The summer term started last week at the University of Michigan, so I’m in the second week of a new class.  I’ve been noticing that there are certain stories that always end up getting told, in one form or another, in pretty much every math class I teach.

Today’s lecture (on vector functions and parametrization of curves), had it been given by anyone else, would have involved the word “counter-clockwise”.

But as the great Red Green said, “I’m not most people; I’m barely me.”

I don’t like to use the terms “clockwise” and “counterclockwise”.  There are at least two reasons for this, one of them rational and one of them frivolous.  (I’ll let you be the judge of which is which.)

To understand the first reason, you have to know that when I was a small child, my father and I had this game.  We would ask each other outlandish questions, such as “Why did you invent Tuesday?”, and then make up answers and explanations.

It so happens that one day I asked my father, quite seriously and with no thought of the question game, what “clockwise” and “counterclockwise” meant. As I recall, he explained that most clocks in the world work like the clock in our family room.  By an ancient tradition, however, clocks which hang behind counters, such as the ones where you pay in diners, have to go the other way.  So there are two directions around a circle, the way normal clocks go and the way counter clocks go.

And I accepted this and went on with my small child life.  Months later, I happened to notice the clock behind a counter when I was out somewhere with my father.  “Dad,” I exclaimed, “That clock moves like the clock at home!” “Well, of course it does…”  “But Dad, you said that…”  <here I can trail off while the class laughs a little>

The bottom line is, ever since then, I’ve never really been sure which was was clockwise and which way was counterclockwise.  So I try to avoid the terms.

The term I use now is widdershins, which is a very old word (older than clocks of the sort we’ve been discussing) meaning counterclockwise.

(I actually first learned the word from that Sierra game about King Arthur and the Holy Grail, where Widdershins was some kind of magic statue that played tricks on you if you didn’t give it copper or tin…does anyone else remember that game?)

This brings us to the next reason.  Of the words “clockwise” and “counterclockwise”, which boil down to “the way clocks go” and “the way clocks don’t go”, there is a natural choice for which is the “right” direction and which is the “wrong” direction.  Syntactically, one is positive and one is negative.  Unfortunately, in mathematics the convention (for measuring angles, traversing curves, etc.) is that counterclockwise is positive (there are reasons for this, not worth getting into now), which is precisely not what the language leads you to expect.  But with “widdershins” and “antiwiddershins”, the negative-sounding word and the negative direction for angle measure coincide.  Improvement!

And another thing.  Have you considered how you’re going to explain “clockwise” to your grandchildren?  You think they’ll ever use a clock with hands?  Those things will be antiquities!  They’ll all tell time with computers and cell phones (and maybe digital watches, which are pretty cool, 42).  Someday your grandchildren will be visiting you, and they’ll find your old game of, I don’t know, Sorry, and try to figure out the rules.

“What does ‘play proceeds clockwise’ mean, Grandma?  To play Quickly?”


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