Good Math, Bad Math

In light of [my recent demolition of a purported improvement on the second law of thermodynamics][2l], an alert reader sent me [a link to this really boneheaded piece of work at Uncommon Descent by Granville Sewell][sewell].

[sewell]: http://www.uncommondescent.com/intelligent-design/introducing-sewells-law/
[2l]: http://scienceblogs.com/goodmath/2007/06/dembskis_buddy_part_2_murphys.php

Sewell is, yet again, trying to find some way of formulating IDist anti-evolution garbage in terms of the second law of evolution. Sewell’s been doing this for ages, and it’s been a
wretched failure. Naturally, according to Sewell that has *nothing* to do with the fact that his argument is a pile of rubbish – it’s all because people have been distracted by
arguments that came about because people don’t understand the second law of thermodynamics. It’s their confusion of 2LOT, *not* any flaw in Sewell’s argument.

So, he’s proposing a new law which he claims subsumes the 2LOT, and which he modestly names after himself:


>However, after making this argument for several years, with very limited success, I have
>come to realize that the biggest disadvantage of my formulation is: it is based on a
>widely recognized law of science, one that is very widely misunderstood. Every time I
>write about the second law, the comments go off on one of several tangents that sometimes
>have something vaguely to do with the second law, but have in common only that they divert
>attention away from the question of probability.
>
>So I have decided to switch tactics, I am introducing Sewell’s law: “Natural forces do not
>do macroscopically describable things which are extremely improbable from the microscopic
>point of view.” I still insist that this is indeed the underlying principle behind all
>applications of the second law, the only thing that all applications have in common, in
>fact.

Only one problem… It’s not true. *Lot’s* of things that are highly improbable from
the microscopic point of view happen at the macroscopic point of view. A rainstorm – the
formation of water droplets from water vapor at a particular time in a particular place – is incredibly unlikely from a microscopic point of view, but it’s inevitable from a macroscopic point of view. *And*…

Ok, so there’s more than one problem. And the second one is in its way even worse than the first.

Sewell’s “law” isn’t just wrong; even if it were true, it couldn’t be a law: it’s not just not true, it’s *not* a scientific statement of *any* *kind*.

As I pointed out in the other “second law replacement” post, the second law is *not*
a statement that things tend towards randomness, or that things tend toward disorder, or anything like that. Those are vague, human language explanations that try to provide some
intuitive handle on the meaning of the law. But the law itself is a *mathematical* statement.

Someone like Sewell might ask, “What’s the difference?”. I’ll tell you the difference: using the real second law, I can make *precise* statements to describe real phenomena. (A friend of mine who’s a physicist insists that he wants the second law on his headstone when he does, only instead of saying “≥”, he wants it to say “>”. That is a precise statement; a *silly* precise statement, but a precise statement nonetheless.)

Using the second law, I can look at a description of a thermodynamic system, and say “That can’t happen.” I can do that with great precision: because it’s a formal mathematical system, I can use it as part of a formal modeling process, and describe what it says, and
based on that whether or not a given phenomenon is possible, and even model what the probabilities of some unlikely but possible events are.

“Sewell’s Law” doesn’t do that – it *can’t* do that, because it’s not a mathematical
statement, and in fact, Sewell *can’t* phrase it as a mathematical statement. It’s an
intrinsically vague statement – one which relies on the fuzziness of his “macroscopic” versus “microscopic”, and “improbable”. He can’t quantify these things, because they’re
imprecise by design.

Comments

  1. #1 Mobius
    June 27, 2007

    I agree completely. The first thing that struck me about “Sewell’s Law” was the lack of precision in what it said. The second was, as you pointed out, that it wasn’t even true.

    Sad. But then, coming from a IDiologist, not unexpected.

  2. #2 Blake Stacey, OM
    June 27, 2007

    Granville Sewell is to thermodynamics as Sal Cordova is to:

    (a) biochemistry
    (b) information theory
    (c) classical mechanics
    (d) all of the above

    Policy question: I seem to recall you not linking directly to UD. Has your stance on traffic, Google rank, etc. changed?

    (I’m just curious, mostly because now I have to deal with the same problem.)

    P.S. The word classical in the text of a hyperlink trips the ScienceBlogs spam filter.

  3. #3 Jonathan Vos Post
    June 27, 2007

    Was it stated here, or in Uncertain Principles, or in another of the Science Blogs, that arguments about the laws of thermodynamics have produced more confusion and nonsense than any other principles in science?

    I know that we’ve discussed Entropy in Good Math, Bad Math, and hit a brick wall in the minds of Intelligent Designers.

    Okay, I’ve got to go teach my first High School Algebra 1 class now. In the Fall I’m expected to also teach Chermistry and Physics and Biotechnology.

    I’ve been an Adjunct Professor of Mathematics for 5 semesters at a private university, and an Adjunct Professor of Astronomy at a community college, and had 2,000+ senior citizens as students through the Center for the Study of The future and Elderhostel. But I suspect now that it is in High School that I can most help students who might otherwise be lost. I’ve taken a pay cut. I’m putting my money where my mouth is.

    I’m going to be even more in the mood for distinguishing Good Math from Bad Math, and Good Science from Bad Science, for the sake of the students. A mind is a terrible thing to waste…

  4. #4 Jake
    June 27, 2007

    It’s worse than that, as far as I’m concerned. ‘Microscopic’ versus ‘macroscopic’, sure, maybe there’s a definition there. But the way ‘improbable’ is used by most layfolk is pretty dangerous. Every occurrence (that is, element of the sample space) is fantastically improbable when you get right down to it, and you don’t need to appeal to evolution to get it. I roll a die 6 times to get 5312562242. That particular run of numbers is quite unlikely: 1 in upwards of 60 million, considerably worse than my chances for winning the lottery. Do I have magic fingers, to roll a die in such a fantastically improbable way? Not really: there are 60 million possibilities, and one of them is going to happen, and no matter which one happened, they were all “fantastically improbable”.

    Anyone who’s serious about trying to use probability to understand natural phenomena had better describe their events and event space a lot more clearly, and have a firm grounding in conditional probability as well. These folks never seem to get beyond “small numbers = small chance”.

  5. #5 Mark Chu-Carroll
    June 27, 2007

    Blake:

    When it comes to linking, I tend to be a bit weasely… On one hand, I hate to send traffic their way – they’ll use any traffic as a way of boosting their credibility. But on the other hand, I want people to be able to see that I’m not doing a Cordova-style quote mine, but that I’m honestly quoting the bozos with appropriate context. I tend to go back and forth between those positions.

  6. #6 Jon
    June 27, 2007

    It never ceases to amaze me that people think they can talk technically and in-depth about science without using math. If you’re a mathematician or scientist, and you don’t understand why informal (non-mathematical) language is dangerous, you’re incompetent and, probably, an idiot.

  7. #7 Paul Carpenter
    June 27, 2007

    Presumably in the second paragraph you mean to say Second Law of Thermodynamics rather than of Evolution.

  8. #8 Lepht
    June 27, 2007

    didn’t someone else try and overthrow 2LOT a couple days ago? am i getting deja-vu, or is this becoming a disturbing little trendette amongst IDers:

    1. take theory nobody knocks because it’s kind of, y’know, verifiable

    2. try to poke holes in it; if you fail, say you didn’t and anyone arguing with you is a heretic

    3. declare you beat theory, which means you beat evolution (regardless of what theory it was you were poking holes in)

    4. declare that therefore, ID wins (because it’s obviously the only other choice) and so all the godless heathens can just give up now and go start a circus or something. damn monkey-lovers.

    maybe i should make one of my own and see if they can tell.

    Lepht

  9. #9 Enigman
    June 27, 2007

    Sewell’s law seems to be a rip-off of Borel’s law, which is a false statement but very reasonable nonetheless.

  10. #10 Rich Reynolds
    June 27, 2007

    But isn’t Sewell popularizing concepts that non-mathematicians and non-scientists can come to understand?

    After all the argot of the physicists is only meant to insulate them from the great unwashed, while firming up their “cult of ingenuity.”

    I like the Sewell approach, and its quantum fuzziness is rather nice for a change….and quantumly correct.

    Rich Reynolds

  11. #11 Mark C. Chu-Carroll
    June 27, 2007

    Rich:

    No, he’s not “popularizing concepts that non-mathematicians and non-scientists can come to understand”.

    Statements like “things tend towards chaos” are attempts to take the second law, and give non-scientists some intuition about what it means.

    That’s not what Sewell is doing. He’s proposing a *new* law, which he claims subsumes most uses of the second law. But his new law is (a) not true, and (b) doesn’t have any actual science behind it.

    It’s fine for a popularizer of science to simplify things and present them informally, so long as they’re honest that that’s what they’re doing. It’s *not* fine for a purported scientist to present a scientific argument in
    the vague terms of popular writing. Sewell has repeatedly made the argument that his law means that evolution could not possibly have happened. But he’s *never* formulated his law with any more precision than the informal statement that I’ve quoted. It’s not just the popularization of the so-called law that’s non-scientific: it’s the entire law itself.

  12. #12 Blake Stacey, OM
    June 27, 2007
  13. #13 Rich Reynolds
    June 27, 2007

    Well, Mark,

    We should get our hands on Sewell and rough him up!

    If he’s actually perverting the Second Law, then he should be anathema.

    What’s interesting to me, is that Sewell continues to provoke discussion, even though he appears to be using scientific canards as his modus.

    And I understand the frustration (and anger) of actual mathematicians and science in general when someone screws around with “provable” theories and laws, using circumlocution to flummox us lay people.

    RR

  14. #14 Coin
    June 27, 2007

    What’s interesting to me, is that Sewell continues to provoke discussion

    Historically speaking, most liars do.

  15. #15 Blake Stacey, OM
    June 27, 2007

    A “discussion” whose undertone usually resembles “Oh my expletiving God, we’ve explained that to you time and time again — why don’t you just listen, you bastard” is not the type of discussion I would personally like to provoke.

  16. #16 Coin
    June 27, 2007

    So perhaps this is a fun opportunity, I’ve never actually gotten a chance to apply Baez’s Index to anything before.

    Let me give this a shot:

    The Crackpot Index
    John Baez
    A simple method for rating potentially revolutionary contributions to physics:

    1. A -5 point starting credit.

    2. 1 point for every statement that is widely agreed on to be false.

    “the underlying principle behind the second law is that natural forces do not do macroscopically describable things which are extremely improbable from the microscopic point of view”

    “Natural forces do not do macroscopically describable things which are extremely improbable from the microscopic point of view.”

    3. 2 points for every statement that is clearly vacuous.

    “Bill Dembski’s argument (in ‘The Design Inference’) that only intelligence can account for things that are ‘specified’ … and ‘complex’”

    “Natural forces do not do macroscopically describable things which are extremely improbable from the microscopic point of view.”

    5. 5 points for each such statement that is adhered to despite careful correction.

    “Bill Dembski’s argument (in ‘The Design Inference’) that only intelligence can account for things that are ‘specified’ … and ‘complex’”

    “all you have to do is point out that the laws of probability [sic] do (contrary to common belief!) still apply in open systems, you just have to take into account the boundary conditions in the case of an open system (see A Second Look at the Second Law ).”

    “that natural forces cannot rearrange atoms into computers and spaceships and the Internet here, whether the Earth is an open system or not”

    “whether the second law applies or not depends on which formulation you buy”

    11. 10 points for beginning the description of your theory by saying how long you have been working on it.

    “In an April 2, 2007 post…” (half credit)

    24. 20 points for defending yourself by bringing up (real or imagined) ridicule accorded to your past theories.

    “However, after making this argument for several years, with very limited success, I have come to realize that the biggest disadvantage of my formulation is: it is based on a widely recognized law of science, one that is very widely misunderstood.”

    25. 20 points for naming something after yourself. (E.g., talking about the “The Evans Field Equation” when your name happens to be Evans.)

    “So I have decided to switch tactics, I am introducing Sewell’s law”

    26. 20 points for talking about how great your theory is, but never actually explaining it.

    *

    29. 30 points for suggesting that a famous figure secretly disbelieved in a theory which he or she publicly supported. (E.g., that Feynman was a closet opponent of special relativity, as deduced by reading between the lines in his freshman physics textbooks.)

    “I argued that the advantage of my formulation is that it is based on a widely recognized law of science, that physics textbooks practically make the design argument for you” (half credit)

    37. 50 points for claiming you have a revolutionary theory but giving no concrete testable predictions.

    *

    …Mr. Sewell scores a 151. Is that impressive, relatively speaking?

  17. #17 Alex, FCD
    June 27, 2007

    A friend of mine who’s a physicist insists that he wants the second law on his headstone when he dies, only instead of saying “≥”, he wants it to say “>”.

    AHAHAHAhahahaha! That’s a good one. Just give me as second to wipe tears of mirth from my eyes.

  18. #18 Torbjörn Larsson, OM
    June 27, 2007

    Oh, Sewell again.

    Catching up quickly on his production, where I left off last time:

    - His 2LOT appendix in a math (!) textbook is chock full of errors when he tries to define a boundary for a system to apply 2LOT in, so the result isn’t at all usable. Maybe he should have consulted with a physicist, he could have sorted out perfect and imperfect differentials for Sewell. (Actually, I seem to vaguely remember some simple sign errors as well. Maybe I should dig up my notes again…)

    - His ” A Second Look at the Second Law” makes the two elementary errors Mark notes (violations of the classical law vs the full statistical law, misapplication). And the post is based on this.

    the second law of evolution

    That would have been freudian, if not Freud’s theories were dead. ;-)

    Sewell’s law seems to be a rip-off of Borel’s law, which is a false statement but very reasonable nonetheless.

    Borel’s initial statement and application is fine. (We can use contingent cutoff probabilities, when generating hypotheses for testing. Approximating with zero probability doesn’t preclude an event, it is “almost surely” true as they say in probability theory.)

    The problem with Borel’s law is when someone like Dembski tries to make a universal non-contingent application out of it, means surely true, and never intends to test the hypothesis.

    But then Dembski is a pseudomathematician.

  19. #19 Torbjörn Larsson, OM
    June 27, 2007

    When it comes to linking, I tend to be a bit weasely…

    I’m just a regular customer here, but that is fine by me.

    As I just mentioned on a thread on brasilian waxing, I like variation and surprises. :-)

  20. #20 Jon L
    June 27, 2007

    1) I’d prefer it if you did link a little more often. Actually you usually are pretty good about it and I do understand why you wouldn’t want to, but in that fruit fly article a while back I wanted to verify something you said IDist had said and had a bitch of a time finding it in google. Also, FYI, you can use the “rel=nofollow” attribute of an <a>nchor tag to tell bots not to follow links (and thus avoiding giving them any pagerank boost).

    2) Well, he is right about one thing. “law of science, one that is very widely misunderstood.” Unfortunately, he’s also an example of that.

  21. #21 Rich Reynolds
    June 28, 2007

    To digress…

    T. Larsson writes that Freud’s theories are dead.

    I didn’t even know they were sick.

    The canard that Freud is passe is as bogus as Sewell’s “hypothesis.”

    A read of Civilization and Its Discontents should disabuse anyone of the idea that Freud isn’t relevant any longer.

    RR

  22. #22 Torbjörn Larsson, OM
    June 28, 2007

    The canard that Freud is passe is as bogus as Sewell’s “hypothesis.”

    I am certainly a layman here, but my impression was that Sigmund Freud is considered a fraud by many, perhaps inventing data or rejecting contrary data. See especially “Critical reactions” at http://en.wikipedia.org/wiki/Freud , but also this:

    Most of Freud’s specific theories–like his stages of psychosexual development–and especially his methodology, have fallen out of favor in modern experimental psychology.

    Since it is neither evidence based medicine nor experimental psychology despite being such an old idea, I suspect that the critical view may be true. But in any case, this is why I characterized his ideas as “dead”.

    “Civilization and Its Discontents” seems to be a book authored by Freud nearly 80 years ago. What relevance does it have in modern evidence based medicine or experimental psychology?

  23. #23 Rich Reynolds
    June 28, 2007

    Torbjorn:

    Freud’s views on sexuality still apply — as is evidenced by what happens to women in civilized and uncivilized countries or societies. (Darfur is an example.)

    If one reads Civilization and Its Discontents, one will see that the ideas presented apply as much today as they did in 1930, when the material was written.

    Freud’s views on religion are particularly apropos, especially in the scientific community.

    Freud’s psychoanalytic methodology applies. That neurotics eschew the method for drugs doesn’t mean that it is ineffective.

    It is simplistic and faddish to dismiss Freud. That Wikipedia is off-handed about Freud should be a clue for his continuing relevance.

    RR

  24. #24 John Marley
    June 28, 2007

    If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations — then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation — well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.

    – Sir Arthur Stanley Eddington, 1927

    The IDiots are trying to redefine 2LoT in such a way that all of science collapses.

    The plan has the same chance of succeeding as ID has of being accepted as science.

  25. #25 Torbjörn Larsson, OM
    June 28, 2007

    Freud’s psychoanalytic methodology applies.

    There is AFAIK nothing of Freud in evidence based medical treatment of psychiatric diagnoses.

    And the quote above seems to say that your assumption above is wrong. (The references in the link I gave you should be a start to find out.)

    In any case you don’t support any of your claims.

  26. #26 Anonymous
    June 28, 2007

    If you dont want to bump UDs google rank could you just add a nofollow tag?

  27. #27 assman
    June 30, 2007

    “fuzziness of his “macroscopic” versus “microscopic””

    Quantum Mechanics relied on a fuzzy undefined macro/micro distinction ever since its inception. Moreover any examination of these types of foundational problems (micro/macro boundary, measurement problem etc) in QM was actively discouraged until recently.

    “It never ceases to amaze me that people think they can talk technically and in-depth about science without using math.”

    Hmm it seems to me that biologists talk about a lot of things in depth without using math. And of course Faraday description of EM which Maxwell formalized was fairly mathematically imprecise and yet vitally important to the development of EM.

    I would also say that though scientists may use a lot of math to model their ideas, it is not true that they develop ideas through mathematical reasoning. Instead intuitive, fuzzy, vague and even contradictory ideas are how a lot of important scientific ideas are developed. The early history of QM is a beautiful example. It is only later when the ideas are formalized that things are made mathematically precise. QM itself required the work of people like Von Neumann, Dirac, Schroedinger, Heisenberg etc before its vague fuzzy ideas could be made precise.

  28. #28 Torbjörn Larsson, OM
    June 30, 2007

    Quantum Mechanics relied on a fuzzy undefined macro/micro distinction ever since its inception.

    If you mean that qualitative math is fuzzy compared to quantitative, sure. (Or, as I’ve seen Terence Tao define it over on his blog, soft vs hard math.)

    Otherwise the correspondence principle is a clear and well-defined principle.

  29. #29 Anonymous
    June 30, 2007

    “Otherwise the correspondence principle is a clear and well-defined principle.”

    No I am not talking about the correspondence principle. And I do not consider the correspondence principle to be mathematically clear, well-defined or even correct. The correspondence principle states that QM systems reduce to classical systems in the limit of large quantum numbers. There are a lot of problems with this principle. What exactly is a precise mathematical definition of a quantum number. Also this principle is false. Electron in a box for instance never reduces to a classical system since there are certain positions where the electron will never be observed even if the so called quantum number is very large. Anyways the closest thing to a real correspondence principle is Ehrenfest’s theorem which is actually formulated completely differently than the correspondence principle.

    What I am talking about is the measurement problem. The original Copenhagen interpretation of QM was that you had a QM microscopic system you were testing and a classical macroscopic measuring device. When you measure the microscopic system the state vector associated with the system as a whole collapses into some eigenvector associated with the eigenvalue you measure. Now how and why does this collapse of the state vector take place. It was obvious that in QM only classical macroscopic things like measuring devices could cause this collapse. So in QM the world was divided into two things the macro and the micro. Only the macroscopic objects had the special property that when they interacted with microscopic things they could cause wavefunction collapse. Microscopic things did not have this property. Also the collapse is a discontinuous process that only happens when macroscopic measuring devices interact with microscopic systems whereas the time evolution of QM systems happens through continuous unitary transformations. So on the one hand we have macro systems causing discontinuous collapse and on the other micro systems that evolve through continuous unitary transformations. Nobody ever defined what macroscopic measuring devices were or why the had the magical powers that could cause wave function collapse. And nobody demonstrated that in the limit of large quantum numbers, the unitary time reversible continuous transformations would reduce to discontinuous time-irreversible measurement projections. Now many of these issues are being resolved through decoherence theory but for years these issues were never touched.

  30. #30 Torbjörn Larsson, OM
    June 30, 2007

    And I do not consider the correspondence principle to be mathematically clear, well-defined or even correct. The correspondence principle states that QM systems reduce to classical systems in the limit of large quantum numbers.

    A limit as used in the correspondence principle is a mathematical well-defined process, so as I hinted the principle is in the domain of soft math. So I don’t think that is a problem.

    I don’t recognize your version of the correspondence principle. As far as I know it is a rule of thumb to check the correct solution by going to the classical limit. It can be done in a number of ways: by decreasing Planck’s constant, by decreasing the de Broglie wavelength, by increasing the set of quantum numbers, by increasing the value of quantum numbers, et cetera.

    I’m not sure that any specific way guarantees the classical limit. But doing “all of them” should, as we are concerned with the procedure being well-defined.

    So in the box case, which I don’t know much about, perhaps the classical limit can be obtained by adding some of the other procedures. (For example, more fermions may be the way to force the volume occupancy to be distributed as in a classical system.)

    What I am talking about is the measurement problem.

    Well, as your previous comment was mainly about a “macro/micro distinction” I wasn’t. :-)

    More seriously, the correspondence principle defines a classical observer, and AFAIK QM theory isn’t elaborated enough to decide all foundational problems like the measurement problem as such. That is why it has “interpretations”.

    I agree that, while decoherence AFAIU doesn’t solve all foundational problems, it was an area which could have been explored much earlier.

  31. #31 Torbjörn Larsson, OM
    June 30, 2007

    “I’m not sure that any specific way guarantees the classical limit.”

    Well, actually I’m pretty sure that decreasing Planck’s constant always does the trick. But only pretty sure.

  32. #32 Jonathan Vos Post
    July 1, 2007

    I’m not sure what thread had Poincare Recurrance as (bad) Theology.

    Eternal return (Eliade)

    The “Eternal return” is, according to the theories of religious historian Mircea Eliade, a belief, expressed (sometimes implicitly but often explicitly) in religious behavior, in the ability to return to the mythical age, to become contemporary with the events described in one’s myths. It should be distinguished from the philosophical concept of eternal return, which holds that, statistically speaking, all arrangements of matter in the universe must necessarily recur if given an infinite amount of time.

  33. #33 Art
    July 2, 2007

    It’s always amusing when an antievolutionist like Sewell “proves” that completely mixed oil and water will never separate into two ordered phases.

  34. #34 Brad Hughes
    July 6, 2007

    Mark, long time listener, first time caller.

    When it comes to linking, I tend to be a bit weasely… On one hand, I hate to send traffic their way – they’ll use any traffic as a way of boosting their credibility. But on the other hand, I want people to be able to see that I’m not doing a Cordova-style quote mine, but that I’m honestly quoting the bozos with appropriate context. I tend to go back and forth between those positions.

    Try using tinyurl.com.

  35. #35 Xanthir, FCD
    July 7, 2007

    Jeez, I never even thought of that. That’s an excellent suggestion, Brad.

    Mark, use TinyUrl. It won’t affect whether or not they get traffic, but at least it’ll prevent them from gaining Google cred. Hell, it might even reduce their google cred over a simple non-link, because readers won’t have to search for it in Google.

  36. #36 Marion Delgado
    July 14, 2007

    What you blind fools don’t realize is the importance of quantum consciousness zero-point-energy biomorphogenetic fields acting in areas of irreducible complexity according to microangelic feedback loops in a fractal dimension! Once you understand that, it’s trivially true!

    For proof I cite Zeno’s metaphysicians. I mean, para-docs.

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