Closing the connection with Shannon and Silicon Valley

The key connection between Shannon and the logic of digital, was the transistor, and then immediately the flip/flop. The rest really were different encodings (read graphs) of nested flip/flops. The original flip/flop was a plug in replacement for the relay, but the flip flop circuit model had already been demonstrated in vacuum tubes. Flip flop, like a light switch, on or off.

Then they started building tiny chips with 8,16,256,... in a row. However many flip flops the programmers had available, Shannon proved that their existed trees arrangements that can get you complex graph algebras. Then came digital indexing, memory. Dennis Richie had enough linear address space to cram a kernel.

Also Shannon appears in Huffman encoding which is big in computers, and is really fundamental to nature. His career started just after the introduction of relays into Ma Bell operator stations, 1923. The manual switch board came about in the 1900 - 1910 period.

What about Harry Nyquist (1889-1976).

e worked at AT&T's Department of Development and Research from 1917 to 1934, and continued when it became Bell Telephone Laboratories in that year, until his retirement in 1954.

This guy follows Samuel Morse. Its a plot I tell you. Nyquist was big, still is all through digital. He tells us how much we can know, in the limit, at a given sample rate. He combines Samuel Morse and Fourier. What else about Morse code? Ham guys? It is a Huffman encode, the most common characters get the short dot/dash sequence.Nyquist also tell us how much voltage differential we need in the flip/flop to be stable.  He was big in designing the vacuum tube flip/flop. He also tells us how close we can separate digital streams in wire data, how fast we can tap morse code.

Who preceded Morse? Ben Franklin and the kite trick! Seriously, first proof of electron transfer, I think. Ben precedes the  battery invention, Ben used a copper key showing that it collected charge. At the time they were just then looking at charge in the lab.

John_von_Neumann, however, might take the prize here.  He was mainly jus a tool maker, a methematician, but he was a great tool maker.  Then there is special mention for Weiner and Levinson. Weiner got the random process, which Nyquist/Shannon got as SNR, but they were independent. Weiner is bounding infinitesimal measures, Shannon building more infinitesimal from the binary. Those two trails meet at Stanford with Burg and that drove a bunch of Silicon Valley, still does in multi-media.

Shannon's last fingerprints were left with Huffman encoding, and patent issues about that were a problem. The deal was Ma Ball wanted a better encoding to get more infor through the satellites. That problem is? An optimal flow problem.  It was a matter of Huffman working through various options of traversing a graph, and the result? I used it to find unattended aggregates in the  SP100, just for grins. Leading to maximum entropy formal Elliot Wave analysis, and a likely explanation for Benford's law.

Oh yes, Von Newman did work in groups, compact groups. He worked with the Haar idea that a bounding operator exists if a group of things meets some nearness criteria.  Von Newman invented the math we gonna use for semantic algebra. You see Von Newman in encoding operators for digital streams. I think you will see Von Newman in name mangling for big tables that Google does.

I have to mention Nyquist again. His job was to move Ma Bell from the electrical relay to the DeForest vacuum tube. In doing that he contributed not only to digital, but his finger prints appear all over analog radio, in channel separation, side lobe propagation.   So he is everywhere the battery operated transistor radio was, for a whole generation, still is. And he showed up in analog  magnetic tape, then in digital magnetic media, including our little hard drives. He tells us ultimately how closed we can put the magnetic pulses.

In special mention, the Levinson and Weiner systems were signal processing, then supporting the foundation for statistical economics. Adaptive Levinson asks: I the economy were a least squared spectral analyzer, what would be the optimum set of 'moments'. You get block statistics, matrix inversions, matrix factoring. The result is a Nyquist sampled economy of finite dimension, but uniform time is assumed.  Nothing Shannon did seemed to need time.
Its a plot, I tell you.