First off let me just say I’m no real mathematician, but am fairly familiar with notation etc., this is mostly just a curiosity/thing I noticed, and so a layman’s explanation of any potential answer would also be appreciated. (And I apologise in advance if this isn’t really in the scope of this SE - I would also welcome edits for the right tags!).
Anyway, to the question at hand:
I was sitting in traffic the other day, watching the indicators of several cars. They all have slightly different periods between flashes, and every now and again, they will synchronise (or at least appear to to the resolving power in time of the eye). This got me to thinking along the following lines:
- Given any 2 arbitrary periodic sequences (obviously with different periods), will they always synchronise at some point? Can it be proven in general that this is true or false?
- Does this still hold for more than 2 sequences?
- Are there arbitrary sequences that can be chosen that would never coincide with one another, even once?
Are there already proofs for all of this?
Just as a last remark, I assume this would essentially describe the same phenomenon observed in this well known physics ‘toy’.