It’s a little bit like the famous liar’s paradox, which we studied in DeLong’s class. Here’s one version of it: “The following sentence is true. The preceding sentence is false.” As soon as you accept the first sentence, you validate the second sentence, which invalidates the first sentence, which invalidates the second, which validates the first,... See more

DeLong and Hofstadter both found great beauty in what the latter called strange loops—occasions when mathematical systems or works of art or pieces of music fold back upon themselves. M. C. Escher’s drawings are a great, overt example of this. Take his famous picture of two hands drawing each other; it’s impossible to say where it starts or ends.... See more