Today I won’t be teaching you a thing you actually will ever need to know: just a concept I find quite interesting, and that is the issue of tropical years versus calendar years. So buckle up because its time for a little bit of a lesson on both history *and* math. (And because large numbers are involved I’m going to write things numerically rather than spell out the words as I usually do. For your convenience.)

As I probably don’t have to explain, one year is not 365 days. In this instance, when I say “one year”, I mean the time it takes for the Earth to make one complete orbit around the sun (i.e. First day of spring to first day of spring). This doesn’t take 365 days: it takes about 365.2421891 days.

As a result of this, making a calendar turns out to be pretty tough. With a calendar that only contains 365 days, you’ll start being further and further behind, marking the first of spring days before it actually occurs. (1 day behind every 4 years, to be precise).

In 46 BCE, Julius Caesar normalized the calendar by adding the leap year rule, which I’m sure you’re familiar with. So every 4 years, we add an extra day, and this largely solved the problem. With a calendar year being 365.25 days, the first of spring will remain the first of spring for a long time. With this system, it’ll take 128 years to be 1 day ahead!

Except, hold on, 128 years isn’t actually very long. Longer than pretty much anyone has been alive, sure, but about 1500 years later, the Julius calendar was an entire 10 days ahead!

This introduced the Gregorian calendar, named after Pope Gregory XIII. What’s the difference between the Julius calendar and this one, you ask? Well, it’s largely the same, but it takes out 3 leap days every 4 centuries. Specifically, the rule is this. If the year is divisible by 4, there is a leap year. *Unless* the year is divisible by 100 (ex. 1800,1900), in which case you do *not* add a leap year. *Double unless* that year is *also* divisible by 400 (ex. 2000), where you *do* add a leap year. Basically, we have a leap year every 4 years unless its the dawn of a new century. In most cases.

As a result of this calendar being implemented, we had to shave off some days on the calendar. October 5th-14th of 1582 never happened in most countries. Except a few countries don’t like the Pope (England), so they didn’t adopt the Gregorian calendar until 1752. This meant that for England and its colonies, September 3-13th of 1752 never happened.

The Gregorian calendar is what we still use to this day. With the new rules, its so accurate, we will only be 1 day off after every 3,216 years. So, while you won’t get the leap day you may or may not expect in the year 2100, you can rest easy knowing that the first of spring by our standard *was* the first of spring so many years ago.

As it turns out, the rotation of the Earth and its orbit around the Sun (along with some small but measurable factors) make calendars pretty complicated. In the year 2000, we calculated the tropical year to be 365.2421897 days long. Only 10 years later, that same number was calculated to be 365.2421891! Pretty close, but still noticeably different. It’s why mathematicians haven’t solved this problem after so many millennia: the number we’re trying to hit is one that is in constant fluctuation.

In any case, here are the two videos where I got this information. The first video, by StandUpMaths, focuses primarily on the calendar issue, whereas the second, VSauce, talks about how time works in general. VSauce in particular I find extremely interesting, and I’d highly recommend if you enjoy learning things like this!