In an instant – the probability of February 29

If your birthday or wedding anniversary is February 29, your special day will pass this year in an infinitesimal moment at midnight. [1] The year 2019, when this is posted, is not a leap year, but given any random year, we usually think that the probability of it being a leap year, with a February 29, is one in four, or 25%. But in our current calendar system, the odds are actually a bit less than that, at 24.25%.

This is because the “official” international rule for determining leap years is more complex than our common one-out-of-four rule-of-thumb. It turns out that the Earth orbits the sun in a tiny bit less than 365.25 days, about 11 minutes less in fact. So, in order to compensate for this small difference, every year divisible by 100 is not a leap year. Unless, that is, the year is divisible by 400, in which case it is a leap year. Got that? And so, the years 1800 and 1900 were not leap years, but 2000 was. Thus, for 1515 out of every 2000 years, February 29 comes and goes in an instant between February 28 and March 1.

For most of us, the one-out-of-four rule is close enough for any calendar figuring we need to do. Indeed, very few readers of this blog will need to remember those strange exceptions to the rule. As our planet bolts through the universe while “circling” the sun [2] Isaac Newton used his “new math” of “infinitesimal calculus” to put formulas to gravitational force, and these formulas were close enough to get the first airplanes off the ground. Albert Einstein’s refinements to gravitational force were close enough to get the first spacecraft to the moon and back home again. But as things get really small, down at the subatomic level, Einstein’s original calculations are not good enough, because other forces besides gravity come into play.

Physicists continue to refine these calculations. But Einstein was not wrong, nor was Newton. The slide rule on which I first solved mathematics problems at my university in the late 1960s was not wrong, rather the handheld calculator that became ubiquitous in the 1970s, and the better one you likely have in the computer in your cell phone, just take us more places into the human understanding of the universe.

Likewise, Charles Darwin was not wrong about biological evolution, even though he never imagined that probabilistic, recombinant DNA was at the (approaching infinitesimally-small) core of living things. But he was “close enough” for 1859. Today, every new sequencing of a living organism’s DNA continues to confirm and enhance Darwin’s theory. The universe reveals itself in its own time.

I was a moderator for an online discussion board almost 20 years ago that had a contributor who would regularly “trigger” on the mere mention of Darwin or the word “evolution,” and then go into long litanies about how “Darwin was wrong” based on some science or pseudoscience article he had read. He did not understand, nor do an amazing number of fundamentalist religious believers yet today, that when scientists use the word “Darwin,” they are speaking using a “shorthand” for, not the original On the Origin of Species claims, but rather everywhere science has brought us since to refine that conceptual 1859 breakthrough.

Stay tuned for a couple posts on the still-visible theological challenges to evolution, which I think are readily overcome, and one related “science vs. religion” topic that is not so easy to reconcile.

Back to our original story, if you were born on a February 29, or if you were married, or some other significant event happened to you on this date, this “infinitesimal” day matters, whether the rest of us experience it or not. I personally will likely be asleep for its entire duration. Sometimes life in this universe seems to take billions of years to do anything significant. Sometimes, it passes by in an instant.


  1. I wrote about the math and the theology behind infinitesimals, infinitely-small distances and moments, about a year ago in this post about how the Protestant Reformation helped to bring about Calculus.
  2. The Earth makes its way around the Sun at a velocity of about 30 kilometers per second, but it is not really a circle because the Sun is itself orbiting the Milky Way galaxy at a velocity of 200-250 kilometers per second. But at this scale, velocity likely does not mean what you think it does. Back in January I linked to a great video that helps visualize how our planet and sun traverse space-time:

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.