Remember Granville Sewell? He's the alleged mathematician who wrote the very non-mathematical "A Mathematician's View of Evolution", which I fisked [a few weeks ago](http://scienceblogs.com/goodmath/2006/10/second_law_slop_from_granville.php). Well, he's back with a response to the people who criticized him, called ["Can Anything Happen in an Open System?"](http://www.math.utep.edu/Faculty/sewell/articles/open.pdf)
Did he actually address any of the criticisms in a substantial way? Did he actually say *anything* new?
Of course not. Do these idiots *ever* really address criticisms?
He starts off with an introduction that seriously makes me question his competence as a mathematician:
>Mathematicians are trained to value simplicity. When we have a simple, clear
>proof of a theorem, and a long, complicated, counter-argument, full of hotly
>debated and unverifiable points, we accept the simple proof, even before we find the
>errors in the complicated argument. Mathematicians are trained to value simplicity. When
>we have a simple, clear proof of a theorem, and a long, complicated, counter-argument,
>full of hotly debated and unverifiable points, we accept the simple proof, even before
>we find the errors in the complicated argument.
This is an utterly ridiculous statement for a mathematician to make. In math, we *don't* accept simple arguments over complicated ones because they're simpler. *Ever*.
It's true that if we have a simple proof and a complex counterargument, we'll accept the simple proof. But not because one is simple and one is complex. It's because a proof of a theorem and a counter-example to that theorem *are mutually exclusive*. If the proof is correct, the complex counterexample *can't* be, and it's *usually* easier to check the validity of a simple proof than a complex counter-argument. Whichever one we can verify with less effort is generally the one we attack: because *a valid proof* of a theorem disproves the existence of a counterexample; and a *valid proof* of a counterexample to a theorem *disproves* the theorem.
He then uses this argument to handwave away any arguments about his claims about gradualism, and focus the rest of the paper on his "second law of thermodynamics" argument. And basically, from there on, he just starts to repeat, almost verbatim, the arguments from the *original* paper, simply pretending that the criticisms of that crappy argument don't exist.
Just as a reminder, the basic criticisms of his original argument included:
1. He tries to conflate evolution with randomness.
2. He uses a strawman version of the "open system" argument about why evolution does'n violate the second low, to characterize evolution's thermodynamic where evolution is equivalent to a computer being able to assemble itself in one room (allegedly decreasing entropy in that room) because two computers in the next room fall apart (increasing entropy more than the decrease of the computer assembling itself.)
3. He separates entropy into multiply different *kinds* of entropy, and asserts (incorrectly) that they are totally distinct. (So "heat entropy" can only produce heat; "carbon diffusion" entropy concerns only the diffusion of carbon, and you can't reduce "carbon diffusion" entropy by adding a bunch of heat.)
It's amazing that he considers this a *response* to criticism, because he doesn't actually acknowledge any of these real criticisms of his arguments.
The closest he comes to acknowledging any criticisms is to come up with a really stupid strawman, which is itself just a rehash of the garbage from the original paper:
>It requires only a modicum of common sense to see that it is extremely improbable that
>atoms should rearrange themselves into mammalian brains, computers, cars, and airplanes,
>even if the Earth does receive energy from the Sun. We will see that the idea that
>anything can happen in an open system is based on a misunderstanding of the second law;
>that order can increase in an open system, not because the laws of probability are
>suspended when the door is open, but simply because order may walk in through the door.
This is just a rehash of the same-old argument from the original paper. Sure Granville, *no one* would be inclined to believe that a powerbook like I'm typing this on would spontaneously assemble itself from a pile of sand on a beach. But that's *not* an accurate metaphor for evolution. You see, *computers don't reproduce*; they don't *consume* resources to provide themselves with power; they don't *produce* waste.
Living things don't violate the second law. We create some small decreases in entropy (for example, in producing the structure of our cells) by consuming energy in the form of resources, and in the process, we create a *much larger* increase in entropy in the form of waste heat and waste materials.
From this, he moves on to reiterate his nonsense about different kinds of entropy:
>If we take a book of random letters and blow vowels into the
>front of the book (pretend letters can diffuse!) and suck them out the back, we
>can import order into the book, if randomness of the vowel distribution is used to
>measure order. Vowels are essential for words, just as solar energy is essential for
>life, but this process is not going to produce a great novel-that is a different KIND
Sorry Granville, but this is just pure obfuscatory math: come up with a meaningless distinction, throw some equations at it to make it look credible, and then talk really fast. Thermodynamics doesn't define a bunch of different non-interchangeable "kinds" of order. It defines *one* thing: thermodynamic entropy. There aren't "different kinds" of order in thermodynamics. Your equations are pointless and irrelevant, because *they have nothing to do with thermodynamics*. They're built on an invalid, unjustified distinction. The fact that you can write some equations doesn't make your fabricated distinctions any less invalid. Unless you can show *how your equations for different kinds of non-interchangeable entropy necessarily follow from the second law of thermodynamics*. And you don't do that - because you *can't* do that.
It comes back to that little ditty from the beginning of this post: the existence of a valid counterexample disproves a theorem. We can quite easily show how, for example, the addition of heat to a system reduces some kind of diffusion entropy: just look at how we purify silicon. *If* this "kinds of entropy" nonsense were valid, it couldn't work. But it does - therefore your theory is wrong.