WEBVTT 1 00:00:00.200 --> 00:00:04.827 A description that works for what we see now may still fail to predict what happens 2 00:00:04.827 --> 00:00:06.173 after an action. 3 00:00:06.173 --> 00:00:11.356 If hidden conditions have different consequences, treating them as the same can hide a 4 00:00:11.356 --> 00:00:12.813 difference that matters. 5 00:00:12.813 --> 00:00:17.784 Watch which distinctions are needed to predict change, and which details can safely be 6 00:00:17.784 --> 00:00:18.520 left out. 7 00:00:19.760 --> 00:00:21.180 Start a fresh run. 8 00:00:21.180 --> 00:00:24.752 The observer receives zero: the lamp is off. 9 00:00:24.752 --> 00:00:30.480 That reading fits either hidden configuration u or hidden configuration v. 10 00:00:30.480 --> 00:00:33.660 We do not get a cutaway showing which one is actual. 11 00:00:33.660 --> 00:00:39.408 The letters name hidden configurations; zero and one name lamp outputs. 12 00:00:39.408 --> 00:00:42.507 Zero means off and one means on. 13 00:00:42.507 --> 00:00:46.128 We want to predict the lamp after a button called PULSE. 14 00:00:46.128 --> 00:00:48.400 Does the current reading tell us enough? 15 00:00:49.190 --> 00:00:52.330 The rules are supplied with this teaching model. 16 00:00:52.330 --> 00:00:56.343 If the device started in u, PULSE would take it to w. 17 00:00:56.343 --> 00:00:59.283 The lamp is one in w. 18 00:00:59.283 --> 00:01:02.743 If it started in v, PULSE would leave it in v. 19 00:01:02.743 --> 00:01:05.143 The lamp there is zero. 20 00:01:05.143 --> 00:01:08.796 These are calculations from the known rule. 21 00:01:08.796 --> 00:01:11.809 We have not pressed the button on the actual device. 22 00:01:12.599 --> 00:01:15.719 Before comparing the results, predict the answer. 23 00:01:15.719 --> 00:01:28.479 Given only the received zero, must the lamp be on after PULSE, must it be off, or is the result still undetermined? 24 00:01:28.479 --> 00:01:32.977 The two possible runs start with the same lamp output, zero. 25 00:01:32.977 --> 00:01:37.208 Starting in u gives w and then output one. 26 00:01:37.208 --> 00:01:41.066 Starting in v gives v and then output zero. 27 00:01:41.066 --> 00:01:43.539 So the result is still undetermined. 28 00:01:43.539 --> 00:01:47.786 The current reading has not selected one of those starting configurations. 29 00:01:47.786 --> 00:01:51.199 No predicted output has become a new received reading. 30 00:01:52.069 --> 00:01:55.920 Now build prediction groups for all four configurations in the model. 31 00:01:55.920 --> 00:02:02.842 Configurations can share a group only when the group supports the same future lamp predictions for the available buttons. 32 00:02:02.842 --> 00:02:08.136 We must give u and v different groups: PULSE is a concrete reason to separate them. 33 00:02:08.136 --> 00:02:11.056 These boxes are a description of possibilities. 34 00:02:11.056 --> 00:02:14.869 Splitting a box does not create a new physical configuration. 35 00:02:15.659 --> 00:02:19.563 Compare the other two configurations, w and z. 36 00:02:19.563 --> 00:02:21.115 Both have output one. 37 00:02:21.115 --> 00:02:28.259 They are not candidates for our earlier zero reading; we are comparing model cases to finish the prediction groups. 38 00:02:28.259 --> 00:02:31.486 PULSE leaves w at w and z at z. 39 00:02:31.486 --> 00:02:32.966 Their lamps stay on. 40 00:02:32.966 --> 00:02:35.939 Press PULSE again and the same thing happens. 41 00:02:35.939 --> 00:02:39.339 Any number of PULSE presses keeps both outputs one. 42 00:02:39.339 --> 00:02:42.539 There is one other available button: RESET. 43 00:02:42.539 --> 00:02:45.926 Its known rule sends every configuration to u. 44 00:02:45.926 --> 00:02:53.232 Starting in w or starting in z, the first RESET therefore brings both cases to that same state u. 45 00:02:53.232 --> 00:02:58.799 Every finite sequence either has no RESET, or has a first RESET. 46 00:02:58.799 --> 00:03:02.909 Without RESET, we just checked the repeated PULSE case. 47 00:03:02.909 --> 00:03:10.133 With RESET, both cases reach u together; the same later buttons then give the same states and outputs. 48 00:03:10.133 --> 00:03:12.917 That is why w and z can stay together. 49 00:03:13.707 --> 00:03:17.087 The full model has four configurations. 50 00:03:17.087 --> 00:03:25.557 For lamp predictions using PULSE and RESET, three groups suffice: u, v, and w-or-z. 51 00:03:25.557 --> 00:03:31.467 Members of each group are predictively equivalent: they make the same specified future predictions. 52 00:03:31.467 --> 00:03:35.387 The combined w-or-z group reports one. 53 00:03:35.387 --> 00:03:40.007 PULSE keeps it in that group; RESET takes it to the u group. 54 00:03:40.007 --> 00:03:42.931 From u, PULSE actually goes to w. 55 00:03:42.931 --> 00:03:52.171 Its group destination is called w-or-z because that label groups w with z; it does not mean the button might send u to z. 56 00:03:52.171 --> 00:03:57.671 The other rows are shown too, so we can update the group without choosing a member inside it. 57 00:03:57.671 --> 00:04:00.358 But the group cannot answer every question. 58 00:04:00.358 --> 00:04:06.111 If the task were to report the exact configuration name, w or z would matter. 59 00:04:06.111 --> 00:04:11.291 Our grouping preserves this lamp-prediction task, not all possible information. 60 00:04:12.081 --> 00:04:13.781 Return to the fresh run. 61 00:04:13.781 --> 00:04:17.241 The only received reading is still zero. 62 00:04:17.241 --> 00:04:21.901 All the button presses we traced were hypothetical model cases. 63 00:04:21.901 --> 00:04:24.854 The actual device has not been operated. 64 00:04:24.854 --> 00:04:28.977 We now know why u and v need separate prediction groups. 65 00:04:28.977 --> 00:04:37.801 Does the observer know which of those groups its device occupies? 66 00:04:37.801 --> 00:04:41.361 No. Both u and v still fit the evidence. 67 00:04:41.361 --> 00:04:46.494 A table can show which difference matters without giving us an experiment that obtains it. 68 00:04:46.494 --> 00:04:51.401 Later episodes ask what observations and actions are actually available. 69 00:04:52.271 --> 00:04:57.671 u and v look the same now but must be separated for future lamp predictions. 70 00:04:57.671 --> 00:05:03.871 w and z are different configurations that can stay together for this specified task. 71 00:05:03.871 --> 00:05:08.084 A useful description preserves the distinctions the task needs. 72 00:05:08.084 --> 00:05:12.251 We have not assigned probabilities or measured the cost of finding out. 73 00:05:12.251 --> 00:05:16.591 Episode four asks how uncertainty and usefulness differ.