Diving into the Deeps of Decarbonization

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

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

Guest Post by Willis Eschenbach

pathways to deep decarbonizationAnother day, another new piece of mad garbage put out by the UN. It’s called “pathways to deep decarbonization”, all in lower case (8 Mb PDF). Their proposal is to get CO2 emissions down to zero.  I didn’t get far into it before I cracked up laughing and lost the plot.

It starts with the following definition:

Deep decarbonization requires a very significant transformation of energy systems. The ultimate objective of this transformation is to phase out fossil fuel combustion with uncontrolled CO2 emissions. Only fossil fuels in conjunction with CCS [carbon capture and storage] would remain.

But that wasn’t the funny part. That was just depressing. The funny part came later.

Now, out here in the real world the most charitable way to describe this lunacy of forcing the nations of the world to give up fossil fuels is to … to … well, now that I think about it, there is no way to describe this as anything but a pathetic joke which if implemented will cause untold economic disruption, disaster, and death.

In any case, in order to figure out how to “phase out fossil fuel combustion”, they go on to describe what they call the “principal drivers” of CO2 emissions, viz:

The simplest way to describe the deep decarbonization of energy systems is by the principal drivers of energy-related CO2 emissions—for convenience, since the focus of this chapter is on energy systems, we simply refer to them as CO2 emissions. CO2 emissions can be expressed as the product of four inputs: population, GDP [gross domestic production] per capita, energy use per unit of GDP, and CO2 emissions per unit of energy:

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

That was where I lost it …

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

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

CO2_{emissions} = CO2_{emissions}

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

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

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

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

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

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

Best wishes to all,

w.

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

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

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

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

Willis Eschenbach says:

Well, yesterday was a long day. Up early to get to the airport, and this time the flight actually flew. Go deal with the rental car. Roll on home.

Then change clothes, I’d spent the night without luggage. Hang out with the gorgeous ex-fiancee and catch up. Put in a load of wash. Put the trash in the trash bin, the recyclables in their bin, the kitchen scraps in the garden waste bin. Roll all three of them up the driveway to the street. Unpack. Pack. Wash the dishes. Make coffee. Scrub the toilet.

Then when I got around to opening up my computer in the afternoon, after waking up from its normal sleep and running for about 15 minutes … it died. Dead. As in when I turned it on, It ran for about 5 seconds, and croaked …

So … that meant another 45 minute drive to the “local” Apple store. It also meant about an hour’s worth of waiting for an appointment. Then another three hours while they worked on the machine before finally getting It to run again. Net result?

It’s now 10 PM, and I’m back where I was last night … on line again. Oh, and a couple hundred bucks lighter.

Anyhow, that was how my day went. I hope Bart had more fun than I did.

Regarding the comments, I’m overjoyed that there is much discussion of the issue. My point, albeit poorly expressed given some of the comments, was that since the Beer Identity Is equally as true and valid as the Kaya Identity, it is obvious that we cannot use the Kaya Identity to “prove” anything.

So yes, the Kaya Identity is true, but trivially so. We cannot depend on it to represent the real world, and it can’t show us anything.

For example, folks upstream said that we can use the Kaya Identity to show what happens if the GDP per capita goes up by say 10%. According to the Kaya Identity, emissions will also go up by 10%.

But according to the Beer Identity, if Gross Beer Production per capita goes up by 10%, then CO2 emissions have to go up by 10% … and we know that’s not true. So clearly, neither identity can serve to establish or demonstrate anything about the real world.

What I tried to say, apparently unsuccessfully, is that by itself, the Kaya Identity cannot demonstrate or show or prove anything about the real world. If there is anythlng true about it, that truth must exist outside of the Kaya Identity. Otherwise the Beer Identity would be a valuable guide to CO2 emissions … but we know that’s not true.

Finally, l hear rumblings that Anthony shouldn’t have published this piece of mine. This totally misunderstands Anthony’s position in the game. The strength of WattsUpWithThat is not that it is always right or that it publishes only the best stuff guaranteed to be true.

The beauty and value of WUWT that it is the world’s premier location for public peer review of climate science. On a personal level, WUWT is of immense use to me, because my work either gets falsified or not very quickly … or else, as in this case, there’s an interesting ongoing debate. For me, being shown to be wrong is more valuable than being shown to be right. If someone can point out my mistakes, it saves me endless time following a blind alley.

And indeed, there is much value in the public defenestration of some hapless piece of bad science. It is as important to know not only which ideas are wrong but exactly why they are wrong. When Anthony publishes scientific claims from the edges, generally they are quickly either confirmed or falsified. This is hugely educational for scientists of all kinds, to know how to counter some of the incorrect arguments, as well as giving room for those unusual ideas which tomorrow will be mainstream ideas.

So it is not Anthony’s job to determine whether or not the work of the guest authors will stand the harsh light of public exposure. That’s the job of the peer reviewers, who are you and I and everyone making defensible scientific comments. Even if Anthony had a week to analyze and dissect each piece, there’s no way that one man’s wisdom can substitute for that of the free marketplace of ideas … which is why it’s not his job. Bear in mind that even with peer review, something like two-thirds of peer reviewed science is falsified within a year. And Anthony is making judgements publish/don’t publish on dozens of papers every week.

So please, dear friends, cut Anthony some slack. He’s just providing the arena wherein in 2014 we practice the blood sport of science, the same sport we’ve had for a few hundred years now, ripping the other guys ideas to bits, also known as trying to scientifically falsify another person’s claims that you think don’t hold water. It is where we can get a good reading on whether the ideas will stand up to detailed hostile examination.

It is not Anthony’s job to decide if mine or any other ideas and expositions and claims will wtthstand that test … and indeed, it is often of value for him to publish things that will not stand the test of time, so that we can understand exactly where they are lacking.

So please remember, Anthony is just providing the boxing ring. It is not his job to predict in advance who is going to win the fight. His job is to fill the cards with interesting bouts … and if this post is any example, he is doing it very well.

Best to everyone,

w.

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

And a final update from Anthony:

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

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

I thought this was relevant, and worth sharing:

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

Thanks for your consideration – Anthony Watts

The climate data they don't want you to find — free, to your inbox.
Join readers who get 5–8 new articles daily — no algorithms, no shadow bans.
0 0 votes
Article Rating
682 Comments
Inline Feedbacks
View all comments
Pete Brown
July 10, 2014 10:17 am

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

Daniel G.
July 10, 2014 10:20 am

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

Pete Brown
July 10, 2014 10:20 am

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

Daniel G.
July 10, 2014 10:28 am

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

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

Frederick Davies
July 10, 2014 10:31 am

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

Zeke
July 10, 2014 10:32 am

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

john robertson
July 10, 2014 10:35 am

Thanks Willis,terrible and funny, more and more I come to believe the UN uses Monty Python as an instruction/training manual.
So some here say; “Its an Identity”.
Sure is , identifies you as being from the new math school, how does this “equation make you feel?”.
Richard Courtney clearly defines the identity of this idiocy.As a political statement devoid of any value dressed up as algebra.
It does not matter how much you modify the variables, short of dividing by 0, this equation is CO2=CO2.
This is intergovernmental maths.
Perfect for those policy meetings , where absolute idiocy abounds as all the mandarins nod wisely and cover their butts.
Actually the equation is a perfect summary of modern govt policy.
Predetermined conclusion=(consultation/verbiage)* (verbiage/consultation)*Predetermined conclusion.

Dr. Doug
July 10, 2014 10:45 am

Nancy C (10:10 a.m.):
You address me but then respond to someone else.
Nonetheless, the issue is simply this:
The ratios as such express regularities. The components (numerator and denominator) do not vary independently. Thus, Energy/GDP is meaningful, but Willis’s Energy/GBP is not.
GDP and population do not vary independently of each other.
Neither do GDP and energy use, nor energy use and carbon emissions.
The ratios among these “variables” exhibit regularities — although, of course, the values and details of these regularities may change over time. GDP per capita may rise.
The separate ‘variables’ (GDP etc.) do not vary independently. Their interdependence is expressed in ratios.
Daniel G. (9:55 a.m.):
I take it that by “variables” you mean that the ratios (not their components) are meaningful and vary more or less independently of each other. Yes!

gnomish
July 10, 2014 10:46 am

“so the equations for how many M&Ms I’ve got is M = C * B/C * P/B * M/P
So if I know how many M&M per packet, and packets per box, and boxes per crate, and the number of crates, I can easily calculate the number of M&Ms. This is the Kaya method.”
john wright! remember this page!
look at C * B/C
the first C should be replaced by a different label, like N (the number of crates)
the fallacy of the M&M analogy comes from false declaration of 2 independent entities as the same,
when you change the first C, you must also change the second C.
doing that is just dividing by reciprocal and is always 1. this is a useless result.
heh- once i was looking at illuminated manuscripts. i noticed that sometimes the creator would run out of space for the words and crowd them into the margin or jam them in somewhere.
it was like he had to have them in there cuz they were holy writ he was garnering spiritual coin by copying so devotedly. and then it struck me- he was copying- he was illiterate and was not copying words, to him it was copying divine symbols.
that’s what this numerology of the crimatologist cult reminded me of.
(the comment that ‘they are using common core and their algorithms work as expected’ was too brilliant!)
another thing came to mind:
the hadith’s say a mozzie man must sit to pee. i got to wondering, tho- if you’re wearing a jellaba, do you really need to be told? and why would i tell somebody? wouldn’t it be far more useful to spot a real dummy from a distance by the wet spot?
and yet, here i find myself trying it… maybe cuz i like to sit around and don’t like puddles on the seats…

JK
July 10, 2014 10:51 am

Nancy C mistakes me for Dr Doug (which is OK as I think Dr Doug was making the same point as me, only more concisely).
She says ‘You can’t arbitrarily change them or hold them constant. PLEASE, do yourself a favor and just plug some numbers into that equation. You’ll quickly find that what you said, “CO2 emissions are proportional to population” is not actually true according to that equation, no matter what you try!’
Ok, let’s try it with some numbers.
Take a desert island, maybe with some coal near the surface.
population = 100
GDP / population = 10
(that means GDP must equal 1000)
energy / GDP = 10
(on average the islanders need to burn 10 lumps of coal to produce 1 unit of GDP)
CO2 / energy = 1
(each lump of coal releases 1 unit of CO2).
CO2 = 100 x 10 x 10 x 1 = 10,000
What happens if we try doubling population ASSUMING that
GDP / population
energy / GDP
CO2 / energy
stay constant?
Now:
population = 200
GDP / population = 10
(that means IF our assumption holds, THEN GDP must equal 2000)
energy / GDP = 10
(on average the islanders need to burn 10 lumps of coal to produce 1 unit of GDP)
CO2 / energy = 1
(each lump of coal releases 1 unit of CO2).
CO2 = 100 x 10 x 10 x 1 = 20,000
So, making this assumption was somthing I tried and found it was true that CO2 is proportional to population.
Nancy C said that I “can’t arbitrarily change [these ratios] or hold them constant”. But you can see that is just what I did above. However, what we really need to ask what does this assumption mean in the real world? It can be done, but is it useful? What it means is that on average each person on the island is producing and consuming the same goods as before.
Is that realistic? It depends. If the demographics are the same we have doubled the number of workers and the number of dependents such as children, it could be a good starting point. If we started with 100 workers and added 100 children, then probably not – likely GDP / population would drop.
Even if we just double the number of workers, GDP / population may rise. We have known since Adam Smith that the division of labour is limited by the size of the market. With more people we can get more specialisation and raise productivity.
But thinking about constant GDP / population as an imaginary analytic starting point is useful.
The other ratios are useful in a similar way. Energy / GDP held constant means that the make up of economic activity remains the same. The balance between energy intensive iron making and low energy yoga instruction stays in the same ratio. Again this is a useful analytic starting point for thinking about economic change. CO2 / energy held constant means that energy technology does not change. The islanders do not invent more efficient boilers, or move from coal to gas. Once again, this will never be exactly true, but it is a useful analytic starting point.
Compare this to the breakdown:
CO2 emissions = Al Gore’s Waistline * GDP/Al Gore’s Waistline * energy/GDP * CO2 emissions/energy
It’s just as true as arithmetic. And it’s true that IF we ASSUME
GDP / Al Gore’s Waistline
is constant then CO2 emissions would be proportional to Al Gore’s Waistline. But we need to ask the exact same question: what does this assumption mean in the real world? The answer is nothing at all. It is not an assumption that corresponds to anything meaningful, even as an imaginary analytic starting point.
So I think that’s the difference. If you want to say that GDP / population is just as useless for understanding the economy as GDP / Al Gore’s Waistline then that’s another argument. But again I would point to the way that GDP / population is very widely thought of as an important statistic both before and outside the climate debate.

July 10, 2014 10:52 am

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

Pete Brown
July 10, 2014 10:53 am

richardscourtney says:
July 10, 2014 at 8:56 am
“So, I have no intention of answering meaningless questions which divert from the important fact that
The equation is a political tool provided by a political organisation for political purposes.”
It’s a policy tool, but you’re nearly there. You only disagree with it though because you think it disagrees with you! And you only think that because you haven’t taken the time to understand it or its uses. And you’ll disagree with anything that you think disagrees with you, whether you’ve taken the time to think it through and research it or not!
Think about this:
FIRST, Willis Eschenbach wrote and published on the world’s leading climate science site a sneering, mocking piece laughing at how stupid the Kaya identity is and all the people who ever referred to it, and
ONLY THEN did he even find out for the first time that it has a name and that it is called the Kaya identity!,
AND ONLY THEN, presumably, did he start to research it and find out what it is and what it is used for, and by whom.
And that is the kind of arrogance people used to have to go to SKS for…
I absolutely despair of the lot of you…

Nancy C
July 10, 2014 10:57 am

sigh. It doesn’t matter whether my ratios are meaningless, all that matters is that they can be calculated.
Daniel G, whether ratios that share variables can be set independently of one another depends on how many ratios and how many variables. Sometimes there’s independence, sometimes not. In the case of the kaya identity as expressed above, definitely not. It’s a simple case of number of variables and number of equations.
Let’s try something. Let’s do as Dr. Doug suggested and hold those 3 ratios constant. For convience, let’s say they are:
GDP/Population = 1
energy/GDP = 1
CO2emis/Energy = 1
Now you have an equation where, as Dr Doug said, CO2 Emissions are proportional to population:
CO2emis = Population * 1 * 1* 1
Let’s say population is 9 billion. Now CO2emis = 9,000,000,000. It’s unitless, but that’s fine, we’re working a math problem now, not a physics problem. (If we wanted to we could get it back to a physics equation by just multiplying population by a constant of appropriate size and units. But it shouldn’t matter, if the math in one works, the math in the other should work.)
Okay, since now we know CO2emis = 9E9 we should be able to calculate the other variables.
CO2emis/Energy = 1, so we know energy = 1.1E-10
energy/GDP = 1 so, GDP = 9E9
GDP/Population = 1 so, Population = 1.1E-10
So clearly population can’t be 9 billion because that would imply that population must be .00000000001111…
The only way this set of equations works is if population is = 1. There is only one option. In fact, since we have 4 equations and 4 variables, we knew from the start there would only be one solution. You could set any of the ratios to any constants you could imagine, and you’d get a similar unique solution because you’d always have 4 equations and 4 variables. Population would never be able to vary, it would always be completely determined by the values of the other ratios.
So, if as Dr. Doug said, you hold those 3 ratios constant, then, yeah, I guess in some sense CO2 emissions are proportional to population, but only trivially, since as soon as you set those 3 ratios to constants you also set population to a constant: it can’t be varied or the relationship no longer holds.

Pete Brown
July 10, 2014 10:58 am

As I think American idiom would have it,
I can’t believe how much Dr Roy Spencer was low-balling it…

Alan Robertson
July 10, 2014 10:58 am

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

TerryS
July 10, 2014 10:59 am

Here is the equation with the terms re-arranged.
CO2 = CO2 *(Population/Population)*(GBP/GBP)*(Energy/Energy)
Since everything in any of the brackets evaluates to one, for all values except zero, you can not infer any relationship between any of the terms so, for example, you can not infer that increasing or decreasing Energy will have any impact on CO2. Neither can you infer that a change in Population will result in a change in CO2, Energy or GBP.
The authors of the report might have called the equation the “Kaya Identity” but that does not make it an identity. It is, in fact, a tautology since it evaluates, for all values of all terms except zero, to 1.

July 10, 2014 11:00 am

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

Lichanos
July 10, 2014 11:02 am

You are not being fair here. It’s called an “identity” because it is supposed to express a simple relationship, i.e., the component elements to aggregate CO2 emissions. If it did not reduce to a tautology, it would be wrong.
It’s not a ‘scientific’ equation, such as the ones physicists work with when they try to solve for an unknown variable. (Or algebra students, for that matter.) It’s intended for policy maker – economist types. I believe the way they have stated it is very bad – and you have demonstrated why – because the CO2 emissions on the left is the aggregate emissions (observed or desired), and the CO2 emissions on the right is actually part of an average efficiency rating to be observed or set as desired. When I dip into economics texts, I find this stuff sort of mind boggling, but that’s the way it is.
Despite its rather glorious sounding name, all it’s supposed to do is allow you to demonstrate that, given CO2 emissions held steady, and, say, population rising, something else has to change, such as the ratio of CO2 emitted to energy produced. Or, given the desire to reduce CO2 emissions, something else has to change. Nothing fancy.

Alan Robertson
July 10, 2014 11:03 am

pimf… good one, Willis
there’s a learning curve to my new scaled- down keyboard and I ain’t learned much yet

RH
July 10, 2014 11:04 am

Daniel G. says:
July 10, 2014 at 10:28 am
“…snip….
Take voltage for example. In a diode, the relation between voltage and current is not linear, but resistance is still defined the same way. And:
V = IR”
—————-
Also:
V = Population*GDP/Population*Energy/GDP*V/Energy

Daniel G.
July 10, 2014 11:05 am

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

Nope. When GDP increases alongs with the population increase, GDP per capita doesn’t decrease porportionally to population increase.
In this very long comment section, people have said I’m making unfounded asssumptions. Ok, what assumptions I’ve made that are still unfounded?

TRM
July 10, 2014 11:06 am

I am so embarrassed. I totally missed the cancellation 🙁
Population = Population / 1 ….. so CO2=C02
Nice.

Daniel G.
July 10, 2014 11:08 am

RH says:

Also:
V = Population*GDP/Population*Energy/GDP*V/Energy

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

Nancy C
July 10, 2014 11:09 am

JK, thanks for sticking with this, as I’m sure most people find it tedious. I bothered to look at the pdf and find the relationship expressed this way:
CO2emissions = Population x (GDP/Population) x (Energy/GDP) x (CO2/Energy)
This is different from Willis’ version in that he’s given the CO2 variables the same name, implying they were the same thing, but actually they’re not.
I think I admitted in previous comments that I was only referring to the relationship “as expressed here” and that if there was a problem with the way Willis represented it, that would be a valid criticism.
If someone upthread had already expressed it this way “the CO2 on the right is not the same variable as the CO2 on the left”, and I missed it, I apologize.
But yeah, it looks like that’s the problem. If they were the same, Willis would have been right, since they’re different, he was wrong.

JK
July 10, 2014 11:09 am

Nancy C
wrote:
“Okay, since now we know CO2emis = 9E9 we should be able to calculate the other variables.
CO2emis/Energy = 1, so we know energy = 1.1E-10
energy/GDP = 1 so, GDP = 9E9
GDP/Population = 1 so, Population = 1.1E-10
So clearly population can’t be 9 billion because that would imply that population must be .00000000001111…”
Seriously?
If CO2emis = 9e9 and CO2emis/Energy = 1 then Energy = 9E9
then energy/GDP = 1 implies GDP = 9E9
then GDP/Population = 1 implies Population = 9E9
This looks consistent to me.
Anyway, I’m afraid I don’t have time to continue with this thread.

1 10 11 12 13 14 28