“By convention”

The previous post reminded me of something that happened in 7th grade pre-algebra:

Someone (perhaps me) asked the teacher one day why we used x to represent an unknown quantity.  Without hesitation, the teacher answered, "By convention."  He then moved on to solve 2x+6 = 16, or whatever the equation was we were working with.

At the time, I thought nothing of the response.  It wasn’t until years later, when I’d read all 399 of Isaac Asimov’s science essays from The Magazine of Fantasy and Science Fiction that I realized what a cop-out the answer was.  It was always possible to explain something clearly to a young audience, as Asimov had proved on a monthly basis for more than 30 years.  I grew visibly annoyed for several reasons:

  1. "By convention" while generally true, does not mean very much to a 7th grader.  Truth be told, I had no idea what "by convention" meant at the time.
  2. If I had know what it meant, I would have interpreted it as a synonym for "Because I said so."
  3. There are some fascinating reasons for why x is used, some of which are discussed in Unknown Quantity: A Real and Imaginary History of Algebra by John Derbyshire.

All my life I have been turned off by things that couldn’t be explained.  When I was young, I tended to ignore them.  As I grew older (and particularly after I read Asimov’s science essays), I began to embrace them and look for a better understanding of them.  It seems to me that my math teachers callous casting off of the question with "by convention" probably detracted from my early interest in math.  I wonder how much more interested I would have been if he had supplied a more reasonable answer.