by Robert Waltz
Not for the faint of art.
A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.
The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.
Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.
Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.
One of the most amusing typos I see is when someone is trying to say "angel" and they end up saying "angle."
I mean, that cracks me right up. Every. Time.
"You're a real angle!"
"She's my guardian angle."
"My baby is such a little angle!"
I know I shouldn't make fun. But I do.
It's not like I'm trying to be obtuse, but I just think it's really acute thing to do. Though my reaction is just not right.
It doesn't help that there was historically a people called the Angles. They migrated from Jutland or some shit like that to an island off the north coast of Europe, where they eventually merged with the Saxons but still gave their name to part of the island: England, a shortening of Angle-land. Hell, in French it's still called Angleterre.
From what I hear, though, they were no angels, often at war, engaging in pointless (and sometimes worthwhile) battles, and eventually conquering more than half the land area of the globe, before finally backing off from a lot of that. But, you know, angels were no angels either; if you really look at the mythology surrounding them, those are some scary-ass motherfuckers. Not the fluffy haloed humanoids with wings that somehow made it into popular culture.
The Angles' language lives on, though. Nealy half the world still speaks it, to one degree or another. (Yes, to be clear, that's totally another "angle" pun.) But it's nothing like Enochian, the purported language of the angels. No, it's way easier to make puns in Angle-ish, and all too easy to mistake similarly-spelled words for each other.
But that's part of the joy of English, you know. I don't think I'd have nearly as much fun punning in another language. After all, when it comes to humor, that's my angle.