1 00:00:04,069 --> 00:00:07,061 We begin with a problem. 2 00:00:07,061 --> 00:00:15,048 [WIND BLOWING] 3 00:00:15,048 --> 00:00:18,427 Alice and Bob live in tree forts which are far apart 4 00:00:18,427 --> 00:00:21,225 with no line of sight between them. 5 00:00:21,225 --> 00:00:23,733 And they need to communicate. 6 00:00:23,733 --> 00:00:28,410 So they decide to run a wire between the two houses. 7 00:00:28,410 --> 00:00:41,113 [wind still blowing] 8 00:00:41,113 --> 00:00:48,693 They pull the wire tight and attach a tin can to each end... 9 00:00:48,693 --> 00:00:52,436 [clinking of metal] 10 00:00:52,436 --> 00:00:57,842 ...allowing them to send their voices faintly along the wire. 11 00:00:57,842 --> 00:01:02,213 [muffled "Hello" through wire] 12 00:01:02,213 --> 00:01:05,815 [Alice]: I can't hear you. 13 00:01:05,815 --> 00:01:09,005 [Bob]: I can hear you but barely 14 00:01:09,005 --> 00:01:14,690 [Alice]: 1,2,3,4,5 15 00:01:14,690 --> 00:01:20,897 However, there is a problem: Noise 16 00:01:20,897 --> 00:01:22,944 Whenever there is a high wind, 17 00:01:22,944 --> 00:01:29,415 it becomes impossible to hear the signal over the noise. 18 00:01:29,415 --> 00:01:32,881 So they need a way to increase the energy level of the signal 19 00:01:32,881 --> 00:01:35,421 to separate it from the noise. 20 00:01:35,421 --> 00:01:40,968 This gives Bob an idea. 21 00:01:40,968 --> 00:01:47,016 They can simply pluck the wire, which is much easier to detect over the noise. 22 00:01:47,016 --> 00:01:49,226 But this leads to a new problem: 23 00:01:49,226 --> 00:01:56,983 how do they encode their messages as plucks? 24 00:01:56,983 --> 00:02:03,782 Well, since they want to play board games across a distance, they tackle the most common messages first: 25 00:02:03,782 --> 00:02:07,387 the outcome of two dice rolls. 26 00:02:07,387 --> 00:02:09,197 In this case the messages they are sending 27 00:02:09,197 --> 00:02:14,120 can be thought of as a selection from a finite number of symbols, 28 00:02:14,120 --> 00:02:17,171 in this case, the eleven possible numbers, 29 00:02:17,171 --> 00:02:24,553 which we call a discrete source. 30 00:02:24,553 --> 00:02:27,765 At first, they decide to use the simplest method. 31 00:02:27,765 --> 00:02:31,210 They send the result as the number of plucks. 32 00:02:31,210 --> 00:02:34,229 So, to send a three, they send three plucks. 33 00:02:34,229 --> 00:02:38,525 Nine is nine plucks, and twelve is twelve plucks. 34 00:02:38,525 --> 00:02:44,823 However, they soon realize that this takes much longer than it needs to. 35 00:02:44,823 --> 00:02:51,288 From practice, they find that their maximum pluck speed is 2 plucks per second. 36 00:02:51,288 --> 00:02:53,966 Any faster, and they will get confused. 37 00:02:53,966 --> 00:02:57,727 So two plucks per second can be thought of as the rate, 38 00:02:57,727 --> 00:03:01,991 or capacity for sending information in this way. 39 00:03:01,991 --> 00:03:06,387 [sound of plucking] 40 00:03:06,387 --> 00:03:10,265 And it turns out that the most common roll is a seven, 41 00:03:10,265 --> 00:03:15,235 so it takes 3.5 seconds to send the number seven 42 00:03:15,235 --> 00:03:22,152 [7 plucks sound] 43 00:03:22,152 --> 00:03:27,574 Alice then realizes they can do much better if they change their coding strategy. 44 00:03:27,574 --> 00:03:32,121 She realizes that the odds of each number being sent follows a simple pattern. 45 00:03:32,121 --> 00:03:34,205 There is 1 way to roll a 2, 46 00:03:34,205 --> 00:03:36,039 2 ways to roll a 3, 47 00:03:36,039 --> 00:03:38,042 3 ways to roll a 4, 48 00:03:38,042 --> 00:03:40,044 4 ways to roll a 5, 49 00:03:40,044 --> 00:03:42,960 5 ways to roll a six, 50 00:03:42,960 --> 00:03:46,721 6 ways to roll a seven, the most common, 51 00:03:46,721 --> 00:03:50,097 and 5 ways to roll an eight, 4 ways for a nine 52 00:03:50,097 --> 00:03:54,383 and so on back to one way for a twelve. 53 00:03:54,383 --> 00:03:58,354 This is a graph showing the number of ways each result can occur, 54 00:03:58,354 --> 00:04:00,566 and the pattern is obvious. 55 00:04:00,566 --> 00:04:06,029 So now lets change the graph to number of plucks vs. each symbol. 56 00:04:06,029 --> 00:04:13,192 She proceeds by mapping the most common number, 7 to the shortest signal, 1 pluck. 57 00:04:13,192 --> 00:04:14,746 [hear one pluck] 58 00:04:14,746 --> 00:04:17,582 She then proceeds to the next most probable number, 59 00:04:17,582 --> 00:04:20,335 and if there is a tie, she picks one at random. 60 00:04:20,335 --> 00:04:23,223 In this case, she selects 6 to be two plucks 61 00:04:23,223 --> 00:04:25,638 and then 8 to be three plucks, 62 00:04:25,638 --> 00:04:28,635 and then back to 5 to be four plucks, 63 00:04:28,635 --> 00:04:34,141 and 9 is five plucks, and back and forth until we reach 12, 64 00:04:34,141 --> 00:04:36,768 which is assigned to 11 plucks. 65 00:04:36,768 --> 00:04:44,425 Now the most common number, seven, can be sent in less than a second, a huge improvement. 66 00:04:44,425 --> 00:04:47,571 This simple change allows them to send more information 67 00:04:47,571 --> 00:04:52,284 in the same amount of time on average. 68 00:04:52,284 --> 00:04:56,196 In fact, this coding strategy is optimal for this simple example 69 00:04:56,196 --> 00:05:00,083 in that it is impossible for you to come up with a shorter method 70 00:05:00,083 --> 00:05:05,298 of sending two dice rolls using identical plucks. 71 00:05:05,298 --> 00:05:08,967 However, after playing with the wire for some time, 72 00:05:08,967 --> 00:05:11,929 Bob hits on a new idea. 73 00:05:11,929 --> 00:05:21,647 [plucking sounds running backward] 74 00:05:21,647 --> 00:05:24,021 [all sound stops] 75 00:05:24,021 --> 00:05:49,945 [silence] 76 00:05:49,945 --> 00:05:55,302 [one last low rumbling pluck]