ID creationist “scholarship” sinks to new depths

[Edit: I regret turning nasty here. See the comments section for something rather more kind I would say to Winston Ewert.]

I mentioned a couple posts ago that I was annoyed with the editors and reviewers of an article, apparently to be published in an IEEE journal, by Winston Ewert, William Dembski, and Robert J. Marks II. [Edit 9/18/2014: Marks has removed the paper from his website. The IEEE Transactions on Systems, Man, and Cybernetics presently offers "Algorithmic Specified Complexity in the Game of Life" as a preprint.] Although I focus on the authors here, it will be clear enough what the folks responsible for quality control, including those on Ewert’s dissertation committee at Baylor, should have done. The short version is that, Googling obvious keywords, it takes at most a minute to discover that prior work, of which the authors claim to have no knowledge, exists in abundance.

Before continuing, I want to emphasize that my response to ID creationism is anything but knee-jerk. Consider, if nothing else, that the way I dealt with a dubious theorem supplied by Ewert et al. was to attempt to prove it. I not only succeeded in doing so, but supplied the proof here. I have since proved a fundamental theorem that some might take as advancing ID theory, though I see it otherwise.

Back to the article. There is no way around concluding that the veterans, Dembski and Marks, are either incompetent or dishonest. (You can guess which way I lean from a subtitle I’ve considered for this blog: Truth Is the First Casualty of Culture War.) And Youngman Ewert is either lazy, dishonest, or intellectually hobbled. (I see many signs of hero worship and true-believerism.)

You need no clear idea of what information theory is to grasp the significance of Dembski allowing himself to be promoted as the “Isaac Newton of information theory.” Marks edited a volume on engineering applications of information theory. The two have repeatedly cited standard texts that I own, but have not studied thoroughly. I am not an information theorist. So how is it that I should be thunderstruck by a flatly incorrect statement in the second sentence of the abstract, and then be floored by an intensification of it in the second paragraph of the text?

You may think that you are unqualified to judge whether Ewert, Dembski, and Marks are right or wrong. But Google Scholar settles the matter unequivocally. That is what makes the falsehood so atrocious. The authors state in the introduction:

Both Shannon [1], [2] and Kolmogorov-Chaitin-Solomonoff (KCS)¹ [2]-[9] measures of information are famous for not being able to measure meaning. [...] We propose an information theoretic method to measure meaning. To our knowledge, there exists no other general analytic model for numerically assigning functional meaning to an object.

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¹Sometimes referred to as only Kolmogorov complexity or Kolmogorov information.

My immediate thoughts, incomprehensible to most of you, but eminently sensible to many who’ve had a course in information theory, were Kolmogorov structure function and Kolmogorov sufficient statistic. I first learned about Kolmogorov complexity from a chapter in reference [2]: Cover and Thomas, Elements of Information Theory. See Section 14.12, “Kolmogorov Sufficient Statistic.” If Dembski and Marks do not understand the relevance, then they are incompetent. If they do, then they are dishonest.

Back to Google. And to Ewert. And to Baylor. The article clearly draws on Ewert’s dissertation, which had better include a chapter with a title like “Literature Review.” Actually, his dissertation proposal should have surveyed the relevant literature. A scholar should comprehend a body of knowledge before trying to extend it — right? Let’s make the relatively charitable assumptions that Ewert, though presuming to make a fundamental contribution to information theory, never took a course in information theory, and failed to grasp some aspects of the introduction to Kolmogorov complexity in Cover and Thomas. He nonetheless had obvious keywords to enter into Google Scholar. There are 41,500 results for the unclever search

meaningful information Kolmogorov.

(The term meaning is too general, and meaningful is the last word of the first sentence in the abstract.) Close to the top are two articles by Paul Vitányi, both entitled “Meaningful Information.” With the search narrowed to

"meaningful information" Kolmogorov,

there are about 1,310 results. This is what I did first. I immediately went to the more recent of Vitányi's articles, because he’s a prominent researcher in Kolmogorov complexity, and also the coauthor of the standard text on the topic (reference [24] in Ewert et al.). I have highlighted key phrases in the abstract for those of you who don’t care to grapple with it.

Abstract—The information in an individual finite object (like a binary string) is commonly measured by its Kolmogorov complexity. One can divide that information into two parts: the information accounting for the useful regularity present in the object and the information accounting for the remaining accidental information. There can be several ways (model classes) in which the regularity is expressed. Kolmogorov has proposed the model class of finite sets, generalized later to computable probability mass functions. The resulting theory, known as Algorithmic Statistics, analyzes the algorithmic [Kolmogorov] sufficient statistic when the statistic is restricted to the given model class. However, the most general way to proceed is perhaps to express the useful information as a total recursive function. The resulting measure has been called the “sophistication” of the object. We develop the theory of recursive functions statistic, the maximum and minimum value, the existence of absolutely nonstochastic objects (that have maximal sophistication—all the information in them is meaningful and there is no residual randomness), determine its relation with the more restricted model classes of finite sets, and computable probability distributions, in particular with respect to the algorithmic (Kolmogorov) minimal sufficient statistic, the relation to the halting problem and further algorithmic properties.

So what are you up to in this paper, Dr. Ewert? When you feed us the “to our knowledge” guano, knowingly creating the misimpression that you tried to acquire knowledge, you are essentially lying. You have exaggerated the significance of your own work by failing to report on the prior work of others. I doubt highly that you are capable of understanding their work. Were you so inept as to not Google, or so deceitful as to sweep a big mound of inconvenient truth under the rug? Assuming the former, you need to catch on to the fact that your “maverick genius” coauthors should have known what was out there.

Proving a theorem of Ewert, Marks, and Dembski

[Edit: This post essentially does right what Ewert, Dembski, and Marks did wrong. I’ve since shown that the theorem follows from a very simple result in probability.]

In what appears to be a forthcoming journal article [published version], ID creationists Winston Ewert, William Dembski, and Robert J. Marks II state a formal result, and justify it merely by citing a three-page paper in the proceedings of a symposium. I was already annoyed with the reviewers and the editors for missing a huge defect, and decided to while away the sleepless hours by checking the putative proof in On the Improbability of Algorithmic Specified Complexity.

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. Then I decided to provide some explanation that is missing in the paper.

The theorem is correct. As Ewert, Marks, and Dembski put it, "The probability of obtaining an object exhibiting $\alpha$ bits of [algorithmic specified complexity] is less than or equal to $2^{-\alpha}$." It is something that they can establish a property like this. But algorithmic specified complexity is a sum of bits of Shannon self-information and bits of Kolmogorov complexity, which seem like apples and oranges to me.

I should mention that the result probably comes from Ewert's doctoral dissertation, Algorithmic Specified Complexity, still under wraps at Baylor. Evidently Dembski, a mathematician, did not edit the paper.

The following makes more sense if you read Sections I and II of the paper. Those of you with a bit of math under your belts will be amazed by the difference.

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$\newcommand{\suppmu}{\mathrm{supp}(\mu)} \newcommand{\B}{\mathcal{B}} \newcommand{\X}{\mathcal{X}} \renewcommand{\S}{\mathcal{S}} \newcommand{\P}{\mathcal{P}} \newcommand{\Bprime}{\mathcal{B}^\prime}$The set of all strings (finite sequences) on $\B = \{0, 1\}$ is $\B^*.$ Assume that the binary encoding $e: \S \rightarrow \B^*$ of the set $\S$ of objects of interest is 1-to-1. This allows use of the set of codewords $e(\S)$ in place of $\S.$

The set of all programs $\P$ for universal computer $U$ is a prefix-free subset of $\B^*.$ That is, no program is a proper prefix of any other. The conditional Kolmogorov complexity $K(x|y)$ is the length $\ell(p)$ of the shortest program $p$ that outputs $x$ on input of $y,$ i.e., \[ K(x|y) = \hspace{-0.3em} \min_{p : U(p, y) = x} \hspace{-0.4em} \ell(p). \] The Kraft inequality \[ \sum_{x \in \X} 2^{-\ell(x)} \leq 1 \] holds for all prefix-free sets $\X \subset \B^*,$ including the prefix-free set of programs $\P.$ It follows that for all $\X \subseteq \B^*,$ \[ \sum_{x \in \X} 2^{-\!K(x|y)} \leq \sum_{p \in P} 2^{-\ell(p)} \leq 1, \] where $y$ is a string in $\B^*.$ In the first sum, all terms correspond to distinct programs, and each exponent $-\!K(x|y)$ is the negative length of a program that outputs $x$ on input of $y$.

Theorem 1. Let $\mu$ be a probability measure on encoded objects $e(\S).$ Also let \[ X = \{x \in \suppmu \mid -\!\log_2 \mu(x) - K(x | y) \geq \alpha\}, \] where $y$ is a string in $\B^*$ and $\alpha \geq 0.$ Then $\mu(X) \leq 2^{-\alpha}.$

Proof. Rewrite the property of string $x$ in $X$ to obtain a bound on $\mu(x):$ \begin{align*} -\!\log_2 \mu(x) - K(x | y) &\geq \alpha \\ \log_2 \mu(x) + K(x | y) &\leq -\alpha \\ \log_2 \mu(x) &\leq -\alpha - K(x | y) \\ \mu(x) &\leq 2^{-\alpha - K(x | y)}. \end{align*} Applying the bound, \begin{align*} \mu(X) &= \sum_{x \in X} \mu(x) \\ &\leq \sum_{x \in X} 2^{-\alpha -K(x | y)} \\ &= \sum_{x \in X} 2^{-\alpha} \cdot 2^{-K(x | y)} \\ &= {2^{-\alpha} \sum_{x \in X} 2^{-K(x | y)}} \\ &\leq 2^{-\alpha}. \end{align*} The last step follows by the Kraft inequality. Q.E.D.

Bronowski, Michelangelo, Moore, and Einstein

I'm watching Jacob Bronowski's documentary series The Ascent of Man. You'll find in the following transcript a better account of how sculpture takes form than you'll get from any intelligent-design theorist. The notion that there's an independent design that the sculptor forces upon the stone is simply wrong. But to dwell on that would be to miss what Bronowski emphasizes, an interesting analogy of science to sculpture. On reflection, I saw the similarity of his remarks to some by Einstein, which I quote below. Hopefully someone out there will find the connection interesting.

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BRONOWSKI: A popular cliche in philosophy says that science is pure analysis or reductionism, like taking the rainbow to pieces, and art is pure synthesis — putting the rainbow together. This is not so. All imagination begins by analysing nature. Michelangelo said that.

When that which is divine in us doth try
    To shape a face, both brain and hand unite
    To give, from a mere model frail and slight,
    Life to the stone by Art's free energy.

BRONOWSKI: The material asserts itself through the hand and thereby prefigures the shape of the work for the brain. The sculptor, as much as the mason, feels for the form within nature.

The best of artists hath no thought to show
    Which the rough stone in its superfluous shell
    Doth not include: to break the marble spell
    Is all the hand that serves the brain can do.

[TOM: See Sonnets XIV and XV here.]

BRONOWSKI: By the time Michelangelo carved the head of Brutus, other men quarried the marble for him. But Michelangelo had begun as a quarryman in Carrara and he still felt that the hammer in their hands, and in his, was groping in the stone for a shape that was already there. The quarrymen work in Carrara now for the modern sculptors who come here — Marino Marini, Lipschitz and Henry Moore. Their descriptions of their work are not as poetic as Michelangelo's, but they carry the same feeling.

HENRY MOORE: To begin with, as a young sculptor, I couldn't afford expensive stone. And I got my stone by going round the stone yards, and finding what they would call a random block. Then I had to think in the same way that Michelangelo might have done, so that one had to wait until an idea came that fitted the shape of the stone. And that was seeing the idea in that block.

BRONOWSKI: Of course, it can't be literally true that what the sculptor imagines and carves out is already there, hidden in the block. And yet the metaphor tells the truth about the relation of discovery that exists between man and nature. In one sense, everything that we discover is already there. A sculptured figure and the law of nature are both concealed in the raw material. And in another sense, what a man discovers is discovered by him. It would not take exactly the same form in the hands of someone else. Neither the sculptured figure nor the law of nature would come out in identical copies when produced by two different minds in two different ages. Discovery is a double relation of analysis and synthesis together. As an analysis it probes for what is there. But then, as a synthesis, it puts the parts together in a form in which the creative mind transcends the bare limits, the bare skeleton that nature provides.

BRONOWSKI: Sculpture is a sensuous art. The Eskimos make small sculptures that are not even meant to be seen, only handled. So it must seem strange that I choose as my model for science sculpture and architecture. And yet it's right. We have to understand that the world can only be grasped by action, not by contemplation. The hand is more important than the eye. We are not one of those contemplative civilisations of the Far East or the Middle Ages that believed that the world has only to be seen and thought about and who practised no science. We are active, and indeed we know in the evolution of man, that it is the hand that drives the subsequent evolution of the brain. We find tools made by man before he became man. Benjamin Franklin called man the "tool-making animal." And that's right. And the most exciting thing about that is that even in prehistory, man already made tools that have an edge finer than they need have.

[TOM: I've cleaned up this transcript.]

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EINSTEIN: The reciprocal relationship of epistemology and science is of noteworthy kind. They are dependent upon each other. Epistemology without contact with science becomes an empty scheme. Science without epistemology is — insofar as it is thinkable at all — primitive and muddled. However, no sooner has the epistemologist, who is seeking a clear system, fought his way through to such a system, than he is inclined to interpret the thought-content of science in the sense of his system and to reject whatever does not fit into his system. The scientist, however, cannot afford to carry his striving for epistemological systematic that far. He accepts gratefully the epistemological conceptual analysis; but the external conditions, which are set for him by the facts of experience, do not permit him to let himself be too much restricted in the construction of his conceptual world by the adherence to an epistemological system. He therefore must appear to the systematic epistemologist as a type of unscrupulous opportunist: he appears as realist insofar as he seeks to describe a world independent of the acts of perception; as idealist insofar as he looks upon the concepts and theories as the free inventions of the human spirit (not logically derivable from what is empirically given); as positivist insofar as he considers his concepts and theories justified only to the extent to which they furnish a logical representation of relations among sensory experiences. He may even appear as Platonist or Pythagorean insofar as he considers the viewpoint of logical simplicity as an indispensable and effective tool of his research. [Wikiquote]

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BOUNDED SCIENCE: There can be no scientific explanation of science.

Black-box “optimization” is merely sampling

[Edit: The replacement is here at last. There have been many visits to this page since I retracted the post. I apologize to those who have been waiting.]

The main points of this post were correct, but the math contained some errors. I am working on a replacement.

Dembski’s perennial misconception of fitness

DiEb has begun a response to the latest morph of the creationist model of “search” (Dembski, Ewert, and Marks, “A General Theory of Information Cost Incurred by Successful Search” [pdf]). Here, slightly modified, is a rather general comment I made.

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In the conventional “no free lunch” analytic framework, the objective (cost, fitness) function is a component of the problem. Dembski, Ewert, and Marks turn the objective function into an “oracle” that is part of the problem-solver itself. This model is inappropriate to most, if not all, of the evolutionary computations they purport to have analyzed.

Back in the 1990’s, Dembski committed himself to the misconception that Richard Dawkins’ Weasel program uses the fitness function in order to “hit the target.” Various people have tried, with no apparent success, to explain to him that one of the offspring in each generation survives because it is the most fit. The so-called target is nothing but the fittest individual.

To put it simply, the fitness function comes first. The “target” is defined in terms of the fitness function. Dembski gets this backwards. He believes that the target comes first, and that the fitness function is defined in terms of the target.

Dembski and Marks carry this to extreme in “Life's Conservation Law.” They claim that biological targets exist implicitly in nature, and that if Darwinian evolution “hits” them, then fitness functions necessarily have guided evolution. A remarkable aspect of this claim is that they treat fitness functions, which are abstractions appearing in mathematical models of evolution, as though they really exist.

The “search for a search” is another abstraction that they reify. A probability measure on the sample space is a mathematical abstraction. They merely assert that a search practitioner, in selecting a search, searches the uncountably infinite set of probability measures. To that I say, “Give me a physical description of the process.”

Open access to Biological Information: New Perspectives

I previously raised an eyebrow at an editor of Springer’s “Intelligent Systems Reference Library,” in which the creationist volume Biological Information: New Perspectives (eds. Robert J. Marks II, Michael J. Behe, William A. Dembski, Bruce L. Gordon, and John C. Sanford) was scheduled to appear. The proceedings of the secret scientific symposium of scientists and “scientists”…

In the spring of 2011 a diverse group of scientists gathered at Cornell University with an eye on the major new principles that might be required to unravel the problem of biological information. These scientists included experts in information theory, computer science, numerical simulation, thermodynamics, evolutionary theory, whole organism biology, developmental biology, molecular biology, genetics, physics, biophysics, mathematics, and linguistics. Original scientific research was presented and discussed at this symposium, which was then written up, and constitute most of the twenty-four peer-edited papers in this volume.

… (did I mention science?) that took place at, but not under the auspices of, Cornell University have migrated to World Scientific. You can read the volume online, free of charge.

The big surprise is that “Section Four: Biological Information and Self-Organizational Complexity Theory” comprises two dissenting papers, one by Stuart Kauffman (whose views on many things are similar to my own), and the other by Bruce H. Weber. Although editor Gordon is none too clear on the matter in his introduction to the section, it appears that Kauffman and Weber actually contributed to a previous secret meeting, the proceedings of which were never published.

Their involvement in this project traces back to a 2007 conference I organized in Boston under the auspices of the Discovery Institute’s Center for Science and Culture. The conference commemorated the famous 1967 Wistar Symposium on “Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution.” [...] The general perception among the participants in the Boston symposium, as with the participants in the Cornell University conference giving rise to this compendium, is that the mathematical and biological challenges posed to the modern evolutionary synthesis (neo-Darwinism) have not been resolved, but actually have grown more acute as our knowledge of molecular biology, cell biology, developmental biology, and genetics has exploded.

Gee, that sounds like “these guys are on our side.” But here’s the second half of Weber’s abstract:

Presently, however, there is ferment in the Darwinian Research Tradition as new knowledge from molecular and developmental biology, together with the deployment of complex systems dynamics, suggests that an expanded and extended evolutionary synthesis is possible, one that could be particularly robust in explaining the emergence of evolutionary novelties and even of life itself. Critics of Darwinism need to address such theoretical advances and not just respond to earlier versions of the research tradition.

So Gordon contradicts Weber while trying to paint him as an ally. He makes a fine point of the inadequacy of the “modern evolutionary synthesis (neo-Darwinism),” which is hardly where Darwinian evolutionary theory stands today. Kauffman highlights in his abstract the essential reason that the information measures of Dembski and Marks go nowhere in biology.

Biological evolution rests on both quantum random and classical non-random natural selection and whole-part interactions that render the sample space of adjacent biological possibilities unknowable.

I’ve heard him put it more simply: We don’t know the phase space. This means that it is impossible to assign probabilities to evolutionary trajectories. And taking logarithms of probabilities is how Dembski and Marks get information.

I wrote “scientists and ‘scientists’” above because only two of the five editors are scientists, and because engineers, computer scientists, and mathematicians have contributed heavily.

Unsurprisingly, about half of the “new perspectives” are variations on old themes of why evolution doesn’t work. John C. Sanford, a young-earth creationist who believes that genomes have been going to hell in a handbasket since the Fall of Man, authored seven of the papers and one of the section introductions. Dembski, Marks, Montañez and Ewert continue to bash evolutionary computation, including artificial life.

Jonathan Wells shocks us by reporting, “Not Junk After All: Non-Protein-Coding DNA Carries Extensive Biological Information.” Other papers show that the genetic code is fine-tuned, and furthermore that DNA sequences and computer code look much alike, with appropriate visualization. I’m sure there are other sensations to be found on closer inspection of the volume.

Oppose the Scientific Education and Academic Freedom Act

The Common Education Committee of the Oklahoma House of Representatives will consider House Bill 1674 on Tuesday, February 19 at 10:30 a.m. Here I make it easy for Oklahomans who use a mail application to contact the committee members. Those of you who contacted the Senate Education Committee regarding the Oklahoma Science Education Act (Senate Bill 758) can quickly modify your note to apply to HB 1674. (Do please oppose SB 758, which has not yet been scheduled for consideration.)

The National Center for Science Education has provided background information on both the Senate and the House bills. The Oklahomans for Excellence in Science Education have analyzed HB 1674 [PDF].

My characterization of how the bills are related: SB 758 is essentially HB 1674 stripped of motivation, indications of legislative intent, examples of "scientific controversy," and the requirement that students learn what is in the curriculum. The author of HB 1674, Rep. Gus Blackwell, has in fact become a coauthor of SB 758.

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House Common Education Committee

Clicking on a link below creates an email note that begins with a personalized salutation, e.g., "Dear Representative Coody." You need only paste in the rest of the note, and then send it. (Contact Rep. Blackwell only if you live in District 61.) Please be brief and respectful. Include your full name and street address.

HT: Oklahomans for Excellence in Science Education.

Name	Position	Phone	Email
Ann Coody	Chair	557-7398	anncoody@okhouse.gov
Dennis Casey	Vice Chair	557-7344	dennis.casey@okhouse.gov
Gus Blackwell	Member	557-7375	gusblackwell@okhouse.gov
Ed Cannaday	Member	557-7375	ed.cannaday@okhouse.gov
Donnie Condit	Member	557-7376	donnie.condit@okhouse.gov
Doug Cox	Member	557-7415	dougcox@okhouse.gov
Lee Denney	Member	557-7304	leedenney@okhouse.gov
Dale DeWitt	Member	557-7332	daledewitt@okhouse.gov
Curtis McDaniel	Member	557-7363	curtis.mcdaniel@okhouse.gov
Jeannie McDaniel	Member	557-7334	jeanniemcdaniel@okhouse.gov
Jason Nelson	Member	557-7335	jason.nelson@okhouse.gov
Jadine Nollan	Member	557-7390	jadine.nollan@okhouse.gov
Dustin Roberts	Member	557-7366	dustin.roberts@okhouse.gov
Jason Smalley	Member	557-7368	jason.smalley@okhouse.gov
Todd Thomsen	Member	557-7336	todd.thomsen@okhouse.gov
Emily Virgin	Member	557-7323	emily.virgin@okhouse.gov

Oppose the Oklahoma Science Education Act

Oklahoma’s Senate Education Committee will consider yet another “science education” bill introduced by Senator Josh Brecheen. Below, I make it easy to contact members of the committee. You can learn about the history of Senator Brecheen and the ancestry of Senate Bill 758 here. The Oklahomans for Excellence in Science Education provide an analysis, "Why SB 758 by Brecheen is a Bad Bill."

Synopsis of SB 758

The science curriculum addresses "scientific controversies." All school boards and administrators must

1. try to help teachers find effective ways to teach about scientific controversies;
2. try to encourage science students not only to engage in traditional learning, but also to "respond appropriately and respectfully to differences of opinion about controversial issues;" and
3. permit teachers to instruct pupils in "scientific strengths and scientific weaknesses of existing scientific theories covered in the course being taught."

This has nothing to do with promotion of religion, non-religion, etc.

Comments

The phrases "scientific controversies" and "scientific strengths and scientific weaknesses of existing scientific theories covered in the course" appear in adjacent sentences, but the bill actually does not connect the two. The restriction in scope of "strengths and weaknesses" does not apply to "scientific controversies." Thus a teacher might regard "intelligent design vs. Darwinism" as a scientific controversy, even though intelligent design is not a theory covered in the course. There is no "scientific" qualifier of the "controversial issues" on which students have "differences of opinion." A teacher might feel compelled to allow debate after a student brings up creationism.

The bill neither defines nor identifies "scientific controversies," but asserts that the science curriculum already addresses them, and requires that administrators help teachers present them effectively. This shrewdly establishes that teaching effectiveness is an issue. Administrators may evaluate teachers on their handling of "scientific controversies," as well as their moderation of student debate. Thus administrators have the power to identify controversies that an effective teacher should address, and also the power to specify that effective teaching of them requires presentation of certain "strengths and weaknesses" of theories.

Teachers are free to impose nonstandard "strengths and weaknesses" instruction on students, even in cases where administrators do not recommend it. Although a principal might respond legitimately by assigning a low performance rating to a teacher, the legal risk in doing so would be high. Then again, the teacher might also place the local school district at risk of lawsuit. If enacted, the bill would put some school administrators between rocks and hard places.

The guts of the bill

The five paragraphs of Section 2 contain the substance of the bill. I have quoted them here, and added emphasis.

A. The State Board of Education, school district boards of education, school district superintendents and school principals shall endeavor to create an environment within public school districts that encourages students to explore scientific questions, learn about scientific evidence, develop critical thinking skills and respond appropriately and respectfully to differences of opinion about controversial issues.

Start by requiring public schools to do what they already are required to do, and in fact do. Then indicate that civil debate of "controversial issues" belongs in science class. The omission of scientific here must be intentional, as repetitiously as it is used elsewhere.

B. The State Board of Education, school district boards of education, school district superintendents and school principals shall endeavor to assist teachers to find effective ways to present the science curriculum as it addresses scientific controversies. Teachers shall be permitted to help students understand, analyze, critique and review in an objective manner the scientific strengths and scientific weaknesses of existing scientific theories covered in the course being taught.

Posit that the curriculum already addresses "scientific controversies," without making it clear what they are. Open up opportunity for school boards and administrators to change instruction top-down, and for individual teachers to make radical changes at the classroom level.

C. Neither the State Board of Education, nor any school district board of education, school district superintendent or school principal shall prohibit any teacher in a public school district in this state from helping students understand, analyze, critique and review in an objective manner the scientific strengths and weaknesses of existing scientific theories covered in the course being taught.

"This means you!"

D. This section only protects the teaching of scientific information and shall not be construed to promote any religious or non-religious doctrine, promote discrimination for or against a particular set of religious beliefs or non-beliefs or promote discrimination for or against religion or non-religion.

"Ignore that creationist behind the curtain. We are the mighty Legislature!"

E. By no later than the start of the 2013-2014 school year, the State Department of Education shall notify school district boards of education and school district superintendents of public schools in the state of the provisions of this act. Each school district board of education and school district superintendent shall notify all employees within the school district of the provisions of this act.

"Glad tidings to all — nurses, cooks, and janitors!"

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Senate Education Committee

Clicking on one of the links below creates an email note that begins with a personalized salutation, e.g., "Dear Senator Ford." (Contact Senator Brecheen only if you live in his district.) You need only paste in the rest of the note, and then send it. Please be brief and respectful. Include your full name and street address.

Thanks to Oklahomans for Excellence in Science Education for supplying the contact information.

Name	Position	Party	Room	Phone	Email
John Ford	Chair	R	424A	521-5634	fordj@oksenate.gov
Gary Stanislawski	Vice Chair	R	427A	521-5624	stanislawski@oksenate.gov
Josh Brecheen	Member	R	513A	521-5586	brecheen@oksenate.gov
Earl Garrison	Member	D	533	521-5533	whitep@oksenate.gov
Jim Halligan	Member	R	425	521-5572	halligan@oksenate.gov
David Holt	Member	R	411A	521-5636	holt@oksenate.gov
Clark Jolley	Member	R	519	521-5622	jolley@oksenate.gov
Charlie Laster	Member	D	522	521-5539	laster@oksenate.gov
Susan Paddack	Member	D	533A	521-5541	paddack@oksenate.gov
Wayne Shaw	Member	R	513A	521-5574	shaw@oksenate.gov
Ralph Shortey	Member	R	514A	521-5557	shortey@oksenate.gov
John Sparks	Member	D	513B	521-5553	sparks@oksenate.gov
Ron Sharp	Member	R	533	521-5539	sharp@oksenate.gov

The theorem that never was: Diversionary “erratum” from Dembski and Marks

In my last post, I showed that the research program of William A. Dembski and Robert J. Marks II depends on making performance gain in so-called search look like information gain, and calling it active information. It was clear that the misrepresentation arose from severe misunderstanding of the "no free lunch" theorems, not an intent to deceive. I would call it an honest error, if it were not the result of intrinsically dishonest activities — apologetics and culture war.*

Now, unfortunately, I indict both the math and the men. When things like Marks' approval of a master's thesis plagiarizing his and Dembski's publications present themselves to me, I feel honor-bound to report on them. Also, people who know of Marks' considerable technical achievements need to know also that he has, in late career, begun using his reputation and connections to pursue socio-poltical ends. They may want to give him the benefit of the doubt, as I did when he began collaborating with Dembski. This post shows why that's not such a good idea. (And so do this, this, and this.)

There never was a Horizontal No Free Lunch Theorem

In the abstract of "The Search for a Search: Measuring the Information Cost of Higher Level Search," Dembski and Marks write:

We prove two results: (1) The Horizontal No Free Lunch Theorem, which shows that average relative performance of searches never exceeds unassisted or blind searches, and (2) The Vertical No Free Lunch Theorem, which shows that the difficulty of searching for a successful search....

That has the ring of a grand contribution. They've extended the famous "no free lunch" results both horizontally and vertically. Problem is, they knew long before publication of the paper that the statement of the first "theorem" was semantically ill-formed (not even a proposition, let alone a theorem).

How can I say that they knew? The paper was originally scheduled for publication in 2008, in an obscure Polish journal that shut down after two years of operation. Dembski and Marks disseminated the paper themselves, however, after it was accepted, and soon heard of several errors from the mathematically talented D. Eben. I saw not only Eben's detailed criticisms on the Web (e.g., here and here), but also some of the email he sent to Marks. The version of the paper subsequently published in July 2010, in a Japanese open-access journal, includes revisions of arcane mathematics, and acknowledges Eben. But it leaves in place the "theorem" made into gobbledy-gook by an error in sophomore-level discrete math.

Was Marks too dumb to see the mistake, or was he unwilling to dismantle the lovely "horizontal-and-vertical" rhetoric, perhaps believing that he could produce the theorem later? I have never suggested that Marks is anything less than a very bright man.

Dembski and Marks release a diversionary “erratum”

Now, almost two years later, Dembski and Marks have added an erratum to the end of the paper. (Here are Eben's announcement and subsequent discussion of it, along with some of my comments.) They begin by acknowledging the mistake. Then they give a theorem and a corollary that seem, at first blush, to correct those in the original paper. However, they've pulled the old switcheroo. The theorem is actually a lemma, and the corollary is the main result. "Search" is reduced to the utterly uninteresting case of a single draw from the sample space. And, hilariously, the average "active information" in the corollary is undefined. The cause of this is a) correct consideration of insoluble problems, for which expected performance is 0, and b) logarithmic transformation of expected performance to make it into faux information. That is, $\log 0 = -\infty$. Oops.

Dembski and Marks can predicate magical knowledge that the problem has a solution, and make it so that the average "active information" is not always undefined. But there is no way for them to arrange for it always to be defined. As discussed in more detail on Mr. Eben's blog, the "erratum" predicates a condition in which average performance does not depend on the choice of "search" (sampler). Yet the average "active information" varies from 0 to $-\infty$, depending on the "search." This contradicts claims in the paper like this:

If no information about a search exists, so that the underlying measure is uniform, then, on average, any other assumed measure will result in negative active information, thereby rendering the search performance worse than random search.

Yet the "erratum" does nothing to identify and correct this crucial error. Dembski and Marks never had a Horizontal No Free Lunch Theorem, could not possibly have believed that they published one, evidently know that they cannot produce one, and clearly seek to admit to absolutely as little as possible.

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* To get an idea of how Dembski will exploit what he and Marks have published in the next judicial test of public-school instruction in "intelligent design" creationism, see Expert Witness Report: The Scientific Status of Intelligent Design and Rebuttal to Reports by Opposing Expert Witnesses, which he prepared for Kitzmiller v. Dover Area School District (2005). After the trial, Dembski, who had backed out of testifying, dubbed a Flash animation, now heavily redacted, with the judge in the case "represented as a pull-to-speak doll spouting snippets of his decision in a high-pitched voice with added farting noises, and various pro-science advocates... represented as pulling the string."

Marks makes no secret of how he feels about Kitzmiller in the following bait-and-switch guest lecture he gave in "Introduction to Engineering" at Baylor University (Fall 2011). He reads [1:00:00] from the transcript of the trial, supplying a dopey voice for Robert Pennock, who testified on the artificial-life system Avida. Ever so coincidentally, this is followed by a dubbed "OK" in a high-pitched voice.

I hope to devote an entire post to this video: "Academic Freedom Does Not Entail Instructional Freedom." My guess is that program review teams from the Accreditation Board for Engineering and Technology would frown on "the universe is not old enough nor big enough to allow the evolution of complex life" [49:55] indoctrination of freshmen.

Bob Marks grossly misunderstands “no free lunch”

And so does Bill Dembski. But it is Marks who, in a “Darwin or Design?” interview, reveals plainly the fallacy at the core of his and Dembski's notion of “active information.” (He gets going at 7:50. To select a time, it's best to put the player in full-screen mode. I've corrected slips of the tongue in my transcript.)

[The “no free lunch” theorem of Wolpert and Macready] said that with a lack of any knowledge about anything, that one search was as good as any other search. [14:15]

And what Wolpert and Macready said was, my goodness, none of these [“search”] algorithms work as well as [better than] any other one, on the average, if you have no idea what you're doing. And so the question is… and what we've done here is, if indeed that is true, and an algorithm works, then that means information has been added to the search. And what we've been able to do is take this baseline, that all searches are the same, and we've been able to, in cases where searches work, measure the information that is placed into the algorithm in bits. And we have looked at some of the evolutionary algorithms, and we found out that, strikingly, they are not responsible for any creation of information. [14:40]

And according to “no free lunch” theorems, astonishingly, any search, without information about the problem that you're looking for, will operate at the same level as blind search. And that's... It's a mind-boggling result. [28:10]

Bob has read into the “no free lunch” (NFL) theorems what he believed in the first place, namely that if something works, it must have been designed to do so. Although he gets off to a good start by referring to the subjective state of the practitioner (“with a lack of knowledge,” “if you have no idea what you're doing”), he errs catastrophically by making a claim about the objective state of affairs (“one search is as good as any other search,” “all searches are the same”).

Does your lack of knowledge about a problem imply that all available solution methods (algorithms) work equally well in fact? If you think so, then you're on par with the Ravenous Bugblatter Beast of Traal, “such a mind-bogglingly stupid animal, it assumes that if you can't see it, it can't see you.” Your lack of knowledge implies only that you cannot formally justify a choice of algorithm. There not only may be, but in practice usually will be, huge differences in algorithm performance.

What boggles my mind is that Marks and Dembski did not learn this from Wolpert and Macready (1997), “No Free Lunch Theorems for Optimization.” In Section III-A, the authors observe that “it is certainly true that any class of problems faced by a practitioner will not have a flat prior.” This means that some problems are more likely than others, and the NFL theorems do not hold in fact. So what is the significance of the theorems?

First, if the practitioner has knowledge of problem characteristics but does not incorporate them into the optimization algorithm, then... the NFL theorems establish that there are no formal assurances that the algorithm chosen will be at all effective. Second, while most classes of problems will certainly have some structure which, if known, might be exploitable, the simple existence of that structure does not justify choice of a particular algorithm; that structure must be known and reflected directly in the choice of algorithm to serve as such a justification. [emphasis mine]

So don't take my word for it that Bob has twisted himself into intellectual contortions with his apologetics. This comes from an article with almost 2600 citations. If memory serves, Marks and Dembski have cited it in all 7 of their publications.

Marks and Dembski believe, astonishingly, that the NFL theorems say that an algorithm outperforms “blind search” only if some entity has exploited problem-specific information in selecting it, when the correct interpretation is that the practitioner is justified in believing that an algorithm outperforms “blind search” only if he or she exploits problem-specific knowledge [justified true belief, not just information] in selecting it. This leads them to the fallacious conclusion that when a search $s$ outperforms blind search, they can measure the problem-specific information that an ostensible "search-forming process” added to $s$ to produce the gain in performance. They silently equate performance with information, and contrive to transform the gain in performance into an expression that looks like gain of Shannon information.

Their name-game depends crucially on making the outcome of a search dichotomous — absolute success (performance of 1) or absolute failure (performance of 0). Then the expected performance of a search is also its probability of success. There is a probability $p$ that blind search solves the problem, and a probability $p_s > p$ that search $s$ solves the problem, and the ratio $p_s / p$ is naturally interpreted as performance gain. But to exhibit the “added information” (information gain), Marks and Dembski do a gratuitous logarithmic transformation of the performance gain, $$I_+ = \log \frac{p_s}{p} = \log p_s - \log p = -\!\log p + \log p_s,$$ and call the result active information. (The last step is silly, of course. Evidently it makes things look more “Shannon information-ish.”) To emphasize, they convert performance into “information” by sticking to a special case in which expected performance is a probability.

Here's a simple (in)sanity check. Suppose that I have a “pet” algorithm that I run on all problems that come my way. Obviously, there's no sense in which I add problem-specific information. But Marks and Dembski cherry-pick the cases in which my algorithm outperforms blind search, and, because active information is by definition the degree to which an algorithm outperforms blind search, declare that something really did add information to the algorithm.

Now, a point I'll treat only briefly is that Marks and Dembski claim that the cases in which my pet algorithm greatly outperforms blind search are exceedingly rare. The fact is that they do not know the distribution of problems arising in the real world, and have no way of saying how rare or common extreme performance is for simple algorithms. In the case of computational search, we know for sure that the distribution of problems diverges fabulously from the uniform. Yet Marks and Dembski carry on about “Bernoulli's Principle of Insufficient Reason and Conservation of Information in Computer Search,” doing their damnedest to fob off subjective assignment of uniform probability as objective chance.

A bit of irony for dessert [35:50]:

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.