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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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May 26, 2024 at 8:30am
May 26, 2024 at 8:30am
#1071700
Way back in May of 2008, I did an early version of my "comment on a link" thing, combined with a mini-rant: "Big Bang

As that was 16 years ago (I can math), it's not surprising that the link is no longer functional, but I think we can all get the general idea: someone found a stash of expired fireworks, and authorities decided to blow them up using plastic explosive.

Looking back on this now, I'd still take the attitude that they only did it because they could. From what I've heard since then, the proper and safe way to dispose of stale firebangers is to immerse them in water and let them soak for a good long time. But where's the fun in being proper and safe? I may be older and (arguably) wiser now than I was when I found that link, and I may have turned into the neighbor who moans about other people in the neighborhood illegally making booms and whistles around every Fourth of July, but that doesn't mean there isn't, somewhere inside me, Kid Me, who would definitely have wanted to see a bunch of old fireworks get blasted by 30 pounds of C-4.

The only difference is nowadays, I'd be more careful about where I did so.

As for the rant, it was about Mother's Day, which apparently was the day of that entry:

I thought about writing something about Mothers' Day here, but what's the point?

This year, I completely ignored it.

My mom died nine years ago this summer...

Obviously, that's 25 years ago now. That's a longer span of time than I spent living with her.

...and why the hell is there a special day reserved for people who managed to reproduce?

In fairness, there's a special day reserved for just about anything. Today, for example, is Sally Ride Day,   celebrating the birthday and legacy of the first female US astronaut (and who had one of the most awesome names in the history of names, thanks to a certain Wilson Pickett song). Now, there's a woman who accomplished something.

Hell, hamsters can do that. How about reserving a day for those who care enough about the planet and its other life forms that we did not breed like rabbits?

Note to self: stop mixing rodent and lagomorph metaphors.

And that goes double for Father's Day.

Lest anyone labor under the misconception that my rant was reserved for females alone.

Of course, at the end of the entry, I clarified that the whole rant was satire:

Oh, about the first paragraph? I'm just kidding. Mothers - and fathers - should definitely be acknowledged, not for breeding, but for bringing you up right.

If, that is, they did so.

About the only thing I truly regret about that long-ago entry was not being more explicit in tying the "Big Bang" of the fireworks disposal with the "Big Bang" usually associated with the conception of offspring. It's even possible that I didn't make the connection back then, but now, being older and (arguably) more foolish, it jumped right out at me like a rabbit. Or a hamster.


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