I think that a good deal of the 'mathematical thinking' that goes on in our heads is not mathematics at all, but rather thinking about physical analogies.
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"The brain is a logical machine, but it is not a computer."
"I would like to make a confession which may seem immoral: I do not believe absolutely in Hilbert space any more."
"Truth is much too complicated to allow anything but approximations."
"The computer is the only machine that can be taught to do anything."
"The only way to understand a system is to build it."
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