There’s a much simpler argument that gets the same conclusion.
Suppose we write down the position of every particle in the universe. That’s a very big bitstring. But every possible bitstring is contained within N, the set of natural numbers. Therefore, a Turing machine that prints successive integers will also enumerate all possible finite universes.
You can also omit the Turing machine and just say “consider the set N. It includes an encoding of every possible universe.”
I don’t think this has any very deep significance, though. The only lesson I draw is that the set of all natural numbers includes some large integers that have very high information content.
I don’t think so. You’re saying ‘Library of Babel’ to my ‘Simple Process that Computes Everything’. And obviously there’s a continuum between them which includes ‘a program to print out all the integers’
But I get a much stronger emotional reaction to a computation that’s actually being performed than to a record of one having been performed.
It feels like the difference is something to do with swapping space and time is important.
So now I think: What about a 1-d turing-equivalent cellular automaton running that SPCE program? Where every new row appears below the previous row, so that you can look at it either as a flat piece of paper where consciousnesses exist, or as a process in which consciousnesses exist.
But yes, I think the entire content of my post is something like OMGintegerswoo!? And even after admitting that, I still find the idea of these tables mind-blowing in an ontologically-reassuring sort of way.
I think people really care about the distinction between ‘results’ and ‘computation’.
There’s a much simpler argument that gets the same conclusion.
Suppose we write down the position of every particle in the universe. That’s a very big bitstring. But every possible bitstring is contained within N, the set of natural numbers. Therefore, a Turing machine that prints successive integers will also enumerate all possible finite universes.
You can also omit the Turing machine and just say “consider the set N. It includes an encoding of every possible universe.”
I don’t think this has any very deep significance, though. The only lesson I draw is that the set of all natural numbers includes some large integers that have very high information content.
is there some subtle point here that I’m missing?
I don’t think so. You’re saying ‘Library of Babel’ to my ‘Simple Process that Computes Everything’. And obviously there’s a continuum between them which includes ‘a program to print out all the integers’
But I get a much stronger emotional reaction to a computation that’s actually being performed than to a record of one having been performed.
It feels like the difference is something to do with swapping space and time is important.
So now I think: What about a 1-d turing-equivalent cellular automaton running that SPCE program? Where every new row appears below the previous row, so that you can look at it either as a flat piece of paper where consciousnesses exist, or as a process in which consciousnesses exist.
But yes, I think the entire content of my post is something like OMGintegerswoo!? And even after admitting that, I still find the idea of these tables mind-blowing in an ontologically-reassuring sort of way.
I think people really care about the distinction between ‘results’ and ‘computation’.