You propound a complicated arithmetical problem: say cubing a number containing four digits. Give me a slate and half an hour's time, and I can produce a wrong answer.
We are consuming our forests three times faster than they are being reproduced. Some of the richest timber lands of this continent have already been destroyed, and not replaced, and other vast areas are on the verge of destruction. Yet forests, unlike mines, can be so handled as to yield the best results of use, without exhaustion, just like grain fields.
A line is not made up of points. ... In the same way, time is not made up parts considered as indivisible 'nows.' Part of Aristotle's reply to Zeno's paradox concerning continuity.
From a certain temperature on, the molecules 'condense' without attractive forces; that is, they accumulate at zero velocity. The theory is pretty, but is there some truth in it.
By an application of the theory of relativity to the taste of readers, today in Germany I am called a German man of science, and in England I am represented as a Swiss Jew. If I come to be represented as a bête noire, the descriptions will be reversed, and I shall become a Swiss Jew for the Germans and a German man of science for the English!
The creative scientist studies nature with the rapt gaze of the lover, and is guided as often by aesthetics as by rational considerations in guessing how nature works.
Since Copernicus, man seems to have got himself on an inclined plane-now he is slipping faster and faster away from the center into-what? into nothingness? into a 'penetrating sense of his nothingness?' ... all science, natural as well as unnatural-which is what I call the self-critique of knowledge-has at present the object of dissuading man from his former respect for himself, as if this had been but a piece of bizarre conceit.
For myself, I like a universe that, includes much that is unknown and, at the same time, much that is knowable. A universe in which everything is known would be static and dull, as boring as the heaven of some weak-minded theologians. A universe that is unknowable is no fit place for a thinking being. The ideal universe for us is one very much like the universe we inhabit. And I would guess that this is not really much of a coincidence.
The nation behaves well if it treats the natural resources as assets which it must turn over to the next generation increased; and not impaired in value.
The great pagan world of which Egypt and Greece were the last living termsonce had a vast and perhaps perfect science of itsown, a science in terms of life. In our era this science crumbled into magic and charlatanry. But even wisdom crumbles.
We cannot step aside and say that we have achieved our goal by inventing a new drug or a new way by which to treat presently incurable diseases, a new way to help those who suffer from malnutrition, or the creation of ideal balanced diets on a worldwide scale. We cannot rest till the way has been found, with our help, to bring our finest achievement to everyone.
I think that I am among the few lucky ones who are exploiting complexity. Most people are unhappy with the emergence of complexity, they would prefer it if the world were very simple, but then it would be a doom for a cryptographer like myself.