I suggest to close Bounding an analytic function on the closed unit disk as a duplicate of the more general math.stackexchange.com/q/94122/42969. I had chosen a wrong duplicate target first, therefore I cannot vote anymore.

[ SmokeDetector | MS ] Chinese character in title, mostly non-latin title (170): 关于一元线性回归误差方差的估计 by xiaoxiao on math.SE

@quid Oh I didn't know. However, it's true that there was too little effort shown in my opinion. There isn't even any collision (it's just two independently bouncing balls), so it isn't at all hard to start finding out what the trajectory would be like for each ball. Yet no effort to do so was shown.

[ SmokeDetector | MS ] Few unique characters in body (94): deleted........................ ✏️ by Katja on math.SE

@user21820 reasonable people can certainly disagree about the level of effort that should be shown in such a case. I personally think that the post was not careless, even if there was a glitch, and OP had said they are far away from this type of mathematics. I think that this is actually one of the more relevant use-cases for mathematically educated people of this site. Asking questions detached from their actual expertise. What they did do is try to formalize the problem.

Completely tangentially, the still present comment and the answer seem contradictory to me.

"There are some initial positions and velocities where that straight-line path stays away from grid points, but mostly they will collide."

" in 3D space. The balls collide if and only if those two lines meet at some point. How often do two lines in space intersect? "

The answer says the almost always collision. The comment reduces it to intersection of two lines in space, which almost never happens.

@quid Sure, that's why I clarified that it was my opinion. As for the nature of the deleted account, unfortunately we normal users can't see beyond the number of a deleted account... Unrelated, if a crank posts one good comment and then deletes their account, that comment can get upvoted highly. Heh...

@quid I can't make sense of that comment, and it seems to me that it is simply false under an ordinary interpretation of it. I didn't check the one answer, but the conclusion (almost always collides) sounds right to me.

@user21820 "unfortunately we normal users can't see beyond the number of a deleted account" Indeed, that's the primary reason why I commented. Otherwise I'd have left it to everyone to make up their mind about that account. (In retrospect I maybe should have just stayed out of it, but that account is a bit of a special case, eg, see math.stackexchange.com/a/3554518 for more typical activity)

I see.

@user21820 I think the argument is that if one does the tesselation, the line is the of all points reached by a ball. So the two lines are the places where the balls are at some point in time. But then they have to be there at the same time, so one adds a time coordinate.

@quid But that doesn't make sense. The actual position of a ball in time is the line mod the even-numbered walls and then reflected down to the original square.

@user21820 yes I agree. I just rephrased what I believe they meant to convey.

Ah okay. Lol I can't paraphrase sentences that make no sense to me heh.

Anyway, in case anyone is paying attention to this, it's different if one takes the difference between the velocities and then plots a line and then observes that is likely to pass near some grid intersection.

The answer seems good, yes. Intuitively they should meet (since they are actual balls or disks, and not just points). IIRC the trajectory of a single point is almost always dense.

That's in fact why I am of the opinion that too little effort was put in, because it is not my area either and yet I see less effort than the thoughts that went through my head. Anyway, it doesn't matter now given that other people disagree with my assessment.

@user21820 yes, as said at the start, I think that reasonable people can disagree about the merits of that question.

Yup. =)

This seems like it should be discarded math.stackexchange.com/q/3697136/29335

"Alas, Math.SE is being destroyed by puerile political battles. Users who strive to uphold site quality are having their actions grossly misinterpreted and used as the basis for unfounded suspensions. Ad hominem attacks on political opponents run rampant. Fair, unbiased moderation is rare nowadays, so divisiveness rules unity. This does not bode well for the future of the site." Oh boy.

@rschwieb Yeesh...