Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe | Lex Fridman Podcast #124
the following is a conversation with Steven Wolfram his second time in the podcast he's a computer scientist mathematician theoretical physicist and the founder and CEO of Wolfram research a company behind Mathematica wol from alpha Wolfram language and the new wolf from physics project he's the author of several books including a new kind of Science and the new book a project to find the fundamental Theory of physics this second round of our conversation is primarily focused on this latter Endeavor of searching for the physics of our universe in simple rules that do their work on hypergraphs and eventually generate the infrastructure from which space time and all of modern physics can emerge quick summary of the sponsors Simply Safe Sun basket and masterclass please check out these sponsors in the description to get a discount and to support this podcast as a side note let me say that to me the idea that seemingly infinite complexity can arise from very simple rules and initial conditions is one of the most beautiful and important mathematical and philosophical Mysteries and science I find that both cellular aoma and the hypography working on to be the kind of simple clear mathematical playground within which fundamental ideas about intelligence Consciousness and the fundamental laws of physics could be further developed in totally new ways in fact I think I'll try to make a video or two about the most beautiful aspects of these models in the coming weeks especially I think trying to describe how fellow curious minds like myself can jump in and explore them either just for fun or potentially for publication of new Innovative Research In Math computer science and physics but honestly I think the emerging complexity in these hypergraphs can capture the imagination of everyone even if you're someone who never really connected with mathematics that's my hope at least to have these conversations that Inspire everyone to look up to the skies and into our own minds in awe of our amazing Universe let me also mention that this is the first time I ever recorded a podcast Outdoors as a kind of experiment to see if this is an option in times of Co I'm sorry if the audio is not great I did my best and promis to keep keep improving and learning as always if you enjoy this thing subscribe on YouTube review it with five stars and apple podcast follow on Spotify support on patreon or connect with me on Twitter at Lex Friedman as usual I'll do a few minutes of ads now and no ads in the middle I Tred to make these interesting but I do give you time stamp so you're welcome to skip but still please do check out the sponsors by clicking the links in the description it's the best way to support this podcast also so let me say even though I'm talking way too much that I did a survey and it seems like over 90% of people either enjoy these ad reads somehow magically or don't mind them at least that honestly just warms my heart that people are that supportive this show is sponsored by simplysafe a home security company go to Simply safe.com to get a free HD camera it's simple no contracts 15 bucks a month easy setup even I figured it out I have set up in my apartment of course I also welcome Intruders one of my favorite movies is Leon or the professional with Jean Reno Gary Oldman and the brilliant young Natalie Portman if you haven't seen the movie he's a Hitman with a minimalist life that resembles my own fact when I was younger the idea of being a Hitman or targeting evil in a skilled way which is how I thought about it really appealed to me the the skill of it the planning the craftsmanship in another life perhaps if I didn't love engineering and science so much I can see myself being something like a Navy SE and in general I love the idea of serving my country of serving Society by contributing my skill in some small way anyway go to Simply safe.com Lex to get a free HD camera and to support this podcast they're a new sponsor and this is a 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calories I was thinking of doing a video with my mom as she makes it I thought it'd be a fun thing to to do together anyway go to sunbasket.com Lex and use code Lex do it now so they sign a long-term contract for this podcast this show is also sponsored by masterclass sign up at masterclass.com Lex 180 bucks a year you get an all access pass to watch lessons from Chris Hatfield Neila grass Tyson Tony Hawk Carlo Santana Garrick Kasparov Daniel Nano and many more brilliant World experts master class has been a really special sponsor they believe in this podcast in a way that gives me strength and motivation to take intellectual risks I'm thinking of doing a few solo podcast episodes on difficult topics especially in history like the rise and fall of the Third Reich or Stalin Putin and many other difficult topics that I'm fascinated by I have a worldview that seeks inspiring positive insights even and perhaps especially from periods of tragedy and evil that perhaps some folks may find Value in if I can only learn to convey the ideas in my mind as clearly as I think them I think deeply and rigorously and precisely but to be honest have trouble speaking in a way that reflects that rigor of thought so it really does mean a lot the love and support I get as I try to get better at this thing at this talking thing anyway go to masterclass.com Lex to get a discount and to support this podcast and now finally here's my conversation with Stephen wlfr you said that there are moments in history of physics it may be mathematical physics or even mathematics where breakthroughs happen and then a flurry of progress follows so if you look back through the history of physics are what moments stand out to you as important such breakthroughs where a flurry of progress follows so the big famous one is 1920s the invention of quantum mechanics where you know in about 5 or 10 years lots of stuff got figured out that's now quantum mechanics can you mention the people involved yeah that kind of the shener Heisenberg you know Einstein had been a key figure originally plank then dur was a little bit later that was something that happened at that time that's sort of before my time right in my time was in the 1970s uh there was this sort of realization that Quantum field theory was actually going to be useful in physics and uh qcd Quantum thermodynamics theory of ques and gluons and so on was really getting started and uh there was again sort of big flurry of things happened then I happened to be a teenager at that time and happened to be uh really involved in physics and so I got to be part of that which was really cool who were the key figures aside from your young selves at that time you know who won the Nobel Prize for qcd okay people David Gross Frank wilchek you know um David poiter the people who are the sort of the slightly older generation dick feineman Murray Gman people like that uh uh who were Steve Weinberg GED Hof he's younger he's he's in the younger group actually but um these are these are all you know characters who are involved I mean it was uh you know it's funny because those are all people who are kind of in my time and I know them and they don't seem like sort of uh historical uh you know iconic figures they seem more like uh everyday characters so to speak um and uh uh so it's always you know when you look at history from long afterwards it always seems like everything happened instantly um and that's usually not the case there was usually a long buildup but usually there's you know there's some method iCal thing happens and then there's a whole bunch of low hanging fruit to be picked and that usually lasts 5 or 10 years you know we see it today with machine learning and you know deep learning neural Nets and so on you know methodological Advance things actually started working in you know 2011 2012 and so on and uh you know there's been this sort of Rapid uh picking of loow hanging fruit which is probably you know some significant fraction of the way way done so to speak do you think there's a key moment like if I had to really introspect like what was the key moment for the Deep learning quote unquote Revolution I mean it's probably the Alex net business Alex net with imag net so is there something like that with physics where so deep learning neural networks have been around for a long time there's a bunch of 1940s yeah there's a bunch of little pieces that came together and then all of a sudden everybody's eyes lit up like wow there's something here like even just looking at your own work just you're thinking about the universe that there's Simple Rules can create complexity you know at which point was there a thing where your eyes light up it's like wait a minute there's something here is it the very first idea or is it some moment along the line of implementations and experiments and so on there's there's a couple of different stages to this I mean one is the think about the world computationally you know can we use programs instead of equations to make models of the world that's something that I got interested in in the at the beginning of the 1980s you know I did a bunch of computer experiments uh you know when I first did them I didn't really I I could see some significance to them but took me a few years to really say wow there's a big important phenomenon here that lets sort of complex things arise from very simple programs um that kind of happened back in 198 4 or so then you know bunch of other years go by then I start actually doing a lot of much more systematic computer experiments and things and find out that the you know this phenomenon that I could only have said occurs in one particular case is actually something incredibly General and then that led me to this thing called principle of computational equivalence and that was a a long story and then you know as part of that process I was like okay you can make simple programs can make models of complicated things what about the whole universe that's our sort of ultimate example of a complicated thing yeah and so I got to thinking you know could we use these ideas to to study fundamental physics uh you know I happen to know a lot about you know traditional fundamental physics my um uh my first you know I I had a bunch of ideas about how to do this in the early 1990s I made a bunch of technical progress I figured out a bunch of things I thought were pretty interesting you know I wrote about them back in 2002 with the new kind of Science and the cellular ainal world there's echo in the cellular aomin world with your new wol from physics project World we'll get to all that allow me to sort of romanticize a little more on the philosophy of science uh so Thomas philosopher of science describes that you know the progress in science is made with uh these Paradigm shifts and so to linger on the sort of original line of discussion do you agree with this view that there is Revolutions in science that just kind of flip the table what happens is it's a different way of thinking about things it's a different methodology for studying things and that opens stuff up this is this idea of uh he's a famous biographer but I think it's called the innovators the biographer of Steve Jobs of Albert Einstein he also wrote a book I think it's called an evaders where he discusses uh how a lot of uh the Innovations in the history of computing has been done by groups there's a complicated group dynamic going on but there's also a romanticized notion that the individual is at the core of the Revolution like where does your sense fall is is uh ultimately like one person responsible for these revolutions that that creates the spark or one or two whatever but or is it just the big mush and mess and Chaos of of people interacting the personalities interacting I think it ends up being like many things there's leadership and there ends up being it's a lot easier for one person to have a crisp new idea than it is for a big committee to have a crisp new idea and um I think you know but I think it it can happen that you know you have a great idea but the world isn't ready for you for it and um you know you can you can I mean this has happened to me plenty right it's you know you have an idea it's actually a pretty good idea but things aren't ready either either you're not really ready for it or the ambient world isn't ready for it and it's hard to get the thing to to get traction it's kind of interesting I mean when I look at a new kind of science you're now living inside history so you can't tell the story of these decades but it seems like the new kind of science has not had the Revolutionary impact I would think it uh might like it feels like at some point of course it might be but it feels at some point people will return to that book and say there was something special here this was incredible what happened or do you think that's already happened oh yeah it's happened except that people aren't you know the the sort of the heroism of it may not be there but the what's happened is for 300 years people basically said if you want to make a model of things in the world mathematical equations are the best place to go last 15 years doesn't happen you know new models that get made of things most often are made with programs not with equations mhm now you know was that sort of going to happen anyway was that a consequence of you know my particular work in my particular book it's hard to know for sure I mean I am always amazed at the amount of feedback that I get from people where they say oh by the way you know I started doing this whole line of research because I read your book blah blah blah blah blah it's like well can you tell that from the academic literature you know were was there a chain of you know academic references probably not one of the interesting side effects of publishing in the way you did this toome is it serves as an education tool and an inspiration to hundreds of thousands millions of people but because it's not a single it's not a chain of papers with piffy titles it doesn't create a splash of citations like it's had it's had plenty of citations but it's it's you know I think that the IT people think of it as probably more you know conceptual inspiration than uh than kind of a you know this is a line from here to here to here in our particular field right I think that the you know the thing which I am disappointed by and which will eventually happen is this kind of study of the this sort of pure computationalism this kind of study of the abstract behavior of the reputational universe that should be a big thing that lots of people do you mean in mathematics purely almost like it's still mathematics but it isn't mathematics but it isn't it isn't it's a new kind of mathematics it's atitle the book yeah right that's why the book is called that right that's not coincidental yeah it's interesting that I haven't seen really rigorous investigation by thousands of people of this idea I mean you look at your competition around rule 30 I mean that's fascinating if if you can say something right is there some aspect of this thing that could be predicted that's a fundamental question of science that's the core that has been a question of science I think that's a that is a some people's view of what science is about and it's not clear that's the right view in fact as we as we live through this pandemic full of predictions and so on it's an interesting moment to be pondering what what science's actual role in those kinds of things is oh you think it's possible that in science clean beautiful simple prediction may not even be possible in real systems that's the open right question I don't think it's open I think that question is answered and the answer is no well no no the answer could be just humans are not smart enough yet like we don't have the tools no that's that's the whole point I mean that's that's sort of the big discovery of this principle of computational equivalence of mine and um the uh you know this is something which is kind of a follow on to girdle's theorem to turing's work on the halting problem all these kinds of things that there is this fundamental limitation built into science this idea of computational irreducibility that says that you know even though you may know the rules by which something operates that does not mean that you can uh readily sort of be smarter than it and jump ahead and figure out what it's going to do yes but do you think there's a hope for pockets of computational reducibility computational re reducibility reducibility that's so and then and then a set of tools and Mathematics that help you discover such pockets that's where we live is in the pockets of reducibility right that's why you know and this is one of the things that sort of come out of this physics project and actually something that again I should have realized many years ago but didn't um is uh you know the it it could very well be that everything about the world is computationally irreducible and completely unpredictable but you know in our experience of the world there is at least some amount of prediction we can make and that's because we have sort of chosen a slice of um probably talk about this in in much more detail but I mean we've kind of chosen a slice of how to think about the universe in which we can kind of sample a certain amount of computational reducibility and that's that's sort of where we where we exist um and uh it may not be the whole story of how the universe is but it is the part of the universe that we care about and we sort of operate in and um that's you know in science that's been sort of a very special case of that that is science has chosen to talk a lot about places where there is this computational reducibility that it can find you know the motion of the planets can be more or less predicted you know the uh uh something about the weather is much harder to predict something about you know other kinds of things the the um are much harder to predict and it it's um uh these are but science has tended to you know concentrate itself on places where its methods have allowed successful prediction so you think rule 30 if it could Linger on it because it's just such a beautiful simple formulation of the essential concept underlying all the things we're talking about do you think there's pockets of reducibility inside rule 30 yes but it's a question of how big are they what will they allow you to say and so on and that's and figuring out where those pockets are I mean in a sense that's the that's sort of a uh uh you know that is an essential thing that one would like to do in science um but it's it's also the the important thing to realize that that has not been you know is is that science if you just pick an arbitrary thing you say what's the answer to this question that question may not be one that has a computationally reducible answer that question if you if you choose you know if you walk along the series of questions and you've got one that's reducible and you get to another one that's nearby and it's reducible too if you stick to that kind of stick to the land so to speak yeah then you can go down this chain of sort of reducible answerable things but if you just say I'm just pick a question at random I'm going to have my computer pick a question at random yeah uh most likely it's going to be irreducible most likely it will be irreducible and and what we're throwing in the world so to speak uh we you know when we engineer things we tend to engineer things to sort of keep in the zone of reducibility when we're thrown things by the natural world for example not not at all certain that we will be kept in this kind of zone of reducibility can we talk about this pandemic then for a second is so how do we there's obviously huge amount of economic pain that people are feeling there's a huge incentive and medical pain uh Health just all kind psychological there's a huge incentive to figure this out to walk along the trajectory of reducible of reducibility there's there's a a lot of disperate data you know people understand generally how virus is spread but it's very complicated because there's a lot of uncertainty there's a there could be a lot of variability like so many obviously a nearly infinite number of variables that uh that represent human interaction and so you have to figure out in ter from the perspective of reducibility figure out which variables are really important in this kind of uh from an epidemiological perspective so why aren't we you kind of said that we're clearly failing well I I think it's a complicated thing so so I mean you know when this pandemic started up you know I happen to be in in the middle of being about to release this whole physics project thing but I thought you know the timing is just uh cosmically but but um but you know but I thought you know I I should do the public service thing of you know trying to understand what I could about the pandemic and you know we've been curating data about it and all that kind of thing but but you know so I started looking at the data and started looking at modeling and I decided it's just really hard you need to know a lot of stuff that we don't know about human interactions it's actually clear now that there's a lot of stuff we didn't know about viruses um and about the way immunity works and so on and um it's you know I think what will come out in in the end is there's a certain amount of of what happens that way you just kind of have to trace each step and see what happens there's a certain amount of stuff where there's going to be a big narrative about this happened because you know of te- cell immunity this happened because there's this whole giant sort of field of of of asymptomatic viral stuff out there you know there will be a narrative and that narrative whenever there's a narrative that's kind of a sign of reducibility but when you just say let's from first principles figure out what's going on then you can potentially be stuck in this kind of uh mess of irreducibility where you just have to simulate each step and you can't do that unless you know details about you know human interaction networks and so on and so on and so on the thing that has has been very sort of frustrating to see is the mismatch between people's expectations about what science can deliver and what science can actually deliver so to speak um because people have this idea that you know it's science so there must be a definite answer and we must be able to know that answer and you know this is it is both uh uh you know that when you after you've played around with sort of little programs in the computational universe you don't have that intuition anymore you know it's it's I always I'm always fond of saying you know the the the the computational animals are always smarter than you are that is you know you look at one of these things and it's like it can't possibly do such and such a thing then you run it and it's like wait a minute it's doing that thing how does that work okay now I can go back can understand it but that's the brave thing about science is that in the chaos of the irreducible universe we nevertheless persist to find those pockets that's kind of the whole point that's like you say that the limits of science but that you know yes it's highly limited but there there's a hope there and like there there's so many questions I want to ask here so one you said narrative which is really interesting so obviously from uh at every level of society you look at Twitter everybody's constructing narratives about the pandemic about not just the pandemic but all the cultural tension that we're going through so there's narratives but they're not necessarily connected to the underlying reality of these systems so our human narratives I don't even know if they're I don't like those pockets of reducibility Cu we're uh it's like constructing things that are not actually representative of reality well and thereby not giving us like good solutions to how to predict the system look it it gets complicated because you know people want to say explain the pandemic to me explain what's going to happen in the future like yes but but also can you explain it is there a story to tell what already happened in the past yeah what's going to happen but I mean in you know it's similar to sort of explaining things in AI or in any computational system it's like like you know explain what happened well it could just be this happened because of this detail and this detail and this detail and a million details and there isn't a big story to tell there's no kind of Big Arc of the story that says oh it's because you know there's a viral field that has these properties and people start showing symptoms you know when when the seasons change people will show symptoms and people don't even understand you know seasonal variation of flu for example it's a it's a um uh it's something where where you know that that could be a big story or it could be just a zillion little details that that mount up see but okay let's let's uh pretend that this pandemic like the Corona virus resembles something like the 1D rule 30 cellular aoma okay so I mean that's how epidemiologists model virus spread indeed yes sometimes use cellometer yes yes and okay so you can say it's simplistic but okay let's say it it is it's representative of actually what happens uh you know the the dynamic of you have a graph it probably is closer to the hypergraph uh model is yes it's it's actually that's another funny thing as as we were getting ready to release this physics project we realized that a bunch of things we'd worked out about about foliations of causal graphs and things were directly relevant to thinking about contact tracing and interaction of cell phones and so on which is really weird but like it just feels like uh it feels like we should be able to get some beautiful core insight about the spread of this particular virus on the hypergraph of human civilization right they I tried I didn't I didn't manage to figure it out but you're one person yeah but I mean I think actually it's a funny thing because it turns out the um the main model you know this sir model I I only realized recently was invented by the the grandfather of a good friend of mine from high school so that was just a you know it's a weird thing right the question is you know okay so you know you know on this graph of how humans are connected you know something about what happens if this happens and that happens that graph is made in complicated ways that depends on on all sorts of issues that where we don't have the data about how Human Society works well enough to be able to make that graph there's actually um uh one of my kids did a study of sort of what happens on different kinds of graphs and how robust are the results okay his basic answer is there are few General results that you can get that are quite robust like you know a small number of big gatherings is worse than a large number of small Gatherings okay that's quite robust but when you ask more detailed questions it seemed like it just depends it depends on details in other words it's kind of telling you in that case you know the irreducibility matters so to speak it's not there's not going to be this kind of one sort of Master theorem that says and therefore this is how things are going to work yeah but the there's a certain kind of from a graph perspective the certain kind of dynamic to human interaction so like large groups and small groups I think it matters who the groups are for example you could imagine large depends how you define large but you can imagine groups of 30 people as long like as long as they are uh cleaks or whatever like right as as long as the outgoing degree of that graph is small or something like like that like you can imagine some beautiful underlying rule of human Dynamic interaction where I can still be happy where I can have a conversation with you and a bunch of other people that mean a lot to me in my life and then stay away from the bigger I don't know not going to Miley Cyrus concert or something like that and and figuring out mathematically some nice see this is an interesting thing so I mean in you know this is the question of what you're describing as kind of uh the problem of many situations where you would like to get away from computational irreducibility a classic one in physics is thermodynamics the you know the second law of Thermodynamics the law that says you know entropy tends to increase things that you know start orderly tend to get more disordered or which is also the thing that says given that you have a bunch of heat it's hard heat is you know the microscopic motion of molecules it's hard to turn that heat into systematic mechanical work it's hard to you know just take something being hot and turn that into oh the the you know the all the atoms are going to line up in the bar of metal and the piece of metal is going to shoot in some Direction that's essentially the same problem as how do you go from this this computationally irreducible mess of things happening and get something you want out of it right it's kind of mining you know you're kind of now you know actually I've I've understood in recent years that that the story of of thermodynamics is actually precisely a story of computational irreducibility but it is a um it is already an analogy you know you can you can kind of see that is can you take the um you know what you're asking to do there is you're asking to go from the um uh the kind of um the mess of all these complicated human interactions and all this kind of computational processes going on and you say I want to achieve this particular thing out of it I want to kind of extract from the heat of what's happening I want to kind of extract this useful piece of sort of mechanical work that I find helpful I mean do you have a hope for the pandemic so we'll talk about physics but for the pandemic can that be extracted do you think what's your intuition the good news is the curves basically you know for reasons we don't understand the curves you know the the the clearly measurable mortality curves and so on for the Northern Hemisphere have gone down yeah but the bad news is that it could be a lot worse for future viruses and what this pandemic revealed is we're highly unprepared for the dis discovery of the pockets of reducibility within a pandemic that's much more dangerous well my my guess is the specific risk of you know viral pandemics you know that the pure virology and you know Immunology of the thing this will cause that to advance to the point where this particular risk is probably considerably mitigated but you know it's uh you know does is is the structure of modern society robust to all kinds of risks well the answer is clearly no and you know it's it's surprising to me the extent to which people uh you know as I say it's it's a it's kind of scary actually how much people believe in science that is people say oh you know because the science does this that and the other we'll do this and this and this even though from a sort of Common Sense point of view it's a little bit crazy and and people are not prepared and it doesn't really work in in society as it is for people to say well actually we don't really know how the science Works people say well tell us what to do yeah because then yeah what's the alternative the for the masses it's difficult to sit it's difficult to meditate on computational reducibility it's difficult to sit it's difficult to enjoy a good dinner meal while while knowing that you know nothing about the world I think this is a this is a place where you know this is this is what politicians you know and political leaders do for a living so to speak because you got to make some decision about what to do and it's um tell some narrative that uh while amidst the mystery and knowing not much about the the past or the future still telling a narrative that somehow gives people hope that we know what the heck we're doing yeah get Society through the issue you know even even though you know the idea that we're just going to you know sort of be able to get the definitive answer from science and it's going to tell us exactly what to do unfortunately you know uh that it's interesting because let me point out that if that was possible if science could always tell us what to do then in a sense our you know that would be a big Downer for our lives if science could always tell us what the answer is going to be it's like well you know it's kind of fun to live one's life and just sort of see what happens if one could always just say Let me let me check my science oh I know you know the result of everything is going to be 42 I don't need to live my life and do what I do it's just we already know the answer it's actually good news in a sense that there is this phenomenon of computational irreducibility that doesn't allow you to just sort of jump through time and say this is the answer so to speak um and that's so that's a good thing the bad thing is it doesn't allow you to jump through time and know what the answer is it's scary do you think we're going to be okay as a human civilization you said we don't know absolutely do you think it's do you think we'll Prosper or destroy ourselves as a in general in general I'm an optimist the no I think that that you know it'll be interesting to see for example with this you know pandemic I you know to me you know when you look at like organizations for example you know having some kind of pertubation some kick to the system usually the end result of that is actually quite good you know unless it kills the system it's actually quite good usually and I think in this case you know people I mean my impression you know it's it's a little weird for me because you know I've been a remote Tech CEO for 30 years it doesn't you know this is bizarrely uh you know in the fact that you know like this coming to see you here is is one of the rare moments the first time in six months that I've been like you know in a building other than my house okay so so so you know it's I'm I'm a kind of ridiculous outlier in these kinds of things but overall your sense is when you shake up the system and throw in chaos that you you uh challenge the system we humans emerge better seems to be that way who's to know but I think that you know people you know my my sort of vague impression is that people are sort of you know oh what's actually important you know what's uh what what is worth caring about and so on and that seems to be something that perhaps is is more you know emergent in this kind of situation it's so fascinating that on the individual level we have our own complex cognition we have Consciousness we have intelligence we're trying to figure out little puzzles and then that somehow creates this graph of collective intelligence where we figure out and then you throw in these viruses of which there's Millions different you know this entire taxonomy and the viruses are thrown into the system of collective human intelligence and we little humans figure out what to do about it we get like we Tweet stuff about information there's doctors as conspiracy theorists and then we play with different information I mean the whole of it is fascinating um I I like you also very optimistic but uh there's a fe just you said uh the computational reducibility there's always a fear of the darkness of the uncertainty be before us yeah it's scary I mean the thing is if you knew everything it will be boring and and it would be and and then um uh and worse than boring so to speak it would be you it would reveal the pointlessness so to speak and in a sense the the fact that there is this computational ability it's like as we live our lives so to speak something is being achieved we're Computing what our lives you know uh you know what happens in our lives that's funny so the computation reducibility is kind of like it gives the meaning to life it is the meaning of life computation reducibility is the meaning of life there you go it it gives it meaning yes I mean it it it it it's what it's what causes it to not be something where you can just say uh you know you went through all those steps to live your life but we already knew what the answer was was right hold on one second I'm going to use my handy wol from alfha sunburn computation thing so long as I can get network here there we go oh actually you know what it says sunburn unlikely this is a QA moment this is a good moment okay okay well let me just check what it thinks see why it thinks that it doesn't seem like my intuition this is one of these cases where we can the question is do we do we trust the science or do we um use common sense the UV thing is cool the yeah yeah well we'll see this is a QA moment as I say it's uh do we trust the product yes we trust the product so and then there'll be a data point either way if if I'm desperately sunburned I will send in a angry feedback because we mention the concept so much and a lot of people know it but can you say what competition reducibility is yeah right so I mean the question is if you think about things that happen as being computations you think about the uh some process in physics something that you compute in mathematics whatever else it's a computation in the sense it has definite rules you follow those rules you uh follow them many steps and you get some result so then the issue is if you look at all these different kinds of computations that can happen whether they're computations that are happening in the natural world whether they're happening in our brains whether they're happening in our mathematics whatever else the big question is how do these computations compare is are there dumb computations and smart computations or are they somehow all equivalent and the thing that I kind of uh was sort of surprised to realize from a bunch of experiments that I did in the early 90s and now we have tons more evidence for it this thing I call the principle of computational equivalence which basically says when one of these computations one of these processes that follows rules doesn't seem like it's doing something obviously simple then it has reached the sort of equivalent level of sophistic of computational sophistication of everything so what does that mean that means that you know you might say gosh I'm I'm studying this little tiny you know tiny program on my computer I'm studying this little thing in in nature but I have my brain and my brain is surely much smarter than that thing I'm going to be able to systematically outrun the computation that it does because I have a more sophisticated computation that I can do but what the principle of computational equivalence say say is that doesn't work our our brains are doing computations that are exactly equivalent to the kinds of computations that are being done in all these other sorts of systems and so what consequences that have well it means that we can't systematically outrun these systems these systems are computationally irreducible in the sense that there's no sort of shortcut that we can make that jumps to the answer now in a general case right right but but the so what has happened you know what science has become used to doing is using the little sort of pockets of computational reducibility which by the way are an inevitable consequence of computational irreducibility that there have to be these Pockets scattered around of computational reducibility to be able to find those particular cases where you can jump ahead I mean one one thing sort of a little bit of a parable type thing that I think is is fun to tell you know if you look at ancient Babylon they were trying to predict three kinds of things they tried to predict you know where the planets would be what the weather would be like and who would win or lose a certain battle and they had no idea which of these things would be more predictable than the other that's funny and and you know it turns out you know where the planets are is a is a piece of computational reducibility that you know 300 years ago or so we pretty much cracked I mean it's been technically difficult to get all the details right but it's basically we we got that you know who's going to win or lose the battle no we didn't crack that one that one that one right game theorist are trying and then the weather kind of halfway on that halfway yeah I think we we're doing okay at that one I you know longterm climate different story but but the weather you know we're we're much closer on that but do you think eventually we'll figure out the weather so do you think eventually most thing will figure out the local pockets in everything essentially the local pockets of reducibility no I think that the it's a it's an interesting question but I think that the you know there is an infinite collection of these local Pockets we'll never run out of local pockets and by the way those local pockets are where we build engineering for example that's how we you know when we if we want to have a predictable life so to speak then you know we have to build in these sort of pockets of reducibility otherwise you know if we were if we were sort of existing in this kind of irreducible world we'd never be able to you know have definite things to know what's going to happen you know I I have to say I think one of the features you know when we look at uh sort of today from the future so to speak I suspect one of the things where people will say I can't believe they didn't see that is stuff to do with the following kind of thing so so you know if we describe oh I don't know something like um heat for instance we say oh you know the air and in here it's you know it's this temperature this pressure that's as much as we can say otherwise just a bunch of random molecules bouncing around people will say I just can't believe they didn't realize that there was all this detail and how all these molecules were bouncing around and they could make use of that I mean actually I realized there's a thing I realized last week actually was um was a thing that people say you know one of the scenarios for the very long-term history of our universe is a so-called heat death of the universe where basically everything just becomes thermodynamically boring everything is just this big kind of gas and thermal equilibrium people say that's a really bad outcome but actually it's not a really bad outcome it's an outcome where there's all this comp computation going on and all those individual gas molecules are all bouncing around in very complicated ways doing this very elaborate computation it just happens to be a computation that right now we haven't found ways to understand we haven't found ways you know our brains haven't you know and our mathematics and our science and so on haven't found ways to tell an interesting story about that it just looks boring to us there's a there you're saying there's a hopeful view of the he death quote unquote of the universe where there's actual beautiful complexity going on similar to the kind of complexity we think of that creates Rich experience in human life and life on Earth yes so those little molecules interact in complex ways that there could be intelligence in that there could be absolutely I mean this this is this is what you learn from this hopeful message right I mean this is what you kind of learned from this principle of computational equivalence you learn it's both a a message of of sort of Hope and a message of kind of you know there you're not as special as you think you are so to speak I mean because you know we we imagine that with sort of all the things we do with with human intelligence and all that kind of thing and all of the stuff we've constructed in science it's like we're very special but actually it turns out well no we're not we're just doing computations like things in nature do computations like those gas molecules do computations like the weather does computations the only the only thing about the computations that we do that's really special is that we understand what they are so to speak in other words we have a you know to us they're special because kind of they're connected to our purposes our ways of thinking about things and so on and that's um but so so that's very human Centric that's we're just attached to this kind of thing so let's talk a little bit of physics maybe let's ask the uh the biggest question what is a theory of everything in general what does that mean yeah so I mean the question is can we kind of reduce what has been physics as a something where we have to sort of pick away and say do we roughly know what how the world Works to something where we have a complete formal Theory where we say if we were to run this program for long enough we would reproduce everything you know down to the fact that we're having this conversation at this moment etc etc etc any physical phenomena any phenomena in this world any phenomenon in the universe but the you know because of computational irreducibility it's not you know that's not something where you say okay you've got the fundamental Theory of Everything then you know tell me whether you know uh lions are going to eat tigers or something you know that's a no you have to run this thing for you know 10 to the 500 steps or something to know something like that okay so at some moment potentially you say this is a rule and run this rule enough times and you will get the whole universe right that's that's what it means to kind of have a fundamental Theory of physics as far as I'm concerned is you've got this rule it's potentially quite simple we don't know for sure it's simple but we have various reasons to believe it might be simple and then you say okay I'm showing you this rule you just run it only 10 500 times and you'll get everything in other words you you've kind of reduced the problem of physics to a problem of mathematics so to speak it's like it's a if you know you like you generate the digits of pi there's a definite procedure you just generate them and it' be the same thing if you have a a fundamental Theory physics of the kind that that I'm imagining you you know you get a this Rule and you just run it out and you get everything that happens in the universe so a Theory of Everything is a mathematical framework within which you can explain everything that happens in the universe it's kind of in a unified way it's not there's a bunch of disparate modules of does it feel like if you create a rule and we'll talk about the wol from physics model which is fascinating but if if you if you have a simple set of rules with a with a data structure like a hypergraph does that feel like a satisfying Theory of Everything because then you really run up against the uh irreducibility computational reducibility right so that's a really interesting question so I I I you know what I thought was going to happen is I thought we you know I thought we had a pretty good I had a pretty good idea for what the structure of this sort of theory that's sort of underneath space and time and so on might be like and I thought gosh you know in my lifetime so to speak we might be able to figure out what happens in the first 10us 100 of the universe MH and that would be cool but it's pretty far away from anything that we can see today and it will be hard to test whether that's right and so on and so on and so on to my huge surprise although it should have been obvious and it's embarrassing that it wasn't obvious to me but but um to my huge surprise we managed to get unbelievably much further than that and basically what happened is that it turns out that even though there's this kind of bed of computational irreducibility that sort of uh these all these Simple Rules run into there is a there are certain pieces of computational reducibility that quite generically occur for large classes of these rules and and this is the really exciting thing as far as I'm concerned the the the big pieces of computational reducibility are basically the pillars of 20th century physics that's the amazing thing that general relativity and Quantum field Theory the sort of the pillars of 20th century physics turn out to be precisely the stuff you can say there's a lot you can't say there's a lot that's kind of at this irreducible level where you kind of don't know what's going to happen you have to run it you know you can't run it within our universe etc etc etc etc etc um but the thing is there are things you can say and the things you can say turn out to be very beautifully exactly the structure that was found in 20th century physics namely general relativity and quantum mechanics and general relativity and quantum mechanics are these pockets of reducibility that we think of as that that you know 20th century physics is essentially pockets of reducibility and then it's it is incredibly surprising that any kind of model that's generative from Simple Rules would have would have such Pockets yeah well I think what what's surprising uh is we didn't know where those things came from it's like general relativity it's a very nice mathematically elegant Theory why is it true you know quantum mechanics why is it true what we realized is that from this that they are these theories are generic to a huge class of systems that have these particular very unstructured underlying rules and that's the that's the thing that is sort of uh remarkable and that's the thing to me that's just it's really beautiful I mean it's and the thing that's even more beautiful is that it turns out that you know people have been struggling for a long time you know how does general relativity theory of gravity relate to Quantum Mechanics they seem to have all kinds of incompatibilities it turns out what we realized is at some level they are the same Theory and that's just it's it's just great as far as I'm concerned so maybe like taking a little step back from your perspective not from the low not from the beautiful hypog graph well from physics model perspective but from the perspective of 20th century physics what is general relativity what is quantum mechanics how do you think about these two theories from the context of the theory of everything like just even definitions yeah yeah yeah right so so I mean you know little bit of history of physics right so so I mean the the you know okay very very quick history of right so so I mean you know physics you know in ancient Greek times people basically said we can just figure out how the world works as you know we're philosophers we're going to figure out how the world works you know some philosophers thought there were atoms some philosophers thought there were you know continuous flows of things people had different ideas about how the world works and they tried to just say we're going to construct this idea of how how the world Works they didn't really have sort of Notions of doing experiments and so on quite the same way as developed later so that was sort of an early tradition for thinking about sort of models of the world then by the time of 1600s time of Galileo and then Newton um sort of the big the big idea there was you know you know title of Newton's book you know Pria Mathematica mathematical principles of natural philosophy we can use mathematics to understand natural philosophy to understand things about the way the world works and so that then led to this kind of idea that you know we can write down a mathematical equation and have that represent how the world works so Newton's one of his most famous ones is his universal law of gravity inverse Square law of gravity that allowed him to compute all sorts of features of of the planets and so on although some of them he got wrong and it was took another hundred years for people to actually be able to do the math uh to the level that was needed but but um but so that that had been this sort of tradition was we write down these mathematical equations we don't really know where these equations come from we write them down then we figure out we work out their consequences and we say yes that agrees with what we actually observe in astronomy or something like this so that tradition continued and um then the first of these two sort of great 20th century uh Innovations was uh well the history is a little bit more complicated but let's let's say the the the um the the the there were two quantum mechanics and general relativity quantum mechanics kind of 1900 was kind of the very early uh stuff done by plank that led to the idea of photons particles of light um but let's let's take general relativity first one one feature of the story is that special relativity thing Einstein invented in 1905 was something which surprisingly was a kind of logically invented Theory Theory it was not a theory where it was something where given these ideas that were sort of axiomatically thought to be true about the world it followed that such and such a thing would be the case it was a little bit different from the the kind of methodological structure of some of some existing theories in more in the more recent times or it just been we write down an equation and we find out that it works so what happened there so there's some reasoning about the light the basic idea was you know the speed of light is appears to be constant uh you know even if you're traveling very fast you shine a flashlight the light will come out even if you're going at half the speed of light the light doesn't come out of your flashlight at one and a half times the speed of light um it's still just the speed of light and to make that work you have to change your view of how space and time work um to be able to account for the fact that when you're going faster it appears that you know uh length is foreshortened and time is dilated and things like this that's special relativity that's special relativity so then Einstein went on with sort of vaguely similar kinds of thinking 1915 invented general relativity which is a theory of gravity and the basic point of general relativity is is it's a theory that says when there is mass in space space is curved and what is that mean you know you usually you think of what's the shortest distance between two points like in in a ordinarily in on a plane in space it's a straight line you know photons light goes in straight lines well then the question is is if if you have a curved surface a straight line is no longer straight on the surface of the Earth the shortest distance between two points is a great circle it's a circle um it's uh so you know Einstein's observation was maybe the physical uh structure of space is such that space is curved D so the shortest distance between two points the the path the straight line in quotes won't be straight anymore and in particular if a if a photon is is you know traveling near near the Sun or something or if a particle is going something is traveling near the sun maybe the shortest path will be one that is is uh is is something which looks curved to us because it seems curved to us because space has been deformed by the presence of mass associated with that that massive object so so the kind of the idea uh there is um think of the structure of space as being a dynamical changing kind of thing but then what Einstein did was he wrote down these differential equations that basically represented the curvature of space and its response to the presence of mass and energy and that ultimately is connected to the force of gravity which is one of the forces that seems to based on it strength operate on a different scale than some of the other forces so it operates at a scale as very large what happens there is is just this this curvature of space which causes you know the paths of objects to be deflected that's what gravity does it causes the paths of objects to be deflected and this is an explanation for Gravity so to speak and the surprise is that from 1915 until today everything that we measured about gravity precisely agrees with General and that's um uh and that you know it wasn't clear black holes were sort of predict well actually the expansion of the universe was an early potential prediction although Einstein tried to sort of patch up his equations to make it not cause the universe to expand because it was kind of so obvious the universe wasn't expanding and um uh you know turns out it was expanding and he should have just trusted the equations and that's a lesson for for those of us um interested in making fundamental theories of physics is you should trust your theory and not try and Patch it because of something that you think might be the case that um uh that that might turn out not to be the case even if the theory says something crazy is happening yeah right like the universe the universe is expanding right which is but but um but you know then it took until the 1940s probably even really until the 1960s until people understood that black holes were a consequence of of general relativity and so on but that's um you know the big surprise has been that so far this theory of gravity has perfectly agreed with you know these collisions of black holes seen by their gravitational waves you know it all just works so that's that's been kind of one pillar of the story of physics it's mathematically complicated to work out the consequences of general relativity but it's not there's there's no I mean and and and some things are kind of squiggly and complicated like people believe you know energy is conserved okay well energy conservation doesn't really work in general activity in the same way as it ordinarily does and it's all a big mathematical story of how you actually nail down something that is definitive that you can talk about it and not specific to the you know reference frames you're operating in and so on and so on and so on but fundamentally general relativity is a straight shot in the sense that you have this Theory you work out its consequences and and that that theory is useful in terms of basic science and trying to understand the way black holes work the way the creation of Galaxy's work s of all these kind of cosmological thing understanding what happened like you said at the Big Bang Yeah like all those kinds of well no not not at the Big Bang actually right but the well features of the expansion of the universe yes and and there are there are lots of details where we don't quite know how it's working you know is there you know where's the dark matter is there Dark Energy you know etc etc etc but but fundamentally the the you know the testable features of general relativity it all works very beautifully and it's it's in a sense it is mathematically sophisticated but is not conceptually hard to understand in some sense okay so that's general relativity and what's its friendly neighbor like you said two theories quantum mechanics right so quantum mechanics the the the sort of the way that that originated was one question was is the world continuous or is it discret you know in ancient Greek times people have been debating this people debated it you you know throughout history as light made of waves is it continuous as it discrete as it made of particles cor pusles whatever um you know what had become clear in the 1800s is that atoms that you know materials are made of discrete atoms you know when you take some water the water is not a continuous fluid even though seems like a continuous fluid to us at our scale but if you say let's look at it smaller and smaller and smaller and smaller scale eventually you get down to these you know these molecules and then atoms it's made of discrete things the question is sort of how important is this discreetness just what's discret what's not discret is energy discrete is you know is what's discrete what's not and so does it have mass those kinds of questions yeah yeah right well there's question I for example is mass discreet is an interesting question which is now something we can address but but um you know what what happened in um uh the in in the coming up to the 1920s there was this kind of mathematical theory developed that could explain certain kinds of discreetness in in particularly and in features of atoms and so on and uh you know what developed was this mathematical theory that was a theory the theory of quantum mechanics theory of wave functions sh's equation things like this that's a mathematical theory that allows you to calculate lots of features of the microscopic World lots of things about how atoms work etc etc etc now the calculations all work just great the um uh the question of what does it really mean is a complicated question now I mean to to just explain a little bit historically the you know the early calculations of things like atoms worked great 1920s 1930s and so on there was always a problem there were uh in Quantum field Theory which is a theory of uh uh in quantum mechanics you're dealing with a certain number of at a certain number of electrons and you fix the number of electrons you say I'm dealing with a two electron thing um in Quantum field Theory you allow for particles being created and destroyed so you can emit a photon that didn't exist before you can absorb a photon things like that that's a more complicated mathematically complicated Theory and it had all kinds of mathematical issues and all kinds of Infinities that cropped up and it was finally figured out more or less how to get rid of those but there were only certain ways of doing the calculations and those didn't work for Atomic nuclei among other things um and that led to a lot of development up until the 1960s of alternative ideas for how how one could understand what was happening in atomic nuclei etc etc etc end result in the end the kind of most quotes obvious mathematical structure of quantum field Theory seems to work although it's mathematically difficult to deal with but you can calculate all kinds of things you can calculate to you know a dozen decimal plac places certain certain things you can measure them it all works it's all beautiful now you way the underlying fabric is the model of that particular theory is Fields like you keep saying Fields those are quantum Fields those are different from classical Fields uh a field is something like you say um there's like you say the temperature field in this room it's like there is a value of temperature at every Point around the room that's um or or you can say the wind field would be the the vector Direction of the wind at every point it's continuous yes and it's a that's a classical field a Quantum field is a much more mathematically elaborate kind of thing um and I should explain that that one of the pictures of quantum mechanics that's really important is you know in classical physics one believes that sort of definite things happen in the world you pick up a ball you throw it the ball goes in a definite trajectory that's has certain equations of motion it goes in a parabola whatever else in quantum mechanics the picture is definitely things don't happen instead sort of what happens is this whole sort of structure of of all you know many different paths being followed and um we can calculate certain aspects of what happens certain probabilities of different outcomes and so on and you say well what really happened what's really going on what's the sort of uh what's the underlying you know what's the underlying story what how do we how do we turn this this mathematical theory that we can calculate things with into something that we can really understand and have a narrative about out and that's been really really hard for quantum mechanics my my friend dick feeman always used to say nobody understands quantum mechanics even though he'd made his you know whole career out of calculating things about quantum mechanics um and uh you know so so it's nevertheless it's uh what the quantum field theory is very uh very accurate at predicting a lot of the physical phenomena so it works yeah and but there are things about it you know it has certain when we apply it the standard model of particle physics for example we uh you know which we apply to calculate all kinds of things it works really well and you say Well it has certain parameters it has a whole bunch of parameters actually you say why is the you know why does the muon particle exist why is it 206 times the mass of the electron we don't know no idea but so the standard model physics is is is one of the models that's very accurate for describing three three of the fundamental forces of physics and look looking at the the world of the very small right and then there's back to the neighbor of uh gravity general relativity so and in the context of a Theory of Everything what's traditionally the task of the unification of these theories and why the issue is you try to use the methods of quantum field Theory to talk about gravity and it doesn't work just like there are photons of light so there are gravitons which are sort of the particles of gravity and when you try and compute sort of the properties of the of the particles of gravity the kind of mathematical tricks that get used um in working things out in Quantum field Theory don't work and um that's um so that's been a sort of fundamental issue and when you think about black holes which are a place where uh sort of the the the structure of space is um uh you know has has sort of Rapid variation and you get kind of quantum effects mixed in with effects from general relativity things get very complicated and there are apparent paradoxes and things like that and people have you know there been a bunch of mathematical developments in in physics over the last I don't know 30 years or so which have kind of picked away at those kinds of issues and got hints about how things might work um and but it hasn't been uh you know and the other thing to realize is as far as physics is concerned it's just like his general relativity his Quantum field Theory you know be happy yeah so do you think there's a quantization of gravity so quantum gravity what do you think of efforts that people have tried to yeah what do you think in general of the efforts of the physics Community to try to unify these laws so I think what's it's interesting I mean I would have said something very different before what's happened with our physics project um I mean you know the remarkable thing is what we've been able to do is to make from this very simple structurally simple underlying set of ideas we've been able to build this this you know very elaborate structure that's both very abstract and very sort of mathematically rich and the big surprise as far as I'm concerned is that it touches many of the ideas that people have had so in other words things like string theory and so on uh twister Theory it's like the you know we might have thought I had thought we're out on a prong we're building something that's computational it's completely different from what other people have done but actually it seems like what we've done is to provide essentially the machine code that you know these things are are various features of domain specific languages so to speak that talk about various aspects of this machine code and I think there's a this is something that to me is is is very exciting because it allows one both for us to provide sort of a new foundation for what's been thought about there and for the all the work that's been done in those areas to you know to give us you know more more momentum to be able to figure out what's going on now you know people have sort of hoped oh we're just going to be able to get you know String Theory to just answer everything that hasn't worked out and I think we now kind of can see a little bit about just sort of how far away certain kinds of things are from being able to explain things some things one of the big surprises to me actually I literally just got a message about one aspect of this is um uh the uh uh you know it's turning out to be easier I mean this project has been so much easier than I could ever imagine it would be that is I thought we would be you know just about able to understand the first 10us 100 seconds of the universe and um you know it would be 100 years before we get much further than that it's just turned out it actually wasn't that hard I me we're not finished but you know so you're you're you're seeing Echoes of all the disperate theories of physics in this framework yes I mean it's a very interesting you know sort of History of Science likee phenomenon I mean the best analogy that I can see is what happened with the early early days of of computability and computation Theory you know touring machines were invented in 1936 people sort of understand computation in terms of touring machines but actually there had been pre-existing theories of computation combinators General recursive functions Lambda calculus things like this but people hadn't those hadn't been concrete enough that people could really wrap their arms around them and understand what was going on and I think what we're going to see in this case is that a bunch of these mathematical theories um including some very I one of the things that's really interesting is one of the most abstract things that's come out of of sort of uh mathematics higher category Theory things about Infinity groupoids things like this which to me always just seemed like they were floating off into the stratosphere ionosphere of mathematics um turn out to be things which our sort of theory anchors down to something fairly definite and says our super relevant to the way that we can understand how physics Works give me a sec by the way I just threw a hat on you've said that um with this metaphor analogy that Theory of Everything is a big mountain and you have a sense that however far we are up the mountain that the the wolf from physics model a view of the universe is at least the right Mountain we're the right Mountain yes without question which aspect of it is the right Mountain so for example I mean so there's so many aspects to Just The Way of the wol from physics project the way it approaches the world that's um that's clean crisp uh and uh unique and Powerful so you know there's a there's discreet nature to it there's a hypergraph there's a computational nature there's a generative aspect you start from nothing you generate everything which do you think the actual model is actually a really good one or do you think this General principle of from Simplicity generating complexity is the right like what aspect of the mountain yeah right I mean I I think that the the kind of the meta idea about using simple computational systems to do things that's you know that's the ultimate big Paradigm that is you know sort of super important the details of the particular model are very nice and clean and allow one to actually understand what's going on they are not unique and in fact we know that we know that there's a there's a large number of different ways to describe essentially the same thing I mean I can describe things in terms of hypergraphs I can describe them in terms of higher category Theory I can describe them in a bunch of different ways they are in some sense all the same thing but our sort of story about what's going on and and the kind of kind of cultural mathematical resonances are a bit different I think it's it's it's perhaps worth sort of saying a little bit about kind of the the you know foundational ideas of of uh of uh uh you know of these of these models and things great so can you maybe uh can we like rewind we've talked about a little bit but can you say like what the central idea is of the Wolfram physics project right so so the question is we're interested in finding a sort of simple computational rule that describes our whole universe can we just pause on that I just so be that's such a beautiful that's such a beautiful idea that we can generate our universe from a from a uh from a data structure a simple structure simple set of rules and we can generate our entire universe yes that's all inspiring right but but so so you know the question is how do you actualize that what might this rule be like and so one thing you quickly realize is if you're going to pack everything about our universe into this tiny rule not much that we are familiar with in our universe will be obvious in that rule so you don't get to fit all these parameters of the universe all these features of you know this is how space works this is how time works etc etc etc you don't get to fit that all it all has to be sort of packed in to this this thing something much smaller much more basic much lower level machine code so to speak than that and all the stuff that we're familiar with has to kind of emerge from the operation of so the rule in itself because of the computational reducibility is not going to tell you the story it's not going to give you the answer to uh it's not going to let you predict what you're going to have for lunch tomorrow and it's not going to let you predict basically anything about your life about the universe right but and you're not going to be able to see in that rule oh there's the three for the number of dimensions of space and so on that's not going to be there so space time is not going to be obviously right so the question is then what what is the universe made of that's that's a it's a basic question and we've had some assumptions about what the universe is made of for the last few thousand years that I think in some cases I just turn out not to be right and you know the most important assumption is that space is a continuous thing that is that you can if you say let's pick a point in space we're going to do geometry we're going to pick a point we can pick a point absolutely anywhere in space precisely numbers we can specify of where that point is in fact you know uclid who kind of wrote down the original kind of atiz of geometry back in 300 BC or so um you know his his very first definition he says a point is that which has no part a point is this is this you know uh this indivisible you know infinitesimal thing okay so we might have said that about material objects we might have said that about water for example we might have said water is a continuous thing that we can just uh you know pick any point we want in in in some water but actually we know it isn't true we know that water is made of molecules that are discrete and so the question one fundamental question is what is space made of and so one of the things that's sort of a starting point for what I've done is to think of space as a discrete thing to think of there being sort of atoms of space just as there are atoms of material things although very different kinds of atoms and by the way I mean this idea you know there were ancient Greek philosophers who had this idea there were you know Einstein actually thought this is probably how things would work out I mean he said you know repeatedly he thought that is way it would work out we don't have the mathematical Tools in our time which was 1940s 1950s and so on to explore this like the way he thought you mean that there is something very very small and discreete that's underlying space space yes and that that means that so you know the mathematical Theory mathematical theories in physics assume that space can be described just as a continuous thing you can just pick coordinates and the coordinates can have any values and that's how you define space space is this just sort of background uh sort of theater on which the universe operates but can we draw a distinction between space as a thing that could be described by uh three values coordinates and how you're are you are you using the word space more generally when you say no I'm I'm just talking about space as in what we experience in in in the universe so you think this 3D aspect of it is fundamental no I don't think that 3D is fundamental at all actually I think that the what's the the the thing that has been assumed is that space is this continuous thing where you can just describe it by let's say three numbers for instance but most important thing about that is that you can describe it by PR prise numbers because you can pick any point in space and you can talk about motions any infinitesimal Motion in space and that's what continuous means that's what continuous means that's what you know Newton invented calculus to describe these kind of continuous small variations and so on that was that's kind of a fundamental idea from uclid on that's been a fundamental idea about space and so is that right or wrong uh it's it's not right it's not right it's it's it's it's right at the level of our experience most of of the time it's not right at the level of the machine code so to speak and so machine code yeah of the simulation that's right that's right they're the very lowest level of the fabric of the universe at least under the the the will from physics model is your sense is as discreet right so so now what does that mean so it means what what is space then so in in um models the basic idea is you say there are these sort of atoms of space they're these points that represent you know represent places in space but they're just discrete points and the only thing we know about them is how they're connected to each other we don't know where they are they don't have coordinates we don't get to say this is a position such and such it's just here's a big bag of points like in our universe there might be 10 to the 100 of these points and all we know is this point is connected to this other point so it's like you know all we have is the friend nwor so to speak we don't we don't have you know people's you know physical addresses all we have is the friend network of these points yeah the underlying nature of reality is kind of like a Facebook uh we don't know their location but we have the friends yeah yeah right we we we know which point is connected to which other points and and that's all we know and so you might say well how on Earth can you get something which is like our experience of of you know what seems like continuous space well the answer is by the time you have 10 to the 100 of these things there they those connections can work in such a way that on a large scale it will seem to be like continuous space in let's say three dimensions or some other number of Dimensions or 2.6 Dimensions or whatever else because they're much much much much larger so like the uh the number of relationships here we're talking about is just a humongous amount so the the kind of thing you're talking about is very very very small relative to our experience of daily life right so I mean you know we don't know exactly the size but maybe maybe uh uh 10 Theus uh maybe around 10 Theus 100 m so you know the size of to give a comparison you know the size of a of a proton is 10us 15 M and so this is something incredibly tiny compared to that um and and the the idea that from that would emerge the experience of continuous space is mindblowing what's your intuition why that's possible like first of all I mean we'll get in into it but I don't know if we will through the medium of conversation but the construct of hypergraphs is just beautiful right cellometer beautiful we'll talk about it but okay but but but this thing about you know continuity arising from discrete systems is in today's world is actually not so surprising I mean you know your average computer screen right every computer screen is made of discrete pixels yet we have the you know we have the idea that we're seeing these continuous pictures I mean it's you know the fact that on a large scale continuity can arise from lots of discrete elements this is at some level unsurprising now but wait but the pixels have uh a very definitive structure of Neighbors on on a computer screen right there is no concept of spatial of space inherent in the underly fabric of reality right right right so so the the the point is but there are cases where there are so for example let's just imagine you have a square grid okay and at every point on the grid you have one of these atoms of space and it's connected to four other four other atoms of space on the you know Northeast southwest corners right um there you have something where if you zoom out from that it's like a computer screen yeah so the relationship creates the the spatial like the relationship creates a constraint which then in an emerging sense creates a like yeah like a uh basically a spatial coordinate for that thing yeah right even though the individual point doesn't have a space even though the individual point doesn't know anything it just knows what it's you know what its neighbors are the on a large scale it can be described by saying oh it looks like it's a you know this grid zoomed out grid you can say well you can describe these different points by saying they have certain positions coordinates Etc now in the in the sort of real setup it's more complicated than that it isn't just a square Grid or something it's something much more Dynamic and complicated which we'll talk about but um uh so you know first the first idea the first key idea is you know what's the universe made of it's made of atoms of space basically with these connections between them what kind of connections do they have well so a the simplest kind of thing you might say is we've got something like a graph where every uh every atom of space uh where we have these edges that go between atom these connections that go between atoms of space we're not saying how long these edges are we're just saying there is a connection from from this place to the from this atom to this atom just a quick pause because there's a lot of very people that listen to this just to clarify because I did a poll actually what do you think a graph is a long time ago and it's kind of funny how few people know the term graph uh outside of computer science it's let's call it a network I think that's that's call a network is better so but every time I like the word graph though so let's define let's just say that graph we'll use terms nodes and edges maybe and it's just uh nodes represent some abstract entity and then the edges represent relationships between those entities right exactly so that's what graph say sorry so so there you go so that's the basic structure that is that is the simplest case of a basic structure actually uh it tends to be better to think about hypergraphs so a hypergraph is just instead of saying uh there are connections between Pairs of things we say there are connections between any number of things so there might be Turner edges so instead of instead of just having uh two points are connected by an edge you say three points are all associated with a hyperedge are all connected by hyper Edge that's just at some level that's at some level that's a detail it's a detail that happens to make the um for me you know sort of in the history of this project the realization that you could do things that way broke out of certain kinds of arbitrariness that I felt that there was in the model before I had seen how this worked I mean all a hypergraph can be mapped to a graph it's just a convenient representation mathematically speaking right that's correct that's correct but so then so okay so the the first question the first idea of these models of ours is spaces made of these know connected sort of atoms of space the next idea is space is all there is there's nothing except for this space So In traditional ideas in physics people have said there's space it's kind of a background and then there's matter all these particles electrons all these other things which exist in space right but in this model one of the key ideas is there's nothing except space so in other words everything that has that exists in the universe is a feature of this hypergraph so how can that possibly be well the way that works is that there are certain uh structures in this hypergraph where you say that little twisty knotted thing we don't know exactly how this works yet but but we we have sort of idea about how it works mathematically this sort of Twisted knotted thing that's the core of an electron this thing over there that has this different form that's something else so the different peculiarities of the structure of this graph are the very things that uh we think of as the particles inside the space but in fact it's just a property of of space mindblowing first of all that it's mind-blowing and we'll probably talk in its Simplicity and Beauty yes I think it's very beautiful I this is I'm but okay so but that's space and then there's another concept we didn't really kind of mention but you thinking of computation as a like a transformation let's talk about time in a second let's let's just let's just I mean on the subject oface that you know there's this question of kind of what you know there's this idea there is this hypergraph it represents space and it represents everything that's in Space the features of that hypergraph you can say certain features in this part we do know certain features of the hypergraph represent the presence of energy for example or the presence of mass or momentum and we know what the features of the hypergraph that represent those things are but it's all just the same hypergraph so one thing you might ask is you know if you just look at this hypergraph and you say and we're going to talk about sort of what the hypergraph does but if you say you know how much of what's going on in this hypergraph is things we know and care about like particles and atoms of electrons and all this kind of thing and how much is just the background of space so it turns out so far as in one rough estimate of this all everything that we care about in the universe is only one part in 10 to 120 of what's actually going on the vast majority of what's Happening is purely things that maintain the structure of space that in other words that the things that are the features of space that are the things that we consider notable like the presence of particles and so on that's a tiny little piece of froth on the top of all this activity that mostly is just intended to you know mostly I can't say intended there's no intention here that just maintains the structure of space let me let me load that in it's uh it just makes me feel so good as a human being well to be the froth on the one and the 10 to the 120 or something of well and also just humbling um how in this mathematical framework how much work needs to be done on the infrastructure right of our universe right to maintain the infrastructure of our universe is a lot of work we are we are merely writing a little tiny things on top of that infrastructure but but you know you you were just starting to to talk a little bit about what I you know we talked about you know space that represents all the stuff that's in the universe the question is what does that stuff do and for that we have to start talking about time and what is time and so on and you know one of the the basic idea of this model is time is the progression of computation so in other words we have a a structure of space and there is a rule that says how that structure of space will change and it's the application the repeated application of that rule that defines the progress of time um and what does the rule look like in in the space of hyperg grass right so what the rule says is something like if you have a little tiny piece of hypergraph that looks like this then it will be transformed into a piece of hypergraph that looks like this so that's all it says it says you pick up these elements of space and the you can think of these these uh edges these hyper edges as being relations between elements in space you might pick up uh these two relations between elements in space and we're not saying where those elements are or what they are but every time there's a certain arrangement of elements in space then arrangement in the sense of the way they're connected then we transform it into some other Arrangement so there's a little tiny pattern and you transform it into another little pattern that's right and then because of this I mean again it's kind of similar to Cellular atomine that like yes on paper the rule looks like super simple it's like uh yeah okay yeah like yeah right from this the universe can be born uh but like once you start applying it beautiful structure starts being potentially can be created and what you're doing is you're applying that rule to different parts like to anytime you match it within the hypergraph exactly and then one of the like incredibly beautiful and interesting things to think about is the order in which you apply that rule yes because that pattern appears all over the place right so this is a big complicated thing very hard to wrap one's brain around okay so so you you say the rule is every time you see this little pattern transform it in this way but yet you know as you look around the space that represents the universe there may be zillions of places where that little pattern occurs yeah so so what what what it says is just do this apply this rule wherever you feel like and what what is extremely non-trivial is well okay so so this is happening sort of in in computer science terms sort of asynchronously you're just doing it wherever wherever you feel like doing it and the only constraint is that if you're going to apply the rule somewhere the the things to which you apply the rule the the little you know elements to which you apply the rule if they if they have to be okay well you can think of each application of the rule as being kind of an event that happens in the universe Y and these the input to an event has to be ready for the event to occur that is if one event occurred if one transformation occurred and It produced a particular atom of space then that atom of space has to already exist before another uh transformation that's going to apply to that atom of space can occur so like the prerequisite for the event that's exist that's right so it it that defines a kind of uh this sort of set of causal relationships between events it says this event Happ has to have happened before this event but that is um but that's that's not a very limiting constraint no it's not and what's still you still get the zillion uh that's a technical term options that's correct but but okay so this is where things get a little bit more elaborate but they're mindblowing so right but so so what what what happens is so the first thing you might say is you know let's well okay so so this question about the freedom of which which event you do when well let me let me sort of State an answer and then explain it okay the the um the validity of special relativity is a consequence of the fact that in some sense it doesn't matter in what order you do these underlying things so long as they respect this kind of set of causal relationship ship so and that's that's uh in a the the part that's in a certain sense is a really important one but the fact that it it sometimes doesn't matter that's a I don't know what that's another like beautiful thing okay so so there's this idea of what I call causal invariance causal invariance exactly that's so really really powerful powerful idea a powerful idea which has actually Arisen in different forms many times in the history of mathematics mathematical logic even computer science has many different names um I mean our particular version of it is a little bit tighter than other versions but it's basically the same idea here's here's how to think about that idea so imagine that well let's talk about it in terms of math for a second let's say you're doing algebra and you're told you know multiply out this series of polinomial that are that are multiplied together okay you say well which order should I do that in so well do I multiply the third one by the fourth one and then do it by the first one or do I do the fifth one by the sixth one and then do that well it turns out it doesn't matter you can you can multiply them out in any order you'll always get the same answer that's a that's a a property if you think about kind of making a kind of network that represents in what order you do things you'll get different orders for different ways of multiplying things out but you'll always get the same answer same thing if you let's say you're sorting you've got a bunch of A's and B's they're in random some random order you know baa BBB AA whatever and you you have a little rule that says every time you see ba flip it around to AB okay eventually you apply that rule enough times you'll have sorted the string so that it's all the A's first and then all the B's again you there are many different orders in which you can do that that many different sort of places where you can apply that update in the end you'll always get the string sorted the same way I know I know with sorting a string it's it sounds obvious that's to me surprising that that there is in complicated systems obviously with a with a string but in in a hypergraph that the application of the rule a asynchronous rule can lead to the same results sometimes yes yes that is it is not obvious and it was something that um you know I I sort of discovered that idea for these kinds of systems in back in the 1990s and for various reasons I I I was not I was not satisfied by how sort of fragile finding that particular property was was and let me let me just make another point which is that that it turns out that even if the underlying rule does not have this property of causal invariance it can turn out that every observation made by observers of the rule can they can impose what amounts to causal invariance on the rule we can explain that it's a little bit more complicated I mean technically that has to do with this idea of completions which is something that comes up in term re writing systems automated theorem proving systems and so on but that let's let's ignore that for a second we can come to that later but is it useful to talk about observation not yet not yet so so great so there's some concept of causal invariance as uh you apply these rules in an asynchronous way you can think of those Transformations as events so there's this hypergraph that represents space and all of these events happening in the space and the graph grows in interesting complicated ways and eventually the froth arises to of a what we experience as human existence so that's that's the that's some version of the picture but but let's explain a little bit more exactly what's a little a little more detailed like right well so so one thing that is sort of surprising in this in this theory is one of the sort of achievements of 20th century physics was kind of bringing space and time together that was you know special relativity people talk about SpaceTime this sort of unified thing where space and time kind of are mixed and there's a nice mathematical formula M um that uh in which you know space and time sort of appear as part of the SpaceTime Continuum the SpaceTime you know four vectors and things like this um you know we talk about spe time as the fourth dimension and all these kinds of things it's you know that and it seems like the theory of relativity sort of says space and time are fundamentally the same kind of thing so one of the things that took a while to understand in in this approach of mine is that uh in in in my kind of approach space and time are really not fundamentally the same kind of thing space is the extension of this hypergraph time is the kind of progress of this inexorable computation of these rules getting applied to the hypergraph so it's they seem like very different kinds of things and and so that at first seems like how can that possibly be right how can that possibly be lorensen variant that's the term for things being you know following the the rules of special artivity well it turns out that when you have causal invariance that and let's see we can it's worth it's worth explaining a little bit how this works it's a little bit little bit elaborate but but the basic point is that um uh the even though space and time sort of come from very different places it turns out that the rules of sort of space time that special relativity talks about um come out of this model when you're looking at large enough systems MH so so a way to think about this you know in terms of the when you're looking at large enough systems um the U part of that story is when you look at some fluid Like Water for example there are equations that govern the flow of water um those equations are things that apply on a large scale if you look at the individual molecules they don't know anything about those equations it's just the the the sort of the large scale effect of those molecules turns out to follow those equations and it's the same kind of thing happening in our models I know this might be a a small point but it might be a very big one we've been talking about space and time at the lowest level of the model which is space the hypergraph time is the evolution of this hypergraph but there's also SpaceTime that we think about in general relativity for special relativity like what how does how do you go from the uh lowest source code of space and time we're talking about to the more traditional terminology of space and time right so so the the key thing is this thing we call the causal graph so the causal graph is the graph of causal relationships between events so every one of these little updating events every one of these little transformations of the hypergraph happens somewhere in the hypergraph happens at some stage in the computation that's an event that event is has a causal relationship to other events in the sense that if the if another event needs as its input the output from the first event there will be a causal relationship of the the the future event will depend on the past event so you can say it's it has a causal connection and so you can make this graph of causal relationships between events that graph of causal relationships causal invariance implies that that graph is unique it doesn't matter even though you think oh I'm I'm you know let's say we were sorting a string for example I did that particular transposition of of characters at this time and then I did that one then I did this one turns out if you look at the network of of connections between those updating events that network is the same it's it's the if if you were to see the the the structure so in other words if you were to draw that that if you were to put that Network on a picture of where you're doing all the updating the places where you put the the nodes of the network will be different but the way the nodes are connected will always be the same so but the causal graph is a is I don't want it's kind of an observ it's not uh enforced it's just emergent from set of events well it's a it's a feature of of okay so what it is characteristic I guess of the way events happen right it's an event can't happen until its input is ready right and so that creates this this network of causal relationships and that's that's the causal graph and the thing the next thing to realize is okay we when you're going to observe what happens in the universe you have to sort of make sense of this causal graph so and you are an observer who yourself is part of this causal graph and so that means so let me give you an example of of how that works so so imagine we have a really weird Theory of physics of the world where it says this updating process there's only going to be one update at every moment in time and it's just going to be like a touring machine it has a little head that runs around and just is always just updating one thing at a time so you say you know I have a theory of physics and The Theory of physics says there's just this one little place where things get updated you say that's completely crazy because you know it's plainly obvious that things are being updated sort of you know at the same syn yeah at the same time but but the fact is that the thing is that if I'm you know talking to you and you seem to be being updated as I'm being updated but but if there's just this one little head that's running around updating things I will not know whether you've been updated or not until I'm updated so in other words when you draw this causal graph of the causal relationship between the updatings and you and the updatings in me it'll still be the same causal graph whether even though the underlying sort of story of what happens is oh there's just this one little thing and it goes and updates in different places in the universe so is that is that clear or is that a hypothesis is that is that clear that there's a unique causal graph uh if there's causal invariance there's unique coal growth that's so so it's okay to think of what we're talking about as a hypergraph and the operations on it as a kind of touring machine with a single head like a single guy running around updating stuff um is that safe to intuitively think of it this way um let me think about that for a second yes I think so I think that I think there's nothing it doesn't matter I mean you you can you can say okay there is one the reason I'm pausing for a second is that um I'm wondering well well when you say running around depends how far it jumps every time it runs around yeah yeah that's right but I mean like one operation at yeah you can think of it one operation it's easier for the human brain to think of it that way as opposed to uh simultaneous it's not okay but the thing is that's not how we experience the world what we experience is we look around everything seems to be happening at successive moments in time everywhere in space yes that is the um and that's partly a feature of our particular construction I mean that is the speed of light is really fast compared to you know we look around you know I can see maybe 100 feet away right now um you know it's uh the my brain does not process very much in the time it takes light to C 100 ft the brain operates at a scale of hundreds of milliseconds or something like that I don't know and and speed of light is much faster right you know light goes in a billionth of a second light has gone a foot so it goes a billion feet every second there's certain moments through this conversation where I I I uh imagine the absurdity of the fact that there's two descendants of Apes modeled by hypergraph that are communicating with each other and experiencing this whole thing as a real time simultaneous update with uh I'm taking in photons from you right now but there's something much much deeper going on right here it it does have a it's paralyzing sometimes just yes to remember that right no I mean you know but so you know yes yes as a small little tangent I I just remembered that we're talking about I mean this the about the fabric of reality right so we we've got this causal graph that represents the sort of causal relationships between all these events in the universe yeah that causal graph kind of is a representation of space time but our experience of it requires that we pick reference frames this is kind of a key idea Einstein had this idea that what that means is we have to say what are we going to pick as being the uh sort of what we Define as simultaneous moments in time so for example we can say um you know we we set how do we set our clocks you know if we've got a a spacecraft landing on Mars you know do we say that it you know what what time is it landing at was it you know even though there's a 20 minute speed of light delay or something thing you know what time do we say it landed at how do we how do we set up sort of time coordinates for for the world and that turns out to be that there's kind of this arbitrariness to how we set these reference frames that Define sort of what cils simultaneous and what is the the essence of special relativity is to think about reference frames going at different speeds and to think about sort of how they assign what counts as space what counts as time and so on um that's all well a bit technical but the basic bottom line is that the this causal invariance property that means that it's always the same causal graph independent of how you slice it with these reference frames you'll always sort of see the same physical processes go on and that's basically why special relativity works so there's something like special relativity uh like everything around space and time that uh that fits this idea of the causal graph right well you know one way to think about it is given that you have a a basic structure that just involves updating things in in these you know connected updates and looking at the causal relationships between connected updates that's enough when you unravel the consequences of that that together with the fact that there are lots of these things and that you can take a Continuum limit and so on implies special RS of a day and um so that it's kind of a not a big deal because it's kind of it's kind of a you it was completely unobvious when you started off with saying we've got this graph it's being updated in time etc etc etc that just looks like nothing to do with special arts every day and yet you get that and and what I mean then the thing I mean this was stuff that I figured out back in the 1990s the um the the next big thing you get is General Arts of day um and so the in this hypergraph the this sort of limiting structure when you have a very big hypergraph you can think of as being just like you know water seems continuous on a large scale so this hypergraph seems continuous on a large scale one question is you know how many dimensions of space does it correspond to so one question you can ask is if you just got a bunch of points and they're connected together how do you deduce what effective dimension of space that bundle of points corresponds to and that's that's pretty easy to explain so basically if you say you got a point and you look at how many neighbors does that point have okay imagine it's on a square grid then it'll have four neighbors go another level out how many neighbors do you get then what you realize is as you go more and more levels out as you go more and more distance on the graph out you're you're capturing something which is essentially a circle in two Dimensions so that you know the the number of the area of a circle is p pi r squ so the it's the number of points that you get to goes up like the distance you've gone squared and in general in D dimensional space it's R to the^ D it's the the number of points you get to if you go R steps on the graph grows like the number of steps you go to the power of the dimension and that's a that's a way that you can estimate the effective dimension of one of these graphs so what does that grow to so how does the dimension grow because uh I mean obviously the visual aspect of these hypergraphs they're often visualized in three dimensions right and then there's a certain kind of structure uh like you said there's the I mean a circle a sphere uh there there's a planer aspect to it to this graph to where it kind of it almost starts creating a surface like a complicated surface but a surface so how does that connect to affected Dimension okay so if you can lay out the graph in such a way that the that the points in the graph that uh you know the the points that are neighbors on the graph are neighbors as you lay them out out MH and you can do that in two dimensions then it's going to approximate a two- dimensional thing if you can't do that in two Dimensions if everything would have to fold over a lot in two dimensions then it's not an approximating a two- dimensional thing maybe you can lay it out in three dimensions maybe you have to lay it out in five Dimensions to have it be the case that it sort of smoothly lays out like that well but okay so uh and I apologize for the different tangent questions but you know there's an Infinity number of possible rules so we have to look for rules that uh that create the kind of structures that that're reminiscent for uh that have Echoes of the different physics theories in them so what kind of rules is there something simple to be said about the kind of rules that you have found beautiful that you have found powerful right so so I mean what you know one of the features of computational ir reducibility is it's very you you can't say in advance what's going to happen happen with any particular you can't say I'm going to pick these rules from this part of rule space so to speak because they're going to be the ones that are going to work that's you can make some statements along those lines but you can't generally say that now you know the state of what we've been able to do is you know different properties of the universe like dimensionality you know integer dimensionality features of of other features of of quantum mechanics things like that at this point what we've got is we've got rules that that uh any one of those features we can get a rule that has that feature yeah so we don't have the the sort of the final here's a rule which has all of these features we do not have that yet so so if I were to try to summarize the wolf from physics project which is uh you know something that's been in your brain for a long time but really has just exploded in activity you know only just months ago yes uh so it's an evolving thing and next week I'll try to publish this conversation as quickly as possible because by the time it's published already new things will probably have come out so uh so if I were to summarize it we've talked about the basics of there's a hypergraph that represents space there is uh Transformations and that hypergraph that represents um time progress of time the progress of time there's a cause a graph that's a characteristic of this and the basic process of science of yeah of science within the wol from physics model is to try different rules and see which properties of physics that we know of known physical theories are appear within the graphs that emerg from that rule that's what I thought it was going to be uh oh okay so what so what is it turns out we can do a lot better than that it turns out that using kind of mathematical ideas we can say and computational ideas we can we can make General statements and those General statements turn out to correspond to things that we know from 20th century physics in other words the idea of you just try a bunch of rules and see what they do that's what I thought we were going to have to do um but in in fact we can say given causal invariance and computational irreducibility we can derive and this is where it gets really pretty interesting we can derive special relativity we can derive general relativity we can derive quantum mechanics and that's where things really start to get exciting is you know it wasn't at all obvious to me that even if we were completely correct and even if we had you know this is the rule you know even if we found the rule to be able to say yes it corresponds to things we already know I did not expect that to be the case and so for somebody who is uh simple mind and definitely not a physicist not even close what does derivation mean in this case okay so so let me this is interesting question okay so there's so one one thing in the context of computational reducibility yeah yeah right right so what you have to do let me give let me go back to again the mundane example of fluids and water and things like that right so so you have a bunch of molecules bouncing around you can say uh just as a piece of mathematics I happen to do this from cellular autometer back in the mid 1980s you can say just as a matter of mathematics you can say the Continuum limit of these little molecules bouncing around is the Navia Stokes equations that's just a piece of mathematics it's not it doesn't rely on uh you have to make certain assumptions that you have to say there's enough Randomness in the way the molecules bounce around that certain statistical averages work etc etc etc okay it is a very similar derivation to derive for example the Einstein equations okay so the way that Works roughly the einin equations are about curvature of space uh curvature of space I talked about sort of how you can figure out dimension of space there's a similar kind of way of figuring out if you if you just sort of say um uh you know you're making a larger larger ball or larger and larger if you draw a circle on the surface of the Earth for example you might think the area of a circle is pi r squ but on the surface of the Earth because it's a sphere it's not flat the the area of a circle isn't precisely P pi r s as the circle gets bigger the area is slightly smaller than you would expect from the formula P Pi R square has a little correction term that depends on the the ratio of the size of the circle to the radius of the Earth okay so it's the same basic thing allows you to measure from one of these hyper graphs what is its effective curvature and that's oh so um the little piece of mathematics that uh explains special general relativity is uh can map nicely to describe fundamental property of the hyps the curvature of H so special relativity is about the relationship of time to space general relativity is about curvature in in this space represented by this hypergraph so what is the curvature of a hypergraph okay so first I have to explain what was explaining is first thing you have to have is a notional Dimension you don't get to talk about curvature of things if you say oh it's a curved line but I don't what a line is yet so yeah what is the dimension of a hypography hypergraph it's got a trillion nodes in it yeah what is it roughly like is it roughly like a grid a two-dimensional grid is it roughly like all those all those nodes are arranged on line what's it roughly like and there's a pretty simple mathematical way to estimate that by just looking at the the the this thing I was describing this sort of the size of a ball that you construct in the hypergraph that's a you just measure that you can just you know comput it on a computer for a given hypergraph and you can say oh this thing is wiggling around but it's it's roughly corresponds to two or something like that it roughly corresponds to 2.6 or whatever so that's how you that's how you have a notion of dimension in these hypergraphs curvature is something a little bit beyond that it's if you look at the how the size of this ball increases as you increase its radius curvature is a correction to the SI size increased associated with Dimension it's a sort of a second order term in in the in determining the size just like the area of a circle is roughly P pi r s so it goes up like R squar the two is because it's in two Dimensions but when that circle is drawn on a big sphere the the actual formula is pi r 2 * 1 minus uh R 2 over a 2 and some coefficient so in other words there's a correction to and that correction term that gives you coverture and that correction term is what makes this hypergraph correspond have the potential to correspond to curved space now the next question is is that curvature is the way that curvature works the way that Einstein's equations of general relativity you know is it the way they say it should work and the answer is uh yes and the and so how does that work the I mean you the the calculation of the curvature of this hypergraph for for some some set of rules no it doesn't matter what the rules are it doesn't so long as they have causal invariance and computational irreducibility and and they lead to finite dimensional space f non infinite dimensional space nonin dimensional it can grow infinitely but it can't be infinite dimensional so what ises a infinitely dimensional hypog graph look like so that mean for example so in a you start from one root of the tree it Doubles Doubles again doubles again doubles again and that means if you ask the question starting from a given point how many points do you get to remember in like a circle you get to r squ with a two there on a tree you get to for example 2 to the r it's exponential dimensional so to speak or infinite dimensional do you have a sense of in the space of all possible rules how many uh lead to uh infinitely dimensional hypog grass is that U no okay is that an important thing to know yes it's an important thing to know I would love to know the answer to that and but but you know it gets a little bit more complicated because for example it's very possibly the case that in our physical universe that the Universe started infinite dimensional and it only uh it as it as the you know at the big bang it was very likely infinite dimensional and as um as the universe sort of expanded and cooled its Dimension gradually went down and so one of the bizarre possibilities which actually there are experiments you can do to try and look at this the universe can have Dimension fluctuations so in other words we think we live in a three-dimensional universe but actually there may be places where it's actually 3.01 dimensional or where it's you know 2.99 dimensional and it may be that in the in the very early Universe it was actually infinite dimensional and it's only a late stage phenomenon that we end up getting three-dimensional space but from your perspective of the hypergraph the one of the underlying assumptions you kind of implied but you have a sense a hope um set of assumptions that the the rules that underly our universe or the rule that underlies our universe is static is that the one of the assumptions you're currently operating under uh yes but there's a there's a footnote to that which we should get to because it requires a few more steps okay well actually then let's backtrack to the curvature because we're talking about as long as it's finite dimensional uh finite dimensional computational irreducibility and causal invariance then it follows that uh the uh that the large scale structure will follow Einstein's equations and now let me again qualify that a little bit more there's a little bit more complexity to it the um uh okay so Einstein's equations in their simplest form apply to the vacuum no matter just the vacuum and they say in particular what they say is if you have um uh so there's this term jisc that's a term that means shortest path comes from measuring shortest paths on the earth so you you look at a bunch of a bundle of jd6 a bunch of shortest paths it's like the paths that photons would take between two points then the statement of Einstein's equations is basically a statement about a certain the that as you look at a bundle of gd6 the structure of space has to be such that although the the cross-sectional area of this bundle May although the actual shape of the cross-section may change the cross-sectional area does not that's a version that's a that's the most simple-minded version of amuu minus a half r g mu new equals z which is the the more mathematical version of Einstein's equations it's a statement it's a statement of thing called the Richie tensor is equal to zero um that's that's Einstein's equations for the vacuum okay so we get that in um as a result of this model but footnote big you know big footnote because all the matter in the universe is the stuff we actually care about the vacuum is not stuff we care about so the question is how does matter come into this and for that you have to understand what energy is in these models and um one of the things that we realized um you know last late last year was um that there's a very simple interpretation of energy in these models okay and energy is basically well intuitively it's the amount of activity in these hypergraphs and the way that that remains over time so a little bit more formally you can think about this causal graph as having these edges that represent causal relationships you can think about oh boy there's one more concept that we didn't get to is that the the notion of space-like hypersurfaces so this is this is a is not as scary as it sounds the the um it's a it's a common notion in general it's a the notion is you are you're defining what is a possibly what is what um where in SpaceTime might be a particular moment in time so in other words what what is a consistent set of places where you can say this is happening now so to speak and you make this series of of of sort of slices through the SpaceTime uh through this causal graph to rep represent sort of what we consider to be successive moments in time okay it's somewhat arbitrary because you can you can deform that if you're going at a different speed and special relativity you tip those things if you're you can you know there there are different kinds of defamations but only certain defamations are allowed by the structure of the causal graph anyway be there as it may the the the basic point is there is a way of figuring out you know you say what is the energy associated with what's going on in this in this hypergraph and the answer is there is a precise definition of that and it is the formal way to say it is it's the Flux Of causal edges through space likee hypersurfaces the slightly less formal way to say it it's basically the amount of activity the the see the reason it gets tricky is you might say it's the amount of activity per unit volume in in this hyper graph but you haven't defined what volume is so it's it's it's a little bit that you have to but this hypersurface gives some more formalism to that yeah it gives a way to connect that to but intuitive we should think about is the just the amount of activity right so so the amount of activity that kind of remains in one place in the hypergraph corresponds to energy the amount of activity that is kind of where an activity here affects an activity somewhere else C corresponds to momentum and um and so one of the things that's kind of cool is that I'm trying to think about how to say this intuitively the mathematics is easy but the the intuitive version I'm not sure but basically the way that things sort of stay in the same place and have activity is associated with rest mass and so one of the things that you get to derive isal mc^2 um that is a consequence of this interpretation of energy in terms of the way the causal graph Works which is a the whole thing is sort of a consequence of this whole story about updates and hypergraphs and so on so can you Linger on that a little bit how do we get eals mc² so where does the mask come from so okay okay I mean without is there an intuitive so okay F first of all you're pretty deep in the mathematical explorations of this thing right now we're in a very we're in a flux uh currently so maybe you haven't even had time to think about intuitive explanations uh but yeah I mean this one this one is is look roughly what's happening that derivation is actually rather easy and everybody and I've been saying we should pay more attention to this derivation because it's such you know because people care about this one and everybody says it's just easy it's it's easy so there's some concept of energy that's uh can be intuitively thought of as the activity the the flux the level the level of uh changes that occurring based on the Transformations within a certain volume however the heck do you find the volume okay so and then Mass well mass is is mass is associated with kind of the energy that does not cause you to that does not somehow propagate through time yeah I mean one of the things that was not obvious in the usual formulation of speciality is that space and time are connected in a certain way energy moment and momentum are also connected in a certain way the fact that the connection of energy to momentum is analogous to the connection to space between space space and time is not self-evident in ordinary relativity it is a consequence of this of the way this model works it's an intrinsic consequence of the way this model works and it's all to do with that with with unraveling that connection that ends up giving you this this relationship between energy and and well it's energy momentum Mass they're all connected and and so like uh that's hence the general relativity you have a sense that uh it appears to be baked in to the fundamental properties of the way these hypergraphs are evolved well I didn't yet get to so I I got as far as special relativity and equals mc^ s the one last step is in general relativity the the final connection is energy Mass cause curvature in space and that's something that when you understand this interpretation of energy and you kind of understand the correspondence to coverture and hypergraphs then you can finally sort of the the big final answer is you derive the full version of Einstein's equations for space time and matter um and that's um so is that have you that last piece with curvature have is that have you arrived there yet oh yeah we're we're there yes and and here's the here's the way that we here's how we're really really going to know we've arrived okay so you know we have the mathematical derivation it's all fine but but you know mathematical derivations okay so one thing that's sort of a a uh you know we're taking this limit of what happens when you the limit you have to look at things which are large compared to the size of an elementary length small compared to the whole size of the universe large compared to certain kinds of fluctuations blah blah blah there's a there's a there's a tower of many many of these mathematical limits that have to be taken so if you're a pure mathematician saying where's the precise proof it's like well there are all these limits we can you know we can try each one of them computationally and we can say yeah it really works but the formal mathematics is really hard to do I mean for example in the case of deriving the equations of fluid dynamics from molecular dynamics that derivation has never been done MH there is no rigorous version of that derivation so so because you can't do the limits yeah because you can't do the limits um but so the limits allow you to try to describe something general about the system and very very particular the kinds of limits that you need to take with these very right and and the limits will definitely work the way we think they work and we can do all kinds of computer exp hard deration yeah it's just it's just the mathematical structure kind of in you know ends up running right into computational reducibility and you end up with a bunch of a bunch of difficulty there but here's the way that we're getting really confident that we know completely what we're talking about which is when people study things like black hole mergers using Einstein's equations what do they actually do well they actually use Mathematica a whole bunch to analyze the equations and so on but in the end they do numerical relativity which means they take these nice mathematical equations and they break them down so that they can run them on a computer and they break them down into something which is actually a discrete approximation to these equations then they run them on a computer they get results then you look at the gravitational waves and you see if they match okay turns out that our model gives you a direct way to do numerical relativity so in other words instead of saying you start from these Continuum equations from Einstein you break them down into these discrete things you run them on a computer you say we're doing it the other way around we're starting from these discrete things that come from our model and we're just running big versions of them on the computer and uh you know what we're saying is and this is this is how things will work so what I'm the way I'm calling this is is proof by compilation so to speak Pro by that is in other words you're you're taking um something where you know we've got this description of a black hole system and what we're doing is we're we're showing that the you know what we get by just running our model agrees with what you would get by doing the computation from the Einstein equations as a small tangent or actually a very big tangent but uh proof by compilation is a beautiful Concept in a sense the way of doing physics with this model is by running it or compiling it and some level yes it have you thought about and these things can be very large is there totally new possibilities of computing hardware and Computing software which allows you to perform this kind of compilation well algorithms software Hardware so so first comment is these models seem to give one a lot of inition about distributed computing a lot of different intuition about how to think about parallel computation and that particularly comes from the quantum mechanic side of things which we didn't talk about much yet but uh the question of what you know given our current computer hardware how can we most efficiently simulate things yeah that's actually partly a story of the model itself because the model itself has deep parallelism in it yes the ways that we're simulating it we're just starting to be able to use that deep parallelism to be able to be more efficient in the way that we simulate things but in fact the structure of the model itself allows us to think about parallel computation in different ways and one of my realizations is that you know so it's very hard to get in your brain how you deal with parallel computation and you're always worrying about you know if multiple things can happen at different on different computers at different times oh what happens if this thing happens before that thing and we've really got you know we have these race conditions where something can race to get to the answer for another thing and you get all tangled up because you don't know which thing is going to come in first and usually when you do parallel Computing there's a big Obsession to lock things down to the point where you've you've had locks and mutexes and God knows what else where where you've you've um you've arranged it so that there can only be one sequence of things that can happen so you don't have to think about all the different kinds of things that can happen well in these models physics is throwing us into forcing us to think about all these possible things that can happen but these models together with what we know from physics is giving us new ways to think about all possible things happening about all these different things happening in parallel and so I'm I'm guessing they have buil-in protection for some of the parallelism well causal invariance is the built-in protection causal invariance is what means that even though things happen in different orders it doesn't matter in the end as a as a as a person who struggle with concurrent programming in in like Java uh with all all the basic concepts of uh concurrent programming that that if there could be built up a strong mathematical framework for causal invariance that's so liberating and that that could be not just liberating but really powerful for massively distributed computation absolutely no I mean you know what's eventual consistency in in distributed databases is essentially the causal invariance idea yeah okay so that's but but but have you thought about uh you know we're like really large simulations yeah I mean I'm also thinking about look the fact is you know I've spent much of my life as a language designer right so I can't possibly not think about you know what does this mean for Designing languages for parallel computation in fact another thing that's one of these you know I I'm always embarrassed at how long it's taking me to figure stuff out but you know back in the 1980s I worked on trying to make up languages for parallel computation I thought about doing graph rewriting I thought about doing these kinds of things but I couldn't see how to actually make the connections to actually do something useful I think now physics is kind of showing us how to make those things useful and so my guess is that in time we'll be talking about you know we do parallel programming we'll be talking about programming in a certain reference frame just as we think about thinking about physics in a certain reference frame it's a certain coordination of what's going on we say we're going to program in this reference frame oh let's change the reference frame to this reference frame and then our program will seem different and we'll have a different way to think about it but it's still the same program underneath so let me ask on this topic because I put out that I'm talking to you I got way more questions that I can deal with but what Pops to mind is a question somebody asked on Reddit I think is uh please ask uh Dr wlr uh what are the specs of the computer running the universe so we we're talking about specs of hardware and software simulations of a large scale thing what about a scale that is comparative to something that eventually leads to the two of us talking and about right right right so so actually I I did try to estimate that and we have to go a couple more stages before we can really get to that answer because because we're we're talking about um this this thing um you know this is what happens when you when you build these abstract systems and you're trying to explain the universe there quite a number of levels deep so to speak um but uh the um you mean conceptually or like literally cuz you're talking about small object and there's 10 to the something number right it's it's it it is conceptually deep and one of the things that's happening sort of structurally in this project is you know there were ideas there's another layer of ideas there's another layer of ideas to get to the different things that correspond to physics they're just different layers of ideas and they are um you know it's actually probably if anything getting harder to explain this project because I'm realizing that the fraction of way through that I am so far and explaining this to you is less than than you know it might be because because we know more now you know in the every every week basically we know a little bit more and like those are just layers on the initial fundamental yes structure the layers are you know you you might be asking me you know how do we get uh you know the difference between Fons and bosons the difference between particles that can be all in the same state and particles that exclude each other okay last 3 days we've kind of figured that out okay but um and it's very interesting it's very cool um and it's very uh and those are some kind of properties at a certain level layer of abstraction on the hypog graph yes and there's a and there's but the layers of abstraction are kind of there compounding stacking up so it's difficult but but okay but this but the specs nevertheless remain the same the the specs underneath so I I have an estimate so the question is what are the units so we've got these different fundamental constants about the world so one of them is the speed of light which is the so the thing that's always the same in all these different ways of thinking about the universe is the notion of time because time is computation and so there's an elementary time which is sort of the the the amount of time that we ascribe to elapsing in a in a single computational step yeah okay so that's the elementary time so then there's an El parameter or whatever that it's a constant it's whatever we Define it to be because I mean we we don't you know it's all relative right it doesn't matter it doesn't matter what it is because we could be it could be slow it's just a number which which we use to convert that to Second so to speak because we are experiencing things and we say this amount of time has elapsed so to speak but we're within this thing so AB it doesn't it doesn't matter right but what does matter is the ratio what we can uh the ratio of the spatial distance and this hypergraph to this uh to this moment of time again that's an arbitrary thing but we measure that in me/ second for example and that ratio is the speed of light so the ratio of the elementary distance to the elementary time is the speed of light okay perfect and so there's another there are two other levels of this okay so there is a thing which we can talk about uh which is the maximum entanglement speed which is a thing that happens at another level in this whole sort of story of how these things get constructed um that's a sort of maximum speed in Quantum in the space of quantum States just as the speed of light is a maximum speed in physical space this is a maximum speed in the space of quantum States there's another level which is associated with what we call Ral space which is a another one of these maximum speeds we get to this so these are limitations on the system that are able to capture the kind of physical Universe which we live in the quantum mechanic they are inevitable features of having a a rule that has only a finite amount of information in the rule so long as you have a rule that only involves a a a bounded amount a limited amount of only involving a limited number of elements limited number of relations it is inevitable there are these speed constraints we knew about the one for speed of light we didn't know about the one for maximum entanglement speed which is actually something that is possibly measurable particularly in black hole systems and things like this anyway this is long long story short you're asking what the processing specs of the universe of the of the sort of computation of the universe there's a question of even what are the units of some of these measurements okay so the units I'm using are wol from language instructions per second okay because you got to have some you know what the quad computation are you do it there got to be some kind of frame of reference right right so and because it turns out in the end there will be there's sort of an arbitrariness in the language that you use to describe the universe so in those terms I think it's like 10 the 500 or from language operations per second I think is the um I think it's of that order you know B that's scale of computation what about memory if there's an interesting thing to say about storage and memory well there a question of how many sort of atoms of space might there be you know maybe 10 to 400 we don't know exactly how to estimate these numbers I mean this is this is based on some some I would say somewhat rickety way of estimating things uh you know when there start to be able to be experiments done if lucky there will be experiments that can actually nail down some of these numbers and uh because of computation reducibility there's no much hope for very efficient compression like very uh efficient representation to this good question I mean there's probably certain things you know the fact that we can deduce any okay the question is how deep does the reducibility go right okay and I keep on being surprised that it's a lot deeper than I thought okay and so um one of the the things is that that there's a question of sort of how much of the whole of physics do we have to be able to get in order to explain certain kinds of phenomena like for example if we want to study Quantum interference do we have to know what an electron is turns out I thought we did turns out we don't I thought to know what energy is we would have to know what electrons were we don't you get a lot of really powerful shortcuts right there's a there's a bunch of sort of bulk information about the world the the thing that I EX Ed about last few days okay is um uh the idea of fion versus boson fundamental idea that I mean it's the the reason we have matter that doesn't just self-destruct is because of the exclusion principle that means that two electrons can never be in the same Quantum state is it uh useful for us to maybe first talk about how quantum mechanics let's talk about quantum mechanics the wol from physics model yes let's go there so we talked about general relativity now what uh what have you found uh the story of quantum mechanics right within and outside of the wol from physics right so I mean the the the key idea of quantum mechanics that sort of the the the typical interpretation is classical physics says a definite thing happens quantum physics says there's this whole set of Paths of things that might happen and we are just observing some overall probability of of how those paths work okay so when you think about our hypergraphs and all these little updates that are going on there's a very remarkable thing to realize which is if you say well which particular sequence of updates should you do say well it's not really defined you can do any of a whole collection of possible sequences of updates okay that set of possible sequences of updates defines yet another kind of graph that we call a multi-way graph and a multi-way graph just is a graph where at every node there is a choice of several different possible things that could happen so for example you go this way go that way those are two different edges in the multi-way graph and you're building up the set of possibilities so actually like for example I just made the one the multi-way graph for Tic Tac Toe okay so Tic Tac Toe you start off with some some board that you know is everything is blank and then somebody can put down a an X somewhere an O somewhere and then there are different possibilities at each stage there are different possibilities and so you build up this multi-way graph of all those possibilities now notice that even in Te tactoe you have the feature that there can be something where you have two different things that happen and then those branches merge because you end up with the same shape of you know the same configuration of the board even though you got there in two different ways so what the the thing that's sort of an inevitable feature of our models is that just like quantum mechanics suggests definite things don't happen instead you get this whole multi way graph of all these possibilities okay so then the question is so that okay so that's sort of a a picture of what's going on now you say okay well quantum mechanics has all these features of uh you know all this mathematical structure and so on how do you get that mathematical structure okay couple of couple of things to say so quantum mechanics is actually in a sense two different theories glued together quantum mechanics is a theory of how Quantum amplitudes work that more or less give you the probabilities of things happening and it's the theory of quantum measurement which is the theory of how we actually conclude definite things because the mathematics just gives you these Quantum amplitudes which are more or less probabilities of things happening but yet we actually observe definite things in the world um Quantum measurement has always been a bit mysterious it's always been something where people just say well the mathematics says this but then you do a measurement and they're philosophical arguments about what the measurement is but it's not something where there's a theory of the measurement some on Reddit also asked uh please ask Stephen to tell his story of this the double slit experiment okay yeah I can does that does that make sense oh yeah makes sense absolutely makes sense why is this like a good way to discuss uh a little bit let me let me go let me explain a couple of things first so so the structure of quantum mechanics is is mathematically quite complicated um one of the features let's see well how to how to describe this okay so first point is there's this multi-way graph of all these different Paths of of things that can happen in the world and the important point is that that uh these you can have branchings and you can have mergings Okay so this property turns out causal invariance is the statement that the number of mergings is equal to the number of branchings yeah so in other words every time there's a branch eventually there will also be a merge in other words every time there were two possibilities of what might have happened eventually those will merge beautiful concept by the way yeah yeah yeah so so that so that idea okay so then uh so that's that's one thing and that's closely related to the the sort of objectivity in quantum mechanics the fact that we believe definite things happen it's because although there are all these different paths in some sense because of causal invariance they all imply the same thing that's I'm I'm cheating a little bit in saying that but that's roughly the essence of what's going on okay next next thing to think about is uh you have this multi-way graph it has all these different possible things that are happening now we ask this multi-way graph is sort of evolving with time o over time it's branching it's merging it's doing all these things okay um the question we can ask is if we slice it a at a particular time what do we see and that slice represents in a sense something to do with the state state of the universe at a particular time so in other words we've got this multi-way graph of all these possibilities and then we're asking an an okay we take this slice this slice represents aent okay each of these different paths corresponds to a different Quantum possibility for what's happening right when we take this slice we're saying what are the set of quantum possibilities that exist at a particular time and when you say slice are these you slice the graph and then there's a bunch of leaves a bunch of and those represent the state of things right but but then okay so the important thing that you are quickly picking up on is that um what what matters is kind of how these leaves are related to each other so a good way to tell how leaves are related is just to say on the step before did they have a common ancestor so two leaves might be they might have just branched from one thing or they might be far away you know way far apart in this graph where to get to a common ancestor maybe you have to go all the way back to the beginning of the graph all the way back to the beginning so there's some kind of measure of distance right and and that but the what you get is by making the slice what we call it branchial space the space of branches um and in this branchial space um you have a graph that represents the relationships between these Quantum States in branchial space you have this notion of distance in branchial space okay so it's connected to Quant entanglement yes yes it's it's it's basically the the distance in branchial space is kind of an entanglement distance so this that's a very nice model right it is very nice it's very beautiful it's it's I mean it's it's so clean I mean it's it's really you know and it it it tells one okay so anyway so then then this this branchial space uh has this sort of map of the the entanglements between Quantum States so in physical space we have so so you know you can say take let's say the causal graph and we can slice that um at a particular time and then we get this map of how things are laid out in physical space when we do the same kind of thing there's a thing called the multi-way causal graph which is the analog of a causal graph for the multi-way system we slice that we get essentially the relationships between things not in physical space but in the space of quantum States it's like which Quantum state is similar to which other Quantum State okay so now I think next thing to say is just to mention how Quantum measurement works so Quantum measurement has to do with reference frames in bronchial space so okay so measurement in in physical space it matters whether how we assign spatial position and how we how we Define coordinates in space and time and that's that's how we make measurements in ordinary space are we making a measurement based on us sitting still here are we traveling at half the speed of light light in making measurements that way these are different reference frames in which we're making our measurements and the relationship between different events and different points in space and time uh will be different depending on what reference frame we're in okay so then we have this idea of quantum observation frames which are the analog of reference frames but in branchial space and so what happens is what we realize is that a Quantum measurement is the The Observer is sort of arbitrarily determining this reference frame The Observer is saying I'm going to understand the World by saying that space and time are coordinati this way I'm going to understand the World by saying that Quantum States and time are coordinatization frames so in a sense the obser the way the Observer enters is by their choice of these Quantum observation frames and what happens is that the Observer um because okay this is again another stack of other Concepts but anyway because the Observer is computationally bounded there is a limit to the type of quantum observation frames that they can construct interesting okay so there's okay so some constraints some limit on and that's on the choice of observation frames right and by the way I just want to mentioned that there's a I mean it's it's bizarre but there's a hierarchy of these things so in in um uh in thermodynamics the the fact that we believe entropy increases we believe things get more disordered is a consequence of the fact that we can't track each individual molecule if we could track every single molecule we could run every movie in Reverse so to speak and we would you know we would not see that things are getting more disordered but it's because we are computationally bounded we can only look at these big blobs of what all these molecules collectively do that we think that things are that we describe it in terms of of entropy increasing and so on and it's the same phenomenon basically also the consequence of computational irreducibility that causes us to basically be forced to conclude that definite things happen in the world even though there's this Quantum you know this set of all these different Quantum processes that are going on so I I mean I'm I'm I'm I'm skipping a little bit and the the but that that's a that's a a rough picture and in the evolution of the wol from physics project where do you feel we stand on the some of the puzzles that are along the way see you're skipping along a bunch of it's amazing how much these things are unraveling I mean you know these things look it used to be the case that I would agree with dick fan nobody understands quantum mechanics including me okay I'm getting to the point where I think I actually understand quantum mechanics my my exercise okay is can I explain Quantum Mechanics for real at the level of kind of Middle School type explanation right and I'm getting closer it's getting it's getting there I'm not quite there I've tried it a few times and I realize that there are things that um uh where I have to start talking about elaborate mathematical Concepts and so on but I think and and you know you got to realize it's not self-evident that we can explain you know at an intuitively graspable level something which uh you know about the way the universe works the universe wasn't built for our understanding so to speak um but but I think then then um uh okay so another important important idea is um uh this idea of branchial space which I mentioned this sort of space of quantum states it is okay so I mentioned Einstein's equations describing you know the effect of uh the effect of mass and energy on uh trajectories of particles on gd6 the curvature of of um of physical space is associated with uh the presence of energy according to Einstein's equations Okay so turns out that rather amazingly the same thing is true in branchial space so it turns out the presence of energy or more accurately lran density which is a kind of relativistic invariant version of energy um the presence of that causes essentially deflection of jd6 in this branchial space okay so you might say so what Well turns out that the sort of the best formulation we have of quantum mechanics this the fine path integral is a thing that describes Quantum processes in terms of mathematics that can be interpreted as well in quantum mechanics the the big thing is you get these Quantum amplitudes which are complex numbers that represent when you combine them together represent probabilities of things happening and so the big story has been how do you derive these Quantum amplitudes and people think these Quantum amplitudes they have a complex number has you know real part and imaginary part you can also think of it has a magnitude and a phase um and it um people have sort of thought these Quantum amplitudes have magnitude and phase and you compute those together turns out that magnitude the magnitude and the phase come from completely different places the magnitude comes okay so what do you how do you compute things in quantum mechanics roughly I'm I'm telling you I'm I'm getting there to be able to do this at a middle school level but I'm not there yet um the the roughly what happens is you're asking does this state in quantum mechanics evolve to this other state in quantum mechanics and you can think about that like a particle traveling or something traveling through physical space but instead it's traveling through branchial space MH and so what's happening is does this Quantum State evolve to this other Quantum State it's like saying does this object move from this place in space to this other place in space okay now the way that you these quantum amplitudes udes characterize kind of um to what extent the thing will successfully reach some particular point in branchial space just like in physical space you could say oh it had a certain velocity and it went in this direction in branchial space there's a similar kind of concept is there a nice way to visualize for me now mentally Branch space it's just you have this hypergraph sorry you have this multi-way graph it's this big branching thing branching and merging thing but I mean like moving through that space I I'm just trying to understand what that looks like is you know that space is probably exponential dimensional which makes it again another can of worms in understanding what's going on that space as in in ordinary space this hypergraph the spatial hypergraph limits to something which is like a manifold like a like something like threedimensional space almost certainly the multi-way graph limits to a hbert space which is something that I mean it's it's just a weirder exponential dimensional space and by the way you can ask I mean there are much weirder things that go on for example one of the things I've been interested in is the expansion of the universe in branchial space so we know the universe is expanding in physical space but the universe is probably also expanding in BR space so that means the the number of quantum states of the universe is increasing with time the diameter of the thing is growing right so that means that the and and by the way uh this is related to whether Quantum Computing can ever work um and uh uh why okay so let me explain why so so let's talk about okay so first of all just just to finish the thought about Quantum amplitudes the the incredibly beautiful thing just this is just I'm just very excited about this the the um the F path integral is is this formula it says that the amplitude the quantum amplitude is e to the i s overh bar where s is the thing called the action and um it uh okay so that can be thought of as representing a deflection of the angle of this path in the multi-way graph so it's a deflection of a jisc in the multi-way path that is caused by this thing called the action which is essentially associated with energy okay and so this is a deflection of a path in branchial space that is described by this path integral which is the thing that is the mathematical essence of quantum mechanics m turns out that deflection is the deflection of gd6 and branchial space follows the exact same mathematical setup as the deflection of gd6 in physical space except the deflection of gd6 in physical space is described with Einstein's equations the deflection of gd6 and branchial space is defined by the F and path integral and they are the same in other words they are mathematically the same so that means that general relativity is a story of essentially Motion in physical space uh quantum mechanics is a story of essentially Motion in bronchial space and the underlying equation for those two things although it's presented differently because one's interested in different things in branchial space and physical space but the underlying equation is the same so in other words it's the this it's just you know these two theories which are the two sort of pillars of 20th century physics which have seemed to be off in different directions are actually facets of the exact same Theory there and this I mean that's exciting to see to see where that evolves and exciting that that just is there right I mean to me you know look I having spent some part of my early life you know working in these in the context of these theories of of you know 20th century physics it's they just they seem so different and the fact that they're really the same is just really amazing actually let me you you mentioned double slit experiment okay so the double experiment is a is an interference phenomenon where you say there are you know you can have a photon or an electron and you say there are these two slits it could have gone through either one but there is this interference pattern where it's there's destructive interference where you might have said in classical physics oh well if if there are two slits then there's a better chance that it gets through one or the other of them but in quantum mechanics there's this phenomenon of destructive interference that means that even though there are two slits two can lead to nothing as opposed to two leading to more than than for example one slit and in what happens in this model and we've just been understanding this in the last few weeks actually is that the um what essentially happens is that the the double slit experiment is a story of the interface between branchial space and physical space and what's essentially happening is that the destructive interference is the result of the two possible paths associated with photons going through those two slits winding up at opposite ends of branchial space and so they don't and so that's why there's sort of nothing there when you look at it is because these two different sort of branches couldn't get merged together to produce something that you can measure in physical space is there a lot to be understood about brancho space like is mathematically speaking yes it's a very beautiful mathematical thing and it's very I mean by the way this whole is just amazingly rich in terms of the mathematics that it says should exist okay so for example calculus you know is a story of infinite decimal change in integer dimensional space onedimensional two- dimensional threedimensional space we need a theory of infinitesimal change in fractional dimensional and dynamic dimensional space No Such Theory exists so there's a tools of mathematics that are needed here right and this is a motivation for that actually right and it's it's you know there are there are indications and we can do computer experiments and we can see how it's going to come out but we need to you know that the actual mathematics is doesn't doesn't exist and in branchial space it's actually even worse there's there's even more sort of layers of mathematics that are you know we can see how it works roughly by doing computer experiments but to really understand it we need more more sort of mathematical sophistication so quantum computers okay so the basic idea of quantum computers the the promise of quantum computers is quantum mechanics does things in parallel and so you can sort of intrinsically do computations in parallel and somehow that can be much more efficient than just doing them uh one after another and you know I actually worked on Quantum Computing a bit with dick fan back in 1981 2 3 um that kind of time frame and and we a fascinating image you you and findan work on quantum computers well we we tried to work the the big thing we tried to do was invent a Randomness chip that would generate Randomness at a high speed using quantum mechanics and the discovery that that wasn't really possible uh was part of the um the story of we never really wrote anything about it I think maybe he wrote some stuff but I we didn't we didn't write stuff about what we figured out about sort of the fact that it really seemed like the measurement process in quantum mechanics was a serious damper on what was possible to do in sort of you know the possible advantages of quantum mechanics mecs and for computing but anyway so so the the the sort of the promise of quantum Computing is let's say you're trying to you know Factor an integer well you can instead of you know when you factor an integer you might say well does this Factor work does this Factor work does this Factor work um in ordinary Computing it seems like we pretty much just have to try all these different factors um you know kind of one after another but in quantum mechanics you might have the idea oh you can just sort of have the physics try all of them in parallel mhm okay and um the you know and there's this algorithm shaes algorithm which which uh allows you according to the formalism of quantum mechanics to do everything in parallel and to do it much faster than you can on a classical computer okay the only little footnote is you have to figure out what the answer is you have to measure the result so the quantum mechanics internally has figured out all these different branches but then you have to pull all these branches together to say and the classical answer is this okay the standard theory of quantum mechanics does not tell you how to do that it tells you how the branching works but it doesn't tell you the process of corralling all these things together and that process which intuitively you can see is going to be kind of tricky but our model actually does tell you how that process of pulling things together works and the answer seems to be we're not absolutely sure we've only got to two * three so far in in uh you know which is kind of in in in this um in this factorization in quantum computers but we can um uh the you know what seems to be the case is that the advantage you get from the parallelization from quantum mechanics is lost from the amount that you have to spend pulling together all those parallel threads to get to a classical answer at the end now that phenomenon is not unrelated to various decoherence phenomena that are seen in Practical quantum computers and so on I mean I should say as a as a very practical point I mean it's like should people stop ing to do Quantum Computing research no because what they're really doing is they're trying to use physics to get to a new level of what's possible in Computing and that's a completely valid activity whether whether you can really put you know whether you can say oh you can solve an MP complete problem you can reduce exponential time to polinomial time you know we're not sure and and I'm suspecting the answer is no but that's not relevant to the Practical speedups you can get by using different kinds of Technologies different kinds of physics um to do basic Computing so you're saying I mean some of the models you're playing with the indication is that uh to uh get all the Sheep back together uh and you know to to Coral everything together to get the actual solution to the algorithm is uh you lose all the you lose use all by the way I mean so so again this question do we actually know what we're talking about about Quantum Computing and so on so again again uh we're doing proof by compilation so we have a Quantum Computing framework yeah in wolam language and which is you know a standard Quantum Computing framework that represents things in terms of the standard uh you know formalism of quantum mechanics and we have a compiler that simply compiles the representation of quantum Gates into multi-way systems so and in fact the the message that I got was from somebody who's working on the project who has managed to compile one the sort of uh a core formalism based on category Theory um in of core Quantum formalism into multi-way systems so this when you say multi-way system these multi-way graphs yes yes so you're comp yeah okay that's awesome and then you can do all kinds of experiments on that multiway graph right well but the point is that what we're saying is the thing we've got this representation of let's say Shaw's algorithm in terms of standard Quantum Gates and it's just a pure matter of sort of computation to just say that is a equivalent we will get the same result as running this multi-way system can you do complexity analysis on that multi-way system well that's what we've been trying to do yes we're getting there we haven't done that yet I mean we we there's a pretty good indication of how that's going to work out and we've done it as I say our computer experiments we've unimpressively gotten to about 2 * three in terms of factorization which is kind of about how far people have got with physical quantum computers as well but but that's um but yes we will be able to we definitely will be able to do complexity analysis and we will be able to know so the one remaining hope for Quantum Computing really really working at this formal level of you know Quantum brand exponential stuff being done in polinomial time and so on the one hope which is very bizarre is that you can uh kind of uh piggyback on the expansion of bronchial space so here's here's how that might work so you think you know energy conservation standard thing in high school physics energy is conserved right but now you imagine you think about energy in the context of cosmology and the context of the whole universe it's a much more complicated story The expansion of the universe kind of violates energy conservation and so for example if you imagine you've got two galaxies they're receding from each other very quickly they've got two big Central black holes you connect a spring between these two Central black holes not easy to do in practice but let's imagine you could do it now that spring is being pulled apart it's getting getting more potential energy in the spring as a result of the expansion of the universe so in a sense you are you are piggybacking on the expansion that exists in the universe and the sort of violation of energy conservation that's associated with that cosmological expansion to essentially get energy you're essentially building a perpetual motion machine by using the expansion of the universe and that is a physical version of that it is conceivable that the same thing can be done in branchial space to essentially uh mine the expansion of the universe in Branch Hill space as a way to get uh sort of uh Quantum Computing for free so to speak just from the expansion of the universe in branchial space now the physical space version is kind of absurd and involves you know Springs between black holes and so on it's conceivable that the branchial space version is not as absurd and that it's actually something you can reach with physical things you can build in lab and so on we don't know yet okay so yeah like you were saying the branch of space might be uh expanding and there might be some something that could be exploited right in the same kind of way that that um that you can exploit the um uh you know that expansion of the universe in principle in physical space you just have like a glimmer of hope right I think that the look I think the real answer is going to be that for practical purposes you know the official brand that says you can you can you know do exponential things in po time is probably not going to work for people curious to kind of learn more so this is more like this is not Middle School we're going to go to elementary school for a second maybe Middle School let's go to middle school so if I were to try to maybe write a write a pamphlet of like wolf from physics project for dummies AKA for me or maybe make a video on the basics but not just the basics of the physics project but the basics plus the most beautiful Central ideas um how would you go about doing that could you help me out a little bit yeah yeah I mean we covered a l really practical matter we have this kind of visual summary picture that we made um which I think is a pretty good you know when I've tried to explain this to people and you know it's a pretty good place to start is you got this rule you know you apply the rule you're building up this this big hypergraph um you've got all these possibilities you're kind of thinking about that in terms of quantum mechanics I mean that's a that's a that's a decent place to start so basically the things we've talked about which is space represented as a hypergraph transformation of that space is kind of time yes and then uh structure of that space in the curvature of that space as gravity that's that can be explain without going anywhere near quantum mechanics um I would say that's actually easier to explain than special robots of day um oh so going into General so going to curvature yeah I mean special relativity I I think is it's a little bit elaborate to explain yeah and honestly you only care about it if you know about special relativity if you know how special relativity is ordinarily derived and so on general relativity is easier is easier yes and what about what's the easiest way to reveal uh I think the the basic point is just this fact that there are all these different branches that there's this kind of map of how the branches work and that um I mean I think I think actually the recent things that we have about the double experiment are pretty good because you can actually see this you can see how the double slit you know phenomenon arises from just features of these graphs now you know having said that right there is a little bit of of slight of hand there because the the true story of the way that double slit thing works depends on a coordinatization of branchial space that for example in our internal team there is still a vigorous battle going on about how that works and it's it's what's becoming clear is I mean what's becoming clear is that it's mathematically really quite interesting I mean that is that there's a you know it involves essentially putting space fill in curves you basically have a thing which is naturally two-dimensional and you're sort of mapping it into one dimension and with a space filling curve and it's like why is it this space filling curve and not another space filling curve and that becomes a story about reman surfaces and things and it's quite elaborate and um but but the there's a a more little bit slight of hand way of doing it where it's you know it's surprisingly direct it's so a question that might be difficult to answer but uh for several levels of people could you give me advice on how we can learn more specifically there is people that are completely outside and just curious and are captivated by the beauty of hypergraphs actually uhhuh so people there just want to explore play around with this uh second level is people from say people like me who somehow got a PhD and computer science but are not physicists and but fundamentally the work you're doing is computational nature so it feels very accessible yes so what are what can a person like that do to learn enough physics or not to be able to uh one explore the beauty of it and two the the final level of contribute something right of a level of even publishable you know like strong interesting ideas at all those layers complete beginner yeah I see person and the Cs person that wants to publish right I mean I think that you know I've written a bunch of stuff uh bu called Jonathan gorod who's been a key person working on this project has also written a bunch of stuff um and some other people have started writing things too and he's a physicist physicist well he's I would say a mathematical physicist he pretty mathematically sophisticated he's he regularly out mathematized me yeah strong yeah strong mathematical physicist yeah I looked at some of the papers right but but so so I mean you know I wrote this kind of original announcement blog post about this project which people seem to have found uh I've been really happy actually that people um who uh you know people seem to have gred key points from that much deeper key points people seem to have gred than I thought they would grock um and that that's a kind of a Long blog post that explains some of the things we talked about like the hypergraph and the basic rules and uh I don't does it I forget doesn't have any quantum mechanics goes through quantum mechanics yes it does but we we know a little bit more since that blog post that probably clarifies but that blog post is does a pretty decent job um and you know talking about things like again something you didn't mention the fact that the uncertainty principle as a consequence of curvature in bronal space how much physics should a person know to be able to understand the beauty of this framework and to contribute something novel okay so I I think that those are different questions so I mean I think that the why does this work why does this make any sense um uh to really know that you have to know a fair amount of physics okay um and for example have a why does this work you're you're referring to the connection between this model and general relativity for example you have to understand something about General of there there's also a side of this where just as the pure mathematical framework is fascinating yeah yes if you throw the physics out then it's quite accessible to I mean you know I I wrote this sort of long technical introduction to the project which seems to have been very accessible to people who are you know who understand computation and and formal abstract ideas but are not specialists in physics or or other kinds of things I mean the thing with the physics part of it is you know it's there's both a way of thinking and a literally a mathematical formalism I mean it's like you know to know that we get the Einstein equations to know we get the ener of momentum tensor you kind of have to know what the energ of momentum tensor is and that's physics I mean that's kind of graduate level physics basically um and uh so so that you know making that final connection is requires some depth of physics knowledge I mean that's the unfortunate thing the difference between machine learning in physics in the 21st century is it uh really Out Of Reach of a year or two worth of study no you could get it in a year or two but you can't get it in a in a month right I mean so but it doesn't require necessarily like 15 years no it does not and and in fact a lot of what has happened with this project makes a lot of this stuff much more accessible there are things where it has been quite difficult to explain what's going on and it it requires much more you know having the concreteness of being able to do simulations knowing knowing that this thing that you might have thought was just an analogy is really actually what's going going on makes one feel much more secure about just sort of saying this is how this works um and I think it will be you know the I'm hoping the textbooks of the future the physics textbooks of the future there will be a certain compression there will be things that used to be very much more elaborate because for example even doing continuous mathematics versus this discret mathematics you know to know how things work in continuous mathematics you have to be talking about stuff and waving your hands about things whereas with discreet the discreet version it's just like here is a picture this is how it works and there's no oh did we get the limit right did this you know did this thing that is of you know uh zero you know measure zero object you know interact with this thing in the right way you don't have to have that whole discussion it's just like here's a picture you know this is what it does and you know you can then it takes more effort to say what does it do in the limit when the picture gets very big but you can do experiments to build up an intuition actually yes right and you can get sort of core intuition for what's going on now in terms of contributing to this the you know I would say that the study of the computational universe and how all these programs work in the computational universe there's just an unbelievable amount to do there and it is very close to the surface that is you know high school kids you can do experiments it's not um you know and you can discover things I mean you know we you can discover stuff about I don't know like this thing about expansion of bronal space that's an absolutely accessible thing to look at now now you know the main issue with doing these things is not there isn't a lot of technical depth difficulty there the actual doing of the experiments you know all the code is all on our website to do all these things the real thing is sort of the Judgment of what's the right experiment to do how do you interpret what you see that's the part that you know people will do amazing things with and that's the part that but but it isn't like you have to have done 10 years of of study to get to the point where you can do the experiments you D the cool thing you can do experiments day one basically it's that that that's the amazing thing about and you've actually put the tools out there it's beautiful it's mysterious uh there's still I would say maybe you can correct me it feels like there's a huge number of L hanging fruit oh on the mathematical side at least not the not the physics side perhaps no no there's look on the on the okay on the physics side we are we're definitely in harvesting mode you know of which which fruit the low hanging ones or the low hanging ones yeah right I mean basically here's the thing there's a certain list of you know here are the effects in quantum mechanics here are the effects in general activity it's just like industrial harvesting it's like can we get this one this one this one this one this one and and the thing that's really you know interesting and satisfying and it's like you know is one climbing the right Mountain does one have the right model the thing that's just amazing is you know we keep on like are we going to get this one one how hard is this one it's like oh you know it looks really hard it looks really hard oh actually we can get it um and uh and you're you're continually surprised I mean it seems like I've been following your progress It's kind of exciting all the in harvesting mode all the things you're picking up along the way right right no I mean it's it's the thing that is I keep on thinking it's going to be more difficult than it is now that's a you know that's a who knows what um I mean the one thing so the the the um the thing that's been was big thing that I think we're we're pretty close to I mean I can give you a little bit of the road map it's sort of interesting to see is like what are particles what are things like electrons how do they really work um are you close to get like what what's uh are you close to trying to understand like the atom the electrons neutrons protons this is this is the stack so the first thing we want to understand is uh the quantization of spin so particles they they kind of spin they have a certain Ang angular momentum that angular momentum even though the masses of particles are all over the place you know the electron has a mass of 511 M the but you know the proton is 938 M etc etc etc they're all kind of random numbers the the spins of all these particles are either integers or half integers and that's a fact that was discovered in the 1920s I guess um the U uh I think that we are close to understanding why spin is quantized um and that's a and it it appears to be a quite elaborate mathematical story about homotopic groups in twist space and all kinds of things but bottom line is that seems Within Reach and that's that's a big deal because that's a very core feature of understanding how particles work in quantum mechanics another core feature is this difference between particles that obey the Exclusion Principle and sort of stay apart that leads to the stability of matter and things like that and particles that love to get together and be in the same state things like photons that um and that's what leads to phenomena like lasers um where you can get sort of coherently everything in the same state that difference is the particles of integer spin or bons like to get together in the same state the particles of half integer spin of ferons like electrons that they tend to stay apart and um so the question is can we can we get that in our models and uh oh just the last few days I think we made um I mean I think the story of um I mean it's it's it's one of these things where we're really close it's is this connect to fans and bans you you talking so this was what happens is what seems to happen okay it's you know subject to revision next even next few days but what seems to be the case is that uh bons are associated with essentially merging in multi-way graphs and firion are associated with branching in multi-way graphs and that essentially the Exclusion Principle is the fact that in branchial space things have a certain extent in branchial space that in which things are being sort of forced apart in branchial space whereas the case of bans they get they they Clump together in branchial space and the real question is can we explain the relationship between that and these things called Spinners which are the representation of half integer spin particles that have this weird feature that usually when you go around 360° rotation you get back to where you started from but for a spinner you don't get back to where you started from it takes 720 of rotation to get back to where you started from and we are just it feels like we are we're just incredibly close to actually having that understanding how that works and it turns out it looks like my current speculation is that it's as simple as the uh directed hypergraphs versus undirected hypergraphs interesting uh the relationship between Spinners and vectors so which is just nice interesting yeah that would be interesting if these are all these kind of uh nice properties of this multiway graphs of of branching andjoin Spinners have been very mysterious and if that's what they turn out to be there's going to be an easy explanation directed vers undirected it's just and that's why there's only two different cases it's why are Spinners important in quantum mechanics can you just give a yeah so Spinners are important because they are um they're the representation of of for electrons which have half anra spin they are the the wave functions of electrons are spin Spinners just like the wave functions of photons are vectors the wave functions of electrons are Spinners and and they have this property that when you rotate by by 360° they come back to minus1 of themselves and take 720° to get back to the original value and and they are a consequence of of um uh in we usually think of of of rotation in space as being you know when you have this notion of rotation invariance and rotational invariance as we ordinarily experience it doesn't have the feature you know if you go through 360° you go back to where you started from but that's not true for electrons and so that's that's why understanding how that works is important yeah I've been playing with Mobius uh strip quite a bit lately just for fun and yes yes it adds some funk it has the same kind of funky properties yes right exactly you can have this the So-Cal belt trick which is this way of taking an extended object and you can see properties like SP with that kind of extended object that um yeah it would be very cool if there's it somehow connects to direcor versus undirected I think that's what it's going to be I think it's going to be as simple as that but we'll see I mean this is this is the thing that that you know this is the big sort of bizarre surprise is that you know because you know I I I learned physics as probably let's say let's say a fifth generation in the sense that you know if you go back to the 1920s and so on there were the people who were originating quantum mechanics and so on maybe it's a little less than that maybe I was like a a a third generation or something I don't know but but you know the people from whom I learned physics were the people who were you know have been students of the students of the the people who originated the the current understanding of physics and we're now at you know probably the seventh generation of physicists or something from the from the early days of 20th century physics and you know whenever a field gets that many generations deep it seems the foundations seem quite inaccessible and they seem you know it seems like you can't possibly understand that we've gone through you know seven academic generations and that's been you know that's been this thing that's been difficult to understand for for that long it just can't be that simple um and well in a sense maybe that Journey takes you to a to a simple explanation that was there all along as the whole right right right I mean you know and the thing for me personally the thing that's been quite interesting is you know I didn't expect this project to work in this way and I you know but I had this sort of weird piece of personal history that I used to be a physicist and I used to do all this stuff and I know you know the the standard Canon of physics I knew it very well and um you know but then I've been working on this kind of computational Paradigm for basically 40 years and uh the fact that you know I'm sort of now coming back to to you know trying to apply that in physics it kind of felt like that Journey was necessary was this uh when did you first try to play play with a hypergraph so I what happen yeah so so what I had was okay so this is again you know one one always feels dumb after the fact it's it's um it's obvious after the fact but but so back in the early 1990s I realized that using graphs as a sort of underlying thing underneath space and time was going to be a useful thing to do I figured out about multi-way systems um I figured out the things about general relativity I figured out by the end of the 1990s but I always felt there was a certain inelegance because I was using these graphs and there were certain constraints on these graphs that seemed like they were they were kind of awkward it was kind of like you can pick it's like you couldn't pick any rule it was like pick any number but the number has to be prime was kind of like you couldn't it was a kind of an awkward special constraint I had these trivalent graphs graphs with just three connections from every node okay so but but I discovered a bunch of stuff with that but I thought it was kind of inelegant and you know the other piece of sort of personal history is obviously I spent my life as a language computational language designer and so the story of computational language design is a story of how do you take all these random ideas in the world and kind of grind them down into something that is computationally as simple as possible and so you know I've been very interested in kind of simple computational Frameworks for representing things and have you know ridiculous amounts of experience in in trying to do that and actually all of those trajectories of your life kind of came together so you make it sound like you could have come up with uh everything you're working on now decades ago but in reality look two things slowed me down I mean one thing that slowed me down was I couldn't figure out how to make it elegant and and that turns out hypergraphs were the key to that and that I figured out but about less than two years ago now um and um the other I mean I I think so that was that was sort of a a key thing well okay so the real embarrassment of this project okay is that the final structure that we have that is the foundation for this project is basically a a kind of an idealized version a formalized version of the exact same structure that I've used to build computational languages for more than 40 years yeah but it took me but I didn't realize that and and you know and there yet may be other so we're focused on physics now but I mean that's what the new kind of science is about same kind of stuff and this in terms of mathematically um the beauty of it so so there could be entire other kind of objects they're useful for like we we're not talking about you know machine learning for example maybe there's other variants of the hypog graph that are very useful for reasoning well we'll see whether the multi-way graph for machine Learning System is interesting okay let's leave it at that that's conversation number three that's that's that's we're not going to go there right now but so one of the things you've mentioned is um the space of all possible rules that we kind of discussed a little bit uh that you know there could be I guess the set of possible rules is infinite right well so here's here's the big sort of one of the conundrums that that I'm kind of trying to deal with is let's say we think we found the rule for the universe and we say here it is you know write it down it's a little tiny thing and then we say gosh that's really weird why did we get that one right and then we're in this whole situation because let's say it's fairly simple how did we come up the winners getting one of the simple possible Universe rules why didn't we get what some incredibly complicated rule why do we get one of the simpler ones and and that's a thing which you know in the history of science you know the whole sort of story of kernus and so on was you know we used to think the Earth was the center of the universe but now we find out it's not and we're actually just and some you know random corner of some random Galaxy out in this big universe there's nothing special about us so if we get you know Universe number 3177 out of all the infinite number of possibilities how do we get something that small and simple right so I was very confused by this and it's like what are we going to say about this how are we going to explain this and I thought it was might be one of these things where you just you know you can get it to the threshold and then you find out its rule number such and such and you just have no idea why it's like that yeah okay so then I realized it's actually more bizarre than that okay so we talked about multi-way graphs we talked about this idea that you take these underlying transformation rules on these hypergraphs and you apply them wherever the rule can apply you apply it and that makes this whole multi-way graph of possibilities okay so let's go a little bit weirder let's say that at every place not only do you apply a particular rule in all possible ways it can apply but you apply all possible rules in all possible ways they can apply okay so you say that's just crazy that's way too complicated you're never going to be able to conclude anything okay however turns out oh that don't tell me there's some kind of invariance yeah yeah so so what happens is man that would be amazing right so so this thing that you get this this kind of Ral multi-way graph this multi-way graph that is a branching of rules as well as a branching of possible applications of rules this thing has causal invariance it's a it's an inevitable feature that it shows causal invariance and that means that you can take different reference frames different ways of slicing this thing and they will all in some sense be equivalent if you if you make the right translation they will be equivalent so okay so the the basic Point here is that that's true that would be beautiful it is true and it is beautiful so you you it's not just an intuition there is some no no no there's real mathematics behind this and it and it's it is it is okay so here's here's how it comes yeah that that would be that's amazing right so so by the way I mean the mathematics that's connected to is the mathematics of higher category Theory and groupoids and things like this which I've always been afraid of but now I'm I'm I'm finally wrapping my arms around it but um um it's also related to uh it also relates to computational complexity Theory um it's also deeply related to the P versus NP problem and other things like this again seems completely bizarre that these things are connected but here's why it's connected the this space of all possible okay so a touring machine very simple model of computation you know you just got a this tape where you write down you know ones and zeros or something on the tape and you have this this rule that says you know you you change the number you move the head of the on the tape Etc you have a definite rule for doing that a deterministic touring machine just does that deterministically given the configuration of the tape it will always do the same thing a non-deterministic touring machine can have different choices that it makes at every step yeah and so you know um you know this stuff you probably teach this stuff the um it um uh you know so a non-deterministic touring machine has the set of branching possibilities which is in fact one of these multi-way graphs and in fact if you say imagine the extremely non-deterministic touring machine the touring machine that can just do uh that takes any possible rule at each step that is this Ral multi-way graph the set of the set of trans the set of possible histories of that extreme non-deterministic tur machine is a ruo multi-way graph and you're uh what term you using ruo ruo it's a weird word yeah it's a weird word right multi-way graph okay so this so that I'm trying think of I'm trying to think of the space of rules uh so these are basic Transformations so in a turning machine it's like it says move left move you know if it's a one if it's a black Square under the head move left and right a green square that's a rule that's a very basic rule but I'm trying to see the rules on the hypergraphs how rich of the programs can they be or do they all ultimately just map into something simple yeah they will I mean hypergraphs that's another layer of complexity on this whole thing you can you can think about these in transformations of hypergraphs but touring machines are a little bit put touring machines okay right they're a little bit simpler so if you look at these extreme non-deterministic touring machines you're mapping out all the possible non-deterministic paths that the turing machine can follow yeah and and if you ask the question uh can you reach okay so so a deterministic turing machine follows a single path the non-deterministic turing machine fills out this whole uh sort of ball of possibilities and so then the P versus MP problem ends up being questions about and we haven't completely figured out all the details of this but it's basically has to do with questions about the the growth of that ball relative to what happens with individual paths and so on so essentially there's a geometrization of the P versus MP problem that comes out of this that's a sideshow okay the main the main event here is the statement that you can look at this multi-way graph where the branches correspond not just to different applications of a single rule but to different application to Applications of different rules okay and that then that when you say I'm going to be an observer embedded in that system and I'm going to try and make sense of what's going on in the system and to do that I essentially I'm picking a reference frame and that turns out to be uh well okay so the way this comes out essentially is the reference frame you pick is the rule that you infer is what's going on in the universe even though all possible rules are being run although all those possible rules are in a sense giving the same answer because of causal invariance MH but what you see will be could be completely different if you pick different reference frames you essentially have a different description language for describing the universe okay so how does what does this really mean in practice so imagine there's us we think about the universe in terms of space and time and we have various kinds of description models and so on now let's imagine the friendly aliens for example right how do they describe their Universe well you know our description of the universe probably is affected by the fact that you know we are about the size we are you know meter is tall so to speak we have brain processing speeds we about the speeds we have we're not the size of planets for example we the speed of light really would matter you know in our everyday life the speed of light doesn't really matter everything can be you know the fact that speed of light is finite is irrelevant it could as well be infinite we wouldn't wouldn't make any difference you know it affects the the Ping times on the internet that's about that's about the level of of um of how we notice the speed of light in our sort of everyday existence we don't really notice it um and so we have a way of describing the universe that's based on our sensory you know our senses our uh in these days also on the mathematics we've constructed and so on but the realization is it's not the only way to do it there will be completely completely utterly incoherent descriptions of the universe which correspond to different reference frames in this sort of Ral space in the Ral space that's fascinating so we're we have some kind of reference frame in this Ral space right and from that that's why we are attributing this rule to the universe so in other words when we say why is it this Rule and not another the answer is just you know Shine the Light back on us so to speak it's because of the reference frame that we've picked in our way of understanding what's happening in the sort of uh space of all possible rules and so on but also in the space from this reference frame because of the royal the the the invariance that simple that the rule on which the universe with which you can run the universe might as well be simple yes yes but okay so so here's another point so this is again these are a little bit mind twisting in some ways but but the the the um um okay another thing that's sort of we know from computation is this idea of computation universality the fact that given that we have a program that runs on one kind of computer we can as well you know we can convert it to run on any other kind of computer we can emulate one kind of computer with another so that might lead you to say well you think you have the rule for the universe but you might as well be running it on a touring machine because we know we can emulate any computational rule on any kind of machine and that's essentially the same thing that's being said here that is that what we're doing is we're saying um these different interpretations of physics correspond to essentially running physics on different underlying you know thinking about the physics as running in different with different underlying rules as if different underlying computers were running them and but because of computation universality or more accurately because of this principle of computational equivalence thing of mine there's that they are um these things are ultimately equivalent so the only thing that is the ultimate fact about the universe the ultimate fact that doesn't depend on any of these you know we don't have to talk about specific rules etc etc etc the ultimate fact is the universe is computational and it is the the things that happen in the universe are the kinds of computations that the principle of computational equivalence says should happen now that might sound like you're not really saying anything there but you are because you can you could in principle have a hypercomp computer that things that take an ordinary computer in infinite time to do the hypercom computer can just say oh I know the answer it's this immediately what this is saying is the universe is not a hyper Compu it's not simpler than a an ordinary touring machine type computer it's exactly like an ordinary touring machine type computer and so that's the that's in the end the sort of net net conclusion is that's the thing that is the sort of the hard immovable fact about the universe that's sort of the the fundamental principle of the universe is that it is computational and not hyper computational and not sort of for computational it is this level of computational ability and it's um it kind of has and that's sort of the the The Core Fact but now you know this this idea that you can have these different kind of uh Ral reference frames these different description languages for the universe it it makes me you know I I used to think okay you know imagine the aliens imagine the Extraterrestrial intelligence thing you know at least they experience the same physics right and now I've realized isn't true they could have a different roal frame that's that's fascinating they can end up with a a a a description of the universe that is utterly utterly incoherent with ours and and that's also interesting in terms of how we think about well intelligence the nature of intelligence and so on you know I'm I'm fond of the quote you know the weather has a mind of its own because these are you know these are sort of computationally that that system is computationally equivalent to the system that is our brains and so on and what's different is we don't have a way to understand you know what the weather is trying to do so to speak we have a story about what's happening in our brains we don't have a sort of connection to what's happening there so we actually it's funny last time we talked maybe over a year ago uh we talked about how it was more based on your work with a rival uh we talked about how would we communicate with alien intelligences can you maybe comment on how we might how the wol from physics project changed your view how we might be able to communicate with alien intelligence like if they showed up is it possible that because of our com comprehension of the physics of the world might be completely different we would just not be able to communicate at all here's here's the here's the thing you know intelligence is everywhere the fact this idea that there's this notion of oh there's going to be this amazing extraterrestrial intelligence and it's going to be this unique thing it's just not true it's the same thing you know I I think people will realize this about the time when people decide that artificial intelligences are kind of just natural things that are like human intelligences they'll realize that that extraterrestrial intelligences or intelligences associated with physical systems and so on it's all the same kind of thing ultimately computation it's all the same it's all just computation and the issue is can you are you sort of inside it are you are you thinking about it do you have sort of a story you're telling yourself about it and you know the weather could have a story it's telling itself about what it's doing we just it's utterly incoherent with the stories that we tell ourselves based on how our brains work I mean ultimately it must be a a question whether we can align exactly Aline with the kind of intelligence systematic way of doing it right so the question is in the space of all possible intelligences what's the how do you think about the distance between description languages for one intelligence versus another and needless to say I have thought about this and uh um you know I I don't I don't have a great answer yet but but I think that's a that's a thing where there will be things that can be said and there'll be things that where you can sort of start to characterize you know what is the translation distance between this you know version of the universe or this you know kind of set of computational rules in this other one in fact okay so this is a you know there's this idea of algorithmic information Theory there's this question of sort of what is the uh when you have some something what is the sort of shortest description you can make of it where that description could be saying run this program to get the thing right so I'm pretty sure that that the um uh that there will be a physicalization of the idea of GIC information and that okay this is again a little bit bizarre but so I mentioned that there's the speed of light maximum speed of information Transmission in physical space there's a maximum speed of information Transmission in branchial space which is a maximum entanglement speed there's a maximum speed of information Transmission in roual space which is has to do with a maximum speed of translation between different uh description languages and again I'm I'm not fully wrapped my brain around this one yeah that one just blows my mind to think about that but that starts getting closer to the yeah the kind of physicalization right it's a and it's also a physicalization of of algorithmic information and I think there's probably a connection between I mean there's probably a connection between the notion of energy and some of these things which again I I you know hadn't seen all this coming I i' I've always been a little bit resistant to the idea of connecting physical energy to things in in in computation Theory but I I think that's probably coming and that's what essentially at the core with the the physics project is that you're connecting information Theory with well physics yeah it's computation in computation with our physical Universe yeah right I mean the fact that our physical universe is is right that we can think of it as a computation and that we can have discussions like you know the theory of the physical universe is the same kind of a theory as the P versus MP problem and so on is is really uh you know I think that's really interesting and and the fact that well uh okay so this this kind of brings me to one one more thing that I have to in terms of this sort of unification of different ideas which is meta mathematics yeah let's talk about that you mentioned that earlier what the heck is M mathematics and uh okay so here's here's what here's okay so what is mathematics mathematics uh sort of at a a lowest level one thinks of mathematics as you have certain axioms you say you know you say things like x + y is the same as y + x that's an axom um about addition and then you say we got these axioms and we and and from these axioms we derive all these theorems that fill up the literature of mathematics the the the activity of mathematicians is to derive all these theorems actually the axm of mathematics are very small you can fit you know when I did my new kind of science book I fit all of the standard axm of mathematics on basically a page and a half um it's not much stuff it's like a very simple rule from which all of mathematics arises um the way it works though is a little different from the way things work in in sort of uh a computation because in mathematics what you're interested in is a proof and the proof says from here you can use from this expression for example you can use these axioms to get to this other expression so that proves these two things are equal okay so we can we can begin to see how this is going to work what what's going to what happen is there are paths in metam mathematical space so what happens is each um two different ways to look at it you can just look at it as mathematical expressions or you can look at it as mathematical statements postulates or something but either way you think of these things and they are connected uh by these axioms so in other words you have some fact you or you have some expression you apply this axum you get some other expression and in general given some expression there may be many possible different Expressions you can get you basically build up a multi-way graph and a proof is a path through the multi-way graph that goes from one thing to another thing it the path tells you how did you get from one thing to the other thing it's the it's the story of how you got from this to that the theorem is the thing at one end is equal to the thing at the other end the proof is the path you go down to get from one thing to the other you mentioned that G's incompetance theem is not natural it fits naturally there how hard is yeah so so what happens there is that the girdles theorem is basically saying that there are pods of infinite length that is that there's no upper bound if you know these two things you say I'm trying to get from here to here how long do I have to go you say well I've looked at all the paths of length 10 somebody says that's not good enough that path might be of length a billion and and you there's no up bound on how long that path is and that's that's what leads to the incompleteness theorem so I mean the the thing that is kind of an emerging idea is you can start asking what's the analog of Einstein's equations in metam mathematical space what's the analog of a black hole in metam mathematical space what's the whole so yeah it's fascinating to model all the mathematics in this well so so here's here's what it is this is mathematics in bulk so human mathematicians have made a few million theorems they published a few million theorems but imagine the infinite future of mathematics apply something to mathematics that mathematics likes to apply to other things take a limit what is the limit of the infinite future of mathematics what does it look like what is the Continuum limit of mathematics what is the as you just fill in more and more and more theorems what does it look like what does it do how does what kinds of conclusions can you make so for example one thing I've just been doing is taking uid so uclid very impressive he had 10 axioms he derived 465 theorems okay his book you know that was was the sort of defining book of mathematics for 2,000 years um so you can actually map out and I I I I actually did this 20 years ago but I've done it more seriously now you can map out the theorem dependency of those 465 theorems so from the axioms you grow this graph it's actually a multi-way graph of how all these theorems get proved from other theorems and so you can ask questions about you know well you can ask things like what's the hardest theorem in ukle the answer is the hardest theorem is that there are five plutonic solids that turns out to be the hardest theorem in ucle that's actually his his Last Theorem in all his books that's the final what's the hardness the the distance you have to travel yeah that's it's 33 Steps From the the longest path in the graph is 33 steps so that's the there there's a 33 step path you have to follow to go from the axioms according to ukids proofs to the statement there are five platonic solids so so okay so then then then the the question is in uh what does it mean if you have this map okay so in a sense this meta mathematical space is the infrastructural space of all possible theorems that you could prove in mathematics MH that's the geometry of meta mathematics there's also the geography of mathematics that is where did people choose to live right in space and that's what for example exploring the sort of empirical metam mathematics of ID is doing each individual like human mathematician you can embed them into that space I mean they they kind they they represent a path in the things they do maybe a set of paths right so like and a set of axioms that are chosen right so so for example here's an example of of a thing that I realized so one of the surprising things about well there two surprising facts about math one is that it's hard and the other is that it's doable okay so first question is why is math hard you know you've got these axioms they're very small why can't just solve every problem in math easily yeah it's just logic right yeah well logic happens to be a particular special case that does have certain Simplicity to it um but General mathematics even arithmetic already doesn't have the Simplicity that logic has so why is it hard because of computational irreducibility right right because what happens is to know what's true and this is this whole story about the path you have to follow and how long is the path and goal theorem is the statement there could be an in that the path is not a bounded length but the fact that the path is not always compressible to something tiny is a story of computational irreducibility so that's that's why math is hard now the next question is why is math doable because it might be the case that most things you care about don't have finite length paths most things you care about might be things where you get lost in the sea of computational irreducibility and worse undecidability that is there's just no finite length path that gets you there um you know why is mathematics doable you know girdle proved his incompleteness theorem in 1931 most working mathematicians don't really care about it they just go ahead and do mathematics even though it could be that the questions they're asking are undecidable it could have been that format's L theorem is undecidable it turned out it had a proof it's a long complicated proof the twin Prime conjecture might be undecidable the reman hypothesis might be undecidable these things might be the axioms of mathematics might not be strong enough to reach those statements it might be the case that depending on what axioms you choose you can either say that's true or that's not true so and and by the way from as Last Theorem there could be a shorter path absolutely yeah so that the notion of j6 in metam mathematical space is a notion of shortest proofs in metam mathematical space and that's a you know human mathematicians do not find shortest paths nor do automated theorem provs um but the fact and and by the way the I mean this stuff is so bizarrely connected I mean if you if you're into automated theorem proving there are these so-called critical pair Lamas and automated theorem proving those are precisely the branch pairs in our um that in multi-ray graphs let me just finish on the why mathematics is doable oh yes the second part so we know why it's hard why is it doable right why do we not just get lost in undecidability all the time yeah um so and and here's another fact is in doing computer experiments and doing experimental mathematics you do get lost in that way when you just say I'm picking a random integer equation how do I does it have a solution or not and you just pick it at random without any human sort of path getting there often it's really really hard it's really hard to answer those questions when you just pick them up random from the space of possibilities but what's what I think is happening is and that's a case where you just fell off into this ocean of sort of irreducibility and so on what's happening is human mathematics is a story of building a path you you started off you're you're always building out on this path where you are proving things you you you've got this proof trajectory and you're basically the human mathematics is the sort of the exploration of the world along this proof trajectory so to speak you're not you're not just you know uh parachuting In from from you know from from anywhere you're following you know Lewis and Clark or whatever you're actually you're actually going doing the PA and the fact that you are constrained to go along that path is the reason you don't end up with lot every so often you'll see a little piece of undecidability and you'll avoid that that part of the path but that's basically the story of why human mathematics is has seemed to be doable it's a story of exploring these paths that that are by their nature they have been constructed to be paths that can be followed and so you can follow them further now you know what why is this relevant to anything so okay so here's the the my my my belief the fact that human mathematics works that way is I think there's some sort of connections between the way that observers work in physics and the way that the axium systems of mathematics are set up to make mathematics be doable in that kind of way and so in other words in particular I think there is an analog of causal invariance which I think is um and this is again in sort of the upper reaches of mathematics and and stuff that um uh it's a thing there's this thing called homotopy type Theory which is an abstract it's came out of category Theory and it's sort of an abstraction of mathematics mathematics itself is an abstraction but it's an abstraction of the abstraction of mathematics and there is a thing called the univalence axium which is a sort of a a key axom in that set of ideas and I'm pretty sure the univance axium is equivalent to causal variance what was the term you use again uni univance is that something for somebody like me accessible um or is this there's a statement of it that's fairly accessible I mean the statement of it is um uh basically it says things which are equivalent can be considered to be identical in which but in which space yeah it's it's in in higher category okay in Category 3 okay so it's it's a it's a but I mean the thing just to give sketch of how that works so category theory is an attempt to idealize it's an attempt to sort of have a formal theory of mathematics that is at a sort of higher level than mathematics it's where where you just think think about these mathematical objects and these categories of objects and these these morphisms these connections between categories okay so it turns out the morphisms and categories the least weak categories are very much like the paths in our hypergraphs and things and it turns out again this is this is where it all gets gets crazy I mean it's it's the fact that these things are connected is just bizarre so category Theory uh the our causal graphs are like second order category Theory and it turns out you can take the limit of infinite order category Theory so just just give rough roughly the idea this is a this is a roughly explainable idea so a mathematical proof will be a path that says you can get from this thing to this other thing and here's the path you get from this thing to this other thing but in general there may be many paths many proofs that get you many different paths that all successfully go from this thing to this other thing okay now you can define a higher order proof which is a proof of the equivalence of those proofs mhm okay so you're saying there's a go path between those proofs essentially yes a path between the paths yeah okay and so you do that that's the sort of second order thing that path between the paths is essentially related to our causal graphs then take limit wow path between path between path between path the infinite limit that infinite limit turns out to be our Ral multi-way system yeah the Ral the the Ral multi-way system that's a fascinating thing both in the physics world and and as you're saying now that's that's I'm not sure I've loaded it in completely but well I'm not sure I have either and it may be one of these things where where you know in another another five years or something it's like this was obvious but I didn't see it no but the thing which is sort of interesting to me is that there's sort of an upper reach of of mathematics of the abstraction of mathematics um this thing there's this mathematician called grth and deque who's generally viewed as being sort of one of the most abstract sort of creator of the most abstract mathematics of 1970s is time frame um and one of the things that he constructed was this thing he called the infinity groupoid um and he has the sort of hypothesis about the inevitable appearance of geometry from essentially logic in the structure of this thing well it turns out this Ral multiway system is the infinity group void so it's a it's this limiting object and this is an this is an instance of that limiting object so what to me is I mean again I I've been always afraid of this kind of mathematics because it seemed incomprehensibly abstract to me um but what's what's what I'm sort of excited about with this is that that we've sort of concre ified the way that you can reach this kind of mathematics which makes it uh well both seem more relevant and also the fact that that you know I don't yet know exactly what mileage we're going to get from using the sort of the apparatus that's been built in those areas of mathematics to analyze what we're doing but the thing that's so both ways so use mathematics understand what you're doing and using what you're doing computationally to understand that right so so for example the the understand of uh meta mathematical space one of the reasons I really want to do that is because I want to understand quantum mechanics better and and that what you see you know we live that uh kind of the multi-way graph of mathematics because we actually know this is a theorem we've heard of this is another one we've heard of we can actually say these are actual things in the world that we relate to which we can't really do as as readily for the the physics case and so it's kind of a way to help my intuition it's also you know there are bizarre things like the what's the analog of Einstein's equations in metam mathematical space what's the analog of a black hole you know it turns out it looks like not completely sure yet but there's this notion of non-constructive proofs in mathematics and I think those relate to well actually the the they they relate to things and related to event Horizons um so the fact that you can take ideas from physics like event Horizons into the same kind of it's it's really so do you think there'll be do you think you might stumble upon some breakthrough ideas in theorem proving like for from the the other direction yeah yeah yeah no I mean what's really nice is that we are using so this this absolutely directly maps to theorem proving so paths and multi-way graphs that's what a theorem improver is trying to do but I also mean like like automated de yeah yeah yeah that that's what right so the finding of PODS the finding of shortest parts s or finding a paths at all is what automated theorem provs do and actually what what we've been doing so we've you know we've actually been using automated theorem proving both in the physics project to prove things and using that as a way to understand multi-way graphs and because what an automated theorem prover is doing is it's trying to find a path through a multi-way graph and its critical pair lemas are precisely little stubs of Branch pairs going off into branchial space and that's I mean it's really weird you know we have these visualizations in W language of our of of um proof graphs from our automative theorem proving system and they look reminiscent of well it's just bizarre because we made these up a few years ago and they have these little triangle things and they are they are we we didn't quite get it right we didn't quite get the analogy perfectly right but it's very close you know just to say in terms of the how these things are connected so there's another bizarre connection that I I have to mention because because um um which is uh which again we don't fully know but it's a connection to uh uh something else you might not have thought was in the slightest bit connected which is distributed blockchain like things now you might figure out that that's you you would figure out that that's connected because because it's a story of distributed computing yeah and the issue you know with a blockchain you're saying there's going to be this one Ledger that that globally says this is what happened in the world but that's a bad deal if you've got all the different transactions that are happening and you know this transaction in country a doesn't have to be reconciled with a transaction in country B at least not for a while and that story is just like what happens when our causal graphs that whole reconciliation thing is just like what happens with light cones and all that's where the cause in variance comes into play I mean that that's you know most of your conversations are about physics but it's kind of funny that the this probably and possibly might have even bigger impact and uh revolutionary ideas in totally other disciplines right well see see yeah right so the question is why is that happening right and and the reason it's happening I I've thought about this obviously because I like to think about these meta questions of you know what's happening is this model that we have is an incredibly minimal model yeah and once you have an incredibly minimal model and this happened with cellular autometer as well cellular autometer inedibly minimal model and so it's inevitable that it gets you sort of an upstream thing that gets used in lots of different places and it's like you know the fact that it gets used you know cellular autometer as sort of a minimal model of let's say road traffic flow or something and they're also a minimal model of something in you know chemistry and they're also a minimal model of something in in epidemiology right it's because they're such a simple model that they can that they use apply to all these different things similarly this model that we have with the physics project is a is another it's a cellular autometer are a minimal model of parallel of of basically of parallel computation where you've defined space and time these models are minimal models where you have not defined space and time and they have been very hard to understand in the past but the I think the perhaps the most important breakthrough there is the realization that these are models of physics and therefore that you can use everything that's been developed in physics to get intuition about how things like that work and that's why you can potentially use ideas from physics to get intuition about how to do parallel Computing and because the underlying model is the same and but but we have all of this achievement in physics I mean you know you might say oh you've come up with the fundamental Theory of physics that throws out what people have done in physics before well it doesn't but also the real power is to use what's been done before in physics to apply it in these other places yes and absolutely this kind of brings up I know you probably don't particularly love commenting on the work of others but let me let me bring up a couple personalities just because it's fun people are curious about it so there's uh uh Sabine Hassen Felder I don't know if you're familiar with her she uh she wrote this book uh that I need to read but it Bas I forget what the title is but it's uh Beauty leads us astray in physics is a subtitle something like that which so much about what we're talking about now like the simplification is uh to us humans seems to be beautiful like there's a certain intuition with physicists with people that A Simple Theory like this reducibility pockets of reducibility is the ultimate goal and I think what she tries to argue is uh no we just need to come up with theories that are just really good at predicting physical phenomena it's okay to have a bunch of uh disperate theories as as opposed to trying to chase this beautiful Theory of Everything Is the ultimate beautiful Theory uh a simple one you know it's always what's your response to that well so what you're quoting so I don't know the Sabine hassenfeld is you know exactly what she said but I meting the I'm quoting the title of a book okay let me let me let me respond to what you were describing which may or may not have nothing to do with what you know what Sabin Hassen Felder says or thinks sorry San right sorry for misquoting um but I mean the the question is you know does is beauty a guide to whether something is correct that's right which is kind of also the story of aam's Razer you know if you've got a bunch of different explanations of things you know is the thing that is the simplest explanation likely to be the correct explanation and there are situations where that's true and there are situations where it isn't true sometimes in human systems it is true because people have kind of you know in evolutionary systems sometimes it's true because it's sort of been kicked to the point where it's minimized um but uh you know in physics does Arkham's Razer work you know is there a simple quotes beautiful explanation for things or is it a big mess um you know we don't intrinsically no you know I think that the I wouldn't before I worked on the project in recent times I would have said we do not know how complicated the rule for the universe will be and and I would have said you know the one thing we know which is a fundamental fact about science that's the thing that makes science possible is that there is order in the universe I mean you know early theologians would have used that as an argument for the existence of God because it's like why is there order in the universe why doesn't every single particle in the universe just do its own thing yeah um you know something must be making there be order in the universe we you know in in the sort of early theology point of view that's you know the role of God is to do that so to speak in our uh you know we might say it's the role of a formal Theory to do that and then the question is but how simple should that theory be and should that theory be one that that you know where I think the point is if it's simple it's almost inevitably somewhat beautiful in the sense that because all the stuff that we see has to fit into this little tiny Theory and the way it does that has to be you know it it depends on your notion of beauty but I mean in for me the the sort of the surprising con connectivity of it is at least in my aesthetic that's something that uh respond to my aesthetic but the question is uh I mean you're you you're a fascinating person in the sense that you're at once talking about computational the fundamental computational reducibility of the universe and and the other hand trying to come up with a Theory of Everything which simply describes the the the simple origins of that computational reducibility right I mean both of those things are kind of it's paralyzing to think that we can't make any sense of the universe in the general case but in it's hopeful to think like one we can think of a rule and uh that generates this whole complexity and two we can find uh pockets of uh reducibility that are powerful for our everyday life to do different kinds of predictions I suppose sine would wants to find focus on the finding of small pockets of reducibility versus the uh Theory of Everything You know it's a funny thing because because you know a bunch of people have started working on this this you know physics project people who are you know physicists basically um and it is really a fascinating sociological phenomenon because what you know when I was working on this before and the 1990s you know wrote it up put it it's 100 pages of this 1200 page book that I wrote new kind of science it's you know 100 pages of that is about physics right I I saw it at in that at that time not as a pinnacle achievement but rather as a use case so to speak I mean my main point was this new kind of Science and it's like you can apply it to biology you can apply it to you know other kinds of physics you can apply it to fundamental physics it's just it's just an application so to speak it's not the core thing but um but then you know one of the things was interesting with that with that book was you know book comes out lots of people think it's pretty interesting and lots of people start using what it has in different kinds of fields the one field where there was sort of a a heavy pitchforking was from my friends the fundamental physics people yeah which was it's like no this can't possibly be right and you know it's like you know if what you're doing is right it'll overturn 50 years of what we've been doing and it's like no it won't was what I was saying and it's like um but uh you know for a while when I started you know I I was going to go on back in 2002 well 2004 actually I was going to go on working on this project and I actually stopped partly because it's like why am I you know this is like I've been in business a long time right I'm I'm building a product for a target market that doesn't want the product and it's like why work yeah yeah why why work against the swim against the current or whatever but but you see what's happened which is sort of interesting is is that so A couple of things happened and it was it was like uh you know it was like I I I don't want to do this project because I can do so many other things which I'm really interested in where you know people say great thanks for those tools thanks for those ideas Etc whereas you know if you're dealing with kind of a a uh you know sort of a structure where people are saying no no we don't want this new stuff we don't need any new stuff we're really fine with what what we there's like literally like I don't know millions of people who are thankful for wolf from alpha a bunch of people wrote to me how thankful they are they are a different crowd than uh the theoretical physics Community perhaps yeah well right but you know the theoretical physics Community pretty much uniformally uses uh W from language and Mathematica right and so it's it's kind of like like um you know and that that's but the thing is what happens you know this is what happens mature fields do not you know it's like we're doing what we're doing we have the methods that we have and we're we're just fine here now what's happened in the last 18 years or so I think there's a couple of things have happened first of all the the hope that you know String Theory or whatever would would deliver the fundamental Theory of physics that hope has disappeared that the another thing that's happened is the the sort of the interest in computation around physics has been greatly enhanced by the whole Quantum information Quantum Computing story people you know the idea there might be something sort of computational uh related to physics is somehow somehow growing and I think you know it's it's sort of interesting I mean right now if we say you know it's like if you're like who else is trying to come up with the fundamental Theory of physics it's like there aren't professional no professional physic no professional physicists what are your uh I mean you've talked with him but just as a matter of personalities CU it's a beautiful story what are your thoughts about Eric Weinstein's work I you know I I think his his um I mean he did a PhD thesis in mathematical physics at Harvard mathematical physicist and and you know it's it seems like it's kind of you know it's in that framework and it's kind of like I'm not sure how much further it's got than his PhD thesis which was 20 years ago or something and I think that you know the the you know it's a fairly specific piece of mathematical physics that's quite nice and um what trajectory do you hope it takes I mean well I think in his particular case I mean from what I understand which is not everything at all but you know I think I know the rough Tradition at least he's operating in is sort of theory gauge theories gauge theories yeah local gauge and variance and so on okay we are very close to understanding how local gauge and variance Works in our models and it's very beautiful and it's very um and you know does some of the mathematical structure that he's enthusiastic about fit quite possibly yes so there might be a possibility of trying to understand how those things fit how gauge Theory fits well the question is you know so there are a couple of things one might try to get in the world so for example it's like can we get three dimensions of space we haven't managed to get that yet gauge Theory the standard model of particle physics says that it's su3 cross su2 cross U1 those are the designations of these um Le groups um it doesn't but but anyway so those are those are sort of representations of symmetries of the theory and um so you know it is conceivable that it is generically true okay so all those are subgroups of a group called E8 which is a weird exceptional Le group okay it is conceivable I don't know whether it's the case that that will be generic in these models that it will be generic that the gaug and variance of the model has this property just as things like general relativity which corresponds to thing called U general covariance which is another GA like invariance it could conceivably be the case that the kind of local gauge invariance that we see in particle physics is somehow generic and and that would be a you know the thing that's that's really cool I think you know sociologically although this hasn't really hit yet is that all of these different things all these different things people have been working on in these in some cases is quite abstruse areas of mathematical physics an awful lot of them seem to tie into what we're doing and you know it might not be that way yeah absolutely that's a beautiful thing in the theory I mean but the reason I so the reason Eric Weinstein is important is to the point that you mentioned before which is it's strange that The Theory of Everything Is Not at the core of uh the passion the dream the focus the funding of the physics community it's too hard it's too hard and people gave up I mean basically what happened is ancient Greece people thought we're nearly there you know the world is made of platonic solids it's you know water is a tetrahedron or something yes we're almost there okay long period of time where people were like no we don't know how it works you know time of Newton uh you know we're almost there everything is gravitation you know time of Faraday and Maxwell we almost there everything is Fields everything is The Ether you know then the whole time we're making big progress though oh yes absolutely but the fundamental Theory of physics is almost a footnote because it's like it's the machine code it's like we're operating in the high level languages yeah um you know that's what we really care about that's what's relevant for our everyday physics you talked about different centuries and the 21st century will be uh everything is computation yes if that takes us all the way we don't know but it might take us pretty far yes right that's right and but I think the point is that it's like you know if you're doing biology you might say how can you not be really interested in the origin of life and the definition of life well it's irrelevant you know you're studying the properties of some virus it doesn't matter you know where you know you're you're operating at some much higher level and it's the same what what's happened with physics is I was sort of surprised actually I was sort of mapping out this history of of people's efforts to understand the fundamental Theory of physics and it's remarkable how little has been done on this question and it's you know because you know there have been times when there's been bursts of enthusiasm and we're almost there and and then it decays and and people just say oh it's too hard but it's not relevant anyway and I think that the um the thing that um you know so so the question of of you know one question is why does anybody why should anybody care right why should anybody care what the fundamental Theory of physics is I think it's intellectually interesting but what will be the sort of what will be the impact of this what I mean this is the key question what do you think will happen if we figure out the fundamental Theory of physics right outside of the intellectual curiosity of us this my best guess okay so if you look at the history of science I think a very interesting analogy is cernus okay so what did cernus do there had been this toic system for working out the motion of planets it did pretty well it used epicycles etc etc etc it had all this computational ways of working out where planets will be when we work out where planets are today we're basically using epicycles but cernus had this different way of formulating things in which he said you know and the Earth is going around the Sun and that had a consequence the consequence was you can use this mathematical Theory to conclude something which is absolutely not what we can tell from common sense right so it's like trust the mathematics trust the science okay now fast forward 400 years and um you know and now we're in this pandemic and it's kind of like everybody thinks the science will figure out everything it's like from the science we can just figure out what to do we can figure out everything that was before cernus nobody would have thought if the science says something that doesn't agree with our everyday experience where we just have to you know compute the science and then figure out what to do people say that's completely crazy and so your sense is once we figure out the framework of computation that can basically do any understand the the fabric of reality will be able to derive totally counterintuitive things no the the the point I think is the following that that right now you know I talk about computational irreducibility people you know I was was very proud that I managed to get the term computational irreducibility into the Congressional record last year um that's right that's a whole another topic we could talk about different different topic different different topic but but um um in any case you know but so computational reducibility is one of these sort of Concepts that I think is important in understanding lots of things in the world but the question is it's only important if you believe the world is fundamentally computational right and but if you if you know the fundamental Theory of physics and it's fundamentally computational then you've rooted the whole thing that is you know the world is computational and while you can discuss whether you know uh it's not the case that people say well you have this whole computational reducibility all these features of computation we don't care about those because after all the world isn't computational you might say but if you know you know Bas space based thing physics is computational then you know that that stuff is you know that's kind of the grounding for that stuff just as in a sense cernus was the grounding for the idea that you could figure out something with math science that was not what you would intuitively think from your senses so now we've got to this point where for example we say you know once we have the idea that computation is the foundational thing that explains our whole universe then we have to say well what does it mean for other things like it means there's computational irreducibility that means science is limited in certain ways that means this that means that but the fact that we have that grounding means that you know and I think for example for kernus for instance the implications of his work on the sort of mathematics of astronomy were cool but they involved a very small number of people the implications of his work for sort of the philosophy of how you think about things were vast and involved you know everybody more or less but do you think so that's actually the way scientists and people see the world around us so it has a huge impact in that sense do you think it might have an impact more directly to engineering derivations from physics like propulsion systems our ability to colonize the world like for example okay this is like sci-fi but if you if you understand the computational nature say of uh of the different forces of physics you know there's there's a notion of being able to you know warp gravity things like this like can we make warp drive warp drive yeah so like would we be able to will it will uh you know will like Elon Musk start paying attention like it's awfully costly to launch these Rockets do you think we'll be able to yeah create warp drive and uh you know I I I set myself some homework I agreed to give a talk at some NASA Workshop in a few weeks about faster than light travel so I I haven't figured it out yet but but no but you got two weeks yeah right but do you think that kind of understanding of fundamental Theory of physics can lead to those engineering breakthroughs okay I think it's far away but I'm not certain I mean and you know this is the thing that that um I set myself an exercise When Gravity waves gravitational waves were discovered right I set myself the exercise of what would black hole technology look like in other words right now you know black holes are far away they're you know how on Earth can we do things with them but just imagine that we could get you know pet black holes right in our backyard you know what kind of Technology could we build with them I I got a certain distance not that far but I think in in um you know so there are ideas you know I have this one of the weirder ideas is the things I'm calling SpaceTime tunnels which are higher dimensional pieces of the of of SpaceTime where basically you can you know in in our three-dimensional space there might be a five-dimensional you know uh region which actually will appear as a white hole at one end and a black hole at the other end you know who knows whether they exist and then the questions another one okay this is another crazy one is the thing that I'm calling a vacuum cleaner okay so so so I I I mentioned that you know there's all this activity in the universe which is meant Ming the structure of space yes and that leads to a certain uh energy density effectively in space and so the question in fact dark energy is a story of essentially negative mass produced by uh the absence of energy you thought would be there so to speak and we don't know exactly how it works in in our either our model or the physical universe but this notion of a vacuum cleaner is a thing where you know you have all these things that maintaining the structure of space but what if you could clean out some of that stuff that's maintaining the structure of space and make a simpler vacuum somewhere yeah you know what would that do a totally different kind of vacuum right and that that would lead to negative energy density which would need to so gravity is is usually a purely attractive Force but negative Mass would lead to rep repulsive gravity um and uh lead to all kinds of weird things now can it be done in our universe um you know my immediate thought is no but but you know the fact is that okay so so here once you understand the fact because you're saying like at this level abstraction can we reach to the lower levels and mess with it uh once you understand the levels I think you can start and I'm I'm you know I have to say that that this reminds me of people telling one years ago that you know you'll never transmit data over a copper wire at more than a th you know a th000 board or something right and and this is why did that not happen you know why why did why do we have this much much faster data transmission because we've understood many more of the details of what's actually going on and and it's the same exact story here and it it's the same you know I think that this as I say I think one of the features of sort of one of the things about our time that will seem incredibly naive in the future is the belief that you know things like heat is just random motional molecules that that that it's just just throw up your hands it's just random we can't say about it that will seem naive yeah the at the heat depth of the universe those particles would be laughing at us humans thinking yes right that life is not civilization um you know humans used to think they're special with their little brains well right but but also but but and they used to think that this would just be random and uninteresting but that's but so so this question about whether you can you know mess with the underlying structure and how you find a way to mess with the underlying structure that's a you know I have to say you know my immediate thing is boy that seems really hard but then and and you know possibly computational irreducibility will bite you but then there's always some path of computational reducibility and that path of computational reducibility is the engineering invention exact that has to be made those little pockets can have huge engineering impact right and and I think that that's right and I mean we live in you know we make use of so many of those pockets and the fact is you know I I um uh you know this this is yes it's it's a you know it's one of these things where where you know I am a person who likes to figure out ideas and so on and the sort of tests of my level of imagination so to speak and so a couple of places where there's sort of serious humility in terms of my level of imagination one is this thing about different reference frames for understanding the universe where like imagine the physics of the aliens what will it be like like and I'm like that's really hard I don't know you know and and I mean once you have the framework in place you can at least reason about the things you don't know or maybe can't know or like it's too hard for for you to know but then the the mathematics can that's exactly it allow you to reach beyond what you can uh reason about right well so so I'm you know I'm I'm I'm trying to not have you know if you think back to Alan Turing for example and you know when he invented Turing machines you know and and imagining what computers would end up doing so to speak yeah um you know and very difficult it's difficult right and it's it's I mean made a few reasonable predictions but most of it he couldn't predict possibly by the time by 1950 he was making reasonable predictions about something but not the 30s yeah right not not not in the not when he first you know conceptualized you know and he conceptualized Universal Computing for a very specific mathematical reason that wasn't um uh wasn't as general but but yes it's a it's a good sort of exercise and humility to realize that that it's kind of like it's it's really hard to figure these things out the engineering of of um the universe if we know how the universe works how can we engineer it that's such a beautiful Vision that's such a beautiful by the way I have to mention one more which is the the ultimate question of of from physics is okay so we have this abstract model of the universe why does the universe exist at all right so you know we might say there there is a a formal model that if you run this model you get the universe or the model gives you you know a model of the universe right you you you you run this mathematical thing and the mathematics unfolds in the way that corresponds to the universe but the question is why was that actualized why does the actual Universe actually exist and um so this is this is another one of these humility and and um is like can you figure this out I have a guess okay about the answer to that and um my guess is somewhat unsatisfying but my guess is that it's a little bit similar to girdle second incompleteness theorem which is the statement that from within as an axiomatic Theory like P arithmetic you cannot from within that theory prove the consistency of the theory so my guess is that for entities within the universe there is no finite determination that can be made of the the statement the universe exists is essentially undecidable to any entity that is embedded in the universe within that Universe how does that make you feel is that is that does that put you at peace that it's impossible or is it really ultimately frustrating well I think it just says that it's not a kind of question that you know it's there are things that it is reasonable I mean there's kinds of you know you can talk about hypercomputation as well you can say imagine there was a hypercom computer here's what it would do so okay great it would be lovely to have a hypercom computer but unfortunately we can't make it in the universe like it would be lovely to answer this but unfortunately we can't do it in the universe um and you know this is all we have so to speak um and I think it it's it's really just a a statement it's sort of in the end it'll be a a kind of a logical logically inevitable statement I think I think it will be something where it is as you understand what it means to have what it means to have a sort of predicate of existence and what it means to have these kinds of things it will sort of be inevitable that this has to be the case that from within that Universe you can't establish the reason for its existence so to speak you can't prove that it exists and so on and nevertheless because of computation or reducibility the future is uh ultimately not predictable full of mystery and that's what makes life worth living right I mean right and you know it's funny for me because as a just a pure sort of human being doing what I do it's you know I'm I'm uh you know I like I'm interested in people I like sort of the you know the whole Human Experience so to speak and yet it's a little bit weird when I'm thinking you know it's all hypergraphs down there and it's all just uh hypergraphs all the way down right like turtles all the way down right and and and it's kind of you know it's to me it is a funny thing because every so often I get this you know as I'm thinking about I think we've really gotten you know we've really figured out kind of the essence of how physics works and I'm like thinking to myself you know here's this physical thing and I'm like you know this feels like a very definite thing how can it be the case that this is just some Ral reference frame of you know this infinite creature that that is uh so abstract and so on and I kind of it is a it's a it's a funny sort of feeling that that you know we are we're sort of uh um it's like it's in the end it's just sort of um be happy we're just humans type thing and and it's it's kind of like but but we're making we make things as it's not like we're just a tiny Speck we are in a sense the we are more important by virtue of the fact that in a sense it's not like there's there is no ultimate you know it's like we're important because because you know we're here so to speak and we're not it's not like there's a thing where we're saying um you know we are just but one sort of intelligence out of all these other intelligences and so you know ultimately there'll be the Super intelligence which is all of these put together and they'll be very different from us no it's actually going to be equivalent to us and the thing that makes us sort of special is just the details of us so to speak it's not something where we can say oh there's this other thing you know just you think humans are cool just wait until you've seen this you know it's going to be much more impressive well no it's all going to be kind of computationally equivalent and the thing that you know it's not going to be oh this thing is is amazingly much more impressive and amazingly much more meaningful let's say no we're it I mean that's that's that that's the um and and the symbolism of this particular moment so this has been one of the one of the favorite conversations I've ever had Stephen it's a huge honor to talk to you to talk about a topic like this for four plus hours on the fundamental Theory of physics and yet we're just two finite descendants of Apes that have to end this conversation because Darkness have come upon us right and and we're going to get bitten by mosquitoes and all kinds of terrible the symbolism of that we're talking about the most basic fabric of reality and having to end because of the fact that things end um it's tragic and beautiful Stephen thank you so much huge honor I can't wait to see what you do in the next couple of days and next week month we're all watching with excitement thank you so much thanks thanks for listening to this conversation with Stephen wlr and thank you to our sponsors Simply Safe Sun basket and masterclass please check out our sponsors in the description to get a discount and to support this podcast if you enjoy this thing subscribe on YouTube review it with five stars and apple podcast follow on Spotify support on patreon or connect with me on Twitter at Lex Friedman and now let me leave you with some words from Richard fan physics isn't the most important thing love is thank you for listening and hope to see you next time