Elegant Systems, Inelegant Institutions: Building, Designing, and Pursuing Perfection in the Age of Revolution

Historians do their best work when they struggle to find that place where the particulars of authentic lives, times, and events meet the possibility of generalization and the two perspectives illuminate each other. Most authentic lives display the banalities of daily existence punctuated by moments of aspiration and achievement that transcend the mundane. As often as not, achievements fall short of aspirations, scattering frustration and disappointment in their wake. Historians sift the resulting detritus and try to recover the dynamics of this strange relationship between the idiosyncratic individual and the "whole picture." We have before us here two fine examples of seasoned historians striving to do just that. Tamara Plakins Thornton has written an enormously learned book about an intellectually challenging subject—mathematic systems—in the guise of a normal biography of Nathaniel Bowditch, an early American gentleman of Salem, Massachusetts. Edward Gray has written an artful and sophisticated book about a complicated man—Thomas Paine—in the guise of a simple study of Paine's life-long effort to peddle his design for an iron bridge. Both subjects pursued the sublime union of natural law and human freedom. Both were disappointed.

Nathaniel Bowditch grew up in Salem, which, at the time of his youth, was a leading center of New England's maritime economy. Like so many young men in seaport towns, Bowditch took advantage of friendly connections, clerked in a waterfront chandlery, went to sea, learned the ways of saltwater commerce, collected a little capital and parlayed that, in a matter of years, into a comfortable fortune. But his passion was fixed on mathematics, both abstract and applied. While pursuing with one hand a perfectly ordinary practical course for a young man of modest means, with the other Bowditch taught himself mathematics and carved out a name for himself as a genius with numbers, with systems, and with the orderly view of things that proceeded from the two.

Bowditch's first triumph came with the publication of his New American Practical Navigator (1802). Celestial navigation required the comparison of real-time observations of the moon and stars with elaborate, published tables of values designed to yield a global position. Human "computers" produced the requisite tables, crunching out page after page of numbers, setting them in type, and laboriously proof-reading the resulting pages. Errors crept in relentlessly. Starting with the most popular British navigational manual, Bowditch reworked these calculations, added the latitude of hundreds of American reference points, corrected for a serious mistake involving the leap year, included simple tutorials for use by practical seamen, and produced a new manual that quickly became the standard for the next generation. The book secured his reputation as a man of precision and practicality—if not pedantry. Many of his thousands of "corrections" could be found in the third decimal, too insignificant to affect working navigational decisions. (Today we might diagnose Bowditch as some kind of savant, especially in light of the rigid social miscues and lack of impulse control or executive self-regulation he displayed throughout his adult life; in his day he was considered very smart and prickly.)

Bowditch's mathematical studies carried him deep into what we know as calculus, where he began to develop approaches to actuarial probabilities and statistical differentiations that he promptly put to use developing compound interest tables, marine insurance risks, and life insurance tables. On the applied side he developed systems for Salem's East India Marine Society and for the Massachusetts Hospital Life Insurance Company of Boston. To these financial services ventures he brought a degree of method, system, and regularity never before seen in banks or counting houses. He specialized...