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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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| "Don't believe everything you read on the internet." -Abraham Lincoln    PROMPT November 7th Today's prompt is taken from a book I own. "Great Quotes From Great Leaders", published by Motorola, my employer. This one is from Norman Vincent Peale. "The trouble with most of us, is that we would rather be ruined by praise than saved by criticism." Do you feel this is a valid statement? Tell us why you feel the way you do. The trouble with quotes is that they give the unwarranted weight of fame to questionable opinions. Which is not to say I disagree with the quote, but I'll get to that in a minute. Well, okay, more like an hour. What I mean is... well, consider the following quote: Life is like riding a bicycle. To keep your balance, you must keep moving. Sounds kind of simple, right? An almost trite comparison. Think about it, though, and a couple of things come to mind: First, most people who ride bikes are perfectly capable of keeping their balance when they're not on the bike, so you're adding a needless level of complexity to life. Perhaps the reason you're riding the bike is to get to a particular destination, in which case that alone is reason to keep moving; balance is irrelevant to that. Further, however balanced you might be on a bike, there's always the possibility that you'll hit something and wreck, or something will hit you and you'll wreck. These possibilities are greatly diminished if you stay sitting at home instead. In other words, scratch the surface a bit and it's not really a great metaphor. What gives it weight? What enabled me to find it in a quick search on the internet? Well, it's that the quote is attributed to Albert Einstein. The point being not that the quote is bad -- it's got a certain cleverness to it -- but that if Al Smith of Poughkeepsie had said it instead of the great genius Albert Einstein, it would never had survived. Oh, someone else might have said it eventually, because it's really fairly obvious (unlike the things Einstein is rightfully famous for, such as the Theories of Relativity, which are absolutely not obvious, but someone else would have worked them out eventually too). But someone famous says something, and boom, it's suddenly received wisdom. "The trouble with most of us," then, is actually that we attach an unwarranted profundity to random sayings of people we've heard of and admire. I'll call it the Einstein trap. That said, I have no admiration for Norman Vincent Peale and, in actuality, I'm far less likely to consider anything that he wrote to be useful. He was, after all, one of the founders, if not the founder, of Toxic Positivity. Almost worse, it's very likely  that he just made everything up, including, ironically, all the quotes and anecdotes of unnamed Great Men in his writing.But... the best (by which I mean the worst, that is, the most successful) con men don't lie all the time; they sprinkle in just enough truth and/or common sense (which is not the same thing as truth) to persuade people that everything they say is truthful. So by mentally devaluing the quote simply on the basis of who it's attributed to, I fall into the reverse of the Einstein trap; that is, giving words of figures that I don't like less consideration on the basis of that dislike. I'll admit that this is just as wrong as the Einstein trap itself, so let's consider the quote by itself, stripped of attribution: The trouble with most of us, is that we would rather be ruined by praise than saved by criticism. "The trouble" -- this would seem to imply that it's the only trouble, which obviously it's not. But as a rhetorical device, okay, fine. "with most of us" -- kind of a weasel phrase. How "most" is "most?" And who's "us?" I'm going to go with "greater than 50%" and "humans in general" "is that we would rather be ruined by praise than saved by criticism." More rhetoric, in this case the... crap, I don't remember the Greek name for it. All rhetorical devices have Greek names. It's the one where you contrast two different states of being: "ruined" and "saved" in this case. So, can one be ruined by praise? Yes, I think so. Absolutely. It's like when you show your writing to your family and they go "Yes, dear, this is wonderful," and so you gather up the courage to send it to a publisher, who sends back a note like "This isn't fit to line my birdcage." The family's praise isn't helpful. And can one be saved by criticism? Oh, I think it's obvious that we can, if it's given in good faith and taken without anger. So I think the quality of the quote hinges on the word "most." And that's the part I dispute. Where are the psychological studies backing up, or negating, the majority assertion? Did anyone to a poll? Has some grad student made it their thesis? I think "most of us" certainly feel good when praised. Like dogs, we're just made that way. And criticism can be tough to take, but I know I appreciate it if it's not mean-spirited, and I try to use it to improve. But again, I don't have much evidence to generalize that to others. So. If he'd said "some" or "many" instead of "most," I would be less inclined to be critical of the quote, regardless of its source. And that's my criticism. |
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