I would point out that a 20^130 possible combinations does NOT imply a probability of 1:(20^130) of a particular conformation actually occuring -- apples and oranges. This is a very common and slippery fallacy. Some conformations have astronomically smaller probabilities than this, and some have astronomically greater probabilities than this. This is a glaringly obvious flaw to anyone with a background in organic chemistry. The phase spaces are highly biased and irregular, making assessments of probability by a simple combinatorial analysis grossly inaccurate. Heck, if this wasn't the case it would make computational chemistry a LOT easier and simpler than it actually is.
Lots of people cling to this argument, but it is a strawman. The size of the combinatorial space is not the same as the probability of any particular piece of that combinatorial space occurring. Flawed premise, flawed conclusion. For a simple analogy, think of a loaded dice. Just because it has 6 sides does not mean that the probability of any given side coming up is 1:6 if the dice is loaded. The distribution function matters. A lot.
I just wanted to point out that Schroeder was not speaking to probability. He was speaking to the number of combinations. And also he was remarking how strange that nature would use that same combination for all visual systems, that it must have been pre-programmed in the lower life forms which had no use for eyes.
If he were talking probability, a lot of statistical issues would have come up including Bayes theorum no doubt.
That may be true, however, the DNA 'dice' are not loaded. Chemistry does not force in any way a particular order of the DNA molecules. There are two proofs for this:
1. DNA molecules do not touch each other in the linear sequence. Instead they are joined 'on the outside' by sugar/phosphate molecules which make equally easy bonds with all four different DNA molecules.
2. If there was a chemical necessity to any particular scheme, we would be seeing that certain possible combinations do not occur. Instead we see all 64 possible combinations of the three bit code appearing in living things.