarbonization. (2) Other things equal, GDP grows when the population, and thus the labor force, grows. It is not a 1:1 relationship (because of diminishing returns), but it is an empirically (not just theoretically) real relationship, adding to the meaningfulness of the ratio in itself. (3) Empirically, the ratio tends to rise over time due to technological change and capital accumulation, more than offsetting the diminishing returns just noted.
Given the important fact of rising GDP per capita, we might expect rising carbon consumption per capita — but that depends on other things being equal. And they’re not. Why not? Well, the declining energy intensity of GDP and the varying carbon intensity of energy.
And that’s what the equation is useful for getting at.

July 10, 2014 9:31 am

>> Yes, there is. More population increases GDP. Duh.
And each of those increases cancel each other out in the formula.

July 10, 2014 9:32 am

Let’s say we are totally awesome, and reduce the CO2 intensity of our energy to zero.
What variable has changed?
What is our GDP?
What is our population?

The carbon intensity has changed. We would reduce carbon dioxide emissions to zero. We can say nothing about the other three independent variables on the right hand side.
Do you understand the difference between a dependent and an independent variable?

Dave Wendt
July 10, 2014 9:32 am

So the equations for how many M&Ms I’ve got is
M = C * B/C * P/B * M/P
So if I know how many M&M per packet, and packets per box, and boxes per crate, and the number of crates, I can easily calculate the number of M&Ms. This is the Kaya method.
Except that in your equation the variables have different values at each stage. In M/P, P=1. In P/B
P= some number presumably greater than 1 and B=1. In B/C, B= some number presumably greater than 1 and C=1. C would be the same only in the singular case where you have only one crate. What you have constructed is in no way equivalent to the Kaya Identity

Kevin Kilty
July 10, 2014 9:32 am

There is a long history of equations of this sort that are constructed to convey the appearance of understanding.

JohnB
July 10, 2014 9:33 am

@Bones
Miles driven = Gallons * Miles / gallon
– great analogy.
It also tells you that you can get further by EITHER increasing your gas mileage OR getting a bigger tank.

July 10, 2014 9:34 am

Interesting post. Anyone interested in seeing an application of the Kaya Identity in climate policy evaluation might take a look at this paper on Australia:
http://sciencepolicy.colorado.edu/admin/publication_files/2010.36.pdf
More generally, see:
http://www.amazon.com/Climate-Fix-Roger-Pielke/dp/0465025196/ref=tmm_pap_title_0/275-2858781-9562656
Happy to engage those with sincere interest here (I won’t be following this thread):
http://rogerpielkejr.blogspot.com/2014/07/common-ground-on-climate.html
Thanks!

Tamara
July 10, 2014 9:39 am

Thanks, Daniel G., but that’s not what I am asking.
What population can we have with 0 emissions? How rich can we be with 0 emissions?
How many empty crates can I have if I don’t have any M&Ms?
I’m with Mark Bofill. Cheers!

EO Peter
July 10, 2014 9:43 am

Me think they badly labelled variable in this mathematical relation. At left it shall be “CO2emissionsTotal” and at right simply “Co2emissions”.
But the fact remain, that it is still a “childish” kind of a relation…

Frodo
July 10, 2014 9:44 am

“Wayne Delbeke says
Ask Holdren.”
“ Hoser says:
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?”
Yup and Yup. If you haven’t already, Please read Dr. Tim Ball’s excellent June 24th post regarding Holdren. All these unscientific movements are intimately connected with dramatic population control, especially in the suffering 3rd world. Holden’s 1977 book, co-authpored with the head ghoul Erhlich, with numerous evil solutions to the non-existent problem of overpopulation, was entitled “Ecoscience – Population, Resources, Environment”. CAGW is just the evil, unscientific spawn of the 60s/70s overpopulation movement. The people behind it have gotten more devious as time as gone on, so it isn’t as blatantly stated as it was in the 60s/70s, but dramtic population reduction is still the main goal. For (much) more detail on the book written by President Obama’s current Science Poobah, read (and literally weep) the link below :
http://zombietime.com/john_holdren/

Daniel G.
July 10, 2014 9:44 am

@Jason L:
You do not have 1 box. You do not have 1 crate. you do not have 1 package.
CO2 = p * w * e * c
Use these example values:
p = 1,000,000 people
w = $20,000 / 1 person
e = 300 kJ / $1
c = (1 gram of CO2) / 1J
Co2 = pop * (gdp per capita) * (energy intensity) * (co2 efficiency)

Daniel G.
July 10, 2014 9:46 am

Thanks, Daniel G., but that’s not what I am asking.
What population can we have with 0 emissions?

0 energy-related net emissions. Kaya tells us that energy-related emissions will be zero. She doesn’t tell if humans will exist.

How rich can we be with 0 emissions?

Kaya tells us that energy-related emissions will be zero. She doesn’t tell if humans will be rich.

Brian
July 10, 2014 9:47 am

Willis and those who think the Kaya identity is useless are confusing dimensional analysis with the actual equation, as others have already noted. Consider the following equation:
distance traveled = (distance traveled/time)*time
Now that’s a useless equation–all it does is cancel to distance traveled on each side.
Except that the equation is not useless. We replace it with standard useful quantities, each of which can be independently measured.
d = v*t
Now nothing cancels. It tells us that if we know our velocity and time elapsed, we can get the distance traveled. So how is this useful if v is just (distance traveled/time)? Because we can get v by using smaller samples of distance and time. So v could be (distance traveled in 5 sec)/(5 sec). THEN we can use that value to get the total distance traveled in ANY amount of time we want.
That’s what the Kaya identity does also. It’s also what Steveta_UK does above with M&Ms. Sorry Willis, but your argument is a bad mistake.

Chuck Nolan
July 10, 2014 9:50 am

Without actually checking, my guess is energy use per unit of GDP is decreasing. It takes less juice to make stuff. This increases our wealth. (This is climate politiscience so guesses are okay)
CO2 emissions per unit of energy decreasing and adding to our wealth.
Historically, GDP rises faster than population therefore more people enjoy the fruits of being human and this also adds to our wealth.
The problem is not so much too many people but rather wealth.
The rich control freaks don’t have enough, yet.
cn

Daniel G.
July 10, 2014 9:52 am

Willis’ argument evaporates when the ratios and pop are changed by letters. Each of the letters is meaningful, and they are more or less indepedent of each other, creating a linear relationship.

RH
July 10, 2014 9:53 am

I can’t decide if they are inept, or just feel so in control of the dialog that they can say anything they want if it fits their agenda.

Greg
July 10, 2014 9:54 am

Oh my , I’ve never found WUWT to be a strong place for a technical discussion but boy are we going to town on this one. Everyone who wouldn’t no an exponential from an elephant’s tail but can remember his two-times table from school is in on this one.
Well at least we know were to come next time we need to check the subtlties of temperature adjustments or the impluse response of the climate system.
BTW, no one’s leaving here until I get my M&Ms back. I had five red ones six blue ones (my FAVOURITES !).
Now own up ! Who got ’em ?

Daniel G.
July 10, 2014 9:55 am

BTW, even if the relationship between GDP and population is not linear, that is beside the point.
What matters is that all variables are meaningful and more or less indepedent of each other.

Sun Spot
July 10, 2014 9:56 am

I took this post to be a statement of the absurd for reasons of invoking levity. It seemed to me an extension of the recent post on humor as were many of the comments.

John West
July 10, 2014 9:59 am

What’s wrong with saying:
Emissions = number of emitters X (units of production per emitter) X (unit of energy per unit of production) X (emissions per unit of energy)
?

Mark Bofill
July 10, 2014 10:00 am

Gosh Daniel.

BTW, even if the relationship between GDP and population is not linear, that is beside the point.
What matters is that all variables are meaningful and more or less indepedent of each other.

Does it matter? Only if you care whether or not the results are correct. I sort of like it when I the formulas I use give me the correct answers. Stuff doesn’t crash, fail and or explode so much that way.
I guess if what you’re trying to accomplish has little to do with whether or not the results are correct, you’d be right that it doesn’t matter and it’s besides the point.

Chuck Nolan
July 10, 2014 10:01 am

The graphic does not come from science or economics.
This is taught in communications 101.
It’s for propaganda. Made for politicians and those in authority for control purposes only.
cn

EO Peter
July 10, 2014 10:03 am

“What’s wrong with saying:
Emissions = number of emitters X (units of production per emitter) X (unit of energy per unit of production) X (emissions per unit of energy)
?”
As I said, it shall be:
Emissions_tot = number of emitters X (units of production per emitter) X (unit of energy per unit of production) X (emissions per unit of energy)

RockyRoad
July 10, 2014 10:09 am

In Atlas Shrugged, Ayn Rand had much to say about A = A.
Perhaps those stellar wits over at the UN have finally embraced Atlas Shrugged.

Nancy C
July 10, 2014 10:10 am

Dr Doug,
“It’s the same with the NancyC’s proposal:
e = population * (m/GDP) * (GDP*c) * (c/population)
It’s a valid equation. But it’s not useful, because the relationship between mass and GDP is arbitrary.”
You’re starting to understand! You’re right! It’s a valid equation but not useful. The exact same is exactly true of the kaya identity, at least as written here.
You also say:
“IF the following are held constant:
GDP/population
energy/GDP
CO2 emissions/energy
THEN:
CO2 emissions are proportional to population.”
But, think about it. Those ratios aren’t actually independent of each other because of their shared variables. You can’t arbitrarily change them or hold them constant. PLEASE, do yourself a favor and just plug some numbers into that equation. You’ll quickly find that what you said, “CO2 emissions are proportional to population” is not actually true according to that equation, no matter what you try!
Of course in the real world, CO2 emissions will tend to be somewhat proportional to population, although not in any way that can be reduced to a simple law. That’s how we can know the kaya identity is garbage, it doesn’t model the real world in any way. As population goes up, you expect CO2 emissions to change. In the kaya identity as expressed here it doesn’t, no matter what you do to population CO2 emissions never change.
Now, since I haven’t read the source material, I’m willing to accept that Willis maybe misrepresented the kaya identity in some way. If so, that would be a good criticism of his article.
Gerard Harbison says:
July 10, 2014 at 8:55 am
c is a constant. You therefore can’t vary c/population independent of c.
I wouldn’t put my name on that.
You corrected yourself, you meant you can’t vary c/pop without varying pop.
I assume that you also know that since c is a constant you can vary mc^2 without varying m. So what? What’s the value of pointing out the one thing and not the other? I guess I’m missing your point.
If you think there’s a problem with my NANCY identity, please go ahead and plug in some numbers. You’ll find it gives the correct answer every time, which means I’m just as good as einstein. Or at least just as good as this “kaya” person.

July 10, 2014 10:12 am

I guess Willis is trying to be funny. The equation is obviously valid (whether it is exactly correct may be another matter). I had to scroll through many comments to finally find one that explained it (Pete Brown 4:32 am)
Think of CO2 on the left side of the equation as CO2[total]. On the right you have CO2 per unit energy as the input (the last term on the right). In other words in the calculation you do not input total CO2 on the right you input CO2 per unit energy.

Nancy C
July 10, 2014 10:15 am

oops, CAN’T vary mc^2 without varying m.

Ann Banisher
July 10, 2014 10:17 am

If you want to decarbonize the world and wonder how much it costs, there’s an App for that!
Go to the International Carbon Bank’s CO2 Reduction Calculator
http://www.icbe.com/carbondatabase/reductions.asp
to see how truly insane the idea is. They do all the math, This calculator estimates the time and cost required to phase out CO2 production with renewable energy and carbon sinks. It tells you what each system costs, its lifespan, and how much CO2 you will save, and the tells you how much it costs per ton.
To give some perspective, the US alone produces 5.2 GT of carbon/year. If you want to play with math, find the cheapest method to reduce US consumption by 50% and see if you can do it for less that a quadrillion dollars. Seriously.

Daniel G.
July 10, 2014 10:17 am

Those ratios aren’t actually independent of each other because of their shared variables.

False. The M&M ratios also have shared variables. That doesn’t make a problem.

Pete Brown
July 10, 2014 10:17 am

Nancy C says:
July 10, 2014 at 8:51 am
Nancy, seriously, did you do that lobotomy yourself….?

Daniel G.
July 10, 2014 10:20 am

Nancy, this is the problem with your identity:
(m/GDP) is a meaningless ratio.
(GDP*c) is a meaningless product.
(c/population) is meaningless ratio.
Average wealth, energy intensity, and co2 efficiency are not meaningless.

Pete Brown
July 10, 2014 10:20 am

Roger Pielke Jr. (@RogerPielkeJr) says:
July 10, 2014 at 9:34 am
Hurray!!!! The Cavalry…!!!!
Prof Roger, thanks for answering the call…

Daniel G.
July 10, 2014 10:28 am

…although not in any way that can be reduced to a simple law…

We are talking specifically about energy-related emissions. Yes, it can be reduced to a simple law, because you have meaningful ratio variables.The relation between co2 emissions and population might be non-linear because increasing population creates more genius inventors, increasing GDP per capita, but that has nothing to do with the validity of Kaya’s identity.
Take voltage for example. In a diode, the relation between voltage and current is not linear, but resistance is still defined the same way. And:
V = IR

Frederick Davies
July 10, 2014 10:31 am

Reminds me of the Drake equation… all very scientific-looking, but just plain obvious.
FD

Zeke
July 10, 2014 10:32 am

I notice the social sciences have arrived to the level of chemistry. Popper warned about that a long time ago.

john robertson