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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've done entries in here before on dreams. It might even be too many; a search of "dream" in this blog yields five pages of results. But here's one more anyway. Weird dreams train us for the unexpected, says new theory  AI inspires hypothesis that sleeping human brain might try to break its overfamiliarity with daily data A reasonable hypothesis. Let's see if there's anything to back it up, or if it remains speculation. It’s a common enough scenario: you walk into your local supermarket to buy some milk, but by the time you get to the till, the milk bottle has turned into a talking fish. Wait, is this about dreams or LSD? Dreams can be bafflingly bizarre, but according to a new theory of why we dream, that’s the whole point. By injecting some random weirdness into our humdrum existence, dreams leave us better equipped to cope with the unexpected. That's also one reason why we have science fiction and fantasy. Although Hoel’s hypothesis is still untested, an advantage is that it takes the phenomenology of dreams – particularly their sparse, hallucinatory, and narrative content – seriously, rather than viewing it as an unexplained byproduct of other background brain processes. So, no, it remains speculation. But that doesn't mean it's wrong. “However, as with so many theories that dreaming has a function, there is no evidence yet that dreaming is more than an epiphenomenon, a functionless byproduct of neural activity." The idea of "function" can be a tricky one, biologically speaking. The way evolution works, something might start out having no apparent function, and then acquire one that's useful to the organism and promotes survival, which is then passed on. With dreams, well, it seems that dreaming is common to many animals. The question is, even if it is a byproduct of other processes, could it then be useful? I'd guess yes, but I'm hardly an expert. The article finishes with a summation of some of the other possible functions of dreaming. I'm pretty sure I've mentioned some of them in here before. I'm not going to quote them here, but the article should be free to view if you're interested. Of course, there's no reason why it couldn't be a combination of several of these functions (or even others). We have plenty of examples of body parts or processes serving more than one function. The mouth, for example, is used for both talking and chewing (hopefully not at the same time; were you born in a barn?) as well as... well... certain other things. I'm not sure if they've ever been able to tell just when dreaming started along the evolutionary timeline, but as other animals do it, it might have been quite a long time ago -- in which case, it's had plenty of time to gain adaptive function. After all, at first glance, one might think that sleep itself isn't very conducive to individual survival, as it allows predators to sneak up on you. Dreams generally occur during sleep, though, and their benefit might very well outweigh any downsides to periodic unconsciousness. But that's even more speculation, and in this case, coming from someone without any background or credentials. But that's okay -- as with a dream, the meaning can be very personal. |
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Finally. Fascinating stuff. All of them. There is something rather philosophical about comedy. You are certainly right there. 
