Not for the faint of art. |
Complex Numbers 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. |
When it comes to words, "correct" is a bit ambiguous. Or should that read: "korrect" is a bit ambiguous? In honor of the 182nd anniversary of the first-ever appearance in print of O.K. (in The Boston Morning Post) I am here to start an internet copyediting war. Said anniversary was apparently last year, as this article dates from March 2021. Also, "an internet copyediting war?" Right, like anything actually gets copyedited on the internet. As you can see, the original “O.K.” was very clearly an acronym, in this case of “oll korrect,” a popular slang misspelling of “all correct” (we can probably blame this on the teens of the era). Lest anyone think that teens making up expressions to piss off their stodgy elders is a new phenomenon. As with most language that drifts into common usage, the origins of O.K. slowly receded from collective awareness and the word began to assume different shapes and sizes: the slightly more streamlined and dashing OK; the drawling and onomatopoetic okay; the abrupt and minimalist ok. (Who knows, maybe mmmkay will achieve formal status one day.) And yes, the "oll korrect" origin story is disputed, though that seems to be the leading hypothesis. What's not in dispute is that it was made up at some point. All words were; it's just a matter of how long ago. So what is a copyeditor to do? One of the best pieces of advice I ever got was from an old alt-weekly copyeditor at a bar, who didn’t really prescribe to this fixed style or that, but rather believed first and foremost in the “ugly rule.” In truth, I'm pretty sure most style rules are the result of copyeditors going to bars. One thing I think most of them would agree on, though, drunk or sober, is that this author should have either used "...prescribe this fixed style or that..." or "...subscribe to this fixed style or that..." The way it's written makes no linguistic sense. He held (correctly) that language and its rules are slippery and ever-changing, and that convention and usage should always supersede institutional formality. While this may be "korrect," there's still no excuse for mixing up its and it's; there, their, and they're; or prescribe and subscribe. So, within that admittedly wild and wooly ethos he came up with the Ugly Rule, which privileges the reader’s eye above all else, and seeks to minimize typographical distractions (in practical terms, the New Yorker’s truly eccentric insistence on diacritics is a direct and egregious violation of the rule). Which is what I've been saying. Whether it should be "wooly" or "woolly" is also up for debate. He also believed that words, over time, tended to shed their size: compound hyphens disappeared, capitalization faded, and spaces closed up. Hence to-day became today, Band-Aid became band-aid, and (thank god) Web site is becoming website; and if these contractions were inevitable, why not just get in early? They're not inevitable. But it is the way trends go in English. I've done entire blog entries on the phenomenon. Here's one that coincidentally (or is it ironically?) riffs off a New Yorker article: "Dashing" Can you see where I’m going with this? I can, but don't you get paid by the word? This is why, as an editor, I prefer ok to OK or okay. Why fight it? Why waste the extra ink? What ink? The problem with ok is that it looks like it should be pronounced with one syllable, similar to oak or ach. The problem with O.K. is that it's absolutely archaic; hardly anyone puts periods into acronyms or abbreviations these days. OK is a decent compromise, but okay is closest to how the "word" is actually pronounced. Full disclosure: I'm pretty sure I use them all interchangeably, but I think I lean more towards "okay." I also had to go and look up some "texting rules" post I made several years ago, because I had a vague memory of being told not to use "k" for "okay." Here it is: "Unwritten, Expanded" The important excerpt: "So... wait... we're supposed to, on the one hand, condense our texts into emojis and "u" for "you" and acronyms such as IDK or LOL or whatevs, but you're going to get pissed because someone typed "K" for "OK?" Good gods." So, in conclusion, this author doesn't actually answer the headline question. My personal opinion? Look at how The New Yorker handles it, and do whatever they don't. That'll be okay. |