At 12:45 PM 9/22/2014, Benjamin Udell wrote:
The laws seem for all the world like mathematical rules nontrivially operative as laws of physical quantities such as force, mass, velocity, etc. That's why the laws can be formulated as mathematical rules, in conventional mathematical symbols and formulas.
Ben, I am trying to understand how you distinguish laws and rules if "laws seem for all the world like mathematical rules." You say, That's why laws can be described by rules. Why does that work?
Like many physicists, I do not see very clearly why the free creations of pure mathematicians, like complex numbers, matrices, infinite dimensional vector spaces, and Lie groups, have turned out to so accurately and elegantly model physical systems -- systems that are themselves beyond our common sense and even our logic. I agree with Wigner, math appears "unreasonably effective," and with Peirce, " . . . it is probable that there is some secret here which remains to be discovered."
Do you not see a categorical difference between laws and rules? Howard
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