RE: Proportions of Infinity

From: Ben Goertzel <ben.domain.name.hidden>
Date: Sat, 24 May 2003 18:28:47 -0400

> >This is where we make closest contact. There are an uncountable
> >infinity of factorial programs written in Fortran.
>
> I can spot a mistake here: There is a one to one correspondance between
> computer programs and integers. Think of a computer program as
> another way
> of writing an integer, in another base.
>
> Jean-Michel Veuillen

yeah, you're right, that statement about factorial programs in FORTRAN is
not right

If one is willing to consider infinite-length FORTRAN programs, then there
are indeed an uncountable infinity of programs write-able in FORTRAN.

However, a "factorial program" presumably has got to return the answer to "n
factorial" within a finite period of time. So, define two factorial
programs as equivalent if the sets of instructions they execute before
returning the answer to "n factorial" are equivalent. (Two equivalent
programs may differ in (potentially infinite) "junk DNA" segments). Then,
if we assume a computer processor that operates at finite speed, we can
conclude there is a countable number of equivalence classes of factorial
programs, and that each equivalence class contains a finite program.

-- Ben Goertzel
Received on Sat May 24 2003 - 18:28:36 PDT