Posted: Sep 14, 2015 6:26 pm
by crank
scott1328 wrote:
Chaitin was clearly speaking in the context of computing real numbers. He was not making the claim you have put into his mouth.


But to say you can begin writing an uncomputable number out is false because all you have done with your random number generator is generate a number that equally identifies countably infinite rational number, countably infinite computable numbers, and uncountably infinite non-computable numbers.

In what sense of the word have you identified any number whatsoever with your random number generator?


Chaitin is clearly claiming what I said he claimed. All you have to do is watch the video and hear him for yourself, obviously even a quote from a Chaitin paper isn't good enough. You are getting unreasonable in the extreme. How does the context in this case in any way change the meaning of what he explicitly says? "a real number has an infinite number of digits of precision," How much more blatant can something get?

I never said I could identify one, from my very first post I said as much. I never said the random number generator would identify one, only that it could start to generate one. Put another way, stipulate an infinite sequence of random digits, that's an uncomputable. We know what .33... means, we also know what an infinite string of digits means, and we know that all reals will be represented by some combination of those digits. That is exactly what Cali's definition is. This is obvious. Your objections are all way off, either strawman or irrelevant, or plain wrong.