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 |    Not for the faint of art. |
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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. ![Merit Badge in Quill Award
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| I'm not sure there's anything new here, but it's an interesting read. https://getpocket.com/explore/item/how-your-brain-decides-without-you How Your Brain Decides Without You And already we have a misleading headline. Your brain can't decide anything without you, because the concept of "you" is tied up in your brain. Or something. It's not like we really understand consciousness. The structure of the brain, she notes, is such that there are many more intrinsic connections between neurons than there are connections that bring sensory information from the world. From that incomplete picture, she says, the brain is “filling in the details, making sense out of ambiguous sensory input.” The brain, she says, is an “inference generating organ.” She describes an increasingly well-supported working hypothesis called predictive coding, according to which perceptions are driven by your own brain and corrected by input from the world. Okay... but what I'm not seeing in the article is anything about how one's preconceptions are coded in the first place. Genetics? Environment? Some combination? Likely, they don't know. But the fact is there that they are coded, and thus there might be ways to change that code. Nice if you want to change it. Not so nice if there's some external input that can change what "you" are without your conscious consent. This has implications on our conception of "free will," incidentally. I've been saying for a while now that the classical definition of "free will" is bogus - the idea that, given the exact same set of circumstances, we could have decided differently. That's no excuse for acting badly, of course, but it does imply a kind of determinism. Like I said, interesting stuff. But there's a brewery out there called Duck Rabbit, and their logo is based on the duck/rabbit illusion featured in the article. And now I want one of their beers. Apparently I have no control over that. |
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Finally. Fascinating stuff. All of them. There is something rather philosophical about comedy. You are certainly right there. 
