it’s late and I’ve been studying math all day and just thought of this after seeing a post on how the laws on fixed points in time seem to have gone out the window on Doctor Who
Okay so I’m taking a class on Nonlinear Dynamics and chaos which sounds a lot fancier than it probably is but
Basically motion according to an equation or set of equations can be analyzed as a graph of its postion vs velocity. This is called a phase plane, and can either look like a bunch of arrows or as lines with arrows on them. If you have the phase plane you can predict the motion of an object given some initial starting point on the graph. Each point on the graph has an arrow telling you where it goes next and from the next point it’ll follow the next arrow until some path is traced out.
Anyway getting back to Doctor Who, there are points in these graphs called fixed points. Fix points can be stable or unstable. And for certain equations if you vary some parameter the stability or the existence of these fixed points can change.
So let’s think of time as one of these phase planes. You’ve got a fixed point in time which guarantees the stability of the time around it. Then we have a parameter, let’s call it M. If M is altered past a certain point, there is a bifurcation, a change in the topology of the graph - the fixed point could either change stability, disturbing time, or it could disappear entirely - removing the necessity of the fixed point.
I suppose if we were to apply it to Journey to the Center of the TARDIS, at first it was a weakly stable point in time, then shenanigans happened and the TARDIS started leaking time, so things became very unstable, and the parameter was the Doctor, who then altered time enough to removing the fixed point entirely - hence no memories.
So there are key, fixed points in time but as we’ve seen with the Doctor, these can change or disappear. Also I doubt time would follow the simplified 2 dimensional phase plane and it’s more likely to have the chaotic features of an n dimensional problem. But the principles should still be there.