Good day everybody, I would love to ask You a question about proving undecidable statements with hypercomputation.
I have read a paper written by Professor T. Ord named "Hypercomputation: computing more than the Turing machine", where he writes this: " While it is sometimes claimed [4, 10] that Chaitin constant is completely patternless, this is not true. If it was, it would not be so easily describable. " " Chaitin’s results about W show not that some mathematical objects are patternless, but that they seem patternless relative to a certain amount of computational power23. The results do not show that some facts (such as the value of a particular bit of W) are true for no reason, but that a certain level of computational power is insufficient to show why these facts are true "
And this is what I would like to ask You about.
Lets for example assume that the Rieman Hypothesis(RH) is undecidable by Turing machine. Therefore there is no finite proof that would prove that RH is true. Can it be said that for us finite beeings the RH is true for no reason at all, or more precisely for unknown reason, but If we had computational capacity of a sufficiently powerful Hypercomputer we would be able to constructively prove with a proof of infinite length that RH is true?
And by this proof I don´t mean just brute forcing this problem away like computing the zeta function for all reals and look for counter example. I mean a proof more in a sense of some inaccessible uncomputable structure, that would lead to a proof for RH much like for example the use of Eliptic curves lead Professor Wiles to a proof of Fermats Last Theorem.
So basically my question is, whether there are mathematical structures or patterns that would explain, why undecidable/non-recursive functions are true.
Thank You very much for your kind answers, Have a nice day.