Reimagining of Schrödinger’s cat breaks quantum mechanics — and stumps physicists / Nature

I had a question that seemed too vague to put on the main site

Could it be possible to show that the set of computable problems is "dense" in the set of all problems?

That is, any problem P can be at least approximated by computable problems in such a way that solving the computable problems will give as close to a right answer to P as we're likely to care about

e.g. for the halting problem, maybe the set of all programs can be expressed as the union of an increasing sequence of sets $A_n$ such that the problem "given a program in $A_n$, determine if $A_n$ halts" is computable for each $n$

or something like that

and maybe some similar construction can be carried out for any problem

Who's afraid of artificial intelligence in China? / DW

@JackM have been looking into vaguely similar ideas relating to entropy, almost formulated exactly like you state. it appears that different computations/ algorithms are related by entropy. the closest thing have heard of to your query is maybe research into chaitins Omega... anyway chat is rarely frequented though so encourage you to try to post the question to get larger audience, also consider Computer Science...

@JackM if you post this as a question you may want to link to cstheory.stackexchange.com/questions/41424/… and compare your question to that one