Guest Post by Willis Eschenbach
It’s morning here in Reno, and I thought I’d write a bit more about the Kaya Identity and the Beer Identity. My last post about the Kaya Identity was controversial, and I wanted to see if I could clarify my point. On the last thread, a commenter did a good job of laying out the objections to my work:
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.
That is a very clear and succinct description of what the Kaya Identity is supposed to do. The only problem is … it doesn’t do that.
Let me take another shot at explaining why. To start with, the Kaya Identity states:
where “CO2 emissions” are the CO2 emissions of say a given country; “Population” is the population of that country; “GDP” is gross domestic production of the country, which is the total value of all the goods and services produced; and “Energy” is energy consumed by the country.
The Beer Identity, on the other hand, states the following:
Where all of the other variables have the same value as in the Kaya Identity, and “GBP” is gross beer production by the country.
I think that everyone would agree with those two definitions. They would also agree that both of them are clearly true.
Now, as the commenter said above, when we write
6 = 3 x 2
it tells us that six can be broken into factors of three and two. Not only that, but we can say that for example
(6 * 0.9) = 3 x (2 * 0.9)
That is to say, if we change one of the factors by e.g. multiplying it times 0.9, the total also changes by multiplying it by 0.9.
But is that true of the Beer Identity? Suppose we get more efficient at producing beer, so that it only takes 90& of the energy to make the same amount of beer. Will this decrease our CO2 production by 10%, such that
Well … no. It’s obvious that changing our beer production to make it 10% more energy-efficient will NOT reduce CO2 emissions by 10%. In other words, despite it being unquestionably true, we have no guarantee at all that such an identity actually reflects real world conditions. And the reason why it is not true is that it doesn’t include all of the factors that go into the emission of the CO2, it only includes the beer.
Now, I can hear you thinking that, well, it doesn’t work for gross beer production, but it does work for gross domestic production.
And up until yesterday, I was convinced that the Kaya Identity doesn’t work for GDP any more than it works for GBP … but I couldn’t figure out why. Then yesterday, as I was driving along the Lincoln Highway on my holiday with the gorgeous ex-fiancee, I realized the factor that is missing from the Kaya Identity is … me, driving along the Lincoln Highway on my holiday with my gorgeous ex-fiancee.
The problem is … I’m burning energy, and I’m emitting CO2, but I’m not part of the GDP. I’m not producing anything with that energy—no goods, no services, nothing. My CO2 emission is a part of the total, but it is not included in the Kaya Identity anywhere.
So in fact, the Kaya Identity does NOT tell us 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” as the commenter said.
And that to me is the problem with the Kaya Identity. It’s not that it is false. It is that it gives a false sense of security that we’ve included everything, when in fact we haven’t. And because it looks like mathematical truth, we have folks who take it as gospel, and object strongly when it is questioned or laughed at. Steven Mosher thinks I was wrong to laugh at the Kaya Identity, and I do respect his and the other opinions on the matter, his science-fu is strong … but in fact, the Kaya Identity is no more complete than the Beer Identity, which is why I laughed at it.
So that’s my objection. It’s not that the Kaya Identity is false. It can’t be, by definition its true.
It is that it gives the false impression of mathematical certitude, the impression that it represents the real world, the idea that it identifies the “factors of which CO2 emissions are comprised” … but it doesn’t. This false certainty, because people think it’s “mathematically demonstrable”, leads people to not question whether it applies to the real world.
Finally, in closing let me repeat something I said in the comments on the first thread, which likely didn’t get seen because it was somewhere down around the five hundredth comment.
l hear rumblings that people think that Anthony shouldn’t have published this piece of mine, or should disavow it in some fashion. This totally misunderstands both what Watts Up With That (WUWT) does, and Anthony’s position in the game. The strength of WUWT is not that it is always right or that it publishes only the best stuff that’s guaranteed to be valid.
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, the public peer review afforded by 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 I’m right, well, I thought so to begin with or I wouldn’t have published it, and it doesn’t change my direction.
But if someone can point out my mistakes, it saves me endless time following blind alleys and wrong paths. And my opinions on the Kaya Identity may indeed be wrong.
There is much value in this public defenestration of some hapless piece of bad science, whether it is mine or someone else’s. It is important to know not only which ideas are wrong, but exactly why they are wrong. When Anthony publishes scientific claims from the edges of the field, 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 may 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 supported scientific comments. Even if Anthony had a year to analyze and dissect each piece, he couldn’t do that job. There’s no way that one man’s wisdom can substitute for that of the crowd in the free marketplace of scientific ideas. 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 or 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 withstand that test of time … 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 don’t fill up the poor man’s email box with outrage simply because you think a post is not scientifically valid enough to be published. Send your emails to the guest author instead, or simply post your objections in a comment on the thread. 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 fight cards with interesting bouts … and given the number of comments on my previous post about the Beer Identity, and the huge popularity of his website, he is doing it very well.
Regards to each and all of you, my best to Mosher and all the folks who have commented, and my great thanks to Anthony for the huge amount of work he does behind the scenes to keep this all going. I’m on the road again, and my highway CO2 emissions are still not included in the Kaya Identity …
w.
As Always: If you disagree with something that someone has said, please have the courtesy to quote their exact words. It avoids much confusion and misunderstanding.
Shawnhet:
At July 13, 2014 at 9:08 am you say to Daniel G.:
Yes. And in this thread the prime culprit (by a large margin) is Daniel G..
For example, the Kayla identity can only be meaningless nonsense unless there is a definition of “meaningful” “factors” which determines what “factors” should and what “factors” should not be included in the so-called “identity”. Eventually, after much effort, I managed to get Daniel G. to provide his definition which he did at July 13, 2014 at 8:00 am. But his definition is ridiculous and I did ridicule it in my reply at July 13, 2014 at 8:13 am which is here.
As he repeatedly did on the other thread, Daniel G. has conveniently forgotten the matter when shown to be wrong.
Richard
richardscourtney: Can anybody provide a definition of “meaningful” which determines what should and what should not be used as “factors” in the Kaya identity?
There is probably not an abstract definition that you would accept. One can list the usual things (which provides an ostensive defintion), or a rough rubric such as “anything that contributes at least 1% to the R^2 value of the equation. The meaningful things that contribute to GDP are not the same in all countries: Germany doesn’t grow coffee or pineapples; Kenya doesn’t manufacture automobiles or lithium batteries.
Shawnhet says:
July 13, 2014 at 9:23 am
Sigh
If a country moves to all Nuclear/Wind/Hydro/wave power as its input is your ‘identity; true?
The primary hidden assumption (making it mean what you want it to mean) is that all energy generation is equal in creating CO2 as a byproduct. This is false.
The second assumption is that GDP is driven solely by energy consumption, this is also false.
It has as much validity as the medieval proof of the afterlife.
Its fake maths – and Shawnhet – I will have large fries with that. 😉
Cheers
Willis is punching above his weight here and has disqualified himself from ever criticizing the mathematical work of anyone else. His wiggling where there is no wiggle room is surely drawing laughter from Anthony’s peers. His errors are the platform upon which other uninformed people chant the same wrong conclusion: CO2 = CO2! There will be no gracious mea culpa, no apologies to math teachers everywhere for confusing their students, no clarification as emergent phenomena of his failure. The hole he’s dug here is deep enough to be considered one of the wonders of the world. The Willis Eschenbach by-line is now junk stock.
WTFUWT?
Time to move on – nothing to see here
Ian W says: July 13, 2014 at 10:11 am
Its fake maths –
I wouldn’t even call it that – it has absolutely nothing to do with math ! KAYA is just shorthand for 4 true but trivial assertions, namely:
to halve worldwide anthropogenic CO2 emissions, and all other things being equal or held constant,
1) cut the worldwide population in half;
2) cut worldwide consumption in half;
3) cut energy used in production in half;
4) cut carbon used to produce that energy in half.
Pielke in his dispute with Krugman succesfully used KAYA to demonstrate that 1) and 2) are simply not realistic; that 3) offers only limited (and short-term) possibities as it is impossible to produce (or do) anything without using energy; and so that 4) is the only long-term realistic option to drastically cut CO2 emissions.
Does Pielke not know that those factors are dependent! Of course he does! But even IPCC has known that for some odd 20 years, certainly long before Willis had ever heard of KAYA. But that’s not the point. KAYA is not a “model”, let alone a “mathematical model” ! Again, it has absolutely nothing do with mathematics.
richardscourtney says:
July 13, 2014 at 9:40 am
“For example, the Kayla identity can only be meaningless nonsense unless there is a definition of “meaningful” “factors” which determines what “factors” should and what “factors” should not be included in the so-called “identity”. ”
The scientific method gives a standard for determining what should and should not be included in a hypothesis – namely that you should include things that allow/help you to make meaningful predictions of measurable stuff that happens in the real world and exclude those that do not.
As i said previously, I strongly doubt one can actually make such meaningful predictions using the Kaya framework but if one can do it, then the objections raised against it in the thread and its predecessor are moot.
Cheers, 🙂
Ian W says:
July 13, 2014 at 10:11 am
“Sigh
If a country moves to all Nuclear/Wind/Hydro/wave power as its input is your ‘identity; true?”
Sign. Not the point at all. Countries can’t just decide to move to non-carbon sources of energy at the flip of a switch. Rather, it has to happen slowly and gradually, which means that something like Kaya could still provide a valuable picture of the world (in other words its math will not be “fake”).
Bertrand Russell wrote: If you can not know something without knowing everything, then it is obvious that you can not know anything.
People who have been criticizing the Kaya identity (or Kaya equation or Kaya formula) have, I think, established a few things beyond doubt:
1. the units cancel properly;
2. neither CO2, GDP, Energy per GDP, nor CO2 per energy can be known with exquisite accuracy for any place and time.
3. analogies to the Kaya equation can be written that are of no use whatsoever (that is:
LHS = scale*ratio1*ratio2*ratio3.)
4. other important contributors to CO2 are not in the equation.
The history of science is replete with such incompleteness as represented by points 2,3 , and 4. In the early 1800s, three different people showed with statistical analysis that cleaning stuff in hospitals improved the survival rates of patients; no one could explain why, not all deaths were tallied, not all causes of death were well-recorded, and so on. But the knowledge proved useful in the US Civil War even though, is it happened, most of the injured soldiers cared for in clean conditions died anyway.
In 1998 or 1999, Perlman and Ho showed in an article published in Science magazine, using a dynamical model in which most of the really important factors were not included, that HIV reproduced at a high rate in infected individuals and that anti-retroviral medications reduced that reproductive rate to near 0. This important step in the fight against AIDS contained many of the liabilities highlighted in these two threads: the model could be mimicked by other models of the same structure that were totally useless; the HIV viral burden could not be measured very accurately in blood, and hardly at all in other reservoirs of the body; most of the infectious agents that caused deaths in HIV-infected individuals were not measured at all; the life histories of the patients were not included in the model at all (these life histories were considered “meaningful” by some scientists working on AIDS, not meaningful by others, and there was no a priori definition of “meaningful”); and so forth.
The integrate-and-fire and quadratic integrate-and-fire models of the neuron likewise omit many important facts of neural science, but they are extremely useful in simulations anyway (see Izhikevich, “Dynamical Systems in Neuroscience”, and Kass, Eden and Brown, “Analysis of Neural Data”, for other examples of modeling complex systems with models that have known liabilities and systems measured with bias and error.)
If the standards promoted here by Willis Eschenbach had always been followed, nothing would ever have been learned. Since I don’t believe there is any utility in reducing CO2 I don’t think that use of the Kaya equation will prove fruitful. That said, I hope that no one is deterred from working out the details in actual cases merely because of the critiques presented in these 2 threads.
Next up: can you increase GDP by reducing malaria incidence? By how much? Do the components of GDP and the techniques of reducing malaria incidence have to be the same in each country or region? Is malaria the only problem impeding GDP growth? Is malaria itself equally destructive in all economies? Are there equations that that are potentially useful, yet with comical parallels? Do those equations instill overconfidence in people working to eradicate malaria.
Willis Eschenbach: Thanks, Matthew. You’re making the same mistake Mosher did. I’m not canceling the units. I’m canceling the variables.
No, Willis, you cancelled the units. The values of the variables are multiplied together.
“canceling the variables” doesn’t even have a definition.
thallstd says:
July 12, 2014 at 9:37 am
Excellent point that an increase in population does not necessarily imply a corresponding decrease in GDP per capita. In fact, GDP per capita could go up, down or stay the same depending on whether the net population change results in more or fewer people in the workforce.
—
Tom Trevor says:
July 12, 2014 at 9:42 am
The error in your thinking has been thoroughly explained in the other thread. Search for “dimensional analysis”.
—
Michael 2 says:
July 12, 2014 at 9:57 am
Yet readers still insist on thinking they can look at a ratio, e.g. GDP per capita, and fiddle with the numerators and denominators independently. As long as they think that, they’ll never understand their error.
—
Arthur says:
July 12, 2014 at 10:10 am
See my comment to Tom Trevor above, and please stop with this silly and incorrect line of thinking.
—
Arthur says:
July 12, 2014 at 12:03 pm
Please, please, please – when you’re already in a hole, stop digging.
—
Bob Sullivan says:
July 12, 2014 at 12:16 pm
I’ll say this again to all of you who think this logic is correct…
You don’t substitute a value for the denominator of any of the ratios. The value of each denominator is always 1.
“GDP per capita” means “GDP per 1 person”. “Energy per GDP” means “energy per $1 of GDP”. “CO2 emission per energy” means “CO2 emission per 1 Joule of energy”.
You can substitute a value for the entire ratio, which is, in effect, substituting a value for the numerator. But, leave the denominators alone!
—
I’ve only gone about a quarter of the way through the thread, but I’m too fed up to go any farther. If any of you mentioned above have admitted farther down in the thread to the error of your way, I apologize.
“You Keep Using That Word, I Do Not Think It Means What You Think It Means”
1) useless equation (kaya identity as constructed)
total distance traveled = total distance traveled/hours traveled * hours traveled
2) useful equation (kaya identity as intended?)
total distance traveled = distance traveled/hour * hours traveled
hours traveled != hour
total distance traveled != distance traveled
You cannot justify equation 2 algebraically:
total distance traveled = total distance traveled
-> transform total distance traveled into distance traveled algebraically?
total distance traveled = distance traveled
-> multiply by hours traveled/hour algebraically?
total distance traveled = distance traveled/hour * hours traveled
Willis Eschenbach quotes someone else quoting Willis Eschenbach:
Willis Eschenbach says:
July 13, 2014 at 12:57 am
The Kaya Identity incorporates multiple hypotheses: that greater population leads to greater GDP (other things equal), that greater GDP leads to more energy use, that more energy use leads to more CO2 emissions, and that each of these causal linkages can be roughly quantified.
First, whenever a man says “other things being equal”, I have to point out that in this all-too-real world of ours, other things are never equal … and since your claim depends on that clause, your claim is falsified.
And those problems are not solved by cramming them into an identity.
“Other things are never equal” applies to every equation ever applied to anything. Practically, you can only assess whether the omitted variables have changed enough, or will change enough, to add too much to the already present error of approximation.
Has anybody claimed that those problems have been solved “completely”?
At this rate, you will soon establish that the Brooklyn Bridge can’t be built, much less stand.
The implication is there is a wrong way to use the identity and there is, of course, but that is easily corrected. The unspoken claim is there is no right way to use the identity and that is evidence of a deep misunderstanding of math.
richardscourtney says:
July 12, 2014 at 11:40 pm
““I have repeatedly argued that the (Kaya identity) equation is useless and misleading nonsense except as a propaganda tool: the ratios are arguments propagandists want to promote, and a claim that a ratio is “meaningful” is a statement that there is a desire to promote it.
Importantly, the fallacious Kaya identity needs to be rejected now because otherwise it threatens to become THE propaganda tool used to revive the ailing AGW-scare.””
——————
richardscourtney, I liked and agreed with your above commentary, and if I may, I would like to take the liberty to paraphrase said commentary, with my substitutions of specific verbiage, so that it then states what I have repeatedly argued for years and years, to wit:
——————-
““I have repeatedly argued that the Global Average Surface Temperature calculation is useless and misleading nonsense except as a propaganda tool: the “average changes” are arguments propagandists want to promote, and a claim that an average is “meaningful” is a statement that there is a desire to promote it.
Importantly, the fallacious Global Average Surface Temperature calculations need to be rejected now because otherwise they will continue to be THE propaganda tool used to exacerbate the fear mongering CAGW scare.””
—————-
IMO, …. average temperatures are akin to average football/soccer scores …… which makes for “HOT” arguments between opposing fans of the sport.
===============
richardscourtney says:
July 13, 2014 at 7:55 am
“Can anybody provide a definition of “meaningful” which determines what should and what should not be used as “factors” in the Kaya identity?”
————
I think I can, to wit: …. “meaningful” means “author discretion”.
A similar objection that I have with GCMs, elegant, mathematically rigorous, but not actually modeling the total climate system due to limited spatially collected datasets. One can gain insight into a particular subset of the system, but to claim the larger, overall model represents reality, is fundamentally wrong. Then to use such ‘evidence’ for policy directives is borderline corruption…
This is not as hard as all the discussion makes it seem. Willis is both right and wrong. Here is why — The Kaya Identity and the Beer Identity are both trivially true and seriously misleading. As Steve M says, you have to watch the pea very carefully or you will be tricked very easily.
The error is in how these things are used. If you want to estimate CO2 emissions, it is reasonable to break it down into pieces more easily estimated (with the proper caveats of course). If you want to predict what-ifs, that is a different story.
One of the early comments on the first thread said:
This is an example falling into the trap. The key words here are “all other things being equal”. They are not. The so-called identities are like a stopped watch. They look like multiplying numbers, static things, constants. If that is what the terms represent, fine. But if they are really functions, you have to ask what they are functions of. Time, f(t), but probably also many other things, f(x,y,z,…) and those terms share those variables. So the “all other things being equal” line does not work, change one term and the other terms will change too. The stopped watch works for one point in time, but not others.
Talking about change is like taking derivatives. Dig that calculus out of your memory and take the derivative of composed functions.
Matthew R Marler says:
quote: “The history of science is replete with such incompleteness as represented by points 2,3 , and 4.”
Nice shot. Your point sounds pretty profound but …
quote: “In the early 1800s, three different people showed with statistical analysis that cleaning stuff in hospitals improved the survival rates of patients;”
Well, the Kaya identity is everything but a statistical analysis. It is a tautology. An algebraic tautology.
It contains *no information* whatsoever, regarding CO2, population, energy or whatever.
If such identity was used in hospitals, probably nothing would have changed, or worse, the wrong decisions could have been taken, as an identity can be read either way, and contains only the information you wanted to put in (here, for instance: “CO2 is proportional to Population hence we are too many!”)
quote: “If the standards promoted here by Willis Eschenbach had always been followed, nothing would ever have been learned.”
You are too harsh with him. As I understand, he only wants this pedantic Kaya formula to have some relationship with reality and physical processes and measures. It has not. If identities were a good scientific tool, we would know nothing by now…
In fact, if the Kaya identity is a sort of “scientific summum”, the maximum that the warmists and greens can produce after 40 years and billions of dollars, well, … you see my point.
quote: “Since I don’t believe there is any utility in reducing CO2 I don’t think that use of the Kaya equation will prove fruitful”
No. It is not fruitful because it is an algebraic tautology, whatever your opinion on reducing CO2. It is, literally, not a scientific tool in any way.
I hesitate to comment because this is the first I’ve heard of the Kaya identity but knowing it came from the IPCC and having read this post and most of the comments I do have a take on it. Kaya is an identity being treated like a linear equation and as such is a brilliant piece of agitprop. Danny Lofo who struggled through fractions in the third grade but didn’t quite make it to algebra in high school would look at that equation, note population, GDP and energy consumption in the numerators of the factors on the right hand side of the equation and say wow, we have to reduce those to reduce CO2. We can’t reduce the population and don’t want to reduce the GDP so that only leaves energy. WE HAVE TO REDUCE ENERGY! This is as intended, you know, just to put the various factors into the proper perspective as has been noted. Well, and it’s a major purpose of the IPCC to take control of energy use (just to save the planet of course).
I don’t think there’s anything proper about that perspective. It’s not a linear equation, those factors are non linear functions of one another, evidence is that CO2 is more a result of global warming than a cause (rendering the perspective meaningless) and there are extraneous factors that could make nonsense of the whole thing (e.g. we get nuclear fusion going and energy becomes disconnected from CO2). Willis is spot on to treat it lightly, it is not a serious effort to illuminate the subject, it is propaganda.
The Beer Identity:
1 beer = I should have another
2 beers = I should have a third
3 beers = 1 trip to rest room
Deer occasionally wander onto my property. When I want to count the deer in a particular group, I count the number of legs and divide by four.
Gary Hladik says:July 13, 2014 at 11:45 am
Deer occasionally wander onto my property. When I want to count the deer in a particular group, I count the number of legs and divide by four.
Now,now, Gary, and what if one of the deer only has 3 legs ! 🙂
Willis Eschenbach says: July 13, 2014 at 12:34 am
“If I burned that exact amount of gasoline in a furnace to make a tool, that would add to the GDP. But I didn’t. I burned it in an activity that does not add to the GDP.”
You are using a definition of GDP that is not the common definition. GDP is the sum of *consumption*, investment, government spending, and net exports (from Wikipedia).
If you bought the gas in the USA it was counted in US GDP. If you bought the gas in Canada, and smuggled it across the border, then it would not be counted in US GDP but that doesn’t happen often enough to have a significant impact on the answer.
As I said above, the Kaya equation is politically loaded because it includes population and GDP factors, thereby implying that killing, starving or impoverishing the population would be one way to lower CO2 levels.
More importantly, it was “silly” for Kaya to include those factors in his equation. We have a good estimation of how much fossil fuels we burn and how much CO2 is produced when we burn the fuel. We measure how much fuel we fuel burn in coal plants, gas plants, automobiles, heating oil, etc., and we have good estimations of the efficiencies of those processes, so we have good estimates of CO2 emissions.
Therefore, Kaya erred when he included factors for GDP and population. Those factors only make the equation less accurate. Constructing a long equation with factors that don’t make the equation more precise is not helpful. Actually it’s harmful.
Given the above, the logical and most useful equation is CO2 emitted = CO2 emitted. In other words, if you want to know how much CO2 humans are emitting, LOOK IT UP, and if you want to estimate future emissions of CO2, extrapolate the trend.
I’ve come full circle. At first I thought equation was useless, then on closer examination I realized it can predict what it is intended to predict. Now I see that it is not the most efficient equation and the factors that make it less efficient, and less accurate, were probably added for to make a political point.
Silly means ridiculously trivial or frivolous. Adding population and GDP to the equation, to make a political point, is bad science. It makes the identity ridiculously trivial and frivolous.
Willis got this one right. He seems to not fully understand why his gut reaction was the correct reaction. But right is right so I won’t pick any more nits.
I’m putting Wills back on his pedestal where he belongs.
kabend says: July 13, 2014 at 11:34 am
“It is not fruitful because it is an algebraic tautology”
Please define “algebraic tautology.”
Thomas says: July 13, 2014 at 12:01 pm
Please define “algebraic tautology.”
There is no such thing as algebraic tautology. Tautology is a term used in logic.
The KAYA identity is an identity, of the sort: a = a x 1 x 1 x 1
RH says:
July 12, 2014 at 12:34 pm
Sheesh. Mr. Kaya must be laughing his ^%$* off at how seriously everyone is taking his equation. The thing is nothing more than a political statement masquerading as a scientific formula. It deserves ridicule, not serious thought.
RH,
Exactly. I am soooo glad I chose to go up to the EAA Fly In and Airshow yesterday in Arlington WA (and camp overnight to enjoy a phenomenal ‘blood moon’ rise over snow capped mountains, a wonderful jazz/swing performance by the big band Mojo, a night pyrotechnic aerobatics airshow and an outdoor viewing of the movie “Gravity”) instead of wasting time on arguments about this drivel of a pseudoscience political statement.
Now that the truck is unloaded (sans camping gear, cooler, etc), it is time for a good hour long swim in the local lake, before firing up the ‘barbie’ for some hardwood smoke grilled carnivores delight washed down with adult beverages that definitely contributed to CO2 emissions… and I don’t give a damn if my (tasty!) home brewed plum wine from 2009 contributed anything to GDP!
Regards to you RH,
Mac