Einstein's Clocks and Poincare's Maps

by Peter Galison

  Decimalizing Time

  As Lallemand’s “defection” suggested, decisions taken at the Washington Conference of 1884 reverberated through the French Bureau of Longitude. In addition to their fateful decision about Greenwich, the Washington delegates had also “expressed the hope” that the definition of the astronomical and the nautical days might be joined, so both would start at midnight. Astronomers had long started their official day at noon, profiting from the absence of anything of observational interest during the day to keep their precious nights unbroken by a calendar change. Meanwhile the rest of the world utilized nighttime quiet to change its day at midnight, thereby keeping daylight within a single calendar day. Boosted by concern emanating from the Canadian Institute and the Astronomical Society of Toronto, the Minister of Public Instruction asked the French Bureau in 1894 for its opinion.

  Poincaré led the charge and began, characteristically, by weighing inconveniences. “It is evidently inconvenient [incommode] for an astronomer to change the dates in his notebook in the middle of a night of observations.” He could forget to make the switch, leaving records vastly complicated. But this same “incovenience” now exists for the sailor making solar observations at sea. Indeed at every moment the sailor currently faces precisely the same problems as the astronomer, and worse. Where the astronomer works without distraction, the mariner has a million worries; where the astronomer can always give the observations a fresh look later, the mariner could be dashed against shoals by the slightest error. So let the astronomers write “night of 11–12” in their notebooks. What about the discontinuity in time on the day the reform was instituted? Better to straighten out that “inconvenience” now than later, Poincaré responded.

  If there was a serious objection, it was this: any such reform would necessarily scrap the many compilations of astronomical phenomena, such as those inscribed in the British and American astronomical almanacs, the French Connaissance des Temps, or the German Berliner Jahrbuch. Were any of these volumes to alter their time conventions, converting among them would present a vastly greater problem than the current confusion. Only an international accord could implement this laudable effort to simplify time. Until international accords prevailed, the Bureau’s members concluded that the French should wait, though all agreed that a twenty-four-hour clock would be an improvement.13 But soon the French put even the twenty-four hours in a day under scrutiny, following up on the Washington Conference concession that left “hope” for time’s decimalization. In February of 1897 the president of the Bureau of Longitude established a commission with Henri Poincaré as its secretary to determine whether France should scrap the old twenty-four-hour day and 360-degree circle in favor of a truly rational system. The president bluntly asked: why had the great Convention of 1793 failed to extend the decimal system to time and the circumference of a circle, and were objections to such a novel system still valid?14

  One commissioner serving with Poincaré, Bouquet de la Grye, a former Polytechnician and prominent hydrographic engineer, responded. The Convention had aimed to banish everything that recalled the ancient measuring customs of the ancien regime and to consecrate true French unity by deploying common measures across the whole of the country. With the meter, the Revolution succeeded. But the Convention’s time reform of months and weeks had been a disastrous flop, as had Laplace’s valiant but doomed attempt to decimalize the hour. De la Grye reminded his colleagues that few decimal clocks survived, and no one outside of France took any interest in them. From this debacle, de la Grye found clear guidance for the present: “The metric system succeeded because it was the simplest and it put an end to a veritable incoherence in local measures; the decimalization of time and circumference failed because the whole world employed the same measures and the proposals sinned precisely by their lack of unity.”15 Convenience ruled. Where reforms simplified lives, the public went along; when reforms did not help ordinary people, the schemes fluttered softly into oblivion.

  Poincaré duly recorded the debates that followed. President Loewy insisted that if the Revolution’s metric time had failed, it was because French astronomers could not find partners for the reform in other European states. General de la Noë noted that the geographical service had indeed adopted decimal angles, as had the geodesic services in Belgium. Cornu ascribed one difference between the late-eighteenth-century and the late-nineteenth-century present to the loss of habituation to the duodecimal system. The most curious feature of all was that the contemporary British engineers were so trained in their primitive measures of “inches” and “feet” that they simply refused to understand the advantages of the decimal system. Less despairing of his cross-channel colleagues, the director general of the Paris-Lyon-Mediterranean Railroad evinced some sympathy for the Anglophones; he reported that many British engineers suffered under their present system and would love to break out of their island’s archaic conventions. Impressed by the historical French drive toward the revolutionary ten, stirred by their historic role in rationalizing the world, the commission voted to decimalize time.

  But that vote left much undecided. The railroad representative assured his scientific colleagues that any attempt to alter the twenty-four-hour day was doomed to failure. De la Grye held out for a unification of time and geometry by dividing the circle into 240 parts. Loewy admitted that he had dreamed of a full-bore decimal world, but the burden of past maps and measures led him, mournfully, to conclude that the obstacles to such a brave new world were not passing difficulties. He endorsed de la Grye’s compromise; a circle divided into 240 parts would put the globe into synch with the clock as each hour of the earth’s rotation would correspond to a turning of the world by an elegant 10 degrees. Poincaré backed Loewy, adding:

  Were we in the presence of a tabula rasa, the best system would be one that divided the circle into 400 parts [100 grads per quarter circle, or 100 kilometers per grad]. . . . But we cannot break completely with the past, because not only must we take account of public repugnance, but scientists themselves have a tradition to which they remain tied.16

  Keep the twenty-four-hour day, Poincaré said, and divide the circle in 240 parts. Commander Guyou rejected such compromises, insisting on division into 400 parts. The navigational demands at sea and the calculation of tides brought the mariner into a never-ending series of painful and difficult calculations. Why not provide an easy-to-use decimal system for the scientist or navigator while leaving the public to count time according to its old habits? Trainmen, Guyou added, were already habituated to a timekeeping system that was off by five minutes from city time and were equally at ease with a twenty-four-hour clock. Why not a two-time system? Such an amalgam was intolerable, Poincaré replied. Civil time was clearly linked to longitude. Any mixed system necessitated a conversion factor that was truly convenient for any user.17

  Convenience, convention, continuity with the past. These terms arise again and again in Poincaré’s abstract philosophy. Yet here they are written in the less-than-etherial concerns of real-world engineers, seagoing ships’ captains, imperious railroad magnates, and calculation-intensive astronomers. Monsieur Noblemaire, director of the Paris-Lyon-Mediterranean Railroad, argued as follows to reinforce his intervention: Suppose you leave your train station at 8:45 A.M. and arrive at 3:24 P.M. How long is your trip? One has to think. But by expressing travel problems in decimals, the confusions of A.M. and P.M. vanish. All that remains is subtraction:

  start: 15.40h

  end: 8.75h

  duration: 6.65h

  Here was convenience that mattered to a society on the move.18 Mariners, like the Commandant of the Naval School, saw only benefits to the transition to decimal time and longitude. Maps would be easy to alter, and physicists shouldn’t have a problem. After all, according to the good captain, physicists had adapted easily enough to centimeters, grams, and seconds.19

  Decimalizing time, easy? That would have been news to the physicists. When the president of the French Physical S
ociety, Henri Becquerel, got his hands on the proposal in early April 1897, he was not amused. Even leaving aside the expense of changing all clocks, marine chronometers, pendula, and watches, the physicists saw dire consequences for the electrical industries and those that flowed from them. For it had only been in 1881 that the centimeter-gram-second system (CGS) had been adopted internationally and only in April 1896 that the president of the Republic had decreed that the rational CGS system of measure should be used in all matters of State. Needless to say, one of the cornerstones of that newly rational system, the sexigesimal second (1/3,600 of an hour), now lay in the crosshairs of this decimal revival. Not only would the proposed decimal second (1/10,000 of an hour) utterly alter the mechanical and electrical units of current, work, and the like, but all the practical units (amperes, volts, ohms, and watts) that are defined in terms of them would have to change as well. “What an upset in scientific practice and the entire mechanical and electrical industry!” All the instruments would have to be altered. “What a huge expenditure without any profit, neither for science, nor for industry!” If one weighed the advantages against the disadvantages, the physicists’ balance tipped decidedly toward the status quo: keep the old second. For the physicists, this case was closed before it opened.20

  The physicists’ plaintive cries did not move Poincaré. Or rather, in the face of fierce protests from the public, the navigators, and the scientists, Poincaré refused to engage the debate at all, instead proposing to resolve the problem with the technical legerdemain of a reforming Polytechnician. On 7 April 1897, Poincaré brought the commission a table he had prepared that displayed each proposed system, the kinds of multiplications required (ignoring factors of ten) to express angles, to convert time to angles for expressing longitude (degrees per hour of the earth’s rotation), and to convert angles from the old 360-degree system to the proposed decimal ones. For example, to express an angle of a circle and a half (1.5 rotations) in the 100-division system, there’s no conversion factor at all: once the factors of ten are taken into account, you just have 150 units. No mental arithmetic, the multiplier is just 1. For the 400-division system, 1.5 circles would be 600 units; to get from 1.5 to the 6 in that 600 (the additional multiplication by 100 requiring no brainpower), you need to multiply by 4. The second column tells how to switch from parts of the circle into time: if the whole circle is 100 units, you need to multiply by 24 to get hours—100 units of rotation equals a full twenty-four-hour day. If the circle is 400 units, you need to multiply by 6 to get hours. Finally, to switch back into the old 360-degree circle, you would (for the 400-unit circle) just multiply by the factor 9, whereas a 100-unit circle required multiplication by 36.

  Good technocrat that he was, Poincaré had scanned the table to find the simplest conversion factors. Only the 400-unit system required no double-digit multiplication. So there it was. Poincaré had, objectively, the least “inconvenient” solution, one he happily defended to shrieks of protest against the proposed scrapping of every angle-measurement in the world.21

  Divide circle into this many parts

  Factor for angles greater than circle

  Factor to convert arcs into time

  Factor to convert to 360 degrees

  100

  1

  24

  36

  200

  2

  12

  18

  400

  4

  6

  9

  240

  24

  1

  15

  360

  36

  15

  1

  Poincaré’s table presenting the case for dividing the circle into 400 parts. Source: Henri Poincaré, “Rapport sur les résolutions de la commission chargée de l’étude des projets de décimalisation du temps et de la circonférence” [7 April 1897], Archives of the Paris Observatory.

  Here was an engineering-dictated armistice in a war pitting all against all on social, economic, and cultural grounds. When the dust settled, the hostile factions had compromised even further, keeping the twenty-four-hour clock and decimalizing the hour into 100 minutes with each minute split into 100 seconds.22 These half-measures left Captain Guyou cold. Sea captains were habituated to reading complex tables, as he drily noted; it mattered little to him whether the table consulted had simple or complex formulae for conversion. Ultimately, the committee splintered into almost as many opinions as there were members. One camp lobbied for a division of the circle into 400 parts, another wanted 240 parts, and a third (physicists, sea captains, and telegraphers) preferred the traditional 360 divisions with decimal subslices. Astronomer Faye bucked all these proposals, demanding a clean split of the round into 100 parts.

  Amidst this deci-strife, Poincaré and his allies tried to remain above the fray, adjudicating the competing systems with equanimity. Scribe and contributor Poincaré dutifully recorded his own opinion, one entirely consistent with his views about unifying civil and astronomical time: all these “systems are acceptable and one must choose that one which would have the greatest chance of success before an international congress.” With the president on his side, Poincaré’s forces won in a voice vote: the unity of angle would be the “grad,” that is to say 1/400 of the circumference. That decision, while reinforced in a later meeting, did not quiet the debate. Some of the commissioners themselves dissented: the chief engineer of the French hydrographic service filed a report protesting the tremendous burden that would be caused by trying to reprint the 3,000 charts (not to speak of the instructions, tables, and yearbooks), issued by the service. The entire instrumentarium of navigators, moreover, would be rendered obsolete overnight. Sailors might as well throw their chronometers, pendula, watches, theodolites, and sextants into the briny deep. Another protester contended that the decimal commission was merely managing contradictory interests in a way that would disappoint the public with a badly tailored compromise. Cornu argued that there was one rational system and only one: the proposed reform was neither an adventurous, rational charge into the future nor a safe retreat to the status quo. For Loewy, the radical decimalizers had missed the point: the new system cut out much of the irrational and complicated bits of a system that, in its historical bricolage, made no sense. For the moment one could do no better than settle. Loewy and Poincaré had the votes to back their liberal compromise of a partial reform: 12 for, 3 against.23

  Voting silenced no one in the debate over the measurement of time, which tumbled, later in 1897, into the pages of Cornu and Poincaré’s journal, L’Eclairage Electrique. Clearly uncomfortable with the commission’s compromise, Cornu reported that “an unstable and divided majority” had formulated a solution that would have great difficulty in finding universal acceptance. Even before the committee had finished its work, he said, the French Navy and the army’s geographical service both had objected, since the former would gain little simplification in their usual calculations, while the latter would actually be stepping backward. According to Cornu, decimalizing time was harder than decimalizing space. Length reform had met a triple condition: it held clear benefits for a majority, it offered no enormous inconvenience for those not directly concerned, and it fit well with general public enthusiasm for a unity of length. Everyone was glad to escape from the trading confusion that had prevailed at national, provincial, and commune borders. He expected no such celebration of this flawed time reform.24 Cornu insisted that it was the day, the natural unit of time, that should be decimalized—not the wholly artificial hour. If the day were the base, then a hundredth of the day would be just about a quarter of an hour, and a hundred-thousandth of a day would equal 0.86 old-style seconds. That would be a gratifying unit of time because it corresponded so closely to the typical adult heartbeat, our “natural” small temporal unit.

  But “interests trump logic,” Cornu dourly noted, and no interests backed the one logical reform that would bring order to time. Chaos did not currently reign in the world of
time, as it had in spatial measurements before the reform of the meter. In a sense, time was already unified among countries, as length had not been before the meter. Into this unreceptive atmosphere, Cornu observed, the time commission was now dropping a hopelessly confused compromise that sanctified the all-too-artificial number of twenty-four hours in the day, and then decimalizing this useless hour. Decimal fractions of an hour were unnatural, Cornu insisted: a hundredth, thousandth, and ten-thousandth part of an hour were 36, 3.6, and 0.36 seconds, respectively. This was no good; an astronomical clock could not beat at intervals corresponding to these units of time: 3.6 seconds was too long for a pendulum and 0.36 too short. Having spent years building and maintaining his own astronomical clock with a massive pendulum, Cornu charged ahead: the whole human organism made the second special. Not only did our pulse surge every second or so, but our capacity to react, by sight or sound, took about a tenth of a second, adding to the value of a time unit that was approximately a heartbeat long. According to Cornu, the body, the existing clocks, and the sun all militated against decimalizing the hour. Cornu despaired, moreover, at the commission’s other compromises. If the hour was to be maintained (which he opposed), then the logical division of the globe ought to be in 240 parts, making each hour of rotation carry the earth through the even division of ten parts. Yet here, too, the commission had misplayed its hand, dividing the circumference of the world into 400 parts. Since 400 parts did not divide evenly into the twenty-four hours, even the geographers would gain little convenience as they reckoned longitude. As far as Cornu was concerned, this reform had failed to decimalize the only truly natural period of time by refusing to seize the day as the basic temporal unit in our lives: “men of science should . . . prepare the future not by compromises, but by the progressive adoption of [the decimalized day and circle] in the domain in which they are masters of convention.”25