WEBVTT 00:00:07.158 --> 00:00:08.800 We start with a point. 00:00:08.800 --> 00:00:10.430 like the point we know from geometry 00:00:10.430 --> 00:00:13.349 it has no sice, no dimension 00:00:13.349 --> 00:00:15.238 it just an imaginary idea 00:00:15.238 --> 00:00:17.424 that indicates a position in a system 00:00:17.424 --> 00:00:21.943 a second point then can be used to indicate a different position 00:00:21.943 --> 00:00:24.346 but it too is of undetermined size 00:00:24.346 --> 00:00:25.835 to create the first dimension 00:00:25.835 --> 00:00:29.492 all we need is a line joining any two points 00:00:29.492 --> 00:00:32.104 our first dimensional object has length only 00:00:32.104 --> 00:00:36.519 no width or depth 00:00:36.519 --> 00:00:38.844 if we now take our first dimensional like 00:00:38.844 --> 00:00:40.411 and draw a second line 00:00:40.411 --> 00:00:41.848 crossing the first 00:00:41.848 --> 00:00:43.807 we invented the second dimension 00:00:43.807 --> 00:00:46.498 the object we're presenting now has a length, a width 00:00:46.498 --> 00:00:47.856 but no depth 00:00:47.856 --> 00:00:50.155 to help us with imagining with the higher dimensions 00:00:50.155 --> 00:00:52.349 we're going to represend our second dimensional object 00:00:52.349 --> 00:00:56.816 as beeing creating a second line which branches off from the first 00:00:56.816 --> 00:01:02.511 now lets imaging a race of two dimenstional cratures called flatlanders 00:01:02.511 --> 00:01:06.743 what would it be like to be a flatlander living in their two dimensional world 00:01:06.743 --> 00:01:08.598 a two dimensional creature 00:01:08.598 --> 00:01:10.191 would only have length and width 00:01:10.191 --> 00:01:14.266 as if they're the roaylty on a implossibly plain play card 00:01:14.266 --> 00:01:15.337 picture this 00:01:15.337 --> 00:01:17.949 a flatlander couldn't possibly have a digestive tract 00:01:17.949 --> 00:01:19.935 because the pipe from the mouth to the bottom 00:01:19.935 --> 00:01:23.096 would devide them into two peaces 00:01:23.096 --> 00:01:26.439 and a flatlander trying to view our three dimensional world 00:01:26.439 --> 00:01:28.163 would only be able to perceive shapes 00:01:28.163 --> 00:01:30.149 in two dimensional crossections 00:01:30.149 --> 00:01:31.690 a baloon fro instance 00:01:31.690 --> 00:01:33.675 would start as a tiny dot 00:01:33.675 --> 00:01:35.817 become a holow circle 00:01:35.817 --> 00:01:37.802 which .... grows to a certain size 00:01:37.802 --> 00:01:39.448 than shirnks back to a dot 00:01:39.448 --> 00:01:42.191 before popping out of existence 00:01:42.191 --> 00:01:43.863 an we three dimensional human beeings 00:01:43.863 --> 00:01:45.848 would seem very strange indeed to a flatlander 00:01:51.110 --> 00:01:54.338 imaginging the third dimenstion is the easiest for us 00:01:54.338 --> 00:01:59.092 because for every moment of our lives this wat we're in 00:01:59.092 --> 00:02:02.018 a three dimensional object has length, width and hight 00:02:02.018 --> 00:02:04.839 but here is another way to describe the third dimension 00:02:04.839 --> 00:02:07.478 if we imagine an ant walking across a newspaper 00:02:07.478 --> 00:02:08.836 which is lying on a table 00:02:08.836 --> 00:02:11.161 we can pretend that the ant is a flatlander 00:02:11.161 --> 00:02:15.158 walking along in a flat two dimensional newspaper world 00:02:15.158 --> 00:02:18.344 if that paper is now foldet in the middle 00:02:18.344 --> 00:02:20.826 we create a way for our flatlander ant 00:02:20.826 --> 00:02:23.830 to magically diappear from one position in his world 00:02:23.830 --> 00:02:26.469 an be instantly tranported to another 00:02:26.469 --> 00:02:29.917 we can image that we did this by taking a two dimensional object 00:02:29.917 --> 00:02:32.667 and folding it through the dimension above 00:02:32.667 --> 00:02:34.567 which is our third dimension 00:02:34.567 --> 00:02:36.552 once again it would be more convinient for us 00:02:36.552 --> 00:02:39.216 as we imagine the higher dimensions 00:02:39.216 --> 00:02:41.115 if we can think of the third dimension in this way 99:59:59.999 --> 99:59:59.999 [pop]