On 14 May 2013, at 03:32, meekerdb wrote:
Right. It's not computing all possible functions, it's executing
all possible programs - most of which don't terminate and so don't
compute a function at all.
It computes a partial function, undefined on some arguments, but
defined on possible other arguments. That's why we have to dovetail.
Carfeul because computing a non computable function, on an argument
where it is not defined, gives an infinite computation which can be a
relevant (for our consciousness) computable process. A bit like
emulating a steady evolving physical universe: it is a non stopping
program. By the intensional Church thesis (provable from the usual
one), the UD does not just compute function, it emulates all possible
ways to compute those functions, and thus it emulates all Turing
emulable processes. Amazing, but trivial, the UD computes the
factorial function is all manner, which includes programs emulating
you in passing.
Bruno
Brent
On 5/13/2013 3:30 PM, Stephen Paul King wrote:
So all possible functions are computed equally? ISTM that some
functions would take an eternity to compute and that the number of
such vastly outnumber the recursively enumerable ones.
On Mon, May 13, 2013 at 6:24 PM, meekerdb <[email protected]>
wrote:
On 5/13/2013 2:49 PM, Stephen Paul King wrote:
Does the UD compute *all* functions or only those that are
recursively enumerable?
It computes all of them.
Brent
AFAIK, the latter, as a set, has a measure zero as a subset of the
former. This is one reason why I worry about the viability of UDA
(and AUDA), it postulates a severely restricted subset of the
possible functions as ontologically primitive without a good
argument as to why.
Just because we finite mortals can only counts in terms of natural
numbers is not an argument that All-that-Exists is limited to that
standard. Man is NOT the measure of all things!
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