Chaos theory is not as interesting as it sounds. How could it be? After all, the name “chaos theory” makes it seem as if science has discovered some new and definitive knowledge about some utterly random and incomprehensible phenomena….By calling certain physical systems “chaotic,” scientists lead us to think that they are totally unintelligible - just a muddle of things happening with no connections or structures. So when they find interesting mathematical patterns in these unpredictable systems, they can exclaim that they have discovered the secrets of “order within chaos,” even though only by christening these systems chaotic in the first place can they make such an impressive result possible.
— Stephen KellertIn The Wake of Chaos

Archive for the 'Effective Process' Category

Article on the Ubiquity of Undecidability

Saturday, March 6th, 2010

From March’s Notices of the AMS, Chaim Goodman-Strauss authors an article, “Can’t Decide? Undecide!” [1], on the ubiquity of undecidability in mathematics.
References
[1] Goodman-Strauss,C. 2010. “Can’t Decide? Undecide!”. Notices of the AMS. Vol 57:3.

Comments on Wells’ “In Defense of Mechanism”

Saturday, January 5th, 2008

A 2006 paper attempting to criticize some of Rosen’s arguments, entitled “In Defense of Mechanism” by A.J. Wells [1], was recently brought to my attention. The paper makes a lengthy series of erroneous arguments based on misinterpretations of Rosen’s arguments. Wells begins with a list of statements drawn from Rosen’s Life Itself [2]. He then […]

Error and Emergence

Sunday, May 6th, 2007

(Note: This post is a migration of a page form my old Rosen website.)

It is recommended that the reader first understand the Rosen Modeling Relation and Rosennean complexity prior to reading this page.

Introduction

The concept of “error”

Emergence

The mystery of emergence

References and footnotes

Introduction
Once we understand what is meant by Rosennean complexity, it becomes relatively easy to […]

Effective Processes, Computation, and Complexity

Sunday, May 6th, 2007

 

In 1936, two important papers in the field of mathematics and logic were published. One was “An Unsolvable Problem of Elementary Number Theory” by Alonzo Church. [1] The other was “On computable numbers, with an application to the Entscheidungsproblem” by Alan Turing. [2] These papers were aimed at providing formal and rigorous definitions of the […]