On the other hand, in economy on some planes I just literally don't fit in a forward direction because of femur length and cycling muscles, I don't fit in a sideways direction either because of broad shoulders and arm muscles, and I don't comfortably fit vertically on some planes with fixed-position headrests which push into the middle of my shoulder blades and have me hunched the whole flight.

I'm also not _that_ big. I'm 6'2" and have lived my life moderately actively. That's it. I'm biased, but I believe economy should be designed so that I can fit too.

If you agree with that premise, that'd leave plenty of space for most 250lb people too, and there'd be no reason to exclude them.

Recap: 1NN says that given a query Q you choose any pair (X,Y) from your learned "model" (a finite set of (X,Y) pairs) M minimizing |Q-X|. Your output is Y.

The following kind of argument works for linear interpolation too (you can even view 1NN as 1-point interpolation), but it's ever so slightly messier since definitions vary a fair bit, you potentially need to talk about the existence of >1 discrete "nearest" or "enclosing" set of neighbors, and proving that you can get away with fewer points than 1NN or have lower error than 1NN is itself also messier.

Pick your favorite compact-domain, continuous function embedded in some Euclidean space. For any target error you'd like to hit, the uniform continuity of that function guarantees that if your samples cover the domain well enough (no point in the domain is greater than some fixed distance, needing smaller distances for lower errors, from some point in your model) then the maximum error from a 1NN strategy is bounded by the associated error given by uniform continuity (which, again, you can make as small as you'd like by increasing the sampling resolution). The compact domain means you can physically achieve those error bounds with finite sample sizes.

For a simple example, imagine fitting more and more, smaller and smaller, line segments to y=x^2 on [-1,1].

So...T seconds have elapsed since your last frame, and you have a new data point you'd like to incorporate into your EMA (and, for this problem, that data point is T itself). You keep e^-(bT) of the old data, 1 minus that of the new data, and you're done. Alpha is indeed 1-e^-(b * cur_spf) for some constant b, just like the AI said.

Which b do you choose though? I usually prefer to think of it in terms of half lives. Let H be your desired half life, and set 1-e^-(bH) equal to 1/2. You get b=log(2)/H. That's similar to the AI answer, but it rescales window_secs into a parameter you can actually start to reason about. The AI answer gives you a 1/e life instead, which is a less comfortable constant to mentally process.

That answer also naturally generalizes to other "time" axes or denominators. Suppose you want to EMA using discrete events rather than wall-clock time. Replace T in your dynamic alpha with the discrete count of events you haven't updated the EMA with yet (e.g., if something happens every time tick you would usually take T=1, but you can increase that based on a few skipped frames or whatever if you'd like).

As a fun fact, you can tailor this sort of stateless solution to have almost any decay property you'd like. Start with your favorite ODE satisfying a few properties, and this equation falls out as the step a discrete solver would take to approximate the ODE.