Science Frontiers ONLINE No. 86: MarApr 1993  

In extolling J. Barrow's new book, Pi in the Sky, T. Siegfried first reiterates a point made in past issues of SF, namely, that mathematics is a logical system and that we have no right to expect it is correspond structurely with a physical system. In other words, math and nature are fundamentally different entities. Nevertheless, as Barrow stated in a recent interview:
"If we were just inventing mathematics from our everyday experience, we would find that it would work really rather well in those areas from which that intuition was gained. But we find almost the opposite...It works most powerfully and persuasively in areas that are farthest removed from the everyday experience that has led to it."
Mathematics, for example, leads to verities in quantum mechanics far outside the realm of daily experience. Why is this so?
The puzzle deepens when one discovers that there are different kinds of math based upon different forms of logic (as in Euclidian and nonEuclidian geometries). Some brands of mathematics mirror reality better than others. Why?
In trying to dispose of these "whys," both matematicians and scientists fall back on the anthropic principle with all its unsatisfying tautological overtones:
"...the universe is the way it is because that's the way it has to be for anybody to be around to study it. And perhaps math works so well in studying the universe because math, too, must be the way it is in order for anybody to be around to do the calculations. So maybe the existence of communicating creatures requires a correspondence between the physical universe and mathematics. [??]"
(Siegfried, Tom; Dallas Morning News, p. 7D, January 4, 1993. Cr. L. Anderson)
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