In the early 1970s mathematician Donald Knuth spent a sabbatical with his wife in Norway. The time was meant to be spent relaxing. Yet one night he woke up his partner in a state of agitation. He urgently needed to write a book. Don’t worry, he reassured his spouse, it will only take a week. To concentrate on his writing, he reserved a hotel room just for himself in Oslo.
There he drafted what would become Surreal Numbers: How Two Ex-Students Turned On to Pure Mathematics and Found Total Happiness. Though Knuth did not invent the concept of surreal numbers, he was the first to publish a detailed work on the subject and coin the term. To this day, his book is considered the standard work on the subject.
Yet the tome is anything but an ordinary example of nonfiction. It consists of dialogues between two fictional characters, Alice and Bill. It also features the true inventor of surreal numbers, the late mathematician John Horton Conway, who died in 2020.
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“In the beginning, everything was void, and J.H.W.H. Conway began to create numbers,” Knuth wrote. Knuth added extra initials to Conway’s name as an allusion to the Tetragrammaton (the four-letter Hebrew name of God, transliterated as YHWH or Yahweh), he explained in a Numberphile YouTube video.
That’s hardly the only biblical reference; even Knuth’s backstory for writing the book echoes the religious creation story. He put the whole thing to paper in just a week, as he’d promised his wife. “On the sixth day I finished it. On the seventh day I rested,” Knuth told Numberphile.
Surreal numbers are created by adding values between two given preexisting numbers. If you look at 0 and 1, for example, 1/2 is in the middle, 1/4 is between 0…
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