A Quote by Edward Witten
But the beauty of Einstein's equations, for example, is just as real to anyone who's experienced it as the beauty of music. We've learned in the 20th century that the equations that work have inner harmony.
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Like music or art, mathematical equations can have a natural progression and logic that can evoke rare passions in a scientist. Although the lay public considers mathematical equations to be rather opaque, to a scientist an equation is very much like a movement in a larger symphony. Simplicity. Elegance. These are the qualities that have inspired some of the greatest artists to create their masterpieces, and they are precisely the same qualities that motivate scientists to search for the laws of nature. LIke a work of art or a haunting poem, equations have a beauty and rhythm all their own.
It is more important to have beauty in one's equations than to have them fit experiment... It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one's work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further developments of the theory.
If you look at Einstein's equations and put in low speeds and low gravity, they become Newton's equations.
Even before string theory, especially as physics developed in the 20th century, it turned out that the equations that really work in describing nature with the most generality and the greatest simplicity are very elegant and subtle.
Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe?
The power of equations lies in the philosophically difficult correspondence between mathematics, a collective creation of human minds, and an external physical reality. Equations model deep patterns in the outside world. By learning to value equations, and to read the stories they tell, we can uncover vital features of the world around us.
I now want to tell three stories about advances in twentieth-century physics. A curious fact emerges in these tales: time and again physicists have been guided by their sense of beauty not only in developing new theories but even in judging the validity of physical theories once they are developed. Simplicity is part of what I mean by beauty, but it is a simplicity of ideas, not simplicity of a mechanical sort that can be measured by counting equations or symbols.
The most natural beauty in the world is honesty and moral truth. For all beauty is truth. True features make the beauty of the face; true proportions, the beauty of architecture; true measures, the beauty of harmony and music.
It is more important to have beauty in one's equations than to have them fit experiment.
It is not expensive to be beautiful. It takes only a little effort to be presentable and beautiful. But it takes some effort. And unfortunately people think of beauty as luxury, beauty as frivolity, ... or extravagance. Beauty is a discipline, beauty is art, is harmony, in the ideological sense and in the theological sense, beauty is God and love made real. And the ultimate reach in this world is beauty.
As we all know, there is inner beauty and outer beauty. If we examine inner beauty, to me there is nothing more beautiful than inner peace, in a man or a woman.
If there are four equations and only three variables, and no one of the equations is derivable from the others by algebraic manipulation then there is another variable missing.
We already know the limits of Einstein's theories. From the centers of black holes at the very beginning of the universe - we call these singularities - Einstein's equations fail. In fact, people have joked that's where God is dividing by zero.
What can a pencil do for all of us? Amazing things. It can write transcendent poetry, uplifting music, or life-changing equations; it can sketch the future, give life to untold beauty, and communicate the full-force of our love and aspirations.
It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress.
I don't care much for equations myself. This is partly because it is difficult for me to write them down, but mainly because I don't have an intuitive feeling for equations.
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