Friday Hodgepodge

Four Things

Below are (just!) four things I enjoyed or found enlightening when I read A Mind at Play, the biography of the father of information theory, Claude Shannon, by Jimmy Soni and Rob Goodman.

1. Shannon's six methods for attacking a problem.

2. Shannon proved that a message could be sent with an arbitrarily small amount of error:

That insight is embedded in the circuits of our phones, our computers, our satellite TVs, our space probes still tethered to the earth with thin cords of 0's and 1's. In 1990, the Voyager 1 probe turned its camera back on Earth from the edge of the solar system, snapped a picture of our planetary home reduced in size to less than a single pixel -- to what Carl Sagan called "a mote of dust suspended in a sunbeam" -- and transmitted that picture across four billion miles of void. Claude Shannon did not write the code that protected that image from error and distortion, but, some four decades earlier, he had proved that such a code must exist. And so it did. It is part of his legacy; and so is the endless flow of digital information on which the Internet depends, and so is the information omnivory by which we define ourselves as modern. (loc. 104)

The book makes the point elsewhere that Shannon had amazing powers of abstraction. That he did so very well is attested to by the myriad practical applications of the above insight. See also Item 1.

3. As brilliant as Shannon was, he benefited greatly by having a good mentor in Vannevar Bush:

Finally, Bush took it upon himself to find a suitable dissertation project for Shannon in the field of -- genetics. Genetics? It was at least as plausible an object for Shannon's talents as switches. Circuits could be taught, genes could be taught -- but the analytic skill it took to find the logic beneath them seemed more likely to be inborn. Shannon had already used his "queer algebra" to great effect on relays; "another special algebra," Bush explained to a colleague, "might conceivably handle some of the aspects of Mendelian heredity." More to the point, it was a matter of deep conviction for Bush that specialization was the death of genius. "In these days, when there is a tendency to specialize so closely, it is well for us to be reminded that the possibilities of being at once broad and deep did not pass with Leonardo da Vinci or even Benjamin Franklin," Bush said in a speech at MIT. "Men of our profession -- we teachers -- are bound to be impressed with the tendency of youths of strikingly capable minds to become interested in one small corner of science and uninterested in the rest of the world. ... It is unfortunate when a brilliant and creative mind insists upon living in a modern monastic cell." (p. 48)

At many points, Shannon would use insights gleaned from one interest to forge ahead in a seemingly unrelated area. I am glad that Bush saw the value of this practice.

4. A strong impression about Shannon I got from the book was of benevolence. In addition to the title they chose, the authors make note of this in their last chapter:

Shannon demonstrates machine learning with Theseus in a Bell Labs short.

He did none of this consciously; he wasn't straining to give the appearance of fun. Shannon simply delighted in the various curiosities that grabbed his attention, and the testimony of those around him suggests that it was a delight that, like his mind, was polymorphous. He could find himself lost in the intricacies of an engineering problem, and then, just as suddenly, become captivated by a chess position. He had a flair for the dramatic and the artistic; we see it in the flaming trumpet, Theseus the mouse, a flagpole he hand-carved out of an oversize tree on his property, the juggling clowns he built to exacting specifications. Shannon's admirers are just as quick to compare him to M. C. Escher or Lewis Carroll as they are to put him in the company of Albert Einstein or Isaac Newton. He turned arid and technical sciences into vast and captivating puzzles, the solving of which was play of the adult kind. It says something about Claude Shannon and his instinct for play that his work found its way into both the pages of journals and the halls of museums.

In one sense, it may be impossible to draw anything from this. Shannon's enjoyment seems sui generis. But perhaps his example can still remind us of the vast room for lightness in fields usually discussed in sober tones. These days it's rare to talk about math and science as opportunities to revel in discovery. We speak, instead, about their practical benefits -- to society, the economy, our prospects for employment. STEM courses are the means to job security, not joy. Studying them becomes the academic equivalent of eating your vegetables -- something valuable, and state sanctioned, but vaguely distasteful. (p. 278) [link added]

I cannot help but wonder if less "state sanction" -- less meddlesome prodding -- might allow more people to develop a genuine love for science. Perhaps Shannon's joy is normal, save in the scope genius affords. In any event, this book was a pleasure to read and comes highly recommended, in part for the same reasons the authors gave for wanting to write it:

We are biographers, not mathematicians or physicists or engineers. The best we can say for this inexpert book of ours is that we've tried to write as we'd like to live. That is, we began with a nagging sense that there is something harmful in using without understanding, or at least trying to understand. We began with the idea that there is something ungrateful and grasping in enjoying our bounty of information without bothering to understand how it got here. (p. 283)

We should never allow ourselves to become jaded by wonders that men like Shannon have made routine.

-- CAV