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Sewell's thermodynamic failure
By Mark Perakh
Posted January 3, 2006
The young earth creationists (YECs) used to refer to the 2nd
law of thermodynamics as an allegedly insurmountable obstacle to
evolution. When their critics pointed
out that the 2nd law, as used by creationists, is only valid for
"closed" (or "isolated") systems and therefore is not an obstacle to evolution
on our planet which is an open system receiving energy input from the sun, the
YECs suggested various specious arguments designed to circumvent this limitation
of the 2nd law. With time, as straightforward young earth
creationism gradually retreated to such fringe outlets as Answers in Genesis, the Institute of Creation Research, and
Hovind's entertainment shops (being replaced by intelligent design movement as
the main anti-evolution force), reference to the 2nd law of
thermodynamics has rare been heard as an anti-evolution argument.
However, this pseudo-scientific argument has not been
completely abandoned by anti-evolution forces, both of YEC and ID varieties.
From time to time it recrudesces in writing of this or that advocate of
One example of such a misuse of the 2nd law of
thermodynamics is a recent article by
professor of mathematics Granville Sewell titled "Evolution's
When so great a "scientist" as Pat Buchanan endeavors to
speak about evolution there is little to be surprised about when he displays ignorance -- Buchanan is
a "pundit" of dubious integrity, with no credibility as far as any science is concerned,
so we can't expect from him a reasonable discourse about anything scientific.
Likewise, when some of the fellows of the Discovery Institute assault evolution
theory, distortions and misrepresentations are the order of the day, because
that is how they earn their keep. However, when a professor of mathematics at a
quality university misuses thermodynamics, one only can shrug in astonishment.
Since I am not a mathematician, I would never try discussing
the quality of Sewell's mathematical publications. Perhaps he is a very good
mathematician. That not for me to judge. However, having taught all parts of
physics, including thermodynamics, statistical physics, physical kinetics, and
other related disciplines, for over half a century, both on the undergraduate
and graduate levels, I feel qualified to judge Sewell's thermodynamic exercise.
I find it depressingly fallacious.
Let me quote certain passages in Sewell's essay and briefly comment on them.
Sewell starts his essay with the following words:
In the current debate over "Intelligent Design," the strongest
argument offered by opponents of design is this: we have scientific
explanations for most everything else in Nature, what is special about
know where Sewell found the quoted statement: he provides no references. I
can't recall such statement offered as "the strongest argument… by opponents of
design." To me it looks more like a straw-man erected by Sewell to enable him
easily defeat this allegedly "strongest" anti-design argument.
telling start of Sewell's thermodynamic exercise portends the overall level of
his critique of evolution theory (ET). Indeed, as we read Sewell's tract, what
we see described under the label of evolution theory looks more like a
caricature of that theory. Of course Sewell is not a biologist and is
not expected to discuss evolution theory on a professional level, but if this
is the case, would it not be more sensible to leave the discussion of the
strong and weak features of ET to experts (as they have been doing day in and
day out in thousands of papers in scientific journals and in conferences and
meetings)? I guess that if some biologist not versed in mathematics endeavored
to critique Sewell's mathematical output, Professor Sewell would shrug off the
dilettante's exercise with a disdainful smirk.
am not a biologist, I'll limit my discussion of Sewell's essay to narrow
main argument against the ET used by Sewell seems to be based on thermodynamics,
and specifically on its famous 2nd law.
delving into the essence of Sewell's main argument, let me provide a few more
quotes from his essay.
The first formulations of the second law were all about heat: a
quantity called thermal "entropy" was defined to measure the
randomness, or disorder, associated with a temperature distribution, and it was shown that in an
isolated system this entropy always increases, or at least never decreases, as
the temperature becomes more and more randomly (more uniformly) distributed.
of all, this statement is historically wrong. When Clausius introduced the
concept of entropy, it was not connected in any way with "randomness" -- such a
connection was discovered much later, and not in thermodynamics per se but rather in statistical
physics. Furthermore, the expressions
"temperature distribution" and "temperature becomes more and more randomly
(more uniformly) distributed" are rather imprecise. Temperature T is a
thermodynamic parameter which has meaning only for macroscopic assemblies of
particles. T has no meaning for infinitesimally small volumes. We can
meaningfully discuss temperature gradients,
because the concept of a gradient does not require consideration of
infinitesimally small volumes. However, the concept of a "distribution"
involves the concept of a "distribution function," which necessarily incorporates
values defined for infinitesimal volumes where the concept of T is meaningless.
Sewell further writes,
The fact that order is disappearing in the next room does not make
it any easier for computers to appear in our room -- unless this order is
disappearing into our room, and then only if it is a type of order that
makes the appearance of computers not extremely improbable, for example,
computers. Importing thermal order will make the temperature distribution less
random, and importing carbon order will make the carbon distribution less
random, but neither makes the formation of computers more probable.
here the expressions like "order is disappearing in the next room," "Importing
thermal order," and "will make the temperature distribution less random."
expressions like "entropy flows into the system," are common in thermodynamics,
they are just metaphors. Entropy is not a substance which can literally "flow"
from or into a system. Entropy is a measure of disorder and the actual
mechanism of its decrease in one place and accompanying increase in another
place is statistical. It is realized via random motion of particles chaotically
exchanging their energy and momenta through collisions. Likewise, expressions
like "order is imported," have no literal meaning, but Sewell uses such
expressions as if they reflect the actual influx ("import") or outflow
("export") of some non-existing substance called "order." This metaphoric
language sheds no additional light on the discussed phenomena, more so because
his expressions like "temperature distribution becomes less random" are simply
confusing as the temperature is essentially a macroscopic quantity having no
meaning for infinitesimally small volumes and therefore a distribution function
for temperature cannot be defined.
of Sewell may argue that I am nitpicking here on some insignificant semantic
details. Perhaps this is so and these semantic details have no bearing on the
essence of Sewell's argument. They have
a bearing, though, on the overall credibility of Sewell as the interpreter of
subtle nuances of thermodynamics he evidently pretends to be.
Natural forces, such as corrosion, erosion, fire and explosions,
do not create order, they destroy it.
a further "nitpicking" regarding the term "forces" being applied to corrosion and
erosion (which are, strictly speaking, not forces but processes), Sewell's
thesis is contrary to well established facts which testify that there are many
spontaneous natural processes that create order. Has Professor Sewell never
heard about self organization which occurs spontaneously and has been observed
many times in various systems?
Sewell never heard about, say, Benard cells, a Belousov-Zhabotinsky reaction,
spontaneous ordering in various colloidal systems, etc., etc., etc.? (See, for
example, Niall Shanks, God, the Devil,
erosion, it certainly may cause destruction of information-rich structures. For example, erosion may result in a gradual
deterioration of the Mount Rushmore carvings.
However, in other cases erosion can create sculpture-like images. Has
Professor Sewell never heard about erosion
spontaneously creating amazing structures looking like animals, people, bridges,
and the like? I'd recommend Professor Sewell travel to Russia and visit there
the Dombai region in the North Caucasus.
He may see there an amazing phenomenon -- a mountain named Sulakhat -- which looks like a sculpture by an
accomplished artist in the shape of a young woman on her back, but is, in fact,
an accidental grouping of rocks.
If the gradual
destruction of, say, the Great Buddha sculpture is an example of the
destructive force of erosion, which, according to Sewell, "destroys order," then
the appearance of sculpture-like images due to erosion, by the same logic,
should be construed as creating order (of course this is, in fact, rather an
example of creating the illusion of design).
how Sewell offers his main claim:
.... the idea that the four fundamental forces of physics alone
could rearrange the fundamental particles of nature into spaceships, nuclear
power plants, and computers, connected to laser printers, CRTs, keyboards and
the Internet, appears to violate the second law of thermodynamics in a
announced the quoted claim, Sewell proceeds to elaborate, aiming to prove that
the 2nd law of thermodynamics prohibits evolution.
concentrate now on Sewell's thermodynamic argument.
Since Sewell's argument is based on his interpretation of
entropy and of the 2nd law of thermodynamics, perhaps it is proper
to start with a brief discussion of what these concepts entail (see also my
essay Ian Stewart: Entropy vs. disorder and gravitics vs. thermodynamics).
Sewell interprets entropy as a measure of disorder. In the
context of this discussion, I readily accept such an interpretation. Here,
though, my agreement with Sewell ends. IMO,
the rest of his discourse abounds in faulty assertions, incorrect examples, and
As a preamble to the discussion of Sewell's piece, let me
conduct a brief excursion into the chapter of thermodynamics dealing with
entropy and the 2nd law.
The concept of entropy was introduced by Clausius in a
specific form as
Clausius noticed that while dQ is not a real differential
but just an infinitesimal amount of "heat," (because heat Q is not a function
of state) the inverse temperature 1/T is what mathematically is referred to as
integrating coefficient. Unlike dQ, the quantity dQ/T is a real differential.
Integrating dQ/T produces a function S of the system's thermodynamic parameters
(such as pressure P, volume V, temperature T, magnetization B, etc.). This
function (named "entropy" by Clausius) is a "function of state," in many
respect similar to temperature (with an important difference -- T is an
intensive, whereas S is an extensive property).
COMMENT. While entropy
is legitimately construed as a thermodynamic parameter, or as a system's
"property" similar to the way volume, pressure, temperature, magnetization,
etc., of a system are referred to as system's "properties," in fact entropy is
not a physical property of system's material constituents. For example, for a
gas consisting of molecules, entropy is not a property of molecules, but a
measure of disorder in the molecules' distribution over locations in the volume
they occupy, and/or of their momenta, etc. The term "property" is used in
thermodynamics in a semantically different way than in, say, material science
or physics of solids where the term "property" is reserved for, say, mass,
magnetization, polarization, strength, elasticity, and other physical
properties of a material, determined by its structure.
Clausius found that function S is an invariant of a
reversible adiabatic process or of any reversible cycle (similarly T is an
invariant of a reversible isothermal process or of any reversible cycle).
Reviewing various processes and cycles, Clausius postulated that, in an
irreversible process, the net entropy summed
up for all participants of the process always increases. This postulate
cannot be rigorously proven, but has been accepted, based on an extensive
analysis of multiple situations, as the 2nd
law of thermodynamics. (This law has many differing definitions discussed
in textbooks on thermodynamics; however, for the purpose of this review adopting
the above not quite rigorous definition is quite proper, because creationists
usually base their thesis about the 2nd law allegedly prohibiting evolution,
explicitly or implicitly, on a formulation dealing with the prohibition of
entropy's spontaneous decrease).
From the very beginning, it was realized that the postulate prohibiting
a spontaneous decrease of entropy could not be substantiated for "open" systems.
If a system has been chosen as such
part of the universe whose boundaries allow for energy ingress or egress, then the
entropy of such a system may change in various ways and its decrease is
possible. The actual behavior of entropy in such an "open" systems is
determined not by the prohibition of entropy decrease, but by local conditions,
and is not limited to entropy increase (although the net entropy of the
universe will only increase in every irreversible [i.e. in any real] process, regardless
of which system it occurs in). Hence, even in its initial non-statistical
rendition, the prohibition of entropy decrease was only formulated for closed (or
isolated) systems, including the universe as a whole, or any part of it whose
boundaries prohibit egress and/or ingress of energy and matter. Hence, alternatively, the 2nd law
can be stated as "the net entropy of the universe necessarily increases in all
irreversible processes." In this formulation, the universe is considered a
closed system (as there is nothing beyond the universe, no egress from or
ingress to the universe of energy or matter can take place, which is what the
concept of a closed system is all about). Since all real processes are
irreversible, the 2nd law is a very general statement about the
It may be pointed out that Clausius's formula for entropy is
just a particular case since there are an infinite number of functions all
suitable to serve as "entropy." The sole requirement for a function to serve as
"entropy" is its being an invariant of a reversible adiabatic process. Adiabatic
process is such where there is no energy flow through the system's boundaries.
This is a limiting case wherein, unlike in any other processes, entropy remains
constant. A reversible process is just an idealization as all real processes
are irreversible, so the entropy of the universe necessarily increases in all
natural processes, while the entropy of a part of the universe that is an "open"
system may decrease as well, depending on the local conditions and the energy
Moreover, the units (like Joule/Kelvin) of Clausius's
entropy are not inherent in this quantity. In theoretical physics, entropy is
viewed as essentially a dimensionless quantity. (See, for example, L. Landau
and E. Lifshits, Statistical Physics.)
A substantial impetus for a deeper interpretation of entropy
was provided by the realization (by L. Boltzmann) that entropy is a monotonic
function of the number of microscopic states accessible for the system.
Boltzmann suggested a convenient logarithmic transformation from the
"thermodynamic probability" W, which equals the number of accessible states,
into Clausius's entropy:
S= k x logeW
where k is the Boltzmann
coefficient whose value was chosen to make Boltzmann's statistically defined S
coincide quantitatively with Clausius's S.
Boltzmann's work was instrumental in realizing the
statistical nature of laws of thermodynamics (notably of the zeroth, the first,
and the second laws). Laws of thermodynamics are not statements of absolute
truth but just postulates, justified only in a statistical (probabilistic)
sense. The predictions of the laws of
thermodynamics are pointing to the most
probable behavior of a system rather than to the 100% definite behavior.
However, for sufficiently large system and for sufficiently long periods of
time, the probability of a system behaving according to the laws of
thermodynamics is so overwhelming that behavior contrary to the laws in
question can usually be safely excluded.
The fact of the 2nd law (in its formulation prohibiting
spontaneous entropy decrease) having a reasonable interpretation only for
closed systems is profound. Indeed, what does the 2nd law say about
open systems considered separately from the rest of the universe? Nothing in
detail, except for stating that the reversible ingress of heat into it causes
its entropy to increase while a reversible egress of heat causes entropy's
While asserting that in a closed system entropy cannot spontaneously
decrease, the 2nd law cannot say anything like that about entropy's behavior in
open systems. As far as the 2nd
law goes, in open system's entropy can increase, decrease, or remain constant. Therefore
any attempt to apply the 2nd law, in its formulation prohibiting
entropy decrease, to open systems, is meaningless.
Entropy of an open system, whose boundaries allow for energy
ingress or egress, can spontaneously decrease without contradicting the 2nd
law. Contrary to Sewell's thesis, there are many situations where entropy of an
open system decreases spontaneously, and this in no way contradicts the 2nd
Does Professor Sewell not know, say, about the spontaneous
solidification of melted metals? If a melt is cooling down, (as an open system
does when the surrounding is cooler than the melt) at a certain temperature the
disordered liquid spontaneously converts into crystalline structure of a solid,
and its entropy spontaneously decreases. Sewell's ruminations about "import of
order" from the surrounding does not shed any additional light on this
trivially known notion, as it is just Sewell's peculiar way to assert the
simple fact: while heat "flows" out of the system, the temperature and entropy
of the sample drop, but the entropy of the surrounding, and with it of the
entire universe, increases, thus satisfying the 2nd law (as the
universe is considered a closed system).
Likewise, if a sample of a ferromagnetic material is heated
up, at a temperature above its Curie
point, it converts into paramagnetic state where the strong order in its spin
structure disintegrates (and entropy increases, in agreement with the heat
influx). However, if left intact in a cooler surrounding, the sample will
spontaneously cool down (as per the 2nd law) and below its Curie point a
strongly ordered spin structure will spontaneously set in, with a concomitant
entropy decrease (and this is not at all contrary to the 2nd law).
The above explanation leaves no place for any interpretation
of the 2nd law of thermodynamics as allegedly prohibiting evolution: the 2nd
law contains nothing justifying such a conclusion.
If Sewell's conclusion about the 2nd law
prohibiting evolution were true, life would be impossible. A living organism
constantly (and successfully) fights against entropy increase. Were the
organism a closed system, it would not be able to survive as all processes
within the body would, as the 2nd law postulates, lead to the increase of
entropy, and thus to the body's rapid disintegration. Luckily, organisms are
open systems and the 2nd law does not prohibit entropy decrease in
such systems, hence not prohibiting increase of complexity or of informational
contents of the system.
As a female becomes pregnant, a process starts wherein the
entropy of the fetus, and with it of the entire female body gradually decreases
and this is in no way contrary to the 2nd law because this law does
not prohibit entropy decrease in open systems. The mass of the fetus increases along with its development, and
entropy is an extensive quantity, this contributing to the increase of the
total entropy of the "mother + fetus" system, but the differentiation of the
fetus's tissues is a domineering process resulting in a net decrease of entropy
of said system (with a concomitant increase of the universe's net entropy).
An animal's body constantly exchanges energy and matter with
its surrounding, so it is an open system for which entropy decrease is
possible. Were Sewell right, such growth and development would be impossible, as
would be the evolutionary process. The very existence of Sewell as a living
person testifies against his anti-evolution pseudo-thermodynamic arguments.
There is a case where
the decrease of entropy is an observed fact. In this process another (non-thermodynamic) law is at work, ensuring
entropy decrease. Such a law was suggested to be that of gravity (see, for
example the online discussion of papers by Stewart, Ian Stewart: Entropy vs. disorder and gravitics vs. thermodynamics,
and by Davies at Paul Davies: emergentist vs. reductionist).
As living organisms constantly fight against their entropy's
increase, it is achieved at the cost of the overall increase of the universe's
entropy, thus meeting the requirements of the 2nd law. As the
universe has been constantly expanding since the Planck time, the number of
accessible states is increasing thus enabling the increase of the total entropy
of the universe despite the existence of locations whose entropy decreases
(caused, for example, by living organisms, or by gravity, which is one of those
forces working against entropy increase).
The 2nd law has other limitations as well. For
example, the 2nd law is not applicable to systems of small size, or
for short periods of time. In a small system (say, consisting of only 100
particles) the probability of a non-uniform distribution of the particles is
reasonably large, so a spontaneous increase of order is not as highly
improbable as it is for large systems. This is better interpreted as
considering entropy (like temperature) as an essentially macroscopic concept,
having little meaning for small systems, and no meaning whatsoever for
microscopic systems. This limitation may (or may not) be of consequence for the
problem of abiogenesis, since the spontaneous generation of primitive original
replicators might not have required the assembly of a large number of particles,
so the 2nd law in such a case would not have imposed restrictions
upon the outcome of the reactions.
Likewise, during short periods of time, fluctuations in the
particles'distribution may result in a temporary increase of order. This does
not contradict the 2nd law, which is true only statistically and is
not applicable for short times or small systems.
Although the problems of abiogenesis (the origin of life)
are beyond evolutionary biology, Sewell seems to conflate in his arguments two
different problems -- that of the evolution
of the living organisms and that of the origin of life. In this vein, he
repeatedly refers to laws of probability. Since Sewell is a mathematician, he
is supposed to be versed in probabilities on a professional level. Unfortunately,
his arguments based on probabilities are no better than similar arguments
offered many times before by "creation scientists" of various kinds and shown
many times over to be irrelevant to the question of origin of life.
I have discussed this point at length before (see, for
example, the chapter on probabilities in my book Unintelligent Design, or online at Improbable Probabilities) so I'll not repeat this discussion here.
Sewell further refers to Michael Behe's notorious book Darwin's Black Box and to the concept of
Irreducible complexity (IC). He seems to have uncritically swallowed Behe's
argument, and shows no familiarity with the devastating critique of Behe by
many mainstream scientists. Since I have made a modest contribution to the
critique of Behe's book (see, for example, chapter 2 in my book Unintelligent Design, or online Irreducible Contradiction
and Beyond suboptimality) as well as in my article in Skeptical
Inquirer, Nov-Dec 2005 issue, I see no need to repeat my anti-Behe notions
here. The recent evisceration of Behe's views by the plaintiff's attorneys at the
Kitzmiller vs DASD trial (see Kitzmiller Decision: Plaintiffs Prevail) and Judge Jones's decision) have vividly shown Behe's inability to say anything of substance in defense
of his IC concept.
Sewell further writes,
...there is no proof that natural selection has ever done anything
more spectacular than cause bacteria to develop drug-resistant strains, where
is the overwhelming evidence that justifies assigning to it an ability we do
not attribute to any other natural force in the universe: the ability to create
order out of disorder?
this passage remind one of an episode during the Kitzmiller trial? When Behe
claimed the absence of any scientific data about the emergence of IC systems,
the plaintiff's attorneys placed upon a table a pile of 58 peer-reviewed papers
and 9 books doing exactly what Behe claimed to have never been done. While Behe, in his amusing self-assurance,
might not have realized it, the judge and every unbiased observers construed
this episode as a milestone on the way to completely discrediting Behe.
claiming the absence of "proofs" for ET, Sewell just reveals his lack of
familiarity with the pertinent literature. The fact of speciation (often
referred to by creationists as "macroevolution") has been firmly established by
observation and experimentation. (See, for example Jerry Coyne and Alan Orr's
book Speciation or online at, for
example, Observed Instances of Speciation
or 29+ Evidences for Macroevolution.)
believe the above quotations are sufficient to see Sewell's essay for what it
is -- a groundless diatribe which could be expected from a semi-literate
emotional anti–evolutionist, but sounds preposterous coming from a professor
(A general remark: evolution theory cannot be
proven or rejected by applying any mathematical equations or laws of physics.
ET is an empirical science based on immense experimental and observational
material. The fact of evolution has been established beyond a reasonable doubt,
although mechanisms of evolution continue to be discussed by evolutionary
biologists. If certain mathematical equations or laws of physics seem to
contradict ET, the reasonable explanation is that the equations or laws in
question have been misapplied or misinterpreted.)
essay ends with the following sentences:
The development of life may have only violated one law of science,
but that was the one Sir Arthur Eddington called the "supreme" law of
Nature, and it has violated that in a most spectacular way. At least that is my
opinion, but perhaps I am wrong. Perhaps it only seems extremely improbable,
but really isn't, that, under the right conditions, the influx of stellar
energy into a planet could cause atoms to rearrange themselves into nuclear
power plants and spaceships and computers. But one would think that at least
this would be considered an open question, and those who argue that it really is
extremely improbable, and thus contrary to the basic principle underlying the
second law, would be given a measure of respect, and taken seriously by their
colleagues, but we aren't.
fact, the 2nd law of thermodynamics is not really "the supreme law of Nature,"
although it is one of the widely applicable and highly plausible postulates of
science. However, anti-evolutionists often exaggerate its significance and
applicability. A common thesis of anti-evolutionists has been the assertion
that according to the 2nd law "everything" in nature tends to decay,
degenerate, and lose its ability to be used. They often offer examples such as talking
about a glass that fell on the ground and broke, which will never spontaneously
recombine into a whole glass. While this statement is correct in itself, it in fact
has little to do with the 2nd law of thermodynamics (as should be clear from
the explanation of that law given above).
Likewise, the assertion by anti-evolutionists that "everything" in
nature tends to decay, etc, is an exaggeration. Recall the adage "diamonds are
forever." Items made of gold, platinum,
iridium, rhenium, molybdenum, tungsten, stainless steel, and many other
materials, if left alone, remain intact indefinitely. Some metals (liked gold) are corrosion-resistant simply because of their electrochemical properties. Some other resist corrosion because on their surface spontaneously appears a thin but very strong layer of oxides, protecting the item from corrosion. If this layer is mechanically removed, say by filing the
surface, it immediately spontaneously reappears. A gold item can remain intact
indefinitely long, regardless of the 2nd law of thermodynamics. The same is true for many other materials,
such as various semiconductors, dielectrics, etc. The assertion about "everything" necessarily decaying is an
exaggeration, often used by creationists to "prove" that the 2nd law
makes evolution impossible.
to point now to the concluding sentence in Sewell's essay, where he complains
that anti-evolutionists are not "taken seriously by their colleagues," and are
not "given a measure of respect."
like to ask Professor Sewell whether or not he agrees that when "respect" is
requested, it should be a two-way street?
essay I wrote with Wesley Elsberry
we documented multiple examples of ID advocates using insidious comparisons of
their adversaries with the Nazis, Soviet communists, Salem judges, the Taliban,
Lysenko and other similar personalities and regimes.
published my book Unintelligent Design
and posted a number of anti-ID and anti-creationism essays on the internet, I
was honored by pro-ID and pro-creationism advocates with such signs of respect
as publicly calling me in their posts stupid,
moron, pest, liar, hypocrite, "close," and other similar nice appellations.
I was accused on pro-ID sites of lying about my list of publications and
patents. I was accused of not being able to comprehend simple mathematics, of
not comprehending "plain English," of deliberately trying to misrepresent ID, etc.,
etc., etc. Other critics of creationism often get a similar treatment from
advocates of both ID and YEC. The "great philosopher" of ID William Dembski,
who never published a single word in response to the essence of my critique of
ID, called me, apparently trying to be witty, "Boris Yeltsin of higher
learning." While the meaning of that appellation remains Dembski's secret,
nobody would interpret it as a manifestation of respect and of a serious
attitude to my work. Professor Sewell, when requesting respect, please don't
forget the saying "Doctor, heal yourself."
My thanks to Nick Matzke for pointing
to Sewell's essay, and to Marshall Berman, Andrea Bottaro, Glenn Branch, Pete
Dunkelberg, Gordon Elliott, Wesley Elsberry, Erik, Paul Gross, Art Hunt, Mark
Isaak, M. Kim Johnson, Steve Reuland, Jason Rosenhouse, Douglas Theobald and the entire PT team
for pithy comments.