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Comment by ainoobler | Hacker News Reader

Interesting argument. This assumes that cognition must also be happening on a compact manifold which seems like a reasonable assumption but the conclusion is somewhat counterintuitive because it means there are only finitely many personality types and ways of thinking.

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Is that counterintuitive? There's a finite number of electrons in a human brain (which fits in a space of size 1m^3), and information takes time to propagate across any distance, and humans die before 150 years; this all gestures at there being not only finitely many personality types and ways of thinking, but finitely many human mind states.

I guess that means reincarnation is real.

Assuming you're not trolling: nope, that would be an empirical question of how many brain states ever actually arise in the world during the time humans exist, and how much space and time it takes to maintain a given brain state. The universe is currently expected to stop being able to support human life at some point in the future, so the pigeonhole principle argument requires some physical parameters to be known before you can apply it; and even if the pigeonhole principle did apply, you still can't know by that argument whether any given brain-state is repeated (and if so, how many times). Things which you can deduce using only mathematics, and no physical data, are necessarily extremely weak statements about reality.

If you are a mental clone but uncausally linked then is that still reincarnation?

The universe is mathematical, all we can ever know about it is mathematical.

A very strong empirical statement about the nature of reality, and a strong statement about the nature of mathematics, neither of which everyone agrees with! (What will your reply be if we discover a halting oracle at the centre of the galaxy? Mathematics doesn't forbid that: the Church-Turing thesis is an empirical statement, and it's the empirical scientific law of induction which is what tells us that we're extremely unlikely to find a halting oracle.)

But you've missed the point: even assuming that mathematics can perfectly model the universe, you cannot use weak physical hypotheses ("human brains are finite, there is an injection from human mind-states into human brains") and fully general mathematics (the pigeonhole principle) to derive such specific strong truths as "a particular human mind-state is repeated in a predictable way in the universe". You can at best derive general truths such as "at least one human mind-state is repeated at least once, somewhere", if the universe happens to have its physical parameters set in such a way that the pigeonhole principle holds.

We do have https://en.m.wikipedia.org/wiki/Boltzmann_brain

That may appear every (10^10)^50 years according to

https://en.m.wikipedia.org/wiki/Timeline_of_the_far_future

But there may yet be more brain states than number of possible thoughts by the finite humans.

Oh, 100%, it seems extremely unlikely that multiple brain states in this sense don't code for the same thought! If nothing else, you could only avoid that with an absurdly precise definition of "brain"; any practical definition of "brain" is very likely to include matter that is physically irrelevant to at least some thoughts. I hedged with "1m^3" because the argument goes through even if you take the entire body to be the brain.

Who said this had anything to do with cognition at all? I think Turing's argument goes through with humans replaced by automata and eyes by cameras. It's just that perception has finite resolution.

I made the obvious connection. It's an original thought from me and no one else.

That's how the math works out in general unless you think some kind of soul exists.

It all follows from compactness so if the cognitive manifold is not compact then the conclusion is not true.

At this point I kind of do. The matter that goes into forming your body and brain is somewhat special, having accumulated the properties it has experiencing billions of years of traveling through the universe.

Once you die it decomposes and goes on its way, and forms something new.

Its not a "soul" in the same sense but still pretty trippy

Well, this is true only if you think cognition and thought as a pure biological process totally dependent on state of brain.

I don't think that. I'm just explaining what follows logically if the cognitive manifold is compact.

What exactly do you mean with "cognitive manifold"?

It's a made up concept and it includes all possible ways people can think anything. If you want something concrete then you can consider sheaves of finitely presented algebras on the nervous system considered as a topological space with the obvious covering relations, continuous transformations, and algebra morphisms.

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