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Interview: Donald Knuth: A Life's Work Interrupted

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Don switches gears and for awhile becomes what Ed Feigenbaum calls "The World's Greatest Programmer."

There was a revolutionary new way to write programs that came along in the 1970s called "structured programming." At Stanford we were teaching students how to write programs, but we had never really written more than textbook code ourselves in this style. Here we are, full professors, telling people how to do it, but having never done it ourselves except in really sterile cases with no real-world constraints. I was itching to do it. Thank you for calling me the world's greatest programmerI was always calling myself that in my head. I love programming, and so I loved to think that I was doing it as well as anybody. But the fact is the new way of programming was something that I hadn't had time to invest much effort in.

The motivation is his love affair with books...

That goes very deep. My parents disobeyed the conventional wisdom by teaching me to read before I entered kindergarten. I have a kind of strange love affair with books going way back. I also had this thing about the appearance of books. I wanted my books to have an appearance that other readers would treasure, not just appreciate because there were some words in there.

...and what had happened to his books.

Printing was done with hot lead in the 1960s, but they switched over to using film in the 1970s. My whole book had been completely re-typeset with a different technology. The new fonts looked terrible! The subscripts were in a different style from the large letters, for example, and the spacing was very bad. You can look at books printed in the early 1970s and almost everything looked atrocious in those days. I couldn't stand to see my books so ugly. I spent all this time working on them, and you can't be proud of something that looks hopeless. I was tearing out my hair.

At the very same time, in February 1977, Pat Winston had just come out with a new book on artificial intelligence, and the proofs of it were being done at III [Information International, Incorporated] in Southern California. They had a new way of typesetting using lasers. All digital, all dots of ink. Instead of photographic images and lenses, they were using algorithms, bits. I looked at Winston's galley proofs. I knew it was just bits, but they looked gorgeous.

I canceled my plan for a sabbatical in Chile. I wrote saying "I'm sorry; instead of working on Volume 4 during my sabbatical, I'm going to work on typography. I've got to solve this problem of getting typesetting right. It's only zeros and ones. I can get those dots on the page, and I've got to write this program." That's when I became an engineer. I did sincerely believe that it was only going to take me a year to do it.

But, in fact, it was to be a 10-year project. The prototype user was Phyllis Winkler, Don's secretary.

Phyllis had been typing all of my technical papers. I have never seen her equal anywhere, and I've met a lot of really good technical typists. My thought was definitely that this would be something that I would make so that Phyllis would be able to take my handwritten manuscripts and go from there.

The design took place in two all-nighters. I made a draft. I sat up at the AI lab one evening and into the early morning hours, composing what I thought would be the specifications of a language. I looked at my book and I found excerpts from several dozen pages where I thought it gave all the variety of things I need in the book. Then I sat down and I thought, well, if I were Phyllis, how would I like to key this in? What would be a reasonable format that would appeal to Phyllis, and at the same time something that as a compiler writer I felt I could translate into the book? Because TeX is just another kind of a compiler; instead of going into machine language you're going into words on a page. That's a different output language, but it's analogous to recognizing the constructs that appear in the source file.

The programming turned out to be harder than he thought.

I showed the second version of the design to two of my graduate students, and I said, "Okay, implement this, please, this summer. That's your summer job." I thought I had specified a language. To my amazement, the students, who were outstanding students, did not complete it. They had a system that was able to do only about three lines of TeX. I thought, "My goodness, what's going on? I thought these were good students." Later I changed my attitude, saying, "Boy, they accomplished a miracle." Because going from my specification, which I thought was complete, they really had an impossible task, and they had succeeded wonderfully with it. These guys were actually doing great work, but I was amazed that they couldn't do what I thought was just sort of a routine task. Then I became a programmer in earnest, I had to do it.

This experience led to general observations about programming and specifications.

When you're doing programming, you have to explain something to a computer, which is dumb. When you're writing a document for a human being to understand, the human being will look at it and nod his head and say, "Yeah, this makes sense." But there are all kinds of ambiguities and vagueness that you don't realize until you try to put it into a computer. Then all of a sudden, almost every five minutes as you're writing the code, a question comes up that wasn't addressed in the specification. "What if this combination occurs?" It just didn't occur to the person writing the design specification. When you're faced with doing the implementation, a person who has been delegated the job of working from a design would have to say, "Well, hmm, I don't know what the designer meant by this."

It's so hard to do the design unless you're faced with the low-level aspects of it, explaining it to a machine instead of to another person. I think it was George Forsythe who said, "People have said you don't understand something until you've taught it in a class. The truth is you don't really understand something until you've taught it to a computer, until you've been able to program it." At this level, programming was absolutely important.

When I got to actually programming TeX, I had to also organize it so that it could handle lots of text. I had to develop a new data structure in order to be able to do the paragraph coming in text and enter it in an efficient way. I had to introduce ideas called "glue," and "penalties," and figure out how that glue should disappear at boundaries in certain cases and not in others. All these things would never have occurred to me unless I was writing the program.

I wake up in the morning with an idea, and it makes my day to think of adding a couple of lines to my program. It gives me a real high. It must be the way poets feel, or musicians, or painters. Programming does that for me.

Edsger Dijkstra gave this wonderful Turing lecture early in the 1970s called "The Humble Programmer." One of the points he made in his talk was that when they asked him in Holland what his job title was, he said, "Programmer," and they said, "No, that's not a job title. You can't do that; programmers are just coders. They're people who are assigned like scribes were in the days when you needed somebody to write a document in the Middle Ages." Dijkstra said no, he was proud to be a programmer. Unfortunately, he changed his attitude completely, and I think he wrote his last computer program in the 1980s.

I checked the other day and found I wrote 35 programs in January, and 28 or 29 programs in February. These are small programs, but I have a compulsion. I love to write programs. I think of a question that I want to answer, or I have part of my book where I want to present something, but I can't just present it by reading about it in a book. As I code it, it all becomes clear in my head. The fact that I have to translate my knowledge of this method into something that the machine is going to understand forces me to make that knowledge crystal-clear in my head. Then I can explain it to somebody else infinitely better. The exposition is always better if I've implemented it, even though it's going to take me more time.

It didn't occur to me at the time that I just had to program in order to be a happy man. I didn't find my other roles distasteful, except for fundraising. I enjoyed every aspect of being a professor except dealing with proposals, which was a necessary evil. But I wake up in the morning with an idea, and it makes my day to think of adding a couple of lines to my program. It gives me a real high. It must be the way poets feel, or musicians, or painters. Programming does that for me.

The TeX project led to METAFONT for the design of fonts. But it also wasn't smooth sailing.

Graphic designers are about the nicest people I've ever met in my life. In the spring of 1977, I could be found mostly in the Stanford Library reading about the history of letter forms. Before I went to China that summer I had drafted the letters for A to Z.

I found that writing software was much more difficult than anything else I had done in my life. I had to keep so many things in my head at once. I couldn't just put it down and start something else. It really took over my life during this period.

One of the greatest disappointments in my whole life was the day I received in the mail the new edition of The Art of Computer Programming Volume 2, which was typeset with my fonts and which was supposed to be the crowning moment of my life, having succeeded with the TeX project. I think it was 1981, and I had the best typesetting equipment, and I had written a program for the 8-bit microprocessor inside. It had 5,000 dots-per-inch, and all the proofs coming out looked good on this machine. I went over to Addison-Wesley, who had typeset it. There was the book, and it was in the familiar beige covers. I opened the book up and I'm thinking, "Oh, this is going to be a nice moment." I had Volume 2, first edition. I had Volume 2, second edition. They were supposed to look the same. Everything I had known up to that point was that they would look the same. All the measurements seemed to agree. But a lot of distortion goes on, and our optic nerves aren't linear. All kinds of things were happening. I burned with disappointment. I really felt a hot flash, I was so upset. It had to look right, and it didn't, at that time. I'm happy to say that I open my books now and I like what I see. Even though they don't match the 1968 book exactly, the way they differ are pleasing to me.

What it was like writing TeX.

Structured programming gave me a different feeling from programming the old waya feeling of confidence that I didn't have to debug something immediately as I wrote it. Even more important, I didn't have to mock-up the unwritten parts of the program. I didn't have to do fast prototyping or something like that, because when you use structured programming methodology you have more confidence that it's going to be right, that you don't have to try it out first. In fact, I wrote all of the code for TeX over a period of seven months, before I even typed it into a computer. It wasn't until March 1978 that I spent three weeks debugging everything I had written up to that time.

I found that writing software was much more difficult than anything else I had done in my life. I had to keep so many things in my head at once. I couldn't just put it down and start something else. It really took over my life during this period. I used to think there were different kinds of tasks: writing a paper, writing a book, teaching a class, things like that. I could juggle all of those simultaneously. But software was an order of magnitude harder. I couldn't do that and still teach a good Stanford class. The other parts of my life were largely on hold, including The Art of Computer Programming. My life was pretty much typography.

TeX leads to a new way of programming.

Literate programming, in my mind, was the greatest spin-off of the TeX project. I learned a newway to program. I love programming, but I really love literate programming. The idea of literate programming is that I'm writing a program for a human being to read rather than a computer to read. It's still a program and it's still doing the stuff, but I'm a teacher to a person. I'm addressing my program to a thinking being, but I'm also being exact enough so that a computer can understand it as well. Now I can't imagine trying to write a program any other way.

As I'm writing The Art of Computer Programming, I realized the key to good exposition is to say everything twice: informally and formally. The reader gets to lodge it in his brain in two different ways, and they reinforce each other. In writing a computer program, it's also natural to say everything in the program twice. You say it in English, what the goals of this part of the program are, but then you say it in your computer language. You alternate between the informal and the formal. Literate programming enforces this idea.

In the comments you also explain what doesn't work, or any subtleties. You can say, "Now note the following. Here is the tricky part in line 5, and it works because of this." You can explain all of the things that a maintainer needs to know. All this goes in as part of the literate program, and makes the program easier to debug, easier to maintain, and better in quality.

After TeX, Don gets to go back to mathematics.

We finished the TeX project; the climax was in 1986. After a sabbatical in Boston I came back to Stanford and plunged into what I consider my main life's work: analysis of algorithms. That's a very mathematical thing, and so instead of having font design visitors to my project, I had great algorithmic analysts visiting my project. I started working on some powerful mathematical approaches to analysis of algorithms that were unheard of in the 1960s when I started the field. Here I am in math mode, and thriving on the beauties of this subject.

At age 55 I became 'Professor Emeritus of The Art of Computer Programming,' with a capital T.' I love that title.

One of the problems out there that was fascinating is the study of random graphs. Graphs are one of the main focuses of Volume 4, all the combinatorial algorithms, because they're ubiquitous in applications.

Frustrated with the rate of progress, he "retires" to devote himself to "The Art."

I wasn't really as happy as I let on. I mean, I was certainly enjoying the research I was doing, but I wasn't making any progress at all on Volume 4. I'm doing this work on random graphs, and I'm learning all of these things. But at the end of the year, how much more had been done? I've still got 11 feet of preprints stacked up in my closet that I haven't touched, because I had to put that all on hold for the TeX project. I figured the thing that I'm going to be able to do best for the world is finishing The Art of Computer Programming.

The only way to do it was to stop being a professor full time. I really had to be a writer full time. So, at age 55 I became "Professor Emeritus of The Art of Computer Programming," with a capital "T." I love that title.

Don is a master at straddling the path between engineering and science.

I always thought that the best way to sum up my professional work is that it has been an almost equal mix of theory and practice. The theory I do gives me the vocabulary and the ways to do practical things that can make giant steps instead of small steps when I'm doing a practical problem. The practice I do makes me able to consider better and more robust theories, theories that are richer than if they're just purely inspired by other theories. There's this symbiotic relationship between those things. At least four times in my life when I was asked to give a kind of philosophical talk about the way I look at my professional work, the title was "Theory and Practice." My main message to the theorists is, "Your life is only half there unless you also get nurtured by practical work."

Software is hard. My experience with TeX taught me to have much more admiration for colleagues that are devoting most of their life to software than I had previously done, because I didn't realize how much more bandwidth of my brain was being taken up by that work than it was when I was doing just theoretical work.

Computers aren't everything: religion is part of his life, too.

I think computer science is wonderful, but it's not everything. Throughout my life I've been in a very loving religious community. I appreciate Luther as a theologian who said you don't have to close your mind. You keep questioning. You never know the answer. You don't just blindly believe something.

I'm a scientist, but on Sundays I would study with other people of our church on aspects of the Bible. I got this strange idea that maybe I could study the Bible the way a scientist would do it, by using random sampling. The rule I decided on was we were going to study Chapter 3, Verse 16 of every book of the Bible.

This idea of sampling turned out to be a good time-efficient way to get into a complicated subject. I actually got too confident that I knew much more than I actually had any right to, because I'm only studying less than 1/500th of the Bible. But a classical definition of a liberal education is that you know everything about something and something about everything.a

On his working style...

I enjoy working with collaborators, but I don't think they enjoy working with me, because I'm very unreliable. I march to my own drummer, and I can't be counted on to meet deadlines because I always underestimate things. I'm not a great coworker, and I'm very bad at delegating.

I have no good way to work with somebody else on tasks that I can do myself. It's a huge skill that I lack. With the TeX project I think it was important, however, that I didn't delegate the writing of the code. I needed to be the programmer on the first-generation project, and I needed to write the manual, too. If I delegated that, I wouldn't have realized some parts of it are impossible to explain. I just changed them as I wrote the manual.

I'm worried about the present state of programming. Programmers now are... supposed to assemble reusable code that somebody else has written... Where's the fun in that? Where's the beauty in that?

What is the future of programming?

A program I read when I was in my first year of programming was the SOAP II assembler by Stan Poley at IBM. It was a symphony. It was smooth. Every line of code did two things. It was like seeing a grand master playing chess. That's the first time I got a turn-on saying, "You can write a beautiful program." It had an important effect on my life.

I'm worried about the present state of programming. Programmers now are supposed to mostly just use libraries. Programmers aren't allowed to do their own thing from scratch anymore. They're supposed to assemble reusable code that somebody else has written. There's a bunch of things on the menu and you choose from these and put them together. Where's the fun in that? Where's the beauty in that? We have to figure out a way we can make programming interesting for the next generation of programmers.

What about the future of science and engineering generally?

Knowledge in the world is exploding. Up until this point we had subjects, and a person would identify themselves with what I call the vertices of a graph. One vertex would be mathematics. Another vertex would be biology. Another vertex would be computer science, a new one. There would be a physics vertex, and so on. People identified themselves as vertices, because these were the specialties. You could live in that vertex, and you would be able to understand most of the lectures that were given by your colleagues.

Knowledge is growing to the point where nobody can say they know all of mathematics, certainly. But there's so much interdisciplinary work now. We see that a mathematician can study the printing industry, and some of the ideas of dynamic programming apply to book publishing. Wow! There are interactions galore wherever you look. My model of the future is that people won't identify themselves with vertices, but rather with edgeswith the connections between. Each person is a bridge between two other areas, and they identify themselves by the two subspecialties that they have a talent for.

Finally, we always ask for life advice.

When I was working on typography, it wasn't fashionable for a computer science professor to do typography, but I thought it was important and a beautiful subject. Other people later told me that they're so glad I put a few years into it, because it made it academically respectable, and now they could work on it themselves. They were afraid to do it themselves. When my books came out, they weren't copies of any other books. They always were something that hadn't been fashionable to do, but they corresponded to my own perception of what ought to be done.

Don't just do trendy stuff. If something is really popular, I tend to think: back off. I tell myself and my students to go with your own aesthetics, what you think is important. Don't do what you think other people think you want to do, but what you really want to do yourself. That's been a guiding heuristic for me all the way through.

And it should for the rest of us. Thank you, Don.

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Edited by Len Shustek, Chair, Computer History Museum Mountain View, CA.

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a. See 3:16 Bible Texts Illuminated, by Donald Knuth, A-R Editions, 1991.

For Part I of this interview, see Communications, July 2008, page 35.


©2008 ACM  0001-0782/08/0800  $5.00

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