WEBVTT 00:00:00.010 --> 00:00:03.509 Hi, hopefully you have authority figures in your 00:00:03.509 --> 00:00:07.049 life who you admire and respect, such as your 00:00:07.049 --> 00:00:10.449 parents. But despite that respect, you may see 00:00:10.449 --> 00:00:13.650 something in a different way, a different perspective 00:00:13.650 --> 00:00:17.089 than they do. They may feel strongly about their 00:00:17.089 --> 00:00:20.589 perspective, and it's easy to step back and let 00:00:20.589 --> 00:00:23.710 their view become the only view in the conversation. 00:00:24.850 --> 00:00:30.120 And yet, something doesn't quite sit right. So 00:00:30.120 --> 00:00:32.340 how do you enter into that kind of conversation? 00:00:33.320 --> 00:00:36.380 I know I have been there. And in those moments, 00:00:36.539 --> 00:00:40.259 I ask myself, where can I find the courage to 00:00:40.259 --> 00:00:43.679 engage rather than be silent and just conform? 00:00:44.579 --> 00:00:47.820 Can math give us a clue on how to move forward? 00:00:49.219 --> 00:00:51.960 Yesterday, we talked about how different starting 00:00:51.960 --> 00:00:55.960 points can lead to different conclusions. Math 00:00:55.960 --> 00:01:00.119 teaches us that we are allowed to begin in different 00:01:00.119 --> 00:01:05.019 places. Math literally is an invitation to start 00:01:05.019 --> 00:01:09.599 at a different point. But it is not chaos, because 00:01:09.599 --> 00:01:13.439 once we begin, we must follow the logic wherever 00:01:13.439 --> 00:01:17.459 it leads. That means in difficult conversations, 00:01:17.719 --> 00:01:21.959 we can ask, what if we start from a different 00:01:21.959 --> 00:01:26.989 place? What would follow from that? For example, 00:01:27.049 --> 00:01:30.849 rather than judging someone who is angry, how 00:01:30.849 --> 00:01:34.150 about we understand where the anger is coming 00:01:34.150 --> 00:01:38.290 from? Now, you may think math is just about numbers, 00:01:38.409 --> 00:01:43.349 but it is an exercise in digging deeper and considering 00:01:43.349 --> 00:01:47.810 new starting places. Digging deeper and finding 00:01:47.810 --> 00:01:50.909 a different starting point requires courage. 00:01:51.900 --> 00:01:55.420 But the history of math is full of people with 00:01:55.420 --> 00:01:59.420 that kind of courage. Take geometry. In school, 00:01:59.519 --> 00:02:02.019 we learned that the sum of the angles for a triangle 00:02:02.019 --> 00:02:06.680 is 180 degrees. This truth travels all the way 00:02:06.680 --> 00:02:11.039 back to Euclid over 2 ,000 years ago. Euclid 00:02:11.039 --> 00:02:14.439 built this by assuming five postulates were true. 00:02:15.020 --> 00:02:19.960 A starting point, if you will. But in 1854... 00:02:20.560 --> 00:02:24.099 Bernard Riemann and others had the courage to 00:02:24.099 --> 00:02:28.000 change the starting point by changing how parallel 00:02:28.000 --> 00:02:30.800 lines were defined, which is one of the five 00:02:30.800 --> 00:02:33.740 starting points. When that new starting point 00:02:33.740 --> 00:02:37.840 was taken seriously, the math world and eventually 00:02:37.840 --> 00:02:43.439 the entire world completely changed. Entirely 00:02:43.439 --> 00:02:47.800 new geometries emerged. In a very real sense, 00:02:48.479 --> 00:02:52.419 New mathematical worlds were built from a single 00:02:52.419 --> 00:02:57.120 change in assumptions. And those ideas did not 00:02:57.120 --> 00:03:01.719 stay abstract. They became essential to understanding 00:03:01.719 --> 00:03:05.340 curved space, which is what allows systems like 00:03:05.340 --> 00:03:10.180 GPS on our phones to work accurately. Incredible! 00:03:10.840 --> 00:03:14.139 That's what having courage to start at a different 00:03:14.139 --> 00:03:19.199 place makes possible. This courage creates space, 00:03:19.520 --> 00:03:23.439 literally, to explore what we might otherwise 00:03:23.439 --> 00:03:27.300 dismiss. Of course, courage is not just about 00:03:27.300 --> 00:03:31.139 math. It shows up in conversations, in relationships, 00:03:31.400 --> 00:03:35.439 in moments where it would be easier to stay silent 00:03:35.439 --> 00:03:41.620 than to engage in a way that feels honest. Because 00:03:41.620 --> 00:03:46.430 challenging certainty carries risk. Sure. You 00:03:46.430 --> 00:03:50.310 might be wrong. You might be misunderstood. You 00:03:50.310 --> 00:03:53.729 might create tension. But without that courage, 00:03:53.969 --> 00:03:58.650 something else happens. We stop exploring. And 00:03:58.650 --> 00:04:02.289 when we stop exploring, our understanding stays 00:04:02.289 --> 00:04:06.349 smaller than it could be. So my question today 00:04:06.349 --> 00:04:09.870 is, where might I need the courage to stay in 00:04:09.870 --> 00:04:13.969 the conversation long enough to consider a different 00:04:13.969 --> 00:04:14.629 starting point?