Numbers, puzzles that Ben Franklin pursued

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.

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