Eric Weinstein Explains Octonion Numbers to Joe Rogan

And that we just, we live our lives in the most ordinary mesoscale phenomena where, you know, we don't see, we don't see the quantum because we're not, you know, playing with polarized lenses in ways that show us what light actually is. You know, we're not playing with super fluid helium. We're not understanding just how bizarre olfaction is or, you know, whether there's some sort of quantum aspect of biology. And what you see people doing is that they're, they, they start grasping for everything. Like I'm not saying that there's nothing to ancient aliens or UFOs or whatever, but a lot of that is just people want something richer and more, more amazing for their lives. And I'm not going to pass too much judgment on that, but I am going to say if we just restricted the rest of our days to the provable stuff that we know is out there, it could be amazing. People need more meaning with all of the rationality, with all of the mystery we've taken out of the world. It's time to put a ton of it back in. When you say put a ton of it back in, like how are you going to put it back in? Well, you know, if I were to start talking about the Octonians, an eight dimensional number system that no one understands, I can do that totally rigorously. I can show you all sorts of bizarre stuff involving the Octonians. What is the Octonians? Well, that's my point. You don't even know that there are four types of numbers whose dance, it's called the real numbers that we know, complex numbers that you were tortured once with in high school. Maybe during some kind of a trip, a friend of you mentioned the, mentioned the Quaternions to you. And then there's this one system of numbers, which is like the crazy relative nobody discusses, and that's called the Octonians. And the Octonians are so weird that mathematicians don't even really understand why they're there. That's an Octonian, that thing? Well, my guess is that that's probably back to the root lattice of E8, which we discussed last time, which has this kind of Mandela pattern to it. But I could show you their multiplication table. I could describe their symmetries. There's a symmetry group called G2, which involves these strange numbers. But it's a mystery. Like if I got to, I probably know more about the Octonians than most mathematicians. If I got to the end of all of my knowledge of the Octonians, I still wouldn't know what to tell you about why they're there and what they mean. Nobody knows. I promise you that. That's a real mystery. Now we could talk about it, like, you know, my friend said that that event that happened in Siberia in the early, you know, 20th century was actually an alien visitation. Well, maybe, yes, maybe, no, I don't know anything about it. If I just focused us on, like, what we know is out there that we don't grasp, which is 100% rock solid, it provides so much mystery and meaning and invitation to adventure. Like if you're looking for a hero's journey, I'll show you a ton of these things. And it's empowering. It's just incredibly, it's incredibly empowering to know that you're a hair's breath away from superpowers. So I want to help people explore that. So what is that? Like when you're explaining this, when you're saying this is bizarre series of numbers. Right. What is it doing? Like what, how do we interface with it? Well, um, so for example, let's, let's take an easier system that we feel a little bit more confident with. There's this thing called the quaternions, which are based on the number one, the complex number I, if you remember that from some distant math class, and then there's something called J and K. So I times J equals K J times K equals I J times I is equal to the negative of I times J. So negative K there's a multiplication table for these, these objects. And these objects help with computer vision, you know, computer simulation, 3d, uh, projections. They're used all the time in, um, probably video games. They may come up in nature. I mean, we know that nature uses complex numbers and most people never found out why they were being told about complex numbers or imaginary numbers because they never got to the point where you're actually looking at wave functions, uh, that describe photons and electrons and all of, all of that good stuff that you read about in physics. So in essence, um, the, the octonians are a system where I J K keeps going effectively through element on PQR, you know, until you've got eight different objects and they're not even associative, which is one of these rules that you learn about, you know, multiplication is associative. And you think, well, what isn't associative? Right? So if I, you know, if you, if you talk about commutativity, for example, I can't tell whether you put on your shirt first or your shoes first, because it's, it's commutative as to which order you did it. But if you put on your underwear in a different order than you put on your pants, it'll become immediately obvious which order you did it. Right? Okay. Well, there's another thing called associativity and it's almost everything that we deal with in elementary mathematics is associative. So you're like, why do I learn about associative? I've never met anything that isn't associative. Well, the octonians ain't associative. They're a number system that is responsible for most of the platypi of mathematics, if you will, things that just occur anomalously. So that's an example of an invitation out of this planet, you know, if you start to think about the octonians and care about them and say, are they a message? Do they have meaning? We can prove that they're there. I can construct them for you. But they generate so much bizarreness in some sort of abstract space. How would they recognize like, how, how was it? How did it come to be that this was a point of discussion? There's a process. In fact, there are two processes where you can build these number systems up from each other. So you build the complex from the real, you build the quaternions from the complex, you build the octonions from the quaternions and then you can't build anything beyond that because each time you're giving up a magical power to get to the next stage, by the time you get to the octonions, you're exhausted. When you say give me a magical power. Well, like, for example, it's very hard to think about the square root of negative one. So like, what does it mean for something squared to be negative one? So that's like the complex numbers gave up that kind of sensibility. And then the complex numbers are at least commutative, eight times B equals B times A, but the quaternions don't have that property. So then you have a further property called associativity. So you're sort of to eat to build the next system, you're giving up properties that sort of make sense to us. And by the time you've gotten to the act tonions, you've given everything away. There's no way you're going to build the next system. But yet it's real. Yes, yet it's real in a very real mathematical sense. So does it just highlight our lack of understanding? Yeah, and it is a call to adventure. It's like a message from something that isn't human. I'm not going to say that it's God. I'm not going to say that it's logic or design. But it's a more complex system of the universe. That's right. And you have to uncover that these things are there. Or for example, you know, C. elegans. I don't know if you've played with, do you know about C. elegans? No. All right, C. elegans. Do you say elegance? C. The letter. C. Elegans. Elegan. Elegans. I think it's E. Okay. So it's this worm that was chosen by this guy, Sidney Brenner, who just died. And it's a shame because he would have been a great podcast guest. Just like one of the most brilliant biologists that we didn't focus on. And he said, you know what? We're missing a species that we can completely describe. Soup to nuts. Here's the one that's about the simplest thing with the brain. It's only got a thousand cells. And 300 of those cells make up a very primitive neural system. And we're going to track where every goddamn cell, like bring up, Jamie, if I could ask you something, to bring up the cell lineage diagram for C. elegans. So this would be the first of two images. Well, that is a complete map of how one fertilized egg becomes a tiny microscopic worm for every possible division. What in the fuck am I looking at? I love when you say that. That is so wild. Yeah. Right now, here's the thing. Everyone in biology knows how cool this thing is. And very few people, not enough people outside of biology, know that we have completely mapped how one cell, like if you're 30 trillion cells around, it's too big to write a diagram. It's only possible because there are only a thousand cells and this thing has locomotion. It has sexual reproduction. You know, it eats. So you're looking at the architectural plans for an actual organism. And Jamie, when we're done with that, if I could trouble you for the folks that are just falling by kind of pause for a moment for the folks that are falling at home listening, just listening, not watching. What we're looking at, Jamie, explain how someone can see this image if they want to go with themselves. The letter C, it's not the not see like the ocean sea elegance and then that cell lineage. It looks like a really long basketball bracket. Yes. Pushed out forever. That's a good way to describe it. Yeah. So it's fucking wild. Yeah. Talk about March madness. April madness, June madness. February. It just doesn't stop. If we could bring up the wiring diagram or adjacency matrix, the C. elegans wire. All right. Yeah. Perfect. That is a complete map of the 300 neurons in the C. elegans worm, how they are wired to each other. Like that is a map of the mind of the worm. Wow. Okay. So that's the portal. That's another portal. Here's an organism, which is completely mapped and has complex behaviors. It has, I think about half the number of adult cell types that you and I have. So maybe we have like 250, like only 250 different kinds of adult cells, more or less. I don't want to get too precise about that. And yet we are like 10 trillion or 30 trillion copies of those tiny number of different types of cells. Well, I think the C. elegans has about 125 or something like that. Different cell types. And it only has 1000 cells and it's able to do most of what we're able to do. We move around, we eat, we have sex. Pretty simple life. Do you think it's ever possible? Well, I'm sure it's probably possible, but do you think in our lifetime we'll ever see a map like that of a human organism? I don't think so. But the cool thing is we have this map and we still don't understand it. Like we've got this thing dead to rights. We've got it boxed in. It can't, we know every single cell what it does. We have all the wire rings between the neurons. We still don't get it. Right. Right. So like, imagine that you're eight years old. What is that? Well, what a genius this guy, Sidney Brenner was for choosing this organism. Right? Because this organism is the simplest place to look at complex life. This image of the reconstructed biological neural networks. What? Like you're looking at... Now, we could have a discussion about some weird Peruvian structure and whether we've been visited. And I'd be up for that. I'm not going to pretend that I'm too good for it. But I know that this is real. I don't have any doubt. I'm not going to sit around asking, well, do you believe that aliens talk to the federal government in the 40s? Right. That might as well be an alien. And it's an invitation to adventure.