Donald Knut and Surreal Numbers: I worked for six days and rested on the seventh (40,41,42 / 97)

“Computer science experts would say that I made the biggest mistake when I took on this project.”



This is a unique event in my life. It happened in the early 70s. I met John Conway, probably one of the greatest mathematicians. I met him on the way to the University of Calgary in the 71st and we had lunch together. He sketched a new theory on a napkin that came into his head, and in my opinion, it was really amazing. This is a purely mathematical theory about the new method of determining numbers. Its essence is that they can be not only integral or fractional, but there are also infinite numbers, and the square root of infinity, and the infinity of infinity, and the infinity of the square roots of infinity, and all this makes sense. A year later, I was on holiday in Norway and in the middle of the night the thought came to me, “Wow, this theory is so beautiful that it would be interesting to tell a story, write a book in which the characters open Conway’s theory. They will find its rules on the stone tablet, decipher it and will be able to prove all these things about infinity and so on. ”
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The idea is to teach people in such a way to do research, so that students can not only study what other people have done, but also discover something new in mathematics. And all this can be presented in the form of a story where the characters figure out all these things on their own. So I thought that this could make a really cool book, and it can be used as a supplement. I thought that teachers in high schools could advise her to their students so that they could see how discoveries are made in mathematics.





I decided to call these numbers surreal. For you to understand, real numbers have infinitely many decimal places, and surreal, in turn, even more. This was the Conway system. So I decided that I already had a name (Surreal numbers) and the idea that the theory would be put forward by the characters of the book. I woke Jill and said, “Jill, do you know that I’ve been working on the Art of Programming for many years and still haven't moved a single step? I was thinking about writing another book. What do you say? ”And I also said,“ I think I can write it in a week, in fact, in just a week, since it will be a very short book. ”

And she replied, “Okay, Don, come on. This is your vacation year and we are in Norway, why not set aside a week for this project so that you can concentrate on it, so that you can be happy and we can live happily ever after. ”



We all planned out. I decided to rent a hotel room for a week in the center of Oslo, not far from the place where Ibsen lived, so that I could feel his spirit and tune in to the desired mood. And we decided that she could come and visit me a couple of times a week, and we could pretend that we had an affair. We always wondered what it is. So I could be a writer for a week, and then we could fool people in a hotel so that this woman would come to me in secret. That is exactly what happened the next few weeks. I wrote the first page of the novel in my head several times and when I, for example, rode the bus, I was already thinking about the next sentence.

I checked into the hotel in January and it was probably one of the best weeks of my life. A muse came to me that seemed to dictate this book to me. I lived in a cheap hotel run by strict Norwegian church volunteers. But this did not hinder our romance with Jill. American students from the University of St. Olaf, Minnesota, also stayed at the hotel. Every morning we were served a Norwegian breakfast, which is widespread, it does not compare with herring in England, but in any case we were served herring, eggs and much more.

Every morning I spent an hour, very leisurely eating my Norwegian breakfast, which was enough to last until lunch, and listened to what American students talk about. It was fascinating, since I had not heard spoken English for a long time. By that time we already lived in Norway for 6-7 months. Therefore, I could remember the dialect and some expressions, but no more. My story was written in interactive form, and for me it was important to make an authentic focus on the characters. I listened to what the students were talking about, ate, then went to my room and started writing a book.

The book is like an opera. Do you know operas in which there is good music, but little plot? There was a good math in my book and only a little plot. I reproduced the mathematical part on my own. I remembered that Conway sketched theory on a napkin, but I lost it. I tried to remember what was written there and what he told me a year ago. I tried to restore this theory from memory and bring it out on my own, as this is what the characters in my book do. I conducted my own research and decided that if I made a mistake somewhere, I would certainly put it in the book, and my characters would make the same mistake. I wanted the book to be a true representation of mathematical research.

I usually ended up working in the morning and at first I always had sketches from the previous day that needed to be worked out. I thought about the first page of the book for several months, and I was ready to start working on it. When I needed to take a pause before writing the second page, I could dictate the first to you almost literally. Then I wanted to do some math calculations before continuing to write and I was stuck.

I am stumped. I did not know what to do next. Then I went outside and walked around Oslo. It was a little snowy January, and it was not slippery on the streets. About an hour I just wandered around the hotel and hoped that the solution to the problem itself will come to me. I returned to the room, wrote a little, leisurely dinner, wrote a little more, and then I could not turn off the light, because I needed to write a book. I knew from what suggestions I would continue to work before going to bed. I was all in the work, as you can imagine.



I said that it would take me a week to write a book. After 6 days, I finished the last chapter and rested for 7 days. It was very interesting. Day 6 was actually one of those days when my wife came to me and we went to watch the movie “Butterflies Free” with Goldie Hawn. Then we walked around the Royal Palace in Oslo and there was a wonderful frost on these magnificent trees. I was simply enchanted, looking at the snow-covered branches of the trees against the dark blue sky. It was a week when I saw inspiration in everything. I realized that when I got back to myself, I would finally finish the book, but I just looked at the sky and the patterns created by these icy branches, and this was one of the greatest moments in my life.

Then I returned to the hotel and finished the last chapter, and on day 7 I was resting. On this day, I tried to write a letter to my secretary Phyllis. She was going to print the manuscript, and I had to send her a letter with instructions on how to do it. I started writing a sentence, reached the middle and could not finish it. I wrote 6 days without a break, and then the book was over and my writing activity was over. I couldn't figure out how to write a letter to Phyllis. In the end, the letter was written, and we sent her a handwritten manuscript.

She printed it to me and sent it in a couple of months, and I, in turn, sent it to John Conway in England, Cambridge. He politely noted that I understood one of the axioms of his theory incorrectly, that the characters in my book actually worked on a different system, although his system was actually much better. But okay, it's not so bad. We visited him in England and went to Cambridge; I stayed at his house during Easter and found out what I should have originally written.

Then I returned to Norway and took another week, but not in Oslo, but in an abandoned valley, in one of those valleys, which, during the Black Death, lost its entire population. There was a small holiday home called Solhayman, where many people spent time in the summer and all spoke Norwegian there. We ate at the common table, and I did my best to speak Norwegian with them. But most of the time I studied the book, rewriting everything with the axioms that, as Conway said, I had to use from the very beginning. And everything has become much better.

I also received valuable comments from other readers. For example, there were some romantic scenes in the book and my wife advised me on how best to write them. I took it all into account, worked for another week, and the book was finished, Surreal Numbers. She was completely different from the books I had previously written about computers. It became a kind of litmus test for people, depending on whether they are mathematicians or computer scientists.

Mathematicians would look at Surreal Numbers and say that it is quite interesting.

Computer scientists would say that I made the biggest mistake when I took on this project.

In any case, I received information from my publisher, who said that he needed 17 copies of my book. I had to send them corrections next week. The book has been translated into 8 or 9 languages, which means that there is somewhere in the world of mathematics who have appreciated this little book. It has about 90 small pages. I can never write something like that again, but it was an amazing experience.

- Have you ever wanted to write another novel?
- No, you know, when I wrote this book I walked through the streets of Oslo, saw birds, heard sounds and felt part of this world, because I was writing a book and it was important for me how her characters live and what they say.

It automatically made me more receptive to the world. This is a very important part of my writing experience and I can understand why writers enjoy it. Attempting to transfer your own submissions to prose tempers. Maybe I will wake up once in the middle of the night and want to repeat this experience, but I have always perceived the writing of this book as what I will do the first and the last time in my life. And, as I said, many people think so that I made a big mistake when I wrote it.

Translation: Diana Sheremyeva

To be continued ...

Read more

“Two heroes accidentally find a stone with ancient writings and discover new mathematical structures.”

• John Horton Conway: Life is like a game
• John Horton Conway: Life is like a game - ending
• Donald Knut: I sat in the back row and hunted jokes, and the teachers resigned and didn't often beat on the ass (1,2,3,7 / 97)
• Donald Knut: “My advice to the young” (93/97) and “Feeling the need to assert oneself” (9/97)
• Quant, 1979 "Surreal numbers"

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Publishing support is Edison , which tests critical systems for fault tolerance , as well as designs and develops software for cluster computing .