WEBVTT 00:00:02.439 --> 00:00:07.219 Hyatt, why do we find symmetry so beautiful? 00:00:07.940 --> 00:00:11.500 We see it in the wings of a butterfly, in the 00:00:11.500 --> 00:00:14.859 petals of a flower, and the intricate design 00:00:14.859 --> 00:00:18.780 of a snowflake. We use symmetry in architecture, 00:00:19.199 --> 00:00:24.440 in artwork, company logos, and the patterns woven 00:00:24.440 --> 00:00:29.300 into clothing. Even the human face has a general 00:00:29.300 --> 00:00:34.119 symmetry to it. One eye balances the other. One 00:00:34.119 --> 00:00:38.299 side of the smile reflects the other. Something 00:00:38.299 --> 00:00:42.780 about that balance captures our attention. But 00:00:42.780 --> 00:00:46.219 in mathematics, symmetry means more than having 00:00:46.219 --> 00:00:50.119 two sides that look alike. Symmetry is about 00:00:50.119 --> 00:00:55.060 what remains unchanged when something is transformed. 00:00:56.579 --> 00:01:01.170 Imagine a square. Rotate it one quarter of a 00:01:01.170 --> 00:01:04.069 turn, and it still looks like the same square. 00:01:05.129 --> 00:01:10.209 Rotate it again and again. Its appearance remains 00:01:10.209 --> 00:01:14.969 unchanged. The square has moved, but something 00:01:14.969 --> 00:01:19.349 about it has been preserved. A circle has even 00:01:19.349 --> 00:01:22.989 more symmetry. You can rotate it by any amount, 00:01:23.150 --> 00:01:27.629 and it still looks exactly the same. There is 00:01:27.629 --> 00:01:30.510 no single direction that the circle prefers. 00:01:32.609 --> 00:01:37.390 Mathematicians study symmetry by asking a surprisingly 00:01:37.390 --> 00:01:42.390 simple question. What can we do to this object 00:01:42.390 --> 00:01:48.790 without changing what it fundamentally is? We 00:01:48.790 --> 00:01:54.719 might rotate it, reflect it, move it. Sometimes 00:01:54.719 --> 00:01:59.180 we can even stretch it. The object undergoes 00:01:59.180 --> 00:02:04.359 a transformation, but some important things remain 00:02:04.359 --> 00:02:08.699 constant. And this is one of the reasons symmetry 00:02:08.699 --> 00:02:13.580 is important. Scientists use it to study crystals, 00:02:13.800 --> 00:02:17.419 molecules, and the fundamental laws of nature. 00:02:17.939 --> 00:02:20.759 Engineers use it when designing buildings and 00:02:20.759 --> 00:02:24.930 machines. Artists and musicians use patterns 00:02:24.930 --> 00:02:28.729 of repetition and variation to create a sense 00:02:28.729 --> 00:02:33.009 of order. Symmetry helps us recognize structure 00:02:33.009 --> 00:02:39.030 within change. And I think that question extends 00:02:39.030 --> 00:02:43.629 far beyond math. Our lives are filled with transformations. 00:02:44.509 --> 00:02:49.469 We grow older. Our bodies change. Our relationships 00:02:49.469 --> 00:02:55.020 change. We move into new homes or begin new careers 00:02:55.020 --> 00:02:59.379 or take on new responsibilities. Experiences 00:02:59.379 --> 00:03:04.360 reshape the way we see ourselves and the world. 00:03:05.479 --> 00:03:10.139 Sometimes these changes are chosen and sometimes 00:03:10.139 --> 00:03:15.900 they happen to us. But transformation does not 00:03:15.900 --> 00:03:21.069 necessarily mean everything has been lost. Like 00:03:21.069 --> 00:03:25.530 a square being rotated, our orientation may change 00:03:25.530 --> 00:03:31.349 while something important remains. Perhaps our 00:03:31.349 --> 00:03:35.490 deepest values remain. Perhaps it is our love 00:03:35.490 --> 00:03:39.370 for particular people. Perhaps it is a faith 00:03:39.370 --> 00:03:43.090 that continues to hold us even as our understanding 00:03:43.090 --> 00:03:49.389 of that faith grows and changes. Do not confuse 00:03:50.009 --> 00:03:55.030 Beauty with perfection. Beauty does not require 00:03:55.030 --> 00:03:59.229 perfect symmetry. Sometimes beauty is found in 00:03:59.229 --> 00:04:03.569 recognizing a deeper coherence, the thread that 00:04:03.569 --> 00:04:08.650 continues through all the changes, joys, disappointments, 00:04:08.650 --> 00:04:13.810 and unexpected turns. Mathematical symmetry teaches 00:04:13.810 --> 00:04:18.250 us to look for what is preserved during a transformation. 00:04:20.589 --> 00:04:23.069 So as you consider the changes that are taking 00:04:23.069 --> 00:04:26.209 place in your life, a question to start with 00:04:26.209 --> 00:04:32.149 is identifying what is changing. And then a follow 00:04:32.149 --> 00:04:35.310 -up question is that beneath all those changes, 00:04:35.550 --> 00:04:39.009 what do you hope will remain the same?