Re: Man on the sun
All you need is a super-Turing computer. Like, for instance, an Analogue X Machine.
Hypercomputing machines aren't counterexamples to the Halting Problem proof, since the proof only establishes that the HP is not computable (or, if you prefer, "effectively computable").
You could just as well state that the HP can be solved by a magical all-knowing oracle. It's not an interesting claim. (That's not to say there's no value in hypercomputing research,1 just that "hey, a hypercomputing machine could solve the HP!" isn't in itself a productive observation.)
The same applies to "secure" cryptographic backdoors. We can imagine various non-realizable systems for achieving them, but as we're unable to construct any of them, that doesn't support Wray's thesis.
(Technically, of course, there are uncertain2 - possibly-correct - hypercomputing designs which can be realized. That doesn't help with the HP, though, and I don't see it helping with crypto backdoors; we already have classical protocols for converging on the correct output of a decryption function.)
1Though certainly some people have argued there isn't.
2And nothing is certain anyway, if you're logical. Doxastic logic shows that any reasoner of sufficient power can never believe in its own consistency, without thereby becoming inconsistent.
Biting the hand that feeds IT
