Remembering John Conway's FRACTRAN, a ridiculous, yet surprisingly deep language

Summary

On April 8, 2020, John Horton Conway developed symptoms of COVID-19. On April 11, 2020, he succumbed to the disease. Like so very, very many, I mourn Conway’s passing, and yet I also celebrate his life. I celebrate his accomplishments, I celebrate his curiosity, and I celebrate his skill at making important topics in mathematics engaging and interesting. One of the finest examples of that skill is the programming language FRACTRAN, the subject of this essay. Prelude John Horton Conway in 1993 Conway touched my own life from early days. As I described in The Eight Queens Problem… and Raganwald’s Unexpected Nostalgia: My mother had sent me to a day camp for gifted kids once, and it was organized like a university. The “students” self-selected electives, and I picked one called Whodunnit. It turned out to be a half-day exercise in puzzles and games, and I was hooked. One of the things we talked about in “Whodunnit” was Conway’s Game of Life. I don’t recall playing with it much: There was a lot going on, and it’s entirely possible that I was too busy falling in love with Raymond Smullyan to have curiosity left over for John Conway. An infinitely scrolling implementation of Conway’s Game of Life I went on to rediscover Conway’s Game of Life several times in my life. Some years ago, I read William Poundstone’s The Recursive Universe: Cosmic Complexity and the Limits of Scientific Knowledge, and it literally blew my mind. I learned a little about Game Theory. I spotted Games of Strategy: Theory and Applications in a library and picked it up, thinking it would help my Backgammon. That led me to Conway’s On Numbers and Games, and via parallel paths, to Surreal Numbers. Like the Game of Life, Surreal Numbers keep popping up unexpectedly, reigniting my interest in how the way we represent data, affords or hinders working with that data. The subject of numbers and representation leads us to FRACTRAN. Table of Contents “Books” © Stewart Butterfield, 2012, Some Rights Reserved Pr...