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Gödel, Escher, Bach > Chapter 1: The MU-puzzle

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message 1: by Erik (new)

Erik | 165 comments This chapter introducts a nice puzzle-game. I think it does a nice job of keeping the discussion simple, but addresses a very complex concept.

My wife enjoys doing Sudoku puzzles. I often imagine writing software to solve them, but I don't enjoy trying to solve them manually. Sometimes in sudoku, she has take a Guess & Check approach. The MU system doesn't discuss that.

I really like the part about rare people identifying loops, and then having trouble convincing others of their discovery.

The part about the chess software conceiding is great too. I recently played a video game, and the AI says "good game" and conceides near a player's victory. I was almost certain I had been playing another real person the first time the AI conceided to me.


message 2: by Steph (new)

Steph (spthomp) | 20 comments A simple formal system with production rules but no mechanism for proving a production is a theorem. I wish I had kept up with Prolog. It would be fun to create a simple forward chaining inference engine and then code the simple rules for the MU-Puzzle. Then sit back and let it run for a few hours to see if we can generate MU. But that is not the point, I guess. Instead Hofstadter want us to understand that without some mechanism of “proving” theorems we can spend our entire lives exploring the formal system landscape without discovering the one “place” we want to find. In this case, “MU”.

I conceptualize this problem as a 3-D cube. We stand at one corner and may move through the 3-D space by moving forward, backward, up and down. We will move through the cube in specific pathways determined by the rules and the starting point of “MI”. I think of it as a 3D version of Pac Man. I chuckle to think that the spot we wish to find may be right next to our starting point, but we will never reach it by following the “path” defined by the rules. In this way we find we can not generate “MU” given the initial point and definition of the formal system.

This reminds me of the Knight’s Tour too. It is a classic toy problem to learn about the back-tracking algorithm, then testing if the knight can visit every square on the chess board given a specific starting point. However, the chessboard provides a boundary that limits the search-space for the knight. I don’t see the MU-Puzzle having that kind of boundary so it will go on infinitely.

Questions:

1. Can we start with MU and then work the rules backward to get MI?
2. Does MU represent infinity? Is the author foreshadowing?
3. Is the MU-Puzzle analogous to Turing’s Halting Problem?

Finally, he asks us to move from m-mode to i-mode and then to u-mode. Get out of the system and look at it from above like a researcher looking down on a maze with (us) the rats inside. Are the Dialogs episodes we are viewing from “outside”?

The u-mode he called Zen-mode. So the Buddha asked his followers to meditate to achieve enlightenment and thereby “jump out” of the endless cycle of death and rebirth. That theme was explored in the movie The Matrix. Is Dr Hofstadter our Morpheus? What will I have to do in reading this GEB to have Morpheus say “…he is starting to believe...”

The Zen reference now makes me think of the meditative puzzles of the Zen masters. Here are three I read

a. What was your face before you were born?
b. What is the sound of one hand clapping?
c. What foot prints do birds leave on the sky?

So what are the MU-Puzzle versions of those koans?


message 3: by Brad (new)

Brad (bradrubin) | 264 comments Mod
The MU-Puzzle and the associated issues of reachability and "looking from the outside in" are here, I think, to foreshadow the upcoming Turing computability and Godel provability discussion.


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