0:02 [Music]
0:05 I have not heard this word ruad before
0:06 so I'm guessing that many of my
0:09 listeners haven't either so before we
0:11 continue just what is a a roule
0:14 ad right so there's not a rou ad there's
0:19 only one rou ad okay it's um so it's a
0:21 term I invented it what is it a couple
0:25 of years ago now it's um okay let's see
0:28 we probably have to descend to really
0:29 understand it we have to descend a
0:32 couple of levels in a rabbit hole okay
0:34 but but let me let me say what the what
0:37 the sort of nominal definition is uh the
0:41 nominal definition is it is the
0:42 entangled limit of all possible
0:45 computations what do I mean by that so
0:49 let's say you have a touring machine
0:51 simple idealized model of computation
0:53 you start the T you have this touring
0:55 machine you start it in all possible
0:58 States you look at the touring machine
0:59 just does what it does it has rules it
1:01 just keep keeps running does what it
1:04 does so you start in all possible States
1:06 and what you can then do is you say for
1:08 this touring machine let's say they're
1:09 two different states of the touring
1:11 machine at the beginning maybe they
1:14 merge sometime later uh that's you know
1:17 so that that can happen and you kind of
1:19 mapping out what are the processes that
1:22 go on that go from state to state okay
1:24 so now you don't just think about one
1:26 touring machine you think about all
1:29 possible touring machine rules and in
1:31 that situation you start off from one
1:33 state and you can apply one Ching
1:35 machine rule it goes over here you apply
1:36 another Ching machine rule it goes over
1:39 here now maybe subsequently the states
1:41 those two different states will you
1:42 apply some turing machine rule they'll
1:45 merge so you get this whole structure of
1:49 branching merging uh states of let's say
1:52 touring machines then you continue that
1:54 for all time just keep it running
1:57 forever that the and it then turns out
1:59 it doesn't matter that you're talking
2:00 about touring machine
2:02 it's just a change of coordinate system
2:04 it's like rotating coordinates and
2:05 you're still talking about the same
2:07 piece of space so to speak but you're
2:09 describing it with different different X
2:11 and Y and Z values and so on so you
2:13 could change from turning machines to
2:16 Cellular autometer to other all kinds of
2:18 different models of computation this
2:21 limit will always be the same thing so
2:23 this this limit is sort of interesting
2:26 because it is it is it encapsulates all
2:30 that is computationally possible and it
2:32 is it is unique there's you know you can
2:34 describe it in different ways but
2:36 there's just one ruad there's only the
2:39 only way that it isn't unique is to say
2:40 well it only uses touring machines so a
2:42 touring machine has certain limitations
2:44 like for example if I say and it's
2:46 related to computational reducibility if
2:49 I say here's this touring machine is it
2:52 ever going to reach some halt State you
2:54 say well I ran it for a million steps it
2:55 didn't reach a halt State it's not going
2:58 to Halt but you you to it is not in
3:00 general possible to prove with a finite
3:03 proof that the system will eventually
3:05 halt or not and this is a feature of
3:07 computational irreducibility
3:09 computational ir I mean just to just to
3:12 give the logical flow of this the the
3:14 most fundamental principle here is the
3:16 principle of computational equivalence
3:20 the idea that systems are are equivalent
3:22 in their computational sophistication so
3:24 then the question is if you have a
3:26 system and it's running and it's running
3:28 according to certain rules and you are
3:30 saying I'm going to jump ahead I'm going
3:32 to predict what the system does without
3:34 having to follow all those steps well
3:35 how are you going to do that well
3:38 eventually you have to be somehow
3:40 computationally smarter than the system
3:42 itself you have to be able to say well
3:44 it's spent a billion steps but I've got
3:45 this really clever computational
3:47 technique that lets me answer that in
3:49 three steps okay but the principle of
3:51 computational equivalence tells you you
3:54 can't do that it tells you you as a
3:57 brain as a mathematician as whatever
3:59 else you are simply computationally equivalent
4:00 equivalent
4:02 to the system you're studying and so
4:04 that's why you get this phenomenon of
4:06 computational irreducibility so that's
4:07 kind of the that that's that's that
4:11 piece of it now when you're looking at
4:14 so but one thing you could say is okay
4:16 well computational irreducibility is
4:19 something where you can't jump ahead
4:20 because you're just computationally
4:22 equivalent to the system but I could
4:24 just say I just imagine that I have what
4:26 usually gets called an oracle imagine I
4:29 just have this box that answers
4:30 questions which Tak an infinite time for
4:33 a turing machine to answer and You' say
4:35 I'm going to attach this box to my
4:39 computer well with that box you can go
4:41 beyond mere computation you can go to
4:44 hypercomputation so there are there are
4:47 an infinite hierarchy of hyper RADS
4:50 which involve more than just ordinary
4:52 computation but the one sort of
4:54 contingent fact I think about the
4:57 universe is we live in the ruad and not
5:00 in the hyper ruad and there is a a
5:02 necessary Event Horizon kind of a causal
5:05 disconnection between the ruad there's
5:07 the same kind of causal disconnection
5:09 between the ruad and the hyper ruad as
5:11 there is between what we see in the
5:13 physical universe and the interior of a
5:15 black hole it's it has the same kind of
5:18 causal you can't have an effect going
5:21 from one to the other type thing so the
5:24 the it is not self-evident it's not
5:26 something we can prove in some sense
5:29 that we we can find empirical evidence
5:30 that we're in the ruad not in the hyper
5:33 ruad but it's the same it has the same
5:36 kind of status in kind of uh thinking
5:39 about what's necessary and what's not as
5:40 to say you know we are at this place in
5:42 the physical Universe there's not a
5:44 thing where you can say I'm going to
5:45 prove a theorem that the Earth is at
5:47 this place in the universe that doesn't
5:49 really make any sense it's just we
5:50 happen to be at this place in the
5:53 universe and given that we have certain
5:55 Impressions about how the universe works
5:57 well we happen to be in the ruad and not
5:59 in something else but there is only one
6:01 unque unique ruad and so then you ask
6:03 the question well so for example there
6:05 are many many questions you can ask so
6:08 the the you know the important thing is
6:11 we are sampling the ruad at one place in
6:13 the ruad which means that among other
6:17 things we have given the way our minds
6:19 work given the way our senses work and
6:22 so on we have a particular view of how
6:26 the universe is working if we were to
6:27 move ourselves to a different place in
6:29 Ral space sort of a different place in
6:31 the ruad we would have a different point
6:33 of view about how the universe works
6:35 it's still the same underlying ruad but
6:37 we're sampling it in a different way
6:39 just like in physical space we can move
6:41 from here to there and we'll have a
6:42 different point of view about what's
6:45 happening in the universe so in this in
6:48 this case what we uh the way I see it
6:51 actually um and this is sort of a a
6:54 philosophical plong that is not 100%
6:57 worked out but the way I think of it is
6:59 you know different minds are are
7:01 different points in the ruad they're
7:03 different points in Ral space so you
7:05 know you can be physically in a
7:06 different place and you have a different
7:08 point of view about things you can be in
7:10 a different place in Ral space which
7:13 means you have a different view of you
7:15 have a you attribute different rules to
7:17 the way the universe works and it's just
7:20 like you know in in in my mind versus in
7:23 your mind we might uh we might think
7:24 we're talking about the same thing but
7:26 the actual internal operation of our
7:29 minds is quite different and so one one
7:31 of things that's really kind of fun that
7:32 is a place where sort of you see a
7:34 contact between physics and and all of
7:37 this stuff is in physics one of the
7:39 remarkable things in physics is that
7:42 pure motion is possible that is you can
7:44 take an object and you can move it
7:46 somewhere and it's still the same thing
7:48 it's not obvious that will be true you
7:50 know and if you if you happen to move it
7:52 very close to a space-time Singularity
7:55 it won't be true but in most of space
7:56 you move something from here to there
7:59 and it's still the same thing that that
8:00 is there is a sense in which the
8:03 identity of the object is not changed by
8:06 the way in metam mathematical space that
8:09 that same kind of uh sort of uh
8:11 preservation of of identity under motion
8:13 I think is the reason that there are
8:15 these big dualities between different
8:17 areas of mathematics you can think of
8:19 different areas of mathematics as
8:21 existing in different places in MA meta
8:24 mathematical space and this kind of idea
8:26 that sort of you can you can move from
8:28 one to the other is kind of like the
8:30 algebra to Geometry translation things
8:32 like this but back to back to physical
8:34 space so we have this idea of of motion
8:36 in physical space the possibility of
8:39 pure motion the question is what are
8:41 things that are subject to Pure motion
8:44 so for example particles like electrons
8:47 electrons preserve their identity while
8:49 moving through space uh in the in the
8:52 course of time and this is so in a sense
8:53 we can think of an electron as being
8:56 some sort of well in our models of the
8:58 the universe everything is just made of
9:01 space spaces I I should say this this is
9:04 a I'm I'm kind of I'm sort of bizarrely
9:06 ascending some rabbit hole I started
9:07 from the roule ad which is kind of the
9:10 bottom of the rabbit hole but um uh the
9:13 I mean sort of a fundamental piece of
9:14 our just just to outline this because
9:16 it's relevant to the intuition of these
9:19 other things in our kind of current
9:21 theory of fundamental physics um I say
9:23 our there thing that well I'd been
9:25 working on it from the 1990s but really
9:28 got developed in um about 3 years ago now
9:29 now
9:33 and um it's now become I would say
9:34 decent number of physicists and
9:35 mathematicians are working on it and
9:37 it's sort of becoming a bigger bigger
9:40 snowball it's very very very beautiful
9:43 I'm it just it just came out more
9:44 beautifully than I could ever possibly
9:46 have imagine no I can tell the way that
9:48 you talk about it it's like a
9:50 child yeah yeah right well it's kind of
9:52 like I you know I had no idea that for
9:55 example the three fundamental theories
9:57 of 20th century physics general tivity
10:00 theory of SpaceTime Quant mechanics and
10:01 statistical mechanics the thing that
10:02 leads to the second world of
10:04 thermodynamics all three of those
10:07 theories can be derived from the same
10:09 principle they are in a sense the same
10:11 Theory and I had no idea that would come
10:13 out that way and it's really to me it's
10:15 a just an amazing thing and really all
10:16 three of those theories we can talk
10:18 about it are the results of the
10:20 interplay between the way we are as
10:22 observers interacting with this
10:25 underlying ruad object MH but just to
10:26 just to start off from kind of The
10:29 Theory of physics the
10:31 you know the starting point
10:34 is one important point is space is
10:37 discreet in our model so you know people
10:40 have imagined ever since uclid and so on
10:43 space is just this thing where you put
10:45 stuff at different positions in space
10:47 and you can put things anywhere you want
10:50 in space well back you know in in
10:52 ancient times and so on people wondered
10:55 is matter continuous so discreet and you
10:56 know for a long time that was unclear
10:59 and it became clear at the end of the 19
11:01 Century that matter was actually made of
11:04 discrete molecules and then you know
11:06 another big surprise electromagnet the
11:08 electromagnetic field light and so on is
11:11 also made of discrete particles at that
11:13 time at the beginning of the 20th
11:15 century it was like well presumably
11:17 space is also discret but there were
11:19 technical reasons why people didn't
11:21 manage to make that work I mean Einstein
11:25 famously at least famously to me um you
11:27 know had this statement back from 1916
11:29 said in the end space will turn out to
11:31 be discreet but we don't have the
11:33 mathematical tools to understand how
11:36 this will work yet so 100 years later we
11:41 do and turns out that it is so the
11:42 starting point is realizing space is
11:44 discrete it isn't the case you can just
11:46 put things anywhere you want just like
11:48 you know you have water you can't say
11:50 there's a piece of water everywhere
11:51 there's only sort of water where there's
11:54 a molecule type thing so space is
11:57 discrete this the everything that is in
11:59 the universe is a feature of
12:01 space and we have this kind of a good
12:03 way to think about the structure of
12:05 space is it's like a hypergraph you have
12:07 these these atoms of space just these
12:10 points disembodied points and all that
12:11 you can say about them is how they're
12:13 related to other points so building up
12:15 this kind of graph this network of
12:18 connections between the atoms of space
12:20 they don't they're not placed anywhere
12:22 particular all they know is they have
12:24 these relationships between them that
12:25 are defined by these relations
12:27 associated with this graph and that's
12:29 that's the structure of space and
12:31 everything in space so for example just
12:33 like in a fluid you know you might have
12:35 a Vortex when you run your finger
12:36 through the fluid you'll see a little
12:39 Eddie that Eddie is made of the exact
12:40 same molecules as make anything else in
12:44 the fluid and so similarly a particle
12:46 like an electron we think of as being
12:48 something a little bit like an Eddie but
12:52 now in this in this um graph that
12:54 represents the structure of space rather
12:55 than in this bunch of molecules bouncing
12:57 around so an important point in this
12:59 kind of picture is what is time
13:03 and in this in this model the the graph
13:05 is continuously getting Rewritten There
13:07 are rules that say if you see a piece of
13:09 graph that looks like this it's going to
13:11 change into one that looks like that and
13:12 so there's this Progressive computation
13:15 of new graph from old graph and that
13:18 computational process is the progress of
13:21 time and computational irreducibility is
13:22 the reason that there's sort of
13:24 something definite happening in the
13:27 progress of time and it's so we kind of
13:28 have this idea space is a very different
13:31 kind of thing than time and you know
13:33 relativity still works out it works out
13:35 very beautifully it's an emergent
13:37 feature of of how the system works it
13:39 wasn't something space and time start
13:41 very different but they still have this
13:43 relationship the relativity implies and
13:47 so on but then so then the the next
13:49 thing to realize is we got this system
13:52 it's evolving through time and then the
13:53 next thing you realiz is well there are
13:55 all these different rewrites that could
13:57 happen on this graph there are actually
13:58 many different rewrites that could happen
13:59 happen
14:00 to a given graph there are many
14:01 different rewrites that could happen
14:04 next and that means that time is not a
14:06 single thread time is this
14:08 multi-threaded thing that has both
14:11 branching and merging and so then it
14:14 turns out the quantum mechanics is the
14:17 feature is is a consequence of this fact
14:19 that you get these many threads of time
14:21 and one of the one of the strange
14:23 features is one one of the critical
14:25 things about this model is that that we
14:26 are embedded within the model so we have
14:29 to think what is an entity embedded as
14:31 part of this model think about what's
14:32 going on so for example an important
14:35 feature is there are many branches there
14:38 many threads of time but our minds are
14:41 spread across many threads of time so in
14:43 other words it becomes this question of
14:46 what how does a branching mind perceive
14:48 a branching universe and that turns out
14:50 to be what gives one kind of the
14:52 essentially what gives one quantum
14:54 mechanics there are details there that
14:56 still to be worked out but at a at a
14:58 qualitative level that's the story is is
15:00 that it is and and then it becomes very
15:02 critical that we have this idea that we
15:04 have a single thread of existence
15:06 because that's what causes us to be
15:08 forced to knit together all these
15:10 different threads of time so anyway the
15:12 the final part of the rabbit hole
15:14 descending down to the rabbit hole is
15:16 that so we have you know all these
15:17 possible rewrites are happening they
15:19 Define different threads of time and so
15:22 on but then you might ask yourself you
15:23 know what a confusing situation we've
15:25 got all these things happening we got
15:27 this Rule and we can hold in our hands
15:29 the rule for the universe and we say
15:32 look you know it's rule number 156 or
15:35 something and that's a very bizarre
15:38 possibility that we could just say our
15:41 whole universe we got rule number 156
15:43 and Another Universe might have got
15:45 another Rule and it's then very
15:47 mysterious why we got a rule that's kind
15:49 of a low-numbered rule not a rule so
15:51 complicated that we can never make a
15:52 prediction about what happens in the
15:54 universe because we're always you know
15:56 sampling a different part of the rule
15:58 and so on so I was very confused about
16:00 this for a while but then I realized
16:02 actually the right way to think about it
16:04 is the universe is running all possible
16:08 rules and that's what the ruad is is
16:10 this a universe that is you know where
16:12 you could slice it to look at just the
16:14 space part you can slice it to look at
16:15 the quantum mechanics part but in the
16:18 end it's running all possible rules and
16:22 the the sort of the the big fact is that
16:26 knowing that to an observer like us
16:28 there are certain necessary features of
16:30 the perceptions that we have about the
16:32 universe so the universe is is
16:34 ultimately just this ruad that's doing
16:37 all these crazy things but as a
16:39 computationally bounded believing your
16:41 persistent in time Observer there are
16:43 certain necessary features of what you
16:46 perceive about that universe and those
16:48 necessary features turn out to be
16:50 exactly the big theories of 20th century
16:52 physics which I think is really really
16:55 interesting because it's kind of like
16:56 it's on us so to speak but it's not
16:59 completely on us it's any obser
17:00 who has these General attributes that
17:03 are like us will conclude these
17:06 particular things about physics and so
17:08 you know that's that's a a sense in
17:11 which both the universe is inevitable
17:13 and the universe is dependent on the way
17:15 we particularly are but I was going to
17:18 say uh you know in this kind of picture
17:20 so a particle in this in this kind of
17:24 picture is this kind of uh lump of kind
17:27 of structure in this graph that can move
17:30 without change through time so now the
17:32 question is in Ral space and this is
17:33 where it kind of philosophy meets
17:37 science in some strange way in um in Ral
17:39 space you've got two minds that are at
17:42 different places in Ral space and you
17:44 can always translate between them just
17:46 like you can translate between two
17:47 different computers two different
17:49 touring machines there is a way of
17:51 translating between them but if you ask
17:54 what can you propagate what what thing
17:57 can be produced by one mind and kind of
18:00 move un changed through Ral space and
18:04 land at the other mind I think that the
18:06 you know again not not fully worked out
18:08 but I think concepts are the packaging
18:12 of thought that get to be transportable
18:15 like particles through in this case Ral
18:16 space rather than physical space so in
18:19 other words you take what's in your mind
18:21 and there are all these neuron firings
18:22 that are happening and so on and then
18:26 you say a word you you know elicit some
18:29 kind of concept and that's a thing
18:32 that's packaged enough that it can you
18:36 know arrive at my mind and be unpacked
18:37 and it's kind of the same thing in some
18:40 sense it's kind of the analog of motion
18:43 this this idea that there can be a a a
18:46 kind of a a lump of stuff that is
18:48 translated from one mind to another I
18:51 think that's kind of the the uh uh you
18:52 know that that's that's something one
18:55 can think about as um as kind of you
18:57 know that's sort of the analog of
18:58 particles it's a very bizarre idea that
19:01 the analog of an electron in physical
19:05 [Music] concept
