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...