[xyzzyz]

Doesn't this (and by extension, Curch-Turing) rely on the assumption that the universe is discrete? Provided it were not, and one were able to harness infinite precision, one could presumably make a new symbolic system based on it.

That's a valid point -- if you read it in a certain way, the Church-Turing hypothesis indeed states that continuous models are no more powerful than the discrete ones. In fact, we have every reason to believe it's true. See [1], and references [BCGH07], [GCB08] in that paper.

[1] - http://perso.ens-lyon.fr/yassine.hamoudi/wp-content/uploads/...

[nightcracker]

The Church-Turing hypothesis only applies to functions that apply on discrete data. If the data itself is also continuous it does not apply.