Talk:Conservation of Information in Search - Measuring the Cost of Success

Though this is an essay, I'm thankful for direct input: you know how my English sucks :-) 14:14, 13 October 2009 (UTC)
 * You seem like you know a lot more about the mathematics of this than I do. Am I right in thinking that this paper of Demski's doesn't really say anything more than the fairly obvious, that if you want to do better than a naive search in the average case then you need to apply domain knowledge to the problem, and that the application of domain knowledge can be quantified by looking at the difference between the naive search case and what your algorithm actually achieves? Because if that's all he's saying, I can't help but wonder why even bother committing it to paper. It's both an obvious and totally unhelpful observation. -- 19:23, 13 October 2009 (UTC)
 * For the ID movement, it isn't important that this paper describes an obvious and totally unhelpful observation - as you correctly stated. They got this paper in a peer-reviewed journal, and now they are claiming that it is about ID. BTW: it is not :-) 19:41, 13 October 2009 (UTC)
 * The (1,2) analysis may have been done by Marks, but it's got Dembski's preoccupation with ratcheting written all over it. Basically, they set the mutation rate VERY low in order to make the probability of a decrease in fitness VERY low. The way they go from (43) to (44) in the appendix is shady. "Ridding the equation of μ2 terms" indeed yields what they show for the cases of q = 1 and q = -1, but not for the case of q = 0. Rather than add the two positive values together and normalize, they heuristically, and without comment, subtract the q = 1 probability from 1 to get the q = 0 probability. And, golly gee, they have made the (1,2) algorithm into a (1+2) algorithm flipping at most one bit.Tom English 06:41, 14 October 2009 (UTC)
 * Thanks for dropping by! They made it into a (1+1) algorithm, I think: And yes, the approximation falls apart very fast: $$\mu \ll 1$$ isn't sufficient, they need $$\mu \cdot N \ll 1$$ because of all these pesky binomial coefficients piling up.  07:22, 14 October 2009 (UTC)
 * You evidently are right about this, though I don't want to give the impression that I've checked your work closely. Very interesting. Tom English 21:37, 14 October 2009 (UTC)

Queries vs. Generations
In general a query is one evaluation of the fitness function, while a generation may include lots of those. The (1,2)ES takes two queries per generation, the (1+1)ES just one. 07:24, 14 October 2009 (UTC)

Another minus sign
$$Q \approx \frac{2 \log(L)}{\log(1-2\mu)}$$ should be $$Q  \approx -\frac{2 \log(L)}{\log(1-2\mu)}$$, I suppose. These pesky details! But a even number of sign errors cancels itself out, doesn't it? 07:40, 14 October 2009 (UTC)
 * Belly laugh at that one. More power to you in ferreting out this stuff — I look forward to seeing everything you find — but I've got to get down to explaining the fundamental errors in the global argument of the article. What matters most to me is that Dembski and Marks are attacking the notion that the successes of evolutionary computation are evidence in support of Darwinian principles, and are insinuating that my colleagues and I are benighted and / or dishonest in characterizing our research results. Before ducking out, let me mention that the problem addressed by the algorithms is called ONEMAX (the Weasel problem is a generalization), and that the top Google Scholar hit for "'(1+1)' ONEMAX" is Heinz Mühlenbein's 1992 "How genetic algorithms really work: I. Mutation and hillclimbing" ( http://muehlenbein.org/mut92.pdf ). You should find the early pages interesting. Tom English 21:24, 14 October 2009 (UTC)
 * Thanks for the links! Interesting article - though the approximation used by Mühlenberg is similar to the one of Dembski and Marks. Before getting involved in the whole weaseling, I had no idea of ES - and D&M's paper ignores the whole literature on ESs - and that's not an easy thing to do, as it goes back to the 1960s!  Your post (Resolving Difficult Moral Dilemma) was a real eye-opener, thanks again.
 * You are better qualified than I am to argue the principles (ab)used in the article, I just wanted to show that even the handwork is lacking.
 * 15:35, 15 October 2009 (UTC)

Getting some mileage from this essay
Unfortunately, the IEEE does not have a forum for direct rebuttal of articles in journals published by its Systems, Man, and Cybernetics Society. (IEEE Computational Intelligence Magazine publishes peer-reviewed rebuttals, but only of articles appearing in journals of the IEEE Computational Intelligence Society.) I have seen to it that the matter will get some attention in two publication committees of the IEEE. It happens that a higher-up in the IEEE just asked me if there are mathematical errors in the article by Dembski and Marks, and I put to good use something larron discusses: "Here's an example that's easy to relate. Dembski and Marks analyze the (1, 2)-EA operating on ONEMAX. The mutation rate is μ and the bit-string length is L. They give a dandified derivation of an approximation relevant to convergence rate, and say that it holds for μ << 1, when it in fact holds only when μL is considerably less than 1. They 'validate' their approximation with simulation runs in which μ = .00005 and L = 100, i.e., with μL = 0.005 and probability of .99 that neither offspring is mutated. The approximation error goes through the roof for μ > .001 (probability less than .82 that neither offspring is mutated), and they must have known this." Note my minor correction of the article: μL must be considerably less than 1, not much less than 1. ("Considerably less" is not a good term, but I was in a hurry.)

Thanks very much to larron. Tom English 22:24, 15 October 2009 (UTC)


 * Thank you - and I did so in an email to your gmail-account, too :-) 09:36, 16 October 2009 (UTC)

The average information per query
For their version of an (1+1) ES, Dembski and Marks calculated the average information per query:

$$I_{\oplus} = \frac{1}{\mathcal{H}_L}$$

Here, the number of queries is the expected number of queries. So, what did they calculate for their (1,2) ES. Something similar? Not quite :-)

$$I_{\oplus} \approx \frac{2 \mu L}{\ln(L)}$$

is the average information not for the expected number of queries, for the number of queries Q it takes such that after Q/2 generations on average $$L-1/2$$ bits are correct. They don't tell us why they take this number, other than that Q is big. But it doesn't say anything about the average number of queries it takes....

15:24, 16 October 2009 (UTC)

Errata list for W. Dembski
W. Dembski asked for a complete list of errors (Since you are so concerned about errors, none of which impact the substance of the EIL’s papers (or have the IEEE referees been too lenient?), let me urge you to give us here in this thread a complete list of all of those that have not, in your view, been properly corrected or addressed. Please be very specific in terms of links, page numbers, and precise equations. Don’t just cite some other website.)

Here you go:

1. p 1056, 2nd col, line 12 (eq. 27): $$I_+ = - \log (\frac{1 - F^{\Phi}_{\Delta \kappa} (0)}{1 - F_{\Delta \kappa} (0)})\,$$ should read $$I_+ = \log (\frac{1 - F^{\Phi}_{\Delta \kappa} (0)}{1 - F_{\Delta \kappa} (0)})\,$$

2. p 1057, 1st col, line 5: $$Q \approx \frac{2 \log(L)}{\log(1-2\mu)}\,$$ should read $$Q \approx - \frac{2 \log(L)}{\log(1-2\mu)}\,$$

3. p 1057, 1st col, line 7: $$I_{\oplus} \approx \frac{L}{\log(L)} \log(1-2\mu)\,$$ should read $$I_{\oplus} \approx \frac{L}{2 \log(L)} \log(1-2\mu)\,$$

4. p 1057, 1st col, line 9: $$I_{\oplus} \approx \frac{2 \mu L}{\ln(L)}\,$$ should read $$I_{\oplus} \approx \frac{\mu L}{\ln(L)}\,$$

5. p 1057, 1st col, line 10: $$I_{\oplus} \approx 0.0022 b\,$$ should read $$I_{\oplus} \approx 0.00109 b\,$$, if you use the correct formula, but $$I_{\oplus} \approx 0.00094 b\,$$, if it fits the example of Fig. 2

And then there is the list of references: It's full of errors, typos, and unhelpful entries (if you quote a book, you should hint to the relevant pages...) I hoped that you improved the references for your newest paper Efficient Per Query Information Extraction from a Hamming Oracle, but I was somewhat disappointed when I read that the first entry was on Thomas Back instead of Thomas Bäck.

As for the question: have the IEEE referees been too lenient? IMO, at least, they weren't as careful as I would have them expected to be.

Ann: essentially this list was sent to W. Dembski (info AT designinference.com) and Robert Marks (Robert_Marks AT baylor.edu) on Oct 17, 2009. W. Dembski never answered, while R. Marks only stated that he would look into it. Or as W. Dembski put it here Your concerns will get addressed in due course.

06:13, 8 April 2010 (UTC)
 * The page number in item 4 is 1057, not 1058. You've left out the errors in p. 1057, col. 1, line 7. Tom English (talk) 21:14, 8 April 2010 (UTC)


 * As usual, you are right: I corrected the number and inserted a new erratum no. 3 22:00, 8 April 2010 (UTC)