I'm hoping that analog computing will come back in the form of photonic analog computing. This would be more powerful than quantum digital computing (you know the things that people are wasting time on).
Note the fun sentence "If real computation were physically realizable, one could use it to solve NP-complete problems, and even #P-complete problems, in polynomial time. ".
We are on a wrong evolutionary branch of computing. Bits are lame-o-rama, whereas differentiable signals are pure unadulterated flavortown.
What you're describing is generally accepted to be physically unrealizable. In fact, the sentence that follows your quoted sentence cites two commonly known physical limitations that prevent the existence of your "computational class above and beyond Turing".
Whether or not there exist physically realizable computations that are not computable by a turing machine is an open question, but most physicists and computational complexity theorists seem to believe there does not exist such a class.
Roughly, a computer that can solve problems in polynomial time which do not have a polynomial time algorithm on a Turing machine, which is the same class of computers we use today.
Have you read Scott Aaronson's NP-Complete Problems and Physical Reality [1] ? He goes into some detail about why analog computing is not thought to be physically realizable (Section 6).
I'm passingly familiar. I'm not convinced. I can't really explain to you why. I feel like makes many assumptions about the architecture and workings of such a machine.
I know Scott Aaronson and all, but I won't believe it until someone tries to build one and fails.
> I'm familiar with the Turing thesis but he's wrong.
Could you at least explain in what way you think he is wrong. Surely you must guess how participants on a programming forum will react to a statement like that.
Fun fact, with analog computing, one could imagine achieving Real Computation (https://en.wikipedia.org/wiki/Real_computation) which is above and beyond Turing. completeness.
Note the fun sentence "If real computation were physically realizable, one could use it to solve NP-complete problems, and even #P-complete problems, in polynomial time. ".
We are on a wrong evolutionary branch of computing. Bits are lame-o-rama, whereas differentiable signals are pure unadulterated flavortown.