Re: Revised Computing Randomness

From: Hal Ruhl <hjr.domain.name.hidden>
Date: Wed, 18 Apr 2001 23:42:17 -0700

More detail:

Start with an axiom Aj, use it as data for a LISP expression Rj. A program
that computes the value of this expression "B" in AIT has length:
Expression + data + self-delimiter or in this case Rj + Aj +
Self-delimiter. Like this:

P = {Expression(data) + self-delimiter} computes [produces value] "B"

If P is the shortest program to do so then it is called elegant and its
length is the complexity of "B".

In an everywhere elegant cascade each P(i) is longer than P(i -1) because
the data for P(i) alone has the same complexity as P(i - 1) then you add
the complexity of the expression and the self-delimiter.

What is left is to 1) identify "everywhere elegant cascade" = deterministic
evolution of the isomorphism and 2) find an upper bound on the complexity
of the P(i).

Chaitin did the latter by putting an upper limit on the complexity an N-bit
FAS could prove an elegant program has i.e. it own complexity plus a
constant. But a deterministic cascade is already known to be an everywhere
elegant program.

A contradiction is established unless the cascade stops but it can not stop.

The only way out is a spontaneous increase in the complexity of the FAS.

Hal

     
Received on Wed Apr 18 2001 - 20:52:45 PDT