Thinking about Symmetry via Stuart Kauffman, William Blake, AR Ammons, Johann Gottlieb Fichte, Robert Frost—and My Wife

Biologist Stuart Kauffman blogs for the National Public Radio (NPR) website, and recently wrote a post reflecting on the universe’s symmetry breaking:

To begin at the beginning, . . . The universe started extremely hot, dense, and essentially uniform, or isotropic.  Perhaps all four forces, Electro-Magnetic, Weak, Strong and Gravity really were united into a single unified force.  A first essential to a complex universe is that it expanded and cooled.  By cooling symmetries can be broken. Probably the first ones to be broken were those separating the four forces.

For Kauffman, symmetry breaking establishes the boundary conditions for the movement of new energies:

The universe started highly symmetric. So for asymmetries to arise, those initial symmetries must have been, and even today, continue to be broken.

I want next to show that broken symmetries, absolutely natural in physics, biology, economics, cultural evolution, can arise spontaneously, and become new sources of free energy by which work can be done.

I suppose that this is a physicist’s way of saying what William Blake said: “Roll your cart over the bones of the dead.” Blake didn’t say roll your cart through  the bones of the dead, as if you pretended that they weren’t there at all. He spoke, instead, of a deliberate act; of working one’s way over a limitation that you do not ignore. The bones of the dead constitute the boundary condition that made us possible. They are what came before us; the skeletal shoulders we stand on (or roll over). And they are what we must navigate, or Jacob-wrestle with, on our way to something else. Here is one of Kauffman’s examples:

Consider a hollow metal sphere containing an ideal gas in free space, a closed thermodynamic system. It can do no work.  It is symmetric in the density distribution of the gas, except for square root N fluctuations, where N is the number of gas particles. Now (magically) partition the sphere with a rubber membrane into two half spheres. The symmetry is now BROKEN. But also, by chance, thanks to the square root N fluctuations, the pressure on one side of the sphere will be higher than on the other side, so will push into the less dense half of the membrane partitioned sphere. “Work”, good old-fashioned physical work, has been done on the membrane and the gas in the newly compressed half of the membrane partitioned sphere. So: breaking a symmetry imposed a constraint, the membrane, which became a boundary condition, which enabled work to be done.  All of these seem to go together: break a symmetry, by human hand, or spontaneously, as below, and a constraint comes into existence, becomes an embodied boundary condition that enables work to be done.

The poet AR Ammons once wrote that the universe has no floor, “yet we walk the floor.” Ammons’s koan-like paradox, at one level, is certainly beautiful, but maybe it’s not, strictly speaking, true. If I understand what Kauffman is saying, the universe has lots of floors (and walls and ceilings). They are the contingently broken symmetries that function like a partition dropped into a once symmetrical gas. They get particles, other things, and people stirring and pressing into one another. I think of Fichte’s Anstob—impact: you don’t know who you really are until you start crashing into others. And the boundary conditions that result from the unpredictable ways that symmetries break become the floors we walk on (and the walls and ceilings of existence that we hit). And so, contra AR Ammons, we walk the floor of the universe’s (hidden to us) broken symmetries.

Symmetry breaking, in other words, is nature’s way of getting existence’s bumper cars moving. In fact, bumper cars are a nice analogy. Each car is a little bundle of energy walled off from the wider world with other little bundles of energy. Of course, this makes for interesting difficulties (as well as possibilities).

For an interesting game, the universe, like any art, needs rules and boundaries, and these are derived from broken symmetries. What Robert Frost said of free verse is true of the universe as a whole: there’s little value in playing tennis with the net down. But once the net goes up, things can get interesting. Or, as Stuart Kauffman put it (less eloquently):

What is work? Not just force acting through a distance, but the constrained release of energy into a few degrees of freedom.

In other words, work, information, energy, and evolution gin up when tennis is played with a net; when you try to write a poem in a definite form; when a species gets isolated on an island; or when the universe’s symmetry breaks with a Big Bang.

To be or not to be. To do or not to do. To think or not to think. The inner dialogue of consciousness is also a broken symmetry. Who expends energy to think and fret when whole?

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NOTE: I asked my wife, Rachel, to read the above post before I published it. She had an interesting observation, and I asked her to add it. Here my wife taketh over the keyboard . . .

Maybe a helpful analogy is the story of Robinson Crusoe. His symmetry (the ship) is wrecked and shattered. He is spewed up on a beach with a few pieces of driftwood and some scattered remnants from a previous order. And he makes a new world.