What entropy doesn't mean to me

[mmcirvin]

I'm not even sure why I got involved in all the arguing over Leon Wieseltier's review of Daniel Dennett's book last week, given that I haven't even read the book and have no plans to. But one good thing that came out of it was that somebody, probably Brian Leiter, pointed to this article on David Hume and religion, which by way of background brought up a notion Hume rejected, the theological principle of causal adequacy:

The second principle is that of causal adequacy or the order of causes: No cause can produce or give rise to perfections or excellences that it does not itself possess.

I read that and immediately thought, "Hey, it's the creationist misreading of the second law of thermodynamics!" I think that the reason they like to bring up the second law so often, and claim that it forbids evolution, is that it sounds sort of like this 17th/18th-century axiom of religious apologetics. You just take the colloquial reading of entropy as "disorder", go from there to interpreting it as the opposite of perfection or excellence, and Bob's your uncle.

This is also why the common scientific counterattack, that the second law only applies to closed systems (which the Earth definitely is not), is true but rhetorically unsatisfying. The Sun shines down on the Earth and waste heat radiates away, but it's not obvious that it's raining excellence or perfection, so if you still imagine the second law as a translation of the principle of causal adequacy, the response doesn't seem sufficient.

A better opening response would amount to "the principle of causal adequacy is not a physical law, and entropy is not what you think it is." It is, in fact, Boltzmann's constant times the natural logarithm of the number of microstates. In my old tutorial on the Boltzmann factor, I noted that there's some connection here with intuitive concepts of "disorder", but also cautioned that to equate entropy with disorder without making sure you're actually talking about the number of microstates is fraught with peril. To equate it with old theological notions of perfection is deeply incorrect.

In the process of writing something to this effect in a comment on Orac's blog, I Googled for the phrase "causal adequacy", and discovered to my great delight that Intelligent Design advocate William Dembski likes to toss it around as if it were a scientific principle (the author of that essay even assumes that Dembski made it up, little realizing that it's a centuries-old, contested philosophical concept). Case closed.

Comments

[zmook.livejournal.com]

"Ludwig Boltzmann, who spent much of his life studying statistical
mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on
the work, died similarly in 1933. Now it is our turn to study
statistical mechanics." -- David L. Goodstein

Incidentally, entropy can be defined perfectly rigorously in pure thermodynamics as an abstract function of internal energy, volume, and mole numbers, without any reference to counting microstates. But nobody ever learns pure thermo these days.

[mmcirvin.livejournal.com]

Indeed, I've seen writings by physical chemists in which they insist that only the pure thermo version of entropy is real entropy, and even Shannon's informational entropy is just a colorful metaphor whose promulgation corrupts the young. These people are, I think, mostly wrong (the quantum stat. mech. version is at least related to the informational entropy, and you can use that to calculate specific heats), but I can see what got them so upset.

[paracelsvs.livejournal.com]

When you mix the Hawking entropy of black holes into this, I can't help but get the feeling that there's something very profound underlying all this that hasn't quite been untangled yet. Also, Maxwell's demon and Szilard engines and stuff.

[mmcirvin.livejournal.com]

I think the Maxwell demon is pretty well understood by now, but the full role of gravity in stat. mech. is not, because you need to know more than anyone does about the fundamental physics of gravity in order to count microstates confidently (and also because gravity does such funky things with time and space). These days, people who have proposed a quantum gravity theory always feel very proud if they can pull Hawking's formula for the black hole entropy out of it, that being assumed to be an important consistency condition, but then there's also the question of how much that really tells you.

And then there's the question of whether you can explain the thermodynamic arrow of time by somehow deriving the cosmic boundary conditions. It's a fertile area of study and argument.

[paracelsvs.livejournal.com]

I've been trying to track down that quote for YEARS after hearing it somewhere! Thanks!

[ronebofh.livejournal.com]

I think that the reason they like to bring up the second law so often, and claim that it forbids evolution

They WHAT.

Also, Holtzmann field >> Boltzmann factor.

[mmcirvin.livejournal.com]

Someone hasn't been doing the reading in Advanced Stupidology!

[ronebofh.livejournal.com]

You made me look it up. Holy CRAP is that shit stupid. Cretinous. Imbecilic, even for creationistic malarkey.

[mmcirvin.livejournal.com]

This particular trope is so common that talkorigins.org has several comprehensive articles just dealing with it (http://talkorigins.org/faqs/thermo.html).

I should also mention that creationists (and even some religious apologists who accept naturalistic evolution) also read the first law of thermodynamics as "ex nihilo nihil fit" and sometimes use it as physical support for the Cosmological Argument for the existence of God as First Cause.

I think that's a fallacy too, though the sense in which it's a fallacy is trickier; it cuts more to the status of physical laws as provisional generalizations from observed behavior with limited domains of application, rather than as universal axioms that are supposed to explain absolutely everything. The conservation of mass/energy is just an observed regularity in nature, one that even requires a lot of qualification in the context of general relativity. It's not something one can extrapolate past the beginning of the whole universe with such confidence that breaking it requires a miracle (especially considering that inflationary models with dark energy even suggest how the universe might well get around it).

The old philosophical arguments may or may not stand on their own, but trying to ratify them scientifically by assuming that the terms translate directly into this sort of physics language turns out just to muddle the physics.

[beamjockey.livejournal.com]

Looks like you have a lot of links I need to look at, but I wanted to say that Dennett spoke here at Fermilab on 15 February. His talk was videotaped and will, I expect, be available on podcast and streaming video soon. Look here if you're interested.

We have a lot of cool speakers in the Colloquium series.