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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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April 16, 2023 at 9:53am
April 16, 2023 at 9:53am
#1048283
The random number generator for my trips to the past led me, today, to that rarest of all beasts: a short blog entry.

This one's from January of 2009: "Calvin tributeOpen in new Window.

You'd expect, given the proliferation of short-attention-span media such as Twatter, that brevity would be more popular. But no, the view count on this one is actually somewhat lower than for many of my weightier tomes from the same era.

Anyway, since it's short, there's not much to talk about, but I'm going to try anyway.

First, the link: it's dead. Not too surprising, given its age, but the website it was from still exists. Just not the article. Nor did I do my usual (even for the time) selective quoting, so I can't recall exactly what it was about. It was not, as the title may suggest, referring to the stick-in-the-mud Protestant proponent of predestination, but to the play-in-the-mud comic strip kid.

Doesn't matter much. People (including me) are still singing the praises of this now-classic comic strip. One of my most prized possessions is the three-volume hardcover Complete Calvin & Hobbes, and I still occasionally come across retrospectives and "What's that crazy Bill Watterson up to these days?" articles.

Not to mention that at this old entry, I provide a link to a story I wrote imagining a middle-aged Calvin. That one's still in my port here.

What I've hardly ever mentioned is that C&H was instrumental in cementing my decision to never have kids. He was fun to read about, but, as I recall commenting back when the strip was in its heyday of the 1980s, "Calvin is the kid I wish I'd been, and also the kid I desperately don't want to ever have."

Not that this was the only reason, mind you. There's also laziness, appreciation for uninterrupted sleep, and a strong desire to have things I own remain intact and be wherever I left them. Just to name a few.

But I digress. After all these years, those strips still make me laugh uncontrollably.


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