Models, Morals, and Metaphors

From: Moorad Alexanian (
Date: Tue Feb 05 2002 - 10:30:22 EST

  • Next message: Adrian Teo: "RE: Do animals ever "sin" (was something else)"

    Models, Morals, and Metaphors

    Leo P. Kadanoff

    Games of chance are often used as conceptual models of random processes in
    nature. For example, an exhibit on the heart in Chicago's Museum of Science
    and Industry includes a kind of pinball machine. After the balls bounce
    somewhat randomly through this machine, they fall into bins symbolizing the
    different states of health of one's heart. One can bias the outcomes for
    better or for worse by turning knobs related to one's habits (smoking?
    eating too much?) and controllable risk factors. This device is a
    provocative metaphor for the mix of random and controllable processes that
    determine one's health.

    Similar metaphors occur in the Field Museum of Natural History's exhibit
    "Life through Time." Here we find three different kinds of toys--wheels of
    chance, craps, and a horse race--all used to describe the stochastic nature
    of the evolutionary process. One of the toys invites the museum-goer to spin
    a wheel to gain characteristics that might enable an organism to prosper in
    a transition from an aquatic to a land environment. If the spin yields
    gills, that's bad. A strong tail won't help much either. A sturdy skeleton
    would be a boon, though. According to this display, survival is a matter of
    luck, depending on whether the traits developed in one environment might be
    useful in another. Another display shows various species of horses racing
    through the millennia until extinction drags them down, leaving only the
    modern horse. These toys are tabletop illustrations of the point made by
    David Raup in his book, Extinction: Bad Genes or Bad Luck? (W. W. Norton,

    In his book on the evolution of natural history museums, Stuffed Animals &
    Pickled Heads: The Culture and History of Natural History Museums (Oxford U.
    Press, 2001), Stephen T. Asma describes the gambling displays at the Field
    Museum and then points us to a nearby board with Post-it® notes left by
    museum visitors. One thoughtful visitor, Alan, objects quite strongly to
    these toys, saying,

    "What appears to the human mind as mere randomness, may from a divine
    perspective not be random at all. You may argue that this is a biased
    perspective, ridden with personal values and interpretations. However,
    seeing the principal cause and government of the universe as a roulette
    wheel is filled with the same personally subjective views as well as being
    morally bankrupt. Please pick a more objective and socially responsible
    means to convey your concept of evolution."

    Alan sees these displays as having led us into a totally amoral universe. No
    creator, no greater good; the only goal is to survive. But the gambling
    displays only talk about the evolution of different species and groups. Is
    Alan's extrapolation an error?

    Another Post-it commentator disagrees with Alan's specific conclusion. This
    person's note says, "Alan needs to understand that life is a gamble.
    Whenever he walks out his front door, Alan is gambling with his life." Both
    museum visitors recognize the evocative power of these little mechanical
    models and the metaphors they represent. While these displays are not
    precisely science, both observers see them as potential tools for
    extrapolation and generalization. They thus work in somewhat the same way as
    a literary metaphor.

    As a specialist in statistical physics, I could offer Alan some comfort. I
    could point out to him that the observation of apparently stochastic
    features in some behavior does not imply that the underlying laws are
    themselves probabilistic. Often, deterministic motion is so complex or so
    sensitively dependent on initial conditions that the motion is
    indistinguishable from a set of random events. For example, the path taken
    by an individual molecule in a gas is very well modeled as a random walk,
    entirely probabilistic in its nature. The random walk model can be derived
    from more fundamental models of molecular scattering. The scattering events
    could be realized in at least three different ways: using classical
    mechanics (fully deterministic), using quantum mechanics (partially
    deterministic), or prespecifying the probabilities of scattering. Thus the
    probabilistic single-particle model, the random walk, can be equally well
    obtained from a many-particle model that is entirely deterministic,
    partially so, or not deterministic at all. Real gases will all show the same
    behavior independent of the detailed laws governing the scattering. We use
    the word "universality" to describe the rather commonly occurring physical
    situations in which a set of derived laws remains substantially the same
    over a wide range of alternative underlying fundamental laws. In these
    cases, the observable outcome cannot be used to select among the possible
    underlying laws.

    The process of obtaining apparently probabilistic outcomes from
    deterministic laws has acquired its own name, the butterfly effect. This
    metaphor describes the magnification of small differences in initial data to
    ultimately produce a very large effect. To exemplify this process,
    meteorologist Edward Lorenz pointed out that the disturbance produced by the
    flapping of a butterfly's wings in South America has the potential to modify
    or produce a later storm in the United States.

    Conversely, as every student of statistics well knows, if you put together
    many individual stochastic motions, you may well get an essentially
    deterministic situation. A dilute classical gas obeys the deterministic gas
    law, PV = NkT. Through the "miracle" of large numbers, many stochastic
    molecules have produced a deterministic gas.

    These examples show that what one sees in a particular set of observations
    of the world will not and cannot determine what is happening at a deeper
    level. Thus statistical physics has not revealed whether the universe (or
    even a gas) is "really" stochastic or deterministic. We can only say that
    our models, stochastic and deterministic, have each caught some elements of
    what we see when we look at the gas. As we study the models, we better
    understand them and their close correspondence to behaviors of the real gas.
    But that is as far as we get.

    So what can we tell Alan and his Post-it critic? In my view, we should say
    that even the best models we have seen in science are idealizations and
    abstractions of nature and must, of necessity, catch only a piece of
    reality. If Alan wants to believe that deep down the universe has a purpose
    that we have not caught in any of our scientific models, we have no evidence
    to convince him of the contrary. On the other hand, science does have some
    useful information for Alan and other thoughtful people. There is strong
    evidence that the world is old and has been behaving the same way for a very
    long time. Evidence does indicate that the motion of the planets, the
    inheritance of biological characteristics, and everything we have observed
    follows well-defined laws. Wherever we have looked most seriously, we have
    seen phenomena that can be described by simple models of lawful behavior,
    endlessly repeated, without discernible purpose or goal. As Alan says, this
    is a cold and amoral description of reality. This view of the world as
    defined by law does have some support as a model of the Solar System and of
    other situations we have studied carefully. However, to apply this picture
    to the entire universe requires a tremendous extrapolation. Such an
    extrapolation can only have the strength of a metaphor.

    As a scientist, I can say that we do not have (and probably cannot have) any
    evidence to show that nature is just a set of laws operating without purpose
    or goal. But as a person, I find the metaphor congenial. I believe that the
    world is like that.

    Science gives us metaphors that we can use to organize and express our
    experiences in life. One powerful metaphor arises in my own subject of
    dynamical nonlinearity. We study many models that undergo a partially
    recurrent cyclic behavior in which the same basic thing happens through very
    many cycles. Then, in one or a few cycle times, there is a large and
    "unexpected" excursion to a very different behavior. In my thinking about
    the world, I follow the metaphor of these models and conclude that, in real
    life, one should expect "large changes" or perhaps even "disasters." Here I
    am extrapolating the scientific model results far beyond their range of
    scientific validity. Such extrapolations are not science. But they can be

    I close with a final example: The Museum of Science and Industry contains
    another exhibit, on AIDS. Here there are several dice cages, which the
    visitor spins to represent dangerous behavior--for example, unprotected
    sexual contacts. One dice cage models an interaction in which the visitor
    would have a one in six chance of contracting HIV. Is this metaphor
    objective? No. It presents a particular picture of how things work. Is it
    immoral? That's for each individual to decide. I think it's quite moral

    My arguments are based in part upon Michael Ruse's book, Mystery of
    Mysteries: Is Evolution a Social Construction? (Harvard U. Press, 1999).
    Michelle Ditzian provided editorial support. The research behind this work
    was partially supported through the NSF Division of Materials Research.

    Leo P. Kadanoff is a condensed matter theorist at the University of Chicago.

    © 2002 American Institute of Physics

    This archive was generated by hypermail 2b29 : Tue Feb 05 2002 - 10:29:22 EST