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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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| As I prepare to face one of my phobias later today, it's only fitting that this story about spiders came up this time. Why so many of us are casual spider-murderers  It's officially arachnicide season in the Northern Hemisphere. Millions of spiders have appeared in our homes – and they'd better be on their guard. Why do we kill them so casually? Plus, the new Spider-Man movie hits theaters today. I don't know when I'll get a chance to see it, but I do hope it's soon. Now, I kind of like spiders. What I mean by that is: when I encounter one outside, I appreciate its elegance and its insectivorous qualities. When I encounter one inside, I try to turn it into an outside spider -- but sometimes, like when I saw a telltale red hourglass marking on one of them, well... things can get ugly. First I needed to fetch something from the shed – the domain of monstrous spiders the size of baby mice, who lurk in corners with just their furry, gangling legs protruding. On the other hand, I am not a fan of enormous spiders jumping out at me. That doesn't give me time to do a threat assessment. Eventually my journey ended on the patio – and here there was a shock. Lying on the paving, legs splayed out wildly, as though he had fallen from a great height – was the pallid corpse of Stripy. One thing I have never, ever done, though, is give a spider a name. I once had a praying mantis that liked to hang out on my ceiling, and his name was Batman. Mantises (mantes?) share the spiders' penchant for eating annoying bugs without all the extra legs, eyes, and fuzz. Why do many of us kill spiders so casually, swatting out their lives with our god-like power, almost like it's a reflex? Because we're bigger (normally) and prefer to remain unbitten? Spider massacres like these are even more jarring when you consider that spiders and humans are not so different. Though our evolutionary paths diverged at least 530 million years ago, we share many of the same organs and body parts – such as kneecaps – and similar brain chemicals, from dopamine to adrenaline. No one has ever studied spider emotions directly, but it's easy to imagine that they might be more relatable than you would think. Except I don't like to eat bugs. They may also have their own unique kind of intelligence, in which they're able to use their webs to help them think. I've seen articles about this before. The webs act as kind of an external brain. In that, they're not so dissimilar to us, as we use the Web as an external brain. According to Jeffrey Lockwood, there are a number of reasons we struggle to empathise with spiders – in fact, these unlucky creatures possess a constellation of separate features that chance has combined into a package we find uniquely repulsive. All those bloody damn eyes, for starters. Human infants as young as just five months old tend to be more threatened by images of spiders than those of other organisms, suggesting that our aversion to them is partly innate, perhaps having evolved to prevent us from casually picking up ones that are venomous. I do have a vague memory from early childhood of being freaked out by a spider that was webbing down from the ceiling toward my crib. Though whether that's a memory of a real event or of a nightmare, I'm not certain. Many of the most chilling stories about spiders have an element of surprise – such as the time a friend donned an old Halloween costume that had been stashed away in the loft for years, and someone said "wow, I love the spider detail on your neck! It's so realistic…". Much screaming ensued, because this was most certainly not part of the look, but a real spider who had silently slunk down from their hat. This is comedy gold -- if it doesn't happen to me, that is. Apart from their menacing fangs and scampering legs, spiders face another challenge in the looks department, at least from a human perspective: they don't look like human babies. To me, this is a point in favor of spiders. Anyway, a good article to read, and there aren't even that many pictures of spiders to freak people out. The ones that are there are kind of cute. I'm sure most people know intellectually that spiders are our friends, but reason and rationality are poor weapons against the true enemy, which is fear. I'll have to keep that in mind when I freak out as they drill into my eyeball. |
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