Registered: Sep 2006
Posts: 13

As far as I can tell levels of complexity is not dealt with in NKS, this poses a problem when you look at the world you go from subatomic (simple) to things like the human brain (complex) and all are based off those simple systems. If NKS is right how can this be, since Cellular automata won't generate from a simple set of rules a more complex set of primitives and rules to generate rules for those based on all previous, such that you have one system built on top of another. Not what NKS says about a lot parallel arbitrary computer that form a fragmented universe, which I would disagree with for the reason that it doesn't makes sense based on the just stated idea a provable idea at that, that the world is made up of systems built on top of each other that are more closely connected just happening to run in parallel by random chance.

-Simon

Report this post to a moderator | IP: Logged

Registered: Oct 2005
Posts: 403

You don't think rule 110 is an example where you have one system built on top of another?

Report this post to a moderator | IP: Logged

Registered: Jan 2004
Posts: 16

Simon,
Consider taking a look at at the Wolfram and Kurzweil Roundtable Discussion since Kurzweil directly raises the same concerns that you are raising.

Actually NKS touches on the Ackermann function that is a famous hierarchy of systems in mathematics and computation. You might want to consider looking at an article I originally wrote for this forum that is now at Tetration.net:Arithmetic as well as the beginning of an article I am writing at Tetration.net:Physics . I work with iterated functions instead of CAs because they allow complexity to interface with many different areas of mathematics. FaĆ_ di Bruno's formula and the associated Bell polynomials are the foundation of my work with continuous iteration. I have longer wondered whether there is any connection between the principles of continuous iteration and renormalization. Now a new paper, Combinatorial Hopf Algebras in Quantum Field Theory I. points out that FaĆ_ di Bruno's formula is a very important Hopf algebra. The paper explains how Hopf algebras are important in several different areas of quantum field theory including renormalization.
Good Luck,
Daniel Geisler

Report this post to a moderator | IP: Logged

Registered: Nov 2006
Posts: 1

I have attempted to deal with levels of complexity with respect to NKS in a short essay 'Pseudorandom thoughts on complexity' which is found at http://kryptograff.blogspot.com
(If any misconceptions, errors or amateurish blunders are noted, I would like to know.)

__________________
Paulie

Report this post to a moderator | IP: Logged