Of Time and Miracles

Is crossing a large chasm of space and time resources a miracle?

Treating the empirical time scale of the evolution theoretically as infinity they have then an easy game, apparently to avoid the concept of purposesiveness. While they pretend to stay in this way completely ‘scientific’ and ‘rational’, they become actually very irrational, particularly because they use the word ‘chance’, not any longer combined with estimations of a mathematically defined probability, in its application to very rare single events more or less synonymous with the old word ‘miracle’.”
 -- Wolfgang Pauli to Niels Bohr, 2/15/1955, letter 2015 in von Meyenn (2001), p.105

Adleman's K-potency and Kauffman's Atoms

One of the motivations for the sequence-space probability dispersion matrix is that as a model it might estimate the computational depth of nucleotide sequences, or the relative depth between two nucleotide sequences.   How deep is a given nucleotide sequence?

Kauffman writes in a recent foreword that the universe has produced every kind of atom it could produce (an ergodic process, whereas enumerating the realizable proteins is a non-ergodic process), but Leonard Adleman has elsewhere written in "The Rarest Things in the Universe" (among "entropy and information" here) that atoms with higher counts of protons than we've thus far encountered could be considered to have larger depth (and thus be somewhat analogous to Kauffman's sequences).

I am not a physicist, but I suppose it is possible to theorize about an atomic nucleus with a million protons. But what if I want to create one? It appears that producing transuranic elements takes huge amounts of time/energy and the greater the number of protons, the more time/energy it takes. It is even conceivable (to me at least) that there is not enough time/energy available (at least on earth) to actually produce one. Like the prime factorization of , it may exist in theory but not in reality. On the other hand, physicists from Russia and America, using lots of time/energy, have created an atomic nucleus with 118 protons called Ununoctium. Ununoctium is analogous to Childers’ prime factorization; both exist in reality; both were very costly to create.

In his 1979 paper "Time, Space, and Randomness," Adleman develops an idea about "K-potency" motivated by an analogy with thermodynamics, specifically chemical reactions that take much less time going in one direction than the other.

This approach to "one-way functions" is important to crytography, incidentally.  His definition for K-potency follows here:

2^219 states

2²¹⁹ states

But that's just one star, and a measly one at that. A typical supernova releases something like 10⁵¹ ergs. (About a hundred times as much energy would be released in the form of neutrinos, but let them go for now.) If all of this energy could be channeled into a single orgy of computation, a 219-bit counter could be cycled through all of its states.
    https://www.schneier.com/blog/archives/2009/09/the_doghouse_cr.html

The Grammar of DNA

Similar to David Abel's(?) distinction of change contingent and choice contingent variation is Lila Gatlin's D1 and D2 distinctions.  D1 is "context-free" variation in the statistic Shannon sense and D2 is "context sensitive" in a grammatical sense.  Gatlin is/was a biochemist/biophycisist and is not using these terms in their specific computer science meanings, where a grammar-generated language is specifically referred to as context-free.

Gatlin referred to a Law of Conservation of Information, not too coincidently similar to Dembski's interpretation of Wolpert's.  Since at that time, the modern ID Movement had not taken shape, and the guardians of the light of science were only concerned with creation science based on religious axioms, Gatlin wasn't derided, marginalized, and silenced the way that ID proponents now are.  She was published in Nature and the Journal of Molecular Biology (as has Douglas Axe in the latter, if I recall).  Jeremy Campbell leaned quite a bit on her ideas for his Grammatical Man, which garnered praise from mathematician and Skeptic (in the anti-supernatural and anti-creationist sense) Martin Gardner.  Surely, Gardner would be expected to have a negative reaction to a speculative book that depended on pseudoscience.  Way back in the 70s, you must realize, these ideas weren't pseudoscience.

This gets back to my Conjecture:  The opposition leveled at an idea in biology will be in proportion to the perceived utility of the idea to supporting theistic belief.  Professional skeptics would not close ranks against this idea until it was associated with the idea of Intelligent Design.  Note here that all 2nd Law of  θ∆ics arguments are summarily dismissed with a "guilt by association" argument (you know, one of them there fallacies) of the Barbara Forrest kind.

Anyway, Gatlin recognizes that the statistical measure of information of the Shannon sort is insufficient to reason about the interrelatedness of grammatically organized information that has semantic value.  Where here analysis possibly falls short, is that "grammatically correct" strings, or strings that follow grammatical rules, do not necessarily convey meaning, and in fact, are usually nonsense.   But it is certainly a step  in the right direction.  There is a limited context-sensitivity in grammar that is relevant to protein structure.  Subject must have its predicate and vice versa.  In English, the choice of a plural noun will affect the form of the predicate verb.  In protein space, particular "choices" in one part of the protein will have consequences for residue choices in remote parts of the same protein (or possibly, in a part of a co-enzyme).  The context-freedom in grammar is that rules only get you so far:

Greenness is a square light bulb, that grazes in the death of fragrance.  A bus, on the other shoe, does not swim with the lug nuts, but flies in a river of boots.

Grammatically correct, more or less, but not likely to inform the hearer about much of anything.   And for every meaningful sentences, there are many combinatorially more that would be unlikely to be useful sentences in any context.  The birth of tables preceded the art of melting dishes by a trillion dollars.  My sofa isn't feeling well.

See far ogle.