All of Thoroughly Typed's Comments + Replies

I really like this concept!

Reminds me a bit of Scott's Ars Longa, Vita Brevis.

  1. Cars in a parking lot: they enter an leave mostly independently. The turnover time for residential parking might be a day or two. For a shopping center it is a few hours.
  2. Bugs in software: they get introduced and then fixed somewhat independently. The turnover time is on the order of weeks to months, maybe days if the project is very active, or even years for very subtle bugs.
  3. Water molecules in a lake: "new" ones flow in, get mixed up with the existing ones, and roughly independently flow out again. The turnover time depends on the influx/outflux and volume
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  1. Stable equilibrium: The surface of a pond when I throw something in. I might be interested in the overall water level, which slowly changes over days and weeks. At these timescales the surface is always in equilibrium. (Equilibrates quickly re what I'm interested in)
  2. Bistability: The ruling party in a democracy. Mostly stable over a monthly to yearly timescale. I need to worry about who to vote for once every few years, not every day. (Equilibrates quickly re what I'm interested in)
  3. Dynamic equilibrium: The amount of train delays per day in a city. If I'm in
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Good examples. One theme these highlight: we intuitively use timescale separation all the time in our day-to-day lives.
  1. The demand for toilet paper. On a short-term timescale there'll be random peaks and troughs (or not so random ones due to people expecting a lockdown). But in the medium-term it'll be constant, because of each person only needing a fairly constant amount of toilet paper. Although in the long-term there'll be changes again due to a growing or shrinking population.
  2. The amount of train delays per day in a city. Some days have more, e.g. because of some big event or a random accident, while other days have fewer. But on average over weeks or months it is roughl
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Lots of great economic examples here. #2 in particular makes some great points about incentives inducing an equilibrium, in ways that a lot of overly-simple economic models wouldn't capture very well.

I really like the chess example. Anything continuous that gets discretized is similar. Like the color of a pixel in a photo, or whether you have crossed the finish line in a race.

  1. A seesaw on a playground. Either side will come back down again if it's perturbed a little (given it's reasonably well oiled etc).

    People sitting on it and literally kicking with their feet is enough to kick it into a different state. Random noise due to wind is not strong enough, except maybe in a heavy storm.
  2. The handle of a window (usually). Pointing in one direction when closed and another when open. It will stay in either position unless explicitly moved (which makes it different from a door handle).

    The activation energy required to kick it depends on w
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#3 is definitely a useful frame, probably lots of insights to be pumped from that one.
  1. The even surface of a pond. If I throw in a stone it'll ripple for a while, but the additional activity will dissipate again.
  2. The number of tabs I have open in my browser. If it's very few I have no problem opening and keeping new ones. If it's too many, titles become hard to read etc. and I feel reluctant to keep open additional ones and tend to close a bunch of them at once.
  3. The amount of social interaction I get. Too little and I feel lonely and reach out to people. Too much and I feel overwhelmed and keep to myself for a while.
I sympathize with #2, although for me the "titles become hard to read" issue is a lost cause - my equilibrium is way past that.

In economics (and I’m sure in many other fields - I’m just writing about what I know here), something like this is supposedly done in the “robustness checks” section of a paper.

Machine learning sometimes has ablation studies, where you remove various components of your system and rerun everything. To figure out whether the fancy new layer you added actually contributes to the overall performance.