Setting up the episode: symmetry and physics

4:12principle and how that relates to the to the modern world. Now symmetry, everybody knows what symmetry is, right? The my favorite symmetric object is the Taj Mahal in India. Um the first time I saw it was actually I I was quite old even though I was grew up in um grew up and was born in India. I didn't see it until after college. And it is one of the most beautiful buildings I have ever seen on planet earth. And all of that has to do with symmetry. If you look at the Taj Mahal, right? It's an extremely symmetric building. And we kind of know what that means, right? We have this deep sort of intuitive sense that symmetry means

4:52balance beauty harmony right? But when we think of symmetry, we think of it as a static property. It's something that we're looking at for a static object, right? But what do we actually mean when we say symmetry? >> The idea is, and this is something that um the great mathematician Herman While came up with, the idea of symmetry from a mathematical sense is that a thing is symmetrical if there is something we can do to it so that after we have done it, it looks the same as it did before. >> This is a tongue twister. It is. But here here's what's happening. You've got a thing that is symmetric. What does

5:34that mean? That means I can do something to it and when I'm done doing it, it looks just the same. The Taj Mahal. Here's an example. Right. The imagine the Taj Mahal in your head. >> Yes. >> Flip it. Flip it along the XY plane. >> Yes. >> Not on the XY plane, on the vertical. Right. So, so everything that's on the left goes to the right. So, those spires on the left go to the spires on the right. The dome is exactly symmetric to the central axis. The two little domes on the side are symmetric. So they just