Quote of the Day
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.
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 universe is governed by science. But science tells us that we can't solve the equations, directly in the abstract.
Playing a three-hour Rush show is like running a marathon while solving equations.
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.
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.
Friedrich August von Hayek
We have the only cookbook in the world that has partial differential equations in it.
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.
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.
In my own research when I'm working with equations, I never feel like I really understand what I'm doing if I'm solely relying on the mathematics for my understanding. I need to have a visual picture in my mind. I'm constantly translating from the math to some intuitive mind's-eye picture.
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.
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.
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.
Technologies evolve in the strangest ways. Computers were created to calculate ballistics equations, and now we use them to create amusing illusions. Creating amusing illusions is a big business if you play it right.
Global equations undergo changes, this is their nature.
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.
I became an atheist because, as a graduate student studying quantum physics, life seemed to be reducible to second-order differential equations. Mathematics, chemistry and physics had it all. And I didn't see any need to go beyond that.
The complicated, ambiguous milieu of human contact is being replaced with simple, scalable equations. We maintain thousands more friends than any human being in history, but at the cost of complexity and depth. Every minute spent online is a minute of face-to-face time lost.
Daniel H. Wilson
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.
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.
We seem to forget that innovation doesn't just come from equations or new kinds of chemicals, it comes from a human place. Innovation in the sciences is always linked in some way, either directly or indirectly, to a human experience.
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.
We tend to think of science as finding equations, like E=MC2, that are simple and elegant. But maybe some theories are complicated, and we can only find the simple ones.
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.
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?
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