Donald Knuth: Programming, Algorithms, Hard Problems & the Game of Life | Lex Fridman Podcast #219

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 it's 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 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 the year and the program yeah i might have learned about it assembler later that summary i probably did in 1957 hardly anybody had heard of assemblers you looked at the user manuals how did you write a program for this machine it would be it would it would say um you know you would say 69 which meant load the distributor and and then you would give the address of the number you wanted to load into the distributor uh yesterday uh my friend that 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 you know very contemporary with 1957 yes and in 1956 ibm had donated to stanford university on 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 a it's on youtube now um and and it showed the picture from stanford uh that that you know they they said look you know we donated one of these to stanford one to mit and they mentioned one other another college and in in december of 56 they donated to to my university case tech but anyway they showed a picture then a class session where a guy was teaching programming and on the blackboard it said 69 8 000 i mean he it was he was teaching them how to write uh code for this ibm 650 which was in decimal numbers so so the instructions were tended ten decimal digits you had two digits that said what what to do for they just say uh uh what to do it too 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 one 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 and i could write a better manual uh and that he did and so i i started working at the computer center um and and uh wrote some manuals then but but yeah but but this was uh but this was the way we did it and and my first program then was june of 1957 the tic-tac-toe no that was the second program the first the third program the first program was factoring a number okay so you dial a number on the on the um uh their switches that means you sat at this big mainframe and and you turn the dials and set a number and and then it would punch out uh the factors of that number on on cars so that's the input is the number the input was yeah the input what was the number yeah attended a number and and uh and the output was uh its factors and and and i wrote that program uh i still have a copy of it somewhere and um how many lines of code do you remember well yeah it started out as about 20 but then i kept having to debug it and i i discovered debugging of course when i wrote my first program and what does uh debugging look like on a program with just all numbers well you sit there and you uh i don't remember how i got it into the machine but i but i think there was a way to punch punch it on cards so each each instruction would would be one one card or maybe i could get seven instructions on the 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 of course um and and so you have one set of switches where you can dial the number i'm inputting but there's another switch that's it that you know that says okay now execute one instruction and show me what you thought what you did or or you or you there was another four switches and say stop if you get to those if if you get to that instruction so so i can say now go until you get there again and watch okay so i could watch you know it he 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 so then i work on the but if if not divisible by two divide by three okay keep trying and you know until you know you're you're at the end and uh you would find a bug if uh if you were just surprised that something weird happened well certainly i mean first of all i might have it you know try to divide by one instead of two you off by one errors that people make all the time you know but but maybe i go to the wrong instruction maybe i you might maybe i uh i left left something in a register that i shouldn't have done but the first bugs were pretty you know i i 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 um so you're sorry to interrupt you were 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 like what 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 sleep you know i used to do all-nighters when i was in high school i used to i used to do the uh the whole student newspaper every monday night i would i would you know i would just stay up all night and and it would be done on tuesday morning um that was because i i didn't get ulcers and stuff like that until later you know but but but uh well the uh i don't know if you know rodney brooks rod brooks of course yeah he he he told he told me a story that he really you're you know he really looked up to you he was actually afraid of you vice versa i must say but when 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 oh that happened all the time he was really intimidated he's like dr newt is not happy with this that's interesting but no no the the machine at stanford ai lab was uh uh i was down an awful lot because we they had they had many talented programmers changing the operating system every day and so operating system was getting better every day but it was also crashing so so so i i wrote almost the entire manual for tech during down time [Music] that much but that's another story okay well he was saying they uh it's a hardware problem they they uh they tried to fix it and they reinserted something and smoke was everywhere because he was hurt well that didn't happen as often as the operation coming from but yeah and it was it's a funny story because you're saying there's this tall uh don knuth that i look up to and there was pressure to i think it's the computer well it's funny okay the kind of things we remember that stick in our memory well okay yeah well i i i could tell you a bunch of rod brooks stories too but let's let's let let's go back to the 650. so so um so i'm debugging this my first program and and i i i had more bugs in it than a number of lines of code i 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 it i got a 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 my i was my first program i i probably screwed up and you know it it fell off the edge of the card or something like that but but i didn't realize that there are some tentative numbers that have that have more than eight um 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 line the stuff up in memory and then it punched the card but but after you know so by the time i finished i had to i had to deal with lots of lots of things also i uh uh if you if you put a large prime number in there my program might have sat there for for 10 minutes the 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 ten digit ten digits yeah so i think the largest is sort of nine nine nine nine nine nine nine nine nine seven or something like that and that would you know that that would take me a while uh for that first one anyway that was my first program well what was your goal with that program well there's something you were hoping to find a large prime maybe or no the opposite you know 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 uh 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 he had some machi so the the the tic-tac-toe program is interesting on many levels but one of them is that it has some you can call machine learning in it that's yeah that's right uh uh 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 uh uh it it was my first experience with machine learning because 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 um right how was it designed right so so you got a three by three grid and each each each each could be in three states it can be empty or it can have an x or an o yeah right so three to the ninth is a uh well what is how big is it i should know um but it's 80 81 times 81 times three so um anyway eight is like two to the third and so that would be uh that would be like two to the sixth um uh and then uh but that would be 64 then you have to anyway i love how you're doing the calculation anyway the three comes from the fact that it's either empty an x or an o right and the 650 what was it was a machine that had only uh two thousand ten digit words you go from zero zero zero zero to one nine nine nine and that's it and and in each word you have a ten digit number so that's not many bits i mean i gotta 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 but it did have it it did have strange instruction where if if you had a tentative number that but all the digits were either eight or nine uh you you'd be eight nine nine eight or something like that that would uh you you could make a test whether it was eight or nine that was one of the strange things ibm engineers put into to the machine i have no idea what well um hardly ever used but anyway i i needed one digit for every every position i'd seen uh zero meant it was a bad position i meant it was good position i i think i started out at five or six you know but if you if you win a game then you uh then you increase the value of that position for you but you decrease it for your opponent uh uh so but but i i 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 which had to also include my program yes 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 get every every position in tic-tac-toe it is equivalent to roughly eight others because you you you can rotate the board um which gives you factor four and you can also flip it over and that's another factor two so so i might you know so i might have needed only three to the ninth over eight positions about you know plus plus a little bit uh so i had but anyway that was that was a 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 rotation i had to otherwise i couldn't do the learning uh wow so so but but i had three parts to my tic-tac-toe program uh and i called it brain one brain two and brain three so brain one just played a um let's see at random okay it's your turn okay you gotta put an x somewhere he has to go in an empty space but that's that's it okay choose to choose one and and play it uh brain two uh had a canned routine and i think it was it also maybe it had maybe it assumed you were the first player or maybe it allowed you to be first i think you were odd to be either first of a second but had a canned built-in strategy known to be optimum for tic-tac-toe [Music] before i forget by the way i learned uh 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 was never able to finish wow so that was the program he thought about more than a hundred years ago yeah yeah he had he he did that okay and i had but and and i had however 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 uh machine as part of that exhibit so that had been one of my uh you know something i'd seen before i was a freshman in college and and inspired me to see if i could write a program for okay so so anyway i had brain one random you know uh knowing nothing brain two knowing everything then brain three was the learning one and and i could i i could play brain one against brain one brain one against brain two and so on and so uh you could also play against the user against the live members but but uh so so i started going the the learning thing and i said okay you know take two random random people uh just playing uh uh tic-tac-toe uh uh knowing nothing um and after about i i forget the number now but but it converged after about 600 games uh uh to a safe draw the way my program learned was actually it learned how not to make mistakes because you know how to it didn't try to do anything for winning it just tried to yeah drop losing and not lose so that was probably because of the way i did i designed the learning thing i could have you know had a different uh reinforcement function that that would that would reward brilliant play but anyway it didn't and uh and and if if i took a novice against the uh you know the skilled player uh it it was able to learn uh how to play a good game so that was that and that was really mike but after i finished that i i felt i i understood programming was there um did you did a curiosity and interest in learning systems persist for you so why why did you want brain three to learn yeah i i think naturally it's we're talking about rod brooks like he he was teaching all kinds of very small devices to to learn stuff um if a leaf drops off of a tree uh uh you know it he was saying something well it learns if there's wind or not but but i i mean he pushed that a little bit too far but he said he could probably train some little mini bugs to to scour out dishes if he had enough financial support i don't know can i can i ask you about that because he he also mentioned that during those years there was discussion about inspired by touring about computation you know of what is computation yeah and yeah i never thought about any stuff like that that was that that was way too philosophical i mean i i was a i was a freshman after all i mean i i didn't i was pretty much a machine so it's almost like yeah i got you it's a tinkering mindset uh not a philosophical mindset it was just exciting to me to be able to control something but not but not but not to say hmm am i solving a big problem or something like that or is is this a step for humankind right 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 ex i had to take i had to take uh classes on computability 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 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 before stuff but but i i had great fun playing with the machine you know i um i wrote program because it was fun to write programs and and and get this i 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 uh 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 it's the same with music and whatever you can i i i i found uh well during the pandemic i spent a lot more time playing the piano and i i found something that i'd had i i had it right when i was taking lessons uh you know before i was a teenager and uh it was yankee doodle uh played in the style of you know and i you had you had beethoven and you had wc and chopin and you know and the last one was gershwin 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 uh this author mario somebody or other had had been able to uh reverse engineer the styles of of those components so but now specifically uh to 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 uh and it had been written by a team at at carnegie mellon and uh i have no idea which program was responsible for but but it you would get to a part where the guy would just not know how he 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 uh change in style but there were but then 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 it was mostly the the brilliance of the concept more than the uh semicolons and uh or the the you know the use of short sentences versus long sentences something like that so you would see the idea in the code and you can see the the different style of thinking experience right it was yeah so it was stylistic i mean like i could identify authors by their by the amount of technical aptitude they had but not by styling the sense 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 of thinking going on here what do you think and what what would be the defining uh 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 got it you know that i use a lot of global variables that other people don't and and and i expand things inline more than instead of calling anyway i have different subset of c that i use okay but this that's a little bit stylistic yeah but but with literate programming you alternate between english and and c or whatever and um and by the way people listening to this should look up literate programming it's very interesting uh concept that you uh 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 it is that i uh i i realized that uh my programs were to be read by people and not not just by computers and and that typography could massively enhance that and and and so uh i mean it they're just wonderful if they're gonna look it up that they should also look up this book by called physically based rendering by matt farr and anyway it got an academy award but it's but but but all the if on the graphic effects you see in movies uh like you know are accomplished by algorithms and this book it is the whole book is a literate program it tells you not only how you do all the shading and and uh bringing images in that you need for animation and textures and so on but it also uh you can run the code uh so uh and and so uh i find it uh an extension of the way i uh of of how to teach programming is it is but by by telling a story as part of the program so it's uh 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 more or a year later yeah so it it it's uh what's this piece it's the greatest thing since sliced bread programming or literate literate program okay uh you heard it here first okay you uh dodged this question in an interview i listened to uh so let me ask you again here uh 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 personal defined beauty a different way from hour to hour i mean it depends on what and what you're looking for at one level you it's it's beautiful just if it works at all another level it's beautiful if it's if it uh uh it can be understood easily it's beautiful if it if it's illiterate 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 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 uh i remember having this conversation i had this conversation on stack overflow whether humor is good in comments and i think it is whether huma is good in comments like uh when you add comments in code yeah 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 programmers yeah okay so uh a couple days ago i received a wonderful present from my former editor at aston wesley he he's downsizing his house and he found uh that somebody at the company had had found all that all of their internal files about the art of computer programming from the 1960s and they gave it to him uh and then you know before throwing string in the garbage and then so he said oh yeah he 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 and so i just received uh this big big stack of of letters uh some of which i had written to them but 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 uh uh in in the uh in the comments to volume one uh uh the the major the major reader was was bob floyd uh who is my great uh co-worker in the 60s um died early unfortunately but but uh and and he he commented about the humor so we had you know he ran it by me you know says you know keep this joke in or not you know um 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 is it said you know the ideal thing is uh that it's it's it's something where the reader knows that there's probably a joke here if you only understood it and this is a motivation to understand to think about it a little bit um but anyway it it it's a very delicate humor i mean it's it's it's really uh each each century invents a different kind of humor too i mean and different cultures have different different kinds of humor um yeah like uh we met we talked about russia a little bit offline uh you know there's dark humor and you know what when a country goes to something different right any of that life and stuff like this yo 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 but uh yeah it's called the funny men or something like that but yeah okay so anyway i i think it's important to know that that this is part of life and and it should be fun and not yeah and and so you know i wrote this this organ composition which uh uh 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 it's it's there yeah a little humor is okay yeah i mean not egregious humor so in in this correspondence you know there were there were things i said yeah i really shouldn't have i i really shouldn't have done that but uh but other ones i could you know i insisted on and i've got jokes in there that no that nobody has figured out you in fact in volume 2 i've got a cryptogram a message in cypher 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 uh and so you know if computers keep getting faster and faster then you know 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 uh i i don't know if you've heard about this let me explain it maybe you'll find it interesting so open ai is a company that does uh ai work and they have this language model it's a neural network that can generate language pretty well but they also of on top of that develop 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 in any language that it trained on uh 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 whether but how do you know whether it did a good job or not you could see a lot of examples where he did a good job and so you it it's not a thing that generates the code for you it starts it gives you uh 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 seemed to like when i was a professor at caltech uh in this in the 60s we had this this guy who who talked a good game he could give inspiring lectures and you'd think well certainly things he was talking about an hour later you said well what did he say um but what but but he really felt that it didn't matter whether computers got the right answer or not it just mattered whether it made you happy or not in other words if you you know if if if your boss paid for it uh he you know then you had a job you could you know you could 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 you see uh we're going that way i mean so many more things are are taken over by saying well this seems to work and so and when there's when there is uh competing interests involved neither side understands why the decision is being made you know we realize now that it's that is bad but but consider what happens five private ten year year down the line when things get even more further detached and 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 uh some deep experimentally 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 this you know 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 they're that's the that's the positive but of course it does come with the darkness like automation what what's better correct i'm never going to try to write a book about that uh i'm never going to recommend to any of my students to work for them so you you're on the side of i'm on the side i'm on the side of honor happiness understanding i understand and i i think these things are really marvelous if they if if what they do is you know all of a sudden we have a better medical diagnosis or or or you know it will help guide some scientific experiment or something like this uh you know you know curing diseases or what whatever but but when it when it affects people's lives in a serious way uh uh so if you're writing if you're writing code for geeky oh yeah here this is great this will make a slaughter bot 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 the this whole thing ends anyway so um but it it there is a heat death of the universe predicted but i i'm trying to postpone that for 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 to to 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 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 because they they invented it too and so you 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 et cetera yeah people have more more potential to to do harm now than by far than they did a 100 years ago but are you optimistic about so the humans are good at creating destructive things but also humans are good at solving problems yeah i mean there's half empty and have full you know that so how yeah we have full or what i can go yeah so so let me let me put it this way because because it's the only way i can be optimistic but but but think of um of things that have changed because of civilization you know they don't occur just in nature so just uh just imagine that the room we're in for example okay some you know we've got pencils we've got books we've got tables we've got microphones clothing food all these things were added somebody invented them one by one and millions of things uh that we inherit okay and it's inconceivable that that so many millions of billions of things uh wouldn't have problems and we we get it all right um and and each one would have no negative effects and so on so it it's very amazing that it much works as does work it's it's incredibly amazing and actually that's the source of my optimism as well including for artificial intelligence so we we drive over bridges we 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 and i mean that it it works and it doesn't go go wrong often enough to suffer and we can identify things that aren't working and and try to improve on them in a sub often suboptimal way oh absolutely but it's but but the the kind of things that i know how to improve require human beings to be rational and i i'm losing my confidence that human beings are rational yeah yeah now here you go again with the worst case uh worst case analysis they may not be rational but they're um they're they're clever and uh beautiful in their own kind of way yeah i tend to think that most people um 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 uh explain this idea uh what's the wrong time what is the wrong place for our optimization so first of all the word optimization i i started out writing software uh and optimization was i was a compiler writer so optimization meant uh making the uh making a better translation it it so that it would run faster on it on a machine instead of an optimized program it's just like you know you you you run a program and you set the optimization level uh for the compiler so that's one word for optimization um and at that time i i happened to be looking in an unabridged dictionary uh for some reason or other and i came to work optimizing 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 1960 early 1960s that's what optimized me meant okay so people started doing cost optimization other kinds of things uh you know whole subfields of of algorithms and economics and whatever are are based on what they call optimization now but but to me optimization when i was saying that was saying uh uh changing a program to make it more tuned to the machine and i found out that uh when a person writes a program uh he 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 i had to work a week writing this page i i mentally think that when the computer gets to that page it's going to slow down right uh it's chris oh i don't understand what i'm doing i better be more 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 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 [Music] 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 and and and convert that in into something but that was just you know less than one percent of the uh so if we optimized that uh we didn't know what we were doing but but but if if we knew that it was spending eighty percent of his time on the comments card you know in ten minutes we could we could make the the compiler run more than twice as fast and 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 the supplies generally i mean there's something that rings true to this across the board 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 limited context and not and and i'm glad if it makes people think about stuff because i i but it applies in another sense too that is sometimes i will do optimization in a way that does help the the actual running time but makes the program impossible to change next week because i've changed my data structure of something that that made it less adaptable so one of the great uh principles of computer science is is it is laziness or whatever you call it the late binding uh you know don't hold off decisions when you can um and and and you know and we understand now quantitatively how valuable that is what do you mean we understand so you mean people people have written thesis about how you can how late binding will it will improve the 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 gonna allocate thirty percent to this and fifty percent 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 design in order to be flexible uh uh to to change with the uh uh with the way the wind is blowing yeah but so the reason that line resonated with a lot of people is because uh there's something about the programmer's mind that wants that enjoys optimization so it's a constant struggle to balance laziness and lay binding with the desire to optimize the elegance of a well-optimized code is something that's compelling to programming yeah it's a 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 yeah my uh 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 i mean like i i can say yes or no but but but i don't 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 unanswerable question in my opinion is is no better than anybody else you think it's unanswerable so you don't think eventually science angels can dance on the head i mean i don't know but angels anyway there are lots of things that are beyond that that we can speculate about but i don't want somebody to say oh yeah canoe said this and and so he's he's he's smart and so he so that must be i mean i say it's something that uh we'll never know interesting okay that's a strong statement i 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 uh but right now you don't have a good intuition i mean that's also possible you know that and ai you know created the universe you know intelligent design has all been done by an ai yes this is i mean all 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 i i 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 in consciousness 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 john mccarthy i think uh we're totally unimpressed by these statements so you don't think so even like the touring paper on uh on the touring test that you know starts by asking can machines think oh um you don't think these kind of um touring doesn't like that question yeah i don't consider it important let's put it that way because it it's in the category of things that it it it would be nice you know but i think it's beyond knowledge and so i don't i'm not 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 some some day but uh the last time i checked uh it it was still 200 years away i haven't been specializing in this by any means but but but i went to lectures about it 20 years ago when i was uh there was there was a symposium at the american academy in in cambridge and it started out by saying essentially everything that's been written about consciousness is is hogwash i tend to i tend to disagree with that a little bit so well it's so consciousness for the longest time still is in the realm of philosophy so it's just conversations without any basis and yeah 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 starts becoming much more like i feel like yeah yeah don't misunderstand me i i i i i certainly don't disagree with that at all um and even at these lectures that we had you know 20 years ago there were neurologists pointing out that that human beings had actually decided to do something before they were conscious of making that decision yeah uh i mean they could tell that you know that signals were being sent to their arms before they before their they knew that they were anything like this are true and and uh my uh you know less valiant has an architecture for the brain and more recently uh uh christus papadomitrio uh in the academy science proceedings a year ago uh with with two other people but i know chris does very well uh and and he's got this uh uh this model of uh this architecture by which you could uh create a uh things that that correlate well with the uh with experiments that are done on consciousness uh and and and and he he actually you know has a a machine language that in which you can you can write code and and test hypotheses uh and so it it might you know we might have a big breakthrough my personal feeling is that consciousness the the best model i i've heard of uh to explain the the miracle of consciousness uh is that that that somehow inside of our brains we're having a a continual survival for the fittest competition as i'm speaking to you uh 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 is winning and and that's affecting the you know the next sentence and so on yeah uh and uh there was this book machine intelligence or unintelligent on intelligence yeah bill atkinson uh was what was it what 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 uh for us humans it feels like there's a concrete 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 so 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 uh 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 and then things for which i which i'm only a uh you know 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 uh games i think uh the game of life uh it is it is wonderful and uh uh and and shows all kind of stuff about how things can evolve without the creator understanding anything more than the power of learning things in a way but to me the most important thing about the game of life is that is is how it focused for me what what it meant to have free will or not because the game of life is obviously totally deterministic yes and i i i find it hard to believe that anybody who's ever had children cannot believe in free will right 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 um 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 let yourself if 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 if the universe is finite we're all living in the game of life to slow down i mean it's 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 i i've got i've got a dozen exercises in volume for fascicle six uh that actually worked rather well for that purpose but bill gospers came up with the with the algorithm that that allows that allowed golly to uh to you know to run thousands and thousands of times faster to you know the website called golly g-o-l-l-y it simulates the cellular automata like game of life yeah you got you got to check it out yeah can i ask about john conway yes in fact i i i'm just reading now the the issue of mathematical intelligence or that came in last last week it's a whole issue devoted to to uh you know remembrance of of him did you know him i i slept overnight in his house several times i yeah he recently passed away yeah he got he died a year ago may i think it was i've covered what are you what are some memories of him of his work that stand out for you is did uh on a technical level did any of his work inspire you on a personal level that did he himself inspire you in some way you know absolutely to all of those things but let's see when did i first meet him i guess i first met him at oxford in like 1967 when i was wow okay that's a long time ago yeah yeah you were minus 20 years old or something i don't know 1967. but but uh there was a conference where uh and i think i spoke i was speaking about something that known as the canoes bendix algorithm now but but he he gave it famous talk about knots and and at the end i didn't know at the time but but anyway that talk had now the source of thousands and thousands of papers since then uh and it was he was reported on something that he had done in high school uh you know almost ten years earlier [Music] before this conference but he never published it and and he climaxed his stock by building some nozzle you have these lit these little plastic things that you that you could stick together uh it's it's it's 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 so it was a dramatic lecture before he had learned how to give even more dramatic lectures later so all right and were you at that lecture and i was there yeah because i had to i was at the same conference um for some reason i was i i happened to be in in calgary uh at the same day that he was visiting calgary and it was a spring of of 72 i'm pretty sure and and we had lunch together and he wrote down during the lunch on a napkin uh all of the facts about what he called numbers um and i and and he covered the napkin with with the theorems about his his idea of numbers and i thought which was incredibly beautiful um and and later in 1972 my sabbatical year began and i went to norway and and in december of that year uh 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 and i and so i said and i had also read a book in dialogue by by alfred rennie uh where he was kind of a socratic thing where the two characters were talking to each other about mathematics and so i and so at the end in the morning i i woke up my wife and said jill i think i want to write a book about conway's theory and um you know you know i'm supposed to be writing the art of computer programming doing all this other stuff but i got 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 i rented a room in a hotel in downtown austin we were in sabbatical in norway uh and i ran at the hotel in in downtown oslo and um did nothing else except write up conway's theory and and i i changed the name to surreal numbers that so this book is now published as surreal number and um and you know we figured out we'd always wonder what what what would he like to have an affair in a hotel room so 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 yeah so uh 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 but i i i looked for it but i couldn't find it so i tried to recreate from memory what he told me at that luncheon uh in calgary and and as i as i wrote the book i 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 that start out the whole thing and everything is defined it flows from that but you have to discover why and and as a every mistake that i make as i'm trying to discover it i uh my characters make two right you know and and and so it was it's a long long story and i but but i worked through this week uh uh and and it and it was it it was one of the most exciting intense weeks of my life and and and i i described it in other places but but but anyway uh after six days i i finished it and on the seventh day i rested and and i sent the right to my secretary to type it it was flowing as i was writing it uh faster than i could think almost but but but after i finished it uh and tried to write a letter to my secretary telling her how to type it i couldn't write it anymore he gave it 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 it it was almost as if i was channeling 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 is a difference between um 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 um and we visited him at his house in cambridge in april we took a boat actually from norway over to across the channel and and so on and stayed with him for some days and and uh oh he told he talked we talked about all kinds of uh of of things he has he had puzzles that i'd never heard of before he had a great way to to solve the game of solitaire many of the common interests that we you know he'd never written up and but but anyway uh then in the summer time i took another week off and went to a a place in in in the mountains of norway and and rewrote the book using the correct axiom and so so that was the most intensive connection with with conway uh after that uh it started with a napkin it started with an app connect but but but we would run into each other all that well yeah the next really impo i was giving lectures in montreal uh i i was giving a series of um of of seven lectures about the topic called stable marriages and and and he arrived in montreal uh uh between my sixth and seventh lecture and and we met at a party and uh i i started telling him about the topic i was doing and uh he sat and thought about it he came up with a beautiful theory to show that the uh i mean in technical terms it's it's that the that the set of all stable marriages it forms a lattice and and there was a simple way to find the greatest lower bound of of two stable pairings and and least upper bound of two stable married and so i could use it in my lecture the next day and he came up with this theorem you know during the party uh and it it it's a brilliant yeah it's a distributive lesson i mean it it's uh you know uh it it added greatly to the theory of of stable matching so you mentioned your wife jill you mentioned stable marriage can you tell the story of how you two met so we celebrated 60 years of wedded bliss uh last month and and we met because uh uh i was dating her roommate this this was my sophomore year her freshman year i 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 i enjoyed a roommate you guys were majoring the same thing no no no because 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 okay and i'm a you know geek and what was she doing with a computer science book all right 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 uh you're the tutor no no yeah no we yeah we there were tearful times uh you know trying to learn certain concepts but i learned art from her and so we 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 uh when did you fall in love with her that day that i asked her about her her roommate okay i mean no i i okay so i i don't mind telling these things depending on how you for how far you go but [Laughter] but let me promise let me tell you this that i i never really enjoyed kissing uh until i found how she did it and 60 years yeah is there a secret you can uh you can say in terms of stable marriages of how you stayed together so long the topic stable marriage by the way is not it is is the technical term uh yes it's [Music] different people will have to learn how to compromise and and and work together and and and you're going to have ups and downs and and and crises and so on um 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 [Music] so you're going to have to compromise on your notions of beauty when you write christmas cards that's it uh you uh you mentioned that richard feynman was someone you looked up to yep um probably you've met him in caltech well we knew each other yeah at cal tech for sure yeah uh you are one of the seminal personalities of computer science he's one for physics have you ever is there specific things you picked up from him by way of inspiration or uh so we used to go to each other's lectures and and uh but but if i saw him sitting in the front row i would throw me for a loop actually and i i i would i would miss a few a few sentences what unique story do i have about i mean i i i i often refer to his his time in brazil where he uh 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 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 um but but anyway it epitomizes the way education goes wrong uh in all kinds of fields uh and has to periodically be brought back from from from a process of giving credentials to a process of giving knowledge that's probably a story that continues to this day in a bunch of places where it's too easy for educational institutions to fall into credentialism versus uh inspirationalism i don't know if those are words but sort of uh yeah understanding versus just giving a little um it would be plaque and you know it's it's very much like what we were talking about if you want the computer to if you want to be able to believe the answer computer is sure it's doing that one of the things bob floyd showed me in the 60s there was a uh he loved this cartoon there was a there were two guys standing in front of in those days the computer was a big thing you know and and the first guy says to the other guy he said this machine can do in one second what it would take uh a million people to do in a hundred years and the other guy says oh so how do you know it's right [Laughter] that's a good line uh is there some interesting distinction between physics and math to you have you looked at physics much to like speak university 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 are they strongly overlapping it's quite different in my opinion i um 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 like 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 quite a different mentality is it it has to do with your philosophy of geek geekdom i mean some of my computer scientist friends are really good at physics and others are not and and i i'm uh you know i'm really good at algebra but not at geometry you talk about different parts of mathematics you know i just it's so they're 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 uh in discrete ways and then this is more continuous yeah i i i'm not sure if turing would been a great physicist i think it was a pretty good chemist i don't know but but uh but anyway i see things i i i believe that computer science is largely driven by uh a people who have brains who work who are good at resonating with certain kind of of of concepts and like quantum computers it takes a different kind of brain yeah that's interesting yeah it's it's well quantum computers is almost like at the intersection in terms of brain uh between computer science and physics because they it involves both at least at this 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 uh statistical mechanics and you know i mean random processes uh uh are related to algorithms in a lot of a lot of ways and so but there's lots of different flavors of flavors of physics as there are different flavors of mathematics as well um but but the thing is that i 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 so i didn't understand quantum mechanics at all from reading about it in 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 into the book so i couldn't understand his book at all you could say you understood it but i really i really didn't um well feynman also spoke in this way so feynman i think prided himself on a really strong intuition but at the same time he was hiding all the the really good the the deep computation he was doing so so there was one thing that that uh that i i was never able to uh yeah i wish i had more time to 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 uh it i find out that that somebody invented it in in 1830s it's fairly easy to to understand anyway so you start with x plus x plus x plus x n times and and you can call that x n so x n is multiplication then you take x times x times x times x and n time 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 yes just to clarify for the uh so x times x times x n times is obviously x n and x x plus x plus x n times oh yeah okay and then uh xn multiplication is x to the n uh 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 pi so in other words if if if it's two uh double arrow uh three that would be that would be 2 to the 2 to the 2 so that would be 2 to the fourth power that'd be 16 okay okay so so so that's the double arrow and now you can do a triple arrow uh of course uh and and so on and and i i had this this paper called uh well essentially big numbers uh you know you yeah you try to impress your friend but by saying a number they've never thought of before yeah and and and i i gave a special name for it we designed a font for it that has script k and so on but it but it really is 10 i think like 10 quadruple aero 3 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 fine 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 right so you know you have that means x to the x x but what about x x double arrow two 2.5 well that's not too hard to figure out that's interpolate between those but what what what x double arrow i or one plus i or some complex number uh and and uh so he claimed that that that there was no analytic function that would that would do that would do the job uh but i i i 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 [Laughter] yeah okay wow okay okay so so that's that's fine uh that's fine can you describe what the [Music] uh new 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 uh something that everybody knows now if they're if they're using a search engine uh you have a a large collection of text and you want to know if if the word canoeist appears anywhere in the text to say or or some some other word that's less interesting than but anyway that's the most interesting thing or something mega morris right so we have we have a large piece of text and it it's all one long one-dimensional thing you know first or second letter et cetera et cetera et cetera and so uh the question you would like to be able to do this um and the obvious way is that let's say we're looking for morris they don't know that 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 um yeah the next letter is is e so we missed we missed out on morris and so we go back and start looking for another okay all over again so that's the obvious way to do it all right um and and jim morris noticed there was a more clever way to do it the obvious way would have started let's say you know we found that let letter m at character position one thousand so it was started next at character position 1001 [Music] but but he but he said no look we we already read the o and the r and we know that they aren't m's so we could we could start we don't have to read those over again all right so uh 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 uh like repeating patterns at the beginning at the middle right right so so um 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 was some routine i was supposed to find occurrences of patterns in texas and we didn't explain it and 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 what 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 vaughn was studying some technical problem about palindromes or something like that he wasn't really it juan wasn't working on on text searching but he was working on on an abstract problem that that was related well at that time steve cook was a professor at berkeley uh and uh uh 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 um but i but i knew steve while he was at berkeley and he had come up with a with a very peculiar theorem uh about a technical concept called a stack automaton and a stack automaton it is a machine that that it can't do everything a turing machine can do but it 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 of thomas on it can tell you afterwards edcba you know it doesn't have any other memory except except this one thing that it can see 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 um amount of time whatsoever so the stack automaton you 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 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 uh fast the stack of timezone goes slow but 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 thomas undone did you know i i i wrote down and and then i tried to see patterns in that and and how did he convert that into a computer program on a regular machine um 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 uh and now i have an efficient program and and so i uh i i would never have thought about like that if i hadn't had his theorem which was purely abstract thing actually to try to intuit how to use the stack automaton for the the string matching problem yeah so so so the problem i i had started with was not the string matching part but then i realized that the string matching problem was another thing which would also be could be done by a stack of automatons and and so when when i looked at what that told me then i had a nice algorithm for this string matching problem uh and 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 automated theory but it never taught me it never improved my programming for for everyday problems uh 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 automated theory then i knew how to write the program so this was for me uh you know a change in life i started to say maybe i should learn more about thomas and and and and i i showed this note to vaughn pratt and he said that's similar to something i was working on um and then uh and jim morris was at berkeley too at the time anyway he he he's had an illustrious career but i haven't kept track of jim but one is my colleague at stanford and my student uh later but but this was before vaughn ron 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 so it was our algorithm we each discovered it 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 our things together it was my job to write the paper how did the elephants bring to life spring to life was because i i had drafted this paper autonomous theory oh it can be useful which was seen by vaughn 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 history problem let me ask a ridiculous question uh last time we talked you told me what the most beautiful algorithm is actually uh 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 uh it's pretty clear okay because it's uh called the the birth of the giant component okay so now let me explain that because this is actually gets gets into physics too and it gets into something called bose einstein statistics but 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 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 100 points and and we number them from zero zero to nine nine all right now let's let's take pi uh the digits of pi so two at a time so so we had 31 41 59 26 we we can look go go through pi and so so we take the first two 31 41 and let's let's put a connection between point 31 and point 41 that's an edge in the graph so then we take 5 9 2 6 and make another edge and the graph gets bigger it gets more and more connected as we add these things one at a time okay so we start out with end points and and we add uh m edges okay now each edge is completely we forgot about edges we had before we make an edge twice we might get an edge from a point to its selfie but um you know maybe pi is going to have a run of four digits in there so we're gonna but anyway we're evolving a graph at random um and a magical thing happens when the number of edges is like point four nine and uh so maybe n is a million and i have uh you know 490 000 edges uh then it almost all the time it it consists of isolated trees not even any loops right it's a very small number of veggies so far a little less than half n and right but if i had point five one inches so a little more than half in so it's you know million points 510 000 edges now it probably has a one component that's much bigger than the others um and we call that the giant component is that can you clap so can you clarify so is there a name for this kind of random super cool pie random graph well i i call it part the pie graph no no i the pie graph is actually my pie graph is based on on binary representation of pi not the decimal representation of pi but but but but anyway let's suppose i was rolling dice instead what's that so sorry so it doesn't it doesn't have to be pi any source the point is every step choose totally at random one of those endpoints and choose totally at random another one of the end points make that an edge that's the process yeah so there's there's nothing magical about pi they you're no no i was using pi to sort of saying pi is sort of random that nobody knows a pattern in exactly got it i got it but it's not yeah i i could have just as well drawn straws or something um this was a concept invented by erdogan rainey and they called evolution of random graphs and if you start out with with a 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 half have three uh 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 end and we pass one half in 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 it's a phase transition but it's actually it's a double phase transition and turns out it it it happens there's actually two things going on at once at this phase transition which uh which is very remarkable about okay so so um 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 so there are data structures that sort of grow this way okay so so dick carp 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 had found something interesting happening the students are are generating this or simulating this random evolution of graphs and under taking stat snapshots every so often take a look at what the graph is and the rumor was that every time they looked that there was only one component that had loops in it almost always they do a million experience and only three or four times did they ever ever happen to see a loop at at this point no more than one component with the loop so they want you to keep till the graph gets completely full uh so it starts out totally empty and gets more and more more and more edges all the time uh and and so okay certainly a loop comes along once but but now all the loops stay somehow joined to that one they're there never were two guys with loops wow okay in this experiment okay so anyway this one almost always certainly not always yeah but but but with high very high probability that seemed to be true so so we heard about this rumor at stanford and we said if 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 so let's take a look at it and so we look closer and we find out no it 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 and if you don't happen to look at it during that short interval of time then you miss it so that in other words there'll be a period where they're two or three components have loops but they join together pretty soon okay so 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 uh basic problem was to slow down the big bang so that i could watch it happening yeah i i think i can explain it actually in fairly elementary terms deep even without writing a formula that's right like hawking would do uh and and and so uh let's let's watch the evolution and and at first uh 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 it has five edges and five vertices um or or i could put a tail on that and that would be another edge another vertex like a 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 a cyclic component so so 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 uh uh you know like like it might have ten vertices and nine edges to tie the time together so nine minus ten is minus one so so complexity minus one is a tree it's gotta be connected that's what i mean by a component it's gotta be connected so so so if if i have ten things connected i have to have nine edges can you clarify why when complexity goes uh you can go above zero i'm a little yes right so the complexity plus one is the number of loops so if complexity is zero i have one loop if if if complexity is one that means i have one more edge then i have vertex so i might have like 11 edges and 10 vertices it's so it turns we call that a bicycle because it it it's got two loops and it's got to have two loops in it why can't it be trees just going off of the loop that i would need more edges than all right right okay so so every time i get another loop i i get another excess of edges over vertices i got you okay so in other words uh we start out and after i have one loop i have one component that has a cycle in it not now the the next step uh 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 a bicycle but in fact there's a certain probability it goes from cycle to two you know to two different cycles all right um and i worked out the probability it was something like five out of twenty four that was pretty high it was substantial yeah uh but still soon they're going to merge together almost okay so that's so cool but but then it splits again after you have either either two or one one uh the next step is you either have three or you have two one or you have one on one okay and so i worked out the probability for for those transitions and i worked it out up to up to the first five transitions and i had these so i had these strange numbers five twenty fours and i stayed up all night and about three a.m i i had the numbers computed and i looked at them and here were the denominator was something like 20 2 3 0 2 3. so the probability was something over 2 3 0 2 3. i don't know how you worked that out but i had a formula of that you know i could calculate the probability yeah and and i could find the limiting probability as n goes to infinity and and it turned out to be this number but the denominator was 2 0 and i and i looked at the denominator and i said wait a minute this number factors because 1001 is equal to 7 times 11 times 13. i had learned that in my first computer program so so so so 23023 yeah is 7 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 think so all of a sudden that suggested um another way of looking at the problem where small prime factors would occur so what would that be so that said oh yeah let me take the logarithm of this formula and and sure enough it's going to simplify and and it happened so and i wouldn't have noticed it except for this factorization okay so i go to bed and i say 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 uh they're trying to sell him on donating money to uh for a new computer science building sure and and they and uh so they gave me an appointment to talk to bill and i and i wrote down on the blackboard this this evolutionary diagram you're going from one to two five twenty fourths in all this business yeah and i wrote it down and anyway at the end of the day the uh he was discussing people with the with the uh development office and he said boy i was really impressed with what professor knuth said about this giant component and uh and so uh you know i i love this story because it shows that theoretical computer science has is really worthwhile you know does bill have you ever talked to bill gates about it uh since then yeah that's a cool yeah that's a cool little moment in history yeah but but anyway he happened to visit on exactly the day after i had i i had found this pattern and that allowed me to to crack the problem so you know so that i could develop the uh the theory some more and understand what's happening in the big but uh because i could i could now write down explicit formulas for stuff right and so it would you know it would work not only the first few steps but also they'll 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 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 the cycle and and uh so it's a hundred percent the rumor was that was 100 it turned out the actual numbers was like percent or i i don't know i should remember the number but i do 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 anything it was a nice it related to pi yeah um and we could never have done that with but so that's the hardest problem i ever saw in my life was to prove that this probability is is it was proven the probability was proven yeah i was able to prove this that this and and and this should shed light on a whole bunch of other things about random graphs that that was sort of the the major thing we were asked after that's super cool what was the connection to physics that you mentioned well bose einstein statistics is the study of how molecules uh bond together without geometry without distance you created the tech type setting 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 no 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 50s 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 uh is allowed to make fortran compilers too um on the other hand in the typography 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 okay i already i i already had uh 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 if you get over the threshold then you start thinking about philanthropy or else or you're trying to take it with you but uh but anyway there's a i had my income was over the threshold so so that i i didn't need to keep it and so i specifically could see the advantage of of of making it open for everybody do you think uh 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 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 just that my wife and i don't care about but somebody does but i mean but they have built in a fantastic uh uh undo feature for example in photoshop where you you you can go through a sequence of a thousand complicated steps on graphics and it can take you back anywhere in that sequence yeah 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 really yeah i know i mean there's a lot of really subtle nobel prize class like creation of intellectual property in in there and uh and with patents uh you've got a limited time to uh 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 i i i actually i i'm gonna have to upgrade one of these days but to a newer version of ubuntu yeah i'll stick with ubuntu but but uh right now i'm running something that doesn't support a lot of the new software the last stability i don't remember the number like 14 anyway it's it's quite and i'm going to get a new computer um i'm getting new um solid-state memory instead of kind of a hard disk and the basics well let me ask you um sticking on the topic of tech um 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 there or look at the last page at 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 uh s-e-u-s-s he he wrote children's books in the 50s 40s and 50s wait are you talking about cat in the hat doctor yeah that's it yeah i like how you hit this on on beyond zebra did he did did it get to soviet union [Laughter] yeah doctors no we did dr seuss did not come to the soviet union but since you oh actually i think he did actually a little bit when we were um that that was a uh his maybe cat in the hat or or green eggs and ham i think was used to learn english oh okay so i think it made it that way my my okay i i didn't like those as much as bartholomew cubbins but but i used to know bartholomew covens 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 so there's it looks like a bunch of vines uh well is that symbol of existence by the way he he made a movie in the early 50s um i don't remember the name of the movie now you can probably find it on easily enough but it it features uh dozens and dozens of pianos all playing together at the same time and but but the all the scenery is sort of based on the kind of artwork that was in his books and uh the fantasy big you know based of zeus land or so and i saw the movie only once or twice but it's but it's quite i'd like to see it again that's that's really fascinating that you gave him they gave him shout out here okay is there some elegant basic symbol that you're attracted to some uh give something that gives you pleasure something used a lot pi pi of course uh i try to use pi i as often as i can when i need a random example [Music] because it doesn't have any known characters so for so for instance i i don't have it here to show you but do you do you know the put the uh the the game called masu m-a-s-y-u no it's it it's a great recreation i mean sudoku is easier to understand but matthew is it it is more addictive uh uh you you have black and white stones like like on a go board and you have to draw a path that goes straight through a white stone and makes a right angle turn at the black stone um and it turns out to be really really nice puzzle because it doesn't involve numbers but with this visual but it's 3d pleasant to to play with so so i wanted to use it as example in art of computer programming and i have i have exercise on how to design cool massive puzzles and uh you can find that on wikipedia certainly uh as an example m-a-s-y-u um and and so i and so i decided i would take pi the actual image of it and it had pixels and i i would put a stone wherever it belongs in the letter pi in the greek letter pi and and 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 mossview puzzle that was a good test case for my algorithm on how to design master puzzles because i i insisted in advance that the stones had to be placed in exactly the positions that make the letter pie make a juice letter okay all right that's cool and and i saw you know and it turned out there was a a a unique way to do that um and so so pi is a source of of examples where i can where i can prove that i'm starting with something that isn't canned and most most recently i was writing about something called graceful graphs uh graceful graphs is the following you have a graph that has m edges to it all right 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 and that difference is it's got to be tell you what edge it is so so one edge two numbers will be one apart there'll be another edge where the numbers are two apart and so uh great computer problem can you find a graceful way to label a graph so i started with a so i started with a graph that i use for an organic graph not not a mathematically symmetric graph or anything and i take this i take the 49 states of the united states uh the edges that go from one state to the next state so for example california be next to oregon nevada arizona okay and and and i include this district of columbia uh so i have 49 i can't get at la 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 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 right okay so is there a way to do this for for all the states and at that and so i was i was thinking of having a contest uh for people to to get it as graceful as they could uh but my friend tamara kiki actually solved the problem by proving that i mean i was able 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 i had figured out a way to put labels on so that all the all the uh all the edges were labeled somewhere between one and 117 but but there were some some get some gaps in there because i should really have gone from one to 105 or what the 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 grace for labeling and and so i you know i call out the contest uh because the problem is already solid and too easy in a sense because tom was able to do it in an afternoon um he sorry he did the algorithm or for this particular uh for the stick united states for the united states this problem is this problem is incredibly hard i mean for the general generally okay but it's like it's like coloring but it was very lucky that we worked for the united states sure um i think but but i mean the theory is still very uncomplete but but but anyway then tom came back a couple days later and he had been able to not only find a graceful labeling but he but the label of washington was 31. the label of of idaho was 41 following the digits of pi yeah going across the topic of the united states he has the digits of pipeline did he do it on purpose he was able to still get a graceful labeling with that with it's a miracle okay but yeah but um i i i i like to use pie in my book you see and this is all roads lead to pie yeah somehow um somehow often hidden uh in the middle of like the the most difficult problems can i ask you about uh productivity productivity yeah you said that quote my scheduling principle is to do the thing i hate most uh on my to-do list by week's 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 out and what i want i 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 to others well i yeah i i i don't know how to say it during the pandemic i feel my productivity actually went down by half um because i have to um i have to communicate by writing which is slow i have to i mean i i don't like to send out a bad sentence so i you know i go through and reread what i've written and edit and fix it so so everything takes a long a lot longer when i'm when i'm communicating by by text messages um instead of just you know together with somebody in the room and 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 um it's different from what people in robotics field do which is called planning so she had this principle that was see something that needs to be done and do it you know i would just instead of saying i'm going to do this first and do this first just you know just do it oh yeah pick this up you know but you're 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 the one you want to do least right the one i haven't got any good reason i think that i'll never be able to do it any better than i am now i mean there are some things that that i know if i do something else first i'll be able to do that one better yeah but but but there's some that are going to be harder because you know i i i i've forgotten some of the groundwork that went into it or something like that so so i just finished uh a pretty tough part of the book and uh and so and so now i'm you know doing the parts that are more fun but but but the 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 i i'm you know that it's upbeat i i i can have humor i can you know i can i can say this is cool you know wow this uh i have to 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 is there um you've given some advice to people before but can you um can you you give me too too much credit but anyway this is my this is my turn to just not to say things that that that i believe but but i want to preface it by saying um 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 you because it's trendy but but it's something that you personally feel that you were called to do right 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 you or it took or it doesn't work i mean you 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 or or maybe maybe i i could do this if i worked a little bit harder but you try something else and you say wait i have really no intuition for this and it looks like uh you know it looks like it doesn't have my name on it 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 something when i see everybody else do going some way i probably i i'd probably say not too much competition but yeah but but uh but mostly i 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 yeah i mean not to be bored it hurts it makes me very sad when i when i see kids talking to each other and they say that was boring and to me a person should feel upset if he would help if he had to admit that he wasn't able to find something interesting so uh uh you know the skill they they say i haven't learned how to how to enjoy life i have to have somebody entertain me instead of right that's really interesting it is a skill uh david foster wallace i really like the thing he says about this which is the key to life is to be unborable and i do really like you saying that it's a skill because i think that's a really good that's 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 i have learned how to how to find the beauty and how to find the fun in it yeah that's a that's a really really good point you know sometimes it's more difficult than others to do this but i mean during the covet lots of days when i did when i never saw another human being but um but i i i still find other ways to it still was a pretty fun time yeah yeah 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 a beautiful some beautiful flowers at the nursery at home depot a few blocks away life is amazing it's full of amazing things like this yeah i just sometimes i'll i'll sit there and just stare at a tree nature is beautiful uh let me ask you the big ridiculous question i don't think i asked you last time 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 [Laughter] no no you can't you can't i will not allow you to uh to try to escape answering this question you have to answer definitively uh because they're they're surely surely don knuth there must be an answer what is the answer is it 42 or wherever yeah well i don't think it's the numerical that's that's okay but all right so so anyway um it's only for me and but i but i personally think of my belief that that god exists although i have no idea what that means but i believe that there is some something beyond human uh capabilities um and it might be uh uh it might be some ai but but whatever it is but but whatever i but i do believe that that there is something that goes beyond the realm of human understanding but but that that i can try to learn more about how to resonate with whatever that being would like me to do so do you think you can have occasional glimpses of that being i i strive for that not that i ever think i'm going to get close to it but but it's not it's not for me it's it's saying what should i do that that big being wants me to do that's that's you know i i'm trying to ask what that i mean does that being want me to to be talking to lex friedman right now you know and i said yes okay but thank you well thank you but yeah 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 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 to know what they are yeah but that funny little dance well i i i mean this ai or whatever is it probably is it is smart enough to help to give me clues and uh to 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 i read history i i know that things were they they were they 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 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 uh but but the new insight i've gotten him actually in that way was i i was reading uh what what book was i reading now recently it was it was by ken follett and it was called the man from saint petersburg but it but but it was talking about the prequel to world war one and winston churchill according to this book uh sees that that germany has been spending all its gold reserves uh building up a huge military and there's no question that if germany would attack england that england would be wiped out um so he wants russia to help uh to attack germany from the other side because germany doesn't have enough of an army to 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 a thousand thousand people of russia would 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 czar 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 is the war inevitable or is there a way to have peace and and this just did and it struck me that if i were in a position of responsibility work 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 that 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 and the great leaders to arise uh and help build a better world i mean that's the hope of democracy that's done yeah enhance their abilities with uh with algorithms [Laughter] uh well put done it's such a huge honor i've you've been an inspiration to me and to millions for such a long time um 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 you