Exponential Economist Meets Finite Physicist [link]

by Dreaded_Anomaly1 min read13th Apr 201220 comments


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A dialogue discussing how thermodynamics limits future growth in energy usage, and that in turn limits GDP growth, from the blog Do the Math.

Physicist: Hi, I’m Tom. I’m a physicist.

Economist: Hi Tom, I’m [ahem..cough]. I’m an economist.

Physicist: Hey, that’s great. I’ve been thinking a bit about growth and want to run an idea by you. I claim that economic growth cannot continue indefinitely.

Economist: [chokes on bread crumb] Did I hear you right? Did you say that growth can not continue forever?

Physicist: That’s right. I think physical limits assert themselves.

Economist: Well sure, nothing truly lasts forever. The sun, for instance, will not burn forever. On the billions-of-years timescale, things come to an end.

Physicist: Granted, but I’m talking about a more immediate timescale, here on Earth. Earth’s physical resources—particularly energy—are limited and may prohibit continued growth within centuries, or possibly much shorter depending on the choices we make. There are thermodynamic issues as well.

I think this is quite relevant to many of the ideas of futurism (and economics) that we often discuss here on Less Wrong. They address the concepts related to levels of civilization and mind uploading. Colonization of space is dismissed by both parties, at least for the sake of the discussion. The blog author has another post discussing his views on its implausibility; I find it to be somewhat limited in its consideration of the issue, though.

He has also detailed the calculations whose results he describes in this dialogue in a few previous posts. The dialogue format will probably be a kinder introduction to the ideas for those less mathematically inclined.


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Of course, there's an economist with two degrees in physics just over there ... I believe he's opined "I know of no law limiting economic value per atom".

Right, but he's also expressed scepticism that you could produce arbitrarily high value per atom. Ah, found the link and it was in the context of the number of people-equivalents worth of value we could produce per atom:

It seems just physically impossible to create 10^140 or more lives we would value like ours per atom, even considering quantum computing and black hole negentropy. But could individual living standards be that high?

To say that someone had a standard of living 10^140 times a subsistence level means that 10^-140 of their income could buy a subsistence level standard of living. Someone with a subsistence level living standard, and a square root type risk-aversion, would reject an offer to jump to today’s world average living standard, twenty times higher, if they could instead roll 69 ten-sided dice, and only get to jump to this 10^140 higher standard if all the dice came up 1. (Someone with a fourth root risk aversion would prefer to roll 35 dies.) That is just how incredibly fantastic this 10^140 higher living standard would be. A living standard 10^2950 higher is far far more fantastic.

Ah, thanks for that - I just remembered the pithy soundbite.

I find myself somewhat confused then, because my recollection is that he has consistently argued that economic growth will not be able to continue indefinitely, and that from some point in the future for the vast remaining part of human history we will be living in a static society.

As I remember, Robin argued that we will be living in a Malthusian society, not a static one. In a Malthusian society, population growth keeps the per capita resources at a subsistence level, but the overall society continues to grow.

This particular straw physicist seems to suffer greatly from the lack of imagination and a bunch of internal inconsistencies. For example, 400 years at 10x per century growth corresponds to 10000 the current energy consumption, still just 25% of the power provided by the sun, all of which is currently beamed back into space without boiling any oceans along the way.

Well, they rule out a lot of material at the beginning by agreeing to not be 'space cadets'.

Circa 1700...

Second, agricultural limits impose a cap to growth lest we starve ourselves. I’m not talking about French invasion, the nead for enough priests to avoid damnation, etc. I’m talking about being able to grow enough food to support the craftsmen. I assume you’re happy to confine our conversation to England, foregoing the spectre of an industrial revolution, mass production, automating agriculture, international trade, etc.

Why should the economist forgoe all the resources of the light cone?

Because exponential growth is faster than the light cone. If you allow the galaxy, instead of just Sol, you only add on a few centuries; you don't significantly change the underlying reality.

Correct me if I'm merely displaying staggering stupidity, but ... Imagine a future where energy is so abundant per capita and cats are considered so cute that viewing one lolcat image for ten seconds is considered more valuable than the equivalent of a billion barrels of oil. If one is a lolcat image creator, is one not then a contributor to the economy? If you develop a new type of cable which permits faster transmission of lolcats, have you not contributed to economic growth - and, I should add, contributed more meaningfully than someone who invents more efficient solar panels?

I have a feeling this whole "debate" hinges on some jerrymandered definition of "economy."

Awesome! This question bears directly on the intersection of thermodynamics, computational complexity theory, economics, and identity instantiation, and hence I cannot resist answering.

The question boils down to the relave scalability of different effects with respect to each other:

1) How much computation can you produce per unit energy?
2) How much utility (or how many happy-people-equivalents) can you produce per unit of computation?

If reversible computing is possible, then the answer to 1) is that you can produce as much as you want, producing arbitrarily small energy losses (due to the inability to achieve perfect irreversibility e.g. due to friction in implementation.)

This would render pessimism about 2 irrelevant, it seems.

Edit: And furthermore, if we accept the notion that a virtual being's subjective experience of time depends soley on the program that instantiates them (e.g. a species of substrate independence that is widely accepted here), then such beings would subjectively live forever, even if reversible computing is constrained by having to be arbitrarily slow. (Although people would have to accept uploading themselves, of course.)

I don't see what he means by improving the quality of life while the GDP remains constant. I admit that GDP has imperfections, such as only measuring goods and services that are sold, but ignoring that any improvement in the quality of life is an improvement in the GDP. If it makes your life better, it's worth more.

I figure that economic growth would continue forever, but at a decreasing rate. The long-term growth would be more logarithmic, if not asymptotic, than exponential. Also, I think it could last longer than that physicist seems to think. Even assuming we don't leave the solar system, there's no reason to keep it in its current state. If we can do better in a thousand years by disassembling the planets, then at some point it will be worth while to mine from them to build space-stations, in which case we will disassemble the planets.

The physicist in the dialogue says:

We need to ignore inflation as a nuisance in this case: if my 10 units of energy this year costs $10,000 out of my $100,000 income; then next year that same amount of energy costs $11,000 and I make $110,000—I want to ignore such an effect as “meaningless” inflation: the GDP “growth” in this sense is not real growth, but just a re-scaling of the value of money.

This strikes me as just wrong. If energy prices rise proportionally to GDP but other prices don't, there's still real GDP growth.

This strikes me as just wrong. If energy prices rise proportionally to GDP but other prices don't, there's still real GDP growth.

His example didn't need to be there; he could have just said "let's use real values instead of nominal values" and the economist would have agreed with him. I understood that as an aside to the reader that he was going to deal with real changes (in which the percentage of your income you spend on X changes), rather than nominal changes (in which the percentage stays the same).

The next lines in the dialogue are:

Physicist: Then in order to have real GDP growth on top of flat energy, the fractional cost of energy goes down relative to the GDP as a whole.

Economist: Correct.

This seems to require the statement as actually written, not just a steelmanned version of it. If all the physicist had said was "let's use real instead of nominal values", he wouldn't get to make this inference.

I don't think that's the case. Suppose we deal with real numbers- so $10,000 represents my fraction of the static population's static energy consumption. If my consumption grows from $100,000 to $200,000, the fraction of my consumption that energy represents is now 5% instead of 10%. That means that energy is really getting cheaper- if I continued spending 10% of my consumption on energy, I would get more energy (in whatever form it's useful to me in, which may actually represent less watts).

That is, your statement- that energy prices rise with GDP and other prices don't- is not what the physicist is ruling out. The physicist is ruling out that all prices rise. If they don't, then in order for some prices to rise other prices must fall- for GDP growth to continue but energy to have a smaller share of GDP, energy must be getting cheaper, which seems odd for a scarce resource.

I think the economist should argue that energy prices will rise but energy quantities will stay stagnant. It seems to me that you could have a future scenario in which almost all of income is spent on energy.

Indeed, what happens if, instead of talking about this in terms of dollars, we talk about it in terms of watts? (I'm using watts instead of joules because income is typically dollars / year, instead of just dollars.) If energy is scarce, it's a natural store of value. We've built a Dyson sphere, we've grown the population such that the average person has an income of 1 kW. GDP per capita is now stuck at 1 kW forever- but the sort of goods and services that I can buy with my income of 1 kW will get more and more impressive over time. The price of an experience in terms of Joules will decrease as time goes on. Right?

Much of the value increases he's describing- that the physicist later calls "development" rather than "growth"- strikes me as the sort of "inflation" that he's ruling out. Really, what's going on with a static store of value like that chasing higher and higher utilities is deflation. George Selgin put out a book called Less Than Zero that's relevant.

[edit]Hm, thinking about this again, depending on how you count up "GDP" this might depend on how frequent trading is. I'm presuming you count it in terms of net income plus consumption, rather than net revenue; the first is the more physical quantity but the second is easier to measure.

Claim A: "If the price of energy rises as fast as GDP, then this GDP growth is inflation rather than real growth."

Claim B: "If the price of energy and all other prices rise as fast as GDP, then this GDP growth is inflation rather than real growth."

Claim C: "For GDP to continue really growing (exponentially) given constant energy, the price of energy must continue falling (exponentially) relative to GDP."

I claim that C follows from A, and that the physicist asserts A and deduces C, but I claim that A is false and that C is also false. I claim that B is true, but that C does not follow from B, and that the physicist would agree with B but goes beyond claiming B in also claiming A, as indeed he needs to in order to deduce C. What part of this do you disagree with?

Hmm. I think I might be agreeing with you, but I think I need to unpack what we mean by "inflation" to make sure I'm not tripping myself up somewhere.

Suppose I need 10 kW to survive and power my computer, and spent all of my non-energy income on funny cat videos. We start off with me spending $10k on energy and $90k on cat videos, and I get 9,000 cat videos. We then move to me spending:

  1. $11k on 10 kW, and $99k on 9,000 cat videos. (B)
  2. $11k on 10 kW, and $99k on 9,900 cat videos. (A)

The first situation, once nominal changes in the value of the dollar are removed, is identical to the old situation, which is claim B. The second situation appears to have both real and nominal changes- a kW more costs me 990 cat videos when it used to only cost me 900 cat videos.

I think I've found a disagreement: what happens when the price of energy rises faster than GDP growth? Clearly there's a real change going on, but I don't think it has to be real GDP growth. (Suppose the number of dollars it takes to buy energy skyrockets, but it's all "owed to ourselves" in that the static energy budget of humanity is split up in some egalitarian way, and the supply is completely inelastic with regards to price. GDP, as it measures both trade in energy and trade in services, seems like it could get arbitrarily high, and that the percentage of GDP devoted to energy would also approach 100% in that case.)

I think that Claim C does not follow from either Claim A or Claim B, and that the physicist means to assert Claim B. (I agree that B is true and claim that A is underspecified.)

It looks to me like this is the economist off his game. If you use energy as the currency, this issue becomes much, much easier to think about- and it becomes obvious that if you have economic growth (more cat videos per year) and a fixed energy supply (only 10 kW a year) that the price of energy must grow, not fall (one kW must buy more cat videos, not less; one cat video costs less kW, not more).

Yes, it's wrong. Relative price increases != inflation. If GDP growth declined but energy production remained the same, the price of energy wouldn't fall concordantly with GDP (as it would if we were talking about all prices rather than relative prices).

Edit: Which doesn't necessarily affect his point, I think he is actually trying to talk about the general rise in all prices.

Edit again: Never mind, I read further on, he thinks rising energy prices growing in accordance with GDP is "not real growth," just inflation. If people's standard of living has gone up, it's real growth.

Edit once more for an example: A crazy new iphone comes out and it's so awesome! But the input prices of all the other things I normally use also go up by the exact amount the new iphone would cost me, so it's not growth. :(

But that's not right. If you like the iphone more than some of the other things you use--WAY more than some of the other things you use--then you ditch those things and you buy the iphone. Win for you. If we're talking about replacing basic inputs like food, maybe energy prices cancel out some productivity gains there, but for the huge swathe of things we classify as entertainment or information, the claim doesn't apply.

he thinks rising energy prices growing in accordance with GDP is "not real growth," just inflation

And this claim is essential to his argument, because he has an argument why (once we have a Dyson sphere) energy prices won't rise much slower than nominal GDP, but he does not have an argument why prices in general won't rise much slower than nominal GDP.