Chaos and Complexity

Gil’s post With much fear and trepidation, I enter the SZone got somewhat, but interestingly, derailed into a discussion of David Abel’s paper The Capabilities of Chaos and Complexity, which William Murray, quite fairly, challenged those of who expressed skepticism to refute.

Mike Elzinga first brought up the paper here, claiming:

ID/creationists have attempted to turn everything on its head, mischaracterize what physicists and chemists – and biologists as well – know, and then proclaim that it is all “spontaneous molecular chaos” down there, to use David L. Abel’s term.

Hence, “chance and necessity,” another mischaracterization in itself, cannot do the job; therefore “intelligence” and “information.”

And later helpfully posted here a primer on the first equation (Shannon’s Entropy equation), and right now I’m chugging through the paper trying to extract its meaning.  I thought I’d open this thread so that I can update as I go, and perhaps ask the mathematicians (and others) to correct my misunderstandings.  So this thread is a kind of virtual journal club on that paper.

I’ll post my initial response in the thread.

85 thoughts on “Chaos and Complexity

  1. I haven’t read the paper carefully, but I noticed that in the Acknowledgments, Abel writes

    This work was supported by a grant from The Origin of Life Science Foundation, Inc.

    But, but, didn’t Abel himself found TOoLSF? In other words, he might as well have written

    This work was supported by myself

  2. On page 251, just after Abel gives Shannon’s Entropy equation, but which Abel calls the uncertainty measure (Equation 1), Abel writes:

    This of course is Shannon’s basic measurement of uncertainty in linear sequence complexity. We have invested so much confidence and anticipation in “complexity” as a potential source of spontaneous prescriptive information and organization that our senses are jolted by the pristine mathematical definition of sequence complexity reviewed above. We need to re-educate ourselves with the realization that maximum complexity is nothing more than randomness. The most complex of all strings is a random string. Random strings have never been observed to generate non trivial formal function of any kind. Complexity, therefore, has nothing to do with formal function. Complexity possesses no creative or computational talents. No justification exists for attributing exquisite formal organization to mere complexity.

    That equation gives, as I understand it, the average number of bits per item in the string. And, as Mike points out, the flatter the probability distribution, the higher the entropy will be, and the more bits, for given string length [ETA and alphabet size], the string will contain.

    But Abel seems to me conflate “random” with “equiprobable”. He says that the most “complex” string (presumably for a given length) is the most “random” string, whereas the most “complex” string, surely, is a string in which there are a large number of possible characters occurring with equiprobable frequency. So for a string length of 1000, the most complex string of integers would be the integers from 1:1000. And it seems to me it would make no difference to the entropy of the string, and therefore to the complexity whether the integers were rank ordered or totally jumbled, as long as they retained a flat distribution.

    But Abel then says, in the next two paragraphs:

    Well, what about order and pattern? If complexity itself is not what produces utility in a linear digital string, surely order, structure and pattern can. But do they? The answer is no!
    To understand why, we must also define order and pattern. What exactly is “order”? Starting with a single dimension, order in a sequence is defined by an increasing probability of occurrence of each structure, event, or alphabetical character in that string [183]. High probability is high order [185]. As the probability of an event approaches 1.0, its Shannon uncertainty approaches 0 bits [186]. 0 bits of uncertainty is maximum order. Maximum order is minimal complexity. Order and complexity are antithetical. They lie at opposite extremes of a bidirectional vector (Figure 1) [71]

    Is he saying, then, that a string consisting of the integers from 1:1000 in rank order has no complexity in Shannon terms? If so, this seems simply wrong. Shannon complexity/uncertainty doesn’t take into account the order of the items in the string at all, merely the frequency distribution of each item type. If I know the order of the letters in the English alphabet, I can be very confident that the next letter in the string: ABCDEFGHIJKLMNOPQRSTUVWXY will be Z.

    But that doesn’t make the entropy of that string any less than the entropy of this one: NROGYATWHXMLBVIFJDQEKUPCS

    Both have 25 different item types and in both strings the item types are equally distributed (one of each).

    So his idea that complexity (as he seems to define it) and order are at opposite ends of a single dimension is simply wrong. Simple ordered, simple unordered, complex ordered, and complex unordered strings are all perfectly possible, although it will be true of course that if we plot all possible strings by complexity versus order, the highest density will be for complex unordered strings and the lowest density for complex ordered strings.

    At least that’s how it seems to me – any comments? Have I missed something important?

  3. Ido:
    I haven’t read the paper carefully, but I noticed that in the Acknowledgments, Abel writes

    This work was supported by a grant from The Origin of Life Science Foundation, Inc.

    But, but, didn’t Abel himself found TOoLSF?In other words, he might as well have written

    This work was supported by myself

    Well, there are certainly symptoms of crank present! But cranks are occasionally right, so I’m interested here to check out what he’s saying.

    He seems to me to be making the same error as Dembski.

  4. Elizabeth: Is he saying, then, that a string consisting of the integers from 1:1000 in rank order has no complexity in Shannon terms?

    What creationists and ID proponents say about information is mostly nonsense.

    Shannon’s theory was a theory of communication, and his measure of information content is a measure of the channel carrying capacity. That channel capacity can be less than the bit capacity, because some of the bits might be parity bits or other redundant information.

    As you correctly say, Shannon does not distinuish between an unordered string or an ordered string, unless the ordering is imposed by a protocol that has the effect of limiting channel capacity.

    Kolmogorov complexity, sometimes also called Solomonoff complexity or Chaitin complexity, does distinguish between an unordered string and an ordered string. Whether Kolmogorov complexity is useful is probably still controversial, though that never stopped creationists from trying to put it into their dubious arguments.

    Getting back to Shannon information, I’ll note that Shannon was concerned with communication between intelligent agents (mainly humans or technology built by humans). The usefulness of a string would depend on the use to which those intelligent agents put it. Abel seems to be trying to talk of usefulness independent of how intelligent agents use it. I’m inclined to think that’s mostly nonsense.

  5. Elizabeth,

    Those are indeed legitimate points.

    I’ll have much more to say about this when I get home. My time on this computer is limited.

    But if anyone wants to look ahead (it doesn’t make much difference in which order one reads the pages of this paper), jump to pages 255 through 257. This is the only place in the paper that Abel actually does any calculation, and it is this calculation and Abel’s assertions that reveal that this entire paper is a non-sequitur.

    All of Abel’s misconceptions and misrepresentations as well as those of Dembki and Sewell are revealed in just these few paragraphs.

    Everything else in the paper is simply pseudo-philosophical filler and various rephrasing of these fundamental misconceptions.

    Look closely at Abel’s example under the figure on page 256. Make sure you follow it. The calculation itself is done correctly. Make sure you understand what Abel is using as the probabilities. Then finish the rest of Section 3

    For those who may not know the chemistry and physics, the silliness of it may not be evident on its face. But the first thing any respectable chemist or physicist would ask is, “what does any of this have to do with how atoms and molecules actually interact?”

    I’ve used up my time. Gotta go.

  6. I will blog my own impressions as I read through. Here is

    Part I

    Abel’s opus has all the appearances of a serious scientific paper. Lots of technical terms, hundreds of references, and even a funding acknowledgment. On closer inspection, it turns out to be complete gibberish. And yes, the funding is provided by Abel’s own shell foundation.

    The very first sentence of the paper gives a preview of coming attractions.

    Stand-alone chaos, complexity and catastrophe should never be confused with our theories and what we intelligent humans do using abstract conceptual nonlinear dynamic models.

    The reader is left to ponder: WTF? Why would anybody confuse catastrophe with Abel’s theory? What is an “abstract conceptual nonlinear dynamic model?” Why are linear models disqualified? Can a model be non-abstract and/or non-conceptual? Lots of questions.

    The introduction continues with a relentless stream of gibberish. Having given a list of items in which “life-origin science is not especially interested,” Abel tells us that its goal is to understand whether “objective chaos, complexity and catastrophe” can generate “Bona fide Formal Organization [4].” If you don’t know what the heck BFFO means, don’t be ashamed: the only instance of this term exists in the very paper we are discussing. Perhaps realizing that, Abel helpfully explains:

    By “formal” we mean function-oriented, computationally halting, integrated-circuit producing, algorithmically optimized, and choice-contingent at true decision nodes (not just combinatorial bifurcation points).

    Just reflect for a moment on this string of identifiers, taken from different fields of human endeavor and thrown together as a pile of pick-up sticks (Fig. 2a). “Computationally halting” refers to an abstract problem in computer science. Algorithm optimization is an engineering problem, but I am not sure what it means for organization to be “algorithmically optimized.” (Thoughts?) And why does formal organization (“an abstract, conceptual, non physical entity”) have to produce integrated circuits, of all things?

    After some ruminations about emergence and complexity, Abel proceeds to formulate his “null hypothesis,” which he will try very hard to disprove, but in doing so (you guessed it) will fail.

    Physicodynamics alone cannot organize itself into formally functional systems requiring algorithmic optimization, computational halting, and circuit integration.

    “Physicodynamics” is a rarely used term. In Abelspeak it means, presumably, known natural processes such as chemical reactions. I am not a biologist, but I suspect that organisms don’t normally engage in computational halting (unless they are computer scientists) and don’t produce integrated circuts (again, with a few exceptions). Why these are interesting questions remains unclear.

    (to be continued)

  7. Part II

    There is lots more fun to be had with the introduction, but that is left as an exercise for the reader.

    In Section 2, Abel attempts to explain the concept of complexity.

    An unequivocal, pristine, mathematical definition of linear “complexity” already exists in scientific literature [1, 71, 183]: maximum complexity in a linear string, oddly enough, is randomness.

    Ref. 1 is to another paper of his own, so it’s hardly “pristine,” but Ref. 183 is a legitimate book on the Kolmogorov complexity. It means, presumably, that the concept of complexity dealt with in this section is Kolmogorov’s. Except that randomness is an odd term in that context.

    Let me explain. The Kolmogorov complexity is defined for a single object, in this case a string. It is the minimal length of a program that can generate a given string. No randomness involved.

    Randomness is involved in Shannon’s definition of information. Shannon treats messages (bits, words, or sentences) as random variables. They come from a random source with specified probabilities. Shannon’s entropy is a measure of average surprise upon receipt of a message. If only one type of message arrives time after time, there is no surprise. If every message has an equal chance of appearing, the surprise is maximized.

    These concepts are quite different. For instance, the number π has a low Kolmogorov complexity: instructions for computing it are not complicated. At the same time, the Shannon information of a stream of its digits (appearing with equal probabilities) is high.

    Eq. (1) is Shannon’s measure of information. So Abel conflates the two concepts. He does not understand this subject but pontificates about it as crackpots often do.

    (to be continued)

  8. olegt:
    Part II

    [...]

    Randomness is involved in Shannon’s definition of information. Shannon treats messages (bits, words, or sentences) as random variables. They come from a random source with specified probabilities. Shannon’s entropy is a measure of average surprise upon receipt of a message. If only one type of message arrives time after time, there is no surprise. If every message has an equal chance of appearing, the surprise is maximized.

    Let me see if I have this right. Under Shannon’s treatment, the information content of a message is its surprisal value, in other words, whatever is conveyed that was not previously known by the recipient? Thus, as you say, any subsequent transmissions of that same message to the same recipient will have no surprisal value and, therefore, presumably no information content? In other words, if exactly the same message can have provide information on the first transmission but not on any others, is it fair to say that this version of information is not so much a property of the message itself but refers more to a process, the change that it effects in the mind of the recipient?

  9. OK, so it is now clear that by “random”, Abel means “equiprobable”, and by a “complex” string, he means a long string with equiprobable elements.

    He calls a string “ordered” if either the ordering of the elements means that it can be algorithmically compressed (page 252), which of course makes no difference to the Shannon Entropy, so he is simply wrong here, or if the elements aren’t equiprobable (top of page 257), which does.

    So he seems completely muddled regarding a major plank of his argument. According to Abel, the sequence:

    1 2 3 4 5 6 7 8 9

    which is algorithmically simple (each term is the previous term +1), and which indeed I just actually generated using such an algorithm (such is my dedication)

    must be less complex than

    9 6 2 1 3 8 7 4 5

    which was generated by randomly sampling, without replacement, from the previous string. In both strings, as in my alphabetic example above, each item type is equiprobable, so the Shannon Entropy of the two strings is identical:

    3.1699 bits

    On the other hand, the string

    1 1 1 1 1 1 1 1 1

    which I generated simply by omitting “+1″ from the algorithm that generated my ascending series above has much lower Entropy than either of the other two. Indeed the Entropy is zero.

    But Abel ( I assume) would also say that this string:

    2 2 1 2 3 1 2 4 1 2 1 2 2 1 2 2 2 3 1 2 1 1 1 1 2 2 2 1 3 2 1 1 1 2 1 2 2 2 1 3 1 1 2 3 1 3 2 2 2 1 3 1 1 1 3 2 2 1 1 2 1 1 1 2 1 2 2 1 2 2 1 2 2 3 1 1 3 1 2 2 2 2 1 2 1 1 1 2 1 1 4 1 1 1 1 1 1 3 2 3

    as this one:

    1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 4 4

    In both strings, the probability of each digit is as given on page 256: .46; .4; .12;, .02 respectively, i.e. the probabilities are not equal.

    And both strings have the same Shannon Entropy, namely 1.524, as Abel correctly computes.

    Fortunately for Abel, this muddle doesn’t matter because he then says that neither “order” nor “complexity” can generate “utility” aka “bona fide functional organisation”, which, interestingly, is different from Dembski’s argument, which is that some strings can have high “compressibility” (one of Abel’s two kinds of “order”) as well as high complexity (high Entropy in a long string), and that it that pair or properties in a pattern that tell us that a pattern is “designed” even if we do not know what the pattern is for.

    Dembski is right of course that some patterns can be highly compressible as well as highly complex, but he is wrong that only “designed” patterns can have this pair of properties – maybe keep this for another thread!

    So Abel then brings in the idea of “Functional Sequence Complexity”, for which he refers us to work by “Durston and Chiu at the University of Guelph” who “developed a method of measuring what they call functional uncertainty”, for which he disingenuously references a paper (ref 77) by “Durston, K.K.; Chiu, D.K.; Abel, D.L.; Trevor s, J.T.” which is pretty cheeky, I’d say. He repeatedly refers in highly complimentary fashion to this work as being by “Durston and Chiu”, without indicating in the text that he himself is an author on the paper (“Subsequently, Durston and Chiu have developed a theoretically sound method of actually quantifying Functional Sequence Complexity (FSC) [77]”

    Another tick on the crank scale chart I’d say. But no matter. I turn to the referenced paper, and it turns out that “FSC” is essentially a measure of how conserved a functional protein is computed as something like Mutual Information, and also gives a specific measure of how conserved an amino acid is at any given site.

    Cool. It tells us that similar proteins are similar, and that they are most similar at sites that are most important for the function they seem to serve.

    Quick summary so far:

    • Complexity is Shannon Entropy times string length (I think).
    • Order can be algorithmic compressibility (which Abel erroneously states is incompatible with Complexity)
    • Order can also be non-flat probability distribution.
    • Neither results in function.
    • Functional Sequence Complexity is the amount of Mutual Information between proteins with similar function.

    Haven’t reached the punchline yet.

  10. Also the scholarship is terrible. There are 335 references, and not only are some of them to completely irrelevant papers that just happen to contain the phrase referenced (e.g. “Edge of Chaos”) I have no confidence that any of the sources actually say what the author claims they say. Take Monod: Abel writes:

    Chance and necessity, as Monod pointed out [174], are inadequate to describe everything we repeatedly observe, life especially. Science must acknowledge the reality and validity of selection as a fundamental, “properly basic” category.

    Reference 174 is Monod’s book with the English title “Chance and Necessity”. But in that book, which Abel has clearly not read, Monod says no such thing. The title of his book is a quotation from Democritus: “Everything existing in the Universe is the fruit of chance and of necessity”, and for Monod it is “chance” that governs variance generation (“The initial elementary events which open the way to evolution in the intensely conservative systems called living beings are microscopic, fortuitous, and totally unrelated to whatever may be their effects upon teleonomic functioning.”) but “necessity” that drives natural selection (“Drawn from the realm of pure chance, the accident enteres into that of necessity, of the most implacable certainties. For natural selection operates at the macroscopic level, the level of organisms”). In other words Monod agrees with Democritus.

    The reason I am sure that Abel has not read Monod’s book is not simply that he misunderstands Monod’s position re the title, but he totally ignores Monod’s main thesis which is that “function” in biology, refers to what perpetuates the organism and/or the population (what Monod calls teleonomy), which is highly relevant to Abel’s thesis, as far as I can tell. I suggest he reads the book.

    William, are you convinced yet that Abel is not the Great White Hope of ID? ;)

  11. Seversky: Let me see if I have this right. Under Shannon’s treatment, the information content of a message is its surprisal value, in other words, whatever is conveyed that was not previously known by the recipient? Thus, as you say, any subsequent transmissions of that same message to the same recipient will have no surprisal value and, therefore, presumably no information content? In other words, if exactly the same message can have provide information on the first transmission but not on any others, is it fair to say that this version of information is not so much a property of the message itself but refers more to a process, the change that it effects in the mind of the recipient?

    Your understanding is about right, although I would have to sharpen it up a bit.

    In Shannon’s treatment, information is defined not for a single message, but for a large set of messages. If the same message is repeated over and over then the Shannon information content is zero. If two kinds of messages are repeated with the same frequency, then each message is worth −0.5 log(0.5) − 0.5 log(0.5) = 1 bit of Shannon information. (The logarithms are to base 2.) If the message is “Happy birthday” 99 times of 100 and the rest are “I love you” then the Shannon information is −0.99 log(0.99) − 0.01 log(0.01) = 0.081 bits per message.

    One can say that Shannon treats messages as a bulk commodity, sort of like a truck driver who just needs to deliver and unload them. In contrast, Kolmogorov wants to appraise the values of individual messages and treats them as one-of-a-kind objects.

    The book by Li and Vitanyi (Ref. 183 in the paper) has some quotes from Shannon and Kolmogorov on p. 603.

  12. Elizabeth: William, are you convinced yet that Abel is not the Great White Hope of ID? ;)

    Here is a little factoid that will no doubt cheer up ID fans. Discovery Institute maintains a list of Peer-reviewed & peer-edited scientific publications supporting the theory of intelligent design. Currently there are some 50 papers on it. About one quarter of those (13) are authored or coauthored by David L. Abel.

    So this virtual journal club entry is not entirely in vain. We are discussing a paper by the most prolific* ID writer. :)

    *Judged by the number of publications. Dembski probably has the largest page count.

  13. It appears that everyone is picking up on the same problems with Abel’s paper. :-)

    I expect to get home by early evening, and I’ll add some comparisons with physics.

    There are some other issues that come up as well, and these fall into the realm of psychology I would assume. For example, why do papers like this capture the imaginations and devotion of those in the ID/creationist community?

    More generally, what are crackpots able to pick up on that allows them to write so persuasively for such an audience? Those of us in the science community should probably pay attention to this.

    Gotta hit the road.

  14. OK, I have finished the paper. The remainder seems to consists of a string of assertions, AFAIK, supported only by references, not arguments or evidence presented within the paper, most of which are to Abel’s own work.

    It is also very badly written, using anthropomorphic phrases that attribute agency to abstract referents, even though core of his point concerns willed agency:

    “Language, for example, uses arbitrary symbol selections from an alphabet of options…

    No, “Language” doesn’t “use” any such thing. Language users do.

    Physicality cannot plot and scheme…

    Indeed it can’t. Nobody claims it does. Intelligent organisms plot and scheme, not “physicality”.

    Stand-alone physicodynamics is blind to utility…

    Yes indeed.

    In short, Abel constructs (badly) straw men, then asserts (does not demonstrate) that the straw men don’t explain biological function, all the while making rookie mistakes with the basics of information theory.

    Oh, and cites irrelevant papers for no other apparent reason than that they use certain phrases, as well as at least one book he either has not read or has radically misunderstood.

    Next?

  15. Elizabeth: In short, Abel constructs (badly) straw men, then asserts (does not demonstrate) that the straw men don’t explain biological function, all the while making rookie mistakes with the basics of information theory.

    Exactly. The paper’s sections follow the same recipe:
    * mention lots of science-y terms from disparate fields of human knowledge (hey, no one can understand all of them),
    * cite lots of references (look, all these legitimate people support my statements),
    * add some editorial content that does not follow from the above and is just silly if one pauses for a minute to think about it.

    This goes on for 45 pages, so one needs great stamina to read through this crap and make sure that it does not contain anything of value. Fortunately, Section 2 is short (just 4 paragraphs), yet entirely representative of the rest of the paper. If you want to get a flavor, go ahead and read it. As I discussed in Part II, it begins with a discussion of “complexity” that conflates the rather distinct concepts of Kolmogorov complexity and Shannon entropy. Having accomplished that, Abel comes to this conclusion:

    The most complex of all strings is a random string. Random strings have never been observed to generate non trivial formal function of any kind. Complexity, therefore, has nothing to do with formal function. Complexity possesses no creative or computational talents. No justification exists for attributing exquisite formal organization to mere complexity.

    Indeed, if you pick letters at random, the resulting string will likely have high Kolmogorov complexity. But surely no one measures functionality of a DNA molecule by its Kolmogorov complexity. This is one of the straw men sprinkled liberally throughout the paper.

  16. Seversky: Let me see if I have this right. Under Shannon’s treatment, the information content of a message is its surprisal value, in other words, whatever is conveyed that was not previously known by the recipient?

    Not quite. The Shannon entropy is a measure of the compressibility of the symbols of the message based on their frequentist counts relative one another. It really helps to have a visual aid for this so see: Sannon-Fano and Huffman coding for a tree representation of how the bit strings are produced. (Specifically Huffman.) The idea is that you want to represent your alphabet in variable rather than fixed length bit encodings while still being able to uniquely differentiate each symbol from the next. The trees will give a good grasp of where the logarithms come into play.

    So there’s three ways to look at it. The second message *is* the symbol and so has no content. Each message is its own alphabet, which is the way winzip and other file compressors approach the problem. Or that you have a broad language wide frequency count for the alphabet, which is how Shannon approached it. In the last the entropy for any message, for itself, may be different from any other.

    Elizabeth: Cool. It tells us that similar proteins are similar, and that they are most similar at sites that are most important for the function they seem to serve.

    An oft overlooked issue here is that the proteins are encoded from DNA. In which base pairs not only serve as an ‘information’ encoding but also as a structural component of the DNA itself. So any given site may be conserved because it is a necessary structure for the DNA and/or a necessary structure for the folded protein. It would be good to see more research done on this in the future.

  17. Maus:

    An oft overlooked issue here is that the proteins are encoded from DNA.In which base pairs not only serve as an ‘information’ encoding but also as a structural component of the DNA itself.So any given site may be conserved because it is a necessary structure for the DNA and/or a necessary structure for the folded protein.It would be good to see more research done on this in the future.

    Well, I wasn’t overlooking that (although I’m not aware that protein-coding regions of DNA are constrained by the pressure to preserve the structure of DNA itself, althoutg you could be right), and it makes no difference to my point: that what the FSC measure delivers (and it seems pretty well equivalent to MI) is a measure of similarity between the proteins, and specifically, the measure of similarity at specific sites.

    What is that supposed to tell us?

  18. Elizabeth: On the other hand, the string

    1 1 1 1 1 1 1 1 1

    which I generated simply by omitting “+1″ from the algorithm that generated my ascending series above has much lower Entropy than either of the other two. Indeed the Entropy is zero.

    Elizabeth,

    There’s a basic misunderstanding at work here about Shannon info theory and Shannon Entropy. Abel isn’t helping, of course, but a couple points to bear in mind:

    Shannon entropy is always a measure of a string against a model, as a configuration from a known phase space. That means, that you cannot measure the “entropy of a string” in isolation from a model of the source whence it came. The entropy is dependent on the nature of the source. That means that if you have a truly random source for the string in question, “random” is your model, and governs the entropy calculation for any string drawn from the random source: all successive symbols are equally surprising, and thus have maximum entropy.

    Applying this to your post, then, the entropy for:

    1 1 1 1 1 1 1 1 1

    coming from a random source is EXACTLY the same as the entropy for:

    9 6 2 1 3 8 7 4 5

    or
    9 6 2 1 3 8 7 4 5

    when these strings come from that same random source. That means that for a random source, the Shannon entropy for any string from that source will be identical, and the same, for any possible string drawn from that source. This is tru by the definition of ‘random’: every single symbol is equally surprising, and reduces our uncertainty by exactly the same amount as it arrives from the source. If it does not, then by definition, the source is not random.

    Alternatively, then, if our source is a generator for only the symbol “1″, then the entropy for the string:
    1 1 1 1 1 1 1 1 1

    Is zero. In this case, we know a priori, (and this is crucial!) that the source in question only emits the symbol “1″, and so we have zero surprise value when each successive “1″ symbol arrives from the source. We have reduced our uncertainty by nought when each “1″ arrives, as we know ahead of time, what each new symbol must be.

    So, please note that the same string has different entropy values, based on the source when whence it came. The entropy of a string is not meaningful without referring to what is known about the source. Entropy, then, is a measure of the relationship between an emitted string of symbols, and the nature of the emitting source.

    I’ve more to say on this, but have to run out for a bit. Just hoping to keep things in line with how info theory really works in practice.

  19. eigenstate,

    Thanks for that. Yes, I do understand that, I think. I was making the (unsupported) assumption that the frequency distribution of symbols in the message is a representative sample of available symbols – and the reason I did so was because so many ID arguments for intelligent-pattern-detection assume that you don’t have any information about the source other than those in the “message”.

  20. Elizabeth: What is that supposed to tell us?

    Wasn’t rebutting you, just noting that DNA is the poor cousin of DNA.

    But all I take away from bitstring similarity is bitstring similarity. Without context of what the differences cause it doesn’t mean much. For analogy, in computers a single bit flip can be entirely meaningless. Or it can make all the difference in the world, and in completely baffling manners. And that’s in software where there aren’t chaperones to futz with.

    For ID to make their case they need to do a deeper dig into just what it is they’re looking at. Of course, that’s the same thing the Darwin camp ought be doing as well for the same reasons, if not different philosophies.

  21. Elizabeth,

    I am afraid that eigenstate’s comment might saw some confusion. How come strings 111111111 and 962138745 have the same Shannon entropy? One can answer that the entropy refers to the ensemble’s probabilities, rather than to the individual strings. But at the end of the day, Shannon’s entropy is computed for actual systems, where we are given a stream of messages, and not necessarily a probability distribution.

    How do we deal with this in practice? We extract a probability distribution from a long enough sample of messages. The observed frequency of a given message approaches its probability as the number of messages goes to infinity (the law of large numbers). So the frequency of digits in a sufficiently long numerical string should be representative of their actual probability distribution.

    In view of this, a long string of ones is indicative of a random source with the probability distribution where p(1) = 1 and p(0) = p(2) = p(3) = … = p(9) = 0. This probability distribution has zero Shannon information per digit.

    Strings 111111111 and 962138745 exhibited by eigenstate are not sufficiently long to infer their probability distributions reliably. But I would venture that the former comes from a source with low Shannon entropy. The latter is a bit more tricky: each digit occurs exactly once. This is not a typical string with a uniform distribution.

  22. Maus: Wasn’t rebutting you,

    OK :)

    just noting that DNA is the poor cousin of DNA.

    ?

    But all I take away from bitstring similarity is bitstring similarity.Without context of what the differences cause it doesn’t mean much.For analogy, in computers a single bit flip can be entirely meaningless.Or it can make all the difference in the world, and in completely baffling manners.And that’s in software where there aren’t chaperones to futz with.

    For ID to make their case they need to do a deeper dig into just what it is they’re looking at.

    Well, they need to dig deeper into what it is they are claiming, I would agree.

    Of course, that’s the same thing the Darwin camp ought be doing as well for the same reasons, if not different philosophies.

    Not sure what “thing” you are talking about. Can you explain?

  23. olegt: We extract a probability distribution from a long enough sample of messages.

    Yep, nailed it.

    Elizabeth: Not sure what “thing” you are talking about. Can you explain?

    Apologies, both teams need to be tackling the same problems here. Well, I say that, but the Darwin side of things is largely a history issue while the ID side is, whether it intends it or not, a forward going engineering issue. But I’ll still maintain that both camps need dig deeper into structural issues of DNA and the great nasty of protein folding to put the necessary context in place.

  24. Maus:
    Apologies, both teams need to be tackling the same problems here.Well, I say that, but the Darwin side of things is largely a history issue while the ID side is, whether it intends it or not, a forward going engineering issue.But I’ll still maintain that both camps need dig deeper into structural issues of DNA and the great nasty of protein folding to put the necessary context in place.

    ? The Darwin side of DNA structure and protein folding is a history issue? I have no idea what this means?

  25. olegt:
    Elizabeth,

    I am afraid that eigenstate’s comment might saw some confusion.How come strings 111111111 and 962138745 have the same Shannon entropy? One can answer that the entropy refers to the ensemble’s probabilities, rather than to the individual strings. But at the end of the day, Shannon’s entropy is computed for actual systems, where we are given a stream of messages, and not necessarily a probability distribution.

    How do we deal with this in practice? We extract a probability distribution from a long enough sample of messages. The observed frequency of a given message approaches its probability as the number of messages goes to infinity (the law of large numbers). So the frequency of digits in a sufficiently long numerical string should be representative of their actual probability distribution.

    In view of this, a long string of ones is indicative of a random source with the probability distribution where p(1) = 1 and p(0) = p(2) = p(3) = … = p(9) = 0. This probability distribution has zero Shannon information per digit.

    Strings 111111111 and 962138745 exhibited by eigenstate are not sufficiently long to infer their probability distributions reliably. But I would venture that the former comes from a source with low Shannon entropy. The latter is a bit more tricky: each digit occurs exactly once. This is not a typical string with a uniform distribution.

    Well, I actually generated all the strings in my post algorithmically!

    I mean I actually wrote a little script (in MatLab). I take both yours and eigenstate’s point though, that the strings are two short for anyone to have any confidence that the outputs are a representative sample of what might have been output. After all 11111111111111 might mean something rather important, like I’d fallen asleep briefly on my keyboard, although nnnnnnnnnnnnnnn might be more likely in that instance.

    But, yeah.

  26. So, I’m just flabbergasted by this paper. I’m not a scientist by trade, but I am by now comfortable reading scholarly literature on areas of interest, and keep up with scholarly journals of interest in computing (JACM, IEEE journals, etc.)

    I never run across a paragraph like this, at the top of page 250:

    Science celebrates positive and parsimonious descriptions of presumed objectivity. But we must never forget that our knowledge is only “best thus far.” Even the most fundamental laws of physics technically must be viewed as “tentative.” We rightly eschew diatribes of metaphysical pontifications. Science proceeds through open-mindedness and the falsification of null hypotheses, not through the rhetorical pronouncement of dogmas. Popper and many since have exposed the problems associated with trying to prove any positive hypothesis [176, 177]. Neither induction nor deduction is foolproof. Theses that cannot be proven ought not to be proclaimed as positive statements of fact.

    I read that and think I’m reading an April Fool’s day prank in this journal.

    Maybe I’m just not well read enough in the literature. But how does a paragraph like this get by the reviews and the editor?

    Or this, from the previous page (249):

    Attempts to relate complexity to self-organization are too numerous to cite [4, 21, 169-171]. Under careful scrutiny, however, these papers seem to universally incorporate investigator agency into their experimental designs. To stem the growing swell of Intelligent Design intrusions, it is imperative that we provide stand-alone natural process evidence of non trivial self-organization at the edge of chaos.

    Really? Really?

    I know IJoMS is one of the “open access” journals, which means authors and publishers pay to have their work published, and the articles are free to the public, but there is obviously no serious scholarly review in place here.

    I’m just getting to the parts that are at least nominally concerned with complexity, info theory, biology, chemistry, etc., so I’ll try to contribute something substantial to the discussion from reading that, but…. wow.

  27. It is pretty bad.

    I’m checking out The Cybernetic Cut (which I have in fact read, once, but will try harder this time).

  28. Really, David Abel is seriously confused. In The Cybernetic Cut (page 256), he writes:

    It is widely published that “evolution has no goal.” If an evolutionary experiment is “directed,” how could it possibly be evolutionary? If the process is truly evolutionary, it cannot be deliberately directed toward a goal. When an experimenter directs or steers a supposed “evolutionary algorithm,” that experiment constitutes artificial selection, not natural selection, the same as dog breeding.

    He has confounded the fitness function with the evolving solution. Evolution of course does have a goal, or rather, evolution follows the path of greatest fecundity. If greatest fecundity involves solving an environmental problem, like being inconspicuous to predators, or being thought cute by some other species, or outputing investment strategies given market inputs, or not breaking your bones when you fall out of a tree, or being attractive to a mate, then that problem may well be solved, not because that is “evolution’s goal”, but because that serves “evolution’s goal” of persisting.

    This is as true for a GA as it is for a peke as it is for a bacterial population faced with a new antibiotic as it is for a peacock faced with attracting a mate in the face of competition from other peacocks.

    No information is “smuggled in” to GAs that isn’t equally “smuggled in” to evolving populations by the environment they adapt to thrive in.

  29. Elizabeth: I mean I actually wrote a little script (in MatLab). I take both yours and eigenstate’s point though, that the strings are two short for anyone to have any confidence that the outputs are a representative sample of what might have been output. After all 11111111111111 might mean something rather important, like I’d fallen asleep briefly on my keyboard, although nnnnnnnnnnnnnnn might be more likely in that instance.

    Elizabeth,

    Length is a key factor in measuring complexity according to K-C theory; because algorithmic complexity requires both the “runtime” and the specific code to generate a given output string, for short strings a “simple” string may not possibly be generated by a shorter generating program than a “complex” string.

    But here, the length of your strings is not the problem. If you had used strings that were 10,000 chars in length, and having the same constitution (all ’1′s, a random sequence, etc.), nothing would change.

    If you are dealing with a random symbol source for your string, a string of 10,000 ’1′s is just as surprising (reduces uncertainty) as any other string you might pull from the source. Given a source that randomly generates numbers from 0-9, all generated strings, no matter what their content, will be the same.

    It’s definitional; if the entropies are different, then by definition the source if not a random source.

    That said, we often (in fact nearly always) have to deal with limited or incomplete information about the source, so we model the source based on statistical analysis of observed output. There is no authoritative model for the English language as a symbol source, but if we analyze large amounts of English text, we can derive a statistical profile of the symbols. Researchers like Ronald Rosenfeld have analyzed terabytes of English text and come up with entropy at approximate 1.23 bits per character, and have determined observed letter frequencies for each character in the language (see here for example freq data).

    So models for a source can and have been built without normative descriptions of the source, but these require large samples, way more than what you and I would call a “long string”. These samples would be the statistical basis for what you described as “a representative sample of what might have been output”.

  30. Elizabeth: Well, I actually generated all the strings in my post algorithmically!

    Elizabeth, at the risk of harping on this, let me add one more thing. I should really have responded first to this sentence from you, because it’s the key. Since you used MatLab to write a script to generate your strings, you know, authoritatively, the “phase space” for each source, each script.

    For you script generating “1111111111″, you know, with certainty, that the only symbol that can be emitted is “1″. Doesn’t matter how many you emit, a 10 char string or a 10 million char string, there is no reduction in uncertainty in any string that script emits.

    Now, for your “random script”, you know that the symbol space is [0-9], because that’s how you wrote it. Since it’s random (OK, likely pseudo-random because we are using conventional computers), in its symbol generation, “1111111111″ would be highly surprising, and would reduce our uncertainty with every successive character (but no more surprising than any other random string of [0-9]).

    Anyway, I just had the lightbulb moment that your scripts were the key to our joint understanding here. The fact that you wrote them, and have them in hand illustrates how and why the entropy for “”1111111111″ changes as the output from your “1″s script to your random script.

    Ok, back to the Abel…. whatever-it-is.

  31. eigenstate,

    I enjoyed the article on letter frequency. For my itatsi game I computed letter frequency, letter pair frequency, triplets frequency, etc, for six languages and used this to assign fitness values to randomly mutating strings. What I have is an operational definition of what it means for a string to look like a word.
    Such an oracle can evolve words and wordlike strings very efficiently. You can compete against the oracle, but you can’t beat it.

    I don’t claim it’s like biological evolution, but it does demonstrate that “intelligent” selection is not as powerful as an oracle that can integrate all dimensions of fitness.

  32. Elizabeth: Evolution of course does have a goal, or rather, evolution follows the path of greatest fecundity.

    Hmmm… I disagree. Rather than evolution, you’re talking about natural selection, for which greater fecundity is a “goal” only in a teleonomical sense.

    I skimmed through the paper and picked section 4, “Autopoiesis”. There he introduces the concept of autopoiesis* and claims that it is inadequate to explain OOL, claim he supports with a quote explaining that autopoiesis is intended to describe what life is, not how life came to be. That is true, but I see no indication that anyone in OOL research is confused by it (possibly except Abel himself [if we take seriously the claim he's an OOL researcher]). After that, he apparently makes no further use of the concept, so I’m left wondering what was the point of the whole section. Does anyone have a clue?

    I’m not strong enough to read any further.

    * In doing so he incorrectly spells the name of Humberto Maturana, and later “Valari” for Varela.

  33. On Page 255 of his paper, Abel – in referring to a pile of pick-up sticks – says this:

    The degree of complexity would be staggering. But what exactly does this enormous degree of complexity DO? The pile of pick-up sticks achieves no utility of any kind. The imagined capabilities of stand-alone complexity are in reality miniscule at best.

    One has to wonder what Abel thinks could come of such a pile of sticks. He certainly must know that they will eventually combine with other elements in the universe.

    And then he makes this assertion:

    Attributing organization to chaos and complexity employs a combination of fallacious inferences involving category errors and non sequiturs.

    Who does he think is doing this? The implication seems to be that scientists are doing this, and if so, it is a grotesque mischaracterization of scientists and what they think.

    So what comes of Abel’s calculation of the “Shannon uncertainty” for, say, a simple system consisting of only two constituents taken from the imagined “primordial soup” in the way Abel suggests in his example on Page 256?

    Let’s look at two constituents (A, B) and set the “availability probabilities” at p(A) = ½ and p(B) = ½ and then consider various constituents for A and B. Elizabeth already looked at some cases involving letters and numbers and demonstrated that various arrangements of those numbers and letters had the same “Shannon uncertainty” according to Abel’s calculations.

    Consider the following, all of which have exactly the same “Shannon uncertainty” according to Abel’s calculations.

    (black marble, white marble), (0 , 1), (X , Y), (electron , proton), (hydrogen , fluorine), (sodium , water), (carbon , hydrogen), (fluorine , silicon dioxide), (hydrochloric acid , zinc), (fox , rabbit).

    Clearly things with the same “Shannon uncertainty” according to Abel have very different “capabilities.”

    Try another two-constituent case in which p(A) = 1/3 and p(B) = 2/3.

    (black marble , white marble), (white marble , black marble), (0 , 1), (1 , 0), (electron , proton), (proton , electron), (hydrogen , fluorine), (fluorine , hydrogen), (oxygen , hydrogen), (hydrogen , oxygen), (hydrogen , sulfur), (sulfur, hydrogen), (carbon , oxygen), (oxygen , carbon), (fox , rabbit), (rabbit , fox).

    Chemists will recognize the issues of stoichiometry in these examples.

    Abel is projecting a set of preconceived notions and a prescribed set of requirements onto matter and energy and then attempting to leave the impression that “physicodynamic” processes aren’t up to the job. This is supposed to open the way for “information” and “intelligence.”

    But the complete argument is a non-sequitur because matter and energy do not behave in the way that Abel implies. Atoms and molecules and their increasingly complex assemblies are not inert things sitting around waiting to be sampled with a uniform random sampling distribution and placed in pre-specified arrangements.

    With matter and energy, what you get is what you see. Science takes it apart to find the rules and the dynamics. Those are the rules that apply to matter and energy, not Henry Morris’s, rules, not Abel’s nor Dembski’s, nor Sewell’s, nor any other ID/creationist “theorist’s.”

    I’ll do a separate comment on comparing thermodynamic entropy with Shannon entropy.

  34. For those who might be confused by “Shannon entropy” and thermodynamic entropy, here is a comparison.

    From the statistical mechanics perspective, entropy is defined as

    S = – kp(i) ln p(i)

    where k is Boltzmann’s constant, and i goes from 1 to Ω, which is the number of energy microstates consistent with the total energy of the thermodynamic system.

    Note that the summation is exactly the same as in the Shannon entropy and is the purported reason that John von Neumann suggested to Claude Shannon that Shannon call his expression entropy because nobody knew what it meant.

    As such, the expression for thermodynamic entropy behaves in the same way I described earlier for Shannon entropy. It is maximized when the probabilities of all microstates are equal; and for Ω microstates,

    p(i) = 1/Ω for all i.

    Then the above expression reduces to

    S = k ln Ω,

    and this expression is the maximum value the entropy can take on.

    Now here is the important difference from Shannon entropy. In the case of thermodynamics, a system in contact with a much larger heat bath at a fixed temperature will have a distribution over energy microstates for which the probabilities may be all different. So the first expression above applies.

    When the system is removed from its contact with the heat bath and is isolated, all the probabilities become equal and we get the second expression, and the entropy goes to its maximum.

    Here is the critical point. The probabilities become equal for an isolated thermodynamic system because all the microstates interact with each other by exchanging energy. The reason they do this is because matter interacts strongly with matter by various mechanisms such as the exchange of photons, the exchange of phonons (quantized sound waves in solids), or the exchange of other particles.

    If the microstates themselves were isolated from interacting with each other, the entropy would not change by drifting up to a maximum.

    And this is just the case for things like ones and zeros, or any other inert objects that do not interact with each other. When we see the ID/creationist theorists using entropy when discussing inert objects, that entropy can’t change by “isolating the system.”

    There is another important difference with the thermodynamic entropy. Thermodynamic entropy links important state functions of the system to each other. In fact, the temperature, T, of a thermodynamic system is defined buy

    1/T = ∂ S/∂ E

    where E is the total energy of the system. In words, the reciprocal of the temperature is defined by how the entropy changes with the corresponding change in total energy.

    So thermodynamic entropy contains implicitly within it the physical interactions of matter with matter and the physical dynamics of how the number of energy microstates changes with total energy.

    Shannon entropy does none of that. Thermodynamic entropy is about the physical universe, and Shannon entropy is simply one of a number of ways to study patterns in the data of one’s choosing.

  35. Elizabeth,

    It’s not about what Shannon entropy actually is and how it is actually used; it’s about how Abel abused it.

    He was pretty clear at the bottom of Page 256 on how he got his probabilities from his “primordial soup.” He calls the probabilities “prebiotic availability” in one sentence and “hypothetical base-availability probabilities” about two sentences later.

    So he appears to be sampling from an imagined, infinite “soup” in which removing a few of the constituents makes a miniscule change in the probabilities for those constituents.

    If he were sampling from a relatively small “soup” of constituents, he would have to be sampling with replacement in order to keep the probabilities constant for each of the various constituents.

    So Abel is calculating what he calls “Shannon uncertainty” in order to concoct some sort of prescription that “physicodynamic processes” can’t handle. It’s just plain bogus.

    Complexity in physics permits more things to happen; but it is the underlying interactions among atoms and molecules and the energy from the energy bath in which they are immersed that do all the work.

    I might have included another example of Abel’s calculation by using a two-constituent case in which p(A) = 10^-16 and p(B) = (1 – p(A)).

    Then look at (A, B) for (phosphorus, silicon) as compared with (boron, silicon).

    In the physics of solid state devices, the first is what is known as N-type silicon, and the second is P-type silicon. Quite different.

    Just using Abel’s concoction leads to all sorts of silliness.

  36. I see the UD mele has spilled out of the bar into the alley and has now swelled into a full fledged riot in the viral streets. Apparently my ability to add and subtract integers had in fact not eroded, and I can simply no longer post to UD.

    I have been hereby attracted to the mathyness of this post. Now I must look at this paper and see what all the excitement is about.

  37. I take the points of all who have pointed out that the the Shannon Entropy of a message doesn’t simply depend on the distribution of symbols in the message but on the distribution of symbols in the population from which it is drawn. Or something.

    But am I right (and is Abel simply wrong?) that ordering the symbols in a message (by ranking, for instance) makes no difference to the Entropy?

  38. Elizabeth: But am I right (and is Abel simply wrong?) that ordering the symbols in a message (by ranking, for instance) makes no difference to the Entropy?

    Remember that Shannon information is defined not for a single message but for a stream of messages. If you reorder symbols in a single message then you change the message. But that’s probably not what you meant.

    If you treat a message as a stream of symbols and want to compute their Shannon information then the order of symbols has no impact on their frequencies and hence the calculated Shannon information. In that sense, Abel is wrong.

    However, if we are talking about the Kolmogorov complexity of a message then it’s a different story. A message in which symbols are ordered may be described in a shorter way, e.g., “26 As followed by 40 Bs, 37 Cs…, and 25 Zs.”

    The problem with Abel is that he conflates the two concepts.

  39. Neil Rickert,

    Shannon’s theory had nothing to do with information!

    The word information in this theory is used in a special mathematical sense that must not be confused with its ordinary usage. In particular, information must not be confused with meaning.- Warren Weaver, one of Shannon’s collaborators

  40. Joe G:
    Neil Rickert,

    Shannon’s theory had nothing to do with information!

    Well, it had little to do with meaning.

    Abel rightly makes that point, but AFAICT wrongly implies that symbols arranged in a meaningful order has less Shannon Entropy than the same symbols shuffled randomly.

    For this reason he rejects both “complexity” and “order” as measures of “functional sequence complexity”.

    But his measure of “functional sequence complexity” (FSC) seems to mean some measure of the mutual information (the similarity, essentially) between DNA or protein sequences that have the same biological function.

    Then he just sort of leaves it, and talks about something else.

  41. olegt: Remember that Shannon information is defined not for a single message but for a stream of messages. If you reorder symbols in a single message then you change the message. But that’s probably not what you meant.

    If you treat a message as a stream of symbols and want to compute their Shannon information then the order of symbols has no impact on their frequencies and hence the calculated Shannon information. In that sense, Abel is wrong.

    However, if we are talking about the Kolmogorov complexity of a message then it’s a different story. A message in which symbols are ordered may be described in a shorter way, e.g., “26 As followed by 40 Bs, 37 Cs…, and 25 Zs.”

    The problem with Abel is that he conflates the two concepts.

    Well, he both conflates them and says they are incompatible: that a maximally complex string is the opposite of a maximally ordered string (where sometimes ordered seems to mean minimum Kolmogorov complexity, and sometimes means non-equiprobable distributions of symbols).

    I think he’s wrong on both counts.

    But he rejects both, and plumps for “FSC” which doesn’t seem to get him any forrarder as far as I can tell.

  42. Hey if you people could refute Abel you would- but obviously you can’t.

    Your position can’t account for transcription and translation- and that should be a problem.

  43. Joe G:
    Hey if you people could refute Abel you would- but obviously you can’t.

    Well, we can refute his about what his equation 1 indicates because because he’s clearly misunderstood it. We can’t refute much else because it doesn’t even make a lot of sense.

    What do you think his argument actually is?

    Your position can’t account for transcription and translation- and that should be a problem.

    It is, which is why there is a lot of research in that area.

  44. Joe G: Shannon’s theory had nothing to do with information!

    LOL.

    It has a great deal to do with information. It is, however, not a theory of meaning.

    When I started studying human cognition, I had the same view as you of Shannon’s theory. But, as my investigation has progressed, I have had to reassess that and I now have far greater appreciation for Shannon’s ideas.

  45. Elizabeth: I take the points of all who have pointed out that the the Shannon Entropy of a message doesn’t simply depend on the distribution of symbols in the message but on the distribution of symbols in the population from which it is drawn. Or something.
    But am I right (and is Abel simply wrong?) that ordering the symbols in a message (by ranking, for instance) makes no difference to the Entropy?

    Thermodynamic entropy has absolutely nothing to do with order/disorder. I can provide an example if anyone is interested.

    The Shannon entropy uses exactly the same mathematical calculation and simply attaches a number to the average of the logarithms of the probabilities, no matter what those probabilities represent and no matter what order. Like any average, order doesn’t matter.

    In order to discuss order, one has to have some criterion for determining what one means by order of the entities one is discussing, and then one needs to make use of some knowledge of the permutations of those entities.

  46. In order to discuss order, one has to have some criterion for determining what one means by order of the entities one is discussing, and then one needs to make use of some knowledge of the permutations of those entities.

    I sure would like to see some comment on coding sequences that indicates what advantage a designer has over evolution. It’s one thing to assert (without evidence) that functional sequences are rare and isolated. It’s quite another to assert there is some non-magic way of knowing how to find them.

    Human engineers can calculate whether adding a foot or an inch to the length of a cantilever will cause it to break. What is the equivalent body of knowledge for protein design? How does the designer know the effect of a point change?

  47. olegt: Remember that Shannon information is defined not for a single message but for a stream of messages.

    The corresponding concept in thermodynamics is called an ensemble. This represents all possible configurations of the energy microstates that are consistent with the total energy of the thermodynamic system.

  48. Joe G:
    Hey if you people could refute Abel you would- but obviously you can’t.

    Your position can’t account for transcription and translation- and that should be a problem.

    Even you can’t refute gobbledygook, Joe; but if you want to believe it all, that’s no problem.

    As to “our position” not being able to account for transcription and translation, that may be true, but as Febble has pointed out and linked, there is a lot of research oin these areas.

    I wonder if you would be good enough to link to any reasonably recent research on these subjects which you would NOT ignore.

    Or do you prefer to think that somewhere, at some time, there was or is some entity possessing all the necessary information to set these things up from scratch?

  49. Elizabeth: Anyone want to weigh in on FSC?

    Notice that Equation 2 on Page 253 is exactly of the mathematical form of the Shannon entropy. It is an average of the logarithms of probabilities. Again, order makes no difference to an average.

    This formula simply makes use of a continuous distribution of probability rather than a discrete distribution.

    It should be pointed out here that this is simply one in an arsenal of mathematical methods to find a number that is sensitive to some particular feature of the data one studies.

    For example, autocorrelation is simply an integral of a continuous distribution matched against a shifted version of itself. One can do this same game of matching a discrete distribution against itself by sliding the distribution along a copy of itself and making a measurement of the number of entities that match up.

    In either case, whether the distribution is continuous or discrete, if anything changes in the distribution as compared with a previous copy of the distribution, one can pick up on that by the change in the number that falls out in the calculation.

    I should point out that attaching names such as “information” or “complexity” or whatever else one wants to attach to the calculation has absolutely nothing to do with what is calculated. You call it what you want to call it.

    But one of the naming rules in science in the past has been to attach a name that doesn’t carry any intellectual baggage along with it. Calling something “information” or “order” or “complexity” will be extremely misleading if you don’t know what these words mean and what they refer to.

  50. Joe G: Hey if you people could refute Abel you would- but obviously you can’t.

    It’s not clear why you would make such a claim if you haven’t read or cannot read the paper.

    What, specifically, do you find wrong with the critiques of Abel’s calculations so far?

  51. Elizabeth,

    Just because there is research into transcription and translation does not mean your position can account for it.

  52. Joe G:
    Elizabeth,

    Just because there is research into transcription and translation does not mean your position can account for it.

    Jumping in – sorry, Febble

    Elizabeth has already agreed that “her” position cannot account for them, but points out that there is research into their evolution.

    ID is doing no research into it. I think there is probably no way they can, because the mechanisms involved in ID are not amenable to research. Too much of a “pathetic level of detail”, or something – I believe that’s how a leading IDist thinks of such things. ID theory is not “mechanistic”.

    Just pooftastic

  53. Joe G:
    Elizabeth,

    Just because there is research into transcription and translation does not mean your position can account for it.

    I know it doesn’t. I didn’t say it did.

  54. Joe G: Neil R:

    It has a great deal to do with information.

    By what definition of the word?

    I am talking of the ordinary common sense meaning of “information” which includes speech, writing, and what the brain does to provide us with perception.

    This is heading off on a tangent from the topic. I suggest we stick with the topic.

  55. Mike Elzinga: I should point out that attaching names such as “information” or “complexity” or whatever else one wants to attach to the calculation has absolutely nothing to do with what is calculated. You call it what you want to call it.
    But one of the naming rules in science in the past has been to attach a name that doesn’t carry any intellectual baggage along with it. Calling something “information” or “order” or “complexity” will be extremely misleading if you don’t know what these words mean and what they refer to.

    In an earlier comment I had mentioned that the same misconceptions and misrepresentations introduced by Henry Morris back in the early 1970s have propagated throughout ID/creationist writings for something like 40+ years now.

    What we see here in this Abel paper we also find in Dembski and Marks when they refer to “endoginous information,” “exogenous information,” and “active information.” The mathematical formulas they use do not justify those names; and the mere labeling with such names evokes misconceptions in lay readers that something significant has been calculated.

    In Granville Sewell’s second law paper, Sewell makes assertions that have nothing to do with entropy. Again he introduces an equation that might apply to an extremely narrow case and then proceeds to plug things into it that he has no business plugging into it.

    In Sewell’s case, what he does is analogous to taking the formula for calculating the hypotenuse of a right triangle from the lengths of its sides and then plugging in weight and shoe size in order to calculate a person’s IQ.

    Irreducible complexity, complex specified information, genetic entropy and dozens of other terms, such as those we see in this paper by Abel, are all based on the same basic misconceptions and misrepresentations of what actually takes place in the world of biology, chemistry, and physics. The names that ID/creationist authors choose are loaded terms that evoke beliefs about their work that are not justified by the calculations they do.

    There are already sound definitions for terms like order and randomness. Chaotic, random, pseudo-random, indeterminate, noise, signal, entropy, and the like are well-defined in science and in many fields of engineering.

    When Rudolf Clausius coined the term entropy, he was giving a label to a mathematical expression that was constantly showing up in calculations. This is a normal procedure in science and mathematics; to name recurring mathematical expressions for easy reference. Clausius was careful to pick a name that carried no emotional baggage with it. If he had not named it, somebody else may have given it another name, or quite possibly have named it after some physicist.

    Abel muddles these concepts and applies names to things without any justification except to make assertions that appear to be more profound than they are.

  56. The names that ID/creationist authors choose are loaded terms that evoke beliefs about their work that are not justified by the calculations they do.

    In this respect, I’m reminded of the old wish on the part of programmers that the compiler would discard the code and compile the comments. After all, the comments describe what the code is supposed to do.

    In this case, the labels and loaded terms for the calculations are the message, and the calculations themselves are the comments, intended to be discarded by the target reader who remembers and absorbs the words.

    What you describe sounds no different in principle from the common practice of providing reference footnotes for claims which if dug into, turn out either to have nothing to do with the referencing claims, or to be inconsistent with them.

    The purpose of the calculations is to give a good opaque veneer of quantitative “meaning” and precision to something that isn’t being calculated, and generally can’t be calculated anyway.

  57. Flint: In this respect, I’m reminded of the old wish on the part of programmers that the compiler would discard the code and compile the comments. After all, the comments describe what the code is supposed to do.

    :-) Man, I had forgotten that one.

    And that reminds me of a story a computer administrator friend once told me.

    This was way back in the days of the IBM 1620 and card readers, sorters, and collators.

    He had a student show up at the service window (remember those) of the computer center with an armload of lab notebooks and papers. He asked my friend if he could run all that through the computer for him.

    My friend said that he had to resist the very strong urge to put it all in the shredder and then look nervously at the computer and tell the student that the data broke the computer and that he was going to have to call the IBM Customer Engineer.

  58. Mike Elzinga,

    I read the section you suggested. He seems to be talking about a source population of dna bases in Gaussian terms whereas adenine clusters around the mean and cytosine at the tail. Such that the occurrence of cytosine approaching the mean in any string, due to the low p increases the “surprise” factor
    of that particular string, therefore increasing the uncertainty, or it’s information entropy. So Abel seems to suggest that we should expect that the entropy of the set of possible outcomes should be 1.5 bits, but instead we observe this closer to 2 bits.

    The inference being that the uncertainty in an aa string exceeds the expectation (based on the population assumptions of abel) being acted on by physics and chemistry. Such that the information found in aa strings exceeds expectation in shannon terms.

    I’ll finish reading this today at some point. I don’t really feel like it though.

  59. junkdnaforlife:
    Mike Elzinga,

    I read the section you suggested. He seems to be talking about a source population of dna bases in Gaussian terms whereas adenine clusters around the mean and cytosine at the tail. Such that the occurrence of cytosine approaching the mean in any string, due to the low p increases the “surprise” factor
    of that particular string, therefore increasing the uncertainty, or it’s information entropy. So Abel seems to suggest that we should expect that the entropy of the set of possible outcomes should be 1.5 bits, but instead we observe this closer to 2 bits.

    The inference being that the uncertainty in an aa string exceeds the expectation (based on the population assumptions of abel) being acted on by physics and chemistry. Such that the information found in aa strings exceeds expectation in shannon terms.

    I’ll finish reading this today at some point. I don’t really feel like it though.

    Could someone clarify what section is being referred to here? Page number?

    Thanks!

  60. Lizzie:

    I hate to see you struggle with this article. I gave it a close reading shortly after it came out, and concluded that the verbiage related to information and computation is word salad. I looked at some of Abel’s other solo efforts, and resolved never again to waste time on him. The papers he’s coauthored with Trevor are coherent.

    As pointed out above, Shannon entropy is measured on the source, not the string of symbols it emits, and Kolmogorov complexity is measured on the string. The way you have used the string is essentially to estimate the entropy of the source.

    Contrary to what someone indicated, Kolmogorov complexity is related to randomness. Suppose that the alphabet for strings and programs is {0, 1}. If the Kolmogorov complexity of a string is greater than or equal to the length of the string (i.e., no program that outputs the string is shorter than the string itself), then the sequence of bits in the string passes all computable tests for randomness. Thus incompressible strings are referred to as Kolmogorov random. Almost all strings are Kolmogorov random, or very nearly so. (Randomness is a matter of degree.)

    A string may be too “random” to be random. if a string over alphabet {0, 1} has the same number of 0′s as 1′s, then that property can be used to compress it. Furthermore, a string is incompressible only if it has a logarithmically long substring that is compressible. (This leads to speculation is that we live in an orderly region of a random universe.)

  61. Mike Elzinga: What we see here in this Abel paper we also find in Dembski and Marks when they refer to “endoginous information,” “exogenous information,” and “active information.”The mathematical formulas they use do not justify those names; and the mere labeling with such names evokes misconceptions in lay readers that something significant has been calculated.

    Yes, the name game is everything. Dembski and Marks go so far as to apply “-log” to subjective probability and treat the result as physical information created by intelligence. In the Weasel problem, for instance, the target string is not random. The uniform probability D&M introduce is clearly epistemic.

    In search, if performance is 1 for success in obtaining a satisfactory solution to the problem, and 0 for failure, then the probability that an algorithm obtains a satisfactory solution is its expected performance. Endogenous, exogenous, and active “information” are just logarithmic transformations of expected performance.

  62. Elizabeth: Could someone clarify what section is being referred to here? Page number?

    I think he is referring to Abel’s calculation on Page 256.

    The interpretation that one gives to a calculation depends on context. C = A x B can mean many different things depending on what A, B and C stand for.

    In the case of Shannon entropy, when all the probabilities are equal, the Shannon entropy is maximized. Now it is true that this means that if you dip into the set of entities for which this is calculated, you are equally likely to grab any one of them. If the Shannon entropy is low, then sampling successes will be skewed toward the entities with the higher probabilities.

    But one doesn’t need Shannon entropy to tell you that; one could simply use the product of the probabilities, as I pointed out earlier. That wouldn’t generate any voodoo misconceptions about what is happening.

    In the ID/creationists’ minds, and in the writings of the ID/creationist authors, generating these misconceptions by labeling their calculations with loaded words appears to be a big part of their game. Some of the authors appear to actually believe they are delving into deep understanding; but they are simply fooling themselves with their own words.

    Most of that word-gaming comes from their sectarian history of exegesis, hermeneutics, etymology, and from their retranslations of old writings to extract the “proper” meaning.

    If you look at all the discussion with ID/creationist followers of this stuff, you will note that it always gets bogged down into a mud-wrestling contest over the meanings of words. Abel captures that obsession in his writings.

  63. Tom English: Lizzie:
    I hate to see you struggle with this article. I gave it a close reading shortly after it came out, and concluded that the verbiage related to information and computation is word salad. I looked at some of Abel’s other solo efforts, and resolved never again to waste time on him. The papers he’s coauthored with Trevor are coherent.

    In fairness to Elizabeth, I was the one who, in another context, quoted a comment from Abel which then elicited a challenge to prove this particular paper wrong. That somewhat derailed that thread, but Elizabeth thought a virtual journal club might be a good idea.

    As nauseating as these kinds of papers are – and I can assure you that I have to fight the gag reflex when I read them – I think those of us in the science community have some responsibility for clearing this junk out of public discourse.

    This farce has been going on for nearly 50 years now, and somebody with the knowledge and skill needs to inform the public about how these pseudo-scientists operate.

    I personally don’t enjoy it, but I had the misfortune to be in the wrong place at the wrong time back in the 1970s and had to study this stuff and inform students and the public about what was wrong with it.

    However, I have been able to mitigate the nausea by using these kinds of writings to learn how misconceptions and mischaracterizations are generated and propagated. That actually helps in developing instructional materials; and it gives some insight into the psychological make-up of some of these con artists that do this in other areas as well.

    The challenger who wanted me and others here to prove this paper wrong made accusations of handwaving generalities on our part.

    Yet this video by Thomas Kindell is a classic example of what we are up against.

    One can jump over to UD to see all sorts of demonizing and mischaracterizations of science and scientists.

    As I mentioned earlier on that other thread, in the 40+ years I have been watching this phenomenon, I have yet to encounter a follower of the writings of ID/creationist authors who can actually read these works and defend and justify them. Yet they certainly have strong emotions about them and will engage in endless mud-wrestling about words in these papers.

  64. Yes, I do understand that Shannon Entropy is normally evaluated on the source not the string.

    I was (ill-advisedly as it turns out) putting myself in the shoes of the IDists whose project is to take a string of unknown origin and figure out whether it was designed. But I accept that even Abel bothered to figure out what the source must have been (his estimates of frequencies in the prebiotic soup).

    However, I think my two points remain valid:

    1. That Abel is claiming that Shannon “complexity” is necessarily at the opposite pole to an “ordered” string (using some kind of Kolmogorov measure), and that this is wrong.
    2. That Abel’s “FSC” measure is simply a measure of mutual information between proteins that have a similar function, and at no point does he make a coherent argument that “FSC” cannot be produced by non-intelligent agents, or even that the measure is relevant to the question. He merely asserts this.

  65. Elizabeth: However, I think my two points remain valid:
    1. That Abel is claiming that Shannon “complexity” is necessarily at the opposite pole to an “ordered” string (using some kind of Kolmogorov measure), and that this is wrong.

    2. That Abel’s “FSC” measure is simply a measure of mutual information between proteins that have a similar function, and at no point does he make a coherent argument that “FSC” cannot be produced by non-intelligent agents, or even that the measure is relevant to the question. He merely asserts this.

    I would not even use the term “mutual information” in comparing proteins or any other sequences of entities.

    There are better terms that don’t load a false impression onto the comparison. Autocorrelation, or percentage match (or difference), or p-value, whatever; but not some term that contains an implicit assertion that something is being measured that isn’t.

    For example, one can compare sequences with references and count the differences in some way. It could count mismatches, or the number of permutations needed to get back to the original, or any other feature for which one can attach a number. That number could be expressed as a percentage change or whatever one can use to plug into a sensitive calculation.

    Find some neutral term, but don’t call it information. “Information” is an extremely ambiguous term with implications of intention and communication and intelligence. That seems to be the reason ID/creationist theorist like to use it; it matches their preconceptions. Adding the math makes it look scientific.

  66. junkdnaforlife: Mike Elzinga,
    I read the section you suggested. He seems to be talking about a source population of dna bases in Gaussian terms whereas adenine clusters around the mean and cytosine at the tail. Such that the occurrence of cytosine approaching the mean in any string, due to the low p increases the “surprise” factor
    of that particular string, therefore increasing the uncertainty, or it’s information entropy. So Abel seems to suggest that we should expect that the entropy of the set of possible outcomes should be 1.5 bits, but instead we observe this closer to 2 bits.
    The inference being that the uncertainty in an aa string exceeds the expectation (based on the population assumptions of abel) being acted on by physics and chemistry. Such that the information found in aa strings exceeds expectation in shannon terms.

    I don’t know what one could mean by “information entropy” in this context.

    Earlier in the thread I had demonstrated that even simple, two-constituent systems with probabilities of ½ chosen from a “primordial soup” will have vastly different “capabilities” (from Abel’s assertions on pages 255 and 256) depending on what the constituents are. Here are some of those examples. It is easy to make up more.

    (electron, proton) ⇒ hydrogen atoms.

    (water, sodium) ⇒ sodium hydroxide and hydrogen and lots of photons.

    (black marble, white marble) ⇒ a grey mass or line when view from a distance.

    (fox, rabbit) ⇒ an unstable ecosystem.

    Simply change the probabilities to 1/3 and 2/3 and we can get all sorts of other “capabilities” (for exactly the same “Shannon uncertainty”) depending on the constituents.

    Abel’s assertions and “analyses” are just irrelevant silliness; atoms and molecules and their more complex compounds interact strongly or weakly depending on what they are and what kinetic energies they have and what kind of heat bath and environment they are immersed in.

    Abel’s “analysis” doesn’t apply to anything in particular because it doesn’t have anything to do with what actually happens with things in the real world. As I said, the entire argument in this paper is a non-sequitur.

  67. Abel’s argument is not ultra tight, but it’s not as if, (if one were to base their opinion strictly on what the posters here have offered ), that he clenched a pencil between his buttock cheeks, scribbled it across a piece of paper, signed it, and shipped it off for peer review.

    (He should have leaned on the Cytosine issue, with at least a paragraph of why the chemistry put this dna base at the tail in his population assumptions.)

    Your examples indicate some surprise, but I think lower value.

    {electron | proton} -> hydrogen. There is a very small surprise factor here, with H being 1 and 1. Rather, a surprise would be a frequency whereas {U,TH} clustered around the
    mean (most common elements) and {H,He} were clumped in the tail (least common). Instead, save for a couple odd balls, the elements appear to follow a Gaussian distribution whereas the lightest elements cluster around the mean and the heaviest occupy the tail.

    The periodic table is an example of low Shannon entropy.

    {white marble | black marble } = gray. If we dial back and see gray, there would be little surprise. Shannon entropy would be low in this case. A “surprise” would be a population of white and black marbles with a threshold closer to 0 or 255.

    Gray would be an example of low Shannon entropy. I think the rest of your other examples could fit into one of these categories.

    But say for instance this example:

    {a,b,c,…,z} = Great Expectations

    In this case, despite each character being equaprobable, we find that
    the characters {e,t,a,o,i,n} cluster around the mean, and {z,q,x,j,k,v} occupy the tail,

    This book is an example of high Shannon entropy.

    In Abel’s molecular population of dna bases, pg. 256, the roles are reversed, but the outcome is the same. Instead of flat->Gaussian as in the Great Expectations example, his dna base population frequency follows from Gaussian -> flat. Both populations are outputting a similar high surprise ->increased Shannon entropy. His argument appears to be that in these examples the outcomes are different than what we would expect to see (as in your examples) if only chemistry and physics is acting on the population.

    Abel’s argument I believe is that observing a string with high Shannon entropy that
    is also simply describable (as in K-comp terms, and I assume executes some function, but I haven’t got that far yet), than infer some type of intent.

    I done with this guy’s paper. You can have the final curb stomp.

  68. junkdnaforlife,

    You are missing a crucial point. Letters and numbers do not interact strongly with each other. Atoms and molecules do.

    I deliberately picked the simplest examples I could easily put in a comment. And even those simple examples have huge varieties in what falls out for Abel’s version of having exactly the same “Shannon uncertainty.” So Abel’s paper is meaningless.

    Hydrogen has many, many more properties than do just electrons and protons by themselves. And this is just one of the simplest of cases of emergent phenomena that takes place at all levels of complexity with atoms and molecules.

    Condensed matter is extremely complicated; and emergent phenomena appear rapidly with even very small changes in complexity or rearrangements or “contamination.”

    Take just the properties of, say, lead (Pb) alone. I would hazard an assertion that most people cannot list more than a few properties of a chunk of lead. Most people would have no idea what goes on in any collection of atoms or molecules of exactly the same kind or how any of that changes with temperature and with the introduction of small amounts of other elements.

    Do you understand that the formula for Shannon entropy is an average? It is the average of the logarithms of the probabilities, no matter where those probabilities come from. Averages are insensitive to order. And averages of logarithms or the sum of the logarithms or the product of the probabilities have nothing to do with order.

    There is no way this “measure of probabilities” can tell you anything about the interactive properties of things to which those probabilities are tacked on.

    I provided a comment above about the crucial difference between thermodynamic entropy and Shannon entropy. It is worth rereading.

    The periodic table is an example of low Shannon entropy.

    I’m afraid I can find no meaning in this assertion.

    What could it possibly tell us about the periodic table that chemists and physicists don’t already know light years beyond what any average of logarithms of probabilities can tell us?

  69. junkdnaforlife: The periodic table is an example of low Shannon entropy.

    Would you indulge us with an actual calculation of the periodic table’s Shannon entropy? I would pay good money to see that.

  70. I’ve read a few of Abel’s papers, but not this one. Therefore I’ll just make a general comment.

    Abel, and UD’s UprightBiped, are holding to a philosophical position that goes back to HH Pattee and the intellectual father of modern ID, Michael Polanyi. These are the guys that can’t get how “formal” function can arise from raw bits, chemical flotsam and jetsam, etc. because all things formal are necessarily prior to the physical world. In the beginning was the Word, not the World, and God created Man in His Image, not vice versa.

    Abel is simply trying, laboring mightily, to polish Polanyi’s turd. Polanyi’s JASA article (the Journal of the (Christian group) American Scientific Affiliation, not as UpBd thinks, the American Statistical Association) “Life’s Irreducible Structure”, 1968, is the cloaca from which the modern ID thinking flows.

  71. junkdnaforlife:

    Abel’s argument I believe is that observing a string with high Shannon entropy that
    is also simply describable (as in K-comp terms, and I assume executes some function, but I haven’t got that far yet), than infer some type of intent.

    I done with this guy’s paper. You can have the final curb stomp.

    Well, thanks, I will! My final curb stomp is that that can’t be Abel’s argument because he argues that high Shannon “complexity” (for which he gives the formula for Entropy) is at the opposite pole from describability.

    What you describe seems to be Demsbki’s position, not Abel’s (he allows strings to be both complex and describable).

    Dembski’s position is also problematic, though, and Abel seems to attempt to get around Dembski’s problem by adding in “functional” – and then proposes “FSC”. But his “FSC” seems just to be something like the similarity between strings with similar function. I don’t see how it helps him.

    Not that Abel seems to see Dembski’s problem. Perhaps we should have a look at Dembski now?

  72. David vun Kannon: I’ve read a few of Abel’s papers, but not this one. Therefore I’ll just make a general comment.
    Abel, and UD’s UprightBiped, are holding to a philosophical position that goes back to HH Pattee and the intellectual father of modern ID, Michael Polanyi. These are the guys that can’t get how “formal” function can arise from raw bits, chemical flotsam and jetsam, etc. because all things formal are necessarily prior to the physical world. In the beginning was the Word, not the World, and God created Man in His Image, not vice versa.
    Abel is simply trying, laboring mightily, to polish Polanyi’s turd. Polanyi’s JASA article (the Journal of the (Christian group) American Scientific Affiliation, not as UpBd thinks, the American Statistical Association) “Life’s Irreducible Structure”, 1968, is the cloaca from which the modern ID thinking flows.

    I would add here that ID also inherited fundamental misconceptions from Henry Morris, who set up a narrative that pitted a caricature of evolution against a caricature of the second law of thermodynamics.

    So the stage was set when the morph from “creation science” to “intelligent design” occurred after the 1987 US Supreme Court decision. Dragging in Polyani’s writings gave the ID movement a little more panache (in their minds anyway).

    I suspect some of the thoughts of A.E. Wilder-Smith seeped into Morris’s thinking, but I haven’t put much effort into tracking this down.

    Fairly early on, back in the late 1970s and early 1980s, I started moving away from dealing with all the sophistry in the ID/creationist movement and started going directly after their misconceptions about chemistry, physics, and biology. In particular, I found that their mathematics and physics, when taken down to the bare bones, were ludicrously misleading.

    Simply attaching words to calculations doesn’t change what calculations do. And the entities to which the calculations refer in ID/creationism have nothing to do with the forces and dynamics associated with atoms and molecules in the real world.

  73. Elizabeth: Not that Abel seems to see Dembski’s problem. Perhaps we should have a look at Dembski now?

    I have the Dembski and Marks paper as well as Sewell’s paper. Just as Abel does, the Dembski and Marks paper attaches misleading names to calculations without any justification.

    Sewell’s paper is even worse in its misconceptions and mischaracterizations.

    Demolishing these papers might look like pure cruelty to some, but that’s the fault of the papers themselves.

    I think I will still be available for the next few weeks before I have to do some more traveling.

  74. Elizabeth,

    I don’t think Abel would be all that rattled by this post, seeing that half a dozen charges of him being a crank, how wrong he is and all the flaws in his work were pointed about before many of the posters here seemed to have a clue on what Shannon entropy was in the first place. If you follow the evolution of this post, you will see that the Abel hammers come in swiftly, and are then followed quickly by confusion and bickering about what shannon entropy is, to the point where Mike E had to come in and take everybody step by step through the equations to keep the thread from derailing into a fight about entropy rather than the paper.
    So I would recommend having Mike E write a top post about Dembski’s paper first, detailing the issues and problems he sees, before releasing the hounds next time.

  75. I don’t think that abel would be too rattled by this post, seeing that half a dozen charges of him being a crank, that he is wrong, and the pointing out of all the flaws in his work were made before many of the posters here seemed to even understand what shannon entropy was in the first place. If you follow the evolution of this post, you will see the abel hammers come in swiftly, followed by confusion and bickering about what shannon entropy is, to the point where Mike E had to jump in and take everybody through the equations step by step. So if you want to hammer on Dembski or Sewell, I would recommend having Mike E write a top post about the paper, detailing some of the problems and issues first, before releasing the hounds.

  76. Elizabeth,

    I don’t think that abel would be too rattled by this post, seeing that half a dozen charges of him being a crank, that he is wrong, and the pointing out of all the flaws in his work were made before many of the posters here seemed to even understand what shannon entropy was in the first place. If you follow the evolution of this post, you will see the abel hammers come in swiftly, followed
    by confusion and bickering about what shannon entropy is, to the point where Mike E had to junp in and take everybody through the equations step by step. So if you want to hammer on Dembski or Sewell, I would recommend having Mike E write a top post about the paper, detailing some of the
    problems and issues first, before releasing the hounds.

  77. olegt,

    my spectacular naked assertion is based on the premise that in a given population of {proton | electron} we should be less surprised to observe that elements consisting of 1 proton are in fact more abundant than elements consisting of 92. My spectacular naked assertion will nose dive into the Atlantic if U is in fact more probable than H.

  78. junkdnaforlife,

    I can’t make heads or tails of what you are trying to say by this. In any event, periodic tables do not come in ensembles, so there is no way to compute their Shannon entropy.

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