**[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**

Another 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:

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 …

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.

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.

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

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

Orwellian

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?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!

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

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

Ask Holdren.

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

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.

Now that is, sadly, funny.lol

4 eyes says:

July 9, 2014 at 10:39 pm

Sorry, 4 eyes, but neither equation can “work out the amount” of anything. All either one can do is prove that CO2 emissions = CO2 emissions.

w.

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

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.

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.

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.

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.

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

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.

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!

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.

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…

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.

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

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)..

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.

” 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.

Mooloo says:

July 9, 2014 at 10:58 pm

Say what? Since each variable only appears once, you cannot cancel out anything.

On the right side of their equation, on the other hand, each variable appears both on the top and on the bottom so they can be cancelled out.

Mathematically, the Beer Identity and the Kaya Identity both are totally equivalent, because they reduce to CO2 emissions = CO2 emissions, and both are equally valid.

So would you say that the Beer Identity allows us to figure out what effect a 10% growth in beer production will have on the emissions of CO2? Because according to the equations, a 10% growth in beer production will have the same effect as a 10% growth in GDP …

w.

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?

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

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

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.

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/

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.

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.

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

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.

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!!

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.

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. :)

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

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

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.

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.

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.

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

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

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.

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.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.

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 .

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.

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.

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?

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.

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.

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.

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.

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.

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.

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.

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

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

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

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.

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 effectsince 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.

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

{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

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.

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

Friends:

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

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

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

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

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

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.

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 the

Beer Production, Oh my God can’t someone do something to stop these people?!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.

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 :-‘)

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.

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.

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

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?

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?”.

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.

tttt:

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

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

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

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.

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

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

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.

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

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.

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…)

Hlaford says:

July 10, 2014 at 3:29 am

Excellent point.

XCO2 —> T

XCO2 x 112% ——-> T?

Can anyone advise me what T? should be ?

The equation is irrelevant since:

–> CO2 EMISSIONS ≠ TEMP RISING ASSUMPTION

they want they “believe” it does.

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]

“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.

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 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

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

Author, author, name the author.

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.

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.

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.

@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.

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.

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

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.

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

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.

richardscourtney:

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

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.

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.

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.”

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)

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.

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

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.

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.

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.

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.

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).

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

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.

Pete Brown says:

July 10, 2014 at 5:34 am

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.

The Gory details:

CO2 emissions = Al Gore’s Waistline * GDP/Al Gore’s Waistline * energy/GDP * CO2 emissions/energy

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.

” 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.

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

tttt,

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).

they is not.Nice.

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

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.

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.

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

=======

wrong.

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.

e=mc2

v= at

d=1/2at2

a2+b2=c2

these equations are useful, because they are not of the form a=a.

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.

@ferdberple

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

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.

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

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!

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?

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.

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.

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.

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.

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.

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.

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.

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.

tttt,

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.

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.

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

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!

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.

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.

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

http://climatemodels.uchicago.edu/kaya/

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.

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.

tttt says:

July 10, 2014 at 6:49 am

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.

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

Willis excellent mathematical

reductio ad absurdumis 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

@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.

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?

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.

You are thinking too much math if you think increasing population will reduce GDP per capita.

It doesn’t “cancel”.

@ferdberple

GDP/Al Gore’s Waistline

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

GDP?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.

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.

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.

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

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

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.

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

@ferdberple

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?

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

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.

@JohnB:

GDP per capita, not GDP.

Pete Brown says:

July 10, 2014 at 7:27 am

I agree.

Yes.

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

….

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 ridiculous. Put it back in context.

Now think it through. By accepting the identity, we have

assumedwithout 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.

@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.

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

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.

Mark Bofill writes:

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?

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

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

@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.

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.

JohnB

Yes!

Admittedly your way was quicker…

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.

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.

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).

“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.

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.

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.

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

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.

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.

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?

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

@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)

@Mark 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.

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.

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.

@UsUrbrain says:

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

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.

@David in Texas says:

Apparently, you understand the identity’s meaning. It is the math of totalitarianism.

I am for

recarbonizationbecause 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.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 ;(

>> 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.

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

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???@Jason L says:

Everything else remains the same.

Bullshit, GDP decreases.

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.

Daniel G,

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.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.

@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.

>> 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.

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.

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

@Mark 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.

>> 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.

Jason L. writes:

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.

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.

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?

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.

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

c is a constant. You therefore can’t vary c/population independent of c.

I wouldn’t put my name on that.

Daniel,

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.

Pete Brown

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

.

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

And my explanation of that which you have ignored included

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

Jason L. writes:

Doomsday Scenerio.

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.

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

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

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

population.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……..

>> 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.

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.

@Mark 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.

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.

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.

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?

You are using it incorrectly.

Look at steveta wrote:

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.

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!

Tamara says:

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?

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.

tttt:

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

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

Dave Wendt says:

It doesn’t.

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.

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.

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.

>> 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.

@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.]

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

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.

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

And each of those increases cancel each other out in the formula.

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?

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

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

@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.

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:

The Climate Fix: What Scientists and Politicians Won't Tell You About Global Warming

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!

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!

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…

“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/

@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)

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

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

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.

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

climate politiscience so guesses are okay)isCO2 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

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.

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.

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 ?

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.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.

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)

?

Gosh Daniel.

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.

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

“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)

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.

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.

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.

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

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.

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

Nancy C says:

July 10, 2014 at 8:51 am

Nancy, seriously, did you do that lobotomy yourself….?

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.

Roger Pielke Jr. (@RogerPielkeJr) says:

July 10, 2014 at 9:34 am

Hurray!!!! The Cavalry…!!!!

Prof Roger, thanks for answering the call…

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

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

FD

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

Thanks Willis,terrible and funny, more and more I come to believe the UN uses Monty Python as an instruction/training manual.

So some here say; “Its an Identity”.

Sure is , identifies you as being from the new math school, how does this “equation make you feel?”.

Richard Courtney clearly defines the identity of this idiocy.As a political statement devoid of any value dressed up as algebra.

It does not matter how much you modify the variables, short of dividing by 0, this equation is CO2=CO2.

This is intergovernmental maths.

Perfect for those policy meetings , where absolute idiocy abounds as all the mandarins nod wisely and cover their butts.

Actually the equation is a perfect summary of modern govt policy.

Predetermined conclusion=(consultation/verbiage)* (verbiage/consultation)*Predetermined conclusion.

Nancy C (10:10 a.m.):

You address me but then respond to someone else.

Nonetheless, the issue is simply this:

The ratios as such express regularities. The components (numerator and denominator) do not vary independently. Thus, Energy/GDP is meaningful, but Willis’s Energy/GBP is not.

GDP and population do not vary independently of each other.

Neither do GDP and energy use, nor energy use and carbon emissions.

The ratios among these “variables” exhibit regularities — although, of course, the values and details of these regularities may change over time. GDP per capita may rise.

The separate ‘variables’ (GDP etc.) do not vary independently. Their interdependence is expressed in ratios.

Daniel G. (9:55 a.m.):

I take it that by “variables” you mean that the ratios (not their components) are meaningful and vary more or less independently of each other. Yes!

“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.”

john wright! remember this page!

look at C * B/C

the first C should be replaced by a different label, like N (the number of crates)

the fallacy of the M&M analogy comes from false declaration of 2 independent entities as the same,

when you change the first C, you must also change the second C.

doing that is just dividing by reciprocal and is always 1. this is a useless result.

heh- once i was looking at illuminated manuscripts. i noticed that sometimes the creator would run out of space for the words and crowd them into the margin or jam them in somewhere.

it was like he had to have them in there cuz they were holy writ he was garnering spiritual coin by copying so devotedly. and then it struck me- he was copying- he was illiterate and was not copying words, to him it was copying divine symbols.

that’s what this numerology of the crimatologist cult reminded me of.

(the comment that ‘they are using common core and their algorithms work as expected’ was too brilliant!)

another thing came to mind:

the hadith’s say a mozzie man must sit to pee. i got to wondering, tho- if you’re wearing a jellaba, do you really need to be told? and why would i tell somebody? wouldn’t it be far more useful to spot a real dummy from a distance by the wet spot?

and yet, here i find myself trying it… maybe cuz i like to sit around and don’t like puddles on the seats…

Nancy C mistakes me for Dr Doug (which is OK as I think Dr Doug was making the same point as me, only more concisely).

She says ‘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!’

Ok, let’s try it with some numbers.

Take a desert island, maybe with some coal near the surface.

population = 100

GDP / population = 10

(that means GDP must equal 1000)

energy / GDP = 10

(on average the islanders need to burn 10 lumps of coal to produce 1 unit of GDP)

CO2 / energy = 1

(each lump of coal releases 1 unit of CO2).

CO2 = 100 x 10 x 10 x 1 = 10,000

What happens if we try doubling population ASSUMING that

GDP / population

energy / GDP

CO2 / energy

stay constant?

Now:

population = 200

GDP / population = 10

(that means IF our assumption holds, THEN GDP must equal 2000)

energy / GDP = 10

(on average the islanders need to burn 10 lumps of coal to produce 1 unit of GDP)

CO2 / energy = 1

(each lump of coal releases 1 unit of CO2).

CO2 = 100 x 10 x 10 x 1 = 20,000

So, making this assumption was somthing I tried and found it was true that CO2 is proportional to population.

Nancy C said that I “can’t arbitrarily change [these ratios] or hold them constant”. But you can see that is just what I did above. However, what we really need to ask what does this assumption mean in the real world? It can be done, but is it useful? What it means is that on average each person on the island is producing and consuming the same goods as before.

Is that realistic? It depends. If the demographics are the same we have doubled the number of workers and the number of dependents such as children, it could be a good starting point. If we started with 100 workers and added 100 children, then probably not – likely GDP / population would drop.

Even if we just double the number of workers, GDP / population may rise. We have known since Adam Smith that the division of labour is limited by the size of the market. With more people we can get more specialisation and raise productivity.

But thinking about constant GDP / population as an imaginary analytic starting point is useful.

The other ratios are useful in a similar way. Energy / GDP held constant means that the make up of economic activity remains the same. The balance between energy intensive iron making and low energy yoga instruction stays in the same ratio. Again this is a useful analytic starting point for thinking about economic change. CO2 / energy held constant means that energy technology does not change. The islanders do not invent more efficient boilers, or move from coal to gas. Once again, this will never be exactly true, but it is a useful analytic starting point.

Compare this to the breakdown:

CO2 emissions = Al Gore’s Waistline * GDP/Al Gore’s Waistline * energy/GDP * CO2 emissions/energy

It’s just as true as arithmetic. And it’s true that IF we ASSUME

GDP / Al Gore’s Waistline

is constant then CO2 emissions would be proportional to Al Gore’s Waistline. But we need to ask the exact same question: what does this assumption mean in the real world? The answer is nothing at all. It is not an assumption that corresponds to anything meaningful, even as an imaginary analytic starting point.

So I think that’s the difference. If you want to say that GDP / population is just as useless for understanding the economy as GDP / Al Gore’s Waistline then that’s another argument. But again I would point to the way that GDP / population is very widely thought of as an important statistic both before and outside the climate debate.

john robertson: every equation can be reduced to left hand side = right hand side. That’s what an equation is.

richardscourtney says:

July 10, 2014 at 8:56 am

“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.”

It’s a policy tool, but you’re nearly there. You only disagree with it though because you think it disagrees with you! And you only think that because you haven’t taken the time to understand it or its uses. And you’ll disagree with anything that you think disagrees with you, whether you’ve taken the time to think it through and research it or not!

Think about this:

FIRST, Willis Eschenbach wrote and published on the world’s leading climate science site a sneering, mocking piece laughing at how stupid the Kaya identity is and all the people who ever referred to it, and

ONLY THEN did he even find out for the first time that it has a name and that it is called the Kaya identity!,

AND ONLY THEN, presumably, did he start to research it and find out what it is and what it is used for, and by whom.

And that is the kind of arrogance people used to have to go to SKS for…

I absolutely despair of the lot of you…

sigh. It doesn’t matter whether my ratios are meaningless, all that matters is that they can be calculated.

Daniel G, whether ratios that share variables can be set independently of one another depends on how many ratios and how many variables. Sometimes there’s independence, sometimes not. In the case of the kaya identity as expressed above, definitely not. It’s a simple case of number of variables and number of equations.

Let’s try something. Let’s do as Dr. Doug suggested and hold those 3 ratios constant. For convience, let’s say they are:

GDP/Population = 1

energy/GDP = 1

CO2emis/Energy = 1

Now you have an equation where, as Dr Doug said, CO2 Emissions are proportional to population:

CO2emis = Population * 1 * 1* 1

Let’s say population is 9 billion. Now CO2emis = 9,000,000,000. It’s unitless, but that’s fine, we’re working a math problem now, not a physics problem. (If we wanted to we could get it back to a physics equation by just multiplying population by a constant of appropriate size and units. But it shouldn’t matter, if the math in one works, the math in the other should work.)

Okay, since now we know CO2emis = 9E9 we should be able to calculate the other variables.

CO2emis/Energy = 1, so we know energy = 1.1E-10

energy/GDP = 1 so, GDP = 9E9

GDP/Population = 1 so, Population = 1.1E-10

So clearly population can’t be 9 billion because that would imply that population must be .00000000001111…

The only way this set of equations works is if population is = 1. There is only one option. In fact, since we have 4 equations and 4 variables, we knew from the start there would only be one solution. You could set any of the ratios to any constants you could imagine, and you’d get a similar unique solution because you’d always have 4 equations and 4 variables. Population would never be able to vary, it would always be completely determined by the values of the other ratios.

So, if as Dr. Doug said, you hold those 3 ratios constant, then, yeah, I guess in some sense CO2 emissions are proportional to population, but only trivially, since as soon as you set those 3 ratios to constants you also set population to a constant: it can’t be varied or the relationship no longer holds.

As I think American idiom would have it,

I can’t believe how much Dr Roy Spencer was low-balling it…

Two joke threads in as many days… godd one, Willis.

Here is the equation with the terms re-arranged.

CO2 = CO2 *(Population/Population)*(GBP/GBP)*(Energy/Energy)

Since everything in any of the brackets evaluates to one, for all values except zero, you can not infer any relationship between any of the terms so, for example, you can not infer that increasing or decreasing Energy will have any impact on CO2. Neither can you infer that a change in Population will result in a change in CO2, Energy or GBP.

The authors of the report might have called the equation the “Kaya Identity” but that does not make it an identity. It is, in fact, a tautology since it evaluates, for all values of all terms except zero, to 1.

I guess I’m missing your point.The point is that the four variables on the r.h.s of Kaya are independent variables. c/population is not independent of population. It will vary precisely as the reciprocal of population. As Daniel G said succinctly above, Kaya is useful because the variables on the right hand side are meaningful and substantially independent. Your identity fails on both scores.

You are not being fair here. It’s called an “identity” because it is supposed to express a simple relationship, i.e., the component elements to aggregate CO2 emissions. If it did not reduce to a tautology, it would be wrong.

It’s not a ‘scientific’ equation, such as the ones physicists work with when they try to solve for an unknown variable. (Or algebra students, for that matter.) It’s intended for policy maker – economist types. I believe the way they have stated it is very bad – and you have demonstrated why – because the CO2 emissions on the left is the aggregate emissions (observed or desired), and the CO2 emissions on the right is actually part of an average efficiency rating to be observed or set as desired. When I dip into economics texts, I find this stuff sort of mind boggling, but that’s the way it is.

Despite its rather glorious sounding name, all it’s supposed to do is allow you to demonstrate that, given CO2 emissions held steady, and, say, population rising, something else has to change, such as the ratio of CO2 emitted to energy produced. Or, given the desire to reduce CO2 emissions, something else has to change. Nothing fancy.

pimf…

goodone, Willisthere’s a learning curve to my new scaled- down keyboard and I ain’t learned much yet

Daniel G. says:

July 10, 2014 at 10:28 am

“…snip….

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”

—————-

Also:

V = Population*GDP/Population*Energy/GDP*V/Energy

Nope. When GDP increases alongs with the population increase, GDP per capita doesn’t decrease porportionally to population increase.

In this very long comment section, people have said I’m making unfounded asssumptions. Ok, what assumptions I’ve made that are still unfounded?

I am so embarrassed. I totally missed the cancellation :(

Population = Population / 1 ….. so CO2=C02

Nice.

RH says:

Perfectly dodging the question.

But anyway, I guess someone could use that identity to find average used voltage. He just needs the average current.

JK, thanks for sticking with this, as I’m sure most people find it tedious. I bothered to look at the pdf and find the relationship expressed this way:

CO2emissions = Population x (GDP/Population) x (Energy/GDP) x (CO2/Energy)

This is different from Willis’ version in that he’s given the CO2 variables the same name, implying they were the same thing, but actually they’re not.

I think I admitted in previous comments that I was only referring to the relationship “as expressed here” and that if there was a problem with the way Willis represented it, that would be a valid criticism.

If someone upthread had already expressed it this way “the CO2 on the right is not the same variable as the CO2 on the left”, and I missed it, I apologize.

But yeah, it looks like that’s the problem. If they were the same, Willis would have been right, since they’re different, he was wrong.

Nancy C

wrote:

“Okay, since now we know CO2emis = 9E9 we should be able to calculate the other variables.

CO2emis/Energy = 1, so we know energy = 1.1E-10

energy/GDP = 1 so, GDP = 9E9

GDP/Population = 1 so, Population = 1.1E-10

So clearly population can’t be 9 billion because that would imply that population must be .00000000001111…”

Seriously?

If CO2emis = 9e9 and CO2emis/Energy = 1 then Energy = 9E9

then energy/GDP = 1 implies GDP = 9E9

then GDP/Population = 1 implies Population = 9E9

This looks consistent to me.

Anyway, I’m afraid I don’t have time to continue with this thread.

“Greg says:

July 10, 2014 at 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.”

Greg, I think you meant “know” not “no”

But I’m with you on everything apart from your content…

Lichanos says:

I understand how you feel, but I suggest you read the actual paper. You might become a little less frustated.

Everyone criticizing Willis, try plugging simple numbers into the equation and then solve it. Then change one of the values like energy and solve again. The answer is exactly the same. If you were trying to make a point along the line of “decreasing energy has such and such an effect on CO2″ or “increasing GDP has such and such effect on CO2″ this equation would fail to support it. The equation would be useful if someone discovered that CO2=energy x population/GDP or something like that because then you could show what happens when you increase or decrease GDP or Energy or Population. If you want to make the other points mentioned by critics of Willis in these comments surely there’s a better way than using an equation where all the variables cancel out.

I have read most of the comments on this post and, as a result, I have had some pretty good fits of laughter. The one thing I don’t think I have seen discussed however is the fact that this “identity” has quite effectively distracted everyone away from discussing what the “ideal” CO2 production rate should be. Obviously fanatics will assert this value should be ZERO. PFFT! To what end?

IF that could be achieved (IMHO that is impossible) then the net rate of growth of green things on this planet would begin to go down in direct proportion. So instead the IDEAL increase in the rate of CO2 production should be aimed not at ZERO, nor at an attempt to sustain the current value of 30 gigatonnes CO2 but instead at increasing to a value that ideally produces the greatest amount of food and goods necessary for optimal population growth, prosperity, and optimal long term sustainability.

I do not practice the worship of Gaia, but if I did, I would advocate a lot louder for the plants and CO2 consumers on this planet. My argument would be that the O2 consumers have it pretty cushy, since the gas they needed for life is sitting pretty at near 16% while the CO2 consumers are gasping for breath with a measly .04%. I would argue that an increase to twice that amount would hardly affect anything negatively that most other living things desire other than possibly an increase in Florida like weather at higher latitudes. Who wouldn’t like warmer weather in Minnesota? Especially if it means an increase in crop yields, a roll back in desertification, and more green?

So in conclusion, what the UN SHOULD be studying (IMHO) are the answers to the following questions:

What is the historical correlation between the change in CO2 output vs per capita life expenctancy?

What is the historical correlation between the shift from burning grass and dung, to wood, to coal, to gas, to nuclear vs. increase in per capita life expectancy, decrease in death due to starvation, GDP, population growth, self-sufficiency in food production, and sustainability?

What truly IS the optimal increase in CO2 output, and how quickly can we drive up to that value without creating more Madagascars?

But then, since the UN was responsible for the DDT -> increase in malaria disaster, I don’t hold out hope that they will ever get this one right either.

Nancy C says:

Yeah, he misinterpreted it a bit. This show his reading comprehension is not the best.

One of my worries is that most people (including good scientists) are not used to the technical language, methods and conventions of the social sciences. They end up thinking that all social science is gibberish. For example, look at the snarky reactions to the paper indicating that farmers are sceptical of climate change.

TerryS says: July 10, 2014 at 10:59 am You could not be more correct,

Assuming they have a valid equation then the transposition of equal parameters will always give the same results. Yes, as others say the individual “ratios’ MAY BE ‘independent,’ however that does not mean that the rules of math can be ignored. To analyze the effect of one of the parameters on CO2 you must have data for all others. Once you pick, for example , population, then it goes into two positions THAY CANCEL OUT. This is NOT, I REPEAT NOT a case of unit verification. A population of 12 billion is 12 billion PEOPLE – the units are people, not 12 billion! You need to use 12 billion on both positions (you can not use 12 BILLION in one position and 3 Billion in the other, to do so would give you GARBAGE) and they cancel out. PERIOD. The same is true for energy, and GDP. That gives your equation CO2 = CO2 x 1 X1 x 1. PERIOD

JK, ha ha, yeah, I totally blew that too. barrassed.

Still true, though, that if the CO2 variables on the right and left were actually the same number, you couldn’t adjust the ratios independently of population. Whatever the 3 ratios were, population would always have to equal their reciprocal. Since in the real equation the 2 CO2 variables are different numbers it’s a moot point.

I did that after changing the ratios and pop. for letters, which is the correct thing to do.

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

===========

an equation is an equation when it contains an “=” sign.

The equation may be true or it may be false. The equation tell us something useful, or it may not.

For example:

a=b (if true, this may useful)

a=a (this is always true, and thus is not useful)

there is no value in an equation that tells us 1=1, 2=2, etc, because this is simply the definition of the “=” sign.

to be useful the equation must be of the form:

rain = dogs + cats

and not of the form:

rain = dogs * cats/dogs * rain/cats

Re: Nancy C

Lets try it.

CO2emissions = Population x (GDP/Population) x (Energy/GDP) x (CO2/Energy)

Now lets rearrange using standard algebra techniques taught to school children:

CO2emissions = (Population x GDP x Energy x CO2 ) / (Population x GDP x Energy)

Rearrange again and separate the CO2:

CO2emissions = CO2 x (Population x GDP x Energy) / (Population x GDP x Energy)

CO2emissions = CO2 x 1

In other word the CO2 value on both sides of the equation is the same.

@usurbrain

Which rule of math I am ignoring?

If pop increases, so does GDP, so does energy, so does CO2!!!

I will do this once.

co2 = pop * (gdp/pop) * (energy/gdp) * (co2/energy)

Let me use these example values:

pop = 1,000,000 people

gdp = $20,000,000,000

energy = 6e15 J

co2 = 6 GT of CO2

you might say: this is worthless. I want to know co2.

I say: what matters isn’t co2 (because that is what you are going to find out) but co2/energy.

An increase of pop does not affect co2/energy.

But it does affect energy.An increase of pop does not cancel out with a gdp/pop decrease, because gdp increases too.

Willis Eschenbach:

CO2_{emissions} = Population * \frac{GDP}{Population} * \frac{Energy}{GDP} * \frac{CO2_{emissions}}{Energy}That was where I lost it …Yep. You lost it.

Of course you could substitute any commodity for GDP, but not every country has every commodity, but every country has a GDP. Probably better than beer or GDP would be electricity, but then you miss heating oil and cooking with dung for fuel.

It was a small joke, but let’s face it: you and I are not much interested in reducing CO2 in the first place.

You have just repeated Willis’ procedure. I and others have already criticized his conclusions.

Nancy C says: July 10, 2014 at 11:21 am

“Since in the real equation the 2 CO2 variables are different numbers it’s a moot point.”

If that is TRUE, then you are ignoring or not accounting for many of the CO2 emissions produced in the total generation of energy, e.g. from mine to your house, accounting for even the CO2 generated in the production of concrete for foundations of energy producing equipment. And again end up with a garbage equation.

and not of the form:rain = dogs * cats/dogs * rain/catsSo if I want to know the number of calories in 4 oz of butter, and I get it by looking up the number of calories per oz. on the package, and multiply it by the amount of butter (by weighing it) that’s not a useful equation?

Re: Daniel G

They fit the equation perfectly!!

So do the following:

pop = 1,000 people

gdp = $20,000,000,000

energy = 6e15 J

co2 = 6 GT of CO2

and

pop = 1,000,000,000 people

gdp = $20,000,000,000

energy = 6e15 J

co2 = 6 GT of CO2

and

pop = 1,000,000 people

gdp = $20,000

energy = 6e15 J

co2 = 6 GT of CO2

and

pop = 1,000,000,000,000,000,000,000 people

gdp = $20,000,000,000

energy = 6e99 J

co2 = 6 kg

So exactly how does this equation help you determine any relationships?

I am trying to catch up here, so the equation was written wrong? It should be C=P(G/P)(E/G)(N/E)?

People, look at the M&Ms example. It is analogous.

So exactly how does this equation help you determine any relationships?

Simple, all the ratios are more or less independent of each other. So the equation helps to hide the messy details in the related variables. When pop increases, so does Co2 emissions.

if a valid set of values is (because i estimated the ratios and population, finding out co2):

pop = 1,000,000 people

gdp = $20,000,000,000

energy = 6e15 J

co2 = 6 GT of CO2

then this is not valid:

pop = 1,000,000 people

gdp = $20,000

energy = 6e15 J

co2 = 6 GT of CO2

Not that gdp decreased, pop stayed the same. So gdp per capita decreases, so co2 must smaller as well.

The talk tab on the Kaya Identity page is also interesting.

http://en.wikipedia.org/wiki/Talk:Kaya_identity

Do you believe that IPCC, UN, and other alarmist bodies are really interested in CO2 emissions per se? They probably can’t care less whether the air we all breathe contains 0.04% or 0.1% of CO2 (actually, plants would love it). Their stated goal is to prevent a catastrophic global warming. There is no temperature in that equation; the most important piece is missing. We are all beating a dead horse here.

Daniel G. says: July 10, 2014 at 11:32 am

“An increase of pop does not affect co2/energy. But it does affect energy.”

Then why has energy remained almost stable, flat, for the last four (plus) years in the USA?

Then why has the GDP gone DOWN IN TERMS OF GOLD or other hard currency, take your pick, for the last six years?

Why has CO2 emissions in the USA gone down and the above questions still be true?

The equation is GARBAGE.

M&M equation: M = C * B/C * P/B * M/P

As others have pointed out, the above equation simplifies to M=M. Although the simplified equation is not useful, the original equation is. To make it easier to see, let’s shorten the equation to:

M = P * M/P

This equation tells you how many total M&Ms there are if you know how many packets you have and how many M&Ms there are in a packet. Even though it reduces to M = M, the equation can still be useful if you want to know how many M&Ms you have without emptying out all the packets and counting each M&M individually. For example, if you have 10 packets of M&Ms and there are 100 M&Ms per packet, the formula tells you that you have 1000 M&Ms total (M = 10 * 100.) If you simplified the equation to M=M, it would still be valid, but it would become useless for making this calculation.

This M&M example helps me to see why it isn’t always desirable to reduce an equation to it simplest terms. For that reason, the Kaya identity may also have a purpose, even though it becomes meaningless when reduced to its simplest form. But I can’t speak for its accuracy. That’s another issue.

Re: Gerard Harbison

That is a useful equation, but the following isn’t:

Calories = Butter x (Potatoes / Butter) x (Carrots / Potatoes) * (Calories / Carrots)

Read the paper. Or Willis’ quote. It is talking about energy-related emissions.

You are all wrong :-)

The correct, scientifically rigorous, extensively peer-reviewed, 97% guaranteed to be accurate 95% of the time equation IS (wait for it):

CAGW = FRAUD

I scrolled all the way through the comments, and boy is there a lot of confusion here. The best response was by “Brian”, who used the same example I am going to use. The real problem is the poor variable naming used in writing the original equation. That lousy notation allows one to mis-interpret the equation as being a mere unit check rather than something really useful.

The thing to understand is that factors like energy/GDP are intended by the authors to be understood as adjustable factors, not mere units. We can illustrate the point by writing a distance calculation in two different ways using alternative choices for the variable name assignments.

distance = (distance/time)*time

or we could represent this same idea as

change of distance=velocity*(elapsed time)

The first variable assignment very much has the aspect of a mere unit check. The 2nd wording should suggest an obvious utility if we for instance want to know the distance traveled when

velocity = 60m/hr

elapsed time = 10hrs.

However, it should be clear that one COULD interpret the poorly worded equation in the same way. I.e., (distance/time)=60m/hr and time=10hrs yields distance=600m. It is badly and ambiguously written, but not wacko wrong.

Willis confusion is understandable perhaps, given the poor notation and the overall silliness of the thesis of the paper.

So what? Look again:

Calories = Butter * (Calories / Butter) (1)

Calories = Calories

Butter cancels, but how does this tell whether (1) is useful? That is the problem with Mr. Eschenbach’s argument. The things cancel, leaving this:

co2 = pop * (gdp/pop) * (energy/gdp) * (co2/energy) (1′)

co2 = gdp * (energy/gdp) * (co2/energy)

co2 = gdp * (co2/gdp)

co2 = co2

Everything cancels, but how does this tell wheter (1′) is useful?

Again, look at the M&Ms example.

Which falsehood he then proceeds to compound by pretending that the “CO2 emissions” from the original equation and the “CO2 emissions” from his beer pong fantasy are the same thing, since he gave them the same name. They are not. The first is the total energy-related CO2 emissions from all economic activities captured by the GDP. The second is the total energy-related CO2 emissions from only the production of beer, which is but a tiny fraction of GDP. Thus his conclusion:

… is an asinine non-sequitur. Which only serves to further the embarrassment done to Anthony and WUWT caused by Willis’ ridiculous subheading

“The “Kaya Identity” carbon equation has been falsified – due to a stupid maths error“.The only “falsifying” errors here are by Willis and the only question is whether they were stupid or knowing.

Willis,

I think the authors just left time out of the equation. But time is implied. The equation should be understood something like:

CO2 emissions (to the atmosphere in a given unit of time) = population * GDP produced per person * energy consumed pre unit of GPD produce * CO2 emissions per unit of energy.

The equation tell us how much CO2 is produced in a given unit of time by a given population assuming a given amount of CO2 emissions per unit of primary production. It’s not a meaningless equation. It says that human CO2 emissions are related to how many people there are, how much those people produce, how much energy is used for that production, and how efficient the GDP production is with respect to CO2 emissions.

The equation is similar to an equation explaining how much heat is added to a pot of water on a gas stove. Heat added = heat provided by the flame – heat lost to the environment. Heat (added) = Heat (provided) minus Heat (lost). Heat = Heat. Nothing wrong with that so long as you know which bit of heat you’re talking about.

The equation tells us that if we wanted to lower CO2 we could (1) kill people, or (2) starve them, or (3) convert fossil fuels to energy more efficiently (with less CO2 produced), or (4) use non-fossil energy sources.

As usual, there are many underlying assumptions in the document that are not supported by the evidence. The world warmed a degree or so since the dawn of the industrial revolution but the human race prospered like never before. CO2 is plant food, and humans — along with nearly all other non-plant lifeforms — depend on plants for survival. There is no compelling scientific evidence that future warming will be any different than past warming, which we know was mild and mostly beneficial. Climate models are compelling evidence the human capacity to tinker with numbers but they are not compelling evidence of dangerous warming. And the dangerous global warming theory demonstrates nothing more than the human capacity for panic (or an attempt to cause panic in order to increase profits and/or political power).

The document is highly flawed in many ways but the equation is not unscientific or laughable; except that it is poorly phrased in the it implies factors that could have been made more explicit.

This is the UN equation that matters: UN Climate Treaty = Worldwide Death – by law.

The US EPA has nearly 3,000 new regulations since 2009, based on UN IPCC CO2 “science”, that have yet to be widely known or understood – as the volume of regulations exceeds 22 times the entire Harry Potter series. You’d have to have been hiding under a rock for the last two decades to miss that the UN and the US intend to fully implement Agenda 21 after the planned 2015 treaty.

The question is, who will be the newly hired environmental jackboots that will be armed and trained to use AK-47s to move people off their land during the implementation phase of A21? The EPA wants federal control of all waters, including the river or lake where you live. Part of Agenda 21 is “re-wilding” vast tracts of privately held lands, land YOU own. People scoff at that kind of talk – why? The laws and regulations are either on the books already, or soon will be. It’s not a theory – it’s what the high-rollers want for THEIR world – a place, in their view, where WE don’t belong!

*****

I’ll give you credit Willis for unearthing and dishing on the warmists’ wet dream called “deep decarbonization”. Deep decarbonization is the UN’s and Obama’s death wish for everyone but “the chosen” and the few slaves they will need to carry on without the rest of us. That’s the message of the Georgia guidestones. People who won’t believe that are in denial.

Willis, you’ve spent enough precious time over the years ripping on anyone you please. If you want to be of service to humanity from now on, it would be to repeatedly, widely, and effectively state the obvious: the UN and the Obama administration are laying down the legal framework for worldwide population reduction – eco-genocide – all on account of their fallacious global warming CO2 “science”. It’ll be a progressively incremental reduction too – fully justified by “science”.

Just look at how strident Obama is towards anyone who won’t capitulate to his demands. Take heart Willis – he is far nastier than you have ever been, even on a “bad” day. You ought to be nicer to skeptics you disagree with – perhaps the negative feedback you’ve been getting lately is sinking in – one can only hope. Your antagonistic attitude makes you look like a low-class chump.

Willis, I hope you didn’t waste your time at the conference while sitting in your room writing new posts and numerous responses when you could have been out with the others conversing and learning what you could from each one of them. We could use a report on what Dr. Willie Soon and the other solar researchers said – as that is the area where you are weakest – understanding the sun-earth weather-climate connection.

It is clear that you aren’t accepting solar variability as the cause of climate change. How about looking at David Stockwell’s work? It’s right up on the sidebar under Niche Modelling in the Skeptical Views section. The Sun’s heat accumulates and releases over time…

Willis, since you’re so “good”, why don’t you write the ultimate science paper that crushes CAGW.

*****

Repeating: The UN Climate Treaty = Deep Population Reduction = Worldwide Death.

Getting the picture? They will vote us OFF the island – they survive – we don’t – and they intend to enforce that with the barrel of a gun – legally. Our survival is not their concern. Is it yours? We have come along way since “life, liberty, and the pursuit of happiness” was our ‘guidestone’.

*****

The SUN causes warming, cooling, and extreme weather events, not CO2!

Louis says:

July 10, 2014 at 11:49 am

M&M equation: M = C * B/C * P/B * M/P

As others have pointed out, the above equation simplifies to M=M. Although the simplified equation is not useful, the original equation is. To make it easier to see, let’s shorten the equation to:

M = P * M/P

This equation tells you how many total M&Ms there are if you know how many packets you have and how many M&Ms there are in a packet. Even though it reduces to M = M, the equation can still be useful if you want to know how many M&Ms you have without emptying out all the packets and counting each M&M individually. For example, if you have 10 packets of M&Ms and there are 100 M&Ms per packet, the formula tells you that you have 1000 M&Ms total (M = 10 * 100.) If you simplified the equation to M=M, it would still be valid, but it would become useless for making this calculation.

———-

Nah, you are using the total number of M&Ms to derive the per packet number. M&Ms per packet is a new variable and should be treated as such.

PP=M&Ms per packet

M=P*PP is what you want

PP=M/P is the other

You can’t use the same symbol for two different variables and expect no one to have a problem.

Don’t be mislead, Kaya’s identity is both invalid due to non-specific (middle) terms*, and untrue.

Perhaps he meant to obfuscate his readers, or perhaps he was just inept.

Buck IV hints he understands this issue by his question July 10, 2014 at 12:19 am

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

By redacting the appropriate specific terms (shown in parenthesis) Kaya sets (Global) “CO2 emissions” = (Anthropogenic) CO2 emissions.

Which of course is not true.

In effect Kaya misdirects the reader to believe that all CO2 emissions are anthropogenic, thus setting the agenda for his fallacious and untrue argument, independent of the premiss “CO2 causes catastrophic global warming”.

Obviously due to equilibrium lag of CO2 emissions in our warming environment we have yet to experience the peak CO2 level that will occur from all natural causes, including anthropogenic causes, (consider humans are “natural” to Earth’s environment.)

* Kaya’s fallacy employs the non-specific middle term “CO2 emission”;

CO2 emissions cause global warming.

Man causes CO2 emissions.

Therefore Man causes global warming.

and further,

to stop global warming Man must be stopped.

It is tautological relationship, so it is accurate. Not very useful, but still helps thinking of what has to be done to reduce co2 emissions. (It isn’t like that this goal is a good one)

Daniel G. – you say

“you might say: this is worthless. I want to know co2.” We can know the value of CO2, it’s something that has been measured and recorded. Same thing with GDP, Population and Energy. Now that I have read your comments, here is something I am wondering. When CO2 has increased or decreased, have the values of Population, GDP and Energy increased or decreased accordingly? I am wondering if that equation holds up when using real world data. I’m not rebutting you, I’m wondering if that exercise has been done anywhere.

Pete Brown:

I am replying to your post addressed to me at July 10, 2014 at 10:53 am.

I repeatedly wrote

You have replied

NO! ABSOLUTELY NOT! THAT IS AN OUTRAGE!I disagree with the equation because it is bollocks!

The equation is deliberate ‘Alice In Wonderland’ nonsense. As I have repeatedly explained, it means nothing and it says nothing, but it can be pretended to say whatever its user wants to promote.

I don’t think I can state this more clearly that I did in my post addressed to tttt at July 10, 2014 at 9:13 am where I wrote of the equation

I repeat what I wrote in my post addressed to you at July 10, 2014 at 8:56 am which you pretend to be answering.

You have ignored that and have made your untrue assertion presumably because you cannot defend the equation which is – and can only be – a tool for pure political propaganda.

Also, if you have problems with what you think Willis may or may not have done then take them up with him and not me.

Richard

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

Read the paper, (or at least Willis’ quote). They are talking about co2 emissions related to energy production.Peter Sable says: “as many have pointed out, the equation is wrong if the units aren’t the same on both side of the equation” … “Willis you are chasing the wrong thing here…”

See the Kaya Identity:

http://en.wikipedia.org/wiki/Kaya_identity

The UNITS ARE THE SAME.

While I haven’t looked at every comment, I don’t yet see where anyone has stated the obvious — you cannot use an unknown term “X” to discover the value of “X”.

The unknown quantity appears on both sides of the equation.

Giving some made-up numbers: X = 17 * (12/17) * (6/12) * (X/6)

Simplifying the numbers you get X = 1X or just X = X. It tells you nothing.

I am wondering if that equation holds up when using real world data. I’m not rebutting you, I’m wondering if that exercise has been done anywhere.

@sinewave:

First,

they are talking about co2 emissions related to generation of energy.When that has changed, so did the other variables. (pop, gdp per capita, energy intensity, co2 efficiency)

It is an identity! The relationship is tautological.

With respect to the moderator –

My apoligies if I wrote something in my (withheld post) that was demeaning or wrong. I had no such intent to do any such thing. My comments were simply intended to convey my thoughts. If I went beyond these limits, please forgive me.

Thanks

Dan

sinewave says: “I am wondering if that equation holds up when using real world data.”

Of course it does. It is useless, but it holds up.

It is an “identity”. X always equals X and it doesn’t make the slightest difference what you plug into it. You cannot use on the right side of the equation the same variable you are seeking on the left side. It collapses into an identity.

whups, wrong person quoted. Daniel was quoting sinewave, my comment is in reply to Daniel.

No one is trying to discover co2 emissions, we have another measures for that.

But what would happen if for the generation of single unit of energy emitted 2x the Co2.

What would happen with energy-related co2 emissions? It would double too.

That is what the Kaya’s identity says.

Willis was wrong to laugh.

now somebody go apply dimensional analysis to david evans equation.

There are three examples already: the distance example, the miles example, the M&Ms example, the calories example. Everything “collapses” to an identity.

So what is the problem?Replying to Thomas “The equation is similar to an equation explaining how much heat is added to a pot of water on a gas stove. Heat added = heat provided by the flame – heat lost to the environment. Heat (added) = Heat (provided) minus Heat (lost). Heat = Heat. ”

Bad math, bad logic. You have THREE variables here and it does NOT collapse to “heat = heat”. Your formula is Heat(net) = Heat(added) – Heat(lost). It cannot be reduced because each instance of “heat” is really a different variable.

Mr Watts

The equation is missing the units. This of course can lead to a slight misunderstanding. The use of CO2 as a sole parameter is of course a bit off, we do need to factor in other figures such as the amount of trees we cut (or plant), aerosols, and the amount of rice we eat.

[Mr. Watts did not write the article. Mr. Eschenbach did -mod]

Daniel G. says: “Everything collapses to an identity. So what is the problem?”

Problems exist only for the beholder. Therefore if you do not see the problem, then for you there is no problem, although I’m a bit concerned that you don’t see the problem and might therefore subscribe to the scary remedial programs that will fix it.

Let’s put it this way. The Kaya Identity seems to be a method to calculate total CO2 emissions. However, notice the final term — total CO2 emissions. You START with the very thing you are trying to find!

http://en.wikipedia.org/wiki/Kaya_identity

It’s a JOKE. It is like the “Sokal Affair”, punking non-governmental organizations (and quite a few readers of WUWT it seems).

It is called “circular reasoning” and is a classic fallacy of informal logic. In this case it is buried in something that looks like a mathematical formula that is too ‘academic’ for common minds to follow. The fact is that in order to calculate “CO2 emissions” you have to have a number (CO2 emissions / energy) that requires you to *already know* the “CO2 emissions” number.

As the yacht salesman says: “If you have to ask ‘how much?’, you can’t afford it.”

Daniel G. says:

July 10, 2014 at 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.]

—————-

If M&Ms per packet is treated as a seperate variable then it does have meaning. To go to the distance=velocity*time example.

D=(D/T)*T is meaningless unless velocity is treated as an independant variable.

V=D/T has meaning

D=V*T also does

D=(D/T)*T looks like it carries the same information but without velocity as an independant variable it does not. It tells us nothing.

Robert Christopher says:

July 10, 2014 at 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?

___

Oh, please – don’t cloud the issue with FACTS and common sense :)

The warmists at the UN (seemingly that’s the whole crowd) is hung up on CO2. Hence the interest in keeping our attention focused on CO2 emissions as with the Kaya identity. Reality is that CO2 plays a minor role in “global warming”. All of the 114 models for temperature apparently use CO2 as the primary driving force; all fail with predictions greater than reality. CO2 has increased during the last 18 years; temperature has not. Is it not time to skip lightly over the amount of CO2 emitted and focus our attention elsewhere?

Did you see the new article in the WSJ about model building?

Regardless of what this ‘formula’ is supposed to be used for, what it is actually intended to do, is impart some sort of mathematical/scientific authority to any debate around ‘carbon’ emissions. In my former profession this was politely refered to as ‘Blinding the idiots with science’ and impolitely refered to as using B*llsh*t to baffle Brains. I’m afraid I see it as a con-artists tool and nothing more.

4 eyes says:

July 9, 2014 at 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.

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

It’s more laughable than you think. Life emits CO2 (even plants during the night)

The only way to achieve zero CO2 emissions is to sterilize the planet. I would not be surprised if this was the intent.

There are algebraic identities, these tell us how to reduce algebraic expressions.

Then there are trigonometric identities which are not mere algebraic identities, these are useful to know to reduce expressions involving trigonometric functions.

Then there is the Kaya identity which is a mere algebraic identity, a straightfoward one too, it is only useful to people who can’t do very basic algebra by themselves.

richardscourtney says:

July 10, 2014 at 12:02 pm

“I disagree with the equation because it is bollocks! ”

…

Ah. I see. Thanks. I wasn’t quite sure if that was your point from your previous remarks. Now I know. Good of you to take the time to elaborate. Good then. Great.

Now that we’re bollocks out, so to speak, please tell me which of these things you think you think has no impact on CO2 emissions, on an all other thing being equal basis:

1. increasing population?

2. increasing GDP per capita?

3. increasing energy intensity of the economy?

4. increasing carbon intensity of energy?

I asked you before but you bollocksed it.

Actually hang on. In your view, does burning carbon-based fuels cause CO2 to be released? Are we okay with that? I ask so that I know how far back we have to go here.

Bearing in mind I am sceptical of the CAGW thesis, you are doing an awfully good job of making the other guy’s case…

Not really.

Exactly. GDP per capita is separate value, so is energy intensity of the economy, and so is co2 intensity of energy.

Here is the equation for M&Ms:

M = C * B/C * P/B * M/P

Each of the ratios is meaningful variable. You don’t plug P or B directly.

You plug the ratios.The fact is that in order to calculate “CO2 emissions” you have to have a number (CO2 emissions / energy) that requires you to *already know* the “CO2 emissions” number.You know how many MW your power plant produces, and you know how much coal you burn. From the latter, you can calculate how much carbon dioxide you produce.

So, no.

richardscourtney says:

July 10, 2014 at 12:02 pm

“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.”

I’m not sure that we can substitute Bullsh*t for energy, but if YOU could, seriously you’d be onto something…

Daniel G. says:

July 10, 2014 at 1:00 pm

Here is the equation for M&Ms:

M = C * B/C * P/B * M/P

Each of the ratios is meaningful variable. You don’t plug P or B directly. You plug the ratios.

——

That is fine but then it is written incorrectly. M=C*X*Y*Z (There are many ways to write it so it has meaning). The misconception is that the former equation is stating the same thing, it is not. One equation is demonstrating a relationship, the other is not.

Treating each of the factors as a separate variable and varying the numerical value of one factor to see it’s effect of CO2 emissions assumes those factors are independent of one another. That’s called a static model. In reality changing the value of a factor will likely cause the value of another factor to change; a dynamic model. So it’s really difficult to attribute the change in CO2 emissions to one single isolated factor. Yes, people do that, but without realizing the assumption they are relying on. Those factors in the equation are surely correlated with each other. This is one reason simple-minded models often fail to predict actual outcomes. Viz., increase GDP per capita and energy intensity is likely to change with it.

@Daniel G – Your comments/arguments are tautological. You claim the equation is tautological and then claim it is “accurate.” You claim that if you change one of the parameters (ratios) that the effect on TOTAL CO2 emissions will be shown, yet, the math does not support that and then in a latter comment YOU agree the equation is TAUTOLOGICAL..

If any frustrated commenters ever check back here, I just want to say, I appreciate your persistence, and thanks to everything everyone’s said, I think that I, for one, understand what this kaya identity is a little better.

So it’s true that algebraically the two CO2 numbers should have to be the same, but in a way they’re not, because what’s actually important in the functionality of the thing is the ratios. So when you use the identity to calculate something practical, the actual left and right CO2 numbers will probably be different (but so will the 2 “Energy” numbers and probably the 2 “GDP” and “Population” numbers).

Somebody brought up an analogy to mph, which I think was very helpful.

So let’s say time = distance / (distance/time) where time= 3 hours and distance = 360 miles.

3 hours = 360 miles / (360 miles/3 hours) is pretty useless.

On the other hand, since speedometers read in mph, 3 hours = 360 miles / (60 miles / 1 hr) is pretty useful, and totally valid, even though the 2 variables I labelled “time” aren’t the same number anymore.

Same with the kaya thing; you can calculate total CO2 from total CO2 (and total energy and the other stuff which all divide out) or you can calculate total CO2 from the CO2 output per unit energy (and total energy and the other stuff). The first of those is pointless, but the second one might have value if you know how much CO2 is made when you burn a lump of coal.

Anyway, I’m just posting this additional comment to let people like JK, Dr Doug, etc, know you weren’t completely spinning your wheels. I appreciate your forcing me to think about it and see the point.

Gerard Harbison says: July 10, 2014 at 1:01 pm

“You know how many MW your power plant produces, and you know how much coal you burn. From the latter, you can calculate how much carbon dioxide you produce.”

You also need to know the CO2 level produced at EVERY power level, startup ramp, shutdown ramp, testing, construction, efficiency decreases due to carrying VAR (Volts-Amps-Reactive) created due to wind/solar generated power perturbations and load transfers, and a thousand other thing. And then you need to know ALL of them for EVERY source of Energy generation to get the TOTAL CO2 emissions related to energy generation AND usage. Even wind, Solar, Hydro, are NOT CO2 neutral or ZERO producers of CO2. E.g. Hydro causes the CO2 level to increase due to the fact that the vegetation covered by water no longer adsorbs CO2. They claim burning wood is CO2 neutral, yet, If I take the would burnt at a wood burning power plant, spread the hips on my garden, the Carbon will be there 30 – 40 years from now. Enough time to replace the trees with new trees adsorbing many time the amount of Carbon that was burnt. The AGW science is political B/S.

tttt says:July 10, 2014 at 7:16 am

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?‘Miles driven’ and ‘Miles’ are not the same. In this example, ‘Miles/gallon’ is independent of ‘Miles driven’, so this can be used. Which, I think, is what you have said.

A problem occurs when written in a similar way to the Kaya identity:

Miles driven = Gallons * Miles driven / gallon.

Now ‘Miles driven’ (lhs) is of course the same as ‘Miles driven’ (rhs). This form can not be used since you would need to know the answer first, ‘Miles driven’.

As presented above the Kaya Identity has a similar problem:

CO2(emissions) = (a*b*c) * CO2(emissions)/Energy

However this might work:

CO2(Total emissions) = (a*b*c) * CO2(emissions)/Energy

“Bob Weber says”

Wow, that was a tad harsh. Completely agree that population reduction is and always has been the main goal for at least the last 50 years, but I don’t believe that we in the developed, “modern” countries have much to fear at all. As I stated in an earlier topic, it’s the 3rd world that is targeted for population reduction– those poor suffering people always get the worst of it. We, OTOH are destined for a Brave New World where soma is available free of charge under Obamacare and everyone is completely self-actualized, and there are never any problems.

Daniel G. says: “No one is trying to discover co2 emissions”

The left side of the equation is “Global CO2 Emissions”. The left side of any equation is the thing to be found (the unknown), and the right side is the known. Hopefully I don’t have to persuade you of that convention.

http://en.wikipedia.org/wiki/Kaya_identity

The right side PROVIDES “Global CO2 Emissions” as part of the calculation to determine that very thing! Impossible! What value would you actually enter for that parameter? You don’t know!

But you are in good company. This author (link below) STARTS with “CO2 = CO2″ and derives the Kaya Identify from it inserting self-canceling terms along the way. He explains how important it is for these terms to cancel as if that creates meaning.

http://www.manicore.com/anglais/documentation_a/greenhouse/kaya_equation.html

“But what would happen if for the generation of single unit of energy emitted 2x the Co2.

What would happen with energy-related co2 emissions? It would double too.

That is what the Kaya’s identity says.”

No. Where exactly is “unit of CO2 per unit of energy” defined in this equation?

It isn’t. CO2 efficiency is not part of this equation. Perhaps it was MEANT to be, but it isn’t.

UPDATE: It appears from reading the text that CO2 efficiency was indeed meant to be part of the equation, but lacking a mathematician, they just blurted out the identity hoping nobody would notice.

“It states that total emission level can be expressed as the product of four inputs: population, GDP per capita, energy use per unit of GDP, carbon emissions per unit of energy consumed.”

http://en.wikipedia.org/wiki/Kaya_identity

So, yes, the intention was good but the math amazingly BAD. The equation does NOT capture this intention.

No, that is equation is not meaningless. It is an identity. The meaning of that identity is what allows you to treat velocity as an independent variable.

Similarly, permitting the consideration of the primary drivers of CO2 as independent variables is the function of elaborating the identity CO2 = CO2.

See here:

http://www.manicore.com/anglais/documentation_a/greenhouse/kaya_equation.html

Ignore his politics if they do not comport with your own, he gets the algebra right regardless.

It is not written incorrectly. It is written explicitly. M = C*X*Y*Z = C * B/C * P/B * M/P, where

X = B/C

Y = P/B

Z = M/P

It is silly to say that M = C * B/C * P/B * M/P is meaningless, but that M = C*X*Y*Z has meaning, when the X, the Y and the Z in the latter are given their meanings by the former.

This sort of discussion is depressing, because the scientific illiteracy of many otherwise bright correspondents comes to view (sorry, Willis). Did anyone catch the fact (for example) that momentum is defined to be (mass x velocity)? They are the same thing. But if you have access only to mass and velocity data, you will need the equation to find what the momentum is. From analysis of the momentum versus time, you can find out what the forces must have been. And so on, courtesy of Isaac Newton.

The whole subject falls under the heading of dimensional analysis: the dimensions of one side of an equation must equal the dimensions of the other side. Mostly, we need equations to infer the output answer (left hand side) from input quantities (right hand side). Sometimes, we have perfectly valid quantities that have no dimensions, like Mach number (= flight velocity / sound velocity = dimensionless), yet are valid (and extremely useful) for determining actual physical relationships (e.g., stagnation-to-static temperature ratio, or pressure ratio, or density ratio). When you are dealing with supersonic flight, it turns out that the Mach number is a more useful property than flight velocity, because it enables us to construct a concise physical theory of aerodynamics.

Does anyone seriously doubt that the “Kaya (?) Identity” is an objectively valid way to estimate human CO2 production from the referenced statistics? We can only ever estimate something like that, because there is no literal way to measure it.

Just remember, when the traffic cop gives you a speeding ticket based on his radar gun reading, he is using an equation that has the same dimensionality on each side. Complain to the Judge and see how far that gets you.

It is just that you never bothered to read the entire paper.

@west2

“However this might work:

CO2(Total emissions) = (a*b*c) * CO2(emissions)/Energy”

this makes sense too me.

this post is a “mountain out of a molehill”?

Yeah you”re right, richardscourtney is truly onto something and I agree he’s onto whatever stokes his fire. . . . err Bullsh*t. Too bad he doesn’t know anything!!

Increasingly I find this site is frequented by the likes of Scourthneys . . . no-nothing-charlatans !

Dan

This identity only works in modern times with our current civilization. You have to have GDP, Energy and Population or it falls apart, either because you will have zeroes in denominators or at the very least you will get zero on the right side which has never been the value of CO2. Given that, do we have a similar identity that describes CO2 a few million years ago when Population, GDP and Energy were all zero but CO2 was still positive? Other than just CO2=CO2? You may say that’s pointless given the purpose of the identity currently, but if I were using the Kaya identity I would certainly like to know if there is anything from nature that should be added to GPD, Population, and Energy to make it more sound.

Bottom line is that the equation, as presented by the OP, is laughable. Population, GDP, and Energy all cancel out and leave the ridiculously useless solution CO2 = CO2. I, for one, am not going to parse the intent of the creator of the equation. Sometimes it’s just fun picking on the opposition.

Not necessarily, whether you make the asssumption of indepedence or not doesn’t matter. Of course if you decrease energy intensity (increasing energy efficiency), the chances are that the GDP per capita is going to increase, by more consumption of energy, creating a rebound effect.

But this doesn’t make the identity wrong.

@sinewave:

Given that, do we have a similar identity that describes CO2 a few million years ago when Population, GDP and Energy were all zero but CO2 was still positive?

We are talking about energy-related CO2 emissions.

Does this mean everyone will have to eat unleavened bread?

Can I really ruin someone’s day?

The Kaya Identity is UTTERLY USELESS for solving for peanut M&Ms.

Plain M&Ms are of a uniform size, and thus, can be used in such an equation; peanut M&Ms are not.

Thank you…come again.

Michael J. Dunn says: July 10, 2014 at 1:44 pm

A voice of reason. . . not Willis tell us how we are all wrong.

Dan

Pete Brown:

I take sever umbrage at your disgraceful post at July 10, 2014 at 12:56 pm .

At July 10, 2014 at 12:02 pm I objected to your misrepresentation of my opinion then wrote

Your disgraceful post I am answering misrepresents all that by sayingClearly, you are incapable of defending the equation from logical argument, and you know you cannot defend it.You follow that offensive nonsense by trying to put words in my mouth as a method to change the subject presumably in hope that will hide how daft your arguments are. Well, that’s bound to work (not).

Richard

JJ says:

July 10, 2014 at 1:38 pm

————-

One equation is demonstrating a relationship, the other is being used as a sort of memory tool. I shouldn’t say it doesn’t have meaning, it doesn’t have any meaning on its own. I am not arguing with guys anymore (literally, not snarky), I understand the point you are making.

—————–

JJ says:

July 10, 2014 at 1:38 pm

It is silly to say that M = C * B/C * P/B * M/P is meaningless, but that M = C*X*Y*Z has meaning, when the X, the Y and the Z in the latter are given their meanings by the former.

————–

I would say that our ways of thinking are reverse from each other.

Are you still debating this nonsense?

CO2=(pop/pop)(gdp/gdp)(E/E)CO2

Throw in some more variables:

How ABOUT CARBONTAX, CT!…(CT/CT)-and randomly rearrange the terms to gain new insights!

Alrighty: CO2=E(CT/pop)(pop/gdp)(gdp/E)(CO2/CT)

How profound, all this time I was an AGW genious and I didnt know it!

Algebra released the creative genious in me.

Nancy C says:

July 10, 2014 at 1:19 pm

If any frustrated commenters ever check back here, I just want to say, I appreciate your persistence, and thanks to everything everyone’s said, I think that I, for one, understand what this kaya identity is a little better.

…

Nancy, thank YOU for sticking with it, and for your comment at 1:19 pm, which perhaps will help other people understand that an identity can be useful.

yeah, the kaya joke is like telling someone that doing something will make hair grow on his palms.

you don’t care if it’s true or not- you only want to see if he looks.

now we see who looked.

funny, right?

DanMet’al:

At July 10, 2014 at 1:57 pm you say

Well, perhaps you can tell us what use this ridiculous equation is except as a tool to spout political propaganda.

This missing information is especially important when the equation supposedly determines CO2 (emissions) but calculates from CO2 (emissions) per unit energy which requires one to know CO2 (emissions).

Obviously, if you were to explain this in comprehensible fashion then those of us whom you call “know nothing charlatans” would know something because we would know what you explained. Alternatively, if you don’t explain it then we would again know something; i.e. you are merely another anonymous troll come here to spout disruptive nonsense.

Richard

Some years ago, I had a real-world experience that showed at least the potential utility of an identity like this. It was very similar to the M&M example that several people have used here.

At the time, the state of the art for slicing bacon into packages meant that you had to average 17 ounces for a package labeled as 16 ounces so as virtually never to go under the listed weight and risk government penalties. (In other words, there was a +/- 1 ounce variation.)

I helped a major food company (one you’ve all heard of) reduce the average to 16.25 ounces per package (+/-0.25 ounce variation), a 0.75 ounce reduction, by monitoring the accumulated weight from each slice and slightly modifying the thickness of the last couple of slices.

They illustrated the importance of this improvement to me by going through an identity very much like the ones discussed here to show the overall savings in bacon yielded by this reduction per package. In the analysis they showed me, they held the other terms constant, which was at least a good first-cut (sorry!) approximation. (I would guess that their MBAs went beyond this and calculated the increased sales that might result if they cut their prices to reflect their reduced cost, and so on.)

In another area, I use the equation

Force = Pressure x Area

all the time. But pressure is defined as force per unit area. So is this equation just a tautology? No! Often I have a pressure measurement — even if that measurement came from the total force on a spring at the end of a cylinder of a given area in a gauge — and a measured area on which that pressure acts.

So the question is whether the individual terms in an identity like this are useful or not. I think the terms in the Kaya identity are useful. You can say to a politician: So you want to reduce our CO2 emissions by 30% over the next 20 years. Here is ONE valid way of calculating the emissions. What are you going to cut? Population? No? How about GDP per capita? No? OK, that leaves energy per unit of GDP (efficiency) and CO2 per unit of energy (decarbonization). How are you going to get the 30% with those.

I think the Kaya identity is a useful way of focusing analysis here.

Thanks, Nancy C.

I find the first way you explain it (“two CO2 numbers should have to be the same, but in a way they’re not”) a bit confusing, but the way you explain the mph example is very clear: we’re on the same page.

I would only add I wish that other commentators would focus on the meaning of the numbers rather than arithmetic, which seems to me quite straightforward.

The question is whether concepts such as GDP / population, energy / GDP and CO2 / energy are any more useful for understanding the economy than thinking in terms of total beer production or Al Gore’s Waist Line.

To put it in terms of M&Ms, the warehouse manager might say:

M&Ms = crates * (boxes / crate ) * (packets / box) * (M&Ms / packet)

and use this to calculate how many more M&Ms will ship if they put more M&Ms in each packet, more packets in each box, etc.

Willis might come along and point out that actually the following identity works just as well, substituting global beer production for number of boxes shipped:

M&Ms = crates * (GBP / crate ) * (packets / GBP) * (M&Ms / packet)

In terms of arithmetic the second formula is just as true as the first.

But it is not as useful to the warehouse manager. Why? Because in reality there is a definite relationship between boxes and crates (one pack in the other) and also between packets and boxes (again, one pack in the other). In constrast, in reality, there is no relationship between the number of crates shipped and global beer production, or between the number of boxes shipped and global beer production.

The Kaya identity is useful to the extent that GDP / population, energy / GDP and CO2 / energy are useful for understanding the economy, and specifically emissions form energy production. Willis’ version is less useful to the extent that global beer production is less useful for understanding these questions.

Bryan says: “understand that an identity can be useful.”

Really? A formula of the form X = A * (B/A) * (C/B) * (X/C) is not useful.

You see, you must GUESS at the “X” for the forth term on the right hand side. Whatever you choose it will magically appear on the left hand side as though you have proved something.

Consider the special case of ZERO. You decide there is ZERO Global CO2 emission. What happens? The zero cancels everything, giving Zero as the answer. Good math, but stupid.

What about 1? Work it out. What you will end up with is 1.

No matter what you DECIDE is Global CO2 emission, the Kaya Identity will produce that EXACT value. The complexity of it is a smokescreen and serves no purpose. Really! Give it a shot and see for yourself. Pick some random number for the numerator of the 4th term. Pick real or random numbers for everything else (but not zero). You will end up with the number you started with.

Now then, if you simply insert the laboratory measured value of co2 per unit of energy produced, THEN suddenly you have a meaningful formula.

JK says: “Because in reality there is a definite relationship between boxes and crates (one pack in the other) and also between packets and boxes (again, one pack in the other).”

Also tomatoes and olives and a billion other things that relate to each other but have absolutely nothing to do with a magic card trick that always gives back exactly what you put in.

Our argument here is that the Kaya Identity is NOT USEFUL. An equation is designed to produce an answer on the left hand side based on stuff you know and can measure on the right hand side.

But that’s not what is shown. What is shown is the ANSWER being used to develop the ANSWER and what is in the middle is completely irrelevant, a different story.

If it is important to know that M&M’s fit into packets that fit into crates, PLEASE don’t use the Kaya Identity to explain it — just say it.

Jason L says:

It most definitely DOES NOT tell you this. [reduce population… reduce C02]

I concede your point. You are right. I am wrong.

I was imprecise. Given that the ratio of CO2 emissions/Energy remains constant a reduction in population will reduce C02 emissions.

To use the same variable (CO2 emission) here on the same side of the equation may be silly, may be a tautology. But, I don’t believe that it is a math error. Maybe it is error in the sense that the author intended the formula to show four terms, the population and three ratios, but failed with the last term. It would have been better stated as the “average C02 emissions per unit of energy”. Over some limited time frame, say one year, that would be constant.

Calling it “a stupid maths error” is what I object to, because 1) I don’t see a mathematical error, and 2) it is a logical informal fallacy, “Appeal to ridicule”. We, skeptics, should be better than that.

I would be more concerned about how the formula is used. Consider the ratio “average CO2 emissions per unit of energy”. A command economy could quickly change that value through a mandate: “it’s now illegal to use fossil fuels”. The other terms are not fixed though. Surely, almost instantaneously total energy usage would plummet as would GDP. Population would also fall (more slowly) due to deaths and infertility. But, I have no doubt that CO2 emissions would fall.

In a market economy, I would expect that the ratios Energy/GDP (that’s related to the inverse of energy efficiency) and CO2 emissions/Energy would decrease over time. I am less sure than others that CO2 emissions would fall though, especially in the short- to intermediate-run, because I would expect GDP and population to increase.

That is already moving the goalposts, but fine. I already have said multiple times. You plug the ratios in, not the variables in the numerators.

This is another way of expressing the fact that a growing economy needs more energy. More energy means more emissions, so you really need to be efficient and emit little co2 per unit of energy, to reduce emissions. Again, the Kaya identity proves to be useful.

After all that being said, I don’t know why should anyone care to reduce CO2 emissions, but that is not what is in discussion.

Curt says: “You can say to a politician: So you want to reduce our CO2 emissions by 30% over the next 20 years. Here is ONE valid way of calculating the emissions. What are you going to cut? Population? No? How about GDP per capita? No? OK, that leaves energy per unit of GDP (efficiency) and CO2 per unit of energy (decarbonization).”

It is not valid, not the Kaya Identity anyway. The problem is in the 4th term. You must use a laboratory measurement NOT THIS FORMULA.

http://en.wikipedia.org/wiki/Kaya_identity

P.S. — reducing population is the preferred solution for a great many AGW advocates and is the first parameter listed. Of course your instinct will be to have other people reduce their population first.

P.P.S. I haven’t imagined myself saying to a politician that I want to reduce CO2 for any reason. I *would* like cleaner air and solar power for their own benefits and not because I think CO2 is dangerous. Shucks, I put some in my flavored water almost every day!

Daniel G. says: “That is already moving the goalposts”

Yep, and you moved it. The Kaya Identity is right there for the whole world to see — it requires on the right hand side the very item that you are trying to calculate.

Nor is it an accident. It is deliberate. Here is a derivation of it:

http://www.manicore.com/anglais/documentation_a/greenhouse/kaya_equation.html

The result is that you can plug ANY value into “Global CO2 Emissions” in the 4th term and get it right back on the left hand side like a magic card trick.

Along the way you get to display whatever you feel like for the other three terms. It makes no difference to the equation. If you feel those terms are important, it is because you feel they are important.

The CO2 identity and the M&M identity are very different in the following respect. If I’m managing a candy factory and we put a fixed and known number of M&Ms in each package, and a fixed and known number of packages in each retail box, and a fixed and known number of retail boxes in a shipping box, then by knowing how many shipping boxes are loaded on a truck I can do the obvious multiplication and determine how many M&Ms are on the truck. Furthermore, I can change any one of those factors at will and with assurance I’ll always know how many M&Ms are shipped. This is a static model, and it will work as expected. The variables are under my control. They really are independent of one another.

No so with the CO2 example. If we change any one of the cited factors that may cause a change in one or more of the other factors. And it probably will. Unless we know how a change in one factor changes the others, using that model to prediction CO2 emissions is just whistling in the dark. Moreover, the relations among those “independent” (but not really independent) factors will differ from country-to-country. Russia will be different from India. All will be different in various ways because those are different economies. For a given pair of variables the correlation may be negative in one pair of countries and positive in another pair of countries. We don’t know the relationships among those “independent” factors. We may try to estimate them. The only way to truly estimate them is to make some changes and see what happens. If we foolishly use this model as if the situation is static we’ll most likely be disappointed in its ability to predict.

This is very different from the M&Ms.

Nearly all social-economic models are static, but they are used in dynamic environments. That’s one reason government policies disappoint politicians and voters. A recent classic example involves high income people leaving New Jersey and moving to Florida. Raise the taxes in NJ and watch the wealthy people leave. It’s quite predictable. What’s missing, of course, is how many in each tax bracket will leave and even take their jobs with them. So just increase the taxes and see what happens. Politicians do that.

SimCity is a great game and training device. There’s too much crime in the downtown area of the city. Raise taxes and hire more police. Downtown crime goes down but Sims in the suburbs leave and take their money with them. The police pension fund eats up money for fixing streets. The Sims are not happy and more of them leave. That’s a dynamic situation.

Please keep your eye on how models are used. To simplistically say “here is the effect of changing this variable” in the CO2 model looks good at a big show and tell. But it may flop big-time in the real world. The problem is politicians assume somebody knows what they are doing, and they do dumb stuff like killing the coal business without understanding the consequences.

Yes, I created models for a living; about 50 years including 10 years freelance. Not models like we are discussing here, but models for technology and forecasting. In a time when people pump accumulated data through software and build what passes as models with little or no understanding of how those numbers came to be, most models are dangerous. I’d put the Kaya model, or identity, in that category because it will be used in dynamic situations with no clue to how the “independent” variables are related to one another.

I am going to side with Willis on this.

I am seriously concerned about the number of people who think this is useful in some way.

Formulas are useful if you can insert a number of measurable or known things on one side to determine a useful answer.

The identity quoted does not do that. For instance, GDP per capita cannot be measured. You need to measure the GDP; count the people; then divide one by the other. The same for Energy/GDP. You cannot measure it. You have to work out total energy; sum the GDP; then divide one by the other. The same for Emissions/Energy. You can’t measure it. you have to determine both quantities first then divide one by the other.

Let’s look at the sin, cos, tan example to see the difference. http://commons.wikimedia.org/wiki/File:Sin_Cos_Tan_Cot_unit_circle.svg

Sin and cos vary between plus and minus one. Tan varies between plus and minus infinity. So you could measure sin and cos and calculate the length of the tangent even if your ruler is not long enough or your paper is too small.

Anyway, the identity is not right. It says:

CO2 = Pop * GDP/Pop * Energy/GDP * CO2/Energy

This is the real formula:

CO2 = GDP * Energy/Pop * Pop/GDP * CO2/Energy

As can now be clearly seen, CO2 goes up if Pop/GDP increases. The Kaya Identity says the opposite! Useful stuff indeed.

David in Texas says: “I concede your point. You are right. I am wrong.”

True, but not for the reason you suppose.

“Given that the ratio of CO2 emissions/Energy remains constant a reduction in population will reduce C02 emissions.”

No. The correct ratio is amount of energy used per person. If you cut the population in half, and the other half doubles its consumpion, you have not changed energy or CO2.

Africa sometimes reduces its population by large numbers. How large a change was there in global CO2? Probably almost nothing.

But the identity, as published, does not discuss the ratio of CO2 emissions per unit of energy. That is a simple thing to measure in a laboratory, and the 4th parameter should have been exactly that number — a constant that you plug into the formula.

How exactly you derive that constant is a different way and a different formula. You cannot just use the left hand side as a parameter on the right hand side.

Plain to see that the effectiveness of doing so relies upon how few people understand algebra.

I should also point out that GDP is completely irrelevant. It cancels out of the equation and should be.

When a nation, such as Iceland, recalibrates its currency by dropping some decimal points, all values denoted in Kronur suddenly change, including obviously its GDP. But what is the impact on the economy? Nothing. It’s an administrative change.

So global GDP can be changed instantly on a whim by whoever decides what it is and what currency to denote it.

That is the only important part. You can take a smaller sample than actually going and trying to measure everything. Like in d = vt. How do I measure velocity: take 5 secs, then displacement in 5 secs, v = (displacement in 5s)/5s.

Anyway, if people think the use of the identity is to calculate energy-related co2 emissions, they are somewhat misguided. The use is to serve as reference for logical argument regarding co2 emissions.

Michael 2 says:

Well, I guess that is true. If a government institution suddenly remove two zeros of the currency, you are increase the numerical value of energy intensity of the economy proportionally.

Just one more thought. The commenter who said this really isn’t funny is absolutely right. The UN will beat us over the head with deep decarbonization. Politicians will jump on this as the latest and great thing. If it’s to be snuffed out, now is the time to do that. Remember, ALL of this rests on the assumption that CO2 is causing global warming. Carbon dioxide increasing but temperature flatlined for 18 years. 114 models that predict temperatures higher than reality. Pure BS. But they are not going to give up on CO2. They’ve got too much invested in it.

4 eyes says:

July 9, 2014 at 10:39 pm

[...]

anf if the equation doesn’t show CO2 emissions = CO2 emissions i.e. the same units then there is a problem

*********************************

I’m sure somewhere in the 300+ comments this has been pointed out many times, “CO2 emissions” is not a unit, it is a value. So always x = x. Now I can go back and read the rest of the comments in peace.

graphicconception says: For instance, GDP per capita cannot be measured. You need to measure the GDP; count the people; then divide one by the other.”

Backwards. GDP is a summation of all personal gross products. GDP itself cannot be measured. You already have the “per capita” — just average all tax returns.

“The same for Energy/GDP. You cannot measure it. You have to work out total energy; sum the GDP; then divide one by the other.”

Pointless. It serves no purpose and the GDP parameter can be deleted outright without the slightest impact on the formula. GDP is a “fiat”, it is declared by governments and depends on daily changing exchange rates and fluctuating currency rates.

“The same for Emissions/Energy. You can’t measure it.”

Actually, this is the only thing that CAN be measured. Burn a gram of gasoline and measure the energy and CO2. Do the same for coal or any other flammable substance.

This is where we start. Emissions per unit energy can be measured in a laboratory with precision.

“So you could measure sin and cos and calculate the length of the tangent even if your ruler is not long enough or your paper is too small.”

You lose precision or accuracy (or both) as you approach the asymptote. But yes, it can be practical at times.

Of course you have to know both values to calculate the ratio. The problem with the Kaya Identity is that it uses as input its own output. You don’t HAVE both values for the ratio in the 4th term.

“This is the real formula: CO2 = GDP * Energy/Pop * Pop/GDP * CO2/Energy”

It still cancels out and it still uses as input the very thing you are trying to calcuate.

Enter a “1” for CO2 on the right, what will you get for CO2 on the left?

1.

Change any parameter in the middle. What will you get?

1.

It doesn’t matter what you do in the middle; every term is canceled except “CO2″.

Michael 2 says:

July 10, 2014 at 2:49 pm

It is not valid, not the Kaya Identity anyway. The problem is in the 4th term. You must use a laboratory measurement NOT THIS FORMULA.

*****************************

Ummm, the 4th term (CO2 emissions per unit of energy) is from laboratory measurements. Laboratories can measure very well the grams of CO2 per Joule of energy from natural gas, oil, and coal. These numbers are then used for further analysis of this type.

You also say, “I haven’t imagined myself saying to a politician that I want to reduce CO2 for any reason.” Note that I said, “You can say to a politician: So YOU want to reduce our CO2 emissions by 30% over the next 20 years.” This is useful, because if YOU want to do it, tell me how YOU plan to do it.

Switching to renewables effectively (almost paradoxical scenario, but ignore) would cause to carbon intensity to decrease considerably. How would that change GDP per capita, or energy intensity of the economy or population?

For energy intensity of the economy: I’ve already mentioned the rebound effect above, it is not too hard to understand.

There remains two factors: population and gdp per capita.

I guess greens might want to make living standards to fall or to control population growth. That would reduce CO2 emissions, but it is a bad scenario.

So lets look at their use for this equation – “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.”

Well, that is a pretty big project, so let’s require a ‘pilot program’ and have the U.N. and everyone agreeing with this ‘Identity’ reduce their CO2 to nothing. How they get there is up to them, just don’t use any of the non-believers energy.

A big problem I see is that GDP has been adjusted even worse than the temperature record. Did you realize the paid up value in you home is equated to a rent payment and added to the GDP. How about the fact that borrowed money spent today is credited to todays GDP, but when your kids have to pay back the US $17 T they will get no credit to their GDP. Or last weeks reporting of

The federal government’s Economic Classification Policy Committee has come up with a proposal to redefine fact as fantasy in order to hide offshoring’s contribution to the US trade deficit, artificially inflate the number of US manufacturing jobs, and redefine foreign-made manufactured products as US manufactured products. For example, Apple iPhones made in China and sold in Europe would be reported as a US export of manufactured goods.Read Ben Beachy’s important report on this blatant statistical fraud in CounterPunch’s July 4th weekend edition:

China will not agree that the Apple brand name means that the phones are not Chinese production.If the Obama regime succeeds with this fraud, the iPhones would be counted twice, once by China and once by the US, and the double-counting would exaggerate world GDP.GDP is a fake number all over the world.

A Different James says: July 10, 2014 at 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.

All you M&M boys

DD Says

No, You are using unit-less descriptions to calculate volumes. To paraphrase Vincent Nunes says: July 10, 2014 at 1:55 pm and the Monty Python folks “Is that for plain or peanut M&M’s”

So in your trucks, you can cut you production by half and take 2x the number of trucks if you use one 40′ tractor trailer ‘truck’ versus 2 ‘pickup trucks’.

Michael 2:

I have said

since the beginning. You estimate theratios. Read my first comment, I have substituted the ratios for letters.It is not me who invented the importance of the ratios:

Richardscourtney

I’ve addressed all your points, such as they are, including all the shoutey, bold obscenities. I’m not interested in Alice in wonderland for present purposes and I’m not sure she has much to add.

I’ve asked you twice to explain which factors you object to and you’ve ducked it twice.

You started this by being rude and aggressive and you’ve finished by being rude, obscene and aggressive.

I’m not susceptible to bullies as you may have noticed. But I am done with this conversation. You are as bad as the extremists.

JJ says “It is silly to say that M = C * B/C * P/B * M/P is meaningless, but that M = C*X*Y*Z has meaning, when the X, the Y and the Z in the latter are given their meanings by the former.”

Well, when that is the case, then both are silly.

But perhaps you were to MEASURE C, X, Y, Z and then simply calculate M. Ah, but thats the problem — the whole thing is speculative, interdependent, circular.

Wow; talk about a storm in a tea cup.

Willis makes a slightly tongue in cheek (I would wager) derisive comment about a “Kaya Identity”.

What is this; some second coming of the Magna Carta or the Fifteen ; Ooops ; make that ten commandments ??

Who or what the blazes is “Kaya”, and what justifies calling this an “Identity” ??

Now for starters, the very statement “This is an identity.” Should immediately conjure up the response; “Ho-Hum ! ”

What could possibly be less informative than an “identity.”, which tells us nothing we didn’t already know.

So Willis does some 4-H club cancellations, to illustrate the ho-humness of the identity, and gets raked over the coals.

So suppose I were to state:

S = (A/B).(C/B). (D/E).(B/A)^2.(AE/D) where each of my variables has some hi falutin description.

Now there is no question, that following on Willis’s 4-H math, that this too is an identity ; a tautology.

Well Ho-Hum !!

But now the reader is led to believe that each of my bracketed ratios, is actually something of significance, that is magically related to S via my identity.

Any of those ratios might be a factor that is in no way physically connected to what S actually is, but if each of them were somehow observable, then my S could indeed be a function of multiple factors, most of which are unrelated in any way to whatever S is (except via my “identity)

A well know example, is the absurd “Drake Equation” for how many intelligent life forms are out there trying to contact us.

Well Drake and Sagan too, forgot the denominator, which gives the improbabilities of all the sequential chemical syntheses, necessary (in the correct order) to get from inanimate elemental chemicals to all of the necessary block. of life.

But the “Kaya Identity” lures us into believing that each of the stated ratios, is actually related to CO2 emissions.

Incidently, just how old does cow dung have to get, to be classified as a fossil fuel, as used for a major energy source in parts of the world, that have an endless supply of it.

Michael 2 says:

You can throw as many adjectives as feel like, it doesn’t prove anything.

Pete Brown is the winner. This is probably the worst post in the history of WUWT.

Daniel G. says: “You estimate the ratios.”

You are quite right if you use the formula as the text intention says “total emission level can be expressed as the product of four inputs: population, GDP per capita, energy use per unit of GDP, carbon emissions per unit of energy consumed.”

But that’s not how the formula is written. The formula as written does indeed use the answer, “TOTAL emission” in the forth parameter, “Total emission divided by total energy” as a way to CALCULATE emission per unit of energy.

But you cannot actually do that. Suppose you were to work this formula RIGHT NOW. What value are you goiong to use for “Global CO2 Emissions” in the formula as shown?

http://en.wikipedia.org/wiki/Kaya_identity

Whatever you put in, that’s what you’ll get back out! You will feel VINDICATED.

That is why it is written that way. Instant gratification.

Michael 2 says:

Your reading comprehension is just as good as Eschenbach’s one.

I wonder if this error is intended to be deliberate.

I remember a story about missionaries in Japan. Hardly anyone paid them any heed. Finally a friendly Japanese person said, “Your message is too correct. Make an error, and people will correct you, and while correcting you, will see your message.”

I doubt the AGW crowd is that clever but maybe this whole thing is a trick to cause many people to gloat over the error and, while doing so, become familiar with the underlying rather obvious and simple relationships.

I can easily be persuaded to believe that X gigatons of carbon dioxide are being emitted every year. Persuading me that it is bad is not going to be so easy; bad math isn’t going to help me believe claims.

People look at the M&Ms identity:

M = C * B/C * P/B * M/P

It has an “M” on the fourth factor. That doesn’t matter, and it doesn’t make the identity useless. Because you plug in

the ratios.The Kaya Identity is analogous.

usurbrain says:

July 10, 2014 at 11:48 am

Because of decreasing energy intensity.

usurbrain says:

July 10, 2014 at 11:48 am

That is consistent with CO2 emissions reduction.

usurbrain says:

July 10, 2014 at 11:48 am

There is no inconsistency.

Myself earlier:

but then you miss heating oil and cooking with dung for fuel.Further with the burning of dung, India could reduce toxic emissions by increasing GDP, increasing energy from burning fossil fuel, and cooking with electricity instead of dung. That example, and lots more like it from other poor regions, shows how the “equation” does not account well for technological innovation overall. In the US, CO2 emission per megawatt of electricity have been reduced by substituting natural gas for coal. Besides that, continuous technology improvement in manufacturing drives down the cost (labor, capital, energy) to produce stuff. In short, every ratio on the RHS of the equation can be reduced by technological innovation (GDP/person is not a good substitute for wealth/person — reducing the cost of vaccinations reduces GDP/person, while nevertheless increasing wealth, because GDP is measured mostly in currency.)

C02 = P * GDP/P * E/GDP * C02/E

Double or halve P, GDP, or E and nothing changes. That goes for the ratios as well.

C02 = (P * GDP * E * C02) / (P * GDP * E)

True. But worthless.

I think it was Aristotle who said, “give me the value of (P * GDP * E) / (P * GDP * E) and a good calculator and I can move the world.

Michael J. Dunn says: “Does anyone seriously doubt that the Kaya (?) Identity is an objectively valid way to estimate human CO2 production from the referenced statistics?”

Yes. About half the people here. I wonder about the other half — they see something that isn’t in the equation (but IS in the explanation of it). In other words, it is a litmus test — are you so attuned to AGW that you don’t see the math error, or worse, try to justify it as some sort of discussion guide not really meant to be a “formula”?

A simple fix would fix it, but this website explains its derivation — the self-cancelling property is deliberate and intentional, gradually proceeding from a meaningless and valueless identity to a complex, but still meaningless and ultimately valueless equation:

http://www.manicore.com/anglais/documentation_a/greenhouse/kaya_equation.html

But I think he’s just an AGW fanboi and doesn’t grok the original which probably does require an actual, measured ratio of carbon dioxide per unit energy which can be measured with precision in a laboratory.

I argue from the presentatio of it here which I suspect will be fixed PDQ so I’ve got my screenshot (get yours now!)

http://en.wikipedia.org/wiki/Kaya_identity

As it is used in an NGO publication it is less clear that the “CO2 emissions” on the left side are not the same as just “CO2/Energy” on the right. Page 34 of the following:

http://unsdsn.org/wp-content/uploads/2014/07/DDPP_interim_2014_report.pdf

Michael 2 says:

‘Suppose you were to work this formula RIGHT NOW. What value are you going to use for “Global CO2 Emissions” in the formula as shown?’

One example of what people want to do does involve estimating the final ratio directly. That is thinking about the effect of changing the the way energy is produced, e.g. what would happen in a future scenario where:

– We replace half of fossil fuel energy with nuclear energy, which as a first approximation emits no CO2.

– Population has grown by 10%

– The world economy has grown by 30%

– The composition of the economy has shifted from manufacturing towards services, so that each unit of GDP requires 10% less energy

What do we anticipate happening to CO2?

The Kaya Identity tells us:

CO2 changes by a factor of 1.1 x (1.3 / 1.1) x 0.9 x 0.5 = 0.585, so it falls by 42%.

You could also look at the effect of replacing some proportion of coal with gas, or the effect of renewables, etc.

Of course you might have no interest in thinking through such scenarios. But that’s an example where you get an estimate future emissions out without putting a direct estimate in.

I wonder if anyone here has the same difficulty balancing chemical equations. Are you alarmed or bemused when the count of atoms of each element is the same on the LHS and RHS, showing that the LHS is composed of the stuff on the RHS?

daniel, please follow this:

now many cases is the first C?

this is multiplied by boxes per ONE case.

the variable representing the number of cases is declared as C

the ratio of boxes per ONE case is also declared as C

that’s wrong because it leads to absurdities such as ones i won’t mention but also others like:

no matter how many cases you have in that equation, you will have the same number of boxes divided among them; no matter how many boxes you have, you have the same number of packets divided among them; no matter how many m&ms you have.

JK:

One example of what people want to do does involve estimating the final ratio directly. That is thinking about the effect of changing the the way energy is produced, e.g. what would happen in a future scenario where:That is way too sensible. Couldn’t you write some jokes or something? You are correct, but not quite in tune with the spirit of the post.

C is the number of crates.

For references:

M = C * B/C * P/B * M/P

M&Ms = Crates * Boxes / Crates * Packages / Boxes * M&Ms / Package

For admirers of Willis Eschenbach (among whom I count myself), this is embarrassing.

Matthew R Marler says:

There is nothing funny about a minor slip that creates a discussion spanning over 400 comments.

never mind. bless your soul.

this has been illuminating, if not elegant. willis does it again!

Wow, I can’t believe that such a simple mathematical expression has generated so much dialog.

First, I make no claim as to whether the identity expresses the true relationship between the volume of human-produced CO2 and the 4 terms on the RHS. I leave that to people more learned than me and my math degree.

Second, as instructive and entertaining as Willis’ posts always are, he got this one completely wrong.

As many have pointed out, what Willis did was verify that the unit of measure is the same on both sides of the identity. Peter Sable was the first to point this out, and also to say it’s a very useful technique in checking equations. As many have said, when you do dimensional analysis you better reduce down to 1 = 1 or you have a problem.

I didn’t bother counting how many people tried to put in numbers and ended up with CO2 = CO2. The biggest mistake I saw was substituting separately for the numerators and denominators of the terms.

For example, set population at 5 billion, then plug that into the first term (Population) and the second term (GDP / Population). Continue with other similar substitutions, divide like crazy, and you end up with CO2 = CO2. WTF?

But that’s not what the second term is. It’s a ratio – GDP per unit of population. It’s a single quantity expressed as dollars per person. The value of the denominator is held fixed at 1 – you don’t substitute anything for it! If there’s a change in population, you can plug that new value into the first term, and that might mean that there is a new value for the second term, but you don’t plug the new population into the denominator of the second term – it stays at 1!

The same holds true for the other 2 ratios. Energy used per single $ of GDP is expressed as Joules per dollar, and the denominator is 1 dollar. CO2 per unit of energy is expressed as (let’s say) tons per Joule. How many Joules? 1 Joule – that number doesn’t change in the ratio.

Those ratios are a bit esoteric, take one we are all familiar with – miles per hour. If my speed is 60 miles per hour, it means 60 miles in 1 hour. If my speed is 80 miles per hour, it means 80 miles in 1 hour. In any ratio of any type, the “per x” means per unit of x – the denominator is fixed at 1.

I really like steveta_uk’s M&M example – it’s very easy to visualize and understand. But even there, this identity, M = C * B/C * P/B * M/P, can cause confusion with people thinking each letter on the RHS is a quantity to be substituted for. Maybe it would be a bit clearer if we wrote it as M = C * (B/C) * (P/B) * (M/P) – there are 4 measurable values to be substituted for, not 7.

Finally, kudos to Nancy C for finally getting it, and seeing that LHS CO2 is not the same as RHS CO2. I’m not sure she gets the denominator bit like I describe above, but she has come a lot farther on the path to enlightenment than many others.

richardscourtney says: July 10, 2014 at 2:16 pm Well, perhaps you can tell us what use this ridiculous equation is except as a tool to spout political propaganda.

I, Dan, contend that you’ve lost your perspective. . . you don’t read or give thought to what others write. Here’s what I said earlier:

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.

So I refute your assertion that I’m a troll. . . I try to think things out without demeaning others. Well you on the other hand. . . well I’ll let others decide. . . because I don’t care.

Thanks for your passion. . . guide it wisely!

Dan

i’m prolly gonna hate myself, but this is a nagging puzzle…lol

daniel says:

“M = C * B/C * P/B * M/P

M&Ms = Crates * Boxes / Crates * Packages / Boxes * M&Ms / Package”

daniel- let’s say we have 5 boxes. how many cases is that?

(answer: as many as you freakin want!)

not funny?

Yes it is. Apart from the obvious example of the Kaya equation itself – which whether you understand it or not is being used by people who do – there are many equations of similar construction that we use all the time.

The point of the identity is not the X. It is the relationship between A, B, C and X. More precisely, the point is the relationship between A, B/A, C/B, X/C and X. In the real world, those terms have meanings that are interesting to us.

It also produces four other values – A, B/A, C/B, & X/C. And those values are of interest.

What do you mean by cases? (I don’t know)

The point is that you don’t have to measure X directly.

But I think J.K showed how the identity is really useful. Future scenarios.

JK says:

July 10, 2014 at 3:59 pm

[...]

– We replace half of fossil fuel energy with nuclear energy, which as a first approximation emits no CO2.

[...]

CO2 changes by a factor of 1.1 x (1.3 / 1.1) x 0.9 x 0.5 = 0.585, so it falls by 42%.

******************************************************

Oops. In order for that last factor to be given as 0.5 then actually CO2 is 58.5% of initial since the other givens force the energy consumption to increase by 17% (58.5%/117%). So basically this exercise comes down to the given that CO2 decreased to 58.5% of the initial, to solve for final CO2 decreased to 58.5% of the initial.

Joseph Murphy says:

July 10, 2014 at 11:57 am

Louis says:

July 10, 2014 at 11:49 am

M = P * M/P

This equation tells you how many total M&Ms there are if you know how many packets you have and how many M&Ms there are in a packet. Even though it reduces to M = M, the equation can still be useful if you want to know how many M&Ms you have without emptying out all the packets and counting each M&M individually. For example, if you have 10 packets of M&Ms and there are 100 M&Ms per packet, the formula tells you that you have 1000 M&Ms total (M = 10 * 100.) If you simplified the equation to M=M, it would still be valid, but it would become useless for making this calculation.

———-

Nah, you are using the total number of M&Ms to derive the per packet number. M&Ms per packet is a new variable and should be treated as such.

PP=M&Ms per packet

M=P*PP is what you want

PP=M/P is the other

You can’t use the same symbol for two different variables and expect no one to have a problem.

—–

Not so, Joseph. I did not use the total number of M&Ms to derive the per packet number. I didn’t know the total I had, so I used the number of packets and the M&Ms per packet to derive the total. Ten packets would amount to 1000. 25 packets would amount to 2500. No matter how many packets I have, I can use the formula to determine the total M&Ms (assuming the number per packet doesn’t vary).

M&Ms per packet (M/P) is NOT a new variable. It is a ratio using existing variables. Both M’s are the same variable, as are both P’s. Just plug the number of packets in for P and the total M&Ms back in for M on both sides of the equation and you’ll see that the equation holds up: 1000 = 10 * 1000/10. And also 2500 = 25 * 2500/25. The ratio (M/P) = 100 can be known without knowing either M or P separately (perhaps it’s on the packet label or you counted the contents of a packet before you decided how many packets to buy.) Once you know the number of M&M’s per packet (M/P) you can use P to calculate M, or M to calculate P using the formula M = P * M/P. But if you reduce the formula down to its simplest terms of M = M (or 1 = 1), it’s no longer useful for calculating anything.

The formula for calculating distance traveled is similar: d = t * d/t. Using miles and hours it becomes:

m = h * m/h.

If you know your speed (m/h or mph), you can calculate your miles traveled from the number of hours traveled, or hours traveled from the total miles traveled. If you have both the number of hours traveled and the total miles, you can then calculate the average speed in miles per hour (m/h). That is a useful formula. I have used it on occasion. But if you reduce it down to d=d, it is no longer useful. That’s all I’m saying. Just because you can reduce an identity down to it’s simplest terms doesn’t always mean that’s what you should do. Sometimes it’s the relationships of the variables that give a formula meaning.

You wonder why Mann will not release his code.

Or Phil Jones: “WHY SHOULD I MAKE THE DATA AVAILABLE TO YOU, WHEN YOUR AIM IS TO TRY AND FIND SOMETHING WRONG WITH IT.”

Or U.S. Interior Secretary Jewell: “I hope there are no climate change deniers in the Department of Interior.” (They will let the American People know that the science is totally bogus.)

Or former Senator Timothy Wirth: “We’ve got to ride the global warming issue. Even if the theory of global warming is wrong.” (In other words, just screw it. We know it is wrong and we don’t care….It allows us to meet our political agenda.)

Louis says:

July 10, 2014 at 5:13 pm

[...]

m = h * m/h.

**********************************

This is a great equation if you know m ahead of time in order back calculate the ‘m/h’ rate, but you do need to know m first. Given m and h you can solve for m. The general and more useful equation is d = r * t.

Will, you are missing the whole point. Would it be clearer if it were written as:

m = h * (m/h)

You get the (m/h) from your speedometer, let’s say 50 mph. At this speed, if you drive for 6 hours, you would go 300 miles. Let’s say you wanted to go farther. This equation tells you that you could do this by either increasing your speed, or driving for a longer time. The logic is equivalent to the Kaya identity.

Will Nelson says:

July 10, 2014 at 5:52 pm

Louis says:

July 10, 2014 at 5:13 pm

[...]

m = h * m/h.

**********************************

This is a great equation if you know m ahead of time in order back calculate the ‘m/h’ rate, but you do need to know m first. Given m and h you can solve for m. The general and more useful equation is d = r * t.

_________

With d = r * t, if you know any two variables, you can calculate the third. But since the rate (r) is equal to d/t, you can also write the equation as d = d/t * t. Or, using miles for distance and hours for time, it becomes m = m/h * h, which is basically what I wrote above. You don’t have to know m first. You can know the rate (mph) without knowing the total miles traveled. So if you set your cruise control and keep track of the time, you can calculate the distance (m) that you travel from those values. There’s no need need to know m first.

And wouldn’t you label it as EmissionsCO2 ?

From the bit that Willis quoted:

“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:”

Population multiplied by gdp per capita multipled by energy use per unit of GDP is a long winded way of describing total energy use. Multiply that by CO2 emissions per unit of energy and you have determined CO2 emissions. Which is what you already knew as part of CO2 emissions per unit of energy.

The Kaya Identity is useful for policy based evidence making. You decide what level of CO2 emissions you want and gauge how that might be achieved.

Daniel G. 7:53am said: “What happens to CO2 emissions in these scenarios (while keeping other variables constant):

1. increasing population? decreasing population?”

Nothing. CO2 is a variable like all the others. If you keep CO2 constant you keep CO2 constant. If you didn’t mean it quite like that then a change in ‘Population’ is canceled out by the corresponding inverse change in ‘GDP/Population’ and likewise for any variable you wish to change.

For points 2, 3 and 4 you are not changing a single variable but two and the net effect is the same – changes cancel out.

Daniel G 11:45am said: “Simple, all the ratios are more or less independent of each other. ”

The variables are. The ratios are not as they are expressed in variables that overlap. GDP per capita and energy use per unit of GDP necessarily use the same value for GDP. Energy use per unit of GDP and CO2 intensity of energy production necessarily use the same value for energy. If one ratio changes one or both of the other ratios change too depending on which variables have been altered, but the net effect is still no change.

Daniel G 12:11pm said: “No one is trying to discover co2 emissions, we have another measures for that.

But what would happen if for the generation of single unit of energy emitted 2x the Co2.

What would happen with energy-related co2 emissions? It would double too.

That is what the Kaya’s identity says.”

You do not need the Kaya identity to realise that energy related CO2 emissions doubling per unit doubles total energy related CO2 emissions. What the Kaya identity allows you to do is ask questions like ‘If the CO2 intensity of energy doubled, how big a hit might GDP and energy consumption need to take if we wanted to maintain a fixed level of total energy related CO2 emissions?’ However, I view those kinds of question to be a bit pointless and dangerous. Pointless because it supposes that global productivity and consumption can be tinkered with so directly. Dangerous because it becomes a self-fulfilling justification for politicians to try and grant themselves the authority to command global productivity and consumption.

Louis says:

July 10, 2014 at 6:16 pm

d = d/t * t

****************************

I’m not so sure. With this formula please solve for d without knowing d. lets say, t = 1 hr.

Curt says:

July 10, 2014 at 6:16 pm

********************************

Your speedometer does not read m/t (total miles traveled / total hours in trip…how could a speedometer know this?), it reads dm/dt.

I’m sorry. I’ve read both sides of this and then read Pielke’s blog post about it and I still can’t see anything useful in this stupid identity. First, even if it outputs actual answers to inputs, which to me doesn’t look like it, it assumes that all the relationships are linear. Why would any of it be linear?

Curt says:

July 10, 2014 at 6:16 pm

*********************************

I think what we need to be careful of is not to change the meaning of the variables from one side of the eqn to the other. If m = total miles traveled on the left side then so it does on the right. Of course (total miles traveled) / (total time) can be used to calculate average rate. But it is necessary to know both those pieces of information ahead of time to solve your derivation.

Women = Time * Money and Time = Money so,

Women = Money^2

But of course, Money = (Root of Problems),

Squaring both sides, Money^2 = Problems

Therefore, Women = problems

Wow, I never knew what a bunch of Phys.Ed teachers are posting here, and that is giving them a bad name. Good luck with your struggles. Hopefully there isn’t a math problem on the wet paper bags that are clouding your ability to see.

[this sort of condescending attitude towards others is exactly what is wrong with climate science -mod]

[snip - don't comment on personal things you know nothing about -mod]

So cutting to the chase; This identity is PC rubbish, disguised as algebra to fake out the”Math is hard”crowd.

Or the terms are poorly defined and very badly expressed.

If it means something other than its self cancelling algebraic form, it should be written correctly to avoid confusion.

However as it is a mere bureaucratic tool, one must assume the poor expression, resulting in an appearance of information where none exists, is deliberate.

As is so much of bureau speak.

The intentions are moot, the pretence of mathematical information is rubbish.

What wisdom is dispensed by 1×1=1?

Apart from a warm fuzzy feeling of the political creatures…. Oh look I can do math.

Peter Taylor says:

July 10, 2014 at 4:08 am

“The situation is deathly serious. ”

—————————————————————————————————————————-

Peter the whole premise of the original article is that CO2 is bad and that is fundamentally wrong.

Let me repeat that.

The premise that CO2 is bad is fundamentally wrong.

CO2 improves the biosphere and the environment universally and without requiring any bureaucracy to administer it. There has been an 11% “greening” of the planet since the beginning of the sattelite era mostly due to the increase of CO2 in the atmosphere. CO2 will not significantly (if at all) affect ambient temperatures, which is unfortunate because it looks like we are heading into a cold period. The most prolific periods in Earth’s long history of life occurred when CO2 levels are much higher than they are now. The planet is responsible for the production of about 97% of the CO2 that is in the atmosphere. We are at 400 ppm for CO2 concentration. At about 180 ppm it is game over,

.for everythingWith the coming cold period, the only thing that is going to mitigate against the massive loss of grain growing regions in Russia and Canada is going to be the CO2 levels. Cold is orders of magnitude worse than warm. The darkest times in human history have been during cold periods. The brightest times in human history have been during warm periods.

The situation is serious, but not because of CO2. It is serious because we have been wasting resources on a non-problem during a time of abundance and now have nothing in reserve for when the bad times come. So thank you and your alarmist, illogical, power grabbing, destructive friends. You may well have condemned future generations to hardships that could have been mitigated or even avoided.

Curse you and the horse you rode in on.

[snip - again, don't comment on personal things you know nothing about -mod]

Chucky77 says:

July 10, 2014 at 1:10 pm

“Treating each of the factors as a separate variable and varying the numerical value of one factor to see it’s effect of CO2 emissions assumes those factors are independent of one another. That’s called a static model. In reality changing the value of a factor will likely cause the value of another factor to change; a dynamic model. So it’s really difficult to attribute the change in CO2 emissions to one single isolated factor. Yes, people do that, but without realizing the assumption they are relying on. Those factors in the equation are surely correlated with each other. This is one reason simple-minded models often fail to predict actual outcomes. Viz., increase GDP per capita and energy intensity is likely to change with it.”

In a later post he gives examples and explains this further. The point is that you can’t do these kinds of policy tweaks without unintended consequences. My favorite example related to the topic at hand has to do with auto fuel efficiency standards. (Originally the purpose of the efficiency standards was not mainly related to CO2 emissions, but nowadays the standards are partly for that purpose, I think it is safe to say.) The car manufacturers have ways of getting around them to some extent, but let’s say for the sake of argument that the government is successful in improving average fuel efficiency (which I believe is probably true). By doing this they decrease energy, and thus hope to reduce energy/GDP (by the way, for those having trouble with the concept that the identity under discussion could be useful, read “energy/GDP” as “energy per GDP”, and think of it as the amount of energy used per dollar of GDP). But how much will this policy tweak decrease energy/GDP? A static accounting will look at the total miles driven currently, and then assume that miles driven will not change with greater efficiency. But of course that is not correct. When cars are more efficient, people will drive more, which means the energy used (and thus energy per GDP) will not decrease as much as anticipated. Furthermore, what if the requirements are too extreme, and cause the car manufacturers to make design decisions that do not make economic sense, to the extent that the car industry (and thus the GDP) suffer? Now GDP has gone down, as well as energy, so energy/GDP may not go down at all, but instead GDP/population (read GDP per person) goes lower than it otherwise would have been. So emissions may be reduced, but at the cost of reducing GDP/population instead of reducing energy/GDP (as intended).

But what if our policy makers and regulators are geniuses, and are smarter than the marketplace (as they often claim to be). What if they are successful at instituting requirements that not only make cars more efficient, but that also HELP the auto makers, and thus the economy? (Please leave aside the question of whether this is even a theoretical possibility.) If this happens, then GDP (and thus GDP/population) increases! Now that is a good thing, but it works against the goal of reducing CO2 emissions. So, in that scenario, you reduce energy/GDP (but not by as much as anticipated, because driving increases), but you increase GDP/population. So the net effect on CO2 emissions does not work out as anticipated.

However, these considerations DO NOT mean that the “Kaya Identity” is fundamentally useless just because things cancel out. Many have done a good job (using several good examples ) of explaining how such identities can be useful in general. As for the “Kaya Identity”, I think it gives a reasonable look at the basic quantities that policy makers would be concerned with if they have the goal of reducing CO2 emissions. Actually achieving the intended adjustments is another matter, and anticipating the secondary effects (and overall net effect on CO2 emissions) of the instituted policies is yet another matter.

Of course all this also ignores whether reducing CO2 emissions is even a worthy goal, but that is not what the discussion has mostly been about.

Daniel G:

There is nothing funny about a minor slip that creates a discussion spanning over 400 comments.I think it’s funny, and Willis started with a short paragraph and then laughing out loud.

Future total CO2 emissions can be calculated based on changes to the other factors.

Starting Basis

Population = 300M people

GDP = $15T

Energy used = 100Q Btu

CO2 emissions = 5.5M Tons CO2

GDP per capita = $50K / person

Energy use per unit GDP = 6667 Btu / $

CO2 emissions per unit of energy = 5.5×10^-11 Tons CO2 / Btu

Population * GDP per capita * Energy use per unit of GDP * CO2 emissions per unit of energy =

300M people * ($50K / person) * (6667 Btu / $) * (5.5×10^-11 Tons CO2 / Btu) = 5.5M Tons CO2

Scenario 1, assume the following changes every 5 years after the base year:

Population +10M

GDP per capita +5K / person

Energy use per unit GDP -100 Btu / $

CO2 emissions per unit of energy -0.1×10^11 Tons CO2 / Btu

In 5 years

310M people * ($55K / person) * (6567 Btu / $) * (5.4×10^-11 Tons CO2 / Btu) = 6.05M Tons CO2

In 10 years

320M people * ($60K / person) * (6467 Btu / $) * (5.3×10^-11 Tons CO2 / Btu) = 6.58M Tons CO2

In 15 years

330M people * ($65K / person) * (6367 Btu / $) * (5.2×10^-11 Tons CO2 / Btu) = 7.10M Tons CO2

Scenario 2, assume the following changes every 5 years after the base year:

Population +10M

GDP per capita +5K / person

Energy use per unit GDP -500 Btu / $

CO2 emissions per unit of energy -0.5×10^11 Tons CO2 / Btu

In 5 years

310M people * ($55K / person) * (6167 Btu / $) * (4.9×10^-11 Tons CO2 / Btu) = 5.15M Tons CO2

In 10 years

320M people * ($60K / person) * (5667 Btu / $) * (4.4×10^-11 Tons CO2 / Btu) = 4.79M Tons CO2

In 15 years

330M people * ($65K / person) * (5167 Btu / $) * (3.9×10^-11 Tons CO2 / Btu) = 4.32M Tons CO2

Looks like the formula is working fine to me. My numbers are made up and useless other than to show the formula works. The only time you need to know your CO2 emissions before doing the calculation is for the base year.

Let me know if I did anything wrong or miss understood the point of the formula.

[snip - in fairness, since Brad's comments have been snipped, so must be this one in response -mod]

I propose a new Misery Identity. Any area of life in which a Progressive scientist (usually from a certain generation born from 1942-1955 which I cannot mention here and shall remain unnamed), is allowed to mandate his personal proclivities and preferences on society (veiled in sciencey language and equasions) gets dialed in as a variable, giving an Expanding Misery Identity which anyone can figure out.

However, the Misery Identity is less with diversity and personal freedom. If you like solar panels you can joyously use your solar panels, and I will joyously use hydro and coal, and drive a pickup powered by gasoline, hold the corn. In agriculture, organic-only activists should feel free to pay twice as much for half as much, in the Rich Hippy area of the grocery store; however, I do not want expensive, fungus ridden food which was produced by people bent over in fields for hundreds of hours weeding. That has to go in to the Misery Variable. Vegetarians can eat their soy products and ranchers are left alone to tend their cattle in peace, selling milk, cheese, hamburger, and many other products to people who want to buy them, unmolested and without being constantly disquited by slanderous organic soy product activists.

This is just nuts!!

All these crazy formulas:

M = P * M/P

d = d/t * t

m = h * (m/h)

etc, etc!

Put simply, you can’t use the same notation for different variables!!

Yes, you are saying that the number on the left equals the result of the numbers on the right!!!

But what you have said on the right is; ”divide your result by a number, then multiply it by the same number” !

With the formula (d = d/t * t) you are saying that (the speed “d”) is the same as (distance “d”), when you have just finished showing that (speed “d”) equals (distance “d”) divided by time, multiplied by time!

The correct way to write it is either: s = d/t*t or x=d/t*t Or r=d/t*t etc

Otherwise you get the following:

d = d/t * t

d = (d÷t) x t

thus d ÷t = (d÷t)

Or

d = d/t * t

d = (d÷t) x t

d= (d/1 ÷ t/1) x t/1

d= d/1 x (1/t x t/1)

d =d/1 x 1

d =d/1

d=d

Or

d = d/t * t

d ÷ (d/t) = t (solving for t)

d x (t/d) = t (multiply by reciprocal)

d/1 x t/d = t

1 x t = t

t=t

And in the same pattern:

M = P* (M/P)

M ÷ (M/P) = P (solving for P)

M x (P/M) = P (multiply by reciprocal)

P=P

The point of an equation is that it can be rearranged to solve for different variables.

The one you don’t know can be calculated from the ones you do.

C=C is not helpful in this regard!

E=MC2 is useful because it can be written M=E/C2, if you know the energy but not the mass.

As for the equation in the head post, solving for any other variable, reduces to the pattern Willis demonstrated!

c=c, p=p and e=e ect because the terms in it, cancel each other!

Curt says:

July 10, 2014 at 6:16 pm

Will, you are missing the whole point. Would it be clearer if it were written as:m = h * (m/h)In your equation above m on the left and h outside the parenthesis are variables of an equation , (m/h ) are a constant expressed unusually in units ( units are not mixed up in equations) in which the variables are expressed. It is total algebraic confusion to use the same symbols for variables and units. Until we substitute a value for the variables, a constant instant.

You should state: let M be the miles to travel and m the distance in miles traveled in an hour . If I go for H hours how many miles will I travel?

M=H*m

the way we write E=m*c**2, the units are not written explicitly except in order to sort out in what unit system the calculation is made so as to know in what units E is given.

The problem is not the tautology that emerges from the mixing of units with variable/constants in this famous equation.

The equation rewritten

the equation should be expressed as :

Let C be total carbon emissions , to be estimated

C=P*g*e*c

Where for the variables we substitute a constant value given by measurements.

P the population known from tables

g the GDP/population from tables

e energy /GDP from total energy used

c CO2/energy from chemical analysis and measurements in the lab

where everything above are constants expressed in appropriate units.

There is something called dimensional analysis in sophisticated equations. In simple algebra it means that the units on the left of the equation are the units on the right of the equation,

Units, otherwise the equation is wrong. In the confusion of variables with units in the original equation that is what comes out, the dimensional consistency, CO2=CO2 as units, not numbers with useful value.In my opinion the equation is given in a silly non consistent with algebra form, but is not a tautology if written correctly.

[snip see previous reason, if you have issues with how Willis lived his life today while traveling, take it elsewhere -mod]

Jason L, July 10, 2014 at 8:36 am says:

“It’s disheartening to see how many people think this equation is somehow useful.”

Hear, hear! This is a sentiment I share whole heartedly. It also makes me wonder the credibility of so many people that comment on this science blog. Thanks Willis for exposing them.

Agreed. Stop trying so hard to make it worse.

Yes, and that is often a very useful thing to do. And supported by the multiplicative inverse and identity properties of algebra.

Uh, no. Nothing in (d = d/t * t) says that speed is the same as distance. This is a good example of the concept, however.

1) Begin with distance:

d. Not particularly useful.2) Form the identity:

d = d. A true equation, but still not particularly useful.3) Divide and multiply the right side of the equation by time (t):

d = (d/t) * tStill a true equation,andnow it is useful. It defines a relationship between distance (d) and time (t) and speed (d/t) that has application in the real world. A similar gain in utility can be had if you start with 2) CO2 = CO2 and factor in Population, GDP, and Energy to arrive at Kaya’s Identity.It is true that you can step back from (3) to (2) for either equation, but why would you do that? You’d give up the utility you have gained. And the fact that you can choose to give up the utility of the expanded equation doesn’t mean that utility never existed. If it did we’d be screwed, as

anyequation can be reduced to the trivial identity by standard algebraic operations.Attempting to solve the formula in the head post, for any of its variables, is meaningless!

I have supplied my reasoning and ‘model’ code below ;-)

IF

Co2 emission = c

Population = p

Energy= e

GDP= g

THEN

1. c =p*(g/p)*(e/g)*(c/e)

2. c÷p = (g/p)*(e/g)*(c/e)

3. c÷p = (c/p)

4. c= (c/p) x p/1

5. c=c

AND

6. c÷p = (c/p) [From line 3.]

7. c÷p = c÷p

8. p = c/p x 1/c [Solving for p]

9. p=p

OR

1. c =p*(g/p)*(e/g)*(c/e)

2. c/1 ÷ c/e =p*(g/p)*(e/g)

3. c/1 x e/c =p*(g/p)*(e/g)

4. e=p*(g/p)*(e/g) [Solving for e]

5. e=p/1 x e/p

6. e=e

AND

7. e=p*(g/p)*(e/g) [From line 4.]

e/1÷ e/g = p*(g/p)

e/1x g/e = p*(g/p)

g= p*(g/p) [Solving for g]

g/p=(g/p)

g= (g/p) x p/1

g=g

Pete Brown:

I am replying to your post at July 10, 2014 at 3:23 pm which is untrue twaddle and says in total

Before dealing with the important issue, I provide a paragraph which refutes your falsehoods which I have here copied.I am not susceptible to idiocy from extremists so I have been rejecting your tripe by replacing it with logic and rational argument. I have ‘ducked’ nothing but I have repeatedly explained why I will not be side-tracked by your bullying that attempts to get me to answer your red-herring questions, and

your claim of my bullying is a clear example of psychological projection. I began with my post at July 10, 2014 at 2:31 am which is here. You replied to that single, polite and logical post with a series of posts beginning with your post at July 10, 2014 at 4:32 am.Importantly, you have repeatedly and doggedly refused to address my main point which I have repeatedly stated to you and was stated in my post at July 10, 2014 at 2:31 am where I wrote

You have NOT addressed my thesis that the equation is and can only be a tool for propounding political propaganda.Address the real issue and don’t write falsehoods, or clear off.

Richard

I had to read everyone elses, so even though the show’s mostly over, I’m going to contribute my two bits. :)

The big original confusion seems to be with values over units. Lots of people are reading the equations as if the elements of the equations are variables…but they’re not. They’re units.

In the M&M equation, C is a unit: Crates.

“M = C * B/C * P/B * M/P

M&Ms = Crates * Boxes / Crates * Packages / Boxes * M&Ms / Package”

This equation contains no values, and no way to represent values (no variables or constants). It can be used in a very elementary way to see things like, if you increase the number of packages/box, you will deliver more M&Ms. It can be used to show the equation is valid by showing that the units cancel to an identity. But it does not have variable placeholders; it is only units.

If you do put values in the appropriate places, you see that C is a unit, not a variable:

40000M = 20 C * (10B/1C) * (20P/1B) * (10M/1P)

The value next to the first C is not the same as the value next to the second C. C does not represent a variable that must be the same everywhere in the equation; it represents a unit. If the values next to the Cs were represented by variables, they’d be two different variables with the same unit: Crates.

Similarly, in the original equation, the first “population” will have a value next to it like “600,000,000”, while the value next to “population” in the ratio (GDP/Population) will probably be 1.

Population”, by itself, is a valueless unit. The original equation contains only units.

Willis got it wrong on this one, but I was with him in the beginning, and it was a struggle to follow the discussion. Thanks to all who explained this in their various ways. Thanks, too, to those folks that tried to keep the discussion civil.

But I don’t recommend, as others have, that the thread get buried. Hiding their mistakes, and pretending they don’t make any, is the shameful thing the warmists do.

Whether the equation is a political tool or not should be an entirely different thread.

DanMet’al:

At July 10, 2014 at 4:21 pm you say to me

Absolutely untrue, for example, I relied to your offensive and abusive trolling at July 10, 2014 at 1:47 pm.

However, your meaningless waffle in your post I am now replying does not answer my repeated point which you quote from my response at July 10, 2014 at 2:16 pm to your egregious trolling; viz. I asked

Your reply to that question says

And – of course – that has no relation of any kind to my question which you claim to be addressing.

Richard

Consider this a CSI investigation:

Not sure when Willis actually posted the article?

First response post was at 10:30PM PST on 7-9-2014.

First and only Willis post was on 7-9 at 10:51pM. He has been absent for over 24 hours.

Anthony said in his second update that he was able to contact him at 10PM? There were no comments before 10PM, unless Anthony means 10PM on the 10th?

When was his flight home, and when did he get home?

Does he have a home PC?

When did Anthony add his two updates? No time stamps.

What type of phone does Willis carry, internet capable? Could he have accessed the post like I am doing now?

What hotel did he stay at, internet access? Did it have a business center with internet access?

What type of laptop does he have and how was it damaged?

So many questions….I have a hard time thinking the Willis I have come to know would allow for 24+ hours to pass with no internet access. (I can’t handle it, even on a cruise.)

Just asking questions, no accusations.

It is all about transparency.

“The big original confusion seems to be with values over units. Lots of people are reading the equations as if the elements of the equations are variables…but they’re not. They’re units.”

Yes, useless units as I demonstrated in a post, you can also be an AGW genious and make up your own useless units. Just throw in something in the equation that seems to have bearing on CO2 in the form of (entity/entity). You can even randomly rearrange the terms to get new units that gives you new pseudo insights. If this is how economists think, I am not surprised the economy is in huge trouble.

CO2=CO2(pop/pop)(gdp/gdp)(gec/gec)….add whatever you like

try (ct/ct): carbon tax

or (ge/ge): green energy

or (ec/ec): electric cars ….rolling the dice, oh Kaya speak to me, share your wisdom…

CO2=(ge*pop*gdp*gec*CO2*ct*ec)/(pop*gdp*gec*ct*ge*ec)

CO2=(ge/pop)(pop/gdp)(gdp/gec)(gec/ct)(CO2/ge)(ct/ec)*ec

See how easy it is?

Impressive maybe, but is it useful?

Rdcii:

At July 10, 2014 at 11:27 pm you assert without any supporting evidence or argument

I strongly disagree. The usefulness of a model is fundamental to any consideration of it.

The only perceived utility of the equation is as a tool for political propaganda, and even its staunchest supporters have not suggested any other use.

Also, your unjustified assertion which I am writing to refute is the clearest indication, but your entire post can be understood as being an example of concern trolling; e.g.

“Willis got it wrong on this one …” (wrong? RSC)

“I don’t recommend, as others have, that the thread get buried.” (not recommended but suggested. RSC)

Hiding their mistakes, and pretending they don’t make any, is the shameful thing the warmists do.” (mistakes? shameful? RSC)

Richard

Unbelievable.

‘CO2 emissions = population * GDP/population * energy/GDP * CO2 emissions/energy’

As long as this expression uses uses ‘equal’, ‘multiply’ and ‘divide’, it reduces to CO2 = CO2.

Whatever demonstration (and I use the term loosely) has been used to “prove” it proves nothing beyond the fact that a quantity divided by itself is 1.

Indeed, I can replace ‘population’/’population’, ‘GDP’/’GDP’ and ‘energy’/’energy’ with ‘number of rocks on the moon’/’number of rocks on the moon’, ‘number of neurons in whomever wrote this garbage brains’/’number of neurons in whomever wrote this garbage brains’ and ‘pocket change I have in my wallet today’/”pocket change I have in my wallet today’ and I get the same tautology.

The expression shows no influence of these quantities – or any other – on CO2; that’s why it’s a tautology. The quantities chosen are put there for propagandistic purposes, to create the appearance of an influence.

But wait – there’s more.

Apparently, some posters here are under the impression that, if they use enough word salad and rhetoric, they can shove any garbage down our collective throats.

Who knows? Perhaps they’re not shameless deological propagandists; but merely incult fools, confused with regards to how one correctly uses ‘equal’, ‘multiply’ and ‘divide’.

A lot of people here have been confused by the shorthand used in expressing the identity. While common for people used to this type of presentation, for those unfamiliar with this type of shorthand, the use of only the units in the presentation of the equation without a variable to go with each unit doesn’t make much sense.

Without the shorthand convention, the identity would be expressed something like:

C [tons CO2] = P [persons] * G [$GDP / person] * E [GJ / $GDP] * D [tons CO2 / GJ]

Each of the variable values on the right side can be found from many sources in political, economic and scientific references. As a quick way of analyzing the problem, it can be very useful to express the relationship this way. As I pointed out above, to someone who proposes radical cuts in CO2 emissions, ask him which of the four terms on the right he wants to cut radically to achieve these emissions reductions.

The comments of some other posters here reminds me of an old joke Feynman liked to tell in expressing the concept of a derivative. In the joke, a cop stops a driver for speeding and says, “Did you know you were going 70 miles per hour?” The driver responds, “That’s impossible, I’ve only been driving for 20 minutes!”

I was challenged on my use of the equation of D (miles) = T (hours) * V (miles / hour), saying the speedometer expressed an (almost) instantaneous velocity, not the overall distance divided by overall time. But in many cases, such as traveling on an open highway, it is a good approximation to multiply the short-term velocity by time to get distance. All of us have done this type of mental calculation in our travels — the speedometer shows 75 mph, the highway sign says 300 miles to our destination, so we figure 4 hours of driving time left.

The Kaya identity uses similar logic. The “D” term is derived from very small laboratory samples, but multiplied by very large quantities.

Curt

“C [tons CO2] = P [persons] * G [$GDP / person] * E [GJ / $GDP] * D [tons CO2 / GJ]”

Lol.

tons CO2 = persons * $GDP / person * GJ / $GDP * tons CO2 / GJ reduces to tons CO2 = tons CO2.

You can christen any fraction here with P, G, E, D, or the name of your first child; you can pretend that persons * $GDP / person doesn’t equal $GDP – none of this changes the fact that the ‘identity’ reduces to CO2 = CO2, showing no influence of another quantity on CO2.

Feynman would be ashamed – and angry – to see propagadists use his name to push this tautology as showing any influence of any quantity on CO2. You’re actually comparing derivatives (or equations that actually have different terms before and after the ‘equal’ after trivial simplification) with the tautology you’re trying to push?

Well – keep going; show the readers exactly how intelectually dishonest you are. Or, alternatively, how confused you are about mathematics.

This is one way of losing the plot. Like that bunch religiously focused on the pinhead looking for angels while the barbarian hordes gathered on the steppes.

Tonyb….not sure what I have written that might be relevant – I have been trying to warn the ecologists I work with every day on landscapes, community, forests and biodiversity – but got to be careful to go slowly, otherwise they simply switch off – I think most working ecologists cannot take on board the scale of the dissonance we take for granted. I do have an unpublished essay reviewing ‘green economics’ books – it was too long for the journal I normally get published in…I will send it via your website.

Ok, let’s try this again:

CO2 Emissions = Population X (GDP per capita) X (Unit of Energy /GDP) X (CO2 Emissions / Unit of Energy)

CO2 Emissions = C

Population = # of people = P

GDP per capita = Standard of Living = S

Unit of energy /GDP = Production Efficiency = E

CO2 Emissions / Unit of Energy = Fuel Emission Intensity = F

So, now we have:

C = PSEF

And yes “C” is on both sides of the equation since F = C / Unit of Energy. The usefulness is not derived from determining “C” per se but in analyzing the changes in “C” from changes in P, S, E, and F.

Thus:

Denoting: “Change in” = d

Then:

dC = (dP)(dS)(dE)(dF)

I think the problem is that people have been using the wrong equation. They really need to be using the modified Kayla equation that goes like this:

P = M * (B / M) * (P / B)

where

P = Number of puppies that die each year.

M = The amount of money you earn each year that you don’t donate to me.

B = Number of times you disagree with me in this blog.

As long as we are into differentiation we can use the modified Kayla equation I wrote above to compute the rate of change of puppy deaths relative to the money that you don’t donate to me.

I believe it goes like this:

dP/dM = (dB /dM) * (dP / dB)

where as before

P = Number of puppies that die each year.

M = The amount of money you earn each year that you don’t donate to me.

B = Number of times you disagree with me in this blog.

Now it’s all sophisticated like you’ll all believe me right?

John West

“C = PSEF”

Lol.

As already said: tons CO2 = persons * $GDP / person * GJ / $GDP * tons CO2 / GJ reduces to tons CO2 = tons CO2.

You can christen any fraction here with P, G, E, D, or the name of your first child (or P, S, E, F) – none of this changes the fact that the ‘identity’ trivially reduces to CO2 = CO2 (or C = C), showing no influence of another quantity on CO2.

Instead of population, GDP and energy, you can put in the tautology ANY known and unknown concept that can exist in this universe and can get a numerical value.

Let me guess – in your world, the ‘identity’ shows that all of these concepts inflence CO2, yes, John West?

What a bad joke.

Such elementary concepts are clear to a first grader; but we are supposed to believe they are beyond your ability to grasp.

Much more likelly, your posts reveal you for what you are: a true believer that doesn’t let facts or logic get in the way of his ideology.

Bjorn from Sweden…nothing I said agrees or disagrees with your reply. I saw people arguing about the original equation as if the parts were variables instead of units. You seem very clear that the elements of the original equation were units, not variables.

Excellent. My attempt at clarification was clearly not for you. But you do understand that others have not achieved your clarity about the original equation, because many explanations haven’t been clear? And that your argument that the units aren’t useful requires other people besides you to have a clear understanding that those are units, not variables, in the first place? So, if I’m trying to clarify, in your favor, a necessary preface for your argument, why are you taking any issue with my posting?

There is no need to insult chemists or chemistry as a science.

What I think it is insulting is the term “social sciences” It is like “military music” in Marx´s famous quote.

richardscourtney says:

July 10, 2014 at 11:19 pm

…

Richard, I know I am going to regret this but, to address your post:

“It is a political tool provided by a political organisation for political purposes.”

No, not quite. As I have explained, it is a policy tool. It is not in itself political. It doesn’t get to vote. It isn’t a registered member of a political party. And like any good light saber, it can be used equally for good or evil.

As I also have said, you should not just disagree with something simply because you think it disagrees with you, or could be used by people who disagree with you. You have to engage with the substance…

“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 is GDP per capita?”

Just the whole body of economics really, since about the time just after economics started to about now. Seriously, you cannot be suggesting that the industrial revolution for example, wasn’t a bit fueled by, well, fuel? In my opinion, and in the opinions of quite a lot of people, if you were to take carbon-based fuels out of the economy right now, that would have a devastating effect on the economy. The economy (GDP) would collapse, and our ability to generate wealth (GDP per head) would collapse. The theory goes that since CO2 emissions are a by-product of economic activity, throttling economic productivity will reduce CO2 emissions other things (i.e. the other three ‘factors’) being equal. Conversely, economic growth (i.e. increasing GDP, which corresponds with increasing GDP per head if population is fixed) will entail increasing emissions, other things (i.e. the other three ‘factors’) being equal.

To put the point another way, if you seriously think we can de-couple CO2 emissions and economic productivity then you really need to tell us how – because that would absolutely be the holy grail…!!

This is the point of the Kaya identity. It is intended to illustrate that if you seriously want to reduce CO2 emissions in an economy then you either have to reduce the population, or reduce the wealth of the population, or increase the CO2 efficiency of energy generation, or increase the energy efficiency of economic activity. This strikes me as pretty much a logical truism, which again is very much what the identity is intended to show. As I have said several times though, if you disagree that any one or more of these four factors has the effect that is implied by the Kaya identity, please tell us which and why? Better still, if you think there are other factors that are not already covered under these four heads, and have presumably eluded policy makers for the last 40 years, please tell us…

By the way, I am not advocating reducing the population before anybody else gets silly about that. In fact I’m not advocating anything – except perhaps that people should do some research before launching in (Willis Eschenbach).

“You have NOT addressed my thesis that the equation is and can only be a tool for propounding political propaganda.”

Yes I have, many many many times: Please see Prof Roger Pielke Jr…!

I’ll add this: there are people in the world who think that reducing CO2 emissions is just a matter of political will, or that we already have the means to do it. The Kaya identity can help us to illustrate that this is not the case; that if you really want to reduce CO2 emissions then you either have to have some serious technological advances up your sleeve to make our lives and economic activities more CO2 efficient (and that’s not going to be windmills), or you have to be prepared to put people into the most gut-wrenching poverty, cripple our economies and ways of life, and, frankly, end peoples lives prematurely. Those who are quick to accept this as the price of reducing CO2 emissions – especially given the actual state of the science upon which this is based – are really, really, really scary…

My poor old iPad Original is struggling with this long post and one finger typing, is not making for good communication. I think this post deserves a new separate thread. I’ve just spent several hours getting my “poor old” brain around the Kaya e-quack-tion and I now have lots more to say ;-)

Most of it concerning, how a relation is not an equation and why a Kaya relation ≠ an Einstein equation/intelligence * intelligence.

Economics is the propaganda of central banks. It is politics badly disguised as something rigorous! It is the ‘scientifical’ masquerading as the scientific.

Pete Brown

“This is the point of the Kaya identity. It is intended to illustrate that if you seriously want to reduce CO2 emissions in an economy then you either have to reduce the population, or reduce the wealth of the population, or increase the CO2 efficiency of energy generation, or increase the energy efficiency of economic activity.”

The kaya identity is intended to PROPAGANDISE this. It proves nothing of the sort (and your ‘illustrate’ euphemism doesn’t change this in the least).

“This strikes me as pretty much a logical truism, which again is very much what the identity is intended to show.”

Lol.

You need to prove your ‘logical truism’ in order for it to be science and not religious belief. Hint – simply saying it’s a ‘logical truism’ does not make it so.

As said:

Instead of population, GDP and energy, you can put in the ‘kaya identity’ tautology ANY known and unknown concept that can exist in this universe and can get a numerical value.

Let me guess – in your world, it’s a ‘logical truism’ that all of these concepts inflence CO2, yes, Pete Brown?

What a dishonest joke.

Juice says:

July 10, 2014 at 7:04 pm

….

You’ve read two blogs and still haven’t found enlightenment? That’s almost hard to imagine…

But the Kaya identity use meaningful ratios, your arbitrary tautologies don’t. The same can be said M&Ms identity.

@ Edit_XYZ asks:

“in your world, the ‘identity’ shows that all of these concepts inflence CO2, yes, John West?”No, in my world (reality) the “identity” expresses a relationship of variables that influence CO2 emissions. It is a simple UNIT expression. It simply states that if you wish to change anthropogenic CO2 emissions (which I would rather we increase) then you have to change population, standard of living, production efficiency, fuel emission intensity, or some combination thereof. Of course it was written by people who wish to control these very variables and they seem to have “forgotten” a few that could be there. There is no land use changes variable for example. So, there’s plenty to criticize with respect to this “identity” but the fact that it reduces to X=X is not one of them.

That’s how/why algebra works!FYI: I’m the President and Founder of Tropics from Pole to Pole Society of NC.

Also, do you not realize that with a few pounds of each fuel used one could determine CO2 Emissions / Unit of Electricity Generated in a lab or with a pilot study? Therefore, the “CO2 Emissions” on the right side of the equation is not necessarily the same as the “CO2 Emissions” on the left side of the equation.

Edit_XYZ says:

July 11, 2014 at 4:06 am

…

Try putting some of it in bold – trust me it’ll make your point more compelling.

Co2 is the result variable, by other variables staying constant, i mean the control variables.

Rdcii says:

July 11, 2014 at 3:38 am “So, if I’m trying to clarify, in your favor, a necessary preface for your argument, why are you taking any issue with my posting?”

– I didnt know i did!

The paper uses a technical shorthand that some find distasteful, but it is a shorthand that can’t be ignored and is obvious considering the english used.

John West

“It simply states that if you wish to change anthropogenic CO2 emissions (which I would rather we increase) then you have to change population, standard of living, production efficiency, fuel emission intensity, or some combination thereof.”

It states nothing of the sort. You can increase a trillion times the population, GDP, energy or you can decrease them a trillion times – and the tautology still reduces to CO2=CO2.

“No, in my world (reality) the “identity” expresses a relationship of variables that influence CO2 emissions.”

If in your world the tautology shows that your ideologically chosen variables influence the CO2 emissions, then in your world ANY known and unknown concept that can exist in this universe and can get a numerical value inflences CO2 emissions.

That’s because you can put them in the tautology in place of population, GDP and energy.

And I know that, like any true believer, you think your fantasy world to be the reality.

Well, ‘A casual stroll through the lunatic asylum shows that faith does not prove anything’, John West.

“Therefore, the “CO2 Emissions” on the right side of the equation is not necessarily the same as the “CO2 Emissions” on the left side of the equation.”

You already redundantly proved that you, John West, cannot do simple multiplications and divisions – which inevitably, trivially reduce the kaya identity to CO2=CO2.

But, if you feel that you must continue to prove your mathematical analphabetism – by all means, do so.

“I’m the President and Founder of Tropics from Pole to Pole Society of NC.”

What is amusing here is that you think a good idea to name the organisation you’re president of – in the same thread in which you have proven your lack of even elementary mathematical competence.

You must be a fan of the ‘Any publicity is good publicity’ dictum.

It is not hard to prove that Kaya identity is really identity, but it is just too obvious.

for the sake of demonstration, i will do the following:

write gdp per capita (gc) as the ratio of gdp/pop

write energy intensity (ei) of the economy as the ratio of energy/gdp

write co2 intensity (co2i) of energy as the ratio of co2/energy

Then:

pop * gc * ei * co2i = pop * (gdp/pop) * (energy/gdp) * (co2 / energy)

pop * gc * ei * co2i = gdp * (energy/gdp) * (co2 / energy) = energy * (co2 / energy)

co2 = pop * gc * ei * co2i (Kaya Identity)

1) the variables of the identity are the ratios and population.

2) the variables are quite independent of each other.

3) as the variables are ratios, the factorization is “linear”.

4) the actual relationship between co2 and a variable might be non-linear due to dependency, but that doesn’t disprove the Kaya identity.

5) Kaya identity is analogous to M&Ms identity.

6) The paper uses a technical shorthand, to use numerator/denominator symbols to represent a ratio variable.

7) The Kaya identity is useful for purposes explained in the comments above. (It is just an identity, so it isn’t that useful really, but it is a convenient description)

8) all the variables are meaningful, and they completely factor energy-related co2 emissions.

You have to prove your ratio variables are meaningful.

Explain the M&Ms identity then.

Not yet read all the comments but:

The problem isn’t that the Kaya Identity is an Identity and so it reduces to CO2 = CO2.

The problem is that the four terms that cancel are chosen because the author (Kaya?) wants to talk about those terms:

• Population

• Energy

• GDP

• CO2 emissions

Why choose to limit the discussion to these terms? The author has their reasons but what are they and do we agree with them? And why?

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

Imagine a country that produces pig iron for export to generate its GDP. One day it switches to Gold (shiny, shiny gold). But it doesn’t produce as much gold so its GDP is unchanged. Suddenly its energy per GDP has reduced dramatically.

Is this what the Kaya Identity shows us?

No.Innovation is dependent on education (GDP) and number of brains (population) and luck. The Kaya Identity excludes all other factors (such as random chance) and claims the factors they do include are independent. Innovation means that ain’t so.

So the problem isn’t that the Kaya Identity is an Identity.

The problem is that the Kaya Identity is a means of limiting thought and debate.

technical shorthand? technical? no, shorthand? no. algebra? not much.

post normal skience babble? bingo.

and those who don’t grasp the nature of the kaya incantation must wonder why rorschach keeps showing photographs of their parents fighting…lol

5 boxes; how many cases is that, daniel? can’t do it, can you? useful formula?

it is totally awesomely useful – it belongs on the stanford-binet. like a pork sammich for sorting out infidels, it works gangbusters!

Edit_XYZ says:

“you think a good idea to name the organisation you’re president of – in the same thread in which you have proven your lack of even elementary mathematical competence.”ROTFLMAO

1) It’s not a real orginazation, it’s a joke. Read much?

2) I’ve devised new methods for solving ordinary differential equations and have made a decent living from mathematical competence for 20+ years. Assume much?

3) You are a troll.

4) Goodbye.

gnomish still hasn’t told anyone what he means by a case.

John West – Also, do you not realize that with a few pounds of each fuel used one could determine CO2 Emissions / Unit of Electricity Generated in a lab or with a pilot study?

But this is not going to give you a single value for CO2 Emissions / Unit of Electricity Generated is it?

Each fuel (and for that matter each different electricity generator) will have a different value.

Also cows create CO2 without generating electricity. Likewise my car creates CO2 and it’s not an electricity generator (well only a little bit). And different cars create different amounts of CO2 per energy used.

So you need to include all sources of CO2.

Indeed in the Kala equation the term is C02emissions/Energy not C02emissions/electricity generated.

For the Kayla equation to be computable with a single C02emissions/Energy term it would have to use Average CO2emissions/ Average Energy used.

The problem is that with so many different sources of energy all with a different CO2/energy value – a virtual infinitude – you can’t really compute the Average CO2emissions/ Average Energy used without knowing the total CO2 and total energy used. And if you do know the total energy used (not that you will for reasons just given) then you don’t need the Kayla equation as you already know the value of the left hand term.

So the Kayla equation is still a useless tautology. It makes it sound like you know more than you really do.

Daniel G.

“”If in your world the tautology shows that your ideologically chosen variables influence the CO2 emissions, then in your world ANY known and unknown concept that can exist in this universe and can get a numerical value inflences CO2 emissions.

That’s because you can put them in the tautology in place of population, GDP and energy.”

You have to prove your ratio variables are meaningful.”

Let me introduce you to an elementary rule of division (that first graders have no problem understanding): any number divided by itself gives as result 1.

This means that ANY known and unknown concept that can exist in this universe and can get a numerical value, when put in the kaya identity, being divided by itself, simplifies to 1. It does not matter whether the concept (variable) is meaningful or not.

That means that the kaya identity does NOT prove (does not show/illustrate/insert your euphemism) any link between ANY variable, meaningful or not, and CO2 emissions.

It merely PROPAGANDISES a link between your ideologically chosen concepts (variables/insert your synonym) and CO2 emissions, simply by writing them near each other.

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

It is embedded on the ratios.

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

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

Will Nelson says:

July 10, 2014 at 5:52 pm

Louis says:

July 10, 2014 at 5:13 pm

[...]

m = h * m/h.

**********************************

This is a great equation if you know m ahead of time in order back calculate the ‘m/h’ rate, but you do need to know m first. Given m and h you can solve for m. The general and more useful equation is d = r * t.

————–

Now that I have a full education on identities, it is amazing to me that people familiar with them aren’t fully aware and versed in this criticism. They contain no useful information, you need prior information in order to make them useful. And there usefullness is dependant on the accuracy of your prior information rather than the identity. I apreciate all the comments.

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

John West

“2) I’ve devised new methods for solving ordinary differential equations and have made a decent living from mathematical competence for 20+ years. Assume much?”

I assume nothing. I know you cannot do simple divisions because you’ve redundantly proven it in this very thread by not being able to simplify a tautology.

“3) You are a troll.”

Really?

You keep saying the kaya tautology doesn’t trivially reduce to CO2=CO2 – despite the blatant obvious to the contrary – and I’m the troll?

John West – All I’ve said here is the truth, as determied by basic mathematics and your posts from this thread. If you don’t like the image appearing when someone puts a mirror in front of you, you should refrain from posting non-sense.

“1) It’s not a real orginazation, it’s a joke. Read much?”

Is it? Well – your posts mostly read like long bad jokes. So I suppose it fits right in.

For those still discussing the formula in abstract variables only, please see my post

LanceB says:

July 10, 2014 at 9:05 pm

I suspect that this is how the UN report would use the formula. My post showed that the formula is not ‘broken’ because both sides of the equation have CO2 emissions listed. I’m not arguing about the usefulness of the formula or the validity of the ratio relationships, but just showing that using numbers and a future ‘scenario’ will give an output of Total CO2 emissions as expected.

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

This discussion separates the wheat from the chaff. If it did not reduce to a tautology, it would be wrong.

If I know my average walking speed (v or d/t) and the time I will spent walking (t), I can calculate the distance I will cover.

d = (d/t) *t

A=B*A/B

set B=1 to x

for all x –> A doesn’t change

A=D*C/D*B/C*A/B

set B=1 to x

set C=1 to y

set D=1 to z

for all combinations of x,y,z –> A doesn’t change

Any graph that shows A changing has another undeclared variable involved

Edim

“d = (d/t)*t”

This formula is not a tautology.

Why?

Because, after the trivial divisions on each side of the ‘equal’ sign are performed, we have 3 different concepts:

-on one side of ‘equal’ be have ‘d:total distance traversed in a number of hours';

-on the other side of ‘equal’ we have ‘t: number of hours’ and ‘v: the distance traversed in an hour’. We could NOT put here any concepts (variables) we wanted and have their multiplication still equal d.

In the case of a tatutology (such as the kaya tautology), after the trivial simplificatons are done (and, instead of population, GDP and energy you can put in the tautology ANY variable and it will smplify to 1), we have the same concept (variable) – CO2 – on both sides of the ‘equal’ sign.

And a variable is always equal to itself – which is all that the kaya tautology (any tautology) tells you.

EDit_XYZ can’t do basic division:

d = (d/t)*t = d

So sad that Anthony seems to be giving some credibility to the seemingly innumerate majority here who agree with Willis that any equation whose units cancel out correctly must be invalid. None of those people would have made it through my first engineering class. I have great respect for Anthony and have appreciated the insight in many of Willis’ posts, but I’m incredibly disappointed that so many closed minds here are unwilling to admit that the Kaya Identity is valid by definition and that the way the factors (population, standard of living, energy efficiency of wealth creation and CO2 efficiency of energy production) are arranged would serve a useful purpose if one were evaluating how to impact total CO2 emissions from energy production.

Is innumeracy the problem here or are people simply blinded by their (valid) “CO2 drives catastrophic warming” skepticism? What if CO2 in the identity were replaced by an actual pollutant like SO2? Would you then be able to see that population, standard of living, energy efficiency of wealth creation and SO2 efficiency of energy production would serve as useful factors for reducing SO2. In that particular case, nearly all of the gains we’ve made have been with the SO2 efficiency term by shifting to lower-sulfur fuels and scrubbing SO2 from emissions before release, but can anyone deny that reducing the demand for energy by reducing standard of living or population could have had similar effects? I’m glad we made the right choice on that one and I don’t believe we have to make a choice on CO2, but the Kaya Identity sure gives us a handle on what the levers if we had to make that choice.

One final option for where people are going wrong. The factors in the identity are not Population, GDP, Energy production and CO2 emissions as most people seem to believe. Those could be viewed as the units of the factors. The factors are Population (in units of population), standard of living (in units of GDP per population), energy efficiency of wealth creation (in units of energy produced per GDP) and CO2 efficiency of energy production (in units of CO2 emissions per energy produced).

Since none of the other explanations such as the M&M identity, velocity or gas mileage seems to have helped, I’m not hopeful that this will help many understand their error, but it makes me sad that so many here are unable to grasp these concepts. I had thought that the skeptic community was above average in grasping abstract concepts. Sadly, it seems that either that not the case or the level of ability in the population as a whole is even lower than I thought. I suppose my hope is that many here are simply blinded by their anti-CAGW bias in the same way that we observe that the CAGW true believers are blinded by their bias. Perhaps we’re not as skeptical as we think we are.

M Courtney says:

July 11, 2014 at 4:58 am

“The problem isn’t that the Kaya Identity is an Identity and so it reduces to CO2 = CO2.

The problem is that the four terms that cancel are chosen because the author (Kaya?) wants to talk about those terms:

• Population

• Energy

• GDP

• CO2 emissions

Why choose to limit the discussion to these terms? The author has their reasons but what are they and do we agree with them? And why?”

…

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

Your example of moving from iron to gold production would change the energy efficiency of GDP, so yes, the Kaya identity does account for this. Generally, technological changes would fall under energy efficiency of GDP or CO2 efficiency of energy generation. Luck, I guess, could change any of the terms, depending on what the luck is…

Uh, no. The fact that you can algebraically reduce an equation to identity does not prove that the equation is meaningless. It proves that the equation is an equation.

You do realize that

can be algebraically reduced to identity, don’t you? The thing that you and Willis and the rest of the “it cancels out” crowd have discovered is not a math error in the Kaya identity. What you have discovered is the meaning of the equal sign.every equation in the worldCongratulations.

Daniel G.

“EDit_XYZ can’t do basic division:

d = (d/t)*t = d”

So – v (d/t) and t (2 distinct concepts) equal d (another distinct concept), if multiplied*. As such, this formula tells you that d can be decomposed into t and v.

The kaya tautology tells you only that CO2 equals CO2 multiplied by 1 multiplied by 1 etc – after you do basic division and if you can do basic division, of course (Daniel G., you may not be aware, but, trivially, CO2*1*1*1…=CO2).

*BTW, you should really learn the difference between division and multiplication. In truth, you embarassed yourself long ago, but, as it’s said, ‘It’s never too late’.

They are equivalent operations, the only difference is that you can’t divide by zero

So – gdp per capita, energy intensity of the economy, co2 intensity of energy, and population (4 distinct concepts) equal co2 (another distinct concept), if multiplied. As such, the Kaya identity tells you that co2 can be decomposed into those four factors.

d = (d/t)*t = d * (t/t) = d * 1

Therefore the distance equation is worthless too, because it is just d multiplied by 1.

(Edit_XYZ, you may not be aware, but, trivially, d * 1 = d)

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

It is mathematically correct you know.

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

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

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

Daniel G.

d = (d/t)*t = d * (t/t) = d * 1

Therefore the distance equation is worthless too, because it is just d multiplied by 1.

(Edit_XYZ, you may not be aware, but, trivially, d * 1 = d)”

Daniel G., you can’t even keep the concepts straight in a simple formula such as the above? Let me ‘baby-step’ it for you.

After all possible simplifications are done, on one part of ‘equal’ you have:

v=distance traversed in an hour – dv/tv, if you will.

t=the time (several hours)

On the other part of ‘equal’ you have:

d=total distance traversed (in those several hours) – d total, if you will.

As such, t/tv does NOT equal 1, when you try to simplify it.

And dv does NOT equal d.

Unbelievable. Your lack of mathematical competence is not just for show, is it?

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

Well, yes. You are correct in saying that.

But you miss the point that you are being correct in the only way that the Kaya Identity allows you to be correct. It equates GDP per population as a fixed component when it is actually made from two components and then calculated (or measured, loosely).

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

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

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

Edit_XYZ, you can’t even keep the concepts straight in a simple formula such as the above? Let me ‘baby-step’ it for you.

After all possible simplifications are done, on one part of ‘equal’ you have:

co2_intensity=co2 emissions for a unit of energy – co2_part/energy_part, if you will.

pop=the population (several million people)

On the other part of ‘equal’ you have:

co2=total energy-related co2 emitted (for those several people) – co2 total, if you will.

Kaya Identity:

co2 = pop * (gdp/pop) * (energy/gdp) * (co2_part/energy_part)

As such energy never cancels. BUT THAT IS A POINTLESS GAME, as gdp per capita is ultimately calculated by dividing gdp over population. But the really important variable is gdp per capita, as this represents living standards. The detail is that you do not need the total of energy-related co2 emissions to calculate the co2 intensity of energy. What matters is to plug it in

the ratios.And co2_part does NOT equal co2.

Unbelievable. Your lack of mathematical competence is not just for show, is it?

it takes a witchdoctorate in numerology to cast effective spells or prophecy.

M = 10 * B/10…. check

M = 20 * B/20….mmk

M = 4000 * B/4000…. so useful

so we’re shipping 8 trucks, each carrying 500 cases with 1/2 a box in each case. splendid.

now i know just who i want running my warehouse, ubet.

M Courtney says:

See my comments above.

M Courtney says:

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

M Courtney says:

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

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

Daniel G.

“After all possible simplifications are done, on one part of ‘equal’ you have:

co2_intensity=co2 emissions for a unit of energy – co2_part/energy_part, if you will.

[...]

Kaya Identity:

co2 = pop * (gdp/pop) * (energy/gdp) * (co2_part/energy_part)

[...]

But the really important variable is gdp per capita”

It comes as no surprise that you won’t keep the concepts straight with the kaya tautology – when you didn’t do so with the simple d=v*t.

Now you’ve taken the kaya tautology and replaced the CO2 and one of the energy concepts from one side of ‘equal’ with CO2_part and energy_part.

The kaya tautology does no such thing:

http://en.wikipedia.org/wiki/Kaya_identity (‘Global CO2 emissions’ from one part of ‘equal’ is ‘Global CO2 emissions’ from the other part of equal; and ‘Gross Energy Consumption’ is ‘Gross Energy Consumption’).

Tnis is merely an example of you making a poor attempt to hide your incompetence by blatant data fudging.

And the amusing part? After all possible simplifications are done on your new formula (“co2 = pop * (gdp/pop) * (energy/gdp) * (co2_part/energy_part)”), it reduces to:

CO2=energy*CO2_part/energy_part.

Your valuable gdp per capita (GDP and population) were simplified to 1.

You can’t even blatantly fudge your data correctly, Daniel G.

That said, I like how you try to model the format of your posts on mine. Imitation is the sincerest form of flattery, after all.

The Kaya identity is not an equation because it is not a relationship of any kind.

It does not relate units, variables, numbers or words in a rational way.

It is pure propaganda of the most mind numbingly stupid kind.

Yes it balances, but this is not the utility or value of equations.

Equations are useful because they reveal a calculable relationships between things.

Balancing an equation is not the same thing as identity!

Coming up with E=E will not get you into Mensa. Coming up with E=MC2 just might! ;-)

Einstein’s equation can be rearranged to reveal incites such as: M=E/C2 or C2=E/M, because it parts are inextricably related.

Non of the elements of the Kaya ‘Identity’ have a physically definable or testable relationship.

There is no need to even question the use of variables or units or numbers, because it is an arbitrary construction.

In the Kaya identity, CO2 might sensibly be to balanced by Flying Spaghetti Monsters (M) for example:

CO2= CO2/M*M

Yes, the equation above is balanced, yes it is an identity but is it falsifiable; no!

Is it meaningful; no!

Is it useful; no! *

*This is actually false, because it is very useful as propaganda

Pete Brown:

I am replying to your long missive at July 11, 2014 at 3:55 am which begins by saying

Really? I am surprised because you have not shown any regret at your falsehoods, selective quotation and misrepresentations of my earlier posts. Indeed, I expressed umbrage at one of your posts which included all of those and you have shown no regret for that.

You continue by quoting my words concerning the silly equation which is the subject of this thread; I.e. I wrote of the equation

And you reply

That is self-serving nonsense. Only people get to vote but that does not mean e.g. policies are not political. And your use of the phrase “policy tool” is Orwellian: the equation is not a policy but can be used to promote a policy. In other words, you admit that the equation has the purpose of being a propaganda tool.

I have repeatedly pointed out that the equation is a means of political propaganda and has no other apparent use. Nobody has suggested an alternative use and you don’t. You say the propaganda tool “can be used equally for good or evil”, but you don’t say who defines good and evil; I assume you think that should be you.

Then you add this offensive bollocks:

I DO AND YOU DON’T!

I keep addressing the propagandist nature and purpose of the equation which you have not addressed in any way until now. Instead, you have persistently attempted to force me to discuss the existing – and daft – components of the equation when those components can be anything any propagandist wants to promote.

In fact you acknowledge that I pointed out the components are ridiculous when you quote my having said

You then ignore that I had selected that extract of an earlier post as example of your falsely claiming I had not explained why I refused to answer your ridiculous “4 questions”.

I wrote {snip} after that quoted question. If one reverts to the original post at July 10, 2014 at 4:57 am then the true quotation without the snip is

You have made a reply which is refuted by my paragraph you omitted. You say

That is plain nonsense. It is demonstrated to be wrong by my paragraph you omitted. And as I have repeatedly pointed out to you, when one of the variables changes then it alters others so you CANNOT hold everything else equal.

You are conflating “GDP per capita” with “since CO2 emissions are a by-product of economic activity, throttling economic productivity will reduce CO2 emissions”. They are NOT the same, and if you think they are the same then you need to prove it because my paragraph you omitted shows they are NOT the same.

You follow on with more nonsense by writing

Actually, the USA has decoupled its CO2 emissions from the progress of its economic activity and you would know this if you had looked at the data. The USA did it by switching to a lower CO2 fuel (i.e. natural gas).

But, and very importantly, a relationship between CO2 emissions and economic productivity may exist but not be expressed as GDP per capita. You claim the daft equation is worthy so it is your responsibility to show that GDP per capita is a valid component of it. You have not, and I have provided several examples of why you cannot.

And then – at last – you explicitly state the propagandist nature of the equation when you write

The equation as presented – as you say – pretends and “is intended to illustrate” that reduction of CO2 emissions requires fewer people or poorer people. It is an excuse for Malthusianism.This evil is screened by being accompanied with assertions that similar effects may be achieved by more efficient energy production or more efficient energy use, but those efficiency improvements will happen as a by-product of normal economic activity if no interference is adopted.Then you recognise that the equation is an excuse to promote Malthusianism and try to head off that objection saying

That is sophistry intended to hide a falsehood. The equation promotes Malthusianism and you are advocating adoption of the equation.

I accurately wrote

You answer that with yet another of your falsehoods saying

Pete Brown, that is NOT an answer. It is an unfounded assertion that somebody else has provided an answer at some unspecified place and unspecified time.

If you had an answer you would state it.You conclude saying

It is really, really scary that such demonstrably untrue propaganda as the equation you are promoting is being promoted as an excuse to increase poverty and to cull the poor.Richard

ha! it seems the numerologist i had consulted was a pessimist.

i got a second opinion from an optimistic numerologist who has proven by the same equation that one can ship an infinite number of M&Ms with zero cases!

somebody gets fired and somebody gets a consulting contract now!

Scott Wilmot Bennett:

re your post at July 11, 2014 at 7:51 am.

Yes! Thankyou! The equation is a propaganda tool and nothing else.

I have repeatedly said the same first at July 10, 2014 at 2:31 am here.

You can see it, I can see it, and I don’t understand why not everybody can see it.

If this untrue propaganda is not refuted now it will be impossible to refute it when the media start trumpeting it.

Richard

and that’s the last time i take any recommendations from pielke…

That is your illusion.

Because CO2/M is not a meaningful ratio.

People, you need come up with meaningful ratios. Just create the most out-of-nowhere variable won’t refute the Kaya identity.

Daniel G.

“The kaya tautology does no such thing:”

That is your illusion.”

Really? You’re not even trying to come up with data fudging anymore, I see; just some baseless dictum.

If your dictum has any support, then you should have no trouble coming up with a reputable source for your re-writing of the kaya tautology – from “co2 = pop * (gdp/pop) * (energy/gdp) * (co2/energy)” to “co2 = pop * (gdp/pop) * (energy/gdp) * (co2_part/energy_part)”.

Let’s see the link, Daniel G.

Comment from Anthony: …It would seem that the cancellation of terms is the sort of thing that would rate an “F” in a simple algebra test.

I respectfully disagree. There is no mathematical error, and it allows you to build a useful equation. “Dimensional analysis” is a very common practice in engineering and science. That said, I will concede that it would have been better to express the last term as a ratio and not reuse the symbol “CO2 emissions”.

But if this rates an “F” on simple algebra test, what does using Appeal to Ridicule (“a stupid maths error”) rate on a logic test?

But maybe you already agree, I see that that language was removed from the post.

Daniel G. says at July 11, 2014 at 8:08 am

But it is logically scalable. It happens to be meaningless because Flying Spaghetti Monsters (M) are meaningless… but if we disagreed on the Flying Spaghetti Monsters we would be in disagreement about the Kaya Identity.

So why not look at why the Kaya Identity is not meaningless? It certainly isn’t self-sufficient as, if it were, then we open the door to the Flying Spaghetti Monsters.

To avoid circular arguments: Please justify why each term of the Kaya Identity has meaning and no other meanings are legitimate or required.

My opinion is that the Kaya Identity is intended to avoid that very discussion.

A most cynical device.Daniel G.:

At July 11, 2014 at 8:08 am you say

Therein lies the problem.

There are no “meaningful ratios”, there are only political objectives which people want to promote.

And because there are no meaningful ratios the equation is nonsense.

But, as I said of this meaningless equation at July 11, 2014 at 8:01 am,

If this untrue propaganda is not refuted now it will be impossible to refute it when the media start trumpeting it.Richard

J.K. and other have already suggested alternative uses.

If co2 was were to cause massive warming (not going to happen, but it is hypothetical), it would be important to reduce co2 emissions. There is nothing propagandistical about that.

Look at any CO2 emissions table. Where you find a country like Haiti? Where is USA?

That is just a assumption to simplify the proof that the terms don’t cancel. If you say, no! If population increase, GDP per capita or other factor will change! The point is that you have to prove that every relationship will cancel out. As the economy grows when population increases, it is not obvious on how an increase of population would be matched by decrease in GDP per capita.

You can drop the assumption later.

Of course, they are not the same. GDP per capita is the concept the represents average wealth in the Kaya Identity. That wealth comes from economic productivity. “since CO2 emissions are a by-product of economic activity, throttling economic productivity will reduce CO2 emissions” is sentence expressing a reasoning.

Your reasoning is too simplistic. You have to consider more than one factor.

USA is just one country. It is developed one by the way, think of the rest of the world. But anyway, shale gas is expensive compared to burning coal, and it still emits CO2. They managed to decrease the co2 intensity factor (this is the fourth factor). So the relation between co2 emissions and economic growth is still there. It would be long before humans could decouple such relationship.

Sorry Daniel G.

I’m not going to tag team you with my father. It was inadvertent but still unfair.

So I’m ducking out of this debate; my opinion is clear enough.

richardscourtney says:

July 11, 2014 at 8:01 am

I agree Richard. The reaction by many, to blatant propaganda really scares the sh*t out of me!

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.

@Edit_XYZ:

It is not re-writing, it is just that my interpretation is correct. Read the english in the paper.

Let me explain on what i meant by “logically scalable”. Scalable means that it scales with something. They Kaya Identity scales with logic. One can use a very simple logic, where all rhs variables (pop. and ratios) are independent. The Kaya Identity is valid. Or one can use a more complicated logic, where those variables are interdepedent. They Kaya Identity is still valid.

What is the chapter quoted by Willis is discussing: energy-related co2 emission and how this number can be factored. (we could be discussing something else, like photography, but who wants to discuss photography)

Human people use energy (mostly electric, but also direct heating I guess) for purely material reasons, related to economics. So, for this discussion, what matters is economics and energy, in quantitative terms.

An economy can be large or smaller, it can use more or less energy. Economies tend to be larger with more people, but other than that, there is no simple variable. We can discuss things like market regulations or subsidies, but if that matters for the discussion, it will ultimately affect other variables.

Population: Number of people.

GDP per capita: GDP/(pop.). It represents average wealth, coming from economic productivity.

Energy intensity of the economy: energy/GDP. It represents how much energy is need to generate a unit of wealth.

CO2 intensity of energy: co2/energy. It represents how much co2 is emitted in the generation of one unit of energy.

Is there anything missing? Nope, look at the paragraphs above. We are discussing the quantitative aspect of the energy-related co2 emissions.

Are any of the ratios above meaningless? Which political objectives does RGB Jr. want to promote?

The co2 emissions on the lhs and rhs are with respect to beer. So, yes, we know it is true.

Sorry to pour ice-water on a wonderful debate. But an identity is not written with an equal sign. And identity is written with a singe with 3 horizontal bars. Either Kaya is not an identity or there is a typo.

If Kaya is an identity you cannot transpose (cancel out) terms. You have to transform terms on one side only, usually the right hand side.

To cause even more shame to the commentators, I recall this from 1952 when I did trigonometric identities for fun and scored 100 on all term papers and the final.

So you are now a authority on typographical conventions? No? I though you were…

People can write identities in the way they want.

Daniel G.:

I notice that you have ignored my post which replies to you and, instead, at July 11, 2014 at 8:29 am you have replied to my post which replied to Pete Brown.

I understand that. My reply to you is difficult for you, and Pete Brown has yet to substantiate anything he has said in this thread so it makes sense for you to try to help him.

In response to my repeatedly pointing out that the equation is a propaganda tool and that nobody has suggested any other use, you claim “J.K. and other have already suggested alternative uses”.

The only post I have found which could agree with your assertion is by JK and is at July 10, 2014 at 3:59 pm: it is an attempt to show that it is possible to use the equation in the absence of knowledge of actual CO2 emissions which concludes saying

Sorry, but that is merely an example of the equation being used to present propaganda: the estimate is a guess based on a guess by the propagandist. It tells nothing except about the guess.

You make only two other points which are worth the bother of refuting,

You say

Well, since they are not the same then you are admitting that Pete Brown was wrong and GDP per capita is not an appropriate ratio to use in the equation.

This goes to the heart of my point in reply to you. There are no “meaningful ratios”: there are only assertions which propagandists which to promote by use of the equation.

And you say to me

No. I pointed out the fact that the UISA had decoupled its economic activity from its energy use. The equation is too simplistic because it asserts such decoupling is not possible. And a policymaker has to think of her own country because she can only impose a policy there and not on the rest of the world.

I have said enough to show there is no merit in your excuses for the propaganda tool which you call the Kaya Identity.

Richard

Daniel G.

“It is not re-writing, it is just that my interpretation is correct. Read the english in the paper.”

So – after all the blatant data fudging and mathematical incompetence you’ve exhibited in this thread, you still think that you have a shred of credibility left? That, when prompted to povide a link, some lame excuse is enough?

Aren’t you the optimist.

Let’s see the link (and page/paragraph).

No, it doesn’t assert such a thing. The co2 intensity factors and energy intensity factors have decreased somewhat in the USA, so USA energy-related co2 emissions are not growing.

Read what I said again, I explained why GDP per capita is a appropriate ratio.

PROPAGANDA OF WHAT?(if this were oral discussion, that would be a scream)Malthusianism? CAGW Alarmism? Eugenics?

No, the Kaya Identity doesn’t try to prove co2 emissions are harmful.

The same is valid for you.

Nope, I did not ignore. I answered it:

Daniel G. writes:

Daniel G.:

You make a good point in your post at July 11, 2014 at 8:46 am when you ask

Only RGB Jr. can provide an acceptable answer to that question.

But the question can be applied to anybody who uses the equation. The so-called “meaningful ratios” he chooses to include in the equation are what he is promoting.

Richard

I do not expect for people to trust me.

http://unsdsn.org/wp-content/uploads/2014/07/DDPP_interim_2014_report.pdf

Chapter III, section 1, second paragraph:

Michael 2:

You made two very good points.

1. Only if you hold all three ratios constant will the Population have the anticipated effect. You are right. I was sloppy with my statement. I didn’t state all my assumptions.

2. GDP does indeed cancel out of the equation, but we do know that GDP has a great effect on CO2 emissions. The problem is that with a sharp drop in GDP there is also a sharp drop in Energy use, so the ratio Energy/GDP remain more or less constant.

Yes, it would better to express each as ratio and making them a function of other variables, i.e. R1(GDP, Population, Energy, others?), R2(GDP, Population, Energy, others?) and R3(GDP, Population, Energy, others?). Of course, this complicates the formula and makes it much hard to understand. There is a trade-off between precision and easy of communication. We often make statements without stating all the implicit assumptions.

My previous posts are good examples of unstated assumptions. Another example is “… the ratio of CO2 emissions per unit of energy. That is a simple thing to measure in a laboratory…” The unstated assumption, of course, is that you have to make the measure for all sources of energy and weight-average them. Or alternatively you, you could estimate Total CO2 emissions and Total Energy use and divide, and treat that number as a constant until you can make the estimates again.

Or another example, “So global GDP can be changed instantly on a whim by whoever decides what it is and what currency to denote it.” Here you are assuming that they are expressing GDP in nominal dollars (or some other currency) and not in inflation adjusted dollars. I am assuming that they are expressing GDP in inflation adjusted dollars.

We can always criticize whomever for not stating all their assumptions. Some people find that pleasurable.

@ pheonix7

@ July 11, 2014 at 5:03 am

Certainly there are some valid criticisms of the kaya (cumba ya) identity there. I’m merely pointing out that the reduction to CO2=CO2 (units) is not in any way “bad” for an equation. That’s exactly what an equation is supposed to do. It would get an “A” in basic algebra.

“Whether the equation is a political tool or not should be an entirely different thread.”

Smartest comment on the thread.

@richardscourtney:

Ignoring all my other points. Good way to go.

Maybe when I write d = vt, I am “promoting” velocity and time.

Daniel G.:

I write as a courtesy to acknowledge your post addressed to me at July 11, 2014 at 9:19 am.

If there were something there which were worth the bother of refuting then I would, but I am content to leave your sophistry for others to laugh at and I ignore your “No, ’tisn’t” assertions.

Richard

That is irrelevant. Any bureaucratic change in GDP will change energy intensity proportionally.

See my comment about cutting zeros.

I’ll gladly ignore your “Yes, it is.” assertions too.

Daniel G.:

I write in sincere hope of helping you.

At July 11, 2014 at 9:30 am you write this nonsense

So you think energy intensity can be altered by a stroke of a bureaucrat’s pen.

And you immediately follow that with your post at July 11, 2014 at 9:32 am which quotes my explanation of why I cannot be bothered to refute your nonsense.

Please stop typing for a few moments and try to reflect on what you are typing. When even I am not bothered to refute your words then you may wish to evaluate their cogency.

Richard

richardscourtney says:

July 11, 2014 at 7:55 am

…

Richard, you really do seem to be quite a volatile person who does not like being disagreed with at all!

It is particularly difficult to follow your post if you’re going to start using secret hidden paragraphs. You are apparently very pleased with your game but I honestly cannot see what point has been made. Do I really have to piece your secret paragraphs together from the various places in the string where you use the word ‘snip’? Are you three years old? I really cannot be bothered with that.

I notice you do seem to think that the USA has de-coupled it’s CO2 emissions from its economic productivity. That is very strange indeed. I did not for a moment imagine that anyone could live under such a basic misapprehension.

Specifically you say;

“Actually, the USA has decoupled its CO2 emissions from the progress of its economic activity and you would know this if you had looked at the data. The USA did it by switching to a lower CO2 fuel (i.e. natural gas).”

Actually that’s a very fine example of an economy reducing it’s CO2 intensity of energy generation – precisely one of the four terms on the RHS of the identity, and a excellent illustration of the point! If you think the USA no longer emits CO2 as a by-product of economic activity, though, then you’ve clearly forgotten what happens when you burn gas.

You say;

“You are conflating “GDP per capita” with “since CO2 emissions are a by-product of economic activity, throttling economic productivity will reduce CO2 emissions”. ”

Eh? What? Where exactly am I conflating something with something? Show me the quote? Are you a real person or am I actually debating an infinite number of monkeys? GDP per capita is just Gross Domestic Product divided by the number of people in the economy – nothing seems to be wrong there… CO2 emissions are a byproduct of economic activity – that is correct. Throttling economic activity will, other things being equal, reduce CO2 emissions. That’s basic stuff. No problem there. Where’s the conflation, and what with again?

Re-read my comment and try again. Actually don’t. I’m done.

By the way, I see you have your ‘offensive bollocks’ out again. Don’t go near any playgrounds with that…

Amazing post.

Very Alice in Wonderland reasoning.

So this “Identity” expressed as a mathematic expression, can mean whatever the user wishes it to mean.

Either express yourself clearly or accept that you are supporting the use of propaganda.

This is political-speak masquerading as algebra.

As the IPCC cloaks itself in the illusion of science, while avoiding the scientific method.

As for those who attack Anthony Watts, over this posting by Willis and this free ranging discussion that follows.. WTF?

Pompous certainty ring any bells?

If the source of confusion is the use of terms beyond the comprehension of the average school graduate,that dimensional mathematics allows such poor definition..

Umm do not abuse the commenters here, your inability to understand the concept ,well enough to express yourself in clear english, will result in laughter.

The equation as expressed cancels.

If the terms are improperly expressed, correct it.

Otherwise you defend the indefensible, which is the deliberate miss use of an algebraic expression to give false credibility to a political meme.

Here we go again. Willis’s math knowledge has failed him. To understand the Kaya identity you need to understand what a mathematical identity is. Once that is understood we can debate the validity of the terms for the intended purpose and as importantly, if there is a problem this identity will help us mitigate.

Willis Eschenbach:

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.The beer identity is irrelevant to thinking about countries that do not produce their own beer, though perhaps you could use Beer Consumption instead of Beer Production. But every country produces something, so the Kaya identity is more general. For people unlike us who are concerned to reduce CO2 output, the Kaya identity shows the approximate short term effects of changes. For countries that produce beer, reduce the CO2 output from beer production; for countries that produce automobiles or wheat, reduce the CO2 output from automobile production or wheat production. The results of such changes can be computed on a country-by-country basis. What the Kaya identity misses completely are the long-term effects of technology improvement.

I imagine that you personally would, like me, prefer greater GDP and wealth per person, and let the CO2 change as it will. Reducing the energy cost per product is in almost everybody’s interest already, independent of CO2. To me, the problem with the Kaya identity isn’t its limitations, but its irrelevance to solving the important problems.

richardscourtney says:

If that is the case you may want to answer my points even if they were sophistry.

richardscourtney says:

Let’s say I decided to create a new unit of money: the super-dollar, it is worth 100 dollars.

This cuts two zeros of the GDP digits. But to produce 1 super-dollar, one needs to produce energy enough for 100 dollars. So the digits of energy intensity is changed.

Or I might decide to represent energy in ergs, instead of Joules. That change also alters the digits of energy intensity.

richardscourtney says:

1) The Kaya Identity is valid.

2) It doesn’t have to be used as a propaganda tool.

3) I’ve answered to various technical criticism defending Willis idea of “it cancels”

Nothing out of the ordinary.

oops, that should be: ” For people unlike us who are NOT concerned to reduce CO2 output”

sorry

what a wonderfully rich and entertaining world it is where clouds are really elephants if we interpret them as such – with a tail like a rope and ears like leaves and a trunk like a snake!

when one transcends the comic to the surreal, identities can be anything one may choose.

not only that but one can sally forth on the MMORPG blogs and cast level 12 spells of dazzling numerology with magic mathlike runes and symbols. it’s an addiction.

if being limited by reality and so unimaginative as to be unable to interpret something to be what it is not, makes life seem tawdry and trivial, yet another cruel betrayal by the malignant forces of nature, it really is nature’s way punishing a person for missing the clue boat.

some commenters remark that the creation of the kaya spell is deliberate and sinister.

yup- with a lineage that stretches back thousands of years.

I MAKE THE MEMES (i write the songs- barry manilow)

i’ve been alive forever

and i wrote the very first lies

i possessed you with my demons.

i put the lotto look in your eyes-

i make the memes that keep the world confused

i write the talking points and frame all the views

i spin my narrative and call it the news

i make the memes – i make the memes!

My home lies deep within you

and i’ve got a cavity in your mind

so if you’re looking for the truth

it’s a rotten tooth you will find.

i make the memes that keep the world confused

i write the talking points and frame all the views

i spin my narrative and call it the news

i make the memes – i make the memes!

Like a puppet you will dance- and you never stood a chance-

cuz i taught your parents how to teach you too.

when uneasiness fills your heart, and your reasoning falls apart

It’s from me, it’s for you

to believe- and you do

It’s a global industry!

i make the memes that keep the world confused

i write the talking points and frame all the views

i spin my narrative and call it the news

i make the memes – i make the memes!

i’m a spin doctor

i make the memes

The equation is, as stated, an identity. But, it is only valid insofar as population is THE driving factor in emissions (like integrating a partial derivative, the result is ambiguous not just modulo a constant, as for integration of a total derivative, but modulo a function of the other variables which have an impact), and it is only useful insofar as the intermediate partial differences are constant, which they aren’t. Which is to say, the identity is totally useless, and is obviously intended as a slight of hand to push a population control agenda. Willis’ mirth is well justified. It is total crackpottery.

Lets say we use the equation to predict the effect of a change in population of 10% as one of the previous posters suggested. The “Population” variables in both the numerator and in the denominator go up by 10% and the equation predicts that there will be no net change in CO2. The only way out of that is to prove that that the ratios (eg GDP/Population) are constants. But it we instantly dropped 700 million new souls on the planet, does anyone think GDP would rise by 10%? It might even fall. In either event, the the actual ratio in the real world (GDP to Population) would change and the equation would not correctly predict what actually happens. So until proponents prove that any three of the terms on the right side of the equation are constant when the other term is changed by an arbitrary amount, the equation is useless. Put another way, this equation assumes no feedback as between any of the terms.

Bart says:

Not really. The identity has four factors, and we are discussing energy-related co2 emissions.

Bart says:

Willis is saying that “everything cancels”, thus the identity is useless, quite different from your argument.

richardscourtney:

I have repeatedly pointed out that the equation is a means of political propaganda and has no other apparent use. Nobody has suggested an alternative use and you don’t.JK suggested an alternative use. That does not, obviously, imply that it can not also be used as a propaganda tool.

Actually, the USA has decoupled its CO2 emissions from the progress of its economic activity and you would know this if you had looked at the data. The USA did it by switching to a lower CO2 fuel (i.e. natural gas).Actually, the US has substituted a lot of natural gas for a lot of coal. That plus the recession reduced total US CO2 emissions. “Decoupled CO2 from the progress of its economic activity” is a gross exaggeration. Should the US economy ever grow as much as 5% in any year, or increase exports of large quantities of natural gas, then total CO2 emissions will rise. So perhaps CO2/energy will decrease, but be partially offset by GDP per person, while energy/GDP stays within a short range (say, if the conversion from coal to gas declines as more gas is exported. The results of diverse changes can be computed with reasonable accuracy from the Kaya equation, should anybody care to, thus illustrating JK’s suggested use.

Frederick Colbourne says:

July 11, 2014 at 8:50 am

Rest ashord, this ‘Identity” cancels itself on the right hand side. This in fact is how it is constructed!!!

Frank says:

I and other have explained on how this is wrong on the above comments. You might very busy with something else, thus you’d prefer for me to repeat myself. But I’ll only repeat myself if you ask.

Rest assured! ;-)

Frank:

Put another way, this equation assumes no feedback as between any of the terms.that’s why I wrote that it is good for short-term forecasts of the effects of changes, and wrote of energy/GDP that it stays within a range while some other factors change more.

The basic limitation of the equation is that it isn’t about everything that matters. Other writers may have proved that, like any other tool (say a hammer) it isn’t useful for everything.

USA smallish economic growth in the last 5 years only give more evidence towards the idea that GDP per capita is factor of CO2 emissions.

Daniel G. says:

July 11, 2014 at 10:26 am

Main reason for declining US emissions is increasing reliance on natural gas. Economic downturn, improved insulation in new structures & more efficient cars & trucks may also have contributed, however.

Daniel G. says:

July 11, 2014 at 10:17 am

“The identity has four factors, and we are discussing energy-related co2 emissions..Willis is saying that “everything cancels”, thus the identity is useless, quite different from your argument.”But, applicable to

yourargument. It depends how you interpret the increment ratios – as absolute ratios, or as ratios with the denominator driving and everything else held constant.Look, it’s a stupid equation, intended to drive a stupid agenda. Stop being stupid defending it.

@ferdberple says:

>Intentions are a slippery slope. The road to hell is paved with good intentions.

And bad metrics.

gnomish,

If you are against me, or for me, It makes no matter. You Sir are an Artist.

My favourite archetype is the trickster, Shakespeare’s fool.

decarbonize = debiosphere

Frank and others with the same opinion-

I find the Kaya Identity to be irksome. I also think it’s a needlessly complicated way to argue for energy sources that emit less CO2 by people who want that. However, if you take a deep breath, read the article on manicore (http://www.manicore.com/anglais/documentation_a/greenhouse/kaya_equation.html), and rewrite the equation as CO2 emissions= Population * Production per person * Energy intensity of the economy * Carbon content of the energy, it might help you understand where the other side is coming from and discuss it without getting completely red in the face with steam billowing out of your ears :)

I am tired of this discussion, I am really not that interested in the Kaya identity. I have already said multiple times its usability is limited.

I’ll come back tommorow.

As a last note:

sinewave says:

Look I disagree with many people here, but internet writing is the worst proxy for emotions.

The formula under discussion can be properly be re-stated as:

CO2 = CO2 * GDP/P * E/GDP * P/E

We look up GDP/P, E/GDP and P/E in the tables to solve for CO2. If P/E seems to be an entirely new piece of information because it is not an explicit ratio in the original, then just generate our own P/E values: P/E = (GDP/P * E/GDP)^-1. Oh, and one last thing, we will also need to know the value of CO2 but not to worry, all values work.

Your analysis of the “Beer Identity” is incorrect.

“There is no “stupid maths error” in the Kaya Identity that “falsifies” it, as was claimed in your original subhead … that has been quietly disappeared.”

Yes its hard to quote words that have been disappeared.

Note also that the argument now presented is different.

I’m about to give another presentation here in Vegas but mosher you can blame me for the side heading I saw the argument of canceling terms and thought this was just one of those things that no one ever noticed. I also took the side heading down because it was wrong . Now after this comment in this presentation I’m about to do it’ll be my turn to be incognito for a while I’ll be traveling.

Writing all this by phone dictation. But I wanted to give Willis a chance to respond first.

Willis posted the essay without my knowing that he was writing it and I saw argument about terms cancellation after he posted it. . So it is my blog blame me I’m totally responsible for everything posted here. Even stuff I didn’t write. Apologies all around. That should teach me to try to do too many things at once which is what I tried to do this week.

“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.”

That’s not the argument you made. quote yourself.

Its a tool, not a representation

It can show you something. change the population. you will get a number.

that number is a good rough order estimate of what will happen to emissions.

just that and nothing more.

But your criticism of units cancelling was just wrong.

Now, we can criticize it for a whole host of reasons.. but units?

Pete Brown:

I again write to express umbrage at an untrue and offensive post from you. This time it is more of your offensive and egregious bollocks at July 11, 2014 at 9:48 am.

You have the gall to begin by saying to me

No! I like to be shown to be wrong because then I learn. But I object to having my intelligence insulted by silly and devious nonsense such as you provide.

And you really, really like to demonstrate psychological projection. Early in this thread at July 10, 2014 at 4:55 am you posted your second post to the thread and it said in total

Which received the only possible sensible reply which was

Pete Brown, you proclaim yourself to be quite a volatile person who does not like being disagreed with at all!

You follow that abusive and projected comment with this tripe

“Secret hidden paragraphs”!!? Do try not to display your idiocy.

Everybody can see that I quote to what I refer and I cite its time. Sometimes I add a link.

And do not assume that others behave as you do. I do not play games and I do not make arguments of a three year old. Your assertion that I would lower myself to your level is extremely abusive.

You continue from that twaddle by demonstrating you do not understand the energy issues that your daft equation purports to model when you write

Actually, that shows you are semi-literate!I did NOT write

“the USA no longer emits CO2 as a by-product of economic activity”

I wrote

“the USA has decoupled its CO2 emissions from the progress of its economic activity”.

You demonstrate your complete ignorance of the subject when you do not understand that decoupling does NOT mean cessation.You then dig your hole deeper.

You quote my having said to you about GDP per capita

GDP per capita is the equation “ratio” I was discussing and which you were answering. Your answer said “since CO2 emissions are a by-product of economic activity, throttling economic productivity will reduce CO2 emissions”. But you now write

Are you for real!? Those were YOUR words. It was YOUR conflation.Clearly, a single monkey can provide more rational behaviour than you are displaying.

Then you write

You promised to leave before, but didn’t. I see no reason to believe you are now”done” in light of your other several falsehoods in this thread. But, of course, it is to be hoped that you will clear off.

Richard

Daniel G-

Your arguments yesterday convinced me to research the Kaya Identity and understand it better even though I’m not really that interested either. I was just trying to convince other people to do the same. This is a compliment to you and all the information you shared yesterday.

Daniel G, good effort.

GDP, beer, autos, wheat, M&Ms — any commodity can be used. The value of GDP is that every country produces something that can be measured and, potentially, related to personal consumption and energy use. Then to address particular countries, you have to look at the particular relations appropriate to those countries. If energy use per M&M is not known in a country that produces a lot of M&Ms, then the energy use per M&M is worth learning, the consumption per person is worth learning, and so on.

If anyone were interested in telling countries how to reduce their CO2 emissions, it would be worth knowing the values of the ratios in the RHS to determine which sectors might best be targeted for, say, more energy-efficient technology of production.

I have not found where anyone has written a good argument against you, but it might be time for you to take a rest.

richardscourtney says:

July 11, 2014 at 2:06 pm

…

Richard

Seriously, very much 10/10 for stamina!

As you know, the reference to your ‘secret paragraphs’ relates to the text you deleted from your previous post and then sprang on me in a ‘clever’ trap in your subsequent response. Still not sure what the point was there. The response to your secret paragraph, though, is that changes in population – whether through changes in immigration rates or changes in birth rates or whatever – are included in the 4 terms. They’re under the heading “Population”, which seems like a good name for it. So yes, the Kaya identity accounts for this concept, and I thank you for another good example just to illustrate the point, although I am starting to suspect it hasn’t really been your intention to help me out in this way. Clearly you should not imagine, that each of the four terms on the RHS of the identity will move on an all other things being equal basis in practice. It is convention though that in explaining the behaviour of one component part in a compound logical argument, that one does so on an all other parts being equal basis.

I am pretty pleased, obviously, to have scored a “semi-literate”, from you there! I only wish I can do better in future.

“Decouples” means “separate, disengage, or dissociate (something) from something else.” I Googled that. So yes it does very much mean exactly what I said it means; in this context, to break the association between economic productivity and CO2 emissions. And the USA, for all its many achievements, has not yet managed that, and you are entirely wrong to have stated that it has, I’m afraid.

Whilst I’ve got the ‘com pooter’ going, ‘conflate’ means “combine (two or more sets of information, texts, ideas, etc.) into one”. And I’m assuming you mean not only that I have done so but that I made a mistake in doing so. So yes, I am quite ‘for real’ when I ask what on earth was your point there. I worked through the text you quoted at me as you have seen, and everything is fine.

I’ve scanned the rest of your post. There’s the usual shoutey stuff. Good. I see you’ve got your ‘bollocks’ out yet again, Summer sun and all that. Whatever cooks your bacon. You’re making some of the text bold – which is great because I can skip the bits that aren’t.

Constructive feedback though: I’ve noticed that some people use “LOL” quite a lot when they’re trying to be really disparaging and deliver good insults. You should give that a go. I’m always knocked to the ground when people use “LOL”.

I don’t think I will “clear off” though. There’s something about the way you keep asking me to do that which makes me want to stay.

Bottom line though, is the whistle was blown on this game a while ago. Please read Anthony’s updates, and the piece he links at the top.

And, for the love of decency, please a read bit of Prof Roger Pielke Jr’s actual work. He frankly is someone who understands these things as well as anyone I’ve read, and does so far, far better than I do. I don’t know why you find that prospect problematic. I also don’t know why you think that by deferring to him I somehow reveal myself to be weak or, in your terms, an IDIOT. Frankly if more people around here deferred to other experts just every now and again, rather than arrogantly imagining that being sceptical means assuming everyone else is an idiot – which is what got you into trouble here in the first place – I think that would make it a better place.

For the record, yes, I did say at an early stage:

“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.”

It seems I was right about that. And now I need a shower.

Mods, how are you doing today?

**** Mr Anthony Watts, you are a real gentleman, Sir, and someone who should have, and clearly does have, the full respect and appreciation of everyone here. (I hope the presentation went well, and wish you a safe journey.) *****

sinewave says:

Daniel G- Your arguments yesterday convinced me to research the Kaya Identity and understand it better. . . This is a compliment to you and all the information you shared yesterday.

Matthew R Marler says:

Daniel G, good effort. . . I have not found where anyone has written a good argument against you, but it might be time for you to take a rest.

Well, I concur with you both except: Mr. Marler, why, oh why, should Daniel G. concede to Richard S Courtney, whose incessant and nonsensical “foaming at the mouth” diatribes makes no sense and project exactly the animus and preconceived twaddle that he finds fault with when expressed by the warmest crowd. Yes, Mr. Courtney is simply a propagandist of a different stripe! Truly a know nothing!

Wow am I stupid or what. . . now just more spittle from a jerk, coming my way! But it’s often fun to tweak an idiot! . . . but in this case, from a misguided propagandist that I’m happy to ignore.

Dan

Daniel G. says:

July 11, 2014 at 6:41 am

[...]

d = (d/t)*t = d * (t/t) = d * 1

Therefore the distance equation is worthless too, because it is just d multiplied by 1.

*************************************************************

Here we have the eqn d = r * t solved for r and re-entered into the original eqn. This results in a different and special equation known as an identity. To use it in argument without flagging it as such is disingenuous because as the walnut shell moves you must keep your eye on the fact that the “d” on the right side of the first = sign is not the same as the “d” on the left except in the special case of d = d, the identity. When we want to calculate d without knowing d ahead of time we need to calculate it independently of itself. So we need information such as (d1 – d0) / (t1 – t0), that is, r. Or values of distance and time other than the result distance, d, and total elapsed time, t, to calculate a rate.

Oh! I’ve been in my beer too long and it looks like the party is over :( g’nite and sleep well.

It was over 40 years ago that I learned one of the most simple but profound lessons influencing my science and engineering career. I attended a world-class engineering school whose students and graduates had a reputation for arrogance . . . they believed that their intellect and technical capability was limitless.

One of my graduate school professors told us: “All of you are very bright — otherwise you wouldn’t be here — but you don’t yet know much”. And he said, “remember don’t dwell so much on what you do know without acknowledging what you don’t know! Understanding this disparity is a major key to your future success”. He said, “understanding this is the key to your future learning and ultimate success.”

This made sense to me and following his advise has been the brightest beacon in my technical life. It has not only promoted a life-long pursuit of knowledge, but also instilled a sense of humility, a respect for differing viewpoints (to a limit), and an ever vigilant query to sort out the trustworthy fellow technologists from the pretenders. . . a kind of BS detector.

Why bring this up now: well this present post by Willis has exposed an unsupported arrogance within the WUWT community. . . a lack of humility, failure to engage in civil debate, and an inability to acknowledge what we know versus where our knowledge shortfalls lie.

A few names come to mind, but I’ll leave it at that.

thanks

Dan

Willis = clickbait.

Sad.

Poor, sad johanna. Still wrapped up in hate.

CLR II says:

July 11, 2014 at 6:25 am

“…, but I’m incredibly disappointed that so many closed minds here are unwilling to admit that the Kaya Identity is valid by definition and that the way the factors (population, standard of living, energy efficiency of wealth creation and CO2 efficiency of energy production) are arranged would serve a useful purpose if one were evaluating how to impact total CO2 emissions from energy production.

….

I had thought that the skeptic community was above average in grasping abstract concepts. Sadly, it seems that either that not the case or the level of ability in the population as a whole is even lower than I thought. I suppose my hope is that many here are simply blinded by their anti-CAGW bias in the same way that we observe that the CAGW true believers are blinded by their bias. Perhaps we’re not as skeptical as we think we are.”

I would suggest that perhaps it is not as bad as you think. Maybe those who understand that the cancellation to “CO2 emissions = CO2 emissions” does NOT prove the Kaya Identity to be useless are actually in the majority of readers, but are under represented in the comments simply because we saw that several helpful souls had done a pretty good job of explaining it already, and we didn’t think we could do any better. I know that was the case with me. Perhaps it was also the case with you.

I do share your disappointment in the number of people who are stubbornly getting it wrong. And it is particularly discouraging that some of them present their case in such an arrogant manner. It would be unbecoming even if they were right, but since they are incorrect it is just downright embarrassing.

All that being said, I find the comments on WUWT to be generally very valuable, and I particularly appreciate the input from the scientists who comment.

Dan Met’al:

Mr. Marler, why, oh why, should Daniel G. concede to Richard S CourtneyAt some point, re-kicking the tar baby is the least promising strategy. I only suggested rest; if he wants to step back into the arena, that’s up to him.

Willis (8:43 a.m.): “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.”

That last part is true, but an accounting identity is not intended to “prove” anything anyway. Rather, it helps to analyze the situation. As I wrote yesterday (9:31 a.m.), “a mathematical identity has neither empirical content nor theoretical demonstrative power in itself. It is nothing more nor less than an accounting device.”

(Willis:) “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%.”

I’m not sure where anyone here said as much, but it may well have been inferred or implied. See Pielke Jr. for his specific use of the identity, but in general, your posited 10 percent increase in GDP per capita might well be either partially offset or augmented by what happens to the other ratios. That is, the additional GDP might well consist of production of goods that are less (or more) energy intensive than the previous average, or the additional energy needed to produce those goods might well be less (or more) carbon intensive than the previous average. The Kaya Identity remains useful for framing the questions about whether these situations are likely to occur.

I suppose that the Beer Identity is “equally as true” as the Kaya Identity, but it is not equally as “valid”, because the Kaya Identity points to “truth(s) that exist outside the identity”, as you put it, while the beer identity does not. You are quite right that it is those “outside the identity” truths that matter, but the identity is useful precisely because it fits them into an analytical framework.

I hope that this helps in sorting out the issues. Like others, I have greatly valued your sometimes provocative contributions here, and I wish you a fast recovery from your loss of time and money during these past couple days.

Willis frequently points out one of his strongest assets is his humility and his willingness to admit when he is wrong. Surely he will pop in with a heartfelt mea culpa and get back to critiquing Dr. Evan’s math and data processing skills.

Many people here are confusing a mathematical identity with an application of it and are resolving all manner of things to CO2 = CO2. Hopefully Willis, having made the same error, will correct them and clarify for them the error in their thinking. I wish his hard drive all the best.

Regrettably, Willis’s mea culpa consisted of repeated exhortations to not blame Anthony.

Very few even thought to blame Anthony.

Alas, poor Yorick …

These are the 1930s of the AGW movement. It rreminds me of similar studies carried out in the 1930s in Nazi Germany. For instance a German girl studying sociology in the 1930s had a PhD project whiu consisted of living among Roma gypsy people with the aim of deciding if they should be allowed to live or be exterminated. Her conclusion at the end was that although they were cute folks they didn’t quite make the cut and “should be culled”.

So a similar PhD student has concluded that to reduce CO2 you need to reduce human population. What starts as PhD studies can within a decade become real policy when the (eco)fascists start to implement their agenda.

CO2=CO2(pop/pop)(gdp/gdp)(gec/gec)

or

CO2=pop(gdp/pop)(gec/gdp)(CO2/gec)

or

CO2=gdp(gec/gdp)(pop/gec)(CO2/pop)

or

CO2=gec(pop/gec)(gdp/pop)(CO2/gdp)

I call this “the three or four faces of Kaya”

It may look useless at firsta glance, but in economics analysis it is very useful.

Of interest may be this identity, that I found in a childrens book:

The Andersen Identity:

Population if kingdom:pop

Emperor of kingdom:emp

Tailors of kingdom:tail

New Clothes of emperor:nc

nc=pop(emp/pop)(tail/emp)(nc/tail)

This thread is one of my all time favourites on WUWT

Thank You all.

Pete Brown:

You said you would desist but that was merely another of your egregious lies because you continue your nonsense at July 11, 2014 at 5:02 pm.

Let us be clear. I DID NOT USE ANY ‘TRICK’. Your iteration of that lie is tiresome.

You quoted me out of context and I pointed out what you had done. THAT IS NOT A ‘TRICK’.

You are an offensive and tiresome idiot who states nonsense then tries to pretend he said something else. I cannot be bothered to go through all the examples in your latest diatribe so I relate the first.

In a reply to you at July 11, 2014 at 7:55 am I wrote

At this point Daniel G. joined in at July 11, 2014 at 8:29 am by writing of my report of the decoupling

That, of course, is plain wrong: “the relation between co2 emissions and economic growth is” NOT “still there”. The relationship was ended and a new relationship was established. In other words, and as I said, “the USA has decoupled its CO2 emissions from the progress of its economic activity” and there was no clear relationship until the new relationship was established.

But this error from Daniel G. gave you a life-line that you grasped – but misunderstood – in your exceptionally egregious post at July 11, 2014 at 9:48 am where you wrote of my comment

The suggestion that my comment suggests I “think the USA no longer emits CO2 as a by-product of economic activity” is surreal.

I replied to that insane suggestion in my post at July 11, 2014 at 2:06 pm saying

Unfortunately, you had thus made a complete fool of yourself by trying to displace your ignorance of the subject with misunderstanding of an error of Daniel G.. (This is so funny that nobody could make it up).I could go on but there is no point. You only write offensive nonsense. And I take exception to your mention of “decency” because, as with energy issues, you need to learn what it is before you mention it.

Richard

Without comment on the worth of the report, the Kaya Identity is demonstrated here:

http://www.pnas.org/content/104/24/10288.full

To my mind, the usefulness of the formula depends on whether the individual ratios can be determined without having to find the numerator and the denominator and then divide one by the other.

I don’t know how you can determine GDP per capita without knowing the population (in spite of Michael 2). Wikipedia shows three ways and they all need population.

“Emissions per Energy” is also something that cannot be measured directly. You might be able to measure in the lab emissions for a particular fuel but then you need to know the split: how much wood, coal, gas, oil, wind etc etc. You also need to know the efficiency. Is wood burnt in the fireplace at home as efficient as that burnt in a wood-fueled power station? So I still argue that the individual terms are not stand-alone properties.

Temperature can be defined as a ratio involving entropy and internal energy. Temperature can also be measured directly with a thermometer. So an equation with temperature in it could be useful. The fact that you can expand it in to an energy ratio does not detract from that.

I accept that people who have access to these calculated figures may believe they are useful but they should also be aware of the circularity of their reasoning.

It may explain one thing. GDP/capita is effectively Standard of Living. Many who recommend action on climate change think that the consequences of action will not affect our standard of living. That could be because they use a constant for GDP/capita and don’t think it needs recalculating as GDP varies.

graphicconception:

You begin your thoughtful post at July 12, 2014 at 3:26 am saying

Yes, and that is problematic (as I, you and others have pointed out).

However, there are two more fundamental issues that are important whether or not “the individual ratios can be determined without having to find the numerator and the denominator”.

1.

How does one determine which factors to consider, which to ignore, which factors to combine as which ratios, and why?

All these matters are opinions. And the resulting equation is an opinion which defines how analysis is to be conducted. Such constraint of what and how to analyse is politics and it is not science. In other words, the devised equation is a propaganda tool and is not a scientific tool.

2.

What weightings should be provided to individual factors and why?

This is important because the factors affect each other but can be varied independently.

Richard

http://climatemodels.uchicago.edu/kaya/

Willis Eschenbach says:

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.Please remember:

Neither is it your job to decide IF your or any other person’s ideas and expositions and claims are valid”

IF you have valid arguments, not provided in the comment at all, please present them as well as ALL needed premisses for the argument to be proven valid. Remember that this is one step, the very first steep, that everyone needs to take instead of writing things like:

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.Problem is that you Eschenbach as so many others on both sides in the AWG debate lack every essential part of having

provenanything due to not presenting all needed premisses for anyone outside your own backyard’s bagpack. Not only that – as in your comment your subjective view of presenting your day, which lack all contact with the subject and usually is called diversion.In my mind you had better become a Politian. Not many outside the Political sphere has produced so many fallacies and avoiding answering questions. In other word instead of presenting facts for their view!

(richardscourtney 4:51 am, citing graphicconception):

The usefulness of the ratios is precisely that the ratios express causal relationships: More GDP requires more energy, more energy entails more CO2 emissions, etc.

These ratios are neither arbitrary nor simply ‘matters of opinion’. They are indeed well founded.

I very much doubt that you would argue that producing more stuff (GDP) is likely to be done without using more energy, or that producing that energy can often be done without adding CO2 emissions. These are indeed matters of science (including economic science).

You are right, of course, that science can be abused for political and propaganda purposes, but we must be careful in considering where in the analysis any abuse might potentially occur.

Regarding ‘weightings': Strictly speaking, the ratios are not weighted, as they are multiplied in series. However, to address your underlying point, the values of the ratios are matters for investigation. The usefulness of the Kaya Identity is in clarifying what values need to be investigated and how these values matter.

I have not looked sufficiently into any application of the Kaya Identity to venture any opinion as to whether the analysis is done correctly or not. I generally try to balance good-willed presumption of others’ competence with proper ‘nullius in verba’ skepticism and the recognition that even competent scientists make mistakes.

That was some ‘deep decarbonization’.

Seems one of your right side variables was reported as lower, or higher depending on the point of view, but had no effect on the left side. Which seems to be equal to and the same as your identity.

Thanks for the interesting articles and comments.

heh. yeah- run that on your computer. (computers used to be for computing- some old school guys still use them for that)

remember, the kayanic formula is c = p * g/p * e/g * c/e

see what value you get for C when you plug in various values for population, gdp, energy…

who wants a demonstration of the glorious utility of that magical variable assignment function?

the formula shows that no matter how many people, what the gdp or energy consumption-

well, don’t take my word for it. find out the scientific way. test it.

and now that we’ve found out who’s innumerate, we may as well find out who can correct himself when shown to have been foolish.

i want to see who delivers what he demanded of others when it turns out he’s the one who owes…lol

I would like to think that we could agree that:

1) CO2 emissions=Carbon content of the energy*Energy intensity of the economy*Production per Person*Population

(from http://www.manicore.com/anglais/documentation_a/greenhouse/kaya_equation.html)

is an equation that we could discuss the validity of.

Of course we would need to define what each term meant, then we could have a good old fashioned discussion.

Similarly, each of the above terms could be defined and discussed:

2) Carbon content of the energy = CO2/TOE and

3) Energy intensity of the economy = TOE/GDP and

4) Production per Person = GDP/POP

We are on firm ground here, we can argue what these units are and whether the fractions are meaningful. People could even quote research backing up each of these terms.

We can put into each value some real figures and see if we recognise or can prove the validity of these individual fractions.

However, when you write:

5) CO2 = (CO2/TOE)*(TOE/GDP)*(GDP/POP)*POP

You have produced a multiterm equation.

One of the first rules of simplifying an equation is to cancel.

Always, Always, Always.

It cancels to CO2 = CO2.

It is not an ‘identity’.

Identities are useful, they create short circuits to overwise laborious step by step processing through many lines of cancellation, substitution and any other deeper mathematical steps.

If you see your intermediate solution on your paper or whiteboard, taking the shape of a known identity, you have usually ‘proven’ your work or ‘found’ your solution without further processing required.

The fact that this equation can be cancelled down to CO2 = CO2 ‘proves’ to me, and hopefully most others, that it is wrong, pointless, worthless and rather shocking that it is used in a number of papers.

No ‘useful’ equation can be cancelled to x = x.

I am willing to be proven wrong, but you are not allowed to use faulty processing to try to do so!

*SR*

walla, the kayanic runes brought to life!

graphicconception says:

July 12, 2014 at 3:26 am

“To my mind, the usefulness of the formula depends on whether the individual ratios can be determined without having to find the numerator and the denominator and then divide one by the other.”

Some commenters have emphasized that it is the ratios that are important. This is correct. But some of them seemed to concede that the identity loses validity if any of the ratios are determined using the numerator and denominator rather than through some other means. If this is what they meant, then I differ with them at that point. In fact, IT DOES NOT MATTER HOW YOU DETERMINE THE RATIOS, as long as they are determined accurately. The goal would be to determine them as accurately as possible. To calculate GDP/Population, for example, I think Wikipedia is correct that you would definitely want to use Population.

Many people seem to be stubbornly holding onto on the idea that if you can cancel things out and get to a trivially true equation, then the original equation must be a useless tautology. (This was main idea of the original post, in my opinion.) This is the idea that is incorrect. The importance of the ratios IS NOT that by thinking of the terms as ratios you avoid the ability to cancel everything down to a trivially true equation. The importance of the ratios IS that they are important ratios in the real world, and they are ratios that can be influenced by public policy. That is what the Kaya identity is all about. It PURPOSEFULLY arranges the variables into important ratios that can be influenced by public policy, in such a way that things DO cancel out to obtain a trivially true equation. As others have pointed out, if they did not cancel out in that manner, then there would be a problem. So you want to calculate the ratios in the most accurate way possible. You DO NOT need to avoid “the cancel out thing” by calculating them in a way that does not use the numerator and denominator.

Now, as a practical matter, there are definitely issues with the application of the Kaya identity. In a response to another post mentioning some of the difficulties, I discussed an example (inadvertently posted as bryanwoodsmall) showing that when you try to tweak something through public policy, there are unintended consequences that affect the other variables, so the tweak (at best) will not produce exactly the results you anticipated. Some commenters seem to be saying that the practical issues are so big that the identity itself is useless. I will not comment on that idea, except to say that it is a criticism that is completely unrelated to the assertion that if things cancel out to X=X then the original equation is useless.

There are also issues relating to the goals of those who trot out the Kaya identity. Are they trying to tell us that governments had better reduce the population, and/or reduce GDP/capita (standard of living) in order to stave off climate catastrophe? Okay, I admit it, just typing that question raised my blood pressure, because I am aware that there are people who want to do exactly those things, and they predictably will use the Kaya Identity to make their point, arguing for broad (essentially tyrannical) government authority and power to control every aspect of our lives, stomp on our dreams and aspirations, and deny the world’s poor access to affordable energy, all to combat a problem that so far does not even exist. (Okay, my blood pressure is really up now.) However, that is not the only way the Kaya identity can be used. One could also look at it and say, “Okay, I want my government to keep its dirty paws off the first 2 terms (Population and GDP per capita), so if we think CO2 emissions are a problem, then let’s see what we can do about the last 2 terms.”

But the above 2 paragraphs are beside the point about the mathematics that we are talking about.

Steven Mosher says:

July 11, 2014 at 1:53 pm

Thanks, Mosh, always good to hear from you. As Anthony pointed out

, I did not write the subhead, nor did I think it was correct. Anthony has since removed it.aboveAs to your claims about my canceling the units, I didn’t cancel the units. Take a look at the Kaya Identity … do you see any units anywhere? I cancelled the

variables, not the units, which is a totally different operation.Best regards,

w.

bryan – can you use that formula to produce a nice chart showing these meaningful relationships of one variable to another?

actually, i’m only interested in a graph showing how C varies when you change the variables on the right side.

desperate to see it! don’t fail me! maybe mosh? anybody?

Willis – when you cancel the terms in identity it ceases to be the original identity or anything useful even though it remains an identity (A=B is a simple identity as is CO2=CO2). That is not how they’re used. See the RPJ link and PNAS links in the comments above for working examples of how the Kaya Identity specifically is implemented. The results of course, are debatable but not because there is anything wonky about mathematical identities.

oh, i know what my problem is!

i need to set C = 1 so the product is anomalies! that’ll be so much more useful.

omg… how can i do a multi-model average? what do i use for error bars when all the anomalies are zero to the nth decimal place? jeez… how can i do a a collection of scenarios to show a hockey stick for bau if every graph looks like a hockey floor? this kayanic koan is uberzen…

i’m afraid even mosh’s best is not enough to help me now-

i’ll have to go straight to the top:

calling michael mann!

Willis, congratulations.

What an accidental discovery.

For years I have been baffled as to how otherwise intelligent people can talk absolute rubbish, particularly when discussing public policy.

The heart of the government must spend public wealth without limit versus only one taxpayer.

This post reveals an amazing gulf in communication, those of us who understood mathematics to require defined terms and internal consistency, seem to be unable to communicate with those who seem to assign very flexible definitions to what I see as identical terms.

Clearly you have struck oil.

steverichards1984 says:

July 12, 2014 at 9:05 am

“…

However, when you write:

5) CO2 = (CO2/TOE)*(TOE/GDP)*(GDP/POP)*POP

You have produced a multiterm equation.

One of the first rules of simplifying an equation is to cancel.

Always, Always, Always.

It cancels to CO2 = CO2.

…”

steverichards1984:

I saw your post after I put up mine above.

Up until the part I quote above, you are exactly right in my opinion. However, when I got to that part, the source of the confusion became more clear to me.

You say: “One of the first rules of simplifying an equation is to cancel.”

However, I would ask: Is “simplifying an equation” our goal here? And the answer is “NO”. As I noted in my post above (and others have noted), the variables are INTENTIONALLY arranged in a way that is NOT the simplest form, but contains ratios that are important in the real world, and can be influenced by public policy. Of course you can simplify by canceling, but that destroys the ratios that have been intentionally been built. There is no reason to simplify.

What I think I finally see (now it is obvious, and in retrospect I think others mentioned it) is that the confusion comes from looking at the kaya identity as some kind of algebra problem. It is not an algebra problem to be solved or simplified. It is instead an intentional expression of CO2 emissions in terms of important, “tweak-able” ratios, arranged in such a way that they CAN be cancelled to show that the identity has been properly built from the ratios.

So it comes down to seeing something that has named quantities in it, and thinking that it should be simplified, when in fact it does not need to be simplified.

Bryan: have a go at this.

Using my 5) from above, lets substitute some real numbers into the equation and see what happens:

5) CO2 = (CO2/TOE)*(TOE/GDP)*(GDP/POP)*POP

Where

CO2 = 1

TOE = 2

GDP = 3

POP = 4

6) CO2 = (1/2)*(2/3)*(3/4)

7) simplify or just type into a calculator, it will come out to 1

But the mathematically minded new that because the formula tells you CO2 = CO2 *ALWAYS*

Try any number you like in 5) and 6) for the value of CO2 and *SHOCKINGLY* CO2 will equal that number………………