How real are real numbers? (2004)

Re:How real are real numbers? (2004) by xyzzyz on Monday April 10, 2017 @05:57PM (#14082914)

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/...

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Re:How real are real numbers? (2004) by nightcracker on Monday April 10, 2017 @06:02PM (#14082945)

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

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