Po-Shen Loh: Mathematics, Math Olympiad, Combinatorics & Contact Tracing
嘉宾：Po-Shen Loh
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本篇目录18 章节
§01Transcript · 00:00–08:42§02Transcript · 08:42–17:08§03Transcript · 17:09–24:58§04Transcript · 24:58–33:24§05Transcript · 33:24–41:20§06Transcript · 41:20–49:30§07Transcript · 49:30–58:15§08Transcript · 58:15–1:06:40§09Transcript · 1:06:40–1:14:03§10Transcript · 1:14:03–1:22:48§11Transcript · 1:22:48–1:31:15§12Transcript · 1:31:15–1:39:02§13Transcript · 1:39:02–1:47:17§14Transcript · 1:47:17–1:54:44§15Transcript · 1:54:44–2:01:32§16Transcript · 2:01:32–2:10:16§17Transcript · 2:10:16–2:18:54§18Transcript · 2:18:54–2:20:06§01Transcript · 00:00–08:42
The following is a conversation with Po Shen Lou,
a professor of mathematics at Carnegie Mellon University,
national coach of the USA International Math Olympia team,
and founder of XP that does online education
of basic math and science.
He's also the founder of Novid,
an app that takes a really interesting approach
to contact tracing,
making sure you stay completely anonymous
and it gives you statistical information about COVID cases
in your physical network of interactions.
So you can maintain privacy, very important,
and make informed decisions.
In my opinion,
we desperately needed solutions like this in early 2020.
And unfortunately, I think,
we will again need it for the next pandemic.
To me, solutions that require large scale,
distributed coordination of human beings
need ideas that emphasize freedom and knowledge.
Quick mention of our sponsors,
Jordan Harbinger Show, Onnit, BetterHelp,
Aidsleep, and Element.
Check them out in the description to support this podcast.
As a side note, let me say that Po and I
filmed a few short videos
about simple, beautiful math concepts
that I will release soon.
It was really fun.
I really enjoyed Po sharing his passion for math with me
in those videos.
I'm hoping to do a few more short videos
in the coming months that are educational in nature
on AI, robotics, math, science, philosophy,
or if all else fails,
just fun snippets into my life on music, books, martial arts,
and other random things,
if that's of interest to anyone at all.
This is the Lex Friedman Podcast,
and here's my conversation with Po Shenlow.
You know, you mentioned you really enjoy flying
and experiencing different people in different places.
There's something about flying for me,
I don't know if you have the same experience,
that every time I get on an airplane,
it's incredible to me that human beings
have actually been able to achieve this.
And when I look at like what's happening now
with humans traveling out into space,
I see it as all the same thing.
It's incredible that humans are able to get into a box
and fly in the air and safely and land
in the same, it seems like,
and everybody's taking it for granted.
So when I observe them, it's quite fascinating
because I see that cleanly mapping to the world
where we're now in rockets and traveling to the moon,
traveling to Mars, and at the same kind of way,
I can already see the future
where we will all take it for granted.
So I don't know if you have,
you personally, when you fly,
have the same kind of magical experience
of like how the heck did humans actually accomplish this?
So I do, especially when there's turbulence,
which is like on the way here, there was turbulence
and the plane jiggled, even the flight attendant
had to hold onto the side.
And I was just thinking to myself,
it's amazing that this happens all the time
and the wings don't fall off,
given how many planes are flying.
But then I often think about it and I'm like,
a long time ago, I think people didn't trust elevators
in a 40 story building in New York City.
And now we just take it completely for granted
that you can step into this shaft,
which is 40 floors up and down, and it will just not fail.
Yeah, again, I'm the same way with elevators,
but also buildings, when I'll stand on the 40th floor
and wonder how the heck are we not falling right now?
Like how amazing it is with the high winds,
like structurally, just the earthquakes and the vibrations,
I mean, natural vibrations in the ground.
Like how is this, how are all of these,
you go to like New York City, all of these buildings standing.
I mean, to me, one of the most beautiful things,
actually mathematically too, is bridges.
I used to build bridges in high school from like toothpicks,
just like out of the pure joy of like physics,
making some structure really strong.
Understanding like from a civil engineering perspective,
what kind of structure will be stronger
than another kind of structure, like suspension bridges.
And then you see that at scale,
humans being able to span a body of water
with a giant bridge.
And it's, I don't know, it's so humbling.
It makes you realize how dependent we are on each other.
Sort of, I talk about love a lot,
but there's a certain element in which we little ants
have just a small amount of knowledge
about our particular thing.
And then we're depending on a network of knowledge
that other experts hold.
And then most of our lives,
most of the quality of life we have
has to do with the richness of that network of knowledge,
of that collaboration,
and then sort of the ability to build on top of it,
levels of abstractions.
You start from like bits in a computer,
then you can have assembly, then you can have C++,
or you have an operating system,
then you can have C++ and Python, finally,
some machine learning on top.
All of these are abstractions.
And eventually we'll have AI that runs all of us humans.
But anyway, but speaking of abstractions and programming,
in high school, you wrote some impressive games
for MS DOS.
I got a chance to, in browser somehow,
it's magic, I got a chance to play them.
Alien Attack 1, 2, 3, and 4.
What's the hardest part about programming those games?
And maybe can you tell the story about building those games?
Sure.
I actually tried to do those in high school
because I was just curious if I could.
That's a good starting point for anything, right?
Yeah, yeah, yeah, it's like, could you?
But the appealing thing was also,
it was a soup to nuts kind of thing.
So something that has always attracted me is,
I like beautiful ideas, I like seeing beautiful ideas,
but I actually also like seeing execution of an idea
all the way from beginning to end in something that works.
So for example, in high school,
I was lucky enough to grow up in the late 90s
when even a high school student could hope
to make something sort of comparable
to the shareware games that were out there.
I say the word sort of, like still quite far away,
but at least I didn't need to hire a 3D CG artist.
There weren't enough pixels to draw anyway,
even I can draw, right?
Bad art, of course.
But the point is, I wanted to know,
is it possible for me to try to do those things
where back in those days,
you didn't even have an easy way
to draw letters on the screen in a particular font.
You couldn't just say import a font, it wasn't like Python.
So for example, back then,
if you played those games in the web browser,
which is emulating the old school computer,
those, even the letters you see,
those are made by individual calls
to draw pixels on the screen.
So you built that from scratch,
almost building a computer graphics library from scratch?
Yes, the primitive that I got to use
was some code I copied off of a book in assembly
of how to put a pixel on a screen in a particular color.
And the programming language was Pascal?
Ah, yeah, the first one was in Pascal,
but then the other ones were in C++ after that.
How's the emulation in the browser work, by the way?
Is that trivial?
Because it's pretty cool, you get to play these games
that have a very much 90s feeling to them.
Ah, so it's literally making an MSDOS environment,
which is literally running the old.exe file.
Wow, in the browser.
This is, that could be more amazing than the airplane.
So it wasn't so much about the video games,
it was more about,
can you build something really cool from scratch?
Yes.
And you did a bunch of programming competitions.
What was your interest, your love for programming?
What did you learn through that experience?
Especially now that as much of your work
has taken a long journey through mathematics.
I think I always was amazed
by how computers could do things fast.
If I wanted to make it an abstract analysis
of why it is that I saw some power in the computer.
Because if the computer can do things
so many times faster than humans,
where the hard part is telling the computer
what to do and how to do it,
if you can master that asking the computer what to do,
then you could conceivably achieve more things.
And those contests I was in,
those were the opposite in some sense
of making a complete product, like a game is a product.
Those contests were effectively write a function
to do something extremely efficiently.
And if you are able to do that,
§02Transcript · 08:42–17:08
then you can unlock more of the power of the computer.
But also doing it quickly.
There's a time element from the human perspective
to be able to program quickly.
There's something nice.
So there's almost like an athletics component
to where you're almost like an athlete
seeking optimal performance as a human being
trying to write these programs.
And at the same time, it's kind of art
because the best way to write a program quickly
is to write a simple program.
You just have a damn good solution.
So it's not necessarily you have to type fast.
You have to think through a really clean,
beautiful solution.
I mean, what do you think is the use
of those programming competitions?
Do you think they're ultimately something
you would recommend for students,
for people interested in programming,
or people interested in building stuff?
Yes, I think so because especially with the work
that I've been doing nowadays,
even trying to control COVID,
something that was very helpful from day one
was understanding that the kinds of computations
we would want to do,
we could conceivably do on like a four core cloud machine
on Amazon Web Services out to a population
which might have hundreds of thousands
or millions of people.
The reason why that was important
to have that back of the envelope calculation
with efficient algorithms
is because if we couldn't do that,
then we would bankrupt ourselves
before we could get to a big enough scale.
If you think about how you grow anything from small to big,
if in order to grow it from small to big,
you also already need 10,000 cloud servers,
you'll never get to big.
And also the nice thing about programming competitions
is that you actually build a thing that works.
So you finish it, there's a completion thing,
and you realize, I think there's a magic to it,
where you realize that it's not so hard
to build something that works.
To have a system that successfully takes in inputs
and produces outputs and solves a difficult problem,
and that directly transfers to building a startup essentially
that can help some aspect of this world
as long as it's mostly based on software engineering.
Things get really tricky
when you have to manufacture stuff.
That's why people like Elon Musk are so impressive
that it's not just software.
Tesla Autopilot is not just software.
It's like you have to actually have factories
that build cars, and there's like a million components
involved in the machinery required
to assemble those cars and so on.
But in software, one person can change the world,
which is incredible.
But on the mathematics side,
what, if you look back, or maybe today,
what made you fall in love with mathematics?
For me, I think I've always been very attracted
to challenge, as I already indicated
with writing the program.
I guess if I see something that's hard
or supposed to be impossible,
sometimes I say, maybe I want to see if I can pull that off.
And with the mathematics, the math competitions
presented problems that were hard,
that I didn't know how to start,
but for which I could conceivably try to learn
how to solve them.
So, I mean, there are other things that are hard
called like get something to Mars, get people to Mars.
And I didn't, and I still don't think
that I am able to solve that problem.
On the other hand, the math problems struck me
as things which are hard
and with significant amount of extra work,
I could figure it out.
And maybe they would actually even be useful,
like that mathematical skill is the core
of lots of other things.
That's really interesting.
Maybe you could speak to that
because a lot of people say that math is hard
as a kind of negative statement.
It always seemed to me a little bit like
that's kind of a positive statement
that all things that are worth having in this world,
they're hard.
I mean, everything that people think about
that they would love to do, whether it's sports,
whether it's art, music, and all the sciences,
they're going to be hard
if you want to do something special.
So is there something you could say to that idea
that math is hard?
Should it be made easy or should it be hard?
Ah, so I think maybe I want to dig in a little bit
onto this hard part and say,
I think the interesting thing about the math
is that you can see a question
that you didn't know how to start doing it before.
And over a course of thinking about it,
you can come up with a way to solve it.
And so you can move from a state
of not being able to do something
to a state of being able to do something
where you help to take yourself through that
instead of somebody else spoon feeding you that technique.
So actually here, I'm already digging into
maybe part of my teaching philosophy also,
which is that I actually don't want to ever
just tell somebody, here's how you do something.
I actually prefer to say, here's an interesting question.
I know you don't quite know how to do it.
Do you have any ideas?
I'm actually explaining another way
that you could try to do teaching.
And I'm contrasting this to a method of watch me do this,
now practice it 20 times.
I'm trying to say a lot of people consider math to be hard
because maybe they can't remember
all of the methods that were taught.
But for me, I look at the hardness
and I don't think of it as a memory hardness.
I think of it as a, can you invent something hardness?
And I think that if we can teach more people
how to do that art of invention in a pure cognitive way,
not as hard as the actual hardware stuff, right?
But like in terms of the concepts
and the thoughts and the mathematics,
teaching people how to invent,
then suddenly actually they might not even find math
to be that tiresomeness hard anymore,
but that rewardingness hard of I have the capability
of looking at something which I don't know what to do
and coming up with how to do it.
I actually think we should be doing that,
giving people that capability.
So hard in the same way that invention is hard,
that is ultimately rewarding.
So maybe you can dig in that a little bit longer,
which is do you see basically the way to teach math
is to present a problem and to give a person a chance
to try to invent a solution
with minimal amount of information first?
Is that basically,
how do you build that muscle of invention in a student?
Yes, so the way that,
I guess I have two different sort of ways
that I try to teach.
Actually, one of them is, in fact, this semester,
because all my classes were remotely delivered,
I even threw them all onto my YouTube channel.
So you can see how I teach at Carnegie Mellon,
but I'd often say, hey, everyone, let's try to do this.
Any ideas?
And that actually changes my role as a professor
from a person who shows up for class
with a script of what I wanna talk through.
I actually, I don't have a script.
The way I show up for classes,
there's something that we want to learn how to do,
and we're gonna do it by improv.
I'm talking about the same method as improv comedy,
which is where you tell me some ideas,
and I'll try to yes and them.
You know what I mean?
And then together,
we're gonna come up with a proof of this concept
where you were deeply involved in creating the proof.
Actually, every time I teach the class,
we do every proof slightly differently
because it's based on how the students came up with it.
And that's how I do it when I'm in person.
I also have another line of courses that we make
that is delivered online.
Those things are where I can't do it live,
but the teaching method became also similar.
It was just, here's an interesting question.
I know it's out of reach.
Why don't you think about it?
And then automatic hints.
We feed automatically hints through the internet
to go and let the person try to invent.
So that's like a more rigorous prodding of invention.
But you did mention disease and COVID,
and you've been doing some very interesting stuff
from a mathematical, but also software engineering angle
of coming up with ideas.
It's back to the, I see a problem.
I think I can help.
§03Transcript · 17:09–24:58
So you stepped into this world.
Can you tell me about your work there
under the flag of Novid
and both the software and the technical details
of how the thing works?
Sure, sure.
So first I want to make sure that I say,
this is actually team effort.
I happen to be the one speaking,
but there's no way this would exist
without an incredible team of people
who inspire me every day to work on this.
But I'll speak on behalf of them.
So the idea was indeed that we stepped forward
in March of last year, when the world started to become,
our part of the world started to become,
our part meaning the United States
started to become paralyzed by COVID.
The shutdown started to happen.
And at that time it started as a figment of an idea,
which was network theory,
which is the area of math that I work in,
could potentially be combined with smartphones
and some kind of health information anonymized.
Exactly how?
We didn't know yet.
We tried to crystallize it.
And many months into this work,
we ended up accidentally discovering a new way
to control diseases,
which is now what is the main impetus of all of this work
is to take this idea and polish it
and hopefully have it be useful not only now,
but for future pandemics.
The idea is really simple to describe.
Actually, my main thing in the world
is I come up with obvious observations.
That's that, so I'll explain it now.
Einstein did the same thing
and he wrote a few short papers.
But so the idea is like this.
If we describe how usually people control disease
for a lot of history,
it was that you'd find out who was sick,
you'd find out who they've been around
and you try to remove all of those people from society
against their will.
Now that's the problem.
The against their will part
gives you the wrong kind of a feedback loop,
which makes it hard to control the disease
because then the people you're trying to control
keep getting other people sick.
You can see already how I'm thinking
and talking about this feedback loops.
This is actually related to something you said earlier
about even like how skyscrapers stay in the air.
The whole point is control theory.
You actually want to, or even how an airplane stays,
you need to have control loops
which are feedbacking in the right way.
And what we observed was that the feedback control loop
for controlling disease by asking people
to be removed from society against their will
was not working.
It was running against human incentives
and you suddenly are trying to control
seven billion, eight billion people
in ways that they don't individually want
to necessarily do.
So here's the idea.
And this is inspired by the fact
that at the core of our team
were user experience designers.
That's actually, in fact, the first thing I knew
we needed when we started
was to bring user experience at the core.
Okay.
But so the idea was suppose hypothetically
there was a pandemic.
What would you want?
You would want a way to be able to live your life
as much as possible and avoid getting sick.
Can we make an app to help you avoid getting sick?
Notice how I've just articulated the problem.
It is not, can we make an app
so that after you are around somebody who's sick
you can be removed from society.
It's can we make an app so that you can avoid getting sick.
That would run a positive feed.
I don't know if I want to call it positive or negative
but it would run a good feedback loop.
Okay.
So then how would you do this?
The only problem is that you don't know who's sick
because especially with this disease
if I see somebody who looks perfectly healthy
the disease spreads two days before you have any symptoms.
And so it's actually not possible.
That's where the network theory comes in.
You caught it from someone.
What if we changed the paradigm
and we said, whenever there's a sickness
tell everybody how many physical relationships
separate them from the sickness.
That is the trivial idea we added.
The trivial idea was the distance between you and a disease
is not measured in feet or seconds.
It's measured in terms of how many
close physical relationships separate you
like these six degrees of separation like LinkedIn.
Simple idea.
What if we told everyone that?
It turns out that actually unlocks
some interesting behavioral feedback loops
which for example, let me now jump to a non COVID example
to show why this maybe could be useful.
Actually we think it could be quite useful.
Imagine there was Ebola or some hemorrhagic fever.
Imagine it spread through contact through the air.
In fact, pretend, pretend.
That's a disastrous disease.
It has high fatality rate.
And as you die, you're bleeding out of every orifice.
Okay.
So.
Yeah, not pleasant.
Not pleasant.
So the question is, suppose that such a disease broke
who would want to install an app that would tell them
how many relationships away from them
this disease had struck?
Like a lot of people.
A lot of people.
In fact, almost, I don't want to say almost everyone.
That's a very strong statement
but a very large number of people.
That's fascinating framing.
Like the more deadly and transmissible the disease
the stronger the incentive to install it in a positive sense
the, in the good feedback loop sense.
That's a really good example.
It's a really good way to frame it.
Cause with COVID, it was not as deadly
as potential pandemics could have been
viruses could have been.
So it's sometimes muddled with how we think about it
but yeah, this is a really good framing.
If the virus was a lot more deadly
you want to create a system that has a set of incentives
that it quickly spreads to the population
where everybody is using it
and it's contributing in a positive way to the system.
Exactly.
And actually that point you just made
I don't take credit for that observation.
There was another person I talked to
who pointed out that it's very interesting
that this feedback loop is even more effective
when the disease is worse.
And that's actually not a bad characteristic to have
in your feedback loop
if you're trying to help civilization keep running.
Yeah, it's a really, it's in this dynamic
like people figure out, they dynamically figure out
how bad the disease is.
The more it spreads and the deadlier it is
as the people observe it
as long as the spread of information
like semantic information, natural language information
is closely aligned with the reality of the disease
which is a whole nother conversation, right?
We, that's, we might, maybe we'll chat about that
how we sort of make sure there's not misinformation
while there's accurate information
but that aside, okay, so this is a really nice property.
Right, and just going on on that
actually just talking more about what that could do
and why we're so excited about it.
It's that not only would people want to install it
but what would they do if you start to see
that this disease is getting closer and closer?
We surveyed informally people
but they said, as we saw it getting closer, we would hide.
We would try to not have contacts.
But now you notice what this has just achieved.
The whole goal on this whole exercise was
you got the people who might be sick
and you got everyone else, set A and set B.
Set A is the people who might be sick,
set B is everyone else.
And for the entirety of the past
contact tracing approaches, you tried to get set A
to do things that might not be to their liking or their will
because that's removing them from society.
We found out that there's two ways
to separate set A from set B.
You can also let the people at set B
at the fringe of set A
attempt to remove themselves from this interface.
§04Transcript · 24:58–33:24
It's the symmetry of A and B separation.
Everyone was looking at A, we look at B
and suddenly B is in their incentive to do so.
Beautiful.
So there's a virus that jumps from human to human.
So there's a network sometimes called graph
of the spread of a virus.
It hops from person to person to person to person.
And each one of us individuals are sitting
or plopped into that network.
We have close friends and relations and so on.
It's kind of fascinating
to actually think about this network
and we can maybe talk about the shapes
of this kind of network.
Because I was trying to think exactly this,
like how many people do I,
well, I'm kind of an introvert, not kind of,
I'm very much an introvert.
But so can I be explicit about the kind of people
I meet in regular life?
Say when it was completely opened up, there's no pandemic.
There is a kind of network and there's maybe
in the graph theoretic sense, there's some weights
or something about how close that relationship is
in terms of the frequency of visits,
the duration of visits and all of those kinds of things.
So you're saying we might want to be,
to create on top of that network,
a spread of information to let you know
as the virus travels through this network,
how close is it getting to you?
And the number of hops away it is on that network
is really powerful information
that creates a positive feedback loop
where you can act essentially anonymously
and on your own.
Like nobody's telling you what to do,
which is really important, is decentralized
and not whatever the opposite of authoritarian is.
But you get to sort of the American way.
You get to choose to do it yourself.
You have the freedom to do it yourself
and you're incentivized to do it.
And you're most likely going to do it
to protect yourself against you getting the disease
as the closer it gets to you
based on the information that you have.
But can you maybe elaborate, first of all, brilliant.
Whenever I saw the thing you're working on,
so forget for COVID, this is of course,
really relevant for COVID, but it's also probably relevant
for future diseases as well.
So that was the thing I'm nervous about.
I was like, if this whole,
if our society shut down because of COVID,
like what the heck is gonna happen
when there's a much deadlier disease?
Like this, this is disappointing.
The whole time, 2020, the whole time
I'm just sitting like this,
like is the incompetence of everybody
except the people developing vaccines.
The biologists are the only ones
that got their stuff together.
But in terms of institutions and all that kind of stuff,
it's just been terrible.
But this is exactly the power of information
and the power of information
that doesn't limit personal freedom.
So your idea is brilliant.
Okay, mathematically, can you maybe elaborate
what are we talking about?
Like how do you actually make that work?
What's involved?
Sure, first I'm gonna reply to something you said
about the freedom inside this,
because actually that was the idea.
The idea is this is game theory, right?
And effectively what we did is analogous
to free market economy, as opposed to central planning.
If you just line up the set of incentives correctly
so that people have in their purely selfish behavior
are contributing to the optimization of the global function,
that's it.
And the point of what we do, I guess in mathematics
is we try to explore the search space
to go and find out as many possibilities as there are.
And in this case, it's an applied search space.
That's why the inputs from design,
user experience design and actual people are important.
But you asked about, I guess, the mathematical
or the technical things underpinning it.
So I think the first thing I'll say is
we wanted to make this thing
not require your personal information.
And so in order to do that,
what gave me the confidence to, I guess,
lead our team to run at the beginning
is we saw that this could be done without using GPS information.
So technically what's going on is if two smartphones,
it's a smartphone app.
If two smartphones have this thing installed,
they just communicate with each other by Bluetooth
to go and find out how far,
they can detect nearby things by Bluetooth.
And then they can find out that these two phones
were approximately such and such distance apart.
And that kind of relative proximity information
is enough to construct this big network.
Okay, so the physical network is constructed
based on proximity that's through Bluetooth
and you don't have to specify your exact location,
it's the proximity.
I'm not using the Pythagorean theorem basically.
I mean, if I just knew the GPS coordinates,
we could use the Pythagorean theorem too.
Sorry, that's just how I call it.
Distance formula, whatever you want to call it.
Yeah, so we're not doing
the old Pythagorean based violation of privacy.
Okay.
But so is that enough to form,
to give you enough information about physical connection
to another human being?
Is there a time element there?
Is there, so, okay.
That sounds like a really strong, like low hanging fruit.
Like if you have that,
you could probably go really, really far.
My natural question is,
is there extra information you can add on top of that?
Like the duration of the physical proximity?
So first of all, we actually do estimate the duration,
but the way we estimate the duration
is like how a movie is filmed,
in the sense that every so often, every few minutes,
we check what's nearby.
It's like how a movie is filmed.
You take lots of snapshots.
So there's no way in a battery efficient way
to really keep track of that proximity.
However, fortunately, we're using probability.
The fact is the paradigm that we're using
is it's not super important
if you run into that person only for 10 minutes
at the grocery store.
If that's a stranger that you run into 10 minutes
in this grocery store,
that's not gonna be relevant for our paradigm
because our paradigm is not telling you
who were you around before
and might therefore have gotten infected by already.
Ours is about predicting the future.
We change from, I mean, the standard paradigm was
what already happened, quick damage control.
Ours is predict the future.
If you run into that person once in the grocery store today
and never see them again,
it's irrelevant for predicting the future.
And therefore, for ours, what really matters
is the many hours around the other person,
at which point, if you're scanning every five
to eight minutes.
That's going to come out in the problem,
like statistically speaking,
it's going to come out as a strong relationship
and a person in the grocery store is going to wash out
is not an important physical relationship.
I mean, this is brilliant.
How difficult is it to make work?
So you said, one, there's a mathematical component
that we just kind of talked about,
and then there's the user experience component.
So how difficult does it to go,
just like you built the video game, Alien Attack,
from zero to completion, what's involved?
How difficult is it?
So I'm going to answer that question
in terms of building the product,
but then I'm also going to acknowledge
that just having an app doesn't make it useful
because that's actually maybe the easy part.
If you know what I mean,
there's like all of this stuff
about rollout adoption and awareness,
but let's focus on the app part first.
So that's again, why I said the team is incredible.
So we have a bunch of people who,
let's just say that the technology that we use to make it
is not the standard way you make an app.
If you think about a standard iOS app or Android app,
those are a user interface that contacts a web server
and sends some information back and forth.
We're doing some stuff that has to hook
into the operating system of saying,
let's go use Bluetooth for something
it wasn't really meant for, right?
So there's that part.
By the way, what is the app called?
§05Transcript · 33:24–41:20
Oh, it's called Novid, COVID with an N.
Very nice.
So you have to hook into Bluetooth.
You're saying you have to do that beyond the permissions
that are like at the very surface level
provided on the phone?
Well, I don't want to call them permissions.
I just want to say,
that's not what you usually do with Bluetooth.
Gotcha.
Usually with Bluetooth, you say,
do I have headphones nearby?
Yes.
Okay, I'm done.
You don't go and say, do I have headphones nearby?
Or do I have another phone nearby, which is doing something?
And then keep asking that same question.
Keep asking the question.
Right?
So it's actually not easy.
And I mean, there were some parts of it,
which actually a lot of people had tried unsuccessfully.
Actually, it's known that, for example,
the UK was trying to do something similar.
And the problem they ran into was,
when you program things on iOS,
iOS is very good at making it hard
to do things in the background.
And so there was quite a lot of effort required
to go and make this thing work.
So the whole point, this thing would run in the background
and iOS, I mean, most Android probably as well, right?
But yeah, iOS certainly makes it difficult
for something to run in the background,
especially when it's eating up your battery, right?
Well, we wanted to make sure we didn't eat up the battery.
So that one we can,
we actually are very proud of the fact
that ours uses very little battery.
Actually, even if compared to Apple's own system, so.
Beautiful.
So what else is required to make this thing work?
Right, so the key was that you had to do
a significant amount of work on the actual
mobile app development,
which fortunately the team that we brought
was this kind of general thinkers
where we would dig in deep into the operating system
documentation and the API libraries.
So we got that working.
But there's another angle, which is,
you also need the servers to be able to compute fast enough,
which is tying back to this old school
computer programming competitions and math Olympiads.
In fact, our team that was working on the algorithm
and backend side included several people
who had been in these competitions from before,
which I happen to know because I do coach the team
for the math.
And so we were able to bring people in to build servers,
a server infrastructure in C++ actually,
so that we could support significant numbers of people
without needing tons of servers.
Is there some distributed algorithms working here
or you basically have to keep in the same place
the entire graph as it builds?
Cause especially the more and more people use it,
the bigger, the bigger the graph gets.
I mean, this is very difficult scaling problem, right?
Ah, so that's actually why this computer algorithm
competition stuff was handy.
It's because there are only about seven to eight
giga people in the world.
Yeah.
That's not that many.
So if you can make your algorithms linear time
or almost linear time, a computer operates in gigahertz.
I only need to do one run, one recalculation every hour
in terms of telling people how far away these dangers are.
Yes.
So I suddenly have 3,600 seconds
and my CPU cores are running in gigahertz.
And at most they're eight giga people.
Well, you skipping over the fact that there's N squared
potential connections between people.
So how do you get around the fact that, you know,
that we, you know, the potential set of relationship
any one of us could have is a billion.
So it's a billion times squared.
That's the potential amount of data you have to be storing
and computing over and constantly updating.
So the way we dealt with that is we actually expect
that the typical network is very sparse.
The technical term sparse would mean that the average degree
or the average number of connections that a person has
is going to be at most like a hundred strong connections
that you care about.
If you think of it almost in terms of the heavy hitters,
actually in most people's lives,
a hundred, if we just kept track
of their top hundred interactions,
that's probably most of the signal.
Yeah, yeah.
I'm saddened to think that I might not be even
in a double digits, but.
Oh, I was intentionally giving a crazy number
to account for college students.
You call, oh, those are the,
who you call on the heavy hitters,
the people who are like the social butterflies.
Yeah, I need to,
I'd love to know that information about myself,
by the way, that, do you expose the graph,
like how many, like about yourself,
how many connections you have?
We do expose to each person
how many direct connections they have.
That's great.
But for privacy purposes,
we don't tell anybody who their connections,
like how their connections are interconnected.
Yes, gotcha.
But at the same time, we do expose also to everyone
an interesting chart that says,
here's how many people you have
that you're connected to directly.
Here's how many at distance two,
meaning via people.
And then here's how many at distance three.
And the reason we do that,
is that actually ends up being a dynamic
that also boosts adoption.
It drives another feedback loop.
The reason is because we saw, actually,
when we deployed this in some universities,
that when people see on their app
that they are indirectly connected to hundreds
or thousands of other people,
they get excited and they tell other people,
hey, let's download this app.
But you know, we also saw in those examples,
especially looking at the screenshots people gave,
that is hit as soon as the typical person
has two or three other direct connections on the system.
Because that means that our app
has reached a virality or not of two to three.
The key is we were making a viral app to fight a virus
spreading on the same network that the virus spreads on.
So you're trying to out virus the virus.
That's right.
That's exactly right.
Okay, great.
What have you learned from this whole experience
in terms of, let's say for COVID,
but for future pandemics as well,
is it possible to use the power information here
of networked information as a virus spreads and travels
in order to basically keep the society open?
Is it possible for people to protect themselves
with this information?
Or do you still have to have most,
like in this overarching policy
of everybody should stay at home, that kind of thing?
We are trying to answer that question right now.
So the answer is we don't know yet,
but that's actually why we're very happy
that now the idea has started to become more widely known.
And we're already starting to collaborate
with epidemiologists.
Again, I'm just a mathematician, right?
And a mathematician should not be the person
who is telling everybody, this will definitely work.
But because of the potential power of this approach,
especially the potential power
of this being an end game for COVID,
we have gotten the interest of real researchers.
And we're now working together
to try to actually understand the answer to that question.
Because you see, there's a theory.
So what I can share is the mathematics of,
here's why there's some hope that this would work.
And that's because I'm talking about end game now.
End game means you have very few cases.
But everywhere, we're always thinking,
once there's few cases, then does that mean we now open up?
Once you open up in the past, then the cases go up again
until you have to lock down again.
And now when we talk about the dynamic process that makes,
it's guaranteeing you always have cases
until you have the great vaccines,
which is, we both got vaccinated, this is good.
But at the same time, why I'm thinking
this is still important is because we know
that many vaccine makers have said
they're preparing for the next dose next year.
And if we have a perpetual thing
where you just always need a new vaccine every year,
it could actually be beneficial to make sure
we have as many other techniques as possible
for parts of the world that can't afford,
§06Transcript · 41:20–49:30
for example, that kind of distribution.
Yeah, so actually, no matter how deadly the virus is,
no matter how many things,
whether you have a vaccine or not,
it's still useful to be having this information.
Yes.
Because to stay home or not, depending on how risk,
I'm a big fan, just like you said, of having the freedom
for you to decide how risk averse you wanna be, right?
Depending on your own conditions,
but also on the state of like what you,
just how dangerously you like to live.
So I think that actually makes a lot of sense.
And I also think that since we're,
when you think of disease spreading,
it spreads in aggregate in the sense that
if there are some people who maybe are more risk tolerant
because of other things in their life,
well, there might also be other people
who are less risk tolerance.
And then those people decide to isolate.
But what matters is in the aggregate
that this R naught of the infection spreading
drops below one.
And so the key is if you can empower people
with that power to make that decision,
you might actually still be able to drive
that R naught down below one.
Yeah, and also, this is me talking,
people get a little bit nervous, I think,
with information somehow mapping to privacy violation.
But first of all, in the approach you're describing,
that's respecting anonymity.
But I would love to have information
from the very beginning, from March and April of last year,
almost like a map of like where it's risky
and where it's not to go.
And not map based on sort of the exact location of people,
but where people usually hang out kind of thing.
Just, and maybe not necessarily about actual location,
but just maybe activities,
like just to have information about what is good to do
and not, in terms of like safety,
is it okay to run outside and not,
is it okay to go to a restaurant and not,
I just feel like we're operating in the blind.
And then what you had is a very imperfect signal,
which is like basically politicians desperately trying
to make statements about what is safe and not.
They don't know what the heck they're doing.
They have a bunch of smart scientists telling them stuff.
And the scientists themselves also, very important,
don't always know what they're doing.
Epidemiology is not, is as much an art as a science.
You're desperately trying to predict the future,
which nobody can do.
And then you're trying to speak with some level of authority.
I mean, if I were to criticize scientists,
they spoke with too much authority.
It's okay to say, I'm not sure.
But then they think like, if I say, I'm not sure,
then there's going to be a distrust.
What they realize is when you're wrong and you say,
I'm sure, it's going to lead to more distrust.
So there's this imperfect, like just chaotic,
messy system of people trying to figure out
with very little information.
And what you're proposing is just a huge amount
of information, and information is power.
Is there challenges with adoption that you see
in the future here?
So there's, maybe we could speak to,
there's approaches, I guess, from Google.
There's different people that have tried
similar kind of ideas.
Not, you have quite a novel idea, actually.
But speaking, the umbrella idea of contact tracing,
is there something you can comment about
why their approaches haven't been fully adopted?
Is there challenges there?
Is there reasons why Novid might be a better idea
moving forward, in general, just about adoption?
Yeah, so first of all, I want to say,
I always have respect for the methods that other people use.
And so it's good to see the other people I've been trying.
But what we have noticed is that the difference
between our value proposition to the user
and the value proposition to the user delivered
by everything that was made before is that,
unfortunately, the action of installing
a standard contact tracing app will then tell you
after you have already been exposed to the disease
so that you can protect other people from you.
And what that does to your own direct probability
of getting sick, if you think about it,
suppose you were making the decision,
should I or should I not install one of those apps?
What does that do to your own probability of getting sick?
It's close to zero.
This is the sad thing you're speaking to, not sad.
I suppose it's the way the world is.
The only incentive there is to just help other people,
I suppose, but a much stronger incentive
is anything that allows you to help yourself.
Yes, so what I'm saying is that,
let's just say free market capitalism
was not based on altruism, I think it's based on,
if you make a system of incentives
so that everybody trying to maximize their own situation
somehow contributes to the whole,
that's a game theoretic solution to a very hard problem.
And so this is actually basically mechanism design,
that we've basically come up with a different mechanism,
different set of incentives,
which incentivizes the adoption,
because actually whenever we've been rolling it out,
usually the first question we ask people,
like say in a university is,
do you know what Novid does?
And most of them have read about the other apps
and they say, Oh, Novid will tell you
after you've been around someone so you can quarantine.
And we have to explain to them,
actually, Novid never wants to ask you to quarantine.
That's not the principle.
Our principle isn't based on that at all.
We just want to let you know if something is coming close
so that you can protect yourself.
If you want.
If you want, if you want, if you want.
And then the quarantine is like, yes,
in that case, if you're quarantining,
it's because you're shutting the door from the inside,
if that makes sense.
Yes, exactly.
Exactly.
I mean, this is brilliant.
So what do you think the future looks like
for future pandemics?
What's your plan with Novid?
What's your plan with these set of ideas?
I am actually still an academic and a researcher.
So the biggest work I'm working on right now
is to try to build as many collaborations
with other public health researchers at other universities
to actually work on pilot deployments together
in various places.
That's the goal.
That's actually ongoing work right now.
And so, for example, if anyone's watching this
and you happen to be a public health researcher
and you want to be involved in something like this,
I'm just gonna say, I'm still incentive thinking.
There's something in it for the researchers too.
This could open up an entire new way
of controlling disease.
That's my hope.
I mean, it might actually be true.
And people who are involved in figuring out
how to make this work,
well, it could actually be good for their careers too.
I always have to think like,
if a researcher was getting involved,
what are they getting out of it?
Oh, so you mean like from a research perspective,
you can like publications and sets of ideas
about how to, from a sort of network theory perspective,
understand how we control the spread of a pandemic.
Yes, and what I'm doing right now
is this is basically interdisciplinary research
where maybe our side is bringing the technology
and the network theory,
and the missing parts are epidemiology
and public health expertise.
And if the two things start to join,
also because everywhere that you deploy,
let's just say that the world is different
in the Philippines as it is in the United States.
And just the natures of the locality
would mean that someone like me
should not be trying to figure out how to do that.
But if we can work with the researchers
who are based there,
now suddenly we might come up with a solution
that will help scale in parts of the world
where they aren't all getting the Moderna and Pfizer vaccines
which cost like $20 a pop in the US.
So if they want to participate,
who do they reach out to?
Oh, that would just be us.
I mean, the novid.org website has...
Novid.org.
It has a feedback reach out form.
And actually we are, I mean, again,
this is the DNA of being a researcher.
I am actually very excited by the idea
that this could contribute knowledge
that will outlast all of our generations,
like all of our lifetimes.
There you go.
§07Transcript · 49:30–58:15
Reach out to novid.org.
What about individual people?
Should they install the app and try it out?
Or is this really geographically restricted?
Oh, yeah, I didn't come on here to tell everyone
to install the app.
I did not come to tell everyone to install the app
because it works best
if your local health authority is working with us.
Gotcha.
There's a reason.
It's because, this is back to the game theory.
If anyone could just say, I'm positive,
the high school senior prank would be to say that
we have a massive outbreak on finals week.
Let's not have final exams.
So the way that our system works,
it actually borrows some ideas, not borrows,
we came up with them independently.
But this idea is similar to what Google and Apple do,
which is that if the local health authority
is working with this, they can,
for everyone who's positive,
give them a passcode that expires in a short time.
So for ours, if you're on the app and saying, I'm positive,
you can either just say that,
and that's called unverified,
or you can enter in one of these codes
that you got from the local health authority.
So basically, for anyone who's watching this,
it's not that you should just go and download it
unless you want to go and look at it.
That's cool.
But if you, on the other hand,
if you happen to know anyone at the local health authority,
which is trying to figure out how to handle COVID,
well then, I mean, we'd be very happy
to also work with you.
Gotcha.
So the verified there is really important
because you're maintaining anonymity.
And because of that,
you have to have some source of verification
in order to make sure that it's not possible to manipulate
because it's ultimately about trust and information.
So it could be, verification is really important there.
So basically, individual people should
ask their local health authorities
to sign up to contact you.
I hope this spreads.
I hope this spreads for future pandemics
because I'm really, it's the amount,
the millions of people who are hurt by this,
I think our response to the virus,
economically speaking,
the number of people who lost their dream,
lost their jobs, but also lost their dream.
Entrepreneurs, jobs often give meaning.
There's people who financially and psychologically
are suffering because of our,
I'll say, incompetent response to the virus
across the world, but certainly the United States,
that should be the beacon of entrepreneurial hope
for the world.
So I hope that we'll be able to respond
to these kinds of events much better in the future.
And this is exactly the right kind of idea.
And now is the time to do the investment.
Let's step back to the beauty of mathematics.
Maybe ask the big, silly question first,
which is, what do you find beautiful about mathematics?
I think that being able to look at a complicated problem,
which looks unsolvable,
and then to be able to change the perspective
to come from a different angle
and suddenly see that there's a nice solution.
I don't mean that every problem in math
is supposed to be this way,
but I think that these reframings
and changing of perspectives
that cause difficult things to get simplified
and crystallized and factored in certain ways is beautiful.
Actually, that's related to what we were just talking about
with even this fighting pandemics.
The crystal idea was just quantify proximity
by the number of relationships in the physical network,
instead of just by the feet and meters, right?
It's just that if you change that perspective,
now all of these things follow.
And so mathematics to me is beautiful
in the pure sense just for that.
Yeah, it's quite interesting to see a human civilization
as a network, as a graph,
and our relationships as kind of edges in that graph.
And to then do, outside of just pandemic,
do interesting inferences based on that.
This is true for like Twitter, social networks and so on,
how we expand the kind of things we talk about,
think about sort of politically,
if you have this little bubble, quote unquote,
of ideas that you play with,
it's nice from a recommender system perspective,
how do you jump out of those bubbles?
It's really fascinating.
YouTube was working on that, Twitter's working on that,
but not always so successfully,
but there's a lot of interesting work
from a mathematical and a psychological,
sociological perspective there within those graphs.
But if we look at the cleanest formulation of that,
of looking at a problem from a different perspective,
you're also involved
with the International Mathematics Olympiad,
which takes small, clean problems that are really hard,
but once you look at them differently, can become easy.
But that little jump of innovation is the entire trick.
So maybe at the high level,
can you say what is the International Mathematical Olympiad?
Sure, so this is the competition
for people who aren't yet in college, math competition,
which is the most prestigious one in the entire world.
It's the Olympics of mathematics,
but only for people who aren't yet in college.
Now, the kinds of questions that they ask you to do
are not computational.
Usually you're not supposed to find that the answer is 42.
Right?
Instead, you're supposed to explain why something is true.
And the problem is that at the beginning,
when you look at each of the questions,
first of all, you have four and a half hours
to solve three questions, and this is one day,
and then you have a second day,
which is four and a half hours, three questions.
But when you look at the questions,
they're all asking you,
explain why the following thing is true,
which you've never seen before.
And by the way, even though there are six questions,
if you solve any one of them, you're a genius
and you get an honorable mention.
So this is hard to solve.
So what about, is it one person, is it a team?
Ah, so each country can send six people
and the score of the country is actually unofficial.
There's not an official country versus country system,
although everyone just adds up the point scores
of the six people and they say,
well, now which country stacked up where?
Yeah, so maybe as a side comment,
I should say that there's a bunch of countries,
including the former Soviet Union and Russia,
where I grew up, where this is one of the
most important competitions that the country participates in.
It was a source of pride for a lot of the country.
You look at the Olympic sports,
like wrestling, weightlifting,
there's certain sports and hockey
that Russia and the Soviet Union truly took pride in.
And actually the Mathematical Olympiad,
it was one of them for many years.
It's still one of them.
And that's kind of fascinating.
We don't think about it this way in the United States.
Maybe you can correct me if I'm wrong,
but it's not nearly as popular in the United States
in terms of its integration into the culture,
into just basic conversation, into the pride.
Like, if you won an Olympic gold medal
or if you win the Super Bowl, you can walk around proud.
I think that was the case
with the Mathematical Olympiad in Russia.
Not as much the case in the United States, I think.
So I just wanna give that a little aside
because beating anybody from Russia,
from the Eastern Republic or from China
is very, very difficult.
Like, if I remember correctly,
there's people, this was a multiyear training process.
They train hard.
And this is everything that they're focused on.
My dad was a participant in this.
And it's, I mean, it's as serious as Olympic sports.
You think about like gymnastics,
like young athletes participating in gymnastics.
This is as serious as that, if not more serious.
So I just wanna give that a little bit of context
because we're talking about serious high level math,
athletics almost here.
Yeah, and actually I also think that it made sense
from the Soviet Union's perspective
because if you look at what these people do eventually,
even though, let's look at the USSR's
International Math Olympiad record.
Even though they, I say, even though they won
a lot of awards at the high school thing,
many of them went on to do incredible things
in research mathematics or research other things.
And that's showing the generalization,
generalizability of what they were working on.
§08Transcript · 58:15–1:06:40
Because ultimately we're just playing with ideas
of how to prove things.
And if you get pretty good at inventing creative ways
to turn problems apart, split them apart,
observe neat ways to turn messy things into simple crystals.
Well, if you're gonna try to solve any real problem
in the real world, that could be a really handy tool too.
So I don't think it was a bad investment.
I think it clearly worked well for Soviet Union.
Yeah, so this is interesting.
People sometimes ask me, you know,
you go up and under communism, you know,
was there anything good about communism?
And it's difficult for me to talk about it
because it's not, communism is one of those things
that's looked down on like without,
in absolutist terms currently.
But you could still, in my perspective,
talk about the actual, forget communism
or whatever the actual term is,
but you know, certain ways that the society functioned
that we can learn lessons from.
And one of the things in the Soviet Union
that was highly prized is knowledge,
not even knowledge, it's wisdom
and the skill of invention, of innovation at a young age.
So we're not talking about a selection process
where you pick the best students in the school
to do the mathematics or to read literature.
It's like, everybody did it.
Everybody, it was almost treated
as if anyone could be the next Einstein,
anybody could be the next, I don't know,
Hemingway, James Joyce.
And so you're forcing an education on the populace
and a rigorous deep education,
like as opposed to kind of like,
oh, we wanna make sure we teach
to the weakest student in the class,
which American systems can sometimes do
because we don't wanna leave anyone behind.
The Russian system was anyone can be the strongest student
and we're gonna teach you the strongest student
and we're going to pretend or force everybody,
even the weakest student to be strong.
And what that results in, it's obviously,
this is what people talk about,
is a huge amount of pressure.
Like it's psychologically very difficult.
This is why people struggle when they go to MIT,
this very competitive environment.
It can be very psychologically difficult,
but at the same time,
it's bringing out the best out of people.
And that mathematics was certainly one of those things.
And exactly what you're saying,
which kind of clicked with me just now,
as opposed to kind of a spelling bee in the United States,
which I guess you spell, I'm horrible at this,
but it's a competition about spelling,
which I'm not sure, but you could argue
it doesn't generalize well to the future skills.
Mathematics, especially this kind of mathematics
is essentially formalized competition of invention,
of creating new ideas.
And that generalizes really, really well.
So that's quite brilliantly put.
I didn't really think about that.
So this is not just about the competition.
This is about developing minds
that will come to do some incredible stuff in the future.
Yeah, actually, I want to respond
to a couple of things there.
The first one, this one, which is this notion
of whether or not that is possible
in a non authoritarian regime.
I think it is.
And that's actually why I spent some of my efforts
before the COVID thing,
actually trying to work towards there.
The reason is because if you think about it,
let's say in America,
lots of people are pretty serious
about training very hard for football,
or baseball, or basketball.
Basketball is very, very accessible,
but lots of people are doing that.
Why?
Well, actually, I think that what was going on
with the authoritarian thing was at least the message
that was universally sent was being a good thinker
and a creator of ideas is a good thing.
Yes, exactly.
There's no reason why that message can't be sent everywhere.
And I think it actually should be.
So that's the first thing.
The second thing is what you commented about this thing
about the generalizable skill
and what could people do with Olympiads afterwards.
So that's actually my interest in the whole thing.
I don't just coach students how to do problems.
In fact, I'm not even the best person for that.
I'm not the best at solving these problems.
There are other people who are much better
at making problems and teaching people how to solve problems.
In fact, when the Mathematical Association of America,
which is the group which is in charge
of the US participation in these Olympiads,
when they were deciding whether or not to put me in
back in 2013 as the head coach,
I had a conversation with their executive director
where I commented that we might do worse
because my position was I don't,
I mean, I actually didn't want to focus on winning.
I said, if you're going to let me work
with 60 very strong minds as picked through this system,
because the coach works with these,
gets to run a camp for these students.
I said, I'm actually not going to define my success
in terms of winning this contest.
I said, I wanted to maximize the number of the students
that I read about in the New York Times in 20 years.
And the executive director
of the Mathematical Association of America
was fully in support of this
because that's also how their philosophy is.
So in America, the way we run this
is we're actually not just training to win,
even though the students are very good
and they can win anyway.
One reason, for example, I went and even did the COVID thing
involving quite a few of them
is so that hopefully some of them get ideas
because in 20, 30 years, I won't have the energy
or the insight to solve problems.
We'll have another catastrophe.
And hopefully some of these people will step up and do it.
And ultimately have that longterm impact.
I wonder if this is scalable to,
because that's such a great metric for education,
not how to get an A on the test, but how to have,
how to be on the cover of New York Times
for inventing something new.
And do you think that's generalizable to education
beyond just this particular Olympia?
Like, even you saying this feels like a rare statement,
almost like a radical statement as a goal for education.
So actually the way I teach my classes at Carnegie Mellon,
which I will admit right away is not equivalent
to the average in the world,
but it's already not just the top 60 in the country
as picked by something.
Let me just explain.
I have exams in my class, which are 90% of the grade.
So the exams are the whole thing,
or most of the whole thing.
And the way that I let students prepare for the exams
is I show them all the problems I've ever given
on the previous exams.
And the exam that they will take is open notes.
They can take all the notes they want
on the previous problems.
And the guarantee is that the exam problems this time
will have no overlap with anything
you have seen me give in the past,
as well as no overlap with anything I taught in the class.
So the entire exam is invention.
Wow.
But that's how I go, right?
My point is I have explained to people when I teach you,
I don't want you to have remembered a method I showed you.
I want you to have learned enough about this area
that if you face a new question,
which I came up with the night before
by thinking about like,
what could I ask that I have never asked before?
Oh, that's cute.
That's what the answer is.
Aha, that's an exam problem.
That's exactly what I do before the exam.
And then that's what I want them to learn.
And the first exam, usually people have a rough time
because it's like, what kind of crazy class is this?
The professor doesn't teach you anything for the exam.
But then by the second or third,
and by the time they finished the class,
they have learned how to solve anything in the area.
How to invent.
How to invent in that area, yeah.
Can we walk back to the Mathematical Olympiad?
What's the scoring and format like?
And also what does it take to win?
So the way it works is that each of the six students
do the problems and there are six problems.
All the problems are equally weighted.
So each one's worth seven points.
That means that your maximum score
is six problems times seven points,
which is the nice number of 42.
And now the way that they're scored by the way
§09Transcript · 1:06:40–1:14:03
is there's partial credit.
So the question is asking you,
explain why this weird fact is true.
Okay, if you explain why you get seven points.
If you make minor mistake, maybe you get six points.
But if you don't succeed in explaining why,
but you explain some other true fact,
which is along the way of proving it,
then you get partial credit.
And actually now this is tricky
because how do you score such a thing?
It's not like the answer was 72
and you wrote 71 and it's close, right?
The answer is 72 and you wrote 36.
Oh, but that's pretty close
because maybe you're just off by it.
By the way, they're not numerical anyway,
but I'm just giving some numerical analog
to the way the scoring might work.
They're all essays.
And that's where I guess I have some role
as well as some other people
who helped me in the US delegation for coaches.
We actually debate with the country which is organizing it.
The country which is organizing the Olympiad
brings about 50 people to help judge the written solutions.
And you schedule these half hour appointments
where the delegation from one country
sits down at a table like this.
Opposite side is two or three people from the host country.
And they're just looking over these exam papers
saying, well, how many points is this worth
based on some rubric that has been designed?
And this is a negotiation process
where we're not trying to bargain
and get the best score we can.
In fact, sometimes we go to this table
and we will say, we think we want less than what you gave us.
This is how our, these are our principles.
If you give us too much, we say, no, you gave us too much.
We do that.
However, the reason why this is an interesting process
is because if you can imagine every country
which is participating has its own language.
And so if you're trying to grade the Mongolian scripts
and they're written in Mongolian,
if you don't read Mongolian, which most people don't,
then the coaches are explaining to you,
this is what the student has written.
It's actually quite interesting process.
So it's almost like a jury.
Yes.
You have, in the American legal system,
you have a jury that where they're deliberating,
but unlike a jury, there's the members of the jury
speaking different languages sometimes.
Yes. That's fascinating.
But I mean, it's hard to know what to do
because it's probably really, really competitive.
But your sense is that ultimately people,
like how do you prevent manipulation here, right?
Well, we just hope that it's not happening.
So we write in English.
Therefore, everything that the US does,
everyone can look at.
So it's very hard for me.
It's very hard for you to manipulate.
We don't manipulate.
We only hope that other people aren't.
But at the same time, as you see, our philosophy was,
we want to use this as a way to develop general talent.
And although we do this for the six people who go
to the International Math Olympiad,
we really want that everyone at any,
touched at any stage of this process
get some skills that can help to contribute more later.
So I don't know if you can say something insightful
to this question,
but what do you think makes a really hard math problem
on this Olympiad, maybe in the courses you teach
or in general?
What makes for a hard problem?
You've seen, I'm sure, a lot of really difficult problems.
What makes a hard problem?
So I could quantify it by the number of leaps of insight
of changes of perspective that are along the way.
And here's why.
This is like a very theoretical computer science
way of looking at it, okay?
It's that each reframing of the problem
and using of some tool,
I actually call that a leap of insight.
When you say, oh, wow, now I see,
I should kind of put these plugs into those sockets
like so, and suddenly I get to use that machine.
Oh, but I'm not done yet.
Now I need to do it again.
Each such step is a large possible,
large fan out in the search space.
The number of these tells you the exponent.
The base of the exponent is like how big,
how many different possibilities you could try.
And that's actually why,
like if you have a three insight problem,
that is not three times as hard as a one insight problem,
because after you've made the one insight,
it's not clear that that was the right track necessarily.
Well, unless you're very into it.
There's still a branching of possibility.
Yeah.
Right.
You're saying there's problems like on the math Olympia
that requires more than one insight?
Yes.
Those are the hard ones.
And also I can tell you how you can tell.
So this is how I also taught myself math
when I was in college.
So if you are taking a, not taught myself,
I was taking classes, of course,
but I was trying to read the textbook
and I found out I was very bad at reading math textbooks.
A math textbook has a long page of stuff that is all true,
which after you read the page,
you have no idea what you just read.
Yeah.
This is just a good summary of a math textbook.
Okay.
Yeah, because it's not clear why anything was done that way.
And yes, everything is true,
but how the heck did anyone think of that?
So the way that I taught myself math eventually was,
the way I read a math textbook
is I would look at the theorem statement.
I would look at the length of the proof
and then I would close the book
and attempt to reproof it myself.
Yeah.
That's brilliant.
The length of the proof is telling you
the number of insights,
because the length of the proof is linear
in the number of insights.
Each insight takes space.
Yeah.
And if I know that it's a short proof,
I know that there's only one insight.
So when I'm doing my own way of solving the problem,
like finding the proof,
I quit if I have to do too many plugins.
It's equivalent to a math contest.
In a math contest I look,
is it problem one, two, or three?
That tells me how many insights there are.
This is exactly what I did.
That's brilliant.
Linear in the number.
I don't know.
I think it's possible that that's true.
Approximately, approximately.
Approximately, yeah.
I don't know if somebody out there
is gonna try to formally prove this.
Oh no, I mean, you're right.
There are cases where maybe it's not quite linear,
but in general.
Well, some of it's notation too,
and some of it is style and all those kinds of things,
but within a textbook.
Within the same book.
Within the same book with the same.
Within the same book on the same subject.
Yeah.
This is what I was using.
That's hilarious.
Because you know, if it's a two page proof,
you just know this is gonna be insane, right?
That's the scary thing about insights.
You look like Andrew Wiles
working on the Fermat's Last Theorem,
is you don't know.
Something seems like a good idea,
and you have that idea,
and it feels like this is a leap,
like a totally new way to see it,
but you have no idea if it's at all useful.
Even if you think it's correct,
you have no idea if this is like going to go down a path
that's completely counterproductive
or not productive at all.
That's the crappy thing about invention,
is like I have, I'm sure you do.
I have a lot of really good ideas every single day,
but like, and I'll go inside my head along them,
along that little trajectory,
but it could be just a total waste.
And it's, you know what that feels like?
It just feels like patience is required,
not to get excited at any one thing.
So I think this is interesting
§10Transcript · 1:14:03–1:22:48
because you raised Andrew Wiles.
He spent seven years attacking the same thing, right?
And so I think that what attracts
professional researchers to this
is because even though it's very painful
that you keep fighting with something,
when you finally find the right insights
and string them together,
it feels really good, so.
Well, there's also like short term,
it feels good to, whether it's real or not,
to pretend like you've solved something
in the sense like you have an insight
and there's a sense like this might be the insight
that solves it.
So at least for me, I just enjoy that rush of positivity
even though I know statistically speaking
is probably going to be a dead end.
I'm the same way, I'm the same way.
In fact, that's how I know whether
I might want to keep thinking about this general problem.
It's like, if I still see that I'm getting some insights,
I'm not at a dead end yet.
But that's also where I learned something
from my PhD advisor.
Actually, he was a real big inspiration on my life.
His name is Benny Sudakov.
In fact, he grew up in the former Soviet Union.
He was from Georgia, but he's an incredible person.
But one thing I learned was choose the problems to work on
that might matter if you succeed.
Because that's why, for example, we dug into COVID.
It was just, well, suppose we succeed
in finding some interesting insight here.
Well, it actually matters.
That is worth a laugh.
Yeah, and I think COVID, the way you're approaching COVID
has two interesting possibilities.
One, it might help with COVID or another pandemic,
but two, I mean, just this whole network theory space,
you might unlock some deep understanding
about the interaction with human beings.
That might have nothing to do with the pandemic.
There's a space of possible impacts
that may be direct or indirect.
And the same thing is with Andrew Wiles's proof.
I don't understand, but apparently the pieces of it
are really impactful for mathematics,
even if the main theorem is not.
So along the way, the insights you have
might be really powerful for unexpected reasons.
So I like what you said.
This is something that I learned from another friend of mine.
He's a very famous researcher.
All these people are more famous than I am.
His name is Jacob Fox.
He's Jacob Fox at Stanford.
Also a very big inspiration for me.
We were both grad students together at the same time.
Well, most importantly,
you're good at selecting good friends.
Ah, yeah, well, that's the key.
You gotta find good people to learn things from.
But his thing was, he often said,
if you solve a math problem and have this math proof,
math problem for him is like a proof, right?
So suppose you came up with this proof.
He always asks, what have we learned from this
that we could potentially use for something else?
It's not just, did you solve the problem
that was supposed to be famous?
And is there something new in the course of solving this
that you had to invent
that we could now use as a tool elsewhere?
Yeah, there's this funny effect
where just looking at different fields
where people discover parallels.
They'll prove something, it'll be a totally new result.
And then somebody later realizes
this was already done 30 years ago
in another discipline, in another way.
And it's really interesting.
Now, we did this offline
in another illustration he showed to me.
It's interesting to see the different perspectives
on a problem.
It kind of points like there's just like
very few novel ideas that everything else,
that most of us are just looking at different perspective
on the same idea.
And it makes you wonder this old silly question
that I have to ask you is,
do you think mathematics is discovered or invented?
Do you think we're creating new idea?
Are we building a set of knowledge
that's distinct from reality?
Or are we actually like,
is math almost like a shovel
where we're digging to like this core set of truths
that were always there all along?
So I personally feel like it's discovered.
But that's also because I guess the way that
I like to choose what questions to work on
are questions that maybe we'll get to learn something about
why is this hard?
I mean, I'm often attracted to questions
that look simple, but are hard, right?
And what could you possibly learn from that?
Sort of like probably the attraction
of Fermat's last theorem, as you mentioned,
simple statement, why is it so hard?
So I'm more on the discovered side.
And I also feel like if we ever ran into
an intelligent other species in the universe,
probably if we compared notes,
there might be some similarities between both of us
realizing that pi is important.
Because you might say, why, why humans,
do humans like circles more than others?
I think stars also like circles.
I think planets like circles.
They're not perfect circles,
but nevertheless, the concept of a circle
is just point and constant distance.
Doesn't get any simpler than that.
It's possible that like an alien species
will have, depending on different cognitive capabilities
and different perception systems,
will be able to see things
that are much different than circles.
And so if it's discovered,
it will still be pointing at a lot of same
geometrical concepts, mathematical concepts,
but it's interesting to think of how many things
we would have to still align,
not just based on notation, but based on understanding,
like just like some basic mathematical concepts,
like how much work is there going to be
in trying to find a common language?
I mean, this is, I think Stephen Wolfram and his son
helped with the movie Arrival,
like the developing an alien language,
like how would aliens communicate with humans?
It's fascinating,
because like math seems to be the most promising thing,
but even like math,
like how do you visualize mathematical ideas?
It feels like there has to be an interactive component,
just like we have a conversation.
There has to be, this is something we don't,
I think, think about often, which is like,
with somebody who doesn't know anything about math,
doesn't know anything about English
or any other natural language,
how would we describe,
we talked offline about visual proofs.
How would we, through visual proofs, have a conversation
where we say something, here's the concept,
the way we see it, does that make sense to you?
And like, can you mess with that concept
to make it sense for you?
And then go back and forth in this kind of way.
So purely through mathematics,
I'm sure it's possible to have those kinds of experiments
with like tribes on earth that don't,
there's no common language.
Through math, like draw a circle
and see what they do with it, right?
Do some of these visual proofs,
like the summation of the odds and adds up to the squares.
Yes, I wonder how difficult that is
before one or the other species murders themselves.
That's a good question.
I hope that the curiosity for knowledge
will overpower the greedy,
this is back to our game theory thing,
that the curiosity of like discovering math together
will overpower the desire for resources
and ultimately like willing to commit violence
in order to gain those resources.
I think as we progress,
become more and more intelligent as a species,
I'm hoping we would value more and more of the knowledge
because we'll come up with clever ways
to gain more resources so we won't be so resource starved.
I don't know.
That's a hopeful message for when we finally meet aliens.
Yeah, yeah.
The cool thing about the Math Olympiad,
I don't know if you know work from Francois Chollet
from Google, he came up with this kind of IQ test slash,
it kind of has similar aspects to it
that also the Math Olympiad does for AI.
So he came up with these tests
where they're very simple for humans,
but very difficult for AI to illustrate exactly
why we're just not good at seeing a totally new problem.
Sorry, AI systems are not good at looking at a new problem
that requires you to detect
that there's a symmetry of some kind,
§11Transcript · 1:22:48–1:31:15
or there's a pattern that hasn't seen before.
The pattern is like obvious to us humans,
but it's not so obvious to find that kind of,
you're inventing a pattern that's there
in order to then find a solution.
I don't know if you can comment on that.
If you can comment on, but from an AI perspective
and from a math problem perspective,
what do you think is intelligence?
What do you think is the thing
that allows us to solve that problem?
And how hard is it to build a machine to do that?
Asking for a friend.
Yeah.
So I guess, you see,
because if I just think of the raw search space, it's huge.
That's why you can't do it.
And if I think about what makes somebody
good at doing these things, they have this heuristic sense.
It's almost like a good chess player of saying,
let's not keep analyzing down this way
because there's some heuristic reason
why that's a bad way to go.
Where did they get that heuristic from?
Now, that's a good question.
I don't know.
Because that, if you asked them to explain to you,
they could probably say something in words
that sounds like it makes sense,
but I'm guessing that's only a part
of what's really going on in their brain
of evaluating that position.
You know what I mean?
If you ask Gary Kasparov, what is good,
or why is this position good, he will say something,
but probably not approximating everything
that's going on inside.
So there's basically a function being computed,
but it's hard to articulate what that function is.
Now, the question is, could a computer get as good
at computing these kinds of heuristic functions?
Maybe.
I'm not enough of an expert to understand,
but one bit of me has always been a little bit curious
of whether or not the human brain has a particular tendency
due to its wiring to come up with certain kinds of things,
which is just natural due to the way
that the topology of the neurons and whatever is there,
for which if you tried to just build from scratch
a computer to do it,
would it naturally have different tendencies?
I don't know.
This is just me being completely ignorant
and just saying a few ideas.
Well, this is a good thing that mathematics shows
is we don't have to be,
so math and physics or mathematical physics
operates in a world that's different
than our descendants of eight brains operate in.
So it allows us to have multiple, many, many dimensions.
It allows us to work on weird surfaces.
I would like topology as a discipline is just weird to me.
It's really complicated,
but it allows us to work in that space,
the differential geometry and all those kinds of things
where it's totally outside of our natural day to day
four dimensional experience,
3D dimensional with time experience.
So math gives me hope that we can discover
the processes of intelligence outside the limited nature
of our own human experiences.
But you said that you're not an expert.
It's kind of funny.
I find that we know so little about intelligence
that I honestly think like almost children are more expert
at creating artificial intelligence systems than adults.
I feel like we know so little,
we really need to think outside the box.
And those little,
I found people should check out
Francois Chollet's little exams,
but even just solving math problems,
I don't know if you've ever done this for yourself,
but when you solve a math problem,
you kind of then trace back and try to figure out
where did that idea come from?
Like what was I visualizing in my head?
How did I start visualizing it that way?
Why did I start rotating that cube in my head in that way?
Like what is that?
If I were to try to build a program that does that,
where did that come from?
So this is interesting.
So I try to do this to teach middle school students
how to learn how to create and think and invent.
And the way I do it
is there are these math competition problems
and I'm working in collaboration
with the people who run those.
And I will turn on my YouTube live
and for the first time,
look at those questions and live solve them.
The reason I do this is to let the middle school students
and the high school students and the adults
whoever wants to watch,
just see what exactly goes on through someone's head
as they go and attempt to invent what they need to do
to solve the question.
So I've actually thought about that.
I think that, first of all, as a teacher,
I think about that because whenever I want to explain
to a student how to do something,
I want to explain how it made sense,
why it's intuitive to do the following things
and why the wrong things are wrong.
Not just why this one short fast way,
well, why this is the right way, if that makes sense.
So my point is I'm actually always thinking about that.
Like how would you think about these things?
And then I eventually decided the easiest way
to expose this would just be to go live on YouTube
and just say, I've never seen any of these questions before.
Here we go.
Don't you get, that's anxiety inducing for me.
Don't you get trapped in a kind of like little dead ends
of confusion, even on middle school problems?
Yes, that's what the comments are for.
The live comments come in and students say, try this.
Oh wow.
It's actually pretty good.
And I'll never get stuck.
I mean, I'm willing to go on camera and say,
guess what, Potion Dough can't do this.
That's fine.
But then what ends up happening is you will then see
how maybe somebody saying something and I look at the chat
and I say, aha, that actually looks useful.
Now that also shows how not all ideas,
not all suggestions are the same power, if that makes sense.
Because if I actually do get stuck,
I'll go fishing through the chat, if you've got any ideas.
I don't know if you can speak to this,
but is there a moment for the middle school students,
maybe high school as well,
where there's like a turning point for them
where they maybe fall in love with mathematics
or they get it?
Is there something to be said about like discovering
that moment and trying to grab them to get them
to understand that mathematics is something,
no matter what they wanna do in life
could be part of their life?
Yes.
I actually do think that the middle school
is exactly the right time
because that's the place
where your mathematical understanding
gets just sophisticated enough
that you can start doing interesting things.
Because if you're early on and counting,
I'm honestly not very good at teaching you new insights.
My wife is pretty good at that.
But somehow once you get to this part
where you know what a fraction is
and when you know how to add and how to multiply
and what the area of a triangle is,
at that point to me, the whole world opens up
and you can start observing
there are really nifty coincidences,
the things that made the Greek mathematicians
and the ancient mathematicians excited.
Actually back then it was exciting
to discover the Pythagorean theorem.
It wasn't just homework.
So is there,
which discipline do you think
has the most exciting coincidences?
So is it geometry?
Is it algebra?
Or is it calculus?
Well, you see, you're asking me
and I'm the guy who gets the most excited
when the combinatorics shows up in the geometry.
Is it, okay.
So it's the combinatorics in the geometry.
So first of all, the nice thing about geometry,
this is the same nice thing about computer vision
is it's visual.
So geometry, you can draw circles and triangles and stuff.
So it naturally presents itself
to the visual proof, right?
But also the nice thing about geometry,
I think for me is the earliest class,
the earliest discipline where there's,
that's most amenable to the exploration,
the invention through proofs.
The idea of proofs I think is most easily shown in geometry
because it's so visual, I guess.
So that to me is like,
if I were to think about
§12Transcript · 1:31:15–1:39:02
when I first fell in love with math, it would be geometry.
And sadly enough, that's not used.
Geometry only has a little,
appears briefly in the journey of a student.
And it kind of disappears.
And not until much later,
which there may be like differential geometry,
I don't know where else it shows up.
For me in computer science,
like you could start to think about
like computational geometry or even graph theory
as a kind of geometry.
You could start to think about it visually,
although it's pretty tricky.
But yeah, it was always,
that was the most beautiful one.
Everything else, I guess calculus can be kind of visual too.
That can be pretty beautiful.
But is there something you try to look for in the student
to see like, how can I inspire them at this moment?
Or is this like individual student to student?
Is there something you could say there?
So first of all,
I really think that every student
can pick up all of this skill.
I really do think so.
I don't think it's something only for a few.
And so if I'm looking for a student,
actually oftentimes what I'm,
if I'm looking at a particular student,
the question is,
how can we help you feel like
you have the power to invent also?
Because I think a lot of people
are used to thinking about math
as something where the teacher will show you what to do
and then you will do it.
Yes.
So I think that the key is to show that they have some,
let them see that they have some power to invent.
And at that point,
it's often starting by trying to give a question
that they don't know how to do.
You want to find these questions
that they don't know how to do,
that they can think about,
and then they can solve.
And then suddenly they say,
my gosh, I've had a situation,
I've had an experience where I didn't know what to do.
And after a while, I did.
Is there advice you can give on how to learn math
for people, whether it's a middle school,
whether it's somebody as an adult
kind of gave up on math maybe early on?
I actually think that these math competition problems,
middle school and high school are really good.
They're actually very hard.
So if you haven't had this kind of experience before
and you grab a middle school math competition problem
from the state level,
which is used to decide who represents the state
in the country, in the United States, for example,
those are pretty tricky.
And even if you are a professional,
maybe not doing mathematical things
and you're not a middle school student, you'll struggle.
So I find that these things really do teach you things
by trying to work on these questions.
Is there a Googleable term that you could use
for the organization, for the state competitions?
Ah, yeah.
So there are a number of different ones
that are quite popular.
One of them is called Math Counts, M A T H C O U N T S.
And that's a big tournament,
which actually has a state level.
There's also a mathleague.org,
mathleague, L E A G U E dot org,
also has this kind of tiered tournament structure.
There's also the American math competitions, AMC 8.
AMC also has AMC 10, that's for 10th grade and below
and AMC 12.
These are all run by the Mathematical Association
of America.
And these are all ways to find old questions.
What about the daily challenges that you run?
What are those about?
We do that too.
But I mean, the difference was ours isn't,
that one's not free.
So I should actually probably be careful.
The things that I've just mentioned are also not free.
Not all of those things I mentioned just now
are free either.
Well, people can figure out what is free and what's not,
but this is really nice to know what's out there.
But can you speak a little bit to the daily challenges?
Sure, sure.
So that's actually what we did when,
I guess I was thinking about,
how would I try to develop that skill in people
if we had the power to architect the entire system ourselves?
So that's called the daily challenge with Po Shan Luo.
It's not free because that's actually how I pay
for everything else I do.
So that was the idea.
But the concept was, aha, now let's invent from scratch.
So if we're gonna go from scratch
and we're gonna use technology,
what if we made every single lesson
something where first I say,
hey, here's an interesting question.
Recorded, of course, not live.
But it's like, I say,
hey, here's an interesting question.
Why don't we think about this?
But I know you don't know how to do it.
So now you think,
and a minute later a hint pops on the screen.
But you still think.
And a minute later a big hint pops on the screen.
You still think.
And then finally, after the three minutes,
hopefully you got some ideas you tried to answer.
And then suddenly there's like this
pretty extended explanation of,
oh yeah, so here's like multiple different ways
that you can do the question.
And by accident, you also just learned this other concept.
That's what we did.
So yeah.
Is this targeted towards middle school students,
high school students?
It's targeted towards middle school students
with competitions.
But there's a lot of high school students
who didn't do competitions in middle school
where they would also learn how to think.
If you can see the whole concept was,
can we teach people how to think?
How would you do that?
You need to give people the chance to,
on their own, invent without that kid in the front row
answering every question in two seconds.
And people can find it, I think, what daily.
It's daily.potionlo.com.
But if you go to find my website,
you'll be able to find it.
Beautiful.
Can we zoom out a little bit in the,
so day to day, week to week, month to month,
year to year, what does the lifelong educational process
look like, do you think?
For yourself, but for me,
what would you recommend in the world of mathematics
or sort of as opposed to studying for a test,
but just like lifelong expanding of knowledge
in that skill for invention?
I think I often articulate this as,
can you always try to do more than you could do in the past?
Yeah.
But that comes in many ways.
And I will say it's great
if one wants to build that with mathematics,
but it's also great to use that philosophy
with all other things.
In fact, if I just think of myself, I just think,
what do I know now that I didn't know a year ago
or a month ago or a week ago?
And not just know,
but what do I have the capability of doing?
And if you just have that attitude, it brings more.
See, the thing is, there's also a habit,
like it is a skill, like I've been using Anki,
it's an app for helps you memorize things.
And I've actually, a few months ago,
started doing this daily of setting aside time
to think about an idea that's outside of my work.
Like, let's say, it's all over the place, by the way,
but let's say politics, like gun control.
Is it good to have a lot of guns or not in society?
And just, I've set aside time every day,
I do at least 10 minutes, but I try to do 30,
where I think about a problem.
And I kind of outline it for myself from scratch,
from not looking anything up,
just thinking about it, using common sense.
And I think the practice of that is really important.
It's the daily routine of it, it's the discipline of it.
It's not just that I figured something out
from thinking about gun control,
it's more that that muscle is built too,
it's that thinking muscle.
So I'm kind of interested in, you know, math has,
because especially because I've gotten specialized
into machine learning,
and because I love programming so much,
I've lost touch with math a little bit
to where I feel quite sad about it,
§13Transcript · 1:39:02–1:47:17
and I want to fix that.
Even just not math, like pure knowledge math,
but math, like these middle school problems,
the challenges, right?
Is that something you see a person
be able to do every single day,
kind of just practice every single day for years?
So I can give an answer to that,
that gives a practical way you could do it,
assuming you have kids.
So, no, you can do it yourself.
Step one, get kids.
No, no, I'm just saying this
because I'm just thinking out loud right now,
what could I do to suggest?
Because what I have noticed is that, for example,
if you do have kids who are in elementary school
or middle school, if you yourself go and look
at those middle school math problems
to think about interesting ways
that you can teach your elementary school
or middle school kid, it works.
That's what my wife did.
She never did any of those contests before,
but now she knows quite a lot about them.
And I didn't teach her anything.
I don't do that.
She just was messing around with them
and taught herself all of that stuff.
And that had the automatic daily.
I'm always thinking, how do you make it practical, right?
And the way to make it practical
is if the timer on the automatically daily
is that you are going to automatically daily
do something with your own kid.
Now it feeds back.
And that includes the whole lesson
that if you wanna learn something, you should teach it.
Oh, I strongly believe that.
I strongly believe that.
So I currently don't have kids.
So that's, maybe I should just get kids
to help me with the math thing.
But outside of that,
I do want to do great math into daily practice.
So I'll definitely check out the daily challenges
and see, because what is it?
Grant Sanderson, we talked about offline,
the three blue and brown.
He speaks to this as well,
that his videos aren't necessarily,
they don't speak to the thing that I'm referring to,
which is the daily practice.
They're more almost tools of inspiration.
They kind of show you the beauty
of a particular problem in mathematics,
but they're not a daily ritual.
And I'm in search of that daily ritual mathematics.
It's not trivial to find,
but I hope to find that
because I think math gives you a perspective on the world
that enriches everything else.
So I like what you said about the daily also,
because that's also one reason
why I put my Carnegie Mellon class online.
It's not every day.
It's every other day.
Semester is almost over.
But the idea was, I guess my philosophy was,
if I'm already doing the class,
let's just put it there, right?
But I do know that there are people
who have been following it,
who are not in my class at all,
who have just been following it because,
yes, it's combinatorics.
And the value of that is you could,
you don't really need to know calculus to follow it,
if that makes sense.
So it's actually something that people could follow.
So again, and that one's free.
So that one's just there on YouTube.
Well, speaking of combinatorics,
what is it, what do you find interesting,
what do you find beautiful about combinatorics?
So combinatorics to me is the study of things
where they might be more finite and more discreet.
What I mean is like, if I look at a network,
actually a lot of times the combinatorics
will boil down to something,
and the combinatorics I think about
might be something related to graphs or networks.
And they're very discreet because if you have a node,
it's not that you have 0.7 of a node
and 0.3 of a node over there.
It's that you've got one node,
and then you jump one step to go to the next node.
So that notion is different from say, calculus,
which is very continuous,
where you go and say, I have this speed,
which is changing over time.
And now what's the distance I've traveled?
That's the notion of an integral,
where you have to think of subdividing time
into very, very small pieces.
So the kinds of things that you do
when you reason about these finite discreet structures
often might be iterative, algorithmic, inductive.
These are ideas where I go from one step to the next step
and so on and make progress.
I guess I actually personally like all kinds of math.
My area of research just ended up in here
because I met a really interesting PhD advisor,
potential, that's honestly the reason
I went into that direction.
I met a really interesting guy.
He seemed like he did good stuff, interesting stuff,
and he looked like he cared about students.
And I said, let me just go and learn whatever you do,
even though my prior practice and preparation
before my PhD was not combinatorics,
but analysis, the continuous stuff.
So the annoying thing about combinatorics
and discreet stuff is it's often really difficult to solve
from a sort of running time complexity perspective.
Could you speak to the idea of complexity analysis
of problems, do you find it useful, do you find it interesting?
Do you find that lens of studying the difficulty
of how difficult the computer science problem is
a useful lens onto the world?
Oh, very much so.
Because if you want to make something practical
which has large numbers of people using it,
the computational complexity to me is almost question one.
And that's, again, that's at the origin
of when we started doing this stuff with disease control.
From the very beginning, the deep questions
that were running through my mind were,
would we be able to support a large population
with only one server?
And if the answer is no, we can't start
because I don't have enough money.
Yeah, and there the question is very much
linear time versus anything slower than linear time.
As a very specific thing, you have a bunch
of really interesting papers.
If I could ask, maybe we could pull out some cool insights
at the high level.
Can you describe the data structure of a voting tree
and what are some interesting results on it?
You have a paper that I noticed on it.
Yeah, so this is an example of, I guess,
how in math we might say here's an interesting
kind of a question that we just can't seem
to understand enough about.
Maybe there's something else going on here.
And the way to describe this is you could imagine
trying to hold elections where if you have
only two candidates, that's kind of easy.
You just run them against each other
and see who gets more votes.
But as you know, once you have more candidates,
it's very difficult to decide who wins the election.
And there's an entire voting theory around this.
So a theoretical question became,
what if you made like a system of runoffs,
like a system of head to head contests,
which is structured like a tree,
almost looking like a circuit.
I'm using that way of thinking because it's sort of like
in electrical engineering or computer science,
you might imagine having a bunch of leads
that carry signal, which are going through AND gates
and OR gates and whatnot.
And you've managed to compute beautiful things.
This is just from a purely abstract point of view.
What if the inputs are candidates?
And for every two candidates, it is known
which of the candidates is more popular than the other.
Now can you build some kind of a circuit board
which says, first candidate number four
will play against five and see who wins and so on.
Okay, so now what would be a nice outcome, right?
This is a general question of,
could I make a big circuit board to feed an election into?
Like maybe one nice outcome would be whoever wins
at least is preferred over a lot of people.
Yes.
So for example, if you ran in 1,024 candidates,
ideally we would like a guarantee that says
that the winner beats a lot of people.
Actually in any system where there are 1,024 candidates,
there's always a candidate who beats
at least 512 of the others.
This is a mathematical fact
that there's actually always a person who beats
at least half of the other people.
I'm trying to make sense of that mathematical fact.
Is this supposed to be obvious?
No, but I can explain it.
§14Transcript · 1:47:17–1:54:44
No, I can't.
The way it works is that, think of it this way.
Every time I think, imagine I have all these candidates
and everyone is competing,
everyone is like compared with everyone else at some point.
Well, think of it this way.
Whenever there's a comparison, somebody gets a point.
That's the one who is better than the other one.
My claim is there's somebody whose score
is at least half of how many other people there are.
Yeah, I'm just trying to,
like my intuition is very close to that being true,
but it's beautiful.
I didn't at first, that's not an obvious fact.
No, it's not.
And it feels like a beautiful fact.
Well, let me explain it this way.
Imagine that for every match,
you didn't give one point, but you gave two points.
You gave one point to each person.
Now that's not what we're really doing.
We really want to give one point to the winner of the match,
but instead we'll just give two.
If you gave two points to everyone on every matchup,
actually everyone has the same number of points.
And the number of points they get
is how many other people there are.
Does that sort of make sense?
I'm just like saying.
No, no, everything you're saying makes perfect sense.
So the point is if for every comparison between two people,
which I'm doing for every two people,
I gave one point to each person,
your score, everyone's score is the same.
It's how many other people there are.
Now we only make one change.
For each matchup, you give one point only to the winner.
So we're awarding half the points.
So now the deal is if in the original situation,
everyone's score was equal,
which is how many other people there are.
Now there's only half the number of points to go around.
So what ends up happening is that
there's always going to be,
like the average number of points per person
is going to be half of how many other people there are.
And somebody is gonna be above average.
Somebody is going to be above that.
At least average.
Yeah, this is this notion of expected value,
that if I have a random variable,
which has an expected value,
there's going to be some possibility
in the probability space
where you're at least as big as the expected value.
Yeah, when you describe it like that, it's obvious.
But when you're first saying in this little circuit
that there's going to be one candidate better than half,
that's not obvious.
Yeah, it's not obvious.
It's funny.
It's not obvious.
Math, this is nice.
Okay, so you have this,
but ultimately you're trying to with a voting tree,
I don't know if you're trying this,
but to have a circuit that's like, that's small.
Well, you'd like it to be small.
That achieves the same kind of,
I mean, the smaller it is,
if we look at practically speaking,
the lower the cost of running the election,
of running through, of computing the circuit.
That is true.
But actually at this point,
the reason the question was interesting
is because there was no good guarantee
that the winner of that circuit
would have like have beaten a lot of people.
Let me give an example.
The best known circuit,
when we started thinking about this,
was the circuit called candidate one
plays against candidate two,
candidate three plays against four,
and then the winners play against each other.
And then by the way, five plays against six,
seven against eight, the winners play against each other.
You understand, it's like a giant binary tree.
Yeah, it's a binary, like a balanced binary tree.
It's a balanced binary tree.
One, two, three, four, up to 1,024,
everyone going up to find the winner.
Well, you know what?
There's a system in the world
where it could just be
that there's a candidate called number one,
that just beats like 10 other people,
just the 10 that they need to be on their way up
and they lose to everyone else.
But somehow they would get all the way up.
My point is it is possible to outsmart that circuit
in one weird way of the world,
which makes that circuit a bad one
because you want to say,
I will use this circuit for all elections.
And you might have a system of inputs that go in there
where the winner only beat 10 other people,
which is the people they had to beat on the way up.
So you want to have a circuit where there's as many,
like the final result is as strong as possible.
Yes.
And so what ideas do you have for that?
So we actually only managed to improve it
to square root of N.
So if N is number of vertices,
N over two would be the ideal.
We got it to square root of N.
Versus log base two.
Yeah, exactly.
Yeah.
Which is...
Well, that is halfway.
It could be a lot.
Yeah.
Could be a big improvement.
So that's a, okay, cool.
Is there something you can say with words
about what kind of circuit, what that looks like?
I can give an idea of one of the tools inside,
but the actual execution ends up being more complicated.
But one of the widgets inside this
is building a system where you have like a candidate
who plays, like one part of the whole huge, huge tree
is that that same candidate, let's call them seven.
Seven plays against somebody,
let's make up some numbers.
Let's call the others like letters.
So seven plays against A.
Seven's also gonna play against B separately.
And the winners of each of those will play each other.
By the way, seven's also gonna play C.
Seven's gonna play D.
And the winners are gonna play each other.
And the winners are gonna play each other.
We call this seven against all.
Well, seven against like everyone from a bunch of.
Got it.
So there's some nice overlap between the matchups
that somehow has a nice feature to it.
Yes, and I can tell you the nice feature
because if at the base of this giant tree,
at the base of this giant circuit,
like this is a widget.
We build the things out of widgets.
So I'm just describing one widget.
But in the base of this widget,
you have lots of things which are seven against someone,
seven against someone, seven against someone.
In fact, every matchup at the bottom
is seven against someone.
What that means is
if seven actually beat everyone they were matched up against,
well, seven would rise to the top.
So one possibility is if you see a seven
emerge from the top,
you know that seven actually beat everyone
they were against.
On the other hand, if anyone else is on top,
let's call it F.
If F is on top, how did F get there?
Well, F beat seven on the way at the beginning.
So the point is the outcome of this circuit
has a certain property.
If you see a seven,
you know that the seven actually beat a person
but the seven actually beat a bazillion people.
If you see anyone else,
at least you know they beat seven.
Yeah, then you can prove that it has a nice property.
That's really interesting.
Is there something you can say,
perhaps going completely outside
of what we're talking about,
is how we may
have mathematical ideas
of improving the electoral process?
That one, no.
No, I can't give you that one.
I mean, is there, like, do you ever see it as,
do you see as there being a lot of opportunities
for improving how we vote?
Like from your, I don't know if you saw parallels,
but, you know, it seems like if,
this actually kind of maps to your sort of COVID work,
which is there's a network effect, right?
It seems like we should be able to apply similar kind
of effects of how we decide other things in our lives.
And one of the big decisions we'll make
is who represents us in government.
§15Transcript · 1:54:44–2:01:32
Do you ever think about like mathematically
about those kinds of systems?
I think a little bit about those,
because where I went to college,
the way we voted for student government
was based on this, is it called ranked choice?
Where you eliminate the bottom
and there was runoff elections.
So that was the first time I ever saw that.
And I thought that made sense.
The only problem is it doesn't seem so easy
to get something that makes sense adopted
as the new voting system.
That's a whole nother, that's not a math solution.
That's a, well, it's math in the sense that it's game theory.
So you have to come up with incentive,
it's mechanism design.
You have to figure out how to trick us
despite our basic human nature
to adopt solutions that are better.
That's a whole nother conversation, I think.
Can you just, cause it sounded really cool,
talk a little bit about stochastic coalescence
and you have a paper on showing that,
so you could describe what it is,
but I guess it's a super linear, super logarithmic time
and you came up with some kind of trick
that make it faster.
Can you just talk about it a little bit?
Yeah, so this was something which came up
when I was at Microsoft Research for a summer.
And I'm putting that context because that shows
that it has some practical motivation at some point.
Actually, I think it's still.
It doesn't need to.
It doesn't need to.
It can be beautiful and it's all right.
Yeah, so the easiest way to describe this is
suppose you got like a big crowd of people
and everybody knows how many hours of sleep
they got last night.
And you wanna know how many total hours of sleep
were gotten by this big crowd of people.
At the beginning, you might say,
that sounds like a linear time algorithm
of saying, hey, how many hours you got?
How many you got?
How many you got?
Add, add, add.
But there's a way to do this
if you remember that there are people
and they presumably know how to add.
You could make a distributed algorithm
to make this happen.
For example, while we're thinking of these trees,
imagine you had 1,024 people.
If you could just say, hey, person number one
and person number two, you will add your hours of sleep.
Person number two will go away
and person number one is gonna remember the sum.
Person three and four add up
and person three takes charge of remembering it.
Person four goes away.
Now this like person one knows the sum of these two.
Person three knows the sum of those two.
They talk.
You see what I mean?
You're going up this tree,
same tree that we talked about earlier.
Built up a tree from the bottom up.
Yeah, build up a tree from the bottom up.
And the beautiful thing is
since everyone's doing stuff in parallel,
the amount of time it takes to get the total sum
is actually just the number of layers in the tree,
which is 10.
So now that's logarithmic time
to add up the number of hours that people slept today.
Sounds fantastic.
There's only one problem.
How do you decide who's person number one
and person number two?
Yes.
So if, for example, you just went out into the downtown
and said, hey, get these thousand people, go.
Well, if you're gonna go and say,
and by the way, you're one and you're two and you're three,
that's linear time.
Yes.
That's cheating.
So now the question is how to do this
in a distributed way.
And there were some people who proposed
a very elegant algorithm and they wanted to analyze it.
So I came in onto the analyze side,
but the elegant algorithm was like this.
It was like, well, we don't actually know
what this big tree is.
There isn't any big tree.
So what's gonna happen is first,
everyone is going to decide right now.
Oh, one important thing.
Everyone is going to,
at the very beginning of the whole game,
they will have delegated responsibility to themselves
as the one who knows the sum so far.
So the point is there's gonna be,
people are all gonna have like a pointer which says,
you are the one who knows my,
you've taken care of my ticket, my number.
Yeah.
You're the representative for this particular piece
of knowledge.
And at the very beginning, you're your own representative.
The thing has to start simple, right?
So at the beginning, you're your own representative.
You're pointing to yourself, got it.
Yup, yup.
And now the way this works is that at every time step,
someone blares a ding dong on the town clock or whatever.
And each person flips a coin themselves to decide,
am I going to hunt for somebody to give my number to
and let them represent me?
Or am I going to sit here and wait for someone to come?
Okay.
Okay.
Well, they flipped their coin.
Some of the people start asking other people saying,
hey, I would like you to be my representative.
Here is my number.
But the problem is that there's limited bandwidth
of the people who are getting asked.
It's like, you can't get,
you can't go out to prom with five people.
But this is not what we're doing.
We're adding numbers, okay?
But you can only add one number.
So the person who has suddenly gotten asked
by all these people,
well, they'll have to decide who they're going
to take it from.
And they randomly just choose one.
When they randomly choose one,
all the others are rejected
and they don't get to delegate anything in that round.
But now if this person has absorbed this one who said,
okay, here, you take charge of my number.
This person now updates their pointer.
You're in charge.
And this person adds the two numbers.
That was the first round.
In the next round, when they do the coin flipping,
this person doesn't flip anymore
because they're just delegating.
It's that anyone who has the pointers themselves,
that's like a person who is in charge
of some number of informations,
they flip the coin to decide,
should I find other people who are agents?
Or should I wait for people to ask me?
Yes.
Brilliant.
This is somebody else's idea.
And then now the idea is, okay,
if you just keep doing this process,
what ends up happening?
Oh yeah, and also by the way,
if you decide that you want to go reach out
to other people, here's the catch.
When you're one of these agents saying,
okay, I'm going to go look for someone.
You have no idea who in this crowd is an agent
or somebody who delegated it to someone else.
You just pick a random person.
When you pick the random person,
if it lands on someone and the person says,
oh, I actually delegated it to someone,
then you follow the point.
You walk up the delegation chain.
Walk up the delegation chain.
And you can do like path compression in the algorithm
to make it so you don't consistently
do lots of walking up.
But the bottom line is that what ends up happening
is that you end up reaching out.
Whenever you're one of the ones reaching out,
you can think of it as each agent is responsible
for some number of people.
It's almost like they're the leader of a bunch.
As the process is evolving, you have these lumps.
Each lump has an agent.
And when the agent reaches out,
they reach out to another lump
where the probability of them hitting that lump
is proportional to the size of the lump.
That is the one funny thing about this process.
This is not that they can reach out
to a uniformly random lump
where every lump has the same chance
of getting reached out to.
§16Transcript · 2:01:32–2:10:16
The bigger the lump is,
the more likely it is that you end up reaching that lump.
Which is a problem?
Let me explain why that's a problem.
Because you see, you're hoping
that this has a small number of steps,
but here's a bad situation that could happen.
Imagine if you had like,
there are n people that you're adding up.
Imagine that you have exactly square root of n lumps left,
of which almost all of them are just one person
who's still their own boss, their own manager.
Except one giant one.
Now what's gonna happen?
It's gonna be a huge bottleneck
because every round the giant one
can only absorb one of the others.
And now you suddenly have time
which is about square root of n.
The square root of n is chosen
because that is one where the lumps are such
that you really are limited by this large one
slowly sucking up the rest of them.
So the heart of the question became,
well, but is that just so unusual
that it doesn't usually happen?
Because remember you start with everyone
just being independent.
It's like a lot of lumps of size one.
How naturally do the big lumps emerge?
Yes.
And so what that heart of the proof was,
was showing that that was a joint work with Eyal Lubezki.
That one was showing that actually in that thing
the lumps do kind of get out of whack.
And so it's not the purely logarithmic number of steps.
But if you make one very slight change,
which is if you are one of the agents
and you have just been propositioned,
possibly relayed along by a couple of different people.
If you just say, don't take a random one,
but accept the smallest lump.
That actually does enough to even the whole economy.
Distributes the lump size.
I mean, yeah, it's fascinating how
with the distributed algorithms,
a little adjustment can make all the difference
in the world.
Yeah.
Actually, by the way, this does,
back to our voting conversation,
this makes me think of like,
these networking systems are so fascinating to study.
They immediately spring to mind ideas
of how to have representation.
Like maybe as opposed to me voting for a president,
I want to vote for like,
for you, Paul, to represent me,
maybe on a particular issue.
And then you will delegate that further.
And then we naturally construct those kinds of networks
because that feels like I can have a good conversation
with you and figure out that you know what you're doing
and I can delegate it to you.
And in that way, construct a representative government,
a representative decision maker.
That feels really nice as opposed to like us,
like a tree of height one or something,
where it's like everybody's just,
it feels like there's a lot of room for layers
of representation to form organically from the bottom up.
I wonder if there are systems like that.
This is the cool thing about the internet
and the digital space where we're so well connected,
just like with the Novid app to distribute information
about the spread of the disease.
We can in the same way, in a distributed sense,
form anything like any kind of knowledge bases
that are formed in a decentralized way
and in a hierarchical way,
as opposed to sort of old way
where there is no mechanism for large scale,
fast distributed transactional information.
This is really interesting.
This is where almost like network graph theory,
becomes practical.
Most of that exciting work was done in the 20th century,
but most of the application will be in the 21st,
which is cool to think about.
Let me ask the most ridiculous question.
You think P equals NP?
Wow.
I don't know.
I mean, I would say,
I know there are enough people who have very strong interest
in trying to show that it is.
I'm talking about government agencies.
For security purposes.
For security purposes.
And most computer scientists,
we should say believe that P equals NP.
My question almost like,
this is back to our aliens discussion.
You want to think outside the box,
the low probability event,
what is the world,
what kind of discoveries would lead us to prove
that P does not equal to NP?
Like there could be giant misunderstandings
or gaps in our knowledge about computer science,
about theoretical computer science, about computation,
which allow us to think like flatten all problems.
Yeah, so I don't know the answer to this question.
I think it's very interesting, but I actually,
I know, let's put it this way.
By being at Carnegie Mellon
and being around the theoretical computer scientists,
I know enough about what I don't know to say.
To be humble.
I'm the wrong person to answer this question.
It's a great one.
Well, Scott Aaronson, who's now here at UT Austin,
he used to be at MIT,
puts the probability of P not equals to NP at 3%.
I always love it when you ask,
it's very rare in science and academics
because most folks are humble
in the face of the mystery,
the uncertainty of everything around us.
To have both the humor and the guts to say like,
what are the chance that there's aliens in our galaxy,
intelligent alien civilizations?
As opposed to saying, I don't know, it could be zero.
It could be, depending on the fact, you're saying it's 2.5%.
There's something very pleasant about just having,
it's the number thing.
It's powered to the number.
It's just like 42.
It's like, why 42?
I don't know, but it's a powerful number.
And then everything,
this is the power of human psychology
is once you have the number 42,
it's not that the number has meaning,
but because it's placed in a book with humor around it,
it has the meme effect of actually creating reality.
I mean, you could say that 42 has a strong contribution
of helping us colonize Mars
because it created,
it gave the whatever existential crisis to many of us,
including Elon Musk when he was young,
reading a book like that.
And then now 42 is now part of his humor
that he doesn't shut up about,
it's constantly joking about.
And that humor is spreading through our minds
and somehow this like silly number just had an effect.
In that same way, after Scott told me like the 3% chance,
it's stuck in my head.
And I think it's been having a ripple effect
in everybody else.
The believing that P is not equal to NP,
Scott almost as a joke saying it's 3%
is actually motivating a large number of researchers
to work on it.
3% is high.
It's very high.
Because for the potential impact that that would have.
But then 3% is not that high because it's only,
you know, like we're not very good.
I feel like humans are only able to really think about
like 1%, 50%.
And we kind of, I think a lot of people around 3%
up to 50% like in our minds.
Like 3% at this point.
It could happen.
It could happen.
And it could happen and it's like, yeah.
Like half the time it'll probably happen.
So we're not very good at that.
That's the other thing with the pandemic
is we're not the exponential growth
that we also talked about offline
is something that we can't quite intuit.
And that's something we probably should
if we're to predict the future, to anticipate the future
and to understand how to create technologies
that let us sort of control the future.
Can I ask you for some recommendations
maybe for books or movies in your life?
Long ago when you were baby Po or today
that you found insightful or you learned a lot from
what you would recommend to others.
Yeah.
So I think I don't necessarily have an exact name
of these old things, but I was generally inspired
by stories, true or fictional of campaigns.
For example, like the Lord of the rings, that's a campaign.
But the thing that always inspired me was
it could be possible for somebody who's crazy enough
§17Transcript · 2:10:16–2:18:54
to go up against adversity after adversity,
and it succeeds.
I mean, those are false, those are fictitious.
But I also spent a lot of time, I guess, reading about,
I don't know, I was interested somehow
in like World War II history for whatever reason.
That's a campaign which is much more brutal.
But nevertheless, the idea of difficulty, strategy,
fighting even when things,
in that case it was really fighting,
but just pushing on even when things are difficult.
I guess these are the kinds of general stories
that made me, I guess, want to work on things
that would be hard and where it could be a campaign.
It could be that you work on something for a year,
multiple years, because that was the point, I guess.
Yeah, it starts with a single person.
That's the interesting thing.
I've obviously been, don't shut up about it recently
about World War II, especially on the Hitler side
and the Stalin side.
Some of that has really affected my own family.
The roots of my family very much.
But it's interesting to think that it was just an idea
and one person decided to do stuff
and it just builds and builds and builds.
And you can truly have an impact on the world,
both horrendous and exceptionally positive and inspiring.
So yeah, it's like it's a agency of us individuals.
Sometimes we think we're just reacting to the world,
but we have the full power to actually change the world.
Is there advice you can give to young folks?
We talked, we gave a bunch of advice
on middle school, high school mathematics.
Is there more general advice you would give
about how to succeed in life,
how to learn for high school students,
for college students, career or life in general?
So I think the first one would be
to make sure that you're learning to invent
and to make sure you're not just learning how to mimic.
Because a lot of times you learn how to do X
by watching somebody do X and then repeating X
many times with different inputs.
I've just been very generic in explaining this.
But I guess this is just my own attitude towards the world.
I didn't like ever following anyone's directions exactly.
Even if you told me this is the way to do your homework
is to write in pencil, I would say,
but I think pen is nice, let's try, right?
So I've been that kind of a funny person.
But I do encourage that if you can learn how to invent
as your core skill, then you can do a lot.
But then the second piece that comes with that
is something I learned from my PhD advisor,
which was, well, make sure that what you're working on
is big enough.
And so in that sense, I usually advise to people
once they have learned how to invent,
ideally don't just try to settle for something comfortable,
try to see if you can aim for something which is hard,
which might involve a campaign, which might be important,
which might make a difference.
And it's more of, I guess, rather than worrying
what if you didn't achieve that,
there's also the regret of what if I didn't try?
See, that's how I operate.
I don't operate based on did I succeed or fail?
It was hard anyway.
If I did this novid thing and the whole thing failed,
would I feel terrible?
No, it's a very hard problem.
But would I have had the regret of not jumping in?
Yes.
So it's that different mentality of don't worry
about the failing part as much of the,
make sure you give yourself the shot
at those potentially unbounded opportunities.
You almost make it sound like there's a meaning to it all.
Let me ask the big ridiculous question.
What do you think is the meaning of life?
Or maybe the easier version of that
is what brings your life joy?
So I'll just answer that one personally.
For me, I'm a little bit weird.
I sort of, I guess you can tell by now.
See the pen and pencil discussion from earlier, yes.
Yeah, yeah.
So, I mean, my thing is, I guess I personally
just wanted to maximize a certain score,
which was for how many person years
after I'm no longer here anymore,
did what I do mattered?
Yeah.
And it didn't matter if it's necessarily attributed to me.
It's just like, did it matter?
And so that's what I wanted.
I guess that is very inspired by how scientists work.
It's like, why do we keep talking about Newton?
It's because Newton discovered some interesting things.
And so Newton's score is pretty high.
It's going to be infinity, right?
Well, let's hope it's infinity, but pretty high.
Yes, yes.
So you're going for, so person years,
you're going for like triple digits.
You're going for, so like Newton is like four digits,
probably like a thousand years or personal lifetimes.
How do you like to think, well, what are we?
Sorry, I meant people times years.
People times.
So then it's like, actually his is huge.
His is like going to be billions or trillions, trillions.
But I guess for me, I actually changed the metric
after a while.
And the reason is because you may have seen,
I found some simple way to solve quadratic equations
that is easier than every textbook.
So my score might already be not bad,
which is why I decided then let's change it
into the number of hours in the lifetimes as well.
So the way I was doing it before is that
if a person was sort of remembering or using
or appreciating what I had done
for like 10 years of their life.
Oh, I see.
That would count as 10.
I see.
So if there was one person who for 10 years remembered
or appreciated something I did,
that counts as a score of 10 and we add up overall people.
And then, and that was with the hypothesis
that the score would be very finite in the sense
that if I didn't come up with anything
that might potentially help a lot of generations
in a forever way, then your score will be finite
because at some point it's not,
people don't remember that you made like nice bottles
or something, right?
But then after the quadratic equation thing,
it was that there's some chance
that that actually might make it into textbooks.
And if it makes it in textbooks,
the chance that there'll be an easier way discovered
is actually quite small.
So in that case, then the score might get bigger.
I was just saying the score might actually already
have been achieved in a non trivial way.
I see.
Because it's fun to think about,
cause it could be different.
You can achieve a high score by a small number of people
using it for most of their lifetime
and then generations and generations.
Or you can have, if we do dissipate,
if we do split colonize, become multi planetary species,
you could have that little,
a clever way to solve differential equations,
spread through like trillions of people
as they spread throughout the galaxy.
And they would only use it each one,
a few hours in their lifetime,
but their kids will use it,
the kids of kids will use it, it will spread
and you'll have that impact in that kind of way.
Yes, so that's why I renormalized it
because I was like, well, that's kind of dumb
because what's the importance of that?
That'll save people 15 minutes.
But, so what I meant is I didn't want to count that
as the main score.
Well, I'm gonna have to try to come up
with some kind of device that everyone would want to use,
maybe to make coffee,
cause coffee seems to be the prevalent
performance enhancing chemical that everyone uses.
So I'll have to think about those kinds of metrics.
Yeah, but you see that's just giving an idea
of I guess what I found meaningful in general,
like whether or not it's like,
whether or not that quadratic thing is important or not.
The general idea was I wanted to do things
that would outlast me.
And that was what inspired me
and that's just how I choose what problems to work on.
And that's a kind of immortality is ideas
that you've invented living on long after you
in the minds of others.
And humans are ultimately not,
are like meat vehicles that carry ideas for brief
for just a few years may not be the important thing.
It might be the ideas that we carry with us
and invent new ones.
Like we get a bunch of baby ideas in our head.
We borrow them from others
and then maybe we invent a new one
and that new one might have a life of its own.
And it's fun to think about that idea
of living for many centuries to come
unless we destroy ourselves.
§18Transcript · 2:18:54–2:20:06
But maybe AI will borrow it
and we'll remember Po as like that one human
that helped us out before we of course killed him
and the rest of human civilization.
On that note, Po, this is a huge honor.
You're one of the great educators
I've ever gotten a chance to interact with.
So it's truly an honor that you would talk with me today.
It means especially a lot that you would travel a lot
to Austin to talk to me.
It really means a lot.
So thank you so much.
Keep on inspiring.
And I'm one of your many, many students.
Thank you so much for talking today.
Thank you, thank you.
It's actually a real honor for me to talk to you
and to get this chance to have this really
intellectual conversation through all of these topics.
Thanks, Po.
Thanks for listening to this conversation with Po Chenlo
and thank you to Jordan Harmer, the show,
Onnit, BetterHelp, AidSleep and Element.
Check them out in the description to support this podcast.
And now let me leave you with some words from Isaac Newton.
I can calculate the motion of heavenly bodies
but not the madness of people.
Thank you for listening and hope to see you next time.