[misterman0]

>> His precise theorem is this: Define "LISP program-size complexity" to be the size of a LISP subroutine that examines a proof, determines whether it is correct, and returns either the theorem established by the proof (if the proof is correct) or an error message (if the proof is incorrect). Then, given a formal axiomatic system A, with LISP program-size complexity N, A cannot be used to prove that any LISP expression longer than N + 356 characters is elegant.

Doesn't this in fact prove that numbers are discovered, not invented?

He defines elegance to be "N". He defines

N = 1

356 + N != N

Thus, real numbers are real.

[Y_Y]

I'm interested in the argument at the end of your comment, but I cannot understand it as-is. Could you flesh it out a bit please?

[misterman0]

I'm fascinated by Chaitin's Constant and his use of the word "elegance". His ideas challenge my current belief system.

From the article:

>> [what is] the probability that a randomly constructed program will halt [?]

Where are you in life when this is a question that needs to be pondered? My bet is you're at a point where (when?) you question nature and/or human nature.

>> Real numbers are real

I meant to say, real numbers existed all along and were discovered, as opposed to being an invention.

What made me come to this conclusion? Here's Chaitin (paraphrased):

- run a process that through a series of operations produces a scalar, deterministically.

- alter that process.

- observe that the scalar has increased/decreased in value.

I.e. numbers are "real".