Edit: Lots of the responses were welcome, but none really gave me anything conclusive and I eventually lost interest in this problem. I have now released some of the responses I had below, and will try to get all the ones I was emailed online at some point. The experiment was to do with intuition regarding the “angel problem” which has been solved but have variants that have not. When this was published I was thinking about the ‘timebomb angel problem’ in 2D, and the below problem is the same problem in 1D. The keen reader will be able to find the solution online, so I won’t post it here and spoil the problem for other people wishing to try.
I have started having a few thoughts that have led me to propose a quick experiment which could be helpful in solving a problem I’ve been working on. If you (a mathematically inclined blog reader) have about 10 minutes free right now and are keen to try a nice problem, read on. Otherwise, stop reading and come back later when you have a little bit of time.
Basically I need you to try the following problem more-or-less immediately (no subconscious thinking time!) for ONLY 10-15 MINUTES and then send me a quick email (my @cam.ac.uk address is tl309) detailing your thoughts on the problem. You don’t have to have solved it. What I’m really interested in is your reaction to the problem and the heuristics going through your mind. How you *feel* after 10-15 minutes of work could be immensely useful to know, and if I get enough responses I’ll post the interesting ones in a later post explaining what I’m trying to do.
Problem: Imre got lost on the way to his office and has found himself wandering along the infinitely long corridor in the Centre for Mathematical Sciences. The floor is covered with large tiles such that the corridor is only one tile wide but there are infinitely many stretching in both directions. Imre’s arch-enemy (whom we shall denote Ermi) has rigged up the corridor with teleporters so that if Imre is on certain tiles at certain times he is transported to a faraway nightmarish universe where the axiom of choice is false.
Imre takes one second to move one tile in either direction (though he could just pause and wave his arms for a second instead). Owing to power limitations (and his unsophisticated doom teleporter software), each second Ermi can program just a single teleporter to activate for just one second at some specified point in the future (so he *could* keep one teleporter activated for the entire time, or could activate lots of teleporters simultaneously but only for a very short period of time at a specified point quite far away in the future). There is a time delay, so Ermi can’t turn any teleporters on instantly (so Imre will always get a chance to move out of the way if a teleporter is activated where he is standing). Is it possible for Ermi to trap Imre, or can Imre evade him forever (if whenever Ermi programs a teleporter Imre knows about it)?
If you’ve seen and thought about an equivalent problem before, please don’t tell anyone else for the time being (and don’t bother sending me an email). Otherwise, enjoy, and I’ll be interested in hearing your thoughts (obviously, once you’ve sent me the email, feel free to try solving the problem ;)).
Edit: It would actually be ok if you just posted a “comment” underneath this thread instead of emailing. I was worried about people reading what other people had written, but since I can wait until I publish the comments publically this isn’t an issue.