Modeling, they tried modeling all the time. They were always modeling things.

After decades indeed, centuries of employing such tricks, physicists have forgotten that they are modeling phenomena, not necessarily uncovering Divine Truth. For instance, we can easily write down the equations for a ball on a swinging spring, but if we stretch the spring enough and swing the ball hard enough, we can t solve those equations.

Math, differential equations.

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They're seeing adults. They're modeling their behavior.

Space physicists also achieved breakthroughs in computer modeling.

And that's why the equations look so simple.

Whoa, dude. Check out those killer equations. Sweet.

Do you know where these equations come from?

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There is some modeling of ecosystems going on now.

It used to be called rapid prototyping, rapid modeling.

The augmented equations, today known as the Maxwell equations, described a unified theory of electricity and magnetism. The new equations showed that light is a moving, self renewing disturbance in electrical and magnetic fields, and they predicted that new kinds of disturbances are possible.

This is from my group a slightly less glamorous computer modeling.

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We're talking about books on hyper geometric partial differential equations.

We have designed, and we have worked on the modeling and much of these ideas came from Danny and from his team the modeling of cancer in the body as complex system.

Modeling on the right hand side, there's a very complex computational model.

So we started a separate line of research doing driver state modeling.

We first captured the dynamics with a set of differential equations.

We make it come alive with equations, a lot of mathematics.

See, normally in school, you do things like solve quadratic equations.

You know, from physics to medicine, in particular, epidemiology and also mathematical modeling.

Maxwell's equations are of course symmetrical under rotations of all of space.

We've just abstracted what the retina's doing with a set of equations.

It can be used for calculating mathematical equations of all different types.

In the 1860 s, James Clerk Maxwell assembled the equations for electricity and magnetism, as they were then known, and discovered an inconsistency. He repaired the inconsistency by adding new terms to the equations.

But the thing about Charles and Ray is that they were always modeling stuff.

It's done by geologists, engineers, biologists, all sorts of different people modeling and simulation.

And those symmetries, then, make the equations even shorter, and even prettier, therefore.

Look at the world. You don't see equations carved on to the mountainsides.

So what it's doing is, it's replacing the retinal circuitry, really the guts of the retinal circuitry, with a set of equations, a set of equations that we can implement on a chip. So it's just math.

And so, in a way, the equations are serving as sort of a codebook. An image comes in, goes through the set of equations, and out comes streams of electrical pulses, just like a normal retina would produce.

During FY 1994, NASA made significant progress in measuring, modeling, and mitigating the orbital debris environment.

When I'm modeling a plant in a box, literally, I know where to draw the boundary.

We have the only cookbook in the world that has partial differential equations in it.

In particular, complex numerical modeling has led to a detailed conception of the Earth apos s magnetosphere.

Everything comes out of a point you have infinite density. And all the equations break down.

As a result of that modeling I ended up in all places, in Eritrea, in the Horn of Africa.

I was there because I was actually modeling the mangrove portion for a carbon credit program, under the U.N.

We then manipulate these equations with the help of control theory to create algorithms that stabilize the quad.

We live in a society that completely tends to valorize symbolic forms of representation algebraic representations, equations, codes.

And, in fact, the equations that make neurons into electrical generators were discovered by two Cambridge Nobel Laureates.