Grant Sanderson is the creator of 3Blue1Brown. Support this podcast by supporting our sponsors:
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EPISODE LINKS:
3Blue1Brown: http://youtube.com/3blue1brown
Grant's Twitter: https://twitter.com/3blue1brown

PODCAST INFO:
Podcast website: https://lexfridman.com/podcast
Apple Podcasts: https://apple.co/2lwqZIr
Spotify: https://spoti.fi/2nEwCF8
RSS: https://lexfridman.com/feed/podcast/
Full episodes playlist: https://www.youtube.com/playlist?list=PLrAXtmErZgOdP_8GztsuKi9nrraNbKKp4
Clips playlist: https://www.youtube.com/playlist?list=PLrAXtmErZgOeciFP3CBCIEElOJeitOr41

OUTLINE:
0:00 - Introduction
5:13 - Richard Feynman
9:41 - Learning deeply vs broadly
13:56 - Telling a story with visualizations
18:43 - Topology
23:52 - Intuition about exponential growth
32:28 - Elon Musk's exponential view of the world
40:09 - SpaceX and space exploration
45:28 - Origins of the Internet
49:50 - Does teaching on YouTube get lonely?
54:31 - Daily routine
1:00:20 - Social media
1:10:38 - Online education in a time of COVID
1:27:03 - Joe Rogan moving to Spotify
1:32:09 - Neural networks
1:38:30 - GPT-3
1:46:52 - Manim
1:51:01 - Python
1:56:21 - Theory of everything
2:03:53 - Meaning of life

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The following is a conversation with Grant Sanderson, his second time on the podcast.

He's known to millions of people as the mind behind 3Blue1Brown, a YouTube channel where he educates and inspires the world with the beauty and power of mathematics.

Quick summary of the sponsors, Dollar Shave Club, DoorDash, and Cash App.

Click the sponsor links in the description to get a discount and to support this podcast, especially for the 2 new sponsors, Dollar Shave Club and DoorDash.

Let me say as a Side note, I think that this pandemic challenged millions of educators to rethink how they teach, to rethink the nature of education.

As people know, Grant is a master elucidator of mathematical concepts that may otherwise seem difficult or out of reach for students and curious minds.

But he's also an inspiration to teachers, researchers, and people who just enjoy sharing knowledge, like me, for what it's worth.

It's 1 thing to give a semester's worth of multi-hour lectures.

It's another to extract from those lectures the most important, interesting, beautiful, and difficult concepts and present them in a way that makes everything fall into place.

That is the challenge that is worth taking on.

My dream is to see more and more of my colleagues at MIT and world experts across the world summon their inner 3 blue, 1 brown, and create the canonical explainer videos on a topic that they know more than almost anyone else in the world.

Amidst the political division, the economic pain, the psychological medical toll of the virus, masterfully crafted educational content, feels like 1 of the beacons of hope that we can hold on to.

If you enjoy this thing, subscribe on YouTube, review it with 5 Stars on Apple Podcast, follow on Spotify, support on Patreon, or connect with me on Twitter at Lex Friedman, of course, after you go immediately, which you already probably have done a long time ago, and subscribe to 3Blue1Brown's YouTube channel.

As usual, I'll do a few minutes of ads now, and no ads in the middle.

I try to make these interesting, but I give you timestamps so you can skip.

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I have so many memories of working late nights for a deadline with a team of engineers and eventually taking a break to argue about which DoorDash restaurant to order from.

And when the food came, those moments of bonding, of exchanging ideas, of pausing to shift attention from the programs to the humans were special.

These days, for a bit of time, I'm on my own sadly, so I miss that camaraderie.

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Bad design is when the app gets in the way either because it's buggy or because it tries too hard to be helpful.

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And now, here's my conversation with Grant Sanderson.

You've spoken about Richard Feynman as someone you admire.

I think last time we spoke we ran out of time.

Who is Richard Feynman to you in your eyes?

I mean, I think a ton of people like Feynman.

He's probably, It's a little bit cliche to say that you like Feynman, right?

That's almost like when you don't know what to say about sports and you just point to the Super Bowl or something as something you enjoy watching.

But I do actually think there's a layer to Feynman that sits behind the iconography.

1 thing that just really struck me was this letter that he wrote to his wife 2 years after she died.

So during the Manhattan Project, she had polio.

And, you know, the icon of Feynman is this, almost this like mildly sexist womanizing philanderer, at least on the personal side.

But you read this letter, and I can try to pull it up for you if I want, and it's just this absolutely heartfelt letter to his wife saying how much he loves her, even though she's dead, and kind of what she means to him, how no woman can ever measure up to her.

It shows you that the Feynman that we've all seen in Shirley, You're Joking, is different from the Feynman in reality.

I think the same kind of goes in his science, where he sometimes has this output of being this, aw shucks character, like everyone else is coming in with these fancy fallutin formulas, but I'm just going to try to whittle it down to its essentials, which is so appealing because we love to see that kind of thing.

But when you get into it, like what he was doing was actually quite deep, very much mathematical.

That should go without saying, but I remember reading a book about Feynman in a cafe once.

And this woman looked at me and was like, saw that it was about Feynman.

And she started explaining to me how he was never really a math person.

And I don't understand how that can possibly be a public perception about any physicist, but for whatever reason that worked into his aura that he sort of shooed off math in place of true science.

The reality of it is he was deeply in love with math and was much more going in that direction and had a clicking point into seeing that physics was a way to realize that and all the creativity that he could output in that direction was instead poured towards things like fundamental, not even fundamental theories, just emergent phenomena and everything like that.

So to answer your actual question, like what I like about his way of going at things is this constant desire to reinvent it for himself.

Like when he would consume papers the way he described it, he would start to see what problem he was trying to solve and then just try to solve it himself to get a sense of personal ownership.

And then from there, see what others had done.

Like that's actually an interesting point when you first are inspired by a certain idea that you maybe want to teach or visualize or just explore on your own.

I'm sure you're captured by some possibility and magic of it.

Do you try to rediscover everything yourself?

So, I think the things that I've learned best and have the deepest ownership of are the ones that have some element of rediscovery.

The problem is that really slows you down.

And this is, for my part, it's actually a big fault.

Like this is part of why I'm not an active researcher.

I'm not at the depth of the field a lot of other people are.

The stuff that I do learn, I try to learn it really well.

But other times you do need to get through it at a certain pace.

You do need to get to a point of a problem you're trying to solve.

So obviously you need to be well equipped to read things without that reinvention component and see how others have done it.

But I think if you choose a few core building blocks along the way, and you say, I'm really going to try to approach this, before I see how this person went at it, I'm really going to try to approach it for myself.

No matter what you gain all sorts of inarticulatable intuitions about that topic, which aren't going to be there.

For example, you're going to be trying to come up with counter-examples, you're going to try to come up with intuitive examples, all sorts of things where you're populating your brain with data, and the ones that you come up with are likely to be different than the 1 that the text comes up with.

And that like lends it a different angle.

So that aspect also slowed Feynman down in a lot of respects.

I think there was a period when like the rest of physics was running away from him.

But insofar as it got him to where he was, I kind of resonate with that.

I just, I would be nowhere near it because I'm not like him at all, but it's like a state to aspire to.

You know, just to link in a small point you made that you're not a quote unquote active researcher.

Do you, you're swimming often in reasonably good depth about a lot of topics.

Do you sometimes want to like dive deep at a certain moment and say like, cause you probably built up a hell of an amazing intuition about what is and isn't true within these worlds.

Do you ever want to just dive in and see if you can discover something new?

Yeah, I think 1 of my biggest regrets from undergrad is not having built better relationships with the professors I had there.

And I think a big part of success in research is that element of mentorship and people giving you the kind of scaffolded problems to carry along.

For my own goals right now, I feel like I'm pretty good at exposing math to others and want to continue doing that.

For my personal learning, are you familiar with the hedgehog-fox dynamic?

I think either the ancient Greeks came up with it or it was pretended to be something drawn from the ancient Greeks.

I don't know who to point it to, but the idea...

It is that you've got 2 types of people, or especially 2 types of researchers.

There's the fox that knows many different things, and then the hedgehog that knows 1 thing very deeply.

So, like von Neumann would have been a fox.

He's someone who knows many different things, just very foundational in a lot of different fields.

Einstein would have been more of a hedgehog, thinking really deeply about 1 particular thing.

And both are very necessary for making progress.

So between those 2, I would definitely see myself as like the fox, where I'll try to get my paws in a whole bunch of different things.

And at the moment, I just think I don't know enough of anything to make a significant contribution to any of them.

But I do see value in having a decently deep understanding of a wide variety of things.

Most people who know computer science really deeply don't necessarily know physics very deeply, or many of the aspects, like different fields in math even.

Let's say you have an analytic number theory versus an algebraic number theory.

These 2 things end up being related to very different fields, some of them more complex analysis, some of them more algebraic geometry.

And then when you just go out so far as to take those adjacent fields, place 1 PhD student into a seminar of another one's, they don't understand what the other one's saying at all.

Like you take the complex analysis specialist inside the algebraic geometry seminar, they're as lost as you or I would be.

But I think going around and trying to have some sense of what this big picture is certainly has personal value for me.

I don't know if I would ever make like new contributions in those fields, but I do think I could make new like expositional contributions where there's kind of a notion of things that are known but like haven't been explained very well.

Well, first of all, I think most people would agree your videos, your teaching, the way you see the world is fundamentally often new.

Even just like the visualizations, the multi-dimensional visualization we'll talk about.

I mean, you're revealing something very interesting that, yeah, just feels like research, feels like science, feels like the cutting edge of the very thing of which like new ideas and new discoveries are made of.

I do think you're being a little bit more generous than is necessarily true.

And I promise that's not even false humility because I sometimes think when I research a video, I'll learn like 10 times as much as I need for the video itself, and it ends up feeling kind of elementary.

So I have a sense of just how far away like the stuff that I cover is from the actual depth.

think that could also be a mathematics thing.

I feel like in the machine learning world, you like 2 weeks in, you feel like you've basically mastered the field.

Well, everything is either trivial or impossible.

And it's like a shockingly thin line between the 2, where you can find something that's totally impenetrable, and then after you get a feel for it, it's like, oh yeah, that whole subject is actually trivial in some way.

Every researcher is just on the other end of that hump and it feels like it's so far away, but 1 step actually gets them there.

What do you think about Feynman's teaching style or another perspective of use of visualization?

Well, his teaching style is interesting because people have described like the Feynman effect where while you're watching his lectures or while you're reading his lectures, everything makes such perfect sense.

So as an entertainment session, it's wonderful because it gives you this intellectual satisfaction that you don't get from anywhere else, that you finally understand it.

But the Feynman effect is that you can't really recall what it is that gave you that insight, you know, even a week later.

And this is true of a lot of books and a lot of lectures where the retention is never quite what we hope it is.

So there is a risk that the stuff that I do also fits that same bill, where at best it's giving this kind of intellectual candy on giving a glimpse of feeling like you understand something.

But unless you do something active, like reinventing it yourself, like doing problems to solidify it, even things like space repetition memory to just make sure that you have like the building blocks of what do all the terms mean.

Unless you're doing something like that, it's not actually gonna stick.

So the very same thing that's so admirable about Feynman's lectures, which is how damn satisfying they are to consume, might actually also reveal a little bit of the flaw that we should, as educators, all look out for, which is that that does not correlate with long-term learning.

Well, you've done some interactive stuff.

I mean, even in your videos, the awesome thing that Feynman couldn't do at the time is you could, since it's programmed, you can like tinker, like play with stuff.

You can like, here, let's take the value of this variable and change it to build up an intuition, to move along a surface or to change the shape of something.

I think that's almost an equivalent of you doing it yourself.

Yeah, do you think there's some value in that interactive element?

Yeah, well, so what's interesting is you're saying that, and the videos are non-interactive in the sense that there's a play button and a pause button.

And you could ask, like, hey, while you're programming these things, why don't you program it into an interactable version?

You know, make it a Jupyter notebook that people can play with, which I should do and that would be better.

I think the thing about interactives though is most people consuming them just sort of consume what the author had in mind, and that's kind of what they want.

I have a ton of friends who make interactive explanations.

And when you look into the analytics of how people use them, there's a small sliver that generally use it as a playground to have experiments.

And maybe that small sliver is actually who you're targeting and the rest don't matter.

But most people consume it just as a piece of well-constructed literature that maybe you tweak with the example a little bit to see what it's getting at.

But in that way, I do think a video can get most of the benefits of the interactive app, as long as you make the interactive for yourself and you decide what the best narrative to spin is.

As a more concrete example, like my process with...

I made this video about SIR models for epidemics and it's like this agent-based bottling thing where you tweak some things about how the epidemic spreads and you want to see how that affects its evolution.

My format for making that was very different than others where rather than scripting it ahead of time, I just made the playground and then I played a bunch and then I saw what stories there were to tell within that.

So your video had that kind of structure.

It had like 5 or 6 stories or whatever it was and like it was basically Okay, here's a simulation.

And here's 5 things I found after playing with it.

Well, because the thing is, a way that you could do that project is you make the model and then you put it out and you say, here's a thing for the world to play with.

Like come to my website where you interact with this thing.

And people did like sort of remake it in a JavaScript way so that you can go to that website and you can test your own hypotheses.

But I think a meaningful part of the value to add is not just the technology, but to give the story around it as well.

It's not just to make the visuals that someone will look at.

It's to be the 1 to decide what's the interesting thing to walk through here.

And even though there's lots of other interesting paths that 1 could take, that can be kind of daunting when you're just sitting there in a sandbox and you're given this tool with like 5 different sliders and you're told to like play and discover things.

Like a little bit of guidance in that direction can be what actually sparks curiosity to make someone want to imagine more about it.

A few videos I've seen you do, I don't know how often you do it, but there's almost a tangential like pause where you, here's a cool thing, you say like, here's a cool thing, but it's outside the scope of this video essentially.

But I'll leave it to you as homework essentially to like figure out it's a cool thing to explore.

I wish I could say that wasn't a function of laziness.

And that's like, you've worked so hard on making the

minutes already that to extend it out even further, it would take more time.

And 1 of your cooler videos, the homomorphic, like from the Mobius strip to the 3D.

Yeah, that's the super, and you're like, yeah, you can't transform the Mobius strip into a surface without it intersecting itself.

But I'll leave it to you to see why that is.

Well, I hope that's not exactly how I phrase it because I think what my hope would be is that I leave it to you to think about why you would expect that to be true and then to want to know what aspects of a Mobius strip do you want to formalize such that you can prove that intuition that you have.

Because at some point now you're starting to invent algebraic topology.

If you have these vague instincts like, I want to get this Mobius strip, I want to fit it such that it's all above the plane, but its boundary sits exactly on the plane.

I don't think I can do that without crossing itself, but that feels really vague.

And as you're starting to formalize that, that's what's going to get you to try to come up with a definition for what it means to be orientable or non-orientable.

And like once you have that motivation, a lot of the otherwise arbitrary things that are sitting at the very beginning of a topology textbook start to make a little more sense.

Yeah, and I mean that whole video beautifully was a motivation for topology is cool.

That was my, well, my hope with that is I feel like topology is, I don't want to say it's taught wrong, but I do think sometimes it's popularized in the wrong way where, you know, you'll hear these things of people saying, oh, topologists, they're very interested in surfaces that you can bend and stretch but you can't cut or glue.

There's all sorts of things you can be interested in with random imaginative manipulations of things.

Is that really what mathematicians are into?

It's not as if someone was sitting there thinking, like, I wonder what the properties of clay are, if I had some arbitrary rules about when I can't cut it and when I can't glue it.

Instead, there's a ton of pieces of math that can actually be equivalent to these very general structures that's like geometry, except you don't have exact distances.

You just want to maintain a notion of closeness.

And once you get it to those general structures, constructing mappings between them translate into non-trivial facts about other parts of math.

I don't think that's actually popularized.

I don't even think it's emphasized well enough when you're starting to take a topology class.

Because you kind of have these 2 problems.

It's like either it's too squishy, you're just talking about coffee mugs and donuts, or it's a little bit too rigor-first and you're talking about the axiom systems with open sets.

And an open set is not the opposite of closed set, so sorry about that everyone.

We have a notion of clopen sets for ones that are both at the same time.

And just it's not an intuitive axiom system in comparison to other fields of math.

So you as a student like really have to walk through mud to get there.

And you're constantly confused about how this relates to the beautiful things about coffee mugs and Moebius strips and such.

And it takes a really long time to actually see topology in the way that mathematicians see topology.

But I don't think it needs to take that time.

this is making me feel like I need to make more videos on the topic, because I think I've only done 2.

But I've also seen it in my narrow view of, I find game theory very beautiful, and I know topology has been used elegantly to prove things in game theory.

Yeah, you have facts that seem very strange.

Like I could tell you, you stir your coffee, and after you stir it, and let's say all the molecules settle to not moving again, 1 of the molecules will be basically in the same position it was before.

You have all sorts of fixed-point theorems like this, right?

That kind of fixed-point theorem is directly relevant to Nash equilibriums, right?

So you can imagine popularizing it by describing the coffee fact, but then you're left to wonder like who cares about if a molecule of coffee like stays in the same spot?

Is this what we're paying our mathematicians for?

You have this very elegant mapping onto economics in a way that's very concrete, or very, I shouldn't say concrete, very tangible, like actually adds value to people's lives through the predictions that it makes.

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