Thursday, July 4, 2013

BI:NP - A General Theory of Information Cost Incurred by Successful Search

(This is an email I wrote to William Dembski, Winston Ewert and Robert Marks II)


it's nice to be able to read the proceedings of the conference on Biological Information – New Perspectives for free. However, I have a few questions regarding your contribution "A General Theory of Information Cost Incurred by Successful Search":

1) Your quasi-Baysian calculation on p. 56 gets the right result, but IMO it isn't correct: Please see for details.

2) You claim that you have found a representation for searches as measures on the original space. Again, this works for guesses, but seems to be quite problematic when it comes to searches: here, many quite different searches can be constructed which are "represented" by the same $\mu$ in $M(\Omega)$!

3) You are using the uniform measure on $M(\Omega)$. Again, fine with guesses - but when it comes to searches, this becomes questionable: if $\mu_{(X_1, X_2 \dots, X_n)}$ are measures representing searches $S(X_1, X_2 \dots, X_n$), where at each step an element of $\Omega$ is chosen according to a (uniformly random) chosen measure $\theta_k$, then the measures induced by a "discriminator" (which returns an element of $T$ if it was found, otherwise a random element of the first line of the search matrix) aren't again uniformly distributed on $M(\Omega)$. In fact, we will get that for n tending to infinity, the measures approach $\delta_T$!

4) For me, your description of a search is quite convoluted: I don't see the point of the "navigator"'s output, as this can be seen just as the next element of your search path. And then there is the output of the "inspector": you are treating it quite inconsistently - once, it is the probability of an element to be a member of the target, the next time it is the output of a fitness function...

I'd like to see you addressing these issues above. Denyse O'Leary promised a series of posts at Uncommon Descent, each one dedicated to an article of the proceedings. If you don't wish to answer via mail - or comment on my blog - perhaps we can discuss these questions there?



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