Juergen wrote >The infinite computational histories are countable. The continuum is not. > >The concepts of dovetailing and continuum are incompatible.
But you can write a program which dovetails on the reals ! I have already explain in the list why there is no contradiction with cantor diagonal proof of the non enumerability of the real. It is no more astonishing than the existence of a short program which generate all the finite string, including those which are very long and chaitin incompressible. The trick is to generate them *all*. >There is no program generating the uncountable set of all reals. There is no program generating a *list* of all the reals. >There only is a program generating countably many prefixes of reals. Yes, but the dovetailer generates, for each real, all its bigger and bigger prefixes, and that is called traditionnaly, generating the real. And the dovetailer do that for each real, and so generates all the uncountably many reals. >How to distinguish those from the countably many prefixes of the >countable rational numbers? Locally you cannot. Globally the topology is quite different. The invariance lemma (see my last short paper on consciousness) entails that if I am a machine the probabilities are defined globally. Bruno
