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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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This piece, a recent one from The Guardian, is about communication, so it may be of interest to writers here.
Ha! I see what you did there, headline writer.
Since the moment I learned about the concept of the “thought-terminating cliche” I’ve been seeing them everywhere I look: in televised political debates, in flouncily stencilled motivational posters, in the hashtag wisdom that clogs my social media feeds.
No, you've always been seeing them. Now, you recognize them for what they are.
Coined in 1961 by psychiatrist Robert Jay Lifton, the phrase describes a catchy platitude aimed at shutting down or bypassing independent thinking and questioning.
These days, when I see or hear "platitude," I picture an angry platypus (one with an attitude). Look, it helps me, okay? Apparently, the word derives from the French plat, meaning flat or dull (I guess in the same sense that we use "flat" for non-glossy paints). But in that same language, plat also means dish—in the same way that, in English, "dish" can refer to both a plate (a word obviously also derived from plat) and the food you put on it to eat. This makes a platitude feel like something easily prepared and consumed, which is really damned appropriate.
Also, I'm pretty sure it was Ogden Nash who came up with the phrase "duck-billed platitude."
But I digress, as per usual.
In his book Thought Reform and the Psychology of Totalism, Lifton wrote that these semantic stop signs compress “the most far-reaching and complex of human problems … into brief, highly selective, definitive-sounding phrases, easily memorized and easily expressed. They become the start and finish of any ideological analysis.”
That's a whole lot of words to express what I call "bumper-sticker philosophy," which I suppose is my own thought-terminating cliché.
As the article points out, though, TTCs (do not expect me to type the phrase every damn time) aren't necessarily bad. Like any word or phrase, they can be used for good or evil.
Unfortunately, mere awareness of such tricks is not always enough to help us resist their influence. For this, we can blame the “illusory truth effect” – a cognitive bias defined by the unconscious yet pervasive tendency to trust a statement simply because we have heard it multiple times.
This gets weaponized a lot, too. Keep repeating things like "greed is good," and people start to believe it. Or, like someone we all know of, continue to lie and your minions lap it up as divine Truth, even though it's objectively a lie.
But what if we could do that with the actual truth?
To compete in the marketplace of thought-terminating cliches, then, our best bet might be to take what we know about illusory truth and harness it to spread accurate information.
Like that.
Beyond repetition, studies show that people perceive statements as more believable when presented in easy-to-read fonts or easy-to-understand speech styles, such as rhyme.
Or, you know, alliteration like in my example above.
This, of course, is where writers come in.
And a 2021 study showed that humour is among the qualities that make information more memorable and shareable. A titbit is “just more likely to spread if it’s funny”, says Scheirer.
Did you know that we here in America call small morsels of food or information tidbits instead of titbits because our Puritanical sensibilities required the change? Yeah? Then you were subjected to misinformation.
Probably. I mean, it felt right to me, too, because I'm not without bias, myself. But apparently, "tit" has at least two entirely separate etymologies.
It doesn’t only have to be shameless disinformers who exploit the power of repetition, rhyme, pleasing graphics and funny memes. “Remember, it’s OK to repeat true information,” says Fazio.
The trick, of course, is to know what's true, and in a postmodern world, that's becoming increasingly difficult. Even facts that should be universally accepted, such as the approximate shape or age of the Earth, are subject to strong opposition.
As the article implies, though, this doesn't mean we shouldn't make the attempt. |
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