The following is a conversation with Donald Knuth, his second time on this podcast.
Don is a legendary computer scientist, touring award winner, father of algorithm analysis,
author of the art of computer programming, creator of tech that led to late tech,
and one of the kindest and most fascinating human beings I've ever got a chance to talk to.
I wrote him a letter a long time ago, he responded, and the rest, as they say, is history.
We've interacted many times since then, and every time has been joyful and inspiring.
To support this podcast, please check out our sponsors in the description.
This is the Lex Friedman podcast, and here is my conversation with Donald Knuth.
Donald Knuth, your first large-scale program, you wrote it in IBM 650 assembler in the summer of 1957.
I wrote it in decimal machine language. I didn't know about assembler until a year later.
But the year 1957, and the program is tic-tac-toe.
Yeah, I might have learned about assembler later that summer, I probably did.
In 1957, hardly anybody had heard of assemblers. You looked at the user manuals,
how would you write a program for this machine? It would say 69, which meant load the distributor,
and then you would give the address of the number you wanted to load into the distributor.
Yesterday, my friend at Doug Spicer at the Computer History Museum sent me a link to
something that just went on YouTube. It was the IBM's Progress Report from 1956,
which is very contemporary with 1957. And in 1956, IBM had donated to Stanford University
an IBM 650, one of the first ones, when they showed a picture of the assembly line for IBM 650s.
And they said, you know, this is number 500 or something coming off the assembly line.
And I had never seen so many IBM 650s. I did in this movie that was on YouTube now.
And it showed the picture from Stanford. They said, we donated one of these to
Stanford, one to MIT, and they mentioned one other college. And in December of 56,
they donated to my university case deck. But anyway, they showed a picture then
of a class session where a guy was teaching programming. And on the blackboard, it said 69,
8000. I mean, it was, he was teaching them how to write code for this IBM 650, which was in
decimal numbers. So the instructions were 10 decimal digits. You had two digits,
that said what to do. Four digits to say what to do it to. And four more digits to say where
to get your next instruction. And there's a manual that describes what each of the numbers mean.
And the manual was actually, if the manual had been well written, I probably never would have
gone into computer science, but it was so badly written, I figured that I must have a talent for
it because I'm only a freshman and I could write a better manual. And so I started working at the
computer center and wrote some manuals then. But this was the way we did it. And my first
program then was June of 1957. The tic-tac-toe. No, that was the second program. The first program
was factoring a number. So you dial a number on the switches. I mean, you sat at this big main
frame and you turn the dials and set a number. And then it would punch out the factors of that
number on cards. So that's the input? The input was, yeah, the input was a number,
attended a number. And the output was its factors. And I wrote that program.
I still have a copy of it somewhere. How many lines of code do you remember?
Well, yeah, it started out as about 20, but then I kept having me debug it. I discovered
debugging, of course, when I wrote my first program. What does debugging look like on a
program with just all numbers? Well, you sit there and you, I don't remember how I got it
into the machine, but I think there was a way to punch it on cards. So each instruction would be
one card. Or maybe I could get seven instructions on a card, eight instructions, I don't know. But
anyway, so I'm sitting there at the console of the machine. I mean, I'm doing this at night
when nobody else is around. And so you have one set of switches where you dial the number I'm
inputting, but there's another switch that says, okay, now execute one instruction and show me
what you did. Or you could do another four switches and say, stop if you get to that
instruction. So I can see, now go until you get there again and watch. Okay, so I could watch,
you know, it would take that number and it would divide it by two. And if it's,
you know, there's no remainder, then okay, two is a factor. So then I work on them.
But if not divisible by two, divide by three. Okay, keep trying until you know you're at the end.
And you would find a bug if you were just surprised that something weird happened?
Well, certainly, I mean, first of all, I might have, you know, try to divide by one instead
of two off by one error that people make all the time. But maybe I go to the wrong instruction.
Maybe I, you know, maybe I left something in a register that I shouldn't have done.
But the first bugs were pretty, you know, I probably on the first night, I was able to,
I was able to get the factors of 30, you know, as equal to two, three and five. Okay.
So you're sorry to interrupt. You're, so you're sitting there late at night.
Yeah.
So it feels like you spent many years late at night working on a computer.
Oh, yeah.
So what's that like? So most the world is sleeping. And you have to be there at night
because that's when you get access to the computer.
Between my freshman sophomore year, I didn't need to sleep.
I used to do all nighters. When I was in high school, I used to do the whole student newspaper
every Monday night. I would, you know, I would just stay up all night and it would be done on
Tuesday morning. That was, I didn't get ulcers and stuff like that until later, you know, but
I don't know if you know Rodney Brooks.
Rod Brooks, of course.
Yeah. He told me a story that he really looked up to you. He was actually afraid of you.
Well, vice versa, I must say.
But he tells a story when you were working on tech that they screwed up something with a machine.
I think this might have been MIT, I don't know. And you were waiting for them to fix the machine
so you can get back to work late at night.
Oh, that happened all the time.
He was really intimidated. He's like, Dr. Nooth is not happy with this.
Oh, that's interesting. But no, no, the machine at Stanford AI lab was down an awful lot because
we, they had, they had many talented programmers changing the operating system every day.
And so the operating system was getting better every day, but it was also crashing.
So, so, so I wrote almost the entire manual for tech during downtime of that machine.
But that's another story.
Well, he was saying they, it's a hardware problem. They, they tried to fix it and they
reinserted something and smoke was everywhere.
Oh, wow.
Because he was, he was.
Well, that didn't happen as often as the operating system came.
But yeah.
Anyway, it's a funny story because you're saying there's this tall Don Knuth that I look up to
and there was pressure to fix the computer.
It's funny.
Okay.
The kind of things we remember that stick in our memory.
Well, okay. Well, I can tell you a bunch of Rod Brooks stories too, but let's, let's, let's go
back to the 50. So, so, so I'm debugging this my first program and I, I had more bugs in it than
number of lines of code.
I mean, the number of lines of code kept growing.
And let me explain.
So, so I had to punch the answers on cards.
All right.
So, so suppose I suppose I'm factoring the number 30, then I got, then I got to, I got to put two
somewhere on the card.
I got to put a three somewhere on the card.
I got to put a five somewhere on the card.
Right.
And, and you know what, I, it was my first program.
I, I, I probably screwed up and, you know, it fell off the edge of the card or something like that.
But, but I didn't realize that there are some tended numbers that have,
that have more than eight factors.
And the card has only 80 columns.
And so I need 10 columns for every factor.
So my first program didn't take account for the fact that I would have to punch more than one card.
My first program, you know, just lined the stuff up in memory and then I punched the card.
But, but I have to, you know, so by the time I finished, I had to, I had to deal with lots of,
lots of things.
Also, I, if you, if you put a large prime number in there, my program might have sat there
for 10 minutes or 650 was pretty slow.
And so it would sit there spinning its wheels and you wouldn't know if it was in a loop or whatever.
You said 10 digit?
10 digits.
Yeah.
So I think the largest is sort of 99999999997 or something like that.
And that would, you know, that, that would take me a while for that first one.
Anyway, that was my first program.
Well, what was your goal with that program?
My goal?
Was there something you were hoping to, to find a large prime maybe or?
No.
The opposite?
No, my goal was to see the lights flashing and understand how, how this magical machine would
be able to do something that took so long by hand.
So what was your second program?
My second program was, was a converted number from, from binary to decimal or something like
that.
It was much, much simpler.
It didn't have that many bugs in it.
My third program was tic-tac-toe.
Yeah.
And it had some, so the, the, the tic-tac-toe program is interesting on many levels, but
one of them is that it had some, you can call machine learning in it.
That's, yeah, that's right.
I don't know how long it's going to be before the name of our field has changed from computer
science to machine learning.
But, but anyway, it, it, it was my first experience with machine learning.
Okay. So here we had.
Yeah. How does the program, well, first of all, what is the problem you were solving?
What is tic-tac-toe?
What are we talking about?
And then, what, how, how was it designed?
Right. So, so you got, you got a three by three grid and each, each, each can, can be
in three states.
It can be empty or it can have an X or an O.
All right.
So three to the ninth is a, well, what is, how big is it?
I should know, but it's 81 times, 81 times three.
So, anyway, eight is like two to the third.
And so that would be, that would be like two to the sixth.
And then, but that'd be 64.
Then you have to, anyway.
I love how you're doing the calculation.
So the three.
It's a lot of, anyway.
The three comes from the fact that it's either empty and X or an O.
Right. And the 650, what was it, was a machine that had only 2010 digit words.
You go from zero, zero, zero, zero to one, nine, nine, nine, and that's it.
And, and each word, you have a 10 digit number.
So that's not many bits.
I mean, I got to have three, in order to have a memory of every position I've seen,
I need three to the ninth bits.
Okay. But it was a decimal machine too.
It didn't have bits, but, but it did have, it did have strange instruction where if,
if you had a 10 digit number that, but all the digits were either eight or nine.
You'd be eight, nine, nine, eight or something like that.
That would, you can make a test whether it was eight or nine.
That was one of the strange things IBM engineers put into the machine.
I have no idea why.
Well, hardly ever used.
But anyway, I needed one digit for every, every position I'd seen.
Zero meant it was a bad position.
Nine meant it was good position.
I, I think I started out at five or six, you know, but if you win, if you win a game,
then you, then you increase the value of that position for you, but you decrease it for,
for your opponent.
But, but I could, I had that much total memory for every, every possible position was one digit.
And I had a total of 20,000 digits, which had to, which had to also include my program and
all the logic and everything, including how to, how to ask the user what the moves are and things
like this. Okay. So, so I think I had to work it out because every, every position in tic-tac-toe
is equivalent to, to roughly eight others because you, you, you can rotate the board,
which gives you factor four and you can also flip it over. And that's another factor too. So, so I
might, you know, so I might have needed only three to the ninth over eight positions, you know, plus,
plus a little bit. So I had, but anyway, that was, that was a part of the program to, to squeeze it
into this tiny. So you tried to find an efficient representation that took account for that kind
of routine. I had to, otherwise I couldn't do the learning. Wow. So, so, but, but I had three
parts to my tic-tac-toe program. And I called it brain one, brain two, and brain three. So,
so brain one just played a, let's see, at random. Okay. It's your turn. Okay. You got to put an X
somewhere. It has to go in an empty space, but that's, that's it. Okay. Choose, choose one and play
it. Brain two had a canned routine. And I think it was, it also, maybe it had, maybe to assume
you were the first player or maybe it allowed you to be first. I think you ought to be either
first or second, but had a canned built-in strategy known to be optimum for tic-tac-toe. Before I
forget, by the way, I learned many years later that Charles Babbage had, had planned to, had
thought about programming tic-tac-toe for his, for his dream machine that he, that he would never
able to finish. Wow. So that was the program he thought about. More than a hundred years ago.
Yeah. Yeah. He had, he did that. Okay. And I had, and I had how been influenced by a
demonstration at the, at the Museum of Science and Industry in Chicago. It's like,
it's like Boston's science museum. I think Bell Labs had, had prepared a special exhibit about
telephones and relay technology. And they had a tic-tac-toe playing
machine as part of that exhibit. So that had been one of my, you know,
something I'd seen before I was a freshman in college and inspired me to see if I could write
a program for it. Okay. So anyway, I had brain one, random, you know, knowing nothing, brain
two, knowing everything. Then brain three was the learning one. And I could, I could play
brain one against brain one, brain one against brain two, and so on. And so you could also play
against the user, against the live universe. But, but, so I started going, the learning thing. And
I said, okay, you know, take two random, random people, just playing tic-tac-toe, knowing nothing.
And after about, I forget the number now, but, but it converged after about 600 games
to a safe draw. The way my program learned was actually, it learned how not to make mistakes,
because, you know, it didn't try to do anything for winning. It just tried to say not losing.
Yeah, not losing. So that was probably because of the way I designed the learning thing. I could have,
you know, had a different reinforcement function that would, that would reward brilliant play. But
anyway, it didn't, and, and, and if, if I took a novice against, you know, the skilled player,
it was able to learn how to play a good game. So that was, and that was really my,
but after I finished that, I felt I, I understood programming.
Was there, did you, did a curiosity and interest in learning systems persist for you?
So why, why did you want Brain 3 to learn?
Yeah, I think naturally it's, we're talking about Rod Brooks. He was teaching all kinds of
very small devices to learn stuff. If a leaf drops off of a tree, you know,
he was saying something, well, it learns if there's wind or not. But, but, but I mean,
he pushed that a little bit too far, but he said he could probably train some little mini-bugs
to scour out dishes if he had enough financial support, I don't know.
So can I, can I ask you about that? He also mentioned that during those years,
there was discussion about inspired by touring about computation, you know, of what is computation.
Yeah. And, you know, I never thought about any stuff like that. That was,
that, that was way too philosophical. I mean, I was a, I was a freshman after all. I mean,
I didn't, I was pretty much a machine. So it's almost like, yeah, I got you. It's a tinkering
mindset, not a philosophical mindset. It was just exciting to me to, to be able to control
something, but not, but not to, but not to say, hmm, am I solving a big problem or something
like that? Or is this a step for humankind or anything? No, no way. When did you first start
thinking about computation in the big sense, you know, like the universal turing machine?
Well, I mean, I had to pass an exam. I had to take, I had to take classes on
on computer ability when I was a senior. So, you know, we read this book by Martin Davis and
yeah, this is cool stuff. But, you know, I learned about it because I, you know, I needed to pass
the exams, but I didn't, I didn't invent any of that forward stuff. But I had great fun playing
with the machine, you know, I, I wrote program because it was fun to write programs and, and get
this, I mean, it was like watching miracles happen.
You mentioned in, in an interview that when reading a program, you can tell when the author
of the program changed. Oh, okay. Well, how the heck can you do that? Like what makes a distinct
style for a programmer, do you think? You know, there's different Hemingway has a style of writing
versus James Joyce or something. Well, those are pretty, yeah, those are pretty easy to imitate,
but, but it's the same with music and whatever you can. I found, well, during the pandemic,
I spent a lot more time playing the piano and I, and I found something that I'd had,
I had it right when I was taking lessons, you know, before I was a teenager and it was
Yankee Doodle played in the style of, you know, and you had, you had Beethoven and you had WC
and Chopin and, you know, and the last one was Gershwin. And, and I played over and over again.
I thought it was so brilliant because, but, but it was so easy, but also to appreciate how
this, this author, Mario, somebody or other had, had been able to reverse engineer the,
the styles of, of those computers. So, but now, specifically, your question, I mean, there would
be, there, it was, it was pretty obvious in this program I was reading, it was, it was a compiler,
and it had been written by a team at Carnegie Mellon. And I have no idea which program was
responsible for, but, but you would get to a part where the guy would just not know how to,
how to move things between registers very efficiently. And so, and so everything that,
that could be done in one instruction would take three or something like that. That would be a
pretty obvious change in style. But there were, but there were also, you know, flashes of brilliance
where you could do in one instruction. Normally, I used two because, because you knew enough about
the way the machine worked that you could, that, that you could accomplish two goals in one step.
So, so it was mostly the, the brilliance of the concept more than the semicolons and, you know,
or the, you know, the use of short sentences versus long sentences or something like that.
So you would see the idea in the code and you could see the, the different style of thinking
expressed in the code. Right. It was, yeah. So it was stylistic. I mean, I could identify authors by
their, by the amount of technical aptitude they had, but not by the style in the sense of,
of rhythm or something like that. So if you think about Mozart, Beethoven, Bach,
if somebody looked at Don Knuth code, would they be able to tell that this is a distinct style
thinking going on here? What do you think? And what, what would be the defining characteristic
of the style? Well, my code now is, it is literate programming. So I'm, it's a combination of English
and C mostly, but, but, but if you just looked at the C part of it, you would also probably notice
that I don't, you got it, you know, that I use a lot of global variables that other people don't
and I expand things in line more than instead of calling. Anyway, I have different
subset of C that I use. Okay. But that's a little bit stylistic. But with literate programming,
you alternate between English and C or whatever. And by the way, people listening to this should
look up literate programming. It's very interesting concept that you, that you proposed and developed
over the years. Yeah, yeah. I'm, that's the most significant thing I think to come out of the tech
project is that I, I realized that my programs were to be read by people and not just by computers
and, and, and that typography could massively enhance that. And, and, and so, I mean, it,
they're just wonder if they're going to look it up that they should also look up this book by
called physically based rendering by Matt Far and gosh, anyway, it got an Academy Award,
but it's, but, but all the, all the graphic effects you see in movies, you know, are accomplished
by algorithms. And this book is the whole book is a literate program. It tells you not only how
you do all the shading and, and bring images in that you need for animation and textures and so
on. But it also you can run the code. And, and so I find it an extension of the way I,
of how to teach programming is, is by, by telling a story as part of the program.
So it's, it works as a program, but it's also readable by humans.
Yes. And especially by me. Yeah. A week later or a year later.
That's a good test. If you yourself understand the code. Yeah. Easily a week or a year later.
Yeah. So it's, it's, it's the greatest thing since sliced bread.
Programming or literate. Literate program. Okay.
Okay. You heard it here first. Okay. You dodged this question in an interview I listened to.
So let me ask you again here. What makes for a beautiful program?
What makes for a beautiful program? Yeah. What are the characteristics you see,
like you just said, literate programming? What are the characteristics you see in a program
that make you sit back and say, that's pretty good?
Well, the reason I didn't answer is because there are, there are dozens and dozens of answers to
that because, because each, you can define beauty, the same personality, you find beauty
different way from hour to hour. I mean, it depends on what, on what you're looking for.
At one level, it's beautiful just if it works at all. Another level, it's beautiful if it's,
if it can be understood easily. It's beautiful if it,
if it's a literate programming, it's beautiful. It makes you laugh. I mean, yeah.
I'm actually, so I'm with you. I think beauty, if it's readable.
Readable, yeah.
As if you understand what's going on and also understand the elegance of thought behind it.
And then also, as you said, wit and humor. I was always, I remember having this conversation,
I had this conversation on Stack Overflow, whether humor is good in comments.
And I think it is. Whether humor is good in comments.
Like when you add comments and code, I always thought a little bit of humor is good.
It shows personality. It shows character shows wit and fun and all those kinds of things
of the personality of the programmer.
Yeah. Okay. So a couple days ago, I received a wonderful present from my former editor
at Aston Wesley. He's downsizing his house and he found that somebody at the company had
found all of their internal files about the art of computer programming from the 1960s.
And they gave it to him. And then, you know, before throwing in the garbage.
And then, so he said, oh yeah, he planned to keep it for posterity, but now he realized that
posterity is a bit too much for him to handle, so he sent it to me. And so I just received
this big stack of letters, some of which I had written to them, but many of which they had
written to early guinea pigs who were telling them whether they should publish or not.
You know, and one of the things was, in the comments to volume one, the major reader was
Bob Floyd, who is my great co-worker in the 60s, died early, unfortunately.
But, and he commented about the humor in it. And so we had, you know, he ran it by me, you know,
keep this joke in or not, you know, they also sent it out to focus groups. What do you think about
humor in a book about computer programming? What's the conclusion? And I stated my philosophy,
it says, you know, the ideal thing is that it's something where the reader
knows that there's probably a joke here if he only understood it, and this is a motivation
to understand, to think about it a little bit. But anyway, it's a very delicate humor. I mean,
it's really, each century invents a different kind of humor too. I mean, and different cultures
have different kinds of humor. Yeah, like we talked about Russia a little bit offline, you know,
there's dark humor, and you know, when a country goes through something different.
Right, that and that live and stuff like this. And, you know, and Jack Benny, I mean,
Steve Allen wrote this book about humor, and it was the most boring book, but he was one of my
idols. But it's called The Funny Men or something like that. But yeah, okay, so anyway, I think
it's important to know that this is part of life, and it should be fun and not. And so, you know,
I wrote this organ composition, which is based on the Bible, but I didn't refrain from putting
little jokes in it, also, in the music. It's hidden in the music. It's there, yeah.
A little humor is okay? Yeah, I mean, not egregious humor. So in this correspondence, you know, there
were things I said, yeah, I really shouldn't have done that. But other ones I insisted on. And I've
got jokes in there that nobody has figured out. In fact, in volume two, I've got a cryptogram
message in Cyford. And in order to decipher it, you're going to have to have to break an RSA
key, which is larger than people know how to break. And so, you know, if computers keep
getting faster and faster, then it might be 100 years, but somebody will figure out what this
message is, and they will laugh. I mean, I've got a joke in there. So that one you really have to
work for. I don't know if you've heard about this. Let me explain it. Maybe you'll find it interesting.
So OpenAI is a company that does AI work, and they have this language model. It's a neural
network that can generate language pretty well. But they also, on top of that, developed something
called OpenAI Codex. And together with GitHub, they developed a system called OpenAI Copilot.
Let me explain what it does. There's echoes of literate programming in it. So what you do is
you start writing code, and it completes the code for you. So, for example, you start, let's go to
your factoring program, you start, you write in JavaScript and Python and any language that it
trained on, you start, you write the first line and some comments, like what this code does,
and it generates the function for you. And it does an incredibly good job. Like, it's not
provably right, but it often does a really good job of completing the code for you.
I see. But how do you know whether it did a good job or not?
You can see a lot of examples where it did a good job. And so it's not a thing that generates the
code for you. It starts, it gives you, so it puts the human in the seat of fixing issues versus
writing from scratch. Do you find that kind of idea at all interesting? Every year, we're going to
be losing more and more control over what machines are doing and people are saying, well, it seems
to, like, when I was a professor at Caltech in the 60s, we had this guy who talked a good game.
He could give inspiring lectures and you'd think, well, thrilling things he was talking about an
hour later, what did he say? But he really felt that it didn't matter whether computers got the
right answer or not, whether it made you happy or not. If your boss paid for it, then you had a
job, you could take care of your wife. Happiness is more important than truth.
Exactly. He didn't believe in truth, but he was a philosopher.
I like it. And somehow you see... We're going that way. I mean, so many more things are taken
over by saying, well, this seems to work. And when there's competing interests involved,
well, neither side understands why the decision is being made. We realize now that it's bad,
but consider what happens. Private attend you down the line. When things get even more
further detached, each thing is based on something from the previous year.
Yeah. So you start to lose... The more you automate, the more you start to lose track of
some deep human things. Exponentially. Exponentially. But so that's the dark side.
The positive side is the more you automate, the more you let humans do what humans do best.
So maybe programming, maybe humans should focus on a small part of programming that
requires that genius, the magic of the human mind and the mess you let the machine generate.
Yeah. I mean, that's the positive. But of course,
it does come with the darkness of automation. What's better? I'm never going to try to write
a book about that. I'm never going to recommend to any of my students to work for them.
So you're on the side of correctness. I'm on the side of understanding.
I think these things are really marvelous if what they do is, you know,
all of a sudden we have a better medical diagnosis or it'll help guide some scientific
experiment or something like this, curing diseases or whatever. But when it affects
people's lives in a serious way, so if you're writing code, oh, yeah, here, this is great.
This will make a slaughter butt. Okay. So I see. So you have to be very careful.
Like right now, it seems like fun and games. It's useful to write a little JavaScript
program that helps you with the website. But like you said, one year passes, two years passes,
five years and you forget. You start building on top of it and then all of a sudden you have
autonomous weapon systems based. Well, we're all dead. It doesn't matter in that sense.
Well, in the end, this whole thing ends anyway. So, but it pays. There is a heat death of the
universe predicted, but I'm trying to postpone that for a little bit. Well, it'd be nice that
at the end, as we approach the heat death of the universe, there's still some kind of consciousness
there to appreciate it. Hopefully human consciousness. I'll settle for 10 to the 10 to the 10 to the
10th year, some finite number. But things like this might be the reason we don't pick up any
signals from extraterrestrial. They don't want anything to do with us. Oh, because they
invented it too. So you do have a little bit of worry on the existential threats of AI and
automation. So like, like removing the human from the picture, etc. Yeah. People have more
potential to do harm now than by far than they did a hundred years ago.
But are you optimistic about humans are good at creating destructive things,
but also humans are good at solving problems. Yeah. I mean, there's half empty and half full,
you know, so I can go. So let me let me put it this way because because it's the only way I
can be optimistic. But think of things that have changed because of civilization, you know,
they don't occur just in nature. So just just imagine the room we're in, for example,
okay, some, you know, we've got pencils, we've got books, we've got tables, we got microphones,
clothing, food, all these things were added. Somebody invented them one by one.
And millions of some things that we inherit. Okay. And it's inconceivable that that so many
millions of billions of things wouldn't have problems. And we get it all right.
And each one would have no negative effects and so on. So it's very amazing that much works as
does work. It's incredibly amazing. And actually, that's the source of my optimism as well,
including for artificial intelligence. So we drive over bridges, we use all kinds of technology,
we don't know how it works. And there's millions of brilliant people involved in building a small
part of that. And it doesn't go wrong. And it works. I mean, that it works. It doesn't go wrong
often enough for us to suffer. And we can identify things that aren't working and try to
improve on them in a sub often suboptimal way. Oh, absolutely. But it's but the but the
the kind of things that I know how to improve require human beings to be rational. And I'm
losing my confidence that human beings are rational. Yeah. Yeah. Now here you go again with the worst
case, worst case analysis. They may not be rational, but they're, they're, they're, they're
they're clever and beautiful in their own kind of way. I tend to think that most people
have the desire and the capacity to be good to each other. And love will ultimately win out.
Like if they're given the opportunity, that's where they lean. In the art of computer programming,
you wrote, the real problem is that programmers have spent far too much time worrying about
efficiency in the wrong places. And at the wrong times, premature optimization is the root of all
evil in parentheses, or at least most of it in programming. Can you explain this idea?
What's the wrong time? What is the wrong place for optimization? So first of all, the word
optimization. I started out writing software and optimization was, I was a compiler writer. So
optimization meant making the, making a better translation so that it would run faster on a,
on a machine. So an optimized program is just like, you know, you, you, you run a program and you
set the optimization level for the compiler. So that's one word for optimization. And at that
time, I, I happened to be looking in an unabridged dictionary for some reason or other, and I came
to word optimize. So what's the meaning of the word optimized? And it says to view with optimism.
And you look in Webster's dictionary of English language in 19, early 1960s, that's what optimized
me meant. Okay. Now, so people started doing cost optimization, all the kinds of things,
you know, whole subfields of, of algorithms and economics and whatever are based on what they
call optimization now. But, but to me, optimization, when I was saying that was saying, changing a
program to make it more tuned to the machine. And I found out that when a person writes a program,
he or she tends to think that the parts that were hardest to write are going to be hardest for
the computer to execute. So maybe I have 10 pages of code, but I had to work a week writing this
page. I mentally think that when the computer gets to that page, it's going to slow down.
Right. It's gonna say, Oh, I don't understand what I'm doing. I better be more careful. Anyway,
this is, of course, silly, but it's, it's something that we, that we, that we don't know
when we write a piece of code, we don't know what, what, whether the computer is actually
going to be executing that code very much. So, so people had had a very poor understanding of,
of what the computer was actually doing. I made one test where, where we studied a Fortran compiler,
and it was spending more than 80% of its time reading the comments card.
But as a programmer, we were really concerned about how fast it could take a complicated
expression that had lots of levels of parenthesis and convert that into something. But that was
just, you know, less than 1% of the, so if we optimized that, we didn't know what we were
doing. But, but, but if we knew that it was spending 80% of its time on the comments card,
you know, in 10 minutes, we could, we could make the compiler run more than twice as fast.
You can only do that once you've completed the program. And then you empirically study where
I had some kind of profiling that I knew what was important. Yeah.
So you don't think this applies generally? I mean, there's something that rings true to this
across all. I'm glad that it applied generally, but, but it was, it was only my good luck. I said
it, but, you know, but, but I did, but I said it in a limited context and I, and I'm glad if it
makes people think about stuff because I'm, you know, but it applies in another sense too. That is,
sometimes I will do optimization in a way that does help the actual running time,
but makes the program impossible to change next week because I've changed my data structure or
something that made it less adaptable. So one of the great principles of computer science is,
is, it is laziness or whatever you call it, late binding, you know, don't hold off decisions when
you can. And, and, and, you know, and we understand how quantitatively, how valuable that is.
What, what do you mean we understand? So you mean people, people have written
thesis about how you can, how late binding will improve the proof. I mean, you know,
just in time manufacturing or whatever, you can make, you can defer a decision
instead of doing your advanced planning and say, I'm going to allocate 30% to this
and 50%. So in all kinds of domains, there's an optimality to laziness in many cases.
Decision is not made in advance. So instead you, you, you design in order to be flexible
to change with the, with the way the wind is blowing.
Yeah. But so the reason that line resonated with a lot of people
is because there's something about the programmer's mind that wants, that enjoys
optimization. So it's a constant struggle to balance laziness and late binding with
the desire to optimize, to the elegance of a well optimized code is something that's
compelling to programming. Yeah. It's another concept of beauty.
Let me ask you a weird question. So Roger Penrose has talked about computation, computers,
and he proposed that the way the human mind discovers mathematical ideas is something
more than a computer, that, that a universal Turing machine cannot do everything that a human
mind can do. Now, this includes discovering mathematical ideas. And it also includes,
he's written a book about it, consciousness. So I don't know if you know Roger, but
my daughter's kids played with his kids in Oxford.
Nice. So do you think there is such a limit to the computer? Do you think consciousness is more
than a computation? Do you think the human mind, the way it thinks is more than a computation?
I mean, I, I, I can say yes or no, but, but, but I don't think I have no reason.
I mean, so you don't find it useful to have an intuition in one way or the other?
Like when you think about algorithms, do you, isn't it useful to think about the limits?
Unanswerable question. In my opinion, is, is no better than anybody else.
You think it's unanswerable. So you don't think eventually science.
How many angels condense on the head of, I mean, I don't know.
But angels are anyway, there, there are lots of things that are beyond that we can speculate
about. But I don't want somebody to say, oh, yeah, can you set this and, and so he's, he's,
he's smart and so, so that must be, I mean, I say it's something that we'll never know.
Interesting. Okay. That's a strong statement. I don't, I personally think it's something we
will know eventually. Like there's no reason to me why the, the workings of the human mind
are not within the reach of science. That's absolutely possible. And I'm not denying it.
Yeah. But right now you don't have a good intuition. I mean, that's also possible,
you know, that an AI, you know, created the universe, you know, intelligent design has
all been, has all been done by an AI. Yes. This is, I mean, all of these things are,
but, but, but, but you're asking me to, to pronounce on it and, and I don't have any
expertise. I'm a teacher that passes on knowledge, but I don't, but I don't know
the fact that I, that I vote yes or no on. Well, you do have expertise as a human,
not as a, not as a teacher or a scholar of computer science. I mean, that's ultimately the
realm of where the discussion of human thought. Yeah. Well, I know we're unconscious. I know
where, where Penrose is coming from. He, I'm sure he has no proof. He might even thought he proved
it, but no, he doesn't. He doesn't prove it. He is following intuition. But, but I mean, you have
to ask John McCarthy. I think we're totally unimpressed by these statements. So you don't
think, so even like the touring paper on, on the touring tests that, you know, starts by asking,
can machines think? Oh, you don't think these kind of touring doesn't like that question?
Yeah. I don't consider it important. Let's just put it that way. Because it's in the
category of things that it would be nice to know, but I think it's beyond knowledge. And so I don't,
I'm more interested in knowing about the Riemann hypothesis or something.
So when you say, it's an interesting statement beyond knowledge. Yeah. I think what you mean
is it's not sufficiently well, it's not even known well enough to be able to formalize it
in order to ask a clear question. Yeah. And so that's why it's beyond knowledge, but that doesn't
mean it's not eventually going to be formalized. Yeah. Yeah. Maybe consciousness will be understood
someday. But the last time I checked, it was still 200 years away. I haven't been specializing in
this by any means, but I went to lectures about it 20 years ago when I was, there was a symposium
at the American Academy in Cambridge. And it started out by saying, essentially, everything
that's been written about consciousness is hogwash. I tend to, I tend to disagree with that a little
bit. So consciousness for the longest time still is in the realm of philosophy. So it's just
conversations without any basis and understanding. Still, I think once you start creating artificial
intelligence systems that interact with humans, and they have personality, they have identity,
you start flirting with the question of consciousness, not from a philosophical
perspective, but from an engineering perspective. And then it starts becoming much more,
like I feel like... Yeah. Yeah. Don't misunderstand me. I certainly don't disagree with that at all.
And even at these lectures that we had 20 years ago, there were neurologists pointing out that
human beings had actually decided to do something before they were conscious of
making that decision. Yeah. I mean, they could tell that signals were being sent to their arms
before they knew that they were... And things like this are true. And my, you know, Les Valiant
has an architecture for the brain. And more recently, Christos Papadimitriou in the Academy
Science Proceedings a year ago with two other people, but I know Christos very well.
And he's got this model of this architecture by which you could create things that correlate well
with experiments that are done on consciousness. And he actually has a machine language in which
you can write code and test hypotheses. And so it might, you know, we might have a big breakthrough.
My personal feeling is that consciousness, the best model I've heard of to explain the
miracle of consciousness is that somehow inside of our brains, we're having a
continual survival for the fittest competition. As I'm speaking to you, all the possible things I
might be wanting to say are all in there. And there's like a voting going on.
Yeah, right. And one of them is winning. And that's affecting, you know, the next sentence
and so on. And there was this book, Machine Intelligence or something.
On intelligence.
On intelligence, yeah. Bill Atkinson was a total devotee of that book.
Well, I like, whether it's consciousness or something else, I like the storytelling part
that we, it feels like for us humans, it feels like there's a concrete story. It's almost like
literary programming. I don't know what the programming going on on the inside, but I'm
getting a nice story here about what happened. And it feels like I'm in control and I'm getting a
nice, clear story. But it's also possible there's a computation going on. That's really messy.
There's a bunch of different competing ideas. And in the end, it just kind of generates a story
for you to, a consistent story for you to believe. And that makes it all nice.
Yeah. And so I prefer to talk about things that I have some expertise in than things
which I'm only on the sideline.
So there's a tricky thing. I don't know if you have any expertise in this. You might be a little
bit on the sideline. It'd be interesting to ask though, what are your thoughts on cellular
automata and the game of life? Have you ever played with those kind of little games?
I think the game of life is wonderful and shows all kind of stuff about how things can evolve
without the creator understanding anything more than the power of learning in a way. But
to me, the most important thing about the game of life is how it focused for me
what it meant to have free will or not. Because the game of life is obviously
totally deterministic. And I find it hard to believe that anybody who's ever had children
and cannot believe in free will. On the other hand, this makes it crystal clear.
John Conway said, he wondered whether it was immoral to shut the computer off
after he got into a particularly interesting play of the game of life.
Wow. Yeah. So there is, to me, the reason I love the game of life is exactly, as you said,
a clear illustration that from simple initial conditions with simple rules, you know exactly
how the system is operating, is deterministic. And yet, if you allow yourself to lose that
knowledge a little bit enough to see the bigger organisms that emerge, and then all of a sudden
they seem conscious. They seem not conscious, but living. If the universe is finite, we're all living
in the game of life to slow down. I mean, it sped up a lot. But do you think technically
some of the ideas that you used for analysis of algorithms can be used to analyze the game of life?
Can we make sense of it? Or is it too weird? Yeah. I mean, I've got a dozen exercises in volume
for fastical six that actually work rather well for that purpose.
Bill Gosper came up with the algorithm that allowed Golly to run thousands and thousands of times
faster. You know the website called Golly, G-O-L-L-Y. It simulates the cellular automata,
a game of life. Yeah, you got to check it out. Can I ask you about John Conway? Yes. In fact,
I'm just reading now the issue of mathematical intelligence that came in last week. It's a
whole issue devoted to remembrance of him. Did you know him? I slept overnight in his
house several times. He recently passed away. Yeah, he died a year ago, May, I think it was, of COVID.
What are some memories of him, of his work that stand out for you? On a technical level,
did any of his work inspire you? On a personal level, did he himself inspire you in some way?
Absolutely, all of those things. But when did I first meet him? I guess I first met him at
Oxford in 1967. Wow, okay, that's a long time ago. Yeah, you were minus 20 years old or something,
I don't know, 1967. But there was a conference where I think I was speaking about something
that no one has the Knuth Bendix algorithm now, but he gave a famous talk about knots. I didn't
know at the time, but that talk had now the source of thousands and thousands of papers since then.
He was reported on something that he had done in high school almost 10 years earlier
before this conference, but he never published it. And he climaxed his talk by building some
knots. You have these little plastic things that you could stick together. It's something like
Lego, but easier. And so he made a whole bunch of knots in front of the audience and so on and
then disassembled. It was a dramatic lecture before he had learned how to give even more dramatic
lectures later. Were you at that lecture? And I was there because I was at the same conference.
For some reason, I happened to be in Calgary at the same day that he was visiting Calgary.
And it was a spring of 1972, I'm pretty sure. And we had lunch together. And he wrote down
during the lunch on a napkin all of the facts about what he called numbers. And he covered
the napkin with the theorems about his idea of numbers. And I thought this was incredibly
beautiful. And later in 1972, my sabbatical year began, and I went to Norway. And in December
of that year, in the middle of the night, the thought came to me, you know, Conway's theory
about numbers would be a great thing to teach students how to invent research and what the
joys are of research. And so I said, and I had also read a book in dialogue
by Alfred Renye, kind of a Socratic thing where the two characters were talking to each other
about mathematics. And so at the end, in the morning, I woke up my wife and said,
Jill, I think I want to write a book about Conway's theory. And, you know, I'm supposed to be
writing the art of computer programming, doing all this other stuff. But I really want to write
this other book. And so we made this plan. But I said, I thought I could write it in a week.
And we made the plan then. So in January, I rented a room in a hotel in downtown Oslo.
We were in sabbatical in Norway. And I rented the hotel in downtown Oslo and
did nothing else except write Conway's theory. And I changed the name to surreal numbers that
would. And so this book is now published as surreal numbers. And, and, you know, we figured
out we'd always wonder what do you like to have a fair enough hotel room. So we figured out that
she would visit me twice during the week. Things like this, you know, we would, you know, try to
sneak in this was hotel was was run by a mission organization. These ladies were probably very
strict. But anyway, so, so, and, and the wild week in every way. But the thing is, I had lost that,
I had lost that napkin in which you wrote the theory. But I looked for it, but couldn't find it.
So I tried to recreate from memory what he had told me at that lunch in Calgary. And, and as I
wrote the book, I was going through exactly what I what the characters in the book were supposed
to be doing. So I start with the with the two axioms and start out the whole thing. And everything's
defined flows from that. But you have to discover why. And, and as every mistake that I make as
I'm trying to discover it, I my characters make to you know, and, and, and so it was just a long,
long story. And I but I worked through this week. And it was it was one of the most intense weeks
of my life. And, and I described it in other places. But, but, but anyway, after six days, I
finished it. And on the seventh day, I rested and, and I sent to my secretary to type it.
It was flowing as I was writing it faster than I could think almost. But, but, but after I finished
and tried to write a letter to my secretary, telling her how to type it, I couldn't write
anymore. You gave it everything. The muse had left me completely. Can you explain how that
week could have happened? Like, why is that seems like such a magical week? I have no idea,
but anyway, there was some there. It was almost as if I was channeling. So, so, so the book was
typed, they sent it to Conway. And, and he said, well, Don, you got the axiom, the one axiom wrong.
There's a difference between less than or equal and not greater than I don't know.
The opposite of being greater than, yeah, and less than or equal. But anyway,
technically, it can make a difference when you're developing a logical theory. And the way I had
chosen was harder to do than John's original. So, and we visited him at his house in Cambridge.
In April, we took a boat actually from Norway over to across the channel and so on and stayed
with him for some days. And, and he told he talked, we talked about all kinds of things he has.
He had puzzles that I'd never heard of before. He had a great way to solve the game of solitaire.
Many of the common interests that we'd, you know, he'd never written up. But anyway,
then in the summertime, I took another week off and went to a place in the mountains of
Norway and rewrote the book using the correct axiom. And so, so that was the most intensive
connection with, with, with Conway. After that. It started with a napkin. It started with a napkin.
But, but, but we would run into each other. Yeah, the, the next really, I was giving lectures in
Montreal. I was giving a series of, of seven lectures about a topic called stable marriages.
And, and he arrived in Montreal between my sixth and seventh lecture. And, and we met at a party.
And I started telling him about the topic I was doing. And he sat and thought about it.
And he came up with a beautiful theory to show that the, I mean, in technical terms, it's,
it's that the, that the set of all stable marriages forms a lattice. And, and there was a simple way
to find the greatest floor bound and of two stable pairings and least upper bound of two
stable marriage. And so I could use it in my lecture the next day. And he came up with this
theorem, you know, during the party. And it's a brilliant, it's a distributive lesson. I mean,
it's, you know, it added greatly to the theory of, of stable matching.
So you mentioned your wife, Jill, mentioned stable marriage. Can you tell the story of
how you two met? So we celebrated 60 years of wedded lists last month. And, and we met because I
was dating her roommate. This was my sophomore year, her freshman year. I was dating her roommate.
And I wanted her advice on strategy or something like this. And anyway, I found I enjoyed her advice
better than, than I enjoyed her roommate. You guys were majoring the same thing? No, no, no.
Because I read something about working on a computer in grad school on a difficult computer
science topic. So, so she's an artist and I'm a, and I'm a geek. And what was she doing with a
computer science book? Or I read the, was it the manual that she was reading? What was she reading?
I wrote the manual that she had had, she had to take a class in computer science. Okay. And, and
so you're the tutor? No, no, yeah, no, we, yeah, we, there were terrible times,
you know, trying to learn certain concept, but I learned art from her. And so we worked together,
you know, occasionally in design projects, but, but every year we write a Christmas card
and, and we each have to compromise our, our own notions of beauty. Yes. When did you fall in love
with her? That day that I asked her about her roommate. Okay. I mean, no, I'm okay. So you're,
I don't mind telling these things, depending on how far, how far you go, but, but, but, but, but let
me tell you this, that I, I never really enjoyed kissing until I found how she did it.
Wow. And 60 years. Yeah. Is there a secret you can, you can say in terms of stable marriages
of how you stayed together so long? The topic stable marriage, by the way, is not, is a technical
term. Yes. It's a joke down. But two different people will have to learn how to compromise and,
and work together and, and, and you're going to have ups and downs and, and, and crises and so on.
And so as long as you don't set your expectation on having 24 hours of bliss,
then there's a lot of hope for stability. But if you, if, if you decide that it's,
that, that there's going to be no frustration.
So you're going to have to compromise on your notions of beauty when you write Christmas cards?
That's it. You, you mentioned that Richard Feynman was someone you looked up to.
Yeah. Probably you've met him in Caltech. Well, we knew each other.
Yeah. At Caltech, for sure. Yeah. You are one of the seminal personalities of computer science.
He's one for physics. Have you, is there specific things you picked up from him
by way of inspiration or? So we used to go to each other's lectures and,
and, and, but, but if I saw him sitting in the front row,
I would throw me for a loop, actually. And I would, I would miss a few,
a few sentences. What unique story do I have about, I mean, I, I, I often refer to his,
his time in Brazil, where he essentially said they were teaching all the physics
students the wrong way. They were just, they were just learning how to pass exams and not
learning any physics. And he said, you know, if you want me to prove it,
you know, here, I'll turn to any page of this textbook and, and I'll tell you what's wrong
with this page. And, and he did so. And, and the textbook had been written by his host and,
and it was a big embarrassing incident, but he had previously asked his host if,
if he was supposed to tell the truth. But, but anyway, it epitomizes the way
education goes wrong in all kinds of fields, and has to periodically be brought back
from, from, from a process of giving credentials to a process of giving knowledge.
Yeah, that's probably a story that continues through this day in a bunch of places where it's too easy
for educational institutions to fall into credentialism versus inspirationalism.
I don't know if those are words, but sort of understanding versus just giving a little
a plaque. And, you know, it's, it's very much like what we're talking about. If you want the
computer, if you want to be able to believe the answer, computer is doing that. One of the things
Bob Floyd showed me in the 60s, there was a, he loved this cartoon, there was a, there were two
guys standing in front of, in those days, a computer was a big thing, you know, and, and,
and the first guy says to the other guy, he said, this machine can do in one second, what would
take a million people to do in a hundred years. And the other guy says, oh, so how do you know it's
right? Oh, that's a good line. Is there some interesting distinction between physics and math
to you? Have you looked at physics much to like speaking versus Feynman? So the difference between
the physics community, the physics way of thinking, the physics intuition versus the computer science,
the theoretical computer science, the mathematical sciences. Do you see that as a gap or are they
strongly overlapping? It's quite different, in my opinion. I started as a physics major and I switched
into math. And probably the reason was that I could, I could get A plus on the physics exam,
but I, but I never had any idea why I would have been able to come up with the problems that were
on those exams. But, but in math, I, I, I knew, you know, why the teacher set those problems,
and I thought of other problems that I could set too. And I believe it's, it's quite a different
mentality. Has it has to do with your philosophy of geek, geekdom? No, it's, I mean, some of my
computer scientists friends are really good at physics and others are not. And I'm, you know,
I'm really good at algebra, but not at geometry. Talk about different parts of mathematics, you
know, it's so different kind of physical, but physicists think of things in terms of waves.
And I can think of things in terms of waves, but it's like a dog walking on hind legs, if I'm
thinking about it. So you basically, you like to see the world in, in, in discrete ways, and then
yeah, more continuous. Yeah, I'm not sure if Turing would have been a great physicist.
I think it was a pretty good chemist, but I don't know. But, but, but anyway, I see things.
I believe that computer science is largely driven by people who have brains who are good at resonating
with certain kinds of concepts. And quantum computers, it takes a different kind of brain.
Yeah, that's interesting. Yeah. It's, well, quantum computers is almost like at the intersection
in terms of brain between computer science and physics, because they involves both at least at
this time. But there is like the physicists I've known, they have incredibly powerful intuition.
And, and there's a lot, I mean, statistical mechanics. So I, I study
the statistical mechanics and I mean, the random processes are related to algorithms in a lot of,
in a lot of ways. But there's lots of different flavors of flavors of physics,
there are different flavors of mathematics as well. But, but the thing is that I don't see,
well, actually, when they talk to physicists, use a completely different language than when
they're talking to, when they're writing expository papers. And so I didn't understand quantum
mechanics at all, from reading about it and scientific American. But, but when I read,
you know, how they described it to each other, talking about eigen, eigenvalues,
and various mathematical terms that, that made sense, then it made sense to me. But, but Hawking
said that every formula you put in a book, you lose half of your readers. And so he didn't put
any formulas in the book. So I couldn't understand his book at all. You could say you understood it,
but I really, I really didn't. Well, Feynman also spoke in this way. So Feynman, I think,
prided himself on really strong intuition. But at the same time, he was hiding all the,
the really good, the deep computation he was doing. So, so there was one thing that, that,
that I was never able to, I wish I'd had more time to work out with him. But I guess I could
describe it for you. There's, there's something that got my name attached to it, called Knuth
arrow notation. But it's a notation for very large numbers. And so it, I find out that, that
somebody invented it in, in the 1830s. It's fairly easy to, to understand anyway. So you start with
x plus x plus x plus x n times, and you can call that x n. So x n is multiplication. Then you take
x times x times x times x times n times, that gives you exponentiation x to the nth power.
So that's one arrow x. So x n with no arrows is multiplication. x arrow n is x to the nth power.
Yeah. So just to clarify for the, so x times x times x n times is obviously x n.
x plus x plus x n times. Oh yeah. Okay. And then x n, no.
And then multiplications x to the nth. And then, and then here the arrow is when you're
doing the same kind of repetitive operation for the exponential.
So I, so I put in one arrow and I get x to the nth power. Now I put in two arrows,
and that makes, takes x to the x to the x to the x to the x n times power. So in other words,
if it's two double arrow three, that would be, that would be two to the two to the two.
So that would be two to the fourth power. That'd be 16. Okay. So that's the double arrow.
And now you can do a triple arrow, of course, and, and so on. And, and I had this, this paper called,
well, essentially big numbers. You know, you, you try to impress your friend, but by saying
a number they never thought of before. And, and, and I gave a special name for it,
and designed a font for it that has script K and so on. But it, but it really is 10,
I think like 10 quadruple arrow three or something like that. And I claim that that number, if it
is so mind boggling that you can't comprehend how large it is. But anyway, Feynman, I talked to
Feynman about this, and he said, oh, let's just, let's just use double arrow. But instead of taking
integers, let's consider complex numbers. So, you know, you have, I mean, okay, x, x arrow,
arrow two, that means x, x, or x, but what about x, x double arrow to 2.5? Well, that's not too
hard to figure out. That's interpolate between though. But what, what, what x double arrow,
I, or one plus I, or some complex number. And, and so he claimed that, that, that there was no
analytic function that would, that would do, that would do the job. But I didn't know how he could
claim that that was, that wasn't true. And his next question was, did then have a complex number
of arrows? Yeah, okay. Wow, okay. Okay, so that's, that's Feynman. That's Feynman. Yeah.
Can you describe what the Knuth, Morris Pratt algorithm does? And how did you come to develop
it? One of the many things that you're known for, and has your name attached to it? Yeah,
all right. So it should be actually Morris Pratt Knuth. But we decided to use alphabetical order
when we published the paper. The problem is something that everybody knows now if they're,
if they're using a search engine, you have a large collection of text, and you want to know if,
if the word Knuth appears anywhere in the text, to say, or, or some, some other word that's less
interesting than Knuth. But anyway, that's the most interesting word, yeah. Like Morris or something.
Like Morris, right. So anyway, we have, we have a large piece of text, and it's all one long,
one dimensional thing, you know, first letter, second letter, et cetera, et cetera, et cetera.
And so the question, you'd like to be able to do this quickly. And the obvious way is,
let's say we're looking for Morris, then okay, so we would, we would go through and wait till we
get to letter M. Then we look at the next word and sure enough, it's an O and then an R. But then
that, oh, too bad. The next letter is E. So we missed, we missed out on Morris. And so we go
back and start looking for another. Okay. So that's the obvious way to do it. All right.
And Jim Morris noticed there was a more clever way to do it. The obvious way would have started,
let's say we found that letter M at character position 1000. So it started next at character
position 1001. But he said, no, look, we already read the O and the R. And we know that they aren't
M's. So we can start, we don't have to read those over again. So, and this gets pretty tricky when
when the word isn't Morris, but it's more like abracadabra, where you have patterns that are
occurring. Like repeating patterns in the, at the beginning, at the middle. Right. So he worked it
out. And he put it into the system software at Berkeley, I think it was, where he was,
he was writing some Berkeley Unix, I think it was some routine I was supposed to find occurrences
of patterns in text. And, and we didn't explain it. And so he found out that several months later,
somebody had had looked at it didn't look right. And so they ripped it out. So he had this, this
algorithm, but it didn't make it through. You know, because he wasn't understood. Nobody knew
about this particularly. Von Pratt also had independently discovered it a year or two later.
I forget why. I think Von was studying some technical problem
about palindromes or something like that. He wasn't really, Von wasn't working on,
on text searching, but he was working on a, on an abstract problem that that was related. Well,
at that time, Steve Cook was a professor at Berkeley. And it was the greatest mistake that
Berkeley CS department made was not to give him tenure. And so Steve went to, went to Toronto.
But, but I, but I knew Steve while he was at Berkeley. And he had come up with a,
with a very peculiar theorem about a technical concept called a stack automaton.
And a stack automaton is a machine that, that it can't do everything that through a machine
could do, but it can only look at something on at the top of a stack, or it can put more
things on the stack or, or it can take things off the stack. Like it can't remember a long string
of symbols, but, but it can remember them in reverse order. So, so if you tell a stack automaton, A, B,
C, D, E, it can, it can tell you afterwards E, E, D, C, B, A, you know, it doesn't have any other
memory except, except this one thing that it can see. And, and Steve Cook proved this amazing
thing that says, if a stack automaton can recognize a language, where the strings of the language are
length n, in any amount of time whatsoever, for the stack automaton might use a zillion steps,
a regular computer can recognize that same language in time n log n. So Steve had a way of
transforming a computation that goes on and on and on and on into using different data structures
into something that you can do on a regular computer fast. The stack automaton goes slow,
but, but, but somehow the fact that it can do it at all means that there has to be a fast way.
So I thought this was a pretty, you know, cool theorem. And so I tried it out on, on a problem
where I knew a stack automaton could do it. But I couldn't figure out a fast way to do it on a
regular computer. I thought I was a pretty good programmer. But, but by golly, I couldn't think
of any way to recognize this language efficiently. So I went through Steve Cook's construction.
I filled my blackboard with all the, everything that stack automaton did, you know, I wrote down,
and then I tried to see patterns in that. And, and how does he convert that into a computer
program on a regular machine? And finally, I psyched it out. What was, what was the thing I
was missing so that I could say, oh, yeah, this is what I should do in my program. And now I have
an official program. And, and so I, I would never have thought about that if I hadn't had his theorem,
which was purely abstract thing to try to intuit how to use the stack automaton for the string
matching problem. Yeah. So, so, so the problem I, I had started with was not the string matching
problem. But then I realized that the string matching problem was another thing, which would
also be could be done by a stack automaton. And so when, when I looked at what that told me,
then I had a nice algorithm for this string matching problem. And it told me
exactly what I should remember as I'm, as I'm going through the string. And I worked it out and,
and I wrote this little paper called Automata Theory Can Be Useful. And, and the reason was
that it was first, I mean, I had been reading all kinds of papers about automata theory.
But it never taught me, it never improved my programming for, for everyday problems.
It was something that you published in journals and, and, and, you know, it was, it was interesting
stuff. But it, but here was a case where I couldn't figure out how to write the program.
I had a theorem from Automata Theory, then I knew how to write the program. So this was,
for me, you know, a change in life, I started to say, maybe I should learn more about automata.
And, and, and I, I showed this note to Vaughan Pratt. And he said, he, that's similar to something
I was working on. And then, and Jim Morris was at Berkeley too, at the time. Anyway, he, he had,
he had an illustrious career, but I haven't kept track of Jim, but Vaughan is my colleague at
Stanford and my student later. But this was before Vaughan, Vaughan was still a graduate
student and hadn't come to Stanford yet. So we found out that we'd all been working on the same
thing. So it was our algorithm we each discovered independently, but each of us had discovered
a different, a different part of the elephant, you know, a different aspect of it. And so we could
put our, our things together with my job to write the paper. How did the elephant spring to life?
Spring to life was because I, I had drafted this paper, Automata Theory,
oh, can be useful, which was seen by Vaughan and then by Jim. And then, then, then we combined,
because maybe they had also been thinking of writing something up about it.
About specifically the string match.
Specifically the string match problem in a period.
Let me ask a ridiculous question. Last time we talked, you told me what the most beautiful
algorithm is actually for strongly connected graphs. What is the hardest problem,
puzzle, idea in computer science for you personally that you had to work through?
Just something that was just the hardest thing that I've ever been involved with?
Yeah.
Okay. Well, yeah, that's, I don't know how to answer questions like that, but in this case,
it's pretty clear.
Okay.
Because it's called the birth of the giant component. Okay. So now let me explain that,
because this actually gets, gets into physics too. And it gets into something called Bose
Einstein statistics. But, but anyway, it's got some interesting stories and it connected with
Berkeley again. So start with the idea of a random graph. Now this is, here we just say we have
n points that are totally unconnected and, and there's no geometry involved.
There's no saying some points are further apart than others. All points are exactly,
are exactly alike. And let's say we have a hundred points and we number them from zero,
zero to nine, nine. All right. Now let's, let's take pi, the digits of pi. So
two at a time. So we had 31, 41, 59, 26, we can look, go through pi. And so what,
so we take the first two 31, 41, and let's, let's put a connection between 0.31 and 0.41.
That's an edge in the graph. So then we take 5926 and make another edge. And the graph gets bigger,
gets more and more connected as we add these things one at a time. Okay. So we started out
with n points and, and we add m edges. Okay. Each edge is completely, we forgot about edges
we had before. We make an edge twice. We make an edge from a point to itself even.
You know, maybe pi is going to have a run of four digits in there. So we're going to,
but anyway, we're evolving a graph at random. And a magical thing happens when the number
of edges is like 0.49. And so maybe n is a million and I have, you know, 490,000 edges.
Then it almost all the time, it consists of isolated trees, not even any loops.
Right. It's a very small number of edges so far.
About a little less than half n.
And right.
But if I had 0.51 edges, so a little more than half n. So, you know, million points,
510,000 edges. Now it probably has a, one component that's much bigger than the others.
And we call that the giant component.
Okay. Can you clarify? So can you clarify? First of all, is there a name for this kind of random,
super cool pi random graph?
Well, I call it the pi graph. No, no, the pi graph is actually,
my pi graph is based on binary representation of pi, not the decimal representation of pi, but
anyway, let's suppose I was rolling dice instead. So it doesn't have to be pi?
It doesn't have to be any source of, the point is every step, choose totally at random one of
those endpoints. Choose totally at random another one of the endpoints. Make that an edge.
That's the process.
Yeah. So there's nothing magical about pi.
No, no, I was using pi to, I was sort of saying pi is sort of random that nobody knows a pattern.
Exactly. Got it. Got it. Got it. But it's not, yeah, I could have just as well drawn straws or
something. This was a concept invented by Erdos and Rainey and they called the evolution of random
graphs. And if you start out with, with the large number n, and you, and you repeat this process,
all of a sudden a big bang happens at one half n, there'll be two points together,
then maybe we'll have, have three. And then, you know, then they maybe branch out a little bit,
but, but they'll all be separate until we get to one half n. And we pass one half n and all of a
sudden there's substance to it that there are, there's a big clump of stuff that's all joined
together. So it's almost like a phase transition of some kind.
It's exactly, it's a phase transition, but it's actually, it's a double phase transition. It turns
out it, it, it happens. I mean, there's actually two things going on at once at this phase transition,
which is, which is very remarkable about it. Okay. So, so a lot of the most important algorithms
are based on random processes. And so I wanted to, you know, I want to understand random processes
now. And so there are data structures that sort of grow this way. Okay. So, so, so Dick Karp,
one of the leading experts on, on random randomized algorithms, had his students working,
looking at this at Berkeley. And we heard a rumor that the students have found something
interesting happening. The students are generating this, or similarly, this random evolution of
graphs. And they're taking snapshots that were so often, take a look at what the graph is.
And the rumor was that every time they looked, there was only one component that had loops in it,
almost always. They do a million experiments and only three or four times did they ever,
ever happen to see a loop at this, at this point. I mean, no, more than one component with a loop.
So they watch until the graph gets completely full. So it starts out totally empty and gets more and
more, more and more edges all the time. And so, okay, certainly a loop comes along once. But,
but now all the loops stay somehow joined to that one. They're never, there never were two guys
with loops in these experiments. Okay. So anyway, this was almost always, certainly not always.
But, but, but with very high probability, this seemed to be true. So, so, so we heard about
this rumor as Stanford. And we said, if that's true, then must, you know, a lot more must also
be true. So there's a whole bunch, there's a whole theory out there waiting to be discovered that we
haven't ever thought about. So let's take a look at it. And so we look closer and we find out, no,
actually, it's not true. But, but in fact, it's almost true. Namely, there's a very short interval
of time when it's true. And if you don't happen to look at it during that short interval of time,
then you miss it. So that, you know, there'll be a period where there are two or three components
have loops, but they join together pretty soon. Okay. So if you don't have a real fast shutter
speed, you're going to miss, you're going to miss that instant. So separate loops don't exist for
long. That's, that's it. Yeah. You know, I started looking at this to make it quantitative. And
basic problem was to slow down the big bang so that I could watch it happening. Yeah. I think I
can explain it actually in fairly elementary terms, even, even without writing a formula.
Let's try. Like Hawking would do. And, and, and so let's, let's watch the evolution. And, and at
first, these edges are coming along and they're just making things without loops, which we call
trees. Okay. So then all of a sudden the loop first appears. So at that point, I have one
component that has a loop. All right. Now, now I say that the complexity of a component
is the number of edges minus the number of vertices. So if I have a loop, I have like a
loop of length five has five edges and five vertices. Or, or I could put a tail on that.
And that would be another edge, another vertex because zero, one, two complexity kind of thing.
So, so if the, if the complexity is zero, we have one, one loop, I call it a cycle or I call it a
cyclic components. So, so a cyclic component looks like a, a wheel to which you attach fibers
or trees. They go branching, but there's no more loops. There's only one loop and everything else
feeds into that loop. Okay. And that has complexity zero. But, but a tree itself has complexity
minus one because it has, you know, like, like, like it might have 10 vertices and nine edges to
tie the time together. So nine minus 10 is minus one. So, so complexity minus one is a tree.
It's got to be connected. That's what I mean by a component. It's got to be connected. So, so,
so if, if I have 10 things connected, I have to have nine edges.
Can you clarify why when complexity goes, you can go above zero. I'm a little, yes, what, right.
So the complexity plus one is the number of loops. So if complexity is zero, I have one loop.
If, if complexity is one, that means I have one more edge than I have vertices. So I might have
like 11 edges and 10 vertices. So it turns, we call it a bicycle because it, it's got two loops
and it's got to have two loops in it. If you, if you, I, well, why can't it be trees just going off
of the loop that I would need more edges than I, all right, right. Okay. I got so every time I get
another loop, I get another excess of edges over vertices. I got you. Okay. So in other words,
we start out and after I have one loop, I have one component that has a cycle in it. Now the next
step, according to the rumor would be that at the next step, I would have a bicycle in the evolution
of almost all graphs. It would go from cycle to bicycle. But in fact, there's a certain probability
it goes from cycle to two, you know, two, two different cycles. All right. And I worked out the
probability with something like five out of 24. It was pretty high. It was substantial. Yeah.
But still, soon they're going to merge together almost. Okay. So that's so cool. But that, but
then it splits again. After you have either, either two or one, one, the next step is you either have
three, or you have two, one, or you have one, one, one. Okay. And so I worked out the probability
for those transitions. And I worked it out up to, up to the first five transitions.
And I had these, I had these strange numbers, five, 24. And I stayed up all night and about three
a.m. I had the numbers computed. And I looked at them and here were, the denominator was something
like 223023. So the probability was something over 23023.
I don't know how you worked that out. But I had a formula that, you know, I could calculate the
probability. Yeah. And I could find the limiting probability as n goes to infinity. And it turned
out to be this number, but the denominator was 230. And I, and I looked at the denominator,
I said, wait a minute, this number factors because 1001 is equal to seven times 11 times 13. I had
learned that in my first computer program. So, so, so, so 23, oh, 23 is seven times 11 times 13 times
23. That's not a random number. There has to be a reason why those small primes appear in the
denominator. But my, so all of a sudden that suggested another way of looking at the problem
where small prime factors would occur. So, so what would that be? So that said, oh, yeah,
let me take the logarithm of this formula. And sure enough, it's going to simplify. And it happened.
So I wouldn't have noticed it except for this factorization. Okay. So I go to bed and I say,
oh, okay, this is, this looks like I'm slowing down the Big Bang. I can figure out what's going
on here. And the next day it turned out Bill Gates comes to Stanford to visit. They're trying
to sell him on donating money for a new computer science building. Sure. And, and, and so they
gave me an appointment to talk to Bill and I, and I wrote down on the blackboard this
this evolutionary diagram, you know, going from one to two, five, 24, so in all this business.
Yeah. And I wrote it down. And anyway, at the end of the day, he was discussing people with the,
with the development office. And, and he said, boy, I was really impressed with what Professor
Knuth said about this giant component. And, and so, you know, I love this story because it shows
that theoretical computer science is, is really worthwhile. You know, does Bill, have you ever
talked to Bill Gates about it since then? Yeah. That's a cool, that's a cool little moment in
history. Yeah. But, but, but anyway, he happened to visit on exactly the day after I had,
I found this pattern and that allowed me to, to crack the problem. So, so that I could develop
the theory, the theory some more and understand what's happening in the big, but because I could,
I could now write down explicit formulas for stuff. And so it would, you know,
you work not only the first few steps, but also study the whole process. And, and I worked further
and further. And I, with two authors, co-authors, and we finally figured out that the probability
that the rumor was true. In other words, look at the evolution of a random graph going from zero,
zero to, to complete and say, what's the probability that at every point in time,
there was only one component with a cycle. We started with this rumor saying there's only one
site, there's only one component with a cycle. And, and so it'll be the rumor was it's 100%.
Rumor was that was 100%. It turned out the actual numbers is like 87%. I don't remember,
I should remember the number, but I don't, but I don't have it with me. But, but anyway,
but, but the, but the number, it, it turned out to be like 12 over pi squared or, or anyway,
no, sorry, eight over pi. Anyway, it, it, it was a nice, it related to pi. Yeah. And we could never
have done that with it. But so that's the hardest problem I ever saw in my life was to prove that
this probability is, it says you was proven, the probability was proven. Yeah, I was able to prove
this, that this and, and, and this shed shed light on a whole bunch of other things about random graphs
that that was sort of the, the major thing we were after. That's super cool. I, what was the
connection to physics that you mentioned? Well, Bose Einstein statistics is the study of how molecules
bond together without geometry, without this.
You created the tech typesetting system and released it as open source. Just on that little
aspect, why did you release it as open source? What is your vision for open source?
Okay. Well, that, the word open source didn't exist at that time, but we, but I, I didn't want
proprietary rights over it. Because I saw how proprietary rights were holding things back.
In the late fifties, people at IBM developed the language called FORTRAN. They could have
kept it proprietary. They could have said only IBM can use this language. Everybody else has to,
but, but they didn't. They said anybody who can write, who can translate FORTRAN into the,
into the language of their machines is allowed to make FORTRAN compilers too.
On the other hand, in the topography industry, I had seen a lot of languages that were developed
for composing pages. And each manufacturer had his own language for composing pages.
And that was holding everything back because people were tied to a particular manufacturer.
And, and then a new equipment is invented a year later, but printing, printing machines, they have
to expect to amortize the cost over 20, 30 years. So you didn't want that for tech?
I didn't need the income. I already, I already had a good job. And, you know, my books were,
people were buying enough books that I, that, that it would bring me plenty of supplemental
income for everything my kids needed for education, whatever. So there was no reason for me to try
to maximize income any further. Income is sort of a threshold function. If you don't have,
if you don't have enough, you're starving. But if you get over the threshold, then you start
thinking about philanthropy or else, or you're trying to take it with you. But, but anyway,
there's a, I had, my income was over the threshold. So, so I didn't need to keep it. And so I
specifically could see the advantage of, of making it open for everybody.
Do you think most software should be open?
So I think that people should charge for non-trivial software, but not for trivial software.
Yeah. You give an example of, I think, Adobe Photoshop versus GIMP on Linux,
as Photoshop has value, which.
So it's definitely worth paying, paying for all the stuff. I mean, and I mean,
well, they keep adding, adding stuff that my wife and I don't care about, but
somebody obviously does. But I mean, but they have built in a fantastic
undo feature, for example, in Photoshop where, where you, you can go through a
sequence of a thousand complicated steps on graphics and it can take you back anywhere in
that sequence with really beautiful algorithms. I mean, yeah, it's, it's.
Oh, that's interesting. I didn't think about what algorithm, it must be some kind of efficient
representation. It's really, yeah, no, I mean, there's a lot of really subtle
Nobel Prize class creation of intellectual property in, in, in there.
And, and with patents, you get a limited time to, I mean, eventually the idea of patents is that
you publish so that it's not secret. It's not a trade secret. That said, you, you've said that
I currently use Ubuntu Linux on a standalone laptop. It has no internet connection. I occasionally
carry flash memory drives between the machine and the Macs that I use for network surfing and
graphics, but I trust my family jewels only to Linux. Why do you love Linux?
The version of Linux that I use is stable. Actually, I'm going to have to upgrade one of these days,
but to a newer version of Ubuntu. Yeah, I'll stick with Ubuntu, but, but right now I'm running
something that doesn't support a lot of the new software. The last stable, I don't remember the
number, like 14. Anyway, it's, it's, it's quite, and I'm going to get a new computer.
I'm getting new solid state memory instead of a hard disk.
Yeah, the basics. Well, let me ask you, thinking on the topic of tech,
when thinking about beautiful typography, what is your favorite letter, number, or symbol?
I know, I know. Ridiculous question. But is there some
Let me show you. Look at the last page. The very end of the index.
What is that? There's a book by Dr. Seuss called On Beyond Zebra, and he gave a name to that.
Did you say Dr. Seuss gave a name to that? Dr. Seuss. This is a S-E-U-S-S. He wrote
children's books in the 50s, 40s and 50s. Wait, are you talking about Cat in the Hat?
Cat in the Hat, yeah. That's it, yeah. On Beyond Zebra did it get to Soviet Union.
Yeah, Dr. Seuss did not come to the Soviet Union, but since you... Oh, actually, I think he did,
actually, a little bit when we're... Maybe Cat in the Hat or Green Eggs and Ham,
I think was used to learn English, so I think it made it in that way. Okay, I didn't like those as
much as Bartholomew Cubbins, but I used to know Bartholomew Cubbins by heart when I was young.
So what the heck is this symbol we're looking at? There's so much going on.
He has a name for it at the end of his book on Beyond Zebra.
Who made it? He did. He did. It looks like a bunch of vines. Is that symbol
existing? By the way, he made a movie in the early 50s. I don't remember the name of the movie,
now you can probably find it easily enough, but it features dozens and dozens of pianos all playing
together at the same time. But all the scenery is sort of based on the kind of artwork that was in
his books and the fantasy based of Seussland or something. And I saw the movie only once or twice,
but it's quite... I'd like to see it again. That's really fascinating that you gave them...
They gave them a shout-out here. Okay. Is there some elegant basic symbol that you're attracted to?
Something that gives you pleasure? Something used a lot?
Pie? Pie, of course. I try to use pie as often as I can when I need a random example,
because it doesn't have any known characters. So for instance, I don't have it here to show you,
but do you know the game called Masiu, M-A-S-Y-U? No. It's a great recreation. I mean,
Sudoku is easier to understand, but Masiu is more addictive. You have black and white stones
like on a go board, and you have to draw a path that goes straight through a white stone and
makes the right angle turn at the black stone. And it turns out to be a really nice puzzle,
because it doesn't involve numbers, but it's visual, but it's really pleasant to play with.
So I wanted to use it as an example in art of computer programming, and I have
exercised on how to design cool Masiu puzzles. You can find it on Wikipedia, certainly as an
example, M-A-S-Y-U. And so I decided I would take pie, the actual image of it, and I had pixels,
and I would put a stone wherever it belongs in the letter pie, in the Greek letter pie.
But the problem was, find a way to make some of the stones white, some of the stones black,
so that there's a unique solution to the Masiu puzzle. That was a good test case for my algorithm
on how to design Masiu puzzles, because I insisted in advance that the stones had to be placed in
exactly the positions that make the letter pie, make a Greek letter pie. And it turned out there
was a unique way to do that. And so pie is a source of examples where I can prove that I'm
starting with something that isn't canned. And most recently, I was writing about something
called graceful graphs. Graceful graphs is the following. You have a graph that has M edges
to it, and you attach numbers to every vertex in the following way. So every time you have an edge
between vertices, you take the difference between those numbers. And that difference is
got to tell you what edge it is. So one edge, two numbers will be one apart. There'll be another
edge where the numbers are two apart. And so it's a great computer problem. Can you find a
graceful way to label a graph? So I started with a graph that I use for an organic graph,
not a mathematically symmetric graph or anything. And I take 49 states of the United States.
The edges go from one state to the next state. So for example, California,
be next to Oregon, Nevada, Arizona. And I include District of Columbia. So I have 49.
I can't get Alaska and Hawaii in there because they don't touch. You have to be able to
drive from one to the other. So is there a graceful labeling of the United States?
Each state gets a number. And then if California is number 30 and Oregon is number 11,
that edge is going to be number 19. The difference between those. So is there a way to do this
for all the states? And so I was thinking of having a contest for people to get it as graceful
as they could. But my friend, Tom Rukiki, actually solved the problem by proving that.
I mean, I was able to get it down within seven or something like that. He was able to get a
perfect solution. The actual solution or to prove that a solution exists? More precisely. I had
figured out a way to put labels on so that all the edges were labeled somewhere between one and
117. But there were some gaps in there. Because I should really have gone from one to 105 or whatever
the number is. So I gave myself too much, you know, a lot of slack. He did it without any
slack whatsoever. A perfect graceful labeling. And so I call out the contest because the problem
is already solved and too easy in a sense, because Tom was able to do it in an afternoon.
Sorry, he gave the algorithm or for this particular?
For the United States. This problem is incredibly hard.
I mean, for the general outcome. But it was very lucky that it worked for the United States, I
think. The theory is still very incomplete. But anyway, then Tom came back a couple of days later
and he had been able to not only find a graceful labeling, but the label of Washington was 31.
And the label of Idaho was 41, following the digits of Pi.
Going across the topic of the United States, he has the digits of Pi.
Does he do it on purpose?
He was able to still get a graceful labeling with that extra thing.
It's a miracle. But I like to use Pi in my book.
All roads lead to Pi. Somehow often hidden in the middle of the most difficult problems.
Can I ask you about productivity?
Yeah, you said that, quote, my scheduling principle is to do the thing I hate most
on my to-do list. By weeks end, I'm very happy. Can you explain this process to a productive life?
Oh, I see. Well, but all the time I'm working on what I want, what I don't want to do,
but still I'm glad to have all those unpleasant tasks finished.
Yes. Is that something you would advise others?
Yeah, I don't know how to say it. During the pandemic, I feel my productivity actually went
down by half because I have to communicate by writing, which is slow. I don't like to send
out a bad sentence. I go through and reread what I've written and edit and fix it. Everything
takes a lot longer when I'm communicating by text messages instead of just together
with somebody in a room. It's also slower because the libraries are closed and stuff.
But there's another thing about scheduling that I learned from my mother that I should
probably tell you, and that is different from what people in robotics feel do, which is called
planning. So she had this principle that was, see something that needs to be done and do it.
Instead of saying, I'm going to do this first and do this first,
just do it. Oh, yeah, pick this up.
But at any one moment, there's a set of tasks that you can do. And you're saying a good heuristic
is to do the one you want to do least. Right. The one I haven't got any good reasons.
I'll never be able to do it any better than I am now.
I mean, there are some things that I know, if I do something else first, I'll be able to do that
one better. But there's some that are going to be harder because I've forgotten some of the
groundwork that went into it or something like that. So I just finished a pretty tough part
of the book. And so now I'm doing the parts that are more fun. But the other thing is,
as I'm writing the book, of course, I want the reader to think that I'm happy all the time I'm
writing the book. It's upbeat. I can have humor. I can say, this is cool. Well, this, I have to
disguise the fact that it was painful in any way to come up. The road to that excitement is painful.
Yeah. It's laden with pain. Okay. Is there, you've given some advice to people before,
but can you? You give me too much credit. But anyway, this is my turn to say things that I
believe, but I want to preface it by saying, I also believe that other people do a lot of these
things much better than I do. So I can only tell you my side of it. So can I ask you to give advice
to young people today, to high school students, to college students, whether they're geeks
or the other kind about how to live a life that they can be proud of, how to have a successful
career, how to have a successful life? It's always the same as I've said before, I guess,
not to do something because it's trendy, but it's something that you personally feel that you were
called to do rather than somebody else expects you to do. How do you know you're called to do
something? You try it and it works or it doesn't work. I mean, you learn about yourself. Life is
a binary search. You try something and you find out, oh yeah, I have a background that helped me
with this. Or maybe I could do this if I worked a little bit harder, but you try something else
and you say, I have really no intuition for this and it looks like it doesn't have my name on it.
Was there advice along the way that you got about what you should and shouldn't work on or do you
just try to listen to yourself? Yeah, I probably overreacted another way. When I see everybody
else going some way, I probably say too much competition. But mostly I played with things
that were interesting to me and then later on I found, oh, actually, the most important thing I
learned was how to be interested in almost anything. I mean, not to be bored. It makes me
very sad when I see kids talking to each other and they say, that was boring.
And to me, a person should feel upset if he had to admit that he wasn't able to find something
interesting. I haven't learned how to enjoy life. I have to have somebody entertain me instead of
That's really interesting. It is a skill. David Foster Wallace, I really like the thing he says
about this, which is the key to life is to be unboreable. And I do really like you saying that
it's a skill, because I think that's a really good advice, which is if you find something boring,
that's not, I don't believe it's because it's boring. It's because you haven't developed a skill.
I haven't learned how to find the beauty in it, how to find the fun in it. Yeah, that's a really
good point. Yeah, sometimes it's more difficult than others to do this. But I mean, during the
COVID, lots of days when I never saw another human being, but I still find other ways to
It still was a pretty fun time. I came earlier, I came a few minutes early today and I walked around
Foster City. I didn't want, you know, I didn't know what was going on in Foster City. I saw
beautiful, some beautiful flowers at the nursery at Home Depot a few blocks away. Yeah.
Life is amazing. It's full of amazing things like this. Yeah, I just sometimes I'll sit there and
just stare at a tree. Nature is beautiful. Let me ask you the big ridiculous question. I don't think
I asked you last time. So I have to ask this time in case you have a good answer. What is the meaning
of life? Our existence here on earth, the whole thing. No, no, you can't, you can't. I will not
allow you to try to escape the answer in this question. You have to answer definitively.
Because they're surely, surely, Don Knuth, there must be an answer. What is the answer? Is it 42?
Yeah. Well, I don't think it's a numerical. That's the SDS. That was in Zenon.
All right. So anyway, it's only for me. But I personally think of my belief that God exists,
although I have no idea what that means. But I believe that there is something beyond human
capabilities. It might be some AI. But whatever it is. But whatever. But I do believe that
there is something that goes beyond the realm of human understanding. But that I can try to
learn more about how to resonate with whatever that being would like me to do.
So you think you can have occasional glimpses of that being?
I strive for that. Not that I ever think I'm going to get close to it. But it's not,
it's not for me. It's saying, what should I do that that being wants me to do? That's,
you know, I'm trying to ask, what that, I mean, does that being want me to be talking
to Lex Friedman right now, you know, and I said yes. Okay. But thank you. Well, thank you.
What I'm trying to say is, I'm not trying to say what, of all the strategies I could choose or
something, which one, I try to do it not, not strategically, but I try to
to imagine that I'm following somebody's wishes. Even though you're not smart enough to
know what they are. Yeah. But it's a funny little dance. Well, I mean, this AI or whatever is
probably is smart enough to help to give me clues.
And do you make the whole journey from clue to clue, a fun one?
Yeah, I mean, it's, as so many people have said, it's the journey, not the destination.
And people live, live through crises, help each other, all these things come up,
history repeats itself. You try to say, in the world today, is there any government
that's working? I read history, I know that things were.
They were, there were, there were a lot worse in many ways.
There's a lot of bad things all the time. And I read about, you know, I look at
things and people had good ideas, and they were working on great projects. And then I know that
it didn't succeed, though, in the end. But the new insight I've gotten, actually,
in that way was, I was reading, what book was I reading recently? It was,
it was by Ken Follett, and it was called The Man from St. Petersburg. But it, but it was talking
about the prequel to World War One. And Winston Churchill, according to this book, sees that,
that Germany has been spending all its gold reserves, building up a huge military.
And there's no question that if Germany would attack England, that England would be wiped out.
So he wants Russia to help to attack Germany from the other side, because Germany doesn't
have enough of an army to be fighting two wars at one. Okay. Now, then there's an anarchist in
Russia who sees that wars are something that leaders start, but actually people get killed.
And so he wants to stop any alliance between England and Russia, because that would mean that
thousands and thousands of people of Russia would be killed, that wouldn't be otherwise killed.
All right. And so his, his life's goal is to assassinate a Russian prince who's visiting
England, because that will make, will mean the Tsar will not form the alliance. All right.
So we have this question about what should the government do? Should it actually do something
that will lead to, you know, is the war inevitable or is there a way to have peace? And it struck me
that if I were in a position of responsibility for people's lives, in most cases, I wouldn't have,
I wouldn't have any confidence that any of my decisions were good, that these, these questions
are too hard, probably for any human being, but certainly for me. Well, I think, I think coupling
the not being sure that the decisions are right. So that that's actually a really good thing,
coupled with the fact that you do have to make a decision and carry the burden of that.
And ultimately, I have faith in human beings, in the great leaders to arise
and help build a better world. I mean, that's the hope of democracy.
Yeah. And let's hope that we can enhance their abilities with, with algorithms.
Well put, it's such a huge honor. You've been an inspiration to me and to millions for such
a long time. Thank you for spending your really valuable time with me once again. It's a huge
honor. I really enjoyed this conversation. Thanks for listening to this conversation with
Donald Knuth. To support this podcast, please check out our sponsors in the description.
And now, let me leave you with some words from Don Knuth himself.
Science is what we understand well enough to explain to a computer.
Art is everything else we do. Thank you for listening. I hope to see you next time.