I believe that Chaitin’s constant Ω could be approximated, possibly to the point where it could be "computed".<p>It's impossible to emulate a Turing machine, but you can emulate a Turing machine limited to N states. Make A runs of B random bits in said pseudo-Turing(N) machine, observe distribution of programs that halt, or exceed N. Increase A, B or N, and see if some obvious asymptotes arise as you chart the results.
Unfortunately, the article "Turing Uncomputability" is<p><i>incorrect</i> that [Gödel, 1931] was first to prove<p>inferential undecidablity of mathematical foundations. The<p>[Gödel, 1931] proof using the proposition<p><i>I'mUnprovable</i> is incorrect for foundations because the<p>proposition <i>does not exist</i>.<p>See the following for correct proofs of inferential<p>undecidablity in foundations:<p><a href="https://papers.ssrn.com/abstract=3603021" rel="nofollow">https://papers.ssrn.com/abstract=3603021</a>
The Church/Turing Hypothesis is <i>false</i> because there are<p>digital computations that <i>cannot be performed by a<p>Nondeterministic Turing Machine</i>.<p>For example, see the following:<p><a href="https://papers.ssrn.com/abstract=3603021" rel="nofollow">https://papers.ssrn.com/abstract=3603021</a><p><a href="https://www.youtube.com/watch?v=AJP1VL7shiI" rel="nofollow">https://www.youtube.com/watch?v=AJP1VL7shiI</a>
The [Church 1935] proof of the computational undecidability of<p>the halting problem is essentially the same as the [Turing<p>1936] proof. Consequently, the article under discussion<p>would be better titled "Church/Turing Uncomputability".
This blog used to be called Cantor's Paradise or something like that. Article is an ok popular-level description of uncomputability, focusing mostly on biographical details of early researchers in the field (Turing, Church, etc). As with other articles from the same blog, it mostly rehashes info well known from other sources. There's nothing exactly wrong with it, but I don't really see what is gained.<p>I'm nowhere near a real expert in this topic but almost everything I've seen in the blog so far, I've already seen elsewhere, quite a lot of it in Wikipedia. Nothing is copied or anything like that, but there are only so many ways to tell the same stories.