Wednesday, October 17, 2012

Nahin, The Logician and the Engineer

Back when I took high school physics, a course taught by a thoroughly uninspired and uninspiring man whose name I have mercifully forgotten, a group of guys (who I suspect went on to become TV repairmen) and I had a pact. I would do their math homework and they would do my “hands-on” projects, especially those involving electrical circuitry. Left to my own devices I would undoubtedly have sent sparks flying in all directions.

Fast forward. Here I am with Paul J. Nahin’s book The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age (Princeton University Press, 2012). The author promises that no knowledge of electronics is required, just an understanding of polarity, Ohm’s law for resistors, and the circuit laws of Kirchhoff. “No more than a technically minded college-prep high school junior or senior would have.” Well, that stirred up a lot of bad memories.

So, rather than pretend that I relish looking at wiring diagrams I decided on a different tack. Motivated by a book I recently finished but cannot review for a while (Mastery), I thought it might be worthwhile to look at how Boole and Shannon, men from different centuries and very different backgrounds, came to be such remarkable thinkers.

In today’s post I’m not drawing any conclusions, just presenting short biographies.

George Boole was born in Lincoln, England, in 1815. His father was a cobbler who “seems to have been able to do anything well except his own business of managing the shop.” His real interests lay in mathematics and the construction of optical instruments, interests that he shared with George.

Boole’s formal education was scanty—after primary school a brief stint at a commercial school. He taught himself languages in preparation for becoming a clergyman. But fortunately for the world he soon enough found his true calling. At the age of sixteen he became an assistant teacher of Latin and mathematics at a small boarding school, a job he lost after two years. Among his many sins, he did math problems in chapel. In the evenings, “after a day of being a bad teacher to dull boys,” he plowed through a book on differential calculus which prepared him to read the classics of Lagrange, Laplace, Newton, and Poisson. “As Boole later explained to a friend, he managed it all by sheer force of will, just reading and re-reading, over and over, until he understood.” (p. 20)

Boole continued to teach at various day and boarding schools, all the while writing math papers, inspired perhaps by the establishment of a new math journal, the Cambridge Mathematical Journal. The editor of the journal, Duncan F. Gregory, gave Boole “almost incredibly generous aid,” without which “it is not unreasonable to imagine that Boole’s spirit would have been crushed right at the start.” Gregory published Boole’s early papers and then, when one was too elaborate for the Journal, recommended that Boole submit it to the Transactions of the Royal Society of London. This paper earned Boole a Royal Medal as the best mathematics paper published in the Transactions in the previous three years.

At the age of 34, with no university degree, Boole was appointed professor of mathematics at Queen’s College (today’s University College), Cork, Ireland, where he spent the rest of his short life. He continued to publish and moved “from one honor and achievement to the next.” (p. 27) He died, presumably from pneumonia, shy of his fiftieth birthday.

Claude Shannon was born in Michigan in 1916. His father was a business man and probate judge; his mother, a language teacher and high school principal. Early on Shannon displayed an interest in how things work; when he was in high school he earned pocket money by fixing radios at a local department store. He graduated from the University of Michigan with degrees in mathematics and electrical engineering and then, as a graduate student, got a job as a research assistant in MIT’s Department of Electrical Engineering to work part-time on Vannevar Bush’s differential analyzer, the world’s most advanced analog computer.

In Bush Shannon found “an early mentor” (and champion) “every bit as important to him as Gregory had been to Boole.” (p. 29) Shannon’s job involved understanding and maintaining the analyzer’s controller, a complex circuit of over 100 relays. It wasn’t long before Shannon had his epiphany of marrying Boolean algebra with electrical switching circuits. He described his work in his MIT master’s thesis, labeled by many “the most important master’s thesis ever written.”

After a foray into genetics (and eugenics) for his Ph.D., Shannon eventually ended up at Bell Labs for “an astonishingly creative fifteen years,” doing some work early on in cryptography, and in 1948 publishing “the Magna Carta of the information age,” his “Mathematical Theory of Communication.”

Shannon was strange man. Not only did he ride a unicycle through the corridors of Bell Labs while juggling balls, but he created all manner of toylike gadgetry. Some of the gadgets were scientifically intriguing, others pointless. Perhaps the weirdest was Shannon’s “Ultimate Machine.” Arthur C. Clarke described it thus: “It sits on Claude Shannon’s desk driving people mad. Nothing could look 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.” (pp. 35-36)

In 1958 Shannon left Bell Labs to go back to MIT. There he became interested in portfolio theory and, as William Poundstone described in Fortune’s Formula, became wealthy by applying his ideas to his personal finances.

Unfortunately Shannon was eventually afflicted with Alzheimer’s disease and spent the last seven years of his life in a nursing home.

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