Time to share my favorite quote from Symbols, Signals and Noise by John R. Pierce, where he discusses how Shannon achieved a breakthrough in Information Theory:
> This chapter has had another aspect. In it we have illustrated the use of a novel viewpoint and the application of a powerful field of mathematics in attacking a problem of communication theory. Equation 9.3 was arrived at by the by-no-means-obvious expedient of representing long electrical signals and the noises added to them by points in a multidimensional space. The square of the distance of a point from the origin was interpreted as the energy of the signal represented by a point.
> Thus a problem in communication theory was made to correspond to a problem in geometry, and the desired result was arrived at by geometrical arguments.
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