You Only Get One

Welcome to your one and only perfect square year. We have entered 2025 which is 45 squared. It is, for most of us, the only time we will ever live through a year that is a perfect square. It is your once in a lifetime event.

The last time it happened was 89 years ago, in the year 1936. So unless you are already 88 or older (turning 89 or older this year) you haven't reached your second of these rare events.

It will happen again in 91 years, in the year 2116, and most of us aren't going to live to see that occur. Maybe some preschoolers now will, but I suspect preschoolers aren't members of my reading audience.

The thing is it has probably been a once-in-lifetime event for most people throughout history. Perhaps you are saying: hold on, Erich, what about in the first few centuries. I mean between the year 1 and the year 4, there were only 3 years. And from 4 to 9 is only 5, surely lots of people lived for that long.

That's true, but in the year 1, they were not using the Anno Domini designation of years. It wouldn't be invented for centuries. In those times, usually years were marked based on when the current ruler became the current ruler. So the year might be the eleventh year of the reign of Emperor Penguin the Second, or whatever the ruler's name was. But eventually scribes and the educated found this annoying. It was pretty hard to figure out how long ago things happened when you kept restarting at 1 each time your king died or your land was conquered. The intelligentsia wanted some sort of fixed system that would just keep counting.

In sixth century Christian Europe, a monk named Dionysius Exiguus wanted to figure out what day Easter would fall on in the upcoming years. So he decided to set up a numbering system for years based on something having to do with Jesus. Today we think of it as being when Jesus was born, but it isn't clear that this is what Dionysius was considering. It may have been the conception of Jesus or some other event in the early life of Jesus or the life of Mary slightly before the birth. Anyway, according to the system invented by Dionysius, this was in the year 525.

It's also not clear that Dionysius was the first to do so, nor that it was his system which eventually spread and became the one used today. It's all murky. Where there are sufficient records, we know that somewhere in the 8th or 9th century, monks in England were using AD to denote the year. Still no one knows exactly when in the 8th or 9th century this began.

But let's be generous. The first perfect square in the 8th century would have been the year 729 (which is 27 squared.) Let's assume that this system was being used at that time. Then the following perfect square would have occurred 55 years later in 784. So yes, some people probably did live through both of those years, though average life expectancy was much much lower than this (probably somewhere around 24 years.) But keep in mind that is the average, and it is brought down by the fact that so many people died of childhood ailments. So the ones who did make it to adulthood, some of those could have reached ripe old ages like 60.

Still, it wouldn't have been most of them. It would have still been rare to live through two perfect square years, even back when they were closer together.

Because perfect squares get further and further apart in a predictable way. If you want to know how long between two consecutive perfect squares, you can just add the two numbers they are square of. Like today is 45 squared and the next perfect square is 46 squared. But 45 + 46 = 91, and that is the distance between those perfect squares. The distance between 27 squared (729) and 28 squared (784) is 27 + 28 = 55. Another way to think of it is that the nth perfect square is just the sum of the first n odd numbers.

I am not, in general, a big time New Years' Resolutioner (or Resolutionary, maybe?) If I really want to resolve to do something, there is no reason that January is the best time. In some ways, it is the worst time, because I would only be making a resolution because I felt like I was supposed to make one and not because I wanted to accomplish it.

That being said, maybe I should reconsider that this year. After all, this is the only perfect square year I will ever see. So join me: let's embrace this year, this rare event, this moment we are lucky to live through. Let's make 2025 a signature year for each of us. Let's accomplish our most square deal in this most square year. Let the rarity of this moment remind us all that life only gives us so many opportunities. It's certainly a lesson I need to take to heart.