Wolfram Physics Project: Working Session Thursday, June 4, 2020 [New Emerging Understandings]

okay hi everyone so I thought today we would talk a little bit about the current status of the physics project and then do a general QA about what people would like to talk about so okay well things have been progressing really well as far as I'm concerned I mean I think that the it's kind of often this way the more you understand the further you can see and the more you can understand and we're kind of in that loop of progressively understanding more and more and I would say you know there are some sort of meta things were understanding and there's some things were understanding actually about details of physics so in a meta level I think one of the most significant things were understanding is that there are a lot of abstract kind of mathematical structures whether they're from category theory tapas Theory theory of you know all kinds of you know infinity categories or all the all sorts of obscure seemingly obscure and deeply abstract mathematical areas and the thing that's really interesting is it seems like this project is sort of emerging as a kind of rosetta stone of connections between these areas and ways to sort of concrete fi these areas and I think the way I I'm sort of beginning to think about it is it's like you could imagine all sorts of abstract models of computation lambda calculus Combinator's things like that and then you've got Turing machines which are kind of a a much more concrete view of what computation is and I think certainly what we're seeing with this project is that what we've got is a sort of concrete view of a certain kinds of abstraction and in particular I think the kind of abstraction that we're really dealing with is this cut type of when there is a system where there's a lot of freedom in that system but where you're only able to be sensitive to certain sort of modded out aspects of the system so what do I mean by this it's like you're thinking about space-time all you know about our causal connections between things in space-time and you cut kind of your your underlying description of space-time might contain a lot more information but all you as an observer are sensitive to is that kind of causal connection data and so you know we're seeing just a lot of these kinds of systems where there's sort of a an underlying description language that can be quite complicated but we're sort of what you're sensitive to is something which is just a higher level of a in the system and what we're realizing it's sort of physics as it has evolved so far theoretical physics as it has evolved so far is really keying into these places where there is this sort of high-level description that's available I mean we fundamentally expect that from the very lowest level machine code of the universe so to speak that there will be a layer of computational irreducibility that will be very unpredictable so to speak given even given the rule it can take you know 10 to the 100 steps or something for you to work out what will happen but the question but but what we're seeing is that certain aspects of the universe which are the ones that physics has keyed into are ones where you can make statements even without solving that irreducibility problem and I think that some but what we're realizing is those sorts of reducibility aspects of reducibility are the same aspects of reducibility that are showing up in lots of these abstract systems I think that's one of one of the interesting things is the realization that there's this kind of that way we're where this project is sort of emerging as a as a place where you can attach a lot of these abstract formalisms and and get something that is more concretely understandable from these formalisms and potentially take what's been discovered in these formalisms and applied in really interesting ways to what we are doing with this project so that's one thing that's sort of a meta level ok another another thing I would say that you know people ask a lot about ok when will your model predict some new phenomenon in the universe well we'll get to that we've already got some indications of that but I think what has become clear from sort of even just understanding history of science is the first stage here is what one can might call theoretical predictions that is you look at a different area of let's say physics and you say does this explain what we already know in that area of physics and so we've been progressively doing that for different areas of physics we certainly haven't got through everything I would say there's a checklist that we're going down and we're making progress in it and it's really sort of it's very interesting the extent to which one needs new ideas one needs new formalism but one doesn't have to change the model to explain what's going on so the the question here is sort of what so there's sort of as we go down this checklist you know I can say things we've reached things we haven't reached I would say that we're reaching a lot of stuff to do with quite a lot of stuff to do with cosmology black holes things like that I'm really dug in that seriously into the early universe yet we need to do that another area that's really high on the list is particles you know actually finding an electron and so on I think what we've realized is that there's well as some new ideas about about what how we might think about electrons and so on mathematically in these models let me talk a little bit about the sort of the physics side of these models I mean what we're dealing with I think I'm sort of increasingly thinking that we should call these sort of points that are the the things that appear the elements that appear in our hypergraphs they really are kind of atoms of space and what we're doing at the first level is we have these hyper graphs that are the relations between atoms of space and then we have rules that correspond to the updating of those of those relations and the atoms that exist and so on so what we're realizing is there's a sort of hierarchy of levels so the first level is the sort of the the the physical space level of there's this hyper graph and the connections in the hyper graph are sort of laid out in physical space and the the length of each of those connections is something like the elementary time multiplied by the speed of light those those those connections that uh the hypergraph is really laid out in physical space so the next level is to look at all the possible branchings of updates that can happen to this hyper graph and that defines this multi-way graph and the transversals of the multi-way graph are this different kind of space that represents all these different states and it represent as physical space can be thought of as telling us relations between atoms of space between points in space and we can measure distances between points in space and so on so similarly when we're looking at this multi-way graph of all possible of the sort of the the network of all possible updates we can look at the distance between things that are generated by those updates in what we call branch field space the space of of branching structures unproduced in this multi-way graph and that branch field space the extent of that that branching spaces are kind of map the the points in that branch field space are now essentially quantum states and the the the sort of the the extent of branch shell space is kind of a map of entanglements between quantum states and so sort of the distance in branch shell space is kind of an entanglement distance between quantum states and so what we're seeing there is that is the arena in which quantum mechanics plays out quantum mechanics is inevitable in our models it comes because there are multiple choices of how the update rules can get applied to the spatial hypergraph and those different paths correspond to the different possible sort of things that need to be accounted for in quantum mechanics so we have a bunch of new understandings of how quantum mechanics how to think about quantum mechanics let me mention one that term that we haven't really figured out in too much detail but it's it's interesting to think about it's a concept I'm calling multi space and what it is is it's the combination of space physical space and branching space so I've said this this spatial hypergraph is laid out in physical space each instance of the spatial hypergraph is laid out in physical space but there's also this branch filled space that represents in some sense different possible spatial hypergraphs but actually things are much more into one than that and so what when you're looking at physical space there will be you can think of it as there's this region of physical space where sort of all the different branches might agree and then there's this kind of tower there's this place where where there isn't sort of a consensus version of space where instead there's many branches of what space can be like in that particular in that particular place and so we can think about so we have been thinking about physical space it's one instance on the on the multi-way graph branch field space it's the map of all instances of in a sense complete universe is complete quantum states in the multi-bear graph this multi space idea is sort of a merger of those two things in which we're thinking about sort of physical space but in sort of the other direction we're thinking of it sort of budding out in the branch field direction so it's as if you've got physical space but at every point in physical space there might be a whole stack of different possibilities in branch real space now knitting together those things is complicated and I've been doing some experiments on visualizing that max has been working on an actual code that will make local multi way graphs to be able to implement that efficiently but we don't yet know quite how to visualize it but kind of the the qualitative picture is you've sort of got sort of a consensus version of space there won't really be a full consensus pretty much anywhere but but imagine that you could so have a consensus version of space sort of laid out in the horizontal direction and the vertical direction you have these kind of stacks of different branch field possibilities and so it's as if those stacks of branch real possibilities are the different possible quantum states that represent what could be going on at that point in physical space and so this this idea of multi space is kind of a way of packaging physical space together with branch real space to where the quantum space and I think this will be a valuable way to understand more about about how things work one particular example is particles we've been thinking about particles propagating in physical space and we imagine those particles as being essentially some kind of topological like obstructions in the multi-way graph in the same way that you know in something like a fluid you might have a vortex where you have this sort of circulation of fluid and there's a there's you can move this vortex around but there's a Recor to the vortex it has some sort of topological stability to it we're imagining something similar happening in the physical spatial hypergraph but one of the questions then is what happens in the branch field direction what are particles in branch hill space like we don't really know yet and that's very relevant when we think about things like quantization of spin we need to understand what particles are like in branch field space and I think that the the way that that the way that that sort of plays out is something that multi space will help us try to understand and will help us try to give a way of thinking about the notion of what is essentially spatial localization and possibly also branchy localization for particle like excitation so to speak in the system now one of the things I we've been thinking about is is sort of what's the right meta model for particles we know qualitatively what it's about we know it is a somehow stable locally stable lump of stuff propagating in our system but how do we characterize a locally stable lump of stuff you know in in if we look in I don't know condensed matter physics or something we'll find these sort of topological excitations in a continuous system there's a notion of something like homotopy something like whether that whether you can whether there's sort of an irreducible like in a vortex for example there's sort of an irreducible piece of vorticity that even you know you look around sort of a loop around the core of the vortex and you'll always see that things sort of go around that vortex and you can move it around a bit and so long as you're so long as the core of the vortex is inside your loop you'll always conclude by your integrals or something that there is a vortex in that so it's a sort of a way in a continuous system of seeing how some sort of discrete structure arises and the question is to what extent how should we think about particles in our systems should we think about them in terms of something like homotopy should we think about them in terms of you know something some other kind of way of characterizing discrete features of of spaces now having said that our space is not fundamentally continuous a lot of the mathematics of how of extracting discrete things from continuous spaces there's all that mathematics but our space is probably is very very fine and so it's it's been you know that there's there's just a lot of nodes in the universe and so it's reasonable to try and use mathematical ideas that come from continuous mathematics as a way to characterize sort of large-scale discreteness within this fine grained discreteness I think so another thing that sort of an analogy for particles is black holes where there is a a region of a spatial graph or the causal graph that have certain features it's a region that has some sort of stability in the sense that it has for example causal ideas going into it but not coming out of it and there's a definite region that has those properties so one of the kind of questions is you know should we be thinking about particles as something like black holes in our space should we think about them in terms of some map of causal edges and some kind of stability of the some kind of feature of the divergence of course ledges or something you know should we think about them that way remember that we have a model in which the dimension of space is not a constant kind of thing and so it certainly remains a possibility that an electron for example is really a lump of higher dimensional space let's say that is localized in our physical space we don't know yet but so one of the and I think one of the things we need to understand is the relationship between particles and physical space and particles and branch field space because I think that's what's going to give us things like quantization of spin and we just don't really quite know how to do that and we don't really know quite the mathematics that we should be using for it may have something to do with cohomology may have something to do with some other kinds of approaches to continuous some mathematics maybe I mentioned one thing about continuous mathematics you know we sort of there's a in terms of the conceptual side of our models it's really important that space is discrete that there are atoms of space we can talk about hyper graphs we can talk about multi way graphs all those things are discrete but in fact as I say in the actual universe it may be discrete but the actual scale of the discreteness is absolutely tiny and so that means that we can the it's it's useful to think about sort of mathematical idealized idealizations where you're taking the infinite limit where things are continuous in that infinite limit maybe the mathematics that represents that continuous limit exists maybe it's mathematics that's already been developed maybe it hasn't the continuous limit of our multi way graphs seems really interesting but that mathematics probably has not been developed yet we're not sure um the it's some and you know this may drive some development of that mathematics but and it may be that that ideas from other areas of mathematics like ideas from algebraic topology or whatever else might be or differential topology all these different kinds of areas might be applicable even though we don't yet know what kind of mathematical object we're dealing with and that still has to be figured out but I think one thing that is sort of an interesting possibility is we think of what we're doing and we think about what we're doing in terms of atoms of space discrete graphs all these kinds of things but maybe really another way to think about it is there is a continuous underlying mathematical structure and we are seeing the discrete skeleton of that structure now it's worth remembering that what we actually see as observers lives even far above the structures that we are actually describing in our models so in other words when we say we observers are sensitive to certain foliation zuv the space and we're looking at certain things when we are modding down to the point where we have these foliation x' and we're looking at the properties of things on these foliation x' it's we are looking only at the kind of the very we're looking very sort of zoomed out to what our actual underlying model is talking about so in other words our underlying model is a low-level code but what we are sensitive to what we are actually as observers paying attention to is a much higher level description of the universe and so it's not so the sort of the current idea of our models is okay we got the low level we've got something that's a reasonable guess at the low level machine code now let's build up and try and understand those higher-level constructs that we observers are actually sort of engaging with but also you might say well let's actually go down below the machine code let's say there's another form of description that we could use it's just another way of describing things that will when you say well what does that really mean what it really means is the machine code and that even lower level description could be some mathematical structure that could be thought of in terms of continuous mathematics potentially and but then the sort of the low-level machine code that we're identifying as the useful way to describe the universe could be something that could then be thought of as a skeleton of that underlying continuous system now it is very likely that that underlying continuous system is super hard to describe super hard to deal with but there may be some attributes of it that are useful and that carry all the way through to this sort of level the higher level at which we're actually making contact as observers so okay so that's that's one kind of one kind of thing so let me mention another I'll look at a few questions here let me let me address some of those and then I'll I'll talk about about quantum mechanics and I want to talk a little bit about rules space and questions like why the universe exists um okay so as the first question has the glossary seen the light of day I am so embarrassed we have still not finished that I'm going to work on it and my only excuses I've been working on a bulletin we're going to be announcing sort of things we figured out a sort of bulletins from this project and I was doing a bulletin which I thought was gonna be really straightforward and I thought was going to be done in a couple of days and it's called I have it up on my screen here I'll show it to you later it's called rule II all space the case of Turing machines um and I said thought was going to be really easy I think I finally pretty much finished it now um and it's probably 50 pages now I feel it's gonna be like a five-page modest thing that was all going to be straightforward but it wasn't and so that's been my personal excuse for why we haven't gotten the glossary done but we're gonna work on it and thank you for the for the poke here um okay there's a question here from am speak about hypergraphs how they been used in physics and fundamental physics in the past I don't think they have been I mean hypergraphs are just a generalization of graphs in which instead of saying that there's an edge that joins two vertices and nodes in the graph you're saying that there's a hyper edge that can connect multiple vertices there are many applications for hyper graphs whether it's in the description of email conversations or whether it's in something completely different um but in physics I I don't know of uses I mean it's very interesting that something like our multi way graphs I'm going to try and write a bulletin called the many names of multi way graphs many names are multi way systems okay so you know these the same idea of sort of Treeing out all the possibilities of something has arisen many times and it has names they're called bomb trees they're called Paz cow sets they're called semi tui systems they're called canonical systems they're called gosh all kinds of other things um all of these are at some abstract level the same thing and these have been invented the first of the ones I just mentioned was invented in the 1920s um but they sort of the merger of these things to make a co here i'm een our use of them is i would say and possibly even our name for them is is is much more concrete well i mean that maybe is not true it's a it's a more let's say it's a more industrial scale use than has been made before but but these abstract systems are things that have arisen many times and you know making that sort of rosetta stone collection of connections between these different ways that that these these sort of abstractions were arisen i think is important and we're hoping to do that um let's see mark is asking atoms of space on what platform so this is you know this is sort of talking about the basics of our model but but this is purely abstract these are points that are purely abstract things all we know is the relations between these points by looking at that whole network of relations that's what defines the structure of physical space and by looking at the kind of the progression in time the progression through sort of the computations that are applied to that system that's what defines sort of the knitting together of different parts of space and leading to space-time and relativity and all those kinds of things okay there's a question from Sid can you summarize your consideration of a link to category theory I wish I could summarize it better I'm disappointed that I can't summarize it better um I think here's the basic summary I think that one categories ordinary categories we can think of our causal graphs no I'm sorry we can think of our hyper graphs as being a sort of mild generalization of one categories I think we can then think about our causal graphs in which we are talking about that actually let me say that differently I got that wrong let me let me let me back up and say that better um I think the one categories are related to our multi way graphs I think that the two categories are related to the causal graph that emerges from looking at the connections between between sort of states in the causal in the multi way graph that's two categories I think the three categories correspond to the construction of foliation z-- in our causal graphs and the whole hierarchy of categories going up to the infinity category of growth and Deek and so on I'm sure that has an interpretation in our models I just don't know what it is yet is it useful to think about what we're doing in terms of category theory possibly I suspect category theory needs some generalization because I think there are particular axioms of category theory that are effectively not valid for our systems but nevertheless some of the structure and conclusions of category theory might apply even even when those those axioms don't don't work um maybe let's say I think we have Jonathan here maybe Jonathan would like to make a further comment on that okay so I mean the basic hierarchical structure that you mentioned I think is pretty much right but there's beyond just naively expressing you know our formulation in terms of say functors between one categories or something I think that there's there's a deeper level of stuff that category theory potentially has to offer us because so in and unfortunately didn't really very us reasons we didn't get time to sort of discuss many of these things in as much detail as I think we would have liked on Tuesday but so for instance in the in the sort of categorical foundations of quantum mechanics right people study these things called daggers symmetric minoan or categories which are the sort of they're the the generalized notion of a kind of a hilbert space where where your morphisms represent kind of transformations between systems and then and they're endowed with the structure the category is endowed with this thing called a called a dagger operation which is a sort of involution operation that when applied to a morphism gives you a generalization of the notion of a hermitian adjoint in in standard quantum mechanics so it allows you to define the notion of a sort of hermitian morphism or a unitary morphism one of the thing one of the reasons why I think that's interesting is because it's it's a significant generalization of the standard concepts of things like hermiticity and unitarity in quantum mechanics which is also something that we're running into in our interpretation of quantum mechanics in terms of multi way systems because our formulation of unitarity is actually kind of trivial in the context of multi way systems it's it's just a statement of conservation of measure in the multi way evolution grid path and you know that's not something that fits neatly into the standard Hilbert space formalism of quantum mechanics but it seems like something that might fit very neatly into the categorical formulation but we haven't yet figured out the details of that there are many other things like I think we mentioned we talked but on Tuesday about how category theorists have developed a general technique for kind of thinking about the relationship between objects and their representations so you know obviously in algebra you have the notion of a group which is an abstract concept and then you can think about its representation which is an act which is thinking about the group in terms of its action on some concrete thing a vector space category theory produces a jet a grand generalization of that idea called a snackie and duality in which you can define what in category theory is a functor between the object and it and it's and it's tanake and dual it's representation back again and we have reason to believe that what we're doing in our models you know when we look at causal networks and we say that they're representing space-time in some sense one that it's entirely possible that one can think of that as being a representation in in some generalized notion of the group theoretic sense and it's possible that category theory and these notions of tanake and formalism and so on will give us a more general way of understanding that correspondence and therefore will help us solve some of the problems that Stephen was alluding to earlier about exactly how we understand formally what the you know what the continuum limit of the multi-way causal graph is if there's a sort of if there's a tanake and way to think about that correspondence that's potentially really really useful so that was still very easy I don't know that was pretty technical Jonathan and I but but I mean that description but in a kinder ality was I thought that was interesting I I think I'm fair enough well so you know I would say about category theory in general I mean I think I said this in our discussion on Tuesday I mean a lot of people are afraid of category theory and it's it's often couched in this very abstract two terms um it is you know I think I am I am sort of but I'm coming to terms with category theory and I'm realizing that actually it's it's it's educational for me because I've been living kind of symbolic language descriptions for 40 years now and so for me you know higher order functions that uh you know things that apply to functions that apply to this and so on you know I'm super used to this and so it in a sense it's interesting for me to see an alien formalism category theory and to see how comparatively difficult it is for me to wrap my brain around it I think in the end there will be some interesting things that can be done ok so so I have to say that that in some sense our model here of elements and relations that correspond to hypergraphs in a very bizarre sense is a is a content removed version of what I've been doing for 40 years in in the design of symbolic languages and in the idea of transformations between Somali expressions it is a version of that in which rather than having symbolic expressions that mean something that have actual pieces in them that mean operations like addition or whatever else it is just the pure bureaucratic structure in a sense of these symbolic expressions and then we are purely manipulating that and the amazing thing is that we are managing to reproduce physics by essentially purely reproducing that essentially content removed version of the pure structure of symbolic expressions but symbolic expressions in the bulk and by that I mean the following I mean when we think about programs or even the data that we're manipulating in programs we like every piece of the program every piece of data it means something to us it's it's a it's a thing which has a definite meaningful identity to us and there aren't you know in a program there aren't that many of them we might have 50 million lines of code but it's still not that big at some level whereas what we're thinking about in physics is the same infrastructure but really in the bulk in the sense that what we're dealing with is having you know 10 to the 100 of these relations which which are like symbolic expression structures but none of them has a name so to speak they're all just things that exist in the low-level machine code of the universe so to speak in category theory it's had sort of the same situation when we talk about objects and categories morphisms things like that every morphism is somebody's personal friends to speak every you know it actually means something it's supposed to have it's like an addition it's like a it's something which has a a an immediate semantic connotation whereas sort of the analogy to what we're doing in physics is just take the infrastructure of category theory and take it in bulk so instead of having some some you know exact sequence of this's and that's that has you know five elements in it it's like no let's have one with 10 to the 100 elements but none of those elements are anybody's personal friends so to speak they're just being dealt with in the bulk and so I don't really know how that plays out for category theory but that's some that's I think the type of connection that we would expect to see um okay so it's a question here from guns I can't really read it each asymmetry corresponds to a creation of destruction of energy don't quite understand that um yeah question here from William don't remember if he answers but what do the directions of the directed edges in the special hyper graph represent um surprisingly little actually they're really just bookkeeping they're really just saying in fact even in the the technical document that I wrote a sort of launching this project I talked about the case of undirected hyper graphs and you could have undirected hyper graphs as well it's really one of the features of this project is what we're trying to find is the right low-level language to describe physics but we're well aware of the fact that essentially any language we have will be computation universal and will be capable of describing other languages so saying we're going to do everything in terms of these directed hyper graphs great ok they can emulate undirected hyper graphs similarly undirected hyper graphs can emulate directed hyper graphs the question really is in what formalism is it easiest for us to kind of grok what the universe is doing and so it's a pure speculation that these directed hyper graphs are the right thing that it will be somewhat but but nevertheless as I was mentioning before one of the remarkable things is that the set of these metal levels these levels above the low level machine code it actually doesn't even matter what these microscopic details are in much the same way as you know when you look at properties of a continuum fluid or something doesn't matter if it's air or water the same differential equations are obeyed even though the detailed molecules at the lowest level are completely different and so so it's it's really a question of convenience what is the what programming language do we want to write in to think about the universe and the one that we are sort of have found most convenient is this one in terms of Direction hypergraphs whether that is ultimately the the best one is not is not clear the good news is we have something we have a language that we're taking a good distance and we're able to see its higher-level consequences which as I say don't depend on the details of that low-level language so the answer is we don't know a very specific sort of physical representation of that because I think the physics were seeing is far above that low level machine code so to speak let's see consider a constant oscillation of the entire universe hmm we don't have a lot to say about that yet I mean in other words if there's a big bang at the beginning of the universe might there be a good Big Crunch that's not what the observations tend to say will happen in our universe but maybe that will change and there'll be a Big Crunch where the whole thing comes back down instead of a time reversed Big Bang and they may be oscillate we don't know if that's how things will work um so Big Bang black hole model in space-time so the Big Bang is more like a it's more like a white hole it's a different kind of singularity in in space-time well it's a it's a it's a singularity just like inside a black hole certain kinds of black holes you have space like singularities we're essentially time comes to an end in our models that's a very direct thing you basically have these rewrite rules and at some point the rewrite rules just don't apply anymore and that means that time which is sort of the inexorable inexorable kind of development of of the system just comes to an end because there's no rule to apply and the inverse of that is what's happening at the beginning of the universe at the beginning of the universe you've got no rule is applying and then then there's a first step and then the rule starts applying and that's kind of like the time reversed version of a space like singularity something like a white hole and I see that Jonathan is commenting that we discovered some oscillating universes yes they okay so at a toy level we absolutely can find oscillating universes you know since we don't have a full model for the whole universe we can't discuss that but if it's a question of you know just getting an intuition for how oscillation in the universe might work yes you absolutely can do that without with our models how would increase of energy be represented in the model energy is very straightforwardly the flux of course alleges through space like hyper surfaces otherwise you can otherwise say that a little bit less precisely as energy is the continual activity in the network it is the continual process of rewriting the causal edges are generated every time there's a rewrite and so to say that with time with the progression of evolution of the system when there is progressive evolution when there is progressive activity that activity corresponds to energy so it is perfectly possible that there is progressively more activity in the universe and that is sort of an expansion of the universe in physical space now a thing that is interesting to think about is what about the expansion of the universe in branching space we can think about an expansion of the the underlying spatial hyper graph but we can also think about an expansion of the multi-way graph in which the transversals are the branches graphs that correspond to essentially the the progression of generation of more and more quantum states and a speculation that that we are beginning to have is that quantum computers will only officially work in so far as the universe is expanding in broad sheíll space so let me let me pull that back to something slightly you know people say energy is conserved in the universe all good ok well is that really true because when we look at the expansion of the universe there's this Hubble flow of galaxies expanding potentially with dark energy expanding at an increasing rate and if we say what's the energy budget of the universe well actually it might not be conserved but that is something that's happening in a very large scale it's not happening at the scale of things like on earth where everything is gravitationally bound and so on but when you look at general relativity and you ask what's the energy budget of the whole universe it's not conserved and so you might say well gosh we could make some special kind of mechanical device that just takes energy from the vacuum by by leveraging it's kind of like a title but not quite but it's kind of like or like hydroelectric power or something whether this flow of a river all the time and you're and you're making use of that let's let's make hydroelectric the analog of hydroelectric power just mining energy from the expansion of the universe and yeah you could do that according to according to standard relativity that would work it's a tiny effect it's not going to get you very far but in principle it would work so when you do quantum computing one of the things I'll talk about this a little bit more detail in a few moments and is that I think one of the emerging possibilities is that actually quantum computing only works insofar as you're essentially mining the expansion of the universe in broad shale space now it might be more useful than trying to mine the expansion the universe and physical space because the universe may be expanding much faster and branch else pace than it is in physical space but I'm kind of thinking that's that's the kind of connection that will happen and by the way we'll talk later about the deeply abstract question of the expansion of the universe in rural space in the space of all possible rule applications but that's that's a good mind-bending exercise to think about that and even I'll just as a preview to think about what is a particle in rural space and that's that's for Jonathan among others for to keep him entertained here um ok question from mark not quite getting that okay there's a question from Allison here have you thought more about the idea of curvature in real space what would it mean deviation between rules I was just thinking about this last night I will tell you a little bit about what I think I figured out let me but let me let me set some stage in terms of what what happens in rural space first but that's a very good question very interesting question I think I'm gonna I'm going to say that I think that the analog of the uncertainly principle in rural space is a is the is the temporary failure of inductive inference so here's my current speculation okay so if you're trying to figure out what rule in your description language at your position in rural space what rule describes the universe well the way you do that is by inductive inference you would say let me observe pieces of the universe and let me reverse engineer what rule must be being applied to get those those features of the behavior of the universe okay so that's what we would be doing in traditional natural science is that kind of inductive inference from what we observe in the universe what rules make that come to be okay so I think that in rural space we're looking at these sort of local areas where different possible rules are doing very similar things they're just diverging just a little bit they lead to universes which are very similar locally and so my speculation is that the analog the uncertainty principle is the the fact that if you want to determine the rule of the universe that is if you want to determine your precise position in rural space then it will take a certain irreducible amount of time to do that and that there will be an uncertainty relation that relates the accuracy with which you can determine your position in rural space how accurately you can inductively infer what the universe what the rule of the universe is with how long you spend doing it that's that's my guess now you might ask the question and so then okay the fun thing this is last night's efforts is to estimate this parameter Rho which is the analog of the speed of light in rural space once the analog what what in in physical space would be the speed of light what in glass real space is related to Planck's constant quantum constant in in and and related to our maximum entanglement speed there's a similar thing in rural space and I was trying to make some estimate so it's size which I can talk about later but that's a really good question Allison there um how do we understand from Benjamin how do we understand the Big Bang in the perspective of our theory well the the beginning of the universe is just the fact that you have some spatial hypergraph and there are rules that start being applied to that spatial hypergraph and those rules will lead to typically the increase in size of the spatial hydrograph that's the simple version of it then there's a question of what is the effective dimension of that spatial hypergraph maybe it's infinity as the universe sort of cools the universe potentially sort of cools down and dimension so that the effective dimension of the spatial hypergraph converges to something like 3 today now actually I wrote a bulletin about black holes in our and event horizons in our universes and I had a way of computing kind of the causal connections between different parts of the universe so for example when there's a black hole things outside the black hole can affect things inside the black hole but things inside the black hole can't affect things outside the black hole so you're essentially dividing the universe into these separate sort of causal domains where one thing can affect another or not and there's also the notion of a sort of cosmic event horizon where there might be parts of the universe which fundamentally are causally disconnected they can't affect each other ok so I had a way of computing that and max pointed out that my way of computing it was a bit inadequate so I have to update my bulletin and actually the one of the updates gives us a little bit more information about causal connections in the early universe it gives us a different way of seeing how there can be not a sort of fully contained not one causal domain as a subset of another cause of the main but there are partially overlapping causal domains and I think that's going to be relevant to understanding things about the early universe and that will be hopefully an update to that bulletin real soon um let's see okay another question from Allison the analog of Einstein's equations in real space these are great questions I love these questions I've been thinking about that I've got some comments later I think it has to do with um well let me talk about it later um okay minor David from Calais minor deviations would be the way branching happens in real space yeah that that's correct um okay let's see from Victor how to understand time in our models um the time in our models is something incredibly fundamental time is the inexorable process of computation going on in the universe and that means time is in in many theories in in in standard mathematical physics of the 20th century the beginning of the 21st century time it's just a coordinate like space that was something that came out of the theory of relativity and particularly out of the work of Hermann Minkowski around 1909 who said gosh we can think about invariant intervals in relativity which have the mathematical form T squared minus x squared minus y squared minus Z squared we can think about that as a quadratic form he'd studied that in mathematics he said let's just say that we have this thing called space-time which is a Lorentzian manifold that has in which time is just a coordinate like space and it's packaged together in that t squared minus x squared form well I think that was a bad idea because I think in fact time is something very different from space-time is this inexorable process by which computation follows computation by which the output from one computation is fed as input to the next computation and so on and that is the progress of the universe is the progress of that inexorable irreducible computation one thing that's interesting in our model is that we have physical space laid out in the spatial hypergraph we have the space of quantum states lay down in broad chill space we have a space of possible rules laid out in rule space but that's the sort of space direction but all of those in all of those arenas time is the same thing there's still the same notion of time time is what knits all those things together they all involve this sort of inexorable process of computation and that is the progression of time and so time in our models is something very it's very fundamental and it is really time is just compute time is measured by the steps of irreducible computation that go by and in fact I'll talk about in in the the animal of the speed of light in rural space is a measure of that I believe let's see question from legend here can it be that the ruleset behaves like two point five dimensional taste since until a certain large time then becomes three-dimensional is there mathematical apparatus that puts bounds on the source as is impossible that's a really good question the answer is nope mathematics we don't know mathematics that tells us about that we would really really like to basically what you have to do calculus is set up to talk about things like manifolds manifolds are locally like integer dimensional Euclidean space that is how all of sort of modern calculus differential geometry all these kinds of things they're all built on this idea that locally everything is like Euclidean space or a Lorentzian space but same same difference integer numbers of dimensions okay there is presumably a generalization of calculus that applies to where locally what happens is not an integer dimensional Euclidean space but we don't know what that is possibly they're ideas from geometric group theory where you're thinking about the limit and as a matter of fact I have a very concrete example of this in rural space which I just figured out well with help from two other people figured out yesterday um the of how well almost figured out how so in the Cayley graph of groups the sort of representation of the relations between elements and groups the limits of those have been started bidding to geometric group theory and they potentially might be a model for something like fractional dimensional space and calculus in fractional dimensional space unfortunately things where you're just looking at so things like fractals there isn't really sort of truly you're still usually thinking about embedding the fractal in an integer dimensional space to do things on the fractal what we want is something where the fractal is the story so to speak where the where the fractional dimensional space is the whole story of space and we need to build a calculus on that and we just don't know how to do that yet and it's a super interesting question in mathematics it'll generate some very elegant and very important mathematics I think but we don't know how that works yet um okay it's a question from plan Umbra here if gravity can be described as curvature of space by mass might electric charge analogously be described as Koecher in a high dimensional space and does our physics model model the mass induced covert row space at this point the messenger's curvature of space absolutely we can derive einstein's equations involving the energy momentum tensor essentially what's happening is that the presence of causal edges which is what energy is is causing gd6 that are propagating in - in the causal graph to be sort of to be diverted by to be deflected by the presence of lots of causal edges in the causal graph that's that's roughly that sort of a qualitative version of why Einstein's equations work ok what is electric charge well we don't know yet and actually your idea is related a bit to the Colusa klein theories that were popular from the 1930s on that sort of imagined that maybe they're sort of a 5 dimensional space and maybe maybe one could do something like that that didn't work out at that time and it's an interesting question which we have not looked at it's a good question whether there is a way to think about Colusa klein type theory in the context of our our hypergraphs i don't know good question i think that the possibility yeah i simply don't know i think what we know so far is that and we haven't really looked at this more than we did at the time launch the way that local gauge invariance works so local gauge invariance is sort of the way to understand electromagnetism electromagnetism is associated with a sort of a an arbitrariness in the way that you can assign a phase a u one phase to different points in space and there is a connection between the the how you apply those phases and that connection represents the electromagnetic field or the vector potential of magnetism um and so it's essentially the electromagnetic field is the knitting together it describes how you knit together this sort of arbitrary choice a of of orientation in this internal space that's represented by this you engage group and so we have a very very analogous thing because we have an internal degree of freedom that has to do with the way that a rule gets applied there may be many ways that a rule can be applied within our spatial hypergraph and so it's a question of that internal degree of freedom first of all does is there a limit in which those internal on the internal ambiguities limit to something like ally group that's question one and question two when we have those local ambiguities how does that propagate through to to the to the more global system and I think it's okay so so roughly when we look at the spatial hyper graph we can say that the limit of the spatial hyper graph is something like a manifold at least in certain cases we can understand how that limiting process works it's the get our guess that the limit of this ambiguity in the way that rules can get applied the limit of that can be illegal which is essentially a a continuous version of a group just like a manifold is a continuous version of a description of space so Ally group is a continuous version of what would otherwise be a discrete set of elements that correspond to a group and so I looked a little bit at the in the technical document that I that we put out at the time when we launched the project I looked a little bit at how that limiting process limiting to ly groups might work from essentially bundles of permutations that get de bundles of discrete permutations limiting to lis groups and sort of an interesting question how that works and actually it occurs to me that the things I've just been doing in rural space might have some bearing on this let's see a comment from Jonathan here that um okay so he's speculating that the foliation of the multi way system might be thought of as it Colusa klein like reduction from higher dimensional space to ordinary space time that's interesting I mean boy that's some so I mean I understand that idea I think gosh you know that reduction from I okay requires more thought um don't know all right let's just try and get through some more of these questions and I want to talk a little bit about our understanding of quantum mechanics and rule space question from Edie give us a framework for knowing when directed hypergraphs or equivalent I don't particularly think so I mean I think it's just type of graph isomorphism that tells us that but hyper graph isomorphism is a very complicated business and in multi space there is going to be so you see what we've been doing so far sort of an approximation we've just been looking at a whole hyper graph and we've been saying the multi way graph merges when a whole hyper graph when two whole hyper graphs are isomorphic but in reality we want to do something which is a much more local version of that that will ultimately be equivalent when there's course on variants and so on but we'll look much more interwove in' i mean it's kind of like saying i've got a bunch of strings and i could describe them all separately or i could describe the whole bundle of strings as a regular expression in which I have some some wild cards so you can think about a string as being character character character character character you can think about a regular expression as describing a string by having a graph in which there are multiple paths through that graph and it's the same kind of thing in multi space that we are thinking about describing not just a single choice for this is the way things are laid out in space but this kind of set of possibilities and it's subtle a little bit like a regular expression but what we have is a big generalization of that and actually as I'm thinking about it there's a question of what is the analog of a regular expression actually that's an interesting way to think about it a graph with patterns so to speak so a regular expression can be thought of as something where you know it's it's the string C star T or something might be a regular expression which we see and then a you know any sequence of characters in some version of how regular expressions work followed by T um and so the you know there's a question of the one we're thinking about this is an interesting idea when we're thinking about our hyper graphs can we think about the hyper graphs not just concretely as hyper graphs but as pattern hyper graphs in which there might be sub hyper graphs that can be fed in just like there are so sub regular sub strings that can be fed into a regular expression that might be a way to get a bit more of a handle or multi space I've been having a hard time understanding how to visualize multi space I have some some candidate visualizations but they look terrible so far okay let's see um as a question any question about peer review of our papers you know a bit disappointing there I mean after people say so a lot of people have been reading them so I mean that's the good news and and I know that because there are you know most small mistakes that are in pointed out and we've been fixing those and so on and I would say there's a there's a high degree of actual reading in detail which is very encouraging both I think of my my documents and of Jonathan's papers um I think that the we put up a kind of peer review infrastructure because people said we want peer review well so far I cannot report great success there you know if you if everybody wants peer review somebody's got to do the peer review and encourage everybody to do that we think we have a pretty good infrastructure for it um but so far nobody has gone through that effort I think I'm hoping maybe at our summer school that we'll be able to encourage some people to - to write some you know I think the thing to realize is what we think is useful about peer review is somebody saying look I read this I understand that it seems to make sense not the whole thing the whole thing is a great big thing to talk about but just you know say section five point six I understand section five point six here are a few comments about what you know - review section five point six here's what some other things to help one understand section five point six so to speak I just don't think it's it's some you know I'm and maybe we haven't presented sort of I I thought we made it very clear that that's the kind of peer of you who you think will be useful but so far I'm sorry to say I believe no takers it's just disappointing I mean it's one of these things where I could could expound on that at length but I you know the most important thing is people are reading things people are understanding things people are giving feedback about things that's what's important and that's what's going to help move this forward and and move science forward in general okay is the theory compatible with Marx principle I'm not sure maybe Jonathan has a comment on that a Marx principle is a is a slippery creature um but Jonathan any thoughts on that yeah I agree so the the best the most well-defined formulation of machs principle that I am at least aware of is the one by Dennis Shama and the basic idea is that you can use the fixed masses of the universe to define a globally stationary rotational frame you know I get against which all all rotations are effectively measured so it's worth saying and Stephen probably has a CRISPR exposition of this than I do but so the formulation of relativistic angular momentum in our model basically consists of you take the causal network which is our representation of space-time you define essentially like a cylinder through the causal network and then you rotate some some hyperplane through that cylinder and then you look at the net flux of causal edges through that hyperplane as either summed or averaged over overall so all the hyper planes that sort of exist in that cylinder and that gives you some that gives you a direct way of measuring the sort of the rate of turning of causal edges in the causal network so then marks principle in in Sharma's formulation would say that there's some you know that there's some global cylinder that you can define across the entire causal network in which that sum is equal to zero now of course there are some causal networks where that's true where effectively that the net flux in all directions is the same and there are some causal networks where it's where it's profoundly not true where there's some significant asymmetry in the flux of causal edges and so from our point of view that's actually quite good because we know that there are valid solutions to the Einstein equations I mean that the famous one being the girdle metric that dramatically violates max principle machs principle is something that we kind of only suspect observational II to be true we have no mathematical reason to suspect that it you know that it's that it's a you know there's a fundamental feature of our universe so the fact that our model supports the existence of cosmologies that are both consistent and not consistent with max principle and that we have a way of distinguishing between the two I think is actually quite encouraging okay so let me let me restate what you said which i think is much better version of so I mean what you're basically saying is with our recent understanding an angular momentum as this kind of vorticity of causal edges so to speak that there's a question of how you measure the vorticity of causal edges because if there was sort of nothing that it might be said I don't know if this is really right we should we should untangle this a bit I mean that if there was nothing in the universe you couldn't measure the vorticity of course Ledger's maybe or maybe even if there was nothing even in these in these spaces where there's sort of a net spin of the universe so to speak that we can see that to you know what we're close we let's go figure this one out we should we should figure out a crisp version of our Marx principle works because I think now that we understand something about any momentum we should be able to do that um okay let's see okay so as a question can the hypergraph eeveelution behave like five DS space until a certain point and then become 3d afterwards is that the same problem as a whole thing problem yes it could be ensnared in a whole thing like problem that is to know what will be the long-term output long come outcome of one of these computational rules maybe irreducibly hard and and I thought that was going to happen much more as we tried to work out physics from these models it's been mercifully possible to work things out without being ensnared in computational irreducibility but yeah we we don't know about this we we need this generalization of calculus help us help us make that um okay so let's see there's a question from glitch who if we exist as observers within this type of graph does this mean that some hypothetical a large computer could run the rule for the universe and foliate until we humans pop out again yes the answer is yes you from Calais here about um ideas don't move at a constant speed they seem to have acceleration and that's a comment I think about rural space and that's an interesting speculation and comment let me try and talk a bit more about rule space in a few minutes um is there a natural explanation for is there an expression of the natural randomness in our model like the the decay of a radioactive isotope yeah I mean our model randomness is a feature of computational irreducible systems randomness what is randomness randomness is I don't know what's gonna happen randomness is I can't sort of jump ahead and say this system is going to do this it just looks random to me and that is a sign of computational irreducibility that's something that I've seen in rule 30 that one can kind of see a little bit less exactly in the digits of pi it's something where even though you know the underlying rule the process of computation generates something which is irreducible where you can't jump ahead it looks random so in our models there's randomness all over the place not randomness as in just what how random is often enters models we just say oh that's something we don't know it's a throw of a dice we don't have that our model is completely determined but the for effectively just like the digits of pi there is randomness even though it comes from an underlying rule but we particularly as observers within this universe we can't jump ahead and say oh it's not really random because it's going to be the digit 7 in a moment because we are it's it's something where there's irreducible computation going on which we can't outrun so it seems Quotes random to us even though there is this underlying computation and that that's how that works ok question from glitch - how does a DF CFT conjecture fit into this theory it probably fits beautifully and we just need some string theory people to go nail this down and I think some people are working on this and perhaps we'll see some papers in the future on it um most likely it's the it's sort of the knitting together of branch real space and and physical space it's the fact that the multi way causal graph has sort of a slicing that corresponds to physical space and a slicing that corresponds to broad she'll space that's our guess as to how the ATSC of T correspondence works and I think it will be very direct in our models and we may very well learn some things from some of the detailed work that's been done on ATSC of T how many rules can you apply at the same time to compute the universe that's a complicated question because the these rules define the progression of time so in other words the these rules are just applied wherever they can be applied the question of which rules are being applied simultaneously is a question of which foliation you're picking in the causal graph and and so that's really just a matter for the observer these rules just applying everywhere but these two rules that applied in two different places they might be there's like well they just applied separately it doesn't matter what order they're in it only matters what order they're in when some causal when some causal relationship knits those two things together so that that's kind of how that how that works um let's see questions here let's see a model describes that Emma creation of a graph could it be equivalent to pre-existing fabric of some sort being deformed in some way I you know that's a question of of what are other ways to describe what's going on there are undoubtedly many ways to describe what's going on the question is are they useful is it a useful language I don't know as a question from glitch any word from Lee Smolin actually I have not heard from him I sent an email and he hasn't sent me a response now that now that you mention it so I I can say nothing so people who worked on loop quantum gravity have indeed been been corresponding with us and and we may try and do a live stream with some of those folks at some point I think I think we've discovered that a lot of academic scientists are afraid of live streams so we need to kind of find some way to what we may do is have some discussions which are recorded but not live streamed which is kind of a shame because I think it's fun for everybody to livestream these things and I I am I've enjoyed the the livestream discussions that we've been doing to date I think we've really been hoping to to chat with roger penrose but he's seems to be having some health problems right now which hopefully will resolve swiftly um and I think um will will them will be and will be it will be interesting to to chat about lots of kinds of things there let's see is there time slippage like clocks and a CPU well I'm not sure what time slippage you mean there but there's certainly time dilation and in fact you will see by finally get to talk about rural space you will see time dilation and Turing machines which is quite fun and you'll see relativistic the analog of relativistic time dilation and Turing machines um okay so question from Dale have we found applications of Ramsey theory ergodic theory and measure theory to this um yeah yeah well measure theory for sure there are all kinds of interesting measure theoretic questions particularly about the multi way graph they are probably beyond my personal level of measure theory knowledge but they're super interesting things to be done there I mean this is a you know what we're dealing with is these transverse measures in with respect to something like a flow that corresponds to the actual evolution process a ghatak theory well there's a lot of kind of DISA T like things going on we don't so much think about ensembles we might think about ensembles it might be useful to think in terms of ensembles we haven't really been doing that very much but what we what we certainly do need is certain results that say that our statistical averages are consistent with the averages ensembles we haven't really poked in that direction very much I have to say I was a little bit put off because when I looked at cellular automata in fluid dynamics in the 1980s where some of the same issues of deriving continuum equations from underlying discrete dynamics existed it was just far away from what you to prove with anything in a garlic theory that that this specific sort of irreducible computations would lead to audacity but it's worth it's worth looking at it'd be a good thing to look at and there's some questions about ogre that's today that you could look at in the space of hypergraphs even pretty much immediately and i it's it's a complicated thing because when you have like a cellular automata in the space of states is pretty well-defined it's just possible sequences of bits in the case of hypergraphs even the space of states is hard to define and if you say how many hypergraphs with n nodes are there even that is not an easy thing to answer so a gothic theory is a little bit more complicated when the space that you're dealing with is a space of hypergraphs actually you're making me think that in rule space which i'll finally talk about soon there are some organic theory questions that come up where do i should come up with Turing machines let's talk about that later okay Ramsey theory you're asking about Ramsey theory the directly no but doesn't mean that they don't exist a thing that is sort of an emerging interest is the relationship of transfinite numbers to and things like Goodstein sequences and so on which sort of back on to Ramsey theory possibly in ways I don't well understand yet but I think that the transfinite numbers actually looks like very nice applications of transfinite numbers to understand the essentially infinite time limit of a multi-way system that you may be able to characterize the infinite time limit of a multi-way system in terms of transfinite numbers characterizing its state effectively again we don't know that yet and sort of the comparison between between these things okay there's a comment from jonathan which he's going to have to explain on camera here saying Ramsey theory might be related to particle creation in the early universe oh I think I see what Jonathan is thinking of so that there may be properties of certain hypergraph rules that say once once the hyper graph reaches a certain size some topological obstructions will be inevitable and that will be a purely ramsey theoretic results and that may or may not have relevance to sort of particle cool idea right so to explain it I mean Ramsey theory is as a theory about for example graphs any sufficiently large graph has to contain certain kinds of sub graphs just by it is an inevitable feature same thing for certain arithmetic sequences we have enough numbers there'll always be a an arithmetic sequence defined a certain way there's a nice example of Ramsey theory and my notes and the new kind of science book I'm but any case so what Jonathan is suggesting is that in any sufficiently large hyper graph there will necessarily be certain sub graphs that might correspond to particles just as you might say it isn't true that in any sufficiently large graph so there's a characterization of non-linearity in graphs the the Curt off-screen serum for example and you might say though it isn't true that any sufficiently large graph must can contain nearly as a matter of Ramsey theory a sub graph that could that represents non-linearity that's not true for non-linearity but maybe it is true in hyper graphs for something that corresponds to the topological obstruction that represents the presence of a particle that would be that's very interesting good idea don't forget that idea it's good idea um ok question I don't know what has a Rick here talking about his model deals with underlying primitive space I I don't know that you know one of the challenges here is people send us a lot of you know a lot of of their models of things and you know the fact is in my life I'm going to get the chance probably to explore one model of fundamental physics and you know I this one I kind of started on thirty years ago and we've only finally gotten to the to the kind of point we're at right now it's a hard job exploring fundamental theories of physics and so you know it's when somebody sends me something that says I've got a theory of physics to the main you know the main thing I have to say is well great you know it's like go explore it you know by all means I would say that that I have a couple of caveats to make one thing I would say is you know to have a chance of reproducing physics as we know it you kind of have to connect to the big theories of 20th century physics quantum field theory and general relativity these are because those theories are already you know a million miles above sort of basic high school physics so to speak they have aggregated together just gazillions of phenomena that would be treated as separate that wouldn't even be described instead of high school or college level physics they're they're sort of the the the great aggregators and in a sense they are what you know if you can get those you've got everything or you've you've got you know that's a not everything which you've got a big you've got a big you've got everything we currently know in physics if you can get those theories the problem is those theories are complicated those theories are abstract they rely on towers of mathematics that are not you know basically it's like many years of physics school so to speak to get to the point where you're dealing with the mathematics have gone in field theory mathematics with general relativity you know I was sort of lucky in my own life that I happened to start doing those things when I was a kid and so you know I kind of knowing those mathematical structures for a very very long time and but they're they're complicated structures and I wouldn't know them if I hadn't really actually worked in computing things in them you know it's been funny as I've been coming back to doing physics here I have only realised in the last few weeks how comparatively rusty I was I'm finally getting back in the groove here I mean I think I'm not not totally shabby even when I was a bit rusty but I'm finally getting back in the groove of really really knowing sort of in a very agile way um the all these different things now of course the strange experience from me because it's like a you know I've been a way for 40 years and I come back and a few things have changed and I one of the ones that's sort of amusing is people have been asking about this thing that they call the born rule in quantum mechanics and I was sort of rather confused because I'm like well them but you know I know Bohr and had certain things that he computed about transition amplitudes and all this kind of thing but I didn't know what I didn't you know I sort of assumed this was I kind of guessed what they must mean I didn't know for sure well it turns out the born rule is just the statement the probability is there is the modulus squared of the of the amplitude but when I was doing quantum mechanics people didn't call it that it was just I don't think that really had a name that result it was just how you compute the probability may be prizm people talked about as the Copenhagen interpretation things like that which is kind of a miss miss mistaken you know conflation of terms but it doesn't really matter but anyway what I realized only quite recently is that in the last decade with the rise of quantum information the the notion of the born rule which came out of which was described that way and von neumann's mathematical work on quantum mechanics that has become the name for that idea but that's a recent name I mean the idea existed from the 1920s and I certainly understood that idea very well in the 1970s but it only sort of it only got that name it kind of reminds me of when I look at sort of elementary school math textbooks and they have names for mathematical operations and it's like I have never heard of this I've been doing math all my life and I've never heard of this name of you know carry forward you know something or others and I realized that sort of something that's emerged in the kind of meta description of mathematical education but it wasn't part of the Canon of actually doing it but anyway so you know back to to sort of other people's theories you know I think the it will be the case that there are people who've developed who've worked on sort of sophisticated mathematically oriented theories that connect that are typically honestly in the in the professional physics and mathematics domain the that you know relate to you know twister theory relate to whatever else these are things which I fully expect to have have have gotten enough mileage within those theories themselves that they will be useful in understanding things for our theory when it comes to kind of I've got a theory and it's kind of based on high school physics it's really not very promising because you are short cutting you're you're kind of jumping over you're ignoring 20th century physics and you kind of need that to know whether you have a theory that makes any sense now you know having said all of that I will say that that I personally consider people say will you help me with my theory and the answer is well no because you know I only get one shot in my life probably to work on a theory like this and I I almost got 0 shots in my life to work on a theory like this and you know I'm going to my theory is going really well thank you and I'm that's what I'm gonna keep pursuing and I think that um the the question however I will say something if you say well you know that's not very nice you should be contributing to other people's theories I would like to point out that I've spent about 40 years of my life doing exactly that building tools that are basically the tools that get used by most you know theoretical physicists people like that to explore theories and you know that I've sort of built the upstream tools I led the building they have a large team that works on these things the the building of Wolfram language Mathematica and so on which are the upstream tools that people should use and again if you're not using those tools you've just you know kind of you know if you it's like you don't lose 20th century physics huge handicap don't use the tools we built to do sort of the things you need to do in working out theories big handicap so but you know as I say my my major contribution to everybody else's theory which is what I've been mostly doing before I started working on this this this physics again is we've built a bunch of tools and those tools I think are the world's you know have been for the last several decades the primary tools used for exploring these kinds of fundamental physics ideas and so that's one thing to say now I think I'll just make one comment about kind of the the sort of the the I've got a theory to type type type situation I mean I think a lot of people I've been very surprised at how many you know literally probably hundreds now of people sending us things about various different theories and you know I kind of my my instinct is it's kind of like you know I I'm like I'd like to to suggest something do something but you know it's like I I had the experience actually has a funny story I had the experience when I was what was it fifteen years old maybe I was I was starting to physics I published physics paper or so and somehow person was in England the a person who had some some theory of physics got my address and sent me this letter about you know I've got this theory of physics and it was a theory about how there were I don't know loops of wire that correspond to electrons and things like this okay so I you know was just a naive fifteen-year-old and I'm like this theory is obviously wrong you know I can perfectly well see you know if you if you look at how quantum electrodynamics works you look at this whole big bucket of experiments that have been done this theory is just obviously wrong and you know couldn't possibly be correct so so I wrote back to this person and I said look you know that's all well and good but there are these you know these experiments show this theory can't be correct so I then got this whole deluge of letters and it was all a rather rather unfortunate situation and that kind of that kind of put me off for gosh what is it now that was 1975 so so a solid 45 years put me off kind of responding to these kinds of things except in the case of kids kids are different that that's been a different story um but um and actually I'll tell you one very bizarre thing and I'm getting off topic here and I'm just telling stories but I'll tell you this Punk is kind of a kind of interesting I actually found recently an envelope which was a letter I was intending to send that person back in 1975 that I didn't send for some reason or another it was sort of my final iteration in this in this exchange and I was like what am I gonna do with this letter it's from 1975 it's to a person who I remember in his first sort of introductory letter describing himself he he described himself as I think he said I don't know exact age but you know I'm I'm a well-preserved 62 year old that's not something like that and and to me at age 15 that seemed like an impossibly unbelievably ancient kind of age but because it doesn't seem quite so ancient anymore but in any case I I'm I was we did do some research to try and figure out whether we could track down at least descendents of the person to whom I been intending to send this letter 1975 but without luck okay that was a very long answer to her to a comment there um question about the quantum eraser experiment and this is one where I'm I'm well I'd have to I would like to actually get on and talk about some of these other things so let me just um okay there's a question from Dale here how do I think this project might change the academic community for laypeople and does this represent sort of a democratization of scholarship that's a really good question I think the answer to that will depend on to what extent non academics really make big contributions to this project and I know people are starting and I'm really looking forward to seeing what happens and I think what you'll see there I suspect I might be wrong but I suspect there will be some very practical contributions I know people are working on this right now from a sort of computational point of view parallelizing code making things work in virtual reality for visualization those kinds of things that don't require a big stack of kind of mathematical physics knowledge there may be some insights that come from people without that big stack of mathematical physics knowledge maybe some very very interesting insights I mean I don't I certainly consider it not impossible I don't know something like the understanding of multi space no idea whether that's going to be usefully informed by a big stack of mathematical physics knowledge or whether it's just like a good idea um that needs to be had don't know so that could come from sort of the non sort of academic professional people I think that a community that we're seeing is people who have been educated in sort of the traditional Canon of mathematical physics but who for one reason or another their software engineers now with something else and this is kind of a hobby activity I suspect there will be some really big contributions from people like that and I think that that is interesting because it represents you know the value system of academia which is like published papers you know do it rewards certain kinds of things which I don't think are optimal for the progression of science I think that you know for example one of the things we've been doing well I haven't written enough of these yet with these bulletins um you know journal articles the days have a habit to my mind of being extremely boring and extremely incremental not always but but a lot of them are um and they're very much like I am putting down one little step in a long progression and I'm not really explaining why I'm doing this I'm just saying you know recently Smith and Jones did this so I'm going to take another step in that direction and it's pretty boring and unless you know in detail what Smith and Jones did you're kind of up a creek in terms of knowing what this paper is talking about back in the day you know when journals were first invented in the 1600s people were much chattier you read what they said and it's like oh you know I I found this kind of strange animal living in or whatever and they have a kind of a chat about it so in the bulletins that we're writing I'm I'm you know I'm purposefully you know there's a certain amount of chattiness they have a lot of detailed technical content but they're also kind of chatty and that gives one a reason a way of explaining the motivations for things which I think will make things more accessible I hope it will um so I think it's sort of um now in terms of of the kind of you know you have to remember what academia is in a sense you know academia is a lot about universities and the you know what um universities about their longtime mission from the 1200s so to speak was sort of the the passing on of scholarship from generation to generation in my opinion a very important thing to do I sometimes universities lose track of that that motivation and say oh that stuff from from the past that's all irrelevant we don't need to pass it on I think that's a mistake I think we have this sort of unbroken chain of knowledge for a long time it's really important to pass that on but you know universities sort of in the last I don't know 50 60 years really became these places where sort of a lot of in most countries not all countries it doesn't work this way in all countries are the places where research happens the fact that those two things are bundled together is complicated and has led to sort of complicated dynamics back back when I was a professor okay a shocking thing that I will admit to is you know I ended up you know it's like your professor so you do you know you give classes and I realized by some point I signed up to give a physics for non-scientists class I thought it'd be kind of interesting um and I realized oh my gosh I have no idea what to do in an undergraduate class because I've never gone to one myself I I went for various reasons I went to Oxford where I didn't need to go to classes and didn't go to classes and things um and uh you know I'm like I'm in this undergraduate class and I I don't know what to do and and that's sort of a mechanism of Professor I was I was a while ago that was in the mid 1880s so maybe things have changed but but it was sort of shocking that you know I was I was hired as a professor because I you know was doing research that was interesting but nobody ever bothered to say by the way have you ever taught a course ever I've taught graduate I taught graduate courses but they're a different story so so you know I'm a good example of a bad example so to speak of that I think my cost was kind of interesting in the end um okay let's let's um I really want to get to talking about some okay there's a question how much of nothing is there in the universe the interesting questions let's see oh there's a question from Dale thought experiment priority of universes graph growing to surreal numbers yeah yeah that's thinking about it go think about it I don't know I don't know that's growing the surreal numbers interesting question um let's see there's a question from Olli about will we be able to see matter absolutely we have matter both in bulk and potentially for particles um the okay oh boy so many questions here so many interesting questions this is this is terrible interesting thing from Sean here I just noticed why did John 1:9 say he started to not believe in Hilbert space didn't know he'd said that um okay question from Andrew and your theory does quantum entanglement have a limit within physical space that is an interesting question I mean that relates to the multi way causal graph we're mostly quantum entanglement has a maximum speed of how many states are getting entangled um the right listen let me um let me skip I'm gonna try and come back to some of these questions but let me let me skip ahead and just say a few things I wanted to say about quantum mechanics and about rule space okay quantum mechanics alright so this is sort of our our emerging understanding of quantum mechanics okay so first question is okay quantum mechanics usually described in terms of quantum amplitudes quantum amplitude is you know you talk about a state and you talk about you know you represent it as a sum of basis States there's an amplitude for each of those states and so on they're all complex numbers okay so one of the things that we are pretty sure of is that the packaging of quantum amplitudes into complex numbers is misleading and that in fact you should be thinking about separately the magnitude of the number of the amplitude and the phase of the amplitude and roughly the way that comes about in our models is the magnitude has to do with essentially path counting which it's saying in the multi way graph you're going to reach a certain state and what and and how many paths in the multi way graph how many different kinds of rewritings can get you to that same state and that's what determines the magnitude of the quantum amplitude now what determines the phase well the phase we think is corresponding to the position and branch field space that that amplitude is that that state is at that is the amplitude of the state is its it's how much it was fed by paths in the multi-way graph and then its phases where it is in the branch field graph so so in other words unitarity that sort of conservation of probability sort of inevitable by the when you're dealing with this path counting idea but then phase is determined by that there's a separate piece which is the phase of the amplitude okay so in the path integral my friend dick toyman's path integral formulation of quantum mechanics the the kind of approach there is to say what you do is you look at this this bundle of paths in our interpretation propagating through the multi way graph and you're asking the the path integral tells you that the phase associated with one of those pauses e to the is over H bar where s is the action and so in our model that phase represents this turning of the JD SiC which determines where it lands in bonechill space and it's kind of interesting that the path integral is just a phase and the and the measure is what gives you you know there's there's a measure there and that measure corresponds to our counting a paths type thing so and the phase is essentially the way to think about that phase is it's a turning of jd6 that that phase represents the turning of gd6 turning as in changing your position in branch heel space so we don't fully understand how this works we don't fully understand branch field space it's probably some kind of projective hilbert space in some continuum limit don't fully understand that um but this is sort of the picture of what's going on and we can sort of mathematically do things even without really knowing what branch field space is really like but so so first statement is you know really separate these two things okay so the next issue is the born rule that I just mentioned to you the concept that oh actually here is a question so how does interference work how can it be the case that there are two paths and they end up saying that they're two paths that contribute to something one of the mysteries of quantum mechanics is there are two ways the photon can go through the slit two slits but two adds up to zero in the sense that there can be destructive interference and even though there are two paths for something to happen the net result is that nothing happens okay how does that work in our models well the answer it seems is that what's happening is it in this bundle of gd6 the bundle of jd6 is turned so that one judy SiC is basically going off to one corner of branch Hill space and the other judy stick is going off to the other corner of branch Hill space and when it comes to measuring what happened okay I should explain this the observer is themselves and is in some sense the the typical observer who says I'm gonna measure whether we're in this quantum state that means the observer is localized to a patch of racial space the observer is saying my detector is this thing that's measuring was there anything in this patch of broad chill space that's what it means to say did we hit this quantum state um did we you know in the bra ket formulation did we you know is this bra ket thing nonzero the the okay so then the question is in that let's say that these two photons go through these two difference you know slits the paths the gd6 and brought in in multi way space that correspond to those are routed to two different completely different places then in some sense they will and this is I'm being kind of vague here but we have a somewhat more precise mathematical formulation of this they will both sort of miss the observer in Branch Hill space so the observer will say oh nothing happened it didn't you know there was no result because the the kind of the the the the support for these two outcomes were routed to different parts of branch Hill space now we can get a little bit more precise and we can start thinking about when we think about the observer we think about the observer as themselves a bundle of jd6 in multi-way space and so then what we're asking is when we ask this question what's the probability for something to happen what we're essentially asking is how do the threads by which that thing can happen in the multi way graph how do those overlap the threads which are exist inside the observer and we're not you know this is still in gestation it's still being worked through but roughly what happens is that the threads of the observer and the threads of the thing being observed you're essentially to sort of make a correspondence between these things you're matching up every thread with every thread and that's essentially where you end up getting this notion of the squaring of amplitudes to get probabilities is by virtue of the fact that what matters is kind of all the ways that these threads can be matched up at least that's the that's maybe Jonathan has a CRISPR way to say this we're we're actually this is somewhat related to Jonathan's interpretation of quantum mechanics in terms of completions that I think gives a nice way to understand what's going on here and maybe Jonathan wants to wants to make a a better Christmas statement of this I don't think there's that much more to add I think I think you already said it pretty well so yeah I mean when you when you have states that would otherwise just you know in a conventional formulation of quantum mechanics would destructively interfere we've seen you can go back I think you can watch our quantum computing discussion for an explicit example of this you see that they they end up as as B as being on opposite ends of branching spaces as Stephen said which correspond effectively to orthogonal vectors with respect to the multi revolution graph so then Stephen mentioned one kind of operative way we have of modeling quantum measurement is in terms of these completion procedures where we say the observer is met is defining equivalences between these microstates where those equivalents is defined by that observers particular choice of reference frame that particular choice of quantum observation frame and so then what happens is when so those two microstates that happens as destructively interfere they are sort of maximally branch-like separated when you translate that into the language of completions what that means is you cannot consistently perform a completion on those two microstates without destroying all of the information and so as a Steven mentioned sort of the geometrical interpretation for that is in order to be able to measure those two states the observer would have to build some measurement op some piece of measurement apparatus that was so extended in branch real space that it would basically measure everything and therefore would would yield zero net information in the completion case we can actually show that expose that the only symmetric completion procedure they can apply that would define in equivalence between those two states is one that yields exactly zero information and so you can say in a very precise sense that the the path weights for those two states cancel out yeah that's good I mean okay so the thing we're close to you know coming attraction is fermions versus bosons fermions have the feature that when you have these you know these different paths adding up in effect they're adding as opposed to a fermions bosons they add fermions they subtract we're sort of teetering on the brink of being able to say something about that hopefully coming soon that's one of the things we want to look at UM the okay so question okay let me talk a little bit about what I've been doing in rule space and let me actually show you here something about that let me show you this is my oh there's my homework so to speak of the thing I've been writing which will turn into a boat and soon the okay what is real space normally we think of normally we think of our models as looking at we have these rewrites applied to these these rules for rewriting hypergraphs but one thing you can ask is what if you could rewrite hypergraphs with all possible rules that might apply not a particular rule but all possible rules that's a rather a weird concept it's like saying the universe is following all possible rules but it turns out because of Koslow invariance there's a kind of relativity of rules and you can still make definite statements and I kind of suspect this is how the universe actually works um and we can talk about what that means but let's look at um let's look at what it means in the case of Turing machines okay so what does what is rule space in the case of Turing machines so Turing machines are these standard mathematical models in medicine in 1936 bile and Turing for computation this is a concrete Turing machine it has a little head here and it walks that head back and forth along a tape the as a state it can be either up or down in this particular example and it has rules that say how to write colors on to the tape and how to flip the state of the head and how to move the head left or right okay so I have to say I always thought turning machines were a bit of a mess but I've come to like Turing machines better because they actually are very clean mathematically for looking at certain kinds of things here I have a sort of another form called mobile automata and I came up with in the early 90s that that term I think I'm going to look at as well but but I actually i'm liking turing machines but for this right now and they have kind of the the nice historical connections to the theory of computation okay so an ordinary turing machine has a rule like this it's a definite rule the turing machine does a definite thing rules of this type which have two states two colors there are 4096 of those rules here are the things that those do from a blank tape um the okay now if you know theory of computation you've probably heard of non-deterministic turing machines those are turing machines which don't always follow the same rule they might have two sets of possible rules that they could follow and then to represent the the behavior of a turing machine we have a multi-way graph not usually called that in in Turing machine ology but to know what it is called I don't think people really talk give it a name but it is it is the graph of which again people almost never explicitly draw of what the non-deterministic things the what the sort of non-deterministic possibilities are for the Turing machine so this is a Turing machine with these two sets of rules and this is showing a multi-way graph that this is applying one of those rules this is applying the other rule and this is what the weather Turing machine does okay what is the rule multi way system the rule multi way system is something that I had never thought about before for Turing machines which is it's the graph you get by following all possible in other words you make it the maximally it's the extreme non deterministic Turing machine it says at every step use any every one of the 4096 possible rules and apply all of those rules so that thing will make a multi-way graph this is that multi way graph so in the first step what happens is from this state you can go to different among those 4096 rules these are the possible things that happen you go two steps there is some the OL alison silver is really on the ball here asking about the simplest non-deterministic Turing machine could there be a thing such as the universal non-deterministic Turing Train yes I realized that about a week ago there is I'm looking for it um lots of good things to say there um okay in any case the UM so let's sum okay but back to this so this is a a rule graph rule multi way graph I call it a rule graph because it is showing the outcome from all possible rules it's at each step okay now many of those possible rules actually do the same thing that's why there are only two edges coming out here if I were to show all the possible rules separately there would be a big bundle of edges going to the same place okay so the question then is um the okay so so what's happening here at every step I has a piece of my thing that isn't finished yet but at every step is this correct or is this still incorrect um not sure if that's correct yet but in every step every you can apply any one of these should be 32 possible rules so every at every every step in the evolution of the Turing machine you just say I'm gonna do I'm gonna be extreme non-deterministic I'm going to apply every one of these possible rules okay all right so this is this is what happens this is the multi way graph that represents Turing machine evolution that represents the accession of the extreme non-deterministic Turing machine in in multi way space so every one of these dots here is a configuration of a Turing machine and this is staying starting from let's say a blank tape in the middle here this shows sort of the Treeing out of all possible that non-deterministic Turing machine outcomes okay so one little spoiler here this space okay so this this creature this is this is a non-deterministic Turing machine space and unfortunately very big so it takes a long time to my notebook to load here come on come on come on okay so one of the things I was just figuring out is this structure turns out to be the Cayley graph of a group and so I've been on a hunt for the last ten days for what group is it and actually I'm tally who's been on some of our live streams I was talking to yesterday and tally after we we defined some things actually also my okay my son Christopher had done some pieces to this and tally did some pieces to this and anyway the end result is we now have a construction for what this let's see if I can show you I haven't yet put it in here so it's not I'm not quite finished but the this week might call it the Turing machine group this is the Turing machine group for the case of Turing machines with let's see tapes cyclic tapes of length three and it's this is the Kaylie graph of a group and that Kaylie graph is the multi way graph is the rule multi way graph of the Turing machine and so we finally now know what the group is and I would have to pull it up to but we have group relations someplace here which I haven't written down properly but we know the group relations and we know what the scoop is and it's a semi direct product of certain other groups and it has been somewhat studied I think although I need to read more about it as a kind of generalization of symmetric groups so that's kind of interesting so it tells us this there's this Turing machine group that represents non-deterministic Turing machines space okay so this is the rule multi way graph it's the space of all possible not also the a non-deterministic Turing machine follows a path in this graph and so a non-deterministic Turing machine if you say how do I get from this state to this state there's a geodesic you can follow that can be followed by the extreme non deterministic Turing machine that gets from this state to this state ok so that's the life of non-deterministic Turing machines okay next question how does this relate to deterministic Turing machines okay so let's imagine a deterministic Turing machine this is a particular deterministic Turing machine the evolution of that particular deterministic Turing machine corresponds to a path from a particular initial state corresponds to a path in this essentially Turing machine group space okay so every at every step in the evolution of the generic Turing machine it's visiting a new configuration in this in this Turing machine space in effect okay that's that path is not a JD sick the the there is not necessarily the shortest path the deterministic Turing machine might waste a huge amount of time getting to one of these outcomes here um so okay so one question we can ask is what is okay this was for a different initial condition that turning machine follows a different path okay so now we can ask the okay that's one that definitely isn't a JD SiC it has a big kink in it so now we can ask the question if we look at all possible the terminus dick turing machine so we say let's get I really want to get to some state that's out here in the periphery give me the best non-deterministic Turing machine I'm sorry the best deterministic Turing machine that gets me to that state the Turing the deterministic Turing machine that in the fastest the shortest number of steps gets me to that state can I get there can I not get there okay so this picture shows the deterministic Turing machines all 4096 deterministic Turing machines of this type it shows in red where they can get in a certain number of steps and so you see there are states here that no deterministic can work well a non-deterministic Turing machine by using different rules at different steps can get to that state the deterministic Turing machine cannot reach that state in that number of steps okay so okay so some people probably know computational complexity theory here and probably already guessing where this is going um so but what this is saying is the non-deterministic Turing machines can reach a certain place in this Turing machine graph the deterministic ones can't quite reach there okay what does this remind us of this reminds us of the P versus NP problem so the P versus NP problem is the question if you have a deterministic algorithm that as a function of its of the size of the instance of the problem runs at a time that's polynomial a number of steps requires a number of steps it's a polynomial in the size of the problem that's called a P polynomial time algorithm NP is this is the set of non-deterministic polynomial time algorithms the set of algorithms which are among other things polynomial time for a non-deterministic Turing machine so P is the set of algorithms which are polynomial time for a deterministic Turing machine NP the set of algorithms which are polynomial time for a non-deterministic Turing machine and and that can be interpreted as saying if you guess answer you can check it in polynomial time but but the the you know you can also define it as it's polynomial time for a non-deterministic Turing machine okay so what you're seeing here is basically the comparison between deterministic Turing machines space and non-deterministic Turing machine space and so the P versus NP problem is the question of is NP the space of non-deterministic polynomial time algorithms bigger than P the space of polynomial time algorithms ok so this is kind of a the beginning of a geometrization of that question because this is basically saying so I have to be a little bit more precise to talk about what P and NP are and these in these systems um so the so what's happening here is so as we as we scan over the different possible initial conditions for a Turing machine we're scanning over so so this I told you this was the the calligrapher group so if you're math oriented you know that means it's a versa but it's transitive graph it means the graph looks the infinite graph looks the same from every vertex it's homogeneous which is to say doesn't matter what the initial state of the Turing machine was the initial configuration of its tape you'll always have the same set of possible places you can go from that ok so now what we're seeing is this so when we think about a polynomial time algorithm what we're saying is we've picked an algorithm we've picked a particular deterministic Turing machine that represents our algorithm we could also prick a prefix for in a universal machine but let's not go there doesn't matter okay so given that as we scan over the different inputs for our initial condition we are scanning over a certain set of possible positions in this Turing machine graph ok now as we look at as we increase the size of our initial conditions as we increase the problem instance size we're looking at a bigger and bigger ball of initial positions in this graph so effectively what we're doing is we're taking this long snake and we're starting the tail of the snake so to speak listen oh I'd better say the head of the snake and a particular place in this graph and then we're seeing whether the tail of the snake go okay so what will happen is as we move that head of the snake around the tail of the snake will flail around all over the place okay the tail of the snake will baste but every every time wherever we start it the tail of the snake will be will wind up in some position here okay now we could have one of the questions is if what we're trying to sow so the question is how does how a ghatak is the tail of the snake so by which I mean to what extent as we change the initial conditions here to what extent does the tail of the snake scan over all possible configurations okay and essentially that is the question of P versus NP it's the question of whether we know that the complete Turing machine graph is the set of configurations that we reached by an NP a non-deterministic Turing machine in some sense in some time that is that corresponds to a certain number of sort of segments in the snake a certain number of steps a certain there's a certain JD SiC ball of where we can reach in this rule multi-way graph and that is defining the the frontier of NP problems then the question is how far can a deterministic P problem reach okay so I think what we're getting from this is essentially a geometry zation of the P versus NP problem and so what we need to understand is for example what is the limit we understand okay so this is we understand as of last night and I haven't really fully digested it yet what this group structure is for the multivariate rule multi-way graph and so we don't fully understand at least I don't fully as an understand yet the geometric group Theory interpretation of the limit of that group for the infinite case I think that is probably going to be understandable with geometric group theory um so that tells us something about the space of NP problems or the space of NP things so so now the question is what can we say about the space of of P of deterministic things and let me show you an example so this was some yeah the question is always you know is P versus equal to NP the question is always you know can we find an algorithm that is you know is there a Turing machine an algorithm that succeeds in doing this NP complete this problem that is the hardest fret that it can be for NP this np-complete problem in polynomial time if we could we've proved that P is equal to NP but what happens is when you try and really do that when you try and find what is the optimal algorithm for progressively larger instances of a problem that is a very squiggly issue so for example here's the case of sorting networks these are the optimal sorting networks the optimal ways of doing comparisons between between between values to sort different numbers of things and what you see is that the optimum algorithm is a very complicated messy thing and if you ask what's the infinite limit of this it's going to be hard to know what that limit looks like okay so having said that what is the space of deterministic turing machine computations okay so what we're doing now is I've said there's a graph here that is the deterministic turing machine computations that is embedded in the full turing machine graph the full Turing machine group Cayley graph ok but now we could just pluck out that deterministic graph and we can look at that on its own we can just say given the possible Turing machines what which states do they reach and when do they reach common States so let's take a look at that so this creature this sort of sea urchin like creature represents starting from a configuration of a Turing machine at the center that is a head in the middle blank tape this is looking at other possible configurations of the Turing machine and eventually with all possible deterministic turing machine rules but each one is a deterministic Turing machine so the spokes here basically correspond when you get far out in the spoke there's just one surviving deterministic Turing machine that gets you to that configure particular configuration in the central region there are many different deterministic Turing machines the getage are the same to the same state so if we look at that central it has quite a bit of connectivity there but when we get out into the periphery there's only one solitary Turing machine the deterministic Turing machine that's getting you to that particular place so we can ask questions like what's the what how many Turing machines how many distinct States do we reach when we go a certain distance out and you know what do what are those strands in this deterministic turing machine graph look like and that's the strands have a lot of fine structure so that's a strand and what that's representing is there are several Turing machines here are examples on that strand of what Turing machines live on that strand what Turing machines are are doing things which all lead to States they all lead to the same state so they're all living you know they all go to a state on this strand but the Turing machine the the the edges here which corresponds the different Turing machine rules are different but they're all sort of bundled together on the strand okay so so this is kind of the picture of deterministic Turing machines space and its comparison to non-deterministic space and so this I mean I I don't have a conclusion from this other than to say that I think if we could understand the continuum limit of this as I think we now can as a last night maybe have a decent chance of understanding the continuum limit of non-deterministic Turing machine space then I think we could have a geometrical understanding - for for the P versus NP problem which will be quite exciting I might mention you can do the same thing as I've done with Turing machines here you can do it with cellular automata I'm just amazed that having studied teller atomic up for 40 years I've never done this before but anyway this is this is the the difference sort of elementary cellular automata living in this multi way graph showing how they end up with common States or not so it's kind of this is sort of pruning it down there's my favorite rule 30 off on that prong it just diverged from probably rule 94 if I know my cellular automaton rules um the the uh yeah so I'm just looking and dis glancing at the comments here Marcus is commenting the machines are closed topologically yeah that's basically what we're saying here there's a there's a notion of a rule space in which in this multi way graph we can start looking I I should have shown this we can start this defines the connection of machines by virtue of not being far apart in the rule graph having nearby common ancestors in the rule multi way graph that gives a nearness for machines and so we can we can represent that nearness and machines I think I had some pictures of in terms of rule graphs of machine States and machines and so on and this this is a way of representing how close things are it's a way of defining closeness for configurations of machines okay so how does this apply to the universe well I mean I think it applies it's really pretty interesting for a computational complexity theory but um we're also trying to do physics here so so how does it apply to physics alright let's see this was so so one question is how does a universal Turing machine apply here and that just has to do with a Turing machine that's a little complicated but basically it has to do with an agar DISA T of a Turing machine in this some in the space um question for Marcus about partial order on models interesting not sure as the answer that I'm not sure offhand okay this is the craziest part it's not crazy it's it's it's just very abstract okay so let's talk about um okay let's talk about sort of the world of real space okay what is real space what does it mean okay so we've talked about a real space is this rule multi way graph represents the evolution of essentially the universe according to all possible rules at every step every possible rule of the universe is used every possible rule of evolution is used okay now this is where things get a little bit mind-bending we're also now thinking about the observer being part of this universe the observer is themselves a thing that exists in this rule multi-way graph where all these different rules are getting applied it's about like the same as in quantum mechanics and I suspect that Jonathan's interpretation of quantum mechanics in terms of completions can also apply in rural space and that we can start thinking about rural completions but we don't have to go there quite yet what we so one thing I should say about rule multi-way graphs is causal invariants is very easy to get in them and that sort of almost inevitably arises okay in the first approximation okay so now how do we describe the universe we've got this rule multi-way graph that shows all these different possible paths corresponding to different possible specific rules for the universe just like I was showing you deterministic Turing machines living in this space in this background space of non-deterministic Turing machines so similarly here there is a deterministic rule for the universe that lives in this background space of all possible rules for the universe so okay so we've got the we've got this this path that corresponds to a particular rule that we're attributing to being how our universe works okay so what does it mean to move around in rural space okay what it no let me let me put that a different way what does it mean to pick a different reference frame with which we're referring to parts these are both conflated in a certain way the the and again this is very abstract and it's just sort of it'd be at the edge of my understanding so let me say it roughly and it may not be quite quite correct but roughly moving around in rural space is moving around in the description language that you're using to describe the universe so it's not quite right it's really more like the reference frames that you're using but those reference frames might be a rural observation frame might be one that is localizing you to a particular place in real space but the the thing that we can understand is we're picking a particular description of the universe and that's the one that we're using for our universe okay so now we can ask questions like all kinds of questions so one question would be in rural space we have this rural multi-way Gulf it's it's there are all these different possibilities for where we land up in rural space remember the Turing machines there are all these different configurations of the Turing machine and our rule multi-way graph knits together those different configurations by telling us which configuration is near each other one by ancestry and the rule multi-way graph or alternatively said by rule distance between those configurations okay so we're we're basically getting something where we are looking at as time progresses as computation takes place how rapidly do two points diverge in rural space in effect we can think just in physical space we have an event that happens the effect of that event is seen at most at different points in space at the speed of light we have a light cone this region of what part of space can be affected by an event that happened that light cone the size of that light cone after a certain time the size of that light cone is determined by speed of light times the amount of time that's elapsed the maximum distance that we can affect in time T is C times T okay so in in branchial space of quantum mechanics we think there's a similar thing going on that after a certain time the maximum quantum entanglement that could occur the maximum distance you can go in branch chill space is this thing we're calling Zeta times T okay so in in rural space there's a similar kind of thing where there's a thing calling it Rho which is the maximum rate of divergence of a of a cone in rural space of the effect of an event in rural space there is a a divergence of of the effect of that event in real space okay what on earth is that that Rho quantity that Rho quantity is in a sense we can call that cone an emulation cone that cone determines in some sense the maximum rate at which one model of the universe can be converted one rule by which we model the universe can be converted into another rule by which we model the universe so I'm sorry this is pretty abstract and I'm mum but but so what's happening in rural space is this this cone in real space determines if we're an observer in the universe and we say you know we are going to not keep a fixed view of how the universe works we're gonna be changing our view and we're going to be doing it at a certain speed the maximum speed at which we can change our view of the universe is this Rho quantity and in some sense what that means is and why does that happen well we are using our the universe is happening in the universe itself and so it's for that reason that there is when we sort of weave back the effect of the observer to observe the universe that they're in themselves we see that there has to be a maximum rate of this divergence of descriptions a maximum rate at which we can change our view of how the universe works ok so what is this so one thing that we might ask is what is the interpretation of so we can we can think about all kinds of crazy things with this with this Rho quantity we can think about all kinds of crazy things happening in ruel your space so so one thing I don't really understand very well is what the jd6 of rule space saw in the case of Turing machines they are the fastest path non-deterministically to get to a particular result um but I don't really understand what the significance of that is in real space yet um I don't understand yeah so I don't really understand that so there's a question earlier about what the analog of the Einstein equations is in real space and I think we can say a little bit about that so here's a question what is the analog of um what's the hour of the black holes in rural space ok so this we can say something about so normally in rural space we can imagine that there are multiple multiple frames multiple descriptions we can be using we are we're able to say that we take a path through your space and that path is equivalent to another path we we can we can by changing our frame we can make one path do the same as what another path does so in other words we can change our description language we can end up saying there's a different rule for the universe ok well that's all well and good but here's the thing that won't work so let's say that the path we consider the rule we consider is a computational irreducible rule it's not a rule that has universal computation it's not a rule that shows computational irreducibility it's a rule it's just really dumb all it does is to say the answer is 3 every time just says the answer is 3 the answer is 3 the answer 3 well we can't take that the answer is three paths in luleå we can't take that place in rural space and say oh we can somehow convert that to a true description of the universe there just isn't enough stuff going on in that particular sort of path in the universe that roughly that particular position in rural space to be able to give a full-featured description of the universe so that's kind of like a black hole so that's saying that the pockets of computational reducibility in this sort of ocean of computationally irreducible computational processes the places in that space of possible rules that are so dumb in effect that they just they can't they sort of they can't perform an infinite computation they get stuck after a fixed time they they are reducible you can just say the answer is whatever those are the things that that are like black holes or more to the point probably like space like clarity's which live at the center of certain black holes they are places where probably like all black holes actually they're places where the sort of the gd6 that represent the continued computational evolution of the universe just stop so in a sense there is a there's a certain in rural space there would be these sort of computational irreducible theories dotted around rural space that correspond to the black holes of rural space and this Rho quantity will be the escape velocity in luleå space above which you form a black hole in the real space now again I don't really understand how this all fits together yet but I think there's a notion of something I don't yet understand this and and I think that this idea there may very well be at least metaphors of so the development of knowledge development of ideas the development of different rule systems as ways of describing things for this rule space which we're inventing as something to describe the space of all possible physics --is and which we are now applying to understand computational complexity theory in turn machines but it may also have applications in essentially the theory of knowledge and so on at a more general level having nothing to do with the universe in particular but if we talk about the universe in particular we can ask questions like what is the value of Rho in our universe in particular right just like we can say what is the value of Zeta the the the maximum entanglement speed in our universe in particular what is the value of the speed of light in our universe in particular well the speed of light is measured in distance per unit time okay so in order to say the numerical value of the speed of light 2.99 whatever it is 7-9 x mb 8 meters per second we have to know we're measuring in meters per second if it was measured in you know you know fathoms per fortnight or something it would be a it would have a different numerical value so we have to decide what is our unit for for example length what is a unit for time the natural unit for time in our models is the elementary time which is about maybe 10 to minus 100 roughly 10 to the minus 100 seconds so roughly I mean that's it that's a it's a guess based on various things but um so so when we measure length and physical space we have the notion of we have what we what the speed of light is doing is it's converting this one essentially unitless thing the elementary time into which is essentially the the the thing we're attributing to a single computational update is the elementary time it takes an elementary time time is computation and the a single elementary time is a single computational operation and it takes and it takes that it takes a single computational operation takes one elementary time to occur but that computational operations spread out in physical space is speed of light times elementary times elementary time gives the extent in space that can be some that can be reached by a single operation okay in brawn chill space this quantity Zeta is a can be measured is is roughly related Planck's constant Planck's constant as units of energy times time it isn't exactly Planck's constant but the the the the quantity that for us is this maximum entanglement speed ends up being measured in terms of essentially an energy per unit time and and we can convert it to mass and a guess for its possible value is about 10 to the 5 solar masses per second might be the maximum entanglement speed but it's units or energy per unit time okay what are the units of Rho so the units of Rho are essentially we have a let's see they are basically information content per unit time are the units of Rho they are our description length for a rule they description length and they are the the units so in rural space we've got time going down but we've got in in the extent of real space we move from one rule to another we are essentially measuring the information content that the measure of distance I think is information content rules okay so what an earth is the information content of a rule how do we measure that well you know we have Shannon information theory which measures information and bits that's all well and good but Shannon information doesn't say what the bits mean so in other words when we're talking about sharing information just in terms of probabilities on a communication channel those kinds of things we are just counting okay these are the possible things on the communication channel they don't have anything to do with the semantics of what the communication channel means but for us we need our rules to actually say this is what you do to the hypergraph to evolve the universe okay so we actually need semantics in our rules so we need to be able to have what we actually want is a unit of information content that is a semantic unit of information content we need something that can tell us you know if we describe our universe in terms of Turing machine rules if we describe our universe in terms of Wolfram language you know programs we can in each of those cases we can say what is the information content how many bits how many whorfin language tokens does it take to describe the rule for the universe or a rule you know how many differences of tokens do we need to have to go from this one rule to another so I think the the dimensions of row information content per unit time must be measured in some unit of information content and that unit of information content has to be a semantic unit of information content in terms of some language for describing computation and so you know I have to say my favorite one is the language we've been building for last 40 years well from language but we could be Turing machines Turing machines will be much there'll be a big constant of proportionality because it's a lot of effort to you know emulate the whole open language with the Turing machine but you know it's just a constant difference just like the difference between light-years and millimeters it's just a constant difference um it isn't exactly a constant difference there's some footnotes about how you do conversions between these things and you know interpreters and the deviations of length some interpreters and so on let's not go there let's just say you're measuring rural distance in terms of semantic information content which I claim can best be measured in terms of Wolfram language tokens so the units of roe are Wolfram language tokens per second and the sense what Roe is doing then is it's measuring the intrinsic processing speed of the universe it's measuring how many Wolfram language tokens per second can the universe ingest can the universe actually run okay so what's the value of that well I'm not sure but I think that it is related to the size of so there are many parallel threads in the multi way rule your multi way graph that correspond to all these different puzzle rules that are being applied there's also within each rule you can say well what conceivable rules could apply the universe well mostly the biggest rule we could apply the biggest left hand side for the rewrite rule is the size of the universe itself so that gives us sort of a bound on the size of rules we're dealing with and I think in a rough approximation that it may be fair to say that the value of Rho is approximately the number of nodes in the spatial hypergraph measured given that in our update rules it's on the order of one it's not exactly one wolfen language token per per per node in a hyper graph but let's say it's about one maybe it's five I don't know maybe it's but it's of order one and on the and the orders rang shape we're dealing with it's very very close to order one so that would mean that with our other estimate for the size of the special hyper graph and so on and the size the elementary time row would be about ten to the 450 Wolfram language tokens per second so that would be a measure of the intrinsic processing speed of the universe okay so you could ask the question how many Wolfram language tokens have been generat have been processed in the history of the universe the answer that and a first approximation I think would be about 10 to the 10 to the 350 so that's a big number um so there's questions here about whether whether we can observe the weather we can observe the value of Rho can we observe uncertainty can we observe so I mentioned earlier that I think the analog of the uncertainty principle is the failure of the temporary failure of inductive inference for deducing how the universe works based on observations of it but probably that the scale we're talking about so it's a two smaller phenomenon probably um can we observe rule black holes can we observe these pockets of reducibility what's the density of really old black holes okay so this is one actually Jonathan made this disconnection um the acute connection the density of rule black holes is related to a thing called Omega invented by my good friend Greg Chayton as the Omega is the halting probability for a universal Turing machine so imagine you starting universal Turing machine with all possible inputs with some of those inputs in the classical model of Turing machines no actually we don't tend to use Turing machines that do this but but you know do not have to say whether it halts or just reaches a certain state so some of these Turing machines will after a hundred steps they'll reach that special state the whole thing state another one it might reach it out for a thousand steps another one might go into a loop and never reach it at all another one we might be watching for a trillion steps and we still don't know if it reaches it but Omega is the probability that a universal Turing machine holds after from all possible inputs okay so what's the value of Omega I was at point three is it whatever what's its value well here's the difficult thing its value is non computable why why is that well imagine we've got all these Turing machines and some of them we can say up we saw it Holtz it great it's in the halted been up this other Turing machine oh we saw it went into a loop it's in the non halting bin but then there are these these gradually you know these Turing machines that are just very obstinate and they just can't I should perhaps the they just can't decide what they want to do they keep going they're going a trillion steps they're going at quintillion steps they're going ten to the ten to the ten steps and they're still scrag lling around and we don't know what they're going to do because of computational irreducibility there may be no faster way to find out what that Turing machine is going to do than to just trace all those steps but since there's no bound on how many steps the Turing machine may go we have to say that's an undecidable question whether it will halt that's the classic undecidability of the halting problem for Turing machines but that means this quantity Omega is fundamentally non computable because some of the Turing machines that we'd have to know whether they halt fundamentally there's no upper bound to the there's no way to know whether they'll halt so that means the density of black holes in rural space which would be which is essentially the density of black holes there's the density of computational irreducible things which is roughly halting turing machines it's roughly the density of halting turing machines and you have to sort of pull it back to talking about universal turing machines but it'll boil down to the same thing um then that quantity so this the weird thing so the density of black holes in rural space is undecidable is uncomputable so what does that mean well why does that how could that possibly be right well the answer is what's happening is that in rural space let's say we're watching rural space and we're saying did a black hole form and by the way we could do this for our Turing machines and things like that it won't for the for the ordinary non-deterministic change there's nothing terribly exciting will happen because the background space is all the simple but for other systems we might have a more sophisticated thing going on but um and we might be forming actually is that even true I think we might even be able to see black holes in Turing machine real space um any case oh we yeah I thought we should be now that I think about it we should be able to I'm the and and so the problem is you're looking at a piece of rural space you say did this make a black hole oh there's some things where there's some gd6 which seem to be trapped are they really gonna be trapped forever or are they going to find a way to escape that's an undecidable question in general and that's why this density of black holes can be under sizeable so I think come the um okay so so let's let's talk about one more thing about rural space which is imagine we've got an interpretation of a black hole in rural space what about a white hole in rural space what about something that is a maybe this isn't quite right but but um okay so the question is plop a hyper computer into rural space let's say our Turing machine rural space just imagine that we also have in addition to our happy Turing machines we have a hyper Turing machine what is a hyper Turing machine hyper Turing machine is a Turing machine which says oh you don't have to waste all your time waiting for an infinite time to answer that halting problem I the hyper Turing machine just know the answer I can immediately tell you with my hyper operations I can immediately tell you the answer to that halting problem is it doesn't hold or something it's Alan Turing called these Oracle's you you just ask this Oracle machine does my machine halt or not and it just tells you the answer okay so that's hyper computation is and so the question is in rural space imagine that you had rules that corresponding to hyper computation what would those look like to an observer in rural space to the hyper computer our universe our just pure Turing level universe would look like a black hole in hyper computational space but to us that hyper computational space will presumably look like a white hole that is it will be something where it is spewing out essentially I think is sort of spewing out rouille ol gd6 I think not quite sure if this is right um but anyway so the question would be what you know can you make so in hyper computational space you can again make a rule EO multi-way graph where the where the edges of the ruler multi-way graph aren't ordinary Turing machine operations they're hyper Turing machine computations okay so and again in that hyper hyper rule multi-way graph we will appear as a black hole and so now imagine so what about the whole hierarchy of those things is there a whole hierarchy of hyper computational rule multi-way systems well the answer is yes presumably and that hierarchy is defined by the arithmetic hierarchy related to Google check hierarchy the it's a hierarchy of sort of levels of description of first you have a Turing machine then you have a Turing machine with an Oracle then you say okay but what about the whole thing of the Turing machine with the Oracle well then you need a double Oracle to do that and pretty soon you build up this whole hierarchy of ocular Turing machines and you can keep going forever you can start going into up until transfinite numbers transfinite layers of Oracle Ness so to speak so you've essentially extended hyper computation into trance finite hyper computation so hyper transfinite numbers are what can't are invented in 1870s I guess where you're just counting all the numbers so an ordinal transfinite number as you count all the numbers and you say what's the number that's one greater than every number I counted two and let's just call it lowercase Omega and so then we can say what's then we could say well okay we've got lowercase Omega we can say Omega plus one is yet another number distinct from Omega 1 plus Omega the Commuter arithmetic isn't commutative in transfinite numbers um 1 plus Omega is still just Omega because we start off with 1 and we go count count Count count counts and we still only end up with the the last number reach Omega anyway you can you can keep going in transferring out numbers and you can build these whole hierarchies of transfinite numbers and it gets very complicated because there is the notion of a finite number you might say well with my Omega I can say Omega to the Omega to the Omega to the Omega and let's take the limit of that as we go far enough I think that's called epsilon zero and we can then take epsilon zero we can take the limit of the limit of the limit of limits of that and that has to and then we end up getting this whole hierarchy of names there is no absolute infinity there's just a hierarchy of these named infinities which goes on forever so we can imagine a hierarchy of rouille or multi-way graphs that goes on forever like that we won't ever know anything about it we as observers in our universe won't be won't be able to detect what's going on but we can just imagine that there's a sort of hyper universe that contains this whole hierarchy of things and and we can think about mathematically what those kinds of things mean but Tim I mean it's difficult enough dealing with the rule multi-way graph to deal with that um let's see there are so few questions here oh I should say something about quantum computers um oh yeah there's a question from William here saying is the universe the output of computing chayton's constant that's a that's a fascinating question not you know that gives a a very strange twist to a longtime debate between Gregg Chayton and myself the longtime debate is is the universe like pile like Omega so if it's like PI there's a Turing machine that can just compute the states of the universe if it's like Omega the state of the universe is not computable by a Turing machine so I think what we're saying here is that the ultimate state of real space boy that's interesting that's a kind of wheel both right type situation the ultimate States to rule space is presumably governed by Omega because the ultimate state of rule space will have a bunch of presumably I mean just like our universe has a bunch of black holes in it well this is getting it's it's complicated here but there's some sense in which the ultimate state is described by that constant and that's very interesting okay I hadn't thought of that very very interesting idea um so um let's see a question here take these questions probably rather look I do want to say one thing about quantum computers okay so we have this emerging model of quantum computers and one of the things we're doing hopefully Jonathan's been working on this haven't been asking um - let's see Jonathan said sort of in response to something I said so I think that means Jonathan has to has to explain what he means by that okay what that was that was the Chasen's constant question no I I mean I wasn't going to say anything different to what you said that the the late time behavior of our universe is dominated by the ratios of G C and lambda that dictates the you know the rate the propensity of our universe to form black holes and so presumably the analog of general relativity in rural space the same kind of cosmology applies that there's a there's a real interrelationship between Rho Omega and whatever the whatever the non determinism constant for rural spaces yes so so so I think you're saying the analog of the cosmological constant for real space yes exactly yeah that's a complicated thing to think about I mean you know another big issue is the knitting together of space in rural space what on earth does that correspond to um but you know III sent Greg email actually last night because I was literally I'd written the sentence that said you know Greg's Omega is the density of black holes in rural space now I have to append to that the the statement that actually his longtime claim that the universe might be like Omega or not like pi might in some sense be correct as well which is which is really interesting okay quantum computers for a second okay so what I hope Jonathan has been working on is building a compiler that goes from our quantum computing framework a very I could say our classic classical quantum computing framework traditional quantum computing framework in terms of you know gates and and and States and quantum operators and all those kinds of things we have a very nice framework we've been building up for the last few years for Wolfram language for doing quantum for specifying quantum computations that could be fed to a in principle to a quantum computer um so that is a good way of representing all the things that show up in quantum computation point of information theory so the question then is what can we compile that into our multi way graphs and our interpretation of quantum mechanics in terms of branch field space and so on and it looks great we're going to be able to do this we've got to fill some details in but one of the things that we can then do is we not only can compile the operation of the quantum computation and the gates of the quantum computer we can also compile the measurement operations and that's very important because in traditional treatments of quantum computing measurement is just the sort of separate black box that is not part of the story of the micro description of the quantum computer but in our model it is the story of the micro description of the quantum computer and so the picture of a quantum computer ends up being first the quantum computer just like in that non-deterministic Turing machine story it trees out all these possibilities it reaches far out in branching space it's it's populating lots of branches space doing all those non-deterministic threads of figuring out what the possible factors of a number might be and so on it's it's it's Treeing all that stuff out by by occupying a large region not a physical space but a large region of branch hill space it's kind of like a time memory trade-off you could you could do all it's like it's like saying you know it's like talking about parallel threads memory trade-offs things like this and but what we're talking about here is a is something where in branch real space we're parallelizing in branch real space and we're seeing that there are these different pieces of the quantum computation that are happening in different parts of branch chill space okay but when we want to measure things we are just this observer sitting at some place in branch real space in effect and what we have to do is corral those those things that happened all over branch chill space we have to collect it's like a MapReduce we've we've done the map we've you know that's out there in branch chill space now we have to do the reduce we have to actually get everything back to get an answer okay so in traditional views of quantum computing you don't really talk about that you just say well we did a measurement okay in our model you are talking about every little step you have to take in branch chill space to navigate that information from the outer reaches of branch chill space back to where you're observing it okay so the question is how much effort does it take to do that and this is where it gets interesting it probably takes a lot of effort to do that in practically takes about as much effort to do that as it took to as the branching out took so in other words you're you're putting as much effort to corral it back into that thing at the end you're putting all this computational effort you're arranging something so this study of rural space and and so on I mean we're now we're talking about branching space but but I think there's going to be some way of understanding what we're doing with non-deterministic Turing machines and things to see something about whether even in branch real space whether there it is possible to do what a non-deterministic Turing machine does or whether basically the measurement process is going to essentially lose you what you might think you gained by following all these put all those pause non-deterministically okay so where does that leave quantum computing I mean as a practical matter you know the investigation of using sophisticated ideas from physics for computers super good idea lots of great things lots of optical computing methods lots of other kinds of good methods but does it really get the quantum grand not clear because it may be that in fact those practical problems people have been having with decoherence and quantum computers those are actually not just practical problems they're theoretical problems too and they have to do with this corralling back of things from branch field from the outer reaches of branch field space and an understanding that better is going to give one more limits more understanding what's possible in quantity there's what's not and there may still be a very practical important speed-up but the official quantum brand you know I did it all with quantum mechanics and it followed all those parallel paths might not be really justified but for one comment it could be that the expansion of the universe in Branch Hill space is what is that just like you could in some sense make a perpetual motion machine by using the expansion of space you might be able to make you a quantum computer by using the expansion of the universe in branch l space that's a current speculation um let's see so um it's a all right let's see all kinds of questions here it's one from Markos here can we do rural space models for the hyper edge rules just like we did for Turing machines oh yeah yeah we can that's just vastly more complicated I mean I I I did the Turing machine case because it's super easy compared to even the string rewriting case I'm going to do a probably multi mobile automata next and we're working up to being able to do this for the full hypergraph system but this is this is kind of you know it's it's difficult the visualization is difficult telling what on earth is going on is difficult hopefully we're gonna have some good virtual reality ways of visualizing some of our graphs ready soon that might help if I don't get to motion sick and virtual reality but you know it's it's just it's just a lot of technical difficulty to build up to that umm let's see there's a question here there's a question back here does this suggest that P versus NP is undecidable it is one of my guesses that it is undecidable now the question will end up being in this geometry zation of P versus NP it's an interesting question what is the analog what is undecidability and I think what it'll be is you've got this thing it's this basically ball of deterministic computations and it will have little tentacles that it's sending out as the ball gets bigger and bigger and bigger your basic question is do the tentacles always reach out how far do the tentacles reach is there a limiting process in which this ball that's getting bigger and bigger eventually somehow fills an outer ball or not or do other these little tentacles that get these very fine tentacles that start developing and it could very well be the case that what's happening is that to answer the question of in the infinite limit which is what you're concerned about with v versus NP that you can never know whether there are tentacles that reach out and reach to the outer surface that you need or whether whether in fact there are whether that's not the case and I think it might be possible even thinking in these geometrical terms to have a cleaner formulation of of the undecidability of P versus NP and that will be very testing I'm my own guess is that probably it's undecidable in the sense that within connor arithmetic for example within an axiom system if you ask c c whenever you ask one of these infinite limits you're sort of thrown into being talking about in terms of axiom systems if you just say what will the Turing machine do after a billion steps where i can just run it and see you say what is the machine do after an infinite number of steps i have to reason about that i can't just say well i just run it and see i mean i might be able to just run it and see i might be lucky but after a hundred steps i might have the answer but i might have to go arbitrarily far and so the only way to really deal with that reliably is to be able to reason to be able to generate a proof of what the Turing machine does but like the Turing machine itself the proof could be arbitrarily long by the way I might mention that in the one of the things that might come out of category theory is a okay let me actually here is a really weird one all right this is still a speculation but I'll share it with you this is the why does the universe exist question so just because there exists an abstract rule that will generate the universe why should that rule be actualized why should and I think maybe I mentioned this in a previous live stream but it's the thinking is slowly getting a little crisper so what I want is a proof of the existence of the universe so what an earth would that mean so let me give you an analogy of what Kirk Godel did in 1931 so he wanted to turn metamathematics into mathematics metamathematics is things like is there a proof does a proof exist for this statement or you know the predicate is this statement provable and so the the statement is this the predicate is this statement provable doesn't seem like it's a statement about mathematics it doesn't seem like it's a statement about X's and Y's and integers and things like that it seems like it's a meta mathematical statement okay so the but what he did was to show that that meta mathematical statement can be represented in mathematical terms he invents a girdle numbering which was sort of the first form of programming where he said let me just write out the proof bla bla bla bla bla by taking the symbol plus and turning it into a power of a prime and the symbol equals sign and turning it into some other power of some prime or something and out of that proof I will get a number and that number then the the question of whether a proof is valid will turn into a question about that number and that question can then be represented in terms of equations about numbers so then you've turned this meta mathematical statement about proofs into a mathematical statement about numbers and so that's how he took the statement this statement is unprovable showed that that could be compiled into arithmetic and that kind of proves that because that statement it sort of arithmetic would blow itself up if it could be you know is that same approval is it not provable the that establishes that there are statements that are statements of arithmetic like that statement because it's statement of arithmetic because he showed you could compile that meta mathematical statement into arithmetic and then he showed that that's an example of a statement that is is undecidable from arithmetic and it is a statement so there's incompleteness in arithmetic it's a statement that can be stated in terms of arithmetic but it cannot be proved or disproved by finite proof from the axioms provided in arithmetic ok ok why is all this relevant to us well let's imagine that we wanted to prove the existence of the universe ok so right now the statement this our universe exists does not seem to be a statement about physics does not seem to be a statement that we can make in terms of physics but the goal like girdle found a way to make a compilation of the meta mathematical statement about proofs as a statement of arithmetic our goal is to compile the statement the universe exists into a statement that can be stated in terms of operations of the physical universe okay now unfortunately I don't have a great punchline here because I don't know how to do that um there are in fact girdle strangely had a proof of the existence or was it non-existence I'm not sure of God very bizarre thing to do a statement into and there are proofs that go back though there's one famous one due to Saint Anselm it is the so-called ontological argument and the argument goes you know you assume that gosh I'm not sure I can reproduce it maybe Jonathan knows how this works it's a-you know that which there is no greater than there is there must be something which there is no greater than Jonathan can you can you yeah yeah that's pretty much the essence of it you say we define God to be that than which nothing greater can be conceived and then so an Psalms original argument goes so then a God which exists in reality is greater than a God which exists only in the mind and therefore in order for God to be consistent with his own definition of being that than which nothing greater can be conceived God must exist in reality and not just in the mind that's the essence of the argument eventually what it's doing is defining a total order on greatness and then and then specifying there must be a maximal element and then defining that maximal element to be God okay that was so anyway the goal would be to do a similar thing for the proof of existence of the universe and then my speculation is that the proof of existence of the universe is undecidable from within the universe that is that from within the quotes axiom system defined by the rules of the universe the statement the universe exists is not provable within that axiom system so there's an analogy to this girdle second incompleteness theorem given the axioms of arithmetic you can't prove or disprove the consistency of arithmetic in other words if you are living inside arithmetic you can't get out - to see from the outside the consistency of arithmetic so similarly possibly using something like that ontological argument it might be possible to turn the statement this the universe exists into a statement that can be compiled into a statement and then you would be able to show potentially that the existence of the universe is simply not decidable to entities within the universe and rather bizarre results but let that that's so it's kind of a downer because it says we'll never know why the universe exists um and yeah there's a comment here that girdle was a was was a strange person yeah III girdle them died before I was sort of on the scene but but I worked at the Institute for Advanced Study which is where girdle had worked um and so I heard lots of stories when I worked there I started working there in early 1980s and when I worked there there was still lots of stories about girdle that was circulating I mean one of the most bizarre stories was one of the most bizarre meta stories was there were papers from when girdle had been at the Institute and back when I was there I was like oh can I see these papers and say no these papers are locked in a vault you know no nobody can see the papers from the Institute from one girdle was there so I don't maybe they've been released now I don't I don't know whether that's still an ongoing thing I I think that partly might be because girl wasn't treated that well at the Institute people didn't really understand the significance of girdles theorem at the time and it took many years before he was so really accepted he had invented girls theorem long before he came to the Institute when he was in in Austria um but um he in any case he he um so that was sort of the first met a strange thing I think my favorite girdle story from when I was at the Institute it was a astronomer now wasn't a big big fan of that particular person but anyway he told me you know when he had first been at the Institute he had run into girdle and he described all the stuff he was doing with stars and all this kind of thing but an and girdle had said oh that's very nice young man but I do not believe in natural science in other words girdle didn't believe in the idea of inductive inference and science didn't believe in the idea that it was possible to make he only believed in formal theories so to speak I mean he also girdle was also famous for the fact that um his in in you know he didn't know where the girdles theorem applied to minds and he didn't think it did he kind of hoped and thought that there was sort of a spirituality two minds that that went beyond the mere computational or he didn't really think of it as computation that existed in girdle's theorem and in fact he has a footnote even in his original paper that says that um you know maybe human minds evade girdle's theorem by some kind of ramification of types ramified into the transfinite the and that term but anyway I'm I'm trying to remember there was another there was some other good girdle you know girdle was a very you know when when Cohen proved the independence of the Continuum Hypothesis and set theory there's a there's a good story about him about girdle that I've heard but I've heard many stories about girdle so I shouldn't Tim he was a you know I think his strangeness might be a little bit overrated I think he did get a little bit too a little bit strange towards the end he and unfortunately he perhaps for justifiable reasons in some ways he didn't really believe in doctors medical doctors and so that as that that caused some some horrible things to happen but Tim I think it might have been related to his lack of belief in natural science or it might have been very practical experiences in that area but Google I mean Google was was fond of trying to apply his logical ideas to other things like for example his proof the I think it was existence of God he also was famously um you know one of these good stories that I think is a true story not an apocryphal story of when when girdle was um was becoming an American citizen he was supposed to go off and you know do some hearing or something and he'd been prepping for this this you know citizenship test of that time and I guess Einstein said I'll come along with you to help with this and then Goodell was saying that well he had done he had figured out that there existed a logical way based on the Constitution of the u.s. for the u.s. to become a dictatorship and you know he was some which of course was a was the and and so Einstein was like just don't bring that up but this citizenship hearing and and but you know it was it was girdle's way of thinking that he was going to apply these kind of logical thinking methods in all areas whether that was concluding that questions about him and sometimes they're probably more applicable than others okay I need to wrap up here but but Tim I think there were some questions about as a question about Raisa question from Lee about signs of third parties contributing development yeah there are lots of people working on it they're not yet the few papers starting to appear we're going to be collecting ones we think are particularly interesting on our website but expect ones to appear where we we have our summer school coming up we have a lot of people a lot of well qualified people and talented people coming to that and I fully expect a lot of interesting papers to come out of that it's always a funny thing you know I feel like when you throw out a theory like this you it's like what I do for a living which is you know building will from language and building computational language tools you know people say well what do people do with your computational language and I say you know what I don't really know you know I can tell you a few anecdotal stories but there's millions of people using it every day and it's like they don't tell us what they do with it and we don't know what they do with it um and it's it's so it's a funny thing because you know people say well what are people doing with your model and the answer is well I you know anecdotally I hear about people doing things but I can't tell you the global story of what people do with it and and that will be it's an issue in the organization of what we're doing is some uh and I actually like to say something might be relevant to people here I mean we are trying to figure out how do we organize this science going forward and we're actually looking for for people who might be interested in being involved in sort of the organizational side of the science and you know realistically at some level that starts involving you know it involves you know how do you get a group of people and pay them and are they being paid and they're not being paid are they volunteers they this so they work in universities etcetera etcetera etcetera there's a whole sort of ecosystem needs to be built and that ecosystem seems to be you know some version of it will work just fine through existing universities and people who are just doing what they do is their day jobs and working on these these models that's gonna be just fine because because what we're doing is sort of close enough and methodologically close enough to physics and mathematics and computer science there's really not going to be a huge problem with that but I think that in terms of really developing things in the most effective possible way there's going to be need to be a little bit more centralization and push and so on and for that one needs a sort of an ecosystem for the science builds up and we're trying to just as we're trying to invent new science we're trying to invent new parts of the ecosystem like live-streaming things as a as an example of that that like these bulletins as a mechanism for doing things like a you know the way we're doing our summer school and so on but um you know we're kind of interested if there are people interested in the kind of the organizational aspects of how to make the science really really happen in the world we'd be interested in hearing from them because we're we're really trying to figure that out and we kind of need to you know we're thinking about assembling a team to really do this sort of organizational aspects of the science I mean I I will say quite straightforwardly personally that you know I'm I am in a sense more personally interested in pursuing the science than the organizational aspect of it you know I've spent a lot of my life well more than half my life as a CEO of a tech company and you know I understand how that works and I think it's very productive and I'm very pleased with what we've been able to do and in in so far as I can run a piece of the science in the same way that I've that I've CEO tech company I think I can be very productive insofar as it's a more kind of distributed kind of thing I it's I'm less personally able to contribute expertise to that situation and we're trying to understand what you know and also there's an ecosystem you know a tech company it's basically you know we've got you know a ten people working on stuff and you know people buy our software and you know that feeds the people who work on making better software and how that works for physics is not clear and we won't be able to you know we're not going to it's unlikely to scale to support a giant physics project selling swag we haven't yet got swag up and running but we will and hopefully people will buy some but I'm not I'm not expecting that I will say by the way in terms of things that exist there some hour we have the book a hardcover book version of of the launch documents will be coming out in a few weeks um and the okay to just leave a bit of a cliffhanger okay I'm gonna leave an outrageous cough hanger here there may be a thing that I call quantum money that may be a generalization of blockchain that may come out of the formalism of what we're doing and don't yet really know how it works and that would be the most bizarre way to see a kind of a a in a sense a monetization of physics is that its methods allow the construction of a of a quantum version of money so I'll leave that I think we need to wrap up here I'll leave that as my little cliffhanger for for what might come in the future and as some thanks for your enthusiasm for our project and it's very encouraging and really helps feed energy into into what we're doing and look forward to doing doing more of these live streams in the future oh yes let me remind you I have another live stream for a different audience for kids talking about some science and technology tomorrow I can't spend all my time doing live streams these tend to go awfully long and that this because too many good questions probably the kids won't we're going to try and limit it a bit in length otherwise otherwise they don't get to explore rouille old space which I I really like to do and I don't get to do my day job of actually building tools and making a company run but the tomorrow 3:30 Eastern Time QA for kids about science and technology with an emphasis again has been a good topic on how science fiction ideas end up being real or not okay well nice to chat with you all see you another time

Channel: Wolfram

Views: 15,718

Rating: 4.8907104 out of 5

Keywords: Wolfram, Physics, Wolfram Physics, Wolfram Physics Project, Stephen Wolfram, Science, Technology, Wolfram Language, Mathematica, Programming, Engineering, Math, Mathematics, Nature, A New Kind of Science, NKS, Computer Science, Philosophy

Id: GYal5US3HRQ

Length: 182min 40sec (10960 seconds)

Published: Thu Jun 04 2020