Monday, April 13, 2009

A Trivial Exchange

SCENE: A museum containing the persona of historical figures about 100 years in the future.

Fourier: "Mathematicians rule. My particular claim to fame is the discovery that periodic functions can be represented by a sum of sinusoidal functions."

Ptolemy: "Sire, I claim priority with epicycles."

Kepler: "I proved you wrong with my ellipses for the orbital motion of the planets."

Ptolemy: "Did you ever figure out the librations?"

Aristotle: "Don't I get credit for uniform circular motion?"

Archimedes: "Are not epicycles an assembly of cycloids?"

Riesz: "What Fourier did lacks rigor. If one compares the Fourier Transform of a continuous function with that of a similar function which differs only by the value at a particular point one will find that the two transforms are exactly identical."

Nyquist: "That's a rather trivial example. From the perspective of Sampling Theory the transform of the signal with noise should differ at the sampling frequency."

Armstrong: "Suppose you made the frequency of the noise signal a function of time as in FM modulation. The energy of the noise would be distributed over many frequencies and less noticable. So the transforms could be made practically indistinguishable."

Sire: "You scientists never fail to amuse me. Was not all this foreseen and communicated through the Laws of Nature?

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