Stephen Wolfram: Complexity and the Fabric of Reality | Lex Fridman Podcast #234

the following is a conversation with stephen wolfram his third time on the podcast he's a computer scientist mathematician theoretical physicist and the founder of wolfram research a company behind mathematica wolf from alpha wolfram language and the new wolfram physics project this conversation is a wild technical rollercoaster ride through topics of complexity mathematics physics computing and consciousness i think this is what this podcast is becoming a wild ride some episodes are about physics some about robots some are about war and power some are about the human condition and our search for meaning and some are just what the comedian tim dillon calls fun this is the lex friedman podcast to support it please check out the sponsors in the description and now here's my conversation with steven wolfram almost 20 years ago you published a new kind of science where you presented a study of complexity and an approach for modeling of complex systems so let us return again to the core idea of complexity what is complexity i don't know i think that's not the most interesting question it's like you know if you ask a biologist what is life yeah that's not the question they care the most about what i was interested in is how does something that we would usually identify as complexity arise in nature and i got interested in that question like 50 years ago which is really embarrassingly a long time ago and you know i i was uh you know how does snowflakes get to have complicated forms how do galaxies get to have complicated shapes how does you know how do living systems get produced things like that and the question is what's the sort of underlying scientific basis for those kinds of things and the thing that i was at first very surprised by because i've been doing physics and particle physics and fancy mathematical physics and so on and it's like i know all this fancy stuff i should be able to solve this sort of basic science question and i couldn't this was like early maybe 1980-ish time frame and it's like okay what can one do to understand the sort of basic secret that nature seems to have because it seems like nature you look around in the natural world it's full of incredibly complicated forms you look at sort of most engineered kinds of things for instance they tend to be you know we've got sort of circles and lines and things like this the question is what secret does nature have that lets it make all this complexity that we in doing engineering for example don't naturally seem to have and so that was the kind of the thing that i got interested in and then the question was you know could i understand that with things like mathematical physics well didn't work very well so then i got to thinking about okay is there some other way to try to understand this and then the question was if you're going to look at some system in nature how do you make a model for that system for what that system does so you know a model is some abstract representation of the system some formal representation system what are what is the raw material that you can make that model out of and so what i realized was well actually programs are really good source of raw material for making models of things and you know in terms of my personal history the to me that seemed really obvious and the reason it seemed really obvious is because i just spent several years building this big piece of software that was sort of a predecessor to mathematica and multiple language thing called smp symbolic manipulation program which was something that had this idea of starting from just these computational primitives and building up everything one had to build up and so kind of the notion of well let's just try and make models by starting from computational primitives and seeing what we can build up that seemed like a totally obvious thing to do in uh in retrospect it might not have been externally quite so obvious but it was obvious to me at the time given the path that i happened to have been on so you know so that got me into this question of let's use programs to model what happens in nature and the question then is well what kind of programs and you know we're used to programs that you write for some particular purpose it's a big long piece of code and it does some specific thing but what i got interested in was okay if you just go out into the sort of computational universe of possible programs you say take the simplest program you can imagine what does it do and so i started studying these things called cellular automata um actually i didn't know at first they were called cellular automata but i found that out subsequently but it's just a line of cells you know each one is black or white and it's just some rule that says the color of the cell is determined by the color that it had on the previous step and it's two neighbors on the previous step and i had initially thought that's you know sufficiently simple setup it's not going to do anything interesting it's always going to be simple no complexity simple rule simple behavior okay but then i actually ran the computer experiment which was pretty easy to do um i mean it probably took a few hours um originally and um the and the results were not what i'd expected at all now needless to say in the way that science actually works the results that i got a lot of unexpected things which i thought were really interesting but the really strongest results which was already right there in the printouts i made i didn't really understand for a couple more years so it was it was not you know the compressed version of the story is you run the experiment and you immediately see what's going on but i wasn't smart enough to to do that so to speak but the big the big thing is even with very simple rules of that type sort of the minimal tiniest program sort of the the the one line program or something it's possible to get very complicated behavior my favorite example is this thing called rule 30 which is a particular cellular automaton rule you just started off from one black cell and it makes this really complicated pattern and so that for me was sort of a critical discovery that then kind of said playing back onto you know how does nature make complexity i sort of realized that might be how it does it that might be kind of the secret that it's using is that in this kind of computational universe of possible programs it's actually pretty easy to get programs where even though the program is simple the behavior when you run the program is not simple at all and that was so for me that was the the kind of the the story of kind of how that that was sort of the the indication that one had got an idea of what the sort of secret that nature uses to make complexity and that complexity how complexity can be made in other places now if you say what is complexity you know it's it's complexity is it's not easy to tell what's going on that's the informal version of what is complexity but there is something going on but there's a rule to know what right well no the rules can generate just randomness well that that's not obvious in other words that's not how it is not obvious at all and it wasn't what i expected it's not what people's intuition had been and has been for you know for a long time that is one might think you have a rule you can tell there's a rule behind it i mean it's just like you know the early you know robots and science fiction movies right you can tell it's a robot because it does simple things right turns out that isn't actually the right story but it's not obvious that isn't the right story because people assume simple rules simple behavior and that the sort of the key discovery about the computational universe is that isn't true and that discovery goes very deep and relates to all kinds of things that i've spent years and years studying but um you know that that in the end the sort of the the what is complexity is well you can't easily tell what it's going to do you could just run the rule and see what happens but you can't just say oh you know show me the rule great and now i know what's going to happen and you know the key phenomenon around that is this thing i call computational irreducibility this fact that in something like rule 30 you might say well what's it going to do after a million steps well you can run it for a million steps and just do what it does to find out but you can't compress that you can't reduce that and say i'm going to be able to jump ahead and say this is what it's going to do after a million steps but i don't have to go through anything like that computational effort by the way has anybody succeeded at that you had a challenge a competition right for predicting the middle column of rule 30 and indeed anybody a number of people have sent things in and and sort of people are picking away at it but it's hard i mean it's it's uh i've been i've been actually uh even proving that the center column of rule 30 doesn't repeat that's something i think might be doable okay mathematically proving yes and so that's analogous to a similar kind of things like the digits of pi which are also generated in this very deterministic way and so a question is how random are the digits of pi for example does every first of all do the digits of pi ever repeat or we know they don't because it was proved in the 1800s that pi is not a rational number so that means only rational numbers have digit sequences that repeat so we know the digits of pi don't repeat so now the question is does you know 0 1 2 3 or whatever do all the digits base 10 or base 2 or however you work it out do they all occur with equal frequency nobody knows that's far away from what can be understood mathematically at this point and that's that's kind of uh but i'm i'm even looking for step one which is prove that the the the center column doesn't repeat and then prove other things about it like equidistribution of of uh equal numbers of zeros and ones and those are things which i you know i kind of set up this little little prize thing because i thought those were not not too out of range those are things which are within you know a modest amount of time it's conceivable that those could be done they're not they're not far away from what current mathematics might allow they'll require a bunch of cleverness and hopefully some interesting new ideas that you know will be useful other places but you started in 1980 with this idea before i think you realized you know this idea of programs you thought that there might be some kind of thermodynamic like randomness and then complexity comes from a clever filter that uh you kind of like i don't know spaghetti or something you you you filter the randomness and outcomes complexity which is an interesting intuition i mean how do we know that's not actually what's happening so just because you were then able to develop look you don't need this like incredible randomness you can just have very simple predictable initial conditions and predictable rules and then from that emergency complexity still there might be some systems where it's uh filtering randomness and the inputs well the point is when you have quotes randomised in the input that means there's all kinds of information in the input yeah and in a sense what you get out will be maybe just something close to what you put in like people are very in dynamical systems theory sort of big area mathematics that developed from the early 1900s and and really got big in the 1980s you know an example of what people study there a lot and it's popular version is chaos theory um an example what people study a lot is the shift map which is basically taking 2x mod 1 to the fractional part of 2x which is basically just taking digits in binary and shifting them to the left so at every step you get to see if you say how big is this number that i got out well the most important digit in that number is whatever ended up at the at the left-hand end but now if you start off from an arbitrary random number which is quotes randomly chosen so all its digits are random then when you run that sort of chaos theory shift map all that you get out is just whatever you put in you just get to see what you what it's not obvious that you would excavate all of those digits and if you're for example making a theory i don't know fluid mechanics for example if there was that phenomenon in fluid mechanics then the equations of fluid mechanics can't be right because what that would be saying is the equations of that that it matters to the fluid what happens in the fluid at the level of the you know millionth digit of the initial conditions which is far below the point at which you're hitting kind of sizes of molecules and things like that so it's kind of almost explaining if that phenomenon is an important thing it's kind of telling you that the you know fluid dynamics which describes fluids as continuous media and so on isn't isn't really right but so you know so this idea that you know there's a there's it's a tricky thing because as soon as you put randomness in you have to know you know what how much of what's coming out is what you put in versus how much is actually something that's being generated and what's really nice about these systems where you just have very simple initial conditions and where you get random stuff out or seemingly random stuff out is you don't have that issue you don't have to argue about was that something complicated put in because it's plainly obvious there wasn't now as a practical matter in doing experiments the big thing is if the thing you see is complex and reproducible then it didn't come from just filtering some quotes randomness from the outside world it has to be something that is intrinsically made because it wouldn't otherwise be i mean you know the the it could be the case that you set things up and it's always the same each time and you say well it's kind of the same but it's not then it's not random each time because kind of the definition of it being random is it was kind of picked picked at random each time so to speak so is it possible to for sure know that our universe does not at the fundamental level have randomness is it possible to conclusively say there's no randomness at the bottom well it's an interesting question i mean you know science natural science is an inductive business right you observe a bunch of things and you say can we fit these together what is our hypothesis for what's going on the thing that i think i can say fairly definitively is at this point we understand enough about fundamental physics that there is if there was sort of an extra dice being thrown it's something that doesn't need to be there we can get what we see without that now you know could you add that in as an extra little featuroid um you know without breaking the universe uh probably but in fact almost certainly yes but is it necessary for understanding the universe no and i think actually from a a more fundamental point of view it's it's i think i might be able to argue so so one of the things that i've been interested in have been pretty surprised that i've had anything sentient to say about is the question of why does the universe exist i didn't think that was a question that i would you know i thought that was a far out there metaphysical kind of thing uh even the philosophers have stayed away from that question for the most part it's so such a kind of you know difficult to address question but i actually think to my great surprise that from our physics project and so on that it is possible to actually uh address that question and explain why the universe exists and i kind of have a suspicion i've not thought it through i kind of have a suspicion that that explanation will eventually show you that in no meaningful sense can there be randomness underneath the universe that is that if there is it's something that is necessarily irrelevant to our perception of the universe that is that it could be there but it doesn't matter because in a sense we've already you know whatever it would do whatever extra thing it would add is not relevant to our perception of what's going on so why does the universe exist how does uh the irrelevance of randomness connect to uh the big why question of silver so okay so i mean why does the universe exist well let's see and uh is this the only universe we got it's the only one that about that i'm pretty sure so now you may be which one which of these topics is better to enter first why does the universe exist and uh why you think it's the only one that exists well i think they're very closely related okay okay so i mean the first thing let's see i mean this why does the universe exist question is built on top of all these things that we've been figuring out about fundamental physics because if you want to know why the universe exists you kind of have to know what the universe is made of and i think the um well let me let me uh describe a little bit about the why does the universe exist question so the main issue is let's say you have a model for the universe and you say i've got this this program or something and you run it and you make the universe now you say well how do you actually why is that program actually running and people say you've got this program that makes the universe what computer is it running on right what what does it mean what actualizes something you know two plus two equals four but that's different from saying there's two a pile of two rocks another pile of two rocks and so many moves them together and makes four so to speak and so what is it that kind of turns it from being just this formal thing to being something that is actualized okay so there we have to start thinking about well well what do we actually know about what's going on in the universe well we are observers of this universe but confusingly enough we're part of this universe so in a sense we what what what if we say what do we what do we know about what's going on in the universe well what we know is what sort of our consciousness records about what's going on in the universe and so consciousness is part of the fabric of the universe so we're in it yes we're in it and and maybe i should maybe i should start off by saying something about the consciousness story because that that's um yes maybe we should begin even before that at the very base layer of the wolfram physics project maybe you can give a broad overview once again really quick about this hypergraph model yes and also what is it a year and a half ago since you've brought this project to the world what is the status update where what are all the beautiful ideas you have come across uh what are the interesting things you can always mention it's i mean it's a it's a freaking cambrian explosion i mean it's it's crazy i mean there are all these things which i've kind of wondered about for years and suddenly there's actually a way to think about them and i really did not see i mean the real strength of what's happened i absolutely did not see coming and the real strength of it is we've got this model for physics but it turns out it's a foundational kind of model that's a different kind of computation-like model that i'm kind of calling the sort of multi-computational model and that that kind of model is applicable not only to physics but also to lots of other kinds of things and one reason that's extremely powerful is because physics has been very successful so we know a lot based on what we figured out in physics and if we know that the same model governs physics and governs i don't know economics linguistics immunology whatever we know that the same kind of model governs those things we can start using things that we've successfully discovered in physics and applying those intuitions in all these other areas and that's that's pretty exciting and and very surprising to me um and in fact it's kind of like in the original story of sort of you go and you explain why is there complexity in the natural world then you realize well there's all this complexity there's all this computational irreducibility you know there's a lot we can't know about what's going to happen it's kind of it's kind of very confusing thing for people who say you know science has nailed everything down we're going to you know based on science we can know everything well actually there's this computational irreducibility thing right in the middle of that thrown up by science so to speak and then the question is well given computational irreducibility how can we actually figure out anything about what happens in the world why aren't we why are we able to predict anything why are we able to operate in the world and the answer is that we sort of live in these slices of computational reusability that exists in this kind of ocean of computational irreducibility and it turns out that seems that it's a very fundamental feature of the kind of model that seems to operate in physics and perhaps in a lot of these other areas that there are these particular slices of computational reducibility that are relevant to us and those are the things that both allow us to operate in the world and not just have everything be completely unpredictable but there are also things that potentially give us what amount to sort of physics-like laws in all these other areas so that's that's been sort of an exciting thing but but i would say that in general for our project it's been going spectacularly well i mean i you know i it's very honestly it wasn't something i expected to happen in my lifetime i mean it's you know it's something where where it's it's and in fact one of the things about it some of the things that we've discovered are things where i was pretty sure that wasn't how things worked and turns out i'm wrong and you know in a major area in metal mathematics i i'd be realizing that i something i've long believed we can talk about it later that that that uh just just really isn't right but but i think that um the um the thing that uh so so what's happened with the physics project i mean you know it's a it can explain a little bit about how the how the model works but basically we can maybe ask you uh the following question so it's easy through words describe how cellular automotive works you've explained this and uh it's the fundamental mechanism by which you in your book and your kind of science explored the idea of complexity and how to do science in this world of isla reducible islands and irreducible general irreducibility okay so how does the model of hypergraphs differ from cellular and how does the idea of multi-computation differ like maybe that's a way to describe it right we're yeah right this is a you know my life is like all of our lives something of a story of computational irreducibility yes and you know it's been going for a few years now so it's always a challenge to kind of find these appropriate pockets of reducibility but let me see what i can do great so so i mean first of all let's let's talk about physics first of all and you know a key observation that one of the starting point of our physics project is things about what is space what is the universe made of and you know ever since euclid people just sort of say space is just this thing where you can put things at any position you want and they're just points and they're just geometrical things that you can just arbitrarily put at different different coordinate positions so the first thing in our physics project is the idea that space is made of something just like water is made of molecules space is made of kind of atoms of space and the only thing we can say about these atoms of space is they have some identity there's a there's a there is it's this atom as opposed to this atom and you know you could give them if you're a computer person you give them uuids or something yes and and um but that's all there is to say about them so to speak um and then all we know about these atoms of space is how they relate to each other so we say these three atoms of space are associated with each other in some relation so you can think about that as you know what atom of space is friends with what other atom of space you can build this essentially friend network of the atoms of space and the sort of starting point of our physics project is that's what our universe is it's a giant friend network of the atoms of space and so how can that possibly represent our universe well it's like in something like water you know they're molecules bouncing around but on a large scale that you know that produces fluid flow and we have fluid vortices and we have all of these phenomena that are sort of the emergent phenomena from that underlying uh kind of collection of molecules bouncing around and by the way it's important that that collection of molecules bouncing around have this phenomenon of computational irreducibility that's actually what leads to the second law of thermodynamics among other things and that leads to the sort of randomness of the underlying behavior which is what gives you something which on a large scale seems like it's a smooth continuous type of thing and so so okay so first thing is space is made of something it's made of all these atoms of space connected together in this network and then everything that we experience is sort of features of the of that structure of space so you know when we have an electron or something or a photon it's some kind of tangle in the structure of space much like kind of a vortex and a fluid would be just this thing that is you know it it can actually the vortex can move around it can involve different molecules in the fluid but the vortex still stays there and if you zoom out enough the vortex looks like an atom itself like a basic element yes so there's the levels of abstraction if you squint and kind of blur things out it looks like at every level of abstraction you can define what is a basic individual entities yes but but you know in in this model there's a bottom level yeah you know there's an elementary length maybe that's 100 10 to the minus 100 meters let's say which is really small you know proton is 10 to the minus 15 meters the smallest we've ever been able to sort of see where the particle accelerator is around 10 to the minus 21 meters so you know if we don't know precisely what the correct scale is but it's perhaps over the order of 10 to the minus 100 meters so it's pretty small um and but but that's that's the end that's that's what things are made of what's your intuition where the 10 to the minus 100 comes from what's your intuition about this scale well okay so there's a calculation which i consider to be somewhat rickety okay which has to do with comparing so so there are various fundamental constants there's the speed of light the speed of light once you know the elementary time the speed of light is tells you the conversion from the elementary time to the elementary length then there's the question of how do you convert to the elementary energy and how do you convert to between other things and the various constants we know we know the speed of light we know the gravitational constant we know planck's constant and quantum mechanics those are the three important ones and we actually know some other things we know things like the size of the universe the hubble constant things like that and essentially this calculation of the elementary length comes from looking at these sort of combination of those okay so the most obvious thing people have sort of assumed that quantum gravity happens at this thing the planck scale 10 minus 34 meters which is the sort of the the combination of planck's constant and the gravitational constant the speed of light that gives you that kind of length turns out in our model there is an additional parameter which is essentially the number of simultaneous threads of execution of the universe which is essentially the number of sort of independent quantum uh processes that are going on and that number let's see if i remember that number that number is 10 to 170 i think and and so it's a big number but um that number then connects you know sort of modifies what you might think from all these planck uh units to give you the things we're giving and there's been sort of a mystery actually in the in the more technical physics thing that the planck mass the plank energy plank energy is actually surprisingly big the planck length is tiny 10 minus 34 meters that you know planck time 10 minus 43 meters i think seconds i think um but the planck energy is like uh is like the the energy of a of a lightning strike okay which is pretty weird in our models the actual elementary energy is that divided by the number of sort of simultaneous quantum threads and it ends up being really small too and that's sort of explains that mystery that's been around for a while about about how plank units work but but that you know whether that precise estimate is right we don't know yet i mean that that that's one of the things that's sort of been a thing we've been pretty interested in is how do you see through you know how does you how do you make a gravitational microscope that can kind of see through to the atoms of space you know how do you get in in fluid flow for example if you go to hypersonic flow or something you know you've got a mark 20 you know space plane or something it really matters that there are individual molecules hitting the space plane not a continuous fluid the question is what is the analogous kind of what is the analog of hypersonic flow for for our for things about the structure of space time and it looks like uh a a rapidly rotating black hole right at the sort of critical rotation rate um is it looks as if that's a case where essentially the the structure of space time is just about to fall apart and you may be able to kind of see the evidence of sort of discrete uh elements you know you may be able to kind of see there the sort of gravitational microscope of actually seeing these discrete elements of space and there may be some effect in for example gravitational waves produced by rapidly rotating black hole that in which one could actually see some phenomenon where one can say yes they don't come out the way one would expect based on having a continuous structure of space time that it is something where you can kind of see through to the discrete structure um we don't know that yet so you can maybe elaborate a little bit deeper hollow microscope that concedes a 10 to the minus 100 how rotating black holes and uh presumably the the the detailed accurate detection of gravitational waves from since black holes can reveal the discreteness of space okay first thing is what is a black hole uh actually we we need to go a little bit further in the story of what space time is because i explained a little bit about what space is but it didn't talk about what time is and that's sort of important in in understanding space time so to speak and your sense is both space and time in the story are discreet absolutely absolutely but it's a complicated story yes and um needless to say well it's simple at the bottom it's it's very simple at the bottom it's it's very in the end it's simple but deeply abstract and um and something that is simple in conception but kind of wrapping one's head around what's going on is pretty hard um but so so first of all we have this so you know i've described these kind of atoms of space and their connections you can think about these things as a hypergraph you know a graph is just you connect nodes to nodes but a hypergraph you can have you know uh you can have sort of not just friends individual friends to friends but you can have these triplets of of friends or whatever else it's it's um and so we're just saying and that's just the relations between atoms of space are the hyper edges of the hypograph and so we've got some big collection of of these atoms of space maybe 10 to the 400 or something in our in our universe um and that's the structure of space that's and every feature of what we experience in the world is a feature of that that hypergraph that spatial hypograph so then the question is well how does what does that spatial hypergraph do well the idea is that there are rules that that update that spatial hypograph and you know in a cellular automaton you've just got this line of cells and you just say it every step at every time step you've got fixed time steps fixed array of cells at every step uh every cell gets updated according to a certain rule and that's um that's kind of the that's the way it works now in this hypograph it's sort of vaguely the same kind of thing we say every time you see a little piece of hypergraph that looks like this update it to one that looks like this so it's just keep rewriting this hypergraph every time you see something looks like that anywhere in the universe it gets rewritten now one thing that's tricky about that which we'll come to is this multi-computational idea which has to do with you're not saying in in some kind of lock-step way do this one then this one then this one it's just whenever you see one you can do you can go ahead and do it and that leads one not to have a single thread of time in the universe because if you knew which one to do you just say okay we do this one then we do this one then we do this one but if you say just do whichever one you feel like you end up with these multiple threads of time these kind of multiple histories of the universe depending on which order you happen to do the things you could do in so it's fundamentally asynchronous and parallel yes yes which is very uncomfortable for the human brain that seeks for things to be sequential and synchronous right well i think that this is this is part of the story of consciousness is i think the key aspect of consciousness that is important for sort of parsing the universe is this point that we have a single thread of experience right we have a memory of what happened in the past we can say something predict something about the future but there's a single thread of experience and it's not obvious it should work that way i mean we've got 100 billion neurons in our brains and they're all firing in all kinds of different ways but yet our experiences that there is the single thread of of of time that that goes that that goes along and i think that you know one of the things i've kind of realized with a lot more clarity in the last year is the fact that our the fact that we conclude that the universe has the laws it has is a consequence of the fact that we have consciousness the way we have consciousness and so the fact so i mean just to go on with kind of the the basic setup it's uh so we've got this spatial hypograph it's got all these atoms of space they're getting they're getting these little clumps of atoms of space they're getting turned into other clumps of atoms of space and that's happening everywhere in the universe all the time and so one thing it's a little bit weird is there's nothing permanent in the universe the universe is getting rewritten everywhere all the time and if it wasn't getting rewritten it would space wouldn't be knitted together that is space would just fall apart there wouldn't be any way in which we could say this part of space is next to this part of space you know one of the things that i was people were confused about back in antiquity you know the ancient greek philosophers and so on is how does motion work you know how can it be the case that you can take a thing that we can walk around and it's still us when we walked you know a foot forward so to speak and in a sense with our models that's again a question because it's a different set of atoms of space when we you know when i move my hand it's it's moving into a different set of atoms of space it's having to be recreated it's not the thing itself is not there it's it's being continuously recreated all the time now it's a little bit like waves in an ocean you know vortices in a fluid which again the actual molecules that exist in those are not what define the identity of the thing and but it's a little bit uh you know this idea that there can be pure motion that it can that it is even possible for an object to just move around in the universe and not change is it's not self-evident that such a thing should be possible and that is part of our perception of the universe is that we we parse those aspects of the universe where things like pure motion are possible now pure motion even in general relativity the theory of gravity um pure motion is a little bit of a complicated thing i mean if you imagine your average you know teacup or something approaching a black hole it is deformed and distorted by the structure of space time and to say you know is it really pure motion is it that same teacup that's the same shape well it's a bit of a complicated story and this is a more extreme version of that so so anyway the the thing that that's happening is we've got space we've got this notion of time so time is this kind of this rewriting of the hypograph and one of the things that's important about that time is this sort of computationally irreducible process there's something you know time is not something where in kind of the mathematical view of of time tends to be time is just to coordinate we can you know slide a slider turn a knob and we'll change the the time that we've got in this equation but in this picture of time that's not how it works at all time is this inexorable irreducible kind of set of computations that go on that go from where we are now to the future but so so the thing and one of the things that is again something one sort of has to break out of is your average trained physicist like me says you know space and time are the same kind of thing they're related by you know the prank array group and and lawrence transformations and relativity and all these kinds of things and you know space and time uh you know there are all these kind of sort of folk stories you can tell about why space and time is the same kind of thing in this model they're fundamentally not the same kind of thing space is this kind of sort of connections between these atoms of space time is this computational process so the thing that the first sort of surprising thing is well it turns out you get relativity anyway and the reason that happens the few bits and pieces here which one has to understand but but the the fundamental point is if you are an observer embedded in the system that are part of this whole story of things getting updated in this way and that there are there's sort of a limit to what you can tell about what's going on and really in the end the only thing you can tell is what are the causal relationships between events so an event in this sort of an elementary event is a little piece of hypograph got rewritten and that means a few hyper edges of the hyper graph were consumed by the event and you produce some other hyperedges and that's an elementary event and so then the question is uh what we can tell is kind of what the network of causal relationships between elementary events is that's the ultimate thing the causal graph of the universe and it it turns out that well there's this property of causal invariance that is true of a bunch of these models and i think is inevitably true for a variety of reasons um that makes it be the case that it doesn't matter kind of if if you are sort of saying well i've got this hypograph and i can rewrite this piece here and this piece here and i do them all in different orders when you construct the causal graph for each of those orders that you choose to do things in you'll end up with the same causal graph and so that's essentially why uh well that's in the end why relativity works it's why our perception of space and time is is as as having this kind of connection that relativity says they should have and that's that's kind of that's kind of how that works i think i'm missing a little piece uh if you can go there again you said the fact that the observer is embedded in this hypergraph what's missing uh what is the observer not able to state about this universe so basically if you look from the outside you can say oh i see this uh i see this particular place was updated and then this one was updated and and i'm seeing which order things were updated in but the observer embedded in the universe doesn't know which order things were updated in because until they've been updated they have no idea what else happened so the only thing they know is the set of causal relationships let me give an extreme example let's imagine that the universe is a turing machine turing machines have just this one update head which does something and otherwise the turing machine just does nothing right and and the turing machine works by having this head move around and do its updating uh you know just where the head happens to be the question is could the universe be a turing machine could the universe just have a single updating head that's just zipping around all over the place you say that's crazy because you know i'm i'm talking to you you seem to be updating i'm updating etc but the thing is there's no way to know that because if there was just this head moving around it's like okay it updates me but you're completely frozen at that point until the head has come over and updated you you have no idea what happened to me and so if you sort of unravel that argument you realize the only thing we actually can tell is what the network of causal relationships between the things that happened were we don't get to know from some sort of outside sort of god's eye view of the thing we don't get to know what sort of from the outside what happened we only get to know sort of what the set of relationships between the things that happened actually were yeah but if i somehow record like a trace of this i guess would be called multi-computation can't i uh then look back in the way where do you look for the trace some you place throughout the universe like throughout like a log that records in my own pocket of in this hyper graph can i like realizing that i'm getting an outdated picture can't i record see the problem is and this is where things start getting very entangled in terms of what one understands the problem is that any such recording device is itself part of the universe yeah so you don't get to say you never get to say let's go outside the universe and go do this and and that's why i mean lots of the features of this of this model and the way things work end up being a result of that so but what i guess from on a human level what is the cost you're paying what are you missing from not getting an updated picture all the time okay i got i i understand what you should say yeah yeah right but like what like how does consciousness emerge from that like how like what are the limitations of that observer i understand you're getting a delay well that's true there's a okay there's there's a bunch of limitations of the observer i think maybe just explain something about quantum mechanics because that maybe is a is an extreme version of some of these issues which helps to kind of motivate why one should sort of think things through a little bit more carefully so one feature of the of this okay so in standard physics like high school physics you learn you know the equations of motion for a ball and the the you know it says you throw the ball this angle this velocity things will move in this way and there's a definite answer right the story the the key story of quantum mechanics is there aren't definite answers to where does the ball go there's kind of this whole sort of bundle of possible paths and all we say we know from quantum mechanics is certain probabilities for where the ball will end up okay so that's kind of the the core idea of quantum mechanics so in our models you quantum mechanics is not some kind of plug-in add-on type thing you absolutely cannot get away from quantum mechanics because as you think about updating this hyper graph there isn't just one sequence of things one definite sequence of things that can happen there are all these different possible update sequences that can occur you could do this you know piece of the hypograph now and then this one later and etc etc etc all those different paths of history correspond to these quantum quantum paths and quantum mechanics these different possible quantum histories and one of the things that's kind of surprising about it is they they branch you know there can be a certain state of the universe and it could do this or it could do that but they can also merge there can be two states of the universe which their next state the next state they produce is the same for both of them and that process of branching and merging is kind of critical and the idea that they can be merging is critical and somewhat non-trivial for these hypographs because there's a whole graph isomorphism story and there's a whole very elaborate settlement that's where the causal invariance comes in yes among other things right okay yes that's but but so so then what happens is that what what one's seeing okay so we've got this thing it's branching it's merging et cetera et cetera et cetera okay so now the question is how do we perceive that what do you know how do we do we why don't we notice that the universe is branching and merging why you know why is it the case that we just think a definite set of things happen well the answer is we are embedded in that universe and our brains are branching and merging too and so what quantum mechanics becomes a story of is how does a branching brain perceive a branching universe and the key thing is as soon as you say i think definite things happen in the universe that means you are essentially conflating lots of different parts of history you're saying actually as far as i'm concerned because i'm convinced that definite things happen in the universe all these parts of history must be equivalent now it's not obvious that that would be a consistent thing to do it might be you say all these paths of history are equivalent but by golly moments later that would be a completely inconsistent point of view everything would have you know gone to hell in different ways the fact that that doesn't happen is well that's a consequence of this causal and variance thing but that's and the fact that that does happen a little bit is what causes little quantum effects and that term if that didn't happen at all there wouldn't be anything that sort of is like quantum mechanics it would be quantum mechanics is kind of like in this uh in this kind of this bundle of paths it's a little bit like what happens in statistical mechanics and fluid mechanics whatever that most of the time you just see this continuous fluid you just see the world just progressing in this kind of way that's like this continuous fluid but every so often if you look at the exact right experiment you can start seeing well actually it's made of these molecules where they might go that way or they might go this way and that's kind of quantum effects and and so that's so the this kind of idea of where we're sort of embedded in the universe this branching brain is perceiving this branching universe and that ends up being sort of a story of quantum mechanics that's that's part of the the whole picture of what's going on but i think i mean to come back to sort of where does conscious what is what is the story of consciousness so in the universe we've got you know whatever it is 10 to the 400 atoms of space they're all doing these complicated things it's all a big complicated irreducible computation the question is what do we perceive from all of that and the answer is that we are we are parsing the universe in a particular way let me again go back to the the gas molecules analogy you know in the gas in this room there are molecules bouncing around all kinds of complicated patterns but we don't care all we notice is there's you know the gas laws are satisfied maybe there's some fluid dynamics these are kind of features of that assembly molecules that we notice and then lots of details we don't notice when you say we do you mean the tools of physics or do you mean literally are the human brain in its perception system well okay so the human brain is where it starts but we've built a bunch of instruments to do a bit better than the human brain but they still have many of the same kinds of ideas you know their cameras and their pressure sensors and their these kinds of things they're not uh you know at this point we don't know how to make fundamentally qualitatively different sensory devices right and so it's always just an extension of the conscious experience or a sensory experience sensory experience but sensory experience that's somehow intricately tied to consciousness right well so so one question is when we are looking at all these molecules of the in the gas and there might be 10 to 20 molecules in some little little box or something it's like what what do we notice about those molecules so one thing that we can say is we don't notice that much we are you know we are computationally bounded observers we can't go in and say okay i'm they're 10 to the 20th molecules and i know that i can sort of decrypt their motions and i can figure out this and that it's like i'm just going to say what's the average density of molecules and so one key feature of us is that we are computationally bounded and that when you are looking at a universe which is full of computation and doing huge amounts of computation but we are computationally bounded there's only certain things about that universe that we're going to be sensitive to we're not going to be you know figuring out what all the atoms of space are doing because we're just computationally bounded observers and we are only sampling these these small set of features so i i think the two defining features of consciousness that and i you know i would say that the the sort of the the preamble to this is for years you know because i've talked about sort of computation and fundamental features of physics and science people ask me so what about consciousness and i for years i've said i have nothing to say about consciousness and you know i've kind of told this story you know you talk about intelligence you talk about life these are both features where you say what's the abstract definition of life we don't really know the abstract definition we know the one for life on earth it's got rna it's got cell membranes it's got all this kind of stuff similarly for intelligence we know the human definition of intelligence but what is intelligence abstractly we don't really know and so what i've long believed is that sort of the abstract definition of intelligence is just computational sophistication that is that as soon as you can be computationally sophisticated that's kind of the abstract version the generalized version of intelligence so then the question is what about consciousness and what i sort of realized is that consciousness is actually a step down from intelligence that is that you might think oh you know consciousness is the is the is the top of the pile but actually i don't think it is i think that there's this notion of kind of computational sophistication which is the generalized intelligence but consciousness has two limitations i think one of them is computational boundedness that is that we're only perceiving a sort of computationally bounded view of the universe and the other is this idea of a single thread of time that is that we and in fact we know neurophysiologically our brains go to some trouble to give us this one thread of attention so to speak and it isn't the case that you know in all the neurons in our brains that that uh in at least in our conscious know the the you know the correspondence of language in our conscious experience we just have the single thread of attention single thread of of perception um and you know maybe there's something unconscious that's bubbling around that's the kind of almost the quantum version of what's happening in our brain so to speak we've got the the classical flow of what we are mostly thinking about so to speak but there's this kind of bubbling around of other paths that is all those other neurons that didn't make it to be part of our sort of conscious stream of experience so in that sense intelligence as computational sophistication is much broader than uh yes then the the computational constraints which consciousness operates under and also the sequential like the sequential thing yes like the notion of time that's that's kind of interesting but then the the follow-up question is like okay starting to get a sense of what is intelligence and how does that connect to a human brain because you're saying um intelligence is almost like a fabric like what we like plug into it or something like yeah i think you know our consciousness plugs into it yeah i mean the intelligence i think the core i mean you know intelligence at some level is just a word but we're asking you know what is the the notion of intelligence as we generalize it beyond the bounds of humans beyond the bounds of even the ais that we humans have built and so on you know what what is intelligence you know is the weather you know people say the weather has a mind of its own what does that mean you know can the weather be intelligent yeah what does agency have to do with intelligence here so is intelligence just like your conception of computation just intelligence is a is the capacity to perform computation and the sea of yeah i think so i mean i think that's right and i i think that you know this question of of is it for a purpose okay that quickly degenerates into a horrible philosophical mess because you know whenever you say did the weather do that for a purpose yeah right well yes it did it was trying to move a bunch of hot air from the equator to the poles or something that's its purpose but why because i seem to be equally as dumb today as i was yesterday so there's some persistence like uh consistency over time that the intelligence i plugged into so like what's it seems like there's a hard constraint well between the amount of computation i can perform in my consciousness like they seem to be really closely connected somehow well i think the point is that the thing that gives you kind of the ability to have kind of conscious intel intelligence you you can have kind of this okay so so one thing is we don't know intelligences other than the ones that are very much like us yes right and the ones that are very much like us i think have this feature of single thread of time bounded you know computationally bounded now that but you also need computational sophistication having a single thread of time and being computationally bounded you could just be a clock going tick-tock you know that would satisfy those conditions but the fact that we have this uh sort of uh irreducible you know computational ability that's that's an important feature that's that's the sort of the the bedrock on which we can construct the things we construct now the fact that we have this experience of the world that has the single thread of time and computational boundedness the thing that i sort of realized is it's that that causes us to deduce from this irreducible mess of what's going on in the physical world the laws of physics that we think exist so in other words if we say why do we believe that there is you know continuous space let's say why do we believe that gravity works the way it does well in principle we could be kind of parsing details of the universe that were uh you know that okay the analogy is uh again with the you know statistical mechanics and molecules in a box we could be sensitive to every little detail of the swirling around those molecules and we could say what really matters is the you know the wiggle effect yes that is um you know that is something that we humans just never notice because it's some weird thing that happens when there are 15 collisions of air molecules and this happens and that happens we just see the pure motion of a ball yeah moving about right why do we see that right and the point is that that what seems to be the case is that the things that if if we say given this sort of hypergraph that's updating and all the details about all the sort of uh sort of atoms of space and what they do and we say how do we slice that to what we can be sensitive to what seems to be the case is that as soon as we assume you know computational boundedness single thread of time that leads us to general relativity in other words we can't avoid that that that's the way that we we will parse the universe given those constraints we parse the universe according to those particular uh in such a way that we say the aggregate reducible copy sort of computate pocket of computational reducibility that we slice out of this kind of whole computational irreducible ocean of behavior is just this one that corresponds to general relativity yeah but we don't perceive general relativity well we do if we do fancy experiments so you're saying so perceive really does mean the force we drop something that's a that's a great example of general relativity in action the graph no but like what's the difference between that and newtonian mechanics i mean oh it doesn't i this is i when i say general relativity that's gravity uber the uber theory so to speak i mean newtonian gravity is just the approximation that we can make you know on the earth and things like that so so this is you know the phenomenon of gravity is one that is a consequence of you know we would perceive something very different from gravity so so the way to understand that is when we think about okay so we make up reference frames with which we parse what's happening in space and time so in other words one of the one of the things that we do is we say as time progresses uh everywhere in space is something happens at a particular time and then we go to the next time and we say this is what space is like at the next time there's what space is like at the next time that's it's the reason we are used to doing that is because you know when we look around we might see you know 10 100 meters away um the time it takes light to travel that distance is really short compared to the time it takes our brains to know what happened so as far as our brains are concerned we are parsing the universe in this there is a moment in time it's all of space there's a moment in time it's all of space you know if we were the size of planets or something we would have a different perception because the speed of light would be much more important to us we wouldn't have this perception that things happen progressively in time everywhere in space and so that's an important kind of constraint and the reason that we kind of parse the universe in the way that causes us to say gravity works the way it does is because we're doing things like deciding that we can say the universe exists space has a definite structure there is a moment in time space has this definite structure we move to the next moment in time space as another structure that kind of set up is what lets us kind of deduce kind of what to parse the universe in such a way that we say gravity works the way it does so uh that kind of reference frame is that the illusion of that is that you're saying that somehow useful for consciousness that's what consciousness does because in a sense what consciousness is doing is there are uh it's it's insisting that the universe is kind of sequentialized right that is um and it is not allowing the possibility that oh there are these multiple threads of time and they're all flowing differently it's like saying no you know everything is happening in this one thread of experience that we have and that illusion of that one thread of experience cannot happen at the planetary scale so are you saying typical human are you saying we are at a human level especially here for consciousness like well for our kind of consciousness it's it's uh you know if we existed at a scale close to the elementary length for example then our perception of the universe will be absurdly different okay so but this makes this consciousness seem like a weird side effect to this particular scale and so who cares i mean consciousness is not that special i i think look i think that a very interesting question is which i've certainly thought a little bit about is what can you imagine what is a sort of factoring of something you know what are some other possible ways you could exist so to speak right and you know if you were a photon if you were sort of you know some kind of thing that was some uh kind of you know intelligence represented in terms of photons you know for example the photons we receive in the cosmic microwave background those photons as far as they're concerned the universe just started they they they were emitted you know 100 000 years after the beginning of the universe they've been traveling at the speed of light time stayed still for them and then they just arrived and we just detected them so for them the universe just started and that's a different perception of you know that has implications for a very different perception of time they don't have that single thread that seems to be really important for being able to tell a heck of a good story so we humans we can tell a story right we can tell a story what other kind of stories can you tell so photon is a really boring story yeah i mean so that's a i don't know if they're a boring story but i i think it's you know i've been wondering about this and i've been asking you know friends of mine who are science fiction writers and things have you written stuff about this and i've got one example good great great collection of books from my friend rudy rooker which were um uh which i have to say the um they're books about uh that are very informed by a bunch of science that i've done and the thing that i really loved about them is you know you know in the in the first chapter of the of the book the the earth is consumed by these things he called nance which are nano nanobot type things and but so you know so the earth is gone in the first but then it comes back but but um but then spoiler alert yeah right that was uh that was only a microspot it's only chapter one okay it's it's um the but but uh the thing that um is is not a real spoiler alert because it's such a complicated concept but but in the end in the end the the earth is saved by this thing called the principle of computational equivalence which is a kind of a core scientific idea of mine and i was just like like thrilled i i don't read fiction books very often um and i was just thrilled i get to the end of this and it's like oh my gosh you know everything is saved by this sort of deep scientific principle can you can you maybe elaborate how the principle of computational equivalence can save a planet that would that would be a have a terrible spoiler for me that would be a spoiler okay yeah but but no but let me say what the principle of computational equivalence is um so the question is you are you have a system you have some rule you can think of its behavior as corresponding to a computation the question is how sophisticated is that computation the statement of the principle of computational equivalence is as soon as it's it's not obviously simple it will be as sophisticated as anything and so that has the implication that you know rule 30 you know our brains other things in physics they're all ultimately equivalent in the computations they can do and that's what leads to this computational irreducibility idea because the reason we don't get to jump ahead you know and out think rule 30 is because we're just computationally equivalent to rule 30 so we're kind of just both just running computations that are the same sort of raw the same level of computation so to speak so that's kind of the the idea there and the question i mean it's it's like uh the you know in in the science fiction version would be okay somebody says we just need more servers get us more servers the way to get even more servers is turn the whole planet into a bunch of micro servers and that that's uh that's where it starts and so the question of you know computational equivalence principle of computational equivalence is well actually you don't need to build those custom servers actually you can uh you can just use natural computation to compute things so to speak you can use nature to compute you don't need to have done all that engineering i mean it's kind of the it's it's kind of feels a little disappointing that you say we're going to build all these servers we're going to do all these things we're going to make you know maybe we're going to have human consciousness uploaded into you know some elaborate digital environment and then you look at that thing and you say it's got electrons moving around just like in a rock and then you say well what's the difference and the principle of computational equivalence says there isn't at some level a fundamental you know you can't say mathematically there's a fundamental difference between the rock that is the future of human consciousness and the rock that's just a rock now what i've sort of realized with this kind of consciousness thing is there is a there is an aspect of this that seems to be more special that isn't and and for example something i i haven't really teased apart properly is when it comes to something like the weather and the weather having a mind of its own or whatever or your average you know pulsar magnetosphere acting like a sort of intelligent thing how does that relate to you know how how do how is that that entity related to the kind of consciousness that we have and sort of what would the world look like you know to the weather if we think about the weather as a mind what will it perceive what will it laws its laws of physics be i don't really know because it's very parallel it's very parallel among other things and it it it's not obvious i mean this is a a really kind of mind-bending thing because we've got to try and imagine where uh you know we've got to try and imagine a parsing of the universe different from the one we have and by the way when we think about extraterrestrial intelligence and so on i think that's kind of the key thing is you know we've always assumed i've always assumed okay the extraterrestrials at least they have the same physics we all live in the same universe they've got the same physics but actually that's not really right because the extraterrestrials could have a completely different way of parsing that the universe so it's as if you know there could be for all we know right here in this room you know in the in the details of the motion of these gas molecules there could be an amazing intelligence that we were like but we have no way of we're not parsing the universe in the same way if only we could parse the universe in the right way you know immediately this amazing thing that's going on and this you know huge culture that's developed and all that kind of thing would be obvious to us but it's not because we have a particular way of passing the universe would that thing also have us agency i don't know the right word to use but something like consciousness but a different kind of consciousness i think it's a question of just what you mean by the word because i think that the you know this notion of consciousness and the okay so some people think of consciousness as sort of a key aspect of it is that we feel that the the sort of a feeling of that we exist in some way that we have this intrinsic feeling about ourselves you know i i suspect that any of these things would also have an intrinsic feeling about themselves i've been sort of trying to think recently about constructing an experiment about what if you were just a piece of a cellular automaton let's say you know what would your feeling about yourself actually be and you know can we put ourselves in the in the shoes and the cells of the cellular automaton so to speak can we can we get ourselves close enough to that that we could have a sense of what the world would be like if you were operating in that way and it's a little difficult because you know you have to not only think about what are you perceiving but also what's actually going on in your brain and our brains do what they actually do and they don't it's you know i think there might be some experiments that are possible with with uh you know neural nets and so on where you can have something where you can at least see in detail what's happening inside the system and i i've been sort of one of the one of my projects to think about is is there a way of kind of uh kind of getting a sense kind of from inside the system about what its view of the world is and and how it how it you know uh can can we make a bridge see the main issue is this where you know it's a it's a sort of philosophically difficult thing because it's like we do what we do we understand ourselves um at least to some extent we humans understand ourselves that's correct and but yet okay so what are we trying to do for example when we are trying to make a model of physics what are we actually trying to do because you know you say well can we work out what the universe does well of course we can we just watch the universe the universe does what it does but what we're trying to do when we make a model of physics is we're trying to get to the point where we can tell a story to ourselves that we understand that is also a representation of what the universe does so it's this kind of you know can we make a bridge between what we humans can understand in our minds and what the universe does and in a sense you know a large part of my kind of life uh efforts have been devoted to making computational language which kind of is a bridge between what is possible in the computational universe and what we humans can conceptualize and think about in a sense what you know when i built wolfram language and our whole sort of computational language story it's all about how do you take sort of raw computation and this ocean of computational possibility and how do we sort of represent pieces of it in a way that we humans can understand and that map on to things that we care about doing and in a sense when you add physics you're adding this other piece where we can you know mediate it by computer can we get physics to the point where we humans can understand something about what's happening in it and when we talk about an alien intelligence it's kind of the same story it's like is there a way of mapping what's happening there onto something that we humans can understand and you know physics in some sense is like our exhibit one of the story of alien intelligence it's it's a it's a you know it's an alien intelligence in some sense and what we're doing in making a model of physics is mapping that onto something that we understand and i think you know a lot of these other things that have i've recently been kind of studying uh whether it's molecular biology other kinds of things um which we can talk about a bit um the um uh those are other cases where we're in a sense trying to again make that bridge between what we humans understand and sort of the the natural language of that sort of alien intelligence in some sense when you're talking about just uh to backtrack a little bit about cellular automata being able to uh what's it like to be a cellular automata in a way that's equivalent to what is it like to be a conscious human being how do you approach that so is it looking at some subset of the cellular autonomy asking questions of that subset like how the world is perceived how yeah something like as that subset like for that local pocket of computation what are you able to say about the broader something like that and that somehow then can give you a sense of how to step outside of that cell right but but the tricky part is that that little subset it's what it's doing is it has a view of itself and the question is how do you get inside it it's like you know when we with humans right it's like we can't get inside each other's consciousness that doesn't really um you know that doesn't really even make sense it's like there is an experience that somebody is having but you can perceive things from the outside but sort of getting inside it it doesn't it doesn't quite make sense and i you know for me these sort of philosophical issues and this one i have not untangled so let's let's be um sure um the you know for me the thing that has been really interesting and thinking through some of these things is you know when it comes to questions about consciousness or whatever else it's like when i can run a program and actually see pictures and you know make things concrete i have a much better chance to understand what's going on than when i'm just trying to reason about things in a very abstract way yeah but there may be a way to uh map the program to your conscious experience so for example when you play a video game you do a first person shooter you walk around inside this entity yep it's a very different thing than watching this entity so if you can somehow connect more and more connect this full conscious experience to the subset of the cellular automata yeah it's something like that but the difference in the first person shooter thing is they're still your brain and your memory is still remembering you know you you still have it's it's hard to i mean again what one's going to get one is not going to actually be able to be the cellular automaton one's going to be able to watch what the cellular automaton does but this is the frustrating thing that i'm trying to understand you know you know how to how to think about being it so to speak okay so like in virtual reality there's a concept of immersion like with anything with video game with books there's a concept of immersion it feels like over time if the virtual reality experience is is well done and maybe in the future would be extremely well done the immersion leads you to feel like you mentioned memories you forget that you even ever existed outside that experience yeah so immersive i mean you could argue sort of mathematically that you can never truly become immersed but maybe you can i mean well yeah i mean why can't you merge with the cellular automata yeah right i mean you're just part of the same fabric why can't you just like well that's a good question i mean so so let's imagine the following scenario let's imagine you return what's that well but then can you return back well yeah right i mean it's it's like let's imagine you've uploaded you know your brain is scanned you've got every synapse you know mapped out you upload everything about you the brain simulator you upload the brain simulator and the brain simulator is basically you know some glorified cellular automaton and then you say well now we've got an answer to what does it feel like to be a cellular automaton it feels just like it felt to be ordinary you because they're both computational systems and they're both you know operating in the same way so in a sense but i think there's there's somehow more to it because in that sense when you're just making a brain simulator it's just you know we're just saying there's another version of our consciousness the question that we're asking is if we tease away from our consciousness and get to something that is different how do we make a bridge to understanding what's going on there and you know there's a way of thinking about this okay so this is coming on to sort of questions about the existence of the universe and so on but one of the things is there's this notion that we have of rulial space so we have this idea of this physical space which is you know something you can move around in that's that's uh associated with actual the extent of the spatial hypergraph then there's what we call branchial space the space of quantum branches so in this in this thing we call the multi-way graph of all of the sort of branching histories there's this idea of a kind of space where instead of moving around in physical space you're moving from history to history so to speak from one possible history to another possible history and that's kind of a different kind of space that is the space in which quantum mechanics plays out quantum mechanics like for example oh something like uh i think we're slowly understanding things like destructive interference in quantum mechanics but what's happening is branchial space is associated with phase in quantum mechanics and what's happening is the two photons that are supposed to be interfering and destructively destructively interfering are winding up at different ends of branchial space and so us as these poor observers that are trying to that have branching brains that are trying to conflate together these different threads of history and say we've really got a consistent story that we're telling here we're really knitting together these threads of history by the time the two photons wound up at opposite ends of branchial space we just can't knit them together to tell a consistent story so for us that's sort of the analog of destructive interference got it and then there's rule space too which is the space of rules yes well that's that's a another level up so so there's there's the question um actually i i do want to mention one thing because it's something i've realized in recent times and it's i think it's really really kind of cool which is about time dilation and relativity and it kind of helps to understand it's something that kind of helps in understanding what's going on so in according to relativity if you you know you have a clock it's ticking at a certain rate you send in a spacecraft that's going at some significant fraction the speed of light to you as a observer at rest that clock that's in the spacecraft will seem to be ticking much more slowly and so in other words you know it's kind of like the the the twin who goes off to alpha centauri and goes very fast will age much less than the twin who's on earth that um that is just hanging out where they're hanging out okay why does that happen okay so it has to do with what motion is so in in our models of physics what is motion well when you move from somewhere to somewhere it's you're having to sort of recreate yourself at a different place in space when you exist at a particular place and you just evolve with time you're again you're updating yourself you're you're following these rules to update what happens well so the question is when you have a certain amount of computation in you so to speak when there's a certain amount you know you're computing the universe is computing at a certain rate you can either use that computation to work out sitting still where you are what's going to happen successively in time or you can use that computation to recreate yourself as you move around the universe and so time dilation ends up being it's really cool actually that this is explainable in a in a way that isn't just imagine the mathematics of relativity but but um that time dilation is a story of the fact that as you kind of are recreating yourself as you move you are using up some of your computation and so you don't have as much computation left over to actually work out what happens progressively with time so that means that time is running more slowly for you because it is you're you're using up your computation your your clock can't tick as quickly because every tick of the clock is using up some computation but you already use that computation up on moving at you know half the speed of light or something and so that's that's why time dilation happens and so you can you can start so it's kind of interesting that one can sort of get an intuition about something like that because it has seemed like just a mathematical fact about the mathematics of special relativity and so on well for me it's a little bit confusing what the u in that picture is because you're using up computation okay so so we're simply saying the entity is updating itself according to the way that the universe updates itself and the question is your you know those updates let's imagine the u is a clock okay and the clock is you know there's all these little updates the hypograph and a sequence of updates caused the pendulum to swing back the other way and then swing back swinging back and forth okay and all of the all of those updates are contributing to the motion of you know the pendulum going back and forth or the oscillator moving whatever it is okay but but then the alternative is that's sort of situation one where the thing is at rest situation two where it's kind of moving the the what's happening is it is having to recreate itself at every at every moment the thing is going to have to do the computations to be able to sort of recreate itself at a different position in space and that's kind of the intuition behind so it's either going to spend its computation recreating itself at a different position in space or it's going to spend its computation doing the um uh sort of doing the updating of the you know of the the ticking of the clock so to speak so the more updating is doing the less the ticking of the clock update is doing that's right the more it has having to update because of motion yeah the less it can update the the clock so that that's um i mean obviously there's a there's a sort of mathematical version of it that relates to how it actually works in relativity but that's kind of to me that was sort of exciting to me that it's possible to have a a really mechanically explainable story there that that isn't um and similarly in quantum mechanics this notion of branching brains perceiving branching universes to me that's getting towards a sort of mechanically explainable version of what happens in quantum mechanics even though it's a little bit mind-bending uh to see you know these things about under what circumstances can you successfully knit together those different threads of history and when do things sort of escape and and those kinds of things but the you know the thing about this physical space and physical space the the main sort of big theory is general relativity the theory of gravity and that tells you how things move in physical space in bronchial space the big theory is the feynman path integral which it turns out tells you essentially how things move in quantum in the space of quantum phases so it's kind of like motion and branchial space and it's kind of a fun thing to start thinking about what oh you know all these things that we know in physical space like uh event horizons and black holes and so on what are the analogous things in branchial space for example the speed of light what's the analog of the speed of light in branch hill space it's the maximum speed of quantum entanglement so the speed of light is a flash bulb goes off here what's the maximum rate at which the effect of that flash bulb is detectable moving away in space so similarly in bronchial space something happens and the question is how far in this branchial space in the space of quantum states how far away can that get within a certain period of time and so there's this notion of a maximum entanglement speed and that might be observable that's the thing we've been sort of poking at is might there be a way to observe it even in some atomic physics kind of situation um because one of the things that's weird in quantum mechanics is we're you know when we study quantum mechanics we mostly study it in terms of small numbers of particles you know this electron does this this thing on an ion trap does that and so on but when we deal with large numbers of particles kind of all bets are off it's kind of too complicated to deal with quantum mechanics and so what ends up happening is so this question about maximum entanglement speed and things like that may actually play in one of these in the sort of story of many body quantum mechanics and even have some suspicions about things that might happen even in one of the things i i realized i'd never understood and it's kind of embarrassing but i think i now understand a little better is when you have chemistry and you have quantum mechanics it's like well there's two carbon atoms there's this molecule and we do a reaction and we draw a diagram we say this carbon atom ends up in this place and it's like but wait a minute in quantum mechanics nothing ends up in a definite place there's always just some wave function for this to happen how can it be the case that we can draw these reasonable it just ended up in this place and you have to kind of say well the environment of the molecule effectively made a bunch of measurements on the molecule to keep it kind of classical and that's a story that has to do with this whole thing about about you know measurements have to do with this idea of you know can we conclude that something definite happened because in quantum mechanics the the intrinsic quantum mechanics the mathematics of quantum mechanics is all about they're just these amplitudes for different things to happen then there's this thing of and then we make a measurement and we conclude that something definite happened and that has to do with this thing i think about sort of moving about knitting together these different threads of history and saying this is now something where we can definitively say something definite happen in the traditional theory of quantum mechanics it's just like you know after you've done all the sample sheet computation then this big hammer comes down and you do a measurement and it's all over and that's been very confusing for example in quantum computing it's been a very confusing thing because when you say you know in quantum computing the basic idea is you're going to use all these separate threads of of computation so to speak to do all the different parts of you know try these different factors for an integer or something like this and it looks like you can do a lot because you've got all these different threads going on but then you have to say well at the end of it you've got all these threads and every thread came up with the definite answer but we've got to conflate those together to figure out a definite thing that we humans can take away from it a definite so the computer actually produced this output so having this branchial space and this hypergraph model of physics do you think it's possible to then make predictions that are definite about uh many body quantum mechanical systems is that the whole i think it's likely yes but i don't you know this is every one of these things when you when you go from the underlying theory which is complicated enough and it's i mean the theory at some level is beautifully simple but as soon as you start actually trying to it's this whole question about how do you bridge it to things that we humans can talk about it gets really complicated and and this thing about actually getting it to a definite definite prediction um about you know definite thing you can say about chemistry or something like this um you know that's just a lot of work so i'll give you an example there's a thing called the quantum zeno effect so the idea is you know quantum stuff happens but then if you make a measurement you're kind of freezing time in quantum mechanics you and and so it looks like there's a possibility that with sort of the the relationship between the quantum zeno effect and the way that many body quantum mechanics works and so on maybe just conceivably it may be possible to actually figure out a way to measure the the uh the maximum entanglement speed and the reason we can potentially do that is because the systems we deal with in terms of atoms and things they're pretty big you know a mole of atoms is you know it's a lot of atoms and you know but it isn't a very you know it's something where to get you know when we're dealing with how can you see 10 to the minus 100 so to speak well by the time you've got you know 10 to the 30th atoms you're not you know you're within a little bit closer striking distance of that it's not like oh we've just got you know two atoms and we're trying to see down to 10 to the minus 100 meters or whatever so i don't know how it will work but this is a this is a a potential direction if you can tell by the way if we could measure the maximum entanglement speed we would know the elementary length these are all related so if if we get that one number we just need one number if we can get that one number we can you know the theory has no parameters anymore um and uh you know there are there are other places well there's another another hope for doing that is in cosmology uh in this model one of the features is the universe is not fixed dimensional i mean we think we live in three-dimensional space but this hyper graph doesn't have any particular dimension it can emerge as something which on an approximation it's as if you know you say what's the volume of a sphere in the hypergraph where a sphere is defined as how many nodes do you get to when you go a distance r away from a given point and you can say well if i get to about r cube nodes when i go a distance r away in the hypergraph then i'm living roughly in three dimensional space but you might also get to r to the point you know 2.92 you know for for some value for r in you know as as our increases that might be the the sort of fit to what happens and so one of the things we suspect is that the very early universe was essentially infinite dimensional and that as the universe expanded it became lower dimensional and so one of the things that is another little sort of point where we we think there might be a way to to actually measure some things is dimension fluctuations in the early universe that is is there a is there leftover dimension fluctuation of at the time of the cosmic microwave background 100 000 years or something after the beginning of the universe is it still the case that there are there were pieces of the universe that didn't have dimension 3 that had dimension 3.01 or something and can we tell that is that possible to observe uh the fluctuations in dimensions i don't even know what that entails okay so the the question which should be an elementary exercise in electrodynamics except it isn't is um understanding what happens to a photon when it propagates through 3.01 dimensional space so for example the inverse square law is a consequence of the you know the the surface area of a sphere is proportional to r squared but if you're not in three dimensional space the surface area of sphere is not proportional to r squared it's r to the whatever 2.01 or something and so that means that i think when you kind try and do optics you know a common principle in optics is huygens principle which basically says that every piece of a wavefront of a of a of light is a source of new spherical waves and those spherical waves if they're different dimensional spherical waves will have other characteristics and so there will be bizarre optical phenomena which we haven't figured out yet um so you're you're you're what looking for some weird photon trajectories that designate that it's 3.01 dimensional space yeah yeah that would be an example of i mean you know there are there are only a certain number of things we can measure about photons you know we can measure their polarization we can measure their frequency we can measure their direction um those kinds of things and you know how that all works out and you know in the current models of physics uh you know it's been hard to explain how the universe manages to be as uniform as it is and that's led to this inflation idea that um to the to the great annoyance of my then collaborator i we had we figured out in like 1979 we had this realization that that you could get something like this but it seemed implausible that that's the way the universe worked so we put in a footnote and that was uh so that's a but but any case i i've never really completely believed it but this that's an idea for how to sort of puff out the universe faster than the speed of light early moments of the universe that that's the sort of inflation idea and that you can somehow explain how the universe manages to be as uniform as it is in in our model this turns out to be much more natural because the universe just starts very connected the hypergraph is not such that the ball that you grow starting from single point has volume r cubed it might have volume r to the 500 or r to the infinity um and so that means that you you sort of naturally get this much higher degree of connectivity and uniformity in the universe and then the question is uh this is sort of the mathematical physics challenge is in the standard theory of the universe there's the friedman robertson walker universe which is the kind of standard model where the universe is isotropic and homogeneous and you can then work out the equations of general relativity and you can figure out how the universe expands we would like to do the same kind of thing including dimension change this is just difficult mathematical physics i mean the reason it's difficult is there's sort of fundamental reason it's difficult when when people invented calculus 300 years ago calculus was a story of understanding change and change as a function of a variable so people study univariate calculus they study multivariate calculus it's one variable it's two variables three variables but whoever studied you know 2.5 variable calculus turns out nobody turns out that but what we need to have to understand these fractional dimensional spaces uh which don't work like well they're they're spaces where where the effective dimension is not an integer so you can't apply the tools of calculus in naturally and easily to fractional dimensions no so somebody has to figure out how to do that yeah we're trying to figure this out i mean it's it's very interesting it's very connected to very frontier issues in mathematics it's very beautiful but so is it possible is it possible we're dealing with a scale that's so so much smaller than our human scale is it possible to make predictions versus explanations do you have a hope that with this hypograph model you'll be able to make predictions yeah that that could be validated with a physics experiment predictions that couldn't have been done or weren't done otherwise oh yeah yeah i mean you know i think which in which domain do you think okay so they're going to be cosmology ones to do with dimension fluctuations in the universe that's a very bizarre effect nobody you know dimension fluctuation is just something nobody ever looked for that if anybody sees dimension fluctuation that's a huge flag that something like our model is going on if and and how one detects that you know that's a problem of kind of you know that's a problem of traditional physics in a sense of what's the best way to actually figure that out and and for example that that's one there are there are all kinds of things one can imagine i mean there are things that um uh in black hole mergers it's possible that there will be effects of maximum entanglement speed and large black hole mergers um that's another another possible thing and all of that is detected through like what do you have a hope for ligo type of situation like gravitational waves yeah or alternatively i mean i think it's you know look figuring out experiments is like figuring out technology inventions right that is you know you've got a set of raw materials you've got an underlying model and now you've got to be very clever to figure out you know what is that thing i can measure that just somehow you know leverages in to the right place and we've spent less effort on that than i would have liked because i one of the one of the reasons is that that i think that the the this you know the physicists who've been working on on our models we've with now lots of physicists actually it's very very nice it's kind of uh it's one of these cases where i'm almost i'm really kind of pleasantly surprised that the sort of absorption of the things we've done has been uh quite rapid and quite uh sort of you know very positive so it's a cambrian explosion of physicists too not just ideas yes i mean you know a lot of what's happened that's really interesting and again not what i expected is there are a lot of areas of of sort of very uh elaborate sophisticated mathematical physics whether that's causal set theory whether it's higher category theory whether it's categorical quantum mechanics all sorts of elaborate names for these things spin networks perhaps uh you know causal dynamical triangulations all kinds of names of these fields and these fields have a bunch of good mathematical physicists in them who've been working for decades in these particular areas and the question is but but they've been building these mathematical structures and the mathematical structures are interesting but they're not they don't typically sit on anything they're just mathematical structures and i think what's happened is our models provide kind of a machine code that lives underneath those models so a typical example this is uh uh due to jonathan gorad who's one of the key people who's been working on our project um this is uh in okay so i'll give you an example just to give a sense of how these things connect this is in causal set theory so the idea of causal set theory is there are in space-time we imagine that there's space and time it's a three plus one-dimensional you know set up we imagine that there are just events that happen at different times and places in space and time and the idea of causal set theory is the only thing you say about the universe is there are a bunch of events that happen sort of randomly at different places in space and time and then the whole sort of theory of physics has to be to do with this this graph of causal relationships between these randomly thrown down events so they've always been confused by the fact that to get even lorentz and variance even relativistic and variants you need a very special way to throw down those events and they've had no natural way to understand how that would happen so what jonathan figured out is that in fact from our models they instead of just generating events at random our models necessarily generate events in some pattern in space-time effectively that then leads to ransom variants and relativistic invariants and all those kinds of things so it's a place where all the mathematics that's been done on well we just have a random collection of events now what you know what consequences does that have in terms of causal set theory and so on that can all be kind of wheeled in now that we have some different underlying foundational idea for what what the particular distribution of events is as opposed to just we throw down random events and so that's a that's a typical sort of example of what we're seeing in all these different areas of kind of how you can take you know really interesting things that have been done in mathematical physics and connect them and it's really kind of beautiful because the the you know the sort of the abstract models we have just seem to plug into all these different very interesting very elegant abstract ideas but we're now giving sort of a reason for that to be the way for for a reason for one to care i mean it's like saying uh you can you know you can think about computation abstractly you know you can think about i don't know combinators or something as abstract computational things and you can sort of do all kinds of study of them but it's like why do we care well okay turing machines are a good start because you can kind of see they're sort of mechanically doing things but when we actually start thinking about computers computing things we have a really good reason to care and this is sort of what we're what we're providing i think is a reason to care about a lot of these areas of mathematical physics so that's been that's been very nice so i'm not sure we've ever got to the the question of why does the university let's let's let's talk about that yes so we're it's not the simplest question in the world so um so it's it takes a few steps to get to it and it's nevertheless even surprisingly you can even begin to answer this question indeed as you were saying i'm very surprised so the next thing to perhaps understand is this idea of rulial space so we've got kind of physical space we've got branchial space the space of possible quantum histories and now we've got another level of kind of abstraction which is real space and here's the here's where that comes from so you say okay you say we've got this model for the universe we've got a particular rule and we run this rule and we get the universe okay so that's that's interesting why that rule why not another rule and so that confused me for a long time then i realized well actually what if the thing could be using all possible rules what if at every step in addition to saying apply a particular rule at all places in this hyper graph one could say just take all possible rules and apply all possible rules at all possible places in this hypergraph okay and then you make this rulial multi-way graph which both is all possible histories for a particular rule and all possible rules so the next thing you'd say is how can you get anything reasonable how can anything you know real come out of the set of all possible rules applied in all possible ways okay there's a subtle thing so which i haven't fully untangled the there is this object which is the result of running all possible rules in all possible ways and you might say if you're running all possible rules why can't everything possible happen well the answer is because when you there's sort of this entanglement that occurs so let's say that you have a lot of different possible initial conditions a lot of different possible states then you're applying these different rules well some of those rules can end up with the same state so it isn't the case that you can just get from anywhere to anywhere there's this whole entangled structure of what can lead to what and there's a definite structure that's produced i think i'm going to call that definite structure the ruliad the limit of um the limits of kind of uh all possible rules being applied in all possible ways and you're saying that structure is finite so that somehow connects to maybe a similar kind of thing as like causal invariance well there happens necessarily has causal invariance that's a feature of that's just a mathematical consequence of essentially using all possible rules plus universal computation gives you the fact that from any diverging paths you can always the the paths will always convert does that say that the rule does that necessarily infer that the ruliad is finite in the end it's not necessarily finite i mean it's it's a it's a the the just like the history of the universe may not be finite the history of the universe time may keep going forever you can keep running the computations of the ruliad and you'll keep spewing out more and more and more structure it's like time doesn't have to end it's it's um that but the the issue is there are there are three limits that happen in this ruliad object one is how long you run the computation for another is how many different rules you're applying and another is how many different states you start from and the mixture of those three limits i mean this is just mathematically a horrendous object okay and what's what's interesting about this object is the one thing that does seem to be the case about this object is it connects with ideas in higher category theory and in particular it connects to some of the 20th century's most abstract mathematics done by this chap growth indeek growth and leak had a thing called the infinity group void which is closely related to this roulette object although the details of the relationship uh you know i don't fully understand yet um but i think that the what's what's interesting is this thing that is sort of this very limiting object so so okay so a way to think about this that that again will will take us into another direction which is the equivalence between physics and mathematics the way that uh well let's see uh maybe this is um just to give a sense of this kind of um groupoid and things like that you can think about in mathematics you can think you have certain axioms they're kind of like atoms and you well actually let's say let's talk about mathematics for a second so what is mathematics what do what is what is it made of so to speak mathematics there's a bunch of statements like uh for addition x plus y is equal to y plus x that's a statement of mathematics another statement will be you know x squared minus one is equal to x plus one x minus one there are infinite number of these possible statements of mathematics well it's not i mean it's not just i guess a statement but with x plus y it's uh it's a rule the you can it's a i mean you think of it as a rule it's it's a it is a it is a rule it's also just a thing that is true in mathematics right um the statement of truth okay right and and what you can imagine is you you you imagine just laying out this giant kind of ocean of all all statements well actually you first start okay this is where this was segwaying into a different thing let me let me not go in this direction for a second let's not go to meta mathematics just yet yeah we'll we'll maybe get to meta mathematics but it's it's um uh so let me not let me explain the groupoid and things later yes yeah but but so let's come back to the universe um always a good place to be in so yeah so what does the universe have to do with the rouley ad the rulio space and how that's possible lee connected to why the thing exists at all and why there's just one of them yes okay so here's the point so the thing that had confused me for a long time was let's say we get the rule for the universe we hold it in our hand we say this is our universe then the immediate question is well why isn't another one and you know that's kind of the you know the the sort of the lesson of copernicus is we're not very special so how come we got universe number 312 and not universe quadrillion quadrillion quadrillion and i think the resolution of that is the realization that there that the universe is running all possible rules so then you say well how on earth do we perceive the universe to be running according to a particular rule how do we perceive definite things happening in the universe well it's the same story it's the observer there is a reference frame that we are picking in this rule space and that that is what determines our perception of the universe with our particular sensory information and so on we are parsing the universe in this particular way so here's the way to think about it in in in physical space we live in a particular place in the universe and you know we could live in alpha centauri but we don't we live here um and similarly in rural space we could live in many different places in rural space but we happen to live here and what does it mean to live here it means we have certain sensory input we have certain ways to parse the universe those are our interpretation of the universe what would it mean to travel in rule space what it basically means is that we are successively interpreting the universe in different ways so in other words to be at a different point in rule space is to have a different in a sense a different interpretation of what's going on in the universe and we can imagine even things like an analog of the speed of light as the maximum speed of translation in real space and so on so wait what's the interpretation so real space and we is i'm confused by the we and the interpretation and the universe i thought moving about in real space changes the way the universe is is the the way we would perceive it the way that so this ultimately has to do with the perception so it doesn't real real space is not somehow changing like uh branching into another universe something like that no i mean the point is that the whole point of this is the rouliad is sort of the encapsulated version of everything that is the universe running according to all possible yeah we think of uh our universe the observable universe as its thing so we're a little bit loose with the word universe then because wouldn't the ruley ad potentially encapsulate a very large number like combinatorially large maybe infinite set of what we human physicists think of as universes that's an interesting interesting parsing of the word universe right because what we're saying is just as we're at a particular place in physical space we're at a particular place in rural space at that particular place in rural space our experience of the universe is this yeah just as if we lived at the center of the galaxy our universe our experience of the universe will be different from the when it is given where we actually live and so in us what we're saying is our when you might say i mean in a sense this this ruliad is sort of a super universe so to speak um but it's all entangled together it's not like you can separate out you can say let me it's it's like when we take a reference okay it's like our experience of the universe is based on where we are in the universe we could imagine moving to somewhere else in the universe but it's still the same universe so there's not like universes existing in parallel no because because and the whole point is that if we were able to change our interpretation of what's going on we could perceive a different reference frame in this roulette yeah but that's not that's not uh that's just yeah that's the same rule yeah that's the same universe you're just moving about this is just coordinates right so so the way that's the reason that's interesting is imagine the extraterrestrial intelligence so the alien intelligence we should say the alien intelligence might live on alpha centauri but it might also live at a different place in rural space it can live right here on earth it just has a different reference frame that includes a very different perception of the universe right and then because that really all space is very large i mean do we get to communicate with them right that's yeah but it's also well one uh thing is how different the perception of the universe could be i think it could be bizarrely unimaginably completely different and i mean one thing to realize is even in kind of things i don't understand well you know i'm i i know about the kind of western tradition of understanding you know science and all that kind of thing and you know you talk to people who say well i you know i'm really into some you know eastern tradition of this that and the other and it's really obvious to me what how things work i don't understand it at all but you know it is not obvious i think with this kind of realization that there's these very different ways to interpret what's going on in the universe that kind of gives me at least it doesn't help me to understand that different interpretation but it gives me at least more respect for the possibility that there will be other interpretations yeah it humbles you to the possibility that like what is it reincarnation or all all these like uh eternal recurrence with nietzsche like just these ideas yeah well you know the thing that i realized about a bunch of those things is that you know i've been sort of doing my little survey of the history of philosophy just trying to understand you know what what can i actually say now about some of these things and you realize that some of these concepts like the immortal soul concept which you know i remember when i was a kid and you know it was kind of a lots of religion bashing type stuff of people saying you know what we know about physics tell us how much does a soul weigh and people are like well how can it be a thing if it doesn't weigh anything well now we understand you know there is this notion of what's in brains that isn't the matter of brains and it's something computational and there is a sense and in fact it is correct that it is in some sense immortal because this pattern of computation is something abstract that is not specific to the particular material of a brain now we don't know how to extract it you know in our traditional scientific approach but it's still something where it isn't a crazy thing to say there is something it doesn't weigh anything that's a kind of a silly question how much does it weigh um well actually maybe it isn't such a silly question in our model of physics because the actual computational activity has has a consequence for gravity and things but that's a very very subtle because if we start talking about mass and energy and so on there could be a uh what would you call a solatron yes yes yes a particle that somehow contains soulness yeah right well that's what by the way that's what leibniz said and you know one thing i've i've never understood this you know leibniz had the center of monads and monadolology and he had this idea that that what exists in the universe is this big collection of monads and that they that the only thing that one knows about the monads is sort of how they relate to each other which sounds awfully like hypographs right but leibniz had really lost me at the following thing he said each of these monads has a soul and each of them has a consciousness and it's like okay i'm out of here i don't understand this at all i don't know what's going on but i realized recently that in his day the concept that a thing could do something could spontaneously do something that was his only way of describing that and so what i would now say is well as this abstract rule that runs to leibniz that would have been you know in 1690 or whatever that would have been kind of well it has a soul it has a consciousness um and so you know in a sense it's it's like one of these there's no new idea under the sun so to speak that's you know that's a sort of a version of of the same kinds of ideas but couched in terms that are sort of bizarrely different from the ones that we would use today would you be able to maybe play devil's advocate on the your conception of consciousness that uh like the the two characteristics of it that is constrained and there's a single thread of time is it possible the liveness was onto something that the the basic atom the screw atom of space has a consciousness is is that uh so these are just words right but yeah what is there is there some sense where consciousness is much more fundamental than you're making it seem i don't know i mean that you know i think can you construct a world in which it is much more fundamental i think that okay so the question would be is there a way to think about kind of uh if we sort of parse the universe down at the level of atoms of space or something could we say well so that's really a question of a different point of view a different place in real space we're asking you're asking the question could there be a civilization that exists could there be sort of uh conscious entities that exist at the level of atoms of space and what would that be like and i think that comes back to this question of can we you know what's it like to be a cellular automaton type thing um i mean it's it's you know i'm i'm not yet there i don't know i mean i think that the this is a and i don't even know yet quite how to think about this in the sense that i was considering you know i'm i never write fiction but i i haven't written it since i was like 10 years old my my fiction i made one attempt which i sent to some science fiction writer friends of mine and they told me it was terrible so but um this is a long time ago no it was recently recently they said it was terrible that'd be interesting to see you write a short story based on what sounds like it's already inspiring short stories by or stories yeah right science fiction writers but but i think the the interesting thing for me is you know in the what does it what is it like to be a whatever yeah how do you describe that i mean it's like that's not a thing that you describe in mathematics that what is it like to be such and such well see to me when you say what is it like to be something presumes that you're talking about a singular entity so yeah like there there's a some kind of feeling of the the entity the the stuff that's inside of it and the stuff that's outside of it and then that's when consciousness starts making sense but but then um it seems like that could be generalizable if you take some subset of uh a cellular automata you could start talking about what does that subset maybe a few but then you can i think you could just take arbitrary numbers of subsets like to me uh uh like you and i uh individually are consciousnesses but you could also say the two of us together is a singular consciousness maybe maybe i'm not so sure about that i think that the single thread of time thing may be pretty important and that as soon as you start saying there are two different threads of time there are two different experiences and then we have to say how do they relate how are they sort of entangled with each other i mean that may be a different story of a thing that isn't much like you know the the what do the ants you know what's it like to be an ant you know where there's a sort of more collective view of the world so to speak i don't know i think that um i mean this is uh uh you know i don't really have a good i mean you know my best thought is you know can we turn it into a human story it's like the question of you know when we try and understand physics can we turn that into something which is sort of a human understandable narrative and now what's it like to be a such and such you know maybe the only medium in which we can describe that is something like fiction where it's kind of like you're telling you know the life story in that in that uh in that setting but i i'm this is this is beyond what i've what i've yet understood how to do yeah but it does seem so like with human consciousness you know we're made up of cells and like there's a bunch of systems that are networked that work together that at this at the human level feel like a singular consciousness when you take yes and so maybe like an ant colony is just too low level sorry an ant is too low level right maybe you have to look at the ant colony yeah i agree like there's some level at which it's a conscious being and then if you go to the planetary scale then maybe that's going too far so there's a nice sweet spot yeah right consciousness no i mean i agree i think i think the difficulty is that you know okay so in sort of people who talk about consciousness yes one of the one of the terrible things i've realized because i've now interacted with with some of this community so to speak some interesting people who do that kind of thinking but you know one of the things i was saying to one of the leading people in that area i was saying you know uh that um you know it must be kind of frustrating because it's kind of like a poetry story that is many people are writing poems but few people are reading them yes so there are always these different you know everybody has their own theory of consciousness and they are very non-inter sort of interdiscussible and and by the way i mean you know my own approach to sort of the the question of consciousness as far as i'm concerned i'm an applied consciousness operative so to speak because i don't really in a sense the thing i'm trying to get out of it is how does it help me to understand what's a possible theory of physics and how does it help me to say how do i go from this this incoherent collection of things happening in the universe to our definite perception and definite laws and so on and sort of an applied version of consciousness and and i think the reason it sort of segues to a different kind of topic but the reason that um uh one of the things i'm particularly interested in is kind of what's the analog of consciousness and systems very different from brains and so why does that matter well you know this whole description of this kind of uh well i should you know what we haven't talked about why the universe exists so let's let's get to why the universe exists and then we then we can can talk about perhaps a little bit about what these models of physics kind of show you about other kinds of things like molecular computing and so on yes but that's okay that's good why does the universe exist okay so we finally sort of more or less set the stage we've got this idea of this ruliad of this object that is made from following all possible rules the fact that it's sort of not just this incoherent mess it's got all this entangled structure in it and so on okay so what is this ruliad well it is the working out of all possible formal systems so the the sort of the question of why does the universe exist its core question which kind of started with is you've got two plus two equals four you've got some other abstract results but that's not actualized it's just an abstract thing and when we say we've got a model for the universe okay it's this rule you run it and it'll make the universe but it's like but but you know where's it actually running what what what is what is it actually doing right what is is it actual or is it merely a formal description of something okay so the thing to realize with this with this the the thing about the rouliad is it's an inevitable it is the entangled running of all possible rules so you don't get to say it's not like you're saying which roulette are you picking because it's all possible formal rules it's not like it's just um you know well actually it's only footnote the only footnote it's an important footnote is it's all possible computational rules not hyper-computational rules that is it's running all the rules that would be accessible to a turing machine but it is not running all the rules that will be accessible to a thing that can solve problems in finite time that would take a turing machine infinite time to solve so you can even alan turing knew this that you could make oracles for touring machines where you say a touring machine can't solve the whole thing problem for touring machines it can't know what will happen in any touring machine after an infinite time in any finite time but you could invent a box just make a black box you say i'm going to sell you an oracle that will just tell you you know press this button it'll tell you what the touring machine will do after an infinite time you can imagine such a box you can't necessarily build one in the physical universe but you can imagine such a box and so we could say well in addition to so in this ruliad we're imagining that there is a computational that at the end it's it's running rules that are computational it doesn't have a bunch of uh oracle black boxes in it you say well why not well turns out if there are oracle black boxes the ruliad that is you can make a sort of super rouliad that contains those oracle black boxes but it has a cosmological event horizon relative to the first one they can't communicate in other words you can you can end up with what you end up happening what ends up happening is it's it's like in the physical universe we in this causal graph that represents the causal relationships of different things you can have an event horizon where there's where the causal graph is disconnected where the effect here an event happening here does not affect an event happening here because there's a disconnection in the causal graph and that's what happens at an event horizon and so the what will happen between this kind of the ordinary ruliad and the hyper ruliad is there is an event horizon and you you know we in our rouliad will just never know that there is that they're just separate things they're not they're not connected maybe i'm not understanding but just because we can't observe it uh why does that mean it doesn't exist um it might exist but it does it's not clear what it it's so what so to speak whether it exists i mean you know what we're trying to understand is why does our universe exist we're not trying to ask the question what uh you know it's let me say another thing let me make a meta comment okay which is that that i have not thought through this hyper really ad business properly so i'm i'm i can't the the the the the the hyper ruliad is referring to a ruliad in which hyper computation is possible that's correct okay so like what the that footnote the footnote to the footnote is we're not sure why this is important yeah that's right so let's let's ignore that okay it's already abstract enough okay so so okay so the the one question is we have to say if we're saying why does the universe exist one question is why is it this universe and not another universe yeah okay so the the important point about this ruliad idea is that it's in the rouliad are all possible formal systems so there's no choice being made there's no there's no like oh we picked this particular universe and not that one that's the first thing the second thing is the that we have to ask the question so so you say why does 2 plus 2 equals 4 exist that's not really a that is a thing that necessarily is that way just on the basis of the meaning of the terms 2 and plus and equals and so on right so the thing is that this this ruliad object is in a sense a necessary object it is just the thing that is the consequence of working out the consequence of the formal definition of things you don't it is not a thing where you're saying and this is picked as the particular thing this is just something which necessarily is that thing because of the definition of what it means to have computations is there really a it's a formal system yes but does it exist ah well uh where are we in this whole thing we are part of this ruliad and so our so there is no sense to say does two plus two equals four exist well that's that's in some sense it necessarily exists it's a necessary object it's not a thing that where you can ask uh you know it's it's usually in in philosophy there's a sort of distinction made between uh you know necessary truths contingent truths analytic propositions synthetic propositions there are a variety of different versions of this they're things which are necessarily true just based on the definition of terms and there are things which happen to be true in our universe but we're we don't exist in rural space we that's one of the coordinates that define our existence right well okay so so yes yes but this ruliad is the set of all possible rule coordinates so what we're saying is it contains that so what we're saying is we exist as okay so our perception of what's going on is we're at a particular place in this ruling ad and we are concluding certain things about how the universe works based on that but the question is do we understand you know is there something where we say so so why does it work that way well the answer is i think it has to work that way because this there isn't this ruliad is a necessary object in the sense that it is a purely formal object just like two plus two equals four it's not an object that was made of something it's an object that is just an expression of the necessary collection of formal relations that exist and so then the issue is can we in our experience of that is it you know can we have tables and chairs so to speak in that just by virtue of our experience of that necessary thing and you know what people have generally thought and honestly that i don't know of a lot of discussion of this why does the universe exist question it's been a very you know i've been surprised actually at how little i mean i think it's one of these things that's really uh kind of far out there but the thing that that is you know the surprise here is that all possible formal rules when you run them together and that's the critical thing when you run them together they produce this kind of entangled structure that has a definite structure it's not just a you know a random arbitrary thing it's a thing with definite structure and that structure is the thing when we are embedded in that structure when when anything you know the an entity embedded in that structure perceives something which is then we can interpret as physics and things like this so in other words we don't have to ask the question the the the why does it exist it necessarily exists i'm missing this part why does it necessarily exist okay okay so like you need to have it if you want to formalize the relation between entities but why [Music] why do you need to have relations okay okay so so let's say you say um well it's like why does math have to exist okay that's the same question yeah okay fair question um let's see i think the thing to think about is the existence of mathematics is something where given a definition of terms what follows from that definition inevitably follows so now you can say why define any terms but in a sense the well that's okay so the the definition of terms i mean i think the way to think about this let me see so like concrete terms i mean they're just things like you know uh logical or right that's a thing that's a powerful thing well it's a it's a yes okay but it's it's a the point is that it is not a thing about you know people imagine there is i don't know the uh uh you know an elephant or something or the you know elephants are presumably not necessary objects they are they happen to exist as a result of kind of biological evolution and whatever else but the the thing is that in some sense that there is it is a different kind of thing to say does plus exist the the it's not it's not not like an elephant so a plus is seems more fundamental more basic than an elephant yes but you can imagine a world without plus or anything like it like why do formal things that are discreet that can be used to reason have to exist or uh well okay so why okay so that then the question is but the whole point is computation we can certainly imagine computation that is we can certainly say there is a formal system that we can construct abstractly in our minds that is computation and that that's the um uh and you know we can we can imagine it right now the question is um is it is that formal system once we exist as observers embedded in that formal system that's enough to have something which is like our universe yeah and so then the then what you're kind of asking is perhaps is why i mean the point is we definitely can imagine it there's nothing that says that we're not saying that there's it's sort of inevitable that that is a thing that we can imagine we don't have to ask does it exist we're just it is definitely something we can imagine now that's then we have this thing that is a formally constructable thing that we can imagine and now we have to ask the question what you know given that formally constructable thing what is uh what consequences does that if we were to perceive that formally if we were embedded in that formally constructable thing what would be perceived about the world and we would say we perceive that the world exists because we are we are seeing all of this mechanism of all these things happening and but that's something that is just a feature of it's it's it's something where we are see another way of asking this that i'm trying to get at i understand why it feels like this uh rooliad is necessary but maybe it's just me being human but it feels like then you should be able to not us but somehow step outside of the roulette like what's outside the roulette well the ruling out is all formal systems so there's nothing because but that's what a human would say i know that's what a human would say because we're used to the idea that there are there's but the whole point is that by the time it's all possible formal systems it's it's like it is all things you can imagine but not all computations you can imagine but like we don't well so what we don't see that could be other code okay so so that's a that's a fair question is it possible to encode uh all i mean once we is is there something that isn't what we can represent formally right that is that is there's something that um and that's i think related to the hyper rouliad footnote so to speak you know one of the things sort of interesting about this is you know there has been some discussion of this in theology and things like that um but uh which i don't necessarily understand all of um but the the key sort of new input is this idea that all possible formal systems it's like you know if you make a world people say well you make a world with a particular in a particular way with particular rules but no you don't do that you can make a world that deals with all possible rules and then merely by virtue of living in a particular place in that world so to speak we have the perception we have of what the world is like now i have to say the the um uh it's sort of interesting because i i've you know i wrote this piece about this and i i you know this philosophy stuff is not super easy and i i've um i as i'm as i'm talking to you about it and i actually haven't you know people have been interested in lots of different things we've been doing but this why does the universe exist has been i would say one of the one of the ones that you would think people will be most interested in but actually i think they're just like oh that's just something complicated that that um so so i haven't i haven't explained it as as much as i've explained a bunch of other things and i have to say i think i i think i may be missing a couple of pieces of that argument that um uh would be so so it's kind of a like well your your uh conscious being is computationally bounded so you're missing having written quite a few articles yourself you you're now missing some of the pieces yes being human right one of the consequences of this why the unit why the universe exists thing and this kind of concept of ruling ads and and uh you know places in there representing our perception of the universe and so on one of the weird consequences is if the universe exists mathematics must also exist and that's a weird thing because mathematics people have been very confused including me have been very confused about the the question of of kind of what uh what is the foundation of mathematics what is what kind of a thing is mathematics is mathematics something where we just write down axioms like euclid did for geometry and we just build the structure and we could have written down different axioms and we'd have a different structure or is it something that has a more fundamental sort of truth to it and i have to say it's one of these cases where i've i've long believed that mathematics has a great deal of arbitrariness to it that there are particular axioms that kind of got written down by the babylonians and uh you know that's what we've ended up with the mathematics that we have and i have to say actually my my wife has been telling me for 25 years she's a mathematician she's been telling me you're wrong about the foundations of mathematics and and you know i'm like no no no i know what i'm talking about and finally she's she's much more right than i've been so it's um it's wonderful so i mean uh her sense in your sense are we just uh so this is to the question of uh meta mathematics so we're just kind of on the trajectory through rule space except in mathematics through a trajectory a certain kind of thing that's partly the idea so so i think that the notion is this so 100 years ago a little bit more than 100 years ago but people have been doing mathematics for ages but then in the in the late 1800s people decided to try and formalize mathematics and say you know it is mathematics is you know we're going to break it down we're going to make it like logic we're going to make it out of out of sort of fundamental primitives and that was people like fraga and piano and hilbert and so on and they kind of got this idea of let's do kind of euclid but even better let's just make everything just in terms of this sort of symbolic axioms and then build up mathematics from that and that you know they thought at the time as soon as they get these symbolic axioms that they made the same mistake the kind of computational irreducibility mistake they thought as soon as we've written down the axioms then it'll just we'll just have a machine kind of a super mathematica so to speak that can just grind out all true theorems of mathematics that got exploited by godel's theorem which is basically the story of computational irreducibility it's that even though you know those underlying rules you can't deduce all the consequences in any finite way and so so that was but now the question is okay so they broke mathematics down into these axioms and they say now you build up from that so what i'm increasingly uh coming to realize is that's similar to saying let's take a gas and break it down into molecules there's gas laws that are the large-scale structure and so on that we humans are familiar with and then there's the underlying molecular dynamics and i think that the axiomatic level of mathematics which we can access with automated theorem proving and proof assistance and these kinds of things that's the molecular dynamics of mathematics and occasionally we see through to that molecular dynamics we see undecidability we see other things like this one things i've always found very mysterious is that godel's theorem shows that there are sort of things which cannot be finitely proved in mathematics there are proofs of arbitrary length infinite length proofs that you might need but in practical mathematics mathematicians don't typically run into this they just happily go along doing their mathematics and i think what's actually happening is that what they're doing is they're looking at this they are essentially observers in meta mathematical space and they are picking a reference frame in metal mathematical space and they are computationally bounded observers in metamathematical space which is causing them to deduce that the laws of metamathematics and the laws of mathematics like the laws of fluid mechanics are much more understandable than this underlying molecular dynamics and so what gets really bizarre is thinking about kind of the analogy between matter mathematics this idea of of you exist in this kind of uh um in the sort of space of possible um in this kind of mathematical space where the where the individual kind of uh points in the mathematical space are statements in mathematics and they're connected by proofs where one statement you know you take a couple of different statements you can use those to prove some other statement and you've got this whole network of proofs that's the kind of causal network of mathematics so what can prove what and so on and you can say at any moment in the history of a mathematician of a single mathematical consciousness you are in a single kind of slice of this kind of meta-mathematical space you you know a certain set of mathematical statements you can then deduce with proofs you can deduce other ones and so on you're kind of gradually moving through meta-mathematical space and so it's kind of the view is that the reason that mathematicians perceive mathematics to have the sort of integrity and lack of kind of undecidability and so on that they do is because they like we as as observers of the physical universe we have these limitations associated with computational boundedness single thread of time consciousness limitations basically that the same thing is true of mathematicians perceiving sort of meta-mathematical space and so what's happening is that when you look at if you look at one of these formalized mathematics systems something like you know pythagoras theorem it'll be it'll take oh i don't know uh what is it maybe 10 000 individual little steps to prove pythagoras's theorem and one of the bizarre things that's a sort of an empirical fact that i'm trying to understand a little bit better if you look at different proof assists if you look at different formalized mathematics systems they actually have different axioms underneath but they can all prove pythagoras theorem and so in other words it's a little bit like what happens with gases we can have air molecules we can have water molecules but they still have fluid dynamics both of them have fluid dynamics and so similarly at the level that mathematics that mathematicians care about mathematics it's way above the macular dynamics so to speak and there are all kinds of weird things like for example one thing i was realizing recently is that the quantum theory of mathematics that's a very bizarre idea but um basically when you prove what is you know a proof is you've got one statement in mathematics you go through other statements you eventually get to a statement you're trying to prove for example that's a path path in meta-mathematical space and that's a single path a single proof is a single path but you can imagine there are other proofs of the same result there are a bundle of proofs there's this whole set of possible proofs you could think of as branching similar to the quantum mechanics model that you were talking about exactly and so and then there's some invariants that you can formalize in the same way that you can for the quantum mechanical right so the question is in in proof space you know as you start thinking about multiple proofs are there analogs of for example destructive interference of multiple proofs so here's a bizarre idea it's just a couple of days old so not not yet fully formed but um as you try and do that when you have two different proofs it's like two photons going in different directions you have two proofs which at an intermediate stage are incompatible and that's kind of like destructive interference is it possible for this to instruct the engineering of automated proof systems absolutely i mean as a practical matter i mean the you know this whole question in fact jonathan gorad has a nice heuristic for automated theorem provers that's based on our physics project that is looking for essentially using kind of uh using energy and in our models energy is kind of level of activity in this hypograph and so there's sort of a heuristic for automated theorem proving about how do you pick which path to go down that uh is based on essentially physics um and i mean the thing that that gets interesting about this is is the way that one can sort of have the interplay between like for example a black hole what is a black hole in metal mathematics so the answer is what is black hole in physics a black hole in physics is where in the simplest form of black hole time ends that is all you know everything is is crunched down to the space-time singularity and everything just ends up at that singularity so in our models and that's a little hard to understand in general relativity with continuous mathematics and what does singularity look like in our models it's something very pragmatic it's just you're applying these rules time is moving forward and then there comes a moment where the rules no rules apply so time stops it's kind of like the universe dies there's you know the nothing happens in the universe anymore well in mathematics that's a decidable theory that's a theory so theories which have undecidability which are things like arithmetic set theory all the serious models theories in mathematics they all have the feature that there are proofs of arbitrarily long length in something like boolean algebra which is a decidable theory there are you know any question in boolean algebra you can just go crunch crunch crunch and in a known number of steps you can answer it you know satisfiability you know might be hard but it's still a bounded number of steps to answer any satisfiability problem and so that's the the notion of a black hole in physics where time stops that's the that's analogous to in mathematics where there aren't infinite length proofs where when in physics you know you can wander around the universe forever if you don't run into a black hole if you run into a black hole and time stops you're done and it's the same thing in mathematics between decidable decidable theories and undecidable theories that's a that's an example and i think we're sort of the the attempt to understand so so another question is kind of what is the what is the general relativity of uh of metamathematics what is the bulk theory of metamathematics so in the literature of mathematics there are about three million theorems that people have have published and those represent it's kind of on this it's like like on the earth we would be you know uh you know we've put cities in particular places on the earth but yet there is ultimately you know we know the earth is roughly spherical and there's an underlying space and we could just talk about you know the world of space in terms of where our cities happen to be but there's actually an underlying space and so the question is what's that for meta mathematics and as we kind of explore what is for example for mathematics which is always likes taking sort of abstract limits so an obvious abstract limit for mathematics to take is the limit of the future of mathematics that is what will be you know the ultimate structure of mathematics yeah and one of the things that's an empirical observation about mathematics that's quite interesting is that a lot of theories in one area of mathematics algebraic geometry or something might have they play into another area of mathematics that that same the same kind of a fundamental construct seemed to occur in very different areas of mathematics and that's structurally captured a bit with category theory and things like that but i think that there's probably an understanding of this meta-mathematical space that will explain why different areas of mathematics ultimately sort of map into the same thing and i mean you know my little challenge to myself is what's time dilation in um uh in mata mathematics in other words as you as you basically as you move around in this mathematical space of possible statements um you know what's how does that moving around it's basically what's happening is that as you move around in the space of mathematical statements it's like you're changing from algebra to geometry to whatever else and you're trying to prove the same theorem but as you try if you keep on moving to these different places it's slower to prove that theorem because you keep on having to translate what you're doing back to where you started from and that's kind of the beginnings of the analog of time dilation and metamathematics plus there's probably fractional dimensions in this space as well oh this space is a very messy space this space is much messier than physical space i mean even in even in the models of physics physical space is is very tame compared to branchial space and real space um i mean the mathematical structure you know bronchial space probably more like hilbert space but it's a rather complicated hilbert space and rulial space is more like this weird infinity groupoid story of growth and deacon and you know i can explain that a little bit because in you know in in meta mathematical space a a path in mathematical space is a is a a path between two statements is a way to get by proofs is to way to find a proof that goes from one statement to another and so one of the things you can do you can think about is you've got between statements you've got proofs and they are paths between statements okay so now you can go to the next level and you can ask what about a mapping from one proof to another and so that's in in category theory that's kind of a higher category the notion of higher categories where you're where you're mapping not just between not just between objects but you're mapping between the mappings between objects and so on and so you can keep doing that you can keep saying higher order proofs i want mappings between proofs between proofs and so on and that limiting structure oh by the way one thing that's very interesting is imagine in proof space you've got these two proofs and the question is what is the topology of proof space in other words if you take these two parts can you continuously deform them into each other or is there some big hole in the middle that prevents you from continuously deforming them one into the other it's kind of like you know when you when you think about some i don't know some puzzle for example you're moving pieces around on some puzzle and you can think about the space of possible states of the puzzle and you can make this graph that shows from one state to the puzzle to another state of the puzzle and so on and sometimes you can easily get from one state to any other state but sometimes there'll be a hole in that space and they'll be you know you always have to go around the circuitous route to get from here to there there won't be any direct way that's kind of a question of of whether there's sort of an obstruction in the space and so the question is in proof space what is the what are you know what does it mean if there's an obstruction in proof space yeah i don't even know what an uh obstruction means improve space because for it to be an obstruction it should be reachable some other way from some other place right so this is like an unreachable part of the graph no it's not just an unreachable part it's a part where there are paths that go one way there are parts that go the other way and this question of homotopy and mathematics is this question can you continuously deform you know from one path to another path or do you have to go in a jump so to speak so okay so like if you're going around a sphere for example if you're going around i don't know a cylinder or something you can wind around one way and you can there's no paths where you can where you can easily deform one path into another because it's just sort of sitting on the same side of the cylinder but when you've got something that winds all the way around a cylinder you can't continuously deform that down to a point because it's it's stuck wrapped around my intuition about proof space is you should be able to deform it i mean that because then otherwise it doesn't even make sense because if the topology matters of the way you move about the space that i don't even know what that means well what it would mean is that you would have one way of doing a proof of something over here in algebra yeah and another way of doing a proof of something over here in geometry and there would not be an intermediate way to map between those proofs how would that be possible if they start at the same place and end the same place well it's the same thing as you know we've got points on a you know if we've got paths on a cylinder now i understand how it works in physical space but it just doesn't it feels like proof space shouldn't have that i okay i mean i'm not sure i don't know we will know very soon because we get to do some experiments this is the great thing about this stuff is that in fact you know i i'm in the next few days i hope to do a bunch of experiments on this so you're playing with like proofs in in this kind of space yes yes i mean so so you know this is toy you know theories and you know we've got good so this kind of segues to perhaps another thing which is this whole idea of multi-computation so this this um is another kind of bigger idea that so okay this has to do with how do you make models of things and it's going to it's some so i've sort of claimed that they've been sort of four epochs in the history of making models of things and um and this multi-computation thing is is the fourth there's a new epoch what are the first three the first one is is back in antiquity ancient greek times people were like what's the universe made of oh it's made of you know everything is water thales you know or everything is made of atoms it's sort of what are things made of or you know there are these crystal spheres that represent where the planets are and so on it's like a structural idea of how the universe is constructed there's no real notion of dynamics it's just what is the universe how is the universe made then we get to the 1600s and we get to the sort of revolution of mathematics being introduced into physics and then we have this kind of idea of you write down some equation the what happens in the universe is the solving of that equation time enters but it's usually just a parameter we just can you know sort of slide it back and forth and say here's here's where it is okay then we come to this kind of computational idea that i kind of started really pushing in the in the 90 early 1980s as a result you know the things we were talking about before about complexity that was my motivation but the bigger story was the story of kind of computational models of things and the big difference there from the mathematical models is in mathematical models there's an equation you solve it you've got kind of slide time to the place where you want it in computational models you give the rule and then you just say go run the rule and time is not something you get to slide time is something where it just you run the rule time goes in steps and that's how you work out what how the system behaves you don't time is not just a parameter time is something that is about the running of these of these rules and so there's this computational irreducibility you can't jump ahead in time but there's still important thing is there's still one thread of time it's still the case you know the seller automaton state then it has the next state and the next state and so on the thing that is kind of was sort of tipped off by quantum mechanics in a sense although it it actually feeds back even into relativity and things like that that there's these multiple threads of time and so in this multi-computation paradigm the kind of idea is instead of there being this single threat of time there are these kind of distributed asynchronous threads of time that are happening and the thing that's sort of different there is if you want to know what happened if you say what happened in the system in the case of the computational paradigm you just say well after a thousand steps we got this result right but in the multi-computational paradigm after a thousand steps not even clear what a thousand steps means because you've got all these different threads of time but there is no state there's all these different possible you know there's all these different paths and so the only way you can know what happened is to have some kind of observer who is saying here's how to parse the results of what was going on right but that observer is embedded and they don't have a complete picture so in the case of physics that's right yes and then in the but that's but so the idea is that in this multi-computation setup that it's this idea of these multiple threads of time and models that are based on that and this is similar to what people think about in non-deterministic computation so you have a turing machine usually it has a definite state it follows another state follows another state but typically what people have done when they thought about these kinds of things is they've said well there are all these possible paths a non-deterministic turing machine can follow all these possible paths but we just want one of them we just want the one that's the winner that factors the number or whatever else and similarly you know it's the same story in logic programming and so on but we say we've got this goal find us a path to that goal i just want one path then i'm happy or theorem proving same story i just want one proof and then i'm happy what's happening in multi-computation in physics is we actually care about many parts and well there is a case for example probabilistic programming is a version of multi-computation in which you're looking at all the paths you're just asking for probabilities of things um but in a sense in physics we're taking different kinds of samplings for example in quantum mechanics we're taking a different kind of sampling of all these multiple paths and but the thing that is notable is that when you are when you're an observer embedded in this thing etc etc etc with various other sort of footnotes and so on it is inevitable that the thing that you parse out of this system looks like general relativity and quantum mechanics um in other words that just by the very structure of this multi-computational setup it inevitably is the case that you have certain emergent laws now why is this perhaps not surprising in thermodynamics and statistical mechanics there are sort of inevitable emergent laws of sort of gas dynamics that are independent of the of the details of the molecular dynamics sort of the same kind of thing but i think what happens is what's sort of a funny thing that i've just been understanding very recently is when when i kind of introduced this whole sort of computational paradigm complexity-ish thing back in the 80s it was kind of like a big downer because it's like there's a lot of stuff you can't say about what systems will do and then what i realized is and then you might say now we've got multi-computation it's even worse you know it isn't just one thread of time that we can't explain it's all these threads of time we can't explain anything but the following thing happens because there is all this irreducibility and any detailed thing you might want to answer it's very hard to answer but when you have an observer who has certain characteristics like computational boundedness sequentiality of time and so on that observer only samples certain aspects of this incredible complexity going on in this multi-computational system and that observer is sensitive only to some underlying core structure of this multi-computational system there is all this irreducible computation going on all these details but to that kind of observer what's important is only the the core structure of multi-computation which means that observer observes comparatively simple laws and i think it is inevitable that that observer observes laws which are mathematically structured like general relativity and quantum mechanics which by the way are the same law in our in our model of physics so that's an explanation why there are simple laws that explain a lot for this observer potentially yes but the the place where this gets really interesting is there are all these fields of science where people have kind of gotten stuck where they say we'd really love to have a physics-like theory of economics we'd really love to have a physics like lore in linguistics we gotta talk about molecular biology here okay so what where where does multi-computation come in for biology economics is super interesting too but biology okay let's talk about that so let's talk about chemistry for a second okay so i mean i have to say you know this is it's such a weird business for me because you know they're these kind of paradigmatic ideas and then the actual applications and it's like i've always said i i know nothing about chemistry i learned all the chemistry i know you know the night before some exam when i was 14 years old but yeah but i've actually learned a bunch more chemistry and in in more from language these days we have really pretty nice symbolic representation of chemistry and in understanding the design of that i've actually i think learned a certain amount of chemistry though if you quizzed me on sort of basic high school chemistry i would probably totally fail but um uh but but okay so what is chemistry i mean chemistry is sort of a story of you know chemical reactions are like you've got this particular chemical it's represented as some graph of you know these are these are this configuration of molecules with these bonds and so on and a chemical reaction happens you've got these sort of two graphs they interact in some way you get another graph or multiple other graphs out so that's kind of the the the the sort of the the abstract view of what's happening in chemistry and so when you do a chemical synthesis for example you are given certain sort of these are possible reactions that can happen and you're asked can you piece together this a sequence of such reactions a sequence of such sort of axiomatic reactions usually called name reactions in chemistry can you piece together a sequence of these reactions so that you get out at the end this great molecule you were trying to synthesize and so that's a story very much like theorem proving and people have done actually they started in the 1960s looking at at kind of the theorem proving approach to that although it didn't really it didn't it didn't uh was sort of done too early i think um but anyway so that's kind of the view is that that chemistry chemical reactions are the story of of all these different sort of paths of possible things that go on okay let's let's go to an even lower level let's say instead of asking about uh which species of molecules we're talking about let's look at individual molecules and let's say we're looking at individual molecules and they are having chemical reactions and we're building up this big graph of all these reactions that are happening okay so so then we've got this big graph and by the way that big graph is incredibly similar to these hypergraph rewriting things um in fact in the underlying theory of multi-computation there are these things we call token event graphs which are basically you've broken your state into tokens like in the case of a hypergraph you've broken it into hyperedges and each event is just consuming some number of tokens and producing some number of tokens yeah but then you have to there's a lot of work to be done on update rules in terms of what they actually are for chemistry yeah what they are for our observed chemistry yes indeed yes indeed we've been working on that actually because we have this beautiful system in wolfram language for representing chemistry symbolically so we actually have you know this is a this is an ongoing thing to actually figure out what they are for some practical cases does that require human injection or can it be automatically discovered these update rules well if we implement chemistry better we could probably discover them automatically but i think in in reality right now it's like there are these particular reactions and really to understand what's going on we're probably going to pick a particular subtype of chemistry and just because because let me explain where this is going the place that here's here's where this is going so we got this whole network of all these molecules having all these reactions and so on and this is some whole multi-computational story because each each uh sort of chemical reaction event is its own separate event where we're saying they all happen asynchronously we're not describing in what order they happen you know maybe that order is governed by some quantum mechanics thing doesn't really matter we're just saying they happen in some order and then we ask what is the what what's the you know how do we think about the system well this thing is some kind of big multi-computational system the question is what is the chemical observer and one possible chemical observer is all you care about is did you make that particular drug molecule you're just asking you know the for the one path another thing you might care about is i want to know the concentration of each species right i want to know you know at every stage i'm going to solve the differential equations that represent the concentrations and i want to know what those all are but there's more because when and it's kind of like you're going below in statistical mechanics there's kind of all these molecules bouncing around and you might say we're just going to ignore we're just going to look at the aggregate densities of certain kinds of molecules but you can look at a lower level you can look at this whole graph of possible interactions and so the kind of the idea would be what you know is the only chemical observer one who just cares about overall concentrations or can there be a chemical observer who cares about this network of what happened and so that the question then is so let me give an analogy so this is where i think this is potentially very relevant to molecular molecular biology and molecular computing uh when we think about a computation usually we say it's input it's output we you know or chemistry we say there's this input we're going to make this molecule as the output but what if what we actually encode what if our computation whatever the thing we care about is some part of this dynamic network what if it isn't just the input and the output that we care about what if there's some dynamics of the network that we care about now imagine you're a chemical observer what is a chemical observer well in molecular biology there are all kinds of weird sorts of observers there are membranes that exist that have you know different kinds of molecules that can bind to them things like this it's not obvious that the from a human scale we just measure the concentration of something is the relevant story we can imagine that for example when we look at this whole network of possible reactions we can imagine you know at a physical level we can imagine well what was the actual momentum direction of that of that molecule what was it which we don't pay any attention to when we were just talking about chemical concentrations what was the orientation of that molecule these kinds of things and so here's here's the place where i'm i have a little suspicion okay so one of the questions in biology is what matters in biology and that is you know we have all these chemical reactions we have all these all these molecular processes going on in you know in biological systems what matters and you know one of the things is to be able to tell what matters well so a big story of the what mata's question was what happened in genetics in 1953 when dna was figured out how dna worked because before that time you know genetics have been all these different effects and complicated things and then it was realized ah there's something new a molecule can store information which wasn't obvious before that time a single molecule can store information so there's a place where there can be something important that's happening in molecular biology and it's just in the sequence that's storing information in a molecule so the possibility now is imagine this dynamic network this uh you know causal graphs and multi-way causal graphs and so on that represent all of these different reactions between molecules what if there is some aspect of that that is storing information that's relevant for molecular biology in the dynamic aspect of that yes that's right so that it's similar to how the structure of a dna molecule stores information it could be the dynamics of the system somehow stores information and this kind of process might allow you to give predictions of what that would be well yes but also imagine that you're trying to do for example imagine you're trying to do molecular computation okay you might think the way we're going to do molecular computation is we're just going to run the thing we're going to see what came out we're going to see what molecule came out this is saying that's not the only thing you can do there is a different kind of chemical observer that you can imagine constructing which is somehow sensitive to this dynamic network exactly how that works how we make that measurement i don't know but i have a few ideas but but um that that's what's important so to speak and that that means and by the way you can do the same thing even for touring machines you can say if you have a multi-way turing machine you can say how do you compute with a multi-way turing machine you cut you can't say well we've got this input and this output because the thing has all these threads of time and it's got lots of outputs and so then you say well what does it even mean to be a universal multi-way touring machine i don't fully know the answer to that but it has an interesting idea freak touring out for sure because then uh the dynamics of the the trajectory of the computation matters yes yes i mean but but the thing is that that so this is again a story of what's the observer so to speak in chemistry what's what's the observer there now to give an example of of where that might matter a very uh sort of uh present day example is in immunology um where you know we have whatever it is you know 10 billion different kinds of antibodies that are you know all these different shapes and so on we have i'm a trillion different kinds of t cell receptors that we can that we produce and you know the the traditional theory of immunology is this clonal selection theory where we're constantly producing randomly producing all these different antibodies and as soon as one of those binds to an antigen then that one gets amplified and we produce more of that antibody and so on um back in the 1960s um immunologist called nilsiona who was the guy who invented monoclonal antibodies various other things um kind of had this network theory of the immune system where it would be like well we produce antibodies but then we produce antibodies to the antibodies anti-antibodies and we produce anti-anti-antibodies and we get this whole dynamic network of interactions between different immune system cells and that was that that was kind of a qualitative theory at that time and it's i've been a little disappointed because i've been studying immunology a bit recently and i i knew something about this like 35 years ago or something and i knew you know i'd read a bunch of the books and i talked to a bunch of the people and so on and it was like an emerging theoretical immunology world and then i look at the books now and they're very thick because they've got you know there's just a ton known about immunology and you know all these different pathways all these different details and so on but the theoretical sections seem to have shrunk um and so it's um so the question is what you know for example immune memory where is the where does the immune memory reside is it actually some cell sitting in our bone marrow that is you know living for the whole of our lives that's going to spring into action as soon as we're shown the same antigen or is it something different from that is it something more dynamic is it something more like some network of interactions between these different kinds of immune system cells and so on and it's known that there are plenty of interactions between t cells and you know there's plenty of dynamics but what the consequence of that dynamics is is not clear and to have a qualitative theory for that doesn't it doesn't seem to exist in fact i was just just been trying to study this so i'm quite incomplete in my study of these things but i was a little bit taken aback because i i've been looking at these things and it's like and then they get to the end where they have the most advanced theory that they've got and it turns out it's a cellular automaton theory um it's like uh okay well at least i understand that theory yeah um but but uh you know i think that the possibility is that in um uh this is a place where if you want to know you know explain roughly how the immune system works it ends up being this dynamic network and then the the you know the immune consciousness so to speak the observer ends up being something that you know in the end it's kind of like does the human get sick or whatever but it's a it's something which is a complicated story that relates to this whole sort of dynamic network and so on and i think that's another place where this kind of notion of where i think multi-computation has the possibility see one of the things okay you can end up with something where yes there is a general relativity in there there but it turns up but it may turn out that the observer who sees general relativity in the immune system is an observer that's irrelevant to what we care about about the immune system i mean it could be yes there is some effect where you know there's some you know time dilation of t cells interacting with whatever but it's like that's an effect that's just irrelevant and the thing we actually care about is things about you know what happens when you have a vaccine that goes into some place in shape space and you know how does that affect other places in shape space and how does that spread you know what's the what's the analog of the speed of light in shape space for example that's and that's an important issue if you have one of these dynamic theories it's like you you know you you poke into shape space by having you know let's say a vaccine or something that has a particular configuration in shape space how how quickly as this dynamic network spreads out how quickly do you get sort of other antibodies in different places in shape space things like that when you say shape space you mean the shape of the molecules or those and then so this is like uh it could be deeply connected to the protein and multi-protein folding all of that kind of stuff to be able to say something interesting about the the dance of proteins that right exactly that actually has an impact on um helping develop drugs for example or has an impact on virology immunology helping too i think the big thing is you know when we think about molecular biology the um uh you know what what is the qualitative way to think about it you know in other words is it chemical reaction networks right is it you know genetics you know dna big you know big news it's kind of there's a digital aspect to the whole thing you know what is the qualitative way to think about how things work in biology um you know when we think about i don't know some phenomenon like aging or something which is a big complicated phenomenon which just seems to have all these different tentacles is it really the case that that can be thought about in some you know without dna when people were describing you know genetic phenomena there were you know dominant recessive this that and the other got very very complicated and then people realized oh it's just you know and and what is a gene and so on and so on and so on then people realize it's just base pairs and there's this digital representation and so the question is what is the overarching representation that we can now start to think about using a microbiology i don't know how this will work out and this is again one of these things where and and the place where that gets important is you know maybe molecular biology is doing molecular computing by using some dynamic process that is something where it is very happily saying oh i just got a result it's in the dynamic structure of this network now i'm going to go and do some other thing based on that result for example but we're like oh i don't know what's going on you know it's just we just measured them levels of these chemicals and we couldn't conclude anything but it just we're looking at the wrong thing and and so that's the that's kind of the the the potential there and it's it's um i mean these things are i don't know it's it's for me it's it's like i've not really that was not a view i mean i've thought about molecular computing for ages and ages and ages and i've always imagined that the big story is kind of the the original promise of nanotechnology of like can we make a molecular scale constructor that will just build build a molecule in any shape but i don't think i i'm now increasingly concluding that's not the big point the big point is something more dynamic that will be an interesting end point for any of these things but that's perhaps not the thing you know because the one example we have molecular computing that's really working is us biological organisms and you know maybe the thing that's important there is not uh this you know what chemicals do you make so to speak but more this kind of dynamic process it's a dynamic process and then you can have a good model like the hypergraph to to then explore ex what like simulate again make predictions and if they i think just have a way to reason about biology i mean it's it's hard you know but first of all biology doesn't have theories like physics you know physics is a much more successful sort of global theory kind of kind of area you know biology what are the global theories of biology pretty much darwinian evolution that's the only global theory of biology you know other any other theory is just a well the kidneys work this way this thing works this way and so on there isn't i suppose another global theory is digital information in dna that's another sort of global fact about biology but the the difficult thing to do is to match something you uh have a model of in the hyper graph to the actual like how do you discover the theory how do you how do you discover the theory okay you have something that looks nice and makes sense but like you have to match it to validation oh sure right and that's tricky because you're walking around in the dark not entirely i mean so so you know for example in what we've been trying to think about is take actual chemical reactions okay so you know one of my one of my goals is can i compute the primes with molecules okay that's if i can do that then i kind of maybe i can compute things and you know there's this nice automated lab these guys this emerald cloud lab people are built with wolfram language and so on that's an actual physical lab and you send it a piece of wolf and language code and it goes and you know actually does physical experiments and so one of my one of my goals because i'm not a test tube kind of guy i'm more of a software kind of person is can i make something where you know in this automated lab we can actually get it so that there's some gel that we made and you know the positions of the stripes i mean that would be that would be an example of of where and that would be with a particular uh you know framework for actually doing the molecular computing you know with particular kinds of molecules and and there's a lot of kind of ambient technological mess so to speak associated with oh is it carbon is it this is that you know is it important that there's a bromine atom here et cetera et cetera et cetera this is all chemistry that i don't know much about um and you know that's that's a sort of you know unfortunately that's down at the level you know i i would like to be at the software level not at the level of the transistors so to speak but in chemistry you know there's a certain amount we have to do i think at the level of transistors before we get up to being able to do it although you know automated labs certainly help in in setting that up i talked to a guy named charles hoskinson he mentioned that he's collaborating with you he's an interesting guy he sends me papers on uh speaking of automated theorem proving a lot he's exceptionally well read on that area as well so what's the nature of your collaboration with him he's the creator of cardano what's the nature of the color collaboration between cardano and the whole space of blockchain and wolfram or from alpha or from blockchain all that kind of stuff well okay we're segueing to a slightly different world but but um so although not completely unconnected right the whole thing is somehow connected i know i mean the the you know the strange thing in my life is i've sort of alternated between doing basic science and doing technology about five times in my life so far and the thing that's just crazy about it is you know every time i do one of these alternations i think there's not going to be a way back to the other thing and like i thought for this physics project i thought you know we're doing fundamental theory of physics maybe it'll have an application in 200 years um but now i've realized um actually this multi-computation idea is is applicable here and now it's and in fact it's also giving us this way i'll just mention one other thing and then to talk about blockchain um the um the question of um uh actually that relates to several different things but but um one of the things about about okay so our wolfram language which is our attempt to kind of represent everything in the world computationally and it's the thing i kind of started building 40 years ago in the form of actual wolfram language uh 35 years ago um it's kind of this idea of can we can we express things about the world in computational terms and you know we've come a long way in being able to do that well from alpha is kind of the consumer version of that where you're just using natural language as input the um and it turns it into our symbolic language and that's you know the symbolic language wolf and language is what people use and have been using for the last 33 years actually mathematica which is its first instantiation will be one third of a century old in uh in october um and um that it's it's kind of interesting what do you mean one third of a centuries i mean 33 or 30 what are we in the third 33 in the third um so but i've never heard of anyone celebrating that anniversary but i like it i know a third of a century though it's it's like cannot get many many slices of a century that are interesting yeah but but you know i think that the the thing that's really striking about that is that means you know including the whole sort of technology stack i built around that's about 40 years old and that means it's a significant fraction of the total age of the computer industry um and it's i mean i think it's cool that we can still run you know mathematica version 1 programs today and so on and and we've sort of maintained compatibility and we've been just building this big tower all those years of just more and more and more computational capabilities it's sort of interesting we just made this this picture um of kind of the different kind of threads of of of computational content of you know mathematical content and and you know uh all sorts of things with you know data and graphs and whatever else and what you see in this picture is about the first 10 years it's kind of like it's just a few threads and then then about maybe 15 20 years ago it kind of explodes in this whole collection different threads of all these different capabilities that are now part of language and representing different things in the world but the thing that was super lucky in some sense is it's all based on one idea it's all based on the idea of symbolic expressions and transformation rules for symbolic expressions which was kind of what i originally put into this smp system back in 1979 that was a predecessor of the whole world from language stack so that idea was an idea that i got from sort of trying to understand mathematical logic and so on it was my attempt to kind of make a general human comprehensible model of computation of just everything is a symbolic expression and all you do is transform symbolic expressions and you know in in retrospect i was very lucky that i understood as little as i understood then because had i understood more i would have been completely freaked out about all the different ways that that kind of model can can fail because what do you do when you have a a a symbolic expression you make transformations for symbolic expressions well for example one question is there may be many transformations that could be made in a very multi-computational kind of way but what we're doing is picking we're using the first transformation that applies and we keep doing that until we reach a fixed point and that's the result and that's kind of a very it's kind of a way of of sort of sliding around the edge of multi-computation and back when i was working on smp and things i actually thought about these questions about about how you know how what determines the this kind of evaluation path so for example you know you work out fibonacci you know fibonacci is a recursive thing f of n is f of n minus one plus f of n minus two and you get this whole tree of recursion right and there's the question of how do you evaluate that tree of recursion do you do it sort of depth first where you go all the way down one side do you do it breadth first where you're kind of collecting the terms together where you know that you know f of a plus f of seven f of seven plus f of six you can collect the f of sevens and so on these are um you know i didn't realize that at the time it's kind of funny i was working on on gauge field theories back in 1979 and i was also working on the evaluation model in smp and they're the same problem but it took me 40 more years to realize that and this question about how you do this sort of evaluation front that's a question of reference frames it's a question of of kind of the um the story of i mean that that's that is basically this question of in what order is the universe evaluated and that and so what you realize is there's this whole sort of world of different kinds of computation that you can do sort of multi-computationally and that's a that's an interesting thing it has a lot of implications for distributed computing and so on it also has a potential implication for blockchain which we haven't fully worked out which is some and this is not what we're doing with cardano but but this is a different thing um the um this is something where uh one of the questions is um when you have in a sense blockchain is a deeply sequentialized story of time because in blockchain there's just one copy of the of the ledger and you're saying this is what happened you know time has progressed in this way and the other little things around the edge as as you try and reach consensus and so on and and uh you know actually we just recently we've had this little conference we organized about the the theory of distributed consensus because i realized that a bunch of interesting things that some of our science can tell one about that but that's a different let's let's not go down that that part yeah but distributed consensus is that still has a sequential there's like there's still sequentiality so just don't tell me you're thinking through like how to apply multi-computation to uh blockchain yes and so so that becomes a story of you know instead of transactions all having to settle in one ledger it's like a story of all these different ledgers and they all have to have some ultimate consistency which is what causal and variance would give one but it can take a while and the it can take a while as kind of like quantum mechanics so it's kind of what's happening is that these different paths of history that correspond to you know in one part of history you got paid this amount in another path of history you got paid this amount in the end the universe will always become consistent now now the way it will it works is okay it's a little bit more complicated than that what happens is the way space is knitted together in our theory of physics is through all these events and the the the idea is that the way that economic space is knitted together is between is there these autonomous events that essentially knit together economic space so there are all these threads of transactions that are happening and the question is can they be made consistent are there is there something forcing them to be sort of a consistent fabric of economic reality and sort of what this has led me to is trying to realize how does economics fundamentally work and you know what is economics and uh you know what what are the atoms of economics right so to speak and so what i've kind of realized is that that sort of the perhaps i don't even know if this is right yet there's sort of events in economics of transactions there are states of agents that are kind of the atoms of economics and then transactions are kind of agents transact and some transact in some way and that's an event and then the question is how do you knit together sort of economic space from that what is there an economic space well all these transactions there's a whole complicated collection of possible transactions but one thing that's true about economics is we tend to have the notion of a definite value for things we could imagine that you know you buy a cookie from somebody and they want to get a movie ticket and there is some way that ai bots could make some path from the cookie to the movie ticket by all these different trans intermediate transactions but in fact we have an approximation to that which is we say they each have a dollar value and we have this kind of numeric concept of there's just a way of kind of of of taking this whole complicated space of transactions and parsing it in something which is a kind of a simplified thing that is kind of like our parsing of physical space and so my my guess is that the uh yet again i mean it's crazy that all these things are so connected this is another multi-computation story another story of where what's happening is that the economic consciousness the economic observer is not going to deal with all of those a different microscopic transactions they're just going to parse the whole thing by saying there's this value it's a number and that's that's their understanding of their summary of this economic network and there will be all kinds of things like there are all kinds of arbitrage opportunities which are kind of like the quantum effects in this whole thing and um that's uh you know and places where there's where there's sort of different paths that can be followed and and so on and there's so the question is can one make a sort of global theory of economics and then my test case is again what is time dilation and economics and and i know for you know if you imagine a very agricultural economics where people are growing lettuces and fields and things like this and you ask questions about well if you're transporting lettuces to different places you know what is the value of the lettuces after you have to transport them versus if you're just sitting in one place and selling them you can kind of get a little bit of an analogy there but i think there's a there's a better and more complete analogy and that's the question of is there a theory like general relativity that is a global theory of economics and is it about something we care about it could be that there is a global theory but it's about a feature of economic reality that isn't important to us now another part of the story is can one use those ideas to make essentially a distributed blockchain a distributed generalization of blockchain kind of the quantum analog of money so to speak where where you have for example you can have uncertainty relations where you're saying you know well if i if i insist on knowing my bank account right now there'll be some uncertainty if i'm prepared to wait a while then it'll be much more certain um and so there's you know is there a way of using and so we've made a bunch of prototypes of this um which i'm not yet happy with because what i realized is to really understand these prototypes actually have to have a foundational theory of economics and so that's kind of a uh you know it may be that we could deploy one of these prototypes as a practical system but i think it's really going to be much better if we actually have an understanding of how this plugs into kind of the economics that means like a fundamental theory of transactions between entities well that's that's what you mean by economics yes i think so but i mean you know how how there emerge sort of laws of economics i don't even know and i've been asking friends of mine who are who are economists and things what is economics you know is it an axiomatic theory is it a theory that is a kind of a qualitative description theory is it you know what kind of a theory is it is it a theory you know what kind of thinking it's like like in in biology and evolutionary biology for example there's a certain there's a certain pattern of thinking that goes on in evolutionary biology where if you're a you know a good evolutionary biologist somebody says that creature has a weird horn and they'll say well that's because this and this and this and the selection of this kind and that kind and that's the story and it's not a mathematical story it's a story of a different type of thinking about these things by the way evolutionary biology is yet another place where it looks like this multi-computational idea can be applied and that's where where maybe speciation is related to things like event horizons and there's a whole whole other kind of world of that but because it seems like this kind of model can be applicable in so many aspects like at the different levels of understanding of our reality so it could be the biology of the chemistry at the physics level right the economics and you could potentially the thing is it's like okay sure at all these levels it might rhyme it might make sense as a model the question is can you make useful predictions that's one of these levels that's that's right and that's that's really a question of you know it's a weird situation because it's a situation where the model probably has definite consequences the question is are there consequences we care about yeah and and that's some uh you know and so so in the case of in the economic case the um uh we're um so you know the one one thing is this this idea of using kind of physics-like notions to construct a kind of distributed analog blockchain okay the much more pragmatic thing is that it's a different direction and it has to do with this computational language that we built to describe the world that knows about you know different kinds of cookies and knows about different cities and knows about how to compute all these kinds of things one of the things that is of interest is if you want to run the world you need you know with with with contracts and laws and rules and so on there are rules at a human level and there are kind of um things like and so this this gets one into the idea of computational contracts you know right now when we write a contract it's a piece of legalese it's you know it's just written in english and it's not something that's automatically analyzable executable whatever else it's just english you know back in gottfried leibniz back in you know 1680 or whatever was like um i'm gonna you know figure out how to use logic to decide legal cases and so on and he had kind of this idea of let's make a computational language for the huma the human law um forget about modeling nature forgot about natural laws what about human law can we make kind of a computational representation of that well i think finally we're close to being able to do that and one of the projects that i hope to get to as soon as the there's a little bit of slowing down of some of this cambrian explosion that's happening as a project i've been meaning to really do for a long time which is what i'm calling a symbolic discourse language it's is just finishing the job of being able to represent everything like the conversation we're having in computational terms and one of the use cases for that is computational contracts another use case is something like the the constitution that says what the ai's what we want the ais to do so but this is useful so you're saying uh so these are like you're saying computational contracts but smart contracts this is what's in the domain of cryptocurrencies known as smart contracts and so the the language you've developed this symbolic or seek to further develop symbolic discourse language enables you to uh write a contract and right so write a contract that richly represents some aspect of the world yeah but so so i mean smart contracts tend to be right now mostly about things happening on the blockchain yes and sometimes they have oracles in fact our wolfram alpha api is is the main thing people use to get information about the real world so to speak yeah within smart contracts so well from alpha as it stands is a really good oracle yes whoever wants to use it that's perhaps where the relationship with cardano is yeah that's how we started getting involved with blockchains is we realized people were using you know wolfman alpha as the oracle for smart contract so to speak and so that got us interested in blockchains in general and what was ended up happening is orphan language is with its symbolic representation of things is really very good at representing things like blockchains and so i think we now have them we don't really know all the comparisons but we now have a really nice environment within wolverine language for dealing with the sort of uh you know for representing what happens in blockchains for analyzing what happens with blockchains we have a whole effort in blockchain analytics um and uh you know we've sort of published some samples of how that works but but it's you know because our technology stack welcome language and mathematica are very widely used in the quant finance world there's a there's a sort of immediate uh sort of um uh co-evolution there of of sort of the quant finance kind of thing and blockchain analytics and that's um so so it's kind of the representation of blockchain in computational language then ultimately it's kind of like how do you run the world with code that is how do you write sort of all these things which are right now regulations and laws and contracts and things in computational language and kind of the the ultimate vision is that sort of something happens in the world and then there's this giant domino effect of all these computational contracts that trigger based on the thing that happened and there's a there's a whole story to that and of course you know i i like to always pay attention to the latest things that are going on and i i really i kind of like blockchain because it's a it's a it's another rethinking of kind of computation it's kind of like you know cloud computing was a little bit of that of sort of persistent um kind of uh computational resources and so on and uh you know this multi-computation is a big rethinking of kind of what it means to compute blockchain is another bit of rethinking of what it means to compute the idea that you lodge kind of these autonomous lumps of computation out there in the blockchain world and and one of the things that um just sort of uh for fun so to speak is we've been doing a bit of stuff with nfts and we just did some nfts on gardano and we'll be doing some more and uh you know we did some cellular automaton nfts on cadance people like quite a bit um and you know one of the things i've realized about about nfts is that there's kind of this notion and we're really working on this you know i like recording stuff you know one of the things that's come out of of kind of my science i suppose is this this history matters type type story of you know it's not just the current state it's the history that matters and i've kind of i don't think this is actually realizing maybe it's not coincidental that i'm sort of the human who's recorded more about themselves than anybody else and then i end up with these science results that say history matters which was not those those things i didn't think those were connected but they're at least correlated yes yeah right so you know this question about sort of recording what has happened and and having sort of a permanent record of things one of the things that's kind of interesting there is you know you put up a website and it's got a bunch of stuff on it but you know you have to keep paying the hosting fees or the things going to go away but one of the things about blockchain is kind of interesting is if you put something on a blockchain and you pay you know your commission to get that thing you know put on you know mind put on the block blockchain then then in a sense everybody who comes after you is you know they are motivated to keep your thing alive because that's what keeps the consistency of the blockchain so in a sense with sort of the nft world it's kind of like if you want to have something permanent well at least for the life of the blockchain but but even if the blockchain goes out of circulation so to speak there's going to be enough value in that whole collection of transactions that people are going to archive the thing but that means that you know pay once and you're kind of you're lodged in the blockchain forever and so we've been kind of playing around with um a sort of a hobby thing of of mine of of thinking about sort of the nfts and how you um and sort of the consumer idea of kind of the it's the it's the anti you know it's the opposite of the snapchat view of the world so there's a permanence to it this heavily incentivized and uh thereby you can have a permanence of history right and that's that's that's kind of the um now you know so that's so that's one of the things we've been doing with cardano and it's kind of fun i think that that um i mean this whole question about you know you mentioned automated theorem proving and blockchains and so on and as i've thought about this kind of physics inspired distributed blockchain obviously they're the sort of the proof that it works that they're no double spends there's no whatever else that proof becomes a very formal kind of almost a matter of physics so to speak um and uh you know it's been it's been an interesting thing for the for the practical blockchains to do kind of actual automated film proving and i don't think anybody's really managed it in an interesting case yet it's a thing that people you know aspire to but i think it's a challenging thing because basically the point is one of the one of the things about proving correctness of something is well you know people say i've got this program and i'm going to prove it's correct it's like what does that mean you have to say what correct means i mean it's it's kind of like then you have to have another language and people were very confused back in past decades of you know oh we're going to prove the correctness by representing the program in another language which we also don't know whether it's correct and you know often by correctness we just mean it can't crash or it can't scribble on memory but but the thing is that there's this complicated trade-off because as soon as there's as soon as you're really using computation you have computational irreducibility you have undecidability if you want to use computation seriously you have to kind of let go of the idea that you're going to be able to box it in and say we're going to have just this happen and not anything else i mean this is a this is an old fact i mean girdle's theorem tries to say you know piano arithmetic the axioms of arithmetic can you box in the integers and say these axioms give just the integers and nothing but the integers go to theorem showed that wasn't the case there's a you know you can have all these wild weird things that are obey the piano axioms but aren't integers and there's this kind of infinite hierarchy of additional axioms you would have to add and it's kind of the same thing you you don't get to you know if you want to say i want to know what happens you're boxing yourself in and there's a limit to what can happen so to speak so it's a it's a complicated trade-off and it's a it's a it's a big trade-off for ai so to speak it's kind of like do you want to let computation actually do what it can do or do you want to say no it's very very boxed in to the point where we can understand every step and that's a that's kind of a thing that that um that becomes difficult to do but that that's some i mean in in general i would say one of the things that's kind of complicated in my uh sort of life in the whole sort of story of computational language and all this technology and science and so on i mean i i kind of in in the flow of one's life it's sort of interesting to see how these things play out because i you know i've kind of concluded that i'm in the business of making kind of artifacts from the future which means you know there are things that i've done i don't know this physics project i don't know whether anybody would have gotten to it for 50 years you know the fact that mathematica is a third of a century old and i know that a bunch of the core ideas are not well absorbed i mean that is people finally got this idea that i thought was a triviality of notebooks that was 25 years and um you know some of these core ideas about symbolic computation and so on are not not absorbed i mean people people use them every day in wolfram language and you know do all kinds of cool things with them but if you say what is the fundamental intellectual point here it's it's not well absorbed and it's it's something where you kind of realize that you're you're sort of building things and i i kind of made this this thing about you know we're building artifacts from the future so to speak and i mentioned that it's our uh we have a a conference ever it's coming up actually in a couple of weeks our annual technology conference uh where we talk about all the all the things we're doing um and uh you know so i was talking about it last year about you know we're making artifacts from the future and i was kind of like i had some some version of that that was kind of a dark and frustrated thing of like you know i'm building things which nobody's going to care about until long after i'm dead so to speak but um but but then i i realized you know people were sort of telling me afterwards you know that's exactly how you know we're using wolfman language in some particular setting in you know some computational acts field or some organization or whatever and it's like people are saying oh you know what did you manage to do you know well we know that in principle it will be possible to do that but we didn't know that was possible now and it's kind of like that's the that's sort of the business we're in and in a sense with some of these ideas in science um you know i feel a little bit the same way that there are some of these things where you know some some things like for example this whole idea well so so to to relate to another sort of piece of history in the future one of you know i mentioned we mentioned at the beginning kind of complexity as this thing that i was interested in back 40 years ago and so on where does complexity come from well i think we kind of nailed that the answer is in the computational universe even simple programs make it and that's kind of the secret that nature has that allows you to make it so so that's kind of the um uh that that's that part but the bigger picture there was this idea of this kind of computational paradigm the idea that you could go beyond mathematical equations which have been sort of the primary modeling medium for 300 years and so it was like look it is inexorably the case that people will use programs rather than just equations and you know i was saying that in the 1980s and people were you know i published my big book new kind of science that'll be 20 years ago uh next year so in 2002 and people are saying oh no this can't possibly be true you know we know for 300 years we've been doing all this stuff right to be fair i now realize on a little bit more analysis of what people actually said in pretty much every field other than physics people said oh these are new models that's pretty interesting in physics people were like we've got our physics models we're very happy with them yeah in physics there's more resistance because of the attachment and the power of the equations right the idea that programs might be the right way to approach right uh this field was uh there's some resistance and like you're saying it takes time for somebody who likes the idea of time dilation and all these applications i thought you would understand this yeah right but but you know and computational introduceability yes exactly but but i mean it is really interesting that just 20 years a span of 20 years it's gone from you know pitchforks and horror to yeah we get it and um you know it's helped that we've you know in our current effort in fundamental physics we've gotten a lot further and we've managed to put a lot of puzzle pieces together that that makes sense but the thing that i've been thinking about recently is this field of complexity so i i've kind of was a sort of a a field builder back in the 1980s i was kind of like okay you know can we uh you know i i'd understood this point that there was this sort of fundamental phenomenon of complexity and showed up in lots of places and i was like this is an interesting sort of field of science and i was uh recently was reminded i was at this the very first sort of get-together of what became the santa fe institute and i was like in fact there's even an audio recording of me sort of saying people have been talking about oh what should this play you know outfit do and i was saying well there is this thing that i've been thinking about it's this kind of idea of complexity nice and um it's kind of like and that's that's what that ended up you implanted the seat of complexity to santa fe that's beautiful it's a beautiful vision but but i mean so that but what's happened then is this idea of complexity and you know ken you know and i started the first research center at university of illinois for doing that in the first journal complex systems and so on and uh and it's kind of an interesting thing in in my life at least that it's kind of like you plant this seed you have this idea it's a kind of a science idea you have this idea of sort of focusing on the phenomenon of complexity the deeper idea was this computational paradigm but the the nominal idea is this kind of idea of complexity okay then you roll time forward 30 years or whatever 35 years whatever it is um and you say what happened okay well now there are a thousand complexity institutes around the world um i think more or less we've been trying to count them um and uh you know there are 40 complexity journals i think um and so it's kind of like what actually happened in this field right and and i look at a lot of what happened and i'm like uh you know i have to admit to some eye rolling so to speak because it's kind of like like what is what what's what what's actually going on well what people definitely got was this idea of computational models and then they got but they thought one of the one of the kind of cognitive mistakes i think is they say we've got a computational model and it and we're looking at a system that's complex and our computational model gives complexity by goalie that must mean it's right and unfortunately because complexity is a generic phenomenon and computational irreducibility is a generic phenomenon that actually tells you nothing and so then the question is well what can you do you know there's a a lot of things that have been sort of done under this banner of complexity and i think it's been very successful in providing sort of an interdisciplinary way of connecting different fields together which is powerful in itself right i mean that's a biology in economics and yeah it is right and it's a good organizing principle but but in the end a lot of that is around this kind of computational paradigm computational modeling that's the raw material that powers that kind of uh that kind of correspondence i think and the question is sort of what is the you know i was just thinking recently you know we've been i mean the the other we've been we've been for years people told me you should start some will from institute that does basic science you know all i have is a company that that builds software and we you know we have a little piece that does basic science as kind of a hobby people are saying you should start this wolfram institute thing and and i've been you know because i've known about lots of institutes and i've seen kind of that flow of money and and kind of you know what happens in different situations and so on so i've been kind of reluctant but uh but i've i've i have realized that you know what we've done with our company over the last 35 years you know we built a very good machine for doing r d and you know innovating and creating things and i just applied that machine to the physics project that's how we did the physics project in a fairly short amount of time with a you know efficient machine with you know various people involved and so on um and so you know it it works for basic science and it's like we can do more of this and so biology and chemistry so it's it's become an institute yes well it needs to become an institution an official institute right right but the the thing that so i was thinking about okay so what do we do with complexity you know what what there are all these people who've you know what what should happen to that field yeah and what i realized is there's kind of this area of foundations of complexity that's about these questions about simple programs what they do that's far away from a bunch of the detailed applications the people well it's not far away it's it's the it's the under you know the bedrock underneath those applications so i realized recently this is my a recent kind of little uh innovation of a sort um a post that i'll do very soon um about um uh kind of you know the foundations of complexity what really are they i think they're really two ideas two conceptual ideas that i hadn't really enunciated i think before one is what i call meta-modeling the other is ruleology so what is meta modeling so metamodeling is you've got this complicated model and it's a model of you know hedgehogs interacting with this interacting with that and the question is what's really underneath that what is it you know is it a turing machine is it a cellular automaton you know what is the underlying stuff underneath that model and so there's this kind of meta science question of given these models what is the core model and i realized i mean to me that's sort of an obvious question but then i realized i've been doing language design for 40 years and language design is exactly that question you know underneath all of this detailed stuff people do what are the underlying primitives and that's a question people haven't tended to ask about models they say well we've got this nice model for this and that and the other what's really underneath it and what you know because once you have the thing that's underneath it well for example this multi-computation idea is an ultimate meta modeling idea because it's saying underneath all these fields is one kind of paradigmatic structure and you know you can you can imagine the same kind of thing much more sort of uh much sort of shallower levels in in um in different kinds of modeling so this the first activity is this kind of meta modeling the the kind of the the models about models so to speak you know what is the what's what's you know drilling down into models that's one thing the other thing is this this thing that i think we're going to call ruleology which is kind of the okay you've got these simple rules you've got cellular automata you've got turing machines you've got substitution systems you've got registered machines got all these different things what do they actually do in the wild and this is an area that i've spent a lot of time you know working on it's a lot of stuff in my new kind of science book is about this um you know this new book i wrote about combinators is is full of stuff like this and and this journal complex systems has lots of papers about these kinds of things but but there isn't really a home for people who do or whatever as you call the basic science of rules yes yes right so it's it's like you've got some what is it is it mathematics no it isn't really like mathematics in fact from my now understanding of meta mathematics i understand that it's the molecular dynamics level it's not the level that mathematicians have traditionally cared about it's not computer science because computer science is about writing programs that do things you know that were for a purpose not programs in the wild so to speak it's not physics it doesn't have anything to do with you know maybe underneath some physics but it's not physics as such so it just hasn't had a home and if you look at you know but what's great about it is it's a surviving field so to speak it's something where you know one of the things i i find sort of inspiring about mathematics for example is you look at mathematics that was done you know in ancient greece ancient you know babylon egypt and so on it's still here today you know you find an icosahedron that somebody made in ancient egypt you look at it oh that's a very modern thing it's an icosahedron you know it's it's a timeless kind of kind of activity and this idea of studying simple rules and what they do it's a timeless activity and i can see that over the last 40 years or so as you know even with cellular automata it's kind of like you know you can sort of catalogue what what are the different cellular autonomics are used for and you know like the the simplest rules like like one you might even know this one rule 184 it's um rule 184 is a minimal model for road traffic flow and you know it's also a minimal model for various other things but it's kind of fun that you can literally say you know rule 90 is a minimal model for this and this and this rule 4 is a minimal model for this and it's kind of remarkable that you can just by in this raw level of this kind of study of rules they then branch they're the raw material that you can use to make models of different things so it's a it's a very pure basic science but it's one that you know people have explored it but they've been kind of a little bit in the wilderness and i think you know one of the things that i would like to do finally is is uh you know i always thought that sort of this notion of pure and chaos pure and nks being the acronym for my book new kind of science um was um was something that people should be doing and you know we tried to figure out what's the right institutional structure to do this stuff you know we we dealt with a bunch of universities oh you know can we do this here well what department would it be in it well it isn't in a department it's it's its own new kind of thing that's why that's why the book was called the new kind of science um it's kind of the the because that's an increasingly good description of what it is so to speak we're actually we were thinking about kind of the ruleological society because we're realizing that it's kind of it's it's some you know there's a there's it's very it's very interesting i mean i've never really done something like this before because there's this whole group of researchers who are who've been doing things that are really in some cases very elegant very surviving very solid you know here's this thing that happens in this very abstract system but it's like it's like what is that part of you know it's it doesn't have a a home and i think that's something i you know i kind of fault myself for not having been more you know when complexity was developing in the 80s i didn't understand the the the danger of applications that is it's really cool that you can apply this to economics and you can apply it to evolutionary biology and this and that and the other but what happens with applications is everything gets sucked into the applications and the pure stuff it's like the pure mathematics there isn't any pure mathematics so to speak it's all just applications of mathematics and i i failed to kind of make sure that this kind of pure area was was kind of um maintained and and and developed and i think now you know one of the things i i want to try to do and and you know it's a funny thing because i'm used to look i've been a a tech ceo for more than half my life now so you know this is what i know how to do and um you know i can i can make stuff happen and get projects to happen even as it turns out basic science projects in that kind of setting and and how that translates into kind of you know there are a lot of people working on for example our physics project sort of distributed through the academic world and that's working just great but the question is you know can we have a sort of accelerator mechanism that makes use of kind of what we've learned in in sort of r d innovation and you know but on the other hand it's a funny thing because you know in a company in the end the thing is you know it's a company it makes products that sell things sells things to people um in you know when you're doing basic research one of the challenges is there isn't that same kind of of sort of mechanism and so it's it's it's you know how do you drive the thing in a in a kind of a led kind of way so that it really can can make forward progress rather than you know what can often happen in you know in in academic settings where it's like well there are all these flowers blooming but it's not clear that they're you know that it's that yeah they have a central mission and a drive just like you do with the company that's delivering a big overarching product and that's that's uh but the the challenges you know when you have a the the the economics of the world are such that you know when you're delivering a product and people say well that's useful we'll buy it and then that kind of feeds back and okay then you can then you can pay the people who build it to eat you know so they can eat and so on and with basic science the the payoff is very much less visible and and you know with this physics project as i say the big surprise has been that i mean you know for example well the big surprise with the physics project is that it's looks like it has near-term applications and i was like i'm guessing this is 200 years away it's um i was kind of using the analogy of of you know newton uh starting a satellite launch company which would have been kind of wrong time um and uh you know but but it turns out that's not the case but but we can't guarantee that and if you say we're signing up to do basic research basic radiology let's say and you know and we can't we don't know the horizon you know it's it's an unknown horizon it's kind of like an undecidable kind of proposition of when is this proof going to end so to speak when is it going to be something that that that gets applied i i hope this is this becomes a vibrant new field of radiology i love it like i told you many many times it's one of the most amazing ideas that has been brought to this world so i hope you get a bunch of people to explore this world thank you once again for spending your really valuable time with me today fun stuff thank you thanks for listening to this conversation with stephen wolfram to support this podcast please check out our sponsors in the description and now let me leave you with some words from richard feynman nature uses only the longest threads to weave her patterns so each small piece of our fabric reveals the organization of the entire tapestry thank you for listening and hope to see you next time you

Channel: Lex Fridman

Views: 1,104,432

Keywords: agi, ai, ai podcast, artificial intelligence, artificial intelligence podcast, black holes, cellular automata, computational irreducibility, computer science, intelligence, lex ai, lex fridman, lex jre, lex mit, lex podcast, math, mathematics, mit ai, quantum mechanics, ruliology, stephen wolfram, theoretical physics, wolfram alpha, wolfram mathematica, wolfram physics project

Id: 4-SGpEInX_c

Length: 218min 43sec (13123 seconds)

Published: Tue Oct 26 2021

Reddit Comments

[u/mostinho7]

Blew my mind when he said the universe does everything it can do at once (parallel, asynchronous), while our conscious experience is a single thread of time

[u/needsMoreGoodstuff]

Every other guest talks about these great but fairly everyday topics, like bitcoin, drug addiction, ai...

And then here comes Stephen Wolfram. "I think I know why the universe exists. Also here's the answer for basically everything."

Absolute mental unit.

[u/convie]

One of the few guests where it all goes over my head.

[u/UncleWeyland]

I don't disagree with Scott Aaronson often, but I genuinely think Wolfram and Gorard might be onto something promising here. I'm not a domain expert by any stretch though, so take that with a grain of salt.

What are the odds that a random computational formalism can extract both QM and GR behaviors? Is this really just a case of "fine tuning" a theory until it spits out known models?

Hopefully they can extract more testable hypotheses out of it than some extremely difficult to detect anomaly in gravitational waves from rotating black holes.

[u/mathplusU]

Stephen Wolfram is going to go down as the Einstein of our generation. Came from outside the establishment revolutionized the world of physics. I hope his ideas start gaining traction and begin to get taken more seriously and he one days wins a Nobel Prize.

(Just gotta run the program a few more steps forward)

[u/qrhn]

Always enjoy this guy!

[u/HBJ10]

A fascinating episode - so to speak! 🤣

[u/motherfuckingriot]

I love the idea of space being how things connect and time being how things compute. That clicks for me.

[u/MajorValor]

Was Lex sick or something during this interview? He seemed off…can’t put my finger on it. Hope he’s ok.