WEBVTT 00:00:02.179 --> 00:00:06.960 Hi, have you ever encountered an idea so beautiful 00:00:06.960 --> 00:00:11.939 that you wanted it to be true? The ancient Greeks 00:00:11.939 --> 00:00:15.240 were fascinated by a special group of three -dimensional 00:00:15.240 --> 00:00:18.440 shapes that we now call the platonic solids. 00:00:19.420 --> 00:00:23.600 These shapes are remarkable because every face 00:00:23.600 --> 00:00:27.699 is the same regular shape, every edge has the 00:00:27.699 --> 00:00:31.320 same length, and every corner is arranged. in 00:00:31.320 --> 00:00:35.159 exactly the same way. A cube is one example. 00:00:35.479 --> 00:00:39.179 Each of its six faces is an identical square. 00:00:40.119 --> 00:00:43.700 Another is the tetrahedron. It's formed from 00:00:43.700 --> 00:00:48.000 four identical triangles. There are also shapes 00:00:48.000 --> 00:00:51.579 that are made from eight triangles, 20 triangles, 00:00:51.840 --> 00:00:57.500 and 12 pentagons. And that is the complete list. 00:00:58.219 --> 00:01:03.420 There are exactly five platonic solids. Not six, 00:01:03.659 --> 00:01:09.180 not a hundred, only five. The ancient Greeks 00:01:09.180 --> 00:01:12.379 found this deeply significant. And personally, 00:01:12.500 --> 00:01:17.000 I find it pretty cool. These shapes seem to possess 00:01:17.000 --> 00:01:21.620 a kind of mathematical perfection. Plato even 00:01:21.620 --> 00:01:24.060 connected them to the structure of the physical 00:01:24.060 --> 00:01:28.930 world. He associated four of the solids with 00:01:28.930 --> 00:01:31.890 what were believed at that time as the basic 00:01:31.890 --> 00:01:37.769 elements, earth, water, air, and fire. The fifth 00:01:37.769 --> 00:01:41.670 was connected to the cosmos itself. That theory 00:01:41.670 --> 00:01:45.549 was beautiful. Each fundamental part of nature 00:01:45.549 --> 00:01:50.049 had its own perfect shape. Mathematics appeared 00:01:50.049 --> 00:01:53.209 to reveal the hidden architecture of the universe. 00:01:54.890 --> 00:01:58.629 Nearly 2 ,000 years later, the astronomer Johannes 00:01:58.629 --> 00:02:02.489 Kepler was captivated by these same five shapes. 00:02:03.349 --> 00:02:07.069 At the time, only six planets were known, and 00:02:07.069 --> 00:02:10.590 Kepler noticed that five platonic solids could 00:02:10.590 --> 00:02:14.830 be placed between six spheres, and he wondered 00:02:14.830 --> 00:02:17.669 whether these shapes explained the distances 00:02:17.669 --> 00:02:21.949 between the planets. He imagined one sphere representing 00:02:21.949 --> 00:02:25.719 the orbit of a planet. Inside it, he placed a 00:02:25.719 --> 00:02:29.060 platonic solid. Then he placed another sphere 00:02:29.060 --> 00:02:32.120 inside that solid, followed by another solid, 00:02:32.219 --> 00:02:36.180 and so on. It was an extraordinarily beautiful 00:02:36.180 --> 00:02:41.639 model. But it was wrong. As measurements of the 00:02:41.639 --> 00:02:44.840 planets became more accurate, the distances did 00:02:44.840 --> 00:02:49.219 not fit Kepler's model. Now, I find Kepler's 00:02:49.219 --> 00:02:52.699 story encouraging. because his mistake did not 00:02:52.699 --> 00:02:56.539 make him a poor scientist. His desire to understand 00:02:56.539 --> 00:02:59.520 the heavens eventually contributed to a much 00:02:59.520 --> 00:03:02.680 greater discovery that the planets travel in 00:03:02.680 --> 00:03:06.900 ellipses rather than perfect circles. Kepler 00:03:06.900 --> 00:03:10.419 was willing to release a beautiful theory when 00:03:10.419 --> 00:03:15.340 reality would not support it. But that can be 00:03:15.340 --> 00:03:19.360 difficult. We are drawn to explanations that 00:03:19.360 --> 00:03:26.069 feel, balanced, complete, and elegant. When all 00:03:26.069 --> 00:03:30.610 the pieces fit neatly together, we experience 00:03:30.610 --> 00:03:38.069 the satisfaction of seeing a pattern. But our 00:03:38.069 --> 00:03:42.050 ability to find a pattern does not guarantee 00:03:42.050 --> 00:03:47.689 that the pattern is true. Sometimes we discover 00:03:47.689 --> 00:03:52.020 the hidden structure of reality. Other times, 00:03:52.039 --> 00:03:56.699 we impose a structure because we want reality 00:03:56.699 --> 00:04:02.780 to be simpler and more orderly than it is. Now, 00:04:02.800 --> 00:04:06.319 this does not mean beauty should make us suspicious. 00:04:07.039 --> 00:04:10.639 Beauty is often a valuable guide in mathematics 00:04:10.639 --> 00:04:15.819 and science and art and faith. It awakens curiosity 00:04:15.819 --> 00:04:20.420 and invites us to look more closely. But beauty 00:04:20.420 --> 00:04:25.160 is an invitation to investigate, not permission 00:04:25.160 --> 00:04:29.660 to stop asking questions. The platonic solids 00:04:29.660 --> 00:04:34.480 really are beautiful. Kepler's model really was 00:04:34.480 --> 00:04:39.660 imaginative. But reality was larger than the 00:04:39.660 --> 00:04:45.339 beautiful shape he had created for it. Perhaps 00:04:45.339 --> 00:04:51.339 humility means allowing reality to correct even 00:04:51.339 --> 00:04:56.800 our favorite ideas. So, here is a challenging 00:04:56.800 --> 00:05:01.839 question for you and for me. Are there ideas 00:05:01.839 --> 00:05:06.100 that we are so passionate about that our passion 00:05:06.100 --> 00:05:11.000 sometimes leads us astray? And to be honest, 00:05:11.139 --> 00:05:14.680 that is a difficult lesson that I have had to 00:05:14.680 --> 00:05:19.500 learn. Passion can inspire us to see possibilities 00:05:19.500 --> 00:05:24.339 that others miss. But if we're not careful, it 00:05:24.339 --> 00:05:28.480 can persuade us to see patterns that are not 00:05:28.480 --> 00:05:34.079 really there. Humility allows us to remain passionate 00:05:34.079 --> 00:05:38.699 while still giving reality the final word.