Meta-commentary: I found this frame bizarre. That’s a good thing—I’ve never thought about anything quite like it before.
I feel like “semistable equilibrium” isn’t quite the right way to frame the frame, but the examples were good enough to make up for that.
Minor editorial note:
If you get stuck, look for:
Systems made of lots of similar parts which are all constantly in motion
Systems with a stable equilibrium only if you “zoom out” from the details
Systems for which your expectations are roughly constant sufficiently far into the future, even if the system itself is constantly in motion.
I think you probably meant to replace this bit with something else.
Finally: I had been thinking about offering a monetary reward for framing practicum posts which I find valuable. I hereby award this post $40. For AllAmericanBreakfast: message me a payment method to collect it. For everyone: this is not a commitment to do this for every framing post, but I will likely do this for framing posts which meet my highly subjective quality bar in the near future. I would have awarded $10 more if the post had a better-in-my-judgement name for the concept, along with a formalization which felt like a cleaner fit to the examples. I would have awarded $10-$20 less (but still nonzero) if the post had been worse in various other ways, but still generated interesting ideas when I did the exercise.
That’s very kind of you! Thanks also for pointing out the edit—fixed! Incidentally, this example is taken directly from my differential equations textbook, which describes asymptotically stable, unstable, and semistable equilibrium points.
You may already be familiar with these concepts if you’ve studied this subject. If not, an asymptotically stable equilibrium point is a point at which velocity is zero, and that nearby velocities on both sides of the point move us closer to the equilibrium point (they are attractive). This tracks with your “stable equilibrium” frame. Unstable equilibrium points have zero velocity at the point, but a velocity that moves us away from the point on both sides (they are repulsive). Because of this, objects are rarely found at unstable equilibrium points, since any disturbance from that point will cause repulsion from it. An example might be a coin standing on its edge.
A semistable equilibrium point is a place at which velocity is zero, and where velocity tends to move us closer to the point on one side (attraction) and away from it on the other side (repulsion).
Meta-commentary: I found this frame bizarre. That’s a good thing—I’ve never thought about anything quite like it before.
I feel like “semistable equilibrium” isn’t quite the right way to frame the frame, but the examples were good enough to make up for that.
Minor editorial note:
I think you probably meant to replace this bit with something else.
Finally: I had been thinking about offering a monetary reward for framing practicum posts which I find valuable. I hereby award this post $40. For AllAmericanBreakfast: message me a payment method to collect it. For everyone: this is not a commitment to do this for every framing post, but I will likely do this for framing posts which meet my highly subjective quality bar in the near future. I would have awarded $10 more if the post had a better-in-my-judgement name for the concept, along with a formalization which felt like a cleaner fit to the examples. I would have awarded $10-$20 less (but still nonzero) if the post had been worse in various other ways, but still generated interesting ideas when I did the exercise.
That’s very kind of you! Thanks also for pointing out the edit—fixed! Incidentally, this example is taken directly from my differential equations textbook, which describes asymptotically stable, unstable, and semistable equilibrium points.
You may already be familiar with these concepts if you’ve studied this subject. If not, an asymptotically stable equilibrium point is a point at which velocity is zero, and that nearby velocities on both sides of the point move us closer to the equilibrium point (they are attractive). This tracks with your “stable equilibrium” frame. Unstable equilibrium points have zero velocity at the point, but a velocity that moves us away from the point on both sides (they are repulsive). Because of this, objects are rarely found at unstable equilibrium points, since any disturbance from that point will cause repulsion from it. An example might be a coin standing on its edge.
A semistable equilibrium point is a place at which velocity is zero, and where velocity tends to move us closer to the point on one side (attraction) and away from it on the other side (repulsion).
This is where the name comes from.