- The Washington Times - Sunday, February 24, 2008

BENJAMIN FRANKLIN’S NUMBERS: AN UNSUNG MATHEMATICAL ODYSSEY

By Paul C. Pasles

Princeton University Press, $26.95, 254 pages

REVIEWED BY JAMES SRODES

Can there be anything left to say about Benjamin Franklin? With the publication of this book the answer is yes, to a mathematical certainty.

This is certainly the book to give your favorite math fancier, the manic Sudoku puzzle solver, the armchair geometrician, demographer, or quantum mechanic. Equally, the mass of ordinary folk who idealize Franklin and those historians who make a living feeding the need for more Ben all the time, will revel in this newly discovered dimension to the American Founding Father who put the “poly” in polymath.

A confession: Like most newcomers to trolling through the endless archival stacks of Franklin’s life I accepted the assertion of most of the biographers who went before me that while Franklin was a genius in many areas of learning — physics, meteorology, economics, intelligence, diplomacy, politics — his one shortcoming was that he was not too hot with numbers.

Author Paul C. Pasles, who teaches mathematical sciences at Villanova University, explodes this myth with a book that is an easy read for the innumerate but which also provides nourishment for those more skilled in the niceties of math. All of his adult life Franklin was fascinated with the sophisticated exercise known as magic squires (or circles) which at their simplest are grids of numbers which, when added in all possible directions produce the same total number.

Mr. Pasles has assembled every single one Franklin created as well as some other math exercises that have lain undiscovered until now. Also included are some contemporary math puzzles that offer the reader the chance to contest skills with Franklin himself.

“Our object is not to show that Franklin would have identified himself as a mathematician, only that he was adept at the systematic and creative ways of thinking about numbers, arrangements, and relationships that characterize mathematical thought. He was skilled in logical argument, taught himself mathematics as a teenager, and even learned some of the art of navigation on his own,” Mr. Pasles argues.

One of Franklin’s accomplishments that earned the greatest public praise was his first mapping of the path of the Gulf Stream which he devised by charting the changes in seawater temperatures on a grid of latitude and longitude.

When one thinks about it at all, it is an embarrassing but inescapable conclusion that Franklin must have been skilled at the relationships of numbers and their calculation. He was first and foremost a printer and one of the most gifted engravers of his day.

Math was essential in setting up the graphic relationships for designing new fonts of type to be both legible and to fit the tight constraints of the space of a composing matrix. Then there was printing itself, during which many smaller pages were impressed on a large single sheet and then folded into octavo (eight) or sextodecimo (16) pages for binding so that each page was in the right order and right side up.

The paper currencies he designed for colonial circulation used such ornate geometrical patterns that they were judged to be counterfeit-proof.

Both Franklin’s newspaper, The Pennsylvania Gazette and his wildly popular annual Poor Richard’s Alamacks included puzzles and methods of calculating acreage, measurements, and distances.

During the political turbulence leading up to the War of Independence and during his wartime intelligence/diplomatic foray in Paris, Franklin’s creative codes based on math sequences baffled the decryption efforts of British spymasters. And of course, part of the genius of his electrical physics discoveries lay in his use of the arithmetical terms positive and negative that are still used today.

Twenty years before the Revolution, Franklin began to argue that Britain’s real economic interest lay in enhancing the prosperity and population of North America. To make his case he was one of the earlier developers of a science that scarcely existed at the time — demography.

In an essay published in 1755 he predicted that the population of the colonies would “at least be doubled every twenty years.” He later hedged a bit to an estimate of a doubling every 25 years — between 1790 and 1850; the actual doubling he forecast came every 23 years. Others who followed in the new science of demographic economics — notably Richard Price and Thomas Malthus — publicly credited Franklin as the father of this most contemporary of our social sciences.

Franklin also was adept at marshalling mathematical support for his political causes and he often used statistical arguments to make moral points. Such as his comments on war:

“When will princes learn arithmetic enough to calculate, if they want pieces of one another’s territory, how much cheaper it would be to buy them, than to make war for them, even though they were to give a hundred years’ purchase?”

Or his cold calculation in his economic argument against slavery: “The labor of slaves can never be so cheap here as the labor of working men is in Britain. Anyone can compute it, (sic) Interest of money is in the colonies from 6 to 10 percent. Slaves, one with another, cost $30 a head. Reckon then the interest of the purchase of the first slave, the insurance or risk on his life, his clothing and diet, expenses in his sickness … .”

In time, Franklin made the moral march from small time slave owner and trader to a leader of the new nation’s abolition movement; but his sense of the logic of math pushed him into that first step.

And the new rage for the Sudoku puzzles? Mr. Pasles recounts that the publisher of the Japanese magazine generally credited with its invention has acknowledged that it is based on a “number place puzzle” that appeared in an American magazine in 1979.

That puzzle turns out to be nothing more than a version of the very magic squares that Franklin and his international circle of friends exchanged for their own amusement more than two centuries ago. An entire section of them are included in this fresh take on a familiar Founding Father.

Washington author James Srodes’ latest book is “Franklin: The Essential founding Father.”


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