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Journal, Day Five
The Square Root of Negative One
I’ve been reading books about math—The Men of Mathematics (sexist, yes, but published in 1937), The History of Mathematics, Classics of Mathematics, and The Universal History of Numbers among others—because, in spite of what you may believe about me, I would like to know the truth. I type my lies on the keyboard and I notice that upper row, the other part of the alphanumerical set, the buttons that I don’t push, and I wonder what kind of things I could say with those symbols. X equals X. Not-X doesn’t equal X. Poems have possibilities but math has answers. A discovery in math is of a different order than a discovery in literature. The history of math is the history of peoples from every culture and every period in time all assaying the same set of question. Literature doesn’t do this, right? And math doesn’t lie, it spools it all out honestly, by the book, showing its work as it goes, right?
Four hundred sixty-one years ago, in 1545, fairly early in the history of algebra, a man named Girolamo Cardano, messing around squares and square roots, found himself faced with insoluble equations. The problem was the square root of negative one. It didn’t fall on the number line. It wasn’t a “real” number but it made certain kinds of problems easier to solve. By 1777, 232 years later, Leonhard Euler was referring to this number with the symbol i—from the German word for imaginary—indicating its difference from the supposedly “real” positive and negative numbers. Only 20 years later, 1797, Caspar Wessel found a place to put i and its multiples: he invented a new number line. It crossed the traditional number line vertically. He took the “real” number line and his “imaginary” number line and turned the whole tangle into a number plane.
Can you do that? Can you just plug in some made up thing and end up with solutions? Can you simply draw some imaginary lines and end up with a better map? You don’t expect to be acclaimed as a great scientist until you discover something, something big and useful, but shouldn’t this something have to be real? Let’s jump ahead 125 years. It’s 1922 and Ludwig Wittgenstein has just published his Tractatus Logico-Philosophicus which insists, among other things, that the limits of my language mean the limits of my world. Or, put another way: how you say it is how you think it. And, more dramatically: if you can’t say it, you can’t think it. And, if you can’t think it, how can you solve it?
To imagine a language means to imagine a form of life. That’s Wittgenstein again. So, go ahead: imagine a form of life. Imagine your life. Think about what you say and ask yourself if you want to be the kind of person who says those kinds of things. Change your language and you change your thoughts. Change your thoughts and you change yourself. Imagine your possible selves and decide which ones you want to inhabit. The history of math is the history of peoples from every culture and every period in time all assaying the same set of question. Literature doesn’t do this, right? Or does it?
Doesn’t it? Isn’t there some kind of emotional math, spiritual math, that develops in literature? Can’t we, don’t we already, take specific literary inventions and manipulate them—isolate and solve for X—to count and measure, define a space, build a bridge, a house? Consider Gertrude Stein’s rose or Wallace Stevens’ blackbird or even Isaac Asimov’s robot—they solve something, don’t they? Wittgenstein compared philosophy to a ladder, said it was useful until you got to the top rung but then you had arrived at a place where philosophy could take you no further, and it was time to throw the ladder away. He has a ladder. And thanks to him, I do too. And a rose. And a blackbird. And a robot. And that’s what I do with my day, my good days; I try to make useful things. I like the intent and I like the tradition. I like the materials and I like the sound. I’m a liar, I realize that. And I’m in it for the long haul.