- More on “multiple world-size economies per atom”
By Holden Karnofsky 8 min read

More on “multiple world-size economies per atom”

A follow up on "This Can't Go On" for the skeptical.

In This Can’t Go On, I argued that 8200 more years of today’s growth rate would require us to sustain “multiple economies as big as today's entire world economy per atom.”

Feedback on this bit was split between “That is so obviously impossible, 8200 years of 2% growth is an absurd idea - growth will have to slow much before then” and “Why is that impossible? With ever-increasing creativity, we could increase quality of life higher and higher, without needing to keep using more and more material resources.”

Here I’m going to respond to the latter point, which means expanding on why 8200 years of 2% growth doesn’t look like a reasonable thing to expect. I’m going to make lots of extremely wild assumptions and talk about all kinds of weird possibilities just so that I cover even far-fetched ways for 2% growth to continue.

If you are already on team “Yeah, I don’t see the world economy growing that much,” you should skip this post unless you'd enjoy seeing the case made in a fair amount of detail.

How we COULD support “multiple world-size economies per atom”

I do think it’s conceivable that we could support multiple world-size economies per atom. Here’s one way:

Say that we discover some new activity, or experience, or drug, that people really, really, REALLY value.

Specifically, the market values it at 10^85 of today’s US dollars (that’s ten trillion trillion trillion trillion trillion trillion trillion dollars). That means it's valued about 10^71 times as much as everything the world produces in a year right now (combined).1

Then, one person having this experience2 would mean the size of the economy is at least $10^85. And that would, indeed, be the equivalent of multiple of today’s world economies per atom.3

To be clear, it’s not that we would’ve crammed multiple of today’s world economies into each atom. It’s that we would’ve crammed something 10^71 times as valuable as today’s world economy into a mere 10^28 atoms that make up a human being.

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.”4
  • 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.5
  • But this really isn’t coming anywhere close to communicating how bad the odds would be for this gamble. It’s more like: if there were one person for each atom in the galaxy, and each of them took the gamble, they'd probably still all lose.6
  • 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.

Blowing out the numbers more

Imagine the single best second of your life, the kind of thing evoked by Letter from Utopia:

Have you ever experienced a moment of bliss? On the rapids of inspiration maybe, your mind tracing the shapes of truth and beauty? Or in the pulsing ecstasy of love? Or in a glorious triumph achieved with true friends? Or in a conversation on a vine-overhung terrace one star-appointed night? Or perhaps a melody smuggled itself into your heart, charming it and setting it alight with kaleidoscopic emotions? Or when you prayed, and felt heard?

If you have experienced such a moment – experienced the best type of such a moment – then you may have discovered inside it a certain idle but sincere thought: “Heaven, yes! I didn’t realize it could be like this. This is so right, on whole different level of right; so real, on a whole different level of real. Why can’t it be like this always? Before I was sleeping; now I am awake.”

Yet a little later, scarcely an hour gone by, and the ever-falling soot of ordinary life is already covering the whole thing. The silver and gold of exuberance lose their shine, and the marble becomes dirty.

Now imagine, implausibly, that this single second was worth as much as the entire world economy outputs in a year today. (It doesn’t seem possible that it could be worth more, since the world economy that year included that second of your life, plus the rest of your year and many other people’s years.)

And now imagine a full year in which every second is as good as that second. We’ll call this the “perfect year.” According to the assumptions above, the perfect year would be no more than about 3*10^8 times as valuable as the world economy (there are about 3*10^8 seconds in a year).

And now imagine that every atom in the galaxy could be a person having the perfect year. This would now be about 10^70 * (3 * 10^8) = 3*10^78 as much value as today’s world economy. 2% growth would get us there in 9150 years.

(A crucial and perhaps counterintuitive assumption I'm making here, throughout, is that "2% growth" means "2% really real growth" - that whatever is valuable, holistically speaking, about annual world output today, we'll get 2% more of it each year. I think this is already the kind of assumption many people are making when they say we don't need more material to have ever-increasing wealth. If you think the 2% growth of the recent past is more "fake" than this and that it will continue in a "fake" way, that would be a debate for another time.)

And 1200 years after that, if each year still had 2% growth, the economy would be another ~20 billion times bigger. So now, for every atom in the galaxy, there’d have to be someone whose year was in some sense ~20 billion times better (or "more valuable") than the perfect year.

We’re still only talking about ~10,000 years of 2% growth.

New life forms

It’s still conceivable! Who knows what the future will bring.

But at this point it’s very intuitive to me that we are not talking about anything that looks like “Humans in human bodies having human kinds of fun and fulfillment.” An economy of this value seems to require fundamentally re-engineering something about the human experience - finding some way of arranging matter that creates far more happiness, or fulfillment, or something, that we would value so astronomically more than even the heights of human experience today.

And I think the most natural way for that to happen is something like: “Discovering fundamental principles behind what we value, and fundamental principles of how to arrange matter to get the most of it.” Which in turn suggests something more like “Once we have that level of understanding, we start to arrange the matter in the galaxy optimally, and quickly get close to the limits of what’s possible” than like “We grow at 2%, every year, for continuing thousands of years, even as (as would happen with e.g. digital people) we become beings who can do as much in a year as humans could do in hundreds or thousands of years.”

But it could still happen?

I guess? This was never meant to be a mathematical proof of the impossibility of 2%/year growth. It’s possible in theory.

But at this point, seeing what a funky and fundamentally transformed galaxy it would require within 10,000 years, what is the affirmative reason to expect 2%/year growth for that long a period of time? Is it that “This is the trendline, and by default I expect the trendline to continue?”

But that trendline is only a couple hundred years old - why expect it to continue for another 10,000?

Why not, instead, expect the longer-term pattern of accelerating economic growth to be what continues, until we approach some sort of fundamental limit on how much value we can cram into a given amount of matter? Or expect growth to fall gradually from here and never reach today's level again?

The last couple of centuries have been a wild ride, with wealth and living conditions improving at a historically high rate. But I don’t think that gives us reason to think that this trend goes to infinity. I believe the limits are somewhere, and it looks like sometime in the next 10,000 years, we’re either going to have to approach those limits, or stagnate or collapse.

Hopefully I’ve given a sense for why it seems so unlikely that there will be 10,000 more years in the future that each have 2% or greater growth. Which would imply that each of the last 100+ years will turn out to be one of the fastest-growing 10,000 years of all time.

If you'd like to comment on this post, this would be a good place to do so.

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  1. Today’s economy is a bit less than $10^14 per year (source). $10^85 = $10^14 * 10^71. 

  2. (And paying full price for it, in a way that gets recorded by GDP statistics, which could get a bit hairy.) 

  3. See previous estimate of 10^70 atoms in the galaxy. 

  4. This assumes that one values one’s own life not much more than a year of the world economy’s output. I do not expect that I will see enough disagreement on this point to want to write another post on the matter, but it’s possible.

    It is also making an iffy assumption about "risk-neutrality." In reality, one might personally value this experience much less than 10^71 times as much as one's own life, while still paying resources for it that would be sufficient to save an extraordinarily large number of other people's lives. It's hard to convey the same kind of magnitudes by appealing to impartiality, so I went with this intuition pump anyway; I think it does give the right basic sense of how mind-bogglingly large the value of this experience would be. 

  5. The calculation here would be: if there are 10^10 people alive today (this is "rounding up" from ~8 billion to 10 billion), and each has a 10^-71 (1 in 10^71) chance of winning the gamble, then each has a (1-10^-71) chance of losing the gamble. So the probability that they all lose the gamble is (1-10^-71)^(10^10), which is almost exactly 100%. 

  6. Similar calculation to the previous footnote, but with a population of 10^70 (one for each atom in the galaxy), so the probability that they all lose the gamble is (1-10^-71)^(10^70), which I think is around 90% (Excel can't actually handle numbers this big but this is what similar calculations imply). 

  7. (Footnote deleted) 

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