Mathematics and the Rights of Man
From the most remote times philosophers have taken number as the exemplar of the intelligible. Once one has grasped a principle in geometry, it was said, not even God Himself could understand it better, although, to be sure, He might know more theorems. Calculating people think for themselves; they despise the unintelligible, capricious, unfounded, authoritarian, and feudal as infringements on their thoughts and actions. In brief, mathematics is a science for free people. Or, to say the truth as the 18th century saw it, for free men. Newton's doctor, Sir John Arbuthnot, praised mathematics for giving "a manly vigour to the mind"; a tonic Newton took to such good effect that he mastered all "the noble and manly sciences" and became "the greatest man that ever liv'd." All this will help to construe the remark made by the representatives of the revolutionary government in 1799, on accepting the prototypes of the meter, liter, and kilogram. The metric measurers, they said, reaching for their highest compliment, had carried through their work "with the confidence of a male and republican spirit."
If mathematics is male, Europe grew increasingly manly during the 18th century. When Samuel Pepys became clerk of the king's ships in
1660, he had to recruit his strength (he was then 27) and repair his education (which was excellent) by learning the multiplication table. In the resulting fit of machismo , he forced his wife to learn arithmetic. Most of learned Europe in the 17th century was "innumerate," if by analogy to "literacy" we take "numeracy" to mean familiarity with numbers. During the 18th century the requirements of government bureaucracies, commerce, colonization, mining, rational agriculture, forest management, the military, and so on, brought dramatic increases in numeracy. Before 1750 Poor Richard enjoins us in rhymes to go early to bed to secure health, wealth, and wisdom; just after 1800 a book called The young man's guide delivers the same message by multiplication. If you stay up to eleven o'clock every night, the Guide admonishes, in fifty years you will uselessly expend $182.50 on candles.
Perhaps the most significant sign of this burgeoning rudimentary numeracy was the multiplication of tables of numerical equivalence. A good survey of the tables in use in commerce has yet to be made; but there is no doubt that their number increased dramatically after the Seven Years' War. They came in several sorts: conversions of weights, measures, and moneys; total cost of goods, tabulated by size and unit cost; tables of interest and annuities; agricultural yields; and so on. It did not require great prowess at mathematics to use these compilations; rather, a degree of numeracy comparable to the literacy of one who could read but not write. The spread of the metric system depended on this widespread rudimentary numeracy, and raised its level.
These tables were required not only because of the number and uncertain equivalence of feudal weights and measures, but also, and
perhaps primarily, because the arbitrary multiples and submultiples of the various units made computation burdensome and complex. Calculation of the price of a piece of cloth 2 yards 1 foot 4 inches square at 3 pence 2 farthings the square foot was a sufficient challenge. To change it into aunes, pieds, livres, and deniers, and to proceed to a problem in bushels and cubic king's feet, would have puzzled Archimedes. According to the Paris Academy, referring to the situation in 1790, people at ease with money computations could not handle weights and measures. "In the present state of affairs, a man who can calculate with sous and deniers cannot calculate with toises, pieds, pouces, and lignes, with livres, onces, gros and grains."
The Paris Academy and many other scientific reformers supposed that by dividing the new standards and the revised coinage decimally they would eliminate the need for specialist computers. The decimal was not free from arbitrariness; but its simplicity and convenience could not be gainsaid, at least by practiced calculators, and, as the Academy observed, although not universal it is as natural as the human hand. Only the hand of the learned had so far employed decimal arithmetic, and by no means universally, as Lavoisier pointed out in his Elements of chemistry , when urging his colleagues to state weights in decimal parts of whatever units they used. This natural arithmetic, "previously locked up in the domain of the sciences," was precisely what the reformers thought they sought. "Those who knew little will know everything; others will hurry to forget what they no longer need to know; all will accept as a true benefit a method of calculation that will save them time, study, and chances for error."
Prieur de la Côte d'Or, a former military engineer who served on the all-powerful Committee of Public Safety (Comité du salut public), expected the decimal calculus to be the technical language of Utopia.
"How happy we will be not to be forced to consult anyone about our prosperity, property, expenses, and drink, and to have nothing to do any more with people who often seek only to profit from our ignorance." The connection between democracy and the decimal was made plain and explicit by Condorcet during the first year of the Revolution. Decimalization, he said, fit perfectly with the political program and mandate of the National Assembly. "It [the Assembly] wants to insure that in the future all citizens can be self-sufficient in all calculations related to their interests; without which they can be neither really equal in rights. . .nor really free." Long after the promulgation of the metric system, Laplace advised Napoleon that its chief advantage as understood by its creators was not the destruction of feudal metrology but the division by tens.
Republican zeal is not easy to curb, and the decimalization of everything measured or metered figured among the excesses of the French Revolution. The Paris academicians demonstrated solidarity with the regime by dividing a right angle into 100 revolutionary degrees, and each such degree into 100 minutes; and they found much pleasant recreation in recomputing the trigonometrical functions in what Jean-Baptiste Joseph Delambre, the most assiduous of the metric measurers, later extolled as "the vastest [calculation] that had ever been done, or even conceived." The innovation neither saved the Academy nor suppressed the reckoning of the Babylonians, with which it still coexists in France. A less enduring initiative, the revolutionary calendar, which came into operation retrospectively on the day of the autumnal equinox of 1792, divided the year into twelve parts of thirty days each, grouped in ten-day blocks. The five
or six additional days required to make up the year were intercalated as necessary.
The unsystematic concession to lunar motions represented by the numbers 12 and 3 in the divisions of the revolutionary year was offset by a revolutionary day of ten "hours," each containing 100 "minutes" and 10,000 "seconds." Several clocks ticking 10,000 "seconds" a day were made, but most clock makers and watchers preferred to divide their time in the manner of the servile peoples of Europe. On 18 germinal an III (7 April 1795), the revolutionary government suspended republican time sine die on the official ground that it was of interest only to scientists. The calendar survived longer, until 1 January 1806, when Napoleon put an end to it.
The cost of conversion to decimal units was borne by the people whose lives the system was intended to ease. In computing prices of old goods in the new currency, sellers naturally rounded up to their advantage. The common man as naturally opposed the change. So did the common woman. According to a squib of 1791, the prostitutes of the Palais Royal, whose rates had been recomputed, complained that the 100 sols they now received for their services devalued their charms, "which opinion had previously reckoned at an écu and six livres," by a sixth. It is not easy to anticipate the effects of reform.
Another conflict between geometry and system arose in the naming of the decimal divisions of the meter. In 1792 the Academy discussed the relative advantages of system (in which divisions would be
designated by the prefixes "deci-," "centi-," "milli-," and the only multiple would be "milliaire") and familiarity (in which submultiples of the meter would have common names, like "palme" and "doigt"), and plumped for the familiar. They erred in calculating revolutionary zeal. The Committee on Public Instruction (Comité d'instruction publique) preferred a clean sweep and adopted the systematic names. This occurred on 1 August 1793, on the eve of the suppression of the Academy. One of the Academy's successors in metric matters explained that "it is almost impossible to reason correctly without a language aptly made."
The language did not please the people. Classicists objected that the prefixes (enriched by "déca-," "hecta-," and "kilo-") violated the grammar of ancient languages, while the uneducated could make no sense of them at all. "These names," declared a delegate to the Convention, "novel and unintelligible to the large majority of our citizens, are not necessary for the maintenance of the Republic." He did not know what he had escaped. Prieur de la Côte d'Or, who had taken an active part in the reform of weights and measures from the onset of the Revolution, had names of his own, derived, he said, from ancient languages and Low Breton. The irrationality of the Convention did not extend to adopting "kilicymbe," "myriadore," "ladedix," "pèzeprime," "centicadil," or "decidol," and Prieur, bending to the political wind in 1795, drew up what became the definitive metric names. The many centicadils of bitterness he then swallowed and decidols of crow he then ate were to damage the work of the metric reformers. All concerned might have spared themselves the trouble. For decades the people stubbornly opposed decimalized units and their jabberwocky names.