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Complex Numbers
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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December 1, 2024 at 8:51am
December 1, 2024 at 8:51am
#1080698
Sundays are when I usually dip into the past, and today is a Sunday, so here's a blog entry I did way, way back in 2007: "UselessOpen in new Window.

The internet has changed somewhat since 2007, so the links aren't what they used to be. They're still active URLs, surprisingly enough, but I wouldn't go in there without a condom.

First was the virtual bubble wrap.  Open in new Window. As I noted, the bubble wrap makes the popping noise as you mouse over it, but then regenerates. Infinite bubble wrap, right? Wrong! It was Flash-powered, and Flash is dead. The Web lost a lot of awesome stuff that day, including the utterly useless bubble wrap site.

I don't, in fact, know why the URL is even still there. Just to taunt us, maybe. Or perhaps for some more nefarious purpose, hence the condom.

The second URL at the site was http://www.papertoilet.com/

That one is, to my vast surprise, still operating. I guess it's not Flash. So many great things on the internet lost to time, and the one that remains is a virtual roll of toilet paper that you can unroll to reveal... absolutely nothing? Fitting.

And I'd recommend staying away from the third link, even if you're behind seven proxies. It was, as far as I can tell, just a stapler that you could make go kachunk. Well, not a stapler. A picture of one. Or whatever. And it seems to be gone, anyway. Useless to us, maybe not to malware producers.

And so the unweirdening of the internet proceeds. We have lost so much that we'll never, ever get back, and what do we have to show for it? Influenzas and trolls.

Useless.


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