WEBVTT 00:00:02.610 --> 00:00:06.030 Hi. Imagine driving your favorite sports car 00:00:06.030 --> 00:00:10.490 down a highway with no speed limit. And with 00:00:10.490 --> 00:00:13.929 modern GPS technology, you can record exactly 00:00:13.929 --> 00:00:17.890 where the car is at at every moment of the trip. 00:00:18.230 --> 00:00:22.370 Yes, geeking out. Now, at first, this seems like 00:00:22.370 --> 00:00:26.769 a simple idea. You can find the car's position, 00:00:26.949 --> 00:00:30.629 where it is. But calculus gives another perspective. 00:00:31.320 --> 00:00:34.020 From that same information, we can determine 00:00:34.020 --> 00:00:38.439 how fast the car is moving, its speed. And from 00:00:38.439 --> 00:00:41.679 its speed, we can determine how quickly that 00:00:41.679 --> 00:00:45.659 speed is changing. That's its acceleration. So 00:00:45.659 --> 00:00:50.140 we have position, speed, and acceleration. Same 00:00:50.140 --> 00:00:53.740 car and same journey, but three different perspectives. 00:00:54.539 --> 00:00:57.920 Now, at its heart, calculus is the mathematics 00:00:57.920 --> 00:01:02.310 of change. And one of the great insights is that 00:01:02.310 --> 00:01:05.890 position, speed, and acceleration are connected. 00:01:06.209 --> 00:01:09.829 They are not separate ideas. They are different 00:01:09.829 --> 00:01:13.670 ways of looking at the same reality. And what's 00:01:13.670 --> 00:01:16.450 even more remarkable is that calculus allows 00:01:16.450 --> 00:01:20.569 us to move between these perspectives. We can 00:01:20.569 --> 00:01:24.090 go from position to speed to acceleration. Or 00:01:24.090 --> 00:01:26.950 we can even go backwards from acceleration to 00:01:26.950 --> 00:01:31.040 speed to position. Calculus helps us to see the 00:01:31.040 --> 00:01:34.980 connections. And in a way, this reminds me of 00:01:34.980 --> 00:01:38.120 something similar in my life. For the first part 00:01:38.120 --> 00:01:41.400 of my life, I was a son. And then I became a 00:01:41.400 --> 00:01:44.319 husband and the father of four children. Now 00:01:44.319 --> 00:01:47.480 today, I'm a grandfather. When I was younger, 00:01:47.620 --> 00:01:50.219 I mostly understood life from the perspective 00:01:50.219 --> 00:01:53.640 of a child. But later, I began seeing life through 00:01:53.640 --> 00:01:56.640 the eyes of a parent. And now I see things from 00:01:56.640 --> 00:01:59.819 yet another perspective. And what surprises me 00:01:59.819 --> 00:02:03.000 is how these perspectives help me understand 00:02:03.000 --> 00:02:07.340 one another. As a parent, I understood my parents 00:02:07.340 --> 00:02:10.620 better. And as a grandparent, I understand my 00:02:10.620 --> 00:02:13.259 children better as they raise families of their 00:02:13.259 --> 00:02:16.560 own. Now the people have not changed, but my 00:02:16.560 --> 00:02:20.900 perspective has. And that new perspective has 00:02:20.900 --> 00:02:23.020 helped me see things I could not see before. 00:02:24.560 --> 00:02:27.439 Perhaps you are experiencing something similar. 00:02:28.030 --> 00:02:30.629 Maybe you're in college and seeing your family 00:02:30.629 --> 00:02:32.909 differently now that you've been away from home. 00:02:33.349 --> 00:02:37.050 Or maybe you started a new job and are beginning 00:02:37.050 --> 00:02:39.729 to understand responsibilities that you had not 00:02:39.729 --> 00:02:42.830 noticed before. Or maybe you have moved to a 00:02:42.830 --> 00:02:45.229 new city and discovered that familiar things 00:02:45.229 --> 00:02:48.050 look a bit different from a new perspective. 00:02:49.530 --> 00:02:52.330 So as we move through different seasons of life, 00:02:52.550 --> 00:02:56.560 we gain new ways of seeing. And sometimes these 00:02:56.560 --> 00:03:00.280 new perspectives helps us understand our old 00:03:00.280 --> 00:03:04.000 ones. Thanks for listening. See you tomorrow.