The Zeroth of March

If I referred to a date as “zeroth of March”, I bet it would make perfect sense for some but no sense for others. Dates are just arbitrary numbers assigned to each day. That’s not to say that there is no logic within them. Months are sometimes 30 days long, sometimes 31, and 28 once, except 29 every so often. However, within a particular month, adding one to today’s date is still, thankfully, tomorrow’s date.

Now that’s a simple, straightforward, mathematically sound statement. It makes logical sense, and we can try to stretch it (which is another way of saying generalise.) Do we need the clause within a particular month? What if we got rid of it and just said

If today’s date is $d$, then $d+1$ is tomorrow’s date.

Think about how one would describe a 24-hour clock in a world where only 12-hour clocks exist. We know that adding one to the current hour tells us the next hour. We stick to that rule even for 12pm and make 1pm the 13th hour. What if we did that for dates too? The 31st of June would be is the day after the 30th of June. If you think this doesn't make sense, I will argue that it makes at least as much sense as February having only 28 days, while July and August both getting 31. If you are happy with that, maybe I can convince you that:

If today’s date is $d$, then $d-1$ is yesterday’s date.

The two statements are not equivalent. The former helps us makes sense of the 32nd of March, but the latter does not. It instead helps us make sense of the 0th of March!

But why are we trying to faff around with dates that everyone already understands? In this case, calling something the “zeroth of March” is really convenient instead of saying “the last day of February” or “28th February in non-leap years but 29th February in a leap year”. Calculations also become simple and consistent. It is especially handy when the result we’re after is only a duration and not a date.

As an example consider this scenario:

I know I will run out of coffee in 10 days, but I cannot buy more before the 26th (which is when I will receive my allowance). How many days do I have in which I must do my shopping? How many days can I afford to procrastinate?

• If today is the 18th, then I will run out on $18$th $+10 = 28$th and $28 - 26 = 2$. I can only procrastinate for two days.
• But if today is the 22nd then I would run out on $22$nd $+ 10 = 32$nd and $32 - 26 = 6$.
• If we aren’t allowed the notion of the 32nd day of a month, this calculation becomes complicated. What dates are allowed? That depends on the current month. We did not require that information to come to the answer earlier (because it doesn’t affect the answer). Say it is Feburary. To add 10 days to the 22nd of February, we first add 7 to make reach the 1st of March, then 3. That’s the 4th of March. Then to find the duration between the 26th of February and 4th of March, we again must split it into 2 days of February and 4 days of March so a total of 6 days. Each addition and subtraction can become two if we’re crossing dates.

The zeroth of March is also a useful anchor day for making date calculations. For more an that, I am happy to point you to Rudy Limeback’s excellent illustrative explanation of John Conway’s Doomsday rule.