Framing Practicum: Semistable Equilibrium

1. Meteors. This one isn’t exactly right since the equilibrium point either happens or gets skipped over entirely but nonetheless...imagine a meteoroid flying through the solar system towards Earth. If it crosses into the atmosphere, it becomes a meteor. And then depending on the composition of the meteor and its size, it may burn up in the atmosphere or it may make it to the surface (at that point, it’s a meteorite).
   
   In this case, you can think of the “zone of attraction” as the entire journey to the atmosphere. Once it hits the atmosphere, it quickly is decelerated by air resistance. And if the meteor burns up, then its velocity “stabilizes” at 0. So “burned up in the atmosphere” is sort of like an equilibrium point. If it doesn’t burn up (e.g. because it’s larger), then it plummets to the surface. In this case, the other side of the equilibrium point is not really repulsive. Rather, it’s just a continuation of the pre-equilibrium point. And then when it hits the Earth the entire system is changed.
    
2. Nuclear Weapon Acquisition. You could argue the initial development of nuclear weapons triggered an “attractive force” for major world powers to stock up on warheads (e.g. an arms race). Eventually, the development and acquisition slowed down and even regressed (as in nuclear disarmament). But supplies were not totally eliminated. You could say an equilibrium point has been reached. The reasoning continues for the “repulsive force”: the equilibrium could be broken if any country were to deploy nuclear attacks on another. It would (probably?) lead to retaliatory strikes and the acquisition of warheads may accelerate drastically. (related: apparently the semistability of nuclear deterrence has a name! stability–instability paradox)
    
3. My Steam library on a weekend night. On weekend nights when I have nothing going on, I am attracted to my steam library. I often arrive at an equilibrium where I will sift through my games but don’t actually play anything. Then, I either decide against playing games, at which point I usually back away from the equilibrium point for the night. Or some “external force” nudges me into playing, in which case +4 hours of my night are gone.
   
   Unsurprisingly, friends-wanting-to-play-something-as-a-group is almost always enough to convince me to go past the point of no return. Similarly, I am also likely to break equilibrium if I am playing through a recently acquired game.

Again, I don’t think my first example is a true semistable equilibrium (neither the second example?) but maybe there’s something there. All in all, this was great. I just came across the Framing Practicum Sequences and love them! Thanks for the post AllAmericanBreakfast!

...now off to sift through some games :p

1. Impact on a slab, like a bullet hitting armor or a rock hitting a windshield. If the projectile is long and dense enough to puncture, then it goes through and just keeps going - possibly even accelerating more, if e.g. it's falling. But if the projectile isn't past that critical point, it collides and either bounces off or blasts a crater in the surface or slows to a stop or whatever.
2. When learning a subject, it often takes a lot of time to get to the point where it feels net-positive-value. Before that, each step is another point at which people "bounce off". But after that, people will just keep delving deeper and deeper.
3. Similarly, a business might need to invest a lot of effort/money in order to become profitable. Each step before profitability has some chance of the founders/investors giving up. But once past the point of profitability, they'll likely keep investing more and more.

One thing I notice in the latter two examples is that we don't necessarily know where the equilibrium point is. We could maybe try to track "how close we are" by looking at e.g. a trendline of a company's profitability, although we don't necessarily know how "expensive" the next few steps will be.

• War and Peace. Two rivals may sharply distinguish between threatening gestures and a clear attack. They can approach the point of no return many times, as a form of negotiation. But there is a threshold beyond which a fight or a war ensues: throwing the first punch, crossing the Rubicon, invading Poland.
• Flirtation and Breaking Up. Two people may approach the point of openly showing romantic interest in each other without crossing that threshold by giving a clear signal of their affection. Likewise, they may display signs of dissatisfaction with their relationship without explicitly showing that they are ready to break up with each other. Their attraction or animosity keep bringing them to the brink, but their hesitation about crossing the line holds them back as they approach it. There are gestures they can make which will cause an acceleration into romance or into social distance. But these moments "on the verge" are fleeting.
• Infection. Minor infections can sometimes be cleared up by the innate immune system without triggering an adaptive immune response. Beyond a certain point, immune signaling is sufficient to activate the beginnings of an adaptive response and trigger T cell proliferation.

 1. Drilling a hole in glass. I was at a class learning glass fusing (just for fun) and we each had to drill a hole in float glass. The drill is a vertical bit, about 3mm diameter, and coated with an abrasive. 8 of the 9 of us in the class followed the instructions as to the angle at which to hold the glass, and to cool it with water frequently. We all cut neat little holes. The 9th person was in a hurry, and at the moment the drill broke through the surface of his piece of glass, it caught and violently span out of control, shattering.

2. This idea of a threshold point reminds me of what happens with exponential growth. In the early stages of the Covid outbreak, our Government were blithely aiming for "herd immunity" - after all, the graphs showed a gradual rise in cases, so everything must be okay, right? It took some serious educating to get them to see the nature of exponential growth, and that a disaster was waiting to happen. Now they seem to be taking the same view with the threat of inflation. Any exponential growth starts off slow and steady, like semistable equilibrium, but reaches the point where it is out of control if there is no intervention.

3. When I was reading this article, the image of a set of traffic lights came into my mind. On one side, you have a red light, with traffic approaching slowly and carefully. On the other is a steadily moving stream of traffic taking its turn to move ahead. In the middle somewhere is a point of equilibrium, where traffic waiting to turn right (I am in the UK; it would be left most other places) is paused in the middle of the road, having passed the red light, but being held up by the oncoming traffic. If one of these vehicles fails to obey the rules of the road, all kinds of chaos and mayhem could occur, with vehicles and other objects being flung and damaged unpredictably.