Steven D'Aprano <st...@remove-this-cybersource.com.au> writes: > I thought we were talking about discontinuities in *nature*, not in > mathematics. There's no "of course" about it.
IIRC we were talking about fractals, which are a topic in mathematics. This led to some discussion of mathematical continuity, and the claim that mathematical discontinuity doesn't appear to occur in nature (and according to some, it shouldn't occur in mathematics either). > In mathematics, you can cut up a pea and reassemble it into a solid > sphere the size of the Earth. Try doing that with a real pea. That's another example of a mathematical phenomenon that doesn't occur in nature. What are you getting at? > Quantum phenomenon are actual mathematical discontinuities, or at > least they can be, e.g. electron levels in an atom. I'm sure you know more physics than I do, but I was always taught that observables (like electron levels) were eigenvalues of underlying continuous operators. That the eigenvalues are discrete just means some continuous function has multiple roots that are discrete. There is a theorem (I don't know the proof or even the precise statement) that if quantum mechanics has the slightest amount of linearity, then it's possible in principle to solve NP-hard problems in polynomial time with quantum computers. So I think it is treated as perfectly linear. -- http://mail.python.org/mailman/listinfo/python-list