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.



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