WEBVTT 00:00:02.120 --> 00:00:06.120 Hi, imagine holding a meter stick and looking 00:00:06.120 --> 00:00:09.900 at the evenly spaced centimeter marks. It feels 00:00:09.900 --> 00:00:12.980 obvious that every distance between 0 and 100 00:00:12.980 --> 00:00:16.859 centimeters exists somewhere on that stick. Not 00:00:16.859 --> 00:00:20.320 just whole numbers like 1 or 57, but fractions. 00:00:20.640 --> 00:00:24.120 Even irrational numbers like pi or square root 00:00:24.120 --> 00:00:29.000 of 2. Somehow, infinitely many numbers fit onto 00:00:29.000 --> 00:00:32.590 a single stick. Now imagine sitting in a race 00:00:32.590 --> 00:00:36.590 car, accelerating from 0 to 100 miles per hour. 00:00:36.869 --> 00:00:41.590 At some instance, did the car go exactly 70 miles 00:00:41.590 --> 00:00:49.270 per hour? What about 70 .5? Or 70 .00001? Did 00:00:49.270 --> 00:00:52.490 it pass through every possible speed between 00:00:52.490 --> 00:00:56.390 0 and 100? Or did it somehow skip some values? 00:00:57.009 --> 00:01:00.500 And digging deeper, What does it really mean 00:01:00.500 --> 00:01:04.640 to say a car is traveling 70 miles per hour at 00:01:04.640 --> 00:01:09.000 an instant? A snapshot of time has no duration, 00:01:09.120 --> 00:01:13.799 but motion seems to require duration. So how 00:01:13.799 --> 00:01:17.239 can something move during an instant that contains 00:01:17.239 --> 00:01:21.920 no time? Okay, for most of us, these questions 00:01:21.920 --> 00:01:25.519 do not affect everyday life. We still drive cars. 00:01:25.659 --> 00:01:30.379 We still trust speedometers. Life moves on. But 00:01:30.379 --> 00:01:34.180 mathematicians refuse to simply dismiss these 00:01:34.180 --> 00:01:38.500 tensions. They stay with them. And one direct 00:01:38.500 --> 00:01:41.099 benefit we have from wrestling with paradoxes 00:01:41.099 --> 00:01:44.859 is the concept of calculus, the mathematics of 00:01:44.859 --> 00:01:48.799 motion and change. Math usually becomes more 00:01:48.799 --> 00:01:51.560 interesting once we kick things into motion. 00:01:52.019 --> 00:01:55.640 A golf ball is a special type of sphere, but 00:01:55.640 --> 00:01:59.180 hit it with a club? and suddenly we find a parabola. 00:02:00.079 --> 00:02:04.439 Calculus and math are full of paradoxes, moments 00:02:04.439 --> 00:02:07.640 where reality seems to pull in two different 00:02:07.640 --> 00:02:12.020 directions at once. Of course, paradox is not 00:02:12.020 --> 00:02:16.199 just a math thing. It's a human thing. In relationships, 00:02:16.460 --> 00:02:19.340 two thoughtful people can experience the same 00:02:19.340 --> 00:02:24.520 situation completely different. In life, many 00:02:24.520 --> 00:02:27.680 of us would gladly choose success over struggle. 00:02:28.039 --> 00:02:31.699 Yet, when I look back on my life, I often realize 00:02:31.699 --> 00:02:35.659 I learned the most during difficult seasons rather 00:02:35.659 --> 00:02:41.039 than easy ones. Why is that? Well, author Brene 00:02:41.039 --> 00:02:43.639 Brown says that one of the greatest challenges 00:02:43.639 --> 00:02:47.180 of life is learning not to run from paradox, 00:02:47.479 --> 00:02:51.300 but to remain inside it long enough for deeper 00:02:51.300 --> 00:02:54.900 understanding to emerge. But that's difficult. 00:02:55.000 --> 00:02:59.159 We naturally move towards certainty because certainty 00:02:59.159 --> 00:03:04.219 feels safe. We want quick conclusions, simple 00:03:04.219 --> 00:03:09.300 categories, clear sides, right or wrong, strong 00:03:09.300 --> 00:03:14.520 or weak, certain or uncertain. But life rarely 00:03:14.520 --> 00:03:18.659 stays inside those neat boxes. Sometimes we feel 00:03:18.659 --> 00:03:23.849 both confident and afraid. Sometimes grief and 00:03:23.849 --> 00:03:28.250 gratitude exist together. Sometimes we feel both 00:03:28.250 --> 00:03:33.210 broken and hopeful at the same time. And perhaps 00:03:33.210 --> 00:03:36.949 one of the dangers of certainty is that our understanding 00:03:36.949 --> 00:03:43.310 of reality becomes too small. I know I often 00:03:43.310 --> 00:03:46.610 want to be right. But over time, I've discovered 00:03:46.610 --> 00:03:49.689 that there are moments when love matters more 00:03:49.689 --> 00:03:53.229 than winning an argument. Moments where reconciliation 00:03:53.229 --> 00:03:58.349 matters more than proving my point. Paradox stretches 00:03:58.349 --> 00:04:02.330 us because it forces us to consider that reality 00:04:02.330 --> 00:04:06.030 may be larger than our current categories can 00:04:06.030 --> 00:04:10.430 hold. So, this week we will explore paradoxes 00:04:10.430 --> 00:04:15.090 that involve motion, infinity, patterns, truth, 00:04:15.250 --> 00:04:18.910 and the strange unity hidden inside mathematics 00:04:18.910 --> 00:04:23.709 itself. Not because math removes mystery, but 00:04:23.709 --> 00:04:26.930 because it teaches us how to thoughtfully live 00:04:26.930 --> 00:04:30.610 within it. And one thing that I've experienced 00:04:30.610 --> 00:04:34.189 is that as I remain open and inside the tension 00:04:34.189 --> 00:04:38.949 of paradox, that it is part of the journey towards 00:04:38.949 --> 00:04:40.350 reasonable hope.