Mathematical Hells

[Warning: Memetic hazard and philosophical trip. Also, probably incorrect. Talks about death and torture and robots.]

The universe is probably infinite, flat, uniform, and ergodic. This means not only that there are an infinity of copies of the Earth, all of them identical, all of them containing “a you” that’s reading this post written by “a me.” In fact, all possible distributions of matter happen somewhere an infinity of times.

The Many-Worlds Interpretation of Quantum Mechanics is probably correct. That means everything that “can happen” will, in “some universe.” This means all possible distributions of matter happen everywhere.

There’s a reasonable chance the process that spawned our universe was some form of Eternal or Chaotic Inflation, in which there’s a huge “field” whose local fluctuations spawn universes. In fact, due to the above, it’s likely that our universe repeats an infinite number of times.

It’s fun to think about the possibility that some strong form of Mathematical Platonism is true, and that the only thing that exists is mathematics, and our universe is no more than a mathematical structure. The implication of a myriad ways all distributions of matter can happen is left as an exercise to the reader.

(Why, yes, these are exactly Tegmark’s multiverses. They’re fun to think about.)

I listed the above possibilities in what I think is a decreasing order of probability. But suppose any one of them is true.

How do you know which “you” you are? If all things happen, why did no one ever see anything unusual? Why doesn’t Santa Claus suddenly materialise in the middle of Times Square, why does everything follow such neat and predictable laws as if there was only one way things could be?

In Quantum Mechanics, there is a thing called an “amplitude,” which is, well, a number. And the frequency with which we observe a certain outcome is proportional to the square of the amplitude of that outcome. Why? Beats me.

Some people call this probability a “measure.” That’s because there’s a part of maths called “measure theory” which deals with, amongst other things, comparing the “relative size” of infinities. So, for example, if there are an infinite number of “yous” that are in Earths and an infinite number of “yous” that are being run in a computer, a measure is something that compares “how many” there are of each of them relative to the other, even if there are an infinity of both.

I call it “magical reality fluid” because I have no idea how it works and it’s misleading to call it something that looks Serious when you don’t understand it. You might start believing you do.

Regardless, this would mean that, somehow, there’s more magical reality fluid in the “yous” that are in Earths identical to yours than in the “yous” that are Boltzmann brains and only exist for a femtosecond.

However, you have no way, even in principle of telling whether “you” are the you in this Earth or that Earth, or whether you’re being run on a computer, or what. In fact, there’s not even a question of the matter; you are all identical, the same person, so asking “which of them” is the real you is like asking whether this 3 or this 3 is the real 3.

However, there are ways of ruling out certain “classes of you” that you’re not. For example, there is probably a “you” that chose something other than you did for breakfast, or didn’t eat breakfast at all, or actually ate it when you didn’t. That you is certainly not you. I mean, it’s not you right now. They might’ve been you until yesterday, but now they’re not.

And likewise, if there is some computer that’s (and therefore an infinity of computers that are) running a you that’s identical to you up until 4AM tomorrow, when it will suddenly turn you into a talking duck with all your memories, then you won’t know until tomorrow at 4AM whether you’re one of those.

However, suppose that all the “yous” suddenly died right now, except for the yous that will turn into a duck tomorrow. Then you will never notice. Subjectively, nothing will change for you. Except now there’s a 100% probability (Well.) that you’ll turn into a duck tomorrow. There’ll be no “yous” that will experience anything different.

We have reason to suppose that the vast majority of your magical reality fluid is in Earths that were formed naturally and follow the inexorable emergent determinism of physics. In those Earths, there is very little room for variation, and most of it is likely in the form of quantum fluctuations that may not affect all that much – or maybe they do, who knows, maybe brains are quantum computers, or maybe quantum fluctuations are enough to make the uncertainty about which sperm fertilises which ovum significant. But in any case, whatever happens to one you in such an Earth probably happens to the vast majority of them. And so when you die in one Earth, you’ll die in most of them.

Subjectively speaking, though, you’ll never notice it. Because there is some magical reality fluid in versions of you that aren’t on Earths, but are nonetheless identical to you. They are you, for all intents and purposes. Except they didn’t die.

I mean, some of them did die. But after they do, subjectively, the only yous that remain are the ones that didn’t – and who, inevitably, broke the laws of physics to do so.  Past that point… all bets are off. We don’t have any way, even in principle, to predict what’s going to happen.

But worse than that is that most of these computer simulations won’t even be someone consciously simulating you. You’ll probably just be a byproduct of some other computation. You might be the consequence of the calculation of some function, or something. There’s no reason to expect, a priori, that your future computation will be benign – quite the opposite, since there are many more ways for a human to suffer and be disfigured beyond recognition than there are ways for them to thrive and have a reasonably satisfactory life.

Before you died, that didn’t really matter; the measure – pardon, magical reality fluid – of “yous” in those awful mathematical hells was so absurdly tiny compared to the fluid in deterministic Earths that the probability you’d face them was effectively zero. After all the deterministic Earths have gotten rid of you, however, you’re left with the effective zero fluid as your total fluid, and subjectively you’re… well, who the hell knows where you’ll be? Some mathematical hell, probably.

A benign superintelligence wishing to offset this risk would probably spend a reasonable amount of resources simulating what it believed were reasonable approximations of people who have died in order to try and make the most post-death magical reality fluid of them not be in a mathematical hell, but who knows if this will work, or be enough?

I have a friend who doesn’t want to be cryo-preserved because he’s afraid that humanity, in the future, has a reasonable chance of becoming horrible people who will torture past humans for fun (I want to link a certain recent SMBC comic here about robots that resurrect humans in order to inflict them the maximal amount of pain they can feel but can’t find it), and his probability for that is high enough that the negative effect offsets any of the positive effect of eternal life. The above argument says we’re screwed anyway, but he doesn’t believe it, though I have no idea why, since he’s already entertaining the idea of future humans torturing us for fun.

Ah, well. I guess it’s far-fetched anyway.

It does give the search for immortality a more urgent tone, however.

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5 Responses to Mathematical Hells

  1. Professor Frink says:

    Why assume that many worlds quantum is “probably correct?” Why not treat it as a Bayesian probability like thermodynamics.

    • pedromvilar says:

      It’s not an assumption, I actually think some form of Many-Worlds is true based on my understanding of Quantum Mechanics. But modulo limits in that understanding, and modulo the fact that “some form” still hasn’t solved the Born Probabilities, I’m not completely confident in it.

  2. If there are many me’s in mathematical hells, I disagree that this makes immortality more urgent. You talk as if, once the sensible me’s die, this makes the fact that all these me’s are in mathematical hells more bad.

    This is because you think that what matters is the magical reality fluid of me’s which are in mathematical hells, which is defined sort of like a fraction of all me’s. So when the rest of me die the fraction gets higher. But I don’t think the fraction of me’s in mathematical hells is really important. The total number, maybe. But certainly not the fraction.

    • pedromvilar says:

      No, not exactly. It’s not that these yous in the mathematical hells have more moral weight than you currently do; it’s just that, with subjective probability ~1, you will end up in one of them, unless something is done that will make your post-death yous majoritarily not in one such hell.

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