The International Date Line has bothered me for decades. Not because I have anything against international agreements and not because I’ve ever traveled across the Pacific. It’s just been very puzzling. Why is it a different day of the week on opposite sides of an imaginary line in the middle of the Pacific Ocean? Is it always one day to the west of the Date Line and another day to the east? Even though it’s, say, the middle of the afternoon? How can that be the place where it’s a different day in adjoining time zones, when it’s a new day in every time zone as soon as the clock strikes 12 midnight? How can there be two places in the world where it’s a new day?

The concept has never made any sense. Which is why it was a relief when I finally figured out the damn thing a few weeks ago. What I apparently needed all these years was a visual representation of the globe showing what happens to the day of the week as the Earth goes about its business. Something like this: 

(1) First off, it isn’t true that it’s always a different day of the week on opposite sides of the Date Line. There is one hour every day when it’s the same day of the week on both sides: when it’s between 11 p.m. and 12 midnight in New Zealand, it’s the same day of the week everywhere. That’s line (1) in the diagram. At 11 p.m. in New Zealand, when Monday is almost done, Monday is just beginning at Midway Island in the middle of the Pacific.

(2) Then, when the clock strikes 12 midnight in New Zealand, the next day of the week makes its first appearance in that single time zone. (That’s why Kiwis celebrate the New Year before the rest of us.)

(3) As the hours proceed, more time zones join the new day. By the time it’s 1 p.m. in New Zealand, it’s 10 a.m. in Beijing, 2 a.m. in London and striking midnight out in the Atlantic. The new day is moving westward around the world as each hour passes. But notice that it’s still the previous day on Midway, even though New Zealand and Midway Island are in adjoining time zones and it’s early afternoon in both places. It’s strange but true.

(4) Eventually, the new day arrives in America. In effect, the new day is growing and the old day is shrinking.

(5) The new day makes its way across the Pacific, engulfing Hawaii but leaving Midway at yesterday.

(6) Until finally, it’s the same day of the week all over the world again (for an hour anyway).

So it isn’t the case that it’s always two different days on opposite sides of the Date Line. And aside from one hour each day, there are always two boundaries between one day and the next: at the Date Line and also where the clock is striking 12 midnight.

One last question: Why do we need an International Date Line? I think it’s to avoid a contradiction. Let’s assume it’s 1 p.m. in New Zealand and 2 p.m. on Midway Island, as shown in line (3) above, but there is no Date Line. So we’ll also assume it’s Sunday in both places.

Then look west toward Africa and Europe. When it’s 1 p.m. in New Zealand, it would be Sunday at 12 midnight in the Atlantic. That means, of course, that it would still be Saturday night a bit further west in New York City.

But then look east from New Zealand toward North and South America. If it’s 1 p.m. Sunday in New Zealand, it’s Sunday night in California and early Monday morning in New York.

However, it can’t be both Saturday night and Monday morning in New York (think of the confusion). That’s why we need an International Date Line. A mathematician could probably explain it in technical terms. In practical terms, the Date Line helps make sure there’s a definite answer to the question: What’s today?