Transcript
00:00:00 The following is a conversation with Po Shen Lou,
00:00:02 a professor of mathematics at Carnegie Mellon University,
00:00:06 national coach of the USA International Math Olympia team,
00:00:09 and founder of XP that does online education
00:00:13 of basic math and science.
00:00:15 He’s also the founder of Novid,
00:00:17 an app that takes a really interesting approach
00:00:19 to contact tracing,
00:00:20 making sure you stay completely anonymous
00:00:23 and it gives you statistical information about COVID cases
00:00:25 in your physical network of interactions.
00:00:28 So you can maintain privacy, very important,
00:00:31 and make informed decisions.
00:00:34 In my opinion,
00:00:35 we desperately needed solutions like this in early 2020.
00:00:38 And unfortunately, I think,
00:00:41 we will again need it for the next pandemic.
00:00:44 To me, solutions that require large scale,
00:00:46 distributed coordination of human beings
00:00:49 need ideas that emphasize freedom and knowledge.
00:00:53 Quick mention of our sponsors,
00:00:55 Jordan Harbinger Show, Onnit, BetterHelp,
00:00:58 Aidsleep, and Element.
00:01:01 Check them out in the description to support this podcast.
00:01:04 As a side note, let me say that Po and I
00:01:07 filmed a few short videos
00:01:08 about simple, beautiful math concepts
00:01:10 that I will release soon.
00:01:12 It was really fun.
00:01:14 I really enjoyed Po sharing his passion for math with me
00:01:16 in those videos.
00:01:17 I’m hoping to do a few more short videos
00:01:19 in the coming months that are educational in nature
00:01:23 on AI, robotics, math, science, philosophy,
00:01:26 or if all else fails,
00:01:28 just fun snippets into my life on music, books, martial arts,
00:01:32 and other random things,
00:01:34 if that’s of interest to anyone at all.
00:01:38 This is the Lex Friedman Podcast,
00:01:40 and here’s my conversation with Po Shenlow.
00:01:43 You know, you mentioned you really enjoy flying
00:01:46 and experiencing different people in different places.
00:01:49 There’s something about flying for me,
00:01:51 I don’t know if you have the same experience,
00:01:53 that every time I get on an airplane,
00:01:55 it’s incredible to me that human beings
00:01:58 have actually been able to achieve this.
00:02:00 And when I look at like what’s happening now
00:02:03 with humans traveling out into space,
00:02:06 I see it as all the same thing.
00:02:08 It’s incredible that humans are able to get into a box
00:02:11 and fly in the air and safely and land
00:02:16 in the same, it seems like,
00:02:18 and everybody’s taking it for granted.
00:02:19 So when I observe them, it’s quite fascinating
00:02:22 because I see that cleanly mapping to the world
00:02:25 where we’re now in rockets and traveling to the moon,
00:02:31 traveling to Mars, and at the same kind of way,
00:02:34 I can already see the future
00:02:36 where we will all take it for granted.
00:02:40 So I don’t know if you have,
00:02:42 you personally, when you fly,
00:02:44 have the same kind of magical experience
00:02:46 of like how the heck did humans actually accomplish this?
00:02:49 So I do, especially when there’s turbulence,
00:02:52 which is like on the way here, there was turbulence
00:02:56 and the plane jiggled, even the flight attendant
00:02:58 had to hold onto the side.
00:03:00 And I was just thinking to myself,
00:03:01 it’s amazing that this happens all the time
00:03:03 and the wings don’t fall off,
00:03:04 given how many planes are flying.
00:03:06 But then I often think about it and I’m like,
00:03:09 a long time ago, I think people didn’t trust elevators
00:03:12 in a 40 story building in New York City.
00:03:14 And now we just take it completely for granted
00:03:17 that you can step into this shaft,
00:03:18 which is 40 floors up and down, and it will just not fail.
00:03:24 Yeah, again, I’m the same way with elevators,
00:03:26 but also buildings, when I’ll stand on the 40th floor
00:03:30 and wonder how the heck are we not falling right now?
00:03:35 Like how amazing it is with the high winds,
00:03:39 like structurally, just the earthquakes and the vibrations,
00:03:42 I mean, natural vibrations in the ground.
00:03:44 Like how is this, how are all of these,
00:03:46 you go to like New York City, all of these buildings standing.
00:03:49 I mean, to me, one of the most beautiful things,
00:03:52 actually mathematically too, is bridges.
00:03:54 I used to build bridges in high school from like toothpicks,
00:03:57 just like out of the pure joy of like physics,
00:04:02 making some structure really strong.
00:04:05 Understanding like from a civil engineering perspective,
00:04:09 what kind of structure will be stronger
00:04:12 than another kind of structure, like suspension bridges.
00:04:14 And then you see that at scale,
00:04:17 humans being able to span a body of water
00:04:20 with a giant bridge.
00:04:22 And it’s, I don’t know, it’s so humbling.
00:04:26 It makes you realize how dependent we are on each other.
00:04:31 Sort of, I talk about love a lot,
00:04:33 but there’s a certain element in which we little ants
00:04:37 have just a small amount of knowledge
00:04:39 about our particular thing.
00:04:41 And then we’re depending on a network of knowledge
00:04:45 that other experts hold.
00:04:47 And then most of our lives,
00:04:49 most of the quality of life we have
00:04:51 has to do with the richness of that network of knowledge,
00:04:56 of that collaboration,
00:04:58 and then sort of the ability to build on top of it,
00:05:02 levels of abstractions.
00:05:03 You start from like bits in a computer,
00:05:05 then you can have assembly, then you can have C++,
00:05:08 or you have an operating system,
00:05:09 then you can have C++ and Python, finally,
00:05:12 some machine learning on top.
00:05:13 All of these are abstractions.
00:05:14 And eventually we’ll have AI that runs all of us humans.
00:05:17 But anyway, but speaking of abstractions and programming,
00:05:21 in high school, you wrote some impressive games
00:05:24 for MS DOS.
00:05:26 I got a chance to, in browser somehow,
00:05:28 it’s magic, I got a chance to play them.
00:05:31 Alien Attack 1, 2, 3, and 4.
00:05:34 What’s the hardest part about programming those games?
00:05:37 And maybe can you tell the story about building those games?
00:05:41 Sure.
00:05:41 I actually tried to do those in high school
00:05:44 because I was just curious if I could.
00:05:46 That’s a good starting point for anything, right?
00:05:49 Yeah, yeah, yeah, it’s like, could you?
00:05:50 But the appealing thing was also,
00:05:52 it was a soup to nuts kind of thing.
00:05:54 So something that has always attracted me is,
00:05:56 I like beautiful ideas, I like seeing beautiful ideas,
00:05:59 but I actually also like seeing execution of an idea
00:06:03 all the way from beginning to end in something that works.
00:06:06 So for example, in high school,
00:06:08 I was lucky enough to grow up in the late 90s
00:06:10 when even a high school student could hope
00:06:13 to make something sort of comparable
00:06:16 to the shareware games that were out there.
00:06:18 I say the word sort of, like still quite far away,
00:06:21 but at least I didn’t need to hire a 3D CG artist.
00:06:25 There weren’t enough pixels to draw anyway,
00:06:27 even I can draw, right?
00:06:29 Bad art, of course.
00:06:30 But the point is, I wanted to know,
00:06:31 is it possible for me to try to do those things
00:06:34 where back in those days,
00:06:36 you didn’t even have an easy way
00:06:38 to draw letters on the screen in a particular font.
00:06:41 You couldn’t just say import a font, it wasn’t like Python.
00:06:44 So for example, back then,
00:06:45 if you played those games in the web browser,
00:06:47 which is emulating the old school computer,
00:06:51 those, even the letters you see,
00:06:53 those are made by individual calls
00:06:55 to draw pixels on the screen.
00:06:56 So you built that from scratch,
00:06:58 almost building a computer graphics library from scratch?
00:07:01 Yes, the primitive that I got to use
00:07:03 was some code I copied off of a book in assembly
00:07:05 of how to put a pixel on a screen in a particular color.
00:07:08 And the programming language was Pascal?
00:07:11 Ah, yeah, the first one was in Pascal,
00:07:14 but then the other ones were in C++ after that.
00:07:18 How’s the emulation in the browser work, by the way?
00:07:20 Is that trivial?
00:07:21 Because it’s pretty cool, you get to play these games
00:07:23 that have a very much 90s feeling to them.
00:07:26 Ah, so it’s literally making an MSDOS environment,
00:07:29 which is literally running the old.exe file.
00:07:32 Wow, in the browser.
00:07:33 This is, that could be more amazing than the airplane.
00:07:37 So it wasn’t so much about the video games,
00:07:40 it was more about,
00:07:41 can you build something really cool from scratch?
00:07:44 Yes.
00:07:45 And you did a bunch of programming competitions.
00:07:50 What was your interest, your love for programming?
00:07:54 What did you learn through that experience?
00:07:56 Especially now that as much of your work
00:07:59 has taken a long journey through mathematics.
00:08:03 I think I always was amazed
00:08:04 by how computers could do things fast.
00:08:08 If I wanted to make it an abstract analysis
00:08:11 of why it is that I saw some power in the computer.
00:08:14 Because if the computer can do things
00:08:16 so many times faster than humans,
00:08:18 where the hard part is telling the computer
00:08:20 what to do and how to do it,
00:08:21 if you can master that asking the computer what to do,
00:08:25 then you could conceivably achieve more things.
00:08:28 And those contests I was in,
00:08:29 those were the opposite in some sense
00:08:31 of making a complete product, like a game is a product.
00:08:35 Those contests were effectively write a function
00:08:38 to do something extremely efficiently.
00:08:40 And if you are able to do that,
00:08:42 then you can unlock more of the power of the computer.
00:08:45 But also doing it quickly.
00:08:47 There’s a time element from the human perspective
00:08:49 to be able to program quickly.
00:08:53 There’s something nice.
00:08:54 So there’s almost like an athletics component
00:08:57 to where you’re almost like an athlete
00:09:01 seeking optimal performance as a human being
00:09:03 trying to write these programs.
00:09:05 And at the same time, it’s kind of art
00:09:07 because the best way to write a program quickly
00:09:11 is to write a simple program.
00:09:13 You just have a damn good solution.
00:09:14 So it’s not necessarily you have to type fast.
00:09:17 You have to think through a really clean,
00:09:19 beautiful solution.
00:09:22 I mean, what do you think is the use
00:09:26 of those programming competitions?
00:09:27 Do you think they’re ultimately something
00:09:29 you would recommend for students,
00:09:30 for people interested in programming,
00:09:32 or people interested in building stuff?
00:09:34 Yes, I think so because especially with the work
00:09:37 that I’ve been doing nowadays,
00:09:38 even trying to control COVID,
00:09:40 something that was very helpful from day one
00:09:42 was understanding that the kinds of computations
00:09:45 we would want to do,
00:09:47 we could conceivably do on like a four core cloud machine
00:09:50 on Amazon Web Services out to a population
00:09:53 which might have hundreds of thousands
00:09:55 or millions of people.
00:09:56 The reason why that was important
00:09:57 to have that back of the envelope calculation
00:10:00 with efficient algorithms
00:10:02 is because if we couldn’t do that,
00:10:04 then we would bankrupt ourselves
00:10:06 before we could get to a big enough scale.
00:10:08 If you think about how you grow anything from small to big,
00:10:11 if in order to grow it from small to big,
00:10:13 you also already need 10,000 cloud servers,
00:10:16 you’ll never get to big.
00:10:19 And also the nice thing about programming competitions
00:10:22 is that you actually build a thing that works.
00:10:26 So you finish it, there’s a completion thing,
00:10:29 and you realize, I think there’s a magic to it,
00:10:32 where you realize that it’s not so hard
00:10:35 to build something that works.
00:10:37 To have a system that successfully takes in inputs
00:10:40 and produces outputs and solves a difficult problem,
00:10:43 and that directly transfers to building a startup essentially
00:10:47 that can help some aspect of this world
00:10:50 as long as it’s mostly based on software engineering.
00:10:53 Things get really tricky
00:10:54 when you have to manufacture stuff.
00:10:58 That’s why people like Elon Musk are so impressive
00:11:00 that it’s not just software.
00:11:02 Tesla Autopilot is not just software.
00:11:05 It’s like you have to actually have factories
00:11:07 that build cars, and there’s like a million components
00:11:11 involved in the machinery required
00:11:14 to assemble those cars and so on.
00:11:16 But in software, one person can change the world,
00:11:19 which is incredible.
00:11:21 But on the mathematics side,
00:11:23 what, if you look back, or maybe today,
00:11:26 what made you fall in love with mathematics?
00:11:29 For me, I think I’ve always been very attracted
00:11:33 to challenge, as I already indicated
00:11:35 with writing the program.
00:11:37 I guess if I see something that’s hard
00:11:40 or supposed to be impossible,
00:11:44 sometimes I say, maybe I want to see if I can pull that off.
00:11:47 And with the mathematics, the math competitions
00:11:49 presented problems that were hard,
00:11:53 that I didn’t know how to start,
00:11:55 but for which I could conceivably try to learn
00:11:57 how to solve them.
00:11:59 So, I mean, there are other things that are hard
00:12:00 called like get something to Mars, get people to Mars.
00:12:03 And I didn’t, and I still don’t think
00:12:05 that I am able to solve that problem.
00:12:08 On the other hand, the math problems struck me
00:12:10 as things which are hard
00:12:11 and with significant amount of extra work,
00:12:13 I could figure it out.
00:12:14 And maybe they would actually even be useful,
00:12:16 like that mathematical skill is the core
00:12:18 of lots of other things.
00:12:22 That’s really interesting.
00:12:23 Maybe you could speak to that
00:12:25 because a lot of people say that math is hard
00:12:29 as a kind of negative statement.
00:12:32 It always seemed to me a little bit like
00:12:35 that’s kind of a positive statement
00:12:37 that all things that are worth having in this world,
00:12:40 they’re hard.
00:12:41 I mean, everything that people think about
00:12:44 that they would love to do, whether it’s sports,
00:12:47 whether it’s art, music, and all the sciences,
00:12:52 they’re going to be hard
00:12:54 if you want to do something special.
00:12:56 So is there something you could say to that idea
00:12:59 that math is hard?
00:13:00 Should it be made easy or should it be hard?
00:13:04 Ah, so I think maybe I want to dig in a little bit
00:13:07 onto this hard part and say,
00:13:09 I think the interesting thing about the math
00:13:12 is that you can see a question
00:13:14 that you didn’t know how to start doing it before.
00:13:18 And over a course of thinking about it,
00:13:20 you can come up with a way to solve it.
00:13:24 And so you can move from a state
00:13:25 of not being able to do something
00:13:28 to a state of being able to do something
00:13:30 where you help to take yourself through that
00:13:33 instead of somebody else spoon feeding you that technique.
00:13:37 So actually here, I’m already digging into
00:13:39 maybe part of my teaching philosophy also,
00:13:42 which is that I actually don’t want to ever
00:13:45 just tell somebody, here’s how you do something.
00:13:48 I actually prefer to say, here’s an interesting question.
00:13:52 I know you don’t quite know how to do it.
00:13:54 Do you have any ideas?
00:13:55 I’m actually explaining another way
00:13:58 that you could try to do teaching.
00:14:00 And I’m contrasting this to a method of watch me do this,
00:14:04 now practice it 20 times.
00:14:06 I’m trying to say a lot of people consider math to be hard
00:14:09 because maybe they can’t remember
00:14:10 all of the methods that were taught.
00:14:12 But for me, I look at the hardness
00:14:15 and I don’t think of it as a memory hardness.
00:14:17 I think of it as a, can you invent something hardness?
00:14:21 And I think that if we can teach more people
00:14:24 how to do that art of invention in a pure cognitive way,
00:14:28 not as hard as the actual hardware stuff, right?
00:14:31 But like in terms of the concepts
00:14:32 and the thoughts and the mathematics,
00:14:34 teaching people how to invent,
00:14:36 then suddenly actually they might not even find math
00:14:38 to be that tiresomeness hard anymore,
00:14:42 but that rewardingness hard of I have the capability
00:14:47 of looking at something which I don’t know what to do
00:14:49 and coming up with how to do it.
00:14:51 I actually think we should be doing that,
00:14:52 giving people that capability.
00:14:55 So hard in the same way that invention is hard,
00:14:58 that is ultimately rewarding.
00:14:59 So maybe you can dig in that a little bit longer,
00:15:03 which is do you see basically the way to teach math
00:15:11 is to present a problem and to give a person a chance
00:15:14 to try to invent a solution
00:15:18 with minimal amount of information first?
00:15:21 Is that basically,
00:15:22 how do you build that muscle of invention in a student?
00:15:26 Yes, so the way that,
00:15:27 I guess I have two different sort of ways
00:15:30 that I try to teach.
00:15:30 Actually, one of them is, in fact, this semester,
00:15:32 because all my classes were remotely delivered,
00:15:35 I even threw them all onto my YouTube channel.
00:15:37 So you can see how I teach at Carnegie Mellon,
00:15:39 but I’d often say, hey, everyone, let’s try to do this.
00:15:43 Any ideas?
00:15:44 And that actually changes my role as a professor
00:15:47 from a person who shows up for class
00:15:50 with a script of what I wanna talk through.
00:15:52 I actually, I don’t have a script.
00:15:54 The way I show up for classes,
00:15:55 there’s something that we want to learn how to do,
00:15:58 and we’re gonna do it by improv.
00:16:00 I’m talking about the same method as improv comedy,
00:16:02 which is where you tell me some ideas,
00:16:05 and I’ll try to yes and them.
00:16:07 You know what I mean?
00:16:09 And then together,
00:16:10 we’re gonna come up with a proof of this concept
00:16:13 where you were deeply involved in creating the proof.
00:16:16 Actually, every time I teach the class,
00:16:18 we do every proof slightly differently
00:16:19 because it’s based on how the students came up with it.
00:16:23 And that’s how I do it when I’m in person.
00:16:25 I also have another line of courses that we make
00:16:27 that is delivered online.
00:16:29 Those things are where I can’t do it live,
00:16:31 but the teaching method became also similar.
00:16:34 It was just, here’s an interesting question.
00:16:37 I know it’s out of reach.
00:16:38 Why don’t you think about it?
00:16:39 And then automatic hints.
00:16:40 We feed automatically hints through the internet
00:16:44 to go and let the person try to invent.
00:16:47 So that’s like a more rigorous prodding of invention.
00:16:52 But you did mention disease and COVID,
00:16:56 and you’ve been doing some very interesting stuff
00:16:58 from a mathematical, but also software engineering angle
00:17:01 of coming up with ideas.
00:17:04 It’s back to the, I see a problem.
00:17:07 I think I can help.
00:17:09 So you stepped into this world.
00:17:11 Can you tell me about your work there
00:17:13 under the flag of Novid
00:17:16 and both the software and the technical details
00:17:20 of how the thing works?
00:17:21 Sure, sure.
00:17:22 So first I want to make sure that I say,
00:17:24 this is actually team effort.
00:17:26 I happen to be the one speaking,
00:17:27 but there’s no way this would exist
00:17:29 without an incredible team of people
00:17:30 who inspire me every day to work on this.
00:17:33 But I’ll speak on behalf of them.
00:17:34 So the idea was indeed that we stepped forward
00:17:40 in March of last year, when the world started to become,
00:17:43 our part of the world started to become,
00:17:44 our part meaning the United States
00:17:46 started to become paralyzed by COVID.
00:17:48 The shutdown started to happen.
00:17:50 And at that time it started as a figment of an idea,
00:17:54 which was network theory,
00:17:57 which is the area of math that I work in,
00:17:59 could potentially be combined with smartphones
00:18:02 and some kind of health information anonymized.
00:18:06 Exactly how?
00:18:07 We didn’t know yet.
00:18:07 We tried to crystallize it.
00:18:09 And many months into this work,
00:18:11 we ended up accidentally discovering a new way
00:18:15 to control diseases,
00:18:17 which is now what is the main impetus of all of this work
00:18:20 is to take this idea and polish it
00:18:23 and hopefully have it be useful not only now,
00:18:25 but for future pandemics.
00:18:27 The idea is really simple to describe.
00:18:29 Actually, my main thing in the world
00:18:31 is I come up with obvious observations.
00:18:33 That’s that, so I’ll explain it now.
00:18:35 Einstein did the same thing
00:18:36 and he wrote a few short papers.
00:18:39 But so the idea is like this.
00:18:41 If we describe how usually people control disease
00:18:46 for a lot of history,
00:18:47 it was that you’d find out who was sick,
00:18:51 you’d find out who they’ve been around
00:18:53 and you try to remove all of those people from society
00:18:56 against their will.
00:18:57 Now that’s the problem.
00:18:58 The against their will part
00:19:00 gives you the wrong kind of a feedback loop,
00:19:03 which makes it hard to control the disease
00:19:05 because then the people you’re trying to control
00:19:07 keep getting other people sick.
00:19:08 You can see already how I’m thinking
00:19:10 and talking about this feedback loops.
00:19:11 This is actually related to something you said earlier
00:19:14 about even like how skyscrapers stay in the air.
00:19:17 The whole point is control theory.
00:19:19 You actually want to, or even how an airplane stays,
00:19:22 you need to have control loops
00:19:24 which are feedbacking in the right way.
00:19:27 And what we observed was that the feedback control loop
00:19:29 for controlling disease by asking people
00:19:32 to be removed from society against their will
00:19:34 was not working.
00:19:35 It was running against human incentives
00:19:37 and you suddenly are trying to control
00:19:39 seven billion, eight billion people
00:19:41 in ways that they don’t individually want
00:19:43 to necessarily do.
00:19:45 So here’s the idea.
00:19:47 And this is inspired by the fact
00:19:48 that at the core of our team
00:19:49 were user experience designers.
00:19:51 That’s actually, in fact, the first thing I knew
00:19:53 we needed when we started
00:19:54 was to bring user experience at the core.
00:19:57 Okay.
00:19:58 But so the idea was suppose hypothetically
00:20:03 there was a pandemic.
00:20:05 What would you want?
00:20:08 You would want a way to be able to live your life
00:20:10 as much as possible and avoid getting sick.
00:20:13 Can we make an app to help you avoid getting sick?
00:20:17 Notice how I’ve just articulated the problem.
00:20:19 It is not, can we make an app
00:20:21 so that after you are around somebody who’s sick
00:20:24 you can be removed from society.
00:20:27 It’s can we make an app so that you can avoid getting sick.
00:20:30 That would run a positive feed.
00:20:33 I don’t know if I want to call it positive or negative
00:20:35 but it would run a good feedback loop.
00:20:36 Okay.
00:20:37 So then how would you do this?
00:20:38 The only problem is that you don’t know who’s sick
00:20:41 because especially with this disease
00:20:44 if I see somebody who looks perfectly healthy
00:20:46 the disease spreads two days before you have any symptoms.
00:20:50 And so it’s actually not possible.
00:20:52 That’s where the network theory comes in.
00:20:54 You caught it from someone.
00:20:56 What if we changed the paradigm
00:20:59 and we said, whenever there’s a sickness
00:21:02 tell everybody how many physical relationships
00:21:06 separate them from the sickness.
00:21:08 That is the trivial idea we added.
00:21:09 The trivial idea was the distance between you and a disease
00:21:13 is not measured in feet or seconds.
00:21:16 It’s measured in terms of how many
00:21:19 close physical relationships separate you
00:21:22 like these six degrees of separation like LinkedIn.
00:21:25 Simple idea.
00:21:26 What if we told everyone that?
00:21:28 It turns out that actually unlocks
00:21:30 some interesting behavioral feedback loops
00:21:33 which for example, let me now jump to a non COVID example
00:21:37 to show why this maybe could be useful.
00:21:39 Actually we think it could be quite useful.
00:21:40 Imagine there was Ebola or some hemorrhagic fever.
00:21:44 Imagine it spread through contact through the air.
00:21:46 In fact, pretend, pretend.
00:21:50 That’s a disastrous disease.
00:21:52 It has high fatality rate.
00:21:54 And as you die, you’re bleeding out of every orifice.
00:22:00 Okay.
00:22:01 So.
00:22:02 Yeah, not pleasant.
00:22:03 Not pleasant.
00:22:04 So the question is, suppose that such a disease broke
00:22:07 who would want to install an app that would tell them
00:22:10 how many relationships away from them
00:22:12 this disease had struck?
00:22:14 Like a lot of people.
00:22:15 A lot of people.
00:22:16 In fact, almost, I don’t want to say almost everyone.
00:22:20 That’s a very strong statement
00:22:21 but a very large number of people.
00:22:22 That’s fascinating framing.
00:22:24 Like the more deadly and transmissible the disease
00:22:28 the stronger the incentive to install it in a positive sense
00:22:32 the, in the good feedback loop sense.
00:22:36 That’s a really good example.
00:22:37 It’s a really good way to frame it.
00:22:38 Cause with COVID, it was not as deadly
00:22:42 as potential pandemics could have been
00:22:45 viruses could have been.
00:22:46 So it’s sometimes muddled with how we think about it
00:22:49 but yeah, this is a really good framing.
00:22:51 If the virus was a lot more deadly
00:22:53 you want to create a system that has a set of incentives
00:22:56 that it quickly spreads to the population
00:22:59 where everybody is using it
00:23:00 and it’s contributing in a positive way to the system.
00:23:04 Exactly.
00:23:05 And actually that point you just made
00:23:06 I don’t take credit for that observation.
00:23:07 There was another person I talked to
00:23:09 who pointed out that it’s very interesting
00:23:11 that this feedback loop is even more effective
00:23:14 when the disease is worse.
00:23:16 And that’s actually not a bad characteristic to have
00:23:19 in your feedback loop
00:23:20 if you’re trying to help civilization keep running.
00:23:24 Yeah, it’s a really, it’s in this dynamic
00:23:27 like people figure out, they dynamically figure out
00:23:30 how bad the disease is.
00:23:31 The more it spreads and the deadlier it is
00:23:35 as the people observe it
00:23:37 as long as the spread of information
00:23:39 like semantic information, natural language information
00:23:43 is closely aligned with the reality of the disease
00:23:46 which is a whole nother conversation, right?
00:23:48 We, that’s, we might, maybe we’ll chat about that
00:23:51 how we sort of make sure there’s not misinformation
00:23:53 while there’s accurate information
00:23:54 but that aside, okay, so this is a really nice property.
00:23:58 Right, and just going on on that
00:24:00 actually just talking more about what that could do
00:24:02 and why we’re so excited about it.
00:24:04 It’s that not only would people want to install it
00:24:07 but what would they do if you start to see
00:24:10 that this disease is getting closer and closer?
00:24:13 We surveyed informally people
00:24:15 but they said, as we saw it getting closer, we would hide.
00:24:18 We would try to not have contacts.
00:24:21 But now you notice what this has just achieved.
00:24:24 The whole goal on this whole exercise was
00:24:27 you got the people who might be sick
00:24:29 and you got everyone else, set A and set B.
00:24:32 Set A is the people who might be sick,
00:24:33 set B is everyone else.
00:24:34 And for the entirety of the past
00:24:37 contact tracing approaches, you tried to get set A
00:24:41 to do things that might not be to their liking or their will
00:24:44 because that’s removing them from society.
00:24:47 We found out that there’s two ways
00:24:49 to separate set A from set B.
00:24:51 You can also let the people at set B
00:24:53 at the fringe of set A
00:24:55 attempt to remove themselves from this interface.
00:24:58 It’s the symmetry of A and B separation.
00:25:01 Everyone was looking at A, we look at B
00:25:04 and suddenly B is in their incentive to do so.
00:25:07 Beautiful.
00:25:08 So there’s a virus that jumps from human to human.
00:25:11 So there’s a network sometimes called graph
00:25:16 of the spread of a virus.
00:25:18 It hops from person to person to person to person.
00:25:21 And each one of us individuals are sitting
00:25:25 or plopped into that network.
00:25:28 We have close friends and relations and so on.
00:25:31 It’s kind of fascinating
00:25:32 to actually think about this network
00:25:33 and we can maybe talk about the shapes
00:25:35 of this kind of network.
00:25:37 Because I was trying to think exactly this,
00:25:39 like how many people do I,
00:25:41 well, I’m kind of an introvert, not kind of,
00:25:43 I’m very much an introvert.
00:25:45 But so can I be explicit about the kind of people
00:25:48 I meet in regular life?
00:25:50 Say when it was completely opened up, there’s no pandemic.
00:25:54 There is a kind of network and there’s maybe
00:25:59 in the graph theoretic sense, there’s some weights
00:26:02 or something about how close that relationship is
00:26:06 in terms of the frequency of visits,
00:26:08 the duration of visits and all of those kinds of things.
00:26:11 So you’re saying we might want to be,
00:26:14 to create on top of that network,
00:26:18 a spread of information to let you know
00:26:22 as the virus travels through this network,
00:26:24 how close is it getting to you?
00:26:26 And the number of hops away it is on that network
00:26:29 is really powerful information
00:26:31 that creates a positive feedback loop
00:26:33 where you can act essentially anonymously
00:26:39 and on your own.
00:26:41 Like nobody’s telling you what to do,
00:26:43 which is really important, is decentralized
00:26:46 and not whatever the opposite of authoritarian is.
00:26:52 But you get to sort of the American way.
00:26:54 You get to choose to do it yourself.
00:26:56 You have the freedom to do it yourself
00:26:58 and you’re incentivized to do it.
00:27:00 And you’re most likely going to do it
00:27:01 to protect yourself against you getting the disease
00:27:08 as the closer it gets to you
00:27:10 based on the information that you have.
00:27:12 But can you maybe elaborate, first of all, brilliant.
00:27:17 Whenever I saw the thing you’re working on,
00:27:20 so forget for COVID, this is of course,
00:27:23 really relevant for COVID, but it’s also probably relevant
00:27:26 for future diseases as well.
00:27:28 So that was the thing I’m nervous about.
00:27:30 I was like, if this whole,
00:27:31 if our society shut down because of COVID,
00:27:34 like what the heck is gonna happen
00:27:38 when there’s a much deadlier disease?
00:27:40 Like this, this is disappointing.
00:27:41 The whole time, 2020, the whole time
00:27:44 I’m just sitting like this,
00:27:45 like is the incompetence of everybody
00:27:49 except the people developing vaccines.
00:27:53 The biologists are the only ones
00:27:54 that got their stuff together.
00:27:56 But in terms of institutions and all that kind of stuff,
00:27:58 it’s just been terrible.
00:28:00 But this is exactly the power of information
00:28:04 and the power of information
00:28:05 that doesn’t limit personal freedom.
00:28:08 So your idea is brilliant.
00:28:09 Okay, mathematically, can you maybe elaborate
00:28:12 what are we talking about?
00:28:14 Like how do you actually make that work?
00:28:16 What’s involved?
00:28:17 Sure, first I’m gonna reply to something you said
00:28:19 about the freedom inside this,
00:28:22 because actually that was the idea.
00:28:24 The idea is this is game theory, right?
00:28:27 And effectively what we did is analogous
00:28:29 to free market economy, as opposed to central planning.
00:28:34 If you just line up the set of incentives correctly
00:28:38 so that people have in their purely selfish behavior
00:28:43 are contributing to the optimization of the global function,
00:28:47 that’s it.
00:28:47 And the point of what we do, I guess in mathematics
00:28:50 is we try to explore the search space
00:28:52 to go and find out as many possibilities as there are.
00:28:54 And in this case, it’s an applied search space.
00:28:58 That’s why the inputs from design,
00:29:00 user experience design and actual people are important.
00:29:02 But you asked about, I guess, the mathematical
00:29:05 or the technical things underpinning it.
00:29:07 So I think the first thing I’ll say is
00:29:09 we wanted to make this thing
00:29:12 not require your personal information.
00:29:14 And so in order to do that,
00:29:16 what gave me the confidence to, I guess,
00:29:18 lead our team to run at the beginning
00:29:20 is we saw that this could be done without using GPS information.
00:29:24 So technically what’s going on is if two smartphones,
00:29:28 it’s a smartphone app.
00:29:29 If two smartphones have this thing installed,
00:29:31 they just communicate with each other by Bluetooth
00:29:35 to go and find out how far,
00:29:38 they can detect nearby things by Bluetooth.
00:29:40 And then they can find out that these two phones
00:29:42 were approximately such and such distance apart.
00:29:44 And that kind of relative proximity information
00:29:47 is enough to construct this big network.
00:29:50 Okay, so the physical network is constructed
00:29:53 based on proximity that’s through Bluetooth
00:29:56 and you don’t have to specify your exact location,
00:29:59 it’s the proximity.
00:30:01 I’m not using the Pythagorean theorem basically.
00:30:03 I mean, if I just knew the GPS coordinates,
00:30:05 we could use the Pythagorean theorem too.
00:30:07 Sorry, that’s just how I call it.
00:30:08 Distance formula, whatever you want to call it.
00:30:10 Yeah, so we’re not doing
00:30:14 the old Pythagorean based violation of privacy.
00:30:18 Okay.
00:30:21 But so is that enough to form,
00:30:27 to give you enough information about physical connection
00:30:31 to another human being?
00:30:32 Is there a time element there?
00:30:35 Is there, so, okay.
00:30:37 That sounds like a really strong, like low hanging fruit.
00:30:41 Like if you have that,
00:30:42 you could probably go really, really far.
00:30:44 My natural question is,
00:30:46 is there extra information you can add on top of that?
00:30:49 Like the duration of the physical proximity?
00:30:53 So first of all, we actually do estimate the duration,
00:30:56 but the way we estimate the duration
00:30:58 is like how a movie is filmed,
00:31:00 in the sense that every so often, every few minutes,
00:31:03 we check what’s nearby.
00:31:04 It’s like how a movie is filmed.
00:31:06 You take lots of snapshots.
00:31:07 So there’s no way in a battery efficient way
00:31:11 to really keep track of that proximity.
00:31:14 However, fortunately, we’re using probability.
00:31:17 The fact is the paradigm that we’re using
00:31:20 is it’s not super important
00:31:22 if you run into that person only for 10 minutes
00:31:24 at the grocery store.
00:31:25 If that’s a stranger that you run into 10 minutes
00:31:27 in this grocery store,
00:31:28 that’s not gonna be relevant for our paradigm
00:31:30 because our paradigm is not telling you
00:31:33 who were you around before
00:31:35 and might therefore have gotten infected by already.
00:31:38 Ours is about predicting the future.
00:31:40 We change from, I mean, the standard paradigm was
00:31:42 what already happened, quick damage control.
00:31:45 Ours is predict the future.
00:31:46 If you run into that person once in the grocery store today
00:31:49 and never see them again,
00:31:50 it’s irrelevant for predicting the future.
00:31:52 And therefore, for ours, what really matters
00:31:54 is the many hours around the other person,
00:31:57 at which point, if you’re scanning every five
00:31:59 to eight minutes.
00:32:00 That’s going to come out in the problem,
00:32:02 like statistically speaking,
00:32:03 it’s going to come out as a strong relationship
00:32:05 and a person in the grocery store is going to wash out
00:32:08 is not an important physical relationship.
00:32:11 I mean, this is brilliant.
00:32:14 How difficult is it to make work?
00:32:15 So you said, one, there’s a mathematical component
00:32:19 that we just kind of talked about,
00:32:21 and then there’s the user experience component.
00:32:24 So how difficult does it to go,
00:32:26 just like you built the video game, Alien Attack,
00:32:29 from zero to completion, what’s involved?
00:32:33 How difficult is it?
00:32:34 So I’m going to answer that question
00:32:36 in terms of building the product,
00:32:39 but then I’m also going to acknowledge
00:32:40 that just having an app doesn’t make it useful
00:32:44 because that’s actually maybe the easy part.
00:32:48 If you know what I mean,
00:32:49 there’s like all of this stuff
00:32:50 about rollout adoption and awareness,
00:32:52 but let’s focus on the app part first.
00:32:53 So that’s again, why I said the team is incredible.
00:32:56 So we have a bunch of people who,
00:32:59 let’s just say that the technology that we use to make it
00:33:02 is not the standard way you make an app.
00:33:04 If you think about a standard iOS app or Android app,
00:33:08 those are a user interface that contacts a web server
00:33:12 and sends some information back and forth.
00:33:14 We’re doing some stuff that has to hook
00:33:16 into the operating system of saying,
00:33:17 let’s go use Bluetooth for something
00:33:19 it wasn’t really meant for, right?
00:33:21 So there’s that part.
00:33:22 By the way, what is the app called?
00:33:24 Oh, it’s called Novid, COVID with an N.
00:33:28 Very nice.
00:33:29 So you have to hook into Bluetooth.
00:33:31 You’re saying you have to do that beyond the permissions
00:33:36 that are like at the very surface level
00:33:39 provided on the phone?
00:33:40 Well, I don’t want to call them permissions.
00:33:42 I just want to say,
00:33:43 that’s not what you usually do with Bluetooth.
00:33:45 Gotcha.
00:33:46 Usually with Bluetooth, you say,
00:33:47 do I have headphones nearby?
00:33:49 Yes.
00:33:49 Okay, I’m done.
00:33:50 You don’t go and say, do I have headphones nearby?
00:33:53 Or do I have another phone nearby, which is doing something?
00:33:55 And then keep asking that same question.
00:33:56 Keep asking the question.
00:33:58 Right?
00:33:59 So it’s actually not easy.
00:34:00 And I mean, there were some parts of it,
00:34:02 which actually a lot of people had tried unsuccessfully.
00:34:05 Actually, it’s known that, for example,
00:34:07 the UK was trying to do something similar.
00:34:11 And the problem they ran into was,
00:34:13 when you program things on iOS,
00:34:16 iOS is very good at making it hard
00:34:19 to do things in the background.
00:34:21 And so there was quite a lot of effort required
00:34:23 to go and make this thing work.
00:34:25 So the whole point, this thing would run in the background
00:34:28 and iOS, I mean, most Android probably as well, right?
00:34:33 But yeah, iOS certainly makes it difficult
00:34:35 for something to run in the background,
00:34:36 especially when it’s eating up your battery, right?
00:34:40 Well, we wanted to make sure we didn’t eat up the battery.
00:34:42 So that one we can,
00:34:43 we actually are very proud of the fact
00:34:44 that ours uses very little battery.
00:34:47 Actually, even if compared to Apple’s own system, so.
00:34:51 Beautiful.
00:34:52 So what else is required to make this thing work?
00:34:54 Right, so the key was that you had to do
00:34:56 a significant amount of work on the actual
00:34:58 mobile app development,
00:35:00 which fortunately the team that we brought
00:35:02 was this kind of general thinkers
00:35:04 where we would dig in deep into the operating system
00:35:07 documentation and the API libraries.
00:35:09 So we got that working.
00:35:10 But there’s another angle, which is,
00:35:12 you also need the servers to be able to compute fast enough,
00:35:15 which is tying back to this old school
00:35:17 computer programming competitions and math Olympiads.
00:35:20 In fact, our team that was working on the algorithm
00:35:23 and backend side included several people
00:35:25 who had been in these competitions from before,
00:35:29 which I happen to know because I do coach the team
00:35:32 for the math.
00:35:33 And so we were able to bring people in to build servers,
00:35:37 a server infrastructure in C++ actually,
00:35:40 so that we could support significant numbers of people
00:35:43 without needing tons of servers.
00:35:45 Is there some distributed algorithms working here
00:35:48 or you basically have to keep in the same place
00:35:51 the entire graph as it builds?
00:35:53 Cause especially the more and more people use it,
00:35:56 the bigger, the bigger the graph gets.
00:35:58 I mean, this is very difficult scaling problem, right?
00:36:02 Ah, so that’s actually why this computer algorithm
00:36:05 competition stuff was handy.
00:36:07 It’s because there are only about seven to eight
00:36:11 giga people in the world.
00:36:12 Yeah.
00:36:14 That’s not that many.
00:36:15 So if you can make your algorithms linear time
00:36:17 or almost linear time, a computer operates in gigahertz.
00:36:22 I only need to do one run, one recalculation every hour
00:36:26 in terms of telling people how far away these dangers are.
00:36:29 Yes.
00:36:29 So I suddenly have 3,600 seconds
00:36:33 and my CPU cores are running in gigahertz.
00:36:36 And at most they’re eight giga people.
00:36:39 Well, you skipping over the fact that there’s N squared
00:36:44 potential connections between people.
00:36:46 So how do you get around the fact that, you know,
00:36:51 that we, you know, the potential set of relationship
00:36:54 any one of us could have is a billion.
00:36:56 So it’s a billion times squared.
00:36:59 That’s the potential amount of data you have to be storing
00:37:02 and computing over and constantly updating.
00:37:05 So the way we dealt with that is we actually expect
00:37:08 that the typical network is very sparse.
00:37:10 The technical term sparse would mean that the average degree
00:37:14 or the average number of connections that a person has
00:37:17 is going to be at most like a hundred strong connections
00:37:21 that you care about.
00:37:22 If you think of it almost in terms of the heavy hitters,
00:37:25 actually in most people’s lives,
00:37:28 a hundred, if we just kept track
00:37:29 of their top hundred interactions,
00:37:32 that’s probably most of the signal.
00:37:35 Yeah, yeah.
00:37:37 I’m saddened to think that I might not be even
00:37:40 in a double digits, but.
00:37:42 Oh, I was intentionally giving a crazy number
00:37:44 to account for college students.
00:37:46 You call, oh, those are the,
00:37:48 who you call on the heavy hitters,
00:37:50 the people who are like the social butterflies.
00:37:52 Yeah, I need to,
00:37:54 I’d love to know that information about myself,
00:37:56 by the way, that, do you expose the graph,
00:38:01 like how many, like about yourself,
00:38:04 how many connections you have?
00:38:06 We do expose to each person
00:38:07 how many direct connections they have.
00:38:09 That’s great.
00:38:10 But for privacy purposes,
00:38:11 we don’t tell anybody who their connections,
00:38:14 like how their connections are interconnected.
00:38:16 Yes, gotcha.
00:38:16 But at the same time, we do expose also to everyone
00:38:19 an interesting chart that says,
00:38:21 here’s how many people you have
00:38:22 that you’re connected to directly.
00:38:24 Here’s how many at distance two,
00:38:26 meaning via people.
00:38:27 And then here’s how many at distance three.
00:38:29 And the reason we do that,
00:38:30 is that actually ends up being a dynamic
00:38:32 that also boosts adoption.
00:38:34 It drives another feedback loop.
00:38:36 The reason is because we saw, actually,
00:38:38 when we deployed this in some universities,
00:38:40 that when people see on their app
00:38:42 that they are indirectly connected to hundreds
00:38:46 or thousands of other people,
00:38:47 they get excited and they tell other people,
00:38:49 hey, let’s download this app.
00:38:50 But you know, we also saw in those examples,
00:38:52 especially looking at the screenshots people gave,
00:38:55 that is hit as soon as the typical person
00:38:58 has two or three other direct connections on the system.
00:39:02 Because that means that our app
00:39:04 has reached a virality or not of two to three.
00:39:07 The key is we were making a viral app to fight a virus
00:39:10 spreading on the same network that the virus spreads on.
00:39:14 So you’re trying to out virus the virus.
00:39:17 That’s right.
00:39:17 That’s exactly right.
00:39:20 Okay, great.
00:39:21 What have you learned from this whole experience
00:39:23 in terms of, let’s say for COVID,
00:39:26 but for future pandemics as well,
00:39:29 is it possible to use the power information here
00:39:33 of networked information as a virus spreads and travels
00:39:38 in order to basically keep the society open?
00:39:41 Is it possible for people to protect themselves
00:39:44 with this information?
00:39:46 Or do you still have to have most,
00:39:48 like in this overarching policy
00:39:50 of everybody should stay at home, that kind of thing?
00:39:53 We are trying to answer that question right now.
00:39:55 So the answer is we don’t know yet,
00:39:57 but that’s actually why we’re very happy
00:39:59 that now the idea has started to become more widely known.
00:40:02 And we’re already starting to collaborate
00:40:04 with epidemiologists.
00:40:06 Again, I’m just a mathematician, right?
00:40:08 And a mathematician should not be the person
00:40:11 who is telling everybody, this will definitely work.
00:40:13 But because of the potential power of this approach,
00:40:17 especially the potential power
00:40:19 of this being an end game for COVID,
00:40:22 we have gotten the interest of real researchers.
00:40:26 And we’re now working together
00:40:27 to try to actually understand the answer to that question.
00:40:30 Because you see, there’s a theory.
00:40:31 So what I can share is the mathematics of,
00:40:34 here’s why there’s some hope that this would work.
00:40:36 And that’s because I’m talking about end game now.
00:40:39 End game means you have very few cases.
00:40:41 But everywhere, we’re always thinking,
00:40:43 once there’s few cases, then does that mean we now open up?
00:40:46 Once you open up in the past, then the cases go up again
00:40:49 until you have to lock down again.
00:40:51 And now when we talk about the dynamic process that makes,
00:40:54 it’s guaranteeing you always have cases
00:40:55 until you have the great vaccines,
00:40:57 which is, we both got vaccinated, this is good.
00:41:00 But at the same time, why I’m thinking
00:41:02 this is still important is because we know
00:41:04 that many vaccine makers have said
00:41:06 they’re preparing for the next dose next year.
00:41:09 And if we have a perpetual thing
00:41:11 where you just always need a new vaccine every year,
00:41:14 it could actually be beneficial to make sure
00:41:16 we have as many other techniques as possible
00:41:18 for parts of the world that can’t afford,
00:41:20 for example, that kind of distribution.
00:41:23 Yeah, so actually, no matter how deadly the virus is,
00:41:26 no matter how many things,
00:41:27 whether you have a vaccine or not,
00:41:29 it’s still useful to be having this information.
00:41:31 Yes.
00:41:32 Because to stay home or not, depending on how risk,
00:41:35 I’m a big fan, just like you said, of having the freedom
00:41:39 for you to decide how risk averse you wanna be, right?
00:41:43 Depending on your own conditions,
00:41:44 but also on the state of like what you,
00:41:47 just how dangerously you like to live.
00:41:50 So I think that actually makes a lot of sense.
00:41:51 And I also think that since we’re,
00:41:54 when you think of disease spreading,
00:41:56 it spreads in aggregate in the sense that
00:42:00 if there are some people who maybe are more risk tolerant
00:42:04 because of other things in their life,
00:42:06 well, there might also be other people
00:42:08 who are less risk tolerance.
00:42:09 And then those people decide to isolate.
00:42:12 But what matters is in the aggregate
00:42:14 that this R naught of the infection spreading
00:42:17 drops below one.
00:42:19 And so the key is if you can empower people
00:42:21 with that power to make that decision,
00:42:23 you might actually still be able to drive
00:42:25 that R naught down below one.
00:42:27 Yeah, and also, this is me talking,
00:42:31 people get a little bit nervous, I think,
00:42:33 with information somehow mapping to privacy violation.
00:42:38 But first of all, in the approach you’re describing,
00:42:42 that’s respecting anonymity.
00:42:46 But I would love to have information
00:42:49 from the very beginning, from March and April of last year,
00:42:54 almost like a map of like where it’s risky
00:42:59 and where it’s not to go.
00:43:01 And not map based on sort of the exact location of people,
00:43:05 but where people usually hang out kind of thing.
00:43:07 Just, and maybe not necessarily about actual location,
00:43:13 but just maybe activities,
00:43:15 like just to have information about what is good to do
00:43:19 and not, in terms of like safety,
00:43:23 is it okay to run outside and not,
00:43:25 is it okay to go to a restaurant and not,
00:43:27 I just feel like we’re operating in the blind.
00:43:29 And then what you had is a very imperfect signal,
00:43:33 which is like basically politicians desperately trying
00:43:37 to make statements about what is safe and not.
00:43:40 They don’t know what the heck they’re doing.
00:43:41 They have a bunch of smart scientists telling them stuff.
00:43:44 And the scientists themselves also, very important,
00:43:47 don’t always know what they’re doing.
00:43:49 Epidemiology is not, is as much an art as a science.
00:43:54 You’re desperately trying to predict the future,
00:43:56 which nobody can do.
00:43:57 And then you’re trying to speak with some level of authority.
00:44:01 I mean, if I were to criticize scientists,
00:44:02 they spoke with too much authority.
00:44:04 It’s okay to say, I’m not sure.
00:44:06 But then they think like, if I say, I’m not sure,
00:44:10 then there’s going to be a distrust.
00:44:12 What they realize is when you’re wrong and you say,
00:44:14 I’m sure, it’s going to lead to more distrust.
00:44:16 So there’s this imperfect, like just chaotic,
00:44:19 messy system of people trying to figure out
00:44:23 with very little information.
00:44:25 And what you’re proposing is just a huge amount
00:44:27 of information, and information is power.
00:44:31 Is there challenges with adoption that you see
00:44:34 in the future here?
00:44:36 So there’s, maybe we could speak to,
00:44:38 there’s approaches, I guess, from Google.
00:44:40 There’s different people that have tried
00:44:42 similar kind of ideas.
00:44:44 Not, you have quite a novel idea, actually.
00:44:49 But speaking, the umbrella idea of contact tracing,
00:44:53 is there something you can comment about
00:44:58 why their approaches haven’t been fully adopted?
00:45:02 Is there challenges there?
00:45:03 Is there reasons why Novid might be a better idea
00:45:06 moving forward, in general, just about adoption?
00:45:09 Yeah, so first of all, I want to say,
00:45:10 I always have respect for the methods that other people use.
00:45:13 And so it’s good to see the other people I’ve been trying.
00:45:16 But what we have noticed is that the difference
00:45:19 between our value proposition to the user
00:45:22 and the value proposition to the user delivered
00:45:24 by everything that was made before is that,
00:45:27 unfortunately, the action of installing
00:45:30 a standard contact tracing app will then tell you
00:45:34 after you have already been exposed to the disease
00:45:37 so that you can protect other people from you.
00:45:40 And what that does to your own direct probability
00:45:43 of getting sick, if you think about it,
00:45:45 suppose you were making the decision,
00:45:47 should I or should I not install one of those apps?
00:45:50 What does that do to your own probability of getting sick?
00:45:55 It’s close to zero.
00:45:56 This is the sad thing you’re speaking to, not sad.
00:46:00 I suppose it’s the way the world is.
00:46:03 The only incentive there is to just help other people,
00:46:06 I suppose, but a much stronger incentive
00:46:09 is anything that allows you to help yourself.
00:46:13 Yes, so what I’m saying is that,
00:46:15 let’s just say free market capitalism
00:46:17 was not based on altruism, I think it’s based on,
00:46:21 if you make a system of incentives
00:46:23 so that everybody trying to maximize their own situation
00:46:26 somehow contributes to the whole,
00:46:28 that’s a game theoretic solution to a very hard problem.
00:46:31 And so this is actually basically mechanism design,
00:46:34 that we’ve basically come up with a different mechanism,
00:46:36 different set of incentives,
00:46:38 which incentivizes the adoption,
00:46:40 because actually whenever we’ve been rolling it out,
00:46:43 usually the first question we ask people,
00:46:45 like say in a university is,
00:46:46 do you know what Novid does?
00:46:48 And most of them have read about the other apps
00:46:50 and they say, Oh, Novid will tell you
00:46:51 after you’ve been around someone so you can quarantine.
00:46:54 And we have to explain to them,
00:46:55 actually, Novid never wants to ask you to quarantine.
00:46:58 That’s not the principle.
00:46:59 Our principle isn’t based on that at all.
00:47:01 We just want to let you know if something is coming close
00:47:04 so that you can protect yourself.
00:47:07 If you want.
00:47:08 If you want, if you want, if you want.
00:47:09 And then the quarantine is like, yes,
00:47:11 in that case, if you’re quarantining,
00:47:13 it’s because you’re shutting the door from the inside,
00:47:16 if that makes sense.
00:47:17 Yes, exactly.
00:47:18 Exactly.
00:47:18 I mean, this is brilliant.
00:47:20 So what do you think the future looks like
00:47:23 for future pandemics?
00:47:24 What’s your plan with Novid?
00:47:26 What’s your plan with these set of ideas?
00:47:28 I am actually still an academic and a researcher.
00:47:31 So the biggest work I’m working on right now
00:47:33 is to try to build as many collaborations
00:47:35 with other public health researchers at other universities
00:47:39 to actually work on pilot deployments together
00:47:42 in various places.
00:47:43 That’s the goal.
00:47:44 That’s actually ongoing work right now.
00:47:45 And so, for example, if anyone’s watching this
00:47:47 and you happen to be a public health researcher
00:47:49 and you want to be involved in something like this,
00:47:52 I’m just gonna say, I’m still incentive thinking.
00:47:55 There’s something in it for the researchers too.
00:47:57 This could open up an entire new way
00:47:59 of controlling disease.
00:48:00 That’s my hope.
00:48:01 I mean, it might actually be true.
00:48:03 And people who are involved in figuring out
00:48:06 how to make this work,
00:48:08 well, it could actually be good for their careers too.
00:48:09 I always have to think like,
00:48:11 if a researcher was getting involved,
00:48:12 what are they getting out of it?
00:48:14 Oh, so you mean like from a research perspective,
00:48:16 you can like publications and sets of ideas
00:48:20 about how to, from a sort of network theory perspective,
00:48:27 understand how we control the spread of a pandemic.
00:48:30 Yes, and what I’m doing right now
00:48:31 is this is basically interdisciplinary research
00:48:33 where maybe our side is bringing the technology
00:48:35 and the network theory,
00:48:37 and the missing parts are epidemiology
00:48:39 and public health expertise.
00:48:40 And if the two things start to join,
00:48:42 also because everywhere that you deploy,
00:48:45 let’s just say that the world is different
00:48:46 in the Philippines as it is in the United States.
00:48:49 And just the natures of the locality
00:48:52 would mean that someone like me
00:48:53 should not be trying to figure out how to do that.
00:48:55 But if we can work with the researchers
00:48:56 who are based there,
00:48:57 now suddenly we might come up with a solution
00:48:59 that will help scale in parts of the world
00:49:01 where they aren’t all getting the Moderna and Pfizer vaccines
00:49:04 which cost like $20 a pop in the US.
00:49:07 So if they want to participate,
00:49:09 who do they reach out to?
00:49:10 Oh, that would just be us.
00:49:11 I mean, the novid.org website has…
00:49:13 Novid.org.
00:49:14 It has a feedback reach out form.
00:49:16 And actually we are, I mean, again,
00:49:18 this is the DNA of being a researcher.
00:49:21 I am actually very excited by the idea
00:49:23 that this could contribute knowledge
00:49:25 that will outlast all of our generations,
00:49:28 like all of our lifetimes.
00:49:29 There you go.
00:49:30 Reach out to novid.org.
00:49:34 What about individual people?
00:49:36 Should they install the app and try it out?
00:49:37 Or is this really geographically restricted?
00:49:40 Oh, yeah, I didn’t come on here to tell everyone
00:49:42 to install the app.
00:49:42 I did not come to tell everyone to install the app
00:49:44 because it works best
00:49:46 if your local health authority is working with us.
00:49:49 Gotcha.
00:49:50 There’s a reason.
00:49:51 It’s because, this is back to the game theory.
00:49:54 If anyone could just say, I’m positive,
00:49:58 the high school senior prank would be to say that
00:50:01 we have a massive outbreak on finals week.
00:50:03 Let’s not have final exams.
00:50:05 So the way that our system works,
00:50:06 it actually borrows some ideas, not borrows,
00:50:08 we came up with them independently.
00:50:10 But this idea is similar to what Google and Apple do,
00:50:13 which is that if the local health authority
00:50:14 is working with this, they can,
00:50:16 for everyone who’s positive,
00:50:17 give them a passcode that expires in a short time.
00:50:20 So for ours, if you’re on the app and saying, I’m positive,
00:50:23 you can either just say that,
00:50:25 and that’s called unverified,
00:50:26 or you can enter in one of these codes
00:50:28 that you got from the local health authority.
00:50:30 So basically, for anyone who’s watching this,
00:50:32 it’s not that you should just go and download it
00:50:34 unless you want to go and look at it.
00:50:35 That’s cool.
00:50:36 But if you, on the other hand,
00:50:37 if you happen to know anyone at the local health authority,
00:50:39 which is trying to figure out how to handle COVID,
00:50:42 well then, I mean, we’d be very happy
00:50:44 to also work with you.
00:50:46 Gotcha.
00:50:47 So the verified there is really important
00:50:49 because you’re maintaining anonymity.
00:50:51 And because of that,
00:50:52 you have to have some source of verification
00:50:54 in order to make sure that it’s not possible to manipulate
00:50:59 because it’s ultimately about trust and information.
00:51:02 So it could be, verification is really important there.
00:51:06 So basically, individual people should
00:51:09 ask their local health authorities
00:51:11 to sign up to contact you.
00:51:15 I hope this spreads.
00:51:16 I hope this spreads for future pandemics
00:51:18 because I’m really, it’s the amount,
00:51:21 the millions of people who are hurt by this,
00:51:25 I think our response to the virus,
00:51:28 economically speaking,
00:51:30 the number of people who lost their dream,
00:51:32 lost their jobs, but also lost their dream.
00:51:35 Entrepreneurs, jobs often give meaning.
00:51:38 There’s people who financially and psychologically
00:51:41 are suffering because of our,
00:51:43 I’ll say, incompetent response to the virus
00:51:47 across the world, but certainly the United States,
00:51:49 that should be the beacon of entrepreneurial hope
00:51:53 for the world.
00:51:54 So I hope that we’ll be able to respond
00:52:00 to these kinds of events much better in the future.
00:52:02 And this is exactly the right kind of idea.
00:52:05 And now is the time to do the investment.
00:52:08 Let’s step back to the beauty of mathematics.
00:52:13 Maybe ask the big, silly question first,
00:52:16 which is, what do you find beautiful about mathematics?
00:52:20 I think that being able to look at a complicated problem,
00:52:26 which looks unsolvable,
00:52:28 and then to be able to change the perspective
00:52:30 to come from a different angle
00:52:32 and suddenly see that there’s a nice solution.
00:52:36 I don’t mean that every problem in math
00:52:37 is supposed to be this way,
00:52:39 but I think that these reframings
00:52:40 and changing of perspectives
00:52:42 that cause difficult things to get simplified
00:52:44 and crystallized and factored in certain ways is beautiful.
00:52:48 Actually, that’s related to what we were just talking about
00:52:50 with even this fighting pandemics.
00:52:52 The crystal idea was just quantify proximity
00:52:57 by the number of relationships in the physical network,
00:53:01 instead of just by the feet and meters, right?
00:53:04 It’s just that if you change that perspective,
00:53:07 now all of these things follow.
00:53:09 And so mathematics to me is beautiful
00:53:12 in the pure sense just for that.
00:53:15 Yeah, it’s quite interesting to see a human civilization
00:53:17 as a network, as a graph,
00:53:20 and our relationships as kind of edges in that graph.
00:53:25 And to then do, outside of just pandemic,
00:53:29 do interesting inferences based on that.
00:53:33 This is true for like Twitter, social networks and so on,
00:53:36 how we expand the kind of things we talk about,
00:53:40 think about sort of politically,
00:53:42 if you have this little bubble, quote unquote,
00:53:44 of ideas that you play with,
00:53:46 it’s nice from a recommender system perspective,
00:53:50 how do you jump out of those bubbles?
00:53:52 It’s really fascinating.
00:53:53 YouTube was working on that, Twitter’s working on that,
00:53:57 but not always so successfully,
00:53:59 but there’s a lot of interesting work
00:54:02 from a mathematical and a psychological,
00:54:05 sociological perspective there within those graphs.
00:54:09 But if we look at the cleanest formulation of that,
00:54:13 of looking at a problem from a different perspective,
00:54:16 you’re also involved
00:54:17 with the International Mathematics Olympiad,
00:54:20 which takes small, clean problems that are really hard,
00:54:27 but once you look at them differently, can become easy.
00:54:31 But that little jump of innovation is the entire trick.
00:54:36 So maybe at the high level,
00:54:38 can you say what is the International Mathematical Olympiad?
00:54:41 Sure, so this is the competition
00:54:44 for people who aren’t yet in college, math competition,
00:54:47 which is the most prestigious one in the entire world.
00:54:50 It’s the Olympics of mathematics,
00:54:52 but only for people who aren’t yet in college.
00:54:55 Now, the kinds of questions that they ask you to do
00:54:58 are not computational.
00:54:59 Usually you’re not supposed to find that the answer is 42.
00:55:02 Right?
00:55:03 Instead, you’re supposed to explain why something is true.
00:55:07 And the problem is that at the beginning,
00:55:09 when you look at each of the questions,
00:55:11 first of all, you have four and a half hours
00:55:13 to solve three questions, and this is one day,
00:55:16 and then you have a second day,
00:55:16 which is four and a half hours, three questions.
00:55:19 But when you look at the questions,
00:55:20 they’re all asking you,
00:55:21 explain why the following thing is true,
00:55:23 which you’ve never seen before.
00:55:25 And by the way, even though there are six questions,
00:55:27 if you solve any one of them, you’re a genius
00:55:29 and you get an honorable mention.
00:55:30 So this is hard to solve.
00:55:32 So what about, is it one person, is it a team?
00:55:35 Ah, so each country can send six people
00:55:38 and the score of the country is actually unofficial.
00:55:42 There’s not an official country versus country system,
00:55:45 although everyone just adds up the point scores
00:55:47 of the six people and they say,
00:55:48 well, now which country stacked up where?
00:55:51 Yeah, so maybe as a side comment,
00:55:53 I should say that there’s a bunch of countries,
00:55:56 including the former Soviet Union and Russia,
00:55:59 where I grew up, where this is one of the
00:56:04 most important competitions that the country participates in.
00:56:08 It was a source of pride for a lot of the country.
00:56:11 You look at the Olympic sports,
00:56:14 like wrestling, weightlifting,
00:56:17 there’s certain sports and hockey
00:56:20 that Russia and the Soviet Union truly took pride in.
00:56:24 And actually the Mathematical Olympiad,
00:56:28 it was one of them for many years.
00:56:30 It’s still one of them.
00:56:32 And that’s kind of fascinating.
00:56:33 We don’t think about it this way in the United States.
00:56:36 Maybe you can correct me if I’m wrong,
00:56:38 but it’s not nearly as popular in the United States
00:56:42 in terms of its integration into the culture,
00:56:45 into just basic conversation, into the pride.
00:56:49 Like, if you won an Olympic gold medal
00:56:52 or if you win the Super Bowl, you can walk around proud.
00:56:56 I think that was the case
00:56:57 with the Mathematical Olympiad in Russia.
00:56:59 Not as much the case in the United States, I think.
00:57:03 So I just wanna give that a little aside
00:57:04 because beating anybody from Russia,
00:57:07 from the Eastern Republic or from China
00:57:09 is very, very difficult.
00:57:11 Like, if I remember correctly,
00:57:14 there’s people, this was a multiyear training process.
00:57:18 They train hard.
00:57:20 And this is everything that they’re focused on.
00:57:25 My dad was a participant in this.
00:57:29 And it’s, I mean, it’s as serious as Olympic sports.
00:57:33 You think about like gymnastics,
00:57:34 like young athletes participating in gymnastics.
00:57:36 This is as serious as that, if not more serious.
00:57:38 So I just wanna give that a little bit of context
00:57:41 because we’re talking about serious high level math,
00:57:44 athletics almost here.
00:57:46 Yeah, and actually I also think that it made sense
00:57:49 from the Soviet Union’s perspective
00:57:51 because if you look at what these people do eventually,
00:57:55 even though, let’s look at the USSR’s
00:57:58 International Math Olympiad record.
00:58:00 Even though they, I say, even though they won
00:58:03 a lot of awards at the high school thing,
00:58:05 many of them went on to do incredible things
00:58:07 in research mathematics or research other things.
00:58:10 And that’s showing the generalization,
00:58:13 generalizability of what they were working on.
00:58:15 Because ultimately we’re just playing with ideas
00:58:20 of how to prove things.
00:58:22 And if you get pretty good at inventing creative ways
00:58:26 to turn problems apart, split them apart,
00:58:29 observe neat ways to turn messy things into simple crystals.
00:58:34 Well, if you’re gonna try to solve any real problem
00:58:36 in the real world, that could be a really handy tool too.
00:58:39 So I don’t think it was a bad investment.
00:58:41 I think it clearly worked well for Soviet Union.
00:58:44 Yeah, so this is interesting.
00:58:47 People sometimes ask me, you know,
00:58:48 you go up and under communism, you know,
00:58:52 was there anything good about communism?
00:58:55 And it’s difficult for me to talk about it
00:58:58 because it’s not, communism is one of those things
00:59:00 that’s looked down on like without,
00:59:02 in absolutist terms currently.
00:59:05 But you could still, in my perspective,
00:59:07 talk about the actual, forget communism
00:59:09 or whatever the actual term is,
00:59:11 but you know, certain ways that the society functioned
00:59:16 that we can learn lessons from.
00:59:18 And one of the things in the Soviet Union
00:59:20 that was highly prized is knowledge,
00:59:25 not even knowledge, it’s wisdom
00:59:27 and the skill of invention, of innovation at a young age.
00:59:34 So we’re not talking about a selection process
00:59:37 where you pick the best students in the school
00:59:40 to do the mathematics or to read literature.
00:59:44 It’s like, everybody did it.
00:59:47 Everybody, it was almost treated
00:59:49 as if anyone could be the next Einstein,
00:59:53 anybody could be the next, I don’t know,
00:59:55 Hemingway, James Joyce.
00:59:56 And so you’re forcing an education on the populace
01:00:01 and a rigorous deep education,
01:00:03 like as opposed to kind of like,
01:00:06 oh, we wanna make sure we teach
01:00:10 to the weakest student in the class,
01:00:14 which American systems can sometimes do
01:00:16 because we don’t wanna leave anyone behind.
01:00:19 The Russian system was anyone can be the strongest student
01:00:25 and we’re gonna teach you the strongest student
01:00:26 and we’re going to pretend or force everybody,
01:00:30 even the weakest student to be strong.
01:00:32 And what that results in, it’s obviously,
01:00:35 this is what people talk about,
01:00:36 is a huge amount of pressure.
01:00:38 Like it’s psychologically very difficult.
01:00:40 This is why people struggle when they go to MIT,
01:00:42 this very competitive environment.
01:00:44 It can be very psychologically difficult,
01:00:46 but at the same time,
01:00:47 it’s bringing out the best out of people.
01:00:49 And that mathematics was certainly one of those things.
01:00:53 And exactly what you’re saying,
01:00:54 which kind of clicked with me just now,
01:00:56 as opposed to kind of a spelling bee in the United States,
01:01:00 which I guess you spell, I’m horrible at this,
01:01:03 but it’s a competition about spelling,
01:01:04 which I’m not sure, but you could argue
01:01:07 it doesn’t generalize well to the future skills.
01:01:10 Mathematics, especially this kind of mathematics
01:01:13 is essentially formalized competition of invention,
01:01:17 of creating new ideas.
01:01:21 And that generalizes really, really well.
01:01:23 So that’s quite brilliantly put.
01:01:25 I didn’t really think about that.
01:01:27 So this is not just about the competition.
01:01:29 This is about developing minds
01:01:31 that will come to do some incredible stuff in the future.
01:01:37 Yeah, actually, I want to respond
01:01:38 to a couple of things there.
01:01:39 The first one, this one, which is this notion
01:01:42 of whether or not that is possible
01:01:43 in a non authoritarian regime.
01:01:46 I think it is.
01:01:47 And that’s actually why I spent some of my efforts
01:01:49 before the COVID thing,
01:01:51 actually trying to work towards there.
01:01:53 The reason is because if you think about it,
01:01:55 let’s say in America,
01:01:57 lots of people are pretty serious
01:01:58 about training very hard for football,
01:02:01 or baseball, or basketball.
01:02:02 Basketball is very, very accessible,
01:02:04 but lots of people are doing that.
01:02:05 Why?
01:02:06 Well, actually, I think that what was going on
01:02:09 with the authoritarian thing was at least the message
01:02:13 that was universally sent was being a good thinker
01:02:17 and a creator of ideas is a good thing.
01:02:21 Yes, exactly.
01:02:23 There’s no reason why that message can’t be sent everywhere.
01:02:26 And I think it actually should be.
01:02:28 So that’s the first thing.
01:02:29 The second thing is what you commented about this thing
01:02:32 about the generalizable skill
01:02:35 and what could people do with Olympiads afterwards.
01:02:37 So that’s actually my interest in the whole thing.
01:02:40 I don’t just coach students how to do problems.
01:02:45 In fact, I’m not even the best person for that.
01:02:47 I’m not the best at solving these problems.
01:02:49 There are other people who are much better
01:02:50 at making problems and teaching people how to solve problems.
01:02:53 In fact, when the Mathematical Association of America,
01:02:57 which is the group which is in charge
01:02:58 of the US participation in these Olympiads,
01:03:01 when they were deciding whether or not to put me in
01:03:04 back in 2013 as the head coach,
01:03:06 I had a conversation with their executive director
01:03:09 where I commented that we might do worse
01:03:12 because my position was I don’t,
01:03:15 I mean, I actually didn’t want to focus on winning.
01:03:17 I said, if you’re going to let me work
01:03:19 with 60 very strong minds as picked through this system,
01:03:24 because the coach works with these,
01:03:26 gets to run a camp for these students.
01:03:27 I said, I’m actually not going to define my success
01:03:30 in terms of winning this contest.
01:03:33 I said, I wanted to maximize the number of the students
01:03:36 that I read about in the New York Times in 20 years.
01:03:40 And the executive director
01:03:41 of the Mathematical Association of America
01:03:44 was fully in support of this
01:03:45 because that’s also how their philosophy is.
01:03:48 So in America, the way we run this
01:03:49 is we’re actually not just training to win,
01:03:52 even though the students are very good
01:03:54 and they can win anyway.
01:03:56 One reason, for example, I went and even did the COVID thing
01:03:59 involving quite a few of them
01:04:01 is so that hopefully some of them get ideas
01:04:04 because in 20, 30 years, I won’t have the energy
01:04:06 or the insight to solve problems.
01:04:08 We’ll have another catastrophe.
01:04:10 And hopefully some of these people will step up and do it.
01:04:13 And ultimately have that longterm impact.
01:04:14 I wonder if this is scalable to,
01:04:17 because that’s such a great metric for education,
01:04:20 not how to get an A on the test, but how to have,
01:04:28 how to be on the cover of New York Times
01:04:31 for inventing something new.
01:04:33 And do you think that’s generalizable to education
01:04:37 beyond just this particular Olympia?
01:04:39 Like, even you saying this feels like a rare statement,
01:04:42 almost like a radical statement as a goal for education.
01:04:45 So actually the way I teach my classes at Carnegie Mellon,
01:04:48 which I will admit right away is not equivalent
01:04:51 to the average in the world,
01:04:52 but it’s already not just the top 60 in the country
01:04:56 as picked by something.
01:04:58 Let me just explain.
01:04:58 I have exams in my class, which are 90% of the grade.
01:05:01 So the exams are the whole thing,
01:05:02 or most of the whole thing.
01:05:03 And the way that I let students prepare for the exams
01:05:06 is I show them all the problems I’ve ever given
01:05:08 on the previous exams.
01:05:10 And the exam that they will take is open notes.
01:05:12 They can take all the notes they want
01:05:13 on the previous problems.
01:05:14 And the guarantee is that the exam problems this time
01:05:17 will have no overlap with anything
01:05:18 you have seen me give in the past,
01:05:21 as well as no overlap with anything I taught in the class.
01:05:24 So the entire exam is invention.
01:05:27 Wow.
01:05:28 But that’s how I go, right?
01:05:29 My point is I have explained to people when I teach you,
01:05:33 I don’t want you to have remembered a method I showed you.
01:05:36 I want you to have learned enough about this area
01:05:39 that if you face a new question,
01:05:40 which I came up with the night before
01:05:42 by thinking about like,
01:05:43 what could I ask that I have never asked before?
01:05:46 Oh, that’s cute.
01:05:47 That’s what the answer is.
01:05:48 Aha, that’s an exam problem.
01:05:49 That’s exactly what I do before the exam.
01:05:51 And then that’s what I want them to learn.
01:05:53 And the first exam, usually people have a rough time
01:05:56 because it’s like, what kind of crazy class is this?
01:05:58 The professor doesn’t teach you anything for the exam.
01:06:01 But then by the second or third,
01:06:03 and by the time they finished the class,
01:06:05 they have learned how to solve anything in the area.
01:06:09 How to invent.
01:06:10 How to invent in that area, yeah.
01:06:12 Can we walk back to the Mathematical Olympiad?
01:06:15 What’s the scoring and format like?
01:06:18 And also what does it take to win?
01:06:20 So the way it works is that each of the six students
01:06:25 do the problems and there are six problems.
01:06:27 All the problems are equally weighted.
01:06:29 So each one’s worth seven points.
01:06:31 That means that your maximum score
01:06:33 is six problems times seven points,
01:06:35 which is the nice number of 42.
01:06:37 And now the way that they’re scored by the way
01:06:40 is there’s partial credit.
01:06:41 So the question is asking you,
01:06:43 explain why this weird fact is true.
01:06:46 Okay, if you explain why you get seven points.
01:06:48 If you make minor mistake, maybe you get six points.
01:06:51 But if you don’t succeed in explaining why,
01:06:53 but you explain some other true fact,
01:06:57 which is along the way of proving it,
01:07:02 then you get partial credit.
01:07:03 And actually now this is tricky
01:07:05 because how do you score such a thing?
01:07:07 It’s not like the answer was 72
01:07:10 and you wrote 71 and it’s close, right?
01:07:13 The answer is 72 and you wrote 36.
01:07:15 Oh, but that’s pretty close
01:07:16 because maybe you’re just off by it.
01:07:18 By the way, they’re not numerical anyway,
01:07:20 but I’m just giving some numerical analog
01:07:22 to the way the scoring might work.
01:07:24 They’re all essays.
01:07:25 And that’s where I guess I have some role
01:07:28 as well as some other people
01:07:29 who helped me in the US delegation for coaches.
01:07:32 We actually debate with the country which is organizing it.
01:07:37 The country which is organizing the Olympiad
01:07:39 brings about 50 people to help judge the written solutions.
01:07:45 And you schedule these half hour appointments
01:07:48 where the delegation from one country
01:07:50 sits down at a table like this.
01:07:52 Opposite side is two or three people from the host country.
01:07:55 And they’re just looking over these exam papers
01:07:58 saying, well, how many points is this worth
01:08:00 based on some rubric that has been designed?
01:08:03 And this is a negotiation process
01:08:05 where we’re not trying to bargain
01:08:07 and get the best score we can.
01:08:09 In fact, sometimes we go to this table
01:08:10 and we will say, we think we want less than what you gave us.
01:08:13 This is how our, these are our principles.
01:08:16 If you give us too much, we say, no, you gave us too much.
01:08:18 We do that.
01:08:19 However, the reason why this is an interesting process
01:08:22 is because if you can imagine every country
01:08:24 which is participating has its own language.
01:08:26 And so if you’re trying to grade the Mongolian scripts
01:08:28 and they’re written in Mongolian,
01:08:31 if you don’t read Mongolian, which most people don’t,
01:08:33 then the coaches are explaining to you,
01:08:36 this is what the student has written.
01:08:38 It’s actually quite interesting process.
01:08:40 So it’s almost like a jury.
01:08:43 Yes.
01:08:44 You have, in the American legal system,
01:08:47 you have a jury that where they’re deliberating,
01:08:49 but unlike a jury, there’s the members of the jury
01:08:53 speaking different languages sometimes.
01:08:55 Yes. That’s fascinating.
01:08:57 But I mean, it’s hard to know what to do
01:09:01 because it’s probably really, really competitive.
01:09:04 But your sense is that ultimately people,
01:09:08 like how do you prevent manipulation here, right?
01:09:14 Well, we just hope that it’s not happening.
01:09:17 So we write in English.
01:09:19 Therefore, everything that the US does,
01:09:21 everyone can look at.
01:09:22 So it’s very hard for me.
01:09:24 It’s very hard for you to manipulate.
01:09:25 We don’t manipulate.
01:09:27 We only hope that other people aren’t.
01:09:29 But at the same time, as you see, our philosophy was,
01:09:32 we want to use this as a way to develop general talent.
01:09:35 And although we do this for the six people who go
01:09:38 to the International Math Olympiad,
01:09:40 we really want that everyone at any,
01:09:42 touched at any stage of this process
01:09:45 get some skills that can help to contribute more later.
01:09:48 So I don’t know if you can say something insightful
01:09:51 to this question,
01:09:52 but what do you think makes a really hard math problem
01:09:56 on this Olympiad, maybe in the courses you teach
01:09:59 or in general?
01:10:01 What makes for a hard problem?
01:10:03 You’ve seen, I’m sure, a lot of really difficult problems.
01:10:06 What makes a hard problem?
01:10:07 So I could quantify it by the number of leaps of insight
01:10:12 of changes of perspective that are along the way.
01:10:14 And here’s why.
01:10:15 This is like a very theoretical computer science
01:10:17 way of looking at it, okay?
01:10:19 It’s that each reframing of the problem
01:10:22 and using of some tool,
01:10:23 I actually call that a leap of insight.
01:10:25 When you say, oh, wow, now I see,
01:10:27 I should kind of put these plugs into those sockets
01:10:30 like so, and suddenly I get to use that machine.
01:10:33 Oh, but I’m not done yet.
01:10:34 Now I need to do it again.
01:10:36 Each such step is a large possible,
01:10:38 large fan out in the search space.
01:10:41 The number of these tells you the exponent.
01:10:44 The base of the exponent is like how big,
01:10:46 how many different possibilities you could try.
01:10:49 And that’s actually why,
01:10:51 like if you have a three insight problem,
01:10:54 that is not three times as hard as a one insight problem,
01:10:57 because after you’ve made the one insight,
01:10:59 it’s not clear that that was the right track necessarily.
01:11:03 Well, unless you’re very into it.
01:11:03 There’s still a branching of possibility.
01:11:06 Yeah.
01:11:07 Right.
01:11:09 You’re saying there’s problems like on the math Olympia
01:11:12 that requires more than one insight?
01:11:13 Yes.
01:11:14 Those are the hard ones.
01:11:15 And also I can tell you how you can tell.
01:11:17 So this is how I also taught myself math
01:11:19 when I was in college.
01:11:20 So if you are taking a, not taught myself,
01:11:23 I was taking classes, of course,
01:11:24 but I was trying to read the textbook
01:11:26 and I found out I was very bad at reading math textbooks.
01:11:29 A math textbook has a long page of stuff that is all true,
01:11:32 which after you read the page,
01:11:34 you have no idea what you just read.
01:11:35 Yeah.
01:11:36 This is just a good summary of a math textbook.
01:11:39 Okay.
01:11:39 Yeah, because it’s not clear why anything was done that way.
01:11:44 And yes, everything is true,
01:11:45 but how the heck did anyone think of that?
01:11:47 So the way that I taught myself math eventually was,
01:11:50 the way I read a math textbook
01:11:52 is I would look at the theorem statement.
01:11:55 I would look at the length of the proof
01:11:58 and then I would close the book
01:12:00 and attempt to reproof it myself.
01:12:01 Yeah.
01:12:02 That’s brilliant.
01:12:03 The length of the proof is telling you
01:12:05 the number of insights,
01:12:06 because the length of the proof is linear
01:12:08 in the number of insights.
01:12:10 Each insight takes space.
01:12:12 Yeah.
01:12:13 And if I know that it’s a short proof,
01:12:14 I know that there’s only one insight.
01:12:16 So when I’m doing my own way of solving the problem,
01:12:19 like finding the proof,
01:12:20 I quit if I have to do too many plugins.
01:12:23 It’s equivalent to a math contest.
01:12:24 In a math contest I look,
01:12:25 is it problem one, two, or three?
01:12:27 That tells me how many insights there are.
01:12:28 This is exactly what I did.
01:12:29 That’s brilliant.
01:12:30 Linear in the number.
01:12:32 I don’t know.
01:12:32 I think it’s possible that that’s true.
01:12:36 Approximately, approximately.
01:12:37 Approximately, yeah.
01:12:38 I don’t know if somebody out there
01:12:41 is gonna try to formally prove this.
01:12:43 Oh no, I mean, you’re right.
01:12:44 There are cases where maybe it’s not quite linear,
01:12:46 but in general.
01:12:47 Well, some of it’s notation too,
01:12:48 and some of it is style and all those kinds of things,
01:12:50 but within a textbook.
01:12:51 Within the same book.
01:12:52 Within the same book with the same.
01:12:54 Within the same book on the same subject.
01:12:56 Yeah.
01:12:57 This is what I was using.
01:12:57 That’s hilarious.
01:12:58 Because you know, if it’s a two page proof,
01:13:00 you just know this is gonna be insane, right?
01:13:02 That’s the scary thing about insights.
01:13:06 You look like Andrew Wiles
01:13:08 working on the Fermat’s Last Theorem,
01:13:11 is you don’t know.
01:13:13 Something seems like a good idea,
01:13:16 and you have that idea,
01:13:17 and it feels like this is a leap,
01:13:20 like a totally new way to see it,
01:13:22 but you have no idea if it’s at all useful.
01:13:25 Even if you think it’s correct,
01:13:27 you have no idea if this is like going to go down a path
01:13:30 that’s completely counterproductive
01:13:32 or not productive at all.
01:13:34 That’s the crappy thing about invention,
01:13:38 is like I have, I’m sure you do.
01:13:41 I have a lot of really good ideas every single day,
01:13:44 but like, and I’ll go inside my head along them,
01:13:49 along that little trajectory,
01:13:52 but it could be just a total waste.
01:13:54 And it’s, you know what that feels like?
01:13:57 It just feels like patience is required,
01:13:59 not to get excited at any one thing.
01:14:01 So I think this is interesting
01:14:03 because you raised Andrew Wiles.
01:14:04 He spent seven years attacking the same thing, right?
01:14:08 And so I think that what attracts
01:14:10 professional researchers to this
01:14:12 is because even though it’s very painful
01:14:14 that you keep fighting with something,
01:14:16 when you finally find the right insights
01:14:19 and string them together,
01:14:20 it feels really good, so.
01:14:23 Well, there’s also like short term,
01:14:26 it feels good to, whether it’s real or not,
01:14:31 to pretend like you’ve solved something
01:14:33 in the sense like you have an insight
01:14:35 and there’s a sense like this might be the insight
01:14:37 that solves it.
01:14:39 So at least for me, I just enjoy that rush of positivity
01:14:44 even though I know statistically speaking
01:14:46 is probably going to be a dead end.
01:14:48 I’m the same way, I’m the same way.
01:14:49 In fact, that’s how I know whether
01:14:51 I might want to keep thinking about this general problem.
01:14:54 It’s like, if I still see that I’m getting some insights,
01:14:57 I’m not at a dead end yet.
01:14:59 But that’s also where I learned something
01:15:00 from my PhD advisor.
01:15:01 Actually, he was a real big inspiration on my life.
01:15:04 His name is Benny Sudakov.
01:15:05 In fact, he grew up in the former Soviet Union.
01:15:08 He was from Georgia, but he’s an incredible person.
01:15:12 But one thing I learned was choose the problems to work on
01:15:16 that might matter if you succeed.
01:15:21 Because that’s why, for example, we dug into COVID.
01:15:23 It was just, well, suppose we succeed
01:15:25 in finding some interesting insight here.
01:15:27 Well, it actually matters.
01:15:29 That is worth a laugh.
01:15:30 Yeah, and I think COVID, the way you’re approaching COVID
01:15:36 has two interesting possibilities.
01:15:38 One, it might help with COVID or another pandemic,
01:15:41 but two, I mean, just this whole network theory space,
01:15:48 you might unlock some deep understanding
01:15:51 about the interaction with human beings.
01:15:53 That might have nothing to do with the pandemic.
01:15:55 There’s a space of possible impacts
01:15:58 that may be direct or indirect.
01:16:00 And the same thing is with Andrew Wiles’s proof.
01:16:03 I don’t understand, but apparently the pieces of it
01:16:08 are really impactful for mathematics,
01:16:12 even if the main theorem is not.
01:16:14 So along the way, the insights you have
01:16:18 might be really powerful for unexpected reasons.
01:16:22 So I like what you said.
01:16:23 This is something that I learned from another friend of mine.
01:16:26 He’s a very famous researcher.
01:16:28 All these people are more famous than I am.
01:16:29 His name is Jacob Fox.
01:16:30 He’s Jacob Fox at Stanford.
01:16:32 Also a very big inspiration for me.
01:16:33 We were both grad students together at the same time.
01:16:36 Well, most importantly,
01:16:36 you’re good at selecting good friends.
01:16:38 Ah, yeah, well, that’s the key.
01:16:40 You gotta find good people to learn things from.
01:16:42 But his thing was, he often said,
01:16:44 if you solve a math problem and have this math proof,
01:16:46 math problem for him is like a proof, right?
01:16:48 So suppose you came up with this proof.
01:16:50 He always asks, what have we learned from this
01:16:53 that we could potentially use for something else?
01:16:56 It’s not just, did you solve the problem
01:16:58 that was supposed to be famous?
01:17:00 And is there something new in the course of solving this
01:17:03 that you had to invent
01:17:04 that we could now use as a tool elsewhere?
01:17:06 Yeah, there’s this funny effect
01:17:08 where just looking at different fields
01:17:12 where people discover parallels.
01:17:15 They’ll prove something, it’ll be a totally new result.
01:17:17 And then somebody later realizes
01:17:19 this was already done 30 years ago
01:17:20 in another discipline, in another way.
01:17:23 And it’s really interesting.
01:17:26 Now, we did this offline
01:17:27 in another illustration he showed to me.
01:17:30 It’s interesting to see the different perspectives
01:17:33 on a problem.
01:17:35 It kind of points like there’s just like
01:17:38 very few novel ideas that everything else,
01:17:42 that most of us are just looking at different perspective
01:17:45 on the same idea.
01:17:47 And it makes you wonder this old silly question
01:17:51 that I have to ask you is,
01:17:53 do you think mathematics is discovered or invented?
01:17:58 Do you think we’re creating new idea?
01:18:02 Are we building a set of knowledge
01:18:06 that’s distinct from reality?
01:18:09 Or are we actually like,
01:18:12 is math almost like a shovel
01:18:13 where we’re digging to like this core set of truths
01:18:16 that were always there all along?
01:18:20 So I personally feel like it’s discovered.
01:18:22 But that’s also because I guess the way that
01:18:25 I like to choose what questions to work on
01:18:27 are questions that maybe we’ll get to learn something about
01:18:31 why is this hard?
01:18:32 I mean, I’m often attracted to questions
01:18:33 that look simple, but are hard, right?
01:18:36 And what could you possibly learn from that?
01:18:38 Sort of like probably the attraction
01:18:40 of Fermat’s last theorem, as you mentioned,
01:18:42 simple statement, why is it so hard?
01:18:44 So I’m more on the discovered side.
01:18:47 And I also feel like if we ever ran into
01:18:49 an intelligent other species in the universe,
01:18:54 probably if we compared notes,
01:18:56 there might be some similarities between both of us
01:19:00 realizing that pi is important.
01:19:02 Because you might say, why, why humans,
01:19:04 do humans like circles more than others?
01:19:06 I think stars also like circles.
01:19:08 I think planets like circles.
01:19:09 They’re not perfect circles,
01:19:10 but nevertheless, the concept of a circle
01:19:13 is just point and constant distance.
01:19:15 Doesn’t get any simpler than that.
01:19:17 It’s possible that like an alien species
01:19:19 will have, depending on different cognitive capabilities
01:19:23 and different perception systems,
01:19:25 will be able to see things
01:19:28 that are much different than circles.
01:19:30 And so if it’s discovered,
01:19:33 it will still be pointing at a lot of same
01:19:35 geometrical concepts, mathematical concepts,
01:19:38 but it’s interesting to think of how many things
01:19:43 we would have to still align,
01:19:45 not just based on notation, but based on understanding,
01:19:48 like just like some basic mathematical concepts,
01:19:53 like how much work is there going to be
01:19:56 in trying to find a common language?
01:19:59 I mean, this is, I think Stephen Wolfram and his son
01:20:02 helped with the movie Arrival,
01:20:04 like the developing an alien language,
01:20:07 like how would aliens communicate with humans?
01:20:10 It’s fascinating,
01:20:11 because like math seems to be the most promising thing,
01:20:14 but even like math,
01:20:15 like how do you visualize mathematical ideas?
01:20:22 It feels like there has to be an interactive component,
01:20:24 just like we have a conversation.
01:20:26 There has to be, this is something we don’t,
01:20:28 I think, think about often, which is like,
01:20:31 with somebody who doesn’t know anything about math,
01:20:33 doesn’t know anything about English
01:20:35 or any other natural language,
01:20:37 how would we describe,
01:20:40 we talked offline about visual proofs.
01:20:42 How would we, through visual proofs, have a conversation
01:20:47 where we say something, here’s the concept,
01:20:50 the way we see it, does that make sense to you?
01:20:53 And like, can you mess with that concept
01:20:57 to make it sense for you?
01:20:58 And then go back and forth in this kind of way.
01:21:01 So purely through mathematics,
01:21:03 I’m sure it’s possible to have those kinds of experiments
01:21:04 with like tribes on earth that don’t,
01:21:07 there’s no common language.
01:21:08 Through math, like draw a circle
01:21:10 and see what they do with it, right?
01:21:13 Do some of these visual proofs,
01:21:15 like the summation of the odds and adds up to the squares.
01:21:19 Yes, I wonder how difficult that is
01:21:21 before one or the other species murders themselves.
01:21:24 That’s a good question.
01:21:27 I hope that the curiosity for knowledge
01:21:29 will overpower the greedy,
01:21:31 this is back to our game theory thing,
01:21:33 that the curiosity of like discovering math together
01:21:37 will overpower the desire for resources
01:21:40 and ultimately like willing to commit violence
01:21:44 in order to gain those resources.
01:21:46 I think as we progress,
01:21:47 become more and more intelligent as a species,
01:21:50 I’m hoping we would value more and more of the knowledge
01:21:53 because we’ll come up with clever ways
01:21:54 to gain more resources so we won’t be so resource starved.
01:21:58 I don’t know.
01:21:59 That’s a hopeful message for when we finally meet aliens.
01:22:01 Yeah, yeah.
01:22:02 The cool thing about the Math Olympiad,
01:22:07 I don’t know if you know work from Francois Chollet
01:22:11 from Google, he came up with this kind of IQ test slash,
01:22:16 it kind of has similar aspects to it
01:22:18 that also the Math Olympiad does for AI.
01:22:24 So he came up with these tests
01:22:25 where they’re very simple for humans,
01:22:29 but very difficult for AI to illustrate exactly
01:22:32 why we’re just not good at seeing a totally new problem.
01:22:38 Sorry, AI systems are not good at looking at a new problem
01:22:43 that requires you to detect
01:22:46 that there’s a symmetry of some kind,
01:22:48 or there’s a pattern that hasn’t seen before.
01:22:53 The pattern is like obvious to us humans,
01:22:56 but it’s not so obvious to find that kind of,
01:22:59 you’re inventing a pattern that’s there
01:23:03 in order to then find a solution.
01:23:09 I don’t know if you can comment on that.
01:23:12 If you can comment on, but from an AI perspective
01:23:16 and from a math problem perspective,
01:23:19 what do you think is intelligence?
01:23:22 What do you think is the thing
01:23:23 that allows us to solve that problem?
01:23:25 And how hard is it to build a machine to do that?
01:23:29 Asking for a friend.
01:23:30 Yeah.
01:23:31 So I guess, you see,
01:23:33 because if I just think of the raw search space, it’s huge.
01:23:35 That’s why you can’t do it.
01:23:37 And if I think about what makes somebody
01:23:38 good at doing these things, they have this heuristic sense.
01:23:42 It’s almost like a good chess player of saying,
01:23:44 let’s not keep analyzing down this way
01:23:45 because there’s some heuristic reason
01:23:47 why that’s a bad way to go.
01:23:49 Where did they get that heuristic from?
01:23:50 Now, that’s a good question.
01:23:51 I don’t know.
01:23:53 Because that, if you asked them to explain to you,
01:23:56 they could probably say something in words
01:23:58 that sounds like it makes sense,
01:23:59 but I’m guessing that’s only a part
01:24:01 of what’s really going on in their brain
01:24:03 of evaluating that position.
01:24:04 You know what I mean?
01:24:05 If you ask Gary Kasparov, what is good,
01:24:06 or why is this position good, he will say something,
01:24:10 but probably not approximating everything
01:24:12 that’s going on inside.
01:24:14 So there’s basically a function being computed,
01:24:16 but it’s hard to articulate what that function is.
01:24:19 Now, the question is, could a computer get as good
01:24:21 at computing these kinds of heuristic functions?
01:24:24 Maybe.
01:24:25 I’m not enough of an expert to understand,
01:24:27 but one bit of me has always been a little bit curious
01:24:30 of whether or not the human brain has a particular tendency
01:24:34 due to its wiring to come up with certain kinds of things,
01:24:37 which is just natural due to the way
01:24:39 that the topology of the neurons and whatever is there,
01:24:43 for which if you tried to just build from scratch
01:24:46 a computer to do it,
01:24:47 would it naturally have different tendencies?
01:24:49 I don’t know.
01:24:50 This is just me being completely ignorant
01:24:52 and just saying a few ideas.
01:24:53 Well, this is a good thing that mathematics shows
01:24:56 is we don’t have to be,
01:24:57 so math and physics or mathematical physics
01:25:00 operates in a world that’s different
01:25:02 than our descendants of eight brains operate in.
01:25:07 So it allows us to have multiple, many, many dimensions.
01:25:11 It allows us to work on weird surfaces.
01:25:15 I would like topology as a discipline is just weird to me.
01:25:19 It’s really complicated,
01:25:21 but it allows us to work in that space,
01:25:23 the differential geometry and all those kinds of things
01:25:25 where it’s totally outside of our natural day to day
01:25:30 four dimensional experience,
01:25:33 3D dimensional with time experience.
01:25:35 So math gives me hope that we can discover
01:25:44 the processes of intelligence outside the limited nature
01:25:49 of our own human experiences.
01:25:51 But you said that you’re not an expert.
01:25:55 It’s kind of funny.
01:25:57 I find that we know so little about intelligence
01:26:02 that I honestly think like almost children are more expert
01:26:08 at creating artificial intelligence systems than adults.
01:26:14 I feel like we know so little,
01:26:15 we really need to think outside the box.
01:26:18 And those little,
01:26:19 I found people should check out
01:26:22 Francois Chollet’s little exams,
01:26:24 but even just solving math problems,
01:26:27 I don’t know if you’ve ever done this for yourself,
01:26:30 but when you solve a math problem,
01:26:33 you kind of then trace back and try to figure out
01:26:38 where did that idea come from?
01:26:40 Like what was I visualizing in my head?
01:26:45 How did I start visualizing it that way?
01:26:48 Why did I start rotating that cube in my head in that way?
01:26:52 Like what is that?
01:26:53 If I were to try to build a program that does that,
01:26:55 where did that come from?
01:26:56 So this is interesting.
01:26:58 So I try to do this to teach middle school students
01:27:02 how to learn how to create and think and invent.
01:27:05 And the way I do it
01:27:06 is there are these math competition problems
01:27:08 and I’m working in collaboration
01:27:10 with the people who run those.
01:27:12 And I will turn on my YouTube live
01:27:14 and for the first time,
01:27:15 look at those questions and live solve them.
01:27:18 The reason I do this is to let the middle school students
01:27:21 and the high school students and the adults
01:27:22 whoever wants to watch,
01:27:23 just see what exactly goes on through someone’s head
01:27:27 as they go and attempt to invent what they need to do
01:27:30 to solve the question.
01:27:32 So I’ve actually thought about that.
01:27:34 I think that, first of all, as a teacher,
01:27:37 I think about that because whenever I want to explain
01:27:39 to a student how to do something,
01:27:42 I want to explain how it made sense,
01:27:44 why it’s intuitive to do the following things
01:27:46 and why the wrong things are wrong.
01:27:48 Not just why this one short fast way,
01:27:51 well, why this is the right way, if that makes sense.
01:27:54 So my point is I’m actually always thinking about that.
01:27:57 Like how would you think about these things?
01:27:58 And then I eventually decided the easiest way
01:28:00 to expose this would just be to go live on YouTube
01:28:04 and just say, I’ve never seen any of these questions before.
01:28:06 Here we go.
01:28:07 Don’t you get, that’s anxiety inducing for me.
01:28:12 Don’t you get trapped in a kind of like little dead ends
01:28:17 of confusion, even on middle school problems?
01:28:20 Yes, that’s what the comments are for.
01:28:21 The live comments come in and students say, try this.
01:28:24 Oh wow.
01:28:25 It’s actually pretty good.
01:28:26 And I’ll never get stuck.
01:28:27 I mean, I’m willing to go on camera and say,
01:28:30 guess what, Potion Dough can’t do this.
01:28:32 That’s fine.
01:28:33 But then what ends up happening is you will then see
01:28:35 how maybe somebody saying something and I look at the chat
01:28:38 and I say, aha, that actually looks useful.
01:28:40 Now that also shows how not all ideas,
01:28:44 not all suggestions are the same power, if that makes sense.
01:28:46 Because if I actually do get stuck,
01:28:48 I’ll go fishing through the chat, if you’ve got any ideas.
01:28:52 I don’t know if you can speak to this,
01:28:53 but is there a moment for the middle school students,
01:28:57 maybe high school as well,
01:28:59 where there’s like a turning point for them
01:29:04 where they maybe fall in love with mathematics
01:29:07 or they get it?
01:29:09 Is there something to be said about like discovering
01:29:13 that moment and trying to grab them to get them
01:29:17 to understand that mathematics is something,
01:29:20 no matter what they wanna do in life
01:29:21 could be part of their life?
01:29:23 Yes.
01:29:23 I actually do think that the middle school
01:29:25 is exactly the right time
01:29:26 because that’s the place
01:29:27 where your mathematical understanding
01:29:30 gets just sophisticated enough
01:29:32 that you can start doing interesting things.
01:29:34 Because if you’re early on and counting,
01:29:37 I’m honestly not very good at teaching you new insights.
01:29:40 My wife is pretty good at that.
01:29:41 But somehow once you get to this part
01:29:44 where you know what a fraction is
01:29:45 and when you know how to add and how to multiply
01:29:49 and what the area of a triangle is,
01:29:51 at that point to me, the whole world opens up
01:29:54 and you can start observing
01:29:55 there are really nifty coincidences,
01:29:57 the things that made the Greek mathematicians
01:29:59 and the ancient mathematicians excited.
01:30:02 Actually back then it was exciting
01:30:03 to discover the Pythagorean theorem.
01:30:05 It wasn’t just homework.
01:30:07 So is there,
01:30:10 which discipline do you think
01:30:11 has the most exciting coincidences?
01:30:14 So is it geometry?
01:30:16 Is it algebra?
01:30:17 Or is it calculus?
01:30:21 Well, you see, you’re asking me
01:30:22 and I’m the guy who gets the most excited
01:30:24 when the combinatorics shows up in the geometry.
01:30:27 Is it, okay.
01:30:30 So it’s the combinatorics in the geometry.
01:30:33 So first of all, the nice thing about geometry,
01:30:35 this is the same nice thing about computer vision
01:30:37 is it’s visual.
01:30:40 So geometry, you can draw circles and triangles and stuff.
01:30:42 So it naturally presents itself
01:30:46 to the visual proof, right?
01:30:49 But also the nice thing about geometry,
01:30:51 I think for me is the earliest class,
01:30:56 the earliest discipline where there’s,
01:30:59 that’s most amenable to the exploration,
01:31:02 the invention through proofs.
01:31:04 The idea of proofs I think is most easily shown in geometry
01:31:09 because it’s so visual, I guess.
01:31:12 So that to me is like,
01:31:14 if I were to think about
01:31:15 when I first fell in love with math, it would be geometry.
01:31:18 And sadly enough, that’s not used.
01:31:21 Geometry only has a little,
01:31:23 appears briefly in the journey of a student.
01:31:29 And it kind of disappears.
01:31:30 And not until much later,
01:31:32 which there may be like differential geometry,
01:31:36 I don’t know where else it shows up.
01:31:37 For me in computer science,
01:31:38 like you could start to think about
01:31:40 like computational geometry or even graph theory
01:31:44 as a kind of geometry.
01:31:45 You could start to think about it visually,
01:31:47 although it’s pretty tricky.
01:31:49 But yeah, it was always,
01:31:51 that was the most beautiful one.
01:31:53 Everything else, I guess calculus can be kind of visual too.
01:31:56 That can be pretty beautiful.
01:31:57 But is there something you try to look for in the student
01:32:05 to see like, how can I inspire them at this moment?
01:32:09 Or is this like individual student to student?
01:32:11 Is there something you could say there?
01:32:13 So first of all,
01:32:14 I really think that every student
01:32:16 can pick up all of this skill.
01:32:17 I really do think so.
01:32:18 I don’t think it’s something only for a few.
01:32:20 And so if I’m looking for a student,
01:32:23 actually oftentimes what I’m,
01:32:25 if I’m looking at a particular student,
01:32:26 the question is,
01:32:28 how can we help you feel like
01:32:30 you have the power to invent also?
01:32:32 Because I think a lot of people
01:32:34 are used to thinking about math
01:32:35 as something where the teacher will show you what to do
01:32:37 and then you will do it.
01:32:39 Yes.
01:32:40 So I think that the key is to show that they have some,
01:32:42 let them see that they have some power to invent.
01:32:44 And at that point,
01:32:45 it’s often starting by trying to give a question
01:32:47 that they don’t know how to do.
01:32:48 You want to find these questions
01:32:49 that they don’t know how to do,
01:32:51 that they can think about,
01:32:53 and then they can solve.
01:32:54 And then suddenly they say,
01:32:55 my gosh, I’ve had a situation,
01:32:57 I’ve had an experience where I didn’t know what to do.
01:33:00 And after a while, I did.
01:33:03 Is there advice you can give on how to learn math
01:33:08 for people, whether it’s a middle school,
01:33:10 whether it’s somebody as an adult
01:33:14 kind of gave up on math maybe early on?
01:33:19 I actually think that these math competition problems,
01:33:22 middle school and high school are really good.
01:33:23 They’re actually very hard.
01:33:25 So if you haven’t had this kind of experience before
01:33:29 and you grab a middle school math competition problem
01:33:32 from the state level,
01:33:33 which is used to decide who represents the state
01:33:36 in the country, in the United States, for example,
01:33:39 those are pretty tricky.
01:33:40 And even if you are a professional,
01:33:43 maybe not doing mathematical things
01:33:45 and you’re not a middle school student, you’ll struggle.
01:33:48 So I find that these things really do teach you things
01:33:51 by trying to work on these questions.
01:33:53 Is there a Googleable term that you could use
01:33:56 for the organization, for the state competitions?
01:33:59 Ah, yeah.
01:34:00 So there are a number of different ones
01:34:02 that are quite popular.
01:34:03 One of them is called Math Counts, M A T H C O U N T S.
01:34:07 And that’s a big tournament,
01:34:08 which actually has a state level.
01:34:10 There’s also a mathleague.org,
01:34:12 mathleague, L E A G U E dot org,
01:34:15 also has this kind of tiered tournament structure.
01:34:18 There’s also the American math competitions, AMC 8.
01:34:22 AMC also has AMC 10, that’s for 10th grade and below
01:34:25 and AMC 12.
01:34:27 These are all run by the Mathematical Association
01:34:29 of America.
01:34:30 And these are all ways to find old questions.
01:34:32 What about the daily challenges that you run?
01:34:34 What are those about?
01:34:36 We do that too.
01:34:36 But I mean, the difference was ours isn’t,
01:34:39 that one’s not free.
01:34:39 So I should actually probably be careful.
01:34:42 The things that I’ve just mentioned are also not free.
01:34:44 Not all of those things I mentioned just now
01:34:45 are free either.
01:34:46 Well, people can figure out what is free and what’s not,
01:34:48 but this is really nice to know what’s out there.
01:34:51 But can you speak a little bit to the daily challenges?
01:34:53 Sure, sure.
01:34:54 So that’s actually what we did when,
01:34:56 I guess I was thinking about,
01:34:58 how would I try to develop that skill in people
01:35:02 if we had the power to architect the entire system ourselves?
01:35:05 So that’s called the daily challenge with Po Shan Luo.
01:35:07 It’s not free because that’s actually how I pay
01:35:09 for everything else I do.
01:35:11 So that was the idea.
01:35:12 But the concept was, aha, now let’s invent from scratch.
01:35:16 So if we’re gonna go from scratch
01:35:17 and we’re gonna use technology,
01:35:19 what if we made every single lesson
01:35:23 something where first I say,
01:35:24 hey, here’s an interesting question.
01:35:25 Recorded, of course, not live.
01:35:27 But it’s like, I say,
01:35:27 hey, here’s an interesting question.
01:35:28 Why don’t we think about this?
01:35:29 But I know you don’t know how to do it.
01:35:32 So now you think,
01:35:32 and a minute later a hint pops on the screen.
01:35:35 But you still think.
01:35:36 And a minute later a big hint pops on the screen.
01:35:38 You still think.
01:35:39 And then finally, after the three minutes,
01:35:41 hopefully you got some ideas you tried to answer.
01:35:43 And then suddenly there’s like this
01:35:45 pretty extended explanation of,
01:35:47 oh yeah, so here’s like multiple different ways
01:35:50 that you can do the question.
01:35:51 And by accident, you also just learned this other concept.
01:35:54 That’s what we did.
01:35:55 So yeah.
01:35:56 Is this targeted towards middle school students,
01:35:58 high school students?
01:35:59 It’s targeted towards middle school students
01:36:01 with competitions.
01:36:02 But there’s a lot of high school students
01:36:04 who didn’t do competitions in middle school
01:36:06 where they would also learn how to think.
01:36:07 If you can see the whole concept was,
01:36:09 can we teach people how to think?
01:36:11 How would you do that?
01:36:12 You need to give people the chance to,
01:36:14 on their own, invent without that kid in the front row
01:36:17 answering every question in two seconds.
01:36:20 And people can find it, I think, what daily.
01:36:24 It’s daily.potionlo.com.
01:36:26 But if you go to find my website,
01:36:27 you’ll be able to find it.
01:36:29 Beautiful.
01:36:30 Can we zoom out a little bit in the,
01:36:32 so day to day, week to week, month to month,
01:36:36 year to year, what does the lifelong educational process
01:36:41 look like, do you think?
01:36:43 For yourself, but for me,
01:36:46 what would you recommend in the world of mathematics
01:36:50 or sort of as opposed to studying for a test,
01:36:52 but just like lifelong expanding of knowledge
01:36:59 in that skill for invention?
01:37:02 I think I often articulate this as,
01:37:05 can you always try to do more than you could do in the past?
01:37:10 Yeah.
01:37:11 But that comes in many ways.
01:37:13 And I will say it’s great
01:37:15 if one wants to build that with mathematics,
01:37:17 but it’s also great to use that philosophy
01:37:20 with all other things.
01:37:21 In fact, if I just think of myself, I just think,
01:37:23 what do I know now that I didn’t know a year ago
01:37:26 or a month ago or a week ago?
01:37:28 And not just know,
01:37:29 but what do I have the capability of doing?
01:37:32 And if you just have that attitude, it brings more.
01:37:35 See, the thing is, there’s also a habit,
01:37:38 like it is a skill, like I’ve been using Anki,
01:37:43 it’s an app for helps you memorize things.
01:37:46 And I’ve actually, a few months ago,
01:37:50 started doing this daily of setting aside time
01:37:54 to think about an idea that’s outside of my work.
01:37:59 Like, let’s say, it’s all over the place, by the way,
01:38:04 but let’s say politics, like gun control.
01:38:08 Is it good to have a lot of guns or not in society?
01:38:11 And just, I’ve set aside time every day,
01:38:15 I do at least 10 minutes, but I try to do 30,
01:38:17 where I think about a problem.
01:38:19 And I kind of outline it for myself from scratch,
01:38:20 from not looking anything up,
01:38:22 just thinking about it, using common sense.
01:38:24 And I think the practice of that is really important.
01:38:29 It’s the daily routine of it, it’s the discipline of it.
01:38:32 It’s not just that I figured something out
01:38:35 from thinking about gun control,
01:38:38 it’s more that that muscle is built too,
01:38:43 it’s that thinking muscle.
01:38:44 So I’m kind of interested in, you know, math has,
01:38:49 because especially because I’ve gotten specialized
01:38:52 into machine learning,
01:38:53 and because I love programming so much,
01:38:55 I’ve lost touch with math a little bit
01:38:59 to where I feel quite sad about it,
01:39:02 and I want to fix that.
01:39:05 Even just not math, like pure knowledge math,
01:39:07 but math, like these middle school problems,
01:39:10 the challenges, right?
01:39:13 Is that something you see a person
01:39:14 be able to do every single day,
01:39:16 kind of just practice every single day for years?
01:39:19 So I can give an answer to that,
01:39:21 that gives a practical way you could do it,
01:39:23 assuming you have kids.
01:39:24 So, no, you can do it yourself.
01:39:26 Step one, get kids.
01:39:28 No, no, I’m just saying this
01:39:29 because I’m just thinking out loud right now,
01:39:31 what could I do to suggest?
01:39:33 Because what I have noticed is that, for example,
01:39:35 if you do have kids who are in elementary school
01:39:37 or middle school, if you yourself go and look
01:39:41 at those middle school math problems
01:39:43 to think about interesting ways
01:39:44 that you can teach your elementary school
01:39:46 or middle school kid, it works.
01:39:48 That’s what my wife did.
01:39:48 She never did any of those contests before,
01:39:51 but now she knows quite a lot about them.
01:39:53 And I didn’t teach her anything.
01:39:53 I don’t do that.
01:39:55 She just was messing around with them
01:39:57 and taught herself all of that stuff.
01:39:59 And that had the automatic daily.
01:40:01 I’m always thinking, how do you make it practical, right?
01:40:03 And the way to make it practical
01:40:04 is if the timer on the automatically daily
01:40:07 is that you are going to automatically daily
01:40:09 do something with your own kid.
01:40:11 Now it feeds back.
01:40:13 And that includes the whole lesson
01:40:14 that if you wanna learn something, you should teach it.
01:40:16 Oh, I strongly believe that.
01:40:19 I strongly believe that.
01:40:21 So I currently don’t have kids.
01:40:23 So that’s, maybe I should just get kids
01:40:25 to help me with the math thing.
01:40:27 But outside of that,
01:40:29 I do want to do great math into daily practice.
01:40:32 So I’ll definitely check out the daily challenges
01:40:35 and see, because what is it?
01:40:39 Grant Sanderson, we talked about offline,
01:40:41 the three blue and brown.
01:40:42 He speaks to this as well,
01:40:44 that his videos aren’t necessarily,
01:40:48 they don’t speak to the thing that I’m referring to,
01:40:50 which is the daily practice.
01:40:52 They’re more almost tools of inspiration.
01:40:56 They kind of show you the beauty
01:40:58 of a particular problem in mathematics,
01:41:03 but they’re not a daily ritual.
01:41:05 And I’m in search of that daily ritual mathematics.
01:41:09 It’s not trivial to find,
01:41:14 but I hope to find that
01:41:16 because I think math gives you a perspective on the world
01:41:20 that enriches everything else.
01:41:23 So I like what you said about the daily also,
01:41:25 because that’s also one reason
01:41:27 why I put my Carnegie Mellon class online.
01:41:29 It’s not every day.
01:41:30 It’s every other day.
01:41:31 Semester is almost over.
01:41:33 But the idea was, I guess my philosophy was,
01:41:35 if I’m already doing the class,
01:41:37 let’s just put it there, right?
01:41:38 But I do know that there are people
01:41:40 who have been following it,
01:41:42 who are not in my class at all,
01:41:43 who have just been following it because,
01:41:45 yes, it’s combinatorics.
01:41:47 And the value of that is you could,
01:41:49 you don’t really need to know calculus to follow it,
01:41:51 if that makes sense.
01:41:52 So it’s actually something that people could follow.
01:41:54 So again, and that one’s free.
01:41:56 So that one’s just there on YouTube.
01:41:58 Well, speaking of combinatorics,
01:42:01 what is it, what do you find interesting,
01:42:03 what do you find beautiful about combinatorics?
01:42:07 So combinatorics to me is the study of things
01:42:11 where they might be more finite and more discreet.
01:42:17 What I mean is like, if I look at a network,
01:42:18 actually a lot of times the combinatorics
01:42:20 will boil down to something,
01:42:21 and the combinatorics I think about
01:42:23 might be something related to graphs or networks.
01:42:25 And they’re very discreet because if you have a node,
01:42:28 it’s not that you have 0.7 of a node
01:42:32 and 0.3 of a node over there.
01:42:33 It’s that you’ve got one node,
01:42:34 and then you jump one step to go to the next node.
01:42:37 So that notion is different from say, calculus,
01:42:39 which is very continuous,
01:42:42 where you go and say, I have this speed,
01:42:44 which is changing over time.
01:42:46 And now what’s the distance I’ve traveled?
01:42:47 That’s the notion of an integral,
01:42:49 where you have to think of subdividing time
01:42:50 into very, very small pieces.
01:42:52 So the kinds of things that you do
01:42:54 when you reason about these finite discreet structures
01:42:59 often might be iterative, algorithmic, inductive.
01:43:03 These are ideas where I go from one step to the next step
01:43:06 and so on and make progress.
01:43:08 I guess I actually personally like all kinds of math.
01:43:11 My area of research just ended up in here
01:43:13 because I met a really interesting PhD advisor,
01:43:17 potential, that’s honestly the reason
01:43:19 I went into that direction.
01:43:20 I met a really interesting guy.
01:43:22 He seemed like he did good stuff, interesting stuff,
01:43:24 and he looked like he cared about students.
01:43:26 And I said, let me just go and learn whatever you do,
01:43:29 even though my prior practice and preparation
01:43:32 before my PhD was not combinatorics,
01:43:34 but analysis, the continuous stuff.
01:43:36 So the annoying thing about combinatorics
01:43:40 and discreet stuff is it’s often really difficult to solve
01:43:45 from a sort of running time complexity perspective.
01:43:53 Could you speak to the idea of complexity analysis
01:43:59 of problems, do you find it useful, do you find it interesting?
01:44:04 Do you find that lens of studying the difficulty
01:44:08 of how difficult the computer science problem is
01:44:12 a useful lens onto the world?
01:44:15 Oh, very much so.
01:44:16 Because if you want to make something practical
01:44:20 which has large numbers of people using it,
01:44:22 the computational complexity to me is almost question one.
01:44:27 And that’s, again, that’s at the origin
01:44:29 of when we started doing this stuff with disease control.
01:44:31 From the very beginning, the deep questions
01:44:33 that were running through my mind were,
01:44:35 would we be able to support a large population
01:44:38 with only one server?
01:44:41 And if the answer is no, we can’t start
01:44:43 because I don’t have enough money.
01:44:48 Yeah, and there the question is very much
01:44:51 linear time versus anything slower than linear time.
01:44:58 As a very specific thing, you have a bunch
01:45:00 of really interesting papers.
01:45:01 If I could ask, maybe we could pull out some cool insights
01:45:04 at the high level.
01:45:06 Can you describe the data structure of a voting tree
01:45:08 and what are some interesting results on it?
01:45:11 You have a paper that I noticed on it.
01:45:13 Yeah, so this is an example of, I guess,
01:45:17 how in math we might say here’s an interesting
01:45:20 kind of a question that we just can’t seem
01:45:24 to understand enough about.
01:45:25 Maybe there’s something else going on here.
01:45:27 And the way to describe this is you could imagine
01:45:30 trying to hold elections where if you have
01:45:33 only two candidates, that’s kind of easy.
01:45:35 You just run them against each other
01:45:37 and see who gets more votes.
01:45:38 But as you know, once you have more candidates,
01:45:40 it’s very difficult to decide who wins the election.
01:45:43 And there’s an entire voting theory around this.
01:45:46 So a theoretical question became,
01:45:49 what if you made like a system of runoffs,
01:45:53 like a system of head to head contests,
01:45:57 which is structured like a tree,
01:45:58 almost looking like a circuit.
01:46:00 I’m using that way of thinking because it’s sort of like
01:46:03 in electrical engineering or computer science,
01:46:05 you might imagine having a bunch of leads
01:46:08 that carry signal, which are going through AND gates
01:46:10 and OR gates and whatnot.
01:46:11 And you’ve managed to compute beautiful things.
01:46:13 This is just from a purely abstract point of view.
01:46:16 What if the inputs are candidates?
01:46:18 And for every two candidates, it is known
01:46:20 which of the candidates is more popular than the other.
01:46:23 Now can you build some kind of a circuit board
01:46:25 which says, first candidate number four
01:46:28 will play against five and see who wins and so on.
01:46:31 Okay, so now what would be a nice outcome, right?
01:46:34 This is a general question of,
01:46:35 could I make a big circuit board to feed an election into?
01:46:39 Like maybe one nice outcome would be whoever wins
01:46:41 at least is preferred over a lot of people.
01:46:44 Yes.
01:46:45 So for example, if you ran in 1,024 candidates,
01:46:48 ideally we would like a guarantee that says
01:46:51 that the winner beats a lot of people.
01:46:54 Actually in any system where there are 1,024 candidates,
01:46:58 there’s always a candidate who beats
01:47:00 at least 512 of the others.
01:47:02 This is a mathematical fact
01:47:04 that there’s actually always a person who beats
01:47:06 at least half of the other people.
01:47:09 I’m trying to make sense of that mathematical fact.
01:47:13 Is this supposed to be obvious?
01:47:15 No, but I can explain it.
01:47:17 No, I can’t.
01:47:17 The way it works is that, think of it this way.
01:47:21 Every time I think, imagine I have all these candidates
01:47:24 and everyone is competing,
01:47:26 everyone is like compared with everyone else at some point.
01:47:29 Well, think of it this way.
01:47:30 Whenever there’s a comparison, somebody gets a point.
01:47:34 That’s the one who is better than the other one.
01:47:37 My claim is there’s somebody whose score
01:47:39 is at least half of how many other people there are.
01:47:42 Yeah, I’m just trying to,
01:47:44 like my intuition is very close to that being true,
01:47:47 but it’s beautiful.
01:47:48 I didn’t at first, that’s not an obvious fact.
01:47:52 No, it’s not.
01:47:53 And it feels like a beautiful fact.
01:47:55 Well, let me explain it this way.
01:47:57 Imagine that for every match,
01:48:00 you didn’t give one point, but you gave two points.
01:48:03 You gave one point to each person.
01:48:05 Now that’s not what we’re really doing.
01:48:07 We really want to give one point to the winner of the match,
01:48:10 but instead we’ll just give two.
01:48:12 If you gave two points to everyone on every matchup,
01:48:15 actually everyone has the same number of points.
01:48:18 And the number of points they get
01:48:19 is how many other people there are.
01:48:22 Does that sort of make sense?
01:48:23 I’m just like saying.
01:48:24 No, no, everything you’re saying makes perfect sense.
01:48:26 So the point is if for every comparison between two people,
01:48:30 which I’m doing for every two people,
01:48:32 I gave one point to each person,
01:48:34 your score, everyone’s score is the same.
01:48:36 It’s how many other people there are.
01:48:38 Now we only make one change.
01:48:40 For each matchup, you give one point only to the winner.
01:48:44 So we’re awarding half the points.
01:48:47 So now the deal is if in the original situation,
01:48:50 everyone’s score was equal,
01:48:52 which is how many other people there are.
01:48:54 Now there’s only half the number of points to go around.
01:48:58 So what ends up happening is that
01:49:01 there’s always going to be,
01:49:02 like the average number of points per person
01:49:04 is going to be half of how many other people there are.
01:49:07 And somebody is gonna be above average.
01:49:08 Somebody is going to be above that.
01:49:09 At least average.
01:49:10 Yeah, this is this notion of expected value,
01:49:13 that if I have a random variable,
01:49:14 which has an expected value,
01:49:16 there’s going to be some possibility
01:49:17 in the probability space
01:49:19 where you’re at least as big as the expected value.
01:49:21 Yeah, when you describe it like that, it’s obvious.
01:49:23 But when you’re first saying in this little circuit
01:49:26 that there’s going to be one candidate better than half,
01:49:32 that’s not obvious.
01:49:33 Yeah, it’s not obvious.
01:49:34 It’s funny.
01:49:35 It’s not obvious.
01:49:35 Math, this is nice.
01:49:37 Okay, so you have this,
01:49:38 but ultimately you’re trying to with a voting tree,
01:49:42 I don’t know if you’re trying this,
01:49:43 but to have a circuit that’s like, that’s small.
01:49:48 Well, you’d like it to be small.
01:49:49 That achieves the same kind of,
01:49:53 I mean, the smaller it is,
01:49:56 if we look at practically speaking,
01:49:59 the lower the cost of running the election,
01:50:01 of running through, of computing the circuit.
01:50:03 That is true.
01:50:04 But actually at this point,
01:50:05 the reason the question was interesting
01:50:08 is because there was no good guarantee
01:50:12 that the winner of that circuit
01:50:15 would have like have beaten a lot of people.
01:50:18 Let me give an example.
01:50:19 The best known circuit,
01:50:20 when we started thinking about this,
01:50:22 was the circuit called candidate one
01:50:24 plays against candidate two,
01:50:26 candidate three plays against four,
01:50:28 and then the winners play against each other.
01:50:30 And then by the way, five plays against six,
01:50:32 seven against eight, the winners play against each other.
01:50:34 You understand, it’s like a giant binary tree.
01:50:36 Yeah, it’s a binary, like a balanced binary tree.
01:50:39 It’s a balanced binary tree.
01:50:40 One, two, three, four, up to 1,024,
01:50:42 everyone going up to find the winner.
01:50:44 Well, you know what?
01:50:45 There’s a system in the world
01:50:47 where it could just be
01:50:49 that there’s a candidate called number one,
01:50:52 that just beats like 10 other people,
01:50:56 just the 10 that they need to be on their way up
01:50:59 and they lose to everyone else.
01:51:02 But somehow they would get all the way up.
01:51:04 My point is it is possible to outsmart that circuit
01:51:11 in one weird way of the world,
01:51:13 which makes that circuit a bad one
01:51:15 because you want to say,
01:51:16 I will use this circuit for all elections.
01:51:18 And you might have a system of inputs that go in there
01:51:22 where the winner only beat 10 other people,
01:51:24 which is the people they had to beat on the way up.
01:51:26 So you want to have a circuit where there’s as many,
01:51:29 like the final result is as strong as possible.
01:51:33 Yes.
01:51:34 And so what ideas do you have for that?
01:51:37 So we actually only managed to improve it
01:51:40 to square root of N.
01:51:41 So if N is number of vertices,
01:51:43 N over two would be the ideal.
01:51:46 We got it to square root of N.
01:51:48 Versus log base two.
01:51:50 Yeah, exactly.
01:51:51 Yeah.
01:51:52 Which is…
01:51:53 Well, that is halfway.
01:51:54 It could be a lot.
01:51:55 Yeah.
01:51:56 Could be a big improvement.
01:51:57 So that’s a, okay, cool.
01:51:59 Is there something you can say with words
01:52:01 about what kind of circuit, what that looks like?
01:52:04 I can give an idea of one of the tools inside,
01:52:08 but the actual execution ends up being more complicated.
01:52:10 But one of the widgets inside this
01:52:12 is building a system where you have like a candidate
01:52:16 who plays, like one part of the whole huge, huge tree
01:52:20 is that that same candidate, let’s call them seven.
01:52:23 Seven plays against somebody,
01:52:25 let’s make up some numbers.
01:52:26 Let’s call the others like letters.
01:52:27 So seven plays against A.
01:52:30 Seven’s also gonna play against B separately.
01:52:33 And the winners of each of those will play each other.
01:52:36 By the way, seven’s also gonna play C.
01:52:38 Seven’s gonna play D.
01:52:39 And the winners are gonna play each other.
01:52:41 And the winners are gonna play each other.
01:52:42 We call this seven against all.
01:52:44 Well, seven against like everyone from a bunch of.
01:52:47 Got it.
01:52:48 So there’s some nice overlap between the matchups
01:52:50 that somehow has a nice feature to it.
01:52:53 Yes, and I can tell you the nice feature
01:52:54 because if at the base of this giant tree,
01:52:56 at the base of this giant circuit,
01:52:57 like this is a widget.
01:52:58 We build the things out of widgets.
01:52:59 So I’m just describing one widget.
01:53:01 But in the base of this widget,
01:53:03 you have lots of things which are seven against someone,
01:53:05 seven against someone, seven against someone.
01:53:07 In fact, every matchup at the bottom
01:53:09 is seven against someone.
01:53:11 What that means is
01:53:12 if seven actually beat everyone they were matched up against,
01:53:16 well, seven would rise to the top.
01:53:18 So one possibility is if you see a seven
01:53:21 emerge from the top,
01:53:22 you know that seven actually beat everyone
01:53:24 they were against.
01:53:25 On the other hand, if anyone else is on top,
01:53:28 let’s call it F.
01:53:29 If F is on top, how did F get there?
01:53:31 Well, F beat seven on the way at the beginning.
01:53:34 So the point is the outcome of this circuit
01:53:37 has a certain property.
01:53:38 If you see a seven,
01:53:39 you know that the seven actually beat a person
01:53:41 but the seven actually beat a bazillion people.
01:53:43 If you see anyone else,
01:53:45 at least you know they beat seven.
01:53:47 Yeah, then you can prove that it has a nice property.
01:53:49 That’s really interesting.
01:53:50 Is there something you can say,
01:53:54 perhaps going completely outside
01:53:55 of what we’re talking about,
01:53:56 is how we may
01:54:00 have mathematical ideas
01:54:03 of improving the electoral process?
01:54:06 That one, no.
01:54:07 No, I can’t give you that one.
01:54:09 I mean, is there, like, do you ever see it as,
01:54:14 do you see as there being a lot of opportunities
01:54:17 for improving how we vote?
01:54:20 Like from your, I don’t know if you saw parallels,
01:54:23 but, you know, it seems like if,
01:54:26 this actually kind of maps to your sort of COVID work,
01:54:29 which is there’s a network effect, right?
01:54:32 It seems like we should be able to apply similar kind
01:54:34 of effects of how we decide other things in our lives.
01:54:39 And one of the big decisions we’ll make
01:54:42 is who represents us in government.
01:54:44 Do you ever think about like mathematically
01:54:46 about those kinds of systems?
01:54:48 I think a little bit about those,
01:54:49 because where I went to college,
01:54:51 the way we voted for student government
01:54:53 was based on this, is it called ranked choice?
01:54:56 Where you eliminate the bottom
01:54:58 and there was runoff elections.
01:55:00 So that was the first time I ever saw that.
01:55:02 And I thought that made sense.
01:55:04 The only problem is it doesn’t seem so easy
01:55:06 to get something that makes sense adopted
01:55:08 as the new voting system.
01:55:09 That’s a whole nother, that’s not a math solution.
01:55:12 That’s a, well, it’s math in the sense that it’s game theory.
01:55:16 So you have to come up with incentive,
01:55:17 it’s mechanism design.
01:55:18 You have to figure out how to trick us
01:55:21 despite our basic human nature
01:55:24 to adopt solutions that are better.
01:55:27 That’s a whole nother conversation, I think.
01:55:30 Can you just, cause it sounded really cool,
01:55:33 talk a little bit about stochastic coalescence
01:55:36 and you have a paper on showing that,
01:55:39 so you could describe what it is,
01:55:40 but I guess it’s a super linear, super logarithmic time
01:55:44 and you came up with some kind of trick
01:55:46 that make it faster.
01:55:47 Can you just talk about it a little bit?
01:55:49 Yeah, so this was something which came up
01:55:51 when I was at Microsoft Research for a summer.
01:55:54 And I’m putting that context because that shows
01:55:56 that it has some practical motivation at some point.
01:56:01 Actually, I think it’s still.
01:56:01 It doesn’t need to.
01:56:02 It doesn’t need to.
01:56:03 It can be beautiful and it’s all right.
01:56:05 Yeah, so the easiest way to describe this is
01:56:07 suppose you got like a big crowd of people
01:56:09 and everybody knows how many hours of sleep
01:56:12 they got last night.
01:56:13 And you wanna know how many total hours of sleep
01:56:15 were gotten by this big crowd of people.
01:56:17 At the beginning, you might say,
01:56:18 that sounds like a linear time algorithm
01:56:20 of saying, hey, how many hours you got?
01:56:22 How many you got?
01:56:23 How many you got?
01:56:24 Add, add, add.
01:56:25 But there’s a way to do this
01:56:26 if you remember that there are people
01:56:28 and they presumably know how to add.
01:56:30 You could make a distributed algorithm
01:56:32 to make this happen.
01:56:33 For example, while we’re thinking of these trees,
01:56:35 imagine you had 1,024 people.
01:56:38 If you could just say, hey, person number one
01:56:40 and person number two, you will add your hours of sleep.
01:56:44 Person number two will go away
01:56:46 and person number one is gonna remember the sum.
01:56:48 Person three and four add up
01:56:50 and person three takes charge of remembering it.
01:56:53 Person four goes away.
01:56:54 Now this like person one knows the sum of these two.
01:56:56 Person three knows the sum of those two.
01:56:58 They talk.
01:56:59 You see what I mean?
01:56:59 You’re going up this tree,
01:57:02 same tree that we talked about earlier.
01:57:03 Built up a tree from the bottom up.
01:57:05 Yeah, build up a tree from the bottom up.
01:57:07 And the beautiful thing is
01:57:09 since everyone’s doing stuff in parallel,
01:57:11 the amount of time it takes to get the total sum
01:57:14 is actually just the number of layers in the tree,
01:57:17 which is 10.
01:57:18 So now that’s logarithmic time
01:57:20 to add up the number of hours that people slept today.
01:57:23 Sounds fantastic.
01:57:25 There’s only one problem.
01:57:26 How do you decide who’s person number one
01:57:27 and person number two?
01:57:29 Yes.
01:57:30 So if, for example, you just went out into the downtown
01:57:32 and said, hey, get these thousand people, go.
01:57:34 Well, if you’re gonna go and say,
01:57:35 and by the way, you’re one and you’re two and you’re three,
01:57:37 that’s linear time.
01:57:38 Yes.
01:57:39 That’s cheating.
01:57:40 So now the question is how to do this
01:57:41 in a distributed way.
01:57:43 And there were some people who proposed
01:57:44 a very elegant algorithm and they wanted to analyze it.
01:57:48 So I came in onto the analyze side,
01:57:50 but the elegant algorithm was like this.
01:57:52 It was like, well, we don’t actually know
01:57:55 what this big tree is.
01:57:57 There isn’t any big tree.
01:57:58 So what’s gonna happen is first,
01:58:01 everyone is going to decide right now.
01:58:04 Oh, one important thing.
01:58:05 Everyone is going to,
01:58:07 at the very beginning of the whole game,
01:58:09 they will have delegated responsibility to themselves
01:58:13 as the one who knows the sum so far.
01:58:16 So the point is there’s gonna be,
01:58:18 people are all gonna have like a pointer which says,
01:58:22 you are the one who knows my,
01:58:24 you’ve taken care of my ticket, my number.
01:58:26 Yeah.
01:58:27 You’re the representative for this particular piece
01:58:30 of knowledge.
01:58:31 And at the very beginning, you’re your own representative.
01:58:33 The thing has to start simple, right?
01:58:35 So at the beginning, you’re your own representative.
01:58:36 You’re pointing to yourself, got it.
01:58:38 Yup, yup.
01:58:38 And now the way this works is that at every time step,
01:58:41 someone blares a ding dong on the town clock or whatever.
01:58:45 And each person flips a coin themselves to decide,
01:58:48 am I going to hunt for somebody to give my number to
01:58:53 and let them represent me?
01:58:55 Or am I going to sit here and wait for someone to come?
01:58:58 Okay.
01:58:59 Okay.
01:59:00 Well, they flipped their coin.
01:59:02 Some of the people start asking other people saying,
01:59:04 hey, I would like you to be my representative.
01:59:08 Here is my number.
01:59:10 But the problem is that there’s limited bandwidth
01:59:12 of the people who are getting asked.
01:59:13 It’s like, you can’t get,
01:59:14 you can’t go out to prom with five people.
01:59:16 But this is not what we’re doing.
01:59:17 We’re adding numbers, okay?
01:59:19 But you can only add one number.
01:59:20 So the person who has suddenly gotten asked
01:59:22 by all these people,
01:59:23 well, they’ll have to decide who they’re going
01:59:25 to take it from.
01:59:27 And they randomly just choose one.
01:59:29 When they randomly choose one,
01:59:30 all the others are rejected
01:59:31 and they don’t get to delegate anything in that round.
01:59:34 But now if this person has absorbed this one who said,
01:59:38 okay, here, you take charge of my number.
01:59:40 This person now updates their pointer.
01:59:42 You’re in charge.
01:59:44 And this person adds the two numbers.
01:59:47 That was the first round.
01:59:50 In the next round, when they do the coin flipping,
01:59:52 this person doesn’t flip anymore
01:59:54 because they’re just delegating.
01:59:56 It’s that anyone who has the pointers themselves,
01:59:59 that’s like a person who is in charge
02:00:01 of some number of informations,
02:00:03 they flip the coin to decide,
02:00:04 should I find other people who are agents?
02:00:08 Or should I wait for people to ask me?
02:00:10 Yes.
02:00:10 Brilliant.
02:00:11 This is somebody else’s idea.
02:00:12 And then now the idea is, okay,
02:00:14 if you just keep doing this process,
02:00:15 what ends up happening?
02:00:16 Oh yeah, and also by the way,
02:00:18 if you decide that you want to go reach out
02:00:20 to other people, here’s the catch.
02:00:23 When you’re one of these agents saying,
02:00:24 okay, I’m going to go look for someone.
02:00:27 You have no idea who in this crowd is an agent
02:00:30 or somebody who delegated it to someone else.
02:00:33 You just pick a random person.
02:00:35 When you pick the random person,
02:00:37 if it lands on someone and the person says,
02:00:38 oh, I actually delegated it to someone,
02:00:41 then you follow the point.
02:00:43 You walk up the delegation chain.
02:00:45 Walk up the delegation chain.
02:00:46 And you can do like path compression in the algorithm
02:00:49 to make it so you don’t consistently
02:00:50 do lots of walking up.
02:00:52 But the bottom line is that what ends up happening
02:00:54 is that you end up reaching out.
02:00:57 Whenever you’re one of the ones reaching out,
02:00:59 you can think of it as each agent is responsible
02:01:01 for some number of people.
02:01:03 It’s almost like they’re the leader of a bunch.
02:01:05 As the process is evolving, you have these lumps.
02:01:09 Each lump has an agent.
02:01:11 And when the agent reaches out,
02:01:13 they reach out to another lump
02:01:15 where the probability of them hitting that lump
02:01:18 is proportional to the size of the lump.
02:01:21 That is the one funny thing about this process.
02:01:25 This is not that they can reach out
02:01:27 to a uniformly random lump
02:01:29 where every lump has the same chance
02:01:30 of getting reached out to.
02:01:32 The bigger the lump is,
02:01:34 the more likely it is that you end up reaching that lump.
02:01:38 Which is a problem?
02:01:40 Let me explain why that’s a problem.
02:01:41 Because you see, you’re hoping
02:01:43 that this has a small number of steps,
02:01:45 but here’s a bad situation that could happen.
02:01:47 Imagine if you had like,
02:01:50 there are n people that you’re adding up.
02:01:52 Imagine that you have exactly square root of n lumps left,
02:01:57 of which almost all of them are just one person
02:02:01 who’s still their own boss, their own manager.
02:02:04 Except one giant one.
02:02:06 Now what’s gonna happen?
02:02:06 It’s gonna be a huge bottleneck
02:02:08 because every round the giant one
02:02:09 can only absorb one of the others.
02:02:11 And now you suddenly have time
02:02:13 which is about square root of n.
02:02:15 The square root of n is chosen
02:02:16 because that is one where the lumps are such
02:02:20 that you really are limited by this large one
02:02:23 slowly sucking up the rest of them.
02:02:26 So the heart of the question became,
02:02:28 well, but is that just so unusual
02:02:30 that it doesn’t usually happen?
02:02:32 Because remember you start with everyone
02:02:34 just being independent.
02:02:36 It’s like a lot of lumps of size one.
02:02:37 How naturally do the big lumps emerge?
02:02:39 Yes.
02:02:40 And so what that heart of the proof was,
02:02:42 was showing that that was a joint work with Eyal Lubezki.
02:02:45 That one was showing that actually in that thing
02:02:49 the lumps do kind of get out of whack.
02:02:50 And so it’s not the purely logarithmic number of steps.
02:02:54 But if you make one very slight change,
02:02:56 which is if you are one of the agents
02:03:00 and you have just been propositioned,
02:03:02 possibly relayed along by a couple of different people.
02:03:05 If you just say, don’t take a random one,
02:03:07 but accept the smallest lump.
02:03:12 That actually does enough to even the whole economy.
02:03:14 Distributes the lump size.
02:03:16 I mean, yeah, it’s fascinating how
02:03:17 with the distributed algorithms,
02:03:19 a little adjustment can make all the difference
02:03:21 in the world.
02:03:22 Yeah.
02:03:23 Actually, by the way, this does,
02:03:25 back to our voting conversation,
02:03:26 this makes me think of like,
02:03:29 these networking systems are so fascinating to study.
02:03:32 They immediately spring to mind ideas
02:03:35 of how to have representation.
02:03:37 Like maybe as opposed to me voting for a president,
02:03:42 I want to vote for like,
02:03:45 for you, Paul, to represent me,
02:03:48 maybe on a particular issue.
02:03:50 And then you will delegate that further.
02:03:52 And then we naturally construct those kinds of networks
02:03:55 because that feels like I can have a good conversation
02:03:58 with you and figure out that you know what you’re doing
02:04:00 and I can delegate it to you.
02:04:01 And in that way, construct a representative government,
02:04:05 a representative decision maker.
02:04:08 That feels really nice as opposed to like us,
02:04:12 like a tree of height one or something,
02:04:14 where it’s like everybody’s just,
02:04:18 it feels like there’s a lot of room for layers
02:04:20 of representation to form organically from the bottom up.
02:04:23 I wonder if there are systems like that.
02:04:25 This is the cool thing about the internet
02:04:27 and the digital space where we’re so well connected,
02:04:29 just like with the Novid app to distribute information
02:04:34 about the spread of the disease.
02:04:37 We can in the same way, in a distributed sense,
02:04:39 form anything like any kind of knowledge bases
02:04:44 that are formed in a decentralized way
02:04:48 and in a hierarchical way,
02:04:51 as opposed to sort of old way
02:04:54 where there is no mechanism for large scale,
02:04:56 fast distributed transactional information.
02:05:01 This is really interesting.
02:05:02 This is where almost like network graph theory,
02:05:06 becomes practical.
02:05:09 Most of that exciting work was done in the 20th century,
02:05:11 but most of the application will be in the 21st,
02:05:14 which is cool to think about.
02:05:15 Let me ask the most ridiculous question.
02:05:17 You think P equals NP?
02:05:19 Wow.
02:05:21 I don’t know.
02:05:22 I mean, I would say,
02:05:26 I know there are enough people who have very strong interest
02:05:29 in trying to show that it is.
02:05:32 I’m talking about government agencies.
02:05:34 For security purposes.
02:05:38 For security purposes.
02:05:39 And most computer scientists,
02:05:40 we should say believe that P equals NP.
02:05:43 My question almost like,
02:05:45 this is back to our aliens discussion.
02:05:47 You want to think outside the box,
02:05:48 the low probability event,
02:05:51 what is the world,
02:05:54 what kind of discoveries would lead us to prove
02:05:58 that P does not equal to NP?
02:06:01 Like there could be giant misunderstandings
02:06:05 or gaps in our knowledge about computer science,
02:06:08 about theoretical computer science, about computation,
02:06:11 which allow us to think like flatten all problems.
02:06:14 Yeah, so I don’t know the answer to this question.
02:06:17 I think it’s very interesting, but I actually,
02:06:19 I know, let’s put it this way.
02:06:21 By being at Carnegie Mellon
02:06:22 and being around the theoretical computer scientists,
02:06:24 I know enough about what I don’t know to say.
02:06:27 To be humble.
02:06:28 I’m the wrong person to answer this question.
02:06:32 It’s a great one.
02:06:33 Well, Scott Aaronson, who’s now here at UT Austin,
02:06:35 he used to be at MIT,
02:06:37 puts the probability of P not equals to NP at 3%.
02:06:45 I always love it when you ask,
02:06:48 it’s very rare in science and academics
02:06:51 because most folks are humble
02:06:54 in the face of the mystery,
02:06:56 the uncertainty of everything around us.
02:06:59 To have both the humor and the guts to say like,
02:07:03 what are the chance that there’s aliens in our galaxy,
02:07:07 intelligent alien civilizations?
02:07:09 As opposed to saying, I don’t know, it could be zero.
02:07:12 It could be, depending on the fact, you’re saying it’s 2.5%.
02:07:15 There’s something very pleasant about just having,
02:07:20 it’s the number thing.
02:07:24 It’s powered to the number.
02:07:25 It’s just like 42.
02:07:26 It’s like, why 42?
02:07:27 I don’t know, but it’s a powerful number.
02:07:29 And then everything,
02:07:30 this is the power of human psychology
02:07:32 is once you have the number 42,
02:07:36 it’s not that the number has meaning,
02:07:39 but because it’s placed in a book with humor around it,
02:07:43 it has the meme effect of actually creating reality.
02:07:49 I mean, you could say that 42 has a strong contribution
02:07:53 of helping us colonize Mars
02:07:55 because it created,
02:07:57 it gave the whatever existential crisis to many of us,
02:08:00 including Elon Musk when he was young,
02:08:03 reading a book like that.
02:08:04 And then now 42 is now part of his humor
02:08:07 that he doesn’t shut up about,
02:08:08 it’s constantly joking about.
02:08:09 And that humor is spreading through our minds
02:08:12 and somehow this like silly number just had an effect.
02:08:15 In that same way, after Scott told me like the 3% chance,
02:08:19 it’s stuck in my head.
02:08:20 And I think it’s been having a ripple effect
02:08:22 in everybody else.
02:08:23 The believing that P is not equal to NP,
02:08:29 Scott almost as a joke saying it’s 3%
02:08:32 is actually motivating a large number of researchers
02:08:34 to work on it.
02:08:35 3% is high.
02:08:37 It’s very high.
02:08:37 Because for the potential impact that that would have.
02:08:39 But then 3% is not that high because it’s only,
02:08:44 you know, like we’re not very good.
02:08:46 I feel like humans are only able to really think about
02:08:48 like 1%, 50%.
02:08:51 And we kind of, I think a lot of people around 3%
02:08:55 up to 50% like in our minds.
02:08:58 Like 3% at this point.
02:09:00 It could happen.
02:09:01 It could happen.
02:09:02 And it could happen and it’s like, yeah.
02:09:04 Like half the time it’ll probably happen.
02:09:07 So we’re not very good at that.
02:09:08 That’s the other thing with the pandemic
02:09:10 is we’re not the exponential growth
02:09:13 that we also talked about offline
02:09:15 is something that we can’t quite intuit.
02:09:20 And that’s something we probably should
02:09:22 if we’re to predict the future, to anticipate the future
02:09:25 and to understand how to create technologies
02:09:27 that let us sort of control the future.
02:09:32 Can I ask you for some recommendations
02:09:35 maybe for books or movies in your life?
02:09:39 Long ago when you were baby Po or today
02:09:45 that you found insightful or you learned a lot from
02:09:50 what you would recommend to others.
02:09:52 Yeah.
02:09:52 So I think I don’t necessarily have an exact name
02:09:55 of these old things, but I was generally inspired
02:09:58 by stories, true or fictional of campaigns.
02:10:05 For example, like the Lord of the rings, that’s a campaign.
02:10:09 But the thing that always inspired me was
02:10:12 it could be possible for somebody who’s crazy enough
02:10:16 to go up against adversity after adversity,
02:10:18 and it succeeds.
02:10:20 I mean, those are false, those are fictitious.
02:10:23 But I also spent a lot of time, I guess, reading about,
02:10:25 I don’t know, I was interested somehow
02:10:26 in like World War II history for whatever reason.
02:10:29 That’s a campaign which is much more brutal.
02:10:31 But nevertheless, the idea of difficulty, strategy,
02:10:37 fighting even when things,
02:10:39 in that case it was really fighting,
02:10:40 but just pushing on even when things are difficult.
02:10:43 I guess these are the kinds of general stories
02:10:46 that made me, I guess, want to work on things
02:10:50 that would be hard and where it could be a campaign.
02:10:54 It could be that you work on something for a year,
02:10:57 multiple years, because that was the point, I guess.
02:11:02 Yeah, it starts with a single person.
02:11:04 That’s the interesting thing.
02:11:05 I’ve obviously been, don’t shut up about it recently
02:11:08 about World War II, especially on the Hitler side
02:11:11 and the Stalin side.
02:11:12 Some of that has really affected my own family.
02:11:15 The roots of my family very much.
02:11:18 But it’s interesting to think that it was just an idea
02:11:24 and one person decided to do stuff
02:11:26 and it just builds and builds and builds.
02:11:29 And you can truly have an impact on the world,
02:11:31 both horrendous and exceptionally positive and inspiring.
02:11:36 So yeah, it’s like it’s a agency of us individuals.
02:11:47 Sometimes we think we’re just reacting to the world,
02:11:49 but we have the full power to actually change the world.
02:11:53 Is there advice you can give to young folks?
02:11:56 We talked, we gave a bunch of advice
02:11:58 on middle school, high school mathematics.
02:12:00 Is there more general advice you would give
02:12:02 about how to succeed in life,
02:12:04 how to learn for high school students,
02:12:07 for college students, career or life in general?
02:12:10 So I think the first one would be
02:12:12 to make sure that you’re learning to invent
02:12:14 and to make sure you’re not just learning how to mimic.
02:12:19 Because a lot of times you learn how to do X
02:12:21 by watching somebody do X and then repeating X
02:12:24 many times with different inputs.
02:12:26 I’ve just been very generic in explaining this.
02:12:28 But I guess this is just my own attitude towards the world.
02:12:31 I didn’t like ever following anyone’s directions exactly.
02:12:34 Even if you told me this is the way to do your homework
02:12:37 is to write in pencil, I would say,
02:12:39 but I think pen is nice, let’s try, right?
02:12:42 So I’ve been that kind of a funny person.
02:12:45 But I do encourage that if you can learn how to invent
02:12:50 as your core skill, then you can do a lot.
02:12:52 But then the second piece that comes with that
02:12:54 is something I learned from my PhD advisor,
02:12:57 which was, well, make sure that what you’re working on
02:13:01 is big enough.
02:13:02 And so in that sense, I usually advise to people
02:13:04 once they have learned how to invent,
02:13:07 ideally don’t just try to settle for something comfortable,
02:13:11 try to see if you can aim for something which is hard,
02:13:15 which might involve a campaign, which might be important,
02:13:18 which might make a difference.
02:13:20 And it’s more of, I guess, rather than worrying
02:13:23 what if you didn’t achieve that,
02:13:27 there’s also the regret of what if I didn’t try?
02:13:30 See, that’s how I operate.
02:13:31 I don’t operate based on did I succeed or fail?
02:13:33 It was hard anyway.
02:13:34 If I did this novid thing and the whole thing failed,
02:13:36 would I feel terrible?
02:13:37 No, it’s a very hard problem.
02:13:39 But would I have had the regret of not jumping in?
02:13:42 Yes.
02:13:44 So it’s that different mentality of don’t worry
02:13:46 about the failing part as much of the,
02:13:48 make sure you give yourself the shot
02:13:50 at those potentially unbounded opportunities.
02:13:55 You almost make it sound like there’s a meaning to it all.
02:13:58 Let me ask the big ridiculous question.
02:13:59 What do you think is the meaning of life?
02:14:01 Or maybe the easier version of that
02:14:04 is what brings your life joy?
02:14:06 So I’ll just answer that one personally.
02:14:07 For me, I’m a little bit weird.
02:14:10 I sort of, I guess you can tell by now.
02:14:13 See the pen and pencil discussion from earlier, yes.
02:14:15 Yeah, yeah.
02:14:16 So, I mean, my thing is, I guess I personally
02:14:20 just wanted to maximize a certain score,
02:14:24 which was for how many person years
02:14:28 after I’m no longer here anymore,
02:14:31 did what I do mattered?
02:14:33 Yeah.
02:14:34 And it didn’t matter if it’s necessarily attributed to me.
02:14:36 It’s just like, did it matter?
02:14:38 And so that’s what I wanted.
02:14:41 I guess that is very inspired by how scientists work.
02:14:45 It’s like, why do we keep talking about Newton?
02:14:47 It’s because Newton discovered some interesting things.
02:14:50 And so Newton’s score is pretty high.
02:14:53 It’s going to be infinity, right?
02:14:56 Well, let’s hope it’s infinity, but pretty high.
02:14:59 Yes, yes.
02:15:00 So you’re going for, so person years,
02:15:03 you’re going for like triple digits.
02:15:05 You’re going for, so like Newton is like four digits,
02:15:08 probably like a thousand years or personal lifetimes.
02:15:13 How do you like to think, well, what are we?
02:15:15 Sorry, I meant people times years.
02:15:17 People times.
02:15:18 So then it’s like, actually his is huge.
02:15:19 His is like going to be billions or trillions, trillions.
02:15:23 But I guess for me, I actually changed the metric
02:15:27 after a while.
02:15:28 And the reason is because you may have seen,
02:15:30 I found some simple way to solve quadratic equations
02:15:33 that is easier than every textbook.
02:15:35 So my score might already be not bad,
02:15:39 which is why I decided then let’s change it
02:15:40 into the number of hours in the lifetimes as well.
02:15:44 So the way I was doing it before is that
02:15:48 if a person was sort of remembering or using
02:15:53 or appreciating what I had done
02:15:56 for like 10 years of their life.
02:16:00 Oh, I see.
02:16:01 That would count as 10.
02:16:01 I see.
02:16:02 So if there was one person who for 10 years remembered
02:16:05 or appreciated something I did,
02:16:06 that counts as a score of 10 and we add up overall people.
02:16:09 And then, and that was with the hypothesis
02:16:13 that the score would be very finite in the sense
02:16:16 that if I didn’t come up with anything
02:16:19 that might potentially help a lot of generations
02:16:21 in a forever way, then your score will be finite
02:16:23 because at some point it’s not,
02:16:25 people don’t remember that you made like nice bottles
02:16:28 or something, right?
02:16:30 But then after the quadratic equation thing,
02:16:33 it was that there’s some chance
02:16:34 that that actually might make it into textbooks.
02:16:37 And if it makes it in textbooks,
02:16:39 the chance that there’ll be an easier way discovered
02:16:40 is actually quite small.
02:16:42 So in that case, then the score might get bigger.
02:16:46 I was just saying the score might actually already
02:16:48 have been achieved in a non trivial way.
02:16:51 I see.
02:16:52 Because it’s fun to think about,
02:16:53 cause it could be different.
02:16:54 You can achieve a high score by a small number of people
02:16:58 using it for most of their lifetime
02:17:01 and then generations and generations.
02:17:03 Or you can have, if we do dissipate,
02:17:05 if we do split colonize, become multi planetary species,
02:17:10 you could have that little,
02:17:12 a clever way to solve differential equations,
02:17:17 spread through like trillions of people
02:17:19 as they spread throughout the galaxy.
02:17:21 And they would only use it each one,
02:17:24 a few hours in their lifetime,
02:17:26 but their kids will use it,
02:17:28 the kids of kids will use it, it will spread
02:17:30 and you’ll have that impact in that kind of way.
02:17:33 Yes, so that’s why I renormalized it
02:17:34 because I was like, well, that’s kind of dumb
02:17:36 because what’s the importance of that?
02:17:37 That’ll save people 15 minutes.
02:17:39 But, so what I meant is I didn’t want to count that
02:17:42 as the main score.
02:17:46 Well, I’m gonna have to try to come up
02:17:47 with some kind of device that everyone would want to use,
02:17:50 maybe to make coffee,
02:17:51 cause coffee seems to be the prevalent
02:17:54 performance enhancing chemical that everyone uses.
02:17:57 So I’ll have to think about those kinds of metrics.
02:17:59 Yeah, but you see that’s just giving an idea
02:18:02 of I guess what I found meaningful in general,
02:18:05 like whether or not it’s like,
02:18:06 whether or not that quadratic thing is important or not.
02:18:08 The general idea was I wanted to do things
02:18:10 that would outlast me.
02:18:12 And that was what inspired me
02:18:13 and that’s just how I choose what problems to work on.
02:18:15 And that’s a kind of immortality is ideas
02:18:18 that you’ve invented living on long after you
02:18:23 in the minds of others.
02:18:24 And humans are ultimately not,
02:18:27 are like meat vehicles that carry ideas for brief
02:18:32 for just a few years may not be the important thing.
02:18:34 It might be the ideas that we carry with us
02:18:37 and invent new ones.
02:18:38 Like we get a bunch of baby ideas in our head.
02:18:41 We borrow them from others
02:18:43 and then maybe we invent a new one
02:18:45 and that new one might have a life of its own.
02:18:47 And it’s fun to think about that idea
02:18:50 of living for many centuries to come
02:18:53 unless we destroy ourselves.
02:18:54 But maybe AI will borrow it
02:18:56 and we’ll remember Po as like that one human
02:19:00 that helped us out before we of course killed him
02:19:04 and the rest of human civilization.
02:19:06 On that note, Po, this is a huge honor.
02:19:09 You’re one of the great educators
02:19:12 I’ve ever gotten a chance to interact with.
02:19:15 So it’s truly an honor that you would talk with me today.
02:19:18 It means especially a lot that you would travel a lot
02:19:21 to Austin to talk to me.
02:19:22 It really means a lot.
02:19:23 So thank you so much.
02:19:25 Keep on inspiring.
02:19:26 And I’m one of your many, many students.
02:19:30 Thank you so much for talking today.
02:19:32 Thank you, thank you.
02:19:32 It’s actually a real honor for me to talk to you
02:19:34 and to get this chance to have this really
02:19:37 intellectual conversation through all of these topics.
02:19:39 Thanks, Po.
02:19:41 Thanks for listening to this conversation with Po Chenlo
02:19:44 and thank you to Jordan Harmer, the show,
02:19:47 Onnit, BetterHelp, AidSleep and Element.
02:19:51 Check them out in the description to support this podcast.
02:19:54 And now let me leave you with some words from Isaac Newton.
02:19:58 I can calculate the motion of heavenly bodies
02:20:01 but not the madness of people.
02:20:03 Thank you for listening and hope to see you next time.