A miniature of people crossing the street.

A toy world in an open universe. (nurpax/via flickr)

By Stuart Kauffman

We are exploring the "open universe", far from Newton, looking to see whether the becoming of the universe can involve ontologically both the Actual and the Possible, where what becomes Actual can acausally change what becomes Possible and what becomes Possible can acausally change what becomes Actual.

We must already pretty well suspect that the answer might be "yes", given both our classical world and quantum mechanics, and our previous discussion of the emergence of adaptive opportunities in evolution which seem, acausally, to change what can happen. I want in this blog to try to explore how the interplay of the two can "make history", a history we cannot foretell. I will use the "vast" chemical reaction graph I introduced in the previous post as our "toy world" to think about.

Warning: we will start with "classical" chemicals in a vast reaction network, then be forced to introduce quantum chemistry-lite, then the presumed passage from the quantum world to the classical world (for all practical purposes) via loss of quantum phase information in "decoherence". In the end, we will be at the edge of a new field of science, called "systems chemistry", and beyond what anyone knows.

So OK. Recall that a set of reacting chemicals that transform into one another can be depicted by a reaction graph. The chemicals are denoted by dots called "nodes", and reactions are denoted by arrows leaving one or more substrate node inputs and going into the reaction "box". Then arrows leave the box and point to the product nodes. For example, if X converts to Y in a one substrate - one product reaction, we would draw an arrow from a dot labeled X to a box, and an arrow from the box to a node labeled Y. The reaction is denoted by the arrows and box.

It is essential that this reaction typically goes in both directions, X to Y and Y to X, so the directions of the arrows in the graph are just used for our convenience to pick out substrates and products of a reaction in one direction of that reaction.

Again, let's recall high school chemistry. If we start with a high concentration of X, say millimolar, or 10 to the 20th power X molecules in a liter, and no Y molecules, then in classical chemical kinetics we assume each X molecule has a probability per unit time to convert to Y. We also assume X may never convert to Y. So X molecules convert to Y. As the Y concentration increases, Y molecules start to convert to X. When the net rate of conversion of X to Y and Y to X is equal, the system has reached chemical equilibrium. No net change in the average concentrations of X or Y occur, except for fluctuations on the order of the square root of the number of X or Y molecules. These fluctuations damp out, so the reaction system hovers at equilibrium with these fluctuations.

Next step: Recall that if we ask how many proteins, which are linear chains of amino acids, there are with 200 amino acids in the chain, and 20 kinds of amino acids, the answer is 20 raised to the 200th power, or about 10 raised to the 260th power. In a previous post I noted that if the 10 to the 80th particles in the known universe were to do nothing on the shortest, Planck, time scale of 10 to the -43 seconds but make proteins length 200, it would take an astonishing 10 to the 39th power times the 13.7 billion year history of the universe to make all these possible proteins just once.

So, above the level of atoms, the universe cannot yet have made all possible proteins length 200, 400, or organs, tissue, organisms, or social systems. The universe is indefinitely "open upward" in complexity and on a unique pathway, or trajectory. History enters when the space of the possible is very much larger than what can happen, so this simple calculation is part of the basis of history in the universe.

On to our toy vast chemical reaction graph, with a tiny amount of each of the atoms: carbon, hydrogen, nitrogen, oxygen, phosphorus, and sulphur - the atoms of organic chemistry.

Imagine 100,000 copies of each of these six kinds of atoms in our toy system, so 600,000 atoms in all. Now let's think up with a chemist's help, all the possible organic molecules we can make using 1,2,... up to 600,000 atoms per molecule.

Well, no one even knows how to count how many such organic molecules there are in our toy world, but no matter. Now imagine the reaction graph connecting all these molecules by one substrate - one product reactions, one substrate - two product reactions, eg. a small protein breaking into two smaller fragments, two substrate - one product reactions, eg. the two smaller fragments ligating to reform the initial small protein. Then we we have two substrate - two product reactions, for example, as in the last post, A + B can react to form C + D by a fragment of A breaking of, converting A to C, then the fragment adds to B to turn B into D. So this A + B converts to C + D reaction has two arrows, one each from A and B nodes, into a reaction box, then two arrows leaving the box and entering the C and D nodes.

Let's begin our thought experiment thinking of these 600,000 atoms and chemicals made from them as classical objects.

How will our reaction system behave? Actually, no one knows. We have a vast reaction graph and a tiny amount of matter "on" it, it is "hypo-populated". No one has studied such systems.

In this toy - real world, we get to place atoms and specific kinds of organic molecules in our reaction system. Now the mathematical way to study such a classical reaction system is by what is called a "chemical master equation". This fancy sounding thing is just this: For any distribution of atoms and molecules on the reaction graph, write down all the single next possible reactions that can happen. Then a neat algorithm, the Gillespie algorithm, simulates the behavior of this system by choosing at in a biased random way, depending upon the number of copies of each kind of molecule, which of the reactions occur and when it occurs. Then one repeats this zillions of times, burning up lots of computer time. The atoms and chemicals "flow" stochastically - that is, non-deterministically - across the reaction graph.

This actually works in simple reaction systems, so in principle should in our vast toy world with enough computer time.

As a next step, let's put our reaction system into a closed thermodynamic system into which no matter or energy can enter.

Now the final preliminary step is to arrange our atoms into atoms and molecules and let them loose to react. We can do this any way we want. No one has ever tried this as a numerical experiment, so I am going to be guessing probable results: Take warning.

Let's start with 10,000 atoms each of carbon, hydrogen, nitrogen, oxygen, phosphorus, and sulphur. Then lets construct exactly one copy each of lots of small and middle sized organic molecules such that they are, with some statistical distribution we choose, neighboring nodes on the reaction graph, but since the graph is vast compared to the number of molecules we can create, almost all nodes representing possible organic molecules have no molecules.

Now let's suppose that in many cases a molecule can enter into more than one reaction. For example A + B can convert to C + D, but A + F can convert to G, or A + H can convert to I + J, so our network is highly branched.

When we run the Gillespie algorithm, and if all the input chemical substrates to a set of reactions are present, it will be a matter of Gillespie algorithm chance which occurs, so on different "runs" of the algorithm, A might go down different pathways in the reaction graph.

But A's presence at different locations on the graph may acausally open up new Adjacent Possibles, or acausally close off other Adjacent Possibles. For example, suppose A + F convert to G above. Then the single copy of A no longer exists, and the A + B converts to C + D reaction can no longer occur. The disappearance of A has non-causally made the Adjacent Possible of A + B converting to C + D disappear! Similarly, if F can convert to L, then the new existence of F by the reaction that the Gillespie algorithm randomly chooses, non-causally opens up a new Adjacent Possible: F can possibly convert to L.

No one knows what such a system will do. My own intuition, (only that, but see what you think,) is that the reacting molecules may be able, on repeat runs of the Gillespie algorithm from the same initial distribution of molecules on the reaction graph, to veer off in widely diverse directions to explore diverse areas of the vast reaction graph.

My intuition is ultimately testable and not nuts. Let's assume for discussion that I'm right. Then there is a first critical consequence: Unlike the X Y reaction system in millimolar concentrations that reached chemical equilibrium and showed square root N fluctuations in the numbers of X and Y molecules where the fluctuations damped out, here it seems that fluctuations need not die out, but may amplify in all kinds of ways!

So, in our perfectly legal, closed thermodynamic system, what happened to chemical equilibrium? If I'm right, there is no chemical equilibrium for, say the lifetime of the universe or vastly longer on the vast reaction graph!

Assuming this is true, it is more than a bit strange. There is, of course, an equilibrium, on vastly vastly long time scales when the system can have explored the vast reaction graph so many times over that the probability of occurrences of all molecular species can be known. But the time scale is vastly vast.

More, we can make the time scale to equilibrium as long as we wish by increasing the size of the reaction graph arbitrarily to allow larger molecules. (Very large molecules are perfectly feasible, for example huge coal seams that can be one huge molecule.)

Now let's think about the behavior of this reaction system for, say 3.7 billion years, the age of life on earth. But, in our imagination, run the 3.7 billion year simulation very many times. Perhaps very different wanderings of the chemical system on the vast graph will occur, each a unique history of the chemical reaction system on a "short" time scale of 13.7 billion years, compared to the time to chemical equilibrium.

Now, as emphasized above, in this still classical setting, as Actual molecles are formed, new Adjacent Possibles come into existence and old ones disappear. Thus, if A + B can convert to C + D, and A alone is present in a single copy, there is no Adjacent Possible to form C + D. But if a B molecule comes to exist in our Gillespie simulation, suddenly the formation of C + D acausally becomes an Adjacent Possible.

Thus, the coming into existence and disappearances in this Gillespie chemical master equation classical chemical world of molecules acausally opens up and close off Adjacent Possibilities that, in this Gillespie world, change what Actual molecules form.

Remember the Gillespie algorithm faithfully captures the assumptions of classical chemical kinetics and is used all the time by chemists.

Alfred North Whitehead spoke of Actuals giving rise to Possibles giving rise to Actuals. We seem to have that here, right in front of us.

But we have not dealt with the issue of whether these possibilities are merely epistemological or ontological.

If we are using the Gillespie algorithm, its biased randomness models our ignorance, based on chaotic dynamics and our incapacity to know the detailed motions of many classical particles in detail. In that case, the "possibilities" are merely epistemological, not ontological.

Given what we know now, to obtain ontological possibilities as real in the universe, we must turn to quantum mechanics and quantum chemistry and the two specific interpretations of quantum mechanics with ontological possibilities, namely the Copenhagen interpretation, Born rule and I'll add and discuss, "decoherence", or alternatively, the "multiple world" interpretation of Everett that assumes that every time a measurement event is made the universe splits, both universes are ontologically real, and it is a matter of ontological fact which of the two branching histories of the universe we are in.

This step, discussed in the previous blog, is actually deeply difficult, and beyond what is known about the quantum chemistry of complex vast hypo-populated reaction graphs.

Let me say the problem, beyond the previous post, briefly. A physicist might well say: The entire system remains entirely quantum! There is some initial state of the time dependent Schrodinger equation giving, by squaring amplitudes, the probabilities of molecules of different types on the reaction graph. Then this Schrodinger equation "propagates unitarily" forever, always quantum across the reaction graph, so the probability of molecules at different locations on the graph change. Here "unitarily" means that the total probability remains 1.0.

If the reaction system remains fully quantum, then no actual molecules ever exist, for the classical world never exists, and all we have is either the uninterpreted Schrodinger equation propagating its mathematics, or we interpret the mathematics and have possibilities and computable probabilities of occurrences of molecules on the vast graph, but no way for actual molecules to occur.

For actual molecules to emerge, we appear to need to add decoherence. Recall that quantum interference requires that all the phase information where peaks and valleys of the Schrodinger waves are, is retained in the system, to give the light and dark patterns in the two slit experiment. If the phase information is lost from the quantum "system" to a quantum "environment" or a quantum + classical "environment, then the capacity to have interference disappears in "decoherence" and, claim many physicists, the classical world is approached as closely as one wishes - ie the classical world appears, "for all practical purposes".

OK. So we need a system and an environment. I'm not a physicist or chemist, so let's pop in lots of photons and electrons into our system to be the quantum environment our atomic and molecular system can lose its phase information into.

Then presumably, in this case, real A and B molecules can form, can ontologically possibly form C + D via an acausal quantum process, and we have what we hope for. We have roughly, Whitehead's Actuals and Possibles, emerging and disappearing as the quantum plus decohering to classicity system evolves on the reaction graph. More the Actuals emerge acausally because loss of phase information in decoherence is acausal, and, by reacting via quantum events, acausally alter the Adjacent Possibles on the evolving reaction graph.

We seem to arrive at an acausal becoming which "wanders" in a history dependent way, ie that depends upon what happens to have occurred, on the reaction graph, yet no law seems able to describe this wandering since the detailed way decoherence happens may, in general, not be knowable. This point was my blog about Popper's argument of indeterminism in a Special Relativity setting applied to decoherence: no function maps the system from event A into its future until just before event B, (B in the future light cone of A), during decoherence in the SR setting.

But there may be a deeper "lawlessness". If the system were to remain purely quantum, physicists know how to use the time dependent Schrodinger equation to propagate the Schrodinger waves and all their superpositions over the entire reaction graph, although no actual molecules occur. But given decoherence of some of these possible molecules though decoherent loss of phase information to the environment, that phase information is lost to the system in ways we do not know in detail. Part of the system of molecules is now classical, but in ways we do not know in detail, wandering in some history dependent way on the vast reaction graph. Taken together, it seems impossible to continue to propagate the Schrodinger waye equation unitarily. This is unexplored physics, but I see no way that a law can describe this becoming of the quantum-classical system in its environment wandering in a history dependent way on the Vast reaction graph.

To summarize, a hypopopulated chemical reaction system on a vast reaction graph seems plausibly to exhibit, via quantum behavior and decoherence, the acausal emergence of actual molecules via acausal decoherence and the acausal emergence of new ontologically real adjacent possibles that alter what may happen next, and give rise to a rich unique history of actual molecules on a time scale of the life time of the universe or longer. The entire process may not be describable by a law.

If so, the universe is open in being partially lawless at the quantum-classical boundary (which may be reversible). As discussed, the universe is open upward in complexity indefinitely. Based on unprestatable Darwinian exaptations, the evolution of the biosphere, economy and culture seem beyond sufficient law, hence the universe is again open. The unstatable evolution of the biosphere opens up new Adjacent Possible adaptations. The adaptive opportunities for biologicalevolution may or may not be taken, due to normal population genetic processes such as random mating, meiosis, recombination, and which sperm reaches the egg first. More, no law describes the selective achievement of such an adaptation, if the right genes come together in the right general environment, since we cannot prestate the necessary and sufficient conditions for successful selection of an adaptation. Thus the adaptive opportunity acausally alters what can happen. It seems true both that the becoming of the universe is partially beyond sufficient natural law, and that opportunities arise and disappear and either ontologically, or epistemologically, or lawlessly, may or may not be taken, hence can change the history of our toy vast reaction system, perhaps change the chemistry in galactic giant cold molecular clouds, and change what happens in the evolution of the biosphere, economy and history.

We next need to look at where opportunities come from. Its a puzzle.

12:08 - February 25, 2010