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Laws, Useless Entailment And No Laws

In a recent post, having asserted that we can have no law, where a law is a compact description of the regularities of a process, for the detailed evolution of the biosphere by Darwinian pre-adaptations. Yet, given Newton's Laws, general relativity and the Schrodinger equation, I raised the obvious questions, if the above is right: When can we have laws? When not? Why? Why not?

It should be clear that, given our reductionist framework, the above are not even questions: all is law and entailment from the hoped for Final Theory.

Thus it seems wise to try to address these issues carefully. In this post I will briefly discuss an example from a past post, vast chemical reaction graphs with a small amount of matter on them. Here it appears that we have entailment, but it is useless and we have no detailed laws for the behavior of the system. Then I broach the evolution of the biosphere, where new empty niches are legitimate causal boundary conditions, but we seem to have no way to pre-state or deduce what these new niches will be. If this is true, and since laws, following Newton, require boundary conditions, we seem not even to have entailment.

Vast Hypo-populated Chemical Reaction Graphs

Recall from high school chemistry the law of mass action: X and Y are two chemicals that interconvert. If one starts with all X, it will convert to Y. As Y builds up, it will convert back to X, until chemical equilibrium is reached and the net rate of conversion of X to Y equals the net rate of conversion of Y to X. Here there are square root N, the number of X and Y atoms, fluctuations that damp out. We have laws: mass action and chemical equilibrium.

Now consider carbon, hydrogen, nitrogen, oxygen, phosphorus, and sulfur, CHNOPS, the atoms of organic chemistry. Now lets imagine all possible molecules made of CHNOPS up to 100,000 atoms per molecule. Next we construct, with advice from quantum chemists, a "reaction graph," showing all possible reactions among all possible CHNOPS atoms and molecules up to 100,000 atoms per molecules. This is a vast reaction graph. No reaction system can explore all the possibilities in vastly many times the life time of the universe.

Now let's sprinkle a small number of CHNOPS atoms and small or large CHNOPS molecules on this reaction graph. This done, we wish to study the dynamical reaction behavior of the small number, say 100,000,000 CHNOPS atoms, whether single atoms or in molecules, as the matter "flows" on the vast reaction graph. A convenient way to do this is to use the famous and widely used "Gillespie algorithm," which considers the current state of the atoms and molecules on the reaction graphs, the possible next reactions, chooses one at random biased by the concentration of substrates, picks a waiting time for the reaction to occur out of an exponential distribution, then updates to create the products of that single reaction.

What will be the behavior? No one really knows although systems chemistry is a new field that begins to address this issue.

I'm going to presume the results. Each time we run the simulation, even from the same starting distribution of CHNOPS atoms and molecules on the graph, we get very different sets of molecules as they spread out in a diversity of ways over the graph. Thus, the behavior is non-ergodic, i.e. the behavior is not at equilibrium, and may be very different on each run.

Let's assume this is true. Then each reaction that occurs is truly entailed by the fundamental laws of quantum chemistry. However, in a deep sense this entailment is utterly useless if we want to know the actual detailed flow of matter on the graph on any particular run, predicted at the outset.

Now if, as Gell-Mann, a Nobel physicist, states, a "law is a compact description of the regularities of a process," it seems we can have no law for the detailed behavior of the mass flowing on the graph.

That does not mean we might not have statistical laws, such as the mean flow of matter from small to large molecules over time.

The Evolution Of The Biosphere By Darwinian Pre-Adaptations And No Entailment

I recall that a Darwinian pre-adaptation is a causal feature of an organism of no selective use in the current environment that may become of selective use in a different environment. I recall again my example of swim bladders, yielding neutral buoyancy in the water column in some fish, derived from the lungs of lung fish.

Now we have a new problem. Let's assert that an empty biological niche is a boundary condition, like the walls of a billiard table. In the latter case, we use Newton's laws, initial positions and momenta, and the boundary conditions of the walls, integrate his equations given the boundary conditions and obtain the detailed trajectory of the balls.

In the case of the evolution of the biosphere by Darwinian preadaptations, the "boundary conditions" are constituted by the selective conditions of the empty niche.

My issue is this: can we pre-state or deduce those selective conditions? I think not. Here is my now-familiar example: name all the possible uses, or functionalities, of a screwdriver. It seems we cannot do so. There is no bounded set of functionalities of a screwdriver. Similarly, we cannot prestate either the feature(s) of an organism that might become preadaptation, nor the selective conditions for which the feature(s) of the organism, like the screwdriver, finds a novel use. But each new functionality is a new "empty biological niche" that constitutes the boundary conditions on selective evolution. Then, if we cannot pre-state or deduce ahead of time what the selective conditions are, we cannot derive the boundary conditions for the evolutionary process. If we do not know the boundary conditions, and must have boundary conditions for entailment, then it seems that we can have no entailment for the evolution of the biosphere by Darwinian pre-adaptations.

And, of course, the becoming of the biosphere is even more vastly non-ergodic than our vast chemical reaction graph. Most organisms will never come to exist. Like the vast reaction graph, even if we did have entailment in the evolution of the biosphere by preadaptations, which we do not, that entailment would be useless with respect to the detailed evolution of the biosphere.

Thus we can have no sufficient law for the becoming of the biosphere, although this in no way breaks the laws of physics.