In pursuit of the trivial and the significant / Just imagine, where would we be without numbers?

Widely regarded as the founder of the discipline of science history, I. Bernard Cohen brought enthusiasm and wide-ranging curiosity to the subject throughout his long career at Harvard University. As if to validate the Greek philosopher Pythagoras’ hypothesis that numbers constitute the true nature of things, Cohen in his new book, “The Triumph of Numbers,” which he was finishing at the time of his death at 89 in 2003, explores the history of numbers and describes how counting has come to occupy an enormous place in modern life.

Numbers, according to Cohen, are essential to “the analysis of society, the conduct of government, the regulation of daily life, and the understanding of how nature came to be.” He traces them to at least 3500 BC and a royal mace that records the capture of 120,000 prisoners, 400,000 oxen and 1,422,000 goats.

But their widespread use is a phenomenon that emerged in the scientific revolution of the 17th century, when scientists began to use numbers to test the validity of theories, according to the prolific author, who in 1972 provided the first modern English translation of Isaac Newton’s groundbreaking “Philosophiae Naturalis Principia Mathematica.” It was only in the generation after Galileo, the generation of Newton (1642-1727), “that theory and data of observation became so closely entwined that the validity of the system lay in its success in numerical prediction,” he writes.

Consider 17th century English artist, architect and inventor Richard Hooke’s law, “Ut tensio, sic vis,” which says that the tension in a spring is proportional to the stretching force. (Note, by the way, how Latin uses fewer words than English to convey an idea.) The truth of this proposition can easily be tested: If a spring is stretched 2 inches by a weight of 3 pounds, then a weight of 6 pounds will stretch it 4 inches. The idea that a theory can be proved false by testing has come to be a hallmark of science.

Statistical analysis debuted with 17th century Englishman John Gaunt, who analyzed births and deaths during London’s plague years and derived a fairly accurate estimate of the city’s population.

Not all the early uses of numbers were what we would call scientific, and Cohen has a fine time exploring these. There is, for example, David’s sin. According to the Bible, King David was urged to take a census, or enumerate, Israel and Judah. But, for reasons that remain murky, the enumeration was judged by God to be a “sin.” As recently as the 18th century, that prohibition deterred various governing bodies and leaders such as Massachusetts Gov. John Winthrop from taking accurate censuses.

Later authorities, unintimidated by the Bible, took to numbers with gusto. Cohen recounts with evident delight how Thomas Jefferson’s interest in numbers led him to persuade George Washington to issue the first presidential veto -- of a bill that provided for the first apportioning of congressional seats. Its flaw, Jefferson said, was that it didn’t describe the exact method to be used and so was open to political mischief.

In this and other anecdotes, Cohen’s little book offers a lively tour of the numerical bases of daily life and thought that we all take for granted. *