Eitan Grinspun

Associate Professor of Computer Science, Columbia University
 
On Modelling the Geometries of Motion

"How objects move, how materials change shape over time, and the physics of how all of this happens can be most naturally described in terms of geometry... When you shake your head and your hair goes all over the place, or when you pour water from a cup into another cup, all of that motion can be written down in terms of a language called differential geometry."
Columbia expert on computer graphics discusses motion in the mathematical modelling of human hair, spaghetti and other mysteries of the physical world.

Interview transcript: Eitan Grinspun

How objects move, how materials change shape over time, and the physics of how all of this happens can be most naturally described in terms of geometry. That's the natural language we're talking about in the motion of objects. When you shake your head and your hair goes all over the place, or when you pour water from a cup into another cup, all of that motion can be written down in terms of a language called differential geometry.

If I had to distill what it is I look for when I try to understand the laws of motion, it's a couple of things. One, I think it's really interesting to look at geometry that can be explained in an integral, holistic sense rather than a differential or specialized sense. For example, if you built up a tensegrity structure, you don't know if it will be a stable structure by looking at any one connection. Looking in that way just tells you about that specific connection. But the only reason the overall structure can stay up and be stable is because everything is collaborating together. If you go back to Kepler's Second Law of Planetary Motion which describes the planetary orbit around the sun, it's not looking at the instantaneous velocity of the planet and the forces, it's looking at what happens over finite pieces of time and furthermore, how it applies to any finite piece of time anywhere. And so, in that sense, it's also a sort of global description of what's going on.

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