# Abstract Math and the Natural World



## Scott (May 1, 2006)

I am listening ot a series of lectures on the history of science in the 20th century. 

Anyway, this is an interesting point that might be relevant to discussions with those who believe that math and logic and mere conventions, or are otherwise not intangible. Paul Dirac used abstract math to predict the existence of the positron, or the electron's anti-particle. He arrived at this conclusion completely mathematically and without observation. He held this view because of his firm conviction that the physical world operates according to the principles of abstract math. His predictions were later verfied experimentally by others. 

There is more to the story, but it is interesting. Anyway, this achievement seems inconsistent with the view that math is simply a convention. It would seem odd that a human convention would happen to correspond to physical reality at a very comlpex and unexplored level. This achievement suggests that math is intangible and universal and yet is related to and governs the material and particular world.

Scott

[Edited on 5-1-2006 by Scott]

Reactions: Like 1


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## SRoper (May 1, 2006)

What about different geometries? Euclidian geometry, spherical geometry, and hyperbolic geometry have contradictory postulates, yet they are all "interesting." Does that mean we should stop studying the others when we are reasonably certain one of them conforms more perfectly to the world?


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## rmwilliamsjr (May 1, 2006)

see:
the unreasonable effectiveness of math at:
http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html


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## Scott (May 10, 2006)

Thanks. That is a good article.


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