A tiny case of this I wrote about long ago: https://markxu.com/stop-asking-people-to-maximize

It's important to distinguish between:

• the strategy of "copy P2's strategy" is a good strategy
• because P2 had a good strategy, there exists a good strategy for P1

Strategy stealing assumption isn't saying that copying strategies is a good strategy, it's saying the possibility of copying means that there exists a strategy P1 can take that is just a good as P2.

You could instead ask whether or not the observer could predict the location of a single particle p0, perhaps stipulating that p0 isn't the particle that's randomly perturbed.

My guess is that a random 1 angstrom perturbation is enough so that p0's location after 20s is ~uniform. This question seems easier to answer, and I wouldn't really be surprised if the answer is no?

Here's a really rough estimate: This says 10^{10} s^{-1} per collision, so 3s after start ~everything will have hit the randomly perturbed particle, and then there are 17 * 10^{10} more collisions, each of which add's ~1 angstrom of uncertainty to p0. 1 angstrom is 10^{-10}m, so the total uncertainty is on the order of 10m, which means it's probably uniform? This actually came out closer than I thought it would be, so now I'm less certain that it's uniform.

This is a slightly different question than the total # of particles on each side, but it becomes intuitively much harder to answer # of particles if you have to make your prediction via higher order effects, which will probably be smaller.

The bounty is still active. (I work at ARC)

Humans going about their business without regard for plants and animals has historically not been that great for a lot of them.

I think Luke told your mushroom story to me. Defs not a coincidence.

If you observe 2 pieces of evidence, you have to condition the 2nd on seeing the 1st to avoid double-counting evidence

A human given finite time to think also only performs O(1) computation, and thus cannot "solve computationally hard problems".