Fisher’s not-so-fundamental theorem

Congratulations to our resident theoretical biologist of high renown, Joe Felsenstein, on his presentation, yesterday, of the 37th Fisher Memorial Lecture. [ETA: I’ll post a separate announcement of the video, when it is released.] Following are the details provided by the Fisher Memorial Trust (with a link added by me).

Title: Is there a more fundamental theorem of natural selection?

Abstract. R.A. Fisher’s Fundamental Theorem of Natural Selection has intrigued evolutionary biologists, who wondered whether it could be the basis of a general maximum principle for mean fitness of the population. Subsequent work by Warren Ewens, Anthony Edwards, and George Price showed that a reasonable version of the FTNS is true, but only if the quantity being increased by natural selection is not the mean fitness of the population but a more indirectly defined quantity. That leaves us in an unsatisfactory state. In spite of Fisher’s assertion that the theorem “hold[s] the supreme position among the biological sciences”, the Fundamental Theorem is, alas, not-so-fundamental. There is also the problem that the additive genetic variances involved do not change in an easily predictable way. Nevertheless, the FTNS is an early, and imaginative, attempt at formulating macro-scale laws from population-genetic principles. I will not attempt to revive the FTNS, but instead am trying to extend a 1978 model of mine, put forth in what may be my least-cited paper. This attempts to make a “toy” model of an evolving population in which we can bookkeep energy flows through an evolving population, and derive a long-term prediction for change of the energy content of the system. It may be possible to connect these predictions to the rate of increase of the adaptive information (the “specified information”) embodied in the genetic information in the organisms. The models are somewhat absurdly oversimple, but I argue that models like this at least can give us some results, which decades of more handwavy papers on the general connection between evolution, entropy, and information have not.

142 thoughts on “Fisher’s not-so-fundamental theorem

  1. stcordova,

    Darwin’s followers are expressing their rage at you for mocking one of their religion’s “cardinals”…
    I don’t see any difference between their behaviour and any other religious extremists…
    Blind faith rules them all alike…

  2. J-Mac:
    Darwin’s followers are expressing their rage at you for mocking one of their religion’s “cardinals”…

    1. I’m not a follower of Darwin. The guy died many years ago. There’s nothing to follow.

    2. Neither me, nor newton expressed rage.

    3. My problem with Salvador is his presumption in the face of his astounding incompetence, in this case expressed as mockery towards a person who has been trying, all too patiently, to help Salvador understand quite a bit of evolutionary biology.

    4. I don’t know Joe, I don’t follow Joe. All I know is that the guy has been very patient trying to teach an idiot who actually could not care less.

    J-Mac:
    I don’t see any difference between their behaviour and any other religious extremists…

    That’s because you have no understanding, no character and no sense of decency.

    J-Mac:
    Blind faith rules them all alike…

    You mean like that of some idiot trying to pass biblical mythology for science? Like that?

  3. Joe Felsenstein: There’s a really easy way to solve that.But instead of me explaining it, why don’t you ask the guy who wrote …

    this

    Ah yes.

    instead of ending in this mess
    e^{T} = e^{\frac{ln(\alpha-\lambda A)}{\lambda} + C}

    starting with the intermediate result from my previous comment

    T=-\frac{ln(\alpha-\lambda A)}{\lambda} + C

    but going down a different path

    T=-\frac{ln(\alpha-\lambda A)}{\lambda} + C

    \lambda T=-ln(\alpha-\lambda A) + \lambda C

    \lambda T - \lambda C=-ln(\alpha-\lambda A)

    -\lambda T + \lambda C=ln(\alpha-\lambda A)

    e^{-\lambda T + \lambda C} = \alpha-\lambda A

    e^{-\lambda T + \lambda C}-\alpha = -\lambda A

    -e^{-\lambda T + \lambda C}-\alpha = \lambda A

    \frac{-e^{-\lambda T + \lambda C}-\alpha}{\lambda} = A

    Which is a decaying exponential where \displaystyle \lim_{t\to\infty} \frac{dA}{dt} = 0

  4. Sal:

    I only pointed out how funny it was to commemorate the deceased (RA Fisher) by pointing out one his great accomplishments in the name of Darwin wasn’t so fundamental.

    “Only”? Why lie about it, Sal? We can read the article, you know. Which contains the following, plus other stuff just like it:

    The comedy continues:

    [Quoting Joe:]

    The models are somewhat absurdly oversimple, but I argue that models like this at least can give us some results, which decades of more handwavy papers on the general connection between evolution, entropy, and information have not.

    Translation: My model is absurd, but it’s better than the other absurd handwavy models out there. This lecture is in honor of RA Fisher. He made a model of evolution that is also oversimplified, was wrong, and now it’s my turn to do the same. In relation to all the bad evolutionary models out there, Fisher’s model doesn’t look so bad. If we had a really good model, I’d be talking about that, but instead let me highlight my model that’s been around for 40 years and which no one seems to pay any attention to. At least Fisher’s model gets more citations than mine.

    You brown-nose Joe while you’re here, and then you trash him when you think he isn’t listening. You are what is known in the jargon as a hypocritical douchebag, and I am as happy to say that directly to your face as I am in your absence.

  5. stcordova: Personally, the best way to learn, imho, is to have a little entertainment mixed in. That Quantum Mechanics book by Griffiths which I’ll be basing my QM series on has subtle humor in every chapter.

    That’s how my kids love to learn not only QM…

  6. Entropy: 2. Neither me, nor newton expressed rage.

    I could tell from day one you commented how angry you were at creationists and anybody that questions the science you worship…

    Did it ever occur to you that solid science, based on evidence, has nothing to worry about? It can defend itself… You are trying to defend science that can’t defend itself… That’s why Sal is having such a good time slapping you all around… lol

  7. Entropy: That’s because you have no understanding, no character and no sense of decency.

    I expose falsehood and blind faith sold as science… That’s what I do…
    You don’t like it… Give me one reason why I should care what you think?

  8. J-Mac:

    I expose falsehood and blind faith sold as science… That’s what I do…

    What you do is embarrass yourself on the internet. And use way too many ellipses in the process.

  9. Entropy: You mean like that of some idiot trying to pass biblical mythology for science? Like that?

    Do you really believe that someone like me is going to accept your mythology as science? Are you that naïve?

    My 12 and 14 year old kids can take apart your “science” at the most fundamental level and leave you without answer, which they actually did…

    Do you want another shot at the chicken and egg paradox ? Or, are you still going to avoid the obvious failure of your object of worship to explain life at the most fundamental level?
    My kids have a bet going that no one on this blog will even attempt to address the abiogenesis chicken and egg paradox…
    This is your chance to shine… I’m betting you will ignore this issue and continue to worship your science as if nothing were wrong… because the commitment to materialism is absolute… whether right or wrong…

  10. Faizal Ali: is 14 billion years old

    That’s highly debatable…
    It’s based on the big bang model, as well as on the many assumptions, such as that nothing travels faster than light…
    There was an experiment done suggesting that neutrinos outrun photos… now deemed as an error but not everyone is convinced…

    The big bang model and the accelerating expansion of the universe contradicts the very fundamentals it is based on as the extremes of the universe are, or will be, traveling faster than light… Due to this very fact all the calculation of the age of the universe are way off…

    BTW: The earth is almost positively much older than 6000 years…

    IMV, there had been an unspecified time period before creative days have begun…

  11. I don’t have any comments on Sal’s articles, except to note it has no actual content. It is entirely rhetorical. He makes not even a single argument why Joe is wrong and Sanford is right. He seems to have based the entirety of his post on Joe describing his model as “somewhat absurdly oversimplified”, which Sal then re-interprets as being synonymous with completely absurd and wrong.

    This is done after setting up the great strawman by asserting how proud Fisher must have been of his theorem. This is the same rhetorical trick Basener & Sanford make in their paper. They spend a lot of time trying to set up the perspective that Fisher’s theorem is this fundamentally crucial aspect of evolution that the truth of evolution depends on (by among other things, asserting that Fisher was so very proud of it and thought of it as a “mathematical proof” of natural selection). That way it will look much more impressive when they knock it down.

    This is the performance, the stage-act being played in Basener & Sanford’s paper, and Sal basically repeats. In this thread where we are posting, Sal is doing a lot of huffing and puffing too. Just look at all those equations. How fancy.

  12. Rumraket:

    I don’t have any comments on Sal’s articles, except to note it has no actual content. It is entirely rhetorical. He makes not even a single argument why Joe is wrong and Sanford is right.

    The point of the article is that both Sanford and Joe have identified problems with Fisher’s theorem.

    The rest is entertainment. It’s show business, but maybe not as good as the Joel Osteen show.

    Along those lines, this Broadway song says it all:
    https://youtu.be/GkYcGExumKs

    The more substantive discussion of Joe’s model is here in this thread, particularly the sections where I mentioned Landauer’s principle, and no one has bothered to say yay or nay over what I said.

    Joe’s math is beautiful. Whether it describes reality or not is beside the point as far as I’m immediately concerned since I’m not an evolutionist. Thus Joe’s work can be studied simply for its mathematical beauty.

    If you want to talk real substance, well that’s stuff like Chromatin and the Phosphoproteome, and Quantum Mechanics etc. We can talk about hat, but that isn’t show business…

  13. Rumraket: Yes. Just to put a little context around the remarks that Sal quotes:

    1. The Fisher Memorial Lecture happens every year. It is not a memorial service. After all, Fisher died 56 years ago.

    2. Early in the talk, I mentioned Fisher’s “Fundamental Theorem of Natural Selection” and basically dismissed it as not-so-fundamental (just as I have in the Original Post for this thread). The abstract for that talk was submitted to the Fisher Memorial Lecture folks long before I had even heard of the Basener-Sanford paper.

    3. All the comments I made about my model being a very limited one are not about any model that is supposed to replace the FTNS. It is a model to check out whether there is a provable relationship between energy flow, increase of entropy, and increase of adaptive information. Sometimes one tests general rules by using simple models. Nothing wrong with that.

    4. As for the contrast between Sal’s fulsome praise of me here, and what he says on creationist sites, well, this isn’t the first time he has behaved like that. It is, as he says, “just business”. My father was an an advertising artist, who laid out ads for a living. Once he was warning me not to trust advertising. He said that, for example, a company might advertise a lawn chair as “the ultimate in outdoor comfort”. Whereas, he said, “the ultimate in outdoor comfort might actually be an outhouse”.

  14. stcordova: If you want to talk real substance, well that’s stuff like Chromatin and the Phosphoproteome, and Quantum Mechanics etc. We can talk about hat, but that isn’t show business…

    Talk is cheap.

  15. Joe Felsenstein:

    As for the contrast between Sal’s fulsome praise of me here, and what he says on creationist sites,

    I’ve praised you on creationists sites as well and my recent article poked fun only what you said about your own work (“absurdly oversimplistic”) and Fisher’s (“not so fundamental”).

    Here was me praising you at UD:

    https://uncommondescent.com/genetics/the-fine-work-of-joe-felsenstein-and-m-wilson-sayres/

    The fine work of Joe Felsenstein and M. Wilson Sayres
    May 29, 2013 Posted by scordova under Genetics

    Joe Felsenstein is an evolutionist that has a unique distinction of having his work favorably cited by creationists and bible scholars (except where he disagrees). For example, religious scholars are using Joe’s work to find descendants of the line of priests from the time of the Bible’s King David. See: Y-Chromosomal Aaron.

    and

    https://uncommondescent.com/genetics/mendels-accountant-and-joe-felsensteins-freely-downloadable-book-on-theoretical-population-genetics/

    Joe Felsenstein is a world class geneticist. Joe is credited with coining the phrase “Muller’s Ratchet” after Nobel Prize winner Hermann Muller. Even though Joe is an evolutionist, Joe holds a unique position of being highly regarded by creationists for his work on population genetics. His work on Muller’s ratchet became a pillar of creationist population genetics.

    Most certainly creationists reject the bulk of his claims on one of his favorite topics, phylogeny, but they have high regard for his works on population genetics. Joe is incredibly generous in making the compilation of his research of 34 years into a freely downloadable textbook for students of population genetics. I can attest to the great effort Joe put into the book to make his book accessible. Much of the math and concepts in theoretical population genetics is almost impenetrable (just read some Kimura, and you’ll get my drift). However, Joe makes a difficult topic accessible. He is a master Jedi of population genetics.

    Here is Joe’s book:
    http://evolution.genetics.washington.edu/pgbook/pgbook.html. Grab your copy while supplies last.

    I want to publicly thank Joe for his generosity. His book gives the public the chance to sit under the tutelage of an expert in the discipline. This book encapsulates many of the ideas expressed in Mendel’s Accountant, such as Mendelian Segregation, the Multiplicative Fitness Model, the Additive Fitness Model, linkage, recombination, migration and stirring, Hardy-Weinberg, recombination, selection coefficients, etc.

    and

    https://uncommondescent.com/news/many-thanks-to-gordon-davisson-and-joe-felsenstein-for-review-and-criticism-of-my-ud-article/

    Many thanks to Gordon Davisson and Joe Felsenstein for review and criticism of my UD article

    FWIW, the origin crev.info article, before it was re-written said, “Felsenstein is the most honest evolutionist I know.” The only reason that statement was deleted was that you saying Fisher’s theorem was not so fundamental and about the simplistic nature of you theory on energy and evolution spoke to your own honesty.

    And I put my money where my mouth is. I shelled out $110 to buy your books and sent you a gift a long time ago (Sanford’s genetic entropy). I put other guys at TSZ on ignore (like Keiths, Glen Davidson, Entropy, DNA_jock, Adapa, Gregory, Phoodoo, Frankie, etc.). If I had no regard for you, I would have treated you like I treat the guys on my ignore list.

  16. stcordova: And I put my money where my mouth is. I shelled out $110 to buy your books and sent you a gift a long time ago (Sanford’s genetic entropy).

    Yes, and I thanked you (I think by email) at the time for the Sanford book. As for purchases of my book, I presume they are done for the person’s own reasons, but I do like getting the royalty check. As for who people put on Ignore, that is their own business.

  17. stcordova: I put other guys at TSZ on ignore (like Keiths, Glen Davidson, Entropy, DNA_jock, Adapa, Gregory, Phoodoo, Frankie, etc.). If I had no regard for you, I would have treated you like I treat the guys on my ignore list.

    You mean, better?

    Of course there’s nothing new about you sucking up to anyone with some clout. You’re one of the cheapest, sleaziest intellectual whores around. And you don’t like anyone who tells the truth about you.

    Glen Davidson

  18. Joe Felsenstein: Yes, and I thanked you (I think by email) at the time for the Sanford book.As for purchases of my book, I presume they are done for the person’s own reasons, but I do like getting the royalty check.As for who people put on Ignore, that is their own business.

    Well, it’s a matter of record, I have praised you on creationists sites (well, technically it’s an UD is an ID site, not a creationist site).

  19. stcordova: Joe’s math is beautiful. Whether it describes reality or not is beside the point as far as I’m immediately concerned since I’m not an evolutionist. Thus Joe’s work can be studied simply for its mathematical beauty.

    Hi Sal,
    I can appreciate beauty in art, nature, human qualities etc.

    However, I have a very hard time appreciating beauty in math that ultimately leads to wrong results or conclusions, just like in case of Joe’s calculations… or do they?

    If my son did his math test, and followed all the mathematical formulas exactly and yet his final results would be wrong, would he be praised by his teacher?

    Would he get 100% or an A as the final mark?

    What count’s in math is not the beauty of the formulas or equations as much as the final, correct results, which from what I was able to gather, Joe failed to accomplish…

  20. J-Mac: Do you want another shot at the chicken and egg paradox ?

    Another shot? I obliterated both the supposed paradoxes and your arrogant posture in one shot. You just failed to read it.

    J-Mac: Or, are you still going to avoid the obvious failure of your object of worship to explain life at the most fundamental level?

    Worship? Your talking about yourself there.

    J-Mac: My kids have a bet going that no one on this blog will even attempt to address the abiogenesis chicken and egg paradox…

    Sad to read that you”re making idiots out of your own kids. You should ask them if they understand what a god-of-the-gaps fallacy is, and then check what your supposed paradox looks like. Then you should allow them to read the answers by themselves. Maybe they’d do better than you and help you out. I bet they’re not as stupid as you are, and they would show so if you allowed them to.

    Poor kids.

  21. J-Mac: Do you really believe that someone like me is going to accept your mythology as science? Are you that naïve?

    It’s you who pretends to pass the biblical mythology for science, not me.

    J-Mac My 12 and 14 year old kids can take apart your “science” at the most fundamental level and leave you without answer, which they actually did…

    So they noticed that you were performing eisegesis of biblical mythology to make it fit the sciences that you actually refuse to accept?

  22. J-Mac: I could tell from day one you commented how angry you were at creationists and anybody that questions the science you worship…

    Questioning science is part and parcel of the scientific endeavour. It’s creationists’ ignorance and lack of understanding, mixed with arrogance, that is offensive.

    J-Mac: Did it ever occur to you that solid science, based on evidence, has nothing to worry about?

    I’m not worried about the science. Idiot creationists have been declaring it dead for as long as I can remember, yet there it is, giving us insights after insights. What worries me is the barrier of misunderstanding that religious nuts put in front of new generations.

    J-Mac: It can defend itself… You are trying to defend science that can’t defend itself… That’s why Sal is having such a good time slapping you all around… lol

    It says a lot about you that you’d think that way about Salvador’s comments, when the poor illiterate quotes articles that say the opposite of what the poor fool thought they said.

  23. Rumraket:
    “Salvador Cordova has appeared on National TV, radio shows, newspapers, books and magazines for his work in promoting Intelligent Design and Creation Science. He is a former scientist and engineer in the aerospace and defense industry and presently serves as a professor and researcher in the area of Christian apologetics at small Bible College through the generous support of a private foundation. He also manages a small privately held investment fund which he has run on the side since 1997. He has 4 science degrees including an MS in Applied Physics from Johns Hopkins University and is presently working on a PhD. On April 28, 2005, he became one of the few creationists to ever appear in a cover story of the prestigious scientific journal Nature which covered his work on behalf of intelligent design. The most famous member of the Intelligent Design club he organized at George Mason in 2005 is Biologist Caroline Crocker who was featured in the Ben Stein’s motion picture documentary Expelled.”

    HAHAHAHA. You wrote that shit yourself didn’t you?

    Well, I’m nothing compared to Jerry Bergman! He just published a new book entitled Evolution’s Blunders, Frauds and Forgeries
    reported in Crev.info:

    https://crev.info/2018/01/book-defrocks-darwin/

    One of Bergman’s others books, The Dark Side of Darwin, even mentioned how Darwin beat a puppy simply for enjoying the sense of power.

    Dr Bergman is proof of intelligent design himself. How one man can generate such prolific writing of high quality is astonishing. He has written 43 books and over 1,200 scientific and general publications. He has nine college degrees (including 5 Masters and 2 PhD’s). He teaches multiple scientific subjects. He travels and speaks on radio and to groups. While he is on a roll, read his material and learn from a prodigious researcher. We are honored to have him as a contributor to CEH. After teaching science at the college level for almost 40 years he now works for The Institute of Creation Research.

    I had the honor of having lunch with him at ICC 2013. Hope to see him at ICC2018.

    Dr. Jerry Bergman has taught biology, genetics, chemistry, biochemistry, anthropology, geology, and microbiology at several colleges and universities including for over 40 years at Bowling Green State University, Medical College of Ohio where he was a research associate in experimental pathology, and The University of Toledo. He is a graduate of the Medical College of Ohio, Wayne State University in Detroit, the University of Toledo, and Bowling Green State University. He has over 600 publications in 12 languages and 40 books and monographs.

    His books and, or books that include chapters that he authored, are in over 1,500 college libraries in 27 countries. So far over 80,000 copies of the 40 books and monographs that he has authored or co-authored are in print.

    Dr. Bergman has spoken over 2,000 times to college, university and church groups in America, Canada, Europe and Africa. He is available to speak primarily in the summer, but events during the rest of the year can often be arranged.

  24. stcordova: One of Bergman’s others books, The Dark Side of Darwin, even mentioned how Darwin beat a puppy simply for enjoying the sense of power.

    A book aiming for nothing else but character assassination? From a creationist fool? Who knew!?

    stcordova: He has nine college degrees (including 5 Masters and 2 PhD’s).

    Having multiple degrees is a sign of incompetence. It means that the person wasn’t able to get what you’re supposed to get from each level, he had to repeat the process many times. No wonder the idiot decided to go for “creation research.”

  25. J-Mac: There was an experiment done suggesting that neutrinos outrun photos… now deemed as an error but not everyone is convinced…

    The authors themselves found the problem. It was a problem with their hardware.

    There’s also other facts. The experiment was done at close range, while the explosion of a star is detected visually (telescopes), at the very same time that “neutrino-traps” detects the neutrinos coming our way from that very explosion. If the experiment was right, then why would neutrinos and light get here at the same time from supernovas? Why doesn’t the difference become more evident instead of disappearing? If neutrinos outrun light, the discrepancy should be much more obvious with supernovas, yet the opposite was true.

    That alone shows that the experiment had to be wrong. Later on the problem was found. Once the problem was fixed the experiment showed that neutrinos don’t outrun light. What’s there to be unconvinced about?

  26. Rumraket:

    stcordova: Jerry is ranked higher than I am #20, I’m ranked #81. But hehe, I beat Sean Hannity.

    The order is chronological. -.-

    You’ve stolen even that dubious bit of glory from him. Poor Sal.

  27. Anyone here is welcome to actually discuss the math and contents of Joe’s paper, rather than me (even though that is one of my favorite topics).

  28. Have no idea why this thread would be right to discuss my 1978 paper. It is not aimed at explaining or correcting Fisher’s Fundamental Theorem of Natural Selection.

    I’m more interested in explaining why Basener and Sanford’s paper got the results it did. I’m working (with a co-author) on a post on that, tentatively for PT. Maybe a day or two more.

  29. Joe FelsensteinHave no idea why this thread would be right to discuss my 1978 paper. It is not aimed at explaining or correcting Fisher’s Fundamental Theorem of Natural Selection..

    It’s because Tom English connected it to your memorial lecture which was, I believe, about your 1978 paper.

  30. stcordova: It’s because Tom English connected it to your memorial lecture which was, I believe, about your 1978 paper.

    In the talk, I noted Fisher’s FTNS, then noted its not-so-fundamentalness, and the work that has been done on trying to figure out a rigorously correct verstion of the FTNS. Then I said that even though I had no sympathy with Fisher’s views on politics and religion, one place I did sympathize was his attempt at grand theories. And that I wanted to present another attempt at a grand theory.

    It was one rather different from the FTNS, and was embodied in a “toy” model.

    That was the only connection.

  31. Joe Felsenstein: In the talk, I noted Fisher’s FTNS, then noted its not-so-fundamentalness, and the work that has been done on trying to figure out a rigorously correct verstion of the FTNS.Then I said that even though I had no sympathy with Fisher’s views on politics and religion, one place I did sympathize was his attempt at grand theories.And that I wanted to present another attempt at a grand theory.

    It was one rather different from the FTNS, and was embodied in a “toy” model.

    That was the only connection.

    I suppose the discussion of Basener and Sanford’s paper would best be pursued in this thread:

    http://theskepticalzone.com/wp/does-all-of-evolutionary-theory-rest-on-fishers-fundamental-theorem/

    I have no opinion about where further to discuss your 1978 paper. If you prefer we discuss your 1978 paper in another thread, I think all of us will honor your wishes.

    I looked back at our discussion here 2 years ago where I pointed out there was no mention of Fisher’s theorem in your book, but in reading your latest revision to your book, it was nice to see the revision includes a paragraph mentioning Fisher’s theorem:
    http://theskepticalzone.com/wp/absolute-fitness-in-theoretical-evolutionary-genetics/#comment-99127

    I was aware the Basener and Sanford paper was being developed as far back as February 2016, and maybe even long before that. I conveyed your comment to them that in your view Fisher’s theorem was not so fundamental. I also conveyed Lewontin and Salthe and Andreas Wagner’s criticism of the notion of fitness. They did request from me where the origin of the term Muller’s ratchet came from and I pointed them to the paper’s by you where you are given attribution for the exact phrase “Muller’s ratchet” which extended Muller’s paper that mentioned a ratchet mechanism. That reference to your paper was reflected in their paper. Those were my passing inputs into discussion of their paper.

    They’ve made no secret of their intent, along with the people affiliated with their work, that they are quite interested in tracking the databases that monitor the present day evolution of genomes, especially the human genome. I’m one of the data clerks and news reporters, since I have some computer background, that has been recruited to monitor and investigate bio-informatics databases.

    I do not know how well the population genetic notion of fitness (which Fisher uses) will be useful to tracking the deterioration of the human genome since the medical notion of fitness is the notion more in play. I’ve thought a revision of the field was in order after Lewontin came out in the Santa Fe 2003 bulletin and said that no one really knew what fitness was, and then shortly after Andreas Wager came out and said the same thing and offered a concept of function more akin to Behe!

    Now, specifically about your 1978 paper, as I’ve said, I believe thermodynamic entropy is a subset of a larger class of Shannon entropies, thus thermodynamic entropy laws are difficult to generalize to notions of other Shannon entropies. I’ve criticized my ID colleagues for trying to equate the two entropies because one (thermodynamic) is a subset of the other (Shannon entropy). I’ve never been quite forgiven for the criticism I’ve given in the past and still hold to.

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