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Fasten your seat belts, the flight is getting bumpy :-)

This is a series on the book Gödel, Escher, Bach: An eternal golden braid by Douglas Hofstadter.  

Earlier diaries are here

Today we'll discuss Chapter 5: Recursive structures and processes.

from the overview:

The idea of recursion is presented in many different contexts: Musical patterns, linguistic patterns, geometric structures, mathematical functions, physical theories, computer programs, and others.

This is a hard chapter!  That said, the chapter is still interesting, and I have some questions and ideas to spur conversation.

I also recommend browsing the comments in the old diaries.  Some very good comments are being made late in the week.

The executive on the phone is pretty clear, but I am not sure how good an exemplar of recursion it is.

The bit on pushing and popping nicely ties in with the previous dialogue; and he then gets into stacks.  But I dislike the way he assumes what a listener can and can't do. Perhaps part of the tension is trying to figure out if we are, in fact, finished?  

On recursive transition networks -

  1.  Wouldn't it be great if we diagrammed sentences this way, instead of the cockamamie methods we learned in grade school? (Or, anyway, the ways people attempted to teach us?).
  1.  How do we avoid infinite loops here? Perhaps there is a sort of 'pressure' gauge on ending the loop, and we know, at some level, that we will lose the reader or listener if we add one more loop?  

Diagram G and recursive sequences

  1. Someone who can program could probably make a program to draw the shapes on p 135 and 136 as they expand.  That might make it clearer.
  1. the Q series is neat.  Probably easy to program - I tried a tiny bit and didn't quite get it.  But one of you can probably do it.

The two graphs - I am just not a visual person.  Discuss amongst yourselves

Feynmann diagrams - aren't these cool?  I mean, at one level, this is how EVERYTHING WORKS

Copies and sameness - I think it was Steven Pinker who came up with the idea (or developed it) that we identify nouns by their closeness to an archetype.  Cats are cats because they are close to some 'cat archetype'.  But this is a big question.  

  1.  You aren't identical to the you you were 10 minutes ago, much less when you  were a kid, so how are you the 'same'?
  1. Is a book the same in different languages?
  1. Why are identical twins NOT the same?
  1. Is a book the same to different people?

Programming - as may be already evident, I am going to need help, here.  Not so much with this chapter, as with later ones.

Tic tac toe - I am such a geek.  At some point in elementary school, I diagrammed all of tic tac toe to prove how to win.

Chess - one big change since this book came out - back then, the best chess program was so-so.  Now, it may be better than anyone alive.  What does this do to arguments about artifiicial intelligence?

Originally posted to plf515 on Sun Feb 08, 2009 at 03:37 AM PST.

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