3 ms·
>> 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 correc
by misterman0 7y ago
>> 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 7y agoI'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 7y agoI'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".