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 |    Not for the faint of art. |
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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. ![Merit Badge in Quill Award
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| Today's article is about an article. https://www.bbc.com/culture/article/20200109-is-this-the-most-powerful-word-in-t... Is this the most powerful word in the English language? Personally I would argue that "fuck" is the most powerful word in the English language. I mean, consider how people react to it, and its versatility. Here on WDC, it's the dividing line between 13+ and 18+ ratings. Well... along with certain other words, but I've already used up my sexually-derived word quota now. So on with the article. āTheā. Itās omnipresent; we canāt imagine English without it. But itās not much to look at. It isnāt descriptive, evocative or inspiring. Technically, itās meaningless. And yet this bland and innocuous-seeming word could be one of the most potent in the English language. Long ago, I looked up the definition of the word "the." Since I've been drinking and it was long ago, I just looked it up again. The dictionary entry is entirely too long to quote here, so here it is.  Words are split into two categories: expressions with a semantic meaning and functional words like ātheā, ātoā, āforā, with a job to do. āTheā can function in multiple ways. This is typical, explains Gary Thoms, assistant professor in linguistics at New York University: āa super high-usage word will often develop a real flexibilityā, with different subtle uses that make it hard to define. One thing I've noticed in my studies of French, as well as in my very surface skimming of linguistics in general, is that different languages use articles differently. The link above from BBC goes into this to some extent, but, for example, if you ever want to fake a really bad Russian accent, just eliminate articles entirely. "Is glorious day in America, comrade." I mean, come on. Just try to say that without sounding like a cartoon Russian. Helping us understand what is being referred to, ātheā makes sense of nouns as a subject or an object. So even someone with a rudimentary grasp of English can tell the difference between āI ate an appleā and āI ate the appleā. This author might be surprised at what even native English speakers are entirely ignorant of, at least over here on this side of the pond. There are many exceptions regarding the use of the definite article, for example in relation to proper nouns. We wouldnāt expect someone to say āthe Jonathanā but itās not incorrect to say āyouāre not the Jonathan I thought you wereā. I have a vague memory of the first time I saw or heard "the" used before a proper name. I don't really remember what the name was, but the context was something like: "So, you're the James T. Kirk." It sounded weird then, and it sounds almost as weird now. This simplest of words can be used for dramatic effect. At the start of Hamlet, a guardās utterance of āLong live the Kingā is soon followed by the apparition of the ghost: āLooks it not like the King?ā Of course my mind immediately went to a Monty Python bit from Holy Grail: "Hey look, it's the King." "How do you know it's the King?" "He hasn't got shit all over him." āTheā can even have philosophical implications. The Austrian philosopher Alexius Meinong said a denoting phrase like āthe round squareā introduced that object; there was now such a thing. According to Meinong, the word itself created non-existent objects, arguing that there are objects that exist and ones that donāt ā but they are all created by language. āāTheā has a kind of magical property in philosophy,ā says Barry C Smith, director of the Institute of Philosophy, University of London. Don't get me started on the philosophy of linguistic paradox and the nature of reality. Oh, hell, I have plenty of blog entries about that, in the past and probably in the future as well. But I'll say this here: "a round square" brings the paradoxical object into being, at least Platonically, just as thoroughly. The British philosopher Bertrand Russell wrote a paper in 1905 called On Denoting, all about the definite article. Russell put forward a theory of definite descriptions. He thought it intolerable that phrases like āthe man in the Moonā were used as though they actually existed. All due respect to Russell, he of teapot fame, you can also speak of Santa Claus, sans definite article, as if he actually existed. And there is a huge difference between "god" and "the god." Scandinavian languages such as Danish or Norwegian and some Semitic languages like Hebrew or Arabic use an affix (or a short addition to the end of a word) to determine whether the speaker is referring to a particular object or using a more general term. Latvian or Indonesian deploy a demonstrative ā words like āthisā and āthatā ā to do the job of ātheā. Thereās another group of languages that donāt use any of those resources, such as Urdu or Japanese. My vague, distant memories of learning Latin tell me that Latin didn't have a definite article, either. I could be wrong about that, though. But it does make me wonder why French, a Romance language, uses one (actually three: le, la, les) in ways we'd never dream of in English -- and then omits it in ways we'd never dream of in English. French is a mess. From an English-speaking perspective, of course. Objectively, it makes so much more sense. Conversely, Smith describes Russian friends who are so unsure when to use ātheā that they sometimes leave a little pause: āI went into... bank. I picked up... pen.ā We go to party, drink vodka, yes? In some ways, this cartoon Russian accent makes Russians sound uneducated, kind of like a Southern accent in the US. Nothing could be further from the truth. They just don't have the dependence on articles that English does. Even within the language, there are subtle differences in how ātheā is used in British and American English, such as when talking about playing a musical instrument. An American might be more likely to say āI play guitarā whereas a British person might opt for āI play the guitarā. One of the things that messed me up in English when I was a kid was that I'd devour British books right alongside US ones, so I was always confused about which side of the pond some word or phrase, or spelling, comes from. Didn't help that some of my favourite bands were British. Dammit, there I go... "favorite." They invented the language. We perfected it. Still... there are many British expressions that we might do well to adopt. According to Culpeper, men say ātheā significantly more frequently. Deborah Tannen, an American linguist, has a hypothesis that men deal more in report and women more in rapport ā this could explain why men use ātheā more often. Oh, shit, here we go. Okay, no, I'mma stop this right here and move on to the next subject. The letter y in terms like āye olde tea shopā is from the old rune Thorn, part of a writing system used across northern Europe for centuries. Itās only relatively recently, with the introduction of the Roman alphabet, that āthā has come into being. I have other vague memories of doing a whole newsletter on thorn (Ć¾) a while back. Fantasy newsletter, maybe? Of course, its use wasn't just in the word "the," but it was, like, the Nordic version of the Greek theta. In Iceland, if I recall correctly, it's actually still a letter in their alphabet, whereas in English it's been completely dropped from the alphabet and its sound replaced by "th." What intrigues me most, though, about "the" is this: you can pronounce it "thee" or "thuh," depending on what comes next, but the rules for that are not nearly as clear-cut as the ones surrounding the indefinite article (where it's "a" before a consonant and "an" before a vowel). Never did fully understand that, but then, if you devote too much time to thinking about "the," you might just wrap your head into a pretzel. And that would be a thorny situation, indeed. Oh, and just because it would be wrong of me to leave this blog entry here without some explanation for the title: |
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