Counting Time

How long is a school year?

This is a question nearly all parents must wonder at some point, and it seems like it should be really easy to answer. After all, we’ve been counting time ever since we were children, and some of us are pretty good at it by now.

When I was little, we went to elementary, middle, and high school from the end of August until the beginning of June. This semi-symmetrical schedule allowed for roughly half of the year to be completed by the end of December, so you could have a little mid-year break for both teachers and kids, then come back ready for the second half of the year.

We were out of school for most of June, July, and August. Those precious three months were a gasp of life in a stifling school environment, or so most of us felt. Three months off doesn’t seem like a lot of time, but we certainly made the most of it.

Let’s keep things simple today and imagine that I started school at the beginning of September, like many kids across the US did back then (and still do today), and let’s say the year ended exactly at the end of May.

Our example makes this project pretty easy, since the year began at the start of a month, and ended when another month ended. That means we can just count those months and add them up with the others. Our history with correspondence counting, where one = September and two = October, gives us the intuitive tools we need to do this effectively and quickly, but if you’re anything like me, you probably need to say the names of the months aloud (or mentally) as you count them.

All right: kids are in school for nine months out of the year. We just counted them, so we know this, and we are pretty confident we should be able to use this trick from now on, solving other time-related problems eagerly and with confidence.

The only problem is that it doesn’t work for all of the ways we measure time.

If you waited in the ER from 7 to 9 PM, should we count the three hours that are included? Is this really just an excuse to make a seven-ate-nine joke in my own mind? No, there’s really something interesting here: we say we waited from 7 to 9 PM, and we mean that we waited for two hours, but if we say that the school year lasts from September to June, we mean that both September and June are included.

If we attended college from 2010 through 2013, did we go for three years or four? This question points us toward the answer: we measure time in two ways. We use exclusive units when we’re talking about hours of the day, or minutes or seconds. This means we can just subtract 7 PM from 9 PM, so we come up with the correct answer: two.

On the flip side, we use inclusive units to describe years, especially if you say you did a thing “from this year to that year.” Even more clearly, when we’re talking about a summer break that lasts from June to August, that’s a three month break, not two.

We use inclusive time units for all longer measures of time. Why should this be?

Essentially, the unit itself becomes significant in the calculation, and it becomes significant as compared to the span of a human life. After all, it is we humans who are making up these rules as we go along, so it’s only natural that we should take significant chunks of our life into account and treat them differently.

“We’ll be doing this workshop from the 12th to the 19th” is pretty clear. We have to include both the 12th and the 19th, so we’re doing this workshop for 8 days.

“We’ll be doing this workshop from 7 to 9 today” is equally obvious, but we know we’re only on the hook for 2 hours.

For days, weeks, months, and years, we include the time interval itself. Something significant might happen to us during those longer time frames, while hours, minutes, and seconds are much easier to view as snapshots of time.

How long is significant for you? A lot can happen in an hour of your life, but then again, nothing much at all can happen for an entire day. Still, these distinctions have got to be made somewhere, and making the inclusive/exclusive break between a day and an hour seems to be about as good of a spot as any to pick.