A Quote by Paul Dirac
A good deal of my research in physics has consisted in not setting out to solve some particular problem, but simply examining mathematical equations of a kind that physicists use and trying to fit them together in an interesting way, regardless of any application that the work may have. It is simply a search for pretty mathematics. It may turn out later to have an application. Then one has good luck. At age 78.
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To do any important work in physics a very good mathematical ability and aptitude are required. Some work in applications can be done without this, but it will not be very inspired. If you must satisfy your "personal curiosity concerning the mysteries of nature" what will happen if these mysteries turn out to be laws expressed in mathematical terms (as they do turn out to be)? You cannot understand the physical world in any deep or satisfying way without using mathematical reasoning with facility.
Just by studying mathematics we can hope to make a guess at the kind of mathematics that will come into the physics of the future... If someone can hit on the right lines along which to make this development, it may lead to a future advance in which people will first discover the equations and then, after examining them, gradually learn how to apply them... My own belief is that this is a more likely line of progress than trying to guess at physical pictures.
I don't have any particular recipe. It is the reason why doing research is challenging as well as attractive. It is like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck, you might find a way out.
It seems that every practitioner of physics has had to wonder at some point why mathematics and physics have come to be so closely entwined. Opinions vary on the answer. ..Bertrand Russell acknowledged..'Physics is mathematical not because we know so much about the physical world, but because we know so little.' ..Mathematics may be indispensable to physics, but it obviously does not constitute physics.
One of the obstacles to recognizing chronic mistreatment in relationships is that most abusive men simply don't seem like abusers. They have many good qualities, including times of kindness, warmth, and humor, especially in the early period of a relationship. An abuser's friends may think the world of him. He may have a successful work life and have no problems with drugs or alcohol. He may simply not fit anyone's image of a cruel or intimidating person. So when a woman feels her relationship spinning out of control, it is unlikely to occur to her that her partner is an abuser.
While physics and mathematics may tell us how the universe began, they are not much use in predicting human behavior because there are far too many equations to solve. I'm no better than anyone else at understanding what makes people tick, particularly women.
The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved.
Why should someone have to retrain themselves to use a new application that does the same basic thing as the old application, just because something as trivial as the operating system changed out from under them?
Money cannot be applied to the *general welfare*, otherwise than by an application of it to some *particular* measure conducive to the general welfare. Whenever, therefore, money has been raised by the general authority, and is to be applied to a particular measure, a question arises whether the particular measure be within the enumerated authorities vested in Congress. If it be, the money requisite for it may be applied to it; if it be not, no such application can be made.
You never can tell whether bad luck may not after all turn out to be good luck.
If you thought you were trying to find out more about it because you're gonna get an answer to some deep philosophical question...you may be wrong! It may be that you can't get an answer to that particular question by finding out more about the character of nature. But my interest in science is to simply find out about the world.
Editing is simply the application of the common sense of any good reader. That's why, to be an editor, you have to be a reader. It's the number one qualification.
To criticize mathematics for its abstraction is to miss the point entirely. Abstraction is what makes mathematics work. If you concentrate too closely on too limited an application of a mathematical idea, you rob the mathematician of his most important tools: analogy, generality, and simplicity. Mathematics is the ultimate in technology transfer.
It's fine to work on any problem, so long as it generates interesting mathematics along the way - even if you don't solve it at the end of the day.
What appear to be the most valuable aspects of the theoretical physics we have are the mathematical descriptions which enable us to predict events. These equations are, we would argue, the only realities we can be certain of in physics; any other ways we have of thinking about the situation are visual aids or mnemonics which make it easier for beings with our sort of macroscopic experience to use and remember the equations.
There was a time when the average reader read a novel simply for the moral he could get out of it, and however na?ve that may have been, it was a good deal less na?ve than some of the limited objectives he has now. Today novels are considered to be entirely concerned with the social or economic or psychological forces that they will by necessity exhibit, or with those details of daily life that are for the good novelist only means to some deeper end.
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