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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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August 25, 2024 at 9:46am
August 25, 2024 at 9:46am
#1075694
Today's trip through the Wonka tunnel of time takes us back about five and a half years, to the end of February, 2019. Or about a month after my last Revisited entry. Random numbers will do that.

The entry itself, "Journeys" , was mostly just a personal update, utterly uninspiring and uninspired. This happens sometimes, too.

Finally, the last day of the hated month of February.

I don't remember when I first noted to myself, "You know? I really, really hate February." But clearly, it was over five and a half years ago.

Unfortunately, the weather report here indicates more cold days ahead, and possibly s**w. But at least the end is in sight: three weeks to the equinox.

Not a big fan of winter in general.

If I can make it that far without straying too far from my healthy-eating-and-exercise plan, begun on the solstice, I'll consider it a win. Then it won't feel so bad when I inevitably fail.

See, this is why I'm a pessimist: I can smugly assert that I totally expected to fail, so I was right, and I love being right.

There follows a couple of links to WDC activities, one of which is currently inactive, the other of which is, as I understand it, on its final round.

I'm starting to get antsy for travel again, too. Part of that, though, is the crappy weather we've been having (normal for February in Virginia, but still crappy), so we'll see if I still have the urge in, say, April.

I don't remember, and can't be arsed to look up, if I actually went anywhere in 2019. That long ago, in the Before Time, stuff starts to blend together into some kind of idyllic swirl, an innocent's last gasp before everything went to shit a year later.

It's nearly the end of August now, and already I'm mourning the end of summer.

Oh well. Soon, Oktoberfest beers will be available, and those always make the transition to autumn more tolerable. And, of course, I have a journey to look forward to.


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