Wednesday, June 17, 2015

Responding to Dr. Ewert

I’ve added the following to A Question for Winston Ewert at The Skeptical Zone.

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 [Elizabeth Liddle] 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.)

Wednesday, June 3, 2015

At least a hint, Dr. Ewert?

Posted in The Skeptical Zone.

I repeat my invitation to Dr. Winston Ewert to join us here for discussion of several questions I raised. It helps immensely to display mathematical formulas, rather than talk about them vaguely. However, he has replied at Uncommon Descent, where that is impossible. I’m genuinely astonished to see:

Thursday, May 14, 2015

A better reason for Dr Ewert to enter The Skeptical Zone



Tuesday, May 12, 2015

At The Skeptical Zone: A question for Winston Ewert

I’ve invited Winston Ewert to join a technical discussion at The Skeptical Zone. I do solemnly vow to keep it perfectly civil. It would be better to comment there than here. But suit yourself.

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).


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?



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.

Sunday, March 29, 2015

Deobfuscating a theorem of Ewert, Marks, and Dembski

Back in July, I found that I couldn’t make heads or tails of the theorem in a paper by Winston Ewert, Robert J. Marks II, and William A. Dembski, On the Improbability of Algorithmic Specified Complexity. As I explained,

The formalism and the argument are atrocious. I eventually decided that it would be easier to reformulate what I thought the authors were trying to say, and to see if I could generate my own proof, than to penetrate the slop. It took me about 20 minutes, working directly in LaTeX.
I posted a much improved proof, but realized the next day that I’d missed something very simple. With all due haste, here is that something. The theorem is best understood as a corollary of an underwhelming result in probability.

The simple

Suppose that $\mu$ and $\nu$ are probability measures on a countable sample space $\Omega$, and that $c$ is a positive real number. What is the probability that $\nu(x) \geq c \cdot \mu(x)$? That’s a silly question. We have two probabilities of the event \[ E = \{x \in \Omega \mid \nu(x) \geq c \cdot \mu(x) \}. \] It’s easy to see that $\nu(E) \geq c \cdot \mu(E)$ when $\nu(x) \geq c \cdot \mu(x)$ for all $x$ in $E$. The corresponding upper bound on $\mu(E)$ can be loosened, i.e., \begin{equation*} \mu(E) \leq \frac{\nu(E)}{c} \leq \frac{1}{c}. \end{equation*} Ewert et al. derive $\mu(E) \leq c^{-1}$ obscurely.

The information-ish

To make the definition of $E$ information-ish, assume that $\mu(x) > 0$ for all $x$ in $\Omega$, and rewrite \begin{align} \nu(x) &\geq c \cdot \mu(x) \nonumber \\ \nu(x) / \mu(x) &\geq c \nonumber \\ \log_2 \nu(x) - \log_2 \mu(x) &\geq \alpha, \end{align} where $\alpha = \log_2 c$. This lays the groundwork for über-silliness: The probability of $\alpha$ or more bits of some special kind of information is at most $2^{-\alpha}$. This means only that $\mu(E) \leq c^{-1} = 2^{-\alpha}.$

The ugly

Now suppose that $\Omega$ is the set of binary strings $\{0, 1\}^*$. Let $y$ be in $\Omega$, and define an algorithmic probability measure $\nu(x) = 2^{-K(x|y)}$ for all $x$ in $\Omega$. (I explained conditional Kolmogorov complexity $K(x|y)$ in my previous post.) Rewriting the left-hand side of Equation (1), we obtain \begin{align*} \log_2 2^{-K(x|y)} - \log_2 \mu(x) &= -\!\log_2 \mu(x) - K(x|y) \\ &= ASC(x, \mu, y), \end{align*} the algorithmic specified complexity of $x$. Ewert et al. express an über-silly question, along with an answer, as \[ \Pr[ASC(x, \mu, y) \geq \alpha] \leq 2^{-\alpha}. \] This is ill-defined, because $ASC(x, \mu, y)$ is not a random quantity. But we can see what they should have said. The set of all $x$ such that $ASC(x, \mu, y) \geq \alpha$ is the event $E$, and $2^{-\alpha} = c^{-1}$ is a loose upper bound on $\mu(E)$.

Tuesday, March 10, 2015

Tolstoy on the studious deceit of children by the church





Sunday, September 28, 2014

Would E.T. notice an icon of ID creationism?




Photo by Volkan Yuksel (cropped).






"Mountfujijapan" by Swollib

Special Added Bonus Feature: Creationist Persecution Fantasy

Thursday, September 25, 2014

Response to Denyse O’Leary at Salvo


Dembski did not invent the underlying idea of conservation of information. Biologist Peter Medawar (1980s) and computer scientist Tom English (1996) advanced the view that information is not created from scratch but rather is redistributed from existing sources. Robert Marks II and his students at Baylor University in Texas have developed the idea in terms of search, and their approach has profound consequences for plausible ideas of how evolution occurs, especially when vast claims are made for WEASEL and other evolution computer programs. As we will see in Part II, they are smuggling in information in order to arrive at their target.

Ms. O’Leary, my 1996 formulation of "search" was needlessly complicated. With simplification, search is clearly a process of sampling a set of alternatives (which Dembski and Marks refer to as the sample space). To my huge embarrassment, conservation of information turns out to be nothing but obfuscation of statistical independence — a concept that undergraduates encounter early in introductory courses on probability and statistics. There can be no conservation of information in random selection of a sample because there is no information whatsoever. It is absurd to speak of conserving what does not exist.

If samplers have no information about the samples they draw, then how do we account for the fact that sampler (search) A is more likely than sampler B to select a sample that includes at least one element of the target (to hit the target)? There is not the least mystery here. Samplers differ in their biases. That is the gist of why I was wrong to indicate in 1996 that information somehow resides in samplers, and why Dembski and Marks are wrong to do so today.



P.S.—Note that much of the misunderstanding is attributable to misnaming. I know that Ms. O’Leary appreciates the powerful impact of language upon thought. If you refer to the process of sample selection as search, designate a particular subset of the sample space as the target, and say that the selection process hits the target when the sample includes an element of the subset, then you will have a very hard time thinking straight about sampling.

Wednesday, September 24, 2014



