I would bet that most of my regular readers have never known of Claude Shannon (or if they do they know of him it is through this blog).
Because of certain aspects of my recent work, I've had the opportunity to peruse some of his writings that seem "obvious" to most engineers doing research in communication theory today, and certainly to most engineers who, like me, studied the analysis and probability because we "knew" that it was needed. But if read properly, with the realization that in 1949 most engineers had never heard of a Hilbert space, one can appreciate the true brilliance of Shannon's work. Even today, come to think of it, I suspect most engineers never heard of Hilbert Spaces or mappings into different dimensions, or understood the connection between the Law of Large Numbers and their Wi-Fi connection.
In invite you to read Shannon's paper Communication in the Presence of Noise. In this paper, Shannon throws out the concept of his famous WT Theorem, the sphere hardening argument for error-free communication, provides an explanation of the threshold effect in FM based on topology - at a level that a good freshman today could understand, and hints at the topological reasoning behind why digital transmission is superior to analog transmission. And he does this all in one paper.
Sure, the math is very sloppy; one gets the feeling that Shannon was afraid of losing his audience if the words "almost everywhere" were almost everywhere. One cannot help but wince at the math in places, but one also understands that the arguments he makes can easily be rigorously formatted. Moreover the clarity of exposition, the forcefulness of his ideas, and the impression that "This guy is actually smarter than this; he's holding pointing towards something even better than what I'm reading here" seem to pervade the work.
When you understand and can extend these ideas, it is like looking into the Orignal Face of the Absolute, the mind of God, Sunyata, whatever you want to call it.
And when you figure out that people will actually pay you money to do this - good money- as long as you can extend the ideas in a way that makes money for the company, you realize you've got a pretty good racket going.
Ah, but I cannot explain William Dembski...
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