Lightbucket

He’s best known for information theory, but that’s just the start of it.

Claude Shannon, 1916 – 2001

He also came up with the sampling theorem. It was his idea to use Boolean logic to describe digital circuits. He was one of the independent inventors of binary computing. He contributed to cryptography and he pioneered computer chess. He made a fortune from his investments in early electronics companies, and he built a juggling robot and the “Ultimate Machine”.

Boolean Algebra For Digital Electronics

INPUT		OUTPUT
A	B	A  AND  B
0	0	0
0	1	0
1	0	0
1	1	1

As his first contribution to engineering, he invented digital electronics in the form we know it today – circuits assembled from “logic gates”.

If you’ve ever dabbled in electronics, you’ll immediately recognise the diagram on the right. It’s the symbol for an AND logic gate and its truth table. The whole of digital electronics is based on switches like these, which perform Boolean logic operations. These “logic gates” are the basic building blocks of all digital electronic circuits.

But who first had the idea that a two-valued Boolean algebra (one with members “true” and “false”, or “1” and “0”) could describe the operation of two-valued electrical switching circuits? After all, it’s quite a conceptual leap to get from electrical switches to Boolean algebra.

Claude Shannon came up with that idea while he was still a graduate student. He had a summer job at Bell Labs in 1937, where he was working with switching networks of bewildering complexity – over a hundred electrical relays wired together to control the operation of a differential analyser. He drew on his mathematical expertise to try to get to grips with the sheer complexity of the problem, and realised that Boolean algebra could be used to analyse and design these large networks of electrical relays. The problem could also be turned around: networks of switches could be used to perform binary arithmetic. He wrote this up as his master’s thesis ^[1] in 1940. This thesis laid the conceptual foundations for digital electronics as we know it. It has been called “one of the most important master’s theses ever written…a landmark in that it helped to change digital circuit design from an art to a science” ^[2].

Information Theory

Having made the connection between Boolean algebra and electrical relays to create the concepts underpinning modern digital electronics and binary computers, Shannon then went one better. He noticed a link between binary information channels and the concept of “entropy” in statistical thermodynamics. He developed these ideas to create information theory ^[3], the work he is best known for. His most notable scientific paper, “A mathematical theory of communication”, was published in 1948.

This was quickly followed by the Nyquist–Shannon sampling theorem. That theorem explains why, for example, a CD needs to have a 44.1 kHz digital data rate to get a 20 kHz analog frequency response.

The impact of information theory is all around us. The maximum data rate possible on a noisy communication channel; the maximum lossless data compression possible on a computer file; the effect of error correction codes – these are all results from information theory. All communication systems rely on the ideas he developed.

Investor In Technology Companies

“If you’re so smart, why aren’t you rich?” goes the saying.

Shannon never had that problem – he became extremely wealthy despite having little interest in his own finances. He had created the key engineering concepts behind the computer and communications industries, and he understood those industries very well indeed. Some of his engineering colleagues had founded small start-up companies, and he put some money into a couple of those start-ups. The companies were called Teledyne and Hewlett-Packard. He also invested in a promising radio company called Motorola. His investments earned a 28% annual return on investment between 1966 and 1986, beating Warren Buffet’s 27% over the same period ^[4].

That Other Stuff

Shannon introduced powerful, simplifying, enormously useful new concepts that transformed electronics and communications. For his own amusement, though, he could also go to the opposite extreme. He built an elaborate mechanical contraption called the “Ultimate Machine” ^[2], whose sole function was to switch itself off – it is perhaps the most perfectly pointless machine conceivable. I’ll let Arthur C. Clarke explain it:

The Ultimate Machine	(by kugelbahn.ch)

“Nothing could be simpler. It is merely a small wooden casket, the size and shape of a cigar box, with a single switch on one face. When you throw the switch, there is an angry, purposeful buzzing. The lid slowly rises, and from beneath it emerges a hand. The hand reaches down, turns the switch off and retreats into the box. With the finality of a closing coffin, the lid snaps shut, the buzzing ceases and peace reigns once more. The psychological effect, if you do not know what to expect, is devastating. There is something unspeakably sinister about a machine that does nothing – absolutely nothing – except switch itself off.”

Arthur C. Clarke, Voice Across the Sea

Then there was THROBAC (THrifty ROman numerical BAckward looking Computer), the calculator operating with Roman numerals, and Theseus, the maze-solving mechanical mouse. And he built a machine to solve Rubik’s Cube, and wrote a poem in praise of the Cube, “A Rubric on Rubik’s Cubics”.

And he pioneered chess-playing computers.

And, of course, there was the juggling^[5]: the juggling theorem, the Massachusetts Institute of Jugglology, and the famous juggling machine…

References