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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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October 12, 2019 at 12:03am
October 12, 2019 at 12:03am
#967679
It's Saturday morning (technically) and I'm feeling oppositional, so...

http://mentalfloss.com/article/57032/25-words-are-their-own-opposites

25 Words That Are Their Own Opposites

English, as I've noted before in here, is weird. I say this as someone with very limited exposure to other languages, so I may be way off base, but as a nearly-lifelong speaker, reader, writer, and punster of the language... it's weird.

Here’s an ambiguous sentence for you: “Because of the agency’s oversight, the corporation’s behavior was sanctioned.” Does that mean, "Because the agency oversaw the company’s behavior, they imposed a penalty for some transgression," or does it mean, "Because the agency was inattentive, they overlooked the misbehavior and gave it their approval by default"? We’ve stumbled into the looking-glass world of contronyms—words that are their own antonyms.

I gotta admit, those two words - "oversight" and "sanction" - confused me for the longest time. I can only imagine how an ESL person can deal with this sort of thing.

4. Dust, along with the next two words, is a noun turned into a verb meaning either to add or to remove the thing in question. Only the context will tell you which it is.

Wait... wait... "dust" can be used as a verb?

23. B**ch can derisively refer to a woman who is considered overly aggressive or domineering, or it can refer to someone passive or submissive.

Really? Do we really have to self-censor "bitch" on Mental Floss? I'm going to rethink my occasional visits to their articles and, clearly, I could never work there.

Anyway, just a fun thing to think about. The article gives some etymology where appropriate. It's way too late at night for me to think of other contronyms, but I'm sure others will come to mind when I'm not expecting them.

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