That's good because you at least identify where your error resides. Chemical reactions can build structures (e.g. double-helix, blank CD-ROM, empty hard drive, plain white paper pages) all day long. Clearly structures can be chemically formed INDEPENDENT of data being sequenced on them. Just because you have a chemical structure doesn't mean that it contains data.
But DNA that is capable of forming life, as well as CD-ROM's that are capable of allowing programs to be run from them, WILL have data stored in/on them.
Sure, you could build a double-helix DNA structure with all A/C bases in between acids, but that would be incapable of forming life because there would be no data present.
However, the correct sequence of A, C, G, and T bases in a double-helix structure will form various types of lives, depending upon the order of said data.
No one cares if chemical double-helix structures can form naturally, just as no one cares that blank CD-ROM's can be molded at the factory.
What matters is the sequence of data, if any, that might be stored in or on such structures.
Watson's math simply applies to the probability / improbability of such data self-forming naturally (i.e. without intelligent intervention or aid).
Any sequence of DNA will be active. There's no such thing as a "blank" sequence of DNA. The activity of the sequence will depend on the molecules in the environment around it. But each base, each atom, no matter what sequence it is in, is active with properties peculiar to it.
What matters is the sequence of data, if any, that might be stored in or on such structures.
Watson's math simply applies to the probability / improbability of such data self-forming naturally (i.e. without intelligent intervention or aid).
So you want to consider DNA as a black box? I believe his argument gets even more tenuous at that point. While he does address the concept that there are some errors, I don't believe that he does enough on this tack. There is no experimental evidence that there aren't many more different combinations than he recommends, enough to blunt the odds that he calls impossible.