April 5, 2020

how to imagine time zones

Time zone conversion can be tricky, partly because specific zones depend on local rules, and partly because the mathematical intuition can be tricky to grasp. Here’s a simple conceptualization to address the later problem.

Greenwich Mean Time (GMT) is the midpoint on an open interval from $(-12, 12)$. The International Date Line is the open boundary when moving from East to West towards $-12$ or West to East towards $+12$. Since there’s two directions you can move, you can compare timezones using just two of these open intervals like a slide rule:

-12 -8 -4 0 +4 +8 +12
-12 -8 -4 0 +4 +8 +12

The table above compares GMT to GMT; noon in Greenwhich, England occurs at 0 hours GMT. Move 12 timezones westward to advance a day (the sun moves East to West); move 12 timezones eastward to suspend a day (like that ridiculous scene in Superman).

Let’s say you live in Denver, Colorado. Noon occurs at GMT/-6. You want to schedule time aligned with Berlin, Germany. Noon occurs there at GMT/+2. Slide the two intervals to align at noon:

+6 +2 -10 -6 -2 +2 +6
-10 -6 -2 +2 +6 +10 -2

In other words, if you know the offset to noon GMT in a timezone, you can adjust the timetable to identify overlaps in the desired interval. When you switch from positive to negative, you add a day, and when you switch from negative to positive, you subtract a day. You need only worry about adding/subtracting one day, as the inverval spans only 24 hours, which is exactly one day.

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