The following is a conversation with Stephen 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, Wolfram Alpha, Wolfram Language and the new Wolfram 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. The 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 hoppergrass 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 Master Class. 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 in science. I find that both cellular automata and the hydrograph data structure that Stephen and team are currently working on to be the kind of simple, clear mathematical playground within which fundamental ideas about intelligent 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 and math, computer science and physics. But honestly, I think the emerging complexity in these hyper graphs 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 covid. I'm sorry if the audio is not great. I did my best and promised to keep improving and learning. As always, if you enjoy this thing, subscribe on YouTube, review it.
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So if you look back through the history of physics, at what moment stands out to you as important such breakthroughs were? A flurry of progress follows.
So the big famous one was 1920s. The invention of quantum mechanics were, you know, in about five or 10 years, lots of stuff got figured out. That's now quantum mechanics. You mentioned the people involved.
Yeah, that was kind of the Schrodinger Heisenberg. You know, Einstein had been a key figure originally Planck. Then Dirac was a little bit later. That was something that happened at that time. That sort of before my time, right in my time was in the 1970s. There was this sort of realization that quantum field theory was actually going to be useful in physics and quantum theory of quarks and gluons and so on was really getting started. And that was, again, sort of a big flurry of things happened then.
I happened to be a teenager at that time and happened to be 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 Kassidy? OK, people, David Gross, Frank will check, you know, David Pulitzer, the people who are sort of the slightly older generation, Dick Feynman, Murray Gulman, people like that, who were Steve Weinberg, Garrett Helft, his younger. He's in the younger group, actually. But these are these are all, you know, characters who are involved. I mean, it was 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 historical, you know, iconic figures.
They seem more like everyday characters, so to speak. And so it's always, you know, when you look at history from long afterwards, it always seems like everything happened instantly. And that's usually not the case. There was usually a long buildup, but usually there's you know, there's some methodological thing happens and then there's a whole bunch of low hanging fruit to be picked. And that usually lost five or 10 years. You know, we see it today with machine learning and deep learning, neural nets and so on.
You know, methodological advanced things actually started working and, you know, 2011, 2012 and so on. And, you know, there's been this sort of rapid picking of low hanging fruit, which is probably, you know, some significant fraction of the way we've done so to speak.
Do you think this is a key moment? Like if I had to really introspect, like what was the key moment for the deep learning revolution?
I mean, it's probably the Alex in that business. Alex, now would imagine that there's something like that with physics where so deep learning neural networks have been around for a long time since the 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 is simple rules can create complexity. You know, at which point was there a thing where your eyes light up 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? So 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 beginning of the 1980s. You know, I did a bunch of computer experiments. 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, that's a big, important phenomenon here, that let's sort of complex things arise from very simple programs that kind of happened back in 1984 or so. Then, you know, a 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 principles, computational equivalence. And that was a long story. And then, you know, as part of that process, I was like, OK, you can make simple programs, can make models of complicated things.
What about the whole universe? That's a sort of ultimate example of a complicated thing. And so I got to thinking, you know, could we use these ideas to study fundamental physics? You know, I happen to know a lot about, you know, traditional fundamental physics. My my first you know, 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 a new kind of science and selling in world and.
Right. There's echoes in the summertime time in a world with your new warfrom physics project where we'll get to all that. Allow me to sort of romanticize a little more on the philosophy of science. So Thomas Kune, philosopher of science, describes that, you know, the progress in science is made with these paradigm shifts. And so Tollinger, on the sort of original line of discussion, do you agree with this view that there is revolutions in science that just kind of off 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.
Does this idea of. 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 The Innovators, where he discusses how a lot of 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 ultimately like one person responsible for these revolutions that decrease the spark or one or two whatever.
But or is it just the big mush and mess and chaos of people interacting of personalities?
And 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 new idea. And I think, you know, but I think it can happen that, you know, you have a great idea, but the world isn't ready for you for it. And, you know, you can you can. I mean, this has happened to me plenty, but 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.
And know 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 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 is, well, what happened or do you think that's already happened?
Oh, yeah, it's happened.
Except that people aren't, you know, the sort of the heroism of it may not be there, but 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. Now, you know, was that sort of going to happen anyway?
Was that a consequence of, you know, my particular work and 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 there was there a chain of academic references?
One of the interesting side effects of publishing in the way you did this tome 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 50 titles, it doesn't create a splash of citations like it's had plenty of citations.
But it's you know, I think the IT people think of it as probably more, you know, conceptual inspiration than than kind of a you know, this is a line from here to here to here in our particular field. 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 the sort of pure computational wisdom, this kind of study of the abstract behavior of the computational universe.
That should be a big thing that lots of people do.
You mean in mathematics? Purely almost like it's like mathematics, but it isn't mathematics.
But it isn't. It isn't. It's a new kind of mathematics. Is it a new title?
Right. The title of the book is called That. Right. But that's not coincidental. Yeah.
It's interesting that I haven't seen really rigorous investigation by thousands of people. This idea. I mean, you look at your competition around rule 30. I mean, that's fascinating. If you if you can say something right. Is there some aspect of this thing that could be predicted? That's the fundamental question of science. That's or has been a question of science. I think that's a that is in 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 lived through this pandemic full of predictions and so on, that's an interesting moment to be pondering. What what science is actual role in those kinds of things is, oh, you think it's possible that in science. Clean, beautiful, simple protection may not even be possible in real systems. That's the open road question.
I don't think it's open. I think that question is answered and the answer is no, no, no.
The answer could be just humans are not smart enough yet.
We don't have the tools. 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 the you know, this is something which is kind of a follow on to Google's theorem, to Turing's work on the halting problem or these kinds of things, that there is this fundamental limitation built into science, this idea of computational or disability that says that, you know, even though you may know the rules by which something operates, that does not mean that you can readily sort of be smarter than that and jump ahead and figure out what it's going to do.
Yes, but do you think there's a hope for pockets of computation or disability, computational reuse, reduce, reduce ability?
Yes, that's so. And then a set of tools and mathematics that help you discover such pockets. That's where we live, is in the pockets of reduced ability. 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 is, you know, the it it could very well be that everything about the world is computational, 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 probably talk about this 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 reusability. And that's that's sort of where we where we exist. And 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 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 reduced ability that it can find. You know, the motion of the planets can be more or less predicted. You know, the something about the weather is much harder to predict something about, you know, other kinds of things. The are much harder to predict.
And it's some these are. But science has tended to concentrate itself on places where its methods have allowed successful prediction.
So do you think Rule 34 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 reduced ability inside Rule 30? Yes, that is 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 you know, that is an essential thing that one would like to do in science.
But it's it's also the important thing to realize that that has not been you know, 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 computational irreducible 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 nearby and it's reducible to 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. Most likely it's going to be reduced. Most likely it will be irreducible. And what we're throwing in the world, so to speak, we you know, when we engineer things, we tend to engineer things to sort of keep in the zone of reduced ability.
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 reduced ability.
Can we talk about this pandemic then? Sure. For a second is so how do we there's obviously a huge amount of economic pain that people are feeling. There's a huge incentive and medical pain. Health is just all psychological. There's a huge incentive to figure this out, to walk along the trajectory of reducible, a reduced ability. There's a lot of disparate data. People understand generally how viruses spread, but it's very. Complicated because there's a lot of uncertainty, there's a there could be a lot of variability.
So like so many others in a nearly infinite number of variables that that represent human interaction. And so you have to figure out from the perspective of disability, figure out which variables are really important in this kind of from an epidemiological perspective. So why aren't we you kind of said that we're clearly failing. Well, I think it's a complicated thing.
So, I mean, you know, when this pandemic started up, you know, I happen to be in the middle of it being about to release this whole physics project. Yes. But I thought, you know, timing is just a little a little bizarre. But but but, you know, but I thought, you know, I should do the public service thing of trying to understand what I could about the pandemic. And, you know, we've been generating data about it and all that kind of thing.
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 and about the way immunity works and so on. And it's you know, I think what will come out 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 t 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 a disability. 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 mess of a disability.
We 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, 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, you know, when you after you've played around with sort of little programs on the computational universe, you don't have that intuition anymore.
You know, it's I always I'm always fond of saying, you know, the the computational animals are always smarter than you are, that, as 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? OK, now I can go back and 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's a hope there and like there's so many questions I want to ask yourself when you said narrative, which is really interesting. So obviously, for me, 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 reusability because we're 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 gets complicated because, you know, people want to say, explain the pandemic to me, explain what's going to happen in the future. Yes. 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 and, you know, it's similar to sort of explaining things. And I 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 in this detail and this detail, 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 it's something where, you know, there could be a big story or it could be just a zillion little details that mount up.
But OK, let's let's pretend that this pandemic, like the coronavirus, resembles something like the one the rule 30 cellular automata. OK, so, I mean, that's how epidemiologists model virus spread. Indeed, yes. There are some groups use cellular automata. Yes.
And OK, so you could say it's simplistic, but OK, let's say it is it's representative of actually what happens. You know, the the dynamic of you have a graph. It probably is closer to the hydrograph.
Yes. That's actually that's another funny thing. Yeah. As we were getting ready to release this physics project, we realized that a bunch of things we'd worked out about, about foliate of causal graphs and things were directly relevant to thinking about contact tracing. Yeah. Cell phones and so really weird. But it just feels like it feels like we should be able to get some beautiful core insight about the spread of this particular virus on the hydrograph of human civilization.
I tried. I didn't I didn't manage to figure it out. You're one person.
Yeah, but I mean, I think actually it's a funny thing because it turns out the the main model, you know, the societal model I only realized recently was invented by the grandfather of a good friend of mine from high school. So that was just you know, it's a weird thing. But the question is, you know, OK, 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. That's actually one of my kids did a study of sort of what happens on different kinds of graphs and how robust are the results of 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.
OK, 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 irreducible two 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 if there's a certain kind of from a graph perspective.
The certain kind of dynamic, the human interaction. So like large groups and small groups, I think it matters who the groups are. For example, you can imagine large depends how you define large, but you can imagine groups of 30 people.
As like as long as there are cliques or whatever, like, right, as long as the outgoing degree of that graph is small or something 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, I'm not going to Miley Cyrus concert or something like that and figuring out mathematically some nice.
See, this is an interesting piece. I mean, in you know, this is the question of what you're describing is kind of the problem of many situations where you would like to get away from computational or disability, a classic quantum physics as 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 hot heaters, 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 the you know, the all the atoms are going to line up in the bar 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? That's 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 thermodynamics is actually precisely a story of computational disability. But it is a it is already an analogy. You know, you can you can kind of see that is can you take the you know, what you're asking to do that is you're asking to go from the the kind of the mass 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 before the pandemic. Can that be extracted, do you think? Well, 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 clearly measurable mortality clothes and so on for the northern hemisphere have gone down.
But the bad news is that it could be a lot worse for future viruses. And what this pandemic revealed is were highly unprepared for the discovery of the pockets of reduced ability within a pandemic that's much more dangerous.
Well, my guess is the specific risk of viral pandemics.
You know, that the pure virology and immunology of the thing, this will cause that to advanced to the point where this particular risk is probably considerably mitigated. But, you know, it's 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 surprising to me the extent to which people 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 the stuff in the other will do this and this and this, even though from a sort of commonsense point of view, it's a little bit crazy and people are not prepared and it doesn't really work. And society as it is for people to say, well, actually, we don't really know how the science works because it well, tell us what to do. Yeah, because then.
Yeah. What's the alternative for the masses? It's difficult to sit. It's difficult to meditate on computational reduced ability. It's difficult right.
To enjoy a good dinner meal while while knowing that you know nothing about the way this is.
This is a place where, you know, this is this is what politicians and political leaders do for a living, so to speak, because you've got to make some decision about what to do. And it's somehow some narrative that 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, don't 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 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 will 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. 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 the sense that there is this phenomenon of computational disability that doesn't allow you to just sort of jump through time and say this is the answer, so to speak. 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 OK as a human civilization? He said, I don't know. Absolutely. Do you think it's do you think will prosper or destroy ourselves as a general in general?
I'm an optimist. No, I think that the you know, it'll be interesting to see, for example, with this pandemic, you know, to me, you know, when you look at like organizations, for example, you know, having some kind of perturbation, 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 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 bizarre, you know, and the fact that, you know, like this coming to see you here is the first time in six months that I've been like, you know, in a building other than my house.
OK, so so so, you know, it's 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 challenge the system. We humans emerge better.
Seems to be that way just 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, what's actually important, you know, what's what is worth caring about and so on. And that seems to be something that perhaps this is more, you know, emergent in this kind of situation.
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 a 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 of different, you know, this entire taxonomy and the viruses are thrown into the system of collective human intelligence. And the little humans figure out what to do about it.
Get like we tweet stuff about information. There's doctors as conspiracy theorists, and then we play with different information. And in the whole of it is fascinating. I like you also very optimistic, but there's a just you said the computational disability. There's always a fear of the darkness, of the uncertainty before us. Yeah, not scary. I mean, the thing is, if you knew everything, it will be boring and it would be and then 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 or disability, it's like as we live our lives, so to speak, something is being achieved. We're computing what our lives you know, you know what happens in our lives. That's fine.
And so the computational disability is kind of like it gives the meaning to life. It is the meaning of life, computational disabilities, the meaning of life. It gives it meaning. Yes.
I mean, it's it's what it's what causes it to not be something where you can just say, you know, you went through all those steps to live your life. But we already knew what the answer was. Right. Hold on one second. I'm going to use my hand. Wolfram Alpha Sunburn computation thing. So long as I can get network. Here I go. No, actually, you know what it says. Sunburn. Unlikely.
This is secure, but this is a good moment. OK. OK, well, let me just check what it thinks.
The CIA 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 use common sense? The other thing is the. Yeah, yeah. Well, we'll see. This is a huge moment.
As I say, it's how can we trust the product? Yes, we trust the planet so.
And then can be a data point.
Either way, if I'm desperately sunburned, I will send in an angry feedback because we mentioned the concept so much and a lot of people know it. But can you say what competition or disability is?
Right. So, I mean, the question is, if you think about things that happen as being computations, you think about the some process and 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 follow them many steps and you get some results. So 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 other dumb computations and smart computations, or are they somehow all equivalent? And the thing that I kind of 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 sophistication, of computational sophistication of everything.
So what does that mean? That means that, you know, you might say, gosh, I'm studying this little, tiny, tiny program on my computer. I'm studying this little thing 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 says is that doesn't work.
Our our brains are doing computations that are exactly equivalent to the kinds of computations that are being done and 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, the general case. Right. Right. But the so what has happened? You know, what science has become used to doing is using the little sort of pockets of computational reusability, which, by the way, are an inevitable consequence of computational irresistibility, that they have to be these pockets scattered around of computational reduce ability 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 fun to tell you. And if you look at ancient Babylon, they were trying to predict three kinds of things. They tried to predict 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 one. And, you know, it turns out, you know, where the planets are is is a piece of computational reusability that, you know, 300 years ago.
So we pretty much cracked. And it's been technically difficult to get all the details right. But it's basically we got that, you know, who's going to win or lose the battle? No, we didn't crack that one. That one. That's right. The game theorists are trying. And the weather, we kind of halfway.
Halfway. I think we're doing OK. That one, you know, the climate different story, but whether, you know, we're much closer on that. But do you think eventually we'll figure out the weather? So do you think eventually most things will figure out the local pockets in everything, essentially the local pockets or disability? No, I think that it's a it's an interesting question. But I think that the you know, there is an infinite collection of these local pockets will 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 reduced ability. Otherwise, you know, if we were if we were sort of existing in this kind of irreducible world, we'd never be able to have definite things to know what's going to happen.
You know, I have to say, I think one of the features, you know, when we look at 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 Pete, for instance, we say, oh, you know, the air.
And 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. And actually, I realized there's the thing I realized last week actually was 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's 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 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, 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.
That's just looks boring to us. So you're saying there's a hopeful view of the heat 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 is this is what you learn from the science hopeful message, right? I mean, this is what you kind of learn from this principle of computational equivalence. You learn it's both a a message of a sort of hope and a message of kind of, you know, you're not as special as you think you are, so to speak, 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 the special because kind of they're connected to our purposes, our ways of thinking about things and so on.
And that's some.
But so so that's very human centric. That's it is attached to this kind of thing. So let's talk a little bit of physics. Maybe let's ask 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 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, et cetera, et cetera, et cetera, any physical phenomena, any phenomena in this world, phenomenon in the universe.
But the you know, because of computational disability, it's not you know, that's not something where you say, OK, you've got the fundamental theory of everything. Then you tell me whether, you know, 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. OK. So at some moment, potentially, you say this is a rule and run this rule enough times and you will get the whole universe.
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, OK, I'm showing you this rule. You just run it only 10 to the 500 times and you'll get everything. In other words, you've kind of reduced the problem of physics to a problem of mathematics, so to speak.
It's like it's as if you'd like to generate the digits of pi. There's a definite procedure. You just generate them and be the same thing. If you have a fundamental theory of physics, of the kind 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 a universe 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 warfrom physics model, which is fascinating, but if you. If you have a simple set of rules with a with a data structure like a hyper graph.
Does that feel like a satisfying theory of everything, because then you really run up against the irresistibility competition or disability, right?
So that's a really interesting question. So 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 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 ten to the minus one hundred seconds of the universe.
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, but it wasn't obvious to me. But but 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 irresistibility that sort of these all these simple rules run into there is there are certain pieces of computational reusability 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 reduced ability 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.. 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 relativity and quantum mechanics and general relativity and quantum mechanics. Are these pockets of disability that we think of as. That 20th century physics is essentially pockets of disability, and then it is incredibly surprising that any kind of model that's generated from simple rules would have would have such pockets.
Yeah, well, I think what's surprising 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 this particular very unstructured underlying rules. And that's that's the thing that is sort of remarkable. And that's the thing to me.
That's just it's really beautiful. I mean, it's another 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 the 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 law, not from the beautiful hydrograph Wolfgramm 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 is just even definition. Yeah, yeah.
Yeah, right. So so, I mean, you know, a little bit of history, physics. Right. So so I mean, the, you know. OK, very, very quick history of this. 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 the world works. They don'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 hundreds time of Galileo and the Newton sort of the big the big idea there was, you know, the title of Newton's book, you know, could be a mathematical, 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 allows him to compute all sorts of features 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 to the level that was needed. But but but so that that had been the 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 the consequences and we say, yes, that agrees with what we actually observe in astronomy or something like this. So that tradition continued. And then the first of these two sort of great 20th century innovations was, well, the history is a little bit more complicated.
But let's say that the the the there were two quantum mechanics and generativity quantum mechanics, the kind of 1900 was kind of the very early stuff done by Planck that led to the idea of photons, particles of light. But let's let's take generativity first one. One feature of the story is that special relativity thing Einstein invented in 1935 was something which surprisingly was a kind of logically invented theory. It was not a theory. Where 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 kind of methodological structure of some of some existing theories and more in the more recent times or just been. We write down an equation and we find out that it works. So what happened there?
So there's some reasoning about that. Like the basic idea was the you know, the speed of light is appears to be constant. You know, even if you're travelling 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. 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 to be able to account for the fact that when you're going faster, it appears that, you know, length is foreshortened and time is dilated and things like this and that special relativity, that special relativity.
So then. Feinstein went on with sort of vaguely similar kinds of thinking, 1915 invents a generativity, which is the 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 does that mean? You know, you usually you think of what's the shortest distance between two points like ordinarily and on a plane and space, it's a straight line. You know, photons light goes in straight lines.
Well, then the question is, is 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. It's so, you know, Einstein's observation was maybe the physical structure of space is such that space is curved. So the shortest distance between two points, the path, the straight line and quotes won't be straight anymore. And in particular, if a if a photon is travelling near near the sun or something or if a particle is going something is travelling near the sun, maybe the shortest path will be one that is is something which looks curved to us because it seems curved to us because space has been deformed by the presence of masses so severe that that massive object.
So so the kind of the idea there is think of the structure of space as being a dynamical changing kind of thing.
But then what Einstein did was he wrote down this differential equations that basically represented the curvature of space on its response to the presence of mass and energy, and that ultimately it's connected to the force of gravity, which is one of the forces that seems to be a sign of strength to operate on a different scale than some of the other forces. So our presence here is very large. What happens there is just this this curvature of space which causes the paths of objects to be deflected.
That's what gravity does. It causes the parts of objects to be deflected. And this is an explanation for gravity, so to speak. And the surprises that from 1915 until today, everything that we've measured about gravity precisely agrees that general relativity and that some and that, you know, it wasn't clear black holes were sort of a predictable 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, you know, it turns out it was expanding and he should have just trusted the equations. And that's the lesson for for those of us interested in making fundamental theories of physics, as you should trust your theory and not try and patch it because of something that you think might be the case, that that might turn out not to be the case, even if the theory says something crazy is happening. Yeah, right. Like spending is expanding.
Right. Which is. But but but, you know, then it took until the 1940s, probably really until the 1960s, until people understood that black holes were a consequence of generativity and so on. But that's 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 the gravitational waves. You know, it all just works. So that's been kind of one pillar of the story of physics.
It's mathematically complicated to work out the consequences of relativity, but it's not there's there's no I mean, and and some things are kind of squiggly and complicated, like people believe, you know, energy is conserved. OK, well, energy conservation doesn't really work in generativity 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 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 that that theory is useful in terms of basic science and trying to understand the way black holes work, the way the creation of galaxies work, sort of all of these kind of cosmological thing, understanding what happened, like you said, at the Big Bang. Yeah, like all those kinds of or not not not at the Big Bang, actually.
Right. But the well.
Features of the expansion of the universe. Yes. I mean, 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 that dark energy, you know, et cetera, et cetera, et cetera. But but fundamentally, the the you know, the testable features of general relativity, it all works very beautifully. And it's in a sense, it is mathematically sophisticated, but it is not conceptually hard to understand in some sense.
OK, so there's general relativity. And what's a friendly neighbor like? Quantum theory, quantum mechanics. Right. So quantum mechanics, the the the sort of the way that that originated was one question was, is the world. Tenuous or is it discrete, you know, in ancient Greek times, people have been debating this, people debated it in, you know, throughout history as light made of waves, as a continuous as discrete as it made of particles corpuscles, whatever.
You know, what had become clear in the hundreds 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 it 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 discrete, what's not discrete is energy discrete, as you know, what's discrete, what's not.
And so does it have mass, those kinds of questions?
Yeah. Yeah, right. Well, there's question. I mean, for example, is mass discrete is an interesting question, which is now something we can address.
But but you know what happened in the in the coming up to the 1920s, there was this kind of mathematical theory developed that could explain certain kinds of discreetness and in particularly in features of atoms and so on. And, you know, what developed was this mathematical theory. That was the theory, the theory of quantum mechanics, theory of wavefunction, Schrödinger'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, et cetera, et cetera, et cetera.
Now, the calculations all work just great. The the question of what does it really mean is a complicated question now. I mean, to just explain a little bit historically, the you know, the early calculations of things like atoms works great, 1920s and 1930s and so on. There was always a problem. There were in quantum field theory, which is the theory of quantum mechanics. You're dealing with a certain number of at a certain number of electrons and you fixed the number of electrons.
You say I'm dealing with a two electron thing in quantum field theory, allow for particles being created and destroyed so you can imitate 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.
And that led to a lot of developments up until the 1960s of alternative ideas for how how one could understand what was happening and atomic nuclei, et cetera, et cetera, et cetera, and result. In the end, the kind of most 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, you know, a dozen decimal places, certain certain things.
You can measure them. It all works. It's all beautiful.
Now, you see, the underlying fabric is the model of that particular theory. Fields like you keep saying fields. Those are quantum fields. Those are different from classical fields are a field is something like you say 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 some 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. The quantum field is a much more mathematically elaborate kind of thing. And I should explain 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 on a definite trajectory that's has certain equations of motion. It goes in a parabola or whatever else.
And quantum mechanics, the picture is definite. Things don't happen. Instead, sort of what happens is this whole sort of structure of all, you know, many different paths being followed. And we can calculate certain aspects of what happens, certain probabilities of different outcomes and so on. And you say, well, what really happen? What's really going on? What's the sort of 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?
And that's been really, really hard for quantum mechanics. My my friend Dick Feynman always used to say nobody understands quantum mechanics, even though he made his whole career out of calculating things about quantum mechanics.
And so so it's that nevertheless, that's what the quantum field theory is very, very accurate at predicting a lot of the physical phenomena.
So it works. Yeah, but there are things about it. You know, it has certain when we apply it the standard model of particle physics, for example, we.
You know, which we apply to calculate all kinds of things that works really well, you say, well, it has certain parameters. It has a whole bunch of parameters, actually. So why is the why does the muon particle exist? Why is it two hundred and six times the mass of the electron? We don't know. No idea.
But so the standard model physics is as one of the models that's very accurate for describing three three of the fundamental forces of physics and looking at the world of the very small right. And then there's back to the neighbor of gravity with general relativity. So and then in the context of a theory of everything. What's traditionally the task of the unification of these theories?
Well, 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 some of the properties of the of the particles of gravity, the kind of mathematical tricks that get used in working things out in quantum field, they don't work. And that's some. So that's been a sort of fundamental issue.
And when you think about black holes, which are a place where sort of the the structure of space is, you know, has has sort of rapid variation and you get kind of quantum effects mixed in with effects from generativity. Things get very complicated and there are apparent paradoxes and things like that. And people have, you know, that been a bunch of mathematical developments and in physics over the last 30 years or so, which have kind of picked away at those kinds of issues and got hints about how things might work.
And but it hasn't been. You know, the other thing to realize is as far as physics is concerned, it's just like his generosity, his quantum field theory, you know, be happy. So do you think there's a quantization of gravity of 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. 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 Twista theory, it's like, 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 of 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 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, literally just got a message about one aspect of this is the 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 ten minus one hundred seconds of the universe.
And, 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 and we're not finished. But, you know, you're seeing echoes of all the disparate theories of physics in this framework. Yes. Yes.
I mean, it's a very interesting, you know, sort of history of science like phenomenon. I mean, the best analogy that I can see is what happened with the early, early days of computability and computation theory. You know, Turing machines were invented in 1936. People sort of understand computation in terms of Turing machines. But actually, there had been pre-existing theories of computation, compensators, general 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, including some very I mean, one of the things that's really interesting is one of the most abstract things that's come out of of sort of mathematics, the higher category theory, things about Infinity Group, Boyds, things like this, which to me always just seemed like they were floating off into the stratosphere. Ionosphere of mathematics turned out to be things which our sort of theory anchors down to something fairly definite and says are super relevant to the way that we can understand how physics works given.
So, by the way, just through a Harran, you've said that. 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's the of the warfrom physics model view. The universe is at least the right mountain where the right mounts. Yes, without question. So I'm 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 Wolfram Physics project, the way it approaches the world.
That's as clean, crisp and unique and powerful. So, you know, there's there's discrete nature to it. There's a hydrograph, there's a computation nature. There's a generative aspect. You start from nothing. You generate everything. What do you think the actual model is actually a really good one, or do you think this general principle of simplicity, generating complexity is the right? What aspect of the mountain? Yeah.
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 superimportant. 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 hieroglyphs. I can describe them in terms of how a Category three can describe them 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 the kind of kind of cultural mathematical resonances are a bit different. And I think it's perhaps worth sort of saying a little bit about kind of the the foundational ideas of of of, you know, of these of these models and things.
Great. So can you maybe can we like, rewind? We've talked about a little bit, but can you say, like, what the central idea is of the warfrom physics project?
Right. So so the question is, we're interested in finding sort of simple computational rule that describes a whole universe.
Isn't that just so beautiful and it's such a beautiful. That's such a beautiful idea that we can generate our universe from a form, 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 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 a universe into this tiny room, not much that we are familiar with in our universe will be obvious.
And that rule. So you don't get to fit all these parameters of the universe, all these pictures of, you know, this is how space works as a time, etc, etc., etc., you don't get to fit at all. And 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 the ruling itself because of the computation or disability is not going to tell you the story.
It's not going to give you the answer to it's not going to let you predict what you're going to have for lunch tomorrow. Right. And it's not going to let you predict basically anything about your life, about the universe. Right. 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. That's not going to be the 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 that'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 it just turned out not to be right. And 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, precise numbers. We can specify of where that point is. In fact, you know, Euclid, who kind of wrote down the original kind of assimilation of geometry back in 300 B.C. or so, 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, this indivisible, you know, infinitesimal thing. OK, 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, you know, pick any point we want and 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 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 this is where it would work up. 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 discreet, that's underlying base space. Yes, and 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 sort of theater on which the universe operates?
But can we draw a distinction between space as something that could be described by three values, coordinates and higher?
Are you using the word space more generally when you say no, I'm just talking about space, like really what we read in in the universe so that you think this 3D aspect of it is fundamental?
No, I don't think a 3D is fundamental at all, actually. I think that the what's 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 precise numbers because you can pick any point in space and you can talk about motions, any infinitesimal motion in space. And that's one continuous means.
That's what continuous means. That's what Newton invented calculus to describe this kind of continuous small variations and so on. That was that's kind of a fundamental idea from Euclid on. That's been a fundamental idea about space. And so that right or wrong? It's not right. It's not right. It's it's it's right at the level of our experience. Most of the time it's not right. But the level the machine code, so to speak. And so the idea of the simulation.
That's right. That's right.
Now the very lowest level of the fabric of the universe, at least under the the the the warfrom physics model is your senses as the square.
Right. So so now what does that mean? So it means what is space then. So in and models, the basic idea is you say there are these sort of atoms of space that 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 the 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 network, so to speak. We don't we don't have, you know, people's physical addresses. All we have is the friend network of these points.
The underlying nature of reality is kind of like a Facebook or another location where you have the friends.
Yeah, 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, you know, what seems like continuous space? Well, the answer is by the time you have ten to one hundred of these things, there are those connections can work in such a way that on a large scale, it will seem to be like continuous space and let's say three dimensions or some other number of dimensions or two point six dimensions or whatever else, because they're much, much, much, much larger.
So like the the number of relationships here we're talking about is just humongous. So the the kind of thing you're talking about is very, very, very small relative to our experience of daily life. Right.
So it's I mean, you know, we don't know exactly the size, but maybe maybe ten to the minus, maybe around ten to the minus 100 metres. So, you know, the size of to give a comparison of size of of a proton is 10 to the minus 15 metres. And so this is something incredibly tiny compared to that.
And the the idea that from that would emerge, the experience of continuous space is mind blowing. What's your intuition? Why that's possible? Like, first of all, I mean, we'll get into it, but I don't know if we will through the medium of conversation. But the construct of hypergraphia is just beautiful. Right. Sally Automator, beautiful. We'll talk about it.
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 the fact that on a large scale, continuity can arise from lots of discrete elements.
This is at some level unsurprising now, but the pixels have a very definitive structure of neighbors on a computer screen. Right. There is no. Concept of space shuttle, a space inherent in the underlying fabric of reality.
Right, right, right. So so the point is that there are cases where there are. So, for example, let's just imagine you have a square grid 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 NSW corners. Right there you have something where if you zoom out from that, it's like a computer screen.
So the relationship creates the the spatial like the relationship creates a constraint, which then in an emergent sense creates a like. Yeah. Like a basically spatial coordinate thing, even though the individual point doesn't have the individual point, doesn't know anything, it just knows what it's what its neighbors are.
They on a large scale, it can be described by saying, oh, it looks like it's, 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 sort of real set up, 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 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 every atom of space where we have these edges that go between eight of these connections that go between atoms of space. We're not saying how long these edges are. We just saying there is a connection from from this place to the from this atom to the sun.
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 outside of computer science. Let's call it a network. I think it's called a network is better. But every time I like the word graph, though, so let's define it. Let's just say the graph will use terms, nodes and edges maybe.
And it's just nodes represent and some abstract entity and then the edges represent relationships between those entities. Right, exactly. So that's what I said. So there you go. So that's the basic structure. That is that is the simplest case. The basic structure. Actually, it tends to be better to think about hyper graphs. So hyper is just instead of saying there are connections between pairs of things, we say there are connections between any number of things.
So there might be ternary edges. So instead of instead of just having two points are connected by an edge, you say three points are all associated with a hyper edge, 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 for me, you know, sort of in the history of this project, the realisation 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 hydrograph can be mapped to a graph. It's just a convenient representation. Mathematics, right? That's correct.
That's correct. But so then so OK. So the the first question, the first idea of these models of ours is space is made of these connected sort of atoms of space. The next idea is space is all there is, does nothing except for the space. So in traditional ideas and physics, people have said the space. It's kind of a background. And then this matter, all these particles, electrons, all these other things which exist in space.
Right. But in this model, one of the key ideas is does nothing except space. So in other words, everything that has that exists in the universe is a feature of this hypergrowth. So how can that possibly be? Well, the way that works is that there are certain structures in this hydrograph where you say that little twistin not a thing. We don't know exactly how this works yet. But but 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 we think of as the particles inside the space. But in fact, it's just the a space mind going, 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.
This is I'm OK, but that's space. And then there's another concept we didn't really kind of mention, but I'm thinking of. Amputation is a transformation. Let's talk about time in a second, let's let's just let's just I mean, on the subject of space, you know, there's this question of kind of what you know, there's this idea there is this type of graph. It represents space and it represents everything that's in space. The features of that hypergrowth, you can say certain features in this part.
We do know certain features of the hydrograph represent the presence of energy, for example, or the presence of mass or momentum. And we know what the features of the hydrograph that represent those things are, but it's all just the same hypergrowth. So one thing you might ask is, you know, if you just look at this hypergrowth and you say we're going to talk about sort of what the hypergrowth does, but if you say, you know, how much of what's going on in this hypergrowth is things we know and care about, like particles and atoms of electrons and all that kind of thing, and how much is just the background of space.
So it turns out so far as one rough estimate of this or everything that we care about in the universe is only one part in 10 to the 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 load that in. Its it just makes me feel so good as a human being. Well to be in the froth on the one and a 10 to the 120 or something of.
Well and also just humbling how in this mathematical framework how much work needs to be done in the infrastructure. Right. Yes. The 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 were just starting to talk a little bit about what 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 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.
And what is the rule look like in in a space of progress? Right. So what the rule says is something like if you have a little tiny piece of hydrograph that looks like this, then it will be transformed into a piece of hydrograph that looks like this. So that's all it says. It says you pick up these elements of space and you can think of these these edges, these hyper edges as being relations between elements in space, you might pick up these two relations between elements in space.
And we're not saying where those elements are, 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 into another little pattern. That's right. And then because of this, I mean, again, it's kind of similar to a cellular automaton like, yes, on paper, the ruler looks like super simple, like, yeah, OK. Yeah, the yeah. Right from the universe can be born, but like when 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 any time you match it within hydrograph.
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. OK, so so 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. 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, OK, so so this is happening sort of 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 rules somewhere, the the things to which you apply the rule, the little, you know, elements to which you apply the rule, if they if they have to be OK, well, you can think of each application of the rule as being kind of an event that happens in the universe.
And these are the inputs 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 transformation that's going to apply to that atom of space can occur. So that's the prerequisite for the event. That's right. That's right. So it that defines a kind of this sort of set of causal relationships between events.
It says this event happens. It has to have happened before this event. But that is some. But that's that's not a very limited constraint. No, it's not. And what you still get the Zaillian? That's the technical term options. That's correct.
But but OK, so this is where things get a little bit more elaborate, but they're mind blowing, so. Right.
So what happens is so the first thing you might say is, you know, let's say, well, OK, so so there's a question about the freedom of which which event to do when. Well, let me let me sort of state an answer and then explain it, OK? The the 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 relationships.
So that's that's the part that's in a certain sense is a really important one. But the fact that it sometimes doesn't matter, that's a I don't know, that's another like.
So there's this idea of what I call causal invariance. Causal variance. Exactly.
So that's really, really powerful, powerful, 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. I mean, our particular version of it is a little bit tighter than other versions, but it's basically the same idea has. 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 polynomials that are that are multiplied together.
OK, you say, well, which order should I do that? And say, 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 the mountain any order. You always got the same answer. That's a that's 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 there in random, some random order, you know, back BBB, AAA or whatever, and you have a little rule that says every time you CBA flip it around to a B, OK, 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, 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 sort of the same way I know with string string sounds obvious. That's to me a surprising. That that there is in complicated systems, obviously, with with a string, but in the hydrograph hypergraphia, the application of the rule is asynchronous rule can lead to the same results sometimes.
Yes. Yes, that is not obvious. And it was something that I sort of discovered that idea for these kinds of systems and 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. And 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 variance, it can turn out every observation made by observers of the rule can they can impose what amounts to causal and variance on the rule.
We can explain that 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 rewriting systems or maybe through improving systems and so on. But that lets let's ignore that for a second. What we can come to that later.
But it's useful to talk about observation, not just point. Not yet. It's so, so great.
So there is some concept of cosmic variance as you apply these rules in an asynchronous way. You can think of those transformations as events. So there is this hydrograph that represent space and all of these events happening in the space and the graph grows and interesting, complicated ways. And eventually the froth arises to of of what we experience as human existence.
So that's some version of the picture.
But but let's explain a little bit what's a little more detail. Right. Well, so one thing that is sort of surprising in this industry 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 space time, the sort of unified thing where space and time kind of a mixed and there's a nice mathematical formalism that in which, you know, space and time sort of appear as part of the space time continuum, the space time for vectors and things like this.
You know, we talk about 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 and this approach of mine is that in my kind of approach, space and time are really not fundamentally the same kind of thing. Space is the extension of this.
Hypergrowth time is the kind of progress of this inexorable computation of these rules getting applied to the hypergrowth. So they seem like very different kinds of things. And so that at first seems like how can that possibly be right? How can that possibly be Lorentz invariant? That's the term for things being, you know, following the rules of special relativity. Well, it turns out that when you have Kosslyn variants that and let's see, we can it's worth it's worth exploring a little bit how this works.
It's a little bit a little bit elaborate. But but the basic point is that 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 come out of this model when you're looking at large enough systems. So, so way to think about the you know, in terms of when you're looking at large enough systems. The part of that story is when you look at some fluid like water, for example, there are equations that govern the flow of water.
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 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.
And this might be a small point. There 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 hydrograph time is the evolution of this type of graph. But there's also space time that we think about and general relativity for special relativity. Like what? How does how do you go from the lowest source code of space and time? We're talking about the more traditional terminology of space.
So 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 dilapidating events, every one of those transformations of the hypergrowth happens somewhere in the hypergrowth, 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 has a causal connection. So you can make this graph of causal relationships between events. That graph of causal relationships, causal and variance 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 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 you were to see the structure. So in other words, if you were to draw that, that if you were to put that network on a picture of why 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 what the cause of graph is, is I it's kind of an observation. It's not enforced. It's just emergent from.
Well, it's a feature of of OK. So what it is characteristic, I guess, the way events happen. Right. It's an event can't happen until its input is ready. Right. And so that creates this network of causal relationships. And that's that's the causal graph. And the thing the next thing to realize is, OK, 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 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 that's just going to be like a term machine 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, it's interesting here, but but the fact is that the thing is that if I'm 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. Right. Draw the causal graph of the causal relationship between the updating Xinyu and the update in ZANMI.
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 and 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?
If there's causal inference, there's unique causal graph. So it's OK to think of what we're talking about as a hydrograph and the operations on it as a kind of touring machine with a single head, like a single guy running around updating stuff that safe to intuitively think of it this way. We 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 can you can say, OK, there is one. The reason I'm pausing for a second is that I'm wondering. Well, when you say running around, depends how far it jumps every time it runs. Yeah, that's right. But I mean, like one operation. Yeah. You can think of one operator. It's easier for the human brain to think of it that way as opposed to well, maybe it's not OK.
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 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 hundred feet away right now. You know, it's the my brain does not process very much in the time it takes light to go 100 feet.
Brain operates at a scale of hundreds of milliseconds or something like that. I don't know, Ryan. And speed of light is much faster.
Right? You know, light goes in a billionth of a second, light is going to foot. So it goes a billion feet every second.
There's a certain moms' through this conversation where I imagine the absurdity of the fact that there's two descendants of apes modeled by a hydrograph that are communicating with each other and experiencing this whole thing as a real time simultaneous update with I'm taking in photons from here right now. But there is something much, much deeper going on right here. It does have a paralyzing just. Yes, I remember that right now. I mean, you know, so.
Yes, yes. As a small little tangent, I just remembered that we're talking about I mean, this about the fabric of reality.
Right. So we've got this causal graph that represents the sort of causal relationships between all these events in the universe. 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 sort of what we define as simultaneous moments in time. So, for example, we can say, you know, we how do we set our clocks?
You know, if we've got a spacecraft landing on Mars, you know, do we say that? What time is it landing? Was it you know, even though there's a 20 minute speed of light delay or something, you know, what time do we say it landed at? How do we how do we set up sort of time coordinates 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 council simultaneous and what is 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 to space, what counts as time and so on.
That's all a bit technical. But the basic bottom line is that the this causal variance property, that means that it's always the same causal graph, independent of how you slice it with his 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, like everything around space and time that that fits this idea of the causal graph.
Right. Well, you know, one way to think about it is given that you have a basic structure that just involves updating things in in these connected updates and looking at the causal relationship 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 limits and so on implies special relativity. And so that it's kind of a not a big deal because it's kind of it's kind of a you know, it was completely obvious when you started off with saying we've got this graph, it's being updated in time, et cetera, et cetera, et cetera.
That just looks like nothing to do with special relativity. And yet you've got that. And what I mean then the thing I mean, this was stuff that I figured out back in the 1990s. The the the next big thing you get is general relativity. And so in the hypergrowth, the the sort of limiting structure, when you have a very big hypergrowth, you can think of as being just like. Water seems continuous on a large scale, so this of 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 dimensions of space that bundle of points corresponds to? And that's that's pretty easy to explain. So basically, if you say you've got a point and you look at how many neighbors does that point have? OK, imagine it's on a square grid, then we'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 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 by R-squared. So the it's the number of points that you get to goes up like the distance you've gone squared and general and dimensional space, it's part of the power.
It's the the number of points you get to if you go are steps on the graph grows like the number of steps you go to the power of the dimension. And that's that's the way that you can estimate the effect of dimension of one of these graphs. So what does that go to? So how does the dimension grow? Because, I mean, obviously the visual aspect to this type of graphs, they're often visualized in three dimensions. Right. And then there is a certain kind of structure, like you said.
I mean, a circle, the sphere, there's a planar aspect to it, a right to this graph to where it kind of almost starts creating a surface like a complicated surface. So how does that connect to affected dimension?
OK, so you can lay out the graph in such a way that the that the points in the graph that, you know, the points that are neighbors on the graph are neighbors as you lay them out 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 of everything would have to fold over a lot in two dimensions, then it's not 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 OK, since I apologize for the different tangent questions, but, you know, there's an infinite number of possible rules.
So we have to look for rules that that create the kind of structures that are reminiscent for 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? So, I mean, what you know, one of the features of computational disability is it's very you can't say in advance what's going to happen with any particular you can't say I'm going to pick these rules from this part of rules space, so to speak, because they're going to be the ones that are going to work that 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 different properties of the universe, like dimensionality, you know, instead dimensionality, features of of other features of quantum mechanics, things like that. At this point, what we've got is we've got rules that that any one of those features we can get a rule that has that feature so that we don't have the sort of the final. Here's a rule which has all of these features. We do not have that.
So if I were to try to summarize the warfrom physics project, which. Is something that's been in your brain for a long time, but really has just exploded in activity, know only just months ago. Yes. So it's an evolving thing. Next week, I'll try to publish this conversation as quickly as possible, because by the time it's published, a new things will probably have come up. So if I were to summarize it, we've talked about the basics of there's a hypergraphia represent space.
There is. Transformation's and hypergraphia represents titans of time, that progress of time, there's a cause of graft that's a characteristic of this and the basic process of science, of the art of science within the warfrom physics model is to try different rules and see which properties of physics that we know of. non-Physical theories are appear within the grasp that emerge from that rule. That's what I thought it was going to be. Oh, OK. So what? So what?
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. But in fact, we can say, given causal inference and computational or disability, 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 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 a simple mind and definitely that is not even close, what is derivation? I mean, in this case. OK, so so let me.
Interesting question. OK, so there's so one one thing in the context of competition or disability.
Right, right. So what you have to do let me 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 just as a piece of mathematics, I happen to do this from cellular automata 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.
It's just a piece of mathematics. It's not it doesn't rely on 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, et cetera, et cetera, et cetera. OK, it is a very similar derivation to derive, for example, the Einstein equations. OK, so the way that works, roughly Dunstone equations are about curvature of space, curvature of space. They 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, you know, you're making a larger and 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 as pie squared. But on the surface of the earth, because it's a sphere, it's not flat. The area of a circle isn't precisely Pyar Square. As the circle gets bigger, there is slightly smaller than you would expect from the formula Pyar Square as a little correction term.
That depends on the ratio of the size of the circle to the radius of the earth. OK, so it's the same basic thing allows you to measure from one of these type of graphs what is its effect of curvature. And so the little piece of mathematics that explains special general relativity is can map nicely to describe fundamental property of the type across the curvature. So. Special relativity is about the relationship of time to space, general relativity is about curvature and in this space represented by the type of graph.
So what is the curvature of a hypergrowth? OK, so first I have to explain what was explaining this. First thing you have to have as a notion of dimension, you don't get to talk about curvature of things. If you say, oh, it's a curved line, but I don't know what line is yet.
So what is the dimension of the hydrograph then? Where from where? We've talked about effective dimension, but.
Right. That's what that's what this is about. That's what this is about is you have your hydrograph. It's got a trillion nodes in it. Yeah. What is it roughly like is it roughly like a grid, 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 this thing I was describing, the sort of the size of a ball that you construct in the hypergrowth, that's a you just measure that you can just computed on a computer for a given hypergrowth and you can say, oh, this thing is wiggling around, but it's roughly corresponds to two or something like that, roughly corresponds to two point six or whatever.
So that's how you that's how you have a notion of dimension. And these type of groff's 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 size increase associated with dimension. It's a sort of a second order term. And in the in determining size, just like the area of a circle is roughly Pyaar squared. So it goes up like R-squared.
The two is because it's in two dimensions. But when that circle is drawn on a big sphere, the the actual formula is squared times one minus are squared over a square and some coefficient. So in other words, there's a correction to and that correction term that gives you curvature. And that correction term is what makes this hypergrowth 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 is that the way they say it should work?
And the answer is yes. And the and so how does that work?
The I mean, you're the calculation of the curvature, this type of graph first for some some set of rules.
No, it doesn't matter what the rules are. It doesn't so long as they have causal inference and computational error, disability and and they lead to finite dimensional space, non-independent dimensional space, along with the match dimensional, it can grow infinitely, but it can't be infinite dimensional.
So what is infinity dimensional hydrograph look like so that, for example, so in a tree 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've got to remember? And like a circle, you've got to square the two there on a tree. You've got two, for example, to do 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 lead to infinity dimensional hoppergrass is that? No.
OK, it's an important thing to know. Yes, it's an important thing to know. I would love to know the answer to that. But, you know, it gets a little bit more complicated because, for example, it's very possible the case that in our physical universe that the universe started infinite dimensional. And it only as it as you know, at the Big Bang, it was very likely infinite dimensional. And as far as the universe sort of expanded and cooled, its dimension gradually went down.
And so one of the bizarre possibilities, which actually they're 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 3.0 one dimensional or where it's two point nine nine dimensional. And it may be that 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 hydrograph, one of the underlying assumptions you kind of implied, but you have a sense of hope, a set of assumptions that the rules that underlie our universe or the rule that underlies the universe is static. Is that the one of the assumptions you're currently operating under? Yes, but there's a there's a footnote to that which we should get to because it requires a few more steps. Well, actually, then let's backtrack to the curvature, because we are talking about as long as it's finite dimensional.
Final dimensional computational disability and causal variants, then it follows that the 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 OK, so Einstein's equations in the simplest form, apply to the vacuum, no matter just the vacuum. And they say in particular, what they say is if you have so there's this term sic. That's a term that means shortest path comes from measuring the shortest boss on the earth.
So you look at a bunch of a bundle of joy, six, 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 joy desex, 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 ammunition. Minus a half of G.M. equals zero, which is the more mathematical version of Einstein's equations. It's a statement that's a statement of thing called the Ritchey tense as equal to zero. And that's that's Einstein's equations for the vacuum. So we get that. And 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 one of the things that we realized, you know, last late last year was that there's a very simple interpretation of energy in these models, like an energy. It's basically well, intuitively, it's the amount of activity in these hyper graphs 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 this, that the notion of space like hyper surfaces. So this is this is a there's not as scary as it sounds. The it's a it's a common notion. And generativity, the notion is you are you're defining what is a possibly what is what where in space time 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 the series of of of sort of slices through the space time, through this causal graph to represent sort of what we consider to be successive moments in time. 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 cosmos anyway.
But be that as it may, 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? And this and this hypergrowth. And the answer is there is a precise definition of that and it is the formal way to say it is. That's the flux, of course, alleges through space like hyper surfaces, the slightly less formal way to say it's basically the amount of activity, the C, the reason it gets tricky, as you might say, it's the amount of activity per unit volume in in this type of graph.
But you haven't defined what volume is.
So it's a little bit you have to the surface give some more formalism to that. Yeah. That gives a way to connect that very intuitive we should think about as the just the amount of activity. Right. So, so the amount of activity that kind of remains in one place in the hydrograph corresponds to energy, the amount of activity that is kind of where an activity here affects an activity somewhere else because corresponds to momentum. And 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 intuitive version, I'm not sure. But basically the way that things sort of stay in the same place then have activity is associated with rest mass. And so one of the things that you get to derive is equals EMC squared. That is a consequence of this interpretation of energy in terms of the way the causal graph works, which is the whole thing is sort of a consequence of this whole story about updates and hyper graphs and so on.
So can you linger on that a little bit? How do we get Eco's squared? So where does the maths come from? OK, ok. I mean, is there an intuitive. OK, first of all, you're pretty deep in the mathematical explorations of this thing right now. We're in a very we're in flux currently. So maybe you haven't even had time to think about intuitive explanations.
But yeah, I mean, this one 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 easy. So there is some concept of energy that can be generally thought of as the activity, the flux, the level, the level of changes that are occurring based on the transformations within a certain volume.
However, the heck do you find the volume? OK, so in the mass?
Well, mass is what mass is associated with, kind of the energy that does not cause you that does not somehow propagate through time. Yeah. I mean, one of the things that was not obvious in the usual formulation of special relativity is that space and time are connected in a certain way and measurement 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 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 unravelling that connection that ends up giving you the this relationship between energy and, well, its energy, momentum, mass, they're all connected and and stuff like that, hence the general relativity. You have a sense that it appears to be Bakhtin. To the fundamental properties of the way these hypergraphia evolved.
Well, I didn't yet get to so I got as far as special relativity and equals C squared, the one last step is in general relativity. 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 curvature and hyper graphs, 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.
And that sum is that have you that last piece with curvature have is that have you arrived there yet? Oh yeah.
We with a yes. And here's here's the way that we here's how we're really, really going to know we've arrived. OK, so we have the mathematical derivation. It's all fine. But but you know, mathematical derivations. OK, so one thing that sort of a a you know, we're taking this limit of what happens when you're 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 always limits. We can you know, we can try each one of them computationally and we could see what 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.
There is no rigorous version of that derivation.
So so you can't do the limits because you can't see the limits.
But the limits allow you to try to describe something, General, about the system and very, very particular kinds of limits that you need to take with these very bright.
And the limits will definitely work the way we think they work and we can do all kinds of computer. It's just a hard derivation. Yeah, it's just it's just the mathematical structure kind of, you know, ends up running right into computational or disability and you end up with a bunch of 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 while they actually use Mathematica or 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 see if they match. OK, turns out that our model gives you a direct way to do numerical relativity.
So in other words, instead of saying you start from this continuum of 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 round. We're starting from these discrete things that come from our model and we're just running big versions of a computer. And, 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 proof by compilation, so to speak, that in other words, you're taking something where, you know, we've got this description of a black hole system.
And what we're doing is we're showing that the 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 have proof compilation is a beautiful concept. In a sense, the way of doing physics with this model is by running it or compiling it. And yes. Have you thought about and these things can be very large. Is there a totally new possibilities of.
Computing hardware and computing software, which allows you to perform this kind of compilation, well, algorithms, software, hardware. So first commentors, these models seem to give one a lot of intuition about distributed computing, a lot of different intuition about how to think about parallel computation. And that particularly comes from the quantum mechanics side of things, which we didn't talk about much yet. But the question of what you know, given our current computer hardware, how can we most efficiently simulate things?
That's actually partly a story of the model itself, because the model itself has deep parallelism in it. Yes, the ways that we are 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 or what happens if this thing happens before that thing.
And we've really got you know, we have these conditions where something can race to get to the answer before another thing and you get all tangled up because you know which things are 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 new taxes and God knows what else where where you've you've 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, but all these different things happening in parallel.
And so I'm guess they have built in protection for some of the parallelism. Well, causal and variance is the built in protection.
Causal and variance is what means that even though things happen in different orders, it doesn't matter in the end, as a as a person who struggle with concurrent programming in and like Java without all the basic concepts of concurrent programming, that that if there could be built up a strong mathematical framework for causal and variance. That's so liberating. Well, that could be not just liberating, but really powerful for massively distributed computation.
Absolutely. No. I mean, you know, what's eventual consistency in industrial databases is essentially the causal invariants idea. Yeah, OK, so that's but but have you thought about, you know what, like really large simulations? Yeah.
I mean, I'm also thinking about look, the fact is, you know, I 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? And in fact, another thing that's one of these you know, I'm always embarrassed at how long it's taken 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 Grofe 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 and a certain reference frame.
It's a certain commoditization 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 there, I'm talking to you. I got way more questions than I can deal with. But or perhaps the mind's question somebody asked and read it, I think is please ask Dr.
Warfrom what are the specs of the computer running the universe. So. We're talking about specs of hardware and software for simulations of a large scale thing. What about a scale that has comparative to something that eventually leads to the two of us talking and about. Right, right. Right. So so actually, I did try to estimate that. And we got a couple more stages before we can really get to that answer because because we're we're talking about this this thing.
You know, this is what happens when you when you build these abstract systems and you're trying to explain the universe that quite a number of levels deep, so to speak.
But the you mean conceptually or like literally because you're talking about small objects and there's 10 to 20 something, right?
No, it's it's it it is conceptually. 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, similar ideas to get to the different things that correspond to physics. They're just different layers of ideas. And they are 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 we know more now, you know, every every week, basically, we know a little bit more.
And those are just layers. And the initial fundamental.
Yes, structure layers are you know, you might be asking me, you know, how do we get, you know, the difference between fermions and bosons, the difference between particles that can be all in the same state and particles that exclude each other. OK, last three days, we've kind of figured that out. OK, but and it's very interesting. It's very cool. And it's very and that those are some kind of properties at a certain level.
Layer of abstraction on. Yes.
Yes. And there's a and there's but the layers of abstraction are kind of they're compounds stacking up.
So it's difficult. But but OK. But the specs nevertheless remain the same, the specs underneath.
So 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 there. So the thing that is always the same and 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 and in a single computational step.
OK, so that's the elementary time.
So then that's or whatever that is, it's a constant it's whatever we define it because I mean, we we don't, you know, and it's all relative.
It doesn't matter. It doesn't matter what it is because we could be it could be slower. It's just a number which which we use to convert that second, so to speak, because we are experiencing things and we say this amount of time has elapsed.
So we're within this thing. So it doesn't it doesn't matter. Right. But what does matter is the ratio, what we can the ratio of the spatial distance and the type of graph to this to this moment of time. Again, that's an arbitrary thing. But we measure that in meters per 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, OK?
And so there's another there are two other levels of this. OK, so there is a thing which we can talk about, which is the maximum entanglement speed, which is a thing that happens at another level. And this whole sort of story of how these things get constructed, that's a sort of maximum speed and quantum and the space of quantum states. Just as the speed of light is a maximum speed and physical space, this is a maximum speed in the space of quantum states.
There's another level which is associated with what we call rule space, which is another one of these maximum speeds we get to this.
These are limitations on the system that are able to capture the kind of physical universe which would limit the quantum inevitable features of having a a rule that has only a finite amount of information in the room.
So long as you have a rule that only involves a a bounded amount, a limited amount of only involving a limited number of elements, a limited number of relations, it is inevitable that 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. But anyway, this is a 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? OK, so the units I'm using are Wolfram language instructions per second.
OK, because you've got to have some you know what the court computation that you're doing, they've got to be some kind of frame of reference. Right.
So because it turns out in the end, there will be that sort of an arbitrariness and the language that you use to describe the universe. So in those terms, I think it's like 10 of the 500 or from language operations per second, I think is the I think it's of that order, you know, so that's the scale of the computation. What about memory? If there's an interesting thing to say about storage and memory?
Well, there's a question of how many sort of atoms of space might there be?
You know, maybe 10 to the 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. You know, when they start to be able to be experiments done. If we're lucky, there will be experiments that can actually nail down some of these numbers. And because of computational disability, there's not much hope for very efficient compression, like very efficient representations of this question.
I mean, there's probably certain things, you know, the fact that we can deduce anything. OK, the question is how deep the reusability go. Right. OK. And I keep on being surprised that it's a lot deeper than I thought, OK? And so one of the things is 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 think a lot of really powerful shortcuts. Right. There's a bunch of sort of bulk information about the world. The thing that I'm excited about last few days, OK, is the idea of fermions versus bosons. Fundamental idea that I mean, that's 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 that useful for us to maybe first talk about how quantum mechanics or quantum mechanics into the Wolfram Physics model? Yes, let's go there. So we talked about general relativity.
Now, what what have you found for quantum mechanics right within and outside of the warfrom physics?
Right. So, I mean, the key idea of quantum mechanics is sort of 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 how those paths work. OK, so when you think about hyper graphs 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 so?
Well, it's not really defined. You can do any of a whole collection of possible sequences of updates. OK, 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. OK, so tic tac toe, you start off with some some board that says everything is blank and then somebody can put down a 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 tic tac toe 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, you know, the same configuration of the board, even though you got there in two different ways.
So 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. OK, so then the question is so that OK, so that's sort of a picture of what's going on now. You say, OK, well, quantum mechanics has all these features of, you know, all this mathematical structure and so on. How do you get that mathematical structure?
OK, a couple of a couple of things to say. So quantum mechanics is actually, in a sense, two different theories glued together. Quantum mechanics is the 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 this quantum amplitudes, which are more or less probabilities of things happening.
But yet we actually observe definite things in the world of 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 the philosophical arguments about what the measurement is. But it's not something where there's a theory of the measurement, somebody on Reddit also asked. Please ask Steven to tell his story of this, the experiment. OK, yeah, I can.
That that makes sense. Oh, it makes sense. Absolutely makes sense. Why is this like a good way to discuss a little bit.
Let me let me go let me explain a couple of things first. So so the structure of quantum mechanics is mathematically quite complicated. One of the features, let's see how to how to describe this. OK, so first point is, does 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 these you can have branch rings and you can have mergence. OK, so this property turns out causal invariance is the statement that the number of merging is equal to the number of branches.
Yeah. So in other words, every time there's a branch, eventually there will also be emerge. In other words, every time there were two possibilities. What might have happened. Eventually those will merge. Beautiful concept, by the way. So so that. So that idea. OK, so then 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 course on variants, they all imply the same thing, that I'm cheating a little bit and saying that.
But that's roughly the essence of what's going on. OK, next next thing to think about is I 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 over time. It's branching, it's merging. It's doing all these things. OK, question we can ask is if we slice it at a particular time, what do we see? And that slice represents, in a sense, something to do with the 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 and OK, we take this slice. This slice represents OK, each of these different paths corresponds to a different quantum possibility for what's happening. Right. When we take the slice, we're saying, what are the set of quantum possibilities that exist at a particular time?
And we say, slice are these. You slice the graph and then there's a bunch of leaves, a bunch of leaves, and those represent the state of things. Right. But then, OK, so the important thing that you are quickly picking up on is that 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 that 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 on 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. There's some kind of measure of distance like this and that. But what you get is by making the slice, we call it bronchial space, the space of branches.
And in the branches of space, you have a graph that represents the relationships between these quantum states and branches of space. You have this notion of distance and branch space. OK, so it's connected to quantum entanglement. Yes. Yes. It's basically the distance and branch space is kind of an entanglement distance.
So this is a very nice model, right? It is very nice. It's very beautiful. It's I mean, it's it's so clean. I mean, it's really, you know, it tells one. OK, so anyway, so then then this this branch space has the sort of map of the the entanglements between quantum states. So in physical space we have so, you know, you can say take, let's say, the causal graph and we can slice that 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 analogue because of graph for the multiverse 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 are the quantum state. OK, so now I think the next thing to say is just to mention how quantum measurement works.
So quantum measurement has to do with reference frames and bronchial space.
So OK, so measurement and 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. So we making a measurement. Based on us sitting still here, are we travelling at half the speed of light and 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 will be different depending on what reference frame we're in.
OK, so then we have this idea of quantum observation frames, which are the analogue of reference frames, but in Bronxville space. And so what happens is what we realize is that a quantum measurement is 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 coordinates. This way I'm going to understand the world by saying that quantum states and time are coordinated in this way.
And essentially what happens is that, you know, the process of quantum measurement is a process of deciding how you slice up this multi-way system in this quantum observation frames. So in a sense, the observer, the way the observer enters is by their choice of these quantum observation frames. And what happens is that the observer, because this is a gun, another stack of other concepts. But anyway, because the observer is computationally bounded, there is a limit for the type of quantum observation frames that they can construct.
Interesting. OK, so there's some constraints, some limit on. And that's the choice of observation frames, right? And by the way, I just want to mention that there's a I mean, it's bizarre, but there's a hierarchy of these things. So in an thermodynamics, the fact that we believe entropy increases, we believe things get more disordered as a consequence of the fact that we can't track each individual molecule. If we can 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, but we describe it in terms of entropy increasing and so on. And it's the same phenomenon, basically, also the consequence of computational or disability that causes us to basically be forced to conclude that definite things happen in the world, even though there's this quantum, you know, the set of all these different quantum processes that are going on.
So, I mean, I'm I'm I'm skipping a little bit. And that that's a that's a rough picture. And in the evolution of the warfrom physics project, where do you stand on some of the puzzles that are along the way?
I see you're skipping along a bunch of 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 Feynman. Nobody understands quantum mechanics, including me. OK, I'm getting to the point where I think I actually understand quantum mechanics. Might my exercise OK is can I explain quantum mechanics for real at the level of kind of middle school type explanation? 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 where I have to start talking about elaborate mathematical concepts and so on. But I think and, you know, you've got to realize that it's not self-evident that we can explain, you know, at an intuitively graspable level, something which, you know, about the way the universe works. The universe wasn't built for our understanding, so to speak.
But I think then then. OK, so another important, important idea is this idea of branch space, which I mentioned, this sort of space of quantum states. It is OK, so I mentioned Einstein's equations describing, you know, the effect of the fact of mass and energy on trajectories of particles, on desex the curvature of of a physical space is associated with the presence of energy, according to Einstein's equations. OK, so it turns out that rather amazingly, the same thing is true in broad scale space.
So it turns out the presence of energy or more accurately, Lagrangian density, which is a kind of relativistic, invariant version of energy, the presence of that causes essentially deflection of Jedi's sex in this broncho space. OK, so you might say, so what? Well, it turns out that the sort of the best formulation we have of quantum mechanics, this the Feynman to grow is a thing that describes quantum processes in terms of mathematics that can be interpreted as well in quantum mechanics, that the big thing is you get this 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 potent imaginary part. You can also think of it has a magnitude and a phase. And it people have sort of thought this 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.
OK, so what do you how do you compute things in quantum mechanics, roughly? I'm telling you, I'm getting there to be able to do this as a middle school level, but I'm not there yet. 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 travelling or something travelling through physical space, but instead it's travelling through Brunskill space.
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? OK, now the way that you these quantum amplitudes characterize kind of to what extent the thing will successfully reach some particular point in broncho space, just like physical space, you could say, oh, it had a certain velocity and it went in this direction and broncho space, there's a similar kind of concept.
Is there a nice way to visualize for me now mentally of space?
It's just you have this hypergraphia. You have this multi-way graph, it's this big branching thing, branching and merging thing, but I mean, moving through that space, I'm just trying to understand what that looks like.
You know, that is probably exponential dimensional, which makes it, again, another can of worms and understanding what's going on in that space, as in ordinary space, this hyper graph, the spatial hypergrowth limits to something which is like a manifold, like a like something like three dimensional space. Almost certainly the multi-way graph limits to a Hilbert space, which is something that I mean, it's just a weird, 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 and Brunskill space. So we know the universe is expanding in physical space, but the universe is probably also expanding in space. So that means 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 by the way, this is related to whether quantum computing can ever work and why. OK, so let me explain why. So so let's talk about. OK, so first of all, just just to finish the thought about quantum amplitudes, the incredibly beautiful thing. I've just just I'm just very excited about this. The the important goal is, is this formula that says that the amplitude, the quantum amplitude is ITER, the isOVER bar where X is the thing called the action.
And it OK, 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 jurisich in the multi-way path that is caused by this thing called the action, which is essentially associated with energy. OK, and so this is a deflection of a path and broncho space that is described by this particle, which is the thing that is the mathematical essence of quantum mechanics. Turns out that deflection is the deflection of Judy six and Broncho Space follows the exact same mathematical set up as the deflection of six and physical space, except the deflection of judicial and physical space as described with Einstein's equations, the deflection of Judy and broncho spaces defined by the Feynman pathological.
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 and physical space. Quantum mechanics is a story of essentially motion and broncho space. And the underlying equation for those two things, although it's presented differently because one's interested in different things and space based the physical space. But the underlying equation is the same. So in other words, it's the 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 I mean, that's exciting to see, to see where there 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 20th century physics, it's they just they seem so different and the fact that they're really the same, it's just really amazing, actually. I mean, you mentioned double slit experiment.
OK, so the double slit 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 there are two slits, then there's a better chance that it gets to one or the other of them.
But in quantum mechanics, there's this phenomenon of destructo interference. That means that even though there are two slits, two can lead to nothing as opposed to two, leading to more than one, 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 what essentially happens is that the the double slit experiment is a story of the interface between Brunskill space and physical space.
And what's essentially happening is that the destructive interference as the result of the two possible paths associated with photons going through those two slits, winding up at opposite ends of bronchial 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 and physical space. Is there a lot to be understood by bandshell space?
I guess, yes, as matter medically speaking.
Yes, it's a very beautiful mathematical thing and it's very I mean, by the way, this whole theory is just amazingly rich in terms of the mathematics that it says should exist. OK, so, for example, calculus, you know, is a story of infinitesimal change in integer dimensional space, one dimensional, two dimensional, three dimensional space. We need a theory of infinitesimal change in fractional dimensional and dynamic dimensional space.
No such theory exists as tools of mathematics that are near to here. Right. And this is the motivation for that action. Right. And 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 know the actual mathematics is doesn't doesn't exist. And branch space, it's actually even worse than 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. But quantum computers. OK, so the basic idea of quantum computers that 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 one after another.
And, you know, I actually worked on quantum computing a bit with Feynman back in 1981 to three, that kind of timeframe. And we have fascinating image. You, you and Feynman working on quantum computers. Well, we tried to work.
The big thing we tried to do is invent a randomness chip that would generate randomness at a high speed using quantum mechanics. And the discovery that that wasn't really possible was part of the the story of we never really wrote anything about it. I think maybe he wrote some stuff, but 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 and quantum mechanics was a serious damper on what was possible to do and sort of, you know, the possible advantages of quantum mechanics and for computing.
But anyway, so so 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 in and you might say, well, does this factor work? Does this factor work? Does this factor work in ordinary computing? It seems like we pretty much just have to try all these different factors, you know, kind of one after another.
But in quantum mechanics, you might have the idea or you can just sort of have the physics, try all of them and parallel, OK, and the you know, and there's this algorithm, Shor's algorithm, which which 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. OK, the only little footnote is you have to figure out what the answer is.
You have to measure the results. 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 OK, the standard theory of quantum mechanics does not tell you how to do that. It tells you how the branch works, but 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 times three so far and in, you know, which is kind of in this in this factorization and quantum computers. But we can 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 have seen a practical quantum computers and so on. I mean, I should say, as a very practical point, I mean, it's like should people stop bothering 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 empty, complete problem, you can reduce exponential time to polynomial time.
You know, we're not sure. 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 to do basic computing.
But so you're saying I mean, some of the models you're playing with, the indication is that to get all the shit back together and, you know, to corral everything together, to get the actual solution to the algorithm is you lose all.
You lose users, 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, we're doing proof by compilation. So we have a quantum computing framework and wolfram language, which is you standard framework that represents things in terms of the standard, 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 message they got was from somebody working on the project who has managed to compile one of the sort of a core formalism based on category theory and of core quantum formalism into multi-way systems.
So this is similar to a system of these modular graphs. Yes. So you're saying, OK, that's awesome. And then you can do all kinds of experiments and a multi-year graph.
Right. But the point is that what we're saying is the thing we've got this representation of, let's say, Shor's algorithm in terms of standard quantum gates. And it's just a pure matter of sort of computation to just say that is 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're there's a pretty good indication of how that's going to work out. And we've done, as I say, our computer experiments. We've unimpressive we've gotten to about two times 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 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 quantum brand exponential stuff being done in polynomial time and so on. The one hope, which is very bizarre, is that you can kind of piggyback on the expansion of Brunskill 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, in 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 broncho space to essentially mine the expansion of the universe and Brunskill space as a way to get sort of quantum computing for free, so to speak, just from the expansion of the universe and broncho 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 broncho space version is not as absurd and that it's actually something you can reach with physical things you can build in labs and so on. We don't know yet.
I like you were saying the branch of space might be expanding and there might be some something that could be exploited.
Right. And the same kind of way that that that you can exploit the, 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 polynomial time is not going to work for people curious to kind of learn more.
So this is more like this is not meniscal. We're going to go to elementary school for a second, maybe let's go to Moscow.
So if I were to try to maybe write a write a pamphlet. Of like Wolfram Physics Project for Dummies, a.k.a. 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. How would you go about doing that? Could you help me out a little bit? Yeah, I mean, you know, it's not really practical matter.
We have this kind of visual summary picture we made, which I think is a pretty good you know, when I try to explain this to people and, you know, it's a pretty good place to start as you got this rule. You know, you apply the rule, you're building up this big hypergrowth, 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 represents a hydrograph. Transformation of that space is kind of time, yes. And then the structure of that space and the curvature of that space has gravity that can be explained without going anywhere near quantum mechanics. I would say that's actually easier to explain than special relativity.
Also going into general. Going to curvature. Yeah, I mean, special relativity, I think is it's a little bit elaborate to explain. 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. So I think relativity is easier. Is easier. Yes. And what about what's the easiest way to reveal? I think the basic point is just the fact that there are all these different branches, that there's this kind of map of how the branches work and that I mean, I think I think actually the recent things that we have about the double slit experiment are pretty good, because you can actually see this.
You can see how the double slit phenomenon arises from just features of these graphs. Now, having said that, there is a little bit of of sleight of hand there, because the the true story of the way that the whole thing works depends on the Corden's position of bronchial space, that, for example, in our internal team, there is still a vigorous battle going on about how that works. And 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 and curves. You'll basically have a thing which is naturally two dimensional and you're sort of mapping it into one dimension with a space filling curve. And it's like, why is that? The space filling in another space falling curve? And that becomes a story about reman surfaces and things. And it's quite elaborate and but but there's a more or a little bit sleight of hand way of doing it, whether it's you know, it's surprisingly direct.
It's so question that might be difficult to answer, but 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 hypergraphia, actually. So people there just want to explore, play around with this second level as people from, say, people like me who somehow got a Ph.D. in computer science but are not physicists. 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, one, explore the beauty of it and to the the final level of contribute something. Right. Of a level of even publishable, real strong, interesting ideas at all those layers, complete beginner, you know, see person and the next person that wants to publish. Right.
I mean, I think that, you know, I've written a bunch of stuff called Jonathan Gorod, who's been a key person working on this project, has also written a bunch of stuff. And some other people started writing things, too. And he's a physicist, physicist? Well, he's also a mathematical physicist, is pretty mathematically sophisticated. He's he regularly out mathematics size as me. Yeah. Yeah. Strong mathematical physicist. Yeah. I've looked at some of the papers.
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. I've been really happy actually, that people who, you know, people seem to have grokked key points from that much deeper key points people seem to have grokked than I thought they would grok.
And then that's a kind of a long blog post that explains some of the things they talked about, like the hydrograph and the basic rules. And I don't does it I forget it doesn't have any quantum mechanics in quantum mechanics.
Yes, it does. But we know a little bit more since that blog post that probably clarifies. But that blog post does a pretty decent job. And, you know, talking about things like, again, something we didn't mention, the fact that the uncertainty principle as a consequence of curvature and bronchial space, how much physics should a person know to be able to understand the beauty of this framework and to contribute something now? OK, so I think that those are different questions.
So, I mean, I think that the why does this work? Why does this make any sense to really know that you have to know a fair amount of physics. OK, and for example, have would you say why does this work?
You're referring to the connection. Between this model and general relativity, for example, you have to understand something about general relativity. There's also a side of this where just as the pure mathematical framework is fascinating. Yes, if you throw the physics out right, then it's quite accessible to I mean, you know, 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 formal abstract ideas, but are not specialists and physics or the 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 initial momentum, Tancer kind of have to know what the initial momentum Tancer is. And that's physics. I mean, that's kind of graduate level physics, basically. And 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 in machine learning in physics in the 21st century, is it 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 month, right? I mean, so but it doesn't require necessarily like 15 years.
No, it does not. 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 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 on, makes one feel much more secure about just sort of saying this is how this works.
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 the discrete mathematics, you know, to know how things work and continuous mathematics, you have to be talking about stuff and waving your hands about things.
Whereas with discrete, discrete version, it's just like here is a picture, this is how it works. And there's no, oh, do we get the limit right to this thing that is of, you know, 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, that's just an unbelievable amount to do there. And it is very close to the surface that, as you know, high school kids, you can do experiments. It's not, 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 Marshall space.
That's an absolutely accessible thing to look at. 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 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 ten years of study to get to the point where you can do the experiments. You does a cool thing. You can do experiments. Day one basic. Right. That and that's the amazing thing about and you actually put the tools out there as beautiful and mysterious. There's still I would say maybe you can correct me. It feels like there's a huge number of low hanging fruit on the mathematical side.
It's not not the physics side, perhaps know that.
Look, on the on the OK, on the physics side, we are we're definitely in harvesting mode, you know, of which which fruit.
The low hanging ones are the low hanging fruit. 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 generativity. It's just like industrial harvesting. It's like, can we get this one, this one. This one, this one. This one. And the thing that's really, you know, interesting and satisfying and it's like, you know, is, one, climbing the right mountain does not have the right model.
The thing that's just amazing is, you know, we keep on like, are we going to get this 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. And and 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. Right. Right.
No, I mean, 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 I mean. The one thing that's so the the thing that's been was a big thing that I think we're pretty close to. I mean, I can give you a little bit of the roadmap. It's sort of interesting to see. It's like, what are particles? What are things like electrons?
How do they really work? Are you close to get think what what are you close to trying to understand? Like the atom, the electrons, neutrons, protons.
OK, so this is this is the stack. So the first thing we want to understand is. The quantization of spin, so particles this, they kind of spin, they have a certain angular momentum, that angular momentum, even though the masses of particles all over the place in the electron has a massive point, five on one a movie, the you know, the proton is 938 movie, etc., etc. They're all kind of random numbers, the the spins of all these particles that are either integers or often teachers.
And that's a fact that was discovered in the 1920s. I guess the I think that we are close to understanding why spin is quantized. And that's a and it appears to be a quite elaborate mathematical story about Homma topic groups and Twista 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 the difference between particles that are by 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 and that's what leads to phenomena like lasers where you can get sort of coherently everything in the same state. That difference is the particles of integer spin or bosons like to get together in the same state, the particles of having to just spend fermions like electrons that they tend to stay apart. And so the question is, can we can we get that in our models?
And, oh, just the last few days, I think we made I mean, I think the story of I mean, it's it's it's one of these things where really close is disconnected from reality bosons.
And so this was what what happens is what seems to happen, OK, it's, you know, subject to revision next the next few days. But what seems to be the case is that bosons are associated with essentially merging and multi-way. Groff's and fermions are associated with branching and multi-way graphs. And that essentially the exclusion principle is the fact that in broncho space, things have a certain extent in broncho space that in which things are being sort of forced apart and broncho space, whereas the case of bosons, they get they they come together and bondsteel space.
And the real question is, can we explain the relationship between that and these things called Spinner's, which are the representation of Halford's jaspin particles that have this weird feature that usually when you go around 360 degree rotation, you get back to where you started from. For España, you don't get back to where you started from. It takes 720 degrees of rotation to get back to where you started from. And we are just 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 directed hyper graphs versus undirected hypergrowth. Just think of the relationship between spinners and vectors. So which is just interesting. Yeah, that's interesting. If these are all these kind of nice properties of this multiple graphs of branching and joins us have been very mysterious.
And if that's what they turn out to be, there's going to be an easy explanation for DirecTV or Sun DirecTV. It's just and that's why there's only two different cases.
It's are spinner's important in quantum mechanics. Can you just give a.
Yeah. So Spinner's are important because they are they're the representation of electrons which have half-finished spin. They are the wave functions of electrons. Aspinall's just like the wave functions of photons, are vectors, the way functions of electrons are spinner's. And they have this property that when you rotate by by turning 60 degrees, they come back to minus one of themselves and take 720 degrees to get back to the original value. And they are a consequence of of and we usually think of of of rotation in space as being, you know, when you have this notion of rotational and variance and rotational invariants, as we ordinarily experience, it doesn't have the feature.
You know, if you go through 360 degrees, 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 Möbius strip quite a bit lately. Just for fun. Yes. Yes, it does add some funk. It has the same kind of funky properties. Yes. Right, exactly. You can have those the so-called Beltz track, which is this way of taking an extended object.
And you can see properties like Spinner's with that kind of extended object. That would be very cool if there's somehow connects the directive or some direct. I think that's what it's going to be. 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 that, you know, because, you know, I, I, I learnt physics is probably, let's say, let's say a fifth generation in the sense that, you know, if you go back to the nineteen.
Twenties and so on, there were the people who were originating quantum mechanics and so on, maybe it's a lesson that maybe I was like a a third generation or something. I don't know. But but, you know, the people from whom I learnt physics were the people who, you know, have been students of the students, of the the people who originated the current understanding of physics. And we're now at 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 the thing that's been difficult to understand for for that long. It just can't be that simple.
And why, in a sense, maybe that journey takes you a to a simple explanation. I was there all along. That's right.
I mean, 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 standard canon of physics. I knew it very well. And, you know, but then I'd been working on this kind of computational paradigm for basically forty years.
And 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. It was just when did you first try to play with the hypergrowth? So, yeah, so so what I had was, OK, so this is a gun, you know, when one always feels dumb after the fact, it's it's obvious after the fact. But but so back in the early 1990s, I realized that using Groff's 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. 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, was kind of like you can pick. It's like you couldn't pick any rule was like pick any number. But the number has to be prime was kind of like you couldn't it was kind of an awkward special constraint.
I had this trivalent Groff's Groff's with just three connections from every note. OK, so but but I discovered a bunch of stuff that I thought it was kind of inelegant. And, you know, the other piece was 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 I've been very interested in kind of simple computational frameworks for representing things and have, you know, ridiculous amounts of experience in and trying to do that. Actually, all of those trajectories of your life kind of came together. So you make it sound like you could have come up with everything you're working on now decades ago. But in reality, look, two things.
Slow 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 hyper were the key to that. And that I figured out about less than two years ago now. And the other I mean, I think so that was that was sort of a key thing.
Well, OK. So the real embarrassment of this project is that the final structure that we have, that is the foundation for this project is basically a kind of an idealized version of 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, you know, and there may be other. So we're focused on physics now, but.
I mean, that's what a new kind of science is about, same kind of stuff, and this in terms of mathematically. Well, the beauty of it. So there could be entire other kind of objects that not useful for like we're not talking about, you know, machine learning, for example. Maybe there is other variants of the hydrograph that are very useful for real.
We'll see whether the multi-way growth for machine learning system is interesting.
OK, let's leave it at that. That's conversation number three. That's. We're not going to go there right now.
But one of the things you've mentioned is. The space of all possible rules that we discussed a little bit 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? 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 universal rules. Why didn't we get what? Some incredibly complicated rules? Why do we get one of the simpler ones? And and that's the thing which, you know, in the history of science, you know, the whole sort of story of Copernicus 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 on some 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 317 out of all the infinite number of possibilities, how do we get something that small and simple? 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 it's rule number of such and such, and you just have no idea why it's like that.
OK. So then I realized it's actually more bizarre than that. OK, so we talked about Multi-way Groff's. We talked about this idea that you take these underlying transmission rules on these hyper graphs and you apply them wherever the rule can apply, you apply it. And that makes this whole multi-way graph of possibilities. OK, 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.
As you say, that's just crazy. That's way too complicated. You're never going to be able to conclude anything, OK? However, it turns out that there's some kind of variance. Yeah, yeah.
But that's so what happens is amazing. Right. So so this thing that you got, this kind of rule, 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 kosslyn variance. That's a it's an inevitable feature that it shows Kosslyn variance. 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, OK, so the basic point here is, if that's true, that would be beautiful. It is true. And it is because you you it's not just an intuition. There is no, no, no real mathematics behind this. And it's. It is. It is. OK, so here's 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 group points 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 it's also related to it also relates to computational complexity theory. It's also deeply related to the process. Nonproblem and other things like this, again, seems completely bizarre that these things are connected. But here's why it's connected to this space of all possible.
OK, so Turing Machine, very simple model of computation. You know, you just got 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 Turing machine just does that deterministically. Given the configuration of the tape, it will always do the same thing.
A nondeterministic Turing machine can have different choices that it makes at every step. Yeah. And so, you know, you know the stuff you probably teach the stuff, the it you know. So Non-Deterministic Turing 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 Turing machine, the term machine that can just do that takes any possible rule at each step. That is this real multi-way graph, the set of the set of the set of possible histories of that extreme Non-Deterministic Turing machine is a rule of multi-way graph.
Imbruglia rule rules like weird word. Yeah, it's a weird word.
Multi-way coff. OK, so this so that I'm trying to think of. I'm trying to think of the space of rules. These are basic transformations, so in the Turing 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. I'm trying to see the rules on the hypergrowth.
How rich of the programs can they be or do they all ultimately snap into something simple?
I mean, hypergrowth, that's another layer of complexity on this whole thing. You can you can think about these and translations of hyper, but term machines are a little bit think of a term machines, but they're a lot simpler. So if you look at these extreme non-deterministic machines, you're mapping out all the possible non-deterministic paths that the machine can follow. Yeah. And and if you ask the question, can you reach OK, so so a deterministic term machine follows a single path.
The non-deterministic term machine fills out this whole sort of ball of possibilities. And so then the pivot's the same 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 resolution of the P. MP problem that comes out of this. That's a sideshow.
OK, 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. OK, 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, well, OK.
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 and variance.
But what you see will be what could be completely different if you picked different reference frames. You essentially have a different description language for describing the universe. OK, so how does that 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 the 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, a metre tall, so to speak. We have brain processing speeds of about the speeds we have. We're not the size of planets, for example, where the speed of light really would matter. You know, in our everyday life, the speed of light doesn't really matter. Everything be you know, the fact the speed of light is finite is irrelevant.
It could as well be infinite. We 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 how we notice the speed of light in our sort of everyday existence. We don't really notice it. And so we have a way of describing the universe that's based on our sensory you know, our senses are these days also on the mathematics we've constructed and so on. But the realization is that it's not the only way to do it.
That will be completely, completely, utterly incoherent descriptions of the universe, which correspond to different reference frames in the sort of rules of space in the royal space. That's fascinating. So we're we have some kind of reference frame and it's really our 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 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's simple that the ruling with the universe with which you can run the universe might as well be simple. Yes, yes.
But OK, so here's another point. So this is again, this is a little bit more interesting in some ways. But but the the the OK, 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 running 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 Turing 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 these different interpretations of physics correspond to essentially running physics on different underlying, you know, thinking about the physics of running in different with different underlying rules as if different underlying computers were running them.
And but that because of computation, universality or more accurately, because of this principle of computational equivalence thing of mine, there's that they are 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, et cetera, et cetera, et cetera. 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 hyper computer that things that take an ordinary computer, an infinite time to do the hyper computer can just say, oh, I know the answer. It's this immediately. What this is saying is the universe is not a hyper computer. It's not simpler than a an ordinary Turing machine type computer. It's exactly like an ordinary Turing 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 in computational. It is this level of computational ability. And it's some kind of has that sort of the the core fact. But now, you know, this idea that you can have these different kind of rules of reference frames, this different description languages for the universe, it makes me you know, I used to think, OK, you know, imagine the aliens, imagine the extraterrestrial intelligence thing.
You know, at least they experience the same physics. And I realize this isn't true. They could have a different royal family that's so fascinating that they can end up with a a a a description of the universe that is utterly, utterly incoherent with ours. And that's also interesting in terms of how we think about while 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, we talked about how it was more based on your work with a rival. We talked about how would we communicate with alien intelligences.
Can you maybe comment on how we might how the warfrom physics project changed your view of how we might be able to communicate with alien intelligence if they showed up? Is it possible that because of our comprehension of the physics of the world might be completely different, we would just not be able to communicate? 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 think people will realize this about the time when people decide that artificial intelligence is a kind of just natural things that are like human intelligences. They'll realize that that extraterrestrial intelligences or intelligence is associated with physical systems and so on. It's all the same kind of thing. It's 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. I question whether we can align exactly I've seen with the kind of intelligence, right, so there's no systematic way of doing it. So the question is, in the space of all possible intelligence is 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, you know, 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 they'll be things that way. 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 and this other one, in fact.
OK, so this is a you know, there's this idea of algorithmic information theory. There's this question of sort of what is the when you have some something, what is the sort of shortest description you can make of it, whether that description could be saying, run this program to get the thing right. So I'm pretty sure that that the that there will be a physical possession of the idea of algorithmic information and that, OK, this is, again, a little bit bizarre.
But so I mentioned that the speed of light, maximum speed of information, transmission of physical space, there's a maximum speed of information transmission and bronchial space, which is a maximum entanglement speed. There's a maximum speed of information transmission and rubial space, which is has to do with a maximum speed of translation between different description languages. And again, I'm not fully wrapped my brain around this one.
Yeah, that one just blows my mind to think about that. But that that's getting closer to the. Yeah. The kind of intelligence. Right.
It's a and it's also a physical sensation 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 hadn't seen all this coming. I've always been a little bit resistant to the idea of connecting physical energy to things and computation theory, but I think that's probably coming. And that's what essentially at the core of the physics project is that you're connecting.
Information theory. Well, physics, its computation and computation, our physical universe. Yeah, right. I mean, the fact that the 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 S&P problem and so on is is really you know, I think that's really interesting. And the fact that. Well, OK, so this kind of brings me to one one more thing that I have in terms of the sort of unification of different ideas, which is matter mathematics.
Let's talk about that. You mentioned earlier, what the heck is mathematics? And so here's here's what has.
OK, so what is mathematics? Mathematics are sort of a lowest level, one thinks of mathematics as you have certain axioms. You say, you know, you say things like X plus, which is the same as Y plus X. That's an axiom about tradition. And then you say we've got these axioms and we and from these axioms, we derive all these theorems that fill up the literature of mathematics. The activity of mathematicians is to derive all these theorems.
Actually, the axioms 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 axioms of mathematics on basically a page and a half. Not much stuff. It's like a very simple rule from which all of mathematics arises the way it works. So it's a little different from the way things work in in sort of 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. OK, so we can we can begin to see how this is going to work. What's going to happen is there are paths and matter, mathematical space. So what happens is each two different ways to look at it. You can just look at it as a mathematical expression so you can look at it as mathematical statements, postulates or something.
But either way, you think of these things and they are connected by these axioms. So in other words, you have some fact you or you have some expression, you apply this axiom, 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. 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 Gaydos and Incompleteness Theorem. Is that natural fits naturally there.
How hard to what happens there is that the girl's theorem is basically saying that there are paths of infinite length, that is that there's no upper bound. If you know these two things you said, 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 possible length. Ten. Somebody says that's not good enough. That path might be of length a billion. And there's no upper bound on how long that path is.
And that's that's what leads them completeness theorem. So, I mean, the thing that is kind of an emerging idea is you can start asking what's the analog Einstein's equations and matter mathematical space? What's the analogue of a black hole? A matter mathematical space? What's the whole picture?
So, yeah, it's fascinating to model all mathematics and so is what it is.
This is mathematics and 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 Euclid. So Euclid very impressive. He had ten axioms. He derived four hundred and sixty five theorems. OK, his book, you know, that was was the sort of defining book of mathematics for 2000 years. So you can actually map out and I actually did this 20 years ago, but I've done it more seriously.
Now you can map out the theorem dependency of those four hundred sixty five theorems. So from the axioms you grow this graph, it's actually 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 thermonuclear. The answer is the hardest theorem is that there are five platonic solids. That turns out to be the hardest. There are many. That's actually his his last theorem and all of his books, that's the point, what's the hardness, the distance you have to travel?
Yeah, that's it's 33 steps from the longest path. And 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 Euclid's proofs to the statement, there are five platonic solids. So. Okay. So then then then the question is in what does it mean if you have this map? OK, so in a sense, this matter, mathematical space is the infrastructural space of all possible theorems that you could prove in mathematics.
That's the geometry of matter mathematics. There's also the geography of mathematics. That is where did people choose to live in space. And that's what, for example, exploring the sort of empirical matter, mathematics, Vuclip, each individual like human mathematician, you can embed them into that space.
I mean, they they represent a path and the things they do may be a set of paths. Right. So instead of axioms that are chosen. Right. So, for example, here's an example of a thing that I realized. So one of the surprising things about, well, the two surprising facts about math, one is that it's hard and the other is that it's doable. OK, so first question is, why is math hard? You know, you've got these axioms, they're very small.
Why can't you just solve every problem in math easily? Yes, just logic, right? Yeah. Well, logic happens to be a particular special case that does have certain simplicity to it. But general mathematics, even arithmetic, already doesn't have the simplicity that logic has. So why is it hard? Because of computational or disability? 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 goals theorem is the statement that could be and that the path is not a bounded length, but the fact that the path is not always compressible to something tiny as a story of computational or disability.
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 or disability and worse undecidable, let's say that is there's just no finite length path that gets you there. You know, why is mathematics doable? You know, Google 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 Fermat's last theorem is undecidable. It turned out it had a proof. It's a long, complicated proof. The twin prime conjecture might be undecidable. The Riemann 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 by the way, from my last theorem, it could be a shorter path.
Absolutely. So the notion of desex and matter mathematical space as a notion of shorters proofs and matter mathematical space, and that's a you know, human mathematicians do not find shortest paths, nor do automated theorem prove us. But the fact 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, Paloma's an automated theorem proving those are precise to the branch pairs an hour that an multi-way groff's.
Let me just finish on the way. Mathematics is doable. Yes.
The second part. Right. You know why it's hard. Why is it doable. Right. Why do we not just get lost and undesirability all the time. Yeah. So and here's another fact is in doing computer experiments and doing experimental mathematics, you do get lost. And 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, but you just pick them at random from space 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 error, disability and so on. What's happening is human mathematics is a story of building a path you started off. You're always building out on this path where you are proving things. 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, 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 the wall doing the path and the fact that you are constrained to go along that path. Is the reason you don't end up with every so often you'll see a little piece of understandability and you'll avoid that that part of the path. But that's basically the story of why human mathematics 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. You know what? Why is this relevant to anything? So. OK, 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 axiom systems of mathematics are set up to make mathematics be doable and that kind of way.
And so, in other words, in particular, I think there isn't a lot of causal variance, which I think is and this is, again, in sort of the upper reaches of mathematics and stuff that are.
It's a thing there's this thing called homophobic type theory, which is an abstract came out of Category three and it's sort of an abstraction of mathematics, mathematics itself as an abstraction, but it's an abstraction of the abstraction of mathematics. And there is a thing called the Union Valence axiom, which is a sort of a key axiom in that set of ideas. And I'm pretty sure the ugly valence axiom as equivalence causal on variance was the term used again universally.
Is that something for somebody like me accessible or that there's a statement of it that's fairly accessible? I mean, the statement of it is basically it says things which are equivalent can be considered to be identical in words, but in which space?
Yeah, it's an entire category and category thing.
So it's a it's a but I mean the thing just to give a 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 a sort of higher level than mathematics. It's where well, you just think about these mathematical objects and these categories of objects and these these Mormonism's these connections between categories. OK, so it turns out the more films and categories, at least weak categories, are very much like the paths in our hyper graphs and things.
And it turns out, again, this is this is where it all gets gets crazy. I mean, it's the fact that these things are connected. It's just bizarre. So category theory are the causal graphs are like second order category theory. And it turns out you can take the limits of infinite order category theory. So just give roughly the idea this is 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've got 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. OK, now you can define a higher order proof, which is a proof of the equivalence of those proofs. OK, so you're saying there's a path between those proofs? Essentially, yes. The path between the paths. Yeah, OK.
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 that wow, OK, path to path to impart between path, the infinite limits. That infinite limit turns out to be a parallel multiverse system. Yeah, the royal the royal motorway system, that's a fascinating thing, both in the physics world and as you're saying. Yeah, yeah, that's OK. 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 seems obvious, but I didn't see it now. But the thing which is sort of interesting to me is that there's sort of an upper reach of of mathematics, of the obstruction of mathematics. This thing there's this mathematician called growth and Deek, who's generally viewed as being sort of one of the most abstract sort of creator of the most abstract mathematics of 1970s ish time frame.
And one of the things that he constructed was this thing he called the Infinity Group, Boyd, and he has the sort of hypothesis about the inevitable appearance of geometry from essentially logic and the structure of this thing. Well, it turns out this really multi-way system is the infinity graboid. 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've been always afraid of this kind of mathematics because it seemed incomprehensibly abstract to me.
But what's what's what I'm sort of excited about with this is that that we've sort of concrete defied the way that you can reach this kind of mathematics, which makes it what both seem more relevant and also the fact that that 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 analyse what we're doing.
But the thing that's sets of both ways right now to understand what you're doing and using. Right. So you're doing computationally to understand them.
So, for example, the understanding of matter, mathematical space, one of the reasons I really want to do that is because I want to understand quantum mechanics better. And that what you see, you know, we live that 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 readily for 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 what's the analogue of Einstein's equations and 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 nonconstructive proofs and mathematics. And I think those relate to well, actually, the there are they relate to things and related to event horizons. So the fact that you can take ideas from physics like event horizon and map them into the same kind of space, it's it's really.
Do you think there will be do you think you might stumble upon some breakthrough ideas in theorem proving like four from the other direction?
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 multiple graphs. That's what if they're improvers trying to.
But I also mean like, like automated. Oh yeah.
That's what. Right. So the finding of Pardes the of shortest paths or finding a paths at all is what Automator improvers do and actually what, what we've been doing. So we've you know, we've actually been using automated they're improving both in the physics project to prove things and using that as a way to understand multi-way graphs. And because what an automated thing improver is doing is it's trying to find a path through a multi-way graph. And it's critical. Paloma's are precisely little Stobbs of branch paths going off into broncho space.
And that's I mean, it's really weird. You know, we have these visualizations and wolfram language of hour of of proof graphs from our automated through improving system. And they look reminiscent. Well, it's just bizarre because we made this up a few years ago and they have this little triangle thing and there 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 have to mention because because, um, which is which, again, we don't fully know, but it's a connection to something else you might not have thought was in the slightest bit connected, which is distributed block chain like things you might figure out that you can figure out that that's connected because because it's a story of distributed computing. Yeah. And the issue, you know, with the block chain, 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 these different transactions that are happening and you know, this transaction in country, eh, doesn't have to be reconciled with the transaction in Country B, at least not for a while. And that story. It's just like what happens when I causal graphs, that whole reconciliation thing is just like what happens with light cones and that's where the Kazimierz comes into play.
I mean, that that's you know, most of your conversations are about physics, but it's kind of funny that. This probably and possibly might have even bigger impact and revolutionary ideas and totally other disciplines, right?
Yeah, right. So the question is, why is that happening right now and the reason it's happening? I've thought about this obviously because I like to think about this matter. 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 automata as well, cellular automata and incredibly 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 automata is sort of a minimal model of, let's say, road traffic flow or something. And they're also a minimal model of something and, you know, chemistry and they're also minimal model of something and and epidemiology. But it's because that's such a simple model that they can apply to all these different things. Similarly, this model that we have, the physics project, is that there's another cellular automata, a minimal model of power of of basically of parallel computation where you've defined space and time.
These models are minimum 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.
Yeah, and but but we have all of this achievement in physics. I mean, you know, you might say, oh, you've come up with a fundamental theory of physics that throws out what people 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 this kind of brings up and you probably don't. Particularly love commenting on the work of others, but let me let me bring up a couple of personalities just because it's fun, people are curious about it.
So there's a. Sabine Hassenfeld there don't if you're familiar with her, she she wrote this book, then I need to read it, but I forgot what the title is. But it's Beauty Leads US Astray in Physics is a subtitle, something like that, which so much about what we're talking about now, like this simplification is to us humans seems to be beautiful. Like there's a certain intuition with physicists, with people that a simple theory like this reusability pockets a disability is the ultimate goal.
And I think she tries to argue is no, we just need to come up with theories that are just really good at predicting physical phenomena. It's OK to have a bunch of disparate theories as opposed to trying to chase this beautiful theory of everything is the ultimate beautiful theory, a simple one.
You know, it's always your what's your response to that? Well, so what you're quoting is, I don't know the Sabeen Hassenfeld, as you know exactly what she said, but I'm quoting the title of a book.
OK, let me let me let me respond to what you are describing, which may or may not have anything to do with what you know, what's been Hassenfeld says or thinks. I'm sorry, be the right example. Misquoting. Um, but I mean, the question is, you know, does is beauty a guide to whether something is correct, which is kind of also the story of Ockham's Razor. 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 in those 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. But, you know, in physics, does Ockham's Razor work? You know, is there a simple, quote, beautiful explanation for things or is it a big mess? You know, we don't intrinsically know.
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 rules for the universe will be. 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 that order in the universe?
Why doesn't every single particle in the universe just do its own thing? Yeah, you know, something must be making that order in the universe. We you know, 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 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? Well, 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 depends on your notion of beauty. But I mean, and for me, the the sort of the surprising connectivity of it is, at least in my aesthetic, that's something that responds to my aesthetic.
But the question is, I mean, you you're a fascinating person in the sense that you're at once talking about computation or the fundamental computation or disability of the universe. And the other hand, trying to come up with a theory of everything, which simply describes the the. The simple origins of that competition or disability, 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 it's hopeful to think like one.
We can think of a rule and that generates this whole complexity. And two, we can find pockets of reduced ability that are powerful for everyday life to do different kinds of predictions. I suppose Would wants to find focus on the finding a small pockets of a disability versus the theory of everything. You know, it's a funny thing because because, you know, a bunch of people started working on this this physics project, people who are, you know, physicists basically.
And it is really a fascinating sociological phenomenon because what you know, when I was working on this before in the 1990s, you know, wrote it up, put it it's 100 pages over this 100 page book that I wrote you kind of science. You're one hundred pages of that is about physics. But I saw 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 but then the one thing that was interesting was 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 pitch forking 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, but, you know, for a while when I started, you know, 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 building a product for a target market that doesn't want the product.
And it's like, why work the way I work against the swim, against the current or whatever.
But but you see what's happened, which is sort of interesting, is that there are a couple of things happened. And it was it was like, you know, it was like 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 you know, a 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 it's like, literally like, I don't know millions of people who are thankful for Wolfram Alpha.
A bunch of people wrote to me how thankful they are. They are different crowd than the theoretical physics community.
Perhaps you're right. But, you know, the theoretical physics community pretty much uniformly uses ah, well, from language and Mathematica.
Right. And so it's kind of like like. Yeah. You know, and that's but the thing is, it 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 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 sort of the interest and 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 related to physics to somehow somehow grown. 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 a fundamental theory of physics? It's like there are professional, no professional, no professional, no professional physicists.
What are your I mean, you've talked with him, but just as a matter of personalities, because it's a beautiful story. What are your thoughts about Eric Stein's work? You know, I think his his I mean, he did it. This is the mathematical physics, that of mathematical physics. 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 the 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 what trajectory do you hope it takes?
I mean. Well, I think in this 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 is operating in this sort of theory, theories, theories, local variance and so on. OK, we are very close to understanding how local governance works and our models. And it's very beautiful and it's very 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 station 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. Gaged theory, the standard model of particle physics says, but it's as you three cross ask you to cross you one. Those are the designations of these groups.
Doesn't. But anyway, so those are those are sort of representations of symmetries of the theory. And so, you know, it is conceivable that it is generically true. OK, so all those are subgroups of a group called Aetate, which is a weird, exceptional group. OK, it is conceivable I don't know if that's the case, that that will be generic and these models, that it will be generic, that the Gaige and variants of the model has this property, just as things like general relativity, which corresponds to the general covariance, which is another gauge like invariance, it could conceivably be the case that the kind of local Gagin variants that we see in particle physics is somehow generic.
And that would be a you know, the thing that's that's really cool. I think, you know, sociologically, although it hasn't really hit yet, is that all of these different things, all these different things people have been working on and these in some cases quite abstruse areas of mathematical physics, an awful lot of them seem to tie in to what we're doing. And, you know, it might not be that way.
Yeah, absolutely. That's a beautiful thing, I think. I mean, but the reason I say the reason it 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 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 were nearly there, you know, the world has made a platonic solids. It's, you know, water is a tetrahedron or something. We're almost there, OK, long period of time where people were like, no, we don't know how it works. You know, time of Newton, you know, we're almost there. Everything is gravitation, you know, time of Faraday and Maxwell.
We're almost there. Everything is fields'.
Everything is the ether, you know, then the whole time. 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. You know, that's what we really care about. That's what's relevant for our everyday physics. We talked about different centuries in the 21st century will be 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. 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 operating at a much higher level and it's the same. What's happening with physics is I was sort of surprised, actually.
I was sort of mapping out the history 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 then it decays and people just say, oh, it's too hard, but it's not relevant anyway. And I think that the the thing that 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 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 about what? My best guess. OK, so if you look at the history of science, I think a very interesting analogy is Copernicus.
So what did Copernicus do? There'd been this Ptolemaic system for working out the motion of planets. It did pretty well. It used epicycles, et cetera, et cetera, et cetera. It had all its computational ways of looking at what planets will be. When we work out what planets are today, we're basically using epicycles. But Copernicus 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. So it's like trust the mathematics, trust the science. OK, now fast forward 400 years and 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 Copernicus.
Nobody would have thought if the science says something that doesn't agree with our everyday experience, where we just have to compute the science and then figure out what to do, people say that's completely crazy.
And so your son says, once we figure out the framework of computation that can basically do anything, understand the fabric of reality, will be able to. Derived totally counterintuitive things, no, the point, I think, is the following that that right now, you know, I talk about computational or disability people. You know, I was I was very proud that I managed to get the term computational or disability into the Congressional Record last year. That's right.
But that's a whole nother topic, a different topic. But but in any case, you know, but so computational or disability 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 its fundamental computational, then you've routed the whole thing. But as you know, the world is computational.
And while you can discuss whether you know, it's not the case that people say, well, you have this whole computational disability, 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, based 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, Copernicus was the grounding for the idea that you could figure out something with math and 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 or disability. 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 Copernicus, for instance, the implications of his work on the 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 that that's actually the way scientists and people see the world around us? It has a huge impact in that sense. Do you think you might have an impact more directly to engineering derivations from physics like propulsion systems, our ability to colonize the world, like, for example? OK, this is like sci fi. But if you if you understand the computational nature, say, of of the different forces of physics, you know, there's there's a notion of being able to warp gravity, things like this.
Can we make warp drive? Warp drive? Yeah.
So, like, would we be able to. Well, it will, 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 create warp drive? And, you know, 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 haven't figured it out yet. But you've got two weeks, right? What do you think that kind of understanding of fundamental theory of physics can lead to those engineering breakthroughs?
OK, I think it's far away, but I'm not certain. I mean, you know, this is the thing that that I set myself an exercise when gravity waves, gravitational waves were discovered. Right. I set myself the exercise of what would hole technology look like. In other words, right now, you know, black holes are far away, that, you know, how on earth can we do things with them? But just imagine that we could get, you know, black holes right in our backyard.
You know, what kind of technology could be built with them? I got a certain distance, not that far, but I think in you know, so they're ideas. You know, I have this one of the weirder ideas is things I'm calling space tunnels, which are higher dimensional pieces of space time, where basically you can you know, in our three dimensional space, there might be a five dimensional, you know, region which actually will appear as a white hold while under the black hole at the other end, you know, who knows whether they exist?
And then the question's another one. OK, there's another crazy one. It's the thing that I'm calling a vacuum cleaner. OK, so so so I mentioned that, you know, there's all this activity in the universe which is maintaining the structure of space. Yes. And that leads to a certain energy density effectively in space. And so the question, in fact, dark energy is a story of essentially negative mass produced by the absence of energy thought would be there, so to speak.
And we don't know exactly how it works in either model or the physical universe. But this notion of a vacuum cleaner is a thing where, you know, you have all these things that are maintaining the structure of space. But what if you could clean out some of that stuff that's maintaining the structure of spacing and make a simpler vacuum somewhere? Yeah, you know, what would that do? A totally different kind of vacuum, right? Yes, the.
That would lead to negative energy density, which would need to so gravity is usually a purely attractive force, but negative mass would lead to repulsive gravity and lead to all kinds of weird things. Now, can it be done in our universe? You know, my immediate thought is no, but but, you know, the fact is that OK, so I want to understand the fact because you're saying, like, at this level of abstraction, can we reach to the lower levels and mess with it?
Yes. Once you understand the levels, I think I know. 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, more than a thousand, you know, a thousand board or something. Right. And this is why did that not happen? You know, why 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 it's the same exact story here. And 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 motion of molecules that that that is just just throw up your hands. It's just random. We can't say anything about it. That will seem naive.
Yet at the heat death of the universe, those particles would be laughing at us humans thinking, yes, right.
That life has not been socialization. You know, humans used to think they're special with their little brains. Well, right.
But but also 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, you know, possibly computational irresistibility will bite you. But then there's always some path of computation, reduced ability.
And that path of computational reduced ability is the engineering invention that has to be made. Those little pockets can have huge engineering impact. Right.
And I think that that's right. I mean, we live in you know, we make use of so many of those pockets. And the fact is, you know, I, I you know, this is yes. It's a you know, it's one of these things where where, you know, I'm 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 were like, imagine the physics of the aliens, what will it be like? And I'm like, that's really hard. I don't know, you know?
And I mean, once you have the framework in place, you can at least reason about the things you don't know. Yeah. Maybe can't know or like it's too hard for for you to know. But then the the mathematics can. That's exactly allow you to reach beyond where you can reason.
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. You know, very difficult. Very difficult. Right.
And it's a reasonable predictions, but most of it he couldn't predict possibly by the time by 1950, he was making reasonable predictions about something was not right. Not not not not when he first conceptualized, you know, and he conceptualized universal computing for a very specific mathematical reason that wasn't wasn't his general. But but, yes, it's a it's a good sort of exercise in 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 the universe.
If we know how the universe works, how can we engineer it? Such a beautiful vision. That's such a beautiful by the way, I have to mention one more thing, which is the ultimate question of from physics is, OK, so we have this abstract model of the universe. Why does the universe exist at all? Right. So, you know, we might say there is 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.
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 actualised? Why does the actual universe actually exist? And so this is this is another one of these humility. And it's like, can you figure this out? I have a guess about the answer to that. And my guess is somewhat unsatisfying. But my guess is that it's a little bit similar to Girl Second and Completeness Theorem, which is the statement that from within as an axiomatic theory, like on arithmetic, you cannot from within that theory prove the consistency of the theory.
So my guess is that four entities within the universe, there is no finite determination that can be made of the statement. The universe exists as essentially undecidable to any entity that is embedded in the universe within the universe.
How does that make you feel? 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, that there's kinds of you know, you can talk about hyper computation as well. You can say, imagine there was a hyper computer has what it would do so great. It would be lovely to have a hyper 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.
And, you know, this is all we have, so to speak. And I think it's really just a a statement. It's sort of in the end, it'll be 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 that will sort of be inevitable, that this has to be the case 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 disability, the future is ultimately not predictable for mystery. And that's what makes life worth living right?
I mean, right. And, you know, it's funny for me because as a is a pure sort of human being doing what I do. It's you know, I'm I'm you know, I like I'm interested in people I like sort of, 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 hypergrowth down there and it's all just us all the way down. Right.
Turtles all the way down. Right. And and that'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 of 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 really reference frame of, you know, this infinite creature that that is 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 it's like in the end, it's just sort of we're just happy. We're just humans thing. And 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, you know, we are just but one set of intelligence out of all these other intelligences. And so, you know, ultimately they'll be the super intelligence, which is all of these put together and will be very different from us.
No, it's actually going to be equivalent to us. And the thing that makes us a 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 that say, no, we're it.
I mean, that's that's that's the 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 and the fundamental theory of physics. And yet we're just too finite descendants of apes that have to end this conversation because darkness have come upon us.
Right. And we're going to get bitten by mosquitoes. And the symbolism of that, we're talking about the most basic fabric of reality and having to end because of the fact that things and 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.
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Connect with me on Twitter Leks Friedman. And now let me leave you with some words from Richard Feynman. Physics is the most important thing. Love is. Thank you for listening. Hope to see you next time.