poemranker ::Replying

ReplyTo a comment on It's Time by PoeticXTC.

-=Dark_Angel=-, P.I.29 Dec 2005

When you say 'deduce everything else' what do you mean? Do you mean deduce all true statements? It can be easily proven that there exist functions which are uncomputable (i.e. for any such function f there is no algorithm* to compute f(x) for all x in the domain). One such function is the function H that maps any computer program P, and input data D, to True or False, depending
on whether P halts on input D, or loops forever on input D:

i.e. H(P, D) = True if and only if program P halts on input D.

The upshot of all this is that there are true statements that are undeducible. Clearly any machine that could 'deduce everything' would have to accept these statements as given. There are infinite such statements. So there is no finite upper bound on the minimum you'd have to program a supersupercomputer to deduce everything. The interested reader is encouraged to have a look at http://en.wikipedia.org/wiki/Halting_problem

* Caveat: by 'algorithm' I mean 'Turing machine'. This covers all algorithms (and a lot more) that can be written on any computer, in any language, today. There might be an as yet undiscovered magical means of computation that could solve such problems, but if such a means exists, only Jesu would know about it, and it would be His little secret.