Richard
Feynman once remarked that unless one is able to make one's ideas
understandable to college freshmen, one doesn't really understand them. On
the other hand, when asked by a reporter to explain why he was awarded the
Nobel Prize, Feynman remarked, "Listen buddy, if I could explain it in
fifty words or less, it wouldn't be worth a Nobel Prize."
There are two truths here: (1) Important ideas can be made accessible without
dumbing them down; (2) The details of a scientific theory are important and
typically inaccessible except to individuals with the requisite training. The
hallmark of good science writingthe Feynman Test, let's call itis the
ability to heed both of these truths at the same time.
Yair Guttmann's project centers on a question of fundamental interest,
growing out of the increasing use of probabilistic reasoning in physics over
the last 150 years: Why do statistical methods work so well at predicting the
behavior of huge numbers of particles enclosed in containers even though the
physics that describes the individual behaviors of those particles is purely
deterministic? Hence, it is an ideal subject for a book that seeks to make
important scientific and philosophical issues accessible without garbling
essential technical details. Alas, Guttmann fails the Feynman Test, but his
failure is instructive.
Guttmann observes that a "philosophical temperament" is needed for
a book such as this "on the nature of probabilities in statistical
mechanics. . . . For most physicists, the topic is too 'academic.'" Guttmann
himself champions what he calls the "pragmatist" approach to
statistical mechanics (statistical mechanics explains the macroscopic
properties of a physical system by a probabilistic description of its
constituent particles). Essentially, the pragmatist approach says that we use
probabilities in statistical mechanics because they workthey give us a
successful theory. As Guttmann puts it in chapter 5:
Pragmatists believe that we have a total freedom to choose the concepts that
appear in our scientific theories. We do not have to justify the initial
choice of concepts at all [here statistical/probabilistic concepts]. All we
need is to make sure that the theories we construct will imply correct
predictions.
Well, I'm certainly sympathetic to pragmatism in science. "The
scientific method, as far as it is a method," the Nobel laureate Percy
Bridgman said, "is nothing more than doing one's damndest with one's
mind, no holds barred." This account of pragmatism is perfectly fine diet
for scientists, whose livelihood depends on getting results. But it's rather
thin gruel for philosophers, whose livelihood depends on analyzing conceptual
difficulties. Here, then, is Guttmann's challenge.
He does a fine job (once one wades through the technical morass and finds the
relevant sections) of showing that an "objectivist" approach to
statistical mechanics cannot succeed. That is, he shows that trying to locate
probabilities in the purely physical properties of a particle system won't
deliver a satisfactory account of why probabilities successfully characterize
such a system. But when he considers nonobjectivist, or what we might call
conceptually based alternatives (the Bayesian or "subjectivist"
approach, the "ergodic" approach, and the pragmatist approach), he is
less successful at distinguishing these and making a case for his own
preferred pragmatist approach.
The problem with subjectivist approaches is that strictly speaking their only
criterion for assigning probabilities is internal coherence (probabilities
have to be assigned so that a betting scheme based on them cannot always be a
loser for one party who betsheads I win, tails you lose is, for instance,
not allowed). But there is a physical tiein with statistical mechanics, and
thus something more than coherence is required.
Guttmann also considers but finds wanting the ergodic approach to statistical
mechanics. The ergodic approach treats probabilities as relative waiting
times during which a particle stays in a given portion of phase space (that is,
the hypothetical space that describes all the potential states of a system).
Thus for a particle that spends half its time in a given portion of phase
space, the corresponding probability of that portion of phase space is 1/2.
Although the ergodic approach offers a powerful way of understanding
statistical mechanics and is a fertile area of mathematical research, it
falls short as a justification for applying probabilities to particle systems
where the individual particles are controlled by deterministic physical laws.
Many assumptions with no physical justification need to be incorporated
(e.g., assumptions about the limiting behavior of particle trajectories and
about the type of flows in phase space).
Which leaves the pragmatist approach. As I indicated, I'm sympathetic to this
approach. Indeed, I think it the best of the alternatives to the objectivist
approaches that Guttmann considers. But Guttmann treats haphazardly what to
my mind is the key question raised by the pragmatist approach. The pragmatist
approach, when applied to statistical mechanics, enjoins us to use
probabilities because they workthey enable us to construct a predictively
ac curate and scientifically fecund theory. But why should they do so? As we
have seen, physicists are not inclined to pursue this question, "be
cause discussing it is not likely to improve our ability to make better
predictions, to discover new effects, or to explain phenomena that we do not
yet under stand." And that is why, Guttmann says, "it is the task
of a philosopher" to answer this question.
Objectivist approaches fail because the underlying dynamics of individual
particles, at least as far as statistical mechanics is concerned, is
deterministic (bringing quantum mechanics into the mix doesn't help here since
we still have to deal with ensembles of particles and statistics gets applied
to the ensembles). And as we've seen, subjective and ergodic approaches are
also unsuccessful, either failing to connect with physical reality or adding
what amounts to a frequentist superstructure with all the problems that
raises. Why then do probabilities work? More precisely, why is the mechanics
for ensembles of particles statistical?
It's precisely at this point, just when he is homing in on the central
question, that Guttmann seems repeatedly to lapse into the sorts of loose
justifications that the founders and shapers of statistical mechanics
employed to motivate their probabilities in the first place. Why, for
instance, in an ensemble of particles does the future behavior of a particle
become stochastically independent of its past behavior as the time separating
past and future increases? As the time increases, the particle, being part of
an ensemble, will undergo a lot of collisions with other particles. All those
collisions will tend to wash out any influence the past behavior of the
particle has on its (distant) future behavior. Justifications like this are
intuitive and vague. But they can be given precise mathematical form, and
such mathematical forms can in turn be used to construct a powerful physical
theory, to wit, statistical mechanics.
The role of such loose justifications and why they could stimulate the
development of statistical mechanics should have been topics of particular
scrutiny in a book that finds a pragmatist approach as "the most
convincing account of statistical mechanics." Guttmann recounts such
justifications, but does not adequately show how they underwrite the approach
he advocates.
This failure at the heart of the book is written large in its conception and
execution. There are some wonderfully lucid passages here which the educated
lay reader would find particularly helpful in understanding the controversies
surrounding the foundations of probability theory, especially as they relate
to statistical mechanics. But these passages, though of general philosophical
interest, are embedded in highly technical discussions aimed at specialists
in probability theory, statistical mechanics, and the philosophical
controversies connected with these fields.
One of the most illuminating passages in the book, for instance, is buried in
Appendix II (the second of three), which is devoted specifically to the
foundations of probability. It comes right after an alltoosuccinct appendix
devoted to measure theory and topology, topics about which most
nonmathematicians will not have a clue. The material in the second appendix
needed to be placed at the very beginning of the book to frame the ensuing
discussionindeed, the ensuing discussion presupposes it. (To his credit,
Guttmann advises nonspecialists to consult the appendixes, but the first
appendix is sufficiently offputting to intimidate readers from going further;
what's more, accessible material that is of central importance deserves more
than an appendix).
Guttmann seems to have written primarily for fellow philosophers who
specialize in the foundations of statistical mechanics, unaccountably
throwing in an appendix here and a summary there for popular consumption.
With more care, this book could have been made accessible to a general
audience while still engaging the technical philosophical and mathematical
concerns that Guttmann raises.
It's evident, though, that care was not exercised. As someone who has
published in the same series in which this volume appears, I can vouch that
the problem would not have been with the copyeditors or the typesetters. The
book is strewn with mathematical typosnothing serious if you're a re search
mathematician and know what the relevant mathematical theory says. But for an
amateur mathematician trying to work through the details, reading this book
will be a nightmare. The chapters themselves are disconnected, and one has
little sense of a unifying framework.
All in all, this is a disappointing book from an author who clearly could
have done much better (there are flashes of insight and lucidity that
convince me of this). The book seems to have been cobbled together, largely
from technical papers addressed to experts in the field. Introductory and
transitional material is minimal, and lacking is a gentle guiding hand into a
highly technical field that nonetheless has wideranging philosophical import.
I would love to see plans for a second edition placed in the hands of an
exacting editor.
William A. Dembski is based at Baylor University's newly founded Michael
Polanyi Center for Complexity, Information, and Design. He is the author of The
Design Inference (Cambridge Univ. Press) and Intelligent Design: The
Bridge Between Science and Theology (InterVarsity).
Copyright © 2000 by the author or Christianity Today, Inc./Books &
Culture Magazine, March/April 2000, Vol. 6, No. 2, Page 42
