Why Is The Universe Complex? Cascading Broken Symmetries : 13.7: Cosmos And Culture Why is the universe complex? Stuart Kauffman argues it's because of broken symmetries.
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Why Is The Universe Complex? Cascading Broken Symmetries

We are, I think, stumbling onto unfamiliar territory in considering why the universe is complex. Our familiar line of thought is that there really is a “Theory of Everything,” perhaps string theory, and it will logically and deductively entail all that happens in the unfolding of the universe.

Thank you Newton.

Your mind was stunning and gave us our entire view of science. Or did so until Darwin, who took himself to be the Newton of biology. But where Newton saw law and its deductive unfolding, hearkening to Aristotle’s argument that explanation in science is deduction, Darwin veered in a different direction: history buried in his heritable variation and natural selection. Evolutionary theory is rarely predictive, rarely deductive, yet explains vast tracts of biological facts about the becoming of the universe in our own biosphere.

Let’s recast where we got to in the last blog: An expanding universe cooling, broken symmetries which become both boundary conditions on the release of energy and, at least sometimes, the very source of that energy, which when released in a constrained way becomes work.  Information, I argued, is precisely these boundary conditions, or constraints that enable the new energy to be released in specific ways, thus enabling specific organized processes.

I gave two plausible examples: a hollow sphere of gas particles as an isolated thermodynamic system, partitioned (say by us) by an elastic membrane, so the chance higher pressure on one side could do work on the the membrane and push into the less pressured side, doing work on the membrane and the less pressured side.  Simultaneously a boundary condition came into existence as a symmetry was broken, energy came into existence, the constraint of the membrane enabled work to be done, and constituted, I claim, embodied information.  Then I gave the simple example of a wooden vertical pole falling over, breaking the symmetry of the plane, but becoming a boundary condition on rain water rilling it up against gravity along its flanks. Same thing.

Then I noted that there is no “law” for how the pole falls. It randomly breaks a symmetry. That is what symmetry breaking  is.

We begin to confront somehow a non-Newtonian, non-Einsteinian view in which what arises sets the stage for further symmetry breaking which may also be, in a sense, lawless, into an entire unfolding creativity of the universe becoming complex.

If so, this is not at all what we expect.

Then we must be careful.

Let me jump ahead to what I hope may be true: As symmetries break and become boundary conditions for specific processes to  happen, on average, each such symmetry breaking gives rise to more than one new organized process that might occur, so the entire process, viewed in whole, is a branching, ramifying one in which ever more sources of energy become available, ever more boundary conditions are formed by symmetry breaking in some general sense, and the universe, biosphere, economy, culture, become ever more complex as all advance into an expanding Adjacent Possible that is both real ontologically and in a sense to be understood, “makes space” for the ever new possibilities that become actual.  This will not yet “defeat” the second law of thermodynamics, but will, I hope, lead to a non deductive account of how the universe, partially lawlessly, and creatively, becomes complex.

Can it be so?

I will return later to think with you about star and galaxy formation in the universe. We need first a hoped for criterion for what such systems may maximize as self maintaining far from equilibrium systems. I will guess that this is: maximization of a power (of self maintainance or growth)  per unit “fuel”.  This will, as we will see, pick out a finite displacement from equilibrium.
First, however, I want to leap over star formation and galaxy formation to the vast reaction graphs underpopulated by matter that I discussed in previous blogs.I hope to find symmetry breaking rich in such systems.

Recall that a protein is made of 20 kinds of amino acids. Beta galactosidase, in E. coli, has over 1000 amino acids within its length.  How many possible proteins are there length 1000?  Well, 20 raised to the 1000th power or 10 raised to the 1600 power.

OK so its a big number. Well it is big. There are “only” 10 raised to the 80 power particles in the known universe!  So by a back of the stamp calculation, the universe cannot make all 10 to the 1600 proteins in gadzillions of lifetimes of the universe.

As I have noted before, above the level of the atom, once into chemistry, the universe cannot in many lifetimes of the universe make all possible complex, say organic, molecules up to, say 600,000 atoms per molecule.

Now, as in the past, consider a vast reaction graph with all possible molecules up to 600,000 atoms per molecule.  The reaction graph among these, for the moment, classical chemicals depicts each reaction as arrows coming from the substrates into a box, and from the box arrows going to the products. An example is A + B -> C + D, a two substrate two product reaction. In reality, the arrows are for our convenience, for the reaction is reversible on some time scale and will flow toward equilibrium where the rate of formation of C + D is equal to the rate of formation of A + B.

But this reaction graph is hypopulated by matter.  To be concrete, imagine we have a total of 100,000 atoms of carbon, of hydrogen, of nitrogen, oxygen, phorphorus, and sulfur, the atoms of organic chemistry.

To be concete, let us place our atoms and modest sized organic molecules on the reaction graph so that each reaction has only the substrates present, one copy of each.  Thus there is one A and one B molecule, and zero C and zero D molecules in the above reaction.

The first thing to notice is that this simple system is displaced from chemical equilibrium! The substrates are there, the products are not, so the reaction is “shifted to the left”, and there is a real chemical potential to form C + D.  That is, if chemical equilibrium for this reaction is symmetry, this system has broken that symmetry.

Next we can imagine that C + D have never once come to exist in the history of the universe. Then I want to say that the coming into existence of something for the first time in the universe is also breaking a symmetry. This may be a wider sense of symmetry breaking than we are used to, but the pole falling over for the first time in the universe picked, for the first time, a direction on the plane. A symmetry was broken, here for the first time in the history of the universe.

Finally, we can imagine that A + B might undergo a number of different reactions: A + B ->  Q.  A + B -> C + F.  A + B -> L + R + J.......
Each of these reactions is genuinely possible on the reaction graph.  Which one occurs might be a quantum process, by the Copenhagen interpretation of quantum mechanics, this occurrence is  random and acausal.  So no law governs, in a deterministic sense, whether C  + D or Q or L + R + J is formed, each driven by a real chemical potential.

Symmetries are being broken all over the place.

More the broken symmetries virtually certainly cascade in an  historically dependent way.

Why?  In contrast, consider two types of molecles, X and Y, each present in millimolar concentrations, each converting to the other. Equilibrium is reached when the net rate of  forming X from Y and Y from X are equal.  But the only molecular species in the system are these two, and all that occurs at equilibrium are square root N (the number of X and Y atoms) fluctuations which DAMP OUT.
On the vast reaction graph (to be verified  using chemical master equations and the Gillespie algorithm) fluctuations do not damp out. Instead, the atoms and molecules on the vast graph wander in some way on the graph that is deeply historically dependent: what happens next is constrained by and enabled by what  happened in the past.

So in this first example of an historically dependent process we have: a thermodynamic driving force, no laws for what happens in detail in this flow, cascading broken symmetries which become both the boundary conditions, (A +B exist) and the source of energy, (C + D do not exist so the reaction is shifted to the left), A and B by existing, become the embodied information that enables the reaction A + B -> C + D to occur releasing energy in a constrained way, so work is done ( C + D are present, A + B are absent, so C + D are present above the equilbrium concentration.

Is something like this happening in space? Probably yes. The famous Murchison meteroite, full of organic molecules, which fell in the 1970s in Austrailia has just been analyzed for the first time for the observable diversity of organic molecules: 14,000 were detected which is enough, in one reaction step, the authors say, to generate hundreds of millions of novel molecules, breaking symmetries in the becoming universe.