WEBVTT 00:00:08.129 --> 00:00:11.550 This question lies at the heart of a fascinating 00:00:11.550 --> 00:00:16.010 area of mathematics called topology. Topology 00:00:16.010 --> 00:00:19.750 studies shapes, but it looks beyond their exact 00:00:19.750 --> 00:00:23.469 measurements. The fascinating thing about topology 00:00:23.469 --> 00:00:27.570 is we usually are not concerned with how long 00:00:27.570 --> 00:00:32.009 an object is or how sharply it bends. or whether 00:00:32.009 --> 00:00:36.549 it is perfectly round. Instead, topology asks 00:00:36.549 --> 00:00:40.409 what properties remain when a shape is stretched, 00:00:40.770 --> 00:00:46.009 twisted, bent, or compressed without cutting 00:00:46.009 --> 00:00:49.289 it apart or attaching pieces that were previously 00:00:49.289 --> 00:00:53.770 separate. The most famous example involves a 00:00:53.770 --> 00:00:57.590 coffee mug and a donut. At first, they seem to 00:00:57.590 --> 00:01:01.479 have completely different shapes. One holds coffee 00:01:01.479 --> 00:01:04.540 and the other might be covered in chocolate frosting. 00:01:05.459 --> 00:01:08.439 But imagine that both are made from soft clay. 00:01:09.040 --> 00:01:12.980 You could gradually shrink the cup while thickening 00:01:12.980 --> 00:01:15.900 and rounding its handle. And if you continued 00:01:15.900 --> 00:01:19.260 reshaping the clay without tearing it or joining 00:01:19.260 --> 00:01:22.920 separate parts, the coffee mug could eventually 00:01:22.920 --> 00:01:30.299 be transformed into the shape of a donut. and 00:01:30.299 --> 00:01:35.659 the donut are essentially the same shape. And 00:01:35.659 --> 00:01:41.079 why? It's because each has exactly one hole. 00:01:41.879 --> 00:01:45.560 Their appearances are different, but an important 00:01:45.560 --> 00:01:48.920 part of their underlying structure is the same. 00:01:50.780 --> 00:01:55.239 Topology teaches us that appearance and identity 00:01:55.239 --> 00:02:00.459 are not always identical. A circle can be stretched 00:02:00.459 --> 00:02:04.019 into an oval. It can be pulled into a long irregular 00:02:04.019 --> 00:02:07.980 loop. It might no longer look much like the perfectly 00:02:07.980 --> 00:02:11.460 round circle we started with, yet as long as 00:02:11.460 --> 00:02:14.759 we do not cut it, open or connect different parts 00:02:14.759 --> 00:02:18.280 together, its basic topological structure remains. 00:02:20.139 --> 00:02:23.319 And this raises an interesting question beyond 00:02:23.319 --> 00:02:30.750 mathematics. What makes us... Us. A pregnant 00:02:30.750 --> 00:02:34.729 woman certainly sees her body shape change. You 00:02:34.729 --> 00:02:37.370 are certainly not shaped exactly as you were 00:02:37.370 --> 00:02:41.689 20 years ago. Your body has changed. Your knowledge 00:02:41.689 --> 00:02:45.189 has changed. Your relationships, responsibilities, 00:02:45.590 --> 00:02:50.789 and beliefs may have changed. Experiences have 00:02:50.789 --> 00:02:54.270 stretched you. Disappointments may have bent 00:02:54.270 --> 00:02:58.509 you. and unexpected events may have pushed your 00:02:58.509 --> 00:03:01.229 life in directions that you never anticipated. 00:03:02.169 --> 00:03:07.250 And yet, through all those transformations, you 00:03:07.250 --> 00:03:12.810 remain you. Now, this does not mean that nothing 00:03:12.810 --> 00:03:17.069 important changes. Some experiences truly do 00:03:17.069 --> 00:03:21.610 reshape us. We grow, we learn, we heal, and sometimes 00:03:21.610 --> 00:03:25.259 become people our younger selves would barely 00:03:25.259 --> 00:03:30.500 recognize. But change is not necessarily the 00:03:30.500 --> 00:03:35.280 loss of identity. Like the circle being stretched, 00:03:35.740 --> 00:03:39.539 our outward shape may change while something 00:03:39.539 --> 00:03:42.719 deeper continues through the transformation. 00:03:43.840 --> 00:03:48.120 Perhaps it is our memories. Perhaps it's the 00:03:48.120 --> 00:03:52.050 relationships that have formed us. Perhaps it 00:03:52.050 --> 00:03:57.930 is a deeply held purpose. Perhaps our identity 00:03:57.930 --> 00:04:01.330 is not something we must preserve by ourselves, 00:04:01.750 --> 00:04:06.189 but something grounded and being known and loved 00:04:06.189 --> 00:04:12.409 by God. Topology invites us to look beneath an 00:04:12.409 --> 00:04:15.469 object's current appearance and search for the 00:04:15.469 --> 00:04:20.699 structure that remains. Maybe. we can learn to 00:04:20.699 --> 00:04:24.839 look at people in the same way. A person's circumstances 00:04:24.839 --> 00:04:28.860 may have changed. Their abilities may have changed. 00:04:29.379 --> 00:04:33.879 Their body or personality may have changed. But 00:04:33.879 --> 00:04:37.060 their value cannot be measured only by their 00:04:37.060 --> 00:04:41.860 present outward shape. I am reminded of that 00:04:41.860 --> 00:04:45.699 every week when I visit my dad at his retirement 00:04:45.699 --> 00:04:52.040 home. Mathematics teaches us that not every transformation 00:04:52.040 --> 00:04:57.939 changes what something fundamentally is. So, 00:04:58.040 --> 00:05:00.819 beneath all the changes that you have experienced, 00:05:01.220 --> 00:05:05.939 what makes you still you?