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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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December 25, 2024 at 9:01am
December 25, 2024 at 9:01am
#1081497
I've banged on in here many times over what is and is not an illusion. Here's a bit from Popular Mechanics (way back in 2020) about things we know are illusions.

    Why We've Fallen for Optical Illusions for Thousands of Years  Open in new Window.
Mammoth or bison? Rabbit or duck? Ambiguous images have tricked our eyes forever.


Forever, huh? Our eyes haven't been around forever.

Okay, okay, no, I'm well aware of the emphatic connotation of "forever," and it's beneath me to rag on that usage. I did it anyway.

So, because pictures in here are hard to do, you'd need to visit the link to see the oldest known optical illusion: a carved mammoth / bison dated to 14,000 years ago, thus showing that humans have been fascinated by optical illusions, if not forever, for at least 14,000 years.

Like many optical illusions, these images play on the human brain’s urge for context and turn our first impressions upside down.

I say it also plays on our predilection for pareidolia. Much of art does, really; it can be deliberately-induced pareidolia, which is why we recognize the smiley-face emoji as a smiley-face. These illusions deliberately induce pareidolia in more than one way.

The ambiguity itself is the point, and researchers have studied how the regular human experiences and preconceived notions we all carry around influence the way we decide between ambiguous options or fill in missing information.

And there's a metaphor in there, somewhere.

There's not a lot more at the article, which doesn't even acknowledge my hypothesis about pareidolia, preferring instead to talk about brain plasticity and resolution of ambiguity. But it did get me wondering why these illusions don't elicit the same kind of groaning hatred that their linguistic equivalent, the pun, does?

Maybe because evolution has worked to keep us punsters from contaminating the gene pool.


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