On 1/12/03 9:43 AM, "Damien Sullivan" <[EMAIL PROTECTED]> wrote:
>
> I'll take the risk of replying to other messages here without reading the 2
> dozen other replies first. It sounds like James is using primitive recursive
> functions, equivalent to Hofstadter's BLoop in _GEB_. Those are a subset of
> the Turing-decidable/total recursive (always halt) functions, themselves a
> subset of the Turing-recognizable/partial recursive (short for partially
> defined, vs. totally defined) functions, which are equivalent to all Turing
> machines.
This is an incorrect characterization. We aren't finding THE answer to any
problem, we are just returning the best answer in the current context,
mostly because it would take unnatural contortions for the machinery to try
and return THE answer. All the primitives down to the machinery itself
operate and compute using BEST answers ("best" in an algorithmic information
theory sense).
You can do lots of interesting quasi-recursive operations on it, and I've
even been working on a LISP-y language that takes advantage of the
machinery, but it is not fundamentally recursive in the sense you are using
it. I can't guarantee that the underlying function won't change in some
context-sensitive fashion while in the middle of computing a "recursive"
function. Changes that do occur are almost always beneficial optimizations
in the context that they occur, and if you assume that the function will be
static during the recursion you may be surprised.
And just to be clear, its obviously a Turing machine since it runs on Turing
machines and you can run any Turing machine on it. It is just very
different from normal conceptions of universal computers. But then, I could
say the exact same thing about the human brain.
Cheers,
-James Rogers
[EMAIL PROTECTED]
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