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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.
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Getting back to articles I found online, here's one that I need...
Finally, I can learn how to be funny!
Have you ever thought of the perfect quip or comeback after it didn’t matter—a minute, hour, or day after your conversation has ended?
Sometimes it takes years. Hell, I'm still working on one from my past life in medieval Bavaria. Unfortunately, I'd have to learn Middle German first, and then find the reincarnation of my verbal sparring partner from the time and hope they have learned it as well.
Well, there’s a name for that phenomenon. It’s called l’esprit de l’escalier, or the spirit of the staircase, and refers to the perfect retort that arises at the wrong time.
Hey, that's not German; it's its polar opposite, French.
Still, you’re not doomed to sit by as clever companions exchange sharp banter. You can practice being wittier, improving your reaction times and ability to land a jab or joke at just the right moment.
By memorizing every sit-com ever aired on TV?
In his new book, Wit’s End: What Wit Is, How It Works, and Why We Need It, released on Nov. 13, author, editor, and journalist James Geary of Harvard University’s Nieman Foundation argues that wit isn’t just for a few gifted linguists.
Hey, look, it's an ad for a book (standard disclaimer: this is a writing site so I'll allow it). Also, the author failed at being witty there. He should have said "cunning linguists."
And it’s worth trying, according to Geary, because playing with language—elevating mundane communication from mere talk into a creative process—is a form of innovation that sheds new light on old ideas. Plus, it makes life less boring and more fun for you and others.
But I've been doing something like that for years. It may make life less boring, but people still hide from me at parties after I talk to them. Back when I got invited to parties, anyway.
“[W]it consists in binding together remote and separate notions, finding similarity in dissimilar things (or dissimilarity in similar things), and drawing the mind from one word to another,” Geary explains.
So... puns. Yeah, that's why people hide from me.
“Uncensored access to associations, conscious and unconscious, is essential to wit,” Geary writes. He notes that some people who experience brain damage or have neuropsychiatric diseases lose their ability to make these associations altogether, while others suffer from witzelsucht. This German term means “wit sickness” or “wit addiction” and results in a compulsion to make jokes that are often socially inappropriate.
Ah... there's some German. And I begin to see the problem: brain damage.
Understanding the neurobiology of people who suffer witzelsucht, and those who are linguistically humorless due to brain damage, could shed light on the mechanisms of wit.
I'll take that as granted, but it is utterly perpendicular to the title of the article, which is, I remind you, "The secret to being witty, revealed." Now, true, beating one's head against the wall might be funny to the viewer, but I don't think it's guaranteed to make someone wittier.
Like other forms of creativity it is borne of knowledge. Having a rich vocabulary is a starting point. Curiosity is another important element. Appreciating language in all the places and ways it’s used—from pop music to literary fiction, scientific writing to slang—makes it easier to generate unusual combinations.
I mean, sure, but "don't be stupid" is good advice for almost everything in life.
Yet writing a book about wit was harder than the writer imagined. Geary couldn’t very well be pedantic and dull while highlighting the need for wise, fun, creative communication.
I can only wish we could say the same about this article.
He raps, rhymes, puns, quips, jives, and dialogues his way through this rich history and analysis. Each section of the book, which reveals the elements of different kinds of wit, and offers insight on developing it, is written in a distinct form.
Writing something funny is distinct from saying something funny. For the former, you have months to work on the jokes. For the latter, you need to be quick like sand. Can you really learn how to be funny by reading a book that the author has spent agonizing weeks preparing?
If we were cracking wise, rather than reacting angrily, and being wittier on Twitter, we might all have a much better time.
Or -- and hear me out here; this is blasphemy of the highest order -- we could all decide to collectively ignore Twatter. |
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