Coincidentally
The idea of two events happening on or around the same time is a surprisingly non-trivial notion, which was brought to mind in recent hours as the world celebrated the commencement of the year 2016. At first it seems that the whole world is in unison as the clock strikes midnight, but then you are constantly reminding by the continuous news segments that earlier time zones have already celebrated the “event”. Indeed, when I woke shortly after 6am this morning, friends of mine on another continent were still waiting for their turn to celebrate.
Of course, the celebrations may extend an hour or two either side of midnight so there is certainly a sense of communal celebration if one allows the continuity found in the overlaps between neighbouring time zones.
This brings me to the more formal notion of the temporal relationship of two events. For this exercise I will allow the definition of “event” to encompass two possible interpretations:
- An instantaneous event that occurs at a precise moment of time and has zero duration. (The “midnight” event that prompts us to shout “Happy New Year” is one such event.)
- An interval event that has a beginning and an end that comes after the beginning. (The party surrounding the midnight celebration, though in practice identifying the end may be somewhat difficult.)
It is clear that the midnight event in different timezones are unconnected, assuming one forgoes examination of the time betwixt. One might imagine these two events (the other person’s midnight happening before yours) as follows:
Or as seen by the person in the other time zone (which, I must point out, in terms of the relationship of two events is the same as the above, just described from a different perspective):
Whereas within the same time zone the striking of midnight in two houses would look like this:
The striking of midnight in a house, and the party surrounding it would be like this:
Some might choose to think of this as two distinct parties, the “End of Year Party” and the “New Year’s Party” as follows:
And…
Now comes the question of the relationship of someone else’s party in a different time zone to the striking of midnight in your own time zone. There are two obvious possibilities, the earlier and the later parties:
And…
If one party were to end when another party starts, then you have the following situation:
And very long parties are going to overlap:
The above overlapping party is an example of one where none of the extremes are equal (i.e. they neither start nor end at the same time). For completeness we should consider the other five possible overlaps:
And…
And…
And (a perspective shift)…
And finally…
This may all seem a little strange, but it’s exactly the kind of thinking that one has to do when contemplating the scheduling of concurrent processes, or any complex parallel system. (Only here it’s with parties.) As an exercise, consider the possible arrangements of three events!
Happy New Year.
Categorised as: LUE