WEBVTT 00:00:02.629 --> 00:00:06.389 Hi, is a coffee mug the same shape as a donut? 00:00:08.009 --> 00:00:11.949 Probably not. Obviously not. Well, at least that's 00:00:11.949 --> 00:00:14.509 what most of us would say. But a mathematician 00:00:14.509 --> 00:00:18.129 studying topology might say something different. 00:00:18.730 --> 00:00:22.949 They might say they're exactly the same. See, 00:00:23.030 --> 00:00:25.910 topology is an area of mathematics that studies 00:00:25.910 --> 00:00:29.250 shapes. but it has a particular definition of 00:00:29.250 --> 00:00:32.009 what it means for two shapes to be the same. 00:00:33.210 --> 00:00:36.450 Imagine that your coffee mug is made out of soft 00:00:36.450 --> 00:00:40.289 clay. You can stretch it and bend it, squish 00:00:40.289 --> 00:00:44.390 it. You just cannot tear it apart or glue separate 00:00:44.390 --> 00:00:48.289 pieces together. And with enough manipulation, 00:00:48.590 --> 00:00:52.090 you could gradually reshape that coffee mug into 00:00:52.090 --> 00:00:55.560 a donut. So hold through the handle, becomes 00:00:55.560 --> 00:00:58.880 the hole through the middle of the donut. So 00:00:58.880 --> 00:01:04.040 topologically, they're the same. This may sound 00:01:04.040 --> 00:01:07.599 like a mathematical game, but it reveals something 00:01:07.599 --> 00:01:12.159 powerful about topology. Topology allows us to 00:01:12.159 --> 00:01:16.260 study properties that remain unchanged while 00:01:16.260 --> 00:01:19.859 an object bends, stretches, twists, or folds. 00:01:20.640 --> 00:01:24.370 Think about a long protein chain. it can fold 00:01:24.370 --> 00:01:28.450 into an incredibly complicated shape. But certain 00:01:28.450 --> 00:01:31.489 properties, such as whether the chain is knotted, 00:01:31.670 --> 00:01:35.349 can remain the same throughout those transformations. 00:01:37.129 --> 00:01:40.430 Topology helps us to identify what is changing 00:01:40.430 --> 00:01:46.689 and what remains fundamentally unchanged. Of 00:01:46.689 --> 00:01:48.650 course, in almost every other way, a coffee mug 00:01:48.650 --> 00:01:51.390 and a donut are different. One holds my coffee. 00:01:51.930 --> 00:01:54.890 The other tastes much better. So which answer 00:01:54.890 --> 00:02:00.409 is correct? Are they the same or different? Well, 00:02:00.430 --> 00:02:03.150 both. It depends on what we mean by the same. 00:02:03.549 --> 00:02:06.769 And that's what I love about mathematics. Mathematics 00:02:06.769 --> 00:02:10.590 often forces us to slow down and ask a more precise 00:02:10.590 --> 00:02:14.849 question. Same in what sense? We could ask that 00:02:14.849 --> 00:02:17.969 question about people. Are two people different? 00:02:18.289 --> 00:02:20.860 Well, of course. We have different personalities, 00:02:21.219 --> 00:02:22.979 abilities, experiences, beliefs, appearances, 00:02:23.300 --> 00:02:26.460 backgrounds, yada, yada, yada. But perhaps there 00:02:26.460 --> 00:02:28.879 are other ways in which we are profoundly the 00:02:28.879 --> 00:02:33.060 same. Last week, I talked about the starting 00:02:33.060 --> 00:02:36.879 points of my worldview. One of them is that every 00:02:36.879 --> 00:02:41.900 human being has value. So, in that sense, I believe 00:02:41.900 --> 00:02:45.400 we're the same. Not because our accomplishments 00:02:45.400 --> 00:02:47.979 are equal or because our behavior is the same. 00:02:48.479 --> 00:02:51.599 or because we agree, but because I do not believe 00:02:51.599 --> 00:02:55.120 our fundamental value depends on any of those 00:02:55.120 --> 00:02:59.360 things. Definitions determine what differences 00:02:59.360 --> 00:03:03.879 we notice and which ones we ignore. Topology 00:03:03.879 --> 00:03:07.300 ignores many obvious differences between a mug 00:03:07.300 --> 00:03:11.599 and a donut to reveal something deeper they share. 00:03:12.819 --> 00:03:15.360 And maybe that's worth remembering when we look 00:03:15.360 --> 00:03:18.840 at each other. So here's our question for today. 00:03:19.800 --> 00:03:22.500 When you encounter someone very different from 00:03:22.500 --> 00:03:27.240 you, which differences do you notice first? And 00:03:27.240 --> 00:03:30.120 what might you be overlooking that you share 00:03:30.120 --> 00:03:30.539 the same?