This week I thought I’d talk about the applications of mathematics to Music Theory. The analogies that Hofstadter puts forward in the book are a bit disappointing. There are many beautiful ways to apply math to music. I will focus on groups and symmetry.
I almost forgot to mention, but there has been a course taught to high school students at MIT a few times, and the lectures have been recorded. You can find them here in RM format. I’ll try to have them converted to avi or mp4 if you have trouble seeing the videos. The MIT course had a slightly different focus that this one, but do let me know if there are topics from it that you would like me to cover. Here are the videos in MP4 format:
The dialogue, and the following chapter, deals with the concept of recursion, and higher order logic, which are all central to the proof of the Incompleteness Theorem. There are several concepts of recursion floating around in Mathematics, Logic and computer science, and Hofstadter seems to confuse them all (the terminology doesn’t help), so I’ll try to explain the different notions a bit more formally.
Apologies for posting this again at the last minute. This week we will ficus on the dialogue preceding chapter 4 of the book. This dialogue introduces several notions central to the proof of the Incompleteness Theorem, the most important one being the concept of recursion and iteration. We will be drawing parallels between the concepts of the dialogue and the process of the proof of the Incompleteness Theorem, and relate it to bootstrapping, booting and the Halting Problem
This week we’ll be covering chapters 3 and 4 of the book.
Better late than never, the course webpage is up. I’ll write a syllabus and post it as soon as I can. Meanwhile, feel free to comment on any post on this page.