Interesting, but I’m neither sure that plastic rulers work that way (as opposed to bending under any force, just imperceptibly for tiny forces, noticeably for greater, and breaking when bent too much) nor that the analogy is close enough to learn anything about the comparison.
Thank you for the reply. I am using the ruler as an informal way of introducing a Pitchfork Bifurcation—see [3]. Although the specific analogy to a ruler may appear tenuous, my article merely attempts to draw links between the underlying dynamics, in which a stable point (with symmetries) splits into two stable branches protruding from a critical point. This setup is used to study a wide variety of physical and biological phenomena—see [Catastrophe Theory and its Applications, Poston and Stewart, 1978].
Interesting, but I’m neither sure that plastic rulers work that way (as opposed to bending under any force, just imperceptibly for tiny forces, noticeably for greater, and breaking when bent too much) nor that the analogy is close enough to learn anything about the comparison.
Thank you for the reply. I am using the ruler as an informal way of introducing a Pitchfork Bifurcation—see [3]. Although the specific analogy to a ruler may appear tenuous, my article merely attempts to draw links between the underlying dynamics, in which a stable point (with symmetries) splits into two stable branches protruding from a critical point. This setup is used to study a wide variety of physical and biological phenomena—see [Catastrophe Theory and its Applications, Poston and Stewart, 1978].