“In science there are no ‘depths’; instead, there is surface everywhere.
ridding him, thanks to the influence of the metaphysician Kant, of any inclination to do metaphysics himself…
As Otto Neurath quipped, “The Austrians figured out how to avoid the detour through Kant.”
Textbooks, then as now, aim to lead the student as quickly as possible to the state of the art. But for a critical analysis of the tools—the concepts and methods—it helps to know how they evolved.
Mach writes: “I know of nothing more depressing than those poor people who have learnt too much. What they have acquired is a spiderweb of thoughts, too weak to offer support but complicated enough to confuse them.”
Those in the fine arts chimed in and painted not things, but light.
he would joke: “I disdain experiments the way a banker
Boltzmann’s interests focused more on theoretical than on experimental physics. Later, he would joke: “I disdain experiments the way a banker disdains coins.”
The next fifteen years in Graz were Boltzmann’s most productive period—not just in terms of progeny but also in scientific output.
“Whereas I felt some qualms about plunging myself into philosophy, philosophers seemed to have none about intruding into science…. I first encountered philosophers a long time ago, and at that time I had no idea what they meant by their utterances, and therefore I tried to become better informed about the basics of philosophy.” Boltzmann’s weapon of choice was the club rather than the foil: “To head straight into the deepest depths, I first turned to Hegel; but oh! what obscure, vacuous balderdash did I find there! My unlucky star then ushered me from Hegel to Schopenhauer….
it seems surprising that the urge to answer these pressing questions does not fade away even after they have been recognized as illusions. Apparently our habit of thinking is too ingrained for us to be able to let them go.
Maybe scientists, knowing when to stop, were wiser than philosophers: “Science has progressed almost more through deciding what to ignore than through deciding what to study.”
“To give up nonsense is not to resign.”
his lectures, which had been announced under the rather bland title On a Thesis of Schopenhauer, with the offhand comment that he had originally intended to use a somewhat more provocative title, to wit: Demonstration That Schopenhauer Is an Insipid and Ignorant Philosophaster Who, by Ceaselessly Propagating Hollow Twaddle, Spreads Nonsense Far and Wide and Forever Perverts Brains from Top to Bottom.
It is comforting to know that Albert Einstein’s four earth-shattering contributions to physics during that spectacular year did not go unnoticed by his peers. On April 1, 1906, he received a promotion in the Swiss patent office: from Technical Expert, Third Class, to Technical Expert, Second Class.
According to him, the laws of nature are free creations of the human mind, and their purpose is to relate observed facts in a consistent manner. Several different models can describe the same set of observations; when that happens, settling on one model rather than another is purely a matter of convention, based on whatever appears to be simpler and handier. There is no objective “fact of the matter.” Moreover, abstract notions such as force and electric charge are defined only by the ways in which they are used. Asking for what lies “beneath them” or what they are “in reality” is useless metaphysics.
Hilbert did not start out in life as a wunderkind. As he later confided: “I did not bother much with mathematics
Hilbert did not start out in life as a wunderkind. As he later confided: “I did not bother much with mathematics at school, because I knew I would do it later.”
The second volume of Frege’s Basic Laws of Arithmetic was just then due to be published; it was too late to modify the manuscript. All that Frege could do was add an afterword. To this day what he wrote remains a monument to intellectual honesty: “Few things can be less welcome to a scientific writer than to have one of the foundations of his edifice shaken after the work is finished.”
He loved the inexorability of mathematics, which he characterized as “the science with the evil eye
He proposed that in between reading two German novels, one should always compute at least one integral, so as to lose weight.
Calculations replace intuition—or to be more precise, they assist it; after all, mathematicians cannot help forming mental pictures of the entities that engage their thinking day after day. But they do this privately, on the sly.
(In science, it is common practice for a result to be named after the person who discovered it last.)
Adler waited patiently over coffee for nearly one hour, until she finally left the room. Then he rose, drew his gun, walked up to the prime minister, and pumped several bullets into the count’s head. Officers dining nearby did not even have time to reach for their swords. After a short commotion, Adler handed over his gun and waited for the police. He had lost his spectacles in the scuffle, but not his sangfroid. When the police officer asked him why he had shot the count, he coolly replied that it was none of the officer’s business.
Einstein spontaneously offered to testify in favor of his old friend Friedrich, “whose selflessness had made him land in the soup
when the judge asked the accused why he had never thought of the effect on his parents and his children, Friedrich Adler haughtily replied that political assassination was admittedly problematic, but “to reserve it for childless orphans is not worth discussing.”
it did not take long before he started being hailed as a martyr for his democratic convictions. His trial had been reported almost in its entirety. Censorship had lost its teeth, and indeed the Austrian parliament was reconvened a few days after Adler’s conviction.
Schlick wrote that he sometimes wondered whether the historians in some far-off and more enlightened future, when asked in what period the Great War had raged, would reply: “The Great War? Ah yes, it took place in the period when Albert Einstein was completing his theory of relativity.”
Einstein congratulated Schlick effusively on his book: “Your presentation is of unsurpassable clarity and transparence. You have not shied away from any difficulty, but have gone straight to the point, spelling out everything that is important while leaving out all irrelevancies. Whoever does not understand your presentation must be completely unable to grasp thoughts of this sort.”
many internationally minded people felt this was a wonderful symbolic event, and they rejoiced in the way that science united people across cultural gaps.
While still a student, Carnap had written to Russell to inquire about an affordable copy of the monumental Principia Mathematica, as the German currency had collapsed. However, Russell had no free copy left; he replied instead by sending to the unknown young German student thirty handwritten pages filled with the most important formulas of the three-volume set.