Luís and João Batalha: Fermat's Library and the Art of Studying Papers | Lex Fridman Podcast #209

1. 0:00 – 2:22

   Introduction

   1. LFLex Fridman0:00

      The following is a conversation with Luis and Joao Batella, brothers and co-founders of Fermat's Library, which is an incredible platform for annotating papers. As they write on the Fermat's Library website, "Just as Pierre de Fermat scribbled his famous Last Theorem in the margins, professional scientists, academics, and citizen scientists can annotate equations, figures, ideas, and write in the margins." Fermat's Library is also a really good Twitter account to follow. I highly recommend it. They post little visual factoids and explorations that reveal the beauty of mathematics. I love it. Quick mention of our sponsors: Skiff, SimpliSafe, Indeed, NetSuite, and Four Sigmatic. Check them out in the description to support this podcast. As a side note, let me say a few words about the dissemination of scientific ideas. I believe that all scientific articles should be freely accessible to the public. They currently are not. In one analysis I saw, more than 70% of published research articles are behind a paywall. In case you don't know, the funders of the research, whether that's government or industry, aren't the ones putting up the paywall. The journals are the ones putting up the paywall while using unpaid labor from researchers for the peer review process. Where is all that money from the paywall going? In this digital age, the cost here should be minimal. This cost can easily be covered through donation, advertisement, or public funding of science. The benefit versus the cost of all papers being free to read is obvious, and the fact that they're not free goes against everything science should stand for, which is the free dissemination of ideas that educate and inspire. Science cannot be a gated institution. The more people can freely learn and collaborate on ideas, the more problems we can solve in the world together, and the faster we can drive old ideas out and bring new, better ideas in. Science is beautiful and powerful, and its dissemination in this digital age should be free. This is the Lex Fridman Podcast, and here's my conversation with Luis and Joao Batella.

2. 2:22 – 17:13

   Backstories to research papers

   1. LFLex Fridman2:22

      Luis, you suggested an interesting idea. Imagine if most papers had a backstory section, the same way that they have an abstract. So, knowing more about how the authors ended up working on a paper can be extremely insightful, and then you went on to give a backstory for the Feynman QED paper.

   2. LBLuís Batalha2:42

      Mm-hmm.

   3. LFLex Fridman2:43

      This was all in a tweet, by the way. We're doing tweet analysis today.

   4. LBLuís Batalha2:45

      (laughs)

   5. LFLex Fridman2:46

      How much of the human backstory do you think is important in understanding the idea itself that's presented in the paper or in general?

   6. LBLuís Batalha2:54

      I think this gives way more context to the work of, of scientists. I think people, a lot of people have this almost kind of romantic misconception that, uh, the way a lot of scientists work is almost as this sum of eureka moments where all of the sudden they sit down and start writing two papers in a row, and the papers are usually isolated, and when you actually look at it, it's the papers are, you know, chapters of a way more complex, uh, story. And, uh, the, the Feynman QED paper is a good example. So, Feynman was actually going through a pretty dark phase before writing that paper. It was he lost enthusiasm with physics and doing physics problems, and there was one time when he was in the cafeteria of Cornell, and he saw a guy that was throwing plates in the air, and he noticed that there was, when the plate was in the air, there were two movements there. The, the plate was wob- wobbling, but he also noticed that the, the Cornell symbol was rotating, and he was able to figure out the equations of motions, uh, the equations of motions of th- those, uh, plates, and that, uh, led him to kind of think a little bit about, uh, electron orbits in relativity, which led to the paper of, um, about quantum electrodynamics. So, that kind of reignited, uh, his interest in physics, and, uh, and ended up publishing the paper that led to the, his Nobel Prize basically. And I think it's, it's, there are a lot of really interesting backstories about papers that readers never get to know. For instance, we did, a couple of months ago, um, an AMA around, uh, a paper, a pretty famous paper, the GANs paper with Ian Goodfellow, and so we did an AMA where everyone was could ask questions about the paper and Ian was, uh, responding to those questions, and he also, he was also, uh, telling the story of how he got the idea for that paper in a bar.

   7. LFLex Fridman4:48

      Mm-hmm.

   8. LBLuís Batalha4:48

      So, there was also an interesting and, uh, a backstory. Uh, I also read a, a book, uh, by, um, Cédric Villani. Uh, This, uh, Cédric Villani is this mathematician, a Fields Medalist, and in his book, he tries to explain how he got from like, um, a PhD student to the Fields Medal, and he tries to be as descriptive as possible about every single step how he got to the Fields Medal. And it's interesting also to see just the amount of random interactions and discussions with other researchers, sometimes over coffee, and how it led to like fundamental breakthroughs and some of his most important papers. So, I think it's super interesting to have that context of, of the backstory.

   9. LFLex Fridman5:28

      Well, the Ian Goodfellow story is kind of interesting and perhaps that's true for Feynman as well, I don't know if it's romanticizing the thing, but it seems like just a few little insights and a little bit of work does most of the leap required. Do you have a sense that for a lot of the stuff you've looked at, just looking back through history, uh, it, it, it wasn't necessarily the grind of like Andrew Wiles with Fermat's Last Theorem, for example?

   10. LBLuís Batalha5:54

       Mm-hmm.

   11. LFLex Fridman5:55

       It was more like a, a brilliant moment of insight. In fact, Ian Goodfellow has a kind of sadness to him almost-

   12. LBLuís Batalha6:02

       Mm.

   13. LFLex Fridman6:02

       ... in that at that time in machine learning-... like, at that time especially, in, uh, for, for GANs, you could code something up really quickly-

   14. JBJoão Batalha6:12

       Mm-hmm.

   15. LFLex Fridman6:12

       ... on a single machine-

   16. JBJoão Batalha6:13

       Mm-hmm.

   17. LFLex Fridman6:14

       ... and almost do the invention f- go from idea to, uh, experimental validation in like a single night, a single person could do it. And now, there's kind of a sadness that a lot of the breakthroughs you might have in machine learning kind of require large-scale experiments. So, it was almost like the early days, uh, uh, so, th- I wonder how many low-hanging fruit there are in science and mathematics and even engineering where it's like you could do that little experiment quickly, like you have an insight in a bar. Why is it always a bar?

   18. JBJoão Batalha6:47

       (laughs)

   19. LFLex Fridman6:47

       But you have an insight at a bar, and then just implement, and the world changes.

   20. JBJoão Batalha6:53

       It- it's- it's a good point. I think it also depends a lot on the maturity of the field. When you look at a f- a field like mathematics, like it's a pretty mature field. Uh, a field like machine learning, um, it's- it's growing pretty fast and, um, it's actually pretty- p- p- pretty interesting. I- I- I looked up like the number of new papers on archive with a keyword machine learning and like 50% of those papers have been published on- in the last 12 months. So, you can see just the sense-

   21. LFLex Fridman7:23

       Five-zero? Or-

   22. JBJoão Batalha7:24

       Five-zero. 50%. So, you can see the- the- the- the magnitude of growth in that field.

   23. LFLex Fridman7:30

       (laughs)

   24. JBJoão Batalha7:30

       And so, I think like, uh, as fields mature, like those types of- of moments, I think naturally, uh, are less frequent. Um, it's just a consequence of- of that. The other point that is interesting about the backstory is that- is that it can really make it more memorable in a way. And- and by making it more memorable, it's- it kind of sediments the knowledge more in your mind. I- I remember also reading the- sort of the backstory to- to Dijkstra's Shortest Path Algorithm-

   25. LFLex Fridman7:58

       Mm.

   26. JBJoão Batalha7:58

       ... right? Where- where he- he came up with it, uh, essentially while he was sitting down at a- at a- at a coffee shop in Amsterdam, and he- and he came up with that algorithm over 20 minutes. And one interesting aspect is th- he didn't have any pen or paper at the time.

   27. LFLex Fridman8:13

       Mm-hmm.

   28. JBJoão Batalha8:13

       And so, he had to do it all in his mind. And so, th- there's only so much complexity that he can handle if you're just thinking about it in your mind. And that- like when you think about the simplicity of Dijkstra's Shortest Path Finding Algorithm, it- it's- you know, knowing that backstory helps sediment that algorithm in your mind, so they don't forget about it as easily.

   29. LFLex Fridman8:33

       It might be from you that I saw a meme about Dijkstra. (laughs)

   30. JBJoão Batalha8:39

       (laughs)
3. 17:13 – 37:14

   Fermat's Library

   1. LBLuís Batalha17:13

      scientists.

   2. LFLex Fridman17:14

      So, could we talk about Fermat's Library?

   3. LBLuís Batalha17:17

      Yeah, absolutely.

   4. LFLex Fridman17:18

      W- what is it? What's the main goal? What's the dream?

   5. LBLuís Batalha17:22

      It is a platform for annotating papers in its essence, uh, right? And so academic papers can be one of the densest forms of content out there an- and generally pretty hard to understand at times. And, um ... and the idea is that you can make them more accessible and easier to understand by adding these rich annotations to the side, right? And so we can just imagine a PDF view on your browser and then you have annotations on each side and then when you click on them, a sidebar expands and then you have, uh, y- annotations that support LaTeX and Markdown. Uh, and so the idea is that you can say explain a tougher part of a paper where there's a step that is not completely obvious, um, or you can add more context to it, and then over time papers can become easier and, and easier to understand and can evolve in a way. But it really came from, uh-... myself, Luis, and two other friends. We've been, ah, we've had this, this, long-running habit of kind of running a journal club amongst us. We come from different backgrounds, right? I, I studied CS, Luis studied physics. And so we'd read papers and present them to each other and, uh, and then we tried to bring some of that online, and that's, that's, that's when we decided to, to, to build Fermat's Library. Um, then over time, it kinda grew into, into something, uh, with, with a broader goal. Uh, and really what we're trying to do is trying to help, uh, move science in the, in the right direction. Um, that's really the ultimate goal and, and where we wanna take it now.

   6. LFLex Fridman18:55

      Well, so there's a lot to be said. So first of all, for people who haven't seen it, it, th- the interface is exceptionally well done. That's, like, execution is really important here.

   7. LBLuís Batalha19:05

      Absolutely.

   8. LFLex Fridman19:06

      The other thing, just to mention, for a large number of people apparently, which is new to me, don't know what LaTeX is. So it's spelled like latex, so be careful googling it if you haven't before.

   9. LBLuís Batalha19:20

      (laughs)

   10. LFLex Fridman19:21

       Uh, it's, uh, uh, sorry, I don't even know the correct terminology.

   11. LBLuís Batalha19:24

       Typesetting language?

   12. LFLex Fridman19:25

       It's a typesetting language, where it's, you're basically program, writing a program that then generates something that looks, from a typography perspective, beautiful.

   13. LBLuís Batalha19:37

       Absolutely.

   14. LFLex Fridman19:38

       And, uh, so a lot of academics use it to write papers. I, I, I think there's, like, a bunch of communities that use it to write papers. I would say it's mathematics-

   15. LBLuís Batalha19:48

       Mm-hmm.

   16. LFLex Fridman19:48

       ... physics, computer science.

   17. LBLuís Batalha19:50

       Yeah. That's, yeah, that's the-

   18. LFLex Fridman19:52

       That's it?

   19. LBLuís Batalha19:52

       That's the, the main-

   20. LFLex Fridman19:52

       Because I'm collaborating currently on a paper with, uh, two neuroscientists from Stanford.

   21. LBLuís Batalha19:57

       And they don't know what? (laughs)

   22. LFLex Fridman19:58

       (laughs) Um, so I'm using, um, Microsoft Word and, uh, Mendeley-

   23. LBLuís Batalha20:05

       Hmm. Uh-huh.

   24. LFLex Fridman20:06

       ... and, like, all of those kinds of things, and it's, and I'm being very zen-like about, about the whole process, but it's fascinating. It's a little heartbreaking, actually, because, um, it actually... it's, it's funny to say, but, uh, and we'll talk about open science, actually, the bigger mission behind Fermat's Library is, like, really opening up the world of science to everybody, is these silly two facts of, like, one community uses LaTeX and another uses Word, is actually a barrier between them. That's like, it's, like, boring and practical in a sense, but it makes it very difficult to collaborate.

   25. LBLuís Batalha20:46

       Just on that, like, I think the, if there is some people that should have received, like, a Nobel Prize that, but will never get it-

   26. LFLex Fridman20:52

       Yeah.

   27. LBLuís Batalha20:52

       ... and I think one of those is, like, Donald Knuth-

   28. LFLex Fridman20:55

       Yeah.

   29. LBLuís Batalha20:55

       ... because of TeX and LaTeX then-

   30. LFLex Fridman20:57

       (laughs)
4. 37:14 – 1:00:54

   Scientific publishing

   1. LBLuís Batalha37:14

   2. LFLex Fridman37:14

      Can we talk about peer review, for example?

   3. LBLuís Batalha37:16

      Absolutely. I- I think, like, in- in terms of the peer review, I think we... It's- it's important to look at the bigger picture here of, like... of what does scientific... the scientific publishing ecosystem looks like. Because for me, there- there are a lot of things that are wrong about that entire process. So if you look at, for ins- at the... what, um, publishing means in like a- a traditional journal, you have, uh, journals that pay, um, authors for their articles, and then they might pay, like, reviewers to, um, review those articles, and finally, they pay people toum... or distributors to distribute the content. In the... In the scientific publishing world, you have scientists that are usually backed by government grants that are giving away their work for free in the form of papers, and then you have other scientists that are reviewing their work. Uh, this process is known as the peer review process, again, for free. And then finally, we have, um, government-backed universities and libraries that are buying back all those... all that work so that other scientists can we- can read. So this is... For me, it's bizarre. You have the government that is funding the research, it's paying the salaries of the scientists, it's paying the salaries of the reviewers, and it's buying back all that, uh, product of their work again. Um, and I think the problem with this system, and it's wh- it's why it's so difficult to- to break this suboptimal equilibrium, is because of- of the way academia works right now and the way you can progress in- in your academic life.

   4. LFLex Fridman38:57

      Mm-hmm.

   5. LBLuís Batalha38:58

      Um, and so in a lot of fields, the- the competition in academia is- is really insane. So you have hundreds of PhD students, they are, um, trying to get to a- a professor position, and- and it's hyper competitive, and the only way for you to get there is if you publish papers, ideally in journals with a high impact factor.

   6. LFLex Fridman39:23

      In computer science, it's al- it's often conferences are also very prestigious or actually more prestigious than journals now.

   7. LBLuís Batalha39:30

      Okay, interesting.

   8. LFLex Fridman39:31

      So- so that's the one discipline where... I mean, that has to do with the thing we've discussed, uh, in terms of the... how quickly the field turns around. But like NeurIPS, CVPR, those conferences are more prestigious, or at the very least, as prestigious as the journals.

   9. LBLuís Batalha39:47

      The- the journals.

   10. LFLex Fridman39:48

       But doesn't matter, the process is what it is.

   11. LBLuís Batalha39:50

       And- and- and so with the- the... So for people that don't know how... the impact factor of a journal is basically the average number of citations that a paper would get if it gets published on that journal. But so, um, you can really think that, um... The problem with the- the impact factor is that it's a way to turn papers into accounting units. And- and- and let me unpack this because it's... the impact factor is almost like a nobility title. So pa- because papers are born with impact even before anyone reads them. So the researchers, they don't have the incentive to care about if this paper is gonna have a- a long term impact on- on- on the world. What they care... their goal... their end goal is the paper to get published-

   12. LFLex Fridman40:35

       Yes.

   13. LBLuís Batalha40:36

       ... so that they get that value upfront. So for me, that- that is one of the problems of- of that, and that really creates a tyranny of- of metrics. Because at the end of the day, if you are a dean, what you want to hire is like people, researchers that publish papers on journals with high impact factors, because that will increase the ranking of your university and will allow you to charge more for tuition, so on and so forth. And, um... And- and that- that... and especially when you are in super competitive areas, you know, that people will try to gamify that system and- and misconduct starts showing up. Um, there's a, um, a really interesting book on this topic called Gaming the Metrics. It's a book by a researcher called, uh, Mario Biagioli. It goes a lot into like how these, um... the impact factor and metrics affect science negatively, and it's interesting to think, especially in terms of citations, if you look at the early work of like looking at citations, there was a- a lot of work that was done by a guy called Eugene Garfield, and this guy, um... The early work in terms of citation, they wanted to use... they wanted to use citations as from a descriptive point of view.

   14. LFLex Fridman41:47

       Mm-hmm.

   15. LBLuís Batalha41:47

       So what they wanted to y- to create was a map, and- and that map would create a- a visual representation of in- of influence. So citations would be links between papers, and ideally what they would show, they would represent is that you read someone else's paper and it had an impact on your research. They weren't supposed to be counted.

   16. LFLex Fridman42:08

       I think th- this inspired like Larry and Sergey's work-

   17. LBLuís Batalha42:11

       Exactly.

   18. LFLex Fridman42:11

       ... right? For Google.

   19. LBLuís Batalha42:12

       Exactly. I- I think they even mentioned that. But what happens is like as you start counting citations, you create a market and- and the same way like... And this was... The- the work of E- Eugene Garfield was a big inspiration for Larry and Sergey for the PageRank algorithm that, um, you know, led to the creation of- of Google.

   20. LFLex Fridman42:31

       Mm-hmm.

   21. LBLuís Batalha42:31

       And they even recognize that. And- and if you think about it, it's like the same way there's a- a gigantic market for search engine optimization, uh, SEO, where people try to optimize, you know, the- the PageRank and how high the, uh, uh, web page will rank on Google.... the same will happen for papers. People will try to optimize, like their ci- their, uh, th- the impact factors and the citations that they get. And that, um, creates a really big problem. And if, it's super interesting to actually analyze them, if you look at the distribution of, of the high impa- the impact factors of journals, you have like Nature with, uh, Nature I believe is like in the low 40s. And then you have, I believe Science is high 30s, and then you have a really good, uh, um, um, a, a good set of good journals that f- ... will f- fall between 10 and 30, and then you have a gigantic tail of, of journals that have, uh, impact factor below two.

   22. LFLex Fridman43:25

       Mm-hmm.

   23. LBLuís Batalha43:26

       And you can really see two economies here. You see the, the, um, you know, the universities that are maybe less prestigious, less known that where the faculty are pressured to just publish papers regardless of the journal, "What I want to do is increase the ranking of my university." And so they end up publishing as many papers as, as they, they can in like journals with low impact factor. And unfortunately, this is, uh, represents a lot of, of, of the global south.

   24. LFLex Fridman43:54

       Mm-hmm.

   25. LBLuís Batalha43:55

       And then you have the luxury good economy. So for instance, for ... And there are also problems here in the luxury good economy. So if you look at the journal like Nature, so with impact factor of like in the low 40s, there's no way that you're gonna be able to sustain that level of impact factor by just grabbing the attention of scientists. So what, what I mean by that is like for, for the journals, the articles that get published in Nature, they need to be New York Times great. So they need to make it to the, you know, to the, to the big media. They need to be captured by the meed media-

   26. LFLex Fridman44:33

       Yes.

   27. LBLuís Batalha44:33

       ... big media. And it's because that's the only way for you to capture enough attention to sustain that level of citations.

   28. LFLex Fridman44:39

       Yes.

   29. LBLuís Batalha44:40

       And that, of course, creates problems because people then will try to, again, gamify the system and have like titles or abstracts-

   30. LFLex Fridman44:48

       Right.
5. 1:00:54 – 1:06:48

   How to read a paper

   1. LBLuís Batalha1:00:55

   2. LFLex Fridman1:00:55

      So, uh, let me ask, you've read quite a few papers.You've, uh, annotated quite a few papers. Let's talk about the process itself. How do you advise people read papers? Or y- or maybe you wanna broaden it beyond just papers, but just read concrete pieces of information to understand the insights that lay within.

   3. LBLuís Batalha1:01:18

      Uh, I would say for papers specifically, I would, I would bring back kinda what Luis was talking about, is, is that it's important to keep in mind that papers are not optimized for ease of understanding. And so, (laughs) right? Th- there's all sorts of restrictions and size, uh, and format and, and, and language that they can use, and so it's important to keep that in mind. And so that if you're struggling to read a paper, doesn't m- it, it might not mean that the underlying material is actually that hard. And so, so that's definitely something that, that especially for us that we, we, we read papers and most of the times it'll be papers that are completely outside of our, of our comfort zone, I guess, and, and, and so it'll be completely new areas to us. Um, so I always try to, to keep that in mind.

   4. LFLex Fridman1:02:05

      So, there's usually a certain kinda structure, like abstract introductions-

   5. LBLuís Batalha1:02:09

      Mm-hmm.

   6. LFLex Fridman1:02:09

      ... methodology, uh, depending on the community and so on. Is there something about the process of, like, how to read it, whether you wanna skim it to try to find the parts that are easy to understand or not, uh, reading it multiple times?

   7. LBLuís Batalha1:02:25

      Mm-hmm.

   8. LFLex Fridman1:02:26

      Is, is there any kinda hacks that you can comment on?

   9. LBLuís Batalha1:02:29

      I remember, like, Feynman had this, this kind of hack when he was reading papers, where he would basically, um... he would dr- I think, I believe he would read the conclusion of the paper, and he would try to just, um, see if he would be able to figure out how to get to the conclusion in, like, a couple of minutes by himself, and, um, and he would read pa- a lot of papers that way. And I think F- Fermi also did that almost. A- and Fermi was known for doing a lot of back-of-the-envelope calculations, so he was a master at, uh, doing that. Um, and, and in terms of, like, uh, especially when, uh, when reading a paper, I think a lot of times people might f- feel discouraged about the first time you read it, you, you know, it's very hard to grasp, or you, you don't understand a lo- a huge fraction of the paper, and I think it's having read a lot of papers in my life, I think I've in peace with, like, the fact that you might spend hours where you're just reading a paper and jumping from paper to paper, reading citations, and, um, like, your level of understanding of, uh, sometimes of the paper is very close to 0%, and all, all of a sudden, you know, everything kind of makes sense then in, in, in your mind, and then, you know, you have this quantum jump where all of a sudden you, you, you understand then the big picture of the paper. And, uh, I, I... and th- and this is an exercise that I have to when reading papers and especially, like, more complex papers, like, okay, you don't understand because you're just going through the process, and just keep going. And, like, and it, it's f- might feel super chaotic, especially if you are jumping from reference to reference. You know, you might end up with, like, 20 tabs open and you're reading a ton of other papers, but it's just trusting that process that at the end, like, you'll find light. Um, and I think for me that's a, a good framework when reading a paper. It's hard, because, you know, you might end up spending a lot of time, and you, it looks like you're lost, but, uh, but th- that's the process to actually, um, you know, understand what they are talking about in a paper.

   10. LFLex Fridman1:04:36

       Yeah, I think that process, uh, I enjoy... I've found a lot of value in the process, especially for things outside my field, uh, reading a lot of related work sections and kinda go- going down that path of getting a big context of the field, because what's... especially when they are well written, there's opinions injected into the rel-

   11. LBLuís Batalha1:04:57

       (laughs)

   12. LFLex Fridman1:04:57

       ... the related work, like what work is important, what is not. And if you read multiple related work sections that cite or don't cite each other, like the papers, uh, you, you get a sense of where the field, where the tensions of the field are-

   13. LBLuís Batalha1:05:10

       Understand.

   14. LFLex Fridman1:05:11

       ... where the s- where the field is striving, uh, and that helps you put into context, like, whether the work is radical, whether it's overselling itself, whether it's underselling itself, all those things, uh, and on t- added on top of that, I find that often the related work section is the most kind of accessible and readable part of a paper, because it's kind of, uh, it's brief, to the point, it's trying to... like summarizing, it's almost like a Wikipedia-style article. The introduction is supposed to be a compelling story or, or whatever, but it's often like overselling. There, there's like an agenda-

   15. LBLuís Batalha1:05:49

       Mm-hmm.

   16. LFLex Fridman1:05:49

       ... in the introduction. (laughs) The related work usually has the least amount of agenda except for the few, like, elements where you're trying to, uh, talk shit about previous work or you're trying to sell that you're doing much better. But other, other than that, when you're just painting where the, where the field, uh, came from or where the field stands, it's, uh, really valuable. And also, again, just w- to agree with Feynman, the conclusion. It's like I get a lot of value from the breadth-first search kinda-

   17. LBLuís Batalha1:06:17

       Mm-hmm.

   18. LFLex Fridman1:06:17

       ... read the conclusion, then read the related work, and then, uh, go through the references and the related work-

   19. LBLuís Batalha1:06:24

       Mm-hmm.

   20. LFLex Fridman1:06:24

       ... read the conclusion, read the related work, and just go down the tree un- until you, like, hit dead ends or run out of coffee.

   21. LBLuís Batalha1:06:32

       (laughs)

   22. LFLex Fridman1:06:32

       And then through that process, you go back up the tree, and now you can see the results in their proper, uh, in their proper context, unless of course the paper is truly revolutionary, which even that process will help you understand that is, uh, in fact, uh, truly, uh, revolutionary.

6. 1:06:48 – 1:15:27

   Taking good notes

   1. LFLex Fridman1:06:48

      You've also, um... uh, you, you talked about just following your Twitter thread in a (laughs) in a depth-first search. You talked about that you read, um, the book on, uh, uh, Grisha Perelman, Grigori Perelman.

   2. LBLuís Batalha1:07:01

      Mm-hmm. Mm-hmm.

   3. LFLex Fridman1:07:02

      And then you would... you, you had a really nice Twitter thread on it-

   4. LBLuís Batalha1:07:05

      Mm-hmm.

   5. LFLex Fridman1:07:06

      ... and you were taking notes throughout, so...At a high level, is there suggestions you can give on how to take good notes? Whether it's, we're talking about annotations or just for yourself to try to, uh, put on paper ideas as you progress through the work in order to then like understand the work better.

   6. LBLuís Batalha1:07:24

      For me, I always try not to (laughs) underestimate how much you can forget, uh, within six months-

   7. LFLex Fridman1:07:30

      Right.

   8. LBLuís Batalha1:07:31

      ... after you've read something. (laughs)

   9. LFLex Fridman1:07:32

      Oh, I thought you were gonna say five minutes, but yeah, six months-

   10. LBLuís Batalha1:07:34

       (laughs)

   11. LFLex Fridman1:07:34

       ... is good.

   12. LBLuís Batalha1:07:35

       Yeah, or, or, e- or even shorter. And so, that's something that I always try to keep in mind. And, uh, and it's, and it's often, I mean, w- every once in a while, I'll, I'll read back a paper of, that I annotated on Fermat and it's, and, uh, and I'll read through my own annotations and it's, uh, and I've completely forgotten what I had written. And, uh, but it also, it, it also, it's interesting because in a way after you just understood something, you're kinda the best possible teacher that can teach your future self. Uh-

   13. LFLex Fridman1:08:08

       Yeah.

   14. LBLuís Batalha1:08:08

       ... you know, after you've forgotten it, uh, y- you can, y- you're kind of your own best possible teacher at that moment. And so, it's, it can be great to, to try to capture that, uh-

   15. LFLex Fridman1:08:19

       It's, it's, it's brilliant. You just made me kinda realize it's really nice to f- to put yourself in the position of teaching an older version of yourself-

   16. LBLuís Batalha1:08:30

       Exactly.

   17. LFLex Fridman1:08:30

       ... that returns to this paper, almost like thinking it literally.

   18. LBLuís Batalha1:08:33

       That's under-explored, but it's, it's super powerful, because you are the person that you c- like, if you, if you look at the scale from like one, not knowing anything about the topic, and 10, like you are the one that progressed from one to 10 and you know which steps you struggled with. So you are the, really the best person to help yourself make that transition from one to 10. And, um, and a lot of the times like, eh, and, and we don't ... I, I really believe that the framework there we have to, like esp- expose our- ourselves to like be talking to, like us when we were an expert, when we were taking that class and we knew everything about quantum mechanics, and then six months later you don't remember half of the things. Like how could we make it easier for, like do we have those conversations between you and your past sel- past expert self? Um, I, I, I think there, there might be, you know, it's an under- underexplored idea. I think notes on paper are probably not the best way. I'm not sure if it's a combination of like video, audio, where it's like you have a guided framework that you follow th- to extract information from yourself, so that you can later kind of revisit to make it easier to, to remember. But that's, I think it's an interesting idea worth, worth exploring that not ... I've n- I haven't seen a lot of people kind of trying to, uh, distill that problem.

   19. LFLex Fridman1:09:54

       Yeah, only cr- creating the kind of tools. I find if I record, it soun- so- sounds weird, but I'll take notes, but if I record audio, like, um, like little clips of-

   20. LBLuís Batalha1:10:04

       Uh-huh.

   21. LFLex Fridman1:10:04

       ... thoughts, or like rants, that's really effective at capturing something that notes can't.

   22. LBLuís Batalha1:10:12

       Mm-hmm.

   23. LFLex Fridman1:10:12

       Because when I replay them, for some reason it loads my brain back into where I was when I was reading that, in a way that notes don't.

   24. LBLuís Batalha1:10:21

       Mm-hmm.

   25. LFLex Fridman1:10:21

       Like, when I read notes, I'll often be like, "Wha- what?"

   26. LBLuís Batalha1:10:25

       (laughs)

   27. LFLex Fridman1:10:26

       "What was I tr- what was I thinking there?" But when I listen to the audio-

   28. LBLuís Batalha1:10:30

       Yeah.

   29. LFLex Fridman1:10:30

       ... it brings you right back to that place. So there might ... And maybe with video, with visual-

   30. LBLuís Batalha1:10:35

       Mm-hmm.
7. 1:15:27 – 1:56:18

   Favorite papers on Fermat's Library

   1. JBJoão Batalha1:15:27

   2. LFLex Fridman1:15:27

      Do you mind if we talk about some of the papers? Do any papers come to mind that, uh, have been annotated on Fermat's Library?

   3. JBJoão Batalha1:15:34

      The- the- the papers that we annotated, uh, can be about completely random topics, but that's part of the, what we enjoy as well. It forces you to explore these topics that otherwise maybe you'd never run into. Uh, and so, s- and so the ones that come to mind, uh, to me are- are fairly random, but one that I- I really enjoyed learning more about is, um, a paper, uh, written by a mathematician actually, Tom Apostol, and, uh, about a, uh, a tunnel in a Greek island off the coast of Turkey. (laughs)

   4. LFLex Fridman1:16:09

      (laughs) I like this already.

   5. JBJoão Batalha1:16:10

      So it's very random. Uh-

   6. LFLex Fridman1:16:11

      Yeah.

   7. JBJoão Batalha1:16:11

      ... so this, uh, okay, so what's interesting about this tunnel? So this tunnel, um, was built in the sixth century BC and, um, and it was built in this, uh, uh, in the island of Samos, uh, which is, uh, as- as I said, off the coast of Turkey, and, um, y- right, they had w- the city on one side and they had a mountain and then they had, um, a bunch of springs on the other side and then they wanted to bring water into the city. Um, did, building an aqueduct would be pretty hard because of the- the way the mountain was shaped and it would also, you know, if they, if they were under a siege, like, it, they- they could just, um, easily destroy that aqueduct and then the water w- wouldn't have any water supply. The- the city wouldn't have any water supply. And so they decided to build a tunnel, and they decided to try to do it quickly. Um, and so the, they started digging, uh, from both ends at the same time through the mountain, right? And so, like, when you start thinking about this, it's- it's a fairly difficult problem and this is like sixth century BC, so you had v- very limited access to- to, you know, the- the mathematical tools that you had at the time were very limited. And so what this paper is about is about the story of how they built it and about the fact that for about 2,000 years, kinda the accepted, the accepted explanation of how they built it was actually wrong. And so th- this tunnel has been famous for a while. There are a number of historians that talked about it since ancient Egypt, and, um, and the method that they described, uh, for- for building it, um, is- is, um, was just wrong. And- and so these- these researchers went there and- and were able to figure, figure that out. Um, and so basically kind of the way that they thought they had built it was basically if you can imagine looking at the mountain from the top and you have the mountain and then you have both entrances, um, and so what they, what they thought and what, this is what the ancient historians described is that they, uh, effectively tried to draw a- a right angle, a right angle triangle, um, with the two entrances at each end of the hypotenuse.

   8. LFLex Fridman1:18:25

      Mm-hmm.

   9. JBJoão Batalha1:18:26

      And the way they did it is like they would w- go around the mountain and kinda walking in a grid fashion and then you can, you can figure out, uh, the two sides of the triangle. And then after you have that triangle, you can effectively draw two smaller triangles at each entrance that are, uh, proportional to that big triangle, uh, and then you kinda have arrows pointing in each way.

   10. LFLex Fridman1:18:49

       Got it.

   11. JBJoão Batalha1:18:50

       And then you can, you- you know at least that these, that you have a line going through the- the mountain that connects both entrances.

   12. LFLex Fridman1:18:57

       Mm-hmm.

   13. JBJoão Batalha1:18:58

       The issue with that is, like, o- once you, once you go to this mountain and you start thinking of doing this, you realize that especially given that the tools that they had at the time, that your error margin would be too small.

   14. LFLex Fridman1:19:10

       Hmm.

   15. JBJoão Batalha1:19:11

       ... you wouldn't be able to do it. Uh, it, you, you, you, the, just the fact of, of trying to, to build this triangle in that fashion, the error would accumulate and you would end up missing. You'd start building these tunnels and they would miss each other.

   16. LFLex Fridman1:19:24

       So, the task ultimately is t- to figure out like really perfectly as c- as close as possible the direction you should be digging.

   17. JBJoão Batalha1:19:30

       Mm-hmm.

   18. LFLex Fridman1:19:31

       First of all, that it's possible to have a straight line through-

   19. JBJoão Batalha1:19:34

       Exactly.

   20. LFLex Fridman1:19:34

       ... and then what that, the direction would be-

   21. JBJoão Batalha1:19:37

       Yeah.

   22. LFLex Fridman1:19:37

       ... and then you're trying to infer that by constructing a, a right triangle by doing ... I, I'm not exactly sure about how to do that rigorously, like, by tracing the mountain? By walking along-

   23. JBJoão Batalha1:19:50

       Uh-huh.

   24. LFLex Fridman1:19:50

       ... the mountain. How to ... you said grids?

   25. JBJoão Batalha1:19:52

       Yeah. You, you kinda walk as if you were in a, in a grid and so you, you just walk in right angles.

   26. LFLex Fridman1:19:57

       I see.

   27. JBJoão Batalha1:19:58

       And so, right, so-

   28. LFLex Fridman1:19:58

       But then you have to walk really precisely, then.

   29. JBJoão Batalha1:20:00

       Exactly.

   30. LFLex Fridman1:20:00

       You, because you have to use tools-

Episode duration: 2:54:52