English longitudinal difference from Paris to London:
9 minutes and 20.85 seconds
French longitudinal difference from Paris to London:
9 minutes and 21.06 seconds.
A fifth of a second. Still too much. So again, in 1892, the year Poincaré was elected a permanent member of the Bureau of Longitude, after years of negotiation, the teams once more wired their telegraphs into place. Again the astronomers secured their instruments on the stone piers, launched electrical waves, and painstakingly reduced data. To their immense embarrassment, the results were no more harmonious than they had been in 1888. The two greatest European observatories, both of which claimed to map the whole world, could not agree on their own positions to within a fifth of a second. Once more the French found a greater expanse between Paris and London than the British did. This telegraphic time crisis finally came to a head in 1897–98, during the Bureau of Longitude presidencies of Loewy and then Cornu. The Paris Observatory, in conjunction with the International Geodetic Conference, insisted that the two observatories stabilize the European map with a proper time exchange.35
Clearly, issues of conventions were not confined to the far reaches of geometry or philosophy, rather, they were ubiquitous. Conventions concerned the prime meridian, decimalized time, submarine cables, map making—even the relative location of Paris and London. Everywhere one looked from the Bureau of Longitude in 1897–98, international concords in the world of space and time seemed urgent.
In this light, Poincaré’s “Measure of Time” reads as something quite different from a purely metaphorical tract. First, the calculation of Paris time from a distant site (whether London, Berlin, or Dakar) was not an abstract problem at the Paris Bureau des Longitudes in 1897: it was the most pressing issue of their map-making mission. Second, 1897 marked an enormous intensification of the long war over conventional decimalization, a debate that Poincaré engaged directly. In short, in 1897 more than ever, it was the Bureau of Longitude that was responsible for the precision simultaneity measurements that would permit the extension of an ever-more accurate map of the world relative to the marble longitude pier of Montsouris.
Indeed, when Poincaré proposes in “The Measure of Time” that simultaneity must be understood as a convention, it is crucial to attend to the literal. Synchronizing distant clocks by the observation of astronomical events was standard practice for French, German, British, and American surveyors. Transits of Venus, occultations of stars by the moon, eclipses of our moon and Jupiter’s moons were all useful events to set clocks by (if only inaccurately) on distant colonial shores. Having been a member of the Bureau for four years in 1897, Poincaré knew perfectly well that clock coordination by astronomical sightings had, for many reasons, long been overtaken by the telegraph as the most accurate standard of simultaneity.
Instead—this is the crucial point—Poincaré invoked telegraphically determined longitude as the basis for establishing simultaneity between distant sites. He insisted, in the most celebrated lines of the essay, that in the synchronization of clocks one had to take the time of transmission into consideration. He immediately added that this small correction makes little difference for practical purposes. And he remarked that the calculation of the precise time of transit for an electrical telegraph signal was complex. From at least 1892–93, Poincaré had taught the theory of telegraphic transmission of signals and reviewed the experimental studies that measured the speed of electrical transmission in wires of iron and copper. That interest did not wane. In 1904, in a series of lectures to the Ecole Supérieure de Télégraphie, he extensively analyzed the “telegrapher’s equation,” comparing it to work by others and specifically referring to the physics of undersea telegraph cables.36
In the practices of signal transmission time lies a key point to our puzzle. At first glance, it might seem impossible that Victorian cartographers were taking account of the time of signal transmission as their electrical pulses sped simultaneity across continents and oceans. But we need to look at what they were actually doing as they struggled against the myriad errors that entered the procedure. In fact, in their error corrections, the electric mappers had long since been taking precisely the transit time into account as they synchronized clocks between Paris and the far reaches of the United States, Southeast Asia, East and West Africa. Or, for that matter, in the intransigent precision measurements between Paris and Greenwich. They did not need to wait for relativity.
Back in 1866, as we saw, the U.S. Coast Survey put a monumental effort into determining the longitude gap between Cambridge, Massachusetts, and Greenwich, England, over the first Atlantic cable. The surveyors corrected for the usual errors in clock rates and in the measurements of star positions. But they were quite aware that the instant a telegraph key was pushed in Calais, it did not register in Valentia. That gap was in part due to the observers—their reactions were not instantaneous—and in part due to the instruments’ inertia. It took time, for example, for the magnet to swing the little mirror around sufficiently to cause a noticeable deflection of the light beam. These difficulties, which the authors dubbed the “personal error in noting,” could largely be eliminated by measuring these delays under controlled circumstances. But there was another crucial contribution to the delay between transmission and receipt, and that was the time it took for the signal to cross the Atlantic from Nova Scotia to Ireland. Amidst the listing of all the other errors, there in plain print are the measured transmission times: 25 October 1866, 0.314 seconds; 5 November 1866, 0.280 seconds; 6 November, 0.248 seconds.37 Or look back at the Coast Survey’s myriad missions to Mexico, Central America, and South America. Or to de Bernardières’s missions, or to the vast web of links among European observatories.
Everywhere the electrical surveyors were measuring the time it took the telegraphic signal to pass through the wires; everywhere surveyors were using that delay correction to establish distant simultaneity. Here is how they reasoned. For simplicity, let’s grossly exaggerate the time the signal takes in transit, and call it 5 minutes. Suppose the eastern observing team sends its signal at 12:00 noon, eastern local time, to their western partners located 1/24 of the way around the globe—that is, exactly 1 hour westward (–1 hour). Because of the transmission time, the westerners would receive the signal at 11:05 A.M., western local time. If they forgot to correct for the 5-minute delay, this naive western mission would conclude that they were at a longitude point that was 55 minutes earlier (–55 minutes) from the eastern stations.
(East-to-west apparent difference) = (real longitude difference) + (transmission time)
(Here –55 minutes = –60 minutes + 5 minutes.) Now let’s imagine what happens for a signal traveling west to east. West sends at local west noon (1:00 P.M. local time in the east). But by the time the signal from the western station arrives in the east, the eastern clock would not read 1:00 P.M., but rather 1:05. Our observers, if they were unaware of the time it took the signal to travel, would conclude that western local time was 65 minutes earlier than eastern local time (–65 minutes). In other words, the actual longitude separation would be shorter than our observers would believe if they forgot to take into account the signal time. This means:
(West-to-east apparent difference) = (real longitude difference) – (transmission time)
(Here: – 65 minutes = – 60 minutes – 5 minutes.)
Now, if you add the measurements (east-to-west apparent difference) and (west-to-east apparent difference), you get exactly twice the real longitude difference. The + and – transmission times simply cancel out. And, if you subtract the (west-to-east apparent difference) from the (east-to-west apparent difference) you get twice the transmission time: (apparent east-to-west – apparent west-to-east) = 2 times (transmission time). So,
Transmission time = 1/2 (east-to-west apparent difference – west-to-east apparent difference)
That simple tool for calculating transmission time formed part of the procedural mantra of every lon
g-distance surveying team in the world: in the West Indies, in Central America, in South America, in Asia, and in Africa. Certainly the Bureau of Longitude’s peripatetic astronomers had long been using it as they hauled their wooden observing shacks from place to place: between Hong Kong and Haiphong or Brest and Cambridge. Telegraphic map-makers saw, understood, and said perfectly clearly that the telegraphic signal time had to be taken into account to establish precise simultaneity and therefore longitude. For Poincaré not to have known this around 1898, we would have to assume that he ignored every Bureau of Longitude report written during the years he had served as a member, as well as avoided hearing any discussion of their actual procedures. We would have to suppose that when, in the “Measure of Time,” he wrote “let us watch [the telegraphic longitude savants] at work and look for the rules by which they investigate simultaneity,” he somehow did not understand what his own longitude crews (and every other British, American, German, and Swiss team) had been doing for the previous quarter century. This begs credulity.
Back in the late 1870s—when Lieutenant de Bernardières, Captain Le Clerc, and astronomer Loewy sought, quite literally, to reattach France to the map of Europe—one of their most important links was to be a telegraphically fixed longitude difference between Paris and Berlin. Time delay was an immediate concern. The authors noted in 1882 that their signals “were affected by small errors with different causes all of which must be taken into account carefully”: errors due to the response of electromagnets, the loss of time caused by the sluggishness of the mechanical parts, the relative separation of the pen tips, and finally the “non-instantaneity of the transmission of the electric flux.” To determine that transmission time, there was work to do in the observatory; the astronomer-surveyors had to be certain, for example, that the currents used were always the same. But there were also assumptions to be made, for example, that the velocity of the electric signal was the same in both directions. In agreeing to the procedures for fixing time through exchange of telegraphic signals, the language of conventions entered up front. To synchronize clocks between Berlin and Paris, protocols had to be established, agreements concluded; they even scripted in advance the greetings between stations. As in the Convention of the Meter, conventions of simultaneity demanded international standards, detailed accords on every step of the process.
Now it makes sense that we find among the headings of the French Bureau of Longitude’s Paris-Berlin report, Conventions Relative to the Exchange of Signals.38 When the Bureau of Longitude nailed Bordeaux to the map in 1890, in the list of other corrections, such as pendulum errors and personal equation errors, we finally come to it: “the delay S of the electrical transmission.”39 For the French team in Senegal, it was therefore fully routine to take account of the finite signal time of their electrical pulse; like so many other telegraph missions by 1897, the team simply applied the by-then usual rule to calculate the transmission time: “The difference between these results [apparent Saint-Louis-to-Dakar and apparent Dakar-to-Saint-Louis], which is [0.326 seconds] represents double the time taken for the transmission of the electrical wave plus other errors.”40 Routinized as they were, such corrections were critical for the highly exacting measurements facing Poincaré and his colleagues at the Bureau. In measurement after measurement, compensating for time delay loomed large as surveyors struggled to eliminate the recalcitrant longitude clashes that still remained between Paris and Greenwich, or between Paris and the far-flung French colonies of West Africa, North Africa, and the Far East.
In a certain, unfairly retrospective sense, it is obvious that the longitude finders had to take into account such a time of transmission. After all, they claimed to be recording longitudes to the thousandth of a second, and the transmission time for light over 6,000 kilometers was about a fiftieth of a second. Electrical waves wound their way through equivalent lengths of copper undersea cable several times more slowly, making the correction nearly a tenth of a second. In the late-nineteenth-century world that vaunted cartographic precision, this was too much—every second of time error at the equator meant half a kilometer of east-west confusion.
Poincaré’s remarks in his 1898 “The Measure of Time” about how to define simultaneity by telegraphic signal exchange were not, therefore, imaginary speculation about conventionality. Here was one of the three permanent Academy members of the French Bureau of Longitude, by far the most famous, just a few months before he was elected president, reporting on standard geodesic practice. All around him he could see simultaneity operationalized through the Bureau’s active network of cables, pendula, and mobile observatories.
Poincaré could also see how scientific procedure crossed into philosophy. Some twelve years before, his Polytechnique friend, physicist-philosopher Auguste Calinon, had urged him toward a naturalized view of time and simultaneity. Poincaré had responded sympathetically. Then, in 1897—at precisely the moment Poincaré was most deeply immersed in the decimalization of time—Calinon published a new book. His thirty-paged tract, A Study of the Various Quantities of Mathematics, laid out the vicious circle of our reasoning about the equality of durations. A container is filled with water, then emptied through a spout at its base. Does the emptying take equally long each time the process is repeated? To answer the question presupposes an independent measure of time. But Calinon pointed out that the same question then would occur in this independent measure: what would calibrate the calibrator? Poincaré clearly was struck by Calinon’s formulation and quoted it in “The Measure of Time”: “One of the circumstances of this phenomenon [the time needed to empty the water from a container] is the rotation of the earth; if this speed of rotation varies, it constitutes, in its reproduction of the phenomenon, a circumstance that no longer remains the same. But to suppose this speed of rotation is constant is to suppose that one knows how to measure time.”41
Calinon went even further than Poincaré indicated. He emphasized the historical arbitrariness of human time divisions; the seasons, for example, were chosen not based on any scientific or metaphysical conception, but for simple material utility. When scientists entered the picture, they simply chose the “simplest and most convenient” mechanism, which for Calinon meant that the motion of the hands of a clock were such that, by their use, the formulae for the movement of the planets would be as “simple as possible.” Calinon concluded that there was an irreducible choice in the measure of time, one that had to be based on convenience: “In reality, measurable duration is a variable, chosen from among all the variables present in the study of movements, because it lends itself particularly well to the expression of simple laws of movement.”42
In the intersecting circles around Polytechnique, Poincaré continually faced “choice,” “convenience,” and “simplicity” in the measure of time, both throughout the technical world (railroaders, electricians, astronomers) and in the scientific philosophy of his circle of Polytechnicians. His “Measure of Time” of January 1898 precisely marks that intersection. The measure of time is a convention, one tied to the realities of scientific procedure. It is essential, however, to also see what the paper was not. Poincaré’s “Measure of Time” was not an inquiry into simultaneity that took this principled correction of simultaneity into the heart of his physics. There is not a single word in this article about frames of reference, electrodynamics, or Lorentz’s theory of the electron. Like his field geodesists, in early 1898 Poincaré saw electromagnetic exchange as key to providing a conventional, rule-governed approach to simultaneity. Also like his geodesist colleagues, he saw the scientific consequence of the time-delay definition of simultaneity as just another correction, wedged between the inertial hesitation of an oscillating mirror and the psychophysiology of the observers. Unlike the geodesists, Poincaré saw a philosophically significant point in that correction. Like Calinon, Poincaré saw philosophy in the scientist’s measurement of time. But unlike Calinon, Poincaré had a direct involvement in the coordination of distant clocks. Only Poincaré
stood precisely at that intersection; only he seized on the exchange of electrical signals to make a routine physical process into the basis for a philosophical redefinition of time and simultaneity. By crossing the electrical surveyor’s moves with those of the naturalizing philosopher, a piece of everyday technology suddenly functioned in both domains at once; it could serve in the clock room at Montsouris and grace the Review of Metaphysics and Morals.
In Poincaré’s 1897 field of action, conventions of simultaneity were everywhere: no one would even bother to claim authorship of the longitude finder’s rule for transmission-time correction. Below the threshold of signed patents or authored scientific papers, the geodesist’s correction was part of the vast sea of anonymous knowledge that structured the telegraphic surveyor’s everyday practice. More generally, conventions surged into the visible in every international technical conference, in every accord over length, electricity, telegraphy, meridians, and time.
Recall Poincaré’s words about the nature of physical laws in the “Measure of Time”: “no general rule, no rigorous rule, [rather] a multitude of little rules applicable to each particular case.” Poincaré believed that the redefinition of time was another longitude hunter’s correction that should not ultimately dent the simplicity of Newton’s epochal laws: “These rules are not imposed on us, and one can amuse oneself by inventing others. Nonetheless we would not know how to deviate from these rules without greatly complicating the formulation of the laws of physics, of mechanics, of astronomy.” We choose these rules, Poincaré insisted in oft-cited words, not because they are true, but because they are convenient. As far as Poincaré was concerned in 1898, that meant guarding the long-established laws of Newton for which a simpler alternative simply could not be imagined. “In other words,” he concluded, “all these rules, all these definitions, are nothing but the fruit of an unconscious opportunism.” In Poincaré’s insistence on the conventionality of time, we hear ideas that we can now recognize as having echoed through the halls and wires of the Bureau of Longitude and Ecole Polytechnique, a technical universe in which diplomats, scientists, and engineers used international conventions to manage the colliding imperial networks of space, time, telegraphs, and maps. This world too was Poincaré’s, a way of being in science that stood a long way from Einstein’s.
Einstein's Clocks and Poincare's Maps Page 18