FOM: Computer-aided proofs

[Robert Tragesser]

        Joe Shipman's pondering the interaction of machines and
mathematics,  and the kinds of uncertainy that could arise (Is it the
machine that's producing this funny stuff,  or is it the mathematics?), Is
it the machine or is it the mathematics,  calls to mind the discovery of
the Gibbs Phenomenon:  Around 1900 Albert Michelson constructed and
mechanical harmonic analyzer that could go down to something like the first
80 Fourier components of a graphically presented function.  The machine
could also synthesize,  so it could as it were check its analyses. When
applied to the square wave,  the synthesis put in little bumps at the
points of "discontinuity".  Was this machine error? Michelson pondered.  He
couldn't say.  He asked Gibbs who showed that it was the mathematics. .
.the Gibbs phenomenon.
        
rbrt tragesser