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Everything Becomes Trivial

March 25, 2011

When I was in elementary school, we were forced to read some "classic" books accessible to our young minds. One of these was Silas Marner, a book by George Eliot, a woman famous for her embrace of feminism long before it was fashionable. The plot of Silas Marner is somewhat engaging, but it's too long to summarize here. What's interesting about the book is that its plot is indistinguishable from that of the many "after school specials" that populate television. Eliot may have labored long on this book, but such stories are now cranked-out routinely and quickly by a small team of writers in a room. Eliot's life work is now a trivial pursuit.

John Napier spent twenty years of hand calculation to obtain the first table of logarithms. The purpose of logarithms was to facilitate calculations involving multiplication and division. Nowadays, a five dollar electronic calculator trivializes such calculations. I'm reminded of a cartoon from the early days of computing. A redundant employee is sitting across the desk from his manager, who just gave him the bad news. To add insult to injury, the manager is saying, "The funny thing is that the computer that's replacing you is no bigger than the head of a pin!"

Computing digits of the mathematical constant, pi, by hand consumed the energies of quite a few individuals as they tried to extend the precision of this number to a greater number of decimal places. John Machin labored hard to bring the number of pi digits to an even hundred in 1706 using his rapidly-converging series. Computers have now increased this to 5,000,000,000,000 decimal places, so Machin's present contribution to our knowledge of pi is just 0.000000002% and falling.

The same is true for science. While I was a graduate student, an aged inorganic chemistry professor confided that his years' long work for his PhD dissertation on determining a crystal structure using X-rays was now done at the push of a button on an inexpensive laboratory instrument with results given in a matter of moments. His PhD work was thus trivialized. And so it's true for all sciences.

Science is like the Red Queen's race in Lewis Carroll's "Through the Looking-Glass," where "...it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!" Carroll, whose real name was Charles Dodgson, was a mathematician, and he may have been lamenting the pressures of his profession.

Alice Liddell, 1860

Alice Liddell, as photographed by Lewis Carroll. Alice is the Alice of Alice's Adventures in Wonderland.

(Via Wikimedia Commons)

Does this mean we should just sit on our hands and let the next generation handle everything? The problem with that approach is that without our present, piddling efforts, the next generation won't have the improved tools to advance our work. Napier's logarithms fueled engineering calculations well into the mid-twentieth century. Our astronauts went to the moon on slide rules as much as rockets. To quote Isaac Newton,
"If I have seen a little further it is by standing on the shoulders of Giants."


  1. History of Technology page on Wikipedia.

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Linked Keywords: Elementary school; Silas Marner; George Eliot; feminism; after school specials; John Napier; logarithms; multiplication; division; electronic calculator; layoff; redundant; add insult to injury; chronology of computation of pi; pi; John Machin; Machin formula; rapidly-converging series; graduate student; inorganic chemistry; professor; PhD dissertation; crystal structure; X-rays; Red Queen's race; Lewis Carroll; Through the Looking-Glass; mathematician; Alice's Adventures in Wonderland; Alice Liddell; engineering; twentieth century; slide rule; rocket; standing on the shoulders of giants; Isaac Newton.

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