> Infinities don't enter into this. You brought it up, not me.
No, you did when you brought in Turing machines:
> Imagine a clocked-down Turing computer, whose operating speed us is so slow that we can see its operations. Now imagine the programs which cannot, in principle be run on this computer. You can't because there aren't any.
If the Turing machine doesn't have infinite capacity, I 100% can imagine programs that "cannot, in principle be run on this computer".
Furthermore, if the Turing machine has many orders of magnitude less capacity than a computer and can only run for a tiny fraction of the number of cycles before it grinds to a halt, I can imagine many, many, many programs that won't be able to run on it.
> An AI isn't infinite either.
It doesn't have to be. Just being many orders of magnitude "larger" than us is enough that it, for all practical purposes, is incomprehensible to us enough that it might as well be an entirely separate category.
An AI would be running on a computer with the same space and time bounds as the human, because the AI is just software running on the human’s computer.
If there are no infinities, then I am not sure why you brought up an infinite machine as an argument. The point is to imagine a being with orders of magnitude more processing power than our brains, it'd be able to fathom things we literally could not, even with any amount of slowness of processing. It'd be a physical limitation.
You brought up infinite machines, hence my and the other person's comment. Turing computers or machines have infinite tape. Maybe you meant to just say "computer," not "Turing computer."
Humans can use computers but only for human readable tasks. There is no guarantee that we could comprehend a superintelligence running off a supercomputer, we already don't understand neural network internals at even their current stage.
I meant a general purpose computer I the sense of a universal Turing machine, but without the infinite storage requirement. Technically that would be a linear bounded automata, but that glosses over the the universal construction of the Turing machine.
Maybe the norms in HN are different, but in my field a Turing machine is primarily a general purpose computer, and “Turing complete” describes models which can represent any Turing machine within its constraints. An “infinite tape Turing machine” is explicitly specified when needed.
Personally I’m a bit outside of the mainstream in that I never use infinities except in the case of representing an unterminated series. I reject that “infinity” as a number even makes sense as a context.
No, you did when you brought in Turing machines:
> Imagine a clocked-down Turing computer, whose operating speed us is so slow that we can see its operations. Now imagine the programs which cannot, in principle be run on this computer. You can't because there aren't any.
If the Turing machine doesn't have infinite capacity, I 100% can imagine programs that "cannot, in principle be run on this computer".
Furthermore, if the Turing machine has many orders of magnitude less capacity than a computer and can only run for a tiny fraction of the number of cycles before it grinds to a halt, I can imagine many, many, many programs that won't be able to run on it.
> An AI isn't infinite either.
It doesn't have to be. Just being many orders of magnitude "larger" than us is enough that it, for all practical purposes, is incomprehensible to us enough that it might as well be an entirely separate category.