This is a good question, and I sometimes do put too much time into answering questions on Math Stack exchange. Right now, though, I'm fairly happy with the time I put into this simulation.

First of all, there's the fact that I did this on a Friday evening, after I came home from work. (I spent about six hours on it, and maybe another hour or two on Saturday morning). There are probably more productive uses of my time, but it was fun, and the most likely alternative was probably something like "read reddit" as opposed to "do something productive". It's nice to have leisure-time activities that are at least marginally related to my career.

Speaking of which, here's a few reasons that this was helpful for me:

1. I got a little better at programming in Mathematica. I use Mathematica a lot for both my teaching and research, so it always helps to practice.

2. I learned about a whole field of physics called contact mechanics, which I otherwise wouldn't have been aware of. It's part of my job as a math professor to know about random things like this.

3. I got some experience with modeling in applied mechanics problems. This may be helpful for me in the future -- as a professor at Bard, I regularly have to supervise senior math majors who want to work on research-level problems. The next time a senior who's interested in applied mechanics wants a research problem, I'll have one available.

That's how it's helpful for me, but I suppose it's less clear that this was helpful for the rest of the world. I guess, at the very least, it certainly seems to have entertained a bunch of people, and maybe someone learned something about modeling or differential equations or physics.

Thanks for both the answer on SO/MS and your comment here. You definitely shed some light on what I was wondering about.

Yes, I have to say, I did not know there were generally accepted models of elastic collisions (i.e., the force/distance law used in the simulation).

I presume you know the story of Feynman and spinning plates [1]. Sense of play is important for productivity, sometimes it is more than just important, it becomes a necessity

[1] http://www.physics.ohio-state.edu/~kilcup/262/feynman.html

    The diagrams and the whole business that I got the Nobel
    Prize for came from that piddling around with the wobbling
    plate. -- Richard Feynman

For those whose day job is modelling pool breaks, this could be a time-saving tool.

Actually, for anyone whose work involves modeling physics and collisions in general.

The fact that it describes a phenomenon with which a great many people are familiar and at least casually interested is only one aspect of this. And there's a long history of useful discoveries and advances coming from gaming and gambling (going back to Blaise Pascal).

You need to stop and smell the billiard-ball-shaped roses, my friend. Not every pursuit needs be in the name of industry. Some people enjoy mathematical puzzles for their own sake.

Going to reply to my own post since I cannot edit it anymore to clarify.

First, I am not saying that this is strictly a waste of time. In fact, I do love learning from things like this.

Second, I am not saying we must always be working instead of stopping to try something different. I personally find switching focus very important and I think it's a great tool for a great many people. I find that when people learn something slightly outside of their field they suddenly are hit with a lot of new ideas they did not have before, so learning about random solutions to random problems can be a great way to spend your time.

What I was trying to ask (not assert) was how answers like this come to be. I am somewhat astonished that I can ask pretty much any question on any given subject and a subject matter expert somewhere in the world will then proceed to spend hours putting together a detailed essay or demonstration (or both) of the concepts involved. What I wanted to know is who are these experts, why are they giving their expertise away for Internet Points (tm) and is this detracting from their actual work.

My other question is whether it's possible that at some point the number of soft, open-ended questions on SO will reach a critical mass where most participants will flock to those rather than the specific and hard questions and detailed expert answers that SO became famous for. Clearly we are not there right now, but is it possible and is it going to happen?

"What I wanted to know is who are these experts, why are they giving their expertise away for Internet Points (tm) and is this detracting from their actual work."

While I don't know about this exact post, for most academics, such theoretical exercises are their work. 'Projects' like this are nice and small and contained. They also give you the opportunity to get 'real' questions from people who aren't as close to the material as you are, almost like 'customers', so if you use a question like this in a lecture, it's almost sure to capture the interest of students better than other textbook examples. While I don't teach many courses, I've used examples derived from hybrid 'real world' / theoretical questions as examples to explain our products.

That said, I've surely spend time on questions that will never pay themselves back in such a way. You never know up front which ones will, so it's like playing the VC game - you 'invest' in 10 questions, with the knowledge that 7 will be duds, 2 will break even and the last one will (hopefully) be a home run.

Stack overflow is clearly both an useful, time-saving tool and a "waste of time" (in the sense that it doesn't look directly productive). If you don't like these kind of questions, don't worry, there are plenty of useful questions and answers with a direct work-related application. The answers for your questions are not going to disappear just because there are another questions answered. You know that Stack Overflow has section on things like gaming and role-playing, right?

By the way, I'd have loved an example like this a year ago, when I had a physics subject where elastic and inelastic collisions were studied. I'm pretty sure I'm not the only one.

"Strange how much human progress and accomplishment comes from contemplation of the irrelevant." - Scott Kim