You also make brief mention that the HNFLT proof assumes a partition of the search space and thus cannot handle the overlapping targets. This is problematic because any target on the original search space will become an overlapping target on the multi-query search space. I think you are correct on this point. Thanks for bringing it to our attention. We've added a description of the problem as well as an alternate proof for the uniform case on overlapping targets to the pdf: http://evoinfo.org/papers/2010_TheSearchForASearch.pdf.Here are some thoughts:
- Here is an excerpt from Tom English's blog Bounded Science:
A "Darwin or Design?" podcast interview (read on while it loads in a new tab, and then skip to 7:52) with Marks includes this cute little exchange:
Question: Are you getting any kind of response from the other side? Are they saying this is kind of interesting, or are they kind of putting stoppers in their ears? What's going on?
Answer: It's more of the stoppers in the ears thus far. We have a few responses on blogs, which are unpleasant,* and typically personal attacks, so those are to be ignored. We're waiting for, actually, something substantive in response.
I made this point on overlapping targets in emails, blogs, wikis over the last two years. Which begs the question: Who is putting stoppers in their ears? What are the odds that I'll hear of the authors of the paper themselves? I now got my second mentioning in this paper, can I expect a bottle of whisky, and a handsigned copy of a book? BTW: I prefer the excellent "Handbook of Fourier Analysis and Its Applications" over "The Design Inference: Eliminating Chance through Small Probabilities"
- By pure coincidence the home-page of Evolutionary Informatics has changed. At least until May 19, 2012 there was a link from it to the sub-page errata. Sadly this link is missing now - and the page on errata doesn't seem to be up-to-date.
- I didn't look into the erratum in detail, but I suspect that the theorem Given a uniform distribution over targets of cardinality k, and baseline uniform distribution, the average active information will be non-positive should be phrased more trivially as Given a uniform distribution over targets of cardinality k, and baseline uniform distribution, the average active information will be zero