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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 6, 2019 at 12:05am
October 6, 2019 at 12:05am
Nothing deep or controversial today, for a change.


20 Slang Terms From World War I

I just find word origins fascinating. Mind you, I didn't fact-check any of these, but the author seems to have done his homework.

So if you ever wanted to know where words like "Blighty" (nickname for England) or "strafe" came from, well, here you go.

I'm wary of etymologies, by the way. That's why I said the bit about fact-checking above. I get tired of hearing people proclaiming that, for instance, the lovely English word "fuck" originated as "For Unlawful Carnal Knowledge" or "Fornicating Under Consent of the King." Those backronyms have been debunked time and time again, but like much bad information, they have sticking power.

One time I got an earful from a woman who heard me use the phrase "rule of thumb." She screeched at me about how that's sexist and hateful because "it's from an old law that you could only beat your wife with a stick as big around as your thumb."

This, of course, is utter twaddle - it comes from a way of estimating lengths, or something like that - but I doubt she ever let go of her dearly-held belief. Victimhood can be alluring.

Point is, don't take any etymology as the last and final word (see what I did there) on the subject. Still - interesting stuff.

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