by Robert Waltz
Not for the faint of art.
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.
PROMPT January 5th
If you could learn the answer to one question about your future, what would the question be?
Hey, why limit it to one question? You can ask all the questions you want and get a true, accurate prediction right here:
Ask The Magic 8-Ball!
Just think of a question that can be answered "Yes" or "No", concentrate very, very hard, and click on the "Ask" button.
Hey, Magic 8-Ball, will I ever get married again?
Cannot predict now
Whoa, that's a tough one, huh? At least I can choose to avoid doing so. How about something easier?
Magic 8-Ball, will I become owned by another cat this year?
My sources say no
Well, that's kind of a relief. Between my two and my housemate's other two cats, we have reached the limit of catitude just below that of Crazy Cat People (the formula is C=N+2, where N is the number of humans in the house and C is the maximum number of cats before you are a CCP).
Anyway, now we're getting somewhere.
So, Magic 8-Ball, will the guy who's supposed to rebuild my deck this fall do a good job?
As I see it yes
Definitely a relief, and this also tells me that he'll actually do it and not make up some excuse to put it off until 2022!
Now, Magic 8-Ball, will I manage to end this year sipping cocktails on a tropical island, being fanned by beautiful bikini-clad women while reading good books?
Cannot predict now
Dammit! We're back to that again. I'll just have to find a way to make that happen on my own.
...I actually had one of those things when I was a kid. Yes, they've been around that long. I guess some relative or other presented it to me as a birthday or Hanukkah gift. I messed with it a little bit, but it didn't take me long to figure out how it worked: 20-sided die (okay, this was before D&D but I already knew about platonic solids) suspended in a semi-opaque liquid inside the black ball. Pretty neat, incredibly simple toy and very clever.
It does not, however, predict the future. Of course.
Sometimes, amusingly, I could get the icosahedron to balance on an edge at the window, rather than a face, thus representing the true uncertainty of any predictions about the future.
There are some things about the future that can be predicted to incredible accuracy, like the next few thousand years' worth of solar eclipses as seen from Earth. Orbital dynamics is well-understood and predictable to a great degree of precision -- and yet, all these predictions assume that nothing happens like a black hole swooping through the neighborhood, or space aliens coming by to mess with the planetary orbits. (Why would they do that? Who knows? I can't tell you how humans think, let alone space aliens.)
On the other hand, we can't predict the weather to any degree of accuracy out past a week or so, and the further you go the less accurate the weather report is. The systems involved are simply too complex.
Hell, last time they predicted "snow tomorrow," we got a few millimeters of ice and that's about it.
Kid Me with his Magic 8-Ball wanted to believe. He really wanted to know what the future actually held, but something in him even then realized that a dollar's worth of plastic and glass wasn't going to cut it.
Now, though? My actual answer to the prompt above is "No, I don't think so. Nothing." It's like, when I had a lot of future I wanted to know what would happen, but now that there's not a lot of future left for me, I think I'd rather be surprised.
Especially since the alternative would be, as Kid Me eventually discovered, profound disappointment.