## Philosophers in SOWPODS

October 27, 2007

A friend played “Quine” in a Scrabble move, and it was accepted by the SOWPODS dictionary. I thought at first that it might have been the computer science term rather than the philosopher, but a check on the SOWPODS dictionary reveals that “Quine” does indeed refer to the philosopher. “Kant” and “Aristotle”, too, are included and refer to the philosophers. However, “Plato”, “Socrates”, “Hume”, “Descartes”, “Hegel”, “Leibniz”, “Locke” and “Wittgenstein” aren’t included. I have yet to find any other philosophers who are included.

## There Goes My Source of Free Music Scores

October 25, 2007

IMSLP has been shut down for the time being after threats from Universal Edition, despite hosting only scores that are in the public domain under Canadian law.

## God Has 100 Dresses.

October 22, 2007

iGod does, at least. And its favourite dress is green.

A friend chanced upon this way of drawing a hilarious reply from the bot:
Me: Peace be with you.

Further enquiries reveal the facts mentioned above. Also, God runs on Linux. Only mortals deserve to have Windows inflicted on them.

## Predigested Formalisms, Spoonfeeding of

October 21, 2007

Finally, the van Kampen paper which is not available in the Premier Institute of Social Engineering has arrived from Oxford (thanks to a friend there who got her friend in the college that had the book in its library to photocopy it — yes, socialising comes in useful sometimes). I’m lucky enough to be in a job where I actually have access to whatever passes for a university library here, but the thought that I could have gotten the paper in ten minutes rather ten days if I was still in Chicago makes me a little unappreciative of my situation. I will probably write a bit on van Kampen’s take on the Gibbs Paradox soon, but for now, van Kampen’s opening message to Dirk ter Haar is worth quoting:

Beste Dik,

It is a long time since we both attended the lectures by Mrs de Haas-Lorentz on thermodynamics. They were excellent from a paedagogical point of view since they forced you to figure out almost everything yourself. That is a much better way of learning physics than the spoonfeeding of predigested formalisms which is nowadays regarded as the highest wisdom in education. I remember how puzzled I was by the sudden appearance of the term $-kN\log N$ in the entropy. After I figured it out I found that there is still much confusion about it in the literature. That is my excuse for bothering you with such a time-worn subject.

“spoonfeeding of predigested formalisms” — how appropriate that this description should also be so undigested.

And, just because it’s also about pedagogy and because I have said similar things: Timothy Gowers explains why “examples first” is his favourite pedagogical principle. I couldn’t agree more.

## Misunderstanding Philosophy of Science

October 12, 2007

A few weeks ago there was an argument between John Wilkins and Jason Rosenhouse about Ian Hacking’s review of Philip Kitcher’s latest book. Jason was annoyed with Hacking’s writing style — he thought that it wasn’t necessary to add so many “caveats and restrictions” in an argument against anti-Darwinism. But Hacking adds those “caveats and restrictions” because he is not primarily concerned with rebutting the claims of anti-Darwinists. His main concern, instead, is to articulate and defend the claim that anti-Darwinism is “degenerate science” as opposed to the “dead science” that Kitcher claims it is in his book. Since he’s primarily staking out a position that is different from Kitcher’s (although still along the lines that anti-Darwinism is bad science), it’s natural that he should discuss the fine details that distinguish his thesis from Kitcher’s thesis. To criticise Hacking for not launching a more direct attack on anti-Darwinism instead is absurd — there is no obligation for Hacking to turn a book review into a full frontal attack on anti-Darwinism.

More worryingly, Jason demonstrates an obvious misconception of what philosophy of science is. His misconception is probably most easily seen in his statement that

[the fact that] evolution is a fruitful research program while ID is not… is a not a philosophical argument and it is not an argument that is enriched by knowing that Lakatos was the one who formulated the idea that a fruitful research program was the hallmark of science.

I submitted a comment at the relevant entry on Jason’s blog pointing out that it is a philosophical argument, but either it got caught in the spam filter (which I doubt, since I included no links or flag-worthy keywords in it) or Jason didn’t let it through the moderation queue. This post was meant to flesh out that argument, but the intense annoyance I initially had about the misconception has rather faded by now, and I no longer feel like writing several hundred words explaining why you need philosophy of science to determine what good science is.

## The Mathematical Universe Redux

October 11, 2007

Max Tegmark’s revised Mathematical Universe paper,1 accepted by Foundations of Physics, is out. The “initial conditions” section I’d criticized for being unclear earlier has been ironed out, but I still think the main thesis is full of holes. What follows is a more detailed take-down of the paper than my previous spiel.

To refresh our memories:

• The External Reality Hypothesis (ERH) states that there exists an external reality completely independent of humans.
• The Mathematical Universe Hypothesis (MUH) states that our external physical reality is a mathematical structure.

## Echoes from a Sombre Empire

October 6, 2007

I think this is one of my favourite Werner Herzog documentaries. One of the best 98 minutes I’ve spent in my life.

The final scene has Michael Goldsmith, the journalist who was tortured under Bokassa’s regime, touring a zoo where Bokassa reputedly threw prisoners to the lions and crocodiles. The zoo employee showing him around asks for a cigarette from Goldsmith, only to give the cigarette to a caged chimpanzee, who smokes it as though he’s done it his whole life. By this point, Goldsmith has interviewed dozens of Bokassa’s relations, employees and prisoners and heard (re-heard, more likely) countless stories of the atrocities committed by Bokassa. It is only when he sees the chimp smoke, though, that he turns to the camera and says:

Werner, I can’t stand this anymore. Can you turn it off now?

Michael, I think this is one of the shots that should hold.

You promise that this will be the end shot — it will be the last shot in the film?

Yes, I promise.

And indeed it was.

The choices of music for the film were also brilliant. In one of the opening scenes, Goldsmith visits Bokassa’s lounge in his mansion in France. It’s filled with opulent-looking furniture and the walls are covered with a bizarre combination of photos of him looking emperor-like, of Napoleon, and Vietnam War-related memorabilia. The accompanying music for this scene is some Shostakovich chamber music, forcing us into an interpretation of the lounge as displaying a sinister and twisted personality.

But the ‘best’ choices, in my opinion, were the Schubert selections. The scenes of pomp and circumstance, grotesque when seen in the context of the film, were accompanied by the Andante con moto from Schubert’s E flat major piano trio. The melancholy of that music, when juxtaposed against the ‘artificiality’ of the pomp and circumstance and our knowledge of what was going on ‘beneath’ those ornate costumes and elaborate processions, creates an intense atmosphere of tragic irony.

The final scene with the smoking chimpanzee has another Schubert excerpt, this time from his Notturno. It has that paradoxical quality of vain yet optimistic endeavour that is so typical of Schubert. Perhaps without the music, it would be difficult to understand why Goldsmith suddenly declares that he ‘can’t stand it anymore’. The music seems to give us the empathy with which to understand Goldsmith’s psyche. How it does so is a fascinating philosophical issue, but since I’ve spent the whole morning watching Echoes and writing about it, I think it’s about time I get back to Tolman.

October 3, 2007

## Boltzmann, Still Misunderstood After 130 Years

October 2, 2007

It satisfies this skeptic of textbooks (and anyone who’s read Kuhn must surely be one) to find examples of significant conceptual mistakes propounded by them. Finding out that a mantra repeated in most textbooks in the subject for decades is baseless is especially gratifying, if a little worrying.

OK, at this point I might seem to be well on the way towards violating the Alternative-Science Respectability Checklist, so I should point out that I’m merely referring to an argument that at least three respected physicists have made, in either edited books or peer reviewed publications. My attention was first drawn to the issue, the non-existence of the Gibbs Paradox, by this E. T. Jaynes paper.1 Looking up the citations of Jaynes’ paper (of which there were surprisingly few), I then came across this paper by Robert Swendsen, which makes the same point using a different approach.2 Swendsen cites N. G. van Kampen as also making the same point via a different approach, but I was unable to get hold of the van Kampen paper.3

There are many facets to the issue, but I shall restrict this post to the one that makes me feel sorry for Boltzmann. Not only was he under-appreciated when he was living; more than a century later, even though we recognise him as a ‘great’ figure, he continues to be misinterpreted. Swendsen, in a paper related to [2],4 points out that the definition of entropy for a system of classical distinguishable particles widely attributed to Boltzmann (even by Jaynes, who you’d think would know better!), $S=kN\left(\ln V + \frac{3}{2} \ln \frac{E}{N} + X \right)$, was never made by Boltzmann. It is often claimed that this expression has to be ‘corrected’ for the case of a system of indistinguishable particles, to account for the permutations allowed between arrangements of particles in the latter case. It is also often claimed that quantum mechanical indistinguishability justifies this correction; that it is quantum mechanics that renders the (non-extensive) entropy defined above extensive.5

It turns out, however, that Boltzmann gets the expression for entropy right. He derives it from purely thermodynamic considerations combined with the ideal gas law, without any statistical mechanical assumptions (we can consider the ideal gas law as an empirical statement free of statistical mechanical baggage). Thus his derivation is independent of assumptions about whether the particles in the gas are distinguishable. In modern notation, his expression for the entropy of an ideal gas is $S=kN \left( \ln \frac{V}{N} + \frac{3}{2} \ln \frac{E}{N} + X + 1 \right)$, and it would apply to both the distinguishable and the indistinguishable cases. This expression is extensive (if we define the constant ‘X’ correctly) so unlike what’s claimed in the textbooks we would not need quantum mechanics to ‘save’ the situation. But almost nobody who took it upon him/herself to write a stat mech textbook went back to check what Boltzmann actually derived and how he derived it. Thankfully, Swendsen, after misattributing the ‘wrong’ expression to Boltzmann in his 2002 paper, checked the original source6 to write his 2006 paper, and I happened to have the source on my desk when I was reading the Swendsen paper, so I was able to check for myself that Boltzmann had indeed been wronged. In his 2002 paper, Swendsen shows, using his own statistical mechanical definition of entropy (Boltzmann had used the thermodynamic definition $S=\int \frac{dQ}{T}$ to derive the expression for entropy), that the entropy comes out to be the same whether the particles are distinguishable or not. In his 2006 paper, Swendsen shows that Boltzmann’s entropy formula correctly describes the entropy of a mixture of ideal gases. Swendsen also excavates evidence from the original writings of Boltzmann (even translating some bits himself that haven’t been translated, a sign of how neglected they are) to show that Boltzmann had axiomatically defined the entropy of a composite system to be the logarithm of the probability of the macroscopic state of the system, not with the logarithm of the volume of the system’s phase space. The latter is what people usually attribute to him, and is the assumption that leads to the wrong, non-extensive formula for the entropy of an ideal gas. So the Gibbs Paradox does not exist, we don’t need quantum mechanics to save statistical mechanics, and my dislike for the Reif textbook is vindicated.

How did the neglect of such a major figure as Boltzmann come about? It’s as though we’ve been interpreting him through a layer of frosted glass for the last 50 years (at least). Swendsen marvels in his 2006 paper:

In the preface to his book on Boltzmann’s life and work, Cercignani commented that: “It is remarkable that, with a few exceptions, Boltzmann’s scientific papers have not been translated into English, whereas this task has been accomplished for other scientists of equal or lesser importance. Because of this, much of Boltzmann’s work is known through somebody else’s presentation, not always faithful.

Secondary sources have dominated Boltzmann’s legacy to such an extent that even the famous equation inscribed on his tombstone, $S=k\log W$, is written in a form due to Max Planck. Planck did correctly choose the notation W to indicate “Wahrscheinlichkeit” (probability).

So at least some of Boltzmann’s contemporaries understood some of his work.

Interestingly, the Jaynes paper is also concerned with the misinterpretation of the writings of another great name in thermodynamics/stat mech: that of Gibbs. And his clearing up of the misinterpretation also leads him to the conclusion that there is no Gibbs paradox (and hence that there is no need to faff about with distinguishability of particles when we’re dealing with entropy). So we can see Jaynes and Swendsen treading parallel paths in revealing that the thoughts of these great physicists were far more subtle than your textbook fairy tales would have you believe.

[1] E. T. Jaynes, The Gibbs Paradox, in Maximum-Entropy and Bayesian Methods, C. R. Smith, G. Erickson, and P. Neudorfer, eds. (Kluwer, Dordrecht), p. 1-22. http://bayes.wustl.edu/etj/articles/gibbs.paradox.pdf
[2] R. H. Swendsen, Statistical mechanics of distinguishable particles, J. Stat. Phys. 107:1143 (2002).
[3] The citation is N. G. van Kampen, The Gibbs Paradox, in Essays in Theoretical Physics, W. E. Parry, ed. (Pergamon, Oxford, 1984), pp. 303-312.
[4] R. H. Swendsen, Statistical mechanics of colloids and Boltzmann’s definition of the entropy, Am. J. Phys. 74:187 (2006).
[5] I don’t have any of the textbooks they cited at hand, so I couldn’t check, but Swendsen cites F. Reif’s Fundamentals of Statistical and Thermal Physics and R. K. Pathria’s Statistical Mechanics as making these claims. K. Huang’s Statistical Mechanics is another culprit.
[6] L. Boltzmann, trans. S. G. Brush, Lectures on Gas Theory (Dover, New York, 1995), p. 72.