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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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March 29, 2023 at 12:09pm
March 29, 2023 at 12:09pm
#1047132
Another prompt from "JAFBG" Open in new Window. [XGC] today...

Do you think that kindness is its own reward or should people be grateful for acts of generosity and kindness? What if they're not?


I find that there's a vast, yawning chasm between "should be" and "are."

Many people seem to labor under the delusion that they should be self-sufficient at all times. Which is silly; every life has its ups and downs. Any "help," therefore, generates not gratitude but resentment—resentment that while they're struggling, someone else is doing just fine; well enough, in fact, to dribble charity from their champagne glass.

They might grit their teeth into a rictus and mutter thanks, but inside, they're seething. Possibly even plotting revenge.

Not everyone is like that, of course. But enough are that, if you're feeling generous, you need to be careful. Read the room. Sometimes, the best help you can give someone is to let them sort things through themselves, kind of like in the "tough love" prompt from a few weeks ago.

On the other side, though, performing an act of generosity or kindness should, by definition, come with no strings attached. No expectations, not even of gratitude. Again, we run up against that chasm: some gifts have strings attached, which is just another source of resentment.

Me? I've been in tight situations, and only gotten out of them because of the kindness of others. I don't rely on the kindness of others, because that would be sort of like relying on the clouds to part when you're trying to view a lunar eclipse (it could happen, I want it to happen, but I don't count on it). Consequently, when in a position to help, I try to do so—always bearing in mind that it could be a trap, because there are also those who would take advantage of kindness.

Still, if someone's scamming, that's on them. If I fail to help in a situation where someone genuinely needs it, that's on me.

Gratitude is optional, but it makes the experience that much more pleasant.


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