IdFug's Godel,Escher,Bach Thread

[IdealFugacity]

So I got this book for my birthday (had never heard of it, I see it has gotten good reviews here though.)

Rather than spam the forum with math questions etc as I happen upon them, I'll keep it organized to this thread when appropriate.

First question, re: Euclid's Theorem, specifically, as Hofstadter puts it (p. 59), [paraphrased] "If N! + 1 isn't prime, it is only divisible by numbers > N, and is therefore either prime or has prime divisors > N"

I don't understand the conclusion...why must it have 'prime divisors' > N??

[gumpzilla]

So the Fundamental Theorem of Arithmetic says that any number can be factored uniquely as a product of primes. N! + 1 is either prime - in which case you have a prime greater than N - or it isn't, in which case there must be a factorization of it as a product of prime numbers. Since it isn't divisible by any number less than or equal to N, there must exist prime numbers greater than N.

Hope that helps.

Also, GEB is a great book, but the math will be a real slog in places. Rather than stop reading all together, I'll just say you can get a lot of the interesting ideas out of it even if you skip a lot of the formalistic math stuff (most notably his TNT proof of Godel's theorem.) The dialogues between Achilles and the Tortoise are great by themselves.

[ChrisV]

I found GEB kind of turgid in places. I own it but I'll probably never reread it.

[luckyme]

[ QUOTE ]
The dialogues between Achilles and the Tortoise are great by themselves.


[/ QUOTE ]

GED was a mind-shifting read for me ( not long after it first came out). It clarified several areas that were quite fresh. Emergent properties, level-confusion and 'greenness disintigrates' discussions were just what I needed at the time.

I turn back to the dialogues at times for refresher nibbles at creative explanations.

luckyme

[IdealFugacity]

Speaking of the dialogues, just finished 'Contrapunctus' (p. 75 of my copy, it's the one about the record player breaking records)

Took me a bit but having a very strong suspicion I found the neat (very basic) acrostic at the very beginning of this section (Each capital layer at the beginning of a line for the first several lines...get out your own damned copy [img]/images/graemlins/tongue.gif[/img])...Now I'm going to kill myself scanning everywhere for these things.

[IdealFugacity]

Wow, I'm dumber than I thought, it's way more than the first several lines.

EDIT: Now that I have the first acrostic, [in white below] I can't figure out what the devil it means. It's got to have something to do with Tortoise's second-to-last comments which directed the reader to finding the original acrostic in the first place...
OR, it could, if the author is truly evil, be a demonstration of something ending "suddenly, without warning...rudely"??

<font color="white"> " hofstadter’s contacrostipunctus acrostically backwards spells J.S. Bach’ " </font>

EDIT again: Sigh, i see it again. Don't understand the significance of the first two letters of the backwards acrostic, (B S), probably just supposed to ignore that