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Rated: 18+ · Book · Personal · #1196512
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.




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March 10, 2022 at 12:02am
March 10, 2022 at 12:02am
#1028667
Been a while since I made words about words.

From respair to cacklefart – the joy of reclaiming long-lost positive words  Open in new Window.
We have been bombarded with negativity recently; but the English language is a treasure trove of joyous vocabulary


While I want negative words as well, these will do for now.

“Dwell on the beauty of life. Watch the stars, and see yourself running with them”: words of positivity from the Roman emperor Marcus Aurelius.

Easy to be positive when you're an emperor, I suppose. As long as you're not dodging assassins.

In recent times I’ve made it a mission to highlight a category of English that linguists fondly call “orphaned negatives”. These are the words that inexplicably lost their mojo at some point in the past, becoming a sorry crew of adjectives that includes unkempt, unruly, disgruntled, unwieldy and inept. Yet previous generations had the potential to be kempt, ruly, wieldy, ept and – most recently thanks to PG Wodehouse – gruntled. Some were even full of ruth (compassion), feck (initiative) and gorm (due care and attention).

Well, that explains a few things from previous entries.

It’s not just these negatives that have been lost. The German schadenfreude – pleasure in the misfortunes of others – is now all too familiar. But how many of us know its near opposite in English, “confelicity”, which is joy in another person’s happiness?

Not me. I'll probably forget that word as soon as I'm done with this entry.

But if we are pessimists at heart, it has never stopped us having a laugh.

I mean, sure, that's pretty much my entire brand. That and science. And drinking.

Some of our happiest words are such because they make us smile, and often involve a bit of fun at our own expense. Who can resist such nicknames as “cacklefarts” for eggs, or “bags of mystery” for sausages (because you never quite know what’s in them)? Even the prudish Victorians knew hankies as “snottingers”, and umbrellas as “bumbershoots”.

The Victorians weren't nearly as prudish  Open in new Window. as they're made out to be.

Also, I'd never heard of "cacklefart," which is, obviously, a fine word. I've been known to call eggs "cackleberries." And milk becomes "moo juice." I get my groceries delivered now, because I'm lazy (been doing it since before anyone had heard of COVID), and before that I made grocery lists on a note app on my phone. But before that , I'd use the traditional ink on paper. One time, I'd written a grocery list that included cackleberries, moo juice, chick tits (what else are you going to call chicken breasts?), and a few other twisted inventions of my own. By the time I got my groceries to the car, though, I realized that I'd dropped my grocery list somewhere.

I can only imagine the look of shock and/or horror on the face of whoever found that thing and read it. And then I laugh. See? I can experience joy.

The fact that "cackleberries" is a longer word than "eggs" and thus takes more time to write out is immaterial.

It’s true too that other languages dish out positivity a little better than us. They have a splash of what the Italians call sprezzatura, a careless, thrown together nonchalance or indifference to life’s curveballs. As for joy, it would be hard to beat gigil from the Philippines. In a single word it conveys the “irresistible desire to squeeze something cute”.

That concept just gave me diabetes.

But one English word surely stands above all others from the corners of the dictionary. I mention it all the time, because I’m determined to bring it back. Or bring it anywhere in fact, for it never really enjoyed more than a day in the sun. “Respair” has just one record next to it in the Oxford English Dictionary, from 1525, but its definition is sublime. Respair is fresh hope; a recovery from despair.

...nah.


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