1 00:00:07,158 --> 00:00:08,800 We start with a point. 2 00:00:08,800 --> 00:00:10,430 like the point we know from geometry 3 00:00:10,430 --> 00:00:13,349 it has no sice, no dimension 4 00:00:13,349 --> 00:00:15,238 it just an imaginary idea 5 00:00:15,238 --> 00:00:17,424 that indicates a position in a system 6 00:00:17,424 --> 00:00:21,943 a second point then can be used to indicate a different position 7 00:00:21,943 --> 00:00:24,346 but it too is of undetermined size 8 00:00:24,346 --> 00:00:25,835 to create the first dimension 9 00:00:25,835 --> 00:00:29,492 all we need is a line joining any two points 10 00:00:29,492 --> 00:00:32,104 our first dimensional object has length only 11 00:00:32,104 --> 00:00:36,519 no width or depth 12 00:00:36,519 --> 00:00:38,844 if we now take our first dimensional like 13 00:00:38,844 --> 00:00:40,411 and draw a second line 14 00:00:40,411 --> 00:00:41,848 crossing the first 15 00:00:41,848 --> 00:00:43,807 we invented the second dimension 16 00:00:43,807 --> 00:00:46,498 the object we're presenting now has a length, a width 17 00:00:46,498 --> 00:00:47,856 but no depth 18 00:00:47,856 --> 00:00:50,155 to help us with imagining with the higher dimensions 19 00:00:50,155 --> 00:00:52,349 we're going to represend our second dimensional object 20 00:00:52,349 --> 00:00:56,816 as beeing creating a second line which branches off from the first 21 00:00:56,816 --> 00:01:02,511 now lets imaging a race of two dimenstional cratures called flatlanders 22 00:01:02,511 --> 00:01:06,743 what would it be like to be a flatlander living in their two dimensional world 23 00:01:06,743 --> 00:01:08,598 a two dimensional creature 24 00:01:08,598 --> 00:01:10,191 would only have length and width 25 00:01:10,191 --> 00:01:14,266 as if they're the roaylty on a implossibly plain play card 26 00:01:14,266 --> 00:01:15,337 picture this 27 00:01:15,337 --> 00:01:17,949 a flatlander couldn't possibly have a digestive tract 28 00:01:17,949 --> 00:01:19,935 because the pipe from the mouth to the bottom 29 00:01:19,935 --> 00:01:23,096 would devide them into two peaces 30 00:01:23,096 --> 00:01:26,439 and a flatlander trying to view our three dimensional world 31 00:01:26,439 --> 00:01:28,163 would only be able to perceive shapes 32 00:01:28,163 --> 00:01:30,149 in two dimensional crossections 33 00:01:30,149 --> 00:01:31,690 a baloon fro instance 34 00:01:31,690 --> 00:01:33,675 would start as a tiny dot 35 00:01:33,675 --> 00:01:35,817 become a holow circle 36 00:01:35,817 --> 00:01:37,802 which .... grows to a certain size 37 00:01:37,802 --> 00:01:39,448 than shirnks back to a dot 38 00:01:39,448 --> 00:01:42,191 before popping out of existence 39 00:01:42,191 --> 00:01:43,863 an we three dimensional human beeings 40 00:01:43,863 --> 00:01:45,848 would seem very strange indeed to a flatlander 41 00:01:51,110 --> 00:01:54,338 imaginging the third dimenstion is the easiest for us 42 00:01:54,338 --> 00:01:59,092 because for every moment of our lives this wat we're in 43 00:01:59,092 --> 00:02:02,018 a three dimensional object has length, width and hight 44 00:02:02,018 --> 00:02:04,839 but here is another way to describe the third dimension 45 00:02:04,839 --> 00:02:07,478 if we imagine an ant walking across a newspaper 46 00:02:07,478 --> 00:02:08,836 which is lying on a table 47 00:02:08,836 --> 00:02:11,161 we can pretend that the ant is a flatlander 48 00:02:11,161 --> 00:02:15,158 walking along in a flat two dimensional newspaper world 49 00:02:15,158 --> 00:02:18,344 if that paper is now foldet in the middle 50 00:02:18,344 --> 00:02:20,826 we create a way for our flatlander ant 51 00:02:20,826 --> 00:02:23,830 to magically diappear from one position in his world 52 00:02:23,830 --> 00:02:26,469 an be instantly tranported to another 53 00:02:26,469 --> 00:02:29,917 we can image that we did this by taking a two dimensional object 54 00:02:29,917 --> 00:02:32,667 and folding it through the dimension above 55 00:02:32,667 --> 00:02:34,567 which is our third dimension 56 00:02:34,567 --> 00:02:36,552 once again it would be more convinient for us 57 00:02:36,552 --> 00:02:39,216 as we imagine the higher dimensions 58 00:02:39,216 --> 00:02:41,115 if we can think of the third dimension in this way 59 99:59:59,999 --> 99:59:59,999 [pop]