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

the following is a conversation with. Steven 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 wolm Alpha. wolm language and the new Wolfram. physics project this conversation is a. wild technical roller coaster 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 Dylan calls. fun this is leex Freedman podcast to. support it please check out the sponsors. in the description and now here's my. conversation with Steven. wolam almost 20 years ago you publ.

lished 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 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.

some 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. is 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 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 got just sort of circles and 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 it. 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 of the 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 mathematic. or morphan language thing called s 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 the path.

that I happen 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 autometer. um actually I didn't know at first they. were called cellular autometer but I. found that out um subsequently but it's. just a 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 its two Neighbors. on the previous step and I had initially. thought that's you know sufficiently. simple setup is 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 is pretty. easy to do um I mean it probably took a. few hours um originally and um the uh. 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. result 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 oneline program or something it's. possible to get very complicated. behavior my my favorite example is this. thing called Rule 30 which is a. particular cellular automon rule you. just started off from one black cell and. it makes this really complicated pattern. and so so that for me was sort of a 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 allh. 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 the 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 it's. not e to know what R right well no the. ru rules can generate just.

Randomness right well that that's not. obvious in other words that's not. obvious it's not obvious at all and it. wasn't what I expected it's not what. people's intuition had been and 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 in science fiction movies. right you can tell it's a robot CU 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 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 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. uh for predicting the middle column of. rule 30 anybody 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 thing is 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 F first of all do the. digits of pi ever repeat well 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 two or however you work it out do. they all occur with equal frequency mhm.

nobody knows that's far away from what. can be understood mathematically at this. point and um that's that's kind of uh. but I'm I'm even looking for step one. which is prove that the that that the. center column doesn't repeat and then. prove other things about it like equ. distribution 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 uh 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 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. complexity still there might be some.

systems where it's uh filtering. Randomness on the inputs well the point. is when you have quotes Randomness than. 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 era in. 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 it its. popular version is chaos theory um and. example of what people study a lot is. the shift map which is basically taking. 2x mod one two 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. H it's not obvious that you would. excavate all of those digits and if. you're for example making a theory out. don't know fluid Mechanics for example. if there was that phenomenon and 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 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 there. 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 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 featur oid 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 fun. 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 MH I didn't think that was a. question that I would you know I thought. that was a far out there metaphysical. kind of um thing uh even the. philosophers have stayed away from that. question for the most part it's so such. a kind of uh you know difficult to. address question but I 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 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 the universe so 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 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 CU if you want. to know why the universe exists you kind. of have to know what the universe is. made of and uh I think. the um well let 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 act 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 2 plus 2 equals 4 but. that's different from saying there's two. a pile of two rocks and another pile of.

two rocks and somebody 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 if we say. what do we what do 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 Consciousness is. part of the fabric of the universe so. we're in it yes we're in it and and and. maybe I should maybe I should start off. by saying something about the. Consciousness story because that that's. some yes uh maybe we should begin even. before that at the very base layer of. the wolf from 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 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 um 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 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 a 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 about what happens. in the world why aren't we why are we.

able to predict anything why are we able. to sort of 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 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 they're 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 metam mathematics I I'd be. realizing that i' something I've long. believed we can talk about it uh 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. can explain a little bit about how the.

how the model works but basically we can. maybe ask you the following question so. it's easy through words to describe how. cellular atomo Works you've you've. explained this and uh it's the. fundamental mechanism by which you in. your book and you kind of science. explored the idea of complexity and how. to do science in this world of Island. reducible islands and irreducible. general irreducibility okay okay so how. does the model of hypergraphs differ.

from cellular aoma and how does the idea. of multic computation differ like maybe. that's a way to describe it all right we. we're yeah right this is a you know my. life is like all of our Lives something. of a story of computational. irreducibility 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 MH and you know a.

key observation the 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 uclid. 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 of the first thing in our. physics project is theide 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 a few were computer. person you give them uu IDs or something. but um 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 there are.

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 low 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 uh 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 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 assume odd enough The Vortex. looks like an atom itself like a basic. El so there's a levels of abstraction if. you squint and kind of uh blur things. out it looks like at every level of. abstraction you can Define what is a. basic individual entity yes but but you. know in in this model. there's a bottom level you know there's.

an elementary length maybe 10 100 10us. 100 m let's say which is really small. you know proton is 10- 15 M the smallest. we've ever been able to sort of see. where the particle accelerator is around. 10us 21 M so you know if we don't know. precisely what the correct scale is but. it's perhaps over the order of 10us 100. Metter 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 10 Theus 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 a 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. um we know Plank's constant in 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 plank scale 10- 34 me. which is the sort of the the combination.

of of Plank's constant and the. gravitational constant the speed of. light that gives you that kind of length. um 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 see if. I remember that number that number is 10. to 170 I think and and and so it's a big. number but. that number then connects you know sort.

of modifies what you might think from. all these plank uh units to give you the. things we're giving and there's been. sort of a mystery actually in the in the. there a more technical physics thing. that the plank Mass the plank energy um. plank energy is actually surprisingly. big the plank length is Tiny 10- 34 M. that you know plank time 10- 43 M I. think seconds I think um but the plank. 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 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 they are individual molecules. hitting the space plane not a continuous. fluid the question is what is the. analogous kind of um 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's it. looks as if that's a case where. essentially the the structure of. SpaceTime 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 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 those don't come out the. way one would expect based on having a. continuous structure of SpaceTime that. is something where you can kind of see. through to the discrete structure um we. don't know that yet so you can you maybe. elaborate a little bit deeper how. microscope that can see to 10. Theus 100. how rotating black holes and uh.

presumably the the the detailed accurate. detection of gravitational waves from. say black holes can reveal the. discreetness of space okay first thing. is what is a black hole actually we we. need to go a little bit further in the. in the story of what space time is cu I. explained a little bit about what space. is but I 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 time in this. 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. spaces and their connections you can. think about these things as a hyper.

graph you know a graph is just you. connect nodes to nodes but a hyper graph. 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 that's just the. relations between atoms of space are the. hyper edges of the hypergraph and so we. 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 an.

every feature of what we experience in. the world is a feature of that that. hypergraph that spatial hypergraph so. then the question is well how does what. what does that spatial hypergraph do. well the idea is that there are rules. that that update that spatial hypergraph. and you know in a cellular autometer and. you've just got this line of cells and. you just say at every step at every time. step you 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 uh that's the way it works now in. this hypergraph 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. will come to is this multicomp. 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 fun Al asynchronous and. parallel yes yes which is very.

uncomfortable for the human brain that. seeks for things to be sequential yes. 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 parceling 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 you know 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 experience is. 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 so I mean just to go.

on with kind of the the basic setup it's. uh so we got this spatial hypergraph. it's got all these atoms of space. they're getting they're getting these. little clumps of atoms of space are. getting turned into other clumps of. atoms of space and that's happening. everywhere in the universe all the time. and so one thing that'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 uh 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 when 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 SpaceTime 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. a more extreme version of that so so. anyway the the the thing that that's. happening is we got space we've got this. notion of time so time is this kind of. this rewriting of the hypergraph and one. of the things that's important about. that time is this sort of. computationally irreducible process. there something you know time is not. something where in kind of the. mathematical view of of time tends to be. time is just a CO ordinate 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. there related by you know the panker.

group and and lawence Transformations. and relativity and all these kinds of. things and you know space and time you. know there are all these kind of sort of. folk stories you can tell about why. space and time are 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 there few bits and pieces.

here which 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 the an. elementary event is a little piece of. hypergraph got Rewritten and that means.

a few hyper edges of the hypergraph were. consumed by the event and you produce. some other hyper edges 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 uh 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 uh. sort of saying well I've got this. hypergraph 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 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 uh 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 oface 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 touring machine touring. machines have just this one update head. which does something and otherwise the. touring machine just does nothing right.

and and the touring 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 touring 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 your 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. relationship between the things that. happened actually were yeah but if I.

somehow record like a trace of this I. guess would be called multic computation. can't I uh then look. back in the you record the trace some. you place throughout the UN like. throughout like a log that records in my. own pocket of in this hypergraph can't 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 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 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're just saying 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 a. delayed well there's a okay so there's. there's 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 mhm. 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 a. 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 hypergraph 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. hypergraph now and then this one later.

and etc etc etc all those different. Paths of History correspond to these. Quantum Quantum paths in in 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 hyper graphs. because there's a whole graph. isomorphism Story and there's a whole. very elaborate set of where caal. invariance comes in among other things. right yes that 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 etc etc etc 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 parts 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. invariance thing but that's and the fact. that that does happen a little bit is.

what causes little Quantum effects and. that um 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 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. the this kind of idea of we're 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 10 400 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. and allery 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 of. molecules that we notice and then are. lots of details we don't notice when you. say we do you mean the tools of physics. or do you mean literally the human brain. and its perception system well okay so. the human brain is where it starts but. we built a bunch of instruments that 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 so it's always. just an extension of the conscious. experience even or sensory experience. sensory experience. but sensory experience is 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 20th. molecules and some 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 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 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. 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 I've. kind of told this story you know you. talk about intelligence you talk about. life uh 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 not 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 than the the. computational. constraints which Consciousness operates. under and also the sequent like the. sequential thing like the notion of time. that's that's kind of interesting but.

then the the followup question is like. okay starting to get a sense of what is. intelligence and how does that connect. to a human brain cuz 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. people 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 cuz. I I seem to be equally as dumb today as. I was yesterday so there's some. persistence like a consistency over time. that the intelligence I plugged into so.

like what's it seems like there's a hard. constraint 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 int. intelligence you you can have kind of. this okay so so one thing is we don't. know no intelligences other than the. ones that are very much like us yes.

right and 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 a. 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 invol 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. Moes we could say what matters is the.

you know the wiggle effect that is you. know that is something that we humans. just never noticed 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 moving about right. why do we see that right and 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 altivity 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 AG. reducible comp sort of comput pocket of.

computational reducibility that we slice. out of this kind of whole. computationally 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 fult we drop. something that's a that's a great. example of general relativity in action. the gravity no but like what's the. difference that and newtonium mechanics. I mean oh it doesn't I this is I when I. say general relativity that's 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 this. is 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 uh things happen. progressively in time everywhere in. space mhm um 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 at 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 setup 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's somehow useful for. Consciousness like 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 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 you're are you saying. typical human are you saying we are at a. human level is special here for. Consciousness like well for our kind of. Consciousness it's it's h 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 this. makes it Consciousness seem like a weird. side effect of 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 um 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 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 tell we can. tell a story we 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 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 great great uh collection of. books from my friend Rudy Rooker which. were um uh which I have to say the um. the 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 of the book The. the Earth is consumed by these things. see called NS which are Nano nanobot. type things and it um 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 a that. was only a micro spoiler it's only. chapter one okay good it's um the but. but 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 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 there would be a spoiler okay yeah. 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 uh 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 and outthink Rule 30. is because we're just computationally. equivalent to rule 30 so we're kind of. just both just running computation. 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. micros servers and that that's uh that's. where it starts and so the question of. you know computational equivalence. principle of computational equivalences. well actually you don't need to build. those custom servers actually you can uh.

you can just um 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 and 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 MH 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 of 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 assed 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 our. particular way of processing the. universe would that thing also have a. 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 link of Consciousness is sort of. a key aspect of it is that we feel that.

there 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 automatan 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 in 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 uh you know I think there might be. some experiments that are possible with. 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 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 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 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 represent. presentation 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. wol from language and our whole sort of. computational language story it's all. about how do you take sort of raw. computation in 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 mediated 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 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 intelligences 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 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 cell. aoma being able to uh what's it like to. be a. cellometer in the way that's equivalent. to what it's it like to be a conscious. human.

being how do you approach that so is it. looking at some subset of the cellular. atom and asking questions of that subset. like how the world is perceived how you. as that subset like for that local. pocket of computation what are you able. to say about the broader something like. and that somehow then can give you a. sense of how to step outside of that. cell 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 it. doesn't it doesn't quite make sense and. I you know for me these sort of.

philosophical issues in this one I have. not untangled so let's let's be um um. the you know for me the thing that has. been really interesting in 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 this full. conscious experience to the subset of. the cell autometer yeah it's something. like that but the difference in the. first person shooter thing is there. 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. automatan one's going to be able to. watch what the cellular automatan 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 if. feel feels like over time if the virtual. reality experience is is well done and.

maybe in the future it be extremely well. done the immersion leads you. to feel like you mentioned memories you. forget that you even ever existed. outside that experience it's 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 why can't you merge with the. cell aom I mean you aren't you 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 can 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 automat and. then you say well now we've got an. answer to what does it feel like to be a. cellular automatan 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 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 Ral space so we have. this idea of there's physical space. which is you know something you can move. around in that's that's 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 a multi-way grow off 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 that what's happening is. branchial space is associ with phase and. 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 consist story so for us that's. sort of the analog of destructive. interference got it and then there's Ral.

space too which is the space of rules. yes well that's a that's another level. up so so there's there's the question um. actually I 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 it in a spacecraft.

that's going at some significant. fraction of the speed of light to you as. a 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 the twin who goes off to Alpha. centur 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 m when you exist at a. particular place and you just evolve. with time you're again you're 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 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 the time. dilation is a story of the fact that as. you kind of 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 your clock can't tick as quickly. because every tick of the clock is using. up some computation but you already used. that computation up on moving at you. know half the speed of light or. something and so that's that's why time. dation 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 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 M okay and the clock is you.

know there's all these little updates. the hypergraph and a sequence of updates. cause 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 the oscillator. moving whatever it is okay but but then. the alternative is that's sort of. situation one 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 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 update. 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 it's 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 F path andral 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 branchial 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 branchial space something. happens and the question is how far in. this branchial space and 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 that. because one of the things that's weird. in quantum mechanics is where 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 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 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 as this molecule and we. do a reaction and we draw a diagram and. we say this carbon atom ends up in this. place 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 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 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 this. amplitude 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 a. definite answer but we 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 uh. Branch 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 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 think. called the quantum Zeno effect so it 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. Xeno 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 is 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 10us. 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. 10us 100 meters or whatever so I don't. know how it will work but this is a this. is a a potential Direction and 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 hypergraph doesn't have. any particular Dimension it can emerge.

as something which on in 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 of R in.

you know as as as R 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 fluctuation in the other. 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 three 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. 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 the. surface area of a sphere is proportional. to r s but if you're not in. three-dimensional space the surface area. of sphere is not proportional to r s. it's R to the whatever 2.01 or something. um and so that means that. I think when you kind try and do Optics. you know a common principle in Optics is.

hen's 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 phot on. 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. in the current models of physics uh you. know uh 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 it in a. footnote right and that was 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 the inflation idea. and that 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 a 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 free Bid 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 univarate 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 the the. they're spaces where where the effective. dimension is not an integer so you can't. apply the tools of calculus and. naturally and easily to fractional.

Dimensions no so somebody has to figure. out how to do that we have yeah yeah. we're trying to figure this out I mean. it's it's very interesting I mean 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 you have a hope that. with this hypergraph model You' be able. to make predictions yeah that then could.

be validated with a physics experiment. predictions that couldn't have been done. or weren't done otherwise yeah yeah yeah. I mean you know I think which in which. domain do you think that okay so there. are 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 dimmension. fluctuation that's a huge flag that the. the something like our 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 when 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 in 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. that's gravitational waves yeah or 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 uh we've spent less. effort on that than I would 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'.

been working on on our models we with. now lots of pH such it's very very nice. it's kind of uh uh you 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 physicist too not. just ideas yes I mean you know lot of. what 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 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 don't 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 um due to Jonathan. gorod who's one of the key people who's. been working on our project um this is. uh in Okay so CA 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 3 plus one dimensional you know setup. 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 the this graph of causal. relationships between these randomly.

thrown down events so they've always. been confused by the fact that to get. even lenen variant even relativistic in. variant 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 are models necessarily generate. events in some pattern in in SpaceTime.

effectively that then leads to R. invariance and relativistic invariance. 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 as. opposed to just where 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 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 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 touring machines are a. good start because we 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 universe exist at all 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. surprising that you can even begin to. answer this question indeed as you were. saying I'm I'm very. surprised so the next thing to perhaps. understand is this idea of Ral 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 Ral 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 and 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 hypog graph one could say just take. all possible rules and apply all. possible rules at all possible places in. this hyper graph okay and then you make. this Ral 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 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 ruad the limit of. um uh the limit of kind of uh all. possible rules being applied in all. possible ways and you're saying that. structure finite so that somehow. connects to maybe a similar kind of. thing as like causal. invariance R 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. converge does that say that the ru does. that necessarily infer that the ruad 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. ruad 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 rad object one is how long you run. the computation for another is how many. different rules you're applying and. another is how 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 and. deque um growth and deque had a thing. called The Infinity groupoid which is. closely related to this ruad object um. or Al though 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 MH the way that uh well. let's see uh maybe this is um just 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 what. is what is it made of so to speak. mathematics there's a bunch of. statements like uh for addition x + y is. equal to y + x that's a statement of. mathematics another statement would be. you know x^2 - 1 is equal to x + 1 x -1. 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 it's a. rule that you can it's I mean you think. of it as a rule it's it's a it is it is.

a rule it's also just a thing that is. true in mathematics right um a 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. we're segueing 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. we'll maybe get to meta mathematics but. 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 to speak yeah so what does the. universe have to do with the ruad the. ruo space and how that's. possible 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 it.

another one and you know that's kind of. the you know the the sort of the lesson. of cernus 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 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 on. Alpha santor but we don't we live here.

um and similarly in Ral space we could. live in many different places in Ral. 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 Ral. 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 Ral. 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 Ral space and so on so. wait what's the. interpretation so Ral space and we is. I'm confused by the we and the. interpretation and the Universe I. thought moving about in Ral space. changes the way the. universe is is the the way we would.

perceive it the way that that ultimately. has to do with the perception so it. doesn't Ral Ral space is not somehow. changing like uh branching into another. Universe something like that no just. part of the point is the the whole point. of this is the ruad is sort of the. encapsulated version. of everything that is the universe. running according to all possible we. think of our universe the observable.

universe as its thing so we're a little. bit loose with the word Universe then. because wouldn't the ru had a. potentially. encapsulate a very large number like. combinator large maybe infinite set of. what we phys human physicists think of. as universes that's an interesting. interesting parsing of the word un. 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 Ral space at that particular.

place in Ral 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. would be different from the one it is. given where we actually live and so in a. what we're saying is our when you might. say I mean in a sense this this ruad is. sort of a super universe so to speak um. but it's all in Tangled 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 univers 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 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 ruad yeah but. that's not that's not uh that's just. yeah that's the same ruad that's the.

same universe you're just moving about. these are just coordinates in the. universe 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. centori but it might also live at a. different place in Ral space yeah it can. live right here on Earth it just has a. different frame that includes a very. different perception of the universe and. then because that Ru 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 occurrence with nature 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 the 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 well 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 right 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. subtle about mass and energy and so on.

there could be a a what would you call. it a solatron. yes yes yes a particle that that somehow. contains sness yeah right well that's. what by the way that's what liet said. and you know one thing i' I've never. understood this you know libbets had. this IDE of monads and monadology 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 hypergraphs right.

but liit 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 there's. this just abstract rule that runs to. libbets 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 ADV it on the your. conception of Consciousness that uh like. the the two characteristics of it that. it's constrained and there's a single.

threat of time is it possible the leness. was on to something. that the the basic atom discreet atom of. space has a Consciousness is is that um. so these are just words right but like. what what is there is there some sense. where Consciousness is much more. fundamental than you're making it seem I. 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 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. exists 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 Automan 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 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 haven't. written it since I was like 10 years old. and my my fiction I I've made one. attempt which I sent to some science WR. to friends of mine and they told me it. was terrible so but um this is a long. time ago no this is recently recently. they said it was terrible that'd be. interesting to see you write a short.

story based on the well it sounds like. it's already inspiring short stories by. or stories yeah right by 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. or 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 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 aoma you could. start talking about what does that. subset maybe feel 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. conscious 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 that are our 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 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 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 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 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 for. Consciousness no I me 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 nonin sort of inter discussable 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 it's sort of an an applied. version of Consciousness and and I think. the reason it sort of segs 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 in. systems very different from brains and. so why is that matter. well you know this whole description of. this kind of uh uh well actually you. know what we 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 let's okay why does. the universe exist okay so we finally. sort of more or less set the stage we've. got this idea of this ruad 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 ruad 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 you kind of started. with is You've Got 2 plus 2 equal 4. you've got some other abstract result. but that's not actualized it's just an. abstract thing. and when we say we 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 ruad 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. rule ad 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 touring machine but is not running. all the rules that will be accessible to. a that can solve problems in finite time. that would take a touring machine. infinite time to solve so you can even. Alan touring knew this that you could. make oracles for touring machines where.

you say a touring machine can't solve. the halting 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. ruad 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 ruad that is you can make a. sort of super ruad 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 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. in an event horizon and so the what will. happen between this kind of the ordinary. ruad and the hyper ruad is there is an.

event horizon and you you know we in our. ruad will just never know that there is. 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 might exist but it does it's. not clear what it it's so what so to. speak whether it exists 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 a. meta comment okay which is that that I. have not thought through this hyper ruad. business properly so I'm I'm I can't the. the the the hyper ruad is referring to a. ruad in which hyper comput is possible. that's correct yes 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 exists one question is. why is it this universe and Not Another. Universe yeah okay so the the important. point about this ruad idea is that it's. in the ruad 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+ 2al 4. exist that's not really that is a thing. that necessarily is that way just on the. basis of the meaning of the term two and. plus and equals and so on right so the. thing is that this this ruad object is. in a sense a necessary object it is just.

a 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. computation the r. 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 ruad and so our so there is no. sense to say does 2 + 2 equals 4 exist. well that's that's in some sense it. necessarily exists it's a necessary. object it's not a thing that way 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 there are 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 we we don't exist in roal space. we that's one of the coordinates that. Define our existence right well okay so. so yes yes but this ruad is the set of. all possible Ral 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 ruad and. we are concluding certain things about. how the universe works based on that M. 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 ruad.

is a necessary object in the sense that. it is a purely formal object just like 2. plus 2al 4 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 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 arbitary thing it's a thing with. definite structure and that structure is. the thing when we are embedded in that. structure when when any 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 let me like you need to have it if. you want to formalize the relation. between entities but why. did 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 fair 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 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 well they're not very concrete I. mean they're just things like you know. um logical. or but 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 the point is that it is. not a thing of a you know people imagine. their 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 is 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. discret that can be used to reason have. to exist or 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. 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 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 constructible thing that we can. imagine and now we have to ask the. question what you know given that formly. constructible thing what is uh what. consequences does that if we were to. perceive that formally con if if we were. embedded in that formally constructible.

thing what will we be perceive 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 I'm trying. trying to get at I understand why it. feels like this uh ruad is necessary.

mhm 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 ruad like what's outside the ruad. well the ruad is all formal systems so. there's nothing because but that's what. a human would say I know that's what. human would say cuz 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 it's it's like it is all.

things you can. imagine but no all computations you can. imagine but like we don't well so the. isue is 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 is isn't what we can. represent formally right that is that is. there something that um and that's I. think related to the hyper ruad footnote. so to speak of which I'm afraid that the.

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 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. 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 uh 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 would 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 you are your um.

conscious being is comput entially. bounded so you're missing having written. quite a few articles yourself you you're. now missing some of the pieces yes the. limitation of Being Human right one of. the consequences of this why the UN why. the universe exists thing and this kind. of concept of ruy 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 MH and that's a weird thing. because mathematics people have been. very confused including me have been. very confused about um uh the 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 aums like uid 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 this is 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 was 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.

than I've been so it's um it's one of so. so I mean her sense and your sense are. we just uh so this is to the question of. meta mathematics are we just kind of on. a trajectory through Ral space except in. mathematics through a trajectory of. certain kind of I think that's partly. the the idea so so I think that the. notion is this so 100 years ago a little. bit more than 100 years ago well 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 frager and piano and Hilbert. and so on and they kind of got this idea. of let's do kind of uclid but even. better let's just make everything just. in terms of this sort of symbolic axioms. and then build up mathematics from that. M 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 axim 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 exploded by. girdle'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 human hum 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 of the things. I've always found very mysterious is. that girdle'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 metam mathematical space. and they are picking a reference frame. in metam mathematical space and they are. computationally bounded observers in. metam mathematical space which is. causing them to deduce that the laws of. meta mathematics 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 meta 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 point in. the 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 of proofs that's the. kind of causal network of mathematics of. what can prove what and so on and you. can say at any moment in the history of. of a mathematician of a single. mathematical Consciousness you are in a. single kind of slice of this kind of. meta mathematic 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 threat. 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 if. you look at one of these formalized.

mathematics systems something like you. know Pythagoras's 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 sort of an. empirical fact that I'm trying to. understand a little bit better if you. look at different proof of Sy if you. look look at different formalized. mathematics systems they actually have. different axioms underneath but they can. all prove Pythagoras's 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 molecular. Dynamics so to speak and there are all. kinds of weird things like for example. one thing I was realizing recently is. the the quantum theory of mathematics. that it's a very bizarre idea but um. basically when you prove what is you. know a proof is you 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 metam. 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 proof you can think of it as. branching similar to the quantum. mechanics model that you talk exactly. and so and then there's some invariance. 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 analoges. 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 gorard has a nice. theistic for automated theorem provs. that's based on our physics project that. is looking for essentially using kind of. um using energy in our models energy is. kind of the level of activity in this. hypergraph and so there sort of a. heuristic for automated theorem proving. about how do you pick which path to go. down that 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 metam. 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 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 the you know the 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 arbitrary 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. knowing 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 not of a black hole in physics where. time stops that's the 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 the attempt to understand so so. another question is kind of what is the. what is the general ativity of uh of. metam mathematics what is the bulk. theory of metam mathematics 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. metam 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. mathema ma algebraic geometry or. something might have they play into. another area of mathematics that that. that same the same kind of fundamental. construct seem 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 metam mathematical. space that will explain why different. areas of mathematics ultimately sort of. map into the same thing and and I mean. you know my little challenge to myself. is what's time dilation in um uh in meta. 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 in metam mathematics 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 Ral space um I. mean the mathematical structure you know. branchial space is probably more like. Hilbert space but it's a rather. complicated Hilbert space and Ral 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. metamathematical space a a path in metam.

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. 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 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 paths 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 of 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 there'll be you know you. always have to go around the Securus. route to get from here to there there.

won't be any direct way that's kind of a. 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 obstruction. means in proof space cuz it for it to be. an obstruction should be reachable some. other way from some other place right so. this is like un 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 paths that go. the other way and this question of. homotopia in mathematics is this. question can you continuously deform you. know from one path to another path or do. you have to go in a in a jump so to. speak so so it's like if you're going. around a sphere for example if you're. going around a I don't know a cylinder. or something you can wind around one way. and you can there's no there 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. spaces you should be able to deform it I. mean that cuz then otherwise it doesn't. even make sense cuz 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 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 but how.

would that be possible if they start at. the same place and end of the same place. well it's the same thing as as you know. we've got points on a you know if if. we've got paths on a cylinder I. understand how it works in physical. space but it just doesn't it feels like. proof space shouldn't have that okay I. mean I'm not sure I don't know we'll. 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'm in the next few days I hope to. do a bunch of experiments on this so 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 so this. kind of segue to perhaps another thing. which is this whole idea of multicomp. 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 um so I. I've sort of claimed that there've been. sort of four epochs in the history of. making models of things and um um and.

this multicomp computation thing is is. the fourth is 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 phes you know or everything is. made of ATS 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 uh started really pushing in the. in the 19 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 mathematic maal models is in. mathematical models there's an equation. you solve it you 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 cellular. automatan State then it has the next.

state and the next state and so on the. thing that is kind of we 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 are these multiple threads of. time and so in this multic computation. Paradigm the kind of idea is instead of. there being the single thread 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 multic. computational Paradigm after a thousand. steps not even clear what a thousand. steps means because you 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 in the but that's but so. the idea is that in this multic. 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 touring machine usually it has a. definite state it follows another state. it follows another state but typically. what people have done when they've. thought about these kinds of things is. they've said well there are all these. possible paths a nondeterministic.

touring 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 um 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. multic computation in physics is we. actually care about many paths and well. there is a case for example. probabilistic programming is a version.

of multic 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 um but the thing that is. notable is that when you are when you're. an observer embedded in this thing etc. etc etc uh 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 and. quantum mechanics um in other words that. just by the very structure of this. multic computational setup it inevitably. is the case that you have certain. emergent laws now why is this perhaps. not surprising in thermodynamics and. stati 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 a sort of a. funny thing that I just been. understanding very recently is when when. I kind of introduced this whole sort of. computational Paradigm complexity is. 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 multic 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 multic computational. system and that Observer is sensitive. only to some underlying core structure. of this multicomp 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 multicomp computation which means. that Observer observes comparatively. simple laws and I think it is inevitable. that that Observer observes laws which. are mathematic 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 what 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 law. in linguistics you got to talk about. molecular biology here okay so where. where where does multic 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. there 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 but I've actually learned a bunch. more chemistry and in in wol 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 uh 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 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 multic. 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. and we've been working on that actually. because we have this beautiful system in. in wol 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 could do Quant. chemistry better we could probably.

discover them automatically but I think. in in in reality right now it's like. there are these particular reactions and. 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 the place the here's. here's where this is going so got this. whole network of all these molecules. having all these reactions and so on and. this is some whole multicomp. computational story because each each uh. sort of chemical reaction event is its.

own separate event we're 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 this system well this. thing is some kind of big multicomp. 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 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 statis mechanics. there's kind of all these molecules. bouncing around and you might say uh. we're just going to ignore we're just. going to look at the aggregate uh. 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 the question then is so 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 we you know well. 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 combin 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 which we don't pay any. attention to when we 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 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 matters question was. what happened in genetics in 1953 when. DNA when it 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. molecu 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 the it's similar to how the. structure of a DNA molecule stores. information it could be the Dynamics of. the system some stores information and. this kind of process might allow you to. give uh predictions of what that would. be well yes but but also imagine that.

you're trying to do uh 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 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 touring machine you can say. how do you compute with a multi-way. touring machine you you can't say well. we 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 it's an interesting idea. it freak touring out for sure because. then uh the Dynamics of the 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 very uh sort of 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 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 are 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 Neils yo 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 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 and. then I look at the books now and they're. very thick because they've got you know. there's just a ton knowing about. immunology and you know all these. different Pathways all these different. details and so on but the theoretical. section 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. showing 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 te- 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 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 automatan. Theory it's like U 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 sort of 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 uh where where I. think multic 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 out 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 tea 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 an 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 the. and then so this is like U could be. deeply connected to the protein and. multiprotein folding all of that kind of.

stuff so to be able to say something. interesting about the the dance of. proteins that exactly then actually has. an impact. on um helping develop drugs for example. or has an impact on virology Immunology. helping 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 is a big complicated. phenomenon which just seems to 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 they were you know dominant. recessive this that and the other it 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 Bas. 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 AIC biology 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 the 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 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 a. dynamic process and then you can have a. good model like the hypergraph 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 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 GL theory is. digital information in DNA that's. another sort of global fact about. biology but the the the difficult thing. to do is to. match something you uh have a model of. in the hypergraph to the act 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 and experiment 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 these. Emerald Cloud lab people are built with. wolf and 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 of the primes I love it.

yeah I mean that would be that would be. an example of 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 as. associated with oh is it carbon is it. this is it that you know is it important. that there's a bromine atom here etc etc. etc this is all chemistry that I don't. know much about um and you know that's. that's a 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 in. setting that up I talked to uh 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 theor improving 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 C collaboration between cardano and. the whole Space of blockchain and wol. from wol from alpha wolf from blockchain. all that kind of stuff well okay we. we're segueing to a a slightly different. world but but um so although not. completely unconnected 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 with doing. fundamental Theory of physics maybe. it'll have an application in 200 years. um but now I've realized um actually. this multicomp computation idea is is. applicable here and now it's and in fact.

it's also giving us this way uh I'll. just mention one other thing and then. then talk about blockchain um the um the. question of um actually that relates to. several different things but but um one. of the things about about okay so our. wolam 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 W 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 wol malfa 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 wol from language is. what people use and have been using for. the last 33 years actually Mathematica. which is its first instantiation will be. onethird of a century old in uh in.

October um and um that uh it's it's kind. of interesting what do you mean one3 of. a century is you mean 33 or 30 what are. we 33 and a third 33 and a thir um. so I've never heard of anyone. celebrating that anniversary but I like. it I know third of a century though it's. it's like you know get many many slices. of a century that are interesting but. but you know I think that the the thing. that's really striking about that is. that means um you know including the. whole sort of Technology stacker 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 one 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 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 of different threads of of. all these different capabilities that. are now part of wol from 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. S&P system back in 1979 that was a. predecessor of the whole W 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 multic 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 a way of of of sort of sliding. around the edge of multicomp computation. and back when I was working on S&P 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 ofn is. f ofn minus1 plus F of n minus 2 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 8 plus F of s f. of S Plus F of six you can collect the F. of sevens and so on these are um you. know I didn't realize it 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. um in S&P 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 of I mean that that's that is. basically this question of in what order. is the universe evaluated mhm 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. multic 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 um and this is not what we're doing. with cardano but but this is a 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 there 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 had this. little conference we organized about the. the theory of distributed consensus. because I realized that there 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 yeah but. distributed consensus that still has a. sequential there's like one still. sequentiality so dist don't tell me. you're thinking through like how to. apply multicomp 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 invariance would give one. but it can take a while and the it can. take a while is kind of like quantum. mechanics so it's kind of what's. happening is there these different Paths. of history that correspond to you know. in One path 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 MH. and the the the idea is that the way. that economics spaces knitted together. is between is is there these autonomous. events that essentially knit together. economic space so there're 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 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 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 are transactions. there are states of agents that are kind. of the atoms of economics and then.

transactions are kind of Agents transact. in 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 in economic. space well all these transactions. there's a whole complicated ction 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 um 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 appr o imation to that. which is we say they each have a dollar. value and we have this kind of numerar. 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 a. parsing of physical space and so my my. guess is that the yet again I mean it's. crazy that all these things are so. connected this is another multicomp. 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. 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 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 in economics and and I know for.

you know if if you imagine a very. agricultural economics where people are. growing Lett uses in fields and things. like this and you ask questions about. well if you're transporting Lett uses to. different places you know what is the. value of the lses 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 more complete analogy. and that that's the question of is there. a theory like General itivity 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 and so. we 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 I actually. have to have a foundational theory of. economics and so that's kind of a uh you. know it maybe that we could deploy a 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 economic system and that. means like a fundamental theory of. transactions between entities well.

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 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 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 in. 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 there 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 multicomp. 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 but it seems like this. kind of model can be applicable so many. aspects like at the different levels of. understanding of uh our reality so it. could be the biology at the chemistry at. the physics level 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 as one of these levels and. that's that's right and 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 and 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 analogue of blockchain. okay the much more pragmatic thing is a. is 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 comp 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 legal ease 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 gotfried. liet back in you know 1680 or whatever. was like um I'm going to 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 human 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 project 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. 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 what we want the AI to do so but. this is useful so you're saying uh so. these are like you're saying. computational contracts but the smart. contracts this is what's in the domain. of cryptocurrencies is 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 write a contract that. richly. represents some aspect of the world yeah. but but so so I mean smart contracts. tend to be right now mostly about things. happening on on the blockchain yes. sometimes they have Oracles in a fact I. wol from alpha API is is the main thing. people use to get information about the. real world so to speak yeah within smart. contract so wol from alpha as it stands. is a really good Oracle for whoever.

wants to use it that's perhaps where the. relationship with cardano is yeah well. that's how how we started getting. involved with blockchains is we realized. people were using you know wolf malfa 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 wol from language. is with its symbolic representation of. things is really very good at. representing things like blockchains and. so I think we now have and we don't. really know all the comparisons but we. now have a really nice environment.

within wolam language for dealing with. the sort of uh you know for representing. what happens in blockchains for. analyzing what happens in blockchains we. have a whole effort in blockchain. analytics um and uh you know we've we've. sort of published some samples of how. that works but but it's you know because. our technology stack both 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 some 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.

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 multicomp. 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. cardano and we'll be doing some more and. uh you know we did some cellular automat. and nfts on kadana people seem to like. 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 and we're we're really working on. this you know I like recording stuff you.

know I 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 uh realizing maybe it's not. coincidental that 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 thing's going to go away but. one of the things about BL chain 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 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 sort of a 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 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 there the sort of the proof. that it works that there 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 theorem 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 and 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. 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 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. undid ability 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 girdles theorem tries.

to say you know piano arithmetic the. axim of arithmetic can you box in the. integers and say these axim give just. the integers and nothing but the. integers goodles theem showed that. wasn't the case there's a you know you. can have all these wild weird things. that are obey the piano aums 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 um I. mean in in. general I would say one of the things. that's kind of complicated in my uh sort. of life and the whole sort of story of. computational language and 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 I've kind of concluded that I'm in the. business of making kind of artifacts. from the future which means you know. they 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 are not. absorbed I mean people people use them. every day in W from 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 at our uh we have a a. conference every it's coming up actually. in a couple of weeks a annual technology. conference uh where we talk about all. the all the things we're doing um and uh. you know so I was 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 were sort of.

telling me afterwards you know that's. exactly how you know we're using wolf. language in some particular setting in. you know some computational X field or. some organization or whatever and it's. like people are saying oh you know what. did you manage to do you know what 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. to relate to another sort of piece of. history and 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 the 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 other 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 it'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 the idea that programs might. be the right way to approach right uh. this field was 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 but you know and. computational irreducibility exct 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 in fundamental physics.

we've gotten a lot further and we've. managed to put put a lot of puzzle. pieces together that that make 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 it 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 you know outfit do and I was saying. well there is this thing that I've been. thinking thinking about it's this kind. of idea of complexity and um it's kind. of like and that's that's what that. ended up you planted the seat of. complexity at Santa Fe that's beautiful. it's a beautiful Vision but but but I. mean so that but what's happened then is. this idea of complexity and you know can.

you know and I started the first. Research Center at University of. Illinois for doing that and 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. look looking at a system that's complex. and our computational model gives. complexity by golly 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 me that's a Ecom yeah it is 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. have told me you should start some wolf. 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 wolam institute thing. and and I've been you know because I've. known about lots of institutes and I've. seen kind of their 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 M 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 it's it's become an. Institute yes well it needs to become an. Institute 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 uh 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 that people well. it's not far away it's it's the it's the.

under you know the 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 the 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. rology so what is metamodeling So Meta.

modeling 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 touring machine is. it a cellular automaton you know what is. is the underlying stuff underneath that. model and so there's this kind of. metascience 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 multicomp 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 in different kinds of. modeling so there's the first activi is. is kind of metamodeling 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. rology which is kind of the the okay. you've got these simple rules you've got. cellular autometer you've got turning. machines you've got substitution systems.

you've got register 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 rology. or what I'm not the 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 metam 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 it may be 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 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. ient 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 autometer it's kind of like you. know you can sort of catalog what what. are the different cellular autom 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 four 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 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 I always.

thought that sort of this notion of pure. nks pure and nks being the acronym for. my book new kind of science um was uh. was something that people should be. doing and 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 a 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 we're thinking about. kind of the rological society because we. we're realizing that it's kind of it's. it's um 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 I think now you know. one of the things I I want to try to do. and and you know it's 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 uh 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 leared 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 it 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 in a Leed kind of way. so that it really can can make forward. progress rather than and 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 that you. know that it's you have to have a. central Mission and a drive just like. you do with a company that's delivering. a big overarching product and that's.

that's uh but the the challenge is you. know when you have a the the the the. economics of the world are such that you. know when you're delivering a product. and people say wow that's useful we'll. buy it m 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. rology 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 uh that gets. applied well I I hope this is this. becomes a vibrant New Field of rology I. love it like I told you many many times. it's one of uh the most amazing ideas. that has been brought to this world so I. hope you uh 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 Steven wilam. to support this podcast please check out. our sponsors in the description and now. let me leave you with some words from. Richard Fineman nature uses only the. longest threads to weave her patterns so. each small piece of her fabric reveals. the organization of the entire.

tapestry thank you for listening and. hope to see you next time.