Diving into the Deeps of Decarbonization

[UPDATE: Comment from Anthony: There has been a tremendous amount of discussion and dissent on this topic, far more than I ever would have imagined. On one hand some people have said in comments that Willis has completely botched this essay, and the Kaya identity holds true, others are in agreement saying that the way the equation is written, the terms cancel and we end up with CO2=CO2. It would seem that the cancellation of terms is the sort of thing that would rate an “F” in a simple algebra test. But, I think there’s room for both views to be right. It seems true that *technically* the terms cancel, but I think the relationship, while maybe not properly technically equated, holds as well. Here is another recent essay that starts with Willis’ premise, where CO2=CO2 and expounds from there. See: What is Kaya’s equation?

Further update (modified 3AM 7/12/14): Willis has posted his response in comments, and due to my own travels, I have not been able to post it into the body of the message until several hours later, see it below. – Anthony]

Guest Post by Willis Eschenbach

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:

$CO2_{emissions} = Population * \frac{GDP}{Population} * \frac{Energy}{GDP} * \frac{CO2_{emissions}}{Energy}$

That was where I lost it …

Now, at first glance that looks kind of reasonable. I mean, emissions must go up with population and with GDP per capita, and go down with energy efficiency.

Here’s why I laughed. Lets apply the usual rules of math to that equation. We know that if a variable occurs both on the top and bottom of a fraction, we can cancel it out. Starting from the left, Population on the top cancels Population on the bottom. Then GDP on the top cancels GDP on the bottom. Then Energy on the top cancels Energy on the bottom … and we’re left with …

$CO2_{emissions} = CO2_{emissions}$

Pretty profound, huh? CO2 emissions are equal to CO2 emissions. Who knew?

OK, now let’s build their equation back up again. But instead of using gross domestic production (GDP), we’ll use gross beer production (GBP) instead.

$CO2_{emissions} = Population * \frac{GBP}{Population} * \frac{Energy}{GBP} * \frac{CO2_{emissions}}{Energy}$

Note that this is identical to and equally as valid as their whiz-bang equation, in that it simplifies down to the same thing: CO2 emissions = CO2 emissions.

And as a result, the clear conclusion from my analysis is that the best way to fight the evil menace of CO2 is to figure out a way to make beer using less energy …

Now, there’s a carbon reduction program I could get behind.

Best wishes to all,

The Usual Request: If you disagree with someone, please quote the exact words you disagree with. This prevents misunderstandings, and lets us all understand your objection.

PS—Due to a cancelled flight, I’m stuck here in a hotel in LA on my way back from the Ninth International Climate Change Conference, which I’ll write about another time, and sitting in my hotel room wishing I were home. Not much to do but read boring UN documents … at least this one was funny.

PPS—Although it’s not mentioned in the document, their goofy equation is known as the “Kaya Identity“. Apparently, the number of innumerate people on the planet is larger than I had feared.

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

Willis Eschenbach says:

July 11, 2014 at 8:43 am

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,

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

And a final update from Anthony:

While Willis wants to cut me some slack, and I thank him for that, I’m ultimately responsible for all the content on this website, whether I write it or not. While some people would like nothing more than to have content they deem “wrong” removed, such things generally present a catch-22, and cause more problems than they solve. Of course some people would be pleased to have WUWT disappear altogether. Some days, I’m one of them, because it would allow me to get my life back.

The value is being wrong is learning from it. If you don’t learn from it, then being wrong deserves every condemnation thrown at you. I plan on being wrong again, maybe as soon as today, though one never knows exactly when your training and experience will lead you down the wrong path. In this case I was wrong in thinking that this simple terms cancellation argument pretty much made the Kaya identity useless. I’m still unsure how useful it is, or whether its usefulness is mainly scientific or political, but rest assured I now know more than I ever thought I would know about it, and so do many of you. And there’s the value.

I thought this was relevant, and worth sharing:

“For a scientist, this is a good way to live and die, maybe the ideal way for any of us – excitedly finding we were wrong and excitedly waiting for tomorrow to come so we can start over.” ― Norman Maclean

Thanks for your consideration – Anthony Watts

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Daniel G.

July 10, 2014 3:08 pm

Michael 2 says:

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

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.

Chucky77

July 10, 2014 3:09 pm

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.

Will Nelson

July 10, 2014 3:10 pm

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.

Michael 2

July 10, 2014 3:14 pm

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”.

Curt

July 10, 2014 3:16 pm

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.

Daniel G.

July 10, 2014 3:16 pm

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.

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.

DD More

July 10, 2014 3:21 pm

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’.

Daniel G.

July 10, 2014 3:23 pm

Michael 2:

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.

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

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:

Pete Brown

July 10, 2014 3:23 pm

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.

Michael 2

July 10, 2014 3:25 pm

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.

george e. smith

July 10, 2014 3:30 pm

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.

Daniel G.

July 10, 2014 3:31 pm

Michael 2 says:

the whole thing is speculative, interdependent, circular.

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

Robert V

July 10, 2014 3:32 pm

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

Michael 2

July 10, 2014 3:34 pm

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.

Daniel G.

July 10, 2014 3:37 pm

Michael 2 says:

But that’s not how the formula is written.

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

Michael 2

July 10, 2014 3:38 pm

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.

Daniel G.

July 10, 2014 3:41 pm

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.

Daniel G.

July 10, 2014 3:50 pm

usurbrain says:
July 10, 2014 at 11:48 am

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

Because of decreasing energy intensity.
usurbrain says:
July 10, 2014 at 11:48 am

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

That is consistent with CO2 emissions reduction.
usurbrain says:
July 10, 2014 at 11:48 am

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

There is no inconsistency.

Matthew R Marler

July 10, 2014 3:51 pm

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.)

Will Nelson

July 10, 2014 3:55 pm

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.

Will Nelson

July 10, 2014 3:57 pm

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 2

July 10, 2014 3:58 pm

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

July 10, 2014 3:59 pm

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.

Matthew R Marler

July 10, 2014 4:03 pm

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?

gnomish

July 10, 2014 4:06 pm

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.