Recent events have piqued my interest (in a very roundabout way) in something that I’ve never fully understood. To wit, what is the International Date Line and why do we need one?

The Basics

Here’s what I already knew about the International Date Line (hereafter, IDL). It is the place on the Earth where a day “begins”. It is at (mostly, disregarding political variations) 180 degrees longitude. That’s exactly half way around the world from the Prime Meridian. Crossing west across it adds 24 hours to the time and crossing east across it subtracts 24 hours. Say you were on a boat and straddled the IDL at 1pm, May 1. Well, the east side of your body is at 1pm on May 1, but the west side of your body is at 1pm on May 2 — a full day later.

This seems so silly and arbitrary. Why have an IDL at all?

The Rolling Date Line

We start out by noting that while the IDL is an artificial and arbitrary construct, there is a physical rolling date line. This is wherever on the world it is currently midnight. That’s the point where the day is “naturally” changing from one date to another. If I’m in the Mountain Timezone (MST) at 11pm, then the natural rolling date line is in Central since it’s midnight there and, therefore, one day later.

At first glance, it seems like this should be enough. Once it hits midnight in a time zone, then we can increase our date counter and that’s that. Why do we need the IDL?

The Problem: It’s Always “Today”

Let’s say we don’t have an IDL, though, and only have the natural midnight date line. Let’s further say that it’s midnight (12am) on Jan 1 in MST. That means that it’s 11pm in PST and 10pm in AKDT — all still in Dec 31. On the other side, it’s 1am in CST and 2am in EST — all already in Jan 1. That makes sense.

But let’s start calculating the time and date in each of the time zones around the world (ignoring political changes). There are 24 natural time zones, each one hour behind the time zone to the east of it and one hour ahead of the time zone to the west of it. So if it’s 12am, Jan 1 in MST, then we go back to Dec 31 by traveling west, subtracting 1 from each time zone as we go. This gives us 11pm PST, 10pm AKDT, 9pm HADT, and so on. Exactly half way around the world in JADT (Java time zone), it’s 12pm (noon) there on Dec 31. We keep traveling west, subtracting an hour each time until we swing around to EST. If we did our math right, it’s 2am there and 1am in CST. That checks out. But what day is it? Dec 31.

Eh? That’s not possible. We know that it was already midnight in CST and EST and so if it’s Jan 1 in MST, then it has to be Jan 1 in CST and EST. But think back through our around the world counting. We started out at 11pm Dec 31 and counted down… but at what point did it stop being Dec 31? The answer is that it didn’t. In this scenario, if you count time going west, then it’s always going to be Dec 31 across the globe.

But what if we calculate the time and date going east instead of west? We do so by adding one hour for each time zone. So 12am, Jan 1 in MST means 1am Jan 1 in CST, and 2am in EST, and so on. We keep adding until we get roughly half way around the world where it is 11am MDT and 12pm JADT. It’s still Jan 1 since we never passed midnight. We keep adding until we get to 9pm HADT, 10pm AKDT, and 11pm PST. Again, the time checks out. But what date is it in PST? It’s already Jan 1!

Like before, that’s not possible. PST never passed midnight so it’s impossible to be Jan 1. However, in circumnavigating the globe, we never passed midnight either and so our date never changed. It has to be Jan 1. In fact, if we always count going west, then it’ll always be Jan 1 forever.

See the problem? If we only have a rolling date line, then the date can never change.

Math vs the Real World

“But wait,” you say, “in the real world, we know that days keep advancing after midnight and if counting time zones don’t show that, then the math is simply wrong.” Indeed, if you keep a counter representing the day and increase it after each midnight, then you have your own local proof that the day is advancing. That is, if your counter was at 1 one day, then it’ll be 2 at midnight and 3 the next midnight and so on. The date is definitely advancing. So what’s up with this “always the same day” assertion?

Let’s work through this. Say there is a time keeper in each time zone, and each has a local counter that tells what day it is. It’s midnight in MST and so my counter is set to 2. What is it set to in PST? Well, since it’s not yet midnight there, it’ll still be set to 1. That’s true of AKDT and HADT and let’s keep going around the globe. When does the counter stop being 1 for each time zone? In fact, if we polled each time keeper around the world, then each will say that their counter is set to 1. But no they won’t! That’s physically impossible! Even if we use the ‘counter’ method, we still run into the exact same problem as before. When does the date change?

The Solution: Reset Everything

Let’s take it one more step back. Just to make sure we’re all on the same page, we decide that the entire globe is now on Dec 31 just so there’s no confusion. Time doesn’t change since that’s a physical property of the sun. But the date is a man-made construct and we can arbitrarily say that it’s now Dec 31 everywhere.

Time keeps marching on, though, and it’s definitely turning to Jan 1 someplace on the globe. So we find out where it’s midnight and find out that it’s CST. We allow CST to be Jan 1. Now 23 of the world’s time zones are still in Dec 31, but CST is in Jan 1. An hour passes and it’s midnight in MST. It’s now Jan 1 in MST. One hour later and the PST counter is in Jan 1.

Let’s look back at CST. It is now 2am and still Jan 1. What time and date is EST, though? Well, the time is 3am… but the date is still Dec 31 since it hasn’t passed midnight since our reset.

That’s a critical observation! CST and EST are still only one hour apart, but CST is a full day ahead of EST. EST isn’t really one hour ahead of CST — it’s 23 hours behind.

We can see this clearly as time swings around the globe until it’s finally midnight in EST. Finally, EST can switch to Jan 1, just like CST. But it’s 12am in EST and 11pm in CST. If we use the 24-hour clock instead of AM/PM, then it’s 00:00 in EST and 23:00 in CST. If both are on Jan 1, then CST is 23 hours later than EST. And, indeed, one hour later, when it’s 12am in CST and 1am in EST, that means it’s Jan 2 in CST but still Jan 1 in EST.

International Date Line

What we just did there is make an arbitrary International Date Line right in CST. We arbitrarily said that “this is where the day changes”. And yes, it’s odd that if you’re standing in EST by the border with CST and it’s 3pm in EST, then you can see a few feet away that it’s 2pm in CST… but a full day head. But that’s the way it has to be for dates to work.

In the real world, when the time masters decided to do this, they arbitrarily put the IDL in the middle of the Pacific Ocean rather than in some populated area. Things could get complicated in a hurry if half of a city was a full day later than the other half of the city.

Postscript: How Long Does a Day Last?

There’s an interesting side note to all this. How long does a particular date last? The answer is 48 hours. Yes, the day itself is still 24 hours but the date persists somewhere in the world for a full 48 hours.

How? Well, let’s look at the point just to the west of the IDL. Jan 1 starts there when it’s still Dec 31 just to the east of the IDL. The western point goes through full day (12am, 1am, 2am, …. 10pm, 11pm) and so when it’s midnight again, we know that it has been Jan 1 for a full 24 hours. But it’s look back at the eastern half of the IDL. As Jan 1 was progressing in the west, it was still Dec 31 in the east. Now it’s finally midnight on the eastern point and so it’s finally Jan 1. It’s the beginning of the day, though, so it needs to go through its own fully 24 hour day. That means that it was Jan 1 for 24 hours on the western side of the IDL and Jan 1 for 24 hours on the eastern side. That’s our 48 hours.