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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 a kind of follow-up from yesterday's post, I thought I'd talk about money. Sometimes I'm reminded that most humans don't have the same kind of thoughts about money that I do. The word "millionaire" still conjures up thoughts of a carefree lifestyle, but consider this: Assuming a fairly modest middle-class budget of $50,000 a year, a million dollars will last (assuming interest basically keeps up with inflation) about 20 years. If you're 80, great. If you're 50, it's a crap shoot. If you're 20, forget it. Now, there are ways to stretch that. Lots of people get by on less, but to have the kind of discipline it would take to, say, live on $40K a year while knowing that there's a lot more money sitting in some account somewhere is rare. Also, with decent investments, your return would be higher. Lots of retirement planners use a 4% rule of thumb - basically, invest the lump sum, live on 4% a year. With a $1M windfall, say from a lottery win or an inheritance, you could invest it in an index fund (average annual return of about 6%), and live off 4% (40K) a year - with the difference allowing for inflation and the inevitable bear markets. Either way, we're left with $40K being not a whole lot to live off of, depending on where you're doing the living of course. The expectation of "millionaires" is a somewhat more comfortable lifestyle, even now. It's even worse if your net worth is $1M but half that is tied up in your house - which is probably an asset, but it's not a productive one; it tends to appreciate, but the only ways to get at that money are to a) sell the house (where are you going to live?) or take out home-equity loans (and get eaten by the interest charges). (Of course, $40K a year would usually let someone work a job they actually like, regardless of salary, so it certainly wouldn't suck - but we're not talking about being able to jet off to Belgium on a moment's notice.) But time and again I run into people who insist on thinking of money as something to spend, rather than something to build on. That's when you get into the lottery winners who blow through their fortunes in a few years. Or, locally, we had a semi-famous ex-wife of a billionaire who somehow couldn't live on only $1M a month and ended up selling a bunch of assets to some orange-faced guy. Popular "wisdom" doesn't help, either. "Money isn't everything." Okay, but it's pretty damn important if you like to sleep indoors and eat. "It's better to be poor and happy than rich and unhappy." No, it's better to be rich and happy - which you can't do if you're not rich, which is what happens when you spend all your money; furthermore, I'll take being rich and unhappy over being poor and any emotional state. "Money can't buy happiness." Well, okay; but only because "buying" implies spending the money, not using it as a tool to get more money. "Money won't keep you warm at night." Um... it literally does. "The best things in life are free." Never had single-malt Scotch, have you? These are things they tell poor people so they don't revolt, not Great Truths of Life. And then there's debt. I knew a girl who was impressed by men with fancy cars. "He must be wealthy," she'd say. Well, maybe - or maybe he's hundreds of thousands of dollars in debt so he can impress shallow girls. They talk about "good debt" and "bad debt," and there's some truth to that, but it's not as cut-and-dried as "a mortgage loan is always good debt." Sometimes, it's a trap. (Though credit-card debt is almost always bad.) Anyway, point is, the outward trappings of wealth are not the same thing as wealth. I won't even go into the problems with thinking about spending some amount per month as being "affordable," as opposed to paying the whole amount up front. Or the absolutely fucked-up system we have regarding health-care delivery. "But the US has some of the best health care on the planet!" Okay, arguably true, but that's only if you can find a way to pay for it. I don't have health insurance because the best plan I could find would cost me enough for me to take a cruse every month (not steerage, either), were I so inclined - with absolutely no guarantee that they'd pay the bills. At least with the cruise I'd maybe see some whales. Anyway, the point is, I could be wrong about all of this - but I've thought about these things, which a lot of people don't. Which I think is why you get the so-called "lottery curse." Again, not a curse, but unproductive attitudes about money in general. |
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