Computational Diversions: Turtle Really and Truly Escapes the Plane

Abstract

Just about anyone, when asked, can respond to the question ‘‘What is your all-time favorite book?’’ I’m no exception–in fact, for me, there’s no contest. The book is Turtle Geometry, by Hal Abelson and Andy diSessa (Abelson and diSessa 1980). Actually, Turtle Geometry is more than just a ‘‘favorite’’ book: it actually changed my life, a story I’ve never written about. In 1980, while working as a fledgling computer programmer at the Rockefeller University (my machine there was a DEC PDP-8), I happened into the University Library and plucked the book from the ‘‘new arrivals’’ shelf, intrigued by the mysterious title. A month later, I was certifiably insane, telling everyone who would listen that there was this really, really important book that you just had to read, that introduced mathematical ideas in a completely wonderful, experimental way, that made everything clear... and so forth. I had no idea who the authors were, but the book jacket said that they worked at MIT, so I applied to graduate school to study with them. My application form must have appeared sufficiently obsessive, and to my shock I was accepted. It sounds arrogant to say that ‘‘the rest is history’’, but in any event, the rest is my history. I still love Turtle Geometry, and have probably re-read the book in its entirety a half dozen times in the three decades since it was published. Abelson and diSessa use a Logolike language to present a remarkably accessible, procedural approach to geometry. In the course of about 500 pages, they introduce ideas of recursion, artificial life, Euclidean geometry, vector algebra, topology, and general relativity, to name a few. The book has lost absolutely none of its joy and freshness for me; by the way, it’s still in print, and if the interested reader wishes to consider this a plug, he or she can be my guest. The purpose of this column is to quench an ambition that has festered within me these past 30 years, since first picking up Turtle Geometry from the new-arrivals shelf. In the