WEBVTT 00:00:02.509 --> 00:00:06.429 This week, math is on trial. Our next charge 00:00:06.429 --> 00:00:10.650 against math is being hopelessly abstract. It's 00:00:10.650 --> 00:00:14.890 filled with imaginary numbers, with unusual geometries, 00:00:14.890 --> 00:00:18.210 and ideas that do not seem to have much connection 00:00:18.210 --> 00:00:22.829 to our real world. So the prosecution might ask, 00:00:22.989 --> 00:00:26.809 what possible use could any of this math be? 00:00:27.710 --> 00:00:32.140 Well, history gives us a surprising answer. For 00:00:32.140 --> 00:00:35.859 example, for centuries, Euclidean geometry gave 00:00:35.859 --> 00:00:39.640 us the obvious description of space. Parallel 00:00:39.640 --> 00:00:44.060 lines never meet, triangles always have 180 degrees, 00:00:44.219 --> 00:00:47.320 and of course the shortest distance between two 00:00:47.320 --> 00:00:51.299 points is always a straight line. And then something 00:00:51.299 --> 00:00:55.079 crazy happened. Mathematicians asked what would 00:00:55.079 --> 00:00:58.079 happen if we changed Euclidean's assumptions. 00:00:58.829 --> 00:01:01.210 Could there be a geometry where parallel lines 00:01:01.210 --> 00:01:04.510 behave differently or the angles of a triangle 00:01:04.510 --> 00:01:09.909 do not total 180 degrees? Well, at first, non 00:01:09.909 --> 00:01:12.810 -Euclidean geometry looked like an interesting 00:01:12.810 --> 00:01:16.930 but not practical thought experiment. And then 00:01:16.930 --> 00:01:20.609 Einstein needed a way to describe gravity as 00:01:20.609 --> 00:01:24.189 the curvature of space -time. The abstract geometry 00:01:24.189 --> 00:01:27.799 that mathematicians had already developed gave 00:01:27.799 --> 00:01:32.540 physics the language it needed. Something similar 00:01:32.540 --> 00:01:35.500 happened with imaginary numbers. The old square 00:01:35.500 --> 00:01:38.659 root of negative one seemed so far removed from 00:01:38.659 --> 00:01:43.719 reality. It was even labeled imaginary. But today, 00:01:43.879 --> 00:01:47.239 complex numbers are essential to electrical engineering. 00:01:47.719 --> 00:01:51.280 We use them in signal processing, in quantum 00:01:51.280 --> 00:01:54.079 physics, and really much of modern technology. 00:01:55.719 --> 00:01:58.939 How about number theory? When we created number 00:01:58.939 --> 00:02:01.739 theory for centuries, we were just exploring 00:02:01.739 --> 00:02:04.480 the properties of whole numbers without much 00:02:04.480 --> 00:02:07.840 thought about how to use them practically. But 00:02:07.840 --> 00:02:11.479 today, those ideas secure our financial transactions, 00:02:11.740 --> 00:02:15.020 and they make our communications private using 00:02:15.020 --> 00:02:20.219 cryptography. So again and again, math has imagined 00:02:20.219 --> 00:02:24.280 possibilities. before the physical world revealed 00:02:24.280 --> 00:02:27.960 why they mattered. What appeared useless was 00:02:27.960 --> 00:02:32.099 not useless. Reality simply had not caught up 00:02:32.099 --> 00:02:35.800 with the idea. Now, to be honest, when I look 00:02:35.800 --> 00:02:38.740 back on my life, I can be impatient with anything 00:02:38.740 --> 00:02:42.979 that does not have any immediate use. I remember 00:02:42.979 --> 00:02:46.240 studying for my actual exams and wondering, when 00:02:46.240 --> 00:02:49.879 will I ever use this stuff? When I could not 00:02:49.879 --> 00:02:52.759 see the purpose, it was easier for me to lose 00:02:52.759 --> 00:02:56.500 interest. Looking back, I can see that I did 00:02:56.500 --> 00:02:59.080 not yet understand the bigger picture of math. 00:03:00.139 --> 00:03:03.180 Yes, some math is taught in ways that do not 00:03:03.180 --> 00:03:05.879 feel useful or even connected to anything important. 00:03:06.620 --> 00:03:09.560 But those experiences can distort our view of 00:03:09.560 --> 00:03:12.620 what math really is and keep us from seeing its 00:03:12.620 --> 00:03:16.379 beauty. In the end, I had to work through a lot 00:03:16.379 --> 00:03:19.310 of details. before I could understand how they 00:03:19.310 --> 00:03:23.210 fit together and to see something greater. And 00:03:23.210 --> 00:03:25.870 what I learned is that I may not yet understand 00:03:25.870 --> 00:03:32.090 what today is preparing me to see tomorrow. So, 00:03:32.150 --> 00:03:35.389 on the charge of being abstract, mathematics 00:03:35.389 --> 00:03:39.949 is guilty. But on the charge of being impractical, 00:03:40.189 --> 00:03:45.729 well, the evidence says otherwise. So, our question 00:03:45.729 --> 00:03:48.800 to finish, Is there a part of your life that 00:03:48.800 --> 00:03:51.780 you may have dismissed because it may not matter 00:03:51.780 --> 00:03:55.780 today, but maybe it's possibly going to be important 00:03:55.780 --> 00:03:56.259 later?