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.
Tommy, GDP does not ignore trade. Look it up. The Kaya index only works for one snapshot of time and only for the aggregate GDP and population. Some consume more, some less, but there is an average consumption and an average of how much energy went into that consumption.
Gary, vacations ARE “something of value.” For example, I’d rather have a vacation than another IPCC report.
Mike M says:
July 13, 2014 at 1:38 am
Mike, as I’ve said many times, there are no units presented in the Kaya Identity …
w.
Willis Eschenbach says (July 13, 2014 at 12:57 am): “However, the GDP appears in both the numerator and the denominator, so the net result is unchanged.
—
Willis, all your posts prior to these two seem so well thought out, I can’t believe you’re making such a mess of this one.
GDP (the economic output of e.g. a country) does not appear in the equation at all! But, there are two GDP-related quantities. The second term is GDP per capita, which is obviously a much smaller value than total GDP. The third term is energy per unit of GDP, or, in other words, energy per $1 of economic output. THE NUMERIC VALUE OF THE DENOMINATOR IN THE THIRD TERM IS 1.
You can’t “cancel” the terms. “Cancel’” is not even an arithmetic operation. You can divide the value of the top term by the value of the bottom term, but the bottom term is 1, so the result is still the value of the top term.
And even that is not the right way to think about it. You insist on performing dimensional analysis and mistaking it for algebraic reduction. KNOCK IT OFF!
bk51 says: ” THE NUMERIC VALUE OF THE DENOMINATOR IN THE THIRD TERM IS 1.”
Well I see “GWP” (in the Wikipedia version of it)
If you re-write the equation well then of course it comes out differently.
Canceling terms is the common name for the operation. Nobody is making you cancel terms but I find it a very handy algebraic shortcut.
Here is a video by Roger Pielke, Jr who has a handle on this:
He actually uses Willis’ canceling operation to demonstrate the validity of the identity. It is a short but three-part speech.
bk51 says:
July 14, 2014 at 10:18 pm
bk51,
The point is, that simplifying this ‘expression’ will save you the time of putting numbers into it.
It is not an equation and it is not a formula. It is an identity and that is all.
If you do exactly as you have just said, you get the same result. Why? Because your new terms (“WITH DENOMINATOR 1”) are the reciprocals of one another.
For example:
CO2 Emissions = Population × (GDP/Population) × (Energy/GDP) × (CO2/Energy)
CO2 Emissions = ?
Population = p
GDP = g
Energy = e
CO2 = c
If
c= 2, g=20, p=4, e=8.
Then
RHS = p x (g/p) x (e/g) x (c/e) = 4 x (20/4) x (8/20) x (2/8) = 4 x 5 x 0.4 x 0.25 = 2
Therefore CO2 Emissions = 2 if c= 2, g=20, p=4, e=8.
OR
CO2 Emissions = 2 if c= 2, g=7, p=9, e=8.
RHS = p x (g/p) x (e/g) x (c/e) = 9 x (7/9) x (8/7) x (2/8) = 9 x 0.777777777777778 x 1.142857142857143 x 0.25 = 2
And etc, etc
CO2 Emissions = 2 if c= 2, g=20, p=4, e=9.
CO2 Emissions = 2 if c= 2, g=20, p=4, e=765.
Some people seem to think that you can not transpose ‘identities’!
Whyever not?
They are a mathematical construct, produced by using normal ‘rules’ of maths.
They can be transposed to make any unknown to be the subject (LHS).
I think we should drop the name ‘identity’ from this discussion.
Reposting this from the original thread, as it has become too long for my old iPad!
I am in complete agreement with Richard Courtney.
I am also on record, for pointing out the propaganda value of this silly e-quack-tion (Yes it is an Identity but that is all it is!). Ok, forget the identity, it is useless as a mathematical tool because it is not an equation or formula in any functional way!
What is apparent, is that nobody who works with it, uses the Identity.
What they do do, is apply it as a product of factors. Simply multiplying across the variables.
Straight up, I find the idea of multiplying the factors, unjustifiable and meaningless; except as propaganda.
Is it true that population and GDP are directly related, or proportional; a product?
The very first three places in the world I looked at, not only challenge this assertion, they wipe the floor with the stupidity of it!
Hong Kong has an inverse relationship of GDP to population, because its massive GDP dwarfs its population.
GDP/ Population : 263.3 Billion / 7.2 million
Singapore, according to current figures has an even greater inverse relationship of GDP to population, because it has a smaller population.
GDP/ Population : 274.7 Billion / 5.3 million
Both are massively inverse in there relationship of GDP to population and both are orders of magnitude above the next place I looked at; Bangladesh.
Bangladesh has the exact opposite but still inverse relationship of GDP per capita, because of its huge population!!
GDP/ Population : 115.6 Billion / 154.7 million
CO2 emission are also in an inverse relationship to GDP for Hong Kong and Singapore and are also inversely proportional to population in Bangladesh.
cheers,
Scott
John Whitman says:
July 14, 2014 at 6:20 am
“Roger Pielke jr writes,
“The Kaya Identity is the centerpiece of the analyses found in The Climate Fix and a lot of my work. It is a very powerful tool for understanding the challenge of emissions reductions. It holds that carbon dioxide emissions are influenced by four factors:
population
GDP per capita
energy intensity of the economy
carbon intensity of energy”
———————-
I’ll say it again, to wit:
I compiled the following statistics via reliable sources, to wit:
Increases in World Population & Atmospheric CO2 by Decade
year — world popul. – % incr. — Dec CO2 ppm – % incr. — avg increase/year
1940 – 2,300,000,000 est. ___ ____ 300 ppm
1950 – 2,556,000,053 – 11.1% ____ 310 ppm – 3.1% —— 1.0 ppm/year
1960 – 3,039,451,023 – 18.9% ____ 316 ppm – 3.2% —— 0.6 ppm/year
1970 – 3,706,618,163 – 21.9% ____ 325 ppm – 2.7% —— 0.9 ppm/year
1980 – 4,453,831,714 – 20.1% ____ 338 ppm – 3.8% —– 1.3 ppm/year
1990 – 5,278,639,789 – 18.5% ____ 354 ppm – 4.5% —– 1.6 ppm/year
2000 – 6,082,966,429 – 15.2% ____ 369 ppm – 4.3% —– 1.5 ppm/year
2010 – 6,809,972,000 – 11.9% ____ 389 ppm – 5.1% —– 2.0 ppm/year
2012 – 7,057,075,000 – 3.62% ____ 394 ppm – 1.3% —– 2.5 ppm/year
Source CO2 ppm: ftp://aftp.cmdl.noaa.gov/products/trends/co2/co2_mm_mlo.txt
Based on the above statistics, to wit:
Fact #1 – In 70 years – population increased 198% – CO2 increased 29% – Heat Islands increased est. 300/400+%
Fact #2 – Atmospheric CO2 has been steadily and consistently increasing at a rate of 1 to 2 ppm per year for the past 70 years, …… whereas human generated CO2 releases have been increasing exponentially every year for the past 70 years.
Fact #3 – Global Temperatures have been steadily and consistently increasing a few hundredths or tenths of a degree for the past 70 years, ……. whereas human created infrastructure, housing, vehicles, etc. (Heat Islands) have been increasing exponentially every year for the past 70 years.
Conclusions:
Given the above statistics, it appears to me to be quite obvious that for the past 70 years there is absolutely no direct association or correlation between:
• Increases in atmospheric CO2 ppm and world population increases.
• Increases in Average Global Temperature and world population increases.
• Increases in Average Global Temperature and Heat Islands construction increases.
• Increases in Average Global Temperature and atmospheric CO2 ppm increases.
But then of course, …… I am not looking through Rose Colored Glasses.
A slight improvement on the Kaya Identity might be to replace GDP in the GDP/Energy factor with GAP (Gross Activity Product) which I’d define as the same as GDP except adding imports and exports instead of subtracting them.
GDP = private consumption + gross private investment + government spending + (exports – imports)
Since exporting and importing requires energy for the purposes of CO2 emissions these should be added instead of subtracted. If a country exports exactly the same value of goods as it imports this term would be 0, yet energy would still be being consumed but not captured in the GDP.
So, Kaya’ Identity would be:
CO2↑ = Population x (GDP/Population) x (Energy/GAP) x (CO2↑/Energy)
Or
CO2↑ = Population x standard of living x Energy per Economic Activity x CO2↑ intensity of Energy production
Since GDP and GAP have the same units ($), they still cross out.
Perhaps a small improvement but I’m still not happy with it. I’m putting way more thought into this than I should. Thanks Willis.
Thomas says:
July 14, 2014 at 12:36 pm
“Value is determined by what people are willing to pay. ………….. Entertainment is a significant part of the average American’s consumption …………… so it’s a significant part of GDP.”
——————-
YES, ….. and YES, ….. and absolutely NO.
Purchasing the entertainment services provided by prostitutes, ….. purchasing the entertainment products provided by drug dealers, …… purchasing entertainment via donations and contributions to churches, charities, benevolent organizations, …… purchasing political favors provided by politicians, ……… purchasing your entertainment via bets and wagers, …. etc., etc. …. are all, … inclusive of, ….. the average American’s YEARLY “entertainment” consumption spending of hundreds of billions of dollars ….. yet not a penny of said consumption spending is included in the GDP.
==============
“A thing doesn’t have to have value to be counted as GDP. Consider for example the billions of dollars spent on climate research.”
————-
Don’t be silly, if an entity has no value ….. then there is no way to count it as part of the GDP. And the billions expended by government on climate research is not counted in the GDP, ….. but the expenditures of the recipients of said billions is counted in the GDP, …… that is, minus the afore mentioned entertainment expenditures.
The GDP is a “fuzzy math” figure that is no more accurate than the “unemployment #” or the number of illegal immigrants residing in the US.
A few brief notes for now:
Scott Wilmot Bennett says:
July 15, 2014 at 4:08 am
“CO2 emission are also in an inverse relationship to GDP for Hong Kong and Singapore and are also inversely proportional to population in Bangladesh.”
I’m not sure how you come to this conclusion but you are mistaken: all three will show a direct relationship for CO2 to GDP. (You can’t simply look at one pair of data points and claim to have found an inverse relationship).
Samuel C Cogar says:
July 15, 2014 at 5:26 am
“Fact #2 – Atmospheric CO2 has been steadily and consistently increasing at a rate of 1 to 2 ppm per year for the past 70 years”
This is a bit misleading. Clearly the rate of atmospheric increase has gone up over time.
Samuel C Cogar says:
July 15, 2014 at 7:24 am
“….. yet not a penny of said consumption spending is included in the GDP.”
Just because not all of the spending on entertainment does not make it into the GDP numbers doesn’t mean that entertainment is not a significant part of American GDP.
Cheers, 🙂
I realize I’m a bit late to the party on this post, but there are a couple of points that need to be made;
1) Any equation that has the variable to be solved for as a numerator on both sides, and where literally all of the other factors cancel out is just mathematical masturbation. I too performed the cancellations in my head immediately upon seeing it, and began to laugh. CO2 emissions = CO2 emissions.
2) The equation is meaningless, but not for the GDP problem you cite; indeed, your consumption of food and fuel is counted in the GDP. There is no requisite that your consumption of fuel produce something of value. You consumed it and it is assumed that you got value for that, whether it be from driving to work or some non-intrinsic value such as driving through the desert. Indeed, our method of measuring GDP has no way to differentiate such things.
3) Although the math is entirely different, in looking at the Kaya ID, I get the same feeling I get when I look at the Drake equation. Neither of these is of any value to science.
Shawnhet
Singapore’s GDP per capita, is 8.5 times that of China, despite having a population (Of 5.3 million.) which is 255 times smaller than China’s 1351 million. And Singapore’s CO2 emissions (Of 13520 kt) are 400 times smaller than China’s (5433057 kt).
Bangladesh has a GDP per capita 70 times smaller than Singapore, despite having, a population 30 times larger. It also has the tiny CO2 emissions per capita of 0.000227.
Bangladesh’s CO2 emissions are 4 times larger than Singapore’s despite having a population 30 times larger.
The alarmist assertion that GDP is proportional to population and CO2 emissions, has no substance in the real world, except perhaps, inversely!
The Kaya is not intended to “calculate” CO2, or any other value at all. All the “factors”, CO2, P, GDP, and E are known ahead of time for input (see Pielke, Jr). Kaya just sets up indexes of ratios between these factors. This is purely arithmetic and has nothing to do with algebra. Kaya is amenable to any arrangement of terms and you CAN cancel terms OR NOT as desired.
CO2/P = GDP/P * E/GDP * CO2/E
CO2/GDP = E/GDP * CO2/E (Pielke, Jr.)
Maybe this is the ultimate arrangement:
GDP/P = CO2/P * GDP/CO2
richardscourtney and rgbatduke are right to ignore the math and argue directly to the philosophy.
I can sleep safer now knowing the “Policy Makers” have it all under control.
Couple more points.
1. Dr. Kaya’s identity as he wrote it is applied to global data, not regional.
2. It is an identity, not a working formula.
Use it to find global CO2 emissions as a function of each contributor, solved independently. Use it to calculate what must be changed in each parameter (independently) to reduce the current emissions to 10%, globally, in 30 years. Or just visit the U of Chicago’s calculator and use that. The link can be found in this thread. That calculator uses simple tabled data for the known era, and your inputs to plot future values INDEPENDENTLY because it is a what-if tool!
Mike M says: July 13, 2014 at 1:38 am ” You can take any linear formula and factor out whatever you wish when only the units are being presented.”
Willis Eschenbach says: July 14, 2014 at 9:51 pm ” Mike, as I’ve said many times, there are no units presented in the Kaya Identity …”
I’m using the term “units” loosely, (and I think it’s rather petty telling me “energy” is not a “unit” when everyone knows energy is measured by some form of unit), but if you wish to push this nonsense further let’s convert all the items to your hard units and see what happens going back to my OP…
“The only ‘problem’ I see with the Kaya formula is that it has no names for the values GDP/population, Energy/GDP or CO2/energy and simply uses the unit ratios instead. ”
GDP/population “L” – dollars/person
Energy/GDP “H” – joules/dollar
CO2/energy “Q” – kg/joule
The formula becomes kg = persons * (dollars/person) * (joules/dollar) * (kg/joule)
You can factor any which way to get any nonsensical “result” you want, kg=kg or persons = persons or 1=1.
Again I challenge you by pointing out other formulas like miles= hours * (miles/hour), in which I’ve intentionally satisfied your “hard units” meme and it’s blatantly clear we can do the same thing to that formula that you did to the Kaya formula also reducing it to 1=1.
I will point out again, when you factor things OUT of any formula is no longer the same formula. Factoring out units of a formula is only a test that the the formula is dimensionally congruent – nothing else.
Scott Wilmot Bennett says:
July 15, 2014 at 9:39 am
“Singapore’s GDP per capita, is 8.5 times that of China, despite having a population (Of 5.3 million.) which is 255 times smaller than China’s 1351 million. And Singapore’s CO2 emissions (Of 13520 kt) are 400 times smaller than China’s (5433057 kt).”
Your comparing apples to televisions here. Singapore’s per *capita GDP* is higher than China’s and China’s *total* population and *total* CO2 is higher than Singapore but this does not mean CO2 is inversely related to GDP. If you use per capita numbers for both GDP and CO2 you can see this easily – take a look at the fourth graph here:
http://mygardenpond.wordpress.com/2014/07/13/a-graphical-look-at-the-kaya-identity/
As you can see, it is pretty much a textbook example of a direct relationship and definitely not an inverse one as you suggest.
Cheers, 🙂
Hey Thomas, I agree with your objection to my statement “GDP ignores trade”. Of course, the market price of domestic products is determined during trade, so my statement was flat out wrong.
What I meant to say was that GDP doesn’t show the effect on value by methods of trade. Examples: Speculation causes value swings completely unrelated to energy. Same product traded in larger units gets an economy-of-scale savings in energy for shipping. Trade with subsidized producers divorces value from energy costs. KI is attempting to relate GDP and CO2, but I wonder if the energy signal in GDP is lost in the noise of non-energy aspects.
Will Nelson says:
July 15, 2014 at 10:27 am
I don’t think it is possible to be more Orwellian or proletarian! ;-{
Scott Wilmot Bennett says:
July 15, 2014 at 10:53 am
Will Nelson says:
July 15, 2014 at 10:27 am
“I can sleep safer now knowing the “Policy Makers” have it all under control.”
I don’t think it is possible to be more Orwellian or proletarian! ;-{
***************************************
It is nice to end with a hearty laugh. Thanks.
The real intent behind the “Kaya Identity”:
V CO2 = W Population × X (GDP/Population) × Y(Energy/GDP) × Z(CO2/Energy)
Note the units properly cancel, so that the result on the RHS is the same units as the LHS.
Note that there is nothing about this that is an identity – without units, it looks like:
V = W * X * Y * Z
V varies for any change in W, X, Y or Z.
You cannot construct this “identity” algebraically:
V = V
…
V = W * X * Y * Z ???
Well Chasmod, I don’t like arbitrary exclusions.
I prefer that “Primes have no factors other than one (1) and themselves.” That pretty much limits it to TWO factors only.
And 1 has only 1 and itself (1) as its two factors.
So in my book, one (1) IS a prime number, and if I wrote a math book, it would say that.
Well my original number theory math book, which I did not write, said precisely that.
The arbitrary exclusion, is juvenile in the extreme.
g
Some real world examples expressed again, in GDP per capita:
Singapore’s GDP per capita is 1.5 times that of Hong Kong’s but it produces half the CO2 emissions per capita of Hong Kong!
Hong Kong’s GDP per capita is 48 times that of Bangladesh but Hong Kong’s CO2 emissions per capita are only 13.5 times larger!
Singapore’s GDP per capita is 70 times that of Bangladesh but Singapore’s CO2 emissions per capita are just 7 times larger!
None of these relationships are directly proportional. They demonstrate either inverse or fractional rates of proportion.
The only way to resolve the impasse is to imagine incredible efficiencies for energy production in the cases that don’t follow the ‘model’.
This of course, would be absurd but in this post-normal world, who knows, anything is possible!
It is clear to me, when looking at real examples, that the directly proportional relationships of the “Kaya” are erroneous.
The the real world is not represented by the model.
krischel says:
July 15, 2014 at 3:28 pm
The point krischel, is that an Identity (A mathematical term.) is tested by replacing its variables with values. An Identity is true for all possible values of its variables such that the RHS equals the LHS.
What you have written (below) is a formula and it is an arbitrary one:
V = W * X * Y * Z
As an identity:
v ≡ w*x*y*z
v=3, w=4, x=5, y=6, z=7
3 ≡ 4x5x6x7
3 ≡ 840
RHS is not equivalent to LHS
As an equation:
v=3, w=4, y=6, z=7
3 = 4xxx6x7
3 ÷ 4x6x7 = x
3 ÷ 168 = x
x = 0.017857142857143
As a formula:
v = w*x*y*z
w=4, x=5, y=6, z=7
v = 4x5x6x7
v = 168
The propaganda value of the Kaya is in its claim to scientific rigour. However, it is meaningless as a formula or equation and is of dubious value as an Identity.
krischel says: July 15, 2014 at 3:28 pm
Exactly; better stated than I. If you then include the units they are supposed factor down so that the units remaining on the right are the same as those on the left – as a check. If they do not then the formula would be invalid.