Douglas Hofstadter – Eclecticism

Ever since I read Douglas Hofstadter’s Gödel, Escher, Bach: An Eternal Golden Braid, I’ve had the paradox postulated by Zeno of Elea (c. 450 B.C.) bouncing around in my head. To summarize the paradox:

Zeno’s Paradox may be rephrased as follows. Suppose I wish to cross the room. First, of course, I must cover half the distance. Then, I must cover half the remaining distance. Then, I must cover half the remaining distance. Then I must cover half the remaining distance…and so on forever. The consequence is that I can never get to the other side of the room.

What this actually does is to make all motion impossible, for before I can cover half the distance I must cover half of half the distance, and before I can do that I must cover half of half of half of the distance, and so on, so that in reality I can never move any distance at all, because doing so involves moving an infinite number of small intermediate distances first.

I knew there must be a solution, as we all do manage to move around quite handily, I just never knew what it was. Luckily enough, I managed to stumble across an explanation of the paradox and its solution today. Nifty!

(Via Jason Kottke)

Ow.

Ow ow ow.

My brain hurts.

It’s a good kind of hurt, though. Gödel, Escher, Bach: An Eternal Golden Braid is an exploration of everything from mathematics to the mechanics of thought and reasoning to Artificial Intelligence, all tied together and interrelated to each other. Fascinating, fascinating stuff.

My big difficulty is that I am really not a math person, so whenever the chapters moved into that realm, I had to muddle my way through as best I could until he moved on to something else that I could comprehend more easily. I haven’t had to work this hard to read and understand a book in a long, long time — and I’ve got to say, I enjoyed it (though I did need to let my brain relax with a bit more light reading afterwards).

Some of the concepts are a bit dated, especially in the areas of AI — the book was first published in 1979, and there’s been a lot of progress since then — but the core concepts that he deals with are most likely the same that we’re dealing with today, just from more advanced positions.

Anyway, neat stuff — definite brain food.