Politics these days seem based more on feelz than on thoughts. Now that the shouting is over -- Biden won, so there are no mobs raging in the street -- and the only sound is the high-pitched whine of a well-known Narcissist. TOF thought to take a moment to review the awful simple-mndedness of standard political thought; to wit, the Left-Right spectrum.
Catastrophe Theory was devised by topologist Rene Thom to model situations where stable behavior suddenly flips to chaotic behavior (and vice versa). These surfaces have been used to model such diverse phenomena as the collapse of nations, the buckling of a beam, the binging of anorexia, the flight/fight of animals, boiling of liquids, et al. According to his Fundamental Theorem, there are seven elementary catastrophe surfaces, classified by the number of independent variables and the number of dependent variables. The behavior of a system governed by a potential function converges to an equilibrium surface, the manifold dM. The bends of folds of this manifold describe the varied behaviors of the system.
Back in the 70s, E. C. Zeeman applied the cusp model to political ideologies. The two parameters were A economic (opportunity versus equality) and B political (the rights of the individuals versus the rights of the group). The state space was a “cloud of points” representing the opinions of the individuals in the society. (These are measurable, at least in theory, by opinion polling.) The cloud was embedded topologically in a one-dimensional space, Y, which turned out to be the traditional left-to-right political spectrum. Zeeman‘s catastrophe surface shows why this simple line really has a complex “anatomy”.
An authoritarian left regime that moves toward economic opportunity without opening up politically is liable to snap suddenly to an authoritarian right regime. But if it moves first toward political freedom, it can transition gradually to an open economy. As a society moves smoothly around the parameter space (AxB at bottom) its equlibrium state moves about on the manifold above. For each position in parameter space there is a single unique state on the manifold... Until the society enters the bifurcation set (triangular region) where there are two equilibrium states. Inertia keeps it on the original sheet until it exits the bifurcation set on the opposite side. The original equilibrium vanishes and, governed by the potential function, snaps rapidly to the other equilibrium.
Projecting the surface dM onto the AY and BY planes reveals why dictatorships of the left and the right resemble each other so closely, and why right-wing populists often sound like left-wingers. It also shows why some social changes must be revolutionary; and why one-party states frequently develop left and right wings within the Party.
In 2016, both "tea party" activists and "occupy movement" activists made the same diagnosis of America's ills: viz., the government was controlled by "oligarchs." However, they differed in their solutions. The one wanted to give the government more power (to be wielded, one supposes, by those self-same oligarchs), while the other wanted to elect a junior varsity oligarch.