By Palle Yourgrau
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Extra resources for A World Without Time: The Forgotten Legacy Of Godel And Einstein
As an undergraduate, Godel was particularly impressed by the lectures on number theory, attended by hundreds of students, given by Philip Furtwangler, a cousin of the legendary orchestral conductor Wilhelm Furtwangler, whose fame in those years would turn to infamy when he declined to leave Germany during the next world war. Godel claimed later that Philip Furtwangler, who was paralyzed from the neck down, gave the best lectures he had ever heard. It was Furtwangler whom Godel credited with his turn to mathematics.
Amazingly, although bullets shot from a moving train have a velocity that is increased by the speed of the engine, the measurable velocity of a light beam sent" out from this same engine is unaffected by the train's speed. The classical principle of "addition of velocities" was in peril. Into the breach stepped the Dutch physicist Hendrik Antoon Lorentz, Einstein's father figure and another of his heroes. It was Lorentz who, having already perfected the form of Maxwell's equations, appeared now to save the day by supplying the exact equations, the "Lorentz transformations," that made measurements in one reference, or inertial, frame equivalent to those obtained in another, including the "absolute" rest frame of the postulated ether.
The crises had a common cause: mathematicians found themselves confronted with a paradoxical new kind of number. If a way could not be found to incorporate this new entity into their thinking, they were faced with the prospect of seeing their edifice crumble. 48 I A WORLD WITHOUT TIME "The sole possible foundations of arithmetic seem to vanish," Frege wrote, when confronted with Russell's paradox. ~it~ the third crisis, the positivists' star had risen. by its very nature as an ·a priori, rationalistic science, had always been a thorn in the side of empiricists.
A World Without Time: The Forgotten Legacy Of Godel And Einstein by Palle Yourgrau