Zitat des Tages über Gleichungen / Equations:
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.
At the age of 12, I developed an intense interest in mathematics. On exposure to algebra, I was fascinated by simultaneous equations and read ahead of the class to the end of the book.
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?
When I got to college, I was intending to study film. But I found that my brain was feeling mushy, so I took a few math classes. I started doing really well at them, and solving equations was this, like, drug rush.
We have the only cookbook in the world that has partial differential equations in it.
I regard it in fact as the great advantage of the mathematical technique that it allows us to describe, by means of algebraic equations, the general character of a pattern even where we are ignorant of the numerical values which will determine its particular manifestation.
The triumph is that the waveform we measure is very well represented by solutions of these equations. Einstein is right in a regime where his theory has never been tested before.
You kind of alluded to it in your introduction. I mean, for the last 300 or so years, the exact sciences have been dominated by what is really a good idea, which is the idea that one can describe the natural world using mathematical equations.
Global equations undergo changes, this is their nature.
Gamers have this tendency to turn games into mathematical equations, breaking them into lists of components like 'presentation' and 'mechanics' and judging each one on its own merits.
I love studying asteroids because they are relatively simple, just rocks in space. They can be understood with physics and described with elegant equations. For the most part, they are serene celestial bodies.
A common misconception about how things such as space shuttles come to be is that engineers simply apply the theories and equations of science. But this cannot be done until the new thing-to-be is conceived in the engineer's mind's eye. Rather than following from science, engineered things lead it.
Concern for man and his fate must always form the chief interest of all technical endeavors. Never forget this in the midst of your diagrams and equations.
Playing a three-hour Rush show is like running a marathon while solving equations.
Science is beautiful when it makes simple explanations of phenomena or connections between different observations. Examples include the double helix in biology and the fundamental equations of physics.
Einstein had looked at the numbers and dimensions that went into his equations for gravitational waves and said, essentially, 'This is so tiny that it will never have any influence on anything, and nobody can measure it.' And when you think about the times and the technology in 1916, he was probably right.
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.
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.
The thing that got me started on the science that I've been building now for about 20 years or so was the question of okay, if mathematical equations can't make progress in understanding complex phenomena in the natural world, how might we make progress?
If God has made the world a perfect mechanism, He has at least conceded so much to our imperfect intellect that in order to predict little parts of it, we need not solve innumerable differential equations, but can use dice with fair success.
The field equations and the whole history of general relativity have been complicated.
The math of quantum mechanics and the math of general relativity, when they confront one another, they are ferocious antagonists and the equations don't work.
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.
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 can summarize electricity, magnetism and gravity into equations one inch long, and that's the power of field theory. And so I said to myself: I will create a field theory of strings. And when I did it one day, it was incredible, realizing that on a sheet of paper I can write down an equation which summarized almost all physical knowledge.
Symmetry does mean something different for physicists than for members of the public. It means that an object or a theory does not change when you make some transformation - either rotating or moving it or doing something to the equations.
I have my hopes, & very distinct ones, too, of one day getting cerebral phenomena such that I can put them into mathematical equations: in short, a law or laws for the mutual actions of the molecules of the brain (equivalent to the law of gravitation for the planetary & sideral world).
My mother was the nicest person in the world. I still have people coming to me to say how she was so warm, generous, and kind-hearted. She never washed her dirty linen in public. She always maintained her equations with people.