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.
Interestingly, biologists have named the phases of the bacterial growth curve: lag phase, exponential phase, stationary phase, death phase. I suspect that having names for these phases helps people think more concretely. We could just say it’s a variant of logistic growth, and give some sort of equation for it. But that wouldn’t make it nearly as easy to talk or think about as naming the phases. Early in the pandemic, we could have been saying “we’re in the lag phase of the pandemic, but the exponential phase is coming.” Likewise, you’re worried we’re in the lag phase of inflation, and that the exponential phase is coming.
I wonder if we can just start talking like this. We know these trends are real, and perhaps the problem is that we talk about them as if they required an education in mathematics to understand. Instead, perhaps the bits of the graph just need some nice handy labels.
Your graph also illustrates perfectly why I find this an example of semistable equilibrium as explained in this article. It even looks like a cliff face, although it is inverted. There is a point at which the lag phase changes and becomes the exponential phase. As long as the correct action is taken before this point, the exponential phase can be avoided; e.g. take the petri dish out of the incubator and put bleach in it. This would be equivalent to the chicken player stopping his car before the cliff edge.
Yep! On the flip side, biologists know that it’s important to passage cells before they enter the death phase, which means splitting them into multiple lower-concentration plates. Otherwise, the cells can be irretrievably damaged by overcrowding.
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.
Interestingly, biologists have named the phases of the bacterial growth curve: lag phase, exponential phase, stationary phase, death phase. I suspect that having names for these phases helps people think more concretely. We could just say it’s a variant of logistic growth, and give some sort of equation for it. But that wouldn’t make it nearly as easy to talk or think about as naming the phases. Early in the pandemic, we could have been saying “we’re in the lag phase of the pandemic, but the exponential phase is coming.” Likewise, you’re worried we’re in the lag phase of inflation, and that the exponential phase is coming.
I wonder if we can just start talking like this. We know these trends are real, and perhaps the problem is that we talk about them as if they required an education in mathematics to understand. Instead, perhaps the bits of the graph just need some nice handy labels.
Your graph also illustrates perfectly why I find this an example of semistable equilibrium as explained in this article. It even looks like a cliff face, although it is inverted. There is a point at which the lag phase changes and becomes the exponential phase. As long as the correct action is taken before this point, the exponential phase can be avoided; e.g. take the petri dish out of the incubator and put bleach in it. This would be equivalent to the chicken player stopping his car before the cliff edge.
Yep! On the flip side, biologists know that it’s important to passage cells before they enter the death phase, which means splitting them into multiple lower-concentration plates. Otherwise, the cells can be irretrievably damaged by overcrowding.
A lesson for humans as the population continues to increase.
Welcome to LessWrong! Thanks for posting, these are interesting examples to consider.
Thank you for being so kind. I want to give 2 karma, but it won’t let me.
You can click and hold down for a strong upvote or downvote. The higher your karma score, the more weight your upvotes and downvotes will have.
Ah, maybe I am too new for more than one vote, because holding down doesn’t do it.