How does that make a difference to your argument? You have a deterministic algorithm that claims to compute the digits of Chaitin's Omega. That contradicts a result established in 1936. That's 83 years ago. Nobody's found a flaw in Turing's argument in all this time. Are you saying Turing's wrong? Or that Chaitin's wrong? Or what exactly?i mean yes technically its deterministic, but i bet you can't predict the hundredth value before hand without doing the math.
Ok first, what is a pseudo-random TM? There is such a thing as a nondeterministic TM in which at each state, all possible paths are taken. It's already been proven that nondeterministic TMs have no more computational power than deterministic ones. That is, the set of functions that each class of machine computes is exactly the same.my argument is: you can a) generate pseudo random turing machines b) estimate whether they halt, and c) use that data to determine an approximate value for chaitin's omega.
i admit, it's not perfect, but it should be close enough for most purposes.
You can't computably approximate Omega because that would solve the Halting problem. That was proven impossible in 1936. Do you understand this point?then use this to approximate Chaitins Omega .
that;s basically what im doing. im generating a rational number that's approximately equal to chaitins omega.Now what you could do, would be to take the sequence of finite truncations of the digits of Omega.
Ok. But you're a long way from your original post. I don't think I understand exactly what your point is anymore. There is no TM that can approximate Omega to arbitrary precision. We seem to be agreed on that now. Or not. I'm no longer sure what we're talking about.that;s basically what im doing. im generating a rational number that's approximately equal to chaitins omega.
(say equal to the first 20 binary bits, and then diverges)
Of course you can approximate any random bitstring with finite truncations. But to do that you already have to have the entire bitstring at your disposal. How do you do that if the bitstring is random? How do you determine the first digit?my point is: you can generate a rational number to any degree accuracy of chaitins omega.
can you come up with a finite string of chaitins omega that cannot be converted to a rational number?