If you keep proving stuff that others have done, getting confidence, increasing the complexities of your solutions - for the fun of it - then one day you'll turn around and discover that nobody actually did that one!
In any decision for action, when you have to make up your mind what to do, there is always a 'should' involved, and this cannot be worked out from, 'If I do this, what will happen?' alone.
In talking about the impact of ideas in one field on ideas in another field, one is always apt to make a fool of oneself.
In the Raphael Room, the secret turned out to be that only some of the paintings were made by the great master; the rest were made by students. I had liked the ones by Raphael. This was a big jab for my self-confidence in my ability to appreciate art.
Is no one inspired by our present picture of the universe? This value of science remains unsung by singers: you are reduced to hearing not a song or poem, but an evening lecture about it. This is not yet a scientific age.
It is a curious historical fact that modern quantum mechanics began with two quite different mathematical formulations: the differential equation of Schroedinger and the matrix algebra of Heisenberg. The two apparently dissimilar approaches were proved to be mathematically equivalent.
It is going to be necessary that everything that happens in a finite volume of space and time would have to be analyzable with a finite number of logical operations. The present theory of physics is not that way, apparently. It allows space to go down into infinitesimal distances, wavelengths to get infinitely great, terms to be summed in infinite order, and so forth; and therefore, if this proposition [that physics is computer-simulatable] is right, physical law is wrong.
It is necessary to look at the results of observation objectively, because you, the experimenter, might like one result better than another.
It's the way I study - to understand something by trying to work it out or, in other words, to understand something by creating it. Not creating it one hundred percent, of course; but taking a hint as to which direction to go but not remembering the details. These you work out for yourself.
I've always been very one-sided about science, and when I was younger, I concentrated almost all my effort on it.
Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry.
Once you have a computer that can do a few things - strictly speaking, one that has a certain 'sufficient set' of basic procedures - it can do basically anything any other computer can do. This, loosely, is the basis of the great principle of 'Universality'.
One of the greatest experimental scientists of the time who was really doing something, William Harvey, said that what Bacon said science was, was the science that a lord-chancellor would do. He [Bacon] spoke of making observations, but omitted the vital factor of judgment about what to observe and what to pay attention to.
Our imagination is stretched to the utmost, not as in fiction, to imagine things which are not really there, but just to comprehend those things which are there.
People are always asking for the latest developments in the unification of this theory with that theory, and they don't give us a chance to tell them anything about one of the theories that we know pretty well. They always want to know things that we don't know.
People often think I'm a faker, but I'm usually honest, in a certain way - in such a way that often nobody believes me!
Perhaps one day we will have machines that can cope with approximate task descriptions, but in the meantime, we have to be very prissy about how we tell computers to do things.
Philosophers say a great deal about what is absolutely necessary for science, and it is always, so far as one can see, rather naive, and probably wrong.
Physicists like to think that all you have to do is say, these are the conditions, now what happens next?
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