## Sunday, June 23, 2013

### Review of "A General Theory of Information Cost Incurred by Successful Search" - Introduction

(For some background information, go here)

There are two main ways to apply mathematics: the first is to shed light on a subject and look for a deeper understanding, the second just wants to create the impression that something important is happening somehow. After looking into the article "A General Theory of Information Cost Incurred by Successful Search" (free download as pdf) I became convinced that the authors are following the second path.

The abstract states:

This paper provides a general framework for understanding targeted search. It begins by defining the search matrix, which makes explicit the sources of information that can affect search progress. The search matrix enables a search to be represented as a probability measure on the original search space. This representation facilitates tracking the information cost incurred by successful search (success being defined as finding the target). To categorize such costs, various information and efficiency measures are defined, notably, active information. Conservation of information characterizes these costs and is precisely formulated via two theorems, one restricted (proved in previous work of ours), the other general (proved for the first time here). The restricted version assumes a uniform probability search baseline, the general, an arbitrary probability search baseline. When a search with probability q of success displaces a baseline search with probability p of success where q > p, conservation of information states that raising the probability of successful search by a factor of q/p(>1) incurs an information cost of at least log(q/p). Conservation of information shows that information, like money, obeys strict accounting principles.
The general framework is introduced pp 26 — 38. In my next post, I'll try to relate it to the usual definitions, but I fail to see how this new frameworks improves e.g., the ideas of David Wolpert and William G. Macready significantly (NFLT at wikipedia). pp 38 — 45 provide examples, interestingly without applying the new framework to them. Then follow a couple of pages with sound math (pp. 45 — 61), it is just not clear what they have to do with the claims the authors are making. For their mathematics to work, they have to show that searches can be represented as measures. Indeed, the authors write:
"This representation will be essential throughout the sequel. (p. 37)
I will elaborate how I think that the authors failed to do so, and that the "representation" is at least a misnomer... Another point will be the subject of "Information Cost": this term isn't defined in the paper...

### The Ithaca Papers

William A. Dembski announces in his CV/Resumé on his web site Design Inference - Education in Culture and Worldview some books which are still in preparation. Top of the list is
Biological Information: New Perspectives (co-edited with Robert J. Marks II, John Sanford, Michael Behe, and Bruce Gordon). Under contract with Springer Verlag.
Well, rejoice, the electronic version of this book has been published (and is free for download!), and the hard copy is announced for August 2013. Albeit the publisher switched from Springer to World Scientific, the announcement hasn't changed:
In the spring of 2011, a diverse group of scientists gathered at Cornell University to discuss their research into the nature and origin of biological information. This symposium brought together experts in information theory, computer science, numerical simulation, thermodynamics, evolutionary theory, whole organism biology, developmental biology, molecular biology, genetics, physics, biophysics, mathematics, and linguistics. This volume presents new research by those invited to speak at the conference.
While the publication of Stephen C. Meyer's new book Darwin's Doubt is hailed with great fanfare at the Discovery Institute's news-outlet Evolution News, the appearance of this volume hasn't made their news yet - though Dembski and Meyer are both fellows of the Discovery Institute's Center for Science and Culture (granted, Meyer is its director). Only at Dembski's (former) blog, Uncommon Descent, there are two posts about the book: Instantly, there arose a discussion about Denyse O'Leary's (commenting under the nom de guerre "News") choice of title, where the usual combatants switched sides: the evolutionists claimed the title was designed to mislead the average reader to think that the Cornell University was somewhat involved in the conference, the apologists of Intelligent Design argued that this was just chance. Unfortunately, no one answered to my comment:
In the interest of discussing the data and the evidence, could we have posts on various articles of the book? I’d be quite interested in a thread on Chapter 1.1.2 “A General Theory of Information Cost Incurred by Successful Search” by William A. Dembski, Winston Ewert and Robert J. Marks II.
I hope that the authors are still reading this blog: this way, we could have a productive discussion, and perhaps some questions could be answered by the people involved!
And for the sake of a swift exchange of ideas: could someone please release me from the moderation queue?
Maybe there is no interest in such a discussion at Uncommon Descent. Maybe no one read the comment - it was hold in the moderation queue for five days, and when it appeared, the article wasn't any longer at the front page. Therefore I'll start a number of posts on “A General Theory of Information Cost Incurred by Successful Search” here at my blog: I just can't believe that this peer-edited article would have been successfully peer-reviewed by Springer....