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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 used to stepping into puddles with indeterminate depths, but this one's going to test the integrity of my hip-waders. From The Conversation, and also from last month, hence the theme: I have a vivid memory of the moment I realised Santa didn’t exist. I was around six years old, it was the height of summer, and I was sitting on the step outside our back door, thinking about God. The existence of God, back then, was something that annoyed me: it meant that every Sunday, we had to go to church. Then I realised: there isn’t actually any evidence God exists. I only think God exists, because this is something people have told me. I'll be honest here: that was way younger than I was when I had that particular epiphany. Well, it wasn't an epiphany for me, and not just because the word itself has religious connotations. No, it was more a gradual realization in my case. I remember bounding up, excited, ready to share with my family this wonderful news. No longer would we be forced to endure the drudgery of weekly Sunday schools and sermons. But then I remember checking myself and thinking, oh no. If God doesn’t exist, by the same logic, Santa must be made up as well. I want to doubt that a six-year-old could leap to such logical conclusions, but peoples' minds work differently. This author went on to be, as the headline notes, a philosopher. I did not. I have too much of a sense of humor to be a philosopher. You know what we call a philosopher with a sense of humor? A comedian. Pays better, though that isn't saying much. Perhaps this was the moment I became a philosopher (though I should say that as an adult, I no longer think that the analogy between God and Santa really holds). You know what the difference is? In most cases, I think, parents know that Santa is mythology, while remaining somewhat certain about the existence of God. Here's a philosophical question: Telling someone something that isn't true is called lying (again, as noted in the article's headline). But isn't there a difference between telling them something that you know isn't true, and telling them something that you believe is true, but isn't? Like, if I'm absolutely convinced that it's about to rain. Clouds are gathering on the horizon, and there's that smell in the air and maybe the wind is picking up. So I turn to my imaginary friend and say, "It's about to pour down rain here." But over the next hour or so, the clouds move off to the north (or whatever), leaving the area where I'm standing completely dry. Did I lie? Obviously, I was wrong (hey, it happens, however rarely). But was it a lie when all signs supported my conclusion? But now the tables have turned. Now I am a parent of young children, and I am the one enforcing hegemonic myths about Santa. Ah, yes, yet another difficult decision avoided by me not wanting or having offspring. We all do it, of course. No, "we" don't. Even if he meant "we parents," not all parents do it. Our culture expects parents, basically, to lie to our children that their presents were left by a jolly fat man who flies in a sleigh pulled by reindeer through the sky. Hell, even my parents did that, and they weren't Christians. Santa's not known for leaving Hanukkah presents. That's jolly old Judah Maccabee. We all surely want our children to grow up to be honest people. Shouldn’t we set a good example, as far as possible, by telling them the truth? Except that, sometimes, honesty doesn't serve us very well. For instance, when someone asks us, "Does this dress make my ass look fat?" we don't necessarily want to tell the bare, unvarnished truth. Here's the thing about lying: it demonstrates empathy. To tell a deliberate lie requires enough knowledge about the other person's mental configuration to be able to tell them what they want to hear. As with all of our superpowers, this can be used for good or evil. But someone who "cannot tell a lie," like the mythological version of George Washington, might very well lack empathy. Amusingly, and possibly even ironically, the "cannot tell a lie" cherry-tree incident is itself a made-up story. A myth. A lie. To which I would say: well, no. We shouldn’t be honest about Santa – at least not at first. It is morally OK, to the point of being actively morally good, for parents to participate in the grand Santa lie. And the rest of the article explains why this particular author believes this. If I felt compelled to tell my children everything, I would pull no punches in relating the wretched state of the world, of existence, of my still-deepening resignation that nothing positive can be done about it. I would inflict the full brunt of my money worries, my health concerns, my (mostly irrational) worries about them. Oh, joy! More existential conundrums that I neatly avoided by means of a simple medical procedure. Now, here's the fun part: Just two days before this piece was published, the same outlet posted an article by a different philosopher (also from the UK, though Scotland, not England): "Why you shouldn’t lie to your children about Father Christmas, according to philosophers"  I'll just note that in the UK, "Santa Claus" and "Father Christmas" are essentially the same figure. The history there is kinda cool; basically, Santa was a US thing after we divorced from the UK, but then the name went back across the pond and, eventually, the stories merged.Point is, these articles, together, present two sides of the argument. That might leave parents even more confused than they were before they read the articles, but it just leaves me with a certain sense of smugness for never having to make that decision. Well, there was the one time I was at a friend's house and accidentally dropped the truth bomb about Santa Claus within earshot of their six-year-old (or thereabouts). I haven't been invited back since. That then-six-year-old would be in college now. I wonder if she's studying philosophy. |
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