The following is a conversation with Grant Sanderson, his second time on the podcast.
He's known to millions of people as the mind behind Three Blue One Brown, a YouTube
channel where he educates and inspires the world with the beauty and power of mathematics.
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world. And now, here's my conversation with Grant Sanderson. You've spoken about Richard Feynman
as someone you admire. I think last time we spoke, we ran out of time. So I wanted to talk to you
about him. Who is Richard Feynman to you in your eyes? What impact did he have on you?
I mean, I think a ton of people like Feynman. 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, or something you enjoy watching. But I do actually think there's
a layer to Feynman that sits behind the iconography. One thing that just really struck me was this
letter that he wrote to his wife two years after she died. So during the Manhattan Project, she had
polio. Tragically, she died. They were just young, madly in love. And the icon of Feynman is this
almost this 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 what she means to him,
how no woman can ever measure up to her. And it shows you that the Feynman that we've all seen
in surely you're joking is different from the Feynman in reality. And I think the same kind
of goes in his science where he sometimes has this output of being this aw-shox character.
Like everyone else is coming in. There's these fancyfalutin 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, 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 saw that it was about Feynman. She was like,
oh, I love him. I read surely you're joking. And she started explaining to me how he was never
really a math person. And I don't understand how that can possibly be a public perception
about any physicist, but for whatever reason that worked into his or that he sort of
shoot off math in place of true science, the reality of it is he was deeply in love with
math and was much more going in that direction and had a clicking point into seeing that physics
was a way to realize that and all the creativity that he could output in that direction was instead
poured towards things like fundamental, not even fundamental theories, just emergent phenomena
and everything like that. So to answer your actual question, what I like about his way of going at
things is this constant desire to reinvent it for himself. Like when he would consume papers
the way he'd describe it, he would start to see what problem he was trying to solve and then just
try to solve it himself to get a sense of personal ownership. And then from there, see what others
had done. Is that how you see problems yourself? Like that's actually an interesting point when
you first are inspired by a certain idea that you maybe want to teach or visualize or just
explore on your own. I'm sure you're captured by some possibility and magic of it. Do you read
the work of others? Do you go through the proofs? 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 for my part,
it's actually a big fault. 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 if you simply go through the proof. For example, you're going to be trying to come
up with counter examples. You're going to try to come up with intuitive examples, all sorts of
things where you're populating your brain with data. And the ones that you come up with are likely
to be different than the one that the text comes up with. And that lends at 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 would be nowhere near it because I not like him at all, but
it's like a state to aspire to. You know, just to link in a small point you made,
that you're not quote unquote, active researcher. You're swimming often in reasonably good depth
about a lot of topics. Do you sometimes want to like dive deep at a certain moment and say like,
because you probably built up a hell of an amazing intuition about what is and isn't true
within these worlds. Do you ever want to just dive in and see if you can discover
something new? Yeah, I think one of my biggest regrets from undergrad is not having built better
relationships with the professors I had there. And I think a big part of success and research is
that element of like mentorship and like people giving you the kind of scaffolded problems to
carry along. For my own like goals right now, I feel like I'm pretty good at exposing math to others
and like want to continue doing that. For my personal learning, are you familiar with like
the hedgehog fox dynamic? I think this was either the ancient Greeks came up with it or
it was pretended to be something drawn from the ancient Greeks that I don't know who to
point it to. But yeah, probably Mark Twain. It is that you've got two types of people or
especially two types of researchers. There's the fox that knows many different things. And then
the hedgehog that knows one thing very deeply. So like Von Neumann would have been a fox,
he's someone who knows many different things, just very foundational, a lot of different fields.
Einstein would have been more of a hedgehog thinking really deeply about one particular thing.
And both are very necessary for making progress. So between those two, I would definitely see
myself as like the fox where I'll try to get my paws and like a whole bunch of different things.
And at the moment, I just think I don't know enough of anything to make like a significant
contribution to any of them. But I do see value in like having a decently deep understanding of
a wide variety of things. Like most people who know computer science really deeply don't necessarily
know physics very deeply or many of the aspects like different fields and math even. Let's say
you have like an analytic number theory versus an algebraic number theory. Like these two things
end up being related to very different fields, like some of them more complex analysis, some of
them more like algebraic geometry. And then when you just go out so far as to take those adjacent
fields, place one PhD student into a seminar of another ones, they don't understand what the
other one's saying at all. Like you take the complex analysis specialist inside the algebraic
geometry seminar, there is lost as you or I would be. But I think going around and like trying to
have some sense of what this big picture is certainly has personal value for me. I don't
know if I would ever make like new contributions in those fields, but I do think I could make new
like expositional contributions where there's kind of a notion of things that are known,
but like haven't been explained very well. Well, first of all, I think most people would agree
your videos, your teaching, the way you see the world is fundamentally often new. Like you're
creating something new. And it almost feels like research, even just like the visualizations,
the multidimensional visualization we'll talk about. I mean, you're revealing something very
interesting that, yeah, just feels like research feels like science feels like the cutting edge
of the very thing of which like new ideas and new discoveries are made of.
I do think you're being a little bit more generous than is necessarily. And I promise that's not
even false humility, because I sometimes think when I research a video, I'll learn like 10 times as
much as I need for the video itself. And it ends up feeling kind of elementary. So I have a sense
of just how far away like the stuff that I cover is from the actual depth.
I think that's natural, but I think that could also be a mathematics thing.
I feel like in the machine learning world, you like two weeks in, you feel like you've basically
mastered the skill. And mathematics, it's like...
Well, everything is either trivial or impossible. And it's like a shockingly thin line between the
two where you can find something that's totally impenetrable. And then after you get a feel for
it's like, oh, yeah, that whole, that whole subject is actually trivial in some way. So maybe
that's what goes on. Every researcher is just on the other end of that hump. And it feels like
it's so far away, but one step actually gets them there.
What do you think about sort of Feynman's teaching style or another perspective of
the 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
even a week later. And this is true of a lot of books and a lot of lectures where the retention
isn't ever 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 the building blocks of what do all the terms mean, unless you're doing something like
that, it's not actually going to stick. So the very same thing that's so admirable about Feynman's
lectures, which is how damn satisfying they are to consume might actually also reveal a little
bit of the flaw that we should, as educators all look out for, which is that that does not correlate
with long-term learning. We'll talk about it a little bit. I think you've done some interactive
stuff. I mean, even in your videos, the awesome thing that Feynman couldn't do at the time is you
could, since it's programmed, you can like tinker, like play with stuff. You could take this value
and change it. You can like, here, let's take the value of this variable and change it to build up an
intuition, to move along the surface or to change your shape of something. I think that's almost
an equivalent of you doing it yourself. It's not quite there, but as a viewer. Yeah, do you think
there's some value in that interactive element? Yeah, well, so what's interesting is you're
saying that, and the videos are non-interactive in the sense that there's a play button and a pause
button, and you could ask like, hey, while you're programming these things, why don't you program
it into an interactable version that, you know, make it a Jupyter notebook that people can play
with, which I should do and that like would be better. I think the thing about interactives,
though, is most people consuming them just sort of consume what the author had in mind. And that's
kind of what they want. Like, I have a ton of friends who make interactive explanations. And
when you look into the analytics of how people use them, there's a small sliver that genuinely
use it as a playground to have experiments. And maybe that small sliver is actually who you're
targeting and the rest don't matter. But most people consume it just as a piece of like, well
constructed literature that maybe you tweak with the example a little bit to see what it's getting
at. But in that way, I do think like a video can get most of the benefits of the interactive,
like the interactive app, as long as you make the interactive for yourself and you decide what the
best narrative to spin is. As a more concrete example, like my process with, I made this video
about SIR models for epidemics. And it's like this agent-based bottling thing where you tweak
some things about how the epidemic spreads and you 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. Yeah, that's cool. So your video had that kind of structure. It had
like five or six stories or whatever it was. And like, it was basically, okay, here's a simulation.
Here's a model. What can we discover with this model? And here's five things I found after playing
with it. Well, because the thing is, a way that you could do that project is you make the model
and then you put it out and you say, here's a thing for the world to play with. Like, come to my
website where you interact with this thing. And people did sort of remake it in a JavaScript way
so that you can go to that website and you can test your own hypotheses. But I think a meaningful
part of the value to add is not just the technology, but to give the story around it as well.
And that's kind of my job. It's not just to make the visuals that someone will look at,
it's to be the one to decide what's the interesting thing to walk through here. And even though
there's lots of other interesting paths that one could take, that can be kind of daunting when
you're just sitting there in a sandbox and you're given this tool with like five different sliders
and you're told to play and discover things. It's like, where do you do? What do you start?
What are my hypotheses? What should I be asking? Like, a little bit of guidance in that direction
can be what actually sparks curiosity to make someone want to imagine more about it.
A few videos I've seen you do. I don't know how often you do it, but there's almost a tangential
like pause where you, here's a cool thing. You say, like, here's a cool thing, but it's outside
the scope of this video, essentially. But I'll leave it to you as homework, essentially, to like
figure out it's a cool thing to explore. I wish I could say that wasn't a function of laziness,
right? And that's like, you've worked so hard on making the 20 minutes already that to extend it
out even further would take more time. And one of your cooler videos, the homomorphic, like from
the Mobius strip to the... Mobius striped rectangle? Yeah, that's a super... And you're like, yeah,
you can't transform the Mobius strip into a surface without intersecting itself. But I'll
leave it to you to see why that is. Well, I hope that's not exactly how I phrase it,
because I think what my hope would be is that I leave it to you to think about why you would
expect that to be true. And then to want to know what aspects of a Mobius strip do you want to
formalize such that you can prove that intuition that you have? Because at some point, now you're
starting to invent algebraic topology. If you have these vague instincts like, I want to get this
Mobius strip, I want to fit it such that it's all above the plane, but its boundary sits exactly
on the plane. I don't think I can do that without crossing itself, but that feels really vague.
How do I formalize it? And as you're starting to formalize that, that's what's going to get you
to try to come up with a definition for what it means to be orientable or non-orientable.
And 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 school. That was my hope with that,
is I feel like topology is, I don't want to say it's taught wrong, but I do think sometimes
it's popularized in the wrong way where, you know, you'll hear these things with people saying,
oh, topologists, they're very interested in surfaces that you can bend and stretch, but you
can't cut or glue. Are they? Why? There's all sorts of things you can be interested in with
random like imaginative manipulations of things. Is that really what like mathematicians are into?
And the short answer is not, not really. That's, it's not as if someone was sitting there thinking
like, I wonder what the properties of clay are, if I add some arbitrary rules about what,
when I can't cut it and when I can't glue it. Instead, it's, there's a ton of pieces of math
that can actually be equivalent to like these very general structures that's like geometry,
except you don't have exact distances, you just want to maintain a notion of closeness.
And once you get it to those general structures, constructing mappings between them translate
into non-trivial facts about other parts of math. And that, I just, I don't think that's
actually like popularized. I don't even think it's emphasized well enough when you're starting
to take a topology class, because you kind of have these two problems. It's like either it's too
squishy, you're just talking about coffee mugs and donuts, or it's a little bit too rigor first.
And you're talking about the axiom systems with open sets. And an open set is not the
opposite of closed set. So sorry about that, everyone. We have a notion of clopen sets
for ones that are both at the same time. And just, it's not, 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 mobius strips and such. And it takes a really long time to actually see,
like see topology in the way that mathematicians see topology. But I don't think it needs to take
that time. I think there's, this is making me feel like I need to make more videos on the
topic, because I think I've only done a few. 100% you do. But I've also seen it in my narrow view
of like, I find game theory very beautiful. And I know topology has been used elegantly
to prove things in game theory. Yeah, you have like facts that seem very strange. Like I could
tell you, you stir your coffee. And after you stir it, and like, let's say all the molecules
settled to like not moving again, one of the molecules will be basically in the same position
it was before. You have all sorts of fixed point theorems like this, right? That kind of fixed
point theorem directly relevant to Nash Equilibrium. So you can imagine popularizing it by describing
the coffee fact, but then you're left to wonder like, who cares about if a molecule of coffee
like stays in the same spot? Is this what we're paying our mathematicians for? You have this very
elegant mapping onto economics in a way that's very concrete, or very, I shouldn't say concrete,
very tangible, like actually adds value to people's lives through the predictions that it makes. But
that line isn't always drawn because you have to get a little bit technical in order to properly
draw that line out. And often, I think popularized forms of media just shy away from being a little
too technical. For sure. By the way, for people who are watching the video, I do not condone the
message in this mug. It's the only one I have, which is the snuggle is real. By the way, for
anyone watching, I do condone the message of that mug. The snuggle is real. Okay, so you mentioned
the SIR model. I think there are certain ideas there of growth, of exponential growth. What
maybe have you learned about pandemics from making that video? Because it was kind of exploratory.
You were kind of building up an intuition. And it's again, people should watch the video. It's
kind of an abstract view. It's not really modeling in detail. The whole field of epidemiology,
those people, they go really far in terms of modeling, like how people move about. I don't
know if you've seen it, but there is the mobility patterns, how many people you encounter in certain
situations when you go to a school, when you go to a mall, they model every aspect of that for a
particular city. They have maps of actual city streets. They model it really well. And natural
patterns of the people have is crazy. So you don't do any of that. You're just doing an abstract
model to explore different ideas. Well, because I don't want to pretend like I'm an epidemiologist.
Like we have a ton of armchair epidemiologists. And the spirit of that was more like,
can we through a little bit of play draw reasonable-ish conclusions? And also just get
ourselves in a position where we can judge the validity of a model. I think people should look
at that and they should criticize it. They should point to all the ways that it's wrong,
because it's definitely naive in the way that it's set up. But to say what lessons from that hold,
like thinking about the R naught value and what that represents and what it can imply.
That's R naught. So R naught is if you are infectious and you're in a population which is
completely susceptible, what's the average number of people that you're going to infect
during your infectiousness? So certainly during the beginning of an epidemic,
this basically gives you the exponential growth rate. If every person infects two others,
you've got that one, two, four, eight exponential growth pattern. As it goes on, and let's say it's
something endemic where you've got a ton of people who have had it and are recovered, then
the R naught value doesn't tell you that as directly because a lot of the people you interact
with aren't susceptible, but in the early phases it does. And this is the fundamental
constant that it seems like epidemiologists look at, and the whole goal is to get that down.
If you can get it below one, then it's no longer epidemic. If it's equal to one, then it's endemic,
and it's above one, then you're epidemic. So just teaching what that value is and giving
some intuitions on how do certain changes in behavior change that value, and then what does
that imply for exponential growth? I think those are general enough lessons, and they're
like resilient to all of the chaoses of the world that it's still valid to take from the video.
I mean, one of the interesting aspects of that is just exponential growth,
and we think about growth. Is that one of the first times you've done a video on
known, of course not, the whole Euler's identity? Okay, so...
Sure. I guess I've done a lot of videos about exponential growth in the circular direction,
and only minimal in the normal direction. I mean, another way to ask, do you think
we're able to reason intuitively about exponential growth?
It's funny. I think it's extremely intuitive to humans, and then we train it out of ourselves
such that it's then really not intuitive, and then I think it can become intuitive again when
you study a technical field. So what I mean by that is, have you ever heard of these studies
where in a anthropological setting where you're studying a group that has been disassociated
from a lot of modern society, and you ask, what number is between one and nine? And maybe you
would ask, you've got one rock, and you've got nine rocks. You're like, what pile is halfway
in between these? And our instinct is usually to say five. That's the number that sits right
between one and nine. But sometimes when numeracy and the kind of just basic arithmetic that we have
isn't in a society, the natural instinct is three because it's in between in an exponential sense
and a geometric sense that one is three times bigger and then the next one is three times
bigger than that. So it's like, if you have one friend versus 100 friends, what's in between that?
Yeah, 10 friends seems like the social status in between those two states. So that's deeply
intuitive to us to think logarithmically like that. And for some reason, we kind of train it
out of ourselves to start thinking linearly about things. So in the sense, the early basic math
forces us to take a step back. It's the same criticism if there's any of science
is the lessons of science make us see the world in a slightly narrow sense
to where we have an over-exaggerated confidence that we understand everything
that's supposed to just understanding a small slice of it.
But I think that probably only really goes for small numbers because the real counterintuitive
thing about exponential growth is like as the numbers start to get big. So I bet if you took
that same setup and you asked them, oh, if I keep tripling the size of this rock pile seven times,
how big will it be? I bet it would be surprisingly big even to a society without numeracy. And that's
the side of it that I think is pretty counterintuitive to us, but that you can basically train into
people. I think computer scientists and physicists when they're looking at the early numbers of
COVID, they were the ones thinking like, oh, God, this is following an exact exponential curve.
And I heard that from a number of people. And almost all of them are techies in some capacity,
probably just because I live in the Bay Area. But for sure, they're cognizant of this kind of
growth that's present in a lot of national systems and a lot of systems. I don't know if you've
seen like, I mean, there's a lot of ways to visualize this obviously, but Raker as well,
I think was the one that had this like chessboard where every square on the chessboard,
you double the number of stones or something in that chessboard. I heard this is like an old
proverb where it's like someone, the king offered him a gift and he said, the only gift I would
like very modest, give me a single grain of rice for the first chessboard and then two
grains of rice for the next square, then twice that for the next square and just continue on.
That's my only modest ask your sire. And it's all more grains of rice than there are
anything in the world by the time you get to the end. And my intuition falls apart there.
Like, I would have never predicted that. Like, for some reason, that's a really compelling
illustration how poorly breaks down. Just like you said, maybe we're okay for the first few
piles of rocks, but after a while, it's game over. You know, the other classic example for
gauging someone's intuitive understanding of exponential growth is I've got like a lily pad
on Lake, really big lake, Lake Michigan. And that lily pad replicates, it doubles
one day and then it doubles the next day and it doubles the next day. And after 50 days,
it actually is going to cover the entire lake. So after how many days does it cover half the lake?
49. So you have a good instinct for exponential growth. So I think a lot of,
like the knee-jerk reaction is sometimes to think that it's like half the amount of time,
or to at least be like surprised that like after 49 days, you've only covered half of it.
Yeah. I mean, that's the reason you heard a pause from me. I literally thought that can't be
right. Exactly. So even when you know the fact and you do the division, it's like, wow. So you've
gotten like that whole time and then day 49, it's only covering half. And then after that,
it gets the whole thing. But I think you can make that even more visceral if rather than
going one day before you say how long until it's covered 1% of the lake. And so what would that be?
How many times do you have to double to get over 100? Like seven, six and a half times,
something like that. So at that point, you're looking at 43, 44 days into it. You're not even
at 1% of the lake. So you've experienced 44 out of 50 days and you're like, yeah, that literally
bad. It's just 1% of the lake. But then next thing you know, it's the entire lake.
You're wearing a SpaceX shirt. So let me ask you one person who talks about exponential,
you know, just the miracle of the exponential function in general is Elon Musk. So
he kind of advocates the idea of exponential thinking, you know, realizing that technological
development can, at least in the short term, follow exponential improvement, which breaks
apart our intuition, our ability to reason about what is and isn't impossible. So he's a big,
one, it's a good leadership kind of style of saying like, look, the thing that everyone
thinks is impossible is actually possible because exponentials. But what's your sense about
that kind of way to see the world? Well, so I think it can be very inspiring
to note when something like Moore's Law is another great example where you have this
exponential pattern that holds shockingly well and it enables just better lives to be led.
I think the people who took Moore's Law seriously in the 60s were seeing that, wow,
it's not going to be too long before like these giant computers that are either batch processing
or time-shared, you could actually have one small enough to put on your desk, on top of your desk,
and you could do things. And if they took it seriously, like you have people predicting
smartphones like a long time ago, and it's only out of like kind of this, I don't want to say
faith in exponentials, but an understanding that that's what's happening. What's more interesting,
I think, is to really understand why exponential growth happens and that the mechanism behind
it is when the rate of change is proportional to the thing in and of itself. So the reason
that technology would grow exponentially is only going to be if the rate of progress is
proportional to the amount that you have. So that the software you write enables you to write more
software. And I think we see this with the internet, like the advent of the internet makes it faster
to learn things, which makes it faster to create new things. I think this is oftentimes why like
investment will grow exponentially, that the more resources a company has, if it knows how to use
them well, the more it can actually grow. So I mean, you reference Elon Musk, I think he seems
to really be into vertically integrating his companies. I think a big part of that is because
you have the sense, what you want is to make sure that the things that you develop, you have ownership
of, and they enable further development of the adjacent parts. So it's not just this, you see
a curve and you're blindly drawing a line through it. What's much more interesting is to ask, when
do you have this proportional growth property? Because then you can also recognize when it breaks
down. Like in an epidemic, as you approach saturation, that would break down. As you do
anything that skews what that proportionality constant is, you can make it maybe not break down
as being an exponential, but it can seriously slow what that exponential rate is.
This is the opposite of a pandemic is you want, in terms of ideas,
you want to minimize barriers that prevent the spread. You want to maximize the spread of
impact. So you want it to grow when you're doing technological development so that you do hold up,
that rate holds up. That's almost like an operational challenge of how you run a company,
how you run a group of people, is that any one invention has a ripple that's unstopped.
And that ripple effect then has its own ripple effects and so on. And that continues.
Yeah, like Moore's Law is fascinating on a psychological level, on a human level,
because it's not exponential. It's just a consistent set of what you would call like
S-curves, which is like it's constantly like breakthrough innovations nonstop.
That's a good point. It might not actually be an example of exponentials because of something
which grows in proportion to itself, but instead it's almost like a benchmark that was set out
that everyone's been pressured to meet. And it's like all these innovations and micro
inventions along the way, rather than some consistent sit back and just let the
lily pad grow across the lake phenomenon. And it's also like there's a human psychological
level for sure of like the four-minute mile. There's something about it saying that, look,
there is Moore's Law. It's a law. It's certainly an achievable thing. We achieved it for the last
decade, for the last two decades, for the last three decades. You just keep going.
And it somehow makes it happen. It makes people, I'm continually surprised in this world,
how few people do the best work in the world, in that particular whatever that field is.
Like it's very often that like the genius, I mean you could argue that community matters,
but it's certain like I've been in groups of engineers where like one person is clearly like
doing an incredible amount of work and just is the genius. And it's fascinating to see
basically, it's kind of the Steve Jobs idea is maybe the whole point is to create an atmosphere
where the genius can discover themselves, like have the opportunity to do the best work of their
life. And yeah, and that the exponential is just milking that. It's like rippling the idea that
it's possible and that idea that it's possible finds the right people for the four-minute mile
and the idea that it's possible finds the right runners to run it and then expose a number of
people who can run faster than four minutes. It's kind of interesting to, I don't know,
basically the positive way to see that is most of us are way more intelligent, have way more
potential than we ever realized. I guess that's kind of depressing. But I mean like the ceiling
for most of us is much higher than we ever realized. That is true. A good book to read if
you want that sense is Peak, which essentially talks about peak performance in a lot of different
ways, like chess, London cab drivers, how many push-ups people can do, short-term memory tasks.
And it's meant to be like a concrete manifesto about deliberate practice and such, but the one
sensation you come out with is, wow, no matter how good people are at something, they can get better
and like way better than we think they could. I don't know if that's actually related to exponential
growth, but I do think it's a true phenomenon that's interesting. Yeah, I mean, there's certainly no
law of exponential growth in human innovation. Well, I don't know. Well, kind of, there is.
I think it's really interesting to see when innovations in one field allow for innovations
in another. Like the advent of computing seems like a prerequisite for the advent of chaos theory.
You have this truth about physics and the world that in theory could be known. You could find
Lorenzo's equations without computers, but in practice, it was just never going to be analyzed
that way unless you were doing like a bunch of simulations and that you could computationally
see these models. So it's like physics allowed for computers. Computers allowed for better physics
and wash, rinse, and repeat. That self-proportionality, that's exponential. So I think it's too far to
say that that's a law of some kind. Yeah, a fundamental law of the universe is that
that these descendants of apes will exponentially improve their technology in one day be taken over
by the AGI. That's built in this. They'll make the video game fun whoever created this thing.
I mean, since you're wearing a SpaceX shirt, let me ask. I didn't realize that. I apologize.
It's on topic. So Crew Dragon, the first crewed mission out into space since the
Space Shuttle. And just by first time ever by a commercial company, I mean, it's an incredible
accomplishment, I think, but it's also just an incredible, it inspires imagination amongst people
that this is the first step in a long, like, vibrant journey of humans into space.
Oh, yeah. So how do you feel? Is this exciting to you?
Yeah, it is. I think it's great. The idea of seeing it basically done by smaller entities
instead of by governments, I mean, it's a heavy collaboration between SpaceX and NASA in this
case, but moving in the direction of not necessarily requiring an entire country and its
government to make it happen, but that you can have something closer to a single company doing it.
We're not there yet, because it's not like they're unilaterally saying, like,
we're just shooting people up into space. It's just a sign that we're able to do more
powerful things with smaller groups of people. I find that inspiring.
Innovate quickly. I hope we see people land on Mars in my lifetime.
Do you think we will?
I think so. I mean, I think there's a ton of challenges there, right? Like,
radiation being the biggest one. And I think there's a ton of people who look at that and say,
why? Why would you want to do that? Let's let the robots do the science for us.
But I think there's enough people who are genuinely inspired about broadening the
worlds that we've touched, or people who think about things like backing up the light of consciousness
with super long-term visions of terraforming. Sorry, backing up the light of consciousness.
Yeah, the thought that if Earth goes to hell, we've got to have a backup somewhere.
A lot of people see that as pretty out there, and it's not in the short-term future. But
I think that's an inspiring thought. I think that's a reason to get up in the morning,
and I feel like most employees at SpaceX feel that way, too.
Do you think we'll colonize Mars one day?
No idea. Either AGI kills us first, or if we're allowed, I don't know if it'll take a second.
For allowed?
Well, honestly, it would take such a long time. Okay, you might have a small colony,
something like what you see in the Martian, but not people living comfortably there.
But if you want to talk about actual second Earth kind of stuff, that's just way far out there,
and the future moves so fast that we might just kill ourselves before that even becomes viable.
Oh, yeah. I mean, there's a lot of possibilities where it could be just,
it doesn't have to be on a planet, where it could be floating out in space,
have a space faring backup solution that doesn't have to deal with the constraints
that a planet provides. I mean, a planet provides a lot of possibilities and resources,
but also some constraints. For me, for some reason, it's a deeply exciting possibility.
Oh, yeah. All of the people who are skeptical about it are like, why do we care about going
to Mars? It's like, what makes you care about anything if that's inspiring?
It's hard. Actually, it's hard to hear that, because exactly as you put it on a philosophical
level, it's hard to say why do anything. I don't know. It's like the people say,
I've been doing an insane challenge last 30-something days.
Your pull-ups?
And the pull-ups and push-ups, and a bunch of people are awesome. You're insane, but awesome.
And then some people are like, why?
Why do anything?
I don't know. There's a calling. I'm with JFK a little bit, because we do these things,
because they're hard. There's something in the human spirit that says, same with a math problem,
there's something you fail once, and it's like this feeling that, you know what,
I'm not going to back down from this. There's something to be discovered in overcoming this
thing.
Well, so what I like about it is, and I also like this about the Moon missions. Sure,
it's kind of arbitrary, but you can't move the target. So you can't make it easier and say that
you've accomplished the goal. And when that happens, it just demands actual innovation,
right? Protecting humans from the radiation in space on the flight there while there.
Hard problem demands innovation. You can't move the goalpost to make that easier.
Almost certainly, the innovations required for things like that will be relevant in a bunch
of other domains, too. So the idea of doing something merely because it's hard is loosely
productive. Great. But as long as you can't move the goalposts, there's probably going to be these
secondary benefits that we should all strive for. Yeah. I mean, it's hard to formulate the Mars
colonization problem as something that has a deadline, which is the problem. But if there
was a deadline, then the amount of things we would come up with by forcing ourselves to
figure out how to colonize that place would be just incredible. This is what people,
like the internet didn't get created because people sat down and tried to figure out how do I
send TikTok videos of myself dancing to people. There's an application. I mean, actually,
I don't even know how. What do you think the application for the internet was when it was?
It must have been very low-level basic network communication within DARPA,
like military-based. How do I send a networking? How do I send information securely between
two places? Maybe it was an encryption. I'm speaking totally outside of my knowledge,
but it was probably intended for a very narrow small group of people.
Well, so there was this small community of people who were really interested in
time-sharing computing and interactive computing in contrast with batch processing,
and then the idea that as you set up a time-sharing center, basically meaning multiple people
logged in and using that central computer, why not make it accessible to others? And this was
kind of what I had always thought, oh, is this fringe group that was interested in this new
kind of computing and they all got themselves together. But the thing is DARPA wouldn't have
the US government funding that just for the funds of it. In some sense, that's what DARPA
was all about, was just really advanced research for the sake of having advanced research,
and it doesn't have to pay out with utility soon. But the core parts of its development
were happening in the middle of the Vietnam War when there was budgetary constraints all over
the place. I only learned this recently, actually. If you look at the documents,
basically justifying the budget for the ARPANET as they were developing it, and not just keeping
it where it was, but actively growing it while all sorts of other departments were having their
funding cut because of the war, a big part of it was national defense in terms of having a
more robust communication system, like the idea of packet switching versus circuit switching.
You could kind of make this case that in some calamitous circumstance where a central location
gets nuked, this is a much more resilient way to still have your communication lines
that traditional telephone lines weren't as resilient to, which I just found very interesting.
Even something that we see as so happy-go-lucky is just a bunch of computer nerds trying to
get interactive computing out there. The actual thing that made it funded and thing that made
it advance when it did was because of this direct national security question and concern.
I don't know if you've read it. I haven't read it. I've been meaning to read it,
but Neil deGrasse Tyson actually came out with a book that talks about science and the context
of the military, basically saying all the great science we've done in the 20th century was because
of the military. He paints a positive. It's not critical. A lot of people say military industrial
complex and so on. Another way to see the military and national security is a source of,
like you said, deadlines and hard things you can't move, almost like scaring yourself into
being productive. It is that. Manhattan Project is a perfect example, probably the quintessential
example. That one is a little bit more macabre than others because of what they were building,
but in terms of how many focused, smart hours of human intelligence get pointed towards a topic
per day, you're just maxing it out with that sense of worry. In that context, everyone there was
saying, we've got to get the bomb before Hitler does. That just lights a fire under you. Again,
like the circumstance is macabre, but I think that's actually pretty healthy, especially for
researchers that are otherwise going to be really theoretical, to take these theorizers
and say, make this real physical thing happen, meaning a lot of it is going to be unsexy.
A lot of it is going to be young fine men sitting there inventing a notion of computation in order
to compute what they needed to compute more quickly with the rudimentary automated tools
that they had available. I think you see this with Bell Labs also, where you've got otherwise
very theorizing minds in very pragmatic contexts that I think is really helpful for the theory,
as well as for the applications. I think that stuff can be positive for progress.
You mentioned Bell Labs and Manhattan Project. This makes me curious for the things you've
created, which are quite singular. If you look at all YouTube, or just not YouTube,
it doesn't matter what it is. It's just teaching content, art, doesn't matter. It's like, yep,
that's Grant. That's unique. You're teaching style and everything.
Does it? Manhattan Project and Bell Labs was famously a lot of brilliant people,
but there's a lot of them. They play off of each other. My question for you is, does it get lonely?
Honestly, that right there, I think is the biggest part of my life that I would like to
change in some way, that I look at a Bell Labs-type situation, and I'm like,
God damn, I love that whole situation. I'm so jealous of it. You're reading about Hamming,
and then you see that he also shared an office with Shannon. You're like, of course he did.
Of course they shared an office. That's how these ideas get like...
And they actually very likely worked separately all the time.
Yeah, totally separate.
But there's a literally magic that happens when you run into each other
on the way to getting a snack or something.
Conversations you over here, it's other projects you're pulled into,
it's like puzzles that colleagues are sharing, all of that. I have some extent of it just because
try to stay well connected in communities of people who think in similar ways,
but it's not in the day-to-day in the same way, which I would like to fix somehow.
That's one of the biggest drawbacks, negative things about this current pandemic
is that whatever the term is, but chance collisions are significantly reduced.
I don't know why I saw this, but on my brother's work calendar,
he had a scheduled slot with someone that he scheduled a meeting and the title of the whole
meeting was, no specific agenda. I just missed the happenstance serendipitous conversations
that we used to have, which the pandemic and remote work has so cruelly taken away from us.
Brilliant.
That was the title of the meeting.
That's brilliant.
I'm like, that's the way to do it. You just schedule those things.
Schedule the serendipitous interaction.
It's like, I mean, you can't do it in an academic setting, but it's basically like going to a bar
and sitting there, just for the strangers you might meet, just the strangers or
striking up conversation with strangers on the train.
Harder to do when you're deeply like maybe myself or maybe a lot of academic types who are
like introverted and avoid human contact as much as possible.
It's nice when it's forced to those chance collisions, but maybe scheduling is a possibility.
But for the most part, do you work alone? I'm sure you struggle a lot.
You probably hit moments when you look at this and you say, this is the wrong way
to show it. It's a long way to visualize it. I'm making it too hard for myself.
I'm going down the wrong direction. This is too long. This is too short.
All those self-doubt that could be paralyzing.
Okay. What do you do in those moments? Honestly, I actually much prefer work
to be a solitary affair for me. That's a personality quirk. I would like it to be
in an environment with others and collaborative in the sense of ideas exchanged.
But those phenomena you're describing, when you say this is too long, this is too short,
this visualization sucks, it's way easier to say that to yourself than it is to say to a collaborator.
I know that's just a thing that I'm not good at.
So, in that way, it's very easy to just throw away a script because the script isn't working.
It's hard to tell someone else they should do the same.
Actually, last time we talked, I think it was very close to me talking to Don Knuth.
It was kind of cool, like two people that...
You can't believe you got that interview.
No, can I brag about something?
Please.
My favorite thing is Don Knuth, after he did the interview, he offered to go out to hot dogs with
me, to get hot dogs. That was never... People ask me, what's the favorite interview you've
ever done? That has to be... But unfortunately, I couldn't. I had a thing after.
So, I had to turn down Don Knuth.
You missed Knuth dogs?
Knuth dogs. Sorry. So, that was a little bragging, but the hot dogs, he's such a sweet.
But the reason I bring that up is he works through problems alone as well.
He prefers that struggle, the struggle of it.
But writers like Stephen King often talk about their process of what they do,
what they eat when they wake up, when they sit down, how they like their desk.
On a perfectly productive day, what they like to do, how long they like to work for,
what enables them to think deeply, all that kind of stuff.
Hunter S. Thompson did a lot of drugs. Everybody has their own thing.
Do you have a thing? If you were to lay out a perfect productive day,
what would that schedule look like, do you think?
Part of that's hard to answer because the mode of work I do changes a lot from day to day.
Some days, I'm writing. The thing I have to do is write a script. Some days, I'm animating.
The thing I have to do is animate. Sometimes, I'm working on the animation library.
The thing I have to do is, I'm not a software engineer, but something in the direction of
software engineering. Some days, it's a variant of research. It's like, learn this topic well
and try to learn it differently. Those are four very different modes of what it...
Some days, it's like get through the email backlog of people I've been,
the tasks I've been putting off. It goes research, scripting. The idea starts with
the research and then there's scripting and then there's programming and then there's the
showtime. The research side, by the way, what I think a problematic way to do it is to say,
I'm starting this project and therefore, I'm starting the research. Instead, it should be
that you're ambiently learning a ton of things just in the background and then once you feel
like you have the understanding for one, you put it on the list of things that there can be a video
for. Otherwise, either you're going to end up roadblock forever or you're just not going to
have a good way of talking about it. Still, some of the days, it's like the thing to do
is learn new things. What's the most painful one? I think you mentioned scripting. Scripting is,
yeah, that's the worst. Writing is the worst. What's your perfectly... Let's take the hardest one.
What's a perfectly productive day? You wake up and it's like, damn it, this is the day I need to
do some scripting. You didn't do anything the last two days, so you came up with excuses
to procrastinate, so today must be the day. Yeah, I wake up early, I guess I exercise
and then I turn the internet off. If we're writing, yeah, that's what's required is having
the internet off and then maybe you keep notes on the things that you want to Google when you're
allowed to have the internet again. I'm not great about doing that, but when I do, that makes it
happen. Then when I hit writer's block, the solution to writer's block is to read. It doesn't even
have to be related. Just read something different just for 15 minutes, half an hour, and then go
back to writing. That, when it's a nice cycle, I think can work very well. When you're writing
the script, you don't know where it ends, right? Problem-solving videos, I know where it ends.
Expositional videos, I don't know where it ends. Coming up with the magical thing that ties this
whole story together, when does that happen? That's the thing that makes it such that a topic
gets put on the list. Oh, that's an issue. You shouldn't start the project unless there's one
of those. You have so many nice bags that you haven't such a big bag of aha moments already
that you could just pull at it. That's one of the things and one of the sad things about time
and that nothing lasts forever and that we're all mortal. Let's not get into that
discussion. If I see, even when I ask for people to ask, I did a call for questions and people
want to ask you questions. There's so many requests from people about certain videos
they would love you to do. It's such a pile. I think that's a sign of admiration from people,
for sure. It makes me sad because whenever I see them, people give ideas, they're all
very often really good ideas. It makes me sad in the same kind of way when I go through a library
or through a bookstore, you see all these amazing books that you'll never get to open.
Yeah. You got to enjoy the ones that you have. Enjoy the books that are open and don't let
yourself lament the ones that stay closed. What else? Is there any other magic to that day?
Do you try to dedicate a certain number of hours? Do Cal Newport has this deep work kind of idea?
There's systematic people who get really on top of, they checklist of what they're going to do in
the day and they count their hours. I am not a systematic person in that way, which is probably
a problem. I very likely would get more done if I was systematic in that way, but that doesn't happen.
You talk to me later in life and maybe I'll have changed my ways and give you a very different
answer. I think Benjamin Franklin later in life figured out the rigor is these very rigorous schedules
and how to be productive. I think those schedules are much more fun to write. It's very fun to
write a schedule and make a blog post about the perfect productive day. It might work for one
person, but I don't know how much people get out of reading them or trying to adopt someone else's
style. I'm not even sure that they've ever followed. You're always going to write it as the best
version of yourself. You're not going to explain the phenomenon of wanting to get out of the bed,
but not really wanting to get out of the bed and all of that. Just zoning out for random
reasons or the one that people probably don't touch at all is I try to check social media once a day,
but only so I post. When I post, I check the previous days. That's what I try to do.
That's what I do 90% of the days, but then I'll have a two-week period where it's just like,
I'm checking the internet. It's probably some scary number of times.
I think a lot of people can resonate with that. I think it's a legitimate addiction. It's a dopamine
addiction. I don't know if it's a problem because as long as it's the kind of socializing, if you're
actually engaging with friends and engaging with other people's ideas, I think it can be really
useful. Well, I don't know. For sure, I agree with you, but it's definitely an addiction
because for me, I think it's true for a lot of people. I am very cognizant of the fact I just
don't feel that happy. If I look at a day where I've checked social media a lot, if I just aggregate,
I did a self-report, I'm sure I would find that I'm just literally less happy with my life and
myself after I've done that check. When I check it once a day, I'm happy. Because I've seen it,
okay, one way to measure that is when somebody says something not nice to you on the internet. It's
like when I check it once a day, I'm able to just smile. I virtually think about them positively,
empathetically. I send them love. I don't ever respond, but I just feel positively about the
whole thing. If I check more than that, it starts eating at me. There's an eating thing that happens
with anxiety. It occupies a part of your mind that doesn't seem to be healthy. Same with,
I mean, you put stuff out on YouTube. I think it's important. I think you have a million
dimensions that are interesting to you, but one of the interesting ones is the study of
education and the psychological aspect of putting stuff up on YouTube. I now have completely stopped
checking statistics of any kind. I've released an episode 100 with my dad, conversation with my dad.
He checks, he's probably listening to this, stop. He checks the number of views on his video,
on his conversation. So he discovered a reason, he's new to this whole addiction,
and he just checks. He'll text me or write to me, I just pass Dawkins. I love that so much.
Can I tell you a funny story in that effect of parental use of YouTube? Early on in the channel,
my mom would text me, she's like, the channel has had 990,000 views. The channel has had
991,000 views. I'm like, oh, that's cute. She's going to the little part on the about page where
you see the total number of channel views. No, she didn't know about that. She had been going
every day through all the videos and then adding them up. And she thought she was doing
me this favor of providing me this global analytic that otherwise wouldn't be visible.
That's awesome. It's just like this addiction where you have some number you want to follow
and it's funny that your dad had this. I think a lot of people have it.
I think that's probably a beautiful thing for parents because they're legitimately,
they're proud. Yeah. It's born of love. It's great. The downside, I feel, one of them,
is this is one interesting experience that you probably don't know much about because
comments on your videos are super positive. But people judge the quality of how something went,
like I see that with these conversations, by the comments. I'm not talking about
people in their 20s and their 30s. I'm talking about CEOs of major companies who don't have time.
They literally, this is their evaluation metric. They're like, ooh, the comments seem to be
positive and that's really concerning to me. The most important lesson for any content creator
to learn is that the commenting public is not representative of the actual public.
This is easy to see. Ask yourself, how often do you write comments on YouTube videos?
Most people will realize, I never do it. Some people realize they do, but the people who realize
they never do it should understand that that's a sign. The kind of people who are like you
aren't the ones leaving comments. I think this is important in a number of respects.
In my case, I think I would think my content was better than it was if I just read comments
because people are super nice. The thing is, the people who are bored by it are put off by it in
some way, are frustrated by it. Usually, they just go away. They're certainly not going to
watch the whole video, much less leave a comment on it. There's a huge underrepresentation of
negative feedback, well-intentioned negative feedback because very few people actively do
that. Watch the whole thing that they dislike, figure out what they disliked, articulate what
they dislike. There's plenty of negative feedback that's not well-intentioned, but for that golden
kind. I think a lot of YouTuber friends, I have at least have gone through phases of anxiety about
the nature of comments that stem from basically just this, that it's people who aren't necessarily
representative of who they were going for or misinterpreted what they were trying to say
or whatever have you. We're focusing on things like personal appearances as opposed to substance.
They come away thinking, oh, that's what everyone thinks. That's what everyone's
response to this video was. A lot of the people who had the reaction you wanted them to have,
they probably didn't write it down. Very important to learn. It also translates to
realizing that you're not as important as you might think you are because all of the people
commenting are the ones who love you the most and are really asking you to create certain
things or mad that you didn't create a past thing. I have such a problem. I have a very real
problem with making promises about a type of content that I'll make and then either not
following up on it soon or just never following up on it. Yeah. Last time we talked, I'm not
sure. Promise to me that you'll have music incorporated into your... I'll share with
you a private link. There's an example of what I had in mind. I did a version of it. I think
there's a better version of this that might exist one day. It's now on the back burner. It's sitting
there. There was a live performance at this one thing. I think next circumstance that I'm doing
another recorded live performance that fits having that in a better recording context. Maybe I'll
make it nice in public. Maybe a while. Exactly. The point I was going to make though is I know
I'm bad about following up on stuff, which is an actual problem. It's born of the fact that I
have a sense of what will be good content when it won't be, but this can actually be
incredibly disheartening because a ton of comments that I see are people who are frustrated usually
in a benevolent way that I haven't followed through on X and X, which I get. I should do that,
but what's comforting thought for me is that when there's a topic I haven't promised, but I am
working on and I'm excited about, it's like the people who would really like this don't know that
it's coming and don't know to comment to that effect. The commenting public that I'm seeing is
not representative of who I think this other project will touch meaningfully.
Yeah, so focus on the future, on the thing you're creating now, just like the art of it.
One of the people is really inspiring to me in that regard because I've really seen it
in person. Joe Rogan, he doesn't read comments, but not just that. He doesn't give a damn.
He's not clueless about it. He's just like the richness and the depth of a smile he has
when he just experiences the moment with you offline. You can tell he doesn't give a damn about
anything, about what people think about whether if it's on a podcast you talk to him or whether
offline about just it's not there. What other people think, how even what the rest of the
day looks like is just deeply in the moment or especially is what we're doing going to make
for a good Instagram photo or something like that. It doesn't think like that at all.
I think for actually quite a lot of people he's an inspiration in that way, but in real life,
I show that you can be very successful not giving a damn about comments. It sounds
bad not to read comments because it's like, well, there's a huge number of people who are
deeply passionate about what you do so you're ignoring them. But at the same time, the nature
of our platforms is such that the cost of listening to all the positive people who are
really close to you, who are incredible people have made a great community that you can learn
a lot from. The cost of listening to those folks is also the cost of your psychology slowly being
degraded by the natural underlying toxicity of the internet. Engage with a handful of people
deeply rather than as many people as you can in a shallow way. I think that's a good lesson for
social media usage. Platforms in general, yeah. Choose just a handful of things to engage with
and engage with it very well in a way that you feel proud of and don't worry about the rest.
Honestly, I think the best social media platform is texting.
That's my favorite. That's my go-to social media platform.
Well, yeah, the best social media interaction is real life, not social media, but social
interaction. Well, yeah, no question there. I think everyone should agree with that.
Which sucks because it's been challenged now with the current situation and we're trying to figure
out what kind of platform can be created that we can do remote communication that's still
as effective. It's important for education. It's important for just-
That is the question of education right now. Yeah.
On that topic, you've done a series of live streams called Lockdown Math.
You want live, which is different than you usually do. Maybe one, can you talk about
how that feel? What's that experience like? In your own, when you look back, is that an
effective way? Did you find being able to teach? If so, is there a lessons for this world where
all of these educators are now trying to figure out how the heck do I teach remotely?
For me, it was very different. As different as you can get. I'm on camera, which I'm usually not.
I'm doing it live, which is nerve-wracking. It was a slightly different level of topics,
although realistically, I'm just talking about things I'm interested in no matter what.
But I think the reason I did that was this thought that a ton of people are looking to learn
remotely, the rate at which I usually put out content is too slow to be actively helpful.
Let me just do some biweekly lectures that if you're looking for a place to point your students,
if you're a student looking for a place to be edified about math, just tune in at these times.
In that sense, I think it was a success for those who followed with it. It was a really
rewarding experience for me to see how people engaged with it. Part of the fun of the live
interaction was to actually do these live quizzes and see how people would answer and
try to shape the lesson based on that or see what questions people were asking in the audience.
I would love to, if I did more things like that in the future, kind of tighten that feedback loop
even more. I think if this can be relevant to educators, 100% online teaching is basically
a form of live streaming now. Usually, it happens through Zoom. I think if teachers view what they're
doing as a kind of performance and a kind of live stream performance, that would probably be
pretty healthy because Zoom can be kind of awkward. I wrote up this little blog post actually just on
what our setup looked like if you want to adopt it yourself and how to integrate the broadcasting
software OBS with Zoom or things like that. It was really sorry to pause on that. Maybe we could
look at the blog post, but it looked really nice. The thing is, I knew nothing about any of that
stuff before I started. I had a friend who knew a fair bit and so he kind of helped show me the
roofs. One of the things that I realized is that you could, as a teacher, it doesn't take that
much to make things look and feel pretty professional. One component of it is as soon as you hook
things up with the broadcasting software rather than just doing screen sharing, you can set up
different scenes and then you can have keyboard shortcuts to transition between those scenes.
So you don't need a production studio with a director calling like, go to camera three,
go to camera two, like onto the screen capture. Instead, you can have control of that. It took
a little bit of practice and I would mess it up now and then, but I think I had it decently smooth
such that I'm talking to the camera and then we're doing something on the paper, then we're doing
playing with a Desmos graph or something. Something that I think in the past would have
required a production team, you can actually do as a solo operation and in particular as a teacher.
I think it's worth it to try to do that because two reasons. One, you might get more engagement
from the students, but the biggest reason, I think one of the best things that can come out of this
pandemic education wise is if we turn a bunch of teachers into content creators and if we take
lessons that are usually done in these one-off settings and start to get in the habit of,
sometimes I'll use the phrase commoditizing explanation, where what you want is whatever
a thing a student wants to learn, it just seems inefficient to me that that lesson is taught
millions of times over in parallel across many different classrooms in the world, year to year.
You've got a given algebra one lesson that's just taught literally millions of times by different
people. What should happen is that there's the small handful of explanations online
that exist so that once someone needs that explanation, they can go to it, that the time
in classroom is spent on all of the parts of teaching and education that aren't explanation,
which is most of it. The way to get there is to basically have more people who are already
explaining, publish their explanations and have it in a publicized forum. If during a pandemic,
you can have people automatically creating online content because it has to be online,
but getting in the habit of doing it in a way that doesn't just feel like a Zoom call that
happened to be recorded, but it actually feels like a piece that was always going to be publicized
to more people than just your students, that can be really powerful.
And there's an improvement process there. So being self-critical and growing,
I guess YouTubers go through this process of putting out some content and nobody
caring about it and then trying to figure out, basically improving, figure out why did nobody
care and they come up with all kinds of answers which may or may not be correct,
but doesn't matter because the answer leads to improvement. So you're
being constantly self-critical, self-analytical, it should be better to say. So you think of
like, how can I make the audio better? Like all the basic things. Maybe one question to ask,
because, well, by way of Russ Tedrick, he's a robotics professor at MIT, one of my favorite
people, a big fan of yours. He watched our first conversation. I just interviewed him
a couple of weeks ago. He teaches this course in the under-actuated robotics, which is
robotic systems when you can't control everything. We as humans, when we walk,
we're always falling forward, which means it's gravity. You can't control it. You just hope
you can catch yourself, but that's not all guaranteed. It depends on the surface. So that's
under-actuated. You can't control everything. The number of actuators, the degrees of freedoms
you have is not enough to fully control the system. So I don't know. It's a really, I think,
beautiful, fascinating class. He puts it online. It's quite popular. He does an incredible job
teaching. He puts it online every time, but he's kind of been interested in crisping it up,
making it, innovating in different kinds of ways. And he was inspired by the work he
do because I think in his work, he can do similar kind of explanations as you're doing,
like revealing the beauty of it and spending months in preparing a single video.
And he's interested in how to do that. That's why he listened to the conversation. He's playing
with Manum. But he had this question of, like in my apartment where we did the interview,
I have curtains, like a black curtain. This is a adjacent mansion that I also own.
But you basically just have, I have a black curtain, whatever, that makes it really easy
to set up a filming situation with cameras that we have here, these microphones. He was asking,
what kind of equipment do you recommend? I guess your blog post is a good one. I said,
I don't recommend this is excessive and actually really hard to work with. So I wonder,
I mean, is there something you would recommend in terms of equipment? Do you think like lapel
mics, like USB mics? For my narration, I use a USB mic for the streams I used a lapel mic.
The narration, it's a Blue Yeti. I'm forgetting actually the name of the lapel mic, but it was
probably like a road of some kind. Is it hard to figure out how to make the audio sound good?
I mean, listen to all the early videos on my channel and clearly, I'm terrible at this.
For some reason, I just couldn't get audio for a while. I think it's weird when you hear your own
voice. So you hear it, you're like, this sounds weird. And it's hard to notice it sound weird
because you're not used to your own voice or they're like actual audio artifacts at play.
And then video is just for the lockdown, just the camera. Like you said,
it was probably streaming somehow through the... Yeah, there were two GH5 cameras,
one that was mounted overhead over a piece of paper. You could also use like an iPad or
a Wacom tablet to do your writing electronically, but I just wanted the paper feel one on the face.
There's two. Again, I don't know. I'm like just not actually the one to ask this because I like
animate stuff usually, but each of them has a compressor object that makes it such that the
camera output goes into the computer USB, but gets compressed before it does that.
The live aspect of it, do you regret doing it live?
Not at all. I do think the content might be much less sharp and tight than if it were
something, even that I just recorded like that and then edited later. But I do like
something that I do to be out there to show like, hey, this is what it's like raw. This is what it's
like when I make mistakes. This is like the pace of thinking. I like the live interaction of it.
I think that made it better. I probably would do it on a different channel, I think, if I did
series like that in the future, just because it's a different style. It's probably a different
target audience and kind of keep clean what Three Blue and Brown is about versus
the benefits of live lectures. Do you suggest like in this time of COVID
that people like Russ or other educators try to go the shorter 20-minute videos that are
like really well planned out or scripted, you really think through, you slowly design,
so it's not live? Do you see like that being an important part of what they do?
Yeah. Well, what I think teachers like Russ should do is choose the small handful of topics that
they're going to do just really well. They want to create the best short explanation of it in
the world that will be one of those handfuls in a world where you have commoditized explanation,
right? Most of the lectures should be done just normally. Still put thought and planning into
it. I'm sure he's a wonderful teacher and knows all about that. But maybe choose those small
handful of topics do what beneficial for me sometimes is if I do sample lessons with people
on that topic to get some sense of how other people think about it, let that inform how you
want to edit it or script it or whatever format you want to do. Some people are comfortable
just explaining it and editing later. I'm more comfortable like writing it out and thinking
in that setting. Yeah. Sorry to interrupt. It's a little bit sad to me to see how much
knowledge is lost. Just as you mentioned, there's professors like we can take my dad, for example,
to blow up his ego a little bit. But he's a great teacher and he knows plasma,
plasma chemistry, plasma physics really well. So he can very simply explain some beautiful but
otherwise complicated concepts. And it's sad that if you Google plasma or like for plasma physics,
like there's no videos. Just imagine if every one of those excellent teachers like your father
like Russ, even if they just chose one topic this year, they're like, I'm going to make the best
video that I can on this topic. If every one of the great teachers did that, the internet would
be replete and it's already replete with great explanations, but it would be even more so with
all the niche great explanations and like anything you want to learn. And there's a self-interest
to it in terms of teachers, in terms of even, so if you take Russ, for example, it's not that he's
teaching something like he teaches his main thing, his thing he's deeply passionate about. And from
a selfish perspective, it's also just like, I mean, it's a, it's a, it's like publishing a paper
in a really like nature has like letters, like accessible publication. It's just going to guarantee
that your work, that your passion is seen by a huge number of people. Whatever the definition
of huge is doesn't matter. It's much more than it otherwise would be. And it's those lectures that
tell early students what to be interested in. Yeah. At the moment, I think students are
disproportionately interested in the things that are well represented on YouTube. So to any
educator out there, if you're wondering, hey, I want more like grad students in my department,
like, what's the best way to recruit grad students? It's like, make the best video you
can and then wait eight years. And then you're going to have a pile of like, excellent grad
students for that department. And one of the lessons I think your channel teaches is there's
appeal of explaining just something beautiful, explaining it cleanly, technically, not doing
a marketing video about why topology is great. There's, yeah, that's the, there's people interested
in this stuff. Yeah. I mean, one of the greatest channels, like Matt, it's not even a math channel,
but the channel with greatest math content is Vsauce. Yeah. You've like interviewed. Imagine
you were to propose making a video that explains the Bonak-Tarski paradox substantively, right? Not,
not shying around. It may be not describing things in terms of like the group theoretic
terminology that you'd usually see in a paper, but the actual results that went into this idea of
like breaking apart a sphere, proposing that to like a network TV station saying, yeah, I'm going
to do this in-depth talk of the Bonak-Tarski paradox. I'm pretty sure it's going to reach 20
million people. They'd say, like, get out of here. Like, no, no one cares about that. No one's
interested in anything even anywhere near that. But then you have Michael's quirky personality
around it and just people that are actually hungry for that kind of depth. Then you don't need like
the approval of some higher network. You can just do it and let the people speak for themselves.
So I think, you know, if your father was to make something on plasma physics or if we were to have
like, under-actualized robotics. Under-actuated. Yes, not under-actualized. Plenty actualized.
Under-actuated robotics. Yeah, most robotics is under-actualized currently.
So even if it's things that you might think are niche, I bet you'll be surprised by how many people
actually engage with it really deeply. Although I just psychologically watching him,
I can't speak for a lot of people. I can speak for my dad. I think there's a little bit of a
skill gap, but I think that could be overcome. That's pretty basic.
None of us know how to make videos when we start. The first thing I made was terrible in a number
of respects. Like, look at the earliest videos on any YouTube channel except for Captain Disillusion.
And they're all like terrible versions of whatever they are now.
But the thing I've noticed, especially like with world experts, is it's the same thing that I'm
sure you went through, which is like fear of like embarrassment. Like, they definitely,
it's the same reason. Like, I feel that anytime I put out a video, I don't know if you still feel
that, but like, I don't know, it's this imposter syndrome. Like, who am I to talk about this?
And that that's true for like even things that you've studied for like your whole life.
I don't know. It's scary to post stuff on YouTube.
It is scary. I honestly wish that more of the people who had that modesty to say,
who am I to post this? We're the ones actually posting it. That's right.
I mean, the honest problem is like a lot of the educational content is posted by people who,
like we're just starting to research it two weeks ago and are on a certain schedule
and who maybe should think like, who am I to explain and choose your favorite topic,
quantum mechanics or something. And the people who have the self-awareness to not post are probably
the people also best positioned to give a good honest explanation of it.
That's why there's a lot of value in a channel like Numberphile, where they basically trap
a really smart person and force them to explain stuff on a broad sheet of paper.
So, but of course, that's not scalable as a single channel. If there's anything beautiful
that it could be done as people take it in their own hands, educators.
Which is again, circling back, I do think the pandemic will serve to force a lot of people's
hands. You're going to be making online content anyway. It's happening, right?
Just hit that publish button and see how it goes.
Yeah, see how it goes. The cool thing about YouTube is it might not go for a while,
but like 10 years later, right? Yeah. It'll be like, this is the thing.
What people don't understand with YouTube, at least for now, at least that's my
hope with it, is it's literally better than publishing a book in terms of the legacy.
It will live for a long, long time. Of course, it's one of the things I mentioned Joe Rogan
before, it's kind of, there's a sad thing because I'm a fan. He's moving to Spotify.
Yeah, nine digit numbers will do that to you.
That he's one person that doesn't actually care about that much about money. Like having
talked to him, it wasn't because of money. It's because he legitimately thinks that
they're going to do a better job. From his perspective, YouTube, you have to understand
where they're coming from. YouTube has been cracking down on people who they, Joe Rogan
talks to Alex Jones in conspiracy theories and YouTube is really careful with that kind of stuff.
That's not a good feeling. Joe doesn't feel like YouTube is on his side.
He's often has videos that they don't put in trending that are obviously should be in trending
because they're nervous about like, is this content going to upset people that all that
kind of stuff have misinformation and that's not a good place for a person to be in. Spotify is
giving them, we're never going to censor you, we're never going to do that. The reason I bring that
up, whatever you think about that, I personally think is bullshit because podcast things should
be free and not constrained to a platform. It's pirate radio. What the hell? You can't,
as much as I lost Spotify, you can't just, you can't put fences around it.
But anyway, the reason I bring that up is Joe's going to remove his entire library from YouTube.
Whoa, really? I didn't know that.
He's going to, his full length, the clips are going to stay, but the full length videos are all,
I mean, made private or deleted. That's part of the deal. And that's the first time where I was
like, oh, YouTube videos might not live forever. Things you find, okay, I'm sorry.
This is why you need IPFS or something where it's like, if there's a content link,
are you familiar with the system at all? Right now, if you have a URL that points to a server,
there's a system where the address points to content and then it's distributed.
So you can't actually delete what's at an address because it's content address.
And as long as there's someone on the network who hosts it, it's always accessible at
the address that it once was. But I mean, that raises a question. I'm not going to
put you on the spot, but like somebody like Vsauce, right? Spotify comes along and gives him,
let's say, $100 billion, okay? Let's say some crazy number and then it removes it from YouTube,
right? It's made me, I don't know. For some reason, I thought YouTube was forever.
I don't think it will be. I mean, another variant that this might take is that you fast forward
50 years and Google or Alphabet isn't the company that it once was and it's kind of struggling
to make ends meet. And it's been supplanted by whoever wins on the AR game or whatever it might
be. And then they're like, you know, all of these videos that we're hosting are pretty costly,
so we're just, we're going to start deleting the ones that aren't watched that much and
tell people to try to back them up on their own or whatever it is. Or even if it does exist in
some form forever, it's like if people are not habituated to watching YouTube in 50 years,
they're watching something else, which seems pretty likely. It would be shocking if YouTube
remained as popular as it is now indefinitely into the future. So it won't be forever.
Makes me sad still, but because it's such a nice, just like you said, of the canonical videos.
Sorry, I don't mean to interrupt. You should get Juan Bennett on the thing and then talk
to him about permanence. I think you would have a good conversation.
Who's that?
So he's the one that founded this thing called IPFS that I'm talking about. And if you have him
talk about basically what you're describing, like, oh, it's sad that this isn't forever,
then you'll get some articulate pontification around it that's been pretty well thought through.
But yeah, I do see YouTube, just like you said, as a place, what your channel creates,
which is a set of canonical videos on a topic. Others could create videos on that topic as
well, but as a collection, it creates a nice set of places to go if you're curious about
a particular topic. And it seems like coronavirus is a nice opportunity to put that knowledge out
there in the world at MIT and beyond. I have to talk to you a little bit about machine learning,
deep learning, and so on. Again, we talked about last time, you have a set of beautiful videos
on neural networks. Let me ask you first, what is the most beautiful aspect of neural networks and
machine learning to you? For making those videos, from watching how they feel this evolving,
is there something mathematically or in applied sense, just beautiful to you about them?
Well, I think what I would go to is the layered structure and how you can have what feel like
qualitatively distinct things happening going from one layer to another, but that are following
the same mathematical rule. Because if you look at it as a piece of math, it's like you got a non-linearity
and then you've got a matrix multiplication. That's what's happening on all the layers.
But especially if you look at some of the visualizations that Chris Ola has done with respect
to convolutional nets that have been trained on ImageNet, trying to say, what does this neuron
do? What does this family of neurons do? What you can see is that the ones closer to the input
side are picking up on very low-level ideas like the texture. Then as you get further back,
you have higher-level ideas like what is the where the eyes in this picture and then how do the eyes
form like an animal? Is this animal a cat or a dog or a deer? You have this series of qualitatively
different things happening even though it's the same piece of math on each one. That's a pretty
beautiful idea that you can have a generalizable object that runs through the layers of abstraction,
which in some sense constitute intelligence, is having those many different layers of an
understanding to something. A form of abstractions in an automated way.
Exactly. It's automated abstracting, which I mean, that just feels very powerful and the idea
that it can be so simply mathematically represented. I mean, a ton of modern in-mail research seems
a little bit like you do a bunch of ad hoc things, then you decide which one worked,
and then you retrospectively come up with the mathematical reason that it always had to work.
Who cares how you came to it? When you have that elegant piece of math,
it's hard not to just smile seeing it work in action.
Well, and we talked about topology before. One of the really interesting things is
beginning to be investigated under the field of science and deep learning, which is the craziness
of the surface that's trying to be optimized in neural networks. The amount of local minima,
local optima there is in these surfaces, and somehow a dumb gradient descent algorithm is
able to find really good solutions. That's really surprising.
On the one hand, it is, but also it's not terribly surprising that you have these
interesting points that exist when you make your space so high-dimensional.
Like GPT-3, what did it have? 175 billion parameters. It doesn't feel as mesmerizing to
think about, oh, there's some surface of intelligent behavior in this crazy high-dimensional space.
There's so many parameters that, of course, but what's more interesting is how is it that
you're able to efficiently get there, which is maybe what you're describing that something as
dumb as gradient descent does it. The reason the gradient descent works well with neural
networks and not just choose however you want to parameterize this space and then apply gradient
descent to it, is that layered structure lets you decompose the derivative in a way that makes
it computationally feasible. Yeah, it's just that there's so many good solutions,
probably infinitely many good solutions, not best solutions, but good solutions.
That's what's interesting. It's similar to Steven Wolfram's idea of if you just look at all space
of computations, of all space of basically algorithms, that you'd be surprised how many
of them are actually intelligent. If you just randomly pick from the bucket, that's surprising.
We tend to think a tiny, tiny minority of them would be intelligent, but his sense is it seems
weirdly easy to find computations that do something interesting.
From a Kalmagorov complexity standpoint, almost everything will be interesting.
What's fascinating is to find the stuff that's describable with low information but still does
interesting things. One fun example of this, Shannon's noisy coding and theorem, noisy
coding theorem and information theory that basically says if I want to send some bits to you,
maybe some of them are going to get flipped. There's some noise along the channel. I can come
up with some way of coding it that's resilient to that noise that's very good. Then he quantitatively
describes what very good is. What's funny about how he proves the existence of good error correction
codes is rather than saying here's how to construct it or even like a sensible non-constructive proof.
The nature of his non-constructive proof is to say if we chose a random encoding, it would be
almost at the limit, which is weird because then it took decades for people to actually find any
that were anywhere close to the limit. What his proof was saying is choose a random one
and it's the best encoding you'll ever find. What that tells us is that sometimes when you
choose a random element from this ungodly huge set, that's a very different task from finding
an efficient way to actively describe it because in that case, the random element to actually
implement it as a bit of code, you would just have this huge table of telling you how to encode
one thing into another that's totally computationally infeasible. On the side of how many possible
programs are interesting in some way, it's like, yeah, tons of them. The much, much more delicate
question is when you can have a low information description of something that still becomes
interesting. And thereby, this gives you a blueprint for how to engineer that kind of thing.
KS Theory is another good instance there where it's like, yeah, a ton of things are hard to
describe, but how do you have ones that have a simple set of governing equations that remain
arbitrarily hard to describe? Well, let me ask you. You mentioned GPT-3. It's interesting to ask
what are your thoughts about the recently released open AI GPT-3 model that I believe
is already trying to learn how to communicate like Grant Sanderson.
You know, I think I got an email a day or two ago about someone who wanted to try to use GPT-3
with Manum where you would like give it a high level description of something and then it'll
like automatically create the mathematical animation, like trying to put me out of a job here.
I mean, it probably won't put you out of a job, but it'll create something visually beautiful,
for sure. I would be surprised if that worked as stated, but maybe there's like variants of it
like that you can get to. I mean, like a lot of those demos, it's interesting. I think
there's a lot of failed experiments, like depending on how you prime the thing,
you're going to have a lot of failed, I'm certainly with code, with program synthesis,
most of it won't even run. But eventually, I think if you pick the right examples,
you'll be able to generate something cool. And I think that even that's good enough, even though
if it's if you're being very selective, it's still cool that something can be generated.
Yeah, that's huge value. I mean, think of the writing process. Sometimes a big part of it is
just getting a bunch of stuff on the page and then you can decide what to whittle down to.
So if it can be used in like a man-machine symbiosis where it's just giving you a spew of
potential ideas that then you can refine down, like it's serving as the generator and then the
human services, the refiner, that seems like a pretty powerful dynamic.
Yeah. Have you gotten a chance to see any of the demos like on Twitter? Is there a favorite
you've seen or? Oh, my absolute favorite. Yeah. So Tim Blay, who runs a channel called Alcapela
Science, he was tweeting a bunch about playing with it. And so GPT-3 was trained on the internet
from before COVID. So in a sense, it doesn't know about the coronavirus. So what he seeded it with
was just a short description about like a novel virus emerges in Wuhan, China and starts to spread
around the globe. What follows is a month-by-month description of what happens, January colon.
That's what he seeds it with. So then what GPT-3 generates is like January, then a paragraph
of a description February and such. And it's the funniest thing you'll ever read because
it predicts a zombie apocalypse, which of course it would because it's trained on like the internet.
The internet. But what you see unfolding is a description of COVID-19 if it were a zombie
apocalypse. And like the early aspects of it are kind of shockingly in line with what's reasonable.
And then it gets out of hand so quickly. And the other flip side of that is I wouldn't be surprised
if it's onto something at some point here. You know, 2020 has been full of surprises.
Who knows? Like we might all be in like this crazy militarized zone as it predicts
just a couple months off. Yeah, I think it's definitely an interesting tool of storytelling.
It has struggled with mathematics, which is interesting, or just even numbers.
It's able to, it's not able to generate like patterns, you know, like you give it
in like five-digit numbers, and it's not able to figure out the sequence, you know, or like,
I didn't look in too much, but I'm talking about like sequences like the Fibonacci
numbers and to see how far it can go. Because obviously it's leveraging stuff from the internet
and it starts to lose it. But it is also cool that I've seen it able to generate some interesting
patterns that are mathematically correct. Yeah, I honestly haven't dug into like what's going on
within it in a way that I can speak intelligently to. I guess it doesn't surprise me that it's
bad at numerical patterns because I mean, maybe I should be more impressed with it. But like
that requires having a weird combination of intuitive and formulaic world view. So you're
not just going off of intuition when you see Fibonacci numbers. You're not saying like intuitively,
what do I think will follow the 13? Like I've seen patterns a lot where like 13s are followed by
21s. Instead, it's that like the way you're starting to see a shape of things is by knowing
what hypotheses to test where you're saying, oh, maybe it's generated based on the previous
terms or maybe it's generated based on like multiplying by a constant or whatever it is.
You have a bunch of different hypotheses and your intuitions are around those hypotheses,
but you still need to actively test it. And it seems like GPT-3 is extremely good at
like that sort of pattern matching recognition that usually is very hard for computers,
that is what humans get good at through expertise and exposure to lots of things. It's why it's
good to learn from as many examples as you can, rather than just from the definitions. It's to get
that level of intuition. But to actually concretize it into a piece of math, you do need to test your
hypotheses and if not prove it, have an actual explanation for what's going on, not just a
pattern that you've seen. Yeah, but then the flip side to play devil's advocate, that's a very kind
of probably correct, intuitive understanding of just like we said, a few layers creating
abstractions, but it's been able to form something that looks like a compression of the data that
it's seen that looks awfully a lot like it understands what the heck it's talking about.
Well, I think a lot of understanding is like, I don't mean to denigrate pattern recognition,
pattern recognition is most of understanding and it's super important and it's super hard.
And so like when it's demonstrating this kind of real understanding, compressing down some data,
like that might be pattern recognition at its finest. My only point would be that
like what differentiates math, I think to a large extent, is that the pattern recognition
isn't sufficient and that the kind of patterns that you're recognizing are not like the end goals,
but instead they are the little bits and paths that get you to the end goal.
So that's only true for mathematics in general. It's an interesting question if that might,
for certain kinds of series of numbers, it might not be true. Because that's a basic
Taylor's… certain kinds of series, it feels like compressing the internet is enough to figure
out because those patterns in some form appear in the text somewhere.
Well, I mean, there's all sorts of wonderful examples of false patterns in math where one
of the earliest videos I put on the channel was talking about you kind of dividing a circle up
using these chords and you see this pattern of 1, 2, 4, 8, 16. I was like, okay, pretty easy to see
what that pattern is. It's powers of two. You've seen it a million times, but it's not powers of
two. The next term is 31. And so it's like almost a power of two, but it's a little bit shy.
And there's actually a very good explanation for what's going on. But I think it's a good test
of whether you're thinking clearly about the mechanistic explanations of things, how quickly
you jump to thinking it must be powers of two. Because the problem itself, there can't be a
good way to think about it as doubling a set because ultimately it doesn't. But even before
it starts to, it's not something that screams out as being a doubling phenomenon. So at best,
if it did turn out to be powers of two, it would have only been so very subtly. And I think the
difference between a math student making a mistake and a mathematician who's experienced
seeing that kind of pattern is that they'll have a sense from what the problem itself is whether
the pattern that they're observing is reasonable and how to test it. And I would just be very
impressed if there was any algorithm that was actively accomplishing that goal.
Yeah, like a learning-based algorithm.
Yeah, like a little scientist, I guess, basically.
Yeah, it's a fascinating thought because GPT-3, these language models are already
accomplishing way more than I've expected. So I'm learning not to doubt.
I bet we'll get there. Yeah, I'm not saying I'd be impressed, but like surprised,
like I'll be impressed, but I think we'll get there on algorithms doing math like that.
So one of the amazing things you've done for the world is, to some degree,
open-sourcing the tooling that you use to make your videos with Manum, this Python library.
Now, it's quickly evolving because I think you're inventing new things every time you make a video.
In fact, I've been working on playing around with something. I wanted to do like an ode to
Three Blue on Brown. I love playing Hendrix. I wanted to do like a cover of a concept I wanted
to visualize and use Manum. And I saw that you had like a little piece of code on like Mobius Strip.
I tried to do some cool things with spinning a Mobius Strip, like continue twisting it,
I guess, is the term. And it was easier to, it was tough. So I haven't figured it out yet.
So I guess the question I want to ask is so many people love it that you've put that out there.
They want to do the same thing as I do with Hendrix. They want to cover it. They want to
explain an idea using the tool, including Rust. How would you recommend they try to,
I'm very sorry, they try to go by about it. And what kind of choices should they choose
to be most effective? That I can answer. So I always feel guilty if this comes up because
I think of it like this scrappy tool that's like a math teacher who put together some code.
People asked what it was. So they made it open source and they kept scrapping it together.
And there's a lot, like a lot of things about it that make it harder to work with than it needs to
be that are a function of like me not being a software engineer. I've put some work this year
trying to make it better and more flexible that is still just kind of like a work in process.
One thing I would love to do is just get my act together about properly integrating with what
the community wants to work with and what stuff I work on and making that not deviate.
And just actually fostering that community in a way that I've been shamefully neglectful of.
So I'm just always guilty if it comes up. So let's put that guilt aside.
Just kind of zen-like. All right, zen-like. I'll pretend like it isn't terrible.
For someone like Russ, I think step one is like make sure that what you're animating
should be done so programmatically because a lot of things maybe shouldn't.
Like if you're just making a quick graph of something, if it's a graphical intuition that
maybe has a little motion to it, use Desmos, use Graffer, use Geogebra, use Mathematica,
certain things that are like really oriented around graph. Geogebra is kind of cool.
It's super cool. You can get very, very far with it. And in a lot of ways, it would make
more sense for some stuff that I do to just do in Geogebra. But I kind of have this cycle of
liking to try to improve Manum by doing videos and such. So do as I say, not as I do.
The original thought I had in making Manum was that there's so many different ways of
representing functions other than graphs. In particular, things like transformations,
like use movement over time to communicate relationships between inputs and outputs instead
of like X direction and Y direction, or like vector fields or things like that. So I wanted
something that was flexible enough that you didn't feel constrained into a graphical environment.
By graphical, I mean like graphs with like X coordinate, Y coordinate kind of stuff.
But also make sure that you're taking advantage of the fact that it's programmatic. You have loops,
you have conditionals, you have abstraction. If any of those are like well fit for what you want
to teach to have a scene type that you tweak a little bit based on parameters, or to have
conditional so that things can go one way or another, or loops so that you can create these
things of like arbitrarily increasing complexity, that's the stuff that's like meant to be
animated programmatically. If it's just like writing some text on the screen or shifting
around objects or something like that, things like that, you should probably just use keynote.
Right. You'd be a lot simpler. So try to find a workflow that distills down
that which should be programmatic into Manum and that which doesn't need to be
into like other domains. Again, do as I say, not as I do.
I mean, Python is an integral part of it. Just for the fun of it, let me ask what's your most
and least favorite aspects of Python? Oh, most and least. I mean, I love that it's like
object oriented and functional, I guess, that you can get both of those benefits for how you
structure things. So if you would just want to quickly whip something together, the functional
aspects are nice. Is your primary language for programmatically generating stuff?
Yeah, it's home for me. It's home. Sometimes you travel, but it's home. Got it. It's home.
I mean, the biggest disadvantage is that it's slow. So when you're doing computationally
intensive things, either you have to think about it more than you should how to make it efficient
or it just takes long. Do you run into that at all with your work?
Well, so certainly old Manum is way slower than it needs to be because of how
it renders things on the back and is kind of absurd. I've rewritten things such that
it's all done with shaders in such a way that it should be just live and actually interactive
while you're coding it if you want to. You have a 3D scene, you can move around, you can have
elements respond to where your mouse is or things. That's not something that the user
of a video is going to get to experience because there's just a play button and a pause button,
but while you're developing that can be nice. So it's gotten better in speed in that sense,
but that's basically because the hard work is being done in the language that's not Python,
but GLSL. But yeah, there are some times when it's like there's just a lot of data that goes
into the object that I want to animate that then it just like Python is slow.
Well, let me ask quickly ask, what do you think about the Walrus operator if you're familiar
with it at all? The reason it's interesting, there's a new operator in Python 3.8. I find it
psychologically interesting because the toxicity over it led Guido to resign, to step down from
this beat. Is that actually true or was it like there's a bunch of surrounding things that also,
was it actually the Walrus operator? Well, it was an accumulation of toxicity,
but that was the most toxic one. The discussion, that's the most number of Python core developers
that were opposed to Guido's decision. He didn't particularly, I don't think,
cared about it either way. He just thought it was a good idea. This is where you approve it,
and the structure of the idea of a BDFL is you listen to everybody, hear everybody out,
you make a decision, and you move forward. He didn't like the negativity that burdened him
after that. People like some parts of the benevolent dictator for Life Mantra, but once
the dictator does things different than you want, suddenly dictatorship doesn't seem so great.
Yeah. I mean, they still liked it. He just couldn't because he truly is the B in the benevolent.
He really is a nice guy. I mean, and I think he can't. It's a lot of toxicity. He's difficult.
It's a difficult job. That's why Alanis Torvald is perhaps the way he is. You have to have a thick
skin to fight off the warring masses. It's kind of surprising to me how many people can threaten
to murder each other over whether we should have braces or not, or whether it's incredible.
Yeah. I mean, that's my knee-jerk reaction to the Walrus operators. I don't actually care that
much. Either way, I'm not going to get really passionate. My initial reaction was, yeah,
this seems to make things more confusing to read, but then again, so does list comprehension until
you're used to it. If there's a use for it, great, if not, great, but let's just all calm down about
our spaces versus tabs debates here and be chill. Yeah. To me, it just represents the value of
great leadership even in open source communities. Does it represent that if he stepped down as a
leader? Well, he fought for it. No, he got it passed. I guess, but I guess. I could represent
multiple things too. It can represent failed dictatorships, or it can represent a lot of
things. But to me, great leaders take risks even if it's a mistake at the end. You have to make
decisions. The thing is, this world won't go anywhere. If whenever there's a divisive thing,
you wait until the division is no longer there. That's the paralysis we experienced with Congress
and political systems. It's good to be slow when there's indecision, when there's people
disagree. It's good to take your time, but at a certain point in results and paralysis,
and you just have to make a decision. The background of the site, whether it's yellow,
blue, or red, can cause people to go to war over each other. I've seen this with design.
People are very touched on color choices. At the end of the day, just make a decision
and go with it. I think that's what the water operator represents to me. It represents the
fighter pilot instinct of quick action is more important than just caring everybody out and
really thinking through it because that's going to lead to paralysis. Yeah, if that's the actual case
that it's something where you're consciously hearing people's disagreement, disagreeing with
that disagreement and saying he wants to move forward anyway, that's an admirable aspect of
leadership. We don't have much time, but I want to ask just because it's some beautiful mathematics
involved. 2020 brought us a couple of, in the physics world, theories of everything. Eric
Weisstein, I mean, he's been working for probably decades, but he put out this idea of geometric
unity or started publicly thinking and talking about it more. Stephen Wolfram put out his
physics project, which is kind of this hypergraph view of a theory of everything. Do you find
interesting, beautiful things to these theories of everything? What do you think about the physics
world and sort of the beautiful, interesting, insightful mathematics in that world? Whether
we're talking about quantum mechanics, which you touched on a bunch of your videos a little bit,
quaternions like just the mathematics involved or general relativity, which is more about surfaces
and topology, all that stuff. Well, I think as far as popularized science is concerned,
people are more interested in theories of everything than they should be. Because the problem is
whether we're talking about trying to make sense of Weinstein's lectures or Wolfram's project,
or let's just say listening to Witten talk about string theory, whatever proposed path to a theory
of everything, you're not actually going to understand it. Some physicists will, but you're
just not actually going to understand the substance of what they're saying. What I think is way, way
more productive is to let yourself get really interested in the phenomena that are still deep,
but which you have a chance of understanding. Because the path to even understanding what
questions these theories of everything are trying to answer involves walking down that.
I mean, I was watching a video before I came here from Steve Mould talking about
why sugar polarizes light in a certain way. So fascinating, really, really interesting.
It's not this novel theory of everything type thing. But to understand what's going on there
really requires digging in depth to certain ideas. And if you let yourself think past what the video
tells you about, what does circularly polarized light mean and things like that, it actually would
get you to a pretty good appreciation of two-state states and quantum systems in a way that just
trying to read about what are the hard parts about resolving quantum field theories with
general relativity is never going to get you. So as far as popularizing science is concerned,
the audience should be less interested than they are in theories of everything.
The popularizers should be less
emphatic than they are about that. For actual practicing physicists,
I might be the case, maybe more people should think about fundamental questions.
It's difficult to create a three-blue-one-brown video on theory of everything. So basically,
we should really try to find the beauty in mathematics or physics by looking at concepts
that are within reach. Yeah, I think that's super important. So you see this in math too with the
big unsolved problems. So the clay millennium problems, Riemann hypothesis. Have you ever
done a video on Fermat's last theorem? No, I have not yet. But if I did, do you know what I would do?
I would talk about proving Fermat's last theorem in the specific case of n equals 3.
Is that still accessible though? Yes, actually. Barely. Mathologer might be able to do a great
job on this. He's had a good job of taking stuff that's barely accessible and making it.
But the core ideas of proving it for n equals 3 are hard, but they do get you real ideas about
algebraic number theory. It involves looking at a number field that lives in the complex plane.
It looks like a hexagonal lattice, and you start asking questions about factoring numbers in this
hexagonal lattice. So it takes a while, but I've talked about this sort of lattice arithmetic
in other contexts. And you can get to a okay understanding of that. And the things that
make Fermat's last theorem hard are actually quite deep. And so the cases that we can solve it for,
it's like you can get these broad sweeps based on some hard, but accessible bits of number theory.
But before you can even understand why the general case is as hard as it is, you have to walk through
those. And so any other attempt to describe it would just end up being shallow and not really
productive for the viewer's time. I think the same goes for most unsolved problem type things where
I think, as a kid, I was actually very inspired by the Twin Prime conjecture that totally sucked
me in. It's this thing that was understandable. I kind of had this dream like, oh, maybe I'll be the
one to prove the Twin Prime conjecture. And new math that I would learn would be viewed through
this lens of maybe I can apply it to that in some way. But you sort of mature to a point where you
realize you should spend your brain cycles on problems that you will see resolved because then
you're going to grow to see what it feels like for these things to be resolved rather than spending
your brain cycles on something where it's not going to pan out. And the people who do make
progress towards these things, like James Maynard, is a great example here of young creative
mathematician who pushes in the direction of things like the Twin Prime conjecture,
rather than hitting that head on. Just see all the interesting questions that are hard for similar
reasons, but become more tractable and let themselves really engage with those. So I think
people should get in that habit. I think the popularization of physics should encourage that
habit through things like the physics of simple everyday phenomena because it can get quite deep.
And yeah, I think I've heard a lot of the interest that people send me messages asking
to explain Mindstein's thing or asking to explain Wolfram's thing. One, I don't understand them,
but more importantly, you shouldn't be interested in those.
The giant ball of interesting ideas, there's probably a million of interesting ideas in there
that individually could be explored effectively.
And to be clear, you should be interested in fundamental questions. I think that's a good
habit to ask what the fundamentals of things are, but I think it takes a lot of steps to...
Certainly, you shouldn't be trying to answer that unless you actually understand quantum
field theory and you actually understand general relativity.
That's the cool thing about your videos, people who haven't done mathematics. If you really give
it time, watch it a couple of times and try to reason about it, you can actually understand
the concept that's being explained. And it's not a coincidence that the things I'm describing
aren't the most up-to-date progress on the Riemann hypothesis cousins. There's context in which the
analog of the Riemann hypothesis has been solved in more discrete feeling finite settings that
are more well-behaved. I'm not describing that because it just takes a ton to get there. And
instead, I think it'll be productive to have an actual understanding of something that you can
pack into 20 minutes. I think that's beautifully put. Ultimately, that's where the most satisfying
thing is when you really understand. Yeah, really understand.
Build the habit of feeling what it's like to actually come to resolution.
As opposed to... Which it can also be enjoyable, but just being in awe of the fact that you don't
understand anything. Yeah. I don't know. Maybe people get entertainment out of that, but...
It's not as fulfilling as understanding. You won't grow.
Yeah. But also just the fulfilling. It really does feel good when you first don't understand
something and then you do. That's a beautiful feeling. Let me ask you one last time. We got
awkward and weird about a fear of mortality, which you made fun of me of. But let me ask you on the
other absurd question is, what do you think is the meaning of our life, of meaning of life?
I'm sorry if I made fun of you about words. No, you didn't. I'm just joking. It was great.
I don't think life has a meaning. I don't understand the question. I think meaning is
something that's ascribed to stuff that's created with purpose. There's a meaning to
like this water bottle label in that someone created it with a purpose of conveying meaning.
And there was one consciousness that wanted to get its ideas into another consciousness.
Most things don't have that property. It's a little bit like if I ask you, what is the height?
All right. So it's all relative.
Yeah. You'd be like the height of what? You can't ask what is the height
without an object. You can't ask what is the meaning of life without like
an intentful consciousness putting it... I guess I'm revealing I'm not very religious.
But the mathematics of everything seems kind of beautiful. It seems like
it seems like there's some kind of structure relative to which I mean, you could calculate the height.
Well, so but what I'm saying is I don't understand the question, what is the meaning of life in that
I think people might be asking something very real. I don't understand what they're asking.
Are they asking like, why does life exist? Like, how did it come about? What are the natural laws?
Are they asking as I'm making decisions day by day for what should I do? What is the guiding light
that inspires like, what should I do? I think that's what people are kind of asking.
But also like, why the thing that gives you joy about education, about mathematics,
what the hell is that? Like, what?
Interactions with other people. Interactions with like-minded people, I think is the meaning of
in that sense.
It's bringing others joy essentially. Like in something you've created,
it connects with others somehow and the same in the vice versa.
I think that that is what when we use the word meaning to mean like you sort of filled with
a sense of happiness and energy to create more things like I have so much meaning taken from
this like that. Yeah, that's what fuels my pump at least.
So a life alone on a deserted island would be kind of meaningless.
Yeah, you want to be alone together with someone.
I think we're all alone together. I think there's no better way to end it. Grant,
you've been first time with talks. That's amazing. Again, it's a huge honor that you make time for
me. I appreciate talking with you. Thanks man. Awesome.
Thanks for listening to this conversation with Grant Sanderson and thank you to our sponsors
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to get a discount and to support this podcast. If you enjoy this thing, subscribe on YouTube,
review it with five stars and up a podcast, follow on Spotify, support on Patreon. I'll
connect with me on Twitter at Lex Freedman. And now let me leave you with some words from Richard
Feynman. I have a friend who's an artist and is sometimes taken a view which I don't agree with
very well. He'll hold up a flower and say, look how beautiful it is. And I'll agree. Then he says,
I as an artist can see how beautiful this is, but you as a scientist take this all apart and it
becomes a dull thing. And I think he's kind of nutty. First of all, the beauty that he sees
is available to other people and to me too, I believe. Although I may not be quite as refined
aesthetically as he is, I can appreciate the beauty of a flower. At the same time,
I see much more about the flower than he sees. I can imagine the cells in there,
the complicated actions inside, which also have a beauty. I mean, it's not just beauty at this
dimension at one centimeter, there's also beauty at smaller dimensions, the inner structure, also
the processes, the fact that the colors in the flower evolved in order to attract insects to
pollinate it is interesting. It means that insects can see the color. It adds a question,
does this aesthetic sense also exist in the lower forms? Why is it aesthetic? All kinds of interesting
questions which the science knowledge only adds to the excitement, the mystery and the awe of a
flower. It only adds, I don't understand how it subtracts. Thank you for listening and hope to see
you next time.