The two great conceptual revolutions of twentieth-century science, the overturning of classical physics by Werner Heisenberg and the overturning of the foundations of mathematics by Kurt Gödel, occurred within six years of each other within the narrow boundaries of German-speaking Europe.Read more at location 2274
In the new era of defeat and misery that begins in November 1918, the exact sciences are discredited together with the military-industrial complex that had sustained them.Read more at location 2295
Decline of the West, the title of the apocalyptic world history of Oswald Spengler. The first volume of Spengler’s prophetic work was published in Munich in July 1918,Read more at location 2300
Even those who disagreed with Spengler were strongly influenced by his rhetoric.Read more at location 2303
He said, among other things, that the decay of Western civilization must bring with it a collapse of the rigid structures of classical mathematics and physics.Read more at location 2305
There is not one sculpture, one painting, one mathematics, one physics, but many, each in its deepest essence different from the other, each limited in duration and self-contained.”Read more at location 2306
This is the origin of the sudden and annihilating doubt that has arisen about things that even yesterday were the unchallenged foundation of physical theory, about the meaning of the energy principle, the concepts of mass, space, absolute time, and causal natural laws generally.”Read more at location 2309
Two people who came early and strongly under the influence of Spengler’s philosophy were the mathematician Hermann Weyl and the physicist Erwin Schrödinger. Both were writers with a deep feeling for the German language, and perhaps for that reason were easily seduced by Spengler’s literary brilliance. Both became convinced that mathematics and physics had reached a state of crisis that left no road open except radical revolution.Read more at location 2313
Weyl had been, even before 1918, a proponent of the doctrine of intuitionism, which denied the validity of a large part of classical mathematics and attempted to place what was left upon a foundation of intuition rather than formal logic.Read more at location 2316
David Hilbert and Albert Einstein found themselves in the unaccustomed role of defenders of the status quo, Hilbert defending the primacy of formal logic in the foundations of mathematics, Einstein defending the primacy of causality in physics.Read more at location 2320
Heisenberg discovered the true limits of causality in atomic processes, and Gödel discovered the limits of formal deduction and proof in mathematics.Read more at location 2323
