RE: Design detection and minimum description length

From: Iain Strachan (
Date: Fri Dec 01 2000 - 22:12:44 EST

  • Next message: Michael Roberts: "Re: Evolution & Identity of the ID designer"

    Thanks, Adrian, for that thoughtful summary of the discussion, which
    gives much to chew on.

    I'd like, if I may, to respond briefly to one of your points; the
    other points need more careful thought & things are busy at the
    moment. I've a short trip up to Edinburgh this week to (finally!)
    collect my PhD, (seven years plus doing a full-time job; not a
    recommended procedure for staying sane :-) so will not be able to
    respond promptly to any further points that may follow on this week.

    >Iain offers the example of a "perfect deal" in a game of bridge.
    >Anyone who has sees this situation would become highly suspicious,
    >BUT, only if that person has some knowledge of card games and
    >numbers. And that is precisely Glenn's point. For a person who has
    >never seen a pack of cards, and don't know anything about written
    >numbers, the "perfect deal" is unintelligible and random.

    Yes, this is what I understand as well to be Glenn's problem with the
    whole thing. You need to have "side knowledge" in order to detect a
    design (or a pattern, to use a less loaded word). Your maths teacher
    told you about prime numbers, and that is the side knowledge you need
    to detect a pattern in a sufficiently long sequence of coin-tosses
    that is based on prime numbers (e.g. "The Nth toss is heads if N is
    the product of exactly two primes, otherwise it is tails"). Of
    course you need to know about prime numbers to get this pattern. But
    I don't see that as equivalent to someone telling you that this
    particular pattern was designed. Your teacher told you about prime
    numbers, and then you used your own intelligence to detect the
    pattern based on primes.

    Dembski also addresses this point in "No Free Lunch" (p63):

    "The SETI researchers [in the film Contact] who inferred that an
    extraterrestrial intelligence was communicating with them needed to
    know about prime numbers before they could ascertain that an incoming
    sequence of radio signals representing an ascending sequence of prime
    numbers was in fact just that and therefore due to another
    intelligence. A design inference is one intelligence inferring the
    activity of another intelligence by the judicious exploitation of
    background knowledge".

    I really can't (sorry, Glenn), see any problem with this, and how one
    can go from this to saying that the method has failed because the
    researchers had to be told it was designed.

    >Iain's examples of detecting mathematical relationships/correlations
    >seems irrelevant to me. What would perhaps be a better analogy would
    >be the detection of causality. As in the case of attempting to
    >detect design, one may be able to say that an event (no pattern) is
    >so improbable that we have to reject the null and conclude that
    >there is a pattern, just as in detecting a correlation, one
    >concludes that the null hypothesis is so improbable that we reject
    >it and therefore conclude that there is a relationship. But it is an
    >entirely different matter to go from pattern to design, which would
    >be analogous to going from relationship (correlation) to causation.

    Perhaps I can explain why I think it is relevant. I think the step of
    going from correlation to causation comes down to how complex the
    specification is, and this is close to the heart of how I currently
    understand the Dembski Complexity/Specificity criterion, and the
    "Explanatory Filter". For design, according to this, we must first
    have a sufficiently long sequence that its probability is very low.
    This constitutes what he calls "complexity". However, that is not
    enough; one must also be able to describe the data in a much shorter
    length than the string itself. "This is a sequence of primes" for
    example. This gets one around the retort "OK, you've found an
    interesting pattern, but how many other interesting patterns could
    you find. I bet you could make any pattern 'interesting' with a
    little ingenuity". The reply to this is the counting argument I've
    used earlier. If the specifier string is M bits long, then there are
    at most 2^M patterns of similar interest (by 'i!
    nteresting' I now mean, "can be described in a compact way"). Then
    if the string itself is N bits long and N >> M, we have a low
    probability of that pattern (or any like it) occurring.

    But there is a third box to the filter, called "contingency". The
    argument here is "but what if it has to be that way via a natural
    cause". This is covered by the case where the specifier string
    itself is so short that it could be attributed easily to a natural

    Such a string might be a third degree polynomial that fits nicely
    through a set of 20 (x,y) points. One has found correlation there,
    but no one would suspect design to be at work.

    But suppose the following happened. I sent you a dataset of 10,000
    (x,y) points, with x monotonically increasing, and y wiggling about
    all over the place, apparently at random. Then you decided to
    analyse it by fitting higher and higher degree polynomials, and you
    use my minimum description length test to decide the best model.
    (i.e. you calculate the bit-length of the model, proportional to the
    model order, plus the number of bits you need to transmit the
    residuals). Suppose you find that actually the best fit comes when
    you try a degree 1000 polynomial. Suppose the numbers are all
    digitised at 16 bits, and the residuals you get from the model can
    all be expressed in 8 bits or less (i.e. the model always gets it
    right to within around 0.5 percent). So the description length will

    16x1001 (for the polynomial coefficients of a degree 1000 polynomial),

    + 10000x8

    This comes to 96016 bits.
    The original data (the y points) would be 160000 bits long and the
    difference in length is 63894 bits. So the probability that you
    could do better than this given the null hypothesis (no
    correlatio/causation) is 2^63984.

    Now, how do we get to the idea that this is design rather than
    correlation? The IDer would argue (I think) that it is because the
    description string is so long itself. How many physical processes do
    we know that are governed by degree 1000 polynomials? I think if you
    received such a dataset from me, you'd suspect that I deliberately
    arranged it by generating the data from a polynomial of degree 1000.
    Would the conclusion be different if you didn't get it from me, but
    it arrived from outer space?

    Here's another example that I kind of like. We know that the
    description "all heads" is much simpler than the description of a
    sequence of coin tosses governed by some relationship involving prime

    There is a party trick that the mathematician John H. Conway (of
    "game of life" fame) performs. I imagine it has won him many a drink
    in a bar. He describes it as being able to "cheat probability". He
    takes around 20 American 1-cent coins, and balances them all
    carefully on their edges on a table. What's the odds you can make
    them all come down heads? Roughly 1 in a million. He taps the
    underside of the table at just sufficient force to get them to all
    topple, and they all come down heads! (I guess this trick requires a
    large amount of practice to bring off). Now, for such a simple
    description (all heads), there could well be a simple naturalistic
    explanation. There is. It is all down to the slight asymmetry in
    the milling process of the coins that biases the way it will fall if
    just toppled. But now supposing you performed a different trick.
    Suppose you stuck labels on the "heads" sides of all the coins, and
    wrote the numbers 1 to 20 on them. Then you tapped th!
    e table and at the end, the only numbers showing were primes.

    I think anyone who saw this done, if it could be done repeatedly
    would suspect a cheat; such a feat might be performed by a magician
    who cheated (i.e. designed it that way), but it couldn't be down to
    natural causes. The difference is down to the complexity of
    describing the pattern of heads and tails.

    Hope this offers some more food for thought.
    Thanks for your comments.

    Best wishes,

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