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“if astronomers in two parts of the world could both pinpoint the time at which the position of the moon reached its highest point on the celestial sphere, then those observations would be simultaneous.”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“Could one have chosen otherwise? Of course, Poincaré says: we have only chosen the most convenient geometry.”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“Step by step, Poincaré reasoned on through the investigation, eliminating other possible sources of gas one by one:”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“convention is a quantity or relation fixed by broad agreement.”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“conventions.”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“The metric system, one of the most glorious creations of French genius, has already conquered half of the world, and its complete triumph is no longer doubted by anyone.”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“Poincaré argued instead that simultaneity was irreducibly a convention, an agreement among people, a pact chosen not because it was inevitably in truth, but because it maximized human convenience.”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“Euclidean geometry had, for centuries, practically defined proper reasoning from sure starting points to inevitable conclusions.”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“Exploring the causes of the accident, Poincaré’s language turned analytic, advancing hypotheses and counterhypotheses, facing them one by one against the evidence.”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“he gave each major theory its moment in the sun, displaying its virtues and vices for the students to judge.”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“Since there are no perfectly rigid bodies that we must use to instantiate straight lines, we would soon “discover” that geometry was simply false: we would find, for example, triangles with angles that did not sum exactly to 180 degrees. Poincaré insisted that our choice of geometry is guided by experimental facts but is ultimately open to choice, subject to our need for simplicity.”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“PARIS, HÔTEL DES AFFAIRES étrangères, 20 May 1875, 2:00 P.M. Represented by their decorated plenipotentiaries, seventeen names will be put to a treaty, their resplendent titles marching across the page: “His Majesty, the Emperor of Germany,” “His Majesty, the Emperor of Austro-Hungary,” “His Excellency, the President of the United States of America,” “His Excellency, the President of the French Republic,” “His Majesty, the Emperor of All Russia. . . .” We are at the solemn signing of the Convention of the Meter.”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“Since Perroz was a coal loader and therefore had no pick, Poincaré reasoned that it must have been Pautot who had accidentally punctured the lamp with his axe, and then inadvertently exchanged lamps with Perroz. Sometime after that switch, the punctured lamp 476 had lit the atmospheric methane, initiating the conflagration, and setting off a secondary explosion at the point where the incompletely burnt gas encountered the principal flow of air.”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“He acknowledged, for example, the commonplace that miners upstream of an explosion in the air supply are usually burned, while those downstream are asphyxiated. In the Magny disaster, all the deceased suffered burns, so it was logical to think that the explosion had occurred down the airstream from the last man,”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“For Dumas, the reason for adopting the metric system was because it divided lengths into sensible units of ten. That was what pure scientists wanted and what pragmatic journeymen demanded.”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“mathematical statements can be made in the language of non-Euclidean just as well as in Euclidean geometry.”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“convenience.”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“Cave-ins seemed to reinforce this deduction and to suggest that the gas explosion occurred in the half-moon (see figure 2.2). Against this seemingly plausible notion stood another hypothesis that “equally well accounts for the facts.” In particular, Poincaré considered whether the explosion might have occurred near the timber peg immediately adjacent to the point where lamp 476 stood:”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“Is Euclidean geometry true? It has no meaning. We might as well ask if the metric system is true, and if the old weights and measures are false; if Cartesian co-ordinates are true and polar co-ordinates false. One geometry cannot be more true than another; it can only be more convenient. Now, Euclidean geometry is, and will remain, the most convenient.”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“What, Poincaré asks, are the rules by which scientists judge simultaneity?”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“Drawing strongly on the Kant revival underway in Germany, Boutroux and his circle rejected both the extremes of idealism and empiricism.”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“Various geometries are simply different ways of presenting relations among things; which we use depends on convenience.”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“there were always many ways to represent mathematical concepts.”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“yard—neither plumber nor physicist could cherish such a hodgepodge.”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time
“pedagogical conventionalism”
― Einstein's Clocks and Poincare's Maps: Empires of Time
― Einstein's Clocks and Poincare's Maps: Empires of Time




