Yeah that is interesting. Maybe one way to paraphrase it is that "infinity" is very big and you can fit a lot of interesting structure there :)
It actually turns out that there are infinitely many other problems that are not Turing reducible to any of these ordinary halting problems and to which none of the halting problems are reducible.18 And all these problems have halting problems of their own, defined by the halting of computers that have access to their solutions, that are strictly harder.
Similarly with the classic essay Who Can Name the Bigger Number?
It actually turns out that there are infinitely many other problems that are not Turing reducible to any of these ordinary halting problems and to which none of the halting problems are reducible.18 And all these problems have halting problems of their own, defined by the halting of computers that have access to their solutions, that are strictly harder.
Similarly with the classic essay Who Can Name the Bigger Number?
https://www.scottaaronson.com/writings/bignumbers.html
If you have infinite space, then you can be infinitely clever ...
Who can name the bigger number? Whoever has the deeper paradigm.