Complex Numbers (Book)

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Complex Numbers

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.

http://www.ddewey.net/mandelbrot/

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June 3, 2022 at 12:02am

#1033272

Like a Version

Note: Tomorrow's entry will be delayed. I'm going to a beer festival in DC tomorrow. Assuming no one opens fire into the crowd (this is America, so it's a nonzero chance), I'll return home on Saturday and then blog. Between expecting to be drunk and having a drunk friend to deal with too, I doubt I'll be able to get online at my usual time.

So, like, time for an article about language.

Why do people, like, say, ‘like’ so much?

Link is from the Guardian so the spelling is, like, British.

Why do people have such a problem with “like”? Is it because it simply won’t go away? In 1992, Malcolm Gladwell wrote a robust defence of the word and the way it carries “a rich emotional nuance”, responding to what had already been a decade of criticism. This did nothing to settle the debate.

Some people get annoyed over the stupidest things. This is one of them. Who cares?

You know what other word gets overused and we don't think about it until it's pointed out? "Up."

Scores of recruitment specialists and public-speaking coaches have publicly bemoaned the word’s rise and say those who use it prevent themselves from getting opportunities.

I don't know what a recruitment specialist actually does, but I think public-speaking coaches are the people that try to get us to stop saying "ummm..." too. Which does nothing to actually promote public speaking; sometimes a speaker has to pause for thought without giving the audience an opportunity to think she's stopped speaking.

Sure, if it becomes a vocal tic, perhaps then it's truly annoying, as with any other word or phrase. Until then, to me, using "like" as an intensifier is merely the sign of a casual conversation. Hell, I even use it in my writing in here. Deliberately.

In 2010, Emma Thompson complained to the Radio Times that she “went to give a talk at my old school and the girls were all doing their ‘likes’ and ‘innits?’ which drives me insane… I told them ‘Just don’t do it. Because it makes you sound stupid.’”

Well... "innit" is unique to England, as far as I know, and it really does make you sound like a chav.

There’s certainly an element of sexism here and the detractors of “like” say it makes you sound girlish and stupid, arguing that this is a newish tic said mostly by women and that it’s a meaningless “filler” word that doesn’t add anything to a sentence’s meaning. But they are, in fact, wrong on every count.

As the article eventually points out, the liberal sprinkling of "like" was popularized in the US in the early 80s, the whole Valley Girl thing. But who made men the gatekeepers of language?

The first of these is the quotative “like”: “He cooked a spag bol for me last night, I was like, that’s delicious.”

Maybe this is because I'm American, but "spag bol" would enrage me way more than the use of "like" there.

The other hated “likes” are as a discourse marker, “What did I do last night? Like, had dinner, hung out”; an adverb to mean approximately, “It was super quick to cook, like 30 minutes”, and what’s known as a discourse particle, which goes in the middle of a phrase, rather than at the end of it, “This dinner is like the best I’ve eaten.” But there are more uses than that, for example the Geordie tradition of finishing sentences with a like. “He cooked dinner for me, like,” and increasingly “like” is also used as a noun because of Facebook and Instagram, “I gave it a like.”

Always good to know what part of speech you're using. As for the social media aspect, hate the media, not the noun.

In Shakespeare’s Twelfth Night, written at the start of the 17th century, Valentine says to Cesario, “If the Duke continue these favours towards you, Cesario, you are like to be much advanced.” The linguist Anatoly Liberman says that this version of “like” was being used as a shorthand for likely, and may be the beginnings of our contemporary usage.

Here's where they lose me. I'd need a bit more support for that hypothesis. The dialogue isn't "You're, like, gonna get promoted," but as noted, a shorthand for "likely," perhaps to fit better in iambic pentameter.

But the biggest lie about “like” is that it’s stupid; that it adds nothing to the meaning of a sentence. “People say language is random. But language is almost never random. You can’t just stick that like in anywhere,” says Fought. “So for example, if I say, ‘Oh look at that boy over there. He’s wearing a top hat. And he’s like, 10.’ That makes perfect sense. But if you say ‘How old is your brother’? And I say ‘He’s like, 10’ that’s a little more unusual. Or if I said, ‘My, like, grandma died.’ That’d be a very strange context to hear it. So there’s patterns. There’s ways to do it more grammatically.”

English evolves, but as with any evolution, there are constraints.

So if linguists are largely agreed that “like” is, at least in some contexts, no bad thing, why does society still bristle at it? Katherine D Kinzler, the author of How You Say It, a book about linguistic bias – which she argues is one of the most persistent prejudices in our society – says that taking someone to task for the way they speak is one of the last societally accepted ways to exercise our prejudices.

I can buy that. I'm in the South, but near the cusp of North, and even around here, a lot of people think a Southern accent marks someone as having lower intelligence. This ain't necessarily so. Sure, plenty of Southerners are dumb as dirt. So are plenty of everyone else.

...the best linguistic studies today suggest people who say “like” may actually be more intelligent than those that don’t. One, published in the Journal of Language and Social Psychology, which examined 263 conversational transcripts, found that “conscientious people” and those who are more “thoughtful and aware of themselves and their surroundings” are the most likely to use discourse markers such as “like”.

"May" is the key word there. (And don't get me started on may vs. might

.) One study does not science make. But it's at least a falsification of the premise "all likers are dumb."

Anyway, just another thing I thought I'd, like, share with y'all.

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