in fact, let's talk about the example that richard feynman talks about when he talks about refractions a dandy. it's in your text. let's suppose you're a lifeguard right here, and this is a top view of the beach. and here's a sandy beach. there's sand and water down here. this is a helicopter view. and down here is a person drowning. drowning in the water, so the sharks are coming and something like that. now, you're the lifeguard-type up here. and you want to get from here to here in the least time, okay? so, you might say, well, i'll take a straight line path. good idea, or not good idea? begin with n, g. not. not good idea. hc. has the person-- oh, you don't-- well--let me ask you a question, how fast can you go across the sand compared to how fast can you swim? fast enough. how can you move faster, across the sand or swimming? how many of you say, "honey, i'm not so good in the land, but man, you should see me in the water." [laughs] come on, come on, most of us could go faster across the land, yeah? so it might be that you would say, "hey, what i'll do, is i wanna go the shortest