To the commenter who asked me elaborate on symmetry, symmetry breaking and social evolution.
Symmetry is the concern of a branch of mathematics called group theory. Stewart and Golubitsky’s “Fearful Symmetry: Is God a Geometer” is good on symmetry and symmetry breaking. For example, they write about the symmetries of animal gaits. For bipeds the choices are limited: either move symmetrically, hopping like a kangaroo, or break the symmetry with alternating strides, as we do walking and running. There are more possibilities for four legged animals, and S&G show how you generate trotting, galloping, cantering, pacing, and so on as you move from perfect symmetry to various broken symmetries. The symmetries involved mean that simple oscillating nerve networks can manage these different gaits. Here group theory is doing some actual work.
When group theory was getting big in basic physics early in the twentieth century, some physicists considered it a pointless abstraction, but it now has a central place in the field. In the human sciences, group theory is ensconced in a few places, like some of economics and kinship theory. One guy who sees a wider scope for the theory is John Bolender, who argues that social life is built around a few abstract conceptual templates – sharing, equal exchange, hierarchy, market pricing — related via symmetry and symmetry breaking.
As I noted previously, the move from an egalitarian to a hierarchical society is a form of symmetry breaking. So is the more benign move from a subsistence, jack-of-all-trades economy to a division of labor. In these cases, symmetry breaking in the form of hierarchy formation and the division of labor results from increases in social scale (noted by Peter Turchin for hierarchy, and all the way back to Adam Smith for the division of labor).