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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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| Superlatives can be difficult to remember. PROMPT September 23rd What is the most spontaneous thing you have ever done? In this case, there's an added level of difficulty: to me, something is either spontaneous, or it isn't. While I dislike the idea of binary thinking, this one's pretty clear: either I plan for something, or I don't. I suppose "least spontaneous" would make more sense, since perhaps you can think of something that you've planned longer than anything else. For me, that would probably be my professional engineering exam. Planned for it for, what, something like 15 years? On the other end of the scale you get what I did yesterday: I was sitting there messing around on WDC when the thought came to me, "My car just passed inspection and is in working order again. I've got nothing pressing to do here. I want to take a drive." And so I selected a random destination, got dressed and took off. Planning time: oh, maybe 20 minutes to generate the coordinates and get dressed for driving. That's probably as spontaneous as I get. If you count things that don't require any preparation at all, maybe you can count the times I've been like, "You know, I could sure use a beer right now," so I open the fridge and pop a cold one. Total time between thought and action: maybe 15 seconds, depending on where I am in the house. Less if I get the idea whilst standing in the kitchen. I guess I was assuming that the prompt is about going somewhere. Consider, then, an equation that takes into account the amount of planning and the distance to be traveled. Less planning, higher coefficient. Further distance, also higher coefficient. Call planning time P and distance to be traveled D, then the "most spontaneous" thing would be whatever has the highest value of S (for spontaneity) = D / P (because if P is in the denominator, then a lower P means a higher value of S). Now, in the Before Time, I have considered upping and taking off to Paris or something on no notice, because I could. I mean, I have an up to date passport, and they were still letting Americans in. But since I've never actually done that, we'll reserve that particular value of S for sometime in the future. I hope. I don't know, maybe D should be T, for time. After all, if I decide to drive to Los Angeles, it's about 36 hours of driving, or call it four days of perfectly reasonable 8-hour drive times. Paris is almost twice as far away from me as L.A., as the plane flies, but it's about, oh, call it 12 hours from my house, to airport, to the inevitable connecting airport, to de Gaulle, to, I dunno, say the Eiffel Tower because everyone knows it's in Paris. (I've always despised when movies have to show both an establishing shot and the full name of the city. It's like *pic of Eiffel Tower* "Paris, France" "REALLY? I HAD NO IDEA!!!" *pic of Sydney Opera House* "Sydney, Australia." "Fuck me, I thought that thing was in Toronto.") But I digress. The point is whether you consider distance or time, it's still in the numerator of the equation: more time or longer distance, divided by the planning time. Now that I think of it, sure, it should be time. That would put S in units of time / time, making S (Spontaneity) dimensionless. That makes sense from an engineering perspective, since there are no actual units of spontaneity. Otherwise it's distance / time, which could be confused for speed. So I'll go with the time a friend of mine called me (we did that sort of thing back then) and said, "Hey, we've got tickets to Dar  Williams in New Jersey, wanna go?" So I threw my shit together, took off, met my friend and her friend, and we all drove up to northern Jersey together. Total travel time, maybe 9 hours. Prep time, 30 minutes. S=9/0.5=18. There, that's my record so far (at least that I can remember). That's just getting there, though. I'm not counting being at the concert, meeting Dar, or the drive back (which I was asleep for most of anyway).It's unlikely I'd ever beat it myself, because I have cats and at a minimum I'd have to arrange for someone to care for them when I'm away for more than half a day or so. Anyone who can beat S=18, let me know. That is, if you're still here after all the math. |
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