Leaplings of the World, Unite!

Today’s “Word of the Day” is “intercalary.” It refers to a day inserted in the calendar to bring it into sync with the solar year. That day is today, the 29^th of February, the Leap Day of the Leap Year 2020.

People born on this day, the Leaplings, are special. They get to celebrate their birthday every four years (although some cheat by celebrating three years on the 1^st of March and one on the 29^th of February) and so make it more special than the yearly birthdays we normal folks celebrate.

Everything comes down to counting. We count a year to consist of 365 days, but the Earth takes a little longer than that to go around the sun in an elliptical orbit, although, since the eccentricity is only 0.0167, or almost zero, the orbit is almost circular. The actual number of days is not 365 but 365.2422 days. Think of that rather annoying additional decimal day. Why couldn’t the number of days be an integer instead of a decimal? Because celestial phenomena do not follow the neat geometry of humans. They follow what they must, according to the laws of physics.

Still, let’s approximate and assume that the number of days in a year is 365.25. A day of 0.25 means quarter of a day, which is 6 hours. So, for three years, we fall short in our counting by a total of about 18 hours. The solution? Make it 24 hours by the 4^th year and add that extra day to the fourth, that is, the Leap Year, and we are in sync with the true celestial year, on the average. Except, we are overcounting the solar year by about 12 minutes on the average per year. The solution? Normalize these extra minutes by skipping “intercalary” for some of the Leap Years. Which ones? Those year that are not exactly divisible by 400. That means the years 1700, 1800 and 1900, although divisible by 4 but not 400, were not Leap Years. The year 2000 was but not 2010. This year 2020 is but 2030 will not be, and so on.

Except that this calculation is still not completely right. 365.2422 of a true solar year means 365 days, 5 hours, 48 minutes and 46 seconds. So, when we add a day every Leap Year, we are overcounting the length of the year by (6 hours - 5 hours 48 minutes 46 seconds), that is, 11 minutes and 14 seconds, not 12 minutes. In other words, the Gregorian Calendar we currently use and adjust with a Leap Day overestimates the average length of a year by 11 minutes and 14 seconds, not 12 minutes. The correction necessary is 365.2425 – 365.2422 = 0.0003 days per year, which means another correction will be necessary in 3,030 years. It is safe to say that most of us will NOT be around to experience THAT correction!

Transcending these 4^th place of decimal correction is, however, this question: What is the probability that a person selected at random from the population will have a 29^th of February birthday?

Leapling, anyone?

Well, in 4 years, there are 4 x 365 days = 1460 days + 1 Leap Day = 1461 days. So the probability that your spouse, niece or cousin, or anyone, was born on the 29^th of February = 1/1461, which is approximately 0.000684, or about seven hundredths of 1 percent. So how many people in the world can we expect to have their birthdays fall on the 29^th of February? This expectation value (not the actual number but close, according to laws of probability), assuming that the population of the world in 2020 is 8 billion, is 1/1461 x 8,000,000,000, or about 5.8 million. In other words, we can expect at least 5 million Leaplings on the Earth today.

If you are looking for an ice-breaker at a party, how about this as you hone in on a potential friend: “Are you a Leapling?” When the response is a puzzled, “Say what?”, you launch into an explanation of Leap Years, why and how they came about, and how, using probability, you can calculate that there are over 5 million Leaplings in the world now.

As you look up with a triumphant smile after your brilliant monologue, you realize with a shock that your "target" has vanished!