Grant Sanderson: Math, Manim, Neural Networks & Teaching with 3Blue1Brown | Lex Fridman Podcast #118

The following is a conversation with Grant Sanderson, his second time on the podcast. He's known to millions of people as the mind behind 3Blue1Brown, a YouTube channel where he educates and inspires the world with the beauty and power of mathematics. Quick summary of the sponsors, Dollar Shave Club, DoorDash, and Cash App. Click the sponsor links in the description to get a discount and to support this podcast, especially for the two new sponsors, Dollar Shave Club and DoorDash. Let me say as a side note, I think that this pandemic challenged millions of educators to rethink how they teach, to rethink the nature of education. As people know, Grant is a master elucidator of mathematical concepts that may otherwise seem difficult or out of reach for students and curious minds. But he's also an inspiration to teachers, researchers, and people who just enjoy sharing knowledge, like me, for what it's worth. It's one thing to give a semester's worth of multi-hour lectures. It's another to extract from those lectures the most important, interesting, beautiful, and difficult concepts and present them in a way that makes everything fall into place. That is the challenge that is worth taking on. My dream is to see more and more of my colleagues at MIT and world experts across the world summon their inner 3Blue1Brown and create the canonical explainer videos on a topic that they know more than almost anyone else in the world. Amidst the political division, the economic pain, the psychological medical toll of the virus, masterfully crafted educational content feels like one of the beacons of hope that we can hold onto. If you enjoy this thing, subscribe on YouTube, review it with 5 Stars on Apple Podcast, follow on Spotify, support on Patreon, or connect with me on Twitter at Lex Friedman. Of course, after you go immediately, which you already probably have done a long time ago, and subscribe to 3Blue1Brown YouTube channel, you will not regret it. 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Now that I can do a read for them just like Joe did all those years ago. For the most part, I've just used the razor and the refills, but they encouraged me to try the shave butter, which I've never used before. So I did, and I love it. Not sure how the chemistry of it works out, but it's translucent somehow, which is a cool new experience. Again, try the Ultimate Shave Starter Set today for just five bucks, plus free shipping at dollarshaveclub.com slash Lex. This show is also sponsored by DoorDash. Get five bucks off and zero delivery fees on your first order of $15 or more when you download the DoorDash app and enter code Lex. I have so many memories of working late nights for a deadline with a team of engineers and eventually taking a break to argue about which DoorDash restaurant to order from. And when the food came, those moments of bonding, of exchanging ideas, of pausing to shift attention from the programs to the humans were special. These days, for a bit of time, I'm on my own, sadly, so I miss that camaraderie. But actually, DoorDash is still there for me. There's a million options that fit into my keto diet ways. Also, it's a great way to support restaurants in these challenging times. Once again, download the DoorDash app and enter code Lex to get five bucks off and zero delivery fees on your first order of $15 or more. Finally, this show is presented by Cash App, the number one finance app in the App Store, when you get it, use code LexPodcast. Cash App lets you send money to friends, buy Bitcoin, and invest in the stock market with as little as $1. It's one of the best design interfaces of an app that I've ever used. To me, good design is when everything is easy and natural. Bad design is when the app gets in the way, either because it's buggy or because it tries too hard to be helpful. I'm looking at you, Clippy. Anyway, there's a big part of my brain and heart that love to design things and also to appreciate great design by others. So again, if you get Cash App from the App Store, Google Play, and use code LexPodcast, you get $10, and Cash App will also donate $10 to FIRST, an organization that is helping to advance robotics and STEM education for young people around the world. And now, here's my conversation with Grant Sanderson. You've spoken about Richard Feynman as someone you admire. I think last time we spoke, we ran out of time. So I wanted to talk to you about him. Who is Richard Feynman to you in your eyes? What impact did he have on you? I mean, I think a ton of people like Feynman. He's probably, it's a little bit cliche to say that you like Feynman, right? That's almost like when you don't know what to say about sports and you just point to the Super Bowl or something as something you enjoy watching. But I do actually think there's a layer to Feynman that sits behind the iconography. One thing that just really struck me was this letter that he wrote to his wife two years after she died. So during the Manhattan Project, she had polio. Tragically, she died. They were just young, madly in love. And the icon of Feynman is this, almost this like mildly sexist, womanizing philanderer, at least on the personal side. But you read this letter, and I can try to pull it up for you if I want. And it's just this absolutely heartfelt letter to his wife saying how much he loves her. Even though she's dead and kind of what she means to him, how no woman can ever measure up to her. And it shows you that the Feynman that we've all seen in like, surely you're joking, is different from the Feynman in reality. And I think the same kind of goes in his science where he kind of sometimes has this output of being this, ah shucks character. Like everyone else is coming in, there's these fancy pollutant formulas, but I'm just gonna try to whittle it down to its essentials, which is so appealing because we love to see that kind of thing. But when you get into it, like what he was doing was actually quite deep, very much mathematical. That should go without saying, but I remember reading a book about Feynman in a cafe once, and this woman looked at me and was like, saw that it was about Feynman. She was like, oh, I love him. I read surely you're joking. And she started explaining to me how he was never really a math person. And I don't understand how that can possibly be a public perception about any physicist, but for whatever reason that like worked into his aura that he sort of is a math person. That he sort of shooed off math and in place of true science. The reality of it is he was deeply in love with math and was much more going in that direction and had a clicking point into seeing that physics was a way to realize that. And all the creativity that he could output in that direction was instead poured towards things like fundamental, not even fundamental theories, just emergent phenomena and everything like that. So to answer your actual question, like what I like about his way of going at things is this constant desire to reinvent it for himself. Like when he would consume papers, the way he'd describe it, he would start to see what problem he was trying to solve and then just try to solve it himself to get a sense of personal ownership. And then from there, see what others had done. Is that how you see problems yourself? Like that's actually an interesting point when you first are inspired by a certain idea that you maybe wanna teach or visualize or just explore on your own. I'm sure you're captured by some possibility and magic of it. Do you read the work of others? Like do you go through the proof? Do you try to rediscover everything yourself? So I think the things that I've learned best and have the deepest ownership of are the ones that have some element of rediscovery. The problem is that really slows you down. And this is, for my part, it's actually a big fault. Like this is part of why I'm not an active researcher. I'm not like at the depth of the field a lot of other people are. The stuff that I do learn, I try to learn it really well. But other times you do need to get through it at a certain pace. You need to get to a point of a problem you're trying to solve. So obviously you need to be well-equipped to read things without that reinvention component and see how others have done it. But I think if you choose a few core building blocks along the way and you say, I'm really gonna try to approach this before I see how this person went at it. I'm really gonna try to approach it for myself. No matter what, you gain all sorts of inarticulatable intuitions about that topic, which aren't gonna be there if you simply go through the proof. For example, you're gonna be trying to come up with counter examples. You're gonna try to come up with intuitive examples, all sorts of things where you're populating your brain with data. And the ones that you come up with are likely to be different than the one that the text comes up with. And that like lends it a different angle. So that aspect also slowed Feynman down in a lot of respects. I think there was a period when like the rest of physics was running away from him. But insofar as it got him to where he was, I kind of resonate with that. I just, I would be nowhere near it because I'm not like him at all, but it's like a state to aspire to. You know, just to link in a small point you made, that you're not a quote unquote active researcher. Do you, you're swimming often in reasonably good depth about a lot of topics. Do you sometimes wanna like dive deep at a certain moment and say like, because you probably built up a hell of an amazing intuition about what is and isn't true within these worlds. Do you ever wanna just dive in and see if you can discover something new? Yeah, I think one of my biggest regrets from undergrad is not having built better relationships with the professors I had there. And I think a big part of success in research is that element of like mentorship and like people giving you the kind of scaffolded problems to carry along. For my own like goals right now, I feel like I'm pretty good at exposing math to others and like want to continue doing that. For my personal learning, are you familiar with like the hedgehog fox dynamic? I think this was either the ancient Greeks came up with it or it was pretended to be something drawn from the ancient Greeks. I don't know who to point it to, but the- Probably Mark Twain. It is that you've got two types of people or especially two types of researchers. There's the fox that knows many different things and then the hedgehog that knows one thing very deeply. So like von Neumann would have been the fox. He's someone who knows many different things, just very foundational in a lot of different fields. Einstein would have been more of a hedgehog, thinking really deeply about one particular thing. And both are very necessary for making progress. So between those two, I would definitely see myself as like the fox where I'll try to get my paws in like a whole bunch of different things. And at the moment, I just think I don't know enough of anything to make like a significant contribution to any of them. But I do see value in like having a decently deep understanding of a wide variety of things. Like most people who know computer science really deeply don't necessarily know physics very deeply or many of the aspects, like different fields in math even. Let's say you have like an analytic number theory versus an algebraic number theory. Like these two things end up being related to very different fields. Like some of them more complex analysis, some of them more like algebraic geometry. And then when you just go out so far as to take those adjacent fields, place one, you know, PhD student into a seminar of another one's, they don't understand what the other one's saying at all. Like you take the complex analysis specialist inside the algebraic geometry seminar, they're as lost as you or I would be. But I think going around and like trying to have some sense of what this big picture is, certainly has personal value for me. I don't know if I would ever make like new contributions in those fields, but I do think I could make new like expositional contributions where there's kind of a notion of things that are known, but like haven't been explained very well. Well, first of all, I think most people would agree your videos, your teaching, the way you see the world is fundamentally often new. Like you're creating something new. And it almost feels like research, even just like the visualizations, the multi-dimensional visualization we'll talk about. I mean, you're revealing something very interesting that yeah, just feels like research, feels like science, feels like the cutting edge of the very thing of which like new ideas and new discoveries are made of. I do think you're being a little bit more generous than is necessarily. And I promise that's not even false humility because I sometimes think when I research a video, I'll learn like 10 times as much as I need for the video itself. And it ends up feeling kind of elementary. So I have a sense of just how far away like the stuff that I cover is from the actual depth. I think that's natural, but I think that could also be a mathematics thing. I feel like in the machine learning world, you like two weeks in, you feel like you've basically mastered. In mathematics, it's like. Well, everything is either trivial or impossible. And it's like a shockingly thin line between the two where you can find something that's totally impenetrable. And then after you get a feel for it, it's like, oh yeah, that whole subject is actually trivial in some way. So maybe that's what goes on. Every researcher is just on the other end of that hump. And it feels like it's so far away, but one step actually gets them there. What do you think about sort of Feynman's teaching style or another perspective is of use of visualization? Well, his teaching style is interesting because people have described like the Feynman effect where while you're watching his lectures or while you're reading his lectures, everything makes such perfect sense. So as an entertainment session, it's wonderful because it gives you this intellectual satisfaction that you don't get from anywhere else that you like finally understand it. But the Feynman effect is that you can't really recall what it is that gave you that insight even a week later. And this is true of a lot of books and a lot of lectures where the retention is never quite what we hope it is. So there is a risk that the stuff that I do also fits that same bill where at best, it's giving this kind of intellectual candy on giving a glimpse of feeling like you understand something. But unless you do something active, like reinventing it yourself, like doing problems to solidify it, even things like space repetition memory to just make sure that you have like the building blocks of what do all the terms mean, unless you're doing something like that, it's not actually gonna stick. So the very same thing that's so admirable about Feynman's lectures, which is how damn satisfying they are to consume might actually also reveal a little bit of the flaw that we should as educators all look out for, which is that that does not correlate with long-term learning. We'll talk about it a little bit. I think you've done some interactive stuff. I mean, even in your videos, the awesome thing that Feynman couldn't do at the time is you could, since it's programmed, you can like tinker, like play with stuff. You could take this value and change it. You can like, here, let's take the value of this variable and change it to build up an intuition, to move along the surface or to change the shape of something. I think that's almost an equivalent of you doing it yourself. It's not quite there, but as a viewer. Yeah, do you think there's some value in that interactive element? Yeah, well, so what's interesting is you're saying that, and the videos are non-interactive in the sense that there's a play button and a pause button. And you could ask like, hey, while you're programming these things, why don't you program it into an interactable version, you know, make it a Jupyter notebook that people can play with, which I should do and that like would be better. I think the thing about interactives though is most people consuming them just sort of consume what the author had in mind. And that's kind of what they want. Like I have a ton of friends who make interactive explanations. And when you look into the analytics of how people use them, there's a small sliver that generally use it as a playground to have experiments. And maybe that small sliver is actually who you're targeting and the rest don't matter. But most people consume it just as a piece of like well-constructed literature that maybe you tweak with the example a little bit to see what it's getting at. But in that way, I do think like a video can get most of the benefits of the interactive, like the interactive app, as long as you make the interactive for yourself and you decide what the best narrative to spin is. As a more concrete example, like my process with, I made this video about SIR models for epidemics. And it's like this agent-based bottling thing where you tweak some things about how the epidemic spreads and you wanna see how that affects its evolution. My format for making that was very different than others where rather than scripting it ahead of time, I just made the playground and then I played a bunch and then I saw what stories there were to tell within that. Yeah, that's cool. So your video had that kind of structure. It had like five or six stories or whatever it was. And like, it was basically, okay, here's a simulation, here's a model. What can we discover with this model? And here's five things I found after playing with it. Well, because the thing is, a way that you could do that project is you make the model and then you put it out and you say, here's a thing for the world to play with. Like come to my website where you interact with this thing. And people did like sort of remake it in a JavaScript way so that you can go to that website and you can test your own hypotheses. But I think a meaningful part of the value to add is not just the technology but to give the story around it as well. And like, that's kind of my job. It's not just to like make the visuals that someone will look at. It's to be the one to decide what's the interesting thing to walk through here. And even though there's lots of other interesting paths that one could take, that can be kind of daunting when you're just sitting there in a sandbox and you're given this tool with like five different sliders and you're told to like play and discover things. Where do you do? What do you start? What are my hypotheses? What should I be asking? Like a little bit of guidance in that direction can be what actually sparks curiosity to make someone want to imagine more about it. A few videos I've seen you do, I don't know how often you do it, but there's almost a tangential like pause where you, here's a cool thing. You say like, here's a cool thing, but it's outside the scope of this video essentially. But I'll leave it to you as homework essentially to like figure out it's a cool thing to explore. I wish I could say that wasn't a function of laziness. Right, and that's like you've worked so hard on making the 20 minutes already that to extend it out even further would take more time. And one of your cooler videos, the homomorphic, like from the Mobius strip to the- What do you describe, rectangle? Yeah, that's a super, and you're like, yeah, you can't transform the Mobius strip into a surface without it intersecting itself. But I'll leave it to you to see why that is. Well, I hope that's not exactly how I phrase it because I think what my hope would be is that I leave it to you to think about why you would expect that to be true and then to want to know what aspects of a Mobius strip do you want to formalize such that you can prove that intuition that you have? Because at some point now you're starting to invent algebraic topology. If you have these vague instincts, like I want to get this Mobius strip, I want to fit it such that it's all above the plane but its boundary sits exactly on the plane. I don't think I can do that without crossing itself, but that feels really vague. How do I formalize it? And as you're starting to formalize that, that's what's going to get you to try to come up with a definition for what it means to be orientable or non-orientable. And like, once you have that motivation, a lot of the otherwise arbitrary things that are sitting at the very beginning of a topology textbook start to make a little more sense. Yeah, and I mean, that whole video beautifully was a motivation for topology is cool. That was my, well, my hope with that is I feel like topology is, I don't want to say it's taught wrong, but I do think sometimes it's popularized in the wrong way where, you know, you'll hear these things with people saying, oh, topologists, they're very interested in surfaces that you can bend and stretch, but you can't cut or glue. Are they? Why? Like, there's all sorts of things you can be interested in with random, like imaginative manipulations of things. Is that really what like mathematicians are into? And the short answer is not, not really. It's not as if someone was sitting there thinking like, I wonder what the properties of clay are. I had some arbitrary rules about what, when I can't cut it and when I can't glue it. Instead, there's a ton of pieces of math that can actually be equivalent to like these very general structures that's like geometry, except you don't have exact distances. You just want to maintain a notion of closeness. And once you get it to those general structures, constructing mappings between them translate into non-trivial facts about other parts of math. And that, I just, I don't think that's actually like popularized. I don't even think it's emphasized well enough when you're starting to take a topology class because you kind of have these two problems. It's like either it's too squishy. You're just talking about coffee mugs and donuts, or it's a little bit too rigor first. And you're talking about the axiom systems with open sets and an open set is not the opposite of closed set. So sorry about that, everyone. We have a notion of clopin sets for ones that are both at the same time. And just, it's not an intuitive axiom system in comparison to other fields of math. So you as the student, like really have to walk through mud to get there. And you're constantly confused about how this relates to the beautiful things about coffee mugs and Movia strips and such. And it takes a really long time to actually see that like C topology in the way that mathematicians see topology. But I don't think it needs to take that time. I think there's, this is making me feel like I need to make more videos on the topic. Cause I think I've only done two. 100% you do. But I've also seen it in my narrow view of like, I find game theory very beautiful. And I know topology has been used elegantly to prove things in game theory. Yeah, you have like facts that seem very strange. Like I could tell you, you stir your coffee and after you stir it, and like, let's say all the molecules settled to like not moving again, one of the molecules will be basically in the same position it was before. You have all sorts of fixed point theorems like this, right? That kind of fixed point theorem, directly relevant to Nash equilibriums, right? So you can imagine popularizing it by describing the coffee fact, but then you're left to wonder like, who cares about if a molecule of coffee like stays in the same spot? Is this what we're paying our mathematicians for? You have this very elegant mapping onto economics in a way that's very concrete, or very, I shouldn't say concrete, very tangible. Like actually adds value to people's lives through the predictions that it makes. But that line isn't always drawn because you have to get a little bit technical in order to properly draw that line out. And often I think popularized forms of media just shy away from being a little too technical. For sure. By the way, for people who are watching the video, I do not condone the message in this mug. It's the only one I have, which is this, the snuggle is real. By the way, for anyone watching, I do condone the message of that mug. The snuggle is real. The snuggle is real. Okay, so you mentioned the SIR model. I think there are certain ideas there of growth, of exponential growth. What maybe have you learned about pandemics from making that video? Because it was kind of exploratory. You were kind of building up an intuition. And it's again, people should watch the video. It's kind of an abstract view. It's not really modeling in detail. The whole field of epidemiology, those people, they go really far in terms of modeling like how people move about. I don't know if you've seen it, but like there is the mobility patterns, like how many people you encounter in certain situations when you go to a school, when you go to a mall, they like model every aspect of that for a particular city. Like they have maps of actual city streets. They model it really well. And natural patterns of the people have, it's crazy. So you don't do any of that. You're just doing an abstract model to explore different ideas of- Simple pedigree. Well, because I don't want to pretend like I'm an epidemiologist. Like we have a ton of armchair epidemiologists. And the spirit of that was more like, can we through a little bit of play, draw like reasonable-ish conclusions? And also just like get ourselves in a position where we can judge the validity of a model. Like I think people should look at that and they should criticize it. They should point to all the ways that it's wrong because it's definitely naive, right? In the way that it's set up. But to say like what lessons from that hold, like thinking about the R naught value and what that represents and what it can imply. What's R naught? So R naught is if you are infectious and you're in a population which is completely susceptible, what's the average number of people that you're going to infect during your infectiousness? So certainly during the beginning of an epidemic, this basically gives you kind of the exponential growth rate. Like if every person infects two others, you've got that one, two, four, eight exponential growth pattern. As it goes on and let's say it's something endemic where you've got like a ton of people who have had it and are recovered, then you would, the R naught value doesn't tell you that as directly because a lot of the people you interact with aren't susceptible, but in the early phases it does. And this is like the fundamental constant that it seems like epidemiologists look at and the whole goal is to get that down. If you can get it below one, then it's no longer epidemic. If it's equal to one, then it's endemic and it's above one, then you're epidemic. So like just teaching what that value is and giving some intuitions on how do certain changes in behavior change that value? And then what does that imply for exponential growth? I think those are general enough lessons and they're like resilient to all of the chaoses of the world that it's still like valid to take from the video. I mean, one of the interesting aspects of that is just exponential growth and the way we think about growth. Is that one of the first times you've done a video on, no, of course not, the whole Euler's identity. Okay, so. Sure. I've done a lot of videos about exponential growth in the circular direction, only minimal in the normal direction. I mean, another way to ask, do you think we're able to reason intuitively about exponential growth? It's funny, I think it's extremely intuitive to humans and then we train it out of ourselves such that it's then really not intuitive and then I think it can become intuitive again when you study a technical field. So what I mean by that is, have you ever heard of these studies where in a anthropological setting where you're studying a group that has been disassociated from a lot of modern society and you ask what number is between one and nine? And maybe you would ask, you've got one rock and you've got nine rocks. You're like, what pile is halfway in between these? And our instinct is usually to say five. That's the number that sits right between one and nine. But sometimes when numeracy and the kind of just basic arithmetic that we have isn't in a society, the natural instinct is three because it's in between in an exponential sense and a geometric sense that one is three times bigger and then the next one is three times bigger than that. So it's like, if you have one friend versus 100 friends, what's in between that? Yeah, 10 friends seems like the social status in between those two states. So that's like deeply intuitive to us to think logarithmically like that. And for some reason, we kind of train it out of ourselves to start thinking linearly about things. So in the sense, yeah, the early basic math forces us to take a step back. It's the same criticism if there's any of science is the lessons of science make us like see the world in a slightly narrow sense to where we have an over-exaggerated confidence that we understand everything as opposed to just understanding a small slice of it. But I think that probably only really goes for small numbers because the real counterintuitive thing about exponential growth is like as the numbers start to get big. So I bet if you took that same setup and you asked them, oh, if I keep tripling the size of this rock pile, you know, seven times, how big will it be? I bet it would be surprisingly big even to like a society without numeracy. And that's the side of it that I think is pretty counterintuitive to us, but that you can basically train into people. Like I think computer scientists and physicists when they're looking at the early numbers of like COVID were, they were the ones thinking like, oh God, this is following an exact exponential curve. And I heard that from a number of people. So it's, and almost all of them are like techies in some capacity, probably just because I like live in the Bay Area, but. But for sure, they're cognizant of this kind of growth that's present in a lot of natural systems and a lot of systems. I don't know if you've seen like, I mean, there's a lot of ways to visualize this obviously, but Ray Kurzweil, I think was the one that had this like chessboard where every square on the chessboard, you double the number of stones or something in that chessboard. I've heard this is like an old proverb where, it's like, you know, someone, the king offered him a gift and he said, the only gift I would like, very modest, give me a single grain of rice for the first chessboard. And then two grains of rice for the next square, then twice that for the next square and just continue on. That's my only modest ask, your sire. And like, it's all, you know, more grains of rice than there are anything in the world by the time you get to the end. And I, my intuition falls apart there. Like I would have never predicted that. Like for some reason, that's a really compelling illustration how poorly breaks down, just like you said, maybe we're okay for the first few piles of rocks, but after a while it's game over. You know, the other classic example for gauging someone's intuitive understanding of exponential growth is I've got like a lily pad on a lake, really big lake, like Lake Michigan. And that lily pad replicates, it doubles one day and then it doubles the next day and it doubles the next day. And after 50 days, it actually is gonna cover the entire lake, okay? So after how many days does it cover? Half the lake. 49. So you have a good instinct for exponential growth. So I think a lot of like the knee jerk reaction is sometimes to think that it's like half the amount of time or to at least be like surprised that like after 49 days, you've only covered half of it. Yeah, I mean, that's the reason you heard a pause from me. I literally thought that can't be right. Right, yeah, exactly. So even when you know the fact and you do the division, it's like, wow, so you've gotten like that whole time and then day 49, it's only covering half and then after that, it gets the whole thing. But I think you can make that even more visceral if rather than going one day before you say, how long until it's covered 1% of the lake, right? And it's, so what would that be? How many times you have to double to get over 100? Like seven, six and a half times, something like that. Right, so at that point, you're looking at 43, 44 days into it, you're not even at 1% of the lake. So you've experienced 44 out of 50 days and you're like, yeah, that's really bad, it's just 1% of the lake. But then next thing you know, it's the entire lake. You're wearing a SpaceX shirt, so let me ask you. Sure. Let me ask you, one person who talks about exponential, just the miracle of the exponential function in general is Elon Musk. So he kind of advocates the idea of exponential thinking. The idea of exponential thinking, realizing that technological development can, at least in the short term, follow exponential improvement, which breaks apart our intuition, our ability to reason about what is and isn't impossible. So he's a big, one, it's a good leadership kind of style of saying like, look, the thing that everyone thinks is impossible is actually possible because exponentials. But what's your sense about that kind of way to see the world? Well, so I think it can be very inspiring to note when something, like Moore's Law is another great example where you have this exponential pattern that holds shockingly well and it enables just better lives to be led. I think the people who took Moore's Law seriously in the 60s were seeing that, wow, it's not gonna be too long before these giant computers that are either batch processing or time-shared, you could actually have one small enough to put on your desk, on top of your desk, and you could do things. And if they took it seriously, like you have people predicting smartphones like a long time ago. And it's only out of like kind of this, I don't wanna say faith in exponentials, but an understanding that that's what's happening. What's more interesting, I think, is to really understand why exponential growth happens and that the mechanism behind it is when the rate of change is proportional to the thing in and of itself. So the reason that technology would grow exponentially is only gonna be if the rate of progress is proportional to the amount that you have. So that the software you write enables you to write more software. And I think we see this with the internet, like the advent of the internet makes it faster to learn things, which makes it faster to create new things. I think this is oftentimes why like investment will grow exponentially, that the more resources a company has, if it knows how to use them well, the more it can actually grow. So I mean, you referenced Elon Musk, I think he seems to really be into vertically integrating his companies. I think a big part of that is cause you have the sense what you want is to make sure that the things that you develop, you have ownership of and that they enable further development of the adjacent parts, right? So it's not just this, you see a curve and you're blindly drawing a line through it. What's much more interesting is to ask, when do you have this proportional growth property? Because then you can also recognize when it breaks down, like in an epidemic, as you approach saturation, that would break down. As you do anything that skews what that proportionality constant is, you can make it maybe not break down as being an exponential, but it can seriously slow what that exponential rate is. This is the opposite of a pandemic, is you want, in terms of ideas, you want to minimize barriers that prevent the spread, you wanna maximize the spread of impact. So like you want it to grow when you're doing technological development, is so that you do hold up, that rate holds up. And that's almost like an operational challenge of like how you run a company, how you run a group of people, is that any one invention has a ripple that's unstopped. And that ripple effect then has its own ripple effects and so on, and that continues. Yeah, like Moore's law is fascinating. On a psychological level, on a human level, because it's not exponential, it's just a consistent set of like, what you would call like S-curves, which is like, it's constantly like breakthrough innovations, nonstop. That's a good point. Like it might not actually be an example of exponentials because of something which grows in proportion to itself, but instead it's almost like a benchmark that was set out that everyone's been pressured to meet. And it's like all these innovations and micro inventions along the way, rather than some consistent sit back and just let the lily pad grow across the lake phenomenon. And it's also, there's a human psychological level for sure of like the four minute mile. Like there's something about it, like saying that, look, there is, you know, Moore's law, it's a law. So like it's certainly an achievable thing. You know, we've achieved it for the last decade, for the last two decades, for the last three decades, you just keep going. And it somehow makes it happen. I mean, it makes people, I'm continuously surprised in this world how few people do the best work in the world, like in that particular, whatever that field is. Like it's very often that like the genius, I mean, you can argue that community matters, but it's certain, like I've been in groups of engineers where like one person is clearly like doing an incredible amount of work and just is the genius. And it's fascinating to see, basically it's kind of the Steve Jobs idea is maybe the whole point is to create an atmosphere where the genius can discover themselves. Like have the opportunity to do the best work of their life. And yeah, and that the exponential is just milking that. It's like rippling the idea that it's possible. And that idea that it's possible finds the right people for the four minute mile. The idea that it's possible finds the right runners to run it and then it explodes the number of people who can run faster than four minutes. It's kind of interesting to, I don't know. Basically the positive way to see that is most of us are way more intelligent, have way more potential than we ever realized. I guess that's kind of depressing. But I mean like the ceiling for most of us is much higher than we ever realized. That is true. A good book to read if you want that sense is Peak, which essentially talks about peak performance in a lot of different ways, like chess, London cab drivers, how many pushups people can do, short term memory tasks. And it's meant to be like a concrete manifesto about deliberate practice and such. But the one sensation you come out with is, wow, no matter how good people are at something, they can get better and like way better than we think they could. I don't know if that's actually related to exponential growth, but I do think it's a true phenomenon. It's interesting. Yeah, I mean, there's certainly no law of exponential growth in human innovation. Well, I don't know. Well, kind of, there is. I think it's really interesting to see when innovations in one field allow for innovations in another. Like the advent of computing seems like a prerequisite for the advent of chaos theory. You have this truth about physics and the world that in theory could be known. You could find Lorenz's equations without computers. But in practice, it was just never gonna be analyzed that way unless you were doing like a bunch of simulations and that you could computationally see these models. So it's like physics allowed for computers, computers allowed for better physics. And wash, rinse, and repeat. That self-proportionality, that's exponential. So I think I wouldn't, it's something it's too far to say that that's a law of some kind. Yeah, a fundamental law of the universe is that these descendants of apes will exponentially improve their technology and one day be taken over by the AGI. That's built in the simulation. That'll make the video game fun, whoever created this thing. I mean, since you're wearing a SpaceX shirt, let me ask. I didn't realize I was wearing a SpaceX shirt. I apologize. It's on point, so it's on topic, I'll take it. So Crew Dragon, the first crewed mission out into space since the space shuttle. And just by first time ever by a commercial company. I mean, it's an incredible accomplishment, I think, but it's also just an incredible, it inspires imagination amongst people that this is the first step in a long, like vibrant journey of humans into space. Oh yeah. So what are your, how do you feel? Is this exciting to you? Yeah, it is. I think it's great. The idea of seeing it basically done by smaller entities instead of by governments. I mean, it's a heavy collaboration between SpaceX and NASA in this case, but moving in the direction of not necessarily requiring an entire country and its government to make it happen, but that you can have something closer to a single company doing it. We're not there yet, because it's not like they're unilaterally saying, like we're just shooting people up into space. It's just a sign that we're able to do more powerful things with smaller groups of people. I find that inspiring. Innovate quickly. I hope we see people land on Mars in my lifetime. Do you think we will? I think so. I mean, I think there's a ton of challenges there, right? Like radiation being kind of the biggest one. And I think there's a ton of people who look at that and say, why? Why would you want to do that? Let's let the robots do the science for us. But I think there's enough people who are like genuinely inspired about broadening the worlds that we've touched. Or people who think about things like backing up the light of consciousness with super long-term visions of terraforming. As long as there's a- Sorry, backing up the light of consciousness? Yeah, the thought that if Earth goes to hell, we gotta have a backup somewhere. A lot of people see that as pretty out there, and it's not in the short-term future, but I think that's an inspiring thought. I think that's a reason to get up in the morning, and I feel like most employees at SpaceX feel that way too. Do you think we'll colonize Mars one day? No idea. Either AGI kills us first, or if we're allowed, I don't know if it'll take us that long. If we're allowed? Honestly, it would take such a long time. Okay, you might have a small colony, something like what you see in The Martian, but not people living comfortably there. But if you want to talk about actual second Earth kind of stuff, that's just way far out there, and the future moves so fast that it's like, we might just kill ourselves before that even becomes viable. Yeah, I mean, there's a lot of possibilities where it could be just, it doesn't have to be on a planet, we could be floating out in space, have a space-faring backup solution that doesn't have to deal with the constraints that a planet, I mean, a planet provides a lot of possibilities and resources, but also some constraints. Yeah, I mean, for me, for some reason, it's a deeply exciting possibility. Oh yeah, yeah, all of the people who are skeptical about it are like, why do we care about going to Mars? It's like, what makes you care about anything? That's inspiring. It's hard, actually, it's hard to hear that because exactly as you put it, on a philosophical level, it's hard to say, why do anything? I don't know, it's like the people say, I've been doing an insane challenge last 30-something days. Your pull-ups? The pull-ups and push-ups, and a bunch of people are like, awesome, you're insane, but awesome. And then some people are like, why? Why do anything? I don't know, there's a calling. I'm with JFK a little bit, it's because we do these things because they're hard. There's something in the human spirit that says, same with a math problem, there's something, you fail once, and it's this feeling that, you know what, I'm not gonna back down from this. There's something to be discovered in overcoming this thing. Well, so what I like about it is, and I also like this about the moon missions, sure, it's kind of arbitrary, but you can't move the target. So you can't make it easier and say that you've accomplished the goal. And when that happens, it just demands actual innovation. Like protecting humans from the radiation in space on the flight there, while there, hard problem, demands innovation. You can't move the goalposts to make that easier. Almost certainly, the innovations required for things like that will be relevant in a bunch of other domains too. So like the idea of doing something merely because it's hard, it's like loosely productive, great. But as long as you can't move the goalposts, there's probably gonna be these secondary benefits that we should all strive for. Yeah, I mean, it's hard to formulate the Mars colonization problem as something that has a deadline, which is the problem. But if there was a deadline, then the amount of things we would come up with by forcing ourselves to figure out how to colonize that place would be just incredible. This is what people, like the internet didn't get created because people sat down and tried to figure out how do I send TikTok videos of myself dancing to people? There's an application. I mean, actually, I don't even know how. What do you think the application for the internet was when it was? It must've been very low-level, basic network communication within DARPA, like military-based, like how do I send, like a networking, how do I send information securely between two places? Maybe it was an encryption. I'm speaking totally outside of my knowledge, but it was probably intended for a very narrow, small group of people. Well, so, I mean, there was this small community of people who were really interested in timesharing computing and interactive computing in contrast with batch processing. And then the idea that as you set up a timesharing center, basically meaning you can have multiple people logged in and using that central computer, why not make it accessible to others? And this was kind of what I had always thought, oh, it was this fringe group that was interested in this new kind of computing, and they all got themselves together. But the thing is, DARPA wouldn't actually, you wouldn't have the US government funding that just for the funds of it, right? In some sense, that's what ARPA was all about, was just really advanced research for the sake of having advanced research, and it doesn't have to pay out with utility soon. But the core parts of its development were happening in the middle of the Vietnam War when there was budgetary constraints all over the place. I only learned this recently, actually. If you look at the documents, basically justifying the budget for the ARPANET as they were developing it, and not just keeping it where it was, but actively growing it while all sorts of other departments were having their funding cut because of the war, a big part of it was national defense in terms of having a more robust communication system, like the idea of packet switching versus circuit switching. You could kind of make this case that in some calamitous circumstance where a central location gets nuked, this is a much more resilient way to still have your communication lines that traditional telephone lines weren't as resilient to, which I just found very interesting. Even something that we see as so happy-go-lucky is just a bunch of computer nerds trying to get interactive computing out there. The actual thing that made it funded and thing that made it advance when it did was because of this direct national security question and concern. I don't know if you've read it. I haven't read it. I've been meaning to read it, but Neil deGrasse Tyson actually came out with a book that talks about science in the context of the military, like basically saying all the great science we've done in the 20th century was because of the military. I mean, he paints a positive. It's not like a critical. A lot of people say military industrial complex and so on. Another way to see the military and national security is like a source of, like you said, deadlines and hard things you can't move, like almost scaring yourself into being productive. It is that. I mean, the Manhattan Project is a perfect example, probably the quintessential example. That one is a little bit more macabre than others because of what they were building, but in terms of how many focused, smart hours of human intelligence get pointed towards a topic per day, you're just maxing it out with that sense of worry. In that context, everyone there was saying, like, we've got to get the bomb before Hitler does. And that just lights a fire under you that I, again, like the circumstances macabre, but I think that's actually pretty healthy, especially for researchers that are otherwise going to be really theoretical. To take these like theorizers and say, make this real physical thing happen, meaning a lot of it is going to be unsexy. A lot of it's going to be like young Feynman sitting there kind of inventing a notion of computation in order to like compute what they needed to compute more quickly with like the rudimentary automated tools that they had available. I think you see this with Bell Labs also, where you've got otherwise very theorizing minds in very pragmatic contexts that I think is like really helpful for the theory as well as for the applications. So I think that stuff can be positive for progress. You mentioned Bell Labs and Manhattan Project. This kind of makes me curious for the things you've create, which are quite singular. Like if you look at all YouTube or just not YouTube, it doesn't matter what it is. It's just teaching content, art, doesn't matter. It's like, yep, that's Grant, right? That's unique. I know your teaching style and everything. Does it, Manhattan Project and Bell Labs was like famously a lot of brilliant people, but there's a lot of them. They play off of each other. So like my question for you is that does it get lonely? Honestly, that right there, I think is the biggest part of my life that I would like to change in some way. That I look at a Bell Labs type situation and I'm like, goddamn, I love that whole situation. And I'm so jealous of it. And you're like reading about Hamming and then you see that he also shared an office with Shannon. And you're like, of course he did. Of course they shared an office. That's how these ideas get like. And they actually probably, very likely worked separately. Yeah, totally separate. But there's a literally, and sorry to interrupt. There's a literally magic that happens when you run into each other, like on the way to like getting a snack or something. Conversations you overhear, it's other projects you're pulled into. It's like puzzles that colleagues are sharing. Like all of that. I have some extent of it just because I try to stay well connected in communities of people who think in similar ways. But it's not in the day to day in the same way, which I would like to fix somehow. That's one of the, I would say one of the biggest, well, one of the many drawbacks, negative things about this current pandemic is that whatever the term is, but like chance collisions are significantly reduced. I saw, I don't know why I saw this, but on my brother's work calendar, he had a scheduled slot with someone that he scheduled a meeting. And the title of the whole meeting was, no specific agenda, I just missed the happenstance serendipitous conversations that we used to have, which the pandemic and remote work has so cruelly taken away from us. Brilliant. That was the whole title of the meeting. That's brilliant. I'm like, that's the way to do it. You just schedule those things. You schedule the serendipitous interaction. It's like, I mean, you can't do it in an academic setting, but it's basically like going to a bar and sitting there just for the strangers you might meet, just the strangers or striking up a conversation with strangers on the train. Harder to do when you're deeply, like maybe myself or maybe a lot of academic types who are like introverted and avoid human contact as much as possible. So it's nice when it's forced, those chance collisions, but maybe scheduling is a possibility. But for the most part, do you work alone? Like, I'm sure you struggle like a lot, like you probably hit moments when you look at this and you say like, this is the wrong way to show it. This is the wrong way to visualize it. I'm making it too hard for myself. I'm going down the wrong direction. This is too long. This is too short. All those self-doubt that's like can be paralyzing. Like, what do you do in those moments? Honestly, I actually much prefer like work to be a solitary affair for me. That's like a personality quirk. I would like it to be in an environment with others and like collaborative in the sense of ideas exchanged. But those phenomena you're describing when you say this is too long, this is too short, this visualization sucks, it's way easier to say that to yourself than it is to say to a collaborator. And I know that's just a thing that I'm not good at. So in that way, it's very easy to just throw away a script because the script isn't working. It's hard to tell someone else they should do the same. Actually, last time we talked, I think it was like very close to me talking Don Knuth was kind of cool. Like two people that- Can't believe you got that interview. It's the hard, no, can I brag about something? Please. My favorite thing is Don Knuth, after we did the interview, he offered to go out to hot dogs with me. We get hot dogs. That was never, like people ask me, what's the favorite interview you've ever done? I mean, that has to be, but unfortunately I couldn't. I had a thing after. So I had to turn down Don Knuth. You missed Knuth dogs? Knuth dogs. Sorry, so that was a little bragging, but the hot dogs, he's such a sweet. But the reason I bring that up is he works through problems alone as well. He prefers that struggle, the struggle of it. So, writers like Stephen King, often talk about their process of what they do, like what they eat when they wake up, like when they sit down, how they like their desk, on a perfectly productive day, like what they like to do, how long they like to work for, what enables them to think deeply, all that kind of stuff. Honoré Stompson did a lot of drugs. Everybody has their own thing. Do you have a thing? If you were to lay out a perfect, productive day, what would that schedule look like, do you think? Part of that's hard to answer, because the mode of work I do changes a lot from day to day. Some days I'm writing. The thing I have to do is write a script. Some days I'm animating. The thing I have to do is animate. Sometimes I'm working on the animation library. The thing I have to do is a little, I'm not a software engineer, but something in the direction of software engineering. Some days it's a variant of research. It's like, learn this topic well and try to learn it differently. So those is four very different modes of what it, some days it's like, get through the email backlog of people I've been, the tasks I've been putting off. It goes research, scripting. The idea starts with research, and then there's scripting, and then there's programming, and then there's the showtime. And the research side, by the way, like what's, I think a problematic way to do it is to say, I'm starting this project, and therefore I'm starting the research. Instead, it should be that you're like, ambiently learning a ton of things just in the background, and then once you feel like you have the understanding for one, you put it on the list of things that there can be a video for. Otherwise, either you're gonna end up roadblocked forever, or you're just not gonna like, have a good way of talking about it. But still, some of the days it's like, the thing to do is learn new things. So what's the most painful one, I think you mentioned, scripting? Scripting is, yeah, that's the worst. Yeah, writing is the worst. So what's your, on a perfectly, so let's take the hardest one. What's a perfectly productive day? You wake up, and it's like, damn it, this is the day I need to do some scripting. And like, you didn't do anything the last two days, so you came up with excuses to procrastinate, so today must be the day. Yeah, I wake up early, I guess I exercise, and then I turn the internet off. If we're writing, yeah, that's what's required, is having the internet off, and then maybe you keep notes on the things that you wanna Google when you're allowed to have the internet again. I'm not great about doing that, but when I do, that makes it happen. And then when I hit writer's block, like the solution to writer's block is to read. Doesn't even have to be related, just read something different, just for like 15 minutes, half an hour, and then go back to writing. That, when it's a nice cycle, I think can work very well. And when you're writing the script, you don't know where it ends, right? Like you have a... Problem-solving videos, I know where it ends. Expositional videos, I don't know where it ends. Like coming up with the magical thing that makes this whole story, like ties this whole story together. When does that happen? That's the thing that makes it such that a topic gets put on the list of videos that you wanna make. Oh, that's initial. There isn't a hop in it. You shouldn't start the project unless there's one of those. And you have so many nice bag, that you have such a big bag of aha moments already that you could just pull at it. That's one of the things, and one of the sad things about time, and that nothing lasts forever, and that we're all mortal. Let's not get into that. And discussion is, you know, if I see like, even when I asked for people to ask, like ask, I did a call for questions that people wanna ask you questions. And there's so many requests from people about like certain videos they would love you to do. It's such a pile. And I think that's a sign of like admiration from people for sure. But it's like, it makes me sad because like whenever I see them, people give ideas, they're all like very often really good ideas. And it's like, it's such a, makes me sad in the same kind of way when I go through a library or through a bookstore, you see all these amazing books that you'll never get to open. So, yeah. So you did, yeah. You gotta enjoy the ones that you have. Enjoy the books that are open and don't let yourself lament the ones that stay closed. What else? Is there any other magic to that day? Did you try to dedicate like a certain number of hours? Do you, Cal Newport has this deep work kind of idea? There's systematic people who like get really on top of, you know, they checklist of what they're gonna do in the day and they like count their hours. And I am not a systematic person in that way. Which is probably a problem. I very likely would get more done if I was systematic in that way, but that doesn't happen. So, you know, you talk to me later in life and maybe I'll have like changed my ways and give you a very different answer. I think Benjamin Franklin like later in life figured out the rigor. He has these like very rigorous schedules and how to be productive. I think those schedules are much more fun to write. Like it's very fun to like write a schedule and make a blog post about like the perfect productive day. That like might work for one person, but I don't know how much people get out of like reading them or trying to adopt someone else's style. And I'm not even sure that they've ever followed. Yeah, exactly. Like you're always gonna write it as the best version of yourself. You're not going to explain the phenomenon of like wanting to get out of the bed, but not really wanting to get out of the bed and all of that. And just like zoning out for random reasons or the one that people probably don't touch at all is, I try to check social media once a day, but I'm like only, so I post and that's it. When I post, I check the previous days. That's like my, what I try to do. That's what I do like 90% of the days, but then I'll go, I'll have like a two week period where it's just like, I'm checking the internet. Like, I mean, it's probably some scary number of times. And- I think a lot of people can resonate with that. I think it's a legitimate addiction. It's like, it's a dopamine addiction. And I don't know if it's a problem because as long as it's a kind of socializing, like if you're actually engaging with friends and engaging with other people's ideas, I think it can be really useful. Well, I don't know. So like for sure, I agree with you, but it's definitely an addiction because for me, I think it's true for a lot of people. I am very cognizant of the fact I just don't feel that happy. If I look at a day where I've checked social media a lot, like if I just aggregate, I did a self-report, I'm sure I would find that I'm just like literally on like less happy with my life and myself after I've done that check. When I check it once a day, I'm very, like, I'm happy. Even like, cause I've seen it. Okay, one way to measure that is when somebody says something not nice to you on the internet, is like when I check it once a day, I'm able to just like, I smile, like I virtually, I think about them positively, empathetically, I send them love. I don't ever respond, but I just feel positively about the whole thing. If I check more than that, it starts eating at me. Like there's an eating thing that happens, like anxiety, it occupies a part of your mind that's not, doesn't seem to be healthy. Same with, I mean, you put stuff out on YouTube. I think it's important. I think you have a million dimensions that are interesting to you, but one of the interesting ones is the study of education and the psychological aspect of putting stuff up on YouTube. I like now have completely stopped checking statistics of any kind. I've released an episode, 100 with my dad, conversation with my dad. He checks, he's probably listening to this, stop. He checks the number of views on his video, on his conversation. So he discovered like a reason, he's new to this whole addiction, and he just checks. And he like, he'll text me or write to me, I just passed Dawkins in the top. So. Oh my God, I love that so much. Oh, can I tell you a funny story in that effect of like parental use of YouTube? Early on in the channel, my mom would like text me. She's like, the channel has had 990,000 views. The channel has had 991,000 views. I'm like, oh, that's cute. She's going to the little part on the about page where you see the total number of channel views. No, she didn't know about that. She had been going every day through all the videos and then adding them up. Adding them up. And she thought she was like doing me this favor of providing me this like global analytic that otherwise wouldn't be visible. That's awesome. It's just like this addiction where you have some number you want to follow and like, yeah, it's funny that your dad had this. I think a lot of people have it. I think that's probably a beautiful thing for like parents because they're legitimately, they're proud. Yeah, it's born of love, it's great. The downside I feel, one of them, is this is one interesting experience that you probably don't know much about because comments on your videos are super positive. But people judge the quality of how something went, like I see that with these conversations, by the comments. I'm not talking about like, you know, people in their 20s and their 30s. I'm talking about like CEOs of major companies who don't have time. They basically, they literally, this is their evaluation metric. They're like, ooh, the comments seem to be positive. And that's really concerning to me. Most important lesson for any content creator to learn is that the commenting public is not representative of the actual public. And this is easy to see. Ask yourself, how often do you write comments on YouTube videos? Most people will realize I never do it. Some people realize they do, but the people who realize they never do it should understand that that's a sign the kind of people who are like you aren't the ones leaving comments. And I think this is important in a number of respects. Like in my case, I think I would think my content was better than it was if I just read comments because people are super nice. The thing is the people who are bored by it or are put off by it in some way, are frustrated by it, usually they just go away. They're certainly not going to watch the whole video, much less leave a comment on it. So there's a huge under-representation of like negative feedback, like well-intentioned negative feedback, because very few people actively do that. Like watch the whole thing that they dislike, figure out what they disliked, articulate what they dislike. There's plenty of negative feedback that's not well-intentioned, but for like that golden kind. I think a lot of YouTuber friends I have at least have gone through phases of like anxiety about the nature of comments that stem from basically just this, that it's like people who aren't necessarily representative of who they were going for, misinterpreted what they were trying to say or whatever have you, or were focusing on things like personal appearances as opposed to like substance. And they come away thinking like, oh, that's what everyone thinks, right? That's what everyone's response to this video was. But a lot of the people who had the reaction you wanted them to have, like they probably didn't write it down. So very important to learn. It also translates to realizing that you're not as important as you might think you are, because all of the people commenting are the ones who love you the most and are like really asking you to like create certain things or like mad that you didn't create like a past thing. I don't know, I have such a problem. Like I have a very real problem with making promises about a type of content that I'll make and then either not following up on it soon or just like never following up on it. Yeah, you actually, last time we talked, I think, I'm not sure, promised to me that you'll have music incorporated into your like- I'll share it with you at private length. But so there's an example of like what I had in mind. I like did a version of it and I'm like, I think there's a better version of this that might exist one day. So it's now on the, like the back burner. It's like, it's sitting there. It was like a live performance at this one thing. I think next circumstance that I'm like doing another recorded live performance that like fits having that then in a better recording context, maybe I'll make it nice and public. Maybe a while. But exactly, right? The point I was gonna make though is like, I know I'm bad about following up on stuff, which is an actual problem. It's born of the fact that I have a sense of what will be like good content when it won't be. But this can actually be incredibly disheartening because a ton of comments that I see are people who are like frustrated, usually in a benevolent way that like, I haven't followed through on like X and X, which I get. And I should do that. But what's comforting thought for me is that when there's a topic I haven't promised, but I am working on and I'm excited about, it's like the people who would really like this don't know that it's coming and don't know to like comment to that effect. And like the commenting public that I'm seeing is not representative of like who I think this other project will touch meaningfully. Yeah, so focus on the future, on the thing you're creating now, just like the art of it. One of the people is really inspiring to me in that regard, because I've really seen it in person is Joe Rogan. He doesn't read comments, but not just that. He doesn't give a damn. He like legitimate, he's not like clueless about it. He's like, just like the richness and the depth of a smile he has when he just experiences the moment with you, like offline. You can tell he doesn't give a damn about like, about anything, about what people think about, whether if it's on a podcast, you talk to him or whether offline about just, it's not there. Like what other people think, how even like what the rest of the day looks like is just deeply in the moment. Or like, especially like, is what we're doing gonna make for a good Instagram photo or something like that? It doesn't think like that at all. It's, I think for actually quite a lot of people, he's an inspiration in that way, but it was, and in real life, I show that you can be very successful not giving a damn about comments. And it sounds bad not to read comments, because it's like, well, there's a huge number of people who are deeply passionate about what you do. So you're ignoring them. But at the same time, the nature of our platforms is such that the cost of listening to all the positive people who are really close to you, who are incredible people, have been, made a great community that you can learn a lot from. The cost of listening to those folks is also the cost of your psychology slowly being degraded by the natural underlying toxicity of the internet. Engage with a handful of people deeply, rather than like as many people as you can in a shallow way. I think that's a good lesson for social media usage. Like, on Twitter. Platforms in general, yeah. Choose just a handful of things to engage with and engage with it very well in a way that you feel proud of and don't worry about the rest. Honestly, I think the best social media platform is texting. That's my favorite. That's my go-to social media platform. Well, yeah, the best social media interaction is like real life, not social media, but social interaction. Well, yeah, no question there. I think everyone should agree with that. Which sucks because it's been challenged now with the current situation. And we're trying to figure out what kind of platform can be created that we can do remote communication that still is effective. It's important for education. It's important for just. That is the question of education right now. Yeah. So on that topic, you've done a series of live streams called Lockdown Math. And you went live, which is different than you usually do. Maybe one, can you talk about how'd that feel? What's that experience like? Like in your own, when you look back, like is that an effective way, did you find being able to teach? And if so, is there a lessons for this world where all of these educators are now trying to figure out how the heck do I teach remotely? For me, it was very different, as different as you can get. I'm on camera, which I'm usually not. I'm doing it live, which is nerve wracking. It was a slightly different like level of topics. Although realistically, I'm just talking about things I'm interested in no matter what. I think the reason I did that was this thought that a ton of people are looking to learn remotely, the rate at which I usually put out content is too slow to be actively helpful. Let me just do some biweekly lectures that if you're looking for a place to point your students, if you're a student looking for a place to be edified about math, just tune in at these times. And in that sense, I think it was a success for those who followed with it. It was a really rewarding experience for me to see how people engaged with it. Part of the fun of the live interaction was to actually, like I'd do these live quizzes and see how people would answer and try to shape the lesson based on that, or see what questions people were asking in the audience. I would love to, if I did more things like that in the future, kind of tighten that feedback loop even more. I think for, you know, you asked about like, if this can be relevant to educators, like 100% online teaching is basically a form of live streaming now. And usually it happens through Zoom. I think if teachers view what they're doing as a kind of performance and a kind of live stream performance, that would probably be pretty healthy because Zoom can be kind of awkward. And I wrote up this little blog post actually, just on like, just what our setup looked like, if you want to adopt it yourself and how to integrate like the broadcasting software OBS with Zoom or things like that. It was really sad to pause on that. I mean, yeah, maybe we could look at the blog post, but it looked really nice. The thing is, I knew nothing about any of that stuff before I started. I had a friend who knew a fair bit. And so he kind of helped show me the roops. One of the things that I realized is that you could, as a teacher, like it doesn't take that much to make things look and feel pretty professional. Like one component of it is as soon as you hook things up with the broadcasting software, rather than just doing like screen sharing, you can set up different scenes and then you can like have keyboard shortcuts to transition between those scenes. So you don't need a production studio with a director calling like, go to camera three, go to camera two, like onto the screen capture. Instead you can have control of that. And it took a little bit of practice and I would mess it up now and then, but I think I had it decently smooth such that, you know, I'm talking to the camera and then we're doing something on the paper. Then we're doing like a, playing with a Desmos graph or something. And something that I think in the past would have required a production team, you can actually do as a solo operation. And in particular as a teacher. And I think it's worth it to try to do that because two reasons, one, you might get more engagement from the students. But the biggest reason, I think one of the like best things that can come out of this pandemic education wise, is if we turn a bunch of teachers into content creators. And if we take lessons that are usually done in these one-off settings and like start to get in the habit of, sometimes I'll use the phrase commoditizing explanation, where what you want is, whatever a thing a student wants to learn, it just seems inefficient to me that that lesson is taught millions of times over in parallel across many different classrooms in the world. Like year to year, you've got a given algebra one lesson that's just taught like literally millions of times by different people. What should happen is that there's the small handful of explanations online that exist so that when someone needs that explanation, they can go to it. That the time in classroom is spent on all of the parts of teaching and education that aren't explanation, which is most of it, right? And the way to get there is to basically have more people who are already explaining, publish their explanations and have it in a publicized forum. So if during a pandemic, you can have people automatically creating online content because it has to be online, but getting in the habit of doing it in a way that doesn't just feel like a Zoom call that happened to be recorded, but it actually feels like a piece that was always gonna be publicized to more people than just your students, that can be really powerful. And there's an improvement process there. So being self-critical and growing, I guess YouTubers go through this process of putting out some content and nobody caring about it and then trying to figure out, basically improving, figure out like, why did nobody care? And they come up with all kinds of answers which may or may not be correct, but doesn't matter because the answer leads to improvement. So you're being constantly self-critical, self-analytical, it should be better to say. So you think of like, how can I make the audio better? Like all the basic things. Maybe one question to ask, because, well, by way of Russ Tedrick, he's a robotics professor at MIT, one of my favorite people, a big fan of yours. He watched our first conversation. I just interviewed him a couple of weeks ago. He teaches this course in underactuated robotics, which is like robotic systems when you can't control everything. We as humans, when we walk, we're always falling forward, which means like it's gravity, you can't control it. You just hope you can catch yourself, but that's not all guaranteed. It depends on the surface. So like that's underactuated, you can't control everything. The number of actuators, the degrees of freedoms you have is not enough to fully control the system. So I don't know. It's a really, I think, beautiful, fascinating class. He puts it online. It's quite popular. He does an incredible job teaching. He puts it online every time, but he's kind of been interested in like crisping it up, like making it, innovating in different kinds of ways. And he was inspired by the work you do, because I think in his work, he can do similar kinds of explanations as you're doing, like revealing the beauty of it and spending like months in preparing a single video. And he's interested in how to do that. That's why he listened to the conversation. He's playing with Manum. But he had this question of, you know, like in my apartment where we did the interview, if I have like curtains, like a black curtain, not this, this is a adjacent mansion that we're in that I also own. But you basically just have like a black curtain, whatever, that, you know, it makes it really easy to set up a filming situation with cameras that we have here, these microphones. He was asking, you know, what kind of equipment do you recommend? I guess like your blog post is a good one. I said, I don't recommend, this is excessive and actually really hard to work with. So I wonder, I mean, is there something you would recommend in terms of equipment? Like, is it, do you think like lapel mics, like USB mics? For my narration, I use a USB mic. For the streams, I used a lapel mic. The narration, it's a Blue Yeti. I'm forgetting actually the name of the lapel mic, but it was probably like a Rode of some kind. But- Is it hard to figure out how to make the audio sound good? Oh, I mean, listen to all the early videos on my channel and clearly like, I'm terrible at this. For some reason, I just couldn't get audio for a while. I think it's weird when you hear your own voice. So you hear it, you're like, this sounds weird. And it's hard to know, does it sound weird because you're not used to your own voice or they're like actual audio artifacts at play. So- And then video is just, for the lockdown, it was just the camera. You said it was probably streaming somehow through the- Yeah, there were two GH5 cameras, one that was mounted overhead over a piece of paper. You could also use like an iPad or a Wacom tablet to do your writing electronically, but I just wanted the paper feel. One on the face, there's two, again, I don't know. I'm like just not actually the one to ask this because I like animate stuff usually, but each of them like has a compressor object that makes it such that the camera output goes into the computer USB, but like gets compressed before it does that. The live aspect of it, do you regret doing it live? Not at all. I do think the content might be like much less sharp and tight than if it were something, even that I just recorded like that and then edited later. But I do like something that I do to be out there to show like, hey, this is what it's like raw. This is what it's like when I make mistakes. This is like the pace of thinking. I like the live interaction of it. I think that made it better. I probably would do it on a different channel, I think, if I did series like that in the future, just because it's a different style. It's probably a different target audience and kind of keep clean what 3Blue1Brown is about versus the benefits of like live lectures. Do you suggest like in this time of COVID that people like Russ or other educators try to go like the shorter, like 20 minute videos that are like really well planned out or scripted. You really think through, you slowly design, so it's not live. Do you see like that being an important part of what they do? Yeah, well, what I think teachers like Russ should do is choose the small handful of topics that they're gonna do just really well. They wanna create the best short explanation of it in the world that will be one of those handfuls in a world where you have commoditized explanation, right? Most of the lectures should be done just normally. So put thought and planning into it. I'm sure he's a wonderful teacher and like knows all about that. But maybe choose those small handful of topics. Do what beneficial for me sometimes is if I do sample lessons with people on that topic to get some sense of how other people think about it. Let that inform how you want to edit it or script it or whatever format you wanna do. Some people are comfortable just explaining it and editing later. I'm more comfortable like writing it out and thinking in that setting. Yeah, it's kind of, sorry to interrupt. It's a little bit sad to me to see how much knowledge is lost, like just like you mentioned, there's professors, like we can take my dad for example, to blow up his ego a little bit. But he's a great teacher and he knows plasma, plasma chemistry, plasma physics really well. So he can very simply explain some beautiful but otherwise complicated concepts. And it's sad that like if you Google plasma or like for plasma physics, like there's no videos. And just imagine if every one of those excellent teachers like your father or like Russ, even if they just chose one topic this year, just they're like, I'm gonna make the best video that I can on this topic. If every one of the great teachers did that, the internet would be replete. And it's already replete with great explanations, but it would be even more so with all the niche great explanations and like anything you wanna learn. And there's a self-interest to it in terms of teachers, in terms of even, so if you take Russ for example, it's not that he's teaching something, like he teaches his main thing, his thing he's deeply passionate about. And from a selfish perspective, it's also just like, I mean, it's like publishing a paper in a really, like nature has like letters, like accessible publication. It's just going to guarantee that your work, that your passion is seen by a huge number of people. Whatever the definition of huge is, it doesn't matter. It's much more than it otherwise would be. And it's those lectures that tell early students what to be interested in. At the moment, I think students are disproportionately interested in the things that are well-represented on YouTube. So to any educator out there, if you're wondering, hey, I want more like grad students in my department, like what's the best way to recruit grad students? It's like, make the best video you can and then wait eight years. And then you're going to have a pile of like excellent grad students for that department. And one of the lessons I think your channel teaches is there's appeal of explaining just something beautiful, explaining it cleanly, technically, not doing a marketing video about why topology is great. Yeah, there's people interested in this stuff. I mean, one of the greatest channels, like it's not even a math channel, but the channel with greatest math content is Vsauce, who I interviewed. Imagine you were to propose making a video that explains the Banach-Tarski paradox substantively, right, not shying around, and maybe not describing things in terms of like the group theoretic terminology that you'd usually see in a paper, but the actual results that went into this idea of like breaking apart a sphere, proposing that to like a network TV station, saying, yeah, I'm going to do this in-depth talk of the Banach-Tarski paradox. I'm pretty sure it's going to reach 20 million people. It's like, get out of here. Like, no one cares about that. No one's interested in anything even anywhere near that. But then you have Michael's quirky personality around it and just people that are actually hungry for that kind of depth, then you don't need like the approval of some higher network. You can just do it and let the people speak for themselves. So I think, you know, if your father was to make something on plasma physics, or if we were to have like underactualized robotics, that would- Underactuated. Underactuated. Yes, not underactualized. It's funny, actualized. Underactuated robotics. Yeah, most robotics is underactualized currently. That's true. So even if it's things that you might think are niche, I bet you'll be surprised by how many people actually engage with it really deeply. Although I just psychologically watching him, I can't speak for a lot of people. I can speak for my dad. I think there's a little bit of a skill gap, but I think that could be overcome. That's pretty basic. None of us know how to make videos when we start. The first stuff I made was terrible in a number of respects. Like look at the earliest videos on any YouTube channel, except for Captain Disillusion. And they're all like terrible versions of whatever they are now. But the thing I've noticed, especially like with world experts, is it's the same thing that I'm sure you went through, which is like fear of like embarrassment. Like they definitely, it's the same reason. Like I feel that anytime I put out a video, I don't know if you still feel that, but like, I don't know, it's this imposter syndrome. Like who am I to talk about this? And that's true for like even things that you've studied for like your whole life. I don't know, it's scary to post stuff on YouTube. It is scary. I honestly wish that more of the people who had that modesty to say who am I to post this were the ones actually posting it. They're posting it, that's right. I mean, the honest problem is like a lot of the educational content is posted by people who like were just starting to research it two weeks ago and are on a certain schedule, and who maybe should think like who am I to explain, choose your favorite topic, quantum mechanics or something. And the people who have the self-awareness to not post are probably the people also best positioned to give a good, honest explanation of it. That's why there's a lot of value in a channel like Numberphile, where they basically trap a really smart person and force them to explain stuff on a brown sheet of paper. But of course, that's not scalable as a single channel. If there's anything beautiful that it could be done is people take it in their own hands, educators. Which is again, circling back, I do think the pandemic will serve to force a lot of people's hands. You're gonna be making online content anyway. It's happening, right? Just hit that publish button and see how it goes. Yeah, see how it goes. The cool thing about YouTube is it might not go for a while, but like 10 years later, it'll be like, this is the thing, what people don't understand with YouTube, at least for now, at least that's my hope with it, is it's literally better than publishing a book in terms of the legacy. It will live for a long, long time. Of course, it's one of the things, I mentioned Joe Rogan before, it's kinda, there's a sad thing, because I'm a fan, he's moving to Spotify. Yeah, nine digit numbers will do that to you. But he doesn't really, he's one of the person that doesn't actually care that much about money. Like having talked to him, it wasn't because of money, it's because he legitimately thinks that they're going to do a better job. So from his perspective, YouTube, you have to understand where they're coming from, YouTube has been cracking down on people who they, Joe Rogan talks to Alex Jones and conspiracy theories and stuff, and YouTube is really careful with that kind of stuff, and that's not a good feeling. And Joe doesn't feel like YouTube is on his side. He's often has videos that they don't put in trending that are obviously should be in trending because they're nervous about if this, is this content going to upset people, all that kind of stuff, have misinformation, and that's not a good place for a person to be in, and Spotify is giving them, we're never going to censor you, we're never going to do that. But the reason I bring that up, whatever you think about that, I personally think that's bullshit because podcasting should be free and not constrained to a platform, it's pirate radio, what the hell, you can't, as much as I love Spotify, you can't just, you can't put fences around it. But anyway, the reason I bring that up is Joe's gonna remove his entire library from YouTube. Whoa, really? I didn't know that. His full length, the clips are gonna stay, but the full length videos are all, I mean, made private or deleted, that's part of the deal. And that's the first time where I was like, oh, YouTube videos might not live forever, things you find, okay, sorry. This is why you need IPFS or something where it's like, if there's a content link, are you familiar with this system at all? Right now, if you have a URL that points to a server, there's a system where the address points to content and then it's distributed. So you can't actually delete what's at an address because it's content addressed. And as long as there's someone on the network who hosts it, it's always accessible at the address that it once was. But I mean, that raises a question. I'm not gonna put you on the spot, but somebody like Vsauce, right? Spotify comes along and gives him, let's say $100 billion, okay? Let's say some crazy number and then removes it from YouTube, right? It's made me, I don't know, for some reason I thought YouTube was forever. I don't think it will be. I mean, another variant that this might take is like that you fast forward 50 years and Google or Alphabet isn't the company that it once was and it's kind of struggling to make ends meet and it's been supplanted by whoever wins on the AR game or whatever it might be. And then they're like, you know, all of these videos that we're hosting are pretty costly. So we're gonna start deleting the ones that aren't watched that much and tell people to try to back them up on their own or whatever it is. Or even if it does exist in some form forever, it's like if people are not habituated to watching YouTube in 50 years, they're watching something else, which seems pretty likely. Like it would be shocking if YouTube remained as popular as it is now indefinitely into the future. So it won't be forever. Makes me sad still, but, cause it's such a nice, it's just like you said of the canonical videos. Sorry, I didn't mean to interrupt. Do you know, you should get Juan Bennett on the thing and then talk to him about permanence. I think you would have a good conversation. Who's that? So he's the one that founded this thing called IPFS that I'm talking about. And if you have him talk about basically what you're describing, like, oh, it's sad that this isn't forever, then you'll get some articulate pontification around it. Yeah. That's like been pretty well thought through. But yeah, I do see YouTube, just like you said, as a place, like what your channel creates, which is like a set of canonical videos on a topic. Now others could create videos on that topic as well, but as a collection, it creates a nice set of places to go if you're curious about a particular topic. And it seems like coronavirus is a nice opportunity to put that knowledge out there in the world at MIT and beyond. I have to talk to you a little bit about machine learning, deep learning, and so on. Again, we talked about last time, you have a set of beautiful videos on neural networks. Let me ask you first, what is the most beautiful aspect of neural networks and machine learning to you? From making those videos, from watching how the field is evolving, is there something mathematically or in applied sense just beautiful to you about them? Well, I think what I would go to is the layered structure and how you can have, what feel like qualitatively distinct things happening going from one layer to another, but that are following the same mathematical rule. Because you look at it as a piece of math, it's like you got a non-linearity and then you've got a matrix multiplication. That's what's happening on all the layers. But especially if you look at some of the visualizations that Chris Ola has done with respect to convolutional nets that have been trained on ImageNet, trying to say, what does this neuron do? What does this family of neurons do? What you can see is that the ones closer to the input side are picking up on very low level ideas like the texture. And then as you get further back, you have higher level ideas like, where are the eyes in this picture? And then how do the eyes form like an animal? Is this animal a cat or a dog or a deer? You have this series of qualitatively different things happening, even though it's the same piece of math on each one. So that's a pretty beautiful idea that you can have like a generalizable object that runs through the layers of abstraction, which in some sense constitute intelligence, is having those many different layers of an understanding to something. You have form abstractions in a automated way. Exactly, it's automated abstracting, which I mean, that just feels very powerful. And the idea that it can be so simply mathematically represented. I mean, a ton of like modern in-mouth research seems a little bit like you do a bunch of ad hoc things, then you decide which one worked and then you retrospectively come up with the mathematical reason that it always had to work. But who cares how you came to it? When you have like that elegant piece of math, it's hard not to just smile seeing it work in action. Well, and we talked about topology before, but one of the really interesting things is beginning to be investigated under kind of the field of like science and deep learning, which is like the craziness of the surface that is trying to be optimized in neural networks. I mean, the amount of local minima, local optima there is in the surfaces, and somehow a dumb gradient descent algorithm is able to find really good solutions. That's like, that's really surprising. Well, so on the one hand it is, but also it's like not, it's not terribly surprising that you have these interesting points that exist when you make your space so high dimensional. Like GPT-3, what did it have? 175 billion parameters. So it doesn't feel as mesmerizing to think about, oh, there's some surface of intelligent behavior in this crazy high dimensional space. Like there's so many parameters that of course, but what's more interesting is like, how is it that you're able to efficiently get there? Which is maybe what you're describing that something as dumb as gradient descent does it. But like the reason the gradient descent works well with neural networks and not just, choose however you want to parameterize this space and then like apply gradient descent to it, is that that layered structure lets you decompose the derivative in a way that makes it computationally feasible. Yeah, it's just that there's so many good solutions, probably infinitely many good solutions, not best solutions, but good solutions. That's what's interesting. It's similar to Steven Wolfram has this idea of like, if you just look at all space of computations, of all space of basically algorithms, that you'd be surprised how many of them are actually intelligent. Like if you just randomly pick from the bucket, that's surprising. I tend to think like a tiny, tiny minority of them would be intelligent. But his sense is like, it seems weirdly easy to find computations that do something interesting. Well, okay, so that, from like a Kolmogorov complexity standpoint, almost everything will be interesting. What's fascinating is to find the stuff that's describable with low information, but still does interesting things. Like one fun example of this, you know, Shannon's noisy coding theorem, noisy coding theorem and information theory, that basically says, if I wanna send some bits to you, maybe some of them are gonna get flipped. There's some noise along the channel. I can come up with some way of coding it that's resilient to that noise, that's very good. And then he quantitatively describes what very good is. What's funny about how he proves the existence of good error correction codes, is rather than saying like, here's how to construct it, or even like a sensible non-constructive proof. The nature of his non-constructive proof is to say, if we chose a random encoding, it would be almost at the limit, which is weird, because then it took decades for people to actually find any that were anywhere close to the limit. And what his proof was saying is choose a random one, and it's like the best kind of encoding you'll ever find. But what that tells us is that sometimes when you choose a random element from this ungodly huge set, that's a very different task from finding an efficient way to actively describe it. Because in that case, the random element, to actually implement it as a bit of code, you would just have this huge table of like, telling you how to encode one thing into another that's totally computationally infeasible. So on the side of like, how many possible programs are interesting in some way? It's like, yeah, tons of them. But the much, much more delicate question is when you can have a low information description of something that still becomes interesting. And thereby, that kind of gives you a blueprint for how to engineer that kind of thing. Right. Chaos theory is another good instance there where it's like, yeah, a ton of things are hard to describe, but how do you have ones that have a simple set of governing equations that remain like arbitrarily hard to describe? Well, let me ask you, you mentioned GPT-3. It's interesting to ask, what are your thoughts about the recently released OpenAI GPT-3 model that I believe is already trying to learn how to communicate like Grant Sanderson? You know, I think I got an email a day or two ago about someone who wanted to try to use GPT-3 with Manim, where you would like give it a high level description of something and then it'll like automatically create the mathematical animation. Like, trying to put me out of a job here. I mean, it probably won't put you out of a job, but it'll create something visually beautiful for sure. I would be surprised if that worked as stated, but maybe there's like variants of it like that you can get to. I mean, like a lot of those demos, it's interesting. I think there's a lot of failed experiments, like depending on how you prime the thing, you're going to have a lot of failed, certainly with code and with program synthesis, most of it won't even run. But eventually I think if you pick the right examples, you'll be able to generate something cool. And I think that even that's good enough, even though if you're being very selective, it's still cool that something can be generated. Yeah, that's huge value. I mean, think of the writing process. Sometimes a big part of it is just getting a bunch of stuff on the page and then you can decide what to whittle down to. So if it can be used in like a man-machine symbiosis where it's just giving you a spew of potential ideas that then you can refine down, like it's serving as the generator and then the human serves as the refiner, that seems like a pretty powerful dynamic. Yeah, have you gotten a chance to see any of the demos like on Twitter? Is there a favorite you've seen? Oh, my absolute favorite. Yeah, so Tim Bley, who runs a channel called Acapella Science, he was like tweeting a bunch about playing with it. And so GPT-3 was trained on the internet from before COVID. So in a sense, it doesn't know about the coronavirus. So what he seeded it with was just a short description about like a novel virus emerges in Wuhan, China and starts to spread around the globe. What follows is a month by month description of what happens, January colon, right? That's what he seeds it with. So then what GPT-3 generates is like January, then a paragraph of description, February and such. And it's the funniest thing you'll ever read because it predicts a zombie apocalypse, which of course it would because it's trained on like the internet data. Yeah, the internet. And it's full of zombie stories. But what you see unfolding is a description of COVID-19 if it were a zombie apocalypse. And like the early aspects of it are kind of shockingly in line with what's reasonable. And then it gets out of hand so quickly. And the other flip side of that is I wouldn't be surprised if it's onto something at some point here. You know, 2020 has been full of surprises. Who knows, like we might all be in like this crazy militarized zone as it predicts just a couple months off. Yeah, I think there's definitely an interesting tool of storytelling. It has struggled with mathematics, which is interesting, or just even numbers. It's able to, it's not able to generate like patterns, you know, like you give it in like five digit numbers and it's not able to figure out the sequence, you know, or like, I didn't look in too much, but I'm talking about like sequences like the Fibonacci numbers and to see how far it can go. Because obviously it's leveraging stuff from the internet and it starts to lose it, but it is also cool that I've seen it able to generate some interesting patterns that are mathematically correct. Yeah, I honestly haven't dug into like what's going on within it in a way that I can speak intelligently to. I guess it doesn't surprise me that it's bad at numerical patterns because, I mean, maybe I should be more impressed with it, but like that requires having a weird combination of intuitive and formulaic worldview. So you're not just going off of intuition when you see Fibonacci numbers, you're not saying like, intuitively, what do I think will follow the 13? Like I've seen patterns a lot where like 13s are followed by 21s. Instead it's the, like the way you're starting to see a shape of things is by knowing what hypotheses to test, where you're saying, oh, maybe it's generated based on the previous terms, or maybe it's generated based on like multiplying by a constant or whatever it is. You like have a bunch of different hypotheses and your intuitions are around those hypotheses, but you still need to actively test it. And it seems like GPT-3 is extremely good at, like that sort of pattern matching recognition that usually is very hard for computers, that is what humans get good at through expertise and exposure to lots of things. It's why it's good to learn from as many examples as you can, rather than just from the definitions. It's to get that level of intuition, but to actually concretize it into a piece of math, you do need to like test your hypotheses. And if not prove it, like have an actual explanation for what's going on, not just a pattern that you've seen. Yeah, and, but then the flip side to play devil's advocate, that's a very kind of probably correct, intuitive understanding of just like we said, a few layers creating abstractions, but it's been able to form something that looks like a compression of the data that it's seen that looks awfully a lot like it understands what the heck it's talking about. Well, I think a lot of understanding is, like I don't mean to denigrate pattern recognition. Pattern recognition is most of understanding and it's super important and it's super hard. And so like when it's demonstrating this kind of real understanding, compressing down some data, like that might be pattern recognition at its finest. My only point would be that, like what differentiates math, I think, to a large extent is that the pattern recognition isn't sufficient and that the kind of patterns that you're recognizing are not like the end goals, but instead they are the little bits and paths that get you to the end goal. So that's only true for mathematics in general. It's an interesting question if that might, for certain kinds of series of numbers, it might not be true. Like you might, because that's the basic, you know, like Taylor's, like certain kinds of series, it feels like compressing the internet is enough to figure out, because those patterns in some form appear in the text somewhere. Well, I mean, there's all sorts of wonderful examples of false patterns in math. One of the earliest videos I put on the channel was talking about you kind of dividing a circle up using these chords and you see this pattern of one, two, four, eight, 16. And I was like, okay, pretty easy to see what that pattern is. It's powers of two. You've seen it a million times, but it's not powers of two. The next term is 31. And so it's like almost a power of two, but it's a little bit shy. And there's actually a very good explanation for what's going on, but I think it's a good test of whether you're thinking clearly about mechanistic explanations of things, how quickly you jump to thinking it must be powers of two. Because the problem itself, there's really no good way to, I mean, there can't be a good way to think about it as doubling a set because ultimately it doesn't. But even before it starts to, it's not something that screams out as being a doubling phenomenon. So at best, if it did turn out to be powers of two, it would have only been so very subtly. And I think the difference between a math student making a mistake and a mathematician who's experienced seeing that kind of pattern is that they'll have a sense from what the problem itself is, whether the pattern that they're observing is reasonable and how to test it. And I would just be very impressed if there was any algorithm that was actively accomplishing that goal. Yeah, like a learning-based algorithm. Yeah, like a little scientist, I guess, basically. Yeah, it's a fascinating thought because GPT-3, these language models are already accomplishing way more than I've expected. So I'm learning not to doubt. I bet we'll get there. Yeah, I'm not saying I'd be impressed, but surprised. I'll be impressed, but I think we'll get there on algorithms doing math like that. So one of the amazing things you've done for the world is to some degree open sourcing the tooling that you use to make your videos with Manum, this Python library. Now, it's quickly evolving because I think you're inventing new things every time you make a video. In fact, I've been working on playing around with some, I wanted to do like an ode to 3Blue1Brown. I love playing Hendrix. I wanted to do like a cover of a concept I wanted to visualize and use Manum. And I saw that you had like a little piece of code on like Mobius strip. And I tried to do some cool things with spinning a Mobius strip, like continue twisting it, I guess is the term. And it was easier to, it was tough. So I haven't figured out yet. So I guess the question I want to ask is so many people love it, that you've put that out there. They want to do the same thing as I do with Hendrix. They want to cover it. They want to explain an idea using the tool, including Russ. How would you recommend they try to, I'm very sorry. They try to go by, about it. And what kind of choices should they choose to be most effective? That I can answer. So I always feel guilty if this comes up because I think of it like this scrappy tool. That's like a math teacher who put together some code. People asked what it was. So they made it open source and they kept scrapping it together. And there's a lot of things about it that make it harder to work with than it needs to be that are a function of like me not being a software engineer. I've put some work this year trying to like make it better and more flexible that is still just kind of like a work in process. One thing I would love to do is just get my act together about properly integrating with what like the community wants to work with and like what stuff I work on and making that not like deviate. And just like actually fostering that community in a way that I've been like shamefully neglectful of. So I'm just always guilty if it comes up. So let's put that guilt aside. Just kind of zen like. All right, zen like. I'll pretend like it isn't terrible. For someone like Russ, I think step one is like make sure that what you're animating should be done so programmatically. Because a lot of things maybe shouldn't. Like if you're just making a quick graph of something, if it's a graphical intuition that maybe has a little motion to it, use Desmos, use Grapher, use Geogebra, use Mathematica. Certain things that are like really oriented around graphs. Geogebra is kind of cool. It's amazing. You can get very, very far with it. And in a lot of ways, like it would make more sense for some stuff that I do to just do in Geogebra. But I kind of have this cycle of liking to try to improve Manim by doing videos and such. So do as I say, not as I do. The original like thought I had in making Manim was that there's so many different ways of representing functions other than graphs. In particular, things like transformations, like use movement over time to communicate relationships between inputs and outputs instead of like X direction and Y direction. Or like vector fields or things like that. So I wanted something that was flexible enough that you didn't feel constrained into a graphical environment. By graphical, I mean like graphs with like X coordinate, Y coordinate kind of stuff. But also make sure that you're taking advantage of the fact that it's programmatic. You have loops, you have conditionals, you have abstraction. If any of those are like well fit for what you want to teach to have a scene type that you tweak a little bit based on parameters or to have conditionals so that things can go one way or another or loops so that you can create these things of like arbitrarily increasing complexity. That's the stuff that's like meant to be animated programmatically. If it's just like writing some text on the screen or shifting around objects or something like that, things like that, you should probably just use Keynote. You'd be a lot simpler. So try to find a workflow that distills down that which should be programmatic into Manim and that which doesn't need to be into like other domains. Again, do as I say, not as I do. I mean, Python is an integral part of it. Just for the fun of it, let me ask, what's your most and least favorite aspects of Python? Ooh, most and least. I mean, I love that it's like object-oriented and functional, I guess, that you can kind of like get both of those benefits for how you structure things. So if you would just want to quickly whip something together, the functional aspects are nice. It's your primary language, like for programmatically generating stuff? Yeah, it's home for me. Python is home. It's home. Yeah. Sometimes you travel, but it's home. Got it. It's home. I mean, the biggest disadvantage is that it's slow. So when you're doing computationally intensive things, either you have to like think about it more than you should, how to make it efficient, or it just like takes long. Do you run into that at all? Like with your work? Well, so certainly old Manim is like way slower than it needs to be because of how it renders things on the back end is like kind of absurd. I've rewritten things such that it's all done with like shaders in such a way that it should be just like live and actually like interactive while you're coding it, if you want to. You know, you have like a 3D scene, you can move around, you can have elements respond to where your mouse is or things. That's not something that user of a video is going to get to experience because there's just a play button and a pause button. But while you're developing, that can be nice. So it's gotten better in speed in that sense, but that's basically because the hard work is being done in the language that's not Python, but GLSL, right? But yeah, there are some times when it's like a, there's just a lot of data that goes into the object that I want to animate that then it just like Python is slow. Well, let me ask, quickly ask, what do you think about the Walrus operator, if you're familiar with it at all? The reason it's interesting, there's a new operator in Python 3.8. I find it psychologically interesting because the toxicity over it led Guido to resign, to step down from his- Is that actually true? Or was it like, there's a bunch of surrounding things that also, was it actually the Walrus operator that- Well, it was an accumulation of toxicity, but that was the most toxic one. Like the discussion, that's the most number of Python core developers that were opposed to Guido's decision. He didn't particularly, I don't think, cared about it either way. He just thought it was a good idea, this is where you approve it. And like the structure of the idea of a BDFL is like, you listen to everybody, hear everybody out, you make a decision and you move forward. And he didn't like the negativity that burdened him after that. People like some parts of the benevolent dictator for life mantra, but once the dictator does things different than you want, suddenly dictatorship doesn't seem so great. Yeah, I mean, they still liked it, he just couldn't, because he truly is the B in the benevolent. He really is a nice guy. I mean, and I think he can't, it's a lot of toxicity, it's difficult, it's a difficult job. That's why Alonis Torvald is perhaps the way he is. You have to have a thick skin to fight off, fight off the warring masses. It's kind of surprising to me how many people can like threaten to murder each other over whether we should have braces or not, or whether, like, it's incredible. Yeah, I mean, that's my knee-jerk reaction to the Walrus Operators. Like, I don't actually care that much. Either way, I'm not going to get personally passionate. My initial reaction was like, yeah, this seems to make things more confusing to read. But then again, so does list comprehension until you're used to it. So, like, if there's a use for it, great. If not, great. But like, let's just all calm down about our spaces versus tabs debates here and like, be chill. Yeah, to me, it just represents the value of great leadership, even in open source communities. Does it represent that? If he stepped down as a leader? Well, he fought for it. No, he got it passed. I guess, but I guess, sure. It could represent multiple things too. It can represent like failed dictatorships, or it can represent a lot of things. But to me, great leaders take risks, even if it's a mistake at the end. Like, you have to make decisions. The thing is, this world won't go anywhere if you constantly, if whenever there's a divisive thing, you wait until the division is no longer there. Like, that's the paralysis we experienced with like Congress and political systems. It's good to be slow when there's indecision, when there's people disagree, it's good to take your time. But like at a certain point, it results in paralysis and you just have to make a decision. The background of the site, whether it's yellow, blue, or red can cause people to like go to war over each other. I've seen this with design. People are very touchy on color. Color choices. At the end of the day, just make a decision and go with it. I think that's what the Walrus operator represents to me. It represents the fighter pilot instinct of like quick action is more important than- Than just like carrying everybody out and really thinking through it, because that's going to lead to paralysis. Yeah, like if that's the actual case, that it's something where you're consciously hearing people's disagreement, disagreeing with that disagreement, and saying he wants to move forward anyway. That's an admirable aspect of leadership. So we don't have much time, but I want to ask just, because it's some beautiful mathematics involved. 2020 brought us a couple of, in the physics world, theories of everything. Eric Weinstein kind of, I mean, he's been working for probably decades, but he put out this idea of geometric unity, or started sort of publicly thinking and talking about it more. Stephen Wolfram put out his physics project, which is kind of this hypergraph view of a theory of everything. Do you find interesting, beautiful things to these theories of everything? What do you think about the physics world and sort of the beautiful, interesting, insightful mathematics in that world? Whether we're talking about quantum mechanics, which you touched on in a bunch of your videos a little bit, or quaternions, like just the mathematics involved, or the general relativity, which is more about surfaces and topology, all that stuff. Well, I think as far as popularized science is concerned, people are more interested in theories of everything than they should be. Because the problem is, whether we're talking about trying to make sense of Weinstein's lectures or Wolfram's project, or let's just say, listening to Witten talk about string theory, whatever proposed path to a theory of everything, you're not actually gonna understand it. Some physicists will, but like, you're just not actually gonna understand the substance of what they're saying. What I think is way, way more productive is to let yourself get really interested in the phenomena that are still deep, but which you have a chance of understanding. Because the path to getting to like, even understanding what questions these theories of everything are trying to answer involves like walking down that. I mean, I was watching a video before I came here about, from Steve Mould, talking about why sugar polarizes light in a certain way. So fascinating, like really, really interesting. It's not like this novel theory of everything type thing, but to understand what's going on there really requires digging in in depth to certain ideas. And if you let yourself think past what the video tells you about, what does circularly polarized light mean and things like that, it actually would get you to a pretty good appreciation of like two state states in quantum systems in a way that just trying to read about like, oh, what's the, what are the hard parts about resolving quantum field theories with general relativity is never gonna get you. So as far as popularizing science is concerned, like the audience should be less interested than they are in theories of everything. The popularizers should be less emphatic than they are about that. For like actual practicing physicists, I might be the case, maybe more people should think about fundamental questions, but. It's difficult to create like a three blue, one brown video on theory of everything. So basically we should really try to find the beauty in mathematics or physics by looking at concepts that are like within reach. Yeah, I think that's super important. I mean, so you see this in math too with the big unsolved problems. So like the clay millennium problems, Riemann hypothesis. Have you ever done a video on Fermat's last theorem? No, I have not yet, no. But if I did, do you know what I would do? I would talk about proving Fermat's last theorem in the specific case of N equals three. Is that still accessible though? Yes, actually, barely. Mathologer might be able to do like a great job on this. He does a good job of taking stuff that's barely accessible and making it. But the core ideas of proving it for N equals three are hard but they do get you real ideas about algebraic number theory. It involves looking at a number field that's, it lives in the complex plane. It looks like a hexagonal lattice and you start asking questions about factoring numbers in this hexagonal lattice. So it takes a while, but I've talked about this sort of like lattice arithmetic in other contexts. And you can get to a okay understanding of that. And the things that make Fermat's last theorem hard are actually quite deep. And so the cases that we can solve it for, it's like you can get these broad sweeps based on some hard but like accessible bits of number theory. But before you can even understand why the general case is as hard as it is, you have to walk through those. And so any other attempt to describe it would just end up being like shallow and not really productive for the viewer's time. I think the same goes for most unsolved problem type things where I think, as a kid, I was actually very inspired by the twin prime conjecture that totally sucked me in. It's this thing that was understandable. I kind of had this dream like, oh, maybe I'll be the one to prove the twin prime conjecture. And new math that I would learn would be viewed through this lens of like, oh, maybe I can apply it to that in some way. But you sort of mature to a point where you realize you should spend your brain cycles on problems that you will see resolved, because then you're gonna grow to see what it feels like for these things to be resolved, rather than spending your brain cycles on something where it's not gonna pan out. And the people who do make progress towards these things, like James Maynard is a great example here of like young creative mathematician who pushes in the direction of things like the twin prime conjecture, rather than hitting that head on, just see all the interesting questions that are hard for similar reasons, but become more tractable and let themselves really engage with those. So I think people should get in that habit. I think the popularization of physics should encourage that habit through things like the physics of simple everyday phenomena, because it can get quite deep. And yeah, I think I've heard a lot of the interest that people send me messages asking to explain Weinstein's thing, or asking to explain Wolfram's thing. One, I don't understand them, but more importantly, it's too big a bite to- You shouldn't be interested in those, right? The giant sort of ball of interesting ideas. There's probably a million of interesting ideas in there that individually could be explored effectively. And to be clear, you should be interested in fundamental questions. I think that's a good habit to ask like what the fundamentals of things are. But I think it takes a lot of steps to, like certainly you shouldn't be trying to answer that unless you actually understand quantum field theory and you actually understand general relativity. That's the cool thing about like your videos, people who haven't done mathematics. Like if you really give it time, watch it a couple of times and like try to reason about it, you can actually understand the concept that's being explained. And it's not a coincidence that the things I'm describing aren't like the most up-to-date progress on the Riemann hypothesis cousins, or like there's context in which the analog of the Riemann hypothesis has been solved in like more discrete feeling, finite settings that are more well-behaved. I'm not describing that because it just takes a ton to get there. And instead I think it'll be like productive to have an actual understanding of something that you can pack into 20 minutes. I think that's beautifully put. Ultimately that's where like the most satisfying thing is when you really understand. Yeah, really understand. Build a habit of feeling what it's like to actually come to resolution. Yeah, yeah. As opposed to, which it can also be enjoyable, but just being in awe of the fact that you don't understand anything. Yeah, that's not like, I don't know, maybe people get entertainment out of that, but it's not as fulfilling as understanding. You won't grow. Yeah, but also just the fulfilling. It really does feel good when you first don't understand something and then you do. That's a beautiful feeling. Hey, let me ask you one last time it got awkward and weird about a fear of mortality, which you made fun of me of. But let me ask you on the other absurd question is, what do you think is the meaning of our life, of meaning of life? I'm sorry if I made fun of you about mortality. No, you didn't. I'm just joking. It was great. I don't think life has a meaning. I think like meaning, I don't understand the question. I think meaning is something that's ascribed to stuff that's created with purpose. There's a meaning to like this water bottle label and that someone created it with a purpose of conveying meaning. And there was like one consciousness that wanted to get its ideas into another consciousness. Most things don't have that property. It's a little bit like if I ask you, like, what is the height? All right, so it's all relative. Yeah, you'd be like the height of what? You can't ask what is the height without an object. You can't ask what is the meaning of life without like an intentful consciousness putting it, well, I guess I'm revealing I'm not very religious. But you know, the mathematics of everything seems kind of beautiful. It seems like there's some kind of structure relative to which, I mean, you could calculate the height. Well, so, but what I'm saying is I don't understand the question, what is the meaning of life, in that I think people might be asking something very real. I don't understand what they're asking. Are they asking like, why does life exist? Like, how did it come about? What are the natural laws? Are they asking, as I'm making decisions day by day for what should I do, what is the guiding light that inspires like, what should I do? I think that's what people are kind of asking. But also like, why, the thing that gives you joy about education, about mathematics, what the hell is that? Like, what? Interactions with other people. Interactions with like-minded people, I think is the meaning of, in that sense. So bringing others joy, essentially. Like, in something you've created, it connects with others somehow. And the same, and the vice versa. I think that is what, when we use the word meaning to mean like, you're sort of filled with a sense of happiness and energy to create more things. Like, I have so much meaning taken from this. Like that, yeah, that's what fuels my pump, at least. So a life alone on a deserted island would be kind of meaningless. Yeah, you wanna be alone together with someone. I think we're all alone together. I think there's no better way to end it, Grant. You've been, first time we talked, it was amazing. Again, it's a huge honor that you make time for me. I appreciate talking with you. Thanks, man. Awesome. Thanks for listening to this conversation with Grant Sanderson. And thank you to our sponsors, Dollar Shave Club, DoorDash, and Cash App. Click the sponsor links in the description to get a discount and to support this podcast. If you enjoy this thing, subscribe on YouTube, review it with Five Stars on Apple Podcast, follow on Spotify, support on Patreon, or connect with me on Twitter at Lex Friedman. And now, let me leave you with some words from Richard Feynman. I have a friend who's an artist and is sometimes taken a view which I don't agree with very well. He'll hold up a flower and say, look how beautiful it is. And I'll agree. Then he says, I, as an artist, can see how beautiful this is, but you, as a scientist, take this all apart and it becomes a dull thing. And I think he's kind of nutty. First of all, the beauty that he sees is available to other people and to me too, I believe. Although I may not be quite as refined aesthetically as he is, I can appreciate the beauty of a flower. At the same time, I see much more about the flower than he sees. I can imagine the cells in there, the complicated actions inside, which also have a beauty. I mean, it's not just beauty at this dimension at one centimeter, there's also beauty at smaller dimensions, the inner structure, also the processes. The fact that the colors in the flower evolved in order to attract insects to pollinate it is interesting. It means that insects can see the color. It adds a question. Does this aesthetic sense also exist in the lower forms? Why is it aesthetic? All kinds of interesting questions which the science knowledge only adds to the excitement, the mystery and the awe of a flower. It only adds. I don't understand how it subtracts. Thank you for listening and hope to see you next time.