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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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Congratulations on winning an honorable mention for Best Blog at the 2018 Quill Awards for [Link To Item #1196512] . *^*Smile*^* This award was sponsored by the blogging consortium including [Link To Item #30dbc] , [Link To Item #blogcity] , [Link To Item #bcof] and [Link To Item #1953629] . For more details, see [Link To Item #quills] .](https://images.Writing.Com/imgs/writing.com/writers/badges/type-Blogging-2180.gif) ![Merit Badge in Highly Recommended
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| Today's link will probably only make sense to people in the US. Or, more accurately, some people in the US. 401(k) Plans No Longer Make Much Sense for Savers  The inherent extra return participants enjoyed for many years has almost disappeared because of changes in tax laws and high fees. So if you don't know what the hell this is all about, congratulations. The tax advantage of a 401(k) depends on four factors, all of which have changed dramatically since 1980 to the detriment of 401(k)s. I'm certainly not going to argue the numbers here; they seem right. I do wonder if one can truly extrapolate the average situation here, as the author does, to give advice to everyone. Nevertheless, the reason I'm sharing this article isn't to nitpick it, but to point out something that I should formalize into a Law of Life, though I'm not quite sure yet how to boil it down to bumper-sticker philosophy (or even if I should) That observation is this: Any advantage the ordinary person might enjoy will promptly be socially engineered out of existence. There's also this bit from the article: Reducing taxes on 401(k)s will cost the government money, but it could be a good investment if it results in retirement security for more middle-income households. Except that it would be an even better investment for the government to ensure that people don't retire, so they can continue to pay higher taxes until death. When I was a kid, saving was considered a virtue. Not that I was any good at practicing that or any other virtue, but at some point, most likely coinciding with the 1980s, we collectively decided that saving was for suckers, and to keep the economy going, we should spend, spend, and spend some more. And then borrowing money became easier for most people, so the economy retooled itself again. Can't afford something? No problem, just go into debt. We offer easy finance terms! Younger people today don't expect to ever retire anyway, so why bother saving anything? This, of course, plays right into the hands of our economic overlords. So how do you get ahead? Well, I don't know. Some people never will, though it's important to hold out a carrot of hope to them, usually in the form of a lottery. Even without state-sponsored gambling, though, a lot of it comes down to luck. The whole deal with any kind of retirement account, at least here in the US, is a trade-off: do I pay taxes now, or defer them until later? Deferring them until later requires that you make some assumptions about "later." What will inflation look like? How will tax brackets be handled, and where do I expect to be in them? Will the government cave in to short-sighted efforts to increase the capital gains tax rate? Will all of this effort be in vain because we're going to get nuked anyway? If you asked these questions in 1982 about 2022, you'd have gotten the answers wrong. Back then, we all figured we'd either be radioactive craters by now, or populating a Mars colony. Or maybe even both. The reality, as always, turned out to be way worse. |
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