Framing Practicum: Semistable Equilibrium
Thanks to John Wentworth for conceiving and executing the concept of a framing practicum, as well as much of the format and language of this post!
This is a framing practicum post. We’ll talk about what a semistable equilibrium is, how to recognize semistable equilibria in the wild, and what questions to ask when you find it. Then, we’ll have a challenge to apply the idea.
Today’s challenge: come up with 3 examples of semistable equilibria which do not resemble any you’ve seen before. They don’t need to be good, they don’t need to be useful, they just need to be novel (to you).
Expected time: ~15-30 minutes at most, including the Bonus Exercise.
What’s Semistable Equilibrium?
In Rebel Without a Cause, Jim Stark and Buzz Gunderson are racing their cars at top speed toward a cliff, with the gas pedal strapped down. The first to jump out of their car is chicken. Buzz’s leather jacket gets caught on the door handle. He’s unable to jump free, and plunges over the cliff to his death.
The cliff is a semistable equilibrium. The idea of the “chickie run” is that the cliff causes the racers to decelerate, so that their velocity approaches zero as they near the cliff’s edge. That’s how it works out for Jim. On the other side of the cliff, however, Buzz’s velocity increases again as he hurtles toward the ground.
In general, a semistable equilibrium will approach an equilibrium point if it starts on one side, but will move away from the equilibrium point if it starts on the other side.
What To Look For
A semistable equilibrium needs a threshold that attracts and slows things down if approached from one side, but repels or launches things away if they’re on the other side. If there’s a point “point of no return,” that may be suggestive of a semistable equilibrium. There’s a zone in which disturbances lead to a return to rest, and a second zone just beyond leading to ongoing activity. It’s possible to have multiple equilibria in the system. All that’s required is that there is a point that attracts things from one zone, but repels things in another adjacent zone.
Whether or not it is common to find the system at the equilibrium point will heavily depend on the direction and relative magnitude of disturbing forces.
Useful Questions To Ask
Unlike with a stable equilibrium, the effect of nudges in a semistable equilibrium depend heavily on how close we are to the equilibrium point. If we’re deep into the “zone of attraction” to the equilibrium point, nudges won’t have much of an effect. But if we’re near or at the equilibrium point, a small nudge could easily move us into the “zone of repulsion,” leading to long-term instability in the system.
What happens if we change the equilibrium point? What are the disturbing forces in the system, and do they differ depending on where we are located relative to the equilibrium point? Can these disturbances “rescue us” from the zone of repulsion by bumping us back to the equilibrium point or into the zone of attraction? Does the zone of repulsion move us rapidly away from the equilibrium point, or is it a slower movement? How strong are the attractive and repulsive forces relative to any random disturbances in the system?
Come up with 3 examples of semistable equilibrium which do not resemble any you’ve seen before. They don’t need to be good, they don’t need to be useful, they just need to be novel (to you).
Any answer must include at least 3 to count, and they must be novel to you. That’s the challenge. We’re here to challenge ourselves, not just review examples we already know.
However, they don’t have to be very good answers or even correct answers. Posting wrong things on the internet is scary, but a very fast way to learn, and I will enforce a high bar for kindness in response-comments. I will personally default to upvoting every complete answer, even if parts of it are wrong, and I encourage others to do the same.
Post your answers inside of spoiler tags. (How do I do that?)
Celebrate others’ answers. This is really important, especially for tougher questions. Sharing exercises in public is a scary experience. I don’t want people to leave this having back-chained the experience “If I go outside my comfort zone, people will look down on me”. So be generous with those upvotes. I certainly will be.
If you comment on someone else’s answers, focus on making exciting, novel ideas work — instead of tearing apart worse ideas. Yes, And is encouraged.
I will remove comments which I deem insufficiently kind, even if I believe they are valuable comments. I want people to feel encouraged to try and fail here, and that means enforcing nicer norms than usual.
If you get stuck, look for:
Systems with a stopping or pause point, that is also a point of no return.
Systems that show a combination of attraction and repulsion in a clearly directional manner.
Systems that tend to slow us down to a stop as we approach a certain area, but move us faster if we go beyond it.
Bonus Exercise: for each of your three examples from the challenge, what forces might allow you to predict, measure or control the approach or repulsion from the equilibrium point? Is there some intervention or disturbance that might push us in one direction or the other if we are near the equilibrium point?