When people say the universe is expanding right what the fuck does that mean? make every smart every smart person says Into what? Right, you know like it's the universe. What is it expanding into right? And where's it going? right And I'm good it it doesn't make any sense because you look the Linguistics of the universe is expanding Isn't really what them but so you're saying the matter in the universe is moving outwards. Is that what the universe is expanding? No, no, what it means is The infinite universe is getting more infinite or no. So the first of all is that they took did you say that? Yeah I Was trying to because the Teva is kicking in. Yeah, so if you think about this bottle, okay, right It's the slices of the bottle that are expanding But if you think of the bottle is the universe the but the bottle isn't expanding. Hmm it's just the cross-sections that are expanding and so that's what they really mean what they really mean is something like the space-time metric on space like Cross-sections has its volume form when integrated is is higher something like that Mm-hmm some mathematical statement, but the universe is expanding is not helpful to me Like if I wasn't able to read the math, I would say I don't get it. Well, I don't get anything Quite honestly, I'm not being self-deprecating. I don't get the Big Bang. Yeah, I don't get it at all Well, okay, here's what somebody should tell you. Okay? There are two Kinds of singularities when you try to solve in Stein's field equations for gravity So gravity is a thing Einstein tells us pretty much What we think gravity is it's the curvature of space and time and when we try to solve his equations We get these black hole singularities, which called Swartz killed Singularities and let me get this initial singularity Which we associate back to the Big Bang with the Friedman Walker Robertson model in some sense. Those singularities are Indications to us that we're not at the end of physics and that Einstein's equations Aren't there aren't the real story? And so rather than sort of saying They're a pretty good model up until this point and then we kind of really don't know what happened. Then we had the observational thing that we would map to the Big Bang and then we have the model thing that we would map to the Big Bang and To be honest with you. We pretty sure that our models don't make sense past a point and now we're having this conversation Past the point where we're pretty sure they don't make sense. That would be much more honest to me but because we have this desire to To blow people's minds gratuitously and Everybody wants to how did everything begin and where are we in? Who are we and we want to sort of answer more of that than we probably should Hmm. That's an interesting way That makes sense. Like let me give you an alternate spin on quantum mechanics okay, so typically people say, you know, the mind-blowing thing about quantum mechanics is that it's probabilistic and That is kind of mind-blowing, but if you actually say it differently you say look in Classical mechanics like Newton stuff that we feel more comfortable with You have good questions and bad questions. Like if you and I go hang out at the beach and I say to you Hey, where is that wave? Concentrated at what point? Does that weight wave live? You look at me and say it's a wave it's not concentrated at a point. It's all along the shore so as a classical physicist, you say that's not a good question Eric and When I asked you a good question like How fast is that wave front moving, you know along this trajectory or something? You can give me an answer and it's definite. So as long as you ask a good question in classical mechanics You get definite answers. Mmm when you go to quantum mechanics, and you ask a good question Technically that means that the state vector is an observable of the hermitian operator representing the question never mind Funny thing happens you get deterministic answers. There's no probability involved whatsoever so if I ask a good question in quantum mechanics I have the same property that I do when I ask a good question in classical mechanics. I get a definite answer. There's no probability when I ask a bad question in quantum Instead of like classical mechanics that says, you know screw off. I'm not answering that. That's ridiculous. It's a bad question Quantum mechanics says you really want to ask me a bad question Alright, I'll give you maybe this answer and maybe that answer and here's the probability distribution that I'll actually give you either those two answers And what's more I'll even kick it into the state that I that you asked about So for example, if you ask where is that wave concentrated? So like let's say this is my coffee cup and I drop a little drop in the center of it that creates a circular wave that radiates out and I say where is the Wave concentrated well at one second it hits the coffee mug. Let's say is a big coffee cup and at one second after that It's concentrated again in the center So that becomes a good question only when the wave becomes recon --scent rated in the center of the cup. Alright But if that wave were a quantum wave I could ask where is the wave? Concentrated and with equal probability suddenly the wave will concentrate at some point along the circle That represents the wave Right. So what would your answer be then? well The point would be it'll concentrate it one of these points around the circle at random with equal With equal probability and suddenly the wave will concentrate Randomly when it's a quantum question so this is why quantum mechanics is so confusing quantum physics are so confusing to people well cuz they Hear that and they go. Okay. This is just infuse this when in my head like jello Well, that's the thing. But the point of if I if I have a wave and I slow it down I can look at a wave in a coffee mug Right and I can see that if I ask where is the wave concentrated? You would say it's concentrated at like half an inch out from the center of the cup. There's no say no No not what ring is a concentrated or what exact point it's not concentrated in exact point But that wave in quantum mechanics, which is not concentrated at an exact point Behaves differently when I ask a bad question. So the point that I'm trying to get across is Good questions have exactly the same properties in classical mechanics and quantum mechanics There's no introduction to probability theory. The weird question is why is quantum mechanics answering bad question? Well, maybe even weird a question is Not just why's is its quantum mechanics in an adolescent state of understanding I mean it is part of the problem that they don't know enough yet, and they're trying to like explain what they do know what they can prove on paper and for a person like me like well What do you know and they're like, well, we know probabilities we know this We know that and a person like me who doesn't have any studying in it just goes love What does that mean? Well, that's great So like let's say we were having a conversation about genetics and we were looking only at the DNA and we didn't see epigenetics Right in terms of like methylation patterns then you'd you'd shove everything onto DNA and maybe you had no concept of like development and The the model would work up to a point would explain why you have blue eyes or brown eyes But it wouldn't explain all sorts of other things. And so now then you over over develop that model So I think that what you're saying is really Einstein's intuition, which is I'm not saying. All right, Stein I'm not saying that this is wrong I'm saying this is incomplete and then when we finally get the answer, we're gonna say oh That's why we used to think of it in those crazy terms. Hmm. So back to gauge theory. Yeah gauge symmetry What the hell was that? All right. Well, here's the here's the craziest thing. Okay there is a very confusing visual image of the Fundamental unit that you need to appreciate what gauge symmetry is all about and I had Jamie loaded up Under the tab called planet hop and this is going to H show pfh opf What the fuck am I looking at you are looking at the most important object in the universe. What? That looks like some trippy screensaver on your laptop take another puff my friend because it's worth it this is what you're looking at is a principal fiber bundle and It's and it is the earth. Those are the continents. Well, yeah, that's the cool part about it, which is This is very confusing to figure out what you're looking at, but it's finite in other words If we stay at for an hour or two on this, and we actually answer all your questions You will actually know what a principle bundle is and you will know the arena in which gauge Theory Exists for folks at home that are just listening and they what the fuck of these guys talking about What is the name of this video Jamie? It's not a video. It's a small file on a page I typed him playing it hops and it was the first thing that showed up on math doctor on Oh dot e-d-u, okay so the extended thing planet h o PF for anybody who wants to look at this if you're just listening and you have no idea why I'm freaking out On this this was done by a friend of mine named R or Barna Tong. I actually coded the same thing up strangely enough didn't do it as brilliant a job of coloring it and it looks amazing by the way, so okay, what you're looking at is a Two-dimensional sphere that is the surface of the earth where an extra circle is included at every point on the surface of that sphere which you're now visualizing and That extra circle which would be called the fiber When you take the totality of all of those circles together one for each point on the surface of the sphere They create something called a three sphere that is all the points that are one unit of distance away from the origin in four dimensional space So that three dimensional sphere is the analog of a two-dimensional sphere sitting in three dimensional space So think about a caramel apple if you've ever made caramel apples you get a disc of caramel and you wrap it around The sphere that is the apple surface, right? So this is the three dimensional version of caramel wrapped around the 3-dimensional sphere Sitting in four dimensional space Now, do you understand any of this Jamie? I'm trying well, dude. It's totally trippy. Right? Yeah, and so we're not gonna get it completely during this session however, I think I lack the tools I Don't think so is that we lack the time? So the first thing is you are finding out that one of your friends thinks This is the most important object in the universe and you've never even heard of it Right much less know that there's one visual example. What's a fuck? How is this happening? I know exactly It does look fucking crazy well okay, this is what was discovered in the mid 1970s as the connection between Mathematics and different what we call differential geometry and the discipline of particle theory so two guys Jim Simons the world's now the world's most successful hedge fund manager and cien Yang a person who might art arguably be the world's first or second greatest living Theoretical physicist had a lunch seminar and they said why don't we figure out how do we talk to each other? and what they found out is they both had developed a version of this picture and Independently independently, so it was the Rosetta Stone that Unleashed a revolution So when Lawrence Krauss was talking to you about gauge Theory He was saying things about chess boards and you color it white and you color it black and super confusing to me I would rather your people be confused about an actual example of the object on which we do gauge theory that you can visually see hmm right now if I started to tell you what gauge theory is It's pretty simple So here's a here's a description. I never hear anyone say When you're doing differential calculus, I don't know if you remember differential calculus You're trying to figure out the slopes of lines. You draw instantaneous rise over the run So that always makes sense to people okay, I figure out how fast it's going up versus how fast it's going across But a question arises which is where do you measure the rise from? So for example, if I say what is the height of Mount Everest? Jamie will say 30 was 35,000. Yeah Something crazy like that. Well, let's just go a thousand say base. Well you get an internet connection Mistake. Yes. What do you think? I don't know if can't remember. I would say it's 35,000. What do you think? That was 29? 29 Oh tonight. No. Okay. What's the highest? What's the highest one? Is it key to all right key to the second, right? Is it as Everest the highest? Yeah Okay, so okay Everest the 29 would you say 29 39 89 look tonight above what? Sea level okay. Where is Mount Everest located the Himalayas? What is that? What see? There's no ocean it sure right. So right like we snuck in it's above sea level and there's no ocean So we start from the center of the earth. We have this structure called the geoid which is the interpolation of sea level as if sea level is if the earth was only ocean and there was no tide right and as if there's some sort of so we snuck in the reference level that's my point is that we teach these kids to repeat why it's 29,000 and change above sea level and there's no sea right so that reference level is the magic of gauge theory, right? Which is that we measure the rise over the run based on a custom Level so a level that we all agree upon. So for example, let's imagine that you and I are in some country experiencing hyperinflation Right, and I'm your boss. And you say dude. I need a raise I said well look I've told you I would hire you for you know, ten thousand dinars a month and You say yeah. I said well your salary is constant. I took the derivative of it I've paid you ten thousand ten thousand this month. So you're getting the same amount derivative equals zero. It's constant salary Now you have to come back at me in calculus and you say No I don't like your notion of the derivative because what you're doing is you're measuring the absolute number of dinars that you're paying me But what I want to do is I want to measure it in purchasing power Because I'm losing money every month that you don't increase my salary So I now come up with a version of the calculus in which Mike salary is not constant because it's being measured Relative to purchasing power rather than absolute units that's gauged Is that you're bringing in a reference level? That does the differentiation. So you're measuring rise over run by Customizing the problem. So these were two different applications of the calculus. The cheating employer says I want to go with constant dinars The gifted employee says not so fast. I know gage theory. I want to use a custom reference level, which is purchasing power Right. So it's like sneaking the geoid into tibet to measure everest. I've got my custom level. Does this make sense to you? Yes, it makes sense. Right but now explain it say what he said by the way, I mean We would need a new reference of what what you want to measure. What would no Conversation to have a rough like a flat level, right? Right, I guess yeah, it would be really difficult for me to recall a day from now Maybe the wheat? We'd might Pop a mushroom cap see what's up. It's um Still in reference to quantum physics, like how you would you gauge symmetry? Well, but like you would let's look at some more cool stuff Okay with the visual cortex because everything that we can do visually should inform what we can do Linguistically, so you should push everything into the visual realm that you can I mean by that like well, I just showed you the hopf fibration, which is the only in some sense the only Mature picture I can show you of a principle fibration in geometry or physics That is honest and has the full complexity. It's got a certain kind of knotted Ness to it it's got something that we would call curvature and it is visualizable and so It would be better that we spent, you know a day or two on this most important object which we think reality is based around and that you visually got comfortable with it and then You said okay now tell me again what gauge symmetry is and then instead of Lawrence talking about this Chessboard and the colors and all this stuff by analogy you'd actually be seeing gauge Theory visually like I could program a computer and have done so To show you visually what engaged theory is and it takes some time to sort of understand what the trippy pictures are But if let's bring up the Escher staircase And Jamie has a nice wrinkle on this that instead of using MC escher staircase He's got this animated guy just keeps going down. Hmm. All right. Now what's going on with those stairs now? The stairs are sort of an optical illusion because obviously it can't just keep going down But then you build these systems systems like rock-paper-scissors. What's the best thing to throw in rock-paper-scissors? Well, it depends on what you throw well But we should be able to agree that rock is better than scissors rock is better than sis to the paper is better than rock Right. So you go around that thing. And now the point is that you get to like rock is much better than rock, right? Yeah, that seems crazy Now that concept would be what we would call Halle Nomi The weird sentence rock is better than rock because of that going around the loot why rock is better than rock I don't get it. Well rock Scissors is better than paper right paper is better than rock So by transitivity rock is therefore better than rock because you went around the loop and came back to rock. It's like anime math Yeah, yeah, or if like your CH if you're changing Currencies and you don't spend any of it because you keep you losing using your credit card By the time you come home you have more money than when you left Because the exchange rates did some thing so that when you changed into each currency You somehow it got richer but by saying Brock is better than Rock you're denying the fact they're exactly the same Well, no, they're not you're not addressing. I just want to get to the listing that the linguistic fallacy, right? So the idea that this system here So those stairs in engage theory would be these reference levels for the derivative Mm-hmm, and you can have situations where the reference levels don't knit flatly together right mm-hmm, and so by virtue of that we would say that this system has curvature curvature is the assuredness of of these Better than transitive statements what we're looking at folks for people. Just listening. We're looking at if you've never seen those s-sure Edges those sketches. They're very strange because what there are is a bunch of staircases That appear to always be going downhill even if one of them is above the other one. It's very strange Very strange and this one we're watching an animated guy roll down this staircase Constantly, even though it really looks like somehow or another it must go up somewhere, but you don't ever see it going up But it's also a factor of the illusion of perspective and how it's drawn and and you know playing games with lines exactly, but If you do this very weird experiment, which we didn't know about until the late 50s called the Aronoff Boehm experiment if you run a Electric current through a wire that's insulated It appears not to have any electromagnetic field outside of the insulation however, if you do some sort of quantum interference experiment You can tell that there's current going through because it affects the phage phase-shift. Let's say of an electron orbiting that insulated Electromagnetic system so nobody thought that was going to happen Because they thought well an insulator would keep we thought the electromagnetic field is what determines the shift in the electron But it's insulated. So there is no electromagnetic field to worry about it turned out that it wasn't the electromagnetic field alone. It was some Previous geometric concept which was called the electromagnetic potential that determines something about the phase shift So this esther staircase in the case of electromagnetism. It's like the photons are the analog of those steps they're partially would determine the derivative operators these reference levels and again in our discussion of the Am I paying you the right amount in a hyper inflationary economy? So all of these things you're trying to figure out well, that's an optical illusion, but that effect actually occurs in some systems Not as an optical illusion. Yes, right. So this weirdness Requires a fair amount in terms of either study of math or learning visualizations, but there's no way to achieve it in my experience with linguistic communication like all the stuff that Gets said about you know The universe is expanding or let me tell you what it ciri is and why there's a reason it's confusing It's because it doesn't make any effing sense, right? I see what you're saying sort of but so this is this is Like what Fineman said if you think you know quantum physics, you don't know quantum physics Well, there's there some of that like there's you know, one of the most important things in the world is this thing called a spinner? like the electrons and the protons Correspond to things called spinners and the average person has no idea that spinners exist. What's more? Spinners have a property that when I tell it to you linguistically won't make any sense All right. Okay, let's do this with coffee Okay, so that's more. Yeah Thank you, sir. Perfect. All right, here's the problem. Okay, hold your cup. Nope. Sorry from the bottom and Here's the first challenge without spilling it. Okay. I want you and without readjusting your grip on the bottom of your cup I want you to turn your cup 360 degrees No, no, sorry turn Your fingers should not change on the cup. Okay, turn the cup 360 degrees without spilling it and try to take a sit Okay, that didn't work no now without coming back How would you take a sip if I got it all the way around that way? Yeah Mr. Jiu-jitsu, man No, no, you're gonna do it. All right, really? Yeah. Okay. Here we go. Oh, you're gonna go around so you go 360, okay All right now I'm screwed if I don't bring it back underneath oh I see so that system required 720 degrees of rotation unexpectedly. Oh, you just keep going, right? Okay Now the idea that there are objects that don't come back to themselves Under 360 degrees of rotation, but require 720 is probably something you've never thought about before in your life But without that you wouldn't have the Pauli exclusion principle, you wouldn't have the stability of matter And this thing is called the Philippine wine. Dance, Jamie. Do you want - That's not very seductive Jeff it seems like some very odd Ethnic dance. Yeah, but like maybe you could do 11th planet jiu-jitsu. Here we go So this spinner Is one of the coolest most important objects anywhere and it was discovered to be important in physics by a guy named Paul Dirac Right, it's fun. Okay. So this 720 theory Is entirely responsible for the world that we live in this is so bizarre - a little bit an animation and nobody knows about it Right, like unless you're hanging out with physicists They don't tell you that Electromagnetism has to do with the fact that there's a secret circle at every point in space and time that's invisible to you They don't tell you that there's stuff that requires 720 degrees of rotation. They just say mind-blowing stuff about whoa So what is happening in is 720 degrees of rotation in the quantum world? There's an object that is requiring this just the way the cup arm system requires 720 degrees of what object is this? It's called a spinner and That spinner is how we model the electron the neutrino porks. All that is spin oriole matter Sir that's a good long pause. I like it. Yeah and What where does this fit in in our model of the universe? Like what is the function of this? Why is it there? What is it? How do we know it's there? Well, we know it's there Because When Dirac so there was this problem with like the Schrodinger equation Schrodinger equation takes one derivative in terms of the direction of time and takes two derivatives in the direction of all the spatial directions But because Einstein told us that space and time are woven together For the theory to be relativistic You need the same number of derivatives of time as of space because space-time is sort of one kind of semi unified object Alright, that means you either have to boost the number of derivatives of time up to two to match the two derivatives in the directions Of space or you have to knock the two direct derivatives in the spatial directions down to one derivative To get it to be equal now one direction gets you to something called the klein-gordon equation What Dirac did is he took a square root of the klein-gordon equation? To get these spinners so he had these numbers He didn't understand at first that he was going to get kicked into this world of spinners he came up with a square root equation in which a times be thought to be numbers was not equal to B times it was Like equal to the negative of B times that so it's like what two numbers when you multiply them matter in which order? It wasn't numbers. It was matrices So this was one of the great insights You know rival tyne stein in terms of the depth of what it told us about the universe Most of us haven't really heard of Paul Dirac We don't realize that he has one of the three most important equations in physics now in When you say three most important important in how it's applicable to everyday life or Important in how its given us an understanding in quantum physics or important how its understand it It's it's understanding is significant to quantum physics we're talking about bedrock reality like you and I are having a conversation and if your a matrix fan and what we might call the Construct. Okay. What is the construct made of? Made, so the way I do it is I think of it as a newspaper story. There's where and when did it happen? There was who and what was involved and there's how and why okay, so where and when is space and time clearly? The who and the what to me, let's say the who is the spin Oriole stuff. It's like electrons protons neutrons quarks the stuff that we're made of and Then you and I are only able to see each other because we're passing photons back and forth Which are forced particles they're not spin oriole They come back to Themselves after 360 degrees they don't require 720 Now so this is sort of the you know If you were going to go to a play it have the the dramatic personnel of the play given to you at the beginning So this is what? this universe is it's a story about space and time where and where and when About what is in that you know? Like who are the players and what equipment are they using? that's like bosons and fermions and then there's the how and the why which is the equations and the lagrangians that govern the rules of play you know, so for example if you and I you know start go to the beach and We've got a ball and a net and you think we're gonna play volleyball and we actually somebody says no no We're gonna play CPAC tuck row, which is like volleyball played with the feet in a martial art style, which is awesome Yeah, we've showed a video in that recently sleeves from Thailand. Yeah, they're they're really good at amazing. It's amazing It's like ballet martial arts. Soccer is volleyball happening. One thing we should we should do this as a nation That's a different set of rules for a ball and a net and two teams that You could have done it one way is volleyball and you could have done it another way Is see packed up row where you're using your feet and on your hands. Mm-hmm So those that's sort of the breakdown of what a physics theory is you got to tell me where and when you have to tell me what's in the game and you got to tell me what the rules are and That's what this place is and so theoretical physics Is the most interesting of all of these fields to me not because it speaks to us about our daily lives Because it speaks to us about well, where are we? Where where is this thing taking place? So it seems to me that there's a small number of people like that are studying this stuff that are They're getting past biology. They're getting past Gravity climate change all those different variables that we're constantly dealing with and they're they're getting to the very things that make Everything and what is it under the wiring? Lift lift up the board what's going on in here, right? It's like getting to a computer down to the zero and one logic gates, right? Yeah, so that thing We've got three or four equations. We've got three or four different kinds of objects in the system We seem to be and people are gonna not like what I'm about to say But screw them we seem to be almost at the end Like these equations are so beautiful. They're so tight That it's almost most mysterious because it feels like this thing like a movie that ended prematurely How so? well When we found the Higgs particle at the LHC There wasn't anything left That needed to to close to explain the system. We know that there's dark matter out there that we don't understand We know that there's dark energy out there that we don't understand because of astronomical observations But all the stuff that we know about When you look at it and collide it at high energies and figure out what mutates into what there's nothing missing anymore. So it's like it's like You have got this odd thing where everything got very very simple very unified and it felt like we were gonna get one or two more giant unifications and the whole thing would be tied up with a bow and Right now we just don't have anything that is needed to close the system So for example when you have radioactive carbon decay What you see is that one of the neutrons flips into being a proton and it spits out an electron when it does that Right, so it's like it's like a trans Nucleon it shifts what it is okay that electron doesn't carry off enough energy to Explain how energy would be conserved there was something missing so this guy Wolfgang Pauli said I Bet there's a particle that's neutral so we can't see it that we won't leave a track in a cloud chamber It won't have any effect that we can see electromagnetically But it's carrying away some of the energy because I'm not going to give up on a conservation of energy Just because this particular process doesn't seem to conserve it and sure enough the the sneaky particle that was Spiriting away some of the energy of the system that couldn't be seen because it didn't interact electromagnetically And it didn't interact according to the strong force the only thing you could use to trap it would be the weak force and the weak force was so weak that it was very Hard to see it Okay. Well, there's no neutrino That I know of left to find there's no thing that's missing In our standard model and I'm just not satisfied. Nobody's satisfied that the play is over Why would the play be over just because we've discovered all the neutrinos? well Know it's that we had an easy job when there was stuff that was missing then you just hypothesize I bet there's some invisible thing. That's carrying away some stuff Let's go look for something that's hard to see so they find it and so they'd find Higgs So they'd find the Higgs. They find the neutrinos they find work gluon plasma no, I wasn't gonna go there but I was gonna say that they found like Alternate generations of matter so you and I are made out of the first generation of matter But there could be like alternate Joe Rogan made out of second-generation matter or third generation We don't know of any generations beyond these to hold up. Yeah, what are you talking about? So like the electron okay has it has a relative called the muon that behaves exactly like the electron except it's heavier and The up-down the up and down quarks that make up protons and neutrons have relatives called strange quarks and charmed quarks So there's like a second copy of Lego that has all the same properties as the first copy of Lego except It's at a different mass level Denser but it's a almost identical copy. Nobody wanted this thing so the famous joke is that there was this guy Isadora Ravi who was like a you know, kind of an ethnic Jew in in New York and when they found the second generation of matter he Responded as if it was a group of people at a deli and he said who ordered that, you know And so that's like that's the joke in physics who ordered that Nobody knew there was a second generation and then like then they hit their self for the head. You know, there's a third one, too everybody's just thank what Why? Where are these things coming from? so the fact that you don't know this like what a profound disconnect that you're having all these physicists on the show and These are the basic secrets that we're these are rock-solid These aren't this isn't speculative multiverse string theory woowoo, Schrodinger's cat stuff, you know, this is like this is ground truth and We don't know it And we don't know it because nobody will show you a picture of the hopf fibration Or there's a concept called the group which is how we think about symmetry that no mathematician or physicist can you know go a day without talking about groups almost and We act as if it doesn't need to be taught in high school Like it's too it'll blow your mind. We're not going to teach you that groups even exist So we've built the professional version of the subject around Objects that we don't even tell you exist when you're studying in school so though if you think about the portal story in childhood There's the story about either it's a rabbit hole or a looking-glass Or a wardrobe or platform nine and a half or whatever these things are I don't know what the Harry Potter version of it is, but How do I get from the world that I'm in? To this new amazing world and even find out that it's there and that's what I think theoretical physics has failed to do it Hasn't built a portal For most people to even understand what the issues are. What are the objects? What is the game? How close are we to understanding? what existence itself is which I think we're very very close and The square root. This was I was gonna say before about Dirac is like the most profound Object in mathematics to me and the reason is is that when I ask you what is the square root of negative 1? That is a question that can be posed entirely within the familiar. So the real the real numbers you're comfortable You know you owe money you have money, so I need plus plus 1 and minus 1 Square root understand what what what times? Itself equals my number and when you say what's the square root of negative 1 there's no answer inside of the real line But there is inside of this extension called the complex numbers. And so it's like you're in flatland And you're trying to figure out is there anything beyond flatland? So the great thing about the square root is it's a question. You can ask in flatland that gets you out of flatland Jesus you confuse the shit on me. Are you with this? I Understood that part of it. Yeah. I got understood that part. The complex numbers thing got weird wind Okay algebra, so when I so when I'm taking like rotations of the coffee cup where my arm isn't involved, right? I say okay. Is there a square root of that rotation? Like what does that even mean, dude? All right Well now I put my arm into the system and my arm plus coffee cup gives you Spinners. Oh Dude, I did not even know that spinners were here. I Did not know that any object required 720 degrees of rotation So the cup arm system, we just exhibited it you don't need to learn Clifford algebras or all of this extra jazz that would get you to spinners mathematically But you need to figure out how do I discover the War of the hidden world? And think about this from the perspective of like ayahuasca somebody takes ayahuasca and they have no idea that their brain is capable of this alternate state or LSD or five mio DMT All of these things are like panic rooms in the mind Where if you lived in a house for 20 years? You think you know your house and then one day you pull an old musty book off the shelf and suddenly the bookshelf swings open? You know and it's like holy crap. There's like a second home inside of my home Well, that's a lot of what psychedelics are like psychedelics are like square roots In that they're portals they can get you from the place that you know Into a place that you never imagined could exist do you think that the teaching of groups and a lot of these concepts in high school would Facilitate a better understanding of it from the general public and adulthood in the yellow. Yes Hell, yeah, and it would what do you think is the resistance to this? It's just too complex are not applicable to jobs You know, is that the idea behind it? It's not something that you use in everyday life so that it's just too weird to think about The fact that there's cousins to the electron that are fat. Yeah It's worse than this bodybuilder cousins. Yeah what a boycott made out of Strange quarks. Yeah, one of your cousin's is made out of laughs No, I think it's much worse than this I think that first of all people are terrified of just how smart children are and the differences between children have to be Buried so some children of graded abstraction. Mm-hmm And a lot of the kids were graded abstraction or learning disabled according to the teaching system now I personally think that most learning disabilities of a particular type are actually teaching disabilities people don't know how to teach the smartest kids and groups and things You're gonna lose some people because of the level of abstraction But you're going to get other people who have never been able to buy a base hit in mathematics Suddenly start over performing. So the problem is that when you teach this stuff It's very disruptive to notions of the hierarchy Have you thought about what are the causes of? These different levels of perception. Is it education is it genetics is it? environmental is it some sort of a Chemical balance of the mind like what do you think causes people to be more? perceptive to some of these concepts It's a good question. So the thing I just showed you with the planet Earth in a way that you've never seen it before Mm-hmm. I know of only two people who've ever created that image Well, I'm one of them Dror Biran eaten as the other Maybe there are many more but I've never heard or met them the number of people who first of all know what the hopf fibration Is I would guess is really deeply no. It is a few thousand people in the world So if none of those people are gifted at trying to visualize or none of them care and none of them program computers The number of people who could present that to the world is so small. It's such a tiny priestly class That your odds of getting anyone figuring out how to make this understandable are very small So we're talking about a very small priesthood Most of whom are too busy trying to do new research to want to care to communicate many of whom are not gifted communicators Many of us realize that we don't fully understand these things like I can I can show you spinners mathematically on a page But if you ask me in my darkest moments do I believe that man really knows what spinners are I don't think so this site There's all this stuff that to me looks like the monolith in 2001. It's just too freaky It comes out of nowhere and it's at the core of reality. Like if you really want to blow your mind Look at a tiny number tiny collection of these objects principle vibrations spinners Exceptional League groups this ei 248 dimensional monster this what is that? there's a 248 dimensional set of symmetries which seems to live only to be the symmetries of itself where everything else seems to live to symmetrize something else and No colonist we might have to spark that joint back up again. Let's do that this you know, there's this thing called the tits Freud and Thal magic square after this guy named Jacques teets and These guys Figured out how to generate these sets of symmetries of dimension 52 78 133 and 248. We don't know why they're there. They're like the platypi and Echidnas of the mathematical world. They're just different they don't seem to relate to anything else that we that we know yet and That's what's so fascinating about them and these are discovered by people that are trying to figure out the nature of reality They're discovered by people are trying to find more of these Bizarre equations, but who's who's discovering these and what's the impetus? Like what? What is well you ask very natural questions. Like you've probably seen you ever played Dungeons and Dragons as a kid luckily No, okay. Oh Well, you were beating people up. I was now beating stop it. I've seen one video Anyway, you had these died right and you know, like the cube died the tetrahedral die. What is this chamber? Pattern beyond space-time. Oh, this is my eight D surface princess my Arch-nemesis when I was telling the story last time their interest over October Yeah, Garrett Lisi Bobby took me into the jungle to meet this Sort of differential geometric warlord who lives in the north of Maui and the jungle. Yeah. Yeah. I don't remember this I do now Yeah, you got off my story man tonight. Yeah, I'm sorry. That's all right. Go for it. Here. We are again Put that back up So whoa, what is that? Well, this is this is based on the eight dimensional. I'm almost certain it's gonna be based on the eight dimensional root system So inside of the 248 dimensions, there's an eight dimensional donut called a torus like an eight tortoise and it generates this pattern and that pattern in some sense encodes the instructions for building the 248 dimensional object so somebody probably pushed an eight dimensional thing into two dimensions for your viewing pleasure and does this Accurate like when you're looking at this this image that we're seeing. Does that make sense to you? I mean I I could make I can related things that makes sense to me if the idea is you know Can I look at it the way I'd look at a barcode right say oh, it's tire done sent it. No No idea, but but this is an accurate representation if you're looking at it in two dimensions Yeah, so what what I'm what I'm trying to say is you don't even know to worry about this pattern, right? Because you've never heard that these things exist and this is like the closest that we come to you know, genuine mysticism where we have these objects if there are aliens they know about I ate Right that because II ate or the aliens What ye ate is the alien. Yeah, I've been I mean I will go to this later I don't want to interrupt your story again. I don't have an idea So what I'm trying to get at is this is the majesty and mystery of being a mathematic Mathematician or physicists these findings. So if let's just say by dungeons dragons, you're given these dice Where the normal die is always a cube? But the Platonic solids you can have an octahedron tetrahedron dodecahedron icosahedron all these There's an analogue of those five platonic solids in the next dimension up which I think are called convex polytopes So each one of those objects has an analogue one dimension op, but it was found out in the late teen 1800's that there's a new platonic solid in dimension four called the twenty four cells. You want to bring up the 24 cell? Let's find an animated video of somebody rotating this thing So like this is something that Plato knew nothing about we don't really understand what it's doing there in four dimensions these are like communications from The cosmos So this is like when Jodie Foster was in the movie contact And they were getting them signals about how to make the time machine. Maybe are the portal machine Yeah, but this is on Athena, right? This just stuff just doesn't come with an instruction manual So part of it is you can prove that these things are there and you don't know why they're there and some of them touch everything and some of them have yet to touch almost anything and it's like a communication from pure design that there is so much beautiful structure and so much grace in the universe that we're just What the fuck is is doing here? What is it? Right. Well, what is everything right? What is the whole thing? No, I mean look if you accept three-dimensional space Let's say this glass right if you accept this glass I Understand that a circle can spin the glass a circle Circles worth of symmetries tells me what to do to spin the last that's not that confusing, right? Why is there something that the analog of a circle where a circle I would call one dimensional because it's got one degree of freedom this thing is 248 dimensions and It doesn't seem to live to symmetrize it in the jargon, we would say it doesn't have a Defining representation of lower dimension So normally you have something of low dimension and you say what are its symmetries and the symmetries are of higher dimension This thing seems like the first thing it wants to symmetrize is itself So it's kind of self referential it's kind of onin istic So it's like a zero point of creation That's poetic language and I would groove on that after 11:00 p.m. But I wouldn't call it that right now I would say it's like it So I was trying to pick somebody up. Hey zero point of creation, right? That's a sexy word Yes a sexy car but like if we're saying the Big Bang existed and that means Some point in the history of the universe it was this really tiny thing and it decided for whatever reason Something happened, right and it became this enormous thing sure impossibly enormous thing yeah, it had there had to be a point where it started right but So what I would say is we can competently take that story back to a point. Mm-hmm And then we have to say we don't really believe that we have any insight beyond that point But people want to go there. Anyway, we absolutely know that it was tiny. Yeah small like Smaller than the head of a pin the whole thing I'm always uncomfortable things right when we settle but in life you can you can say a consensus you can say a lot of Stuff about very early very small and it could that could turn out to be wrong you know possibly long ago 14 billion years ago in our minds as far as off for a guy like you Mathematics you see it on number many numbers and paper it all computes You see the numbers 14 billion is a number that makes sense push but conceptually, yeah Like for a dummy like me 14 billion is like if I really if I'm being honest do I really do you think I really have an accurate understanding what 14? Billion and no, but but it's the Weinberg doesn't feel 14 billion either Right, but you know, we're 100 yds is so hundreds in you can feel that right. I see a hundred yards I'm like, that's too far to shoot a bow Yeah, like you got to get a little closer to be so you have some you have some kind of an intuition pump well You know Distance it's a rational distance that you see in a daily basis A hundred yards is a long distance a mile gets a little weird. Like, is that a mile away? How far is that? Oh, it's six miles away. Wow. I didn't think it was that far, right? there's there's weirdness in distance, right but when you get to a hundred and forty million miles Okay. Yeah, I give up but you get to Fort I get Patil by the year. Yeah, I get fatigued by that stuff So other people get energized like yeah, man, you have no idea how long it's humbling, right? But the length is the concept of infinite. Yeah, right like this is one of the things that Kraus said or maybe with Sean Carroll that said it's really not that we Know that we can see 14 billion years ago, right? It's like but that's just as far back as we're capable of seeing right now And even if we did go further the light is actually moving slower Like you wouldn't be able to see it Right, right, right. So you have this thing about with the space-time metric which sort of how things are Feel like they're moving apart. Yeah, just you know Einstein said four degrees of freedom plus rulers and protractors equals space-time Mm, right so a space-time metric is a collection of rulers and protractors so I can do length and angle including length in the time direction and That generates a derivative operator Which we talked about before which is rise over run relative to a custom reference level the custom reference levels generate the Esther staircase that we did and That generates the curvature tensor which generates gravity. So strangely with all of this kind of like Woowoo stuff that we've been doing we just came to a much better description of what? Theoretical physics actually looks like it's four degrees of freedom plus rulers and protractors gives you derivative operators with custom reference levels The custom reference levels don't knit together that leads to an Escher staircase The degree of Usher nests is the curvature tensor the curvature generates the gravity which is what's keeping you and I in our chair
