Could you post the page number, assuming you have the 20th anniversary edition? 

I've been reading the book Godel Escher Bach: an eternal golden braid and while I can understand most of the concepts in the book some of the math is a little fuzzy. 

157 is a prime number. The next prime is 163 and the previous prime is 151, which with 157 form a sexy prime triplet. Taking the arithmetic mean of those primes yields 157, thus it is a balanced prime.
Women and rhythm section first  Jaco Pastorious
Could you post the page number, assuming you have the 20th anniversary edition? 

N 

I stomp on your ideas.
I think hes talking about recursivity resulting into infinity. Look up recursivity and you will understand Diagram G. I haven't read that book tho, but I'm pretty sure this is what he is talking about. 

"Reject common sense to make the impossible possible." Kamina
Out of interest I downloaded the ebook and started reading so I thought I might as well post the diagrams for those who are interested: 

"Reject common sense to make the impossible possible." Kamina
I may be wrong, but here's what I think. If you look at the bottom picture ChaybaChayba posted, you see that for each circular node (which corresponds to a given n), there is a line under it leading to another node  that node is G(n) for that n. Thus, 1 is under 2 so G(2) is 1. 

It starts on page 135 

157 is a prime number. The next prime is 163 and the previous prime is 151, which with 157 form a sexy prime triplet. Taking the arithmetic mean of those primes yields 157, thus it is a balanced prime.
Women and rhythm section first  Jaco Pastorious
Wildman pretty much explained this. It's an example of a recurrence relation and is a way to define a sequence. 

Last edited by PhilosopherStoned; 01112011 at 01:44 PM.
Guys. Hey guys? 

Abraxas
Originally Posted by OldSparta
Sure. I'm reading it at the moment (I tried and failed a couple of years ago... wasn't intellectually ready) and it's brilliant. 

Ok, finally found time to do this. It made me really wish the forum had LaTeX but no such luck. If you actually want to read it, my condolences. It's a little longish but it's broken up into pieces and isn't too difficult. I would think that somebody with the mathematical maturity to handle calculus should be able to handle this (possibly with some questions). There's no calculus or algebra involved, this is completely elementary. 

Previously PhilosopherStoned
Yeah, I've read past this page now. It's really quite simple compared to some of the preceding stuff. Basically, if you pick a node, and work out G for that node, that value will be below that node. 

I understand this now, I think I'm just really out of practice with math, does anyone know of any websites where I can get some algebra problems with solutions? I feel like I've forgotten everything from high school math. 

Last edited by StonedApe; 01132011 at 06:25 PM.
157 is a prime number. The next prime is 163 and the previous prime is 151, which with 157 form a sexy prime triplet. Taking the arithmetic mean of those primes yields 157, thus it is a balanced prime.
Women and rhythm section first  Jaco Pastorious
I'm sure a quick Google will get you a good site. 

I did, I understood how the diagram functioned right away, I just got confused when I started messing with the equation. I understand the book fine, I just used to be good with math and equations and am not at all anymore. 

157 is a prime number. The next prime is 163 and the previous prime is 151, which with 157 form a sexy prime triplet. Taking the arithmetic mean of those primes yields 157, thus it is a balanced prime.
Women and rhythm section first  Jaco Pastorious
For what it's worth, there's not a lot of algebraic manipulation to be done with the recurrence relation. The fact that these things are recursive means that when you try to do algebra with them, you first have to expand out one side. But then... surprise! You have to expand it out again because it's defined in terms of itself. ad infinitum. 

Last edited by PhilosopherStoned; 01132011 at 09:04 PM.
Previously PhilosopherStoned
Ad baseum, more like. 

Try this: 

Yeah, ad baseum is definitely right. I'm not much on latin. It honestly might as well be ad infinitum for the simple reason that it's a huge pain in the ass to deal with one of these things fully expanded. ugghhh. 

Last edited by PhilosopherStoned; 01132011 at 09:45 PM.
Previously PhilosopherStoned
Actually as far as I'm aware ad baseum is something I made up, ha. I'm sure there's a proper term for it but... yeah, dead language and all. 

Bookmarks