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A good theoretical physicist today might find it useful to have a wide range of physical viewpoints and mathematical expressions of the same theory (for example, of quantum electrodynamics) available to him. This may be asking too much of one man. Then new students should as a class have this. If every individual student follows the same current fashion in expressing and thinking about electrodynamics or field theory, then the variety of hypotheses being generated to understand strong interactions, say, is limited. Perhaps rightly so, for possibly the chance is high that the truth lies in the fashionable direction. But, on the off-chance that it is in another direction—a direction obvious from an unfashionable view of field theory—who will find it?
Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin.
EFFECT, n. The second of two phenomena which always occur together in the same order. The first, called a Cause, is said to generate the other—which is no more sensible than it would be for one who has never seen a dog except in pursuit of a rabbit to declare the rabbit the cause of the dog.
Everybody can be great. Because anybody can serve. You don’t have to have a college degree to serve … You only need a heart full of grace. A soul generated by love.
It has been said that America is like a gigantic boiler in that once the fire is lighted, there are no limits to the power it can generate. Environmentally, the fire has been lit.
Scientific method is concerned with efficient ways of generating knowledge.
So when light generates itself in one direction drawing matter with it, it produces local motion; and when the light within matter is sent out and what is outside is sent in, it produces qualitative change. From this it is clear that corporeal motion is a multiplicative power of light, and this is a corporeal and natural appetite.
The astronomers said, ‘Give us matter and a little motion and we will construct the universe. It is not enough that we should have matter, we must also have a single impulse, one shove to launch the mass and generate the harmony of the centrifugal and centripetal forces.’ ... There is no end to the consequences of the act. That famous aboriginal push propagates itself through all the balls of the system, and through every atom of every ball.
The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.
The line separating investment and speculation, which is never bright and clear, becomes blurred still further when most market participants have recently enjoyed triumphs. Nothing sedates rationality like large doses of effortless money. After a heady experience of that kind, normally sensible people drift into behavior akin to that of Cinderella at the ball. They know that overstaying the festivities—that is, continuing to speculate in companies that have gigantic valuations relative to the cash they are likely to generate in the future—will eventually bring on pumpkins and mice. But they nevertheless hate to miss a single minute of what is one helluva party. Therefore, the giddy participants all plan to leave just seconds before midnight. There’s a problem, though: They are dancing in a room in which the clocks have no hands.
The ‘mad idea’ which will lie at the basis of a future fundamental physical theory will come from a realization that physical meaning has some mathematical form not previously associated with reality. From this point of view the problem of the ‘mad idea’ is the problem of choosing, not of generating, the right idea. One should not understand that too literally. In the 1960s it was said (in a certain connection) that the most important discovery of recent years in physics was the complex numbers. The author [Yuri Manin] has something like that in mind.