Do The Math
"As far as the laws of mathematics refer to reality, they are not certain; as far as they are certain, they do not refer to reality."--Albert Einstein
I have mentioned this before but I think the Feynman Lectures linked here provide a very good example of the connection between mathematics and reality.
Einstein further expounds on the proposition:
"It would be possible to describe everything scientifically, but it would make no sense; it would be without meaning, as if you described a Beethoven symphony as a variation of wave pressure." -- Albert Einstein
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