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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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Not long ago, in "Time After Time"  , I speculated about time travel.And tomorrow is Groundhog Day, which is now more famous for the eponymous movie than for the rodent's weather forecasting abilities, which in turn displaced a much older purpose for observing the beginning of February, but that's not important right now - what's relevant today is that the movie Groundhog Day featured a time loop. I should note once again that an episode of ST:TNG did the time loop thing before GHD did, and that GHD itself was inspired by a novel whose title I've forgotten. But Bill Murray is awesome enough that GHD is the only thing people can compare any time loop movies to. This is fine. I love the movie, myself. I just have to be pedantic about it. Anyway. So today's link, which as usual was chosen at random, relates to both of these things. Sort of. I find that paradoxes tend to resolve themselves once semantic issues are resolved -- if, that is, they ever are. No one has yet managed to travel through time – at least to our knowledge – but the question of whether or not such a feat would be theoretically possible continues to fascinate scientists. "WHAT DO WE WANT?!" "TIME TRAVEL!!" "WHEN DO WE WANT IT?!" "IT'S IRRELEVANT!!" "...if you go back in time and stop your parents from meeting, for instance, how can you possibly exist in order to go back in time in the first place?" People keep going on and on about the multiverse interpretation of quantum mechanics, and I'm still not sure how that works (neither is anyone else), but that would easily resolve such an apparent paradox. "Classical dynamics says if you know the state of a system at a particular time, this can tell us the entire history of the system," says Tobar. Okay, this guy's a physicist and I'm not, and I'm not going to contradict his statement, but the way this quote is presented is, in my opinion, misleading. First of all, classical dynamics doesn't rule here; quantum mechanics does, with the Uncertainty Principle and all that. Second, one would have to know the state of a system to an arbitrarily large number of decimal places, which is practically, if not theoretically, impossible. What the calculations show is that space-time can potentially adapt itself to avoid paradoxes. This is misleading, too, implying an intelligence for which there is as yet no evidence. To use a topical example, imagine a time traveller journeying into the past to stop a disease from spreading – if the mission was successful, the time traveller would have no disease to go back in time to defeat. Tobar's work suggests that the disease would still escape some other way, through a different route or by a different method, removing the paradox. Whatever the time traveller did, the disease wouldn't be stopped. Hey, that sounds like a wonderful idea for a movie- oh, wait. Incidentally, I once saw the movie that inspired 12 Monkeys, a short film called La Jetée. Actually, I saw the short film first, in a cinema class in college in the 80s. If you can find it, it's worth watching. Hell. I might try to find it in the original French now that I have some understanding of that language. Tobar's work isn't easy for non-mathematicians to dig into, but it looks at the influence of deterministic processes (without any randomness) on an arbitrary number of regions in the space-time continuum, and demonstrates how both closed timelike curves (as predicted by Einstein) can fit in with the rules of free will and classical physics. No, no, it's not just you; they lost me here as well. I mean, yeah, I know what a "closed timelike curve" is, sort of, but that doesn't say much. Anyway, the thing I take issue with here is "the rules of free will." There are no such rules. Free will is taken as a given, as a basic assumption, but I'm not convinced free will is anything other than an illusion. That is, it's not a matter of predestination, but that our consciousness is the result of physical activities in our nervous systems, which in turn are subject to the rules of determinism; our decisions aren't predictable, but they are deterministic -- probably with some quantum randomness thrown in; the details are above my pay grade, but that doesn't mean we can just accept "free will" is a real thing. "The maths checks out – and the results are the stuff of science fiction," says physicist Fabio Costa from the University of Queensland, who supervised the research. Technically, anything can be the stuff of science fiction. Just saying. While the numbers might work out, actually bending space and time to get into the past remains elusive – the time machines that scientists have devised so far are so high-concept that for they currently only exist as calculations on a page. Like I said: speculative. I still don't accept that time travel is likely on the kind of large scale that captures the popular imagination (that is, anything larger than subatomic particles). But it sure is fun to read and think about. Especially if you're a writer. |
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