Quotes About Equations

The equations are indifferent to the supposed freedom of human will. Some have taken this to mean that in a classical universe, free will would be an illusion. You are made of a collection of particles, so if the laws of classical physics could determine everything about your particles at any moment—where they'd be, how they'd be moving and so on—your willful ability to determine your own actions would appear fully compromised.

Within the modified equations, Kaluza found the ones Einstein had already used successfully to describe gravity in the familiar three dimensions of space and one of time. But because his new formulation included an additional dimension of space, Kaluza found an additional equation. Lo and behold, when Kaluza derived this equation he recognized it as the very one Maxwell had discovered half a century earlier to describe the electromagnetic field.

You could trust numbers, except perhaps for pi, but he was working on that in his spare time and it was bound to give in sooner or later.

In the words of the systems thinker John Sterman, 'The most important assumptions of a model are not in the equations, but what's not in them; not in the documentation, but unstated; not in the variables on the computer screen, but in the blank spaces around them'.

One of the beautiful things about mathematical physics is that equations contain stories.

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.

Winfree wrote equations for his system of oscillators, describing how fast each one moves through its cycle. At any instant, an oscillator's speed is determined by three contributions: its preferred pace, which is proportional to its natural frequency; its current sensitivity to any incoming influences (which depends on where it is in its cycle); and the total influence exerted by all the other oscillators (which depends on where they all are in their cycles).

What I've just described is called a system of differential equations. Such equations arise whenever we have rules for speeds depending on current positions.

The equations showed that the answer depends on how similar the oscillators are. If they're identical, or nearly so, I found that the disturbances grow exponentially fast as oscillators clump together in phase, in an embryonic form of sync. Then out popped a formula for the exponential growth rate (analogous to the interest rate for how fast your money compounds in the bank). No one had ever found such a formula before.

If we're lucky and skillful enough — if we transform the equations in just the right way — we can get them to reveal their hidden implications. To a mathematician, the process feels almost palpable. It's as if we're manipulating the equations, massaging them, trying to relax them enough so that they'll spill their secrets. We want them to open up and talk to us.

we've come to realize that most systems of differential equations are unsolvable, in that same sense; it's impossible to find a formula for the answer. There is, however, one spectacular exception. Linear differential equations are solvable.

Whenever the whole is different from the sum of the parts—whenever there's cooperation or competition going on—the governing equations must be nonlinear.

My heart was deep space and my head was maths

This is often the way it is in physics. Our mistake is not that we take our theories too seriously, but that we do not take them seriously enough. It is always hard to realize that these numbers and equations we play with at our desks have something to do with the real world.

Finally, there is a more subtle relation among F, E, and V.

If miracles had chemical equations then everyone would believe.

I have many dear friends in the film industry, but finally, the roles come to me on merit, not because of personal equations.

Algebra is the metaphysics of arithmetic.

All variables are independent.

Perhaps, then, the most surprising consequence of a visionary Theory of Everything is that it implies that on the grand scale the universe, including its origins and evolution, though extremely complicated, is not complex but in fact is surprisingly simple because it can be encoded in a limited number of equations, conceivably even just a single master equation.

Psychohistory was the quintessence of sociology; it was the science of human behavior reduced to mathematical equations. The individual human being is unpredictable, but the reactions of human mobs, Seldon found, could be treated statistically.

no human mind has created those equations directly. We have merely spent decades programming more powerful computers and they have devised and stored the equations, but, of course, we don't know if they are valid and have meaning. It depends entirely on how valid and meaningful the programming is in the first place.

For a full day he had checked and rechecked equations and relationships in a rattling uncertainty, mixed with growing excitement and a bitter gratitude that he had been taught at least elementary psychomathematics.

Las palabras son un sustituto bastante confuso de las ecuaciones matemáticas.