In Part 1, I laid out the simmer scenario as an alternative to explosion, stagnation, and collapse, in which growth in the coming millennia slows down but remains significant.

In this post, I want to suggest that if our intuitions contradict the plausibility of large long-run growth rates, that’s so much the worse for our intuitions.

Comparing different sized economies

A large rate of compound economic growth means that pretty soon, we’ll have to support multiple current-world-economies per atom in the galaxy. Holden explains why he thinks this implausible:

What would it mean, though, to value a single experience 10^71 times as much as today’s entire world economy? One way of thinking about it might be:

“A 1 in 10^71 chance of this thing being experienced would be as valuable as all of today’s world economy.”

Or to make it a bit easier to intuit (while needing to oversimplify), “If I were risk-neutral, I’d be thrilled to accept a gamble where I would die immediately, with near certainty, in exchange for a 1 in 10^71 chance of getting to have this experience.”

How near-certain would death be? Well, for starters, if all the people who have ever lived to date accepted this gamble, it would be approximately certain that they would all lose and end up with immediate death.

So to personally take a gamble with those kinds of odds … the experience had better be REALLY good to compensate.

We’re not talking about “the best experience you’ve ever had” level here - it wouldn’t be sensible to value that more than an entire life, and the idea that it’s worth as much as today’s world economy seems pretty clearly wrong.

We’re talking about something just unfathomably beyond anything any human has ever experienced.

Holden is claiming that the reason we can’t have 2% growth for thousands of years is that eventually, this leads to an atom being worth 10^71 times the current world-economy. This would require you to have a 10^71 times preference for that atom over everything the current world produces. And this would mean that you should accept near certain death in exchange for an infinitesimal chance to experience the value this atom produces.

But Holden’s logic leads to some crazy implications when applied to other scenarios:

The GDP per capita of America is more than twice that of Greece. Would you play Russian Roulette with half the chambers loaded in order to migrate from Greece to the US?

The GDP per capita in the Roman Empire was about 50x smaller than that of modern America.^[1] In order to avoid being transported back to ancient Rome, would you accept 50/51 odds of immediately dying?

I think Holden is making two incorrect assumptions:

Happiness scales linearly with economic value.

Holden assumes that because the value of goods produced in the future will be far greater, the value of the experiences those goods will support will be correspondingly large. But this doesn’t seem necessarily true to me. My life is much much better than the life of an average citizen of ancient Rome. But is it 50 times better? Do I have a 50x preference to be in the present than in the past? Is a Greek person’s life only half as good as an American’s? No.

Your willingness to accept death scales linearly with happiness.

Okay, so becoming a median subject of Rome would be a pretty shitty existence. I probably have 5x the net experience (total pleasure - suffering) of someone living back then. Suppose an evil fairy comes to me and says, either you get transported back to the Roman Empire - or you can gamble with your life. If you choose to gamble, you get a 1/6th chance of staying in 21st century America, but you get killed in the remaining 5/6th of draws.^[2] Most people would say no and accept their fate as a Roman peasant.

I don’t think this is just irrational risk-aversion. It has to do with the fact that dying (even painlessly) is a really negative experience - not just the cancellation of a potentially positive future.

Holden’s thought experiment seems like a mistaken way of testing our intuitions about growth. Just because the far future produces MUCH more value than the present does not mean you will have experiences that are proportionally blissful in the future. And even if you did, that still doesn’t mean that you would be willing to trade your current life for this future with almost certain odds of dying in the process.

Against our intuitions of growth

Our intuitions about the amount of value a single atom could sustain are likely to be extremely unreliable.

To show an example of what I mean, I want you to guess how many bits of information just a single hydrogen atom can theoretically encode. I really want you to guess before you continue reading.

It turns out that a single hydrogen atom can store 4 million bits of information^[3]. If your guess was significantly less than that, then you should update against your intuitions about how much valuable stuff we can do with a single atom.

For a more concrete example, per capita GDP in the US over 150x greater than in pre-1000 AD societies. Imagine telling an ancient Egyptian that the stuff an average person 3000 years from now would be producing will be worth 150x what he is producing. Is he likely to understand how that is possible? Just adopt his frame of reference for a minute. Even if each farmer produced 5x the crops, each craftsman built 5x the widgets, and each scribe wrote 5x the manuscripts, that still leaves him with a 30x disparity to account for. This scenario would seem as absurd to him as the notion of one current world economy per atom seems to us.

More broadly, we should expect our intuitions to map onto reality in situations that are close to us (both in time and space) and consistent with our previous experiences. The size of the economy in 10,000 years is neither of those things.

A physical limit on growth would be weird

What would it mean for there to be physical limits on growth? There would have to be some universal constant - like the speed of light or the mass of a neutron - representing the maximum amount of value that can squeezed out of an atom. It would mean that there is a best possible thing - it is physically impossible to create something valuable. It’s possible that the most valuable thing is a constant that can fall out of a physics theorem, but that seems like a weird outcome to me.

Admittedly, it would also be weird if the amount of value you could derive from a single atom was unbounded. But I just want to point out that the weirdness goes both ways. There’s no resolution to the question about the physical limits of growth that is not going to be counterintuitive, so the “huh?” factor shouldn’t be a massive update either direction.

1. ^{^}

   And the Roman Empire was quite wealthy by any but the most modern standards. A recently as the 1776, Edward Gibbon noted in The Decline and Fall of the Roman Empire that, “If a man were called to fix the period in the history of the world, during which the condition of the human race was most happy and prosperous, he would, without hesitation, name that which elapsed from the death of Domitian to the accession of Commodus.”

2. ^{^}

   Unless I’m misunderstanding his argument, Holden has to defend both assumptions. Notice that if you bite the bullet on one of these assumptions, the other one becomes even more absurd. For example, if the ratio of GDP per capita between two places corresponds exactly to my preference between them (as per assumption 1), then that means I have a 50x preference for remaining in the modern US rather than the Roman Empire. With a 50x preference, assumption 2 implies that I should be willing to risk 50/51 odds of death in order to avoid being transported back to the Roman Empire. That seems absurd to me.

3. ^{^}

   From Anders Sandberg’s The Physics of Information Processing Superobjects.