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 three blue one brown 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 three blue one brown 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 on to 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 three blue one brown youtube channel you will not regret it as usual i'll do a few minutes of as now 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donate ten dollars to first an organization that is helping you 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 um who is uh 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 fineman right that's um almost like when you don't know what to say about sports and you just point to the super bowl or something it's something you enjoy watching but i do actually think there's a layer to feynman that like 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 you know the 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 fineman 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 you know he kind of sometimes has this output of being this ah shucks character like everyone else is coming in this with these fancy flute and 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 um 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 uh saw that it was about findman she was like oh i love him i read shirley you're joking and she started explaining to me how he was never really a math person and uh i don't understand how that could possibly be a public perception about any physicist but for whatever reason that like worked into his or that he sort of shoot off math 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 um 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 what i like about uh his way of going at things is this constant desire to reinvent it for himself like when he would consume papers the way he described 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 want to 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 see do you try to rediscover everything yourself so um i think the things that i've like 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 for my part it's actually a big fault like this is part of why i'm 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 um but other times you do need to get through it at a certain pace you do 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 uh 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 going to try to approach this before i see how this person went at it i'm really going to try to approach it for myself no matter what you gain all sorts of inarticulatable intuitions about that topic which aren't going to be there if you simply go through the proof for example you're going to be trying to come up with counter examples you're going to try to come up with um 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 um but in so far he's got it got him to where he was uh i i i kind of resonate with that i just i would i would be nowhere near it because i not like him at all but it's like a state to aspire to you know just to look at 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 want to 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 want to 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 um i'm pretty good at exposing math to others and like want to continue doing that for my personal learning i are you familiar with like the hedgehog fox dynamic i think this was um either the ancient greeks came up with it or it was pretended to be something drawn from the ancient creek said i don't know who to point it to but they had probably mocked 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 a fox he's someone who knows many different things just very foundational 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 um so between those two i would definitely see myself as like the fox where uh 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 um like having a decently deep understanding of a wide variety of things like most people who uh 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 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 uh 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 uh 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 uh the multi-dimensional visualization we'll talk about i mean you're revealing something very interesting that uh 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 um 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's like oh yeah that whole 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 uh visualization well his teaching style is interesting because people have described like the feynman effect where while you're watching his lectures or while he's reading his lectures everything makes such perfect sense so as an entertainment session it's wonderful because it gives you this 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 you know even a week later and this is um this is true of a lot of books in a lot of lectures where the retention is never quite what we hope it is um so there is a risk that uh 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 um to solidify it um 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 findman'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 well 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 a surface or to to change the shape of something i think that's almost an equivalent of you doing it yourself it's not quite there but you as a viewer um 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 um and you could ask like hey while you're programming these things why don't you program it into an interactable version that 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 uh 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 genuinely 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 um 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 um 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 um 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 want to see how that affects its evolution um my my uh 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 uh and then i saw what stories there were to tell within that um yeah that's cool so your video had that kind of structure it had uh 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 here 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 um and 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 uh the visuals that someone will look at it's to be the one to decide what's the interesting thing to walk through here um 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 it's like 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 uh making the 20 minutes already that to extend it out even further it would take more time and one of your cooler videos the homomorphic like from the mobius strip to the described rectangle yeah that's the super and you're like yeah you can't uh you can't transform the mobius strip into uh into a surface without it intersecting itself but i'll leave it to you to to see why that is 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 uh 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 not 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 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 um i don't want to say it's taught wrong but i do think sometimes it's popularized in the wrong way where uh you know you'll hear these things of 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 yeah 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 that's uh it's not as if someone was sitting there thinking like i wonder what the properties of clay are if i had some arbitrary rules about what when i can't cut it and when i can't glue it instead it's 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 pub like popularized um 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 um 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 yeah um and just it's not 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 mobius 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 um this is making me feel like i need to make more videos on the topic because i think you do but you know i've also seen it in my narrow view of uh like i'm i find game theory very beautiful and i know topology has been used uh 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 um after you stir it and like let's say all the molecules settle to like not moving again one of the molecules will be basically in the same position it was before um you have all sorts of fixed point theorems like this right that kind of fixed point theorem directly relevant to nash equilibriums right um 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 um you have this very elegant mapping onto economics in a way that's very concrete or very i shouldn't say concrete very uh tangible like actually adds value to people's lives through the predictions that it makes but that line isn't always drawn because like 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 oh by the way for people who are watching the video i do not condone the message and 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 struggle 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 um pandemics from 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 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 they're it's really their mobility patterns like how like they try 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 i'm an epidemiologist like we have a ton of armchair epidemiologists and the spirit of that was more like uh can we through a little bit of play uh draw like reasonable-ish conclusions um and also just like uh 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 um but to say like what what lessons from that hold like thinking about the are not value and what that represents and what it can imply or not so are not is if you are infectious and you're in a population which is um 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 um as it goes on and let's say it's something um uh endemic where you've got like a ton of people who have had it and are recovered then uh 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 um and this is like the fundamental constant that it seems like epidemiologists look at and you know 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 uh 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 um general enough lessons and they're like resilient to all of the chaoses of the world um 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 we think about growth is that one of the first times you've done a video on on uh no of course not the whole uh oilers identity okay so sure i've done a lot of videos about exponential growth in the circular direction uh only minimal in the normal direction i mean another way to ask like do you think we're able to reason intuitively about exponential growth it's it's funny i think it's um 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 uh so what i mean by that is um have you ever heard of these studies where in a uh like anthropological setting where you're studying a group that has been disassociated from a lot of like modern society and you ask what number is between one and nine and maybe you would ask you you've got like 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 uh numeracy and uh the kind of just basic arithmetic that we have isn't in a society the natural instinct is three because it's uh 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 what's you know if you have one friend versus a hundred friends what's in between that yeah ten friends seems like the social status in between those two states so that's like deeply intuitive to us to think logarithmically like that um 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 early basic math is uh yeah it forces us to take a step back it's 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 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 um seven times how big will it be i bet it would be surprisingly big even to like an a society without numeracy and that's the side of it that um i think is pretty counter-intuitive to us uh but that you can basically train into people like i think computer scientists and physicists when they're looking at the early numbers of um like kovid were they were the ones thinking like oh god this is following an exact exponential curve yeah um and i heard that from a number of people uh 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 this kind of growth is present in a lot of natural systems and a lot of in a lot of in a lot of systems uh 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 chess board where um every every square in the chessboard you double the number of stones or something in that chessboard i've heard this is like an old proverb where you know someone the king offered him a gift and he said uh the only gift i would like very modest give me a single grain of rice right so 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 you're sire yeah and like then it's all you know more grains of rice than there are uh anything in the world um by the time you get to the end and i i my intuition falls apart there like i would have never predicted that like for some reason that's a really compelling uh illustration how poorly breaks down just like you said maybe we're okay for the first few piles but of rocks but after a while it's game over you know the other classic example for um gauging someone's intuitive understanding of exponential growth is uh i've got like a lily pad on a on lake really big lake okay um like lake michigan and that lily pad replicates it doubles um one day and then it doubles the next day and it doubles the next day and after 50 days it actually is going to cover the entire lake okay so after how many days does it cover half the lake 49. so you you have a good instinct for exponential growth right so i think a lot of uh 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 um yeah i mean that's the reason you heard a pause from me i literally thought that can't be right right yeah exactly exactly so even when you know the fact and you do the division it's like wow so you've gone 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 um it's covered one percent of the lake right and it's uh so what would that be um how many times you have to double to get over a hundred 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 one percent of the lake so you've you've experienced you know 44 out of 50 days and you're like ah that lilly bad it's just one percent of the lake but then next thing you know it's the entire lake are you wearing a spacex sure so let me ask you sure let me ask you one one person uh who talks about exponential you know just the miracle of the exponential function in general is elon musk so he kind of advocates the idea of exponential thinking you know 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 isn't 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 what's your sense about um about that kind of way to see the world well so i think it's um 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 um and it enables um just better lives to be led i think the people who took moore's law seriously in the 60s we're seeing that wow it's not going to be too long before like 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 want to 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 the technology would grow exponentially is only going to 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 uh create new things i think this is uh oftentimes why like investment will grow exponentially that the more resources a company has if it knows how to use them well the more uh the more it can actually grow so i mean you know you reference elon musk i think he seems to really be into vertically integrating his companies i think a big part of that is because you have the sense what you want is to make sure that the things that you develop you have ownership of and they enable further development of the adjacent parts right so it's not just this you 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 so the opposite of a pandemic is you want in terms of ideas you want to minimize barriers that uh prevent the spread you want to maximize the spread of impact so like you wanted to to grow when you're doing technological development is so that you do hold up that rate holds up and that's all that's almost like a 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 and the like on a psychological level on a human level because it's not exponential it's it's just a consistent set of like what you would call like s-curves which is like it's constantly like breakthrough innovations non-stop that's a good point like it might not actually be an example of exponential 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 it's there's something about it like saying that look there is um you know moore's law it's a law so like it's uh it's certainly an achievable thing you know we've achieved it for the last decade the last two decades 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 couldn't 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 uh to create an atmosphere where the genius can discover themselves like 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 expose 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 realize 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 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 you know chess london cab drivers of how many push-ups people can do short-term memory tasks and if there's one 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 that'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 like there's 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 going to 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 you know wash rinse and repeat that self-proportionality that's exponential so i think i wouldn't i don't think 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 take be taken over by the agi that's some that's built in this similar they'll make the video game fun whoever created this thing uh so i mean since you're wearing a space actually let me let me ask uh so i didn't realize that i apologize yeah so crew dragon the first uh crude mission out into space since the 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 do you what are your how do you feel is this you know 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 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 um uh 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 um it's just a sign that we're able to do more powerful things with smaller groups of people uh 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 uh 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 like the worlds that we've touched um or people who think about things like backing up the light of consciousness with like super long-term visions of terraforming like as long as there's backing up the light of consciousness yeah yeah the thought that uh you know if we if earth goes to hell we gotta have a backup somewhere um a lot of people see that as pretty out there and it's like not in the short term future but i think that's an inspiring thought i think that's a reason to like 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 like either agi kills us first or if we're like allowed i don't know if it'll take loud well like honestly it takes it would take such a long time like okay you might have a small colony right um something like what you see in um the martian but not like people living comfortably there um but if you want to talk about actual like second earth kind of stuff that that's just like way far out there and the future moves so fast that it's hard to predict like we might just kill ourselves before that even becomes viable i yeah i mean there's 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 uh have a have a space faring backup solution that doesn't have uh that doesn't have to deal with the constraints at a planet but 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 all of the people who are like skeptical about it or like why why do we care about going to mars it's like what makes you care about anything that's not 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 it's like the people say like you know i've been doing like an insane challenge last 30 something days your pull-ups and to pull up some push-ups and like you know a bunch of people are like awesome you're insane but awesome and then some people are like why why do anything i i don't know at this there's a calling it's uh i i'm with jfk a little bit is because we do these things because they're hard there's something in the human spirit that says like same with like a math problem there's something you fail once and it's like this feeling that you know what i'm not going to back down from this there's something to be discovered in overcoming this thing well so what i like about it is um and i also like this about the moon missions sure is 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 right like protecting humans from the radiation in space on the flight there while there heart problem demands innovation you can't move the goal post to make that easier almost certainly the innovations required for things like that will be relevant in a bunch of other domains too um 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 goal posts there's probably going to be these secondary benefits that like 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 uh you know uh send tick tock videos of myself dancing to people they you know it was there's an application i mean actually i don't even know what do you think the application for the internet was when it was it must have 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 totally speaking totally outside of my knowledge but like it was probably intended for a very narrow small group of people well so i mean it was there was like this small community of people who are really interested in time sharing computing and like interactive computing in contrast with uh batch processing and then the idea that as you set up like a time sharing center uh basically meaning you have multiple people like logged in and using that like central computer um why not make it accessible to others yeah and this was kind of what i had always thought like oh is this like fringe group that was interested in this new kind of computing and they all like got themselves together but the thing is like darpa wouldn't act 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 uh like 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 like in the middle of the vietnam war when there was budgetary constraints all over the place uh i only learned this recently actually like if you look at the documents basically justifying the um 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 like 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 you know a central location gets nuked uh this is a this is a much more resilient way to still have your communication lines that like traditional um telephone lines weren't as resilient to which i just found very interesting that that um even something that we see is so happy-go-lucky is just a bunch of computer nerds trying to get like interactive computing out there the actual like thing that made it uh funded and thing that made it advance uh 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 like science and the context of the military like basically saying all the great science we've done in the in the 20th century was like because of the military i mean he paints a positive it's not like a critical it's not you know a lot of people say like 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 like hard things you can't move like almost you know almost like scaring yourself into being productive it is that i mean manhattan project is a perfect example probably the quintessential example that one uh is a little bit more macabre than others because of like 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 like 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 firemen 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 uh 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 yup that's 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 uh i i look at a bell labs type situation and i'm like god damn 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 off with 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 very likely worked separately yeah totally fine totally separate but there's a literally i'm sorry to interrupt there's a literally magic that happens when you run into each other like on the way to like get 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 um i i have some extent of it just because i just try to stay well connected in communities of uh people who think in similar ways but it's not 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 uh one of the biggest well uh one of the many um drawbacks negative things about this current pandemic is that uh whatever the term is but like chance collisions are significantly reduced i i saw um i don't know why i saw this but on my on my brother's work calendar uh he had a scheduled slot with someone um that he scheduled a meeting and the 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 only title of the match i'm like that's the way to do it you just schedule those things schedule the serendipitous interaction it's like i mean you can't do 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 like this like this you probably hit moments when you you look at this and you say like this is the wrong way to show it it's a long 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 could be paralyzing okay what do you do in those 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 um and i know that's just a thing that i'm not good at so in that way it's 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 it was kind of cool like two people that yes you got that interview yeah it's the heart hit uh no can i brag about something please uh my favorite thing is don knuth after he did the interview he offered to go out to hot dogs with me to get hot dogs that was never like people ask me what's the favorite interview you've ever done man that has to be um but unfortunately i couldn't i had a thing after so i had to turn down don knuth you missed knuth dogs canoe dogs sorry so that was a little bragging but the the hot dog is such a sweet so um but the reason i bring that up is he he works through problems alone as well he prefers that struggle the struggle of it you know writers like stephen king you know often talk about like their process of you know what they do like what they eat when they wake up like uh when they sit down like how they like their desk you know on a 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 um hunter s thompson did a lot of drugs uh you know everybody has their own thing uh what's do you have a thing is there 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 i like um the mode of work i do changes a lot from day to day like 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 like working on the animation library the thing i have to do is like a little i'm not a software engineer but something in the direction of software engineering some days it's like a variant of research it's like learn this topic well and try to learn it differently so those is like four very different modes of what it some days is like get through the email backlog of people i've been the tasks i've been putting off um it goes research scripting like the idea starts with the research and then there's scripting and then there's programming and then there's the uh show time 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 um 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 right 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 last two days so you came up with excuses to procrastinate so today must be the day yeah i uh i wake up early i i guess i exercise um and then uh i turn the internet off if we're writing yeah that's that's what's required um is having the internet off and then maybe you keep notes on the things that you want to google when you're allowed to have the internet again i'm not great about doing that but when i do uh that makes it happen and then when i hit writer's block like the solution to writer's block is to read it 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 um that when it's a nice cycle i think can work very well and when you when you're writing the script you don't know where it ends right like you have a like problem solving videos i know where it ends expositional videos i don't know where it ends like coming up with uh with the magical thing that makes this whole story like ties this whole story together is that when does that happen that's that's the thing that makes it such that a topic gets put on the list of like oh that's an issue you shouldn't start the project unless there's one of those uh and you have you have so many nice bag that you haven't 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 um discussion uh is you know if i see like even when i ask for people to ask like ask i did a call for questions and people want to ask you questions i mean so many requests from people about like certain videos that would love you to do it's such a pile and i i think that's a 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 so yeah so so you yeah 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 do you try to dedicate like a certain number of hours do you uh uh cal newport has this deep work kind of idea i'm there's systematic people who like get really on top of you know the checklist of what they're going to do in the day and they like count their hours and i am not a systematic person in that way it's which is probably a problem i very likely would get more done if i was systematic in that way but that doesn't happen um so you know maybe you talk to me 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 what how 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 um 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 you're always going to write it as the best version of yourself um 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 bed and all of that and just like zoning out for random reasons or 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 checked the previous days that's like my what i try to do uh 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 some 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 it's i don't know if it's a problem because as long as it's the kind of socializing like if you're actually engaging with friends and engaging with other people's ideas uh i think it can be really useful well i don't know so like for sure i agree with you but i'm it's a 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 because i've seen it okay one way to measure that is when somebody says something not nice to you on the internet it's like when i check it once a day i'm able to just like like i smile like like i virtually i think about them positively empathetically i send him love i don't don't ever respond but i just feel positively about the whole thing if i check if i check like more than that it starts eating at me like it start there's an eating thing that that happens like anxiety uh it occupies a part of your mind that's not doesn't seem to be healthy same with um i mean you you put stuff out on youtube i think it's important i think you have a million dimensions that are interesting to you but yeah one 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 uh 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 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 yeah so he's uh oh can i tell you a funny story in that effect of like parental use of youtube uh early on in the channel uh my mom would like text me she's like uh the chat the channel has had 990 000 views the channel's had 991 thousand 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 uh otherwise wouldn't be visible it's just like this addiction where you have some number you want to follow and then 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 they're yes it's born of love it's great the downside i feel one one of them is this is one [Music] interesting experience that you probably don't know much about because comments on your videos are super positive uh but people judge the quality of how something went like i see that with these conversations by the comments yeah like 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 oh the comments seem to be positive 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 a number of respects like uh 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 um are bored by it are are put off by it in some way or 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 um 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 uh at least have gone through phases of like anxiety about the nature of comments um that stem from basically just this that it's like people who aren't necessarily represented who they were going for or misinterpreted what they're trying to say or whatever have you or we're 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 uh translates to um realizing that you're not as important as you might think you are right 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 um i don't 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 prom i'm not sure promised to me that you'll have music incorporated into your like uh i'll share with you a private link but so there's an example of like what i had in mind i like did a version of it um 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 next circumstance that i'm like doing another recorded live performance that like fits having that then in a better recording maybe i'll make it nice and public maybe a while but exactly right um the point i was gonna make though is like i know i'm bad about following up on stuff uh 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 um but this can actually be incredibly disheartening because a ton of comments that i see are people who are like uh 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 uh yeah the art of it one of the people is really inspiring to me in that regard because i've really seen it in persons um 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 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 how uh even like what the rest of the day looks like it's just deeply in the moment uh or like especially like is 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 a show that you can be very successful not giving a damn about um about comments and it sounds 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 what 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 you know 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 um like platforms in general yeah choose 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 interactions like real life not social media but social interaction well yeah no no question there i think everyone should agree with that which sucks because uh 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's the question of education right now yeah so on that topic you've done a series of live streams called lockdown math and you know 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 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 um 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 which i usually put out content is too slow to be actively helpful let me just do some bi-weekly 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 um and in that sense i think it was you know 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 um i think for you know you ask about like if this can be relevant to educators like 100 online teaching is basically a form of live streaming now um 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 um that would probably be pretty healthy because zoom can be kind of awkward um 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 um like the broadcasting software obs with zoom or things like that it was really sorry 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 um and so he kind of helped show me the roots one of the thing 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 um like one component of it is as soon as you hook things up with a 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 two 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 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 um 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 uh 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 1 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 um 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 a habit of doing it in a in a way that doesn't just feel like a zoom call that happened to be recorded but it actually feels like a a piece that was always going to be publicized to more people than just your students that can be really powerful and there's an improvement process there like so being self-critical and growing like you know like i guess youtubers go through this process of like putting out some content and like nobody caring about it and then trying to figure out like basically improving figure out like why did nobody care uh uh what can i you know 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 or 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 one question to ask because uh well by way of uh russ dedrick he's a robotics professor at mit one of my favorite people a big fan of yours uh he watched our first conversation i just interviewed him a couple weeks ago he uh he teaches this course in under-actuated robotics which is um like robotic systems when you can't control everything like when you're like 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 under-actuated you can't control everything all the the number of actuators uh 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 um it's quite popular he does an incredible job teaching he puts online every time but he's kind of been interested in like crisping it up like you know making it uh you know innovating in different kinds of ways and he was inspired by the work he do because i think in his work he can do similar kind of explanations as you're doing like revealing the beauty of it and spending like months and preparing a single video uh and he's interested in how to do that that's why he listened to the conversation he's playing with madam but he had this question of you know um of uh you know like in my apartment where we did the interview i have like curtains like the for like a black curtain not this uh this is this is a adjacent mansion that we're in that i also but you basically just i have like a black curtain whatever that you know 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 i wonder i mean is there something you would recommend in terms of equipment like is is it direct do you think like lapel mics like usb mics what do you for my narration i use a usb mic for the streams that used a lapel mic uh the narration it's a blue yeti um i'm forgetting actually the name of the lapel mic but it was probably like a road of some kind um 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 for some reason um i just couldn't get audio for a while i think i it's weird when you hear your own voice yeah so here 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 um so uh and then video is just for the lockdowns just the camera like 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 um electronically but i just wanted the paper feel um on on the face there's two um again i don't know i'm like just not actually the one to ask this because i like animate stuff usually but uh 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 the live aspect of it do you do you regret doing it live not at all um i think i do think the content might be like much less sharp and tight than if it were um 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 um 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 it's a different style it's probably a different target audience and kind of keep clean what three blue and brown is about versus uh the benefits of like live lectures do you uh suggest like in this time of covid that people like russ or other educators try to go like the 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 um what they do yeah well what i think teachers like russ should do is um choose the small handful of topics that they're going to do just really well they want to 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 um still put thought and planning into it i'm sure he's a wonderful teacher and like knows all about that but maybe choose a small handful of topics um do what beneficial for me sometimes 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 want to 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 uh it's it's a little bit sad to me to see how much knowledge is lost like just 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 uh 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 like russ um even if they just chose one topic this year 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 want to learn and there's a self-interest to it for in terms of teachers in terms of even so if you take ross 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 a it's a 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 doesn't matter it's much more than it otherwise uh would be and it's those lectures that tell early students what to be interested in yeah 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 gonna 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 there's yeah that's the there's people interested in this stuff yeah i mean uh one of the greatest channels like matt it's not even a math channel but the channel with greatest math content is vsauce yeah you like interviewed if imagine you were to propose making a video that explains the binochtarsky paradox substantively right not not shying around it maybe not describing things in terms of um like the group theoretic terminology that you'd usually see in a paper but the actual uh results um that went into this idea of like breaking apart a sphere proposing that to like a network tv station saying yeah i'm gonna i'm gonna do this in-depth talk of the binocular ski paradox i'm pretty sure it's gonna reach 20 million people it's like get out of here like no 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 um 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 um if we were to have like uh underactualized robotics under actuated under actuated yes not underactualized plenty actualized under-actuated robotics yeah most robotics is under actualized current 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 um actually engage with it really deeply although i just psychologically watching him i can't speak for a lot of people i speak for my dad i think there's a there's a little bit of a skill gap but i think that could be overcome that's pretty basic you know what none of us know how to make videos when we start the first step 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 um fear of like embarrassment like they they definitely it's 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 impostor syndrome like who am i to talk about this and that that's true for like even things that you've studied for like your whole life uh i don't know it's scary to post stuff on youtube it is scary uh 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 that's right i mean the honest problem is like a lot of the educational content is posted by people who like we're 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 and choose your favorite topic quantum mechanics or something um and the people who have the self-awareness uh to not post are probably the people also best positioned to give a good honest explanation of it that's why there's uh 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 broad sheet of paper so but of course that's not scalable as a single channel if they if there's anything beautiful that they could be done as people take it in their own hands uh 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 right yeah it'll be like this the thing this what people don't understand with youtube at least for now at least that's my hope with it is uh it's a leg it's a it's literally better than publishing a book in terms of the legacy it's it will live for a long long time of course it's uh one of the things i mentioned joe rogan before it's kind of there's a sad thing because i'm a fan he's moving to spotify yeah yeah nine digit numbers will do that to you yeah but he doesn't really that he's one a person that doesn't actually care that much about money like having talked to him he it it wasn't because of money it's because he legitimately thinks that they're going to do like a better job like so they're so from his perspective youtube you have to understand where they're coming from youtube has been cracking down on people who they you know joe rogan talks to alex jones and conspiracy theories and youtube was really like careful that kind of stuff and that's not a good feeling like and joe didn't doesn't feel like youtube was on his side um you know he's often has videos that they don't put in trending that like are obviously should be in trending because they're nervous about like you know if this concept is this is this content uh going to you know upset people that 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 uh 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 uh anyway the reason i bring that up is uh joe's going to remove his entire library from youtube whoa really that's going to his full-length the clips are going to stay but the full-length videos are all i mean made private or deleted that's part of the deal and like that's the first time where i was like oh youtube videos might not live forever like things you find like okay sorry this is why you need um ipfs or something where it's like if there's a content link are you familiar with this system at all like right now if you have a url that points to a server there's like a system where the address points to content and then it's like distributed so you you can't actually delete what's at an address because it's 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 um but i mean that raises a question i'm not going to put you on the spot but like somebody like vsauce right spotify comes along and gives him let's say 100 billion dollars okay let's say some crazy number and then removes it from youtube right it's maybe i don't know for some reason i thought youtube is forever i don't think it will be i mean you know another variant that this might take is like uh that you know um you fast forward 50 years and uh you know google or alphabet isn't the company that it once was and it's kind of struggling to make ends meet and you know it's been supplanted by the 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 just we're going to start deleting the ones that aren't watched that much and tell people to like try to back them up on their own or whatever it is um or even if it does exist in some form forever it's like if people are um 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 that's true so uh it won't be forever it makes me sad still but because it's such a nice it's like just like you said of the canonical videos sorry i don't interrupt you know you should get juan bennett on the uh 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 quantification around it yeah that's like been pretty well thought through uh but yeah i do see youtube just like you said as a 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 your networks uh let me ask you first what is the most beautiful aspect of neural networks and machine learning to you like for making those videos from watching how the field is evolving is there something mathematically or an applied sense just beautiful to you about them well i think what i would go to is the layered structure and how um you can have what feel like qualitatively distinct things happening going from one layer to another but that are um 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 um but especially if you look at like some of the visualizations that like chris ola has done with respect to like convolutional nets that have been trained on imagenet trying to say what does this neuron do what do this 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 right and then as you get further back you have higher level ideas like what is the where 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 as having um those many different layers of an understanding to something yeah 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 email 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 um but you know who cares how you came to it when you have like that elegant piece of math uh it's hard not to just smile seeing it work in action well and when you talked about topology before one of the really interesting things is it's beginning to be investigated under kind of the field of like science and deep learning which is like the craziness of the surface that uh is trying to be optimized uh in neural networks i mean the the amount of local minima local optima there is in these 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 gpt3 what did it have 175 billion parameters so it it doesn't feel as mesmerizing to think about oh there's some surface of intelligent behavior in this crazy high-dimensional space it's like there's so many parameters that of course but what's more interesting is like how 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 re the reason the gradient descent works well with neural networks and not just you know choose however you want to parameterize the 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 um yeah it's just that that there's so many good solutions probably infinitely infinitely many good solutions not best solutions but good solutions that's that's what's interesting it's similar to uh stephen wolfram has this idea of like the 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 we 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 common gore 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 uh like one fun example of this you know um shannon's noisy coding in theorem uh noisy coding theorem and uh information theory that basically says if you know i want to send some bits to you uh maybe uh some of them are gonna get flipped uh 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 um and then he quantitatively describes how 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 um 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's 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 um 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 all 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 yeah 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 uh you mentioned gpt3 it's interesting to ask uh what are your thoughts about the recently released openai gbt3 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 um try to use gpd3 with manum 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 um i mean like a lot of those demos it's interesting i think uh there's a lot of failed experiments like depending on how you prime the thing you're going to have a lot of failed i'm certainly with code no program synthesis most of it won't even run but eventually i think if you if you're if you pick the right examples you'll be able to generate something cool and i think even that's good enough even though if if it's if you're being very selective it's still cool that something can be generated yeah that that's huge value um 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 um 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 uh have you gotten a chance to see any of the demos like on twitter is there a favorite you've seen or oh my absolute favorite yeah uh so tim blay who runs a channel called a cappella science he was like tweeting a bunch about playing with it um and so he so gpt3 was trained on um the internet from before kovid so so in a sense it doesn't know about the coronavirus so what he seeded it with was just a short description about like um a novel virus uh 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 sees it with so then what gpt3 generates is like january then a paragraph of description february and such and it's the funniest thing you'll ever read because um it predicts a zombie apocalypse which of course it would because it's trained on like the internet zombie stories but what you see unfolding is a description of covet 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 uh i wouldn't be surprised if it's on to something at some point here when you know 2020 has been full of surprises who knows like we might i'll be in like this crazy militarized zone as it predicts just a couple months off yeah i think is this definitely an interesting tool of storytelling it has struggled with mathematics which is interesting or in just even numbers it's able to it's not able to generate like patterns you know like you give it um in like five digit numbers and it's not able to figure out the sequence you know or like uh 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 um that are mathematically correct yeah i i honestly haven't dug into like what's going on within it uh 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 um a weird combination of intuitive and uh 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 um and it seems like gpt3 is extremely good at um like that sort of pattern matching recognition that usually is very hard for computers that um 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 um like have an actual explanation for what's going on not just a 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 a few layers creating abstractions but it's been able to form something that looks like a a compression of the data that it's seen that looks awfully a lot like it understands what the heck is talking about well i think a lot of understanding is like i don't mean to uh denigrate pattern recognition pattern recognition is most of understanding and it's super important and it's super hard um and so like when it's demonstrating this kind of real understanding compressing down some data like that 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 um 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're 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 a basic you know like taylor's like certain kinds of series it feels like compressing the internet uh is is enough to figure out because those patterns in some form appear in the text somewhere well i mean there's there's all sorts of wonderful examples of false patterns in math where um one of the earliest videos i put on the channel was talking about you're kind of dividing a circle up using these chords and you see this pattern of one two four eight sixteen i was like okay pretty easy to see what that pattern is it's powers of two you've seen it a million times um but it's not powers of two the next term is thirty one and so it's like almost a power of two but it's a little bit shy and there's there's actually a very good explanation for what's going on um 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 no good way to i mean there can't be a good way to think about it as like 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 like you know a math student making the mistake and a mathematician who's experienced seeing that kind of pattern is that they 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 like uh i would just be very impressed if there was any algorithm that um was actively accomplishing that goal yeah like a learning based algorithm yeah like a little scientist i guess yeah basically yeah it's a it's a fascinating thought because gpg three these language models are already accomplishing way more than i've expected so i'm learning not to doubt but i bet we'll get there yeah i'm not saying i'd be impressed but like surprised like i'll be impressed but i i think we'll get there on um 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 madam 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 wanted um i've been working on playing around with something i wanted to do like an ode three blue one brown like i love playing hendrix i want to do like a cover you know of a concept i wanted to visualize and and use madam 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 um twisting it i guess is the term uh and it was easier to uh it was tough so i haven't figured out yet well so i guess the question i want to ask is so many people love it uh that you've put that out there they want to uh do the same things they 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 they try to go by uh about it well so and what kind of choices should they choose to be most effective oh that i can answer so i always feel guilty if this comes up because um i think of it like the 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 like 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 um i i've put some work this year trying to like make it better and more flexible um that is still just kind of like a work in process um 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 um not like deviate uh and just like actually fostering that community in a way that i've 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 okay send like all right i'll pretend like it isn't terrible for someone like russ um 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 um 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 ground georgia is kind of cool it's amazing you can get very very far with it um 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 mana by doing videos and such so do as i say not as i do the original like thought i had in making manam was that there's so many different ways of representing functions other than graphs um 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 uh like x coordinate y coordinate kind of stuff but also make sure that um 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 you know 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 um things like that you should probably just use keynote right um you'll be a lot simpler so try to find a workflow that distills down that which should be programmatic into manum 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 and just for the fun of it let me ask uh what uh what's your most and least favorite aspects of python oh 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 um uh benefits for how you structure things so if you 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 by calling home yeah sometimes you travel but it's home got it it's home uh 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 that just like takes long do you run into that at all like with your work well so uh certainly old man is like way slower than it needs to be because of uh 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 um coding it if you want to to you know you have like a 3d scene you can move around you can have um 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 um 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 um but yeah there are some times when it's like a um 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 it the toxicity over it led guido to resign to step down from this 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 it was a text it was an accumulation of toxicity but that was the the most 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 um he didn't particularly i don't think cared about 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 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 bee in the benevolent he's really he really is a nice guy he 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 alana's terrible 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 operator is like i don't actually care that much either way i'm not going to get irritably passionate my 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 just represents the uh 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 no he got it passed i guess but i i guess right it could represent multiple things too it can represent like failed dictatorships or it could it could represent a lot of things but to me great leaders take risks even if it 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 const if whenever there's a divisive thing you wait until the division is no longer there like that's the paralysis we experience with like congress and political systems it's good to be slow when there's indecision uh when there's a 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 that's what the walrus operator represents to me is it represents the fighter pilot instinct of like quick action is more important than uh than just like caring everybody out and really thinking through it because that's going to lead to paralysis yeah like if that's the actual case that you know it's something we're consciously hearing people's uh disagreement disagreeing with that disagreement and um 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 uh some beautiful mathematics involved 2020 brought us a couple of in the physics world uh 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 hypograph view of the theory of everything do you uh find uh interesting beautiful things to these theories of everything what do you think about the physics world and sort of uh the beautiful interesting insightful mathematics in in that world whether we're talking about quantum mechanics which you touched on in a bunch of your videos a little bit quaternions like just the mathematics involved or general relativity which is more about surfaces and topology all that stuff well i think um as far as like popularized science is concerned people are more interested in theories of everything than they should be like 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 like listening to uh witten talk about string theory whatever proposed path to a theory of everything um you're not actually going to understand it some physicists will but like all you're just not actually going to 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 mold talking about um 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 and quantum systems um 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 um the popularizers should be less emphatic than they are about that for like actual practicing physicist you know it might be the case maybe more people should think about fundamental questions but it's difficult to create uh like a three blue one brown video on the theory of everything so basically we should really try to find the beauty and mathematics of 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 um the big unsolved problems so like the clay millennium problems riemann hypothesis um have you ever done a video on fermat's last name no i have not yet no but if i did do you know what i would do i would talk about um proving foreign theorem in the specific case of n equals three okay is that still accessible though yes actually barely um 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 the core ideas of proving it for n equals three are hard but they do get you real ideas about algebraic number theory um it involves looking at a number field that's uh 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 fairmont's last theme hard are actually quite deep um 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 viewers time i think the same goes for uh most like unsolved problem type things where i think you know as a kid i was actually very inspired by the twin prime conjecture um that like totally sucked me in as 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 like viewed through this lens of like oh maybe i can apply it to that in some way but uh you sort of mature to a point where you realize that you should spend your brain cycles on problems that you will see resolved because then you're going to 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 it's not going to pan out and the people who do make progress towards these things like james maynard uh is a great example here of like young creative mathematician who like 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 um yeah i think you know i've heard a lot of the interest that you know 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 um you shouldn't be interested in those right it's a giant sort of uh 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 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 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 um up-to-date uh progress on the riemann hypothesis cousins or um like there's context in which the analog of the roman hypothesis has been solved in like more uh 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 can 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 um 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 and 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 last time we got awkward and weird about uh a fear of mortality which you made fun of me off but let me ask you on the the other absurd question is um what do you think is uh the meaning of our life of meaning of life i'm sorry if i made fun of you about much no you didn't i'm just joking it was 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 uh like this water bottle label in that someone created it with the purpose of conveying meaning and there was like one consciousness that wanted to get its ideas into another consciousness um most things don't have that property it's a little bit like if i asked you um 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 like i guess i'm revealing i'm not very religious but you know the mathematics of everything seems kind of beautiful it seems like 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 um 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 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 that is what um 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 fuels my pump at least so a life alone on a deserted island will be kind of meaningless yeah you want to 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's 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 5 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 has 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 of 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 awl of a flower it only adds i don't understand how it subtracts thank you for listening and hope to see you next time you