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:

noon | ||||||
---|---|---|---|---|---|---|

-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:

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.