Added June 17, 2015: Jump in with whatever comments you like, folks. Dr. Ewert has responded nebulously at Uncommon Descent. I’d have worked with him to get his meaning straight. I’m not going to spend my time on deconstruction. However, I will take quick shots at some easy targets, mainly to show appreciation to Lizzie for featuring this post as long as she has. Here, again, is what I put to Dr. Ewert:

Your “search” process decides when to stop and produce an outcome in the “search space.” A model may do this, but biological evolution does not. How do you measure active information on the biological process itself? Do you not reify a model?

Dr. Ewert seemingly forgets that to measure active information on a biological process is to produce a specific quantity, e.g., 109 bits.

One approach is to take the search space not to be the individual organisms, but rather the entire population of organisms currently alive on earth. Or one could go further, and take it to be the history of organisms during the whole of biological evolution. One could also take it to be possible spacetime histories. The target can then be taken to be spacetimes, histories, or populations that contain an individual organism type such as birds.

These “search spaces” roll off the tongue. But no one knows, or ever will know, what they actually contain. Even if we did know, no one would know the probabilities required for calculation of the active information for a given target. And even if we did know the probability of a given “target” for a given “search,” we would not be able to justify designating a particular probability distribution on the search space as the “natural” baseline. By the way, Dr. Ewert should not be alluding to infinite sets, as his current model of search applies only to finite sets.

Another possibility is to model evolution as a process which halts upon finding the target, but distinguish between the active information derived from the evolutionary process itself and the active information contributed by the stopping behavior. The stopping behavior cannot induce birds to show up in the first place, it can only select them as the output of the search when they arrive. By looking at the number of opportunities for birds to arise, we can determine how much active information was added by the stopping process. It was shown in “Conservation of Information in Search: Measuring the Cost of Success” that the active information available from such a process is only the logarithm of the number of queries. Any other active information must derive from the evolutionary search itself.

Dembski and Marks define search differently in the cited paper than Dembski, Ewert, and Marks do. The result that Dr. Ewert invokes does not apply to the active information of a search, as presently defined. With the current definition, we can specify a process that goes through elements of the finite search space, one by one, until it recognizes an element of the target. Then the active information of the process is due almost entirely to recognition of the target by the “stopping process.” I hope this gives you some idea of what’s wrong with Ewert’s claim. Perhaps one of the cognoscenti will supply more of the details in a comment.

Both approaches effectively end up adjusting for the number of trials. Getting a royal flush is improbable, but if you play five million hands of poker it is no longer surprising. Similarly, obtaining a bird is rendered much more probable given the number of chances for it happen in the history of universe. It is a very important point to keep in mind that we cannot simply look at the probability of the individual events but also the number of trials.

Dr. Ewert errs, and has brought to the fore a major weakness of the current definition of search. Here the search space is the set of all five-card poker hands, and the target is the subset containing the royal-flush hands. A search that halts after one step and yields a royal flush with probability 1/2 has exactly the same active information as a search that yields a royal flush with probability 1/2 after five million or fewer steps. In short, a “very important point to keep in mind” is that the number of trials actually does not enter into the calculation of active information.

For birds to have been produced by an evolutionary process, the universe must have been biased towards producing birds.

Must the universe have been biased against producing “flying insects that walk on all fours”? (This is not a cheap dig at religion, but instead a substantive response to Robert “Saying the Bible is not a book about science is like saying a cookbook is not a book about chemistry” Marks. I had forgotten Leviticus 11:20 until I Googled for scientific discussion of why there are no four-legged insects.)

The original post follows.

I actually have three technical questions for Winston, but plan on one post apiece. He should respond first to questions he receives through Google Moderator, including those from DiEb, who has added a relevant post to his blog. Hopefully he will join us here when he’s done with that.

Let’s be clear from the outset that off-topic remarks go straight to Guano. (If you attack Winston personally while I am trying to draw him into a discussion of theory, then I will take it personally.) You shouldn’t make claims unless you have read, and believe that you mostly understand, the material in all three sources in note 3, apart from the proofs of theorems. Genuine requests for explanation are, of course, welcome. They’re especially welcome if you’ve made a genuine effort to get what you can from the sources.

The overall thrust of my questions should be clear enough to Winston, though it won’t be to most readers. I’m definitely not laying a trap for him. The first two questions have answers that are provably right or wrong. The third is more a matter of scientific modeling than of math. I’m starting with it because TSZ isn’t yet configured to handle embedded LaTeX (mathematical expressions).

Questions
[We discuss only the highlighted question in this thread.]

1. What is the formal relationship between active information and specified complexity?

2. What is the formal relationship between active information and average active information per query? Does the conservation-of-information theorem apply to the latter?

3. Your “search” process decides when to stop and produce an outcome in the “search space.” A model may do this, but biological evolution does not. How do you measure active information on the biological process itself? Do you not reify a model?

Notes
[Numbered to indicate correspondence to the questions.]

1. There’s an answer that covers both Dembski’s 2005 version (the probabilistic complexity minus the descriptive complexity of the target) and the algorithmic version of specified complexity. For the latter, it’s apparently necessary to restrict the target (no longer called a target) to a single-element set.

2. The conservation-of-information theorem applies to active information. Winston and his colleagues have measured only average active information per query (several closely related forms, actually), which seems unrelated to active information, in their analyses of computational evolution and metabiology. Yet they refer to “conservation of information” in exposition of those analyses.

3. The “search” process of Dembski, Ewert, and Marks terminates, and generates an outcome. The terminator and the discrim­inator of the “search” in fact contribute to its “active information” — bias, relative to a baseline distribution on outcomes, in favor of a “target” event. However, biological evolu­tion has not come to a grinding halt, and has not announced, for instance, “Here it is — birds!” It seems that Winston, in his ENV response to a Panda’s Thumb post by Joe Felsenstein and me, tacitly assumes that a biologist has provided a model that he can analyze as a “search,” and imputes to nature itself the bias that he would measure on the model of nature. If so, then he erroneously treats an abstraction as though it were something real. Famously, “The map is not the territory.” Perhaps Winston can provide a good argument that he hasn’t lapsed into reification.