a certain amount of time goes by before it closes. During that time, things move, and this causes the image to blur. This blur turns out to be really important for making the motion look smooth, so you have to simulate it in the renderer. Another thing you have to simulate is the aperture of the lens -- the light is not entering the camera in one spot, but all over the lens, and that gives you depth of field. You need to simulate both blur and lens effects, but that means that not only are you integrating the scene around each pixel, you also have to integrate that pixel over time and over the lens and over other things. You end up with this incredibly complex integral, and it turns out that there is a technique in physics called Monte Carlo integration that is perfectly suited to dealing with it. However, none of this stuff was in the undergraduate curriculum -- I had to learn it on my own later. What physics really taught me was how to think about things in a creative and rigorous way. It taught me how to think about hard problems. Are there other ways that physics is used in animation? At Pixar, we use physics a lot to simulate the motion of complex things like clothes or hair. But you have to remember that in the animated world, animators do wacky things. They exaggerate enormously in order to tell the story, so the