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 <meeke...@verizon.net> 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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