In the study of differential equations, there is a type of problem which is solved that involves changing a parameter mu and looking for when this change caused a bifurcation in the system of solutions to a differential equation. A bifurcation means a sudden change in the long-term behavior of a system associated with a change in the parameter. The takeaway from this sort of problem is that sometimes these bifurcations are very severe as a result of an infinitessimal change in an input parameter.

Because most anything in life can be described as a system of differential equations, I think we can take a vital lesson from their behavior that will give us tools to affect change in the future. If we think about making a model of events in our lives using Finite Element Methods, then certainly the boundary conditions that we input so that we can solve for future states must describe our environment. If we let the boundary conditions be the parameters mu, then we can imagine that by varying the set of mu we can achieve wildly different long-term behaviors in the states of the world as time goes on. For instance, maybe the parameter of who is president for the next four years causes wildly different outcomes depending on who is chosen, or maybe it doesn’t. If it does, then the system undergoes a bifurcation with respect to some critical value of this parameter (glossing over the discrete nature of things).

As anarchists, we want to find the bifurcation points. We want to find the actions that change just the right parameters so that the flow of the system is radically redirected toward the society we want to create. The moral of the story here is that sometimes it only takes an infinitessimal push in one direction to radically change the future forever. Sometimes adding epsilon to a parameter can cause the long-term behavior of the system to go from bounded to unbounded, FOR ALL EPSILON, NO MATTER HOW SMALL.

Sometimes a small push happens at just the right time, when the environment variables are just right, and something truly unexpected happens. Sometimes you don’t have to work yourself into the ground trying to change the world when you know you won’t even see the results yourself because you just figured a radical change requires a monumental input. Because sometimes it just doesn’t. Sometimes all it takes is showing up on January 20th with just enough spirit to push that system right over the edge of its most radical fucking bifurcation.

In a particular model, the long-term environmental quality X undergoes bifurcations when the parameter delta>.62. The parameter delta describes how quickly the producers can change their outputs.