Leap years And The Even More Curious Phenomenon Of Non-Leap Years

Autumn has come to Bologna and the past few weeks have been dreary and cold. Today, however, the clouds broke and it was a beautiful, clear, warm-enough day. I took an afternoon break from studying and ran up to my favorite spot in Bologna: Villa Ghigi. My own attempts to capture the view and the ambiance up there have so far been unsuccessful. However, this contributor to wikimedia seemed to do a pretty good job of it. 

View of Bologna from Villa Ghigi

Because of the weather and my battle with a persistent cold over the past couple of weeks, I haven't been running much. Getting out and stretching my legs this afternoon did me a lot of good. Well, maybe. The intellectual result of my run is outlined below. I'll leave it up to the reader to determine the normative value of the outcome which is detailed below.

I've mentioned before that one of my favorite by-products of running is the unpredictable stream of thoughts that go through my head as I settle into an almost meditative state. Today, a particularly lucid stream of thoughts brought me to the question of leap years and how we deal with them. The progression of thoughts that got me to that point are another story entirely, but as I plodded back down the hill, I realized that leap years present a problem. 

The whole idea of celebrating a February 29th every four years comes from our attempt to match the earth's revolutions around the sun to it's axial rotation - i.e. match earth years to earth days. There's no good reason why the earth should rotate on its axis a particular number of times as it revolves around the sun. To make life easy, we typically refer to a year as having 365 days. In fact, it revolves on its axis more like 365.2425 times for every trip around the sun. (I didn't know this as I was running, I just assumed there was a margin of error. Wikipedia told me the exact number when I got back.) Now, if the earth were kind to us, it'd pick a nice even number of days to go around the sun; for example, 365 or, if it were particularly kind, 360 days would make celestial time-keeping very neat and easy. Failing that, it'd be nice if the earth picked an easy fraction of a day to add on or subtract from each year. Granted, 365.2425 rounds up to 365.25 easily enough and so every four years, we add an extra day to even things out. None of us would ever notice a difference over the course of our lifetimes between measuring a year as 365.25 days and the ACTUAL length of 365.2425. But apparently, the Pope Gregory was wise enough to transcend living memory. He wanted a calendar for the ages, and to do that, you need more foresight than a measly lifetime.

Rounding up to .25, adding an extra day every four years and leaving it at that could have DISASTROUS consequences; specifically, the addition of 3/100ths of a day each time we celebrate February 29. The additional .2425 days per year only adds up to .97 days over four years, not a full day. Over the course of many years celebrating February 29, the summer solstice gradually creep up and, instead of happening on June 21, it slips back to June 20. Extrapolate that error over a few thousand years and eventually the summer solstice would be in May. That's just unacceptable. 

So, I came back home and started tooling around on wikipedia. Thank goodness Pope Greg had considered this 3/100ths of a day we were adding every four years and formulated a strategy for correcting it. It turns out that at the turn of each century, the centennial year (e.g. 1700, 1800, 1900, etc.) is NOT counted as a leap year. Even though these years are divisible by four, February 29, 1700, 1800 and 1900 did NOT happen. In 1903, for example, the world had gone without a February 29 for 7 years so that the summer solstice in 1903 didn't happen until more than half way through the 22nd day of June. By comparison, the summer solstice in 1896 (the last leap year) was happening towards the end of the day on June 20th. 

First of all, isn't that wild? There I was, thinking that I knew the calendar that I have spent nearly 30 years interacting with on a near daily basis! Maybe this is all common knowledge, I don't know. Usually I have a chance to talk through blog posts before I write them up but I didn't get a chance to talk through this one. I'm assuming this isn't common knowledge.

There's more.

So, most centennial years omit February 29, but not all of them. As it is, the extra fraction of a day we add each February 29th only adds up to 3/4 of a day each century. So dropping February 29 from centennial years puts us behind a total 1/4 of a day every 100 years. Again, small potatoes, but over the course of thousands of years, that could throw us off by a whole week!

I found this on Wikipedia. Search for "Leap Year" and prepare to sacrifice half a day learning about the calendar that measures your life. Don't worry though, you'll make up for the lost 12 hours over the course of the next 100 years.

Thank goodness the Gregorians saved us from this confusion though. The ultimate correction in solving the leap year problem comes by celebrating February 29th on the centennial years that are divisible by 400. This means that the years 1200, 1600 and yes, 2000, celebrated February 29 in order to correct 400 years of ever so slightly shifting the summer solstice later in the year. 

The exciting conclusion to all of this is that the year 2096 will see the earliest summer solstice since 1696; it will actually occur in the MORNING of June 20 (Greenwich Mean Time) opposed to the average of June 21, and the extreme of the afternoon of June 22 witnessed in 1903.

Unfortunately, I probably won't be around in 2096 to experience this once-in-a-quarter-millennium phenomenon, but maybe my kids will? I'll be sure to forward this blog post along to them at some point.

It also means that I missed the similarly momentous occasion of celebrating February 29 in 2000. It didn't occur to me at all that that specific leap year was so phenomenal. We were so caught up in the whole millennium and Y2K business and I was still riding the high of my 16th birthday. What a shame.

Finally, in my lifetime I will likely never experience an non-leap year. And I have to say, I'm ok with that. Leap years are confusing enough, celebrating a non-February 29 would just be confounding.