Phrases

180 quotes found

"Elegant derivations from first principles — which often proved tractable only when applied to idealized situations — were of little value to the many colleagues who needed to fine-tune electronics components for maximum efficiency... Schwinger rearranged his equations in terms of measurable inputs and outputs, just as his engineering colleagues at the Rad Lab had done with real-world electronics. By recasting the calculation, Schwinger managed to calculate the effects of quantum fluctuations on the electron's energy levels and obtain an answer that matched Lamb's measurement to an extraordinary precision. As it turned out, Japanese physicist Sin-Itiro Tomonaga had accomplished the same goal a few years earlier. Tomonaga's work on radar during the war had proven similarly essential to his theoretical approach. This war-forged pragmatism produced enormously impressive research and influenced a generation of leading scientists... Anything that smacked of 'interpretation', or worse, 'philosophy', began to carry a taint for many scientists who had come through the wartime projects. Conceptual scrutiny of foundations struck many as a luxury. The wartime style was reinforced in the United States by exponentially rising university enrolments after the war. The new classroom realities left little space for informal discussion of philosophy or foundations. The Rad Lab rallying cry of “Get the numbers out” shaded into “Shut up and calculate!”"

- Shut up and calculate

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"The madman. - Haven't you heard of that madman who in the bright morning lit a lantern and ran around the marketplace crying incessantly, 'I'm looking for God! I'm looking for God!' Since many of those who did not believe in God were standing around together just then, he caused great laughter. Has he been lost, then? asked one. Did he lose his way like a child? asked another. Or is he hiding? Is he afraid of us? Has he gone to sea? Emigrated? - Thus they shouted and laughed, one interrupting the other. The madman jumped into their midst and pierced them with his eyes. 'Where is God?' he cried; 'I'll tell you! We have killed him - you and I! We are all his murderers. But how did we do this? How were we able to drink up the sea? Who gave us the sponge to wipe away the entire horizon? What were we doing when we unchained this earth from its sun? Where is it moving to now? Where are we moving to? Away from all suns? Are we not continually falling? And backwards, sidewards, forwards, in all directions? Is there still an up and a down? Aren't we straying as though through an infinite nothing? Isn't empty space breathing at us? Hasn't it got colder? Isn't night and more night coming again and again? Don't lanterns have to be lit in the morning? Do we still hear nothing of the noise of the grave-diggers who are burying God? Do we still smell nothing of the divine decomposi­tion? - Gods, too, decompose! God is dead! God remains dead! And we have killed him! How can we console ourselves, the murderers of all murderers! The holiest and the mightiest thing the world has ever possessed has bled to death under our knives: who will wipe this blood from us? With what water could we clean ourselves? What festivals of atonement, what holy games will we have to invent for ourselves? Is the magnitude of this deed not too great for us? Do we not ourselves have to become gods merely to appear worthy of it?"

- God is dead

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"Up to this point we have restricted our attention to space as a mere extension. But space, as understood in common practice, implies considerably more: it represents a three-dimensional Euclidean continuum. When thus particularised, Kant's arguments as to its a priori character are no longer tenable in the light of modern discovery; and we must assume that this special form we credit to space arises entirely from our co-ordination of sense impressions conducted in the simplest way possible. On no account may we consider three-dimensional Euclidean space to be imposed a priori either by sensibility or by the understanding. ...it is generally conceded by scientists that the a priori doctrine of three-dimensional Euclidean space is one of the most pernicious teachings that philosophy has ever attempted to impose upon science. ... These views on space as professed by the greatest scientists are in large measure to be attributed to the discoveries of non-Euclidean geometry supplemented by the investigations of the psychophysicists. ...By the time men are of an age to philosophise, they have been subjected for so many years to beliefs based on inferences from experience, that the beliefs have remained, whereas the inferences, owing to the monotony of their repetition, have become second nature and appear intuitive. ... Were three-dimensional Euclidean space an a priori condition of the understanding, it would have been quite impossible for mathematicians to wend their way through the non-Euclidean hyperspaces of relativity. Neither can three-dimensional space be considered to be imposed by sensibility, since, as Poincaré tells us, after a certain amount of perseverance, he was aided to a considerable degree by sensibility when investigating the problems of Analysis Situs of four dimensions."

- A priori and a posteriori

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