Societies change, or evolve. Why that is, noone knows. Some physicists (such as Einstein and Julian Barbour) maintain that time is an illusion, so there really is no evolution. What has been has always been and will always be, and same for what is in the future.
Even while change may be an illusion, it is conveniant to imagine it occurs. Babies grow up, the universe expands, species of animals change into other species, and societies undergo political and industrial revolutions, and technological change.
This is typically viewed as a ‘nonlinear’ process—meaning it doesn’t occur in a straight line. A line will have ‘breaks’, ‘curves’, and ‘jumps’. Where the straight line changes is called a ‘bifurcation point’ in math, or a ‘phase transition’ in physics (such as when ice melts into water).
In a 1900’s book ‘Decline of the West’ Oswald Spengler suggested that western civilization evolves through 4 major bifurcations (or changes) into new form. Each form is characterized by a particular kind of mathematics, from Greek geometry of platonic solids, the algebra of Descartes, the calculus of Newton and Gauss, into the current forms of stochastic processes and computational math. Similar histories look at evolution of languages and technologies.
Socioeconomically one sees movements like communism, fascism, capitalism and ‘sustainable economics’. In the world of ‘big data’ it may be possible to predict ‘bifurcations’ and ‘singularities’ from nonlinear dynamics. (Singularities are bifurcation points or ‘singularities’). Is the world evolving into eco-collapse, WW3, and authoritarianism, or into ecological stability, peace and some form of democracy? In what phase will the world be in 100 years from now? In liquid (with seas melted from global warming), in a crystal (from a new ice age), a gas (from nuclear annihilation) or a new state (robot based life, using quasicrystals)?