Good Math, Bad Math

A brief disclaimer before I start. I do not read Uncommon Descent. I didn’t check
it before writing my post yesterday. So I didn’t know about the content of Dembski’s
post there that I’m about to write about, until I saw Bob O’H‘s comment on my post this morning.

Yesterday, I explained how he used Dawkins’ “weasel” experiment as an example
of his and Marks’ approach to quantifying the information in search. I said that
it was a lousy example for what it was purportedly being used to demonstrate. And I
theorized that he wanted to claim peer-review approval for his “critique” of Dawkins.

Unbeknownst to me, before I even wrote those words, Dembski had already
done that, over on UD (as usual, I refuse to link to UD; you know where to find them
if you really must):

P.S. Our critics will immediately say that this really isn’t a pro-ID article but that it’s about something else (I’ve seen this line now for over a decade once work on ID started encroaching into peer-review territory). Before you believe this, have a look at the article. In it we critique, for instance, Richard Dawkins METHINKS*IT*IS*LIKE*A*WEASEL (p. 1055). Question: When Dawkins introduced this example, was he arguing pro-Darwinism? Yes he was. In critiquing his example and arguing that information is not created by unguided evolutionary processes, we are indeed making an argument that supports ID.

Umm… Bill, the reason that your critics say it isn’t a pro-ID article is because
it doesn’t talk about intelligent design. It’s a rather dull math paper
about how to quantify the information content of a search algorithm that that
allows it to perform well in a particular kind of search domain.

And the paper doesn’t critique Dawkins’ experiment at all! It
describes a variant of the “Weasel” experiment as an example of how
to quantify the landscape information in a partitioned search. It doesn’t
critique that at all; it just presents a straightforward analysis of it.
So it doesn’t actually critique anything.

But more importantly: as people have explained to you hundreds of times by now, Dawkins’ didn’t use locking. Dawkins’ search algorithm was not
partitioned search
. In fact, the algorithm that Dawkins’ used can’t be
modeled as a partitioning search at all.

So, as usual… Dembski is a liar. At this point, there’s just no way to
excuse him. I don’t consider him to be a particularly competent mathematician – but
ignorance and incompetence are no longer an adequate explanation of his rubbish. He’s
had the locking error pointed out to him numerous times; he’s had the difference explained
to him, demonstrated to him, proven to him numerous times – but he still keeps
harping on the incorrect version of the experiment, because it’s an easier target.

Comments

  1. #1 Blake Stacey
    August 21, 2009

    Heh heh. “Weasel”. I get it. :-)

  2. #2 J-dog
    August 21, 2009

    So, a Dembski paper is the equivalent of a Bachman / Palin press release. Without the making sense part. Ah Dr. Sr. Billy Boy, how low can you go?!

  3. #3 Mozglubov
    August 21, 2009

    I also found it highly amusing that he turned comments on his blog post off after the 9th comment, stating, “I’m growing weary of these quibblings and thus shutting the comments off.”

  4. #4 Blake Stacey
    August 21, 2009

    He also deleted a comment. His whine about “quibblings” starts off with a response to someone called “NS”:

    NS: Get a textbook on general relativity, and you will typically find a math textbook devoted mainly to Riemannian geometry. So by your reasoning, it actually isn’t about the structure of spacetime.

    I don’t know what NS wrote, because it’s not there any more. None of the eight previous comments still present say anything about general relativity, either. (I have my doubts that Dembski has actually looked at the “physics” section of a university library, let alone that he would appreciate the difference between books for physicists and books for mathematicians.) Not only is he a petty tyrant of his tiny dominion, he’s an incompetent one as well.

  5. #5 Deen
    August 21, 2009

    Not to mention the fact that an argument against evolution doesn’t automatically become an argument for Intelligent Design.

  6. #6 Bob O'H
    August 21, 2009

    I don’t know what NS wrote, because it’s not there any more.

    Ah, but the Church Burnin’ Ebola Boys (don’t ask) are on the case. olegt reveals all

    notedscholar
    08/19/2009
    11:39 am
    Not to burst your bubbles, but this isn’t actually a pro-ID article. It’s more about math than anything else.
    NS
    http://www.sciencedefeated.wordpress.com

    P.S. the software closes my blockquote when there are two returns, even though I close the tag later. FWIW, the br tag seems to do the trick (on preview, at least).

  7. #7 william e emba
    August 21, 2009

    Doctor Dumb said, as quoted from his blog:

    Get a textbook on general relativity, and you will typically find a math textbook devoted mainly to Riemannian geometry.

    I have numerous textbooks on general relativity and on Riemannian geometry, and have mastered a good portion of each subject. They have a small bit of overlap. Confusing the two requires the confuser to be extremely stupid, incapable of understanding either subject, and never once thinking his own personal failure to get past page one made him utterly inadequate to compare the two. Sheesh, is he ever stupid.

    For starters, the mathematics used in relativity is semi-Riemannian geometry. Not Riemannian geometry. You know, Minkowski spacetime? So right there you’ve got your EPIC FAIL in full swing.

    For another, mathematics and physics are seriously different fields of study. A mathematics textbook tries to dot the i’s and j’s and heads for theorems of inherently mathematical interest. A physics textbook plays fast and loose with the details and heads for models of inherently physical interest.

    One of my all-time favorite textbooks is Sachs and Wu General Relativity for Mathematicians. It is not particularly great from the mathematical point of view. It is certainly not particularly great from the physical point of view. It is, however, particularly different, one which twists your head into a much better understanding of just how far apart mathematics and physics really are from either. In the end, the book is a failure, if judged by the standards of good mathematics or of good physics. But it’s a stunning success at showing just how far apart mathematics and physics really are, and for this mathematician at least, decoding the secret language of physicists.

  8. #8 Brian
    August 21, 2009

    METHINKS*HE*IS*LIKE*A*WEASEL

  9. #9 Sal
    August 21, 2009

    How can he claim to be “critiquing” Dawkins, when he doesn’t cite him ???

  10. #10 Bayesian Bouffant, FCD
    August 21, 2009

    #5 Deen: Not to mention the fact that an argument against evolution doesn’t automatically become an argument for Intelligent Design.

    George Gilder sez:

    I’m not pushing to have [ID] taught as an ‘alternative’ to Darwin, and neither are they,” he says in response to one question about Discovery’s agenda. ”What’s being pushed is to have Darwinism critiqued, to teach there’s a controversy. Intelligent design itself does not have any content.

  11. #11 Blake Stacey
    August 21, 2009

    So, if Gilder says, “Intelligent design itself does not have any content”, and if Dembski says that “intelligent design is just the Logos theology of John’s Gospel restated in the idiom of information theory”, then. . . .

    ;-)

  12. #12 Joel
    August 21, 2009

    There is a [12] in the partitioned search section, which is a reference to The Blind Watchmaker. This is the only thing cited in regards to partitioned searches.

    Which means the paper’s referencing is particularly shoddy too. However often Dembski insists on misunderstanding (deliberately or otherwise) what was written in TBW, he introduced partitioned searching without citing anything which described it (if he’s going to claim that TBW actually describes partitioned search, that’s just outright fraud), but whilst pretending that something was cited.

  13. #13 Kristine
    August 21, 2009

    It’s just more street theatre continued from last March:

    William Dembski: Gentlemen: If Dawkins is tuning the parameters differently for the [Weasel] program as described in the book and for it as exhibited in the BBC documentary, isn’t he in effect using a different program?

    Mark, did you know that setting parameters differently for a program run actually changes the program itself? Neither did I. So maybe that’s how “00000000” and “01001101” can have the “same amount” of Shannon information. Or something like that. (Bill Dembski????!!!!LIAR!)

  14. #14 RBH
    August 21, 2009

    The Metropolis Sampler has a short sweet critique called Dembski and Marks publish trivial ID paper.

  15. #15 Paul Burnett
    August 21, 2009

    For even more fun, check out http://www.uncommondescent.com/humor/off-topic-school-answering-machine/ – Billy gets fooled by an “Urban Legend.”

  16. #16 Douglas McClean
    August 21, 2009

    Personally, I’m still waiting for some peer-reviewed ID papers on biogeography. I finished watching all of the The Office DVDs, so I need some new comedy material.

  17. #17 MPL
    August 22, 2009

    So, I just finally skimmed Dembski’s older paper, the abstract of the current one, and some other paper by Marks and Dembski online.

    It’s even dumber than I thought.

    First, he recalls the No Free Lunch theorem, then posits a particular search that does better than random search (can we call random search “bogosearch” instead? It’s so much more evocative). Then he proves that a meta-search search algorithm that looks for a search algorithm then uses it to do the search can’t do better than bogosearch (which is a pretty trivial corollary).

    The idiocy of this is that it only discusses the probability of reaching some “target set”. Unfortunately, this really has nothing to do with evolution at all: the theory of evolution never claimed that evolution finds optimal solutions, merely that its “search path” tends “upwards”. The resulting “destination set” is something like the situation in the Texas Sharpshooter fallacy, where the target is chosen by what you found, rather than trying to find the target.

    In fact, Dembski has provided no evidence that evolution is better at finding “optimal solutions” on average than random search is: the increased chance of finding good solutions (e.g. the body plan of a squirrel) might be offset by the decreased chance of finding really awesome solutions (e.g. fire-breathing, space-dwelling invisible dragons). Indeed, some evolutionary “bad designs” (like the “backwards” retina in the human eye) appear to be the result of an inability of the evolutionary “search algorithm” to reach a better solution.

  18. #18 Richard Wein
    August 23, 2009

    I’ve just read the Dembski/Marks paper. What a joke! It’s all based on a sleight of hand. D&M describe a measure of the effectiveness of a search algorithm (relative to random sampling) on a given problem. They then call this measure “active information” and insist it is therefore a thing that must have come from somewhere, so the programmer must have smuggled it into the search algorithm. But it’s still just a measure of effectiveness.

    D&M write: “If any search algorithm is to perform better than random search, active information must be resident”. This is a tautology. To be better than random sampling is the definition of having “active information”. They say that, “to have integrity”, programmers of a search algorithm “should explicitly state” its active information. But this only means that they should state how much more effective their algorithm is than random sampling.

    In the past Dembski has committed his sleight of hand by dressing up a probability measure as “information”, transforming it by means of the formula i = -log2(p). At least there he was using (or abusing) a quantity invented by information theorists (and known as “surprisal”). But now the measure he is dressing up as information is not even a probability. It’s a ratio of probabilities: active information = -log2(p/q), where p is the probability that random sampling finds the target, and q is the probability that the algorithm in question finds the target. It’s absurd to call this quantity “information”.

  19. #19 Richard Wein
    August 23, 2009

    P.S. It occurs to me someone might object to my last comment on the grounds that -log2(p/q) can be considered the difference between -log2(p) and -log2(q).

    It makes no sense to subtract one surprisal from another. But perhaps it can be argued that Dembski’s new sleight of hand is no more absurd than his old one. If you accept that -log2(p) is an amount of stuff that can be “created” and “smuggled” (as Dembski has always done), then I suppose it follows that one amount of this stuff can be subtracted from another.

  20. #20 Matt
    August 23, 2009

    Even if Dembski’s work were on the real version of Dawkins’ program, it doesn’t change the fact that Dawkins’ program was never meant to model natural selection, just the relative power of selection vs. chance. Also, the argument that the starting information was introduced externally looks more like an attack on abiogenesis than evolution.

  21. #21 Blake Stacey
    August 23, 2009

    They say that, “to have integrity”, programmers of a search algorithm “should explicitly state” its active information. But this only means that they should state how much more effective their algorithm is than random sampling.

    In practical terms, what would “active information” tell us that, say, big-O notation couldn’t be used to say? It seems like the only advantage of “active information” is that Dembski and Marks can reify it for their own dubious purposes.

  22. #22 Jonathan Vos Post
    August 23, 2009

    You are 100% correct again, Mark Chu-Carroll. It doesn’t seem to be possible to keep the undead Dembski in his crypt, however well the stake is sharpened, and however diligently it is pounded in.

  23. #23 Richard Wein
    August 24, 2009

    I’ve thought of an even more damning criticism of “active information”. The amount of active information can be greater than the number of bits in a complete description of the search algorithm (or a computer program that executes it). So how can the active information be “resident” in the search algorithm, as D&M claim?

    To take an extreme example, consider a simple search algorithm that searches an M-dimensional space with N points in each dimension, starting at point X. Now use this algorithm to search a fitness landscape that happens to have its unique target point at X, all other points in the landscape having equal fitness. The search will find its target in one step with probability 1. The probability of random sampling finding the target in one step is 1/(N^M). So the active information is -log2(1/(N^M)), or log2(N^M), or M.log2(N) bits. M and N can be as large as you like. For the sake of example, let them each be 2^30. Then the active information is 30×2^30 bits, or 30 gigabits, or 3.25 gigabytes, more than enough to program the algorithm and specify the fitness landscape.

  24. #24 Blake Stacey
    August 24, 2009

    In that example, if X can be anywhere of N^M possibilities, wouldn’t specifying the location of X require log2(N^M) bits?

  25. #25 Blake Stacey
    August 24, 2009

    Dealing with Dembski’s “Information Theory” is like dealing with Velikovsky’s “astronomy”: there’s so little actual content that you end up doing all the work yourself.

    The ratio of the probabilities of success for a search algorithm and for random sampling says as much about the fitness function as it does about the algorithm trying to optimize that function. “Active information” is a (poor) measure of how correlated the fitness landscape is; it reflects (crudely) how well the fitness landscape obeys the Pure Noise condition.

    When a teenager writes her first WEASEL program, she doesn’t necessarily know in advance what the target of its search will be; in fact, she can code it such that it takes its target as a command-line parameter, so that the target string can be changed from one run to the next. She knows only the most basic generalities of the fitness landscape which will be defined by that target string: the fitness function will be auto-correlated, but even its dimensionality could be unknown. What makes the genetic algorithm converge more rapidly than a random search is the fitness function, not any particular detail about the GA itself.

    If we want to gauge how amenable a problem might be to a solution by GA — to see if it is “GA-hard” — we ought to look at the structure of the function we’re trying to optimize. “Active information” is just a shoddy, muddled way of doing fitness landscape analysis.

  26. #26 R0b
    August 25, 2009

    Richard, if this is the first Evo Info Lab paper you’ve read, you’re in for a real treat when you read this one.

    The connotations of the term “information” are quite misleading when the term is applied to search performance. Unlike classical information, the content of the information is not the event of which the probability is taken. In fact, it’s hard to say just what the content is.

    Superficial readers have been caught in this terminology trap since Marks and Dembski made the papers available a few years ago, much as they did with Dembski’s previous terms, such as “complex”. As you did with Dembksi’s previous work and with the tautology you pointed out in #16, replacing “endogenous info”, “exogenous info”, and “active info” with their actual definitions dispels the fog and reveals the lack of substance underneath.

  27. #27 MPL
    August 25, 2009

    I think it’s worth pointing out that Dembski has never proved that “evolutionary search” actually does do better than “random search” at finding organisms that are unusually good at surviving.

    Remember, all of these arguments rest on the idea of average performance—but unusually good performance in one area can be offset by unusually bad performance elsewhere (which is indeed the whole point of the No Free Lunch Theorems).

    There are conceivable organisms/traits which either could not or probably would not evolve because there is no evolutionary path that reaches them. These drag down the average performance of an “evolutionary search” algorithm. Indeed, the absence of “unevolvable” creatures is a major test of evolutionary theory.

  28. #28 Richard Wein
    August 25, 2009

    Blake, yes, that’s true in the general case. I was originally thinking of a special case where X has some property that makes it more easily describable, e.g. X is the point (1,1,1,…,1). This can be described as “value 1 in each dimension”, instead of listing the value in each dimension. I thought I could drop the restriction to special cases, but I can’t. Still, if you add to my example the stipulation that X is the point (1,1,1,…,1), then I think it remains valid.

    Here’s a less artificial example, with a proper search algorithm and a fitness landscape that’s specified by a simple formula instead of identifying a specific point. Consider a hill climbing algorithm on a search space that has values [1,2,3,…,N] in each of M dimensions. The algorithm starts at point (1,1,1,…,1). It queries all the adjacent points (+1, 0 and -1 in all combinations of dimensions), moves to the highest available point, and then repeats. Consider the following fitness function:

    f(x_1, x_2, … , x_M) = x_1 + x_2 + … + x_M

    On this landscape, the algorithm visits (1,1,1,…,1), (2,2,2,…,2), (3,3,3,…,3) up to the unique maximum at (N,N,N,…,N). So it visits N points, and at each of these it queries approximately 3^M points. In total it makes approximately Nx3^M queries, and finds the target with probability 1. With the same number of queries, random sampling has probability of finding the target approximately (Nx3^M)/(N^M), or N/((N-3)^M),

    So the “active information” is approximately -log2(N/((N-3)^M)), or M.log2(N-3) – log2(N) bits. For large N and M, this is still in the order of M.log2(N), as before. With M and N equal to 2^30, it’s still over 3 gigabytes.

    Have I made any errors?

  29. #29 Richard Wein
    August 25, 2009

    P.S. I just thought. My second algorithm has to remember one or more locations in the search space, and in general each of these requires log2(N^M) bits of storage. But that’s working storage, not part of the algorithm. In computer terms, it can be dynamically allocated memory.

  30. #30 Richard Wein
    August 25, 2009

    I just thought, my second example may work in principle, but it’s going to take more time to run than could possibly be available. Those Nx3^M queries are ridiculous when M=2^30.

  31. #31 Blake Stacey
    August 25, 2009

    I’m sure Google could manage it. ;-)

    I was thinking about this on the bus yesterday, and it struck me that once you actually try to use the term “information” in a technical way, the deceptiveness of this talk of “the Designer encoding information into the landscape” becomes pretty clear. As I said at the Panda’s Thumb:

    From the viewpoint of algorithmic information theory, evolutionary algorithms work because the information content of the fitness landscape is low. If the fitness function is very weakly correlated, i.e., approximating the Pure Noise condition, then hill-climbing or search-by-mutation-and-selection won’t do much better than random sampling. But a function of this type has high Kolmogorov-Chaitin information: random sequences are incompressible. A fitness function which is random in the Martin-Loef sense is exactly the kind of landscape which would make a search algorithm thrash about.

    Dembski and Marks are basically doing a kludgy and vague version of fitness landscape analysis. Their “active information” (which I’m not sure should even be called “information”, being the difference between surprisals) is a functional of the algorithm being evaluated and the fitness function which is being optimized. It mixes up the “hardness” of the fitness function with the complexity of the algorithm used to optimize it; Dembski and Marks then reify this number into something which can be “hidden” or “smuggled”.

    And about that business of Dembski and Marks calling their quantity “information”: the surprisal of an event of probability p is defined to be -log p. Averaging this over all possible outcomes gives the Shannon entropy. The surprisal of a message is only equivalent to the Shannon information of the probability distribution over all messages if all messages are equally likely. (This is the situation in which one can use the entropy formula carved on Boltzmann’s tombstone.) If p is the probability of hitting the target with random sampling, then -log p is how surprised we are when random sampling actually works. But success and failure are certainly not equally likely: p is much, much smaller than 1. Likewise, if q denotes the probability that a search algorithm (hill-climbing or whatever) finds the target, then q is not going to be 0.5, either. The way I see it, “active information” is both useless and poorly named.

  32. #32 Blake Stacey
    August 25, 2009

    Footnote: a Google Scholar search on “fitness landscape analysis” finds some interesting papers.

  33. #33 Richard Wein
    August 26, 2009

    Blake, I quite agree.

    Their “active information” (which I’m not sure should even be called “information”…

    I’m sure it shouldn’t be called information. Calling it that just serves D&M’s purpose of conflating it with genuine senses of the word, enabling their fallacy of equivocation.

  34. #34 Radoslav Harman
    August 26, 2009

    The publication http://evoinfo.org/Publications/ConsInfo_NoN.pdf is, in a sense, an interesting reading. The rationale (yes, I think that there is one) that I derived from the paper is the following:

    The outcome of a human-made evolutionary program is already implicitly determined by the program itself (of course, if we consider it to be deterministic); that is perhaps what the authors mean by “conservation of information”. But in the Nature, the “program” is the physical laws. How come the physical laws are such that they implicitly contain the information about the development of life? Isn’t it strange? Wouldn’t it be immensely improbable with “randomly generated” laws left to develop on their own, that is without the divine intelligence and occasional divine interventions?

    So, in my view, the rational core of the Dembski’s argument, stripped of all the biases, dubious notions and objectionable philosophy, is in fact some version of the so called anthropic principle, or the Goldilocks enigma. That is: how come the physical laws are such they not only permit, but even, as it might seem, foster development of some kind of intelligent life? I think that this is a serious question which should be addressed by scientists.

    Recently, the argument forced me to take a closer look at the various multiverse theories, absurd as they might seem. What do you think about this problem, Mark?

  35. #35 DiEb
    August 26, 2009

    I tried to make some comments on the corresponding threads at Uncommon Descent, but I can’t get trough any longer. So, I put some graphs and thoughts at my blog :-)

  36. #36 Stephen Wells
    August 26, 2009

    @31: explain why you think it is immensely improbably that natural laws should lead to intelligent life. While you’re at it, specify what range of possible natural laws you are discussing.

  37. #37 Blake Stacey
    August 26, 2009

    Indeed. Some wild nights in Amsterdam aside, I’m fairly sure I’ve experienced only one Universe, so I have little data on how the fundamental parameters of physical law might vary.

  38. #38 Blake Stacey
    August 26, 2009

    DiEb (#32):

    I like how Denyse O’Leary is calling for Richard Dawkins to release the code for his original program. As if every nerd in the past twenty years hasn’t written their own! But it is consistent with the creationists’ view of truth as predicated on personal authority (witness their continual attempts to defame the character of Charles Darwin).

    Methinks she wants the long-form birth certificate of the WEASEL.

  39. #39 Radoslav Harman
    August 26, 2009

    @33: I do not think it is immensely improbable that natural laws should lead to intelligent life, although books like Just six numbers by Rees and The Goldilocks Enigma by Davies might suggest it.

    That is, in my comment I just tried to guess what is in the core of thinking of Dembski and co.

    Of course I cannot (most probably nobody can) define something like a “probability space of all possible natural laws”, identify the subset (i.e. event) of “all those possible natural laws that lead to an intelligent life” and calculate its probability. Nevertheless, many people do think about the problem in the way that leads them to conclude that without some “designer” or an insanely extreme luck, there would be no life. Therefore I think that some patient clarification of this problem for “general public” would be desirable.

  40. #40 David
    August 26, 2009

    I’m not a geneticist, or an information systems guru, or anything, but it seems to me that Dembski’s off target on at least 2 issues:

    1) Evolution is exactly a random search, taken one generation at a time. Each generation of offspring has a bunch of random mutations. Most don’t do anything, many are immediately fatal, and a few are minor improvements. But there’s no “search strategy” in finding the mutations. It’s random. And the strategy for finding the progeny that survive is brute force – let ‘em fend for themselves and see who survives and reproduces. So there’s no “active information” or whatever he wants to call it.

    2) Evolution isn’t really like a search algorithm at all. A true search algorithm has to search the entire landscape to find the best solution. Evolution only “searches” small mutations away from the starting point (a limited landscape) and only has to find a marginally better solution that where it started. There’s no guarantee that the solution it finds is “best” – in fact, inguinal hernias, low back pain and inverted retinal neuron layers are proof that evolution only finds “good enough” solutions that are near to the starting point.

  41. #41 Jonathan Vos Post
    August 26, 2009

    #37 misses a crucial point. “Evolution only ‘searches’ small mutations away from the starting point (a limited landscape).”

    Natural Selection in actual genomes is NOT merely point mutations. It significantly includes inversions, crossings over, duplication, and other chromosomal mutations.

    The ID fraudulent criminals intentionally omit this from their discussions. Their straw-man has only one kind of straw, not even the variety in scarecrows stuffed with better high school genetics textbooks.

    Next, the issue is hardly the genotype, but the phenotype, as that is what interacts with the environment as summarized by the fitness function. Google what Stuart Kauffman has written about the “adjacent possible.”

  42. #42 Jonathan Vos Post
    August 26, 2009

    http://www.edge.org/3rd_culture/kauffman03/kauffman_index.html

    Stuart Kauffman is a theoretical biologist who studies the origin of life and the origins of molecular organization. Thirty-five years ago, he developed the Kauffman models, which are random networks exhibiting a kind of self-organization that he terms “order for free.” Kauffman is not easy. His models are rigorous, mathematical, and, to many of his colleagues, somewhat difficult to understand. A key to his worldview is the notion that convergent rather than divergent flow plays the deciding role in the evolution of life. He believes that the complex systems best able to adapt are those poised on the border between chaos and disorder.

    Kauffman asks a question that goes beyond those asked by other evolutionary theorists: if selection is operating all the time, how do we build a theory that combines self-organization (order for free) and selection? The answer lies in a “new” biology, somewhat similar to that proposed by Brian Goodwin, in which natural selection is married to structuralism.

    Lately, Kauffman says that he has been “hamstrung by the fact that I don’t see how you can see ahead of time what the variables will be. You begin science by stating the configuration space. You know the variables, you know the laws, you know the forces, and the whole question is, how does the thing work in that space? If you can’t see ahead of time what the variables are, the microscopic variables for example for the biosphere, how do you get started on the job of an integrated theory? I don’t know how to do that. I understand what the paleontologists do, but they’re dealing with the past. How do we get started on something where we could talk about the future of a biosphere?”

    “There is a chance that there are general laws. I’ve thought about four of them. One of them says that autonomous agents have to live the most complex game that they can. The second has to do with the construction of ecosystems. The third has to do with Per Bak’s self-organized criticality in ecosystems. And the fourth concerns the idea of the adjacent possible. It just may be the case that biospheres on average keep expanding into the adjacent possible. By doing so they increase the diversity of what can happen next. It may be that biospheres, as a secular trend, maximize the rate of exploration of the adjacent possible. If they did it too fast, they would destroy their own internal organization, so there may be internal gating mechanisms. This is why I call this an average secular trend, since they explore the adjacent possible as fast as they can get away with it. There’s a lot of neat science to be done to unpack that, and I’m thinking about it.”

  43. #43 Blake Stacey
    August 28, 2009

    I’m glad I’m not the only one who thinks that O’Leary and her ken are using birther logic.

  44. #44 David
    August 29, 2009

    to Jonathan #38:

    When I wrote “small mutations” I was including point mutations and also inversions, crossings over, duplication, and other chromosomal mutations. All of these are small because they start from the parent’s DNA and can only make new sequences that are in some sense closely related. Evolution doesn’t have to search the entire possible range of DNA sequences.

  45. #45 Tomato Addict
    August 30, 2009

    RE: #4

    The “NS” referred to in the last comment is “NotedScholar” and you can find his delete comment on his blog: Science and Math Defeated.

    I should maybe mention before anyone reads that blog and gets the wrong idea, NS is either a wacko or the best damn Poe I’ve ever seen. I have a strong opinion on the matter, but I won’t spoil your fun.

  46. #46 se-rat-o-SAWR-us
    September 2, 2009

    Efficient perl code for weasel. It allows for variable string lengths, which toggle back and forth, so it obviously doesn’t lock, even on the length of the string. Arbitrary printable ASCII mutations are possible, with the hyperlinked starting point of a relevant Richard Dawkins quote.

    Output:

    % ./weasel
    These people are so unbelievably stupid. –Richard Dawkins (http://bit.ly/Cq8EC)
    These people are so unbelievably stupid. –Richard Dawkins (http://bit.ly/Cq8EC
    These people are so unbelievably stupid. –Richard Dawkins (http://bit.ly/Cq8E
    These people are so unbelievably stupid. –Richard Dawkins (http://bit.ly/Cq8
    These people are so unbelievably stupid. –Richard Dawkins (http://bit.ly/Cq
    These people are so unbelievably stupid. b-Richard Dawkins (http://bit.ly/Cq
    These people a0e so unbelievably stupid. b-Richard Dawkins (http://bit.ly/Cq
    These people a0e so unbelie%ably stupid. b-Richard Dawkins (http://bit.ly/Cq
    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
    METHINKS I]:IH LIKE A WEASEB
    METHINKS I]OIH LIKE A WEASEB
    METHINKS I]OIH LIKE A WEASE
    METHINKS I]OIH LIKE A WEASEo
    METHINKS I]!IH LIKE A WEASEo
    METHINKS I]!IH LIKE A WEASEo
    METHINKS I]-IH LIKE A WEASEo
    METHINKS I]-IH LIKE A WEASE’
    METHINKS I]-IH LIKE A WEASE
    METHINKS I[-IH LIKE A WEASE
    . . . . . . . . . . . . . .
    METH0NKS IT IS LIKE A WEASEL
    METH0NKS IT IS LIKE A WEASEL
    METHtNKS IT IS LIKE A WEASEL
    METHINKS IT IS LIKE A WEASEL

    Perl code:

    #!/usr/bin/perl -w

    $|=1;
    $s=”These people are so unbelievably stupid. –Richard Dawkins (http://bit.ly/Cq8EC)”;
    $e=”METHINKS IT IS LIKE A WEASEL”;
    $try=31; # New offspring per generation.

    @e=unpack(“C*”,$e);

    # Print the starting string
    $n=0;
    # Count the characters in the new string that mismatch the target string
    @ns=unpack(“C*”,$s);
    $j=0;
    $mn = (($#e<$#ns)? $#e : $#ns)+1;
    $mx = (($#e>$#ns)? $#e : $#ns)+1;
    $mm = $mx;
    while($j<$mn){$mm– if $e[$j] == $ns[$j++]}
    printf(“Gen %5d, %-2d mismatches:\t\t\t%s\n”,$n,$mm,pack(“C*”,@ns));

    while($mm > 0) {
    $i=-1;
    # Make $try new strings
    while($i++ < $try){
    $mmi = $mm;

    # Mutate one character of the new string
    $chr = int(rand(126-32+1))+32;
    $chr[$i] = $chr;

    # Delete or add the character to the string
    $p = int(rand($#ns+3))-1;
    $p = 0 if ($p<0 && $#ns==0);
    $p[$i] = $p;

    # Count the characters in the new string that mismatch the target string.
    if (0 <= $p && $p <= $#ns) { # $ns[$p] changes to chr($chr)
    if ($p <= $#e) {
    $mmi– if ($e[$p] == $chr);
    $mmi++ if ($e[$p] == $ns[$p]);
    }
    } elsif ($p == -1) { # $ns[$#ns] is deleted
    $mmi– if ($#ns > $#e);
    $mmi++ if ($#ns <= $#e && $e[$#ns] == $ns[$#ns]);
    } elsif ($p == $#ns+1) { # $ns[$#ns+1] appended with chr($chr)
    $mmi++ if ($#ns >= $#e);
    $mmi– if ($p <= $#e && $e[$p] == $chr);
    }
    $mmc[$i] = $mmi;
    }

    # Find high scoring offspring strings.
    @sc = sort {$mmc[$a]<=>$mmc[$b]}(0..$#mmc);

    @new=(shift @sc);
    while(@sc && $mmc[$sc[0]] == $mmc[$new[0]]){push @new,shift @sc}

    # Set new string to a random offspring strings from among the high scoring offspring.
    $i = int(rand(@new));
    $j = $new[$i];
    $mm = $mmc[$j];
    $p=$p[$j];
    $chr=$chr[$j];
    if ($p<0) { $#ns = $#ns-1; } #delete
    else { $ns[$p] = $chr; } #replace/append character

    printf(“Gen %5d, %-2d mismatches (\$p=%2d,\$chr=%s):\t%s\n”,++$n,$mm,$p,chr($chr),pack(“C*”,@ns));
    }

  47. #47 Celal
    September 7, 2009

    I like your blog because i like math. It’s bookmarked and i follow it regularly.

    Does it make sense to say that one Christian’s misuse of math does not minimise or nullify who Jesus is and what he did for us?

    That question goes beyond the modality of mathematics and i hope you can think outside this modality when making criticisms that may reach out to impinge on the person and work of Jesus Christ.

  48. #48 Jordan Wallace
    September 10, 2009

    Mathmatics seems to impose at least a certain amount of objectivity when brought to bare on any mathmatical proof. Often times ones proof is either accurate or inaccurate. But that seems less the problem here. Dembski is an ID proponent which means his philosophical system differs from many of yours. You all know this. In fact you validate one of the key complaints against Darwinian ideals when your level of critique for Dembski hovers around name calling. Like Dawkins, its easier to be a psuedo-phylosopher than a real scientist. Moderated and informed debate for many in this comment string is a matter of put-down and name calling. I guess shout downs are fun but do they accomplish a validation of ones opinion?

  49. #49 DiEb
    October 22, 2009

    In this podcast W. Dembski announced a follow-up paper called The Search for a Search (draft) with “powerful results”.

    I blogged about my problems with this paper (here, here and here), and I even tried to reach R. Marks and W. Dembski, as I think that they don’t show what they intend to show.

  50. #50 DiEb
    October 23, 2009

    2nd try…

    W. Dembski announced a follow-up paper with some strong results: It’s called “The Search for a Search” – and a draft can be found here.

    I’ve some major problems with their definition of a search, and I don’t think that their Horizontal No Free Lunch Theorem (their name) works as they intended…

  51. #51 Zack
    November 16, 2009

    “that information is not created by unguided evolutionary processes; we are indeed making an argument that supports ID.”
    If the model that Dembski uses is misguided or misunderstood, please post such model or the exact error in his thinking on this blog. How is he using misguided information? If he uses such misguided information why is he considered a “liar”? It would be better to call him a “fool” for not listening and engaging the proper arguments. Why attack his character?
    Life would be so easy if Christians and believers would go away. According to scientists, Christians are irrational for not believing in what is apparently true. Let’s give Dembski some credit for not only engaging the scientific community but pushing them to continue their studies. If the evidence for evolution was so overwhelming it would also be undeniably convincing. May our arguments as Christians not only upset the scientific world, but cause you to continue to pursue your craft in such a way that you will find the answer that shuts us up forever (I know secretly that is what also pushes you).
    Christians now see the challenge ahead as well. We will continue picking at your arguments and educating ourselves in such a way to put us in a place to engage the world in their evolutionary thinking.

  52. #52 Mark C. Chu-Carroll
    November 16, 2009

    I call Dembski a liar because he is a liar. He’s proven it over and over again.

    Just look at his latest action: someone posted a careful, detailed critique of his latest paper – and Dembski’s response is to threaten a lawsuit to get the critique removed.

    He knows that he’s full of crap, but he keeps saying things that he knows are false, because he’s got an agenda that’s served by telling falsehoods. If that’s not the definition of a liar, I don’t know what is.

The site is currently under maintenance and will be back shortly. New comments have been disabled during this time, please check back soon.