On Dec 29, 2008, at 1:22 PM, Ben Goertzel wrote:
Well, some of the papers in the references of my paper give formal mathematical definitions of hypercomputation, though my paper is brief and conceptual and not of that nature. So although the generic concept may be muddled, there are certainly some fully precise variants of it.
My comment was not really against the argument you make in the paper, nor do I disagree with your definition of "hypercomputation". (BTW, run spellcheck.) I was referring to the somewhat anomalous difficulty of deciding whether or not some computational models truly meet that definition as a practical matter.
Anyway the argument in my paper is pretty strong and applies to any variant with power beyond that of ordinary Turing machines, it would seem...
No disagreement with that, which is why I called it a "meta- comment". :-)
Super-recursive algorithms, inductive Turing machines, and related computational models can be made to sit in a somewhat fuzzy place with respect to whether or not they are hypercomputers or normal Turing machines. A Turing machine that asymptotically converges on producing the same result as a hypercomputer is an interesting case insofar as the results they produce may be close enough that you can consider the difference to be below the noise floor, and if they are functionally equivalent using that somewhat unusual definition then you effectively have equivalence to a hypercomputer without the hypercomputer. Not strictly by definition, but within some strictly implied error bound for the purposes of comparing output (which is all we usually care about).
The concept of non-isotropic distributions of random numbers has always interested me for much the same reason, since there seems to be a similar concept at work there.
Cheers, J. Andrew Rogers ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=123753653-47f84b Powered by Listbox: http://www.listbox.com
