Re: Kirk Durston on information theory

From: Denyse O'Leary (oleary@sympatico.ca)
Date: Fri Nov 07 2003 - 16:23:04 EST

  • Next message: Denyse O'Leary: "Re: correction to Kirk Durston message"

    > "Re: "Natural processes, over the history of the universe, have the
    > potential to produce up to 70 bits of information." This sure seems to
    > me to be a remarkable leap from a somewhat arbitrary "let's suppose"
    > number used by Behe to develop his argument. Here the number is >
    rendered> as established fact.Am I missing something (always possible!)?
    > JimA "

    Jim Armstrong queried Durston's figures, and this is his response

    With regard to a reasonable upper limit for the amount of information
    that natural processes could be expected to generate, here is a
    clarification of my thinking.

    First, I am defining functional information as the difference in Shannon
    entropy between a physical system that has no constraints placed upon
    it, and a physical system that has been constrained to perform a
    specified function.

    For a maximum upper limit, we can refer to two recent papers. One by
    Lloyd, S. (2002). Computational capacity of the universe. Phys. Rev.
    Lett. 88, no. 23, 237901-1 to 237901-4. Doi:
    10.1103/PhysRevLett.88.237901, and the other
    paper by Bekenstein, J. (2003). Information in the holographic universe.
    Scientific American. August issue. From these two papers, we can
    calculate the maximum amount of functional information that could be
    produced by the entire universe. The value we get from Lloyd's paper is
    about 400 bits, from Bekenstein's paper, 409 bits. Both of these
    computations assume a capacity that far exceeds what much slower,
    chemical processes involved in organic life are capable of. For example,
    Lloyd's paper assumes that the universe is a quantum computer operating
    over 10 byrs. Chemical processes do not cycle at quantum speeds, so the
    amount of information chemical processes could generate would be far
    less than 400 bits.

    For the next step, we note that functional Shannon information has, at
    it's core, a ratio which represents the number of functional
    configurations (Nf) vs. the total number of configurations possible,
    both functional and non-functional (N). A certain amount of functional
    information can be produced from scratch, in theory, in nature through
    what is known as a 'random walk'. The probability (Pf) of 'finding' a
    functional sequence or configuration that has a ratio of Nf/N is equal
    to Pf = (Nf/N)(R!/R^R) for a random walk. We can use this equation to
    calculate the number of trials or steps that we could expect to undergo
    before achieving a certain level of information. For example, a
    functional string of binary code that contained 70 bits of functional
    information would require approximately 1048 trials to 'find' via a
    random walk. Observing events in nature that have a probability of
    10^-48 is so unlikely that we could hypothesize that such an event will
    never likely be observed with any reasonable expectation. For proteins
    that are not well conserved, say, with a functional information content
    of .46 bits per amino acid, achieving 58 bits of information would take
    roughly 1072 steps in a random walk. Keep in mind that since most of
    protein sequence space is non-folding, natural selection cannot guide
    the evolutionary trajectory. Thus, it becomes a random walk as it
    evolves through non-folding sequence space. The bottom line is that
    somewhere we need to choose an upper limit for the amount of information
    natural processes can generate. Depending upon the 'alphabet' used (e.g.
    binary, or 20 amino acids, or 4 bases) that upper limit will vary. The
    hypothesis I work under is that the upper limit will be somewhere around
    70 bits, due to the number of steps required to achieve that level of
    information via a random walk, the time constraints we have within
    nature, and the amount of material and energy required for larger jumps
    in functional information.

    This hypothesis yields two falsifiable predictions: a) natural processes
    will never be observed to produce more than 70 bits of information, and
    b) any configuration or sequence that is actually observed to be
    produced that contains more than 70 bits, will always be produced by an
    intelligent agent.

    Thus far, there are no cases where either of these two predictions have
    been empirically falsified.

    Having said all the above, I believe that 70 bits is too conservative,
    and the upper limit is closer to 40 - 45 bits. In a recent computer
    simulation (Lenski et al., (2003). ŒThe evolutionary origin of complex
    featuresı Nature 423, 139-144.) an information jump of 32 bits could not
    be achieved (although I believe that in theory it can be achieved). Only
    when intermediate stepping stones were introduced into the virtual
    fitness landscape, could the simulation achieve a 32 bit function. Of
    course, this was achieved by inputting the information into the virtual
    fitness landscape in advance, permitting much smaller information jumps;
    this is a significant 'cheat'. When those intermediate steps were
    removed, the simulation failed to achieve the 32 bit function. In
    reality, we do not have advance information input into the natural
    fitness landscape and if we did, then we would have to account for where
    this information came from. For example, when it comes to the generation
    of novel protein folds, the sequence space between islands of folding
    sequence space is non-folding, hence non-functional, hence no effect on
    the phenotype (assuming the evolving gene is a duplicate and, hence,
    expendable). If there is no effect on the phenotype, natural selection
    cannot influence the evolutionary trajectory of the evolving
    protein-coding gene between the islands of stable folding sequence
    space. Finally, the islands of stable, folding sequence space are
    usually much more than 70 bits removed from each other.

    Bottom line: the 70 bit upper limit is an hypothesis that makes
    falsifiable predictions that, thus far, are still standing.

    Kirk

    -- 
    To see what's new in faith and science issues, go to www.designorchance.com
    My next book, By Design or By Chance?: The Growing Controversy Over the
    Origin of Life in the Universe  (Castle Quay Books, Oakville) will be
    published Spring 2004.
    

    To order, call Castle Quay, 1-800-265-6397, fax 519-748-9835, or visit www.afcanada.com (CDN $19.95 or US$14.95).

    Denyse O'Leary 14 Latimer Avenue Toronto, Ontario, CANADA M5N 2L8 Tel: 416 485-2392/Fax: 416 485-9665 oleary@sympatico.ca www.denyseoleary.com



    This archive was generated by hypermail 2.1.4 : Fri Nov 07 2003 - 16:20:14 EST