Grant Sanderson (@3blue1brown) — Past, present, & future of mathematics

1. 0:00 – 8:24

   Does winning math competitions require AGI?

   1. DPDwarkesh Patel0:00

      ... Grant. (piano music plays)

   2. GSGrant Sanderson0:00

      You know, the videos were really inspiring, like, "You're the reason I'm, like, going into grad school." And there's this little bell in the back of my mind that's like, "Do, do I want that?"

   3. DPDwarkesh Patel0:09

      (laughs)

   4. NANarrator0:09

      (laughs)

   5. GSGrant Sanderson0:09

      To get more people going into math PhDs? Math academia, finance, and computer science almost certainly have an over-allocation of talent. Actually, I'm, I'm quite determined at some point to, like, be a high school math teacher for some number of years. Math lends itself to synthetic data, how AlphaGo is trained. You could have it produce a lot of proofs and just train on a whole bunch of those. And the thing that takes, at most, 30 minutes of the teacher's time, maybe even 30 seconds, has these completely monumental rippling effects for the life of the student they were talking to that then sets them on this whole different trajectory.

   6. DPDwarkesh Patel0:44

      Okay, today, I have the pleasure of interviewing Grant Sanderson of the YouTube channel 3Blue1Brown. You all know who Grant is. I'm really excited about this one. By the time that an AI model can get gold in the International Math Olympiad, is that just AGI, given the amount of creative problem-solving and chain of thought required to do that?

   7. GSGrant Sanderson1:05

      I, to be honest, have no idea what people mean when they use the word AGI.

   8. DPDwarkesh Patel1:09

      Yeah.

   9. GSGrant Sanderson1:10

      I think if you ask 10 different people, like, what they mean by it, you're gonna get 10 slightly different answers. And it seems like what people want to get at is a discrete change that I don't think actually exists, where you've got, okay, AI's up to a certain point, they're not AGI. They might be really smart, but it's not AGI. And then after some point, that's the benchmark when, like, now they're, now it's generally intelligent. The reason that world model doesn't really fit is it feels a lot more continuous, where, you know, GPT-4 feels general in the sense that you have one training algorithm that applies to a very, very large set of different kinds of tasks that someone might wanna be able to do. And that's cool, that's, like, an invention that people in the '60s might not have expected to be true for, um, the nature of how artificial intelligence can be programmed. So it's, it's generally intelligent, but maybe what people mean by, "Oh, it's not AGI," is you've got certain benchmarks where, you know, it's better than most people at some things, but it's not better at most people than others. You know, at this point, it's better than most people at math. You know, it, it's better than most people at solving AMC problems and, like, IMO problems. It's just not better than the best. And so, maybe at the point when it's getting golds in the IMO, that's a sign that, okay, it's, it's as good as the best, and we've ticked off another domain, but I don't know. Like, i- is what you mean by AGI that you've, you've enumerated all the possible domains that something could be good at, and now it's better than humans at all of them?

   10. DPDwarkesh Patel2:34

       Or e- e- enough that it could take over substantial fractions of, you know, h- human jobs or something. Where right now, it's, it, it's impressive, but it's not gonna be even 1% of GDP. But in my mind, if it's getting gold in IMO, I mean, having seen some of those problems-

   11. GSGrant Sanderson2:50

       Yeah.

   12. DPDwarkesh Patel2:50

       ... uh, from your channel, I'm, I'm thinking, "Wow, that's, that's really coming after podcasters and (laughs) video animators." I don't know.

   13. GSGrant Sanderson2:56

       I don't know. That feels orthogonal, 'cause getting a gold in the IMO feels a lot more like being really, really good at Go or chess. Like, tho- those feel analogous. Well, it's, it's super creative. Like, I think anyone who... I don't, I don't know chess as well as the people who are into it, but everything that I hear from them, the sort of moves that are made and choices have all of the air of creativity. Um, I think as soon as they started generating artwork, then everyone else could appreciate, "Oh, there's, there's something that deserves to be called creative here."

   14. DPDwarkesh Patel3:23

       Mm-hmm.

   15. GSGrant Sanderson3:23

       And the creative side of the math, you know, I'm, I don't know how it would look when people get them to be, um, getting golds at the IMO. But I imagine it's something that looks a little bit like how AlphaGo is trained, where you have it, like, play with itself a whole bunch. You know, math lends itself to synthetic data in ways that a lot of other domains don't.

   16. DPDwarkesh Patel3:42

       Mm-hmm.

   17. GSGrant Sanderson3:42

       You could have it produce a lot of proofs in a proof-checking language-

   18. DPDwarkesh Patel3:46

       Mm-hmm.

   19. GSGrant Sanderson3:46

       ... like Lean, for example, and just train on a whole bunch of those, and like-

   20. DPDwarkesh Patel3:48

       Yeah.

   21. GSGrant Sanderson3:48

       ... "Is this a valid proof? Is this not a valid proof?" And then counterbalance that with English written versions of something. And so I imagine what it looks like once you get something that is solving these IMO level things, one of, one of two things. Either it writes a, a very good proof that you feel like is unmotivated, 'cause anyone who reads math papers has this feeling that there are, there are two types. There's the ones where you morally understand why the result should be true, and then there's the ones where you're like, "I can follow the steps. Why would you have come up with that? I don't know, but I guess that shows that the result is true." And you, you're left wanting something a little bit more.

   22. DPDwarkesh Patel4:23

       Yeah.

   23. GSGrant Sanderson4:23

       And so you could imagine if it produces that on the gold, to get a gold in the IMO, is that the same kind of ability as r- what is required to replace jobs? Just, like, not really. Like, the, the, the impediments between where it is now and replacing jobs feels like a whole different set of things, like having a context window that is longer than (laughs) you know, some small things such that you can make connections over long periods of time and build relationships and understand where s- someone's coming from.

   24. DPDwarkesh Patel4:51

       Mm-hmm.

   25. GSGrant Sanderson4:51

       And the actual problem-solving part of it, I mean, it, it's a sign that it would be a, a more helpful tool, but in the same way that, like, Mathematica can help you solve math problems much more effectively.

   26. DPDwarkesh Patel5:01

       Mm-hmm. And tell me why I should be less amazed by it, or maybe put it in a different context, but the reason I would be very impressed is that w- with chess or something, obviously this is not all that chess programs are doing, but there's a level of tree search you can do to narrow down the possibilities. And more importantly, the, i- in the math example, it seems that, w- with some of the examples you've illustrated on your channel, for example, the ability to solve the problem is so dependent on coming up with the right abstraction to think about it, coming up with ways of thinking about the problem that are not evident in the problem itself or in any other problem-

   27. GSGrant Sanderson5:36

       Mm-hmm.

   28. DPDwarkesh Patel5:37

       ... uh, in any other test. That seems different from, uh, just a chess game where you don't have to, like, w- what is the largest structure of this chess game in the same way as you do with a IMO problem.

   29. GSGrant Sanderson5:48

       I think you should ask people who know r- a lot about Go and chess, and I'd be curious to hear their opinions on it, because I imagine what they would say is if you're gonna be as good at Go as AlphaGo is, you're also not doing tree search, at least exclusively. It's not dependent on something as both in that, 'cause you get this combinatorial explosion-

   30. DPDwarkesh Patel6:06

       Yeah.
2. 8:24 – 17:34

   Where to allocate mathematical talent?

   1. DPDwarkesh Patel8:24

      Interesting. Um, okay. Applied mathematicians-

   2. GSGrant Sanderson8:27

      Okay.

   3. DPDwarkesh Patel8:27

      ... where do we put them in society where they can have the biggest benefit? We have, like, a lot of them go into computer science and IT, and b- I'm sure there's been lots of benefits there. But where, you know, where are there parts of society where y- you just have a whole bunch of mathematicians go in and they can make things a lot better? You know, I don't know, transportation or logistics or manufacturing. W- where else do you think they might be useful?

   4. GSGrant Sanderson8:48

      That's such a good question. In some ways, I'm like the worst person to ask about that.

   5. DPDwarkesh Patel8:51

      (laughs)

   6. GSGrant Sanderson8:51

      But this isn't gonna answer your question, but instead is gonna, like, fan the flames of why I feel it's an important question. I have actually been thinking recently about if it's worth making an out of typical video that specifically addressed i- like, in- inspiring people to ask that, especially students who are graduating, 'cause I think this thing happens where when you fall in love with math or some sort of technical field, by default in school, you, you study that. And when you're studying that, effectively you're going through an apprenticeship to be an expert in that or a researcher in that. You know, the structure of studying physics in a university or math in a university, even though they know that not all majors are gonna go into the field, the people that you're gaining mentorship from are academics and are researchers in the field, so it's hard not to effectively be apprenticing in that.

   7. DPDwarkesh Patel9:37

      Yeah.

   8. GSGrant Sanderson9:38

      And I also have noticed that when I go and give talks at universities or things like this and students come up after and they're like saying hi, there's a lot of them that are like, "Grant, you know, your videos were really inspiring. Like, you're the reason that I studied math or that you're the reason I'm, like, going into grad school." And there's this little bell in the back of my mind that's like, "Cool, cool. I'm amazed. I don't know if I believe I was wholly responsible for it, but like, cool to have that impact. Do, do I want that?"

   9. DPDwarkesh Patel10:02

      (laughs)

   10. GSGrant Sanderson10:03

       "Is this a good thing to get more people going into math PhDs?" On the one hand, I unequivocally want more people to self-identify as liking math. That's very good. But that, those who are doing that necessarily get shuffled into the traditional outlets like math academia. Yeah, I think you highlighted it very right. It's like math academia, finance and computer science, data science, something in there in general, um, are very common things to go to. And as a result, they almost certainly have an overallocation of talent.

   11. DPDwarkesh Patel10:31

       Mm-hmm.

   12. GSGrant Sanderson10:32

       All three of those are valuable, right? I'm not saying, like, those are not valuable things to go into. But if you were playing God and like shifting around-

   13. DPDwarkesh Patel10:39

       Yeah.

   14. GSGrant Sanderson10:39

       ... where do you want people to go? Again, I'm not answering your question. I'm just asking it in other words 'cause I don't really know. I think you should probably talk to the people who made that shift of which there aren't a huge number, but like Eric Lander is, uh-

   15. DPDwarkesh Patel10:52

       Yeah.

   16. GSGrant Sanderson10:52

       ... maybe one good example. Um, uh, Jim Simons would maybe be another. Whereas people who were doing a very purely academic thing and then decided to shift to something very different. Now, I, I have sort of had this thought that it's very beneficial to insert some forcing function that gets the pure mathematicians to spend some of their time in a non-pure math setting, you know?

   17. DPDwarkesh Patel11:14

       Mm-hmm.

   18. GSGrant Sanderson11:15

       Uh, NSF grants coming with a, a requirement that 10% of your time goes towards a collaboration with another department or something like that. The thought being these, these are really good problem solvers, um, in a specific category of problems, and to just distribute that talent elsewhere might be helpful. And when I, when I, like, run this by mathematicians, sometimes there's a mixed response where they're like, "Ah, I don't know if we'd be all that useful." (laughs) Like, there's a sense that the aesthetic of what constitutes a good math problem is by its nature rooted in the purity of it, such that it's maybe a little elitist to assume that just because people are really, really good at solving that kind of problem, that somehow their abilities are more generalizable than other people's abilities. You know, why ask about the applied mathematicians rather than saying, like, "Shouldn't the applied biologists go and work in logistics and things like that 'cause they also have a set of problem solving abilities that's maybe generalizable?" In the back of my mind I think, "No, but the mathematicians are special." (laughs)

   19. DPDwarkesh Patel12:11

       (laughs) Yeah.

   20. GSGrant Sanderson12:11

       There, there really is something general about math.

   21. DPDwarkesh Patel12:13

       Right.

   22. GSGrant Sanderson12:14

       Um, so...... I don't have the answers. I will say I'm actually very curious to hear from people for what they think the right answers are, or from people who made that switch. Let's say they were a math major or, or something adjacent like computer science, physics, and then they decided that they wanted to pour themselves into something not because that was the academic itch that scratched, that they were scratching by being good at school and, and getting to appreciate that, but because they stepped back and said, "What impact do I want to make on the world?" Um, I'm hungry for more of those stories because I think it could be very compelling to convey those specifically to my audience who is probably on track to go into just the traditional math-type fields and maybe there's room to have a little bit of influence to disperse them more effectively. But I, I don't know. I don't know what more effectively looks like, because at the end of the day I'm, like, I'm a math YouTuber, right? I'm not someone who, uh, has a career in logistics or manufacturing or all of these things in such a way that I can have an in-tune feel for where is there a, uh, need for this specific kind of abstract problem-solving.

   23. DPDwarkesh Patel13:18

       It might be useful to speculate on how an undergrad or somebody who's a young math whiz might even begin to contemplate, "Here's where I can have an edge." I'm, I'm remembering actually, it just occurred to me, a former podcast guest, Lars Doucet, he was a game designer actually, and he started learning about Georgism, which is this idea that you should tax land and only land. And so he got really interested in not only writing about those ideas, but also with, well, if you're gonna tax land, you gotta figure out what the value of land is. Like, how do you figure out the value of land? There's all these algorithms-

   24. GSGrant Sanderson13:53

       Mm-hmm.

   25. DPDwarkesh Patel13:54

       ... of how you do this optimally based on neighboring land and how to average across land, and it... there's a lot of intricacies there. Um, and so he, he now has a startup where he just contracts with cities to implement these algorithms to help them assess the value of their land, which makes property taxes much more feasible. You know, just that's another example, right? Where the motivation was more philosophical, but his specialty as a technical person helped them, um, you know, h- help to make a contribution there.

   26. GSGrant Sanderson14:21

       I think that's perfect. Probably the true answer is that you're not gonna give a universal thing. For any individual, it's gonna be based on where their life circumstances connect them into something, either because they... you know, he had an interest in Georgism for whatever reason. But if someone, I don't know, their, their dad runs a paper mill and they're, like, connected to the family business in that way and realize they can, like, plug themselves in a little bit more efficiently, you're, you're gonna have this wide diversity of the ways that people are applying themselves that does not take the form of general advice given from some podcast somewhere-

   27. DPDwarkesh Patel14:53

       Yeah.

   28. GSGrant Sanderson14:53

       ... but instead takes the form of simply inviting people to, like, think critically about the question rather than following the momentum of what being good at school implies about your future.

   29. DPDwarkesh Patel15:03

       Uh, we were talking about this before the interview started, but we have a much better grasp on reality based on our mathematical tools. And I'm not talking about anything advanced, literally just it being able to count and, um, in the decimal system that even the Romans didn't have.

   30. GSGrant Sanderson15:17

       Mm-hmm.
3. 17:34 – 26:44

   Grant’s miracle year

   1. GSGrant Sanderson17:34

   2. DPDwarkesh Patel17:34

      Yeah, that's really interesting. What's up with miracle years?

   3. GSGrant Sanderson17:37

      (laughs)

   4. DPDwarkesh Patel17:37

      So this is something that happens... has happened throughout science and especially with mathematicians, where they have a single year in which they make up many, if not most, of the important discoveries that they have in their career. Uh, you know, Newton, Einstein, Gauss, they all had these years. Uh, do you have some explanation of what's going on?

   5. GSGrant Sanderson17:55

      What's your take? (laughs)

   6. DPDwarkesh Patel17:57

      I think there's a bunch of possible explanations. It can't just be youth, because youth last 10 years, not one year. So it must have something to do with-

   7. GSGrant Sanderson18:06

      (laughs) Every 35-year-old right now is like... (laughs) How dare you?

   8. DPDwarkesh Patel18:10

      You know, you know what I mean. (laughs)

   9. GSGrant Sanderson18:12

      Yeah.

   10. DPDwarkesh Patel18:12

       They have 20 years.

   11. GSGrant Sanderson18:13

       Yeah, yeah.

   12. DPDwarkesh Patel18:14

       Um, so yeah, it can't just be that. Um-... I don't know, there's a bunch of possible things you could say. One is, you're in a situation in life where you have nothing else going for you, or you- you're just like really free for that one year and then you become successful after that year is over, based on what you did. Yeah. But- but what is your take?

   13. GSGrant Sanderson18:30

       I- I don't know. I, so I agree, there's probably multiple factors, not one.

   14. DPDwarkesh Patel18:35

       Yeah.

   15. GSGrant Sanderson18:36

       One thing could be that the miracle year is the like exhalation, and there's been many, many years of inhalation.

   16. DPDwarkesh Patel18:44

       Yeah.

   17. GSGrant Sanderson18:44

       Where often, let's say, you know, the classic one is Einstein's, where his mir- miracle year were also some of the first papers, like kind of springing onto the scene.

   18. DPDwarkesh Patel18:53

       Yeah.

   19. GSGrant Sanderson18:53

       And I would guess that a lot of the ideas were not bumping around in his head only in that year, but it's like many, many years of thinking about it and kind of coalescing. And so, you might be in a position where you can build up all of this potential energy and then for whatever reason, there's one time in life that lends itself to actually releasing all of that. Um, if I try to reflect on like my own history with what I'm doing now, I think I didn't appreciate early on how much potential energy I was working from, simply from being a student and in college where there's just a bunch of ways of thinking about things, or empathy with new learners, or just cool concepts, right? The- the basic concept behind a video, that in fact, it was many, many years of like all of my time having learned math before I started putting out stuff online that I was able to eat into, and then maybe it was a little later where, okay, the well never runs dry. There's always a long list of things that I want to cover, but in some sense, like, I recognize that the well was, uh, at risk of running dry in a way that I never thought that it could, and without being a little deliberate about devoting some of my day not just to output and producing but to stepping back and like learning new things and- and touching something I never would have. That doesn't happen by default. I don't know if this is all the, also the case for the people who have genuine miracle years where they were like letting out all of this stuff and then it takes a decade to build up that same level of potential energy. The other thing, you have everything to gain and nothing to lose when you are young. So even if it's not merely youth, there's a willingness to be creative and there's also none of the obligations that come from having found success before, right? Uh, you know, there's- there's certain academics who made an extremely deliberate effort not to let... W- what do they call it? Is it like the curse of success or... ? There's some term for it, but I think maybe, um, James Watson, you know, had this standard reply to invitations for, you know, talks and interviews and things like that. It was basically like, "No to everyone because I just want to be a scientist."

   20. DPDwarkesh Patel20:55

       Yeah.

   21. GSGrant Sanderson20:55

       It was much more articulate than that and he has all these nine points, but that was the gist of it. And short of doing that, I think it's very easy for someone to have a lot of other things that eat into their mind share and time and all of that, that even if it's just 20 hours a week, like, actually that- that really interrupts a creative flow.

   22. DPDwarkesh Patel21:12

       Were you a student when you started the channel?

   23. GSGrant Sanderson21:14

       Technically, yeah. The very, very first video was made when I was a senior at Stanford. Um, basically, I had been like toying around with, uh, just a personal programming project in my last year of college that was the beginnings of what is now like the animation tool I work with. I didn't intend for it to be a thing that I would use as a math YouTuber.

   24. DPDwarkesh Patel21:34

       Right.

   25. GSGrant Sanderson21:34

       I didn't even really know what a YouTuber was. It was really just like a personal project. Um, and it was March of that year, I think, that I published the first ever video. And so it was kind of right at that transition point.

   26. DPDwarkesh Patel21:47

       Do you think you could, you would have done it if you had, let's say, become, uh, I don't know where you're planning on doing after college. I remember you saying somewhere maybe a data scientist, but...

   27. GSGrant Sanderson21:55

       Data scientist and math PhD were the two like-

   28. DPDwarkesh Patel21:57

       I see.

   29. GSGrant Sanderson21:58

       ... um, 50/50 contenders basically.

   30. DPDwarkesh Patel22:00

       Is there a world in which you started doing that but then later on s- made Manim or do you think that that was only possible in a world where you had some time to kill in your senior year?
4. 26:44 – 33:33

   Prehistoric humans and math

   1. DPDwarkesh Patel26:44

      to you that prehistoric humans don't seem to have had, um, just basic arithmetic and numeracy? To me, with, with a sort of, I, I guess to us with modern understanding, that kind of stuff seems so universally useful and so fundamental that it's shocking that it just doesn't come about naturally in the course of interacting with the world. Do you think it's, is it that surprising, that, just the concept of numbers and...?

   2. GSGrant Sanderson27:08

      Y- you're right it's so in our bones that it's hard to empathize with not having-

   3. DPDwarkesh Patel27:12

      Yeah.

   4. GSGrant Sanderson27:12

      ... uh, numeracy. A lot of it's linked to if you think, okay, what's the first place that like people think about numbers-

   5. DPDwarkesh Patel27:19

      Yeah.

   6. GSGrant Sanderson27:19

      ... most people, like in their daily lives? It's linked to commerce, and money, and such. So maybe some ways, the question is the same as saying is it surprising that like early humanity didn't have commerce or didn't deal with money? Maybe when you're below Dunbar's number in your communities, like a tit-for-tat structure just makes a lot more sense and actually works well and it would, it would just be obnoxious to like actually account for everything. The other loosely related idea, h- have you come across those, um, studies where when anthropologists will interview tribes of people that are removed enough from normal society that they don't have the level of numeracy that you or I do? But they, you know, there's some notion of counting. You-

   7. DPDwarkesh Patel28:00

      Yeah.

   8. GSGrant Sanderson28:00

      ... if you have one coconut or nine coconuts, like-

   9. DPDwarkesh Patel28:02

      Yeah.

   10. GSGrant Sanderson28:02

       ... you have a sense of that. That if you ask what number is halfway between one and nine, those groups will answer three, whereas y- you or I or people in our world would probably answer five.

   11. DPDwarkesh Patel28:14

       Yeah.

   12. GSGrant Sanderson28:15

       And because we think on this very linear scale, it's interesting that evidently the like natural way to think about things is logarithmically.

   13. DPDwarkesh Patel28:21

       Mm-hmm.

   14. GSGrant Sanderson28:22

       Which kind of makes sense. Like, the social dynamics of as you go from solitude to a group of 10 people to a group of 100 people have roughly equal steps and increase in complexity more so than if you go from like 1 to 51 to 102.

   15. DPDwarkesh Patel28:37

       Yeah.

   16. GSGrant Sanderson28:37

       And I wonder if it's, it's the case that by adding numeracy in some senses we've also like lost some numeracy or lost some intuition in others. Where now if you ask, you know, uh, middle school teachers, "What's a difficult topic to teach or for students to understand?" They're like, "Logarithms." (laughs)

   17. DPDwarkesh Patel28:53

       (laughs)

   18. GSGrant Sanderson28:53

       We're like, "But that should be deep in our bones," right? So somehow it got unlearned and it needs to be... Maybe it's in the formal sense that it's harder to relearn it. But there's, there's maybe a sense of like numeracy and a sense of quantitative thinking that humans naturally do have that is hard to appreciate when it's not expressed in the same language or in the same ways.

   19. DPDwarkesh Patel29:12

       Yeah. I have seen the thing from Joseph Henrich where the still existing tribes where th- they're in this kind of situation. They can do numeracy and arithmetic when it's in very concrete terms, if you're talking about seeds or something.

   20. GSGrant Sanderson29:26

       Mm-hmm.

   21. DPDwarkesh Patel29:26

       But the, the abstract concept of a number, uh, is not, is not available to them.

   22. GSGrant Sanderson29:32

       Do you think the abstract concept of a number is useful to your life?

   23. DPDwarkesh Patel29:37

       Oh, yeah.

   24. GSGrant Sanderson29:38

       Like, in what ways?

   25. DPDwarkesh Patel29:39

       It, it's almost like asking how is the concept of the alphabet useful? It, it comes up so often that it's... I mean, just like how many lights do I set up for this interview, right?

   26. GSGrant Sanderson29:48

       Right. Is that the concept of an abstract number though? 'Cause it's like two people, two lights, one-to-one correspondence.

   27. DPDwarkesh Patel29:54

       (laughs)

   28. GSGrant Sanderson29:54

       Like, did you leverage the abstraction of two as a object which is simultaneously irrational and a real and an integer?

   29. DPDwarkesh Patel30:03

       I see.

   30. GSGrant Sanderson30:03

       And a, you know, is in the context of a group that has additive structure but also multiplication.
5. 33:33 – 44:44

   Why is a lot of math so new?

   1. GSGrant Sanderson33:33

   2. DPDwarkesh Patel33:33

      This actually raised an interesting question I wasn't planning on asking you, but it, it just occurred to me. Is it surprising how new a lot of mathematics is? Even mathematics that is taught at the high school level. Whereas, with physics or biology, that's also new, but you can tell a story where we didn't have the tools to look at the cell or to inspect an electron until very recently. But we've had mathematicians for 2,000, 3,000 years who were doing, th- you know, pretty sophisticated things, even the ancient Greeks. Not ev- it depends on what you mean by sophisticated, but, eh, eh, impressive things.

   3. GSGrant Sanderson34:03

      Yeah.

   4. DPDwarkesh Patel34:04

      I don't know why linear algebra is so new given that fact.

   5. GSGrant Sanderson34:07

      I wouldn't have thought of math as being, like, new in that way. If anything, especially if we're talking at the high school level, I remember there was always this sensation that it's frustrating that all of the things are actually way more than 100 years old, um, in terms of, you know, the, the names attached to the theorems that you're doing. Like, none of them are remotely modern. Whereas in biology, you know, the, um, the understanding we have for, like-

   6. DPDwarkesh Patel34:29

      Yeah, yeah.

   7. GSGrant Sanderson34:29

      ... how proteins are formed is relatively much more modern and you might be just a couple of generations away. I, to some extent, there's a raw manpower component to it where, like, how many people did pure math-

   8. DPDwarkesh Patel34:41

      Mm-hmm.

   9. GSGrant Sanderson34:41

      ... for most of history? For most of history, no one. No one was a pure mathematician. They were, like, a mathematician plus something else or they were a physicist who, you know, or a natural philosopher. And insofar as you're doing, like, natural philosophy, one component of that is developing math, but it's, it's not the full extent of what you do. You know, even the ones who we think of as, like very, very, mm, pure mathematicians in the sense that a lot of their most famous results are pure math, like Gauss-

   10. DPDwarkesh Patel35:06

       Yeah.

   11. GSGrant Sanderson35:07

       ... like actually, a lot of the work, uh, a lot of his, you know, output was also centered on very practical problems and, um, yeah. And maybe, like since then, that's when you start to get an era of something more like pure mathematicians and the raw number available that you have, the man hours that are being put into developing new theorems is probably just got this huge spike-

   12. DPDwarkesh Patel35:29

       The highest.

   13. GSGrant Sanderson35:29

       ... as, one, the population grows, and then also the percentage of the population that has the economic freedom to do something as indulgent as academia, like, grows. Maybe it's pretty reasonable, um, that most of it is much, much more recent. Um, that would be my guess.

   14. DPDwarkesh Patel35:44

       But the, you know, I mean, some of these things seem a- actually pretty modern. Like information theory is less than 100 years old.

   15. GSGrant Sanderson35:49

       That's true.

   16. DPDwarkesh Patel35:49

       And it's, you know, pretty fundamental. Like theoretically, you could've written that paper a long time ago.

   17. GSGrant Sanderson35:54

       Yeah. That's a really good example. And maybe, like, this is a sign that the math that's developed is more in the service of the world that you live in and the adjacent problems-

   18. DPDwarkesh Patel36:03

       Yeah.

   19. GSGrant Sanderson36:03

       ... that it's used to solve than we typically think of it. On the one hand, information theory, such a good example 'cause it's so pure-

   20. DPDwarkesh Patel36:09

       Yeah.

   21. GSGrant Sanderson36:09

       ... that you could have asked the question, you could have defined the notion of a bit. But evidently, there wasn't a strong enough need to think in that way. Whereas when you're doing error correction or you're thinking about actual information channels over, you know, a wire and you're at Bell Labs, that, that's, that's what prompts it. Another maybe really good example for that would be chaos theory.

   22. DPDwarkesh Patel36:29

       Mm-hmm.

   23. GSGrant Sanderson36:29

       You could easily ask, "Why, why is chaos theory so recent?" Um, you could've-... you know, written the, the Lorenz equations since differential equations existed. Uh, w- why didn't anyone do that and understand that there was this sort of sensitivity to initial conditions? And in that case, it would maybe be the opposite, where it's not that you need the existence of computers as a problem to solve, or the problems that they introduce are the problems to solve, but instead, you need them to even discover the phenomena in the first place. Like, a lot of original concepts in KS Theory came from basically running simulations or doing things that required, uh, a massive amount of computation that simply wouldn't be done by hand. Someone could ask the question, but they wouldn't have observed the unexpected phenomenon. And there, even if it's questions that are as relevant to a pre-computer world as to a post-computer world, like the nature of weather modeling or-

   24. DPDwarkesh Patel37:20

       Yeah.

   25. GSGrant Sanderson37:20

       ... just the nature... three body problem, like all of that kind of stuff, um, somehow without the right tools for thought, it just didn't come into the mind. And so maybe... yeah, maybe there's other things like that where those questions or pieces of technology that start to fundamentally shape everyone's life will then in- invariably also shift like the mathematician's focus.

   26. DPDwarkesh Patel37:44

       Mm. I- I... This actually reminds me, the first day of Scott Aaronson's quantum information class, he said that, "What I'm about to describe to you could have been discovered by a mathematician before, you know, quantum physics existed, if only they'd asked the question-"

   27. GSGrant Sanderson37:59

       Yeah.

   28. DPDwarkesh Patel38:00

       "...we- we're gonna do probabilities, but we're only a- allowed to use unitaries." And the rest of it, a- a... you know, you could've just discovered quantum mechanics or quantum information from there.

   29. GSGrant Sanderson38:09

       I mean, the thing about math, right, especially if you're talking about pure axiomatized math, the experience as a student, as an undergrad, is that you are going through a textbook, and it starts with saying, "Here's the axioms of this field, and then we're gonna deduce from those axioms like various different lemmas and theorems and, uh, proceed from that." And with that as the framing, you get the impression that you could have just come up with any axioms, right?

   30. DPDwarkesh Patel38:32

       (laughs)
6. 44:44 – 56:28

   Future of education

   1. DPDwarkesh Patel44:44

      .1% of educators, should they be exclusively on the internet? Because it, it, it seems like a waste if you were just a college professor or a high school professor and you were teaching 50 kids a year or something. Uh, given the greater scale available, should, should more of them be trying to see if they can reach more people?

   2. GSGrant Sanderson45:01

      I, I think it's not a bad thing for more educators who are good at what they're doing to put their stuff online, for sure. Highly encourage that even if it's as simple as getting someone to put a camera in the back of the classroom. I don't think it would be a good idea to get those people out of the classroom. If anything, I think one of the best things that I could do for my career-

   3. DPDwarkesh Patel45:18

      Mm-hmm.

   4. GSGrant Sanderson45:18

      ... would be to put myself into more classrooms (laughs) , um, and actually, I'm, I'm quite determined at some point to like be a high school math teacher for some number of years.

   5. DPDwarkesh Patel45:26

      Huh. Really?

   6. GSGrant Sanderson45:26

      I don't know when the... There's such opportunity cost, I guess. Um, I, the probab- uh, it's something I would plan on like notably later, as long as there's no other like life logistics that occupy a lot of mind share-

   7. DPDwarkesh Patel45:39

      Yeah.

   8. GSGrant Sanderson45:39

      ... because everything I know about (laughs) high school teaching is like it, it just kicks your ass for the first two-

   9. DPDwarkesh Patel45:43

      Right.

   10. GSGrant Sanderson45:44

       ... two years. But I would say I... One of the most valuable things that you can have if you're trying to explain stuff online is a sense of empathy for what the possible viewers are like that, that are out there. The more distance that you put between yourself and them in terms of life circumstances, you know, I'm not a college student, uh, so I don't have the same empathy with what a college student's like. Certainly not a high school student, so I've lost that empathy. That distance just makes it more and more of an uphill battle to make the content good for them. And I think, uh, keeping people in regular touch with just what people in the classroom actively need is necessary for them to remain as good and as sharp as they are. So yes, get more of those top 0.1% to put their stuff online, but like I would absolutely disagree with the idea of taking them out of their existing circumstances. Maybe for a year or two so they don't lose that sharpness, but then like put them right back in, um, because one, it makes them better at the online expo- position. But also, the other thing I might disagree with is the idea that the reach is lower, uh, because okay, yes, it's a smaller number of people, but you're with them for much, much more time, and you actually have the chance of influencing their trajectory through a, a social connection in a way that you, you just don't over YouTube. And I think you using the word education in a way that I would maybe sub out for the word explanation.

   11. DPDwarkesh Patel47:09

       Mm-hmm.

   12. GSGrant Sanderson47:09

       Like, you want explanations to be online, but like education, the word education derives from, uh, the same root as the word educe, like to bring out. And I really like that as a bit of etymology, 'cause it reminds you that the job of an educator is not to like take their knowledge and shove it into the heads of someone else. The job is to bring it out. That's very, very hard to do in a video. And in fact, even if you can kind of get at it by asking intriguing questions, for the most part, the video is there to answer something once someone has a question and the teacher's job or the educator's job should be to provide the environment such that you're bringing out from your students as much as you can through inspiration, through projects, through the little bits of mentorship and encouragement along the way that requires, you know, eye contact and being there in person and being a, a true figure in their life rather than just an abstract voice behind a screen.

   13. DPDwarkesh Patel48:00

       Should... Then should we think of educators more as motivational speakers? As in the actual job of getting the content in your head is, is maybe for the textbooks or for the YouTube, but now the, the job, like why we have college classes or high school classes is we have somebody who approximates Tony Robbins to, you know, get you to do the thing.

   14. GSGrant Sanderson48:18

       Uh, that would be a subset of it, but there's, there's more than just motivational speech that goes into it, right? There's, um, facilitation of projects or even coming up with what the-proj- projects are or recognizing what a student is interested in so that you can try to tailor a question to their specific set of interests-

   15. DPDwarkesh Patel48:35

       Yeah.

   16. GSGrant Sanderson48:35

       ... or you can maybe act as the curator where, "Hey, there's a lot of online explanations for what a Poisson distribution is," and you're like, "Okay, which of these is the right one that I could serve?" And based on knowing you as a particular student, what might resonate, you might be in a better position to do that. All of that-... goes beyond being a Tony Robbins out, you know, saying like, "Oh, you... be the best person that you can be-"

   17. DPDwarkesh Patel48:58

       (laughs)

   18. GSGrant Sanderson48:58

       ... and, um, all of that. And one, one thing I might say is that any time that I'll chat with mathematicians and try to get a sense for how they got into it, what got them started, so, so often it starts by saying, "Well, there was this one teacher." (laughs) And that teacher did something very small, they like pulled them aside and just said, "Hey, you're really good at this. Have you considered studying more?" Or they give them an interesting problem. And the thing that takes like at most 30 minutes of the teacher's time, maybe even 30 seconds, has these completely monumental rippling effects for the life of the student they were talking to that then sets this, them on this whole different trajectory. Um, two, two examples of this come to mind actually. One is, uh, this woman who was saying she had this moment she got pulled aside from the teacher and he just said like, "Hey, I think you're really good at math. You should st- consider being a math major." Which had been completely outside of her, like, purview at that time. And that, like, changed the way she thought about it. And then later she said she learned that he like did that for a large number of people. (laughs)

   19. DPDwarkesh Patel49:56

       (laughs)

   20. GSGrant Sanderson49:56

       He just pulled them and be like-

   21. DPDwarkesh Patel49:58

       Right.

   22. GSGrant Sanderson49:58

       ... "Hey, you're really good at math." Um, so that's a level of impact-

   23. DPDwarkesh Patel50:01

       Yeah.

   24. GSGrant Sanderson50:01

       ... that you can have in person as a, as a figure in their lives in a way that you can't over a screen. Um, then another one which was very funny, I was asking this guy why he went into th- this specific field that he did. It was a seemingly arbitrary thing in my mind, um, but I guess all, all pure math seems to be. And he said that he, for his first year of grad school, was, um, sitting in this seminar and at the end of the seminar the professor, who was this, you know, old professor, he had never met him before, they didn't have any kind of connection, he seeks this guy out. He comes up and he says, "You. I have a problem for you, a good research problem that I thank- I think might be, um, a good place for you to start in the next couple months." And this guy was like, "Oh, okay." And he like gets this research problem and he spends some mon- months thinking about it and he comes back. And then it later came to light that the professor mistook him for someone else-

   25. DPDwarkesh Patel50:51

       (laughs)

   26. GSGrant Sanderson50:52

       ... (laughs) that was-

   27. DPDwarkesh Patel50:52

       Right.

   28. GSGrant Sanderson50:52

       ... someone he was supposed to be mentoring. And so he was just-

   29. DPDwarkesh Patel50:55

       (laughs)

   30. GSGrant Sanderson50:56

       ... like, like the, the stereotypical image of like a doddering old math professor-
7. 56:28 – 59:25

   Math helped me realize I wasn’t that smart

   1. DPDwarkesh Patel56:28

      exactly. Yeah, exac- that's a great example. I, another valuable experience, at least one I had, was, uh, taking Aaronson's classes in college and realizing I am like at least two standard deviations below him. And that was actually a really valuable experience for me, um, not because it increased my confidence in, uh, well, I, I didn't, I didn't have a moment where (laughs) , uh, w- I was like, "Oh wow, I'm good at this," but it was useful to know, um, you know... But podcasting is a, a, a- an easier thing to do, right? So then it's good to know that there's actual technical things out there where knowing that you can get really deep into something and people are just gonna be like way above you, having that sort of awareness.

   2. GSGrant Sanderson57:07

      Do you think it's fair to have a mental model that has a static G factor type quality here such that you're two sig- center deviations below, and that is forever the state of things? Or do you think that the right mental model is something that allows for flexibility on where contributions actually come from or where intuitions come from that, you know, through many years of experience and certain kinds of problem solving maybe what seemed like a flash of insight was actually like the residue of just years of thinking about certain kinds of puzzles that he had that you maybe didn't?

   3. DPDwarkesh Patel57:39

      Yeah, can I tell you a story from that class actually?

   4. GSGrant Sanderson57:40

      Yeah, yeah, go for it.

   5. DPDwarkesh Patel57:41

      So he's giving some proof about like how one compl... Uh, uh, actually it wasn't that. He was giving a proof of that, I forgot the name of the method but it's a very important method in complexity theory that helped to prove the, the bounds of, um, uh, the complexity of different problems. And he explains it and he says, "You know, in 1999, I o- I, I proved this myself, but I realized that six months before, somebody had already published a paper with this method, and I realized I'm catching up to the frontier now," you know?

   6. GSGrant Sanderson58:12

      Mm-hmm.

   7. DPDwarkesh Patel58:13

      "But, uh, b- when I was a kid I was like doing Euler, that's like 2,000 years-"

   8. GSGrant Sanderson58:16

      (laughs)

   9. DPDwarkesh Patel58:16

      "... in regress, now I'm six months behind." And then so later on in the day I'm like, "Wait, 1999. How old was Scott Aaronson in 1999?"

   10. GSGrant Sanderson58:24

       Mm.

   11. DPDwarkesh Patel58:24

       And I think he was 18 or 19, and he was (laughs) basically proving, uh, proving f- frontier results in complexity theory that were-

   12. GSGrant Sanderson58:32

       Yeah.

   13. DPDwarkesh Patel58:32

       Uh... So at, at that point you're like, (laughs) "All right, Aaronson's a special animal here." And-

   14. GSGrant Sanderson58:36

       You are right, he's probably a special animal.

   15. DPDwarkesh Patel58:39

       Yeah. Uh, but it ju- it just broadly good to know, uh, just like have that sort of upper constraint on your Dunning-Kruger that you can, th- th- this exists in the world.

   16. GSGrant Sanderson58:48

       I, maybe the thing that I would want to say is that whatever the scale is on which he's two standard deviations above you, le- that might not be the one scale that matters.

   17. DPDwarkesh Patel58:57

       Mm-hmm.

   18. GSGrant Sanderson58:58

       And that like contributions to these fields don't always look like genius insights and that, uh, sometimes there's, there's fruit to be born from say becoming kind of an expert in two different things and then finding connections between them. And like, the, the people who make contributions are not necessarily the, the Scott Aaronsons of the world.

   19. DPDwarkesh Patel59:16

       Mm-hmm.

   20. GSGrant Sanderson59:17

       Still, you are probably right about-

   21. DPDwarkesh Patel59:19

       (laughs)

   22. GSGrant Sanderson59:19

       ... that truth, that there are... It's like von Neumann's another example of one of these, right?

   23. DPDwarkesh Patel59:23

       Yeah, yeah, yeah.

8. 59:25 – 1:05:12

   Does Godel’s incompleteness theorem matter?

   1. DPDwarkesh Patel59:25

      Okay, how much does, uh, Godel's Incompleteness Theorem practically matter? Is it, is it something that comes up a lot or is it just a interesting thing to know about the bounds that, uh, isn't day-to-day applicable?

   2. GSGrant Sanderson59:37

      You've asked me another question where I'm not the best one to ask, and I should throw that, um, as a caveat to begin. From what I understand, it really doesn't come up. I mean, the, the analogy to make, um, the paradoxical fact that it's conveying, the idea that you can't have an axiom system that is both, um, that will basically like prove all of the things that are true and which is also self-consistent, the, the contradiction that you construct out of that has the same feeling as the sentence, "This statement is a lie." Where, you know, you think about the statement, and if it's false then it must be true, if it's true it must be false. It's that same flavor. And you might ask, does the existence of that paradox mean that it's hard to speak English unequivocally by computer?

   3. DPDwarkesh Patel1:00:18

      (laughs) Yeah, that's interesting.

   4. GSGrant Sanderson1:00:19

      And so it's, it's so rare that you would come up with something that happens to have a bit of self-reference in it. There were... One of the first times that there was something that came up that didn't feel quite as pathological in that way, if the curious listener wants to go into it, that search would be Paris Harrington theorems-

   5. DPDwarkesh Patel1:00:35

      Mm-hmm.

   6. GSGrant Sanderson1:00:35

      ... where it's, it's a little pathological but it wasn't the very least a question that came up that didn't seem like it was deliberately constructed to be one of these self-referential things where, you know, it, it shows itself to be outside the bounds of whatever axiom system, uh, you are starting with. And it, uh, so it was, you know, shown to be unresolvable in a certain sense, but it, it was asking a... I want, I don't want to say natural because a lot of these math questions aren't natural in the sense that most people would want. But it was asking a question where you wouldn't expect that to be true. So maybe at the edges of theory there are some times when the, um, paradoxes that are possible,

   7. NANarrator1:01:11

      (laughs)

   8. GSGrant Sanderson1:01:11

      ... the Godel's im- um, possibility theorem shows, like do eke their ways in. The impression I get is, no, no mathematician is thinking about it. They're not actively worrying about it. It's not like, "Oh God, now like can I be sure that the stuff that I'm gonna show is true?"

   9. DPDwarkesh Patel1:01:23

      Yeah.

   10. GSGrant Sanderson1:01:23

       For all the practical problems if it's like, you know, the Riemann hypothesis-

   11. DPDwarkesh Patel1:01:26

       Yeah.

   12. GSGrant Sanderson1:01:26

       ... or twin primes, almost everyone's like, "No, there's gonna be an answer." (laughs)

   13. DPDwarkesh Patel1:01:30

       Right.

   14. GSGrant Sanderson1:01:30

       Like it, may- maybe they're, they turn out to be unresolvable in, in one of these, uh, ways. But like, there's just a strong sense that...... that theorem came from a pathology in a way that natural questions that people actually care about don't.

   15. DPDwarkesh Patel1:01:45

       That's, that's really interesting that something from the outside of, in, and in popularizations is, seems to be a very fundamental thing, where people, people have definitely heard about this, right?

   16. GSGrant Sanderson1:01:56

       Yeah.

   17. DPDwarkesh Patel1:01:56

       It's not internally... A good a, a good analogy here is, in computer science, the halting problem.

   18. GSGrant Sanderson1:02:00

       Mm-hmm.

   19. DPDwarkesh Patel1:02:00

       It's like, you take a computer science course, one of the first things you learn is a, you know, the proof of the halting problem. And, uh, i- i- it's another one of those things where y- y- you don't really need to be able to prove that every single, or y- maybe y- have that sort of program available for... Yeah. (laughs) No comment.

   20. GSGrant Sanderson1:02:19

       No more comment. (laughs)

   21. DPDwarkesh Patel1:02:21

       Why are good explanations so hard to find, despite how useful they are? Um, o- obviously there's many other, other than you as well, there's many other cases of good explanations. But, uh, generally, it just seems like there aren't as many as there should be. Is it just a story of economics, where it's nobody's incentive to be making really, spend a lot of time making good e- explanations?

   22. GSGrant Sanderson1:02:40

       (laughs)

   23. DPDwarkesh Patel1:02:40

       Is it just a really hard skill that isn't correlated with being able to come with the discovery itself? W- why are e- good explanations scarce?

   24. GSGrant Sanderson1:02:47

       I think there's maybe two explanations. Um, the first, less important one, is gonna be that there's a difference between knowing something and then remembering what it's like not to know it.

   25. DPDwarkesh Patel1:02:59

       Mm-hmm.

   26. GSGrant Sanderson1:02:59

       And the characteristic of a good explanation is that you're walking someone on a path from the feeling of not understanding up to the feeling of understanding. Earlier, you were asking about societies that are, that lack numeracy. That's such a hard brain state to put yourself in. Like, what's it like to not even know numbers? How would you start to explain what numbers are? Um, maybe you should go from a bunch of concrete examples. But like, the way that you think about numbers and adding things, it's just, you have to really unpack a lot before you even start there. And I think, at higher levels of abstraction, that becomes even harder, 'cause it, it shapes the way that you think so much, that remembering what it's like not to understand it. Uh, you're teaching some kid algebra, and the premise of like, a variable, they're like, "What is X?" And you're like, "Well, it's, it's, it's not necessarily anything, but it's what we're solving for." They're like, "Yeah, but what is it?" Like, trying to answer what is X is a weirdly hard thing, 'cause it is the premise that you're even starting from. Um, the more important one probably is that the best explanation depends heavily on the individual who's learning. And the perfect explanation for you, um, often might be very different from the perfect explanation for someone else. So there's a lot of very good domain-specific explanations. You know, pull up in any textbook and like, chapter 12 of it is probably explaining the content in there, like, quite well, assuming that you've read chapters 1 through 11. But if you're coming in from a cold start, it's a little bit hard. And so, the real golden nugget is like, how do you construct explanations which are as generally useful as possible, as generally appealing as possible? Um, and that, I think, because you can't assume shared context, it becomes this challenge. And I think there's like, tips and tricks along the way. But because the people that are often making explanations have a specific enough audience, it is this classroom of 30 people.

   27. DPDwarkesh Patel1:04:46

       Yeah.

   28. GSGrant Sanderson1:04:46

       Or it's this discipline of majors who are in their third year. All the explanations from the people who are professional explainers in some sense are so targeted that maybe it's the economic thing you're talking about, there's not, or at least until recently in history, there hasn't been the need to, or the incentive to come up with something that would be, um, motivating and approachable and clear to an extremely wide variety of different backgrounds.

9. 1:05:12 – 1:10:13

   How Grant makes videos

   1. GSGrant Sanderson1:05:12

   2. DPDwarkesh Patel1:05:12

      Is the process of making your videos, is that mostly you?

   3. GSGrant Sanderson1:05:15

      Mm-hmm.

   4. DPDwarkesh Patel1:05:16

      Okay. Given the scale you're reaching, it seems that if it was possible, i- i- it would, you know, just like a small increase in productivity would be worth like, an entire production studio. And it's interesting to me or surprising that the transaction cost of having a production, uh, setup are high enough that it's better to literally do y- the mundane details yourself.

   5. GSGrant Sanderson1:05:39

      Yeah, I mean, uh, this could honestly just be a personal flaw. Like, I'm not good at, um, pulling people in, and I've struggled to do this effectively in the past. But a part of it is that the mun- the seemingly mundane details are sometimes just how I even think about constructing it in the first place.

   6. DPDwarkesh Patel1:05:57

      Mm-hmm.

   7. GSGrant Sanderson1:05:58

      You know, the first thing that a lot of YouTubers will do if they can hire is hire an editor. And this will be because they film a lot of things, and so a lot of the editing process is removing the stuff that was filmed that shouldn't be in the video and just leaving the stuff that should be in the video. And that's time-consuming and it's kind of mundane. And it's probably not that relevant to what the creator should be thinking about. When you're not filming stuff, like, the, the editing process for me, you know, I start by laying out all of the animations and stuff that I want in a timeline, and then once I record the voiceover, the actual editing is like a day.

   8. DPDwarkesh Patel1:06:29

      Mm-hmm.

   9. GSGrant Sanderson1:06:29

      And it's not, like I guess I could hire someone and gain a day back of my life, but the, the communication back and forth for saying what specifically I want, like, all of the little cuts that I'm making along the way are my way of even thinking about what I want the final piece to be, such that it would be hard to put it into words. It's s- it's similar for why I maybe find it quite hard to use, um, like Copilot and some of these like-

   10. DPDwarkesh Patel1:06:50

       Mm-hmm.

   11. GSGrant Sanderson1:06:50

       ... um, LLM tools and coding, where for the animation code, i- you know, it can be super great if you're learning some new library and it knows about that library that you don't... But for my library that I know inside and out, if I'm just using it, it feels like, oh, th- this should be the most automatable thing ever, you know?

   12. DPDwarkesh Patel1:07:05

       Yeah.

   13. GSGrant Sanderson1:07:05

       It, it's, uh, it's just text. Uh, like, I should be the first YouTuber who can actually do this better 'cause the, the substance behind each animation is text. It's not like an editing workflow in quite the same way. But it doesn't work. And I think it's because, um, maybe it's just because you need a multi-modal thing that actually understands the look of the output. Like, the output isn't something that is consumable in text.

   14. DPDwarkesh Patel1:07:26

       Mm-hmm.

   15. GSGrant Sanderson1:07:26

       It, it's something about how it looks. But at a deeper level, I can't even put into words what I want to put on the screen except to do so in code. Like, that's just the way that I'm thinking about it.

   16. DPDwarkesh Patel1:07:36

       Mm-hmm.

   17. GSGrant Sanderson1:07:37

       And I, like, if I were to try to put into English the thing that I want as a comment that then gets expanded-... that task is actually harder than writing it in, in the code. Um, and if it's clunky to write in code, that's a sign that I should, like, change the interface of the library such that it's less clunky to be expressive in the way that I want. And it's in that same way where a lot of the creative process th- that feels mundane, those are just like the cogs of thought slowly turning in a way that if they weren't turning for that part, they would have to be turning during the interface of communication with the collaborator.

   18. DPDwarkesh Patel1:08:12

       Yeah. O- on the point of working with Copilot, uh, where we kind of visualize the changes you wanted to make, there we- the paper from Microsoft Research, the Sparks of AGI paper, had an actually really interesting example where it was generating LaTex and they generated some output and they say, "Change this so that the visual that comes up and the rendering is different in this way."

   19. GSGrant Sanderson1:08:35

       Mm-hmm.

   20. DPDwarkesh Patel1:08:35

       And it was actually able to do that, which was th- their evidence that it can understand the higher level of visual abstraction.

   21. GSGrant Sanderson1:08:41

       Yeah.

   22. DPDwarkesh Patel1:08:41

       Um, so but I guess it can't do that for Manim?

   23. GSGrant Sanderson1:08:44

       There's a couple reasons I might, um... it might not be as fair a comparison. One would be the two versions of Manim. There's, uh, a split where there's a community version that is, you know, by the community, for the community, and then mine. The interfaces are largely similar. The rendering engines are quite different. But because of slight differences in that, and you know, it might have a tendency, it learned from one or it saw examples from one and it's intermixing them. So stuff just doesn't quite run when there's discrepancy. I maybe shot myself in the foot where all of my code for videos...

   24. DPDwarkesh Patel1:09:14

       (laughs)

   25. GSGrant Sanderson1:09:14

       Like, I don't really comment it that much because it's-

   26. DPDwarkesh Patel1:09:16

       Mm-hmm.

   27. GSGrant Sanderson1:09:16

       ... it's like a one and done deal.

   28. DPDwarkesh Patel1:09:17

       Yeah.

   29. GSGrant Sanderson1:09:17

       It's, if it's, you know, there's... Also if I made the code for the core library, I could comment and document a lot better. But like, the way that I'm making it feels much more like the editing flow if you were to look at the operation history of someone in After Effects, right? Like written down. It's a little bit more like that where there's not a perfect description in English of the thing that I want to do and then the execution of that. It just, it's just the execution of that. Um, and you know, it's- it's not meant to be editable in hindsight as much because I'm just in the flow of making the scene for the one video. And, you know, maybe I could have given it a better chance to learn what it- is supposed to be happening by having a really well-documented set of like, "This is the input, this is the output, this is the comment describing it in English." But even then that wouldn't hit the problem on like, I would have to articulate what the thing I want is-

   30. DPDwarkesh Patel1:10:07

       Mm-hmm.

Episode duration: 1:31:20