I drop my toothbrush, and then try to pick it up. There’s a well known fallacy of breaking this up into a million steps like “first I have to move my hand forward a bit, and then I have to move it further even more, and then I have to grab the toothbrush, and then I have to lift it up, …” and concluding that the conjunction must be very unlikely given some mild error chance. Sometimes the counter is “the error chance is really low though”, but in this case, I in fact sometimes fail to grab my toothbrush (so it can’t be that low), or drop it, or etc.! The answer here is that there’s also this large disjunction—the specific story you told doesn’t actually have to hold, and at that granularity there’s a lot of different plans.
The reinterpration that seems slightly novel to me is: the successful sequence is a stable equilibrium. The ball doesn’t need to go down a bit then to the right then to the left then down …, actually for a large variety of things it could do it will tend to land in the center. Likewise with my fallen toothbrush
What matters in the long term is my threshold for giving up (fairly high unless I’m very tired, in which case I might actually sleep instead of brushing my teeth), whether I have some weird sudden muscle problems, whether the toothbrush breaks or is super dirty or is discovered by me to be any of those things, whether it falls far into the trash can (in which case I might prefer buying a new toothbrush over digging through it)
The cup on my table. The slightly novel bit here isn’t that it’s in a stable equilibrium (static friction preventing it from being buffeted around by the mild shaking of typing and the air currents), but rather that when I intentionally move the up that what I’m doing is steering the stable equilibrium around.
In the long term, you just need to ask where I want the cup right now (do I have a laptop in front of me? is the cafeteria closing soon? am i leaving soon for any other reason? am i going to refill it or take a drink from it?), since almost every likely change to the cup is due to me intentionally moving it.
...the max entropy distribution in thermodynamics, maybe? Suppose I’m an omnipotent but not omniscient God, and so I can create a box with an ideal gas but where the particles resemble the face of Jesus but with tiny uncertainty in their initial positions. After a while, my uncertainty will have turned into the max entropy distribution given the constraints of energy and particle number as all other info gets wiped out.
The point here is that, no matter what sort of special region of phase space that I put the box in, it’ll end up at the max entropy one (well, my belief distribution about it will). Looks like a stable equilibrium! and that’s a novel (and weird) interpretation to me.
To change this: add or remove constraints to the system that are preserved, like energy or particle number.
I drop my toothbrush, and then try to pick it up. There’s a well known fallacy of breaking this up into a million steps like “first I have to move my hand forward a bit, and then I have to move it further even more, and then I have to grab the toothbrush, and then I have to lift it up, …” and concluding that the conjunction must be very unlikely given some mild error chance. Sometimes the counter is “the error chance is really low though”, but in this case, I in fact sometimes fail to grab my toothbrush (so it can’t be that low), or drop it, or etc.! The answer here is that there’s also this large disjunction—the specific story you told doesn’t actually have to hold, and at that granularity there’s a lot of different plans.
The reinterpration that seems slightly novel to me is: the successful sequence is a stable equilibrium. The ball doesn’t need to go down a bit then to the right then to the left then down …, actually for a large variety of things it could do it will tend to land in the center. Likewise with my fallen toothbrush
What matters in the long term is my threshold for giving up (fairly high unless I’m very tired, in which case I might actually sleep instead of brushing my teeth), whether I have some weird sudden muscle problems, whether the toothbrush breaks or is super dirty or is discovered by me to be any of those things, whether it falls far into the trash can (in which case I might prefer buying a new toothbrush over digging through it)
The cup on my table. The slightly novel bit here isn’t that it’s in a stable equilibrium (static friction preventing it from being buffeted around by the mild shaking of typing and the air currents), but rather that when I intentionally move the up that what I’m doing is steering the stable equilibrium around.
In the long term, you just need to ask where I want the cup right now (do I have a laptop in front of me? is the cafeteria closing soon? am i leaving soon for any other reason? am i going to refill it or take a drink from it?), since almost every likely change to the cup is due to me intentionally moving it.
...the max entropy distribution in thermodynamics, maybe? Suppose I’m an omnipotent but not omniscient God, and so I can create a box with an ideal gas but where the particles resemble the face of Jesus but with tiny uncertainty in their initial positions. After a while, my uncertainty will have turned into the max entropy distribution given the constraints of energy and particle number as all other info gets wiped out.
The point here is that, no matter what sort of special region of phase space that I put the box in, it’ll end up at the max entropy one (well, my belief distribution about it will). Looks like a stable equilibrium! and that’s a novel (and weird) interpretation to me.
To change this: add or remove constraints to the system that are preserved, like energy or particle number.