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This is what language without type inference looks like.
In a way, this book is a statement of my religion. I hope that this will come through to my readers, and that my enthusiasm and reverence for certain ideas will infiltrate the hearts and minds of a few people. That is the best I could ask for.
Hey folks, Max here.
Ok - so today is the first day of our first week! This week we’re going to power through the Introduction, A Musico-Logical Offering, the first dialogue, Three Part Invention, and the first chapter, The MU-Puzzle.
The introduction is a broad overview of Hofstadter’s project. You’ll be introduced to Bach through an amazing story about the creation of the Musical Offering, and we’ll meet M.C. Escher and Kurt Gödel and get a history of the last hundred years of mathematics in 2 pages as well. The first dialogue and chapter are pretty straightforward - they will lay the ground rules for future discussions of mathematical theory and give us our first puzzle.
Don’t be discouraged if you come across a part you struggle with or don’t understand - that’s what the group is here for! Post your question, leave it as a comment, or send it to me and I’ll post it up.
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In my reading of Gödel, Escher, Bach, one of the big themes is the emergent nature of intelligence. Watch how Hofstadter sets this up in his first discussion of the question of intelligence:
No one knows where the borderline between non-intelligent behavior and intelligent behavior lies; in fact, to suggest that a sharp borderline exists is probably silly. But essential abilities for intelligence are certainly:
to respond to situations very flexibly;
to take advantage of fortuitous circumstances;
to make sense out of ambiguous or contradictory messages;
to recognize the relative importance of different elements of a situation;
to find similarities between situations despite differences which may separate them;
to draw distinctions between situations despite similarities may link them;
to synthesize new concepts by taking old them together in new ways; to come up with ideas which are novel.
Here one runs up against a seeming paradox. Computers by their very nature are the most inflexible, desireless, rule-following of beasts. Fast though they may be, they are nonetheless the epitome of unconsciousness. How, then, can intelligent behavior be programmed? Isn’t this the most blatant of contradictions in terms? One of the major theses of this book is that it is not a contradiction at all. One of the major purposes of this book is to urge each reader to confront the apparent contradiction head on, to savor it, to turn it over, to take it apart, to wallow in it, so that in the end the reader might emerge with new insights into the seemingly unbreathable gulf between the formal and the informal, the animate and the inanimate, the flexible and the inflexible.
How do rigidly programmed behaviors become more than the sum of their parts? Check out this unbelievably good RadioLab episode about emergence.
Hey intrepid readers - Max here.
Last week we read Three-Part Invention and The MU-Puzzle. We were left in suspense as to whether MU is a theorem of Hofstadter’s MIU-system… at least, I hope none of you solved it, because I sure as hell didn’t.
Thanks to everyone who posted and shared their thoughts on the introduction and the first chapter - I really enjoyed reading what everyone had to say.
Our second reading week brings us to our second dialogue and chapter, Two-Part Invention and Meaning and Form in Mathematics. It’s a much quicker reading than last week.
This chapter introduces the pq- system, which stands in contrast with the MIU-system for the rest of the book. Hofstadter will give a look at mathematical systems, and we’ll learn a bit about Euclidian geometry.
Euclid’s proof is typical of what constitutes “real mathematics”. It is simple, compelling, and beautiful. It illustrates that by taking several rash short steps one can get a long way from one’s starting point.
P.S. Happy happy happy apple horse.
