Time to butt heads over thermodynamics again!
And the response to claim CF005 ("1.While statistical information theory has a quantity called "entropy", it does not have anything equivalent to the second law of thermodynamics") is flat-out wrong. Thermodynamic entropy is EXACLY the information entropy of the macrostate multiplied by Boltzman's constant.
CF011.1 would have been an ideal place to explain that a phrase written in a language has lower information entropy than a string of random characters of the same language, but it's not discussed at all. It's related to the YEC's objection that evolution results in an increase in information. The claim actually harms the creationist's case, because in fact all real thermodynamic processes result in an increase in information.
But you can't demonstrate that without explaining what thermodynamic entropy actually is.
The whole problem is that while information-theoretic entropy is connected to disorder, information-theoretic disorder is not connected to real-world disorder in the way that creationists think. I wrote a post about this some time back which I thought was great, but I have no idea where it went, so here goes.
Let's take the classic example of gas molecules in a partitioned box. Suppose we have twenty molecules in a box in four separate quadrants labeled A, G, T, and C. In the beginning, all the molecules are kept in the A quadrant by partitions; when we raise the partitions, random diffusion ensures that the molecules are now free to visit the G, T and C quadrants.
Suppose we wanted to use a twenty-letter string to represent where each molecule is (technical note: they are distinguishable). In the beginning the string is just twenty As. This string has low information (there's only one possible box per particle) and thus the physical state has low entropy. But after the partition is raised, the string might become AGTCCCTAA ... it now has more information (because now each particle could be in any one of four boxes) and thus more entropy. A little while later, the string might instead become GTACTCAAG ... but it has the same information as before: all we know is that each particle has a one in four chance of being in each of the boxes, and the latter string is just as likely as the former.
Simple? Now suppose we have a nucleic acid string whose sequence is initially just twenty As. After going through a whole bunch of point mutations, the sequence is now AGTCCCTAA ... And after going through another bunch of point mutations, the sequence is now GTACTCAAG ... By analogy with the earlier example, the first bunch of mutations increases the (information) entropy of the nucleic acid string to a theoretical maximum (two bits of information per bit of sequence), and the second bunch of mutations conserves the entropy of the nucleic acid string (still two bits of information per bit of sequence).
Does this raise a problem for creationists? In a sense, because it's obvious that any string of uniform characters (having low entropy, and thus low information) doesn't code for a working protein while a string of random characters could. But that's only contingent on our choice of transcription codes. One could imagine a genetic code where an isolated base (of any kind) acts as a start codon, a pair of bases (of any kind) acts as a stop codon, and the
nth amino acid is coded for by a sequence of
n+2 successive bases (again, of any kind). In such a code, a "low entropy string" of uniform characters would code for a protein as much as a "high entropy string" of random characters. So it's not just that creating entropy creates genetic information: one can imagine a system in which any number of arbitrarily low-entropy strings can code for proteins.
No, the problem is more fundamentally that
the character-wise entropy of a genetic sequence bears zero correlation to the selective advantage its phenotype confers. Not that the character-wise entropy is correlated to carried information (as shown above, it need not do so).
So take the gene for normal hemoglobin. It can be represented as a long string of A, G, T, and C; this long string can be in turn represented as a long series of flipped coins. It would take two coins to represent one base (for example two heads for A, first head and then tail for G, first tail and then head for T, and two tails for C). Because A, G, T and C are roughly evenly distributed in the hemoglobin gene, there's roughly the same number of heads as tails, and you can't tell just by looking at the previous flips whether the next one will be head or tails: the coin is fair.
Now let's take one of the coins and re-flip them. Oops! The hemoglobin gene now has a point mutation, and the poor sufferer now has sickle-cell trait. But notice something: there's (say) only one tail more and one head less among the hundreds of flips. So the coin flips are still fair, half-half head and tail.
It's true that if we took a fair coin and flipped it hundreds of times, we'd get about half of them tails and half of them heads. That's what the mutations do, make the coin flips fair so that the sequence has about the same number of A, G, T and Cs. And the mutations increase entropy in the sense that if we had an initial sequence with all heads, and randomly reflipped all the coins, it would be much more likely for us to get a sequence with half heads and half tails than for us to get another sequence with almost all heads.
But
what would the sequence exactly be? One fair sequence (half heads and half tails) might code for normal hemoglobin. Another fair sequence might code for sickle-cell hemoglobin. Yet another one might code for insulin. A fourth might not be able to code for anything at all. A fifth might code for bigger brains, and a sixth for predisposition to accepting evolution -
and they would all have about the same number of heads as tails, and therefore be valid results of random mutation (to say nothing of the subsequent effects of natural selection).
The point isn't that more entropy = more information (although by many intuitive definitions of information that's true). The point is that the statistical entropy of a genetic sequence simply doesn't correspond to the biological sort of information that creationists believe can't be generated, the kind of information that codes for wings instead of arms and brains instead of feet.
(BTW, "a phrase written in a language has lower information entropy than a string of random characters of the same language" applies to most human languages, notably English, but not to DNA. The information entropy of an arbitrary coding sequence of DNA will be about the same as the information entropy of an arbitrary non-coding sequence of DNA; in fact, as the sequence gets longer, the entropy difference will
decrease, because less characters relative to the length of the whole sequence need to be fixed (only the start and the stop codon).
This is contrary to human languages where the longer a string of random characters is, the higher the probability that it will be nonsense - therefore, the entropy difference between readable and nonsense strings of characters
increases, nearly exponentially I suspect, as the length of an arbitrary string increases.)
