Quotes About Equations

Einstein's goal as he pursued his general theory of relativity was to find the mathematical equations describing two complementary processes: 1. How a gravitational field acts on matter, telling it how to move. 2. And in turn, how matter generates gravitational fields in spacetime, telling it how to curve. His head-snapping insight was that gravity could be defined as the curvature of spacetime, and thus it could be represented by a metric tensor. For more than three years he

The bushy-bearded Scottish physicist James Clerk Maxwell (1831–1879) subsequently devised wonderful equations that specified, among other things, how changing electric fields create magnetic fields and how changing magnetic fields create electrical ones. A changing electric field could, in fact, produce a changing magnetic field that could, in turn, produce a changing electric field, and so on. The result of this coupling was an electromagnetic wave.

His theory indicated that the universe would have to be either expanding or contracting, not staying static. According to his field equations, a static universe was impossible because the gravitational forces would pull all the matter together.

The general laws of nature are to be expressed by equations that hold true for all systems of coordinates, that is they are covariant with respect to any substitutions whatever.

The infinite zero of a black hole-mass crammed into zero space, curving space infinitely-punches a hole in the smooth rubber sheet. The equations of general relativity cannot deal with the sharpness of zero. In a black hole, space and time are meaningless.

Nature speaks in equations.

One of the most outstanding conclusions of some postmodernists is that all of reality is socially constructed. They have even taken issue with the conclusions of Newton and Einstein, on the basis that the privilege of those scientists is obvious in their equations and, as old white guys, their biases inherently prevented them from knowing anything real of the world.

In 1914, a Finnish physicist named Gunnar Nordstrom found that all you had to do to unify gravity with electromagnetism was increase the dimensions of space by one. He wrote the equations that describe electromagnetism in a world with four dimensions of space (and one of time), and out popped gravity. Just by the extra dimension of space, you got a unification of gravity with electromagnetism that was also perfectly consistent with Einstein's special theory of relativity.

We want to attach ourselves to narratives. We don't act because of equations. We follow our beliefs. We get behind leaders who stir our feelings.

differential equations that can be solved in "closed form," that is, by means of a formula for the unknown function f, are the exception rather than the rule

we do not have anything directly comparable to continued-fraction expansions for a complex quadratic irrationality. In fact, the simple, but true, answer to the problem of how to find an infinite number of rational numbers that converge to such an irrationality is that you cannot! Correspondingly, the analogue of the Pell equation has only finitely many solutions.

Fundamental to understanding the arithmetic of Rd is the following question: which ordinary prime numbers p are irreducible elements of Rd and which ones factorize as products of irreducible elements in Rd? We will see shortly that if a prime number does factorize in Rd, it must be expressible as the product of precisely two irreducible factors.

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.

Music, like the visual arts, is rooted in our experience of the natural world," said Schwartz. "It emulates our sound environment in the way that visual arts emulate the visual environment." In music we hear the echo of our basic sound making instrument-the vocal tract. This explanation for human music is simpler still than Pythagoras's mathematical equations: we like the sounds that are familiar to us-specifically, we like sounds that remind us of us.

Newton's equations of absolute exactitude and certainty ("classical determinism") were replaced by Schrodinger's new equations and Heisenberg's mathematics of fuzziness, indeterminacy, and probability.

Dick Feynman was a genius of visualization (he was also no slouch with equations): he made a mental picture of anything he was working on. While others were writing blackboard-filling formulas to express the laws of elementary particles, he would just draw a picture and figure out the answer.

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.

A book on the new physics, if not purely descriptive of experimental work, must essentially be mathematical.

Did your mathematical studies ever reach to the quadratic equation, Stephen?' 'They did not reach to the far end of the multiplication table.

memories of the Depression faded, economists fell back in love with the old, idealized vision of an economy in which rational individuals interact in perfect markets, this time gussied up with fancy equations. The renewed romance with the idealized market was, to be sure, partly a response to shifting political winds

James Clark Maxwell

Economics is all algebra.

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.

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.