TITLE: Encounters with Large Numbers and the Limits of Programs AUTHOR: Eugene Wallingford DATE: March 22, 2011 4:45 PM DESC: ----- BODY: Yesterday, this xkcd illustration of radiation doses made the round of Twitter. My first thought was computational: this graph is a great way to help students see what "order of magnitude" means and how the idea matters to our understanding of a real-world phenomenon. Late yesterday afternoon, one of my colleagues stopped by to describe a Facebook conversation he had been having with a few of our students, and in particular one of out better students. This student announced that he was going to write a program to generate all possible brackets for the men's NCAA basketball tournament. My colleague said, "Um, there are 2 to the 67th power brackets", to which the student responded, "Yeah, I know, that's why I'm going to write a program. There are too many to do by hand." From this followed a discussion of just how big 2**67 is and how long it would take a program to generate all the brackets. Even using a few heuristics to trim the problem down, such as always picking a 1-seed to beat a 16-seed, the number is astronomically large. (Or, as Richard Feynman suggests, "economically large".) Sometimes, even good students can gain a better understanding of a concept by encountering it in the wild. This is perhaps even more often true when the idea is unintuitive or beyond our usual experience. -----