29 June 2014

Negative 3 Mister Darcys, or How I Came to Love √-1

I have a very good friend who went the extra mile to get two Bachelor's Degrees, one in Math and one in English.  What is more, after that she got her PhD in English Renaissance Drama.  Although she vehemently denies having a good memory, she can, if asked, deliver ex tempore a succinct and accurate plot summary of any play of the period you can possibly come up with.  I'm not talking about Shakespeare, Marlowe, or Ben Jonson here.  I'm talking about writers and plays most people not versed in the period are at best only dimly aware of.  And even 20 years after the last Math class she took, she could still remember and talk about the Math in a meaningful way.  So her memory isn't good.  It's prodigious.

Most of the Math she could discuss was lost on me, however.  Geometry and Trigonometry I loved and did well in, but I haven't taken a Math class since high school.  Never took Calculus.  Never wanted to.  But every now and then I would see some equation somewhere and say to her, "So what does that symbol mean?"  And she would launch into some explanation that before too long made my poor brain swell, but, you know what, it's rather charming to watch someone you like indulging a passion that they don't often get to indulge because they are surrounded by people who won't know what they are talking about.  It was a lovely thing to watch, though I was utterly clueless.

And as long as we didn't touch too much on negative numbers, we were fine.  For some reason I had always found the assertion that negative numbers were real particularly irksome.  (It is somehow akin to the claim that "perception is reality," though I have noticed that the perception which is also reality never ever seems to be my perception.)  I mean, okay, negative numbers come in very handy for solving equations, but they were just tools, a means to an end, a bit of mental mathematical gymnastics.  They didn't exist as a measure of real quantity.  Because of course you cannot actually have -3 apples or anything else.

And in my typical cleverer than thou way my proof of the unreality of negative numbers was that the square root of any negative number was an imaginary number. Because obviously a number that didn't exist would have a square root that was imaginary.  Somehow this failed to persuade her.  In fact it annoyed her. Largely because it was stupid, and she knew and disliked the fact that I was trying to tease her.

In revenge she gave me a book called An Imaginary Tale: The Story of √-1, by Paul J. Nahin, for Christmas.  (Revenge tragedy was her specialty.)  Now from what I have read about this book, it is a good book and very highly thought of by those who are able to think of it, but for me a visitation of three spirits by night would have been kinder.  She kept insisting that the Math wasn't that hard, and perhaps I would have decided she was right if I could have gotten to page three.  I couldn't even claim that it was all Greek to me, because then I would have understood it.  In any event my brain oozed out through my ears.  But I have always maintained that turnabout is fair play, and this was a most palpable hit.

Though I still didn't buy that negative numbers were real.

Because it's true that you can't have -3 apples.

Then one day it hit me.  If negative numbers are real because we can conceive of them, and can hold the idea of them in our heads, and do things with those numbers, well then Mr Darcy is real, too.  And Sam Gamgee.  And Falstaff.  And Colonel Aureliano Buendía.  And Viola.  And Diana Villiers.  And the incomparable Lily Bart.

And I can dance with Miss Elizabeth Bennet.

So don't be telling me if I'm wrong.  I don't want to know.

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