How the universe generates time and space from a single rewriting rule | Stephen Wolfram — Transcript

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1. 0:04When we start thinking about the world in computational terms, there's a question of
2. 0:10sort of what does that mean?
3. 0:12People will say things like, if the world is computational, where's the computer
4. 0:16that it's running on?
5. 0:18This is a confusion.
6. 0:19Models are a way of representing what the natural world does.
7. 0:23They're not mechanistically what the natural world is doing.
8. 0:27This is a deep rabbit hole, but let's go into it.
9. 0:35Let's start off with physics.
10. 0:37And, you know, what is the physical world made of?
11. 0:40We start back in antiquity, people arguing is the universe discrete or continuous.
12. 0:44We learn by the end of the 19th century that matter is discrete, kind of the
13. 0:49realization that we've had in recent times, that's sort of the foundation of
14. 0:53the things I've done.
15. 0:55Is that we can think of space as also discrete.
16. 0:58And so we think, what's in the universe?
17. 1:00What's the universe made of?
18. 1:01Well, we think of it as a bunch of discrete atoms of space.
19. 1:04They're not atoms in the sense of chemical atoms.
20. 1:08They're atoms in the sense of being indivisible units.
21. 1:11are atoms of space.
22. 1:14And the only thing one can say about the atoms of space are how they are related to
23. 1:17each other.
24. 1:18And we can represent that by a network where we say this atom of space is kind of
25. 1:23connected, related to these other atoms of space.
26. 1:26So we represent the whole universe just as a graph, a network.
27. 1:31And we imagine
28. 1:32that the universe and space and everything in it is just features of that network.
29. 1:39What there ultimately is, is just this network that represents space and
30. 1:44everything in it.
31. 1:46Well, another question is, well, what does this network do?
32. 1:48You know, that might be in sort of technological terms, the data structure of
33. 1:52the universe.
34. 1:53But what now is the algorithm of the universe, so to speak?
35. 1:58And for that, what
36. 2:00we imagine is that this network, we look at little pieces of this network and we
37. 2:05say there are a collection of rules that say whenever you see a little piece of
38. 2:08network that looks like this, it gets rewritten to a piece of network that looks
39. 2:13like that.
40. 2:15And this just keeps on happening.
41. 2:17And that process of the rewriting of the network, that is the progress of time.
42. 2:21That is, that time kind of corresponds to this progressive computational process of
43. 2:27the rewriting of this network.
44. 2:29And one thing one can ask is, well, what's the large-scale effect of that?
45. 2:32If there are, you know, 10 to the 400 of these atoms of space, and they're all
46. 2:37getting rewritten in all these ways, what does that do in the aggregate?
47. 2:41And sort of an analogous situation is what happens in a fluid, where we know what
48. 2:45happens at the level of individual molecules colliding and bouncing off each
49. 2:48other and so on.
50. 2:50But then the question is, what is the aggregate effect of that when we look at
51. 2:55zillions of molecules together?
52. 2:57And we know in that case that what emerges is fluid mechanics.
53. 3:01Well, in the case of these networks and atoms of space and so on, what seems to
54. 3:07emerge is general relativity, the theory of gravity, Einstein's equations, and so
55. 3:11on.
56. 3:12That's the thing that is the aggregate effect of all these microscopic processes
57. 3:17associated with the structure of this network.
58. 3:21Well, then what happens is there are all these different sort of ways that the
59. 3:26network can get rewritten, but there are all these different parts of the network
60. 3:30can be rewritten separately, that there isn't sort of a single thread of history
61. 3:34that says the network is in this form and then in this form and then in this form.
62. 3:38There are lots of different possible threads of history that correspond to
63. 3:42different possible orders in which these little pieces of rewriting can be done.
64. 3:46And that possibility of all these different paths of history is what leads
65. 3:50to quantum mechanics in our models.
66. 3:52What's characteristic for quantum mechanics is that whereas in kind of
67. 3:55classical physics, the notion is sort of definite things happen, things follow
68. 4:00definite trajectories.
69. 4:01In quantum mechanics, it's like there are many, many paths that are followed, and we
70. 4:05only get to be able to look at sort of the aggregate effect represented in terms of
71. 4:10probabilities of all those paths.
72. 4:12So kind of the picture here is what there ultimately is in the universe is this
73. 4:18network of atoms of space,
74. 4:21and there are many different sort of paths of history of those atoms of that network,
75. 4:27and that's what kind of leads to physics as we know it,
76. 4:31and we're getting sort of more and more detail about how physics as we know it
77. 4:35emerges from that very simple underlying structure.
78. 4:38But there's one thing that confused me for a long time,
79. 4:41which is with this picture, it's like there's a particular rule for updating
80. 4:47this graph, this network and so on.
81. 4:49Why did our universe get that particular rule and not another one?
82. 4:53How do we understand that?
83. 4:55And of all the infinitely many possible rules, why do we get this particular one?
84. 4:59And what I realized in the end is actually we didn't get a particular one.
85. 5:02Actually, all possible rules are being used.
86. 5:06What's happening is just as there are different paths of history associated with
87. 5:10the different applications of a particular rule, so there are different paths of
88. 5:13history associated with the application of different rules.
89. 5:16And in the end, the way to think about things is that what one has is
90. 5:22that represents all possible computations.
91. 5:25I call it the ruliad.
92. 5:27What is the ruliad?
93. 5:28It is the entangled limit of all possible computations.
94. 5:32The ruliad is a very abstract thing.
95. 5:35It's a unique thing.
96. 5:36Imagine that you have all possible machines that can do computation, all
97. 5:40possible abstract systems that can do computation.
98. 5:44You start them all running.
99. 5:45They are entangled because two different machines may produce the same result.
100. 5:51And that kind of weaves together the different pieces, the structure of the
101. 5:56ruliad
102. 5:57So the ruliad is this very abstract thing.
103. 5:59You can imagine a notion of rulial space.
104. 6:03So as you move around the ruliad, it's as if you are sort of using different kind of
105. 6:10computational devices to figure out what will happen in the world.
106. 6:15And in a sense, you can even think that different minds are embedded in different
107. 6:20places in the ruliad.
108. 6:21Different minds have a different way of thinking about what's going to happen in
109. 6:25the world.
110. 6:26And you can represent that by saying those different minds are at different places in
111. 6:29the ruliad
112. 6:30So minds that are very closely aligned will be close together in rulial space.
113. 6:36You know, human minds might be all clumped together.
114. 6:39You know, cats and dogs might be a bit further away.
115. 6:41The weather with its mind of its own might be much further away.
116. 6:45It's similar to physical space where we would have a different point of view about
117. 6:49kind of what we see out there in the world.
118. 6:52If we're standing very close together, we'll say we see the same things.
119. 6:56If we're standing far apart, we'll say we see different things.
120. 6:59There actually, in our model of physics, there actually are three different kinds
121. 7:03of space that turn out to be important.
122. 7:05Physical space is the kind we're used to experiencing, what we call branchial
123. 7:09space, which is kind of the space of possible histories that's associated with
124. 7:14quantum mechanics,
125. 7:15and rulial space, which is this much more general thing that is these kind of
126. 7:20different points of view about how the universe works.
127. 7:23But the ruliad is a completely inevitable, necessary object.
128. 7:27Given the idea of computation, there is no choice but to have the ruliad
129. 7:32The ruliad is this limit of all possible computations.
130. 7:35It's a unique, inevitable object.
131. 7:37So then the question is, well, how do we fit into that?
132. 7:41We are observers embedded within the ruliad
133. 7:45made of the same stuff as the ruliad and the question is, what is our perception of
134. 7:49the ruliad given that setup?
135. 7:51And what turns out to be crucial is that we are observers of a certain kind, and
136. 7:58observers of the kind we are necessarily perceive the ruliad in certain ways.
137. 8:03Let me try and give a simpler example first.
138. 8:06When we're looking at molecules bouncing around, we can ask the question, what do
139. 8:12you perceive about these molecules bouncing around?
140. 8:15One feature of molecular processes is they're reversible.
141. 8:19If you have a movie of molecules colliding, bouncing off, and so on, you
142. 8:24can't tell whether the movie is being run in the forward direction or in reverse.
143. 8:28The microscopic collisions all look the same.
144. 8:31But yet macroscopically, we know you smash a piece of glass and what you get is
145. 8:38something very different.
146. 8:39It's a very different thing that you don't go backwards from that.
147. 8:42We see the thing smashing.
148. 8:44We don't see the thing assembling itself spontaneously from all the fragments.
149. 8:49And so that's the phenomenon of irreversibility.
150. 8:53That's the phenomenon of law of entropy increase, the second law of
151. 8:55thermodynamics, and so on.
152. 8:57Why does it happen?
153. 8:58Well, it happens actually because of this phenomenon of computational
154. 9:01irreducibility.
155. 9:02What's happening is the original setup of the system is sort of being run forwards
156. 9:08computationally.
157. 9:09That computation is effectively encrypting whatever simplicity there was in the
158. 9:13initial conditions, in the
159. 9:14initial setup of the system.
160. 9:16And then the issue is, well, what do we see from that initial setup?
161. 9:20In principle, we can take whatever comes out and we could reverse it.
162. 9:24But in practice, because we are observers who are computationally bounded, we can't
163. 9:30do all that irreversible, irreducible computation
164. 9:34to go and follow through all those steps.
165. 9:36We're stuck just saying it looks random to us.
166. 9:40If we could do sort of unbounded computation, we could always know this
167. 9:46particular elaborate configuration of molecules, that came from the simple
168. 9:50initial condition.
169. 9:51But because we are computationally bounded, we
170. 9:54have to just say it looks random to us, and we believe in the second law of
171. 9:58thermodynamics.
172. 9:59So the second law of thermodynamics is a consequence of our computational
173. 10:04simplicity relative to the computational irreducibility of the underlying processes
174. 10:09that are going on.
175. 10:10So that's an example of a place where the nature of us as observers
176. 10:14determines essentially the laws of physics that we perceive.
177. 10:18What we're effectively doing is, observers like us kind of are sampling particular
178. 10:24pockets of reducibility.
179. 10:26I have to say that if everything was purely irreducible, we wouldn't believe
180. 10:31there were laws of nature.
181. 10:32We would just say,
182. 10:34Everything about the universe is unpredictable.
183. 10:36We just have to watch the universe unfold to see what's going to happen.
184. 10:40But in fact, we know there are certain pieces of computational reducibility.
185. 10:44There are places in which we know there are regularities in the universe, which
186. 10:48we, with our finite minds, are capable of making use of to be able to say that's
187. 10:53predictable.
188. 10:54That's a law of nature.
189. 10:55That's something that allows us to kind of reduce the complexity of the world to
190. 11:00something that we can kind of tell a narrative about in our minds.
191. 11:04So the question then is not why does the ruliad exist?
192. 11:07The ruliad inevitably exists.
193. 11:09It's an abstract thing that necessarily exists and is unique.
194. 11:13The question that is less obvious is why do we exist?
195. 11:17Why are there observers like us embedded within the ruliad
196. 11:21I think that is something which we are within sight of being able to sort of
197. 11:25derive scientifically.
198. 11:26I mean, one feature of observers like us is that we tend to take huge amounts of
199. 11:31input data.
200. 11:32You know, we're looking around the room and we're seeing all these pixels of
201. 11:37data, and yet we take all that input and we decide we're going to say this word
202. 11:42next.
203. 11:43We're going to reduce all of that input.
204. 11:45We're going to kind of crush it down to at a very slow rate decide what we do next.
205. 11:50That seems to be a feature of our brains.
206. 11:52It seems to be an essential feature of the thing that we perceive as consciousness,
207. 11:56so to speak.
208. 11:57That we are getting the sort of single thread of experience that emerges from the
209. 12:02sort of crushing down of all of this input.
210. 12:05It's something that is different from the rest of the natural world.
211. 12:08I mean, in my principle of computational equivalence, it's not that brains are any
212. 12:13more computationally sophisticated than random things in the world.
213. 12:18You know, people would say sort of whimsically, the weather has a mind of its
214. 12:22own.
215. 12:23And the principle of computational equivalence says, actually, yes, all those
216. 12:26fluid motions in the atmosphere, they're doing a computation that's just as
217. 12:30sophisticated as the computation that happens with all the electrochemistry of
218. 12:34neurons and brains.
219. 12:36But the issue is that computation that's going on in the weather
220. 12:40is very different in character.
221. 12:42It's not aligned with the kinds of computations that we do in our brains.
222. 12:47And it doesn't have the same feature of taking sort of all of its input data and
223. 12:52crushing it down to a single sort of consensus next action.
224. 12:56It seems that that sort of, that feature is something that's very essential
225. 13:01to our particular way of perceiving the universe, and it's relevant to what we
226. 13:05perceive as the laws of physics.
227. 13:07There are other features of this, like, for example, why do we believe in
228. 13:11objective reality?
229. 13:12You know, each one of us has an internal view of how things work and how we're
230. 13:17thinking about things.
231. 13:18But we believe that there is an outside world there that everybody sort of more or
232. 13:23less agrees how it's set up.
233. 13:25And I think what is surprising to me as well, that it seems like the emergence of
234. 13:30sort of a reasonable notion of objective reality depends on the fact that there are
235. 13:34lots of us.
236. 13:35If there was just one of us, we wouldn't have a clear notion of objective reality.
237. 13:39It's because we can all extrapolate that our internal perceptions and feelings are
238. 13:44similar in other people.
239. 13:46And those other people, we're all observing, we're all sort of agreeing
240. 13:49about how the universe, how the world works.
241. 13:52And that's why we sort of believe in objective reality.
242. 13:55It's sort of an interesting feature that extends to lots of different things.
243. 14:00Quantum mechanics, for example, is a place where it's been very confusing to
244. 14:05understand why people think definite things happen in quantum mechanics.
245. 14:09In quantum mechanics, you're always following these many possible paths of
246. 14:12history.
247. 14:13Why is it. then, that people sort of say, yes, a definite thing happened and we
248. 14:16agree about what that was?
249. 14:18I think the answer to that is, it's because, in a sense, we're all very close
250. 14:23together in this thing I call branchial space, the space of possible quantum
251. 14:27branches.
252. 14:28It's similar to physical space.
253. 14:30I mean, if you say, what's the night sky like?
254. 14:33We'll all say, well, it looks roughly like this.
255. 14:35It has these constellations in it.
256. 14:37and so on.
257. 14:37But we all say, we all agree about what the night sky looks like because we're all
258. 14:41sitting on this one planet.
259. 14:43If we were spread throughout the galaxy, we absolutely would not agree what the
260. 14:47night sky was like.
261. 14:48It's because we're sort of close together,
262. 14:50we're many entities close together, that we have certain kinds of perceptions about
263. 14:54the way the world works.
264. 14:56But you can kind of keep going and try to understand the extent to which because we
265. 15:01are the way we are, then it becomes inevitable that
266. 15:04the science that we believe in, the laws of physics that we believe in, must be the
267. 15:08way that they are, which is sort of a very surprising sort of metaphysical conclusion
268. 15:13that I, for one, did not see coming at all.