In From Box Scores to Test Scores I devote a section of the text to the famous “fencepost” problem of mathematics, and the related “off-by-one error” I’m fond of calling the OBOE.
The fencepost problem is described simply enough. For example, how many fenceposts, placed 10 feet apart, are needed for a fence 50 feet long? The obvious answer is five (50 divided by 10) and said obvious answer is, of course, wrong. The correct answer is six, as one needs a post at “zero” as well, the locations of the posts being 0, 10, 20, 30, 40, and 50 feet.
Easy enough.
The corollary tends to annoy more people than it satisfies, but it’s the same principle. Ask someone how old he is and he will answer with the number of years he has completed. I’m 43, but as soon as I turned 43 I began my 44th year, no? The year we’re “on” is always one more than our age. When I hit 44 that’ll be the 45th time I’ve seen that date, because I saw it the day I was born. When I was zero. The first of my fenceposts.
Over the weekend I found a historical example of the fencepost question, not only an interesting story but one that affected the area in which I grew up. After the Revolutionary War, when our newly-formed states were still jockeying for land, the states of Pennsylvania and New York were at odds over their border. Trouble was the language of Pennsylvania’s colonial charter, which was somewhat unclear. Its northern border was “beginning of the three and fortieth degree of northern latitude.”
Three and fortieth degree?
Is that the line that is 43? (My 43rd birthday?) Or where the 43rd degree starts? (Not the line but the “band of land” starting just beyond the 42nd parallel extending to 43, or in our analogy, from the day after my 42nd birthday until I turned 43?)
Hmmm.
And wouldn’t you know the place where I grew up is between 42 and 43 degrees north latitude? Hint: it’s in New York but apparently could well have been part of Pennsylvania.
By 1785 Pennsylvania relinquished its claims above 42 degrees, content with its acquisition of Pittsburgh and parts west. They really couldn’t play the technicality card too much about the 43rd parallel anyway, because after all, a few years before…
they’d played the same trick with Maryland. That time they argued that the line should be 40 degrees, not the 40th degree.
But I suppose it’s all a matter of degree, no?