American Association of Physics Teachers

Evolution and the second law of thermodynamics (manuscript  ID no. 25055 submitted to AJP on February 24, 2012)
The articles published by the American Journal of Physics, “Entropy and evolution” (November 2008) and “Evolution and the second law of thermodynamics” (October 2009) are based on a lack of understanding of thermodynamics and evolutionary biology.

The common descent of species refers to the evolution of mammals from bacteria over a period of 3 billion years. Adaptation refers to the evolution of traits that increase the chance of survival in the various habitats that cover Earth. While there is no easy way to draw the line between adaptation and common descent, natural selection is a theory that explains only adaptation. It does not explain common descent. In other words, natural selection explains why giraffes have long necks, but it does not explain how giraffes evolved from fish and fish evolved from prokaryotes.

I have I a license to teach physics in New York State and can lawfully teach biology if no licensed biology teacher is available. I would give my hypothetical class the following two quotes to support the above assertion.  The first quote should be read slowly. The second quote is from a biologist who I think limits the explanatory power of natural selection more than most biologists:

Facilitated variation is not like orthogenesis, a theory championed by the eccentric American paleontologist Henry Osborn (1857–1935), which imbues the organism with an internal preset course of evolution, a program of variations unfolding over time. Natural selection remains a major part of the explanation of how organisms have evolved characters so well adapted to the environment. (Marc Kirschner and John Gerhart, The Plausibility of Life: Resolving Darwin’s Dilemma, 2005, page 247)

P. falciparum, HIV, and E. coli are all very, very different from each other. They range from the simple to the complex, have very different life cycles, and represent three different fundamental domains of life: eukaryote, virus, and prokaryote. Yet they all tell the same tale of Darwinian evolution. Single simple changes to old cellular machinery that can help in dire circumstances are easy to come by. This is where Darwin rules, in the land of antibiotic resistance and single tiny steps…There is no evidence that Darwinian process can take the multiple, coherent steps needed to build new molecular machinery, the kind of machinery that fills the cell. (Michael J. Behe, The Edge of Evolution: The Search for the Limits of Darwinism, 2007, p. 162)

The following is a quote from a science writer who thinks natural selection does explain the complexity of living organisms. You might ask the author what biology textbook or peer-reviewed article she got this idea from. Christine Kenneally, Steve Pinker, and Paul Bloom have PhDs in linguistics, not biology.

They [Pinker and Bloom] particularly emphasized that language is incredibly complex, as Chomsky had been saying for decades. Indeed, it was the enormous complexity of language that made is hard to imagine not merely how it had evolved but that it had evolved at all.

But, continued Pinker and Bloom, complexity is not a problem for evolution. Consider the eye. The little organ is composed of many specialized parts, each delicately calibrated to perform its role in conjunction with the others. It includes the cornea,…Even Darwin said that it was hard to image how the eye could have evolved.

And yet, he explained, it did evolve, and the only possible way is through natural selection—the inestimable back-and-forth of random genetic mutation with small effects…Over the eons, those small changes accreted and eventually resulted in the eye as we know it. (Christine Kenneally, The First Word: The Search for the Origins of Language, 2007, pp. 59–60)

This is the kind of misinformation the two American Journal of Physics articles are promoting. According to the second law of thermodynamics, an isolated system of non-interacting particles will either be in equilibrium or go to a state of greater disorder. In other words, nature goes from the more complex state of speed and location to the less complex state.  The two articles report scientific calculations showing that evolution does not violate the second law of thermodynamics. Laymen interpret this to mean that natural selection explains the complexity of life.

A very understated measure of the complexity of life is the primary structure of a protein. A large protein has 600 amino acids connected together. Sickle cell anemia is caused by one amino acid in hemoglobin not being the right one, there being 20 different kinds of amino acids. Evolutionary biologists calculate the probability of getting the primary structure of a protein by the random selection of amino acids. They relate this probability to the time available for evolution, which is 3 billion years.  I selected the number 600 because that is the length of an English sonnet, which is made up of approximately 20 letters. Professors Gerhart and Kirschner discuss the chances of getting an English sonnet from the random selection of words and letters in their award-winning book cited above.

These are the same calculations of probabilities used in statistical mechanics to relate microscopic variables to the macroscopic variables of thermodynamics. For example, the connection between temperature (T) and the average kinetic energy (KE) of a molecule in a gas is given by  KE = (3/2)kT, where k is the Boltzmann constant. The two articles use an equation connecting entropy (S) with a quantity called thermodynamic probability (Ω): S = klogΩ.

This means there is a loose connection between evolution and thermodynamics. One might say:

Considered thermodynamically, the problem of neo-Darwinism is the production of order by random events. (Ludwig von Bertalanffy, “Chance or Law,” in Beyond Reductionism: New Perspectives in the Life Sciences, The Macmillan Company, 1969, page 76)

However, the idea that evolution violates the second law of thermodynamics is irrational because the second law is as certain as saying the odds of getting snake eyes in a dice game is 1/36. It is equally irrational to try to prove evolution doesn’t violate the second law by performing entropy calculations on living organisms. It is like calculating the entropy of a deck of playing cards with Boltzmann’s constant. A deck of playing cards has neither entropy nor temperature.

There are more quotes from mainstream biologists in my Youtube video titled, “The Truth About Evolution and Religion.”

Also of interested to any teacher should be the dialog between me and a graduate student at Berkeley majoring in biophysics: http://www.quora.com/Should-scientists-refer-to-evolution-as-a-law-instead-of-a-theory/answer/David-Roemer-1

This is a link to an article by a mathematics professor that criticizes the two articles. The article itself contains three other links that may be of interest: http://www.evolutionnews.org/2011/10/more_philosophical_than_scient052441.html

Report of reviewer  sent to me by David Jackson
This manuscript criticizes two articles on the relationship between entropy and biological evolution that were previously published in the American Journal of Physics. The manuscript fails to present valid and clear scientific arguments and is entirely unsuitable for publication.

The manuscript begins with a desultory sequence of statements that fail to present any sort of argument or indeed to bear any relation to the articles supposedly being critiqued: there is a discourse on the meanings of the terms “common descent,” “adaptation,” and “natural selection,” followed by two quotations of no apparent relevance. Then, perhaps most bizarrely, aspersions are cast on the expertise of three linguists who are not mentioned in the original articles. The author claims that “this is the kind of information” supplied in the two articles under critique. If the author wishes to supply examples of “the kind of misinformation” in these articles, he should cite examples from the articles, not from pieces that bear no discernible relationship to them.

In the entire manuscript, I can find only one substantive criticism, namely the sentence “Laymen interpret [the calculations in the articles] to mean that natural selection explains the complexity of life.” The articles in question are extremely explicit in describing what they do and do not claim. The purpose of both articles is to refute the argument often raised by creationists that claims that the second law of thermodynamics renders evolution by natural selection impossible. They do not make the positive claim attributed by the author. The first article, by Styer, is extremely explicit on this point (see item 4 in the Appendix). I see no evidence that any “layman” has fallen into the error that concerns the author.

After this paragraph, the author resumes his stream of irrelevant observations. The next several paragraphs do not contain any argument clear enough for me to respond to. I will simply conclude by pointing out that the author displays a lack of understanding of standard thermodynamics when he remarks that “a deck of playing cards has neither entropy nor temperature.” The laws of thermodynamics apply to all physical systems. Any time there is a meaningful split between “microstates” and “macrostates,” it makes sense to compute entropy.

Email to present and future president of the American Association of Physics Teachers
Dear Beth and Gay,
I just got the attached response to the pdf document I submitted online.  It should have been obvious that I didn’t intend the article for publication because I included three URLs. I am trying to help the AJP understand its mistake and see the need for corrective action. Anonymous reviewers don’t have to worry about their reputations.

I’ll say the same thing to the reviewer that I said to one of the authors: I have a PhD in physics from New York University, and I think it should be possible for two physicists to come to an agreement about the second law of thermodynamics. He responded to this by saying he was too busy to discuss it.

This matter should be referred back to the two authors and the two sets of reviewers. The reviewers, as I already pointed out to you, helped write the original article. This might be okay ordinarily. But for an article criticizing creationism, the reviewers might have been biased against religion in general or creationism itself.

The review is non-responsive and contains nonsense,  no better than I get when blogging:

I will simply conclude by pointing out that the author displays a lack of understanding of standard thermodynamics when he remarks that “a deck of playing cards has neither entropy nor temperature.” The laws of thermodynamics apply to all physical systems. Any time there is a meaningful split between “microstates” and “macro-states,” it makes sense to compute entropy.

The second law of thermodynamics only applies to a system of non-interacting entities. It does not apply to “all physical systems.”  A deck of cards is an imaginary system of non-interacting particles because card players calculate the odds of getting particular hands.  Just like a physicist calculates the probability of states of a system of particles.

What is absurd about the two articles, as I explained as best I could, is that the articles’s phony equation uses Boltzmann’s constant to calculate the entropy of the biosphere.

The other dumb thing about the two AJP articles is the implication that applying heat to a system decreases its entropy. When you compress a gas its entropy decreases because there is more knowledge about the location of the molecules. However, when you add heat to a gas its entropy increases. I did not mention this in my submission because I included a link to an article by a professor of mathematics who explains this.

Very truly yours, David Roemer

Letter to Associate President of the American Association of Physics Teachers
Dear Dr. Hilborn,

I’v been corresponding with Emory Bunn, David Jackson, Beth Cunningham, and Gay Stewart about two articles published in the American Journal of Physics about the second law of thermodynamics. The articles report calculations with Boltzmann’s constant purporting to show that evolution does not violate the second law of thermodynamics.

I just left a message on Beth’s machine asking for an appointment to explain the harm those articles are doing and the harm she and David Jackson are doing by doing nothing.

My own claim to fame as a physicist is the mention of my name in an erratum published in Physics Review Letters. The solution I suggest for this scandal is the publication of an erratum with apologies. The articles were not properly peer-reviewed.

After consulting with Beth and Gay, I submitted a document to David Jackson, who turned the document over to an anonymous reviewer. My response to this reviewer is at

http://newevangelist.me/2012/02/23/american-association-of-physics-teachers/.

Very truly yours,

David Roemer

Response from the president of the American Association of Physics Teachers
Dear David,

I understand that you continue to be concerned about two articles that appeared in the American Journal of Physics regarding the second law of thermodynamics and evolution.  You also expressed concern about the process used that resulted in these two articles being published.  The established review process for manuscripts submitted to AJP was carefully developed and approved by the Editorial Board.  Included in this process is an evaluation of the manuscript by highly qualified referees who are chosen to have expertise to evaluate the submitted manuscript.  In addition, the editor reviews the referees’ evaluation to determine if further evaluation is needed. A manuscript will only be published if it meets AJP’s criteria for publication, is approved by the referees and editor, and the author(s) work through the final editing stage.  This process is very similar, if not identical, to the process other scientific journals use to evaluate manuscripts.  This is the process that physics, and science in general, is done.  This is the process used that resulted in the publication of the two articles you question and for the manuscript that you submitted.  There is no reason to meet or discuss this issue further.
Best regards, Beth
Letter to Executive Board member
Dear Professor Iona,
I’v been complaining about “Entropy and evolution” (November 2008) and “Evolution and the second law of thermodynamics” (October 2009) in the American Journal of Physics to Beth Cunningham, Robert Hilborn, David Jackson, and Gay Stewart for over a month. Mary Beth Monroe just told me that I should file my complaint with you. Some of my correspondence with these individuals is at

http://newevangelist.me/2012/02/23/american-association-of-physics-teachers/.

The second law of thermodynamics applies to an isolated system of non-interacting particles. The molecules in a gas will fill up the entire container because that is the most probable configuration. A deck of playing cards is a model for a gas with 52 molecules. The cards are identical, non-interacting, and isolated. The advantage of the model over a real gas is that the cards come automatically labeled.

Biologists, in their efforts to understand evolution, have a model for a protein: an English sonnet. A poem is like an isolated system of non-interacting particles. The letters represent the amino acids and the poem represents the protein. Just as every letter in the poem has to be in the right place, so every amino acid has to be in the right place. Given that there is only 3 billion years for evolution, probability calculations place a limit on the explanatory power of natural selection. My understanding is that natural selection explains only adaptation, not common descent.

What drew my attention to these articles is that I was ridiculing the following statement by the famous atheist Richard Dawkins:

“When creationists say, as they frequently do, that the theory of evolution contradicts the Second Law of Thermodynamics, they are telling us no more than that they don’t understand the Second Law (we already knew that they don’t understand evolution). There is no contraction, because of the sun!” (The Greatest Show on Earth: The Evidence for Evolution, page 415)

My ridicule was squelched by no less a person than the Deputy Director of National Center of Science Education (Glenn Branch) by citing your articles. The AJP articles not only say the sun produced evolution, they calculate the entropy of the biosphere using Boltzmann’s constant.

In my opinion, you should publish an erratum with an apology. Feel free to give me a call. I offered to go to Washington, DC, to explain how much harm this article is causing and why you have a moral obligation to put an end to it.

Very truly yours,

David Roemer

Response from Steve Iona
Dear Mr. Roemer (and Dr. Monroe)

I received your email from March 19th.If you have an appeal regarding the rejection of an article for which you are an author, the Publications Committee would be the group to review the documentation.  Comments about other articles should be sent as Letters to the Editor.

FYI-The Publications Committee does not judge whether an article should be published or not (that is the role of the editor with input from the expert reviewers).  The Publications Committee only evaluates the process that was used to review an article to assure that the process was fair and appropriate.  The Committee does not address errata; the editor handles that.

Sincerely, Steve Iona

My response to Steve Iona
Dear Steve,

I first sent an email to Emory Bunn, the author of a note to the original article by Daniel Styer. Bunn responded that he didn’t have time to discuss it. I then complained to David Jackson who told me to submit an article.

I am not an expert in the second law of thermodynamics and am not qualified to write an article about it. I complained to Beth Cunningham who told me to write a letter to the editor, something I had already done. Gay Stewart suggested that I submit an article.

I decided to try to write the article, and contacted a retired professor of physics at New York University, Robert Richardson, who claimed to be an expert on thermodynamics. I never met Richardson, but a professor of physics at NYU I know recommended him to me. I got my Ph.D. in physics from NYU and Richardson surely knows my thesis advisor, who is still there. This is the rude and uncharitable response I got:

“I have spent some time with your work but am not able to make an informed comment. I do sometimes testify as an expert in court. But my rate is $400/hr portal to portal.  I doubt that you can afford a day of my time.”

This is an example of the harm that the two articles are causing. Richardson behaved badly. So has everyone at the American Association of Physics Teachers I have contacted, except Beth Monroe.

Styer may not have been lying when he wrote down that fake equation for the entropy of the biosphere, (3). He may have gotten it from another peer-reviewed publication. Or, I may be mistaken in thinking the equation is erroneous. Until I learn otherwise, the equation is a lie invented to persuade people not to believe in the Bible. Unlike violations of the Fifth Commandment, lies can be undone.

I agree with Beth Monroe that the responsibility of getting the erratum published is yours. I think it is significant that Styer thanked the anonymous peer-reviewers for helping him write the article. My guess is that your peer-review process doesn’t include a red flag when an article is criticizing religious beliefs. The editor should have made sure that the peer-reviewers were not personally involved in criticizing creationism and advocates of intelligent design.

Please feel free to call me. I may be able to persuade you that you should reconsider your decision not to get involved.

Very truly yours, David Roemer

Email to Executive Board of the American Association of Physics Teachers

The American Journal of Physics published articles criticizing creationist literature for saying evolution violates the second law of dynamics [“Entropy and evolution” (November 2008) and “Evolution and the second law of thermodynamics” (October 2009)]. The articles report calculations of the entropy of the biosphere using Boltzmann’s constant and imply that adding heat to a system can decrease its entropy. The articles may have been written in good faith, but I have recently pointed out the errors in the articles to your fellow executive board members. So far, no one is taking responsibility for the articles.

The AJP should publish an erratum that apologizes for the articles. I offered to explain my views of the moral issues involved to Beth Cunningham in person. The offer still stands, and I’ll be happy to discuss the matter with you over the telephone.

The second law of thermodynamics states that a gas will fill up its container because this is the most probable configuration. To do these calculations, physicists give each one of the identical molecules in the gas a label (No. 1, No. 2, No. 3, etc.). One might say, the model for a gas is a deck of playing cards because the playing cards are identical, non-interacting, and isolated.

Biologists use the English sonnet as a model for a protein. The letters in the sonnet represent amino acids and biologists calculate the probability of getting a sonnet by the random selection of letters and dictionary words. This calculation and the fact that the primary structure of the protein doesn’t even begin to describe the complexity of life is why natural selection explains only adaptation, not common descent. In other words, natural selection explains why giraffes have long necks, but does not explain how giraffes evolved from bacteria. This is the sense in which evolution violates the second law of thermodynamics.

My correspondence with your colleagues is at

http://newevangelist.me/2012/02/23/american-association-of-physics-teachers/

Very truly yours,

Email sent on 5/1/12

To the Executive Board of the American Association of Physics Teachers:My accusation that the equations in the article titled “Entropy and evolution” in the American Journal of Physics (November 2008) are absurd was published in England (http://www.catholictruthscotland.com/MAYnewsletter12.pdf).In my opinion, it is extremely important that the American Journal of Physics publish a retraction of this article. It is morally reprehensible to allow this article to continue to spread misinformation about evolution and the second law of thermodynamics. The article undermines the belief that scientists and peer-reviewed journals are dedicated to the truth.Very truly yours, David Roemeremail sent on May 1, 2012 to Beth Cunningham
Dear Beth,

You should terminate David Jackson. He should have forwarded my article to Emory Bunn and Daniel Styer for rebuttal. They have reputations to protect and presumably consciences for moral guidance.

For all you know, Jackson himself wrote the anonymous review.

email sent on May 23, 2012 to all members of the board:
To the American Association of Physics Teachers:

I posted a message about the attached article on the Science Writers of New York LinkedIn Group. A member quoted from a document sent to me by David Jackson saying that I did not understand the second law of thermodynamics. This is my response:

The anonymous reviewer said of the pdf file I uploaded to the American Journal of Physics,“This manuscript….unsuitable for publication.” The pdf file obviously wasn’t intended for publication. It was submitted after the editor told me he didn’t want to discuss the article titled “Entropy and evolution” anymore and after I complained to the president of the American Association of Physics Teachers about the misinformation in the article. The document also contained three links to other articles on the internet and very lengthy quotes about evolution from scholarly works.

The reviewer also said, “The laws of thermodynamics apply to all physical systems. Any time there is a meaningful split between ‘microstates’ and ‘macrostates,’ it makes sense to compute entropy.”

I suppose this is correct. When you take a deck of playing cards out of its wrapper the entropy is log (1/ 52!) joules/degree. But it is not true that the entropy is this multiplied by Boltzmann’s constant: 1.38 X 10 (-28). The AJP article computes the entropy of the biosphere using the Boltzmann constant.

The authors may have made this mistake in good faith. But this reviewer, whoever it was, certainly was not acting in good faith. Also, the AAPT and the AJP are not acting in good faith in refusing to publish a retraction.

There is a clue that explains how such an absurd article could survive peer-review. The first article said, under the acknowledgment heading: “Two anonymous referees made valuable suggestions that improved this article significantly.” The referees many have been atheists eager to refute the creationist the article mentions by name (Henry Morris).

Very truly yours, David Roemer

Email sent on May 24, 2012 to Beth Cunningham
Alan Leshner is saying that it is your responsibility to publish the retraction of the AJP article. If you leave office before this happens, the responsibility will fall on Gay Stewart.

Very truly yours, David Roemer

Email sent on December 16, 2012, to Jill Marshall
Dear Dr. Marshall,
I’m writing to ask you to resign from the AAPT to protest the behavior of Beth Cunningham who has ignored my request for a personal interview to explain why the attached AJP article by Daniel Styer should be retracted.

Dr. Cunningham is not following accepted procedures for peer-reviewed journals:

  1. The article attacks creationism and the reviewers of the article helped the author write the article. The reviewers may have been more interested in attacking belief in the Bible than in scientific truth (see ACKNOWLEDGMENTS).
  2. The editor of AJP did not refer my criticisms of the article to Daniel Styer.

I’v been making the same request of members of the Academy of Catholic Theology, who are behaving the same way Cunningham is behaving. The following is the email I sent to Fr. Stanley, President of Providence College. Feel free to give me a call. (see http://newevangelist.me/2012/08/02/first-things/)

Email received from Beth Cunningham on December 17, 2012
Dear Mr. Roemer,
Thank you for your letter and fax concerning the paper “Entropy and Evolution” which was published in the American Journal of Physics.  The American Association of Physics Teachers has established procedures for publishing papers in AJP.  There is, in those procedures, no role for the Executive Officer or any member of the AAPT Executive Board.  The responsibility for scientific review rests within the editors of the individual journals.  I regret that I am not in a position to give further consideration to your request.

Sincerely yours,
Beth A. Cunningham, Ph.D.
AAPT Executive Officer

Email sent to Beth Cunningham on December 18, 2012
Dear Dr. Cunningham,

Thank you for your email in response to my request for a personal interview. I must repeat this request for the following reasons.

David Jackson, editor of the AJP, should have referred my criticism of “Entropy and evolution” by Daniel Styer (Am. J. Phys., Vol. 76, No. 11, November 2008) to the author. If Styer had said I was wrong, I would have written to his college and said he is not qualified to teach physics. Instead, Jackson suggested I submit my own article to the AJP. I did so, and an anonymous reviewer said that that I was wrong. No one at the AJP or AAPT is taking responsibility for the erroneous equation that makes the entire article worthless.

Prior to my AJP submission, I asked Professor Robert Richardson of New York University whether I was right about the absurd equation. His answer supported my analysis, but his behavior became inexplicably hostile when he realized that I was trying to get the AJP to retract an article about evolution. While we never met, he may have found out from a mutual friend that I was a retired high school teacher. He expressed his contempt for my profession by saying that I could not afford his consultation fee of $400 per hour.

The next two PhDs in physics to behave bizarrely are Randy Isaac and Robert Kaita of the American Scientific Affiliation (ASA), where I posted my criticism of the article on the Open Forum of their website. Isaac’s comments were irrational. (Roemer: A Boeing 747 does not have a temperature. Isaac: Yes it does. Roemer: Natural selection only explains adaptation. Isaac: Not true.) I asked Robert Kaita, the President of the ASA, to assign a moderator for our conversation, to no avail.

The next physicist to behave irrationally is Stephen M. Barr, who is an advisor to First Thing, a Catholic journal of opinion. I sent him an email about the matter, and he responded by saying the AJP article was okay and that I was harming the Catholic Church. I accused him of not reading my analysis and demanded an apology.

The Catholic Church is involved because the newsletter of the Catholic Truth of Scotland published my letter explaining why the AJP article and the atheist Richard Dawkins don’t know what they are talking about when they say evolution does not violate the laws of entropy. I found out about the AJP article when Glen Branch of the National Center for Science Education told me about it to refute my criticisms of Dawkins on www.skeptic.com.

My submission to First Things titled “Evolution and the Culture War” was rejected, and I requested a personal interview with Russell Reno to complain. Reno and Barr are members of the Academy of Catholic Theology. I’v been asking the members of this organization to resign to protest the behavior of Reno and Barr, and am getting very strange reactions.

Fr. Nicano Austriaco, a biology professor at Providence College, said he needed three weeks to go over the material I sent him about the AJP article. After three weeks went by, he said that he was not qualified to pass judgment on the matter. Another professor at Providence College, James Keating, said he knew Russell Reno and that he would ask him why my article was not published. I have not yet heard from Dr. Keating. The three other members of the Academy of Catholic Theology at Providence College did not respond to my email. I sent an email to Fr. Brian Shanley, President of Providence College, about the matter.

I got the following email on 8/27/12 from someone who was obviously distressed by my campaign. If Dr. Davis was harmed professionally by my telling Dr. Phipps, it is on your shoulders, not mine.

Dear Dr Roemer,

This is simply a threat. Shame on you—is this how you respond to people who don’t do your bidding? You dragged me into this entirely on your own, Dr Roemer. I don’t encourage you to contact President Phipps, not because I fear any action she might take—she fully supports my involvement with BioLogos, and she understands that you are simply on a crusade to cause trouble for me (and others), because we won’t help you fight your own battles—but because it will simple waste some of her very valuable time. I needn’t add, that you are doing that already with my time. If you raise this issue with me again, I will have no choice but to block your messages. I have classes to teach, and students to meet with, and your concerns are not high on the agenda.

Since you did not send me information about any articles you’ve written for “First Things,” I gather that you actually are not a writer for that magazine, as you claimed. At least, I can find no evidence of such activity.

Edward B. Davis,Professor of the History of Science
Messiah College

I intend to continue to contact members of the American Association of Physics Teachers, Academy of Catholic Theology, and the American Scientific Affiliation and their bosses until the American Journal of Physics retracts the Styer article and the subsequent note by Emory Bunn (Am. J. Phys., Vol. 77, No. 10, October 2009) . The following are links to my correspondence about this matter. (see above links)



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