The Myth of Hypercomputation

[gusl]

[FOM] The Myth of Hypercomputation

One argument against hypercomputation
is that even if someone hands me a hypercomputer (that solves the halting
problem, say), I cannot verify that it really works as advertised from a
finite set of finite measurements. Without the ability to make a finite
verification, I can never really "know" that the hypercomputer is "really
solving" the halting problem.

This is good stuff. I'll have to look at it later.



Also:

Héctor Zenil & Francisco Hernández-Quiroz - How might the human mind be computationally more powerful than Turing machines?

Finally, there are several arguments by Bringsjord.

I get the impression that all these arguments for hypercomputing minds are made in order to justify "romantic intuitions", i.e. they are not exploratory discoveries, which is what you would expect from unbiased scientists. I confess that I suffer from the symmetrical problem: always trying to justify my computationalist intuitions. (never mind that I may actually be a dualist in philosophy of mind)

Comments

[jcreed.livejournal.com]

A friend of mine (lincoln3) went to RPI for his undergraduate degree and had classes from Bringsjord, so I heard a lot about his arguments --- I never found them very appealing, but I never was fair enough to give them a direct listen. Thanks for the link!

[gustavolacerda.livejournal.com]

Did you forget? You've found a fatal fallacy by Bringsjord, where he claims to be using the Barcan formula.

[jcreed.livejournal.com]

Oh, did we already have a discussion about him? I did forget.

[gustavolacerda.livejournal.com]

http://www.livejournal.com/users/gustavolacerda/179597.html

[jcreed.livejournal.com]

I think the important objection to the Zenil and Hernández-Quiroz link is the one they bury on point 3 of page 19: if there is any noise in the system, then all this talk of encoding oracle tapes in real numbers is absurd. For to be able to make use of that encoding, you really need a real number stored in the brain out to truly infinite precision. Otherwise you have a finite "oracle tape", and that's only as good as plain old Turing machines.

Even as much as the uncertainty principle is abused, I think it takes effect at some point here to limit usable information in the brain to a finite quantity, at least if you want to allow me to demand confinement of the position of particles in the brain to be, well, within the skull that brain is in :)

[gustavolacerda.livejournal.com]

Zenil is now occupying my old room on Forbes!

[jcreed.livejournal.com]

crazy! I'm also impressed you found such an old entry enough to report on such a thing.

[gustavolacerda.livejournal.com]

I found this by accident while searching for entries on "Bringsjord". Last Tuesday, TJ told me about their new "amazing" housemate, so I just recognized his name now as if I'd never seen it in this context before.

Here's his site. We should say hi to him.

[bram.livejournal.com]

I'm really not disturbed at all by the possibility of hypercomputation. Just think the universe would be simpler if it didn't occur.

Really, the "not finitely verifiable" argument is like saying computation of an algorithm that takes a gigabyte is impossible because it can't be verified on a 640 K computer.