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Mark Perakh's Web Site

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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 creationism.

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 Thermodynamic Failure."

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 evolution?

I don't 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.

This 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.

Since I am not a biologist, I'll limit my discussion of Sewell's essay to narrow thermodynamic topics.

The main argument against the ET used by Sewell seems to be based on thermodynamics, and specifically on its famous 2nd law.

Before delving into the essence of Sewell's main argument, let me provide a few more quotes from his essay.

Sewell writes,

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.

First 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.

Note here the expressions like "order is disappearing in the next room," "Importing thermal order," and "will make the temperature distribution less random." 

While 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.

Defenders 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.

Here is another quote:

Natural forces, such as corrosion, erosion, fire and explosions, do not create order, they destroy it.

Without 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?

Has 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, and Darwin).

Regarding 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).

Here is 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 spectacular way.

Having announced the quoted claim, Sewell proceeds to elaborate, aiming to prove that the 2nd law of thermodynamics prohibits evolution.

I'll 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 unsubstantiated conclusions.

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

dS=dQ/T

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 natural world.

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 flow.

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 decrease.

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 law.

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?

Doesn't 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.

Likewise, 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.)

I 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 of mathematics.

(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.)

Sewell's 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.

In 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.

I wish 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."

I'd like to ask Professor Sewell whether or not he agrees that when "respect" is requested, it should be a two-way street?

In an 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.

After I 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.

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