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American Journal of Physics
Moderator(s): Randall D. Isaac
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4/13/2012 at 8:50:11 PM GMT
Posts: 142


  I'm sorry for being slow to respond. I'm dealing with my brother's terminal illness and it is very difficult.

  But let me jump in here. You seem to think I'm being evasive, so let me be very very clear:

1. Equeation 3 in that article is precisely correct. It says that entropy is Boltzmann's constant times the natural log of the number of microstates. That is in fact the definition of entropy and it certainly is not absurd.

2. ALL systems and ALL phenomena without exception follow the second law of thermodynamics, whether biological systems or systems of gases or whatever. There is no system of any kind to which the second law does not apply. And yes, all systems do have a temperature.

3. Adding energy to a system does generally increase the entropy, as the authors of that article actually do specify, but the second law doesn't specify that--it specifies only that the Gibbs Free energy will decrease, where that energy includes the energy source. Normally the entropy does increase.

I hope that's clear. The article is not deceptive and it is not wrong. Evolution does not in any way contradict the second law of thermodynamics. And no, biologists don't calculate probabilities like that. Not at all.

I hope that wasn't evasive.


Last edited Friday, April 13, 2012
4/14/2012 at 7:13:49 AM GMT
Posts: 24

Randy and David,

Randy, your statements support my initial impression that the entropy calculations in the meteorological article derived from the same equation.  Usually in these cases I try to do a some mathematics to translate one into the other or at least identify correspondence between the values.  Haven't had the time to do the work, and unfortunately I'm about ready for qualifying exams, so it may be a bit before I can address this.

David, would it be helpful to show how equations like the ones in the meteorological article, which are not in dispute, are similar to those in the AJP article?  Perhaps that would either confirm your suspicion and provide support for an article, or it would explain what the authors of the AJP article mean and how it relates to a physical system.  Physics really boils down to the math, at least for me.

On the surface I see similar reasoning in both articles, but I haven't checked the math.  This isn't are area of expertise for me, so will will take some time to wrap my head around it.  I want to be sure it will be helpful.

Wow, Randy.  Sorry to hear about your brother.  Will be praying for sure. --S

Last edited Saturday, April 14, 2012
4/14/2012 at 11:27:56 AM GMT
Posts: 142

Thank you very much, Scott. He's moving into hospice today.

David, I wonder if the discrepancy may be in how to apply their Eq 3 to a system of molecules in a gas? Did I understand you correctly that you thought this equation would predict a lower entropy when energy is added to that gas? Actually, the density of microstates would increase, hence the logarithm of the number of microstates increases, and the equation does predict an increase of entropy. All is well, don't you think?


4/17/2012 at 3:26:49 AM GMT
Posts: 60
Dear Randy and Scot,

I’m sorry to say I find you answer evasive because it is not responsive to my critique of the "Entropy and evolution” paper.

Equation (3) for entropy is S = k log W and it is analogous to the equation for temperature:  KE = (3/2)kT. I am mentioning the temperature equation because the thermodynamic concept of temperature is easier to grasp than the concept of entropy, which is defined in terms of heat and temperature. If it was absurd for Styer to use the entropy equation, it is equally absurd to use the kinetic energy equation.

Your statements that biological systems follow the second law of thermodynamics and  "all systems have a temperature” does not respond to my criticism of Equation (3).  I am saying all systems do not have a temperature and entropy. All you are doing is contradicting me. You are not responding to my explanation of why Equation 3 does not apply to the biosphere evolving or a seed in the ground growing into a tree.

An example of a system that does not have a temperature is a three-legged stool. The four parts of the stool may have temperatures, but the stool itself does not.

Let me explain in another way why Eq. 3 is nonsense. Suppose you have a gas in a container with a cylinder at atmospheric pressure. You compress the gas with your arm muscle and extract heat from the gas, so that the entropy of the gas decreases. This does not violate the second law of thermodynamics because the gas is not an isolated system. It is connected to a human arm. Likewise, evolution and a seed growing into a tree do not violate the second law because they are not isolated systems of non-interacting particles.

What the Styer article does, by analogy, is calculate the increase in the arm’s entropy, using the Boltzmann constant, to prove that the increase in the entropy of the arm is greater than the decrease in the entropy of the gas, so that there is no violation of the second law. To justify Equation (3), I think you need to cite peer-reviewed papers which calculate the entropy of biological systems. Alternatively, you can explain to my why my reasoning is wrong.

As to your statement that biologists don’t calculate the probability of getting an English sonnet by the random selection of words and letters by a computer in order to understand evolution, I cite the following:

"By comparison, if we question how long it would take a high-speed computer to write randomly a specific Shakespearean sonnet, we are asking that all the letters of the words of the sonnet will come up simultaneously in the correct order. It is an impossible task, even if all the computers in the world today had been working from the time of the big bang to the present. Even to compose the phrase, ‘To be or not to be, letter by letter, would take a typical computer millions of years.” (Marc W. Kirschner and John C. Gerhart, The Plausiblity of Life: Resolving Darwin's Dilemma, page 32).

David Roemer

4/17/2012 at 11:34:41 AM GMT
Posts: 142


  I'm truly puzzled by your thinking I'm being evasive. Let me try again. Eq. 3 does not need citations--it is the definition of entropy that all thermodynamicists know and it applies to all systems. No exception. I do not understand your argument of why it wouldn't apply. I'm not evading anything. Your argument just doesn't make sense to me. Your examples of compressing a gas with your arm is quite right and so is the argument they give in the paper. I see no contradiction whatsoever. Nothing to evade.

And the last quote you gave is surely correct--but no one writes sonnets that way and no biomolecule is created that way and no one calculates the probability of a biomolecule assembling in that way. It has no relevance to the situation.


4/18/2012 at 6:50:21 AM GMT
Posts: 60


You say,

"And the last quote you gave is surely correct--but no one writes sonnets that way and no biomolecule is created that way and no one calculates the probability of a biomolecule assembling in that way. It has no relevance to the situation.”

Gerhart and Kirschner are mainstream biologists and this is a calculation made in an attempt to understand evolution. Because of this calculation and other considerations, natural selection only explains the adaptation of species to the environment. It does not explain the increase in the complexity of living organisms as they evolved from bacteria to mammals (common descent). The only theory that attempts to explain common descent is intelligent design (ID). However, there is no evidence supporting ID.

The connection between evolution and the second law is that biologists do the same kind of probability calculations that physicists do. Physicists label non-interacting entities No. 1, No. 2, etc. Biologists label amino acids a-No.1, a-No.2, b-No.1, b-No.2, etc.  Your telling me this isn’t so makes sense only if you think Gerhart and Krishner are advocates of ID.

Based on this reasoning, I ridiculed Richard Dawkins for saying evolution does not violate the second law of thermodynamics because of the sun! Glen Branch, the Executive Director of the National Center for Science Education, squelched me by citing the two AJP articles, which use the equation (3) (S = klog W) to calculate the entropy of the biosphere.  

Equation (3) only applies to thermodynamic systems. It does not apply, for example, to a Boeing 707. An airplane does not have a temperature or an entropy. Likewise, a seed planted in the ground and growing into a tree does not have a temperature or an entropy. A newly fertilized cell is much more complex than an airplane. Just as it is absurd to say the growth of a seed into a tree violates the second law, it is absurd to say calculations with the equation S = klog W can prove that the second law is not violated when a seed grows into a tree. The way I am interpreting your statement that equation (3) does not need a citation is that there is no citation that justifies applying the equation to biological systems.

I explained this to Emory Bunn, the author of the note improving on the first article by Daniel Styer, and to David Jackson, the editor of the AJP. They both said they didn’t have time to discuss the matter. David Jackson said I could submit an article to the AJP for publication. The correct procedure, I believe, would have been to forward my comments to Daniel Styer and Emory Bunn. Whether or not Jackson did this and what the response of Styer and Bunn was, I do not know. What this means is that you are the only one taking responsibility for equation (3). All we have is your statement that the equation applies to biological systems. We don’t have such a statement from Styer and Bunn because they have not responded to my explanation of why it is absurd to apply the equation to a biological system.

In the process of writing the article, I sent an email to Robert Richardson, a retired professor at New York University, asking for help. I said:

"I am pretty sure that the entropy equations in the articles are nonsense, but I don’t know enough about statistical mechanics to explain why. They use the equation S = klogW, but there is no justification for the use of Boltzman’s constant for biological systems. Is there?”

This was Richardson's initial response:

"Nice to hear from you. The k in   S = klogW  is just a question of units and has no physical significance. logW  is dimensionless and  S has the dimensions of energy divided by temperature. k makes them match. In the "right” set of units  k=1. Please send me your work as I am always interested.”

I sent him the articles and my ideas on the subject. This was his rude and uncharitable response:

"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.”

In the article I submitted I included a link (
to the work of a mathematics professor, Granville Sewell, who criticized the AJP articles. There were two other links. It was obvious that I was not submitting the paper as something to be published. If the anonymous reviewer was honest, he would not have written the review. For all anyone knows, the reviewer could have been Styer or Bunn.

Let me summarize the things that I am saying with the suggestion that you ask a biologist about 1), and expert on thermodynamics about 2) and 4), and an editor of a scientific journal about 3).

1)    Natural selection only explains adaptation, not common descent.
2)    S = klog W does not apply to airplanes and biological systems.
3)    David Jackson’s behavior was unethical because he didn’t refer my criticisms to the authors.  
4)    Robert Richardson’s behavior was disingenuous. He knows I’m right about equation (3), but he doesn’t want to get involved.

David Roemer

4/20/2012 at 4:17:08 PM GMT
Posts: 60
I’d like to try to explain why the American Journal of Physics is so reluctant to publish a retraction its shocking articles. Saying that evolution violates the second law of thermodynamics is equivalent to saying that the theory of intelligent design is true. Intelligent design is the only theory that attempts to explain evolution, but there is no evidence supporting this theory. It is just a bright idea, like saying free will is an illusion.

Natural selection only explains the adaptation of species to their environment. It does not explain the increase in the complexity of life as it evolved from bacteria to mammals over a period of 3 billion years. Biologists understand this, but many laymen do not. What follows is an excerpt from a book by Kenneth Miller (Only a Theory: Evolution and the Battle for the American Soul) rebutting intelligent design and Michael Behe (The Edge of Evolution:  The Search for the Limits of Darwinism).

In my opinion, Miller is being disingenuous. He never admits that there is a limit to the explanatory power of natural selection. If he said this, the book would not sell. A laymen reading this book might think that Behe says, "Natural selection does not explain the complexity of life” and Miller says, "Natural selection explains the complexity of life."

On page 67 Miller says: "A line in the sand is drawn, and on the other side of that line is intelligent design.” [Behe says that natural selection fails on the other side of the line. Whether or not intelligent design succeeds is a philosophical question, according to Behe.] The next paragraph says:

"How does Behe know where to draw that line? He takes a rough estimate from a 2004 clinical paper as to how often resistance to the antimalarial drug chloroquine has arisen in natural populations. ….1 chance in 10(20th power)…In fact he even invents a term for it, calling it …CCC…..To convert this number into an argument against evolution, Behe engages in a sleight of hand reminiscent of his argument for irreducible complexity.

"…….Given Behe’s estimate that fewer than 10 (40th power) cells have existed during the entire history of life on earth, that means that the evolution of even a moderately complex system of interacting proteins is far beyond the "edge” of what evolution can accomplish. He is so certain of this conclusion he calls it the two binding sites rule. Whenever we see two binding sites in a protein, he assures us, we see the hand of intelligent design. [Again, Miller attacks intelligent design instead of defending natural selection].

"….. Behe’s math requires that all of the mutations that produce a CCC must occur together, and they can be favored by natural selection only when all of these highly improbable events take place. ….Molecular studies of drug resistance in the parasite show that it is not the all-or-nothing one-chance-in-10(20th power) event he claims. Rather, full-blown resistance is preceded by a number of mutations that confer partial resistance, enabling natural selection to work at every step of the process. This means, as Nicholas Matzke wrote in his review of [i]The Edge of Evolution[/i], that chlorozuine resistance "is both more complex and vastly more probable than Behe thinks.

"….What he ignores, of course, is something that we already know to be true in the case of CCC, namely that natural selection can favor intermediate stages on the way to the evolution of the final, fully resistant organism."

The biological disagreement between Behe, Miller, and Matze is over Behe’s mathematics. My interpretation is that Behe is saying there are two evolutionary steps from species A to species B. Miller is saying there are 10 partial steps from species A to species B. Hence, the probability of getting from A to B is much less than what Behe says. Miller and Matze are not saying that the partial steps are the result of natural selection. They are saying that when a partial step occurs, natural selection acts upon that partial step.

David Roemer

6/3/2012 at 8:21:23 PM GMT
Posts: 142


  I'm sorry for the long delay. My brother has now gone on to be with the Lord and the memorial services and related activity are finally over. I'm slowly returning to something close to normalcy.

  As for the Kirschner and Gerhart quote, I do not know them nor have I read the context of their work. But in any case, in science the validity of an assertion is not based on who says it but on the evidence supporting it. If they purport to be simulating evolution, then I would like to see the evidence for it. As far as I know, it does not simulate any evolutionary process advocated by virtually all biologists.

  You make many assertions that I believe are false but it would take too long to address all of them. Let's focus simply on the most basic one.s The equation to which you object is the fundamental definition of entropy and is known to apply to all systems, with no exception. The reason is not the use of probabilities by biologists, as you suggested. Rather, it is a fundamental aspect of physics which applies to every living cell and every Boeing 747. If you have some evidence why it should not apply, please provide it. The equation is not absurd in any sense that I know. The only retraction needed is not from AJP.

 As for your assertion that natural selection does not explain common descent, I suppose it depends on how you are defining your terms. Common descent depends on both reproduction with variation and natural selection. With that clarification, the connection is rather clear.

I will not comment on your other two assertions about who said what or who is unethical. Let's focus only on the ideas and the evidence and logic supporting them.


6/5/2012 at 2:45:34 AM GMT
Posts: 4

I am new to this blog. In a closed system (i.e., no heat passing in or out, and no work done on the system) entropy (disorder) will always increase - and this happens in spite of, or maybe because of, random motion of atoms, say, in a diffusion situation.  The earth is not a closed system, due to, at least, energy input from the sun (and energy radiating out to space).  Thus, entropy can decrease on the earth, meaning that order can increase - I would assume, without any expertise in the area, that that could lead to higher order (less disordered) life forms.  The entire universe, on the other hand, is (likely) a closed system and entropy must decrease in it - not meaning that entropy cannot decrease in parts of the universe.  I take this to mean that order can increase on the earth, but overall, entropy is increasing in the universe.  I do not know what this means in biological systems, but I do know that the overall increase of entropy (disorder) certainly suggests a Creator God.  Also, the eventual effect (taking the really long view) is that the entire universe will be homogeneous - totally unlike the creation event.  Not sure if this is relevant.


Jim Bandstra

6/5/2012 at 2:56:46 AM GMT
Posts: 142
Well said, Jim! You understand it very well and stated it concisely. Thank you.