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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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| The random number trolls have presented us with a second consecutive "money" article. This one's maybe a bit less esoteric and perhaps applicable to people outside the US, though it's still obviously US-centric. Well, here's a guy with a PhD in economics from one of the most prestigious universities in the world, talking about money matters. So everything he says has got to be true, right? Maybe.  I've said before, in here, some version of "ask six economists, get ten answers." Moreover, expertise in macroeconomics doesn't necessarily mean expertise in microeconomics, and vice versa. So of course I'm going to argue with the professor. We all want money — some of us dangerously so. Thankfully, there are simple and powerful ways to get rich without gambling your hard-earned savings. Off the top of my head and not following his link: 1) inherit it 2) steal it 3) win the lottery 4) marry it 5) run a ponzi scheme For sure, they won’t all just stick in your brain. And many will change over time as Uncle Sam reforms our taxes and benefits, and as new and better financial products come on board. By "reforms," I think he means "screws with;" and by "new and better," I assume he means "for the banks." This not being Cracked, the numbered list actually increments rather than decrements. I won't copy all of his advice here. If I leave something out, it doesn't mean I agree or disagree; it means I'm way too hung over to say anything relevant. In other words, make up your own minds. 1. Don’t borrow for college. It’s far too risky and expensive. I don’t say this lightly. I’m a college professor. But you can get a fine education without mortgaging your future and potentially dashing your career plans. It simply involves pursuing scholarships and applying to less expensive, if generally less prestigious, institutions. 2. If your parents are borrowing for your tuition, discuss who will repay. I'm considering these two together because after I got done being stunned by the degree of privilege assumed, and marveling at the usual Harvard snobbery, I noticed the contradiction. 3. Strive to own your home, not rent — and try to buy in cash. I'm just. I. Wow. I'm not saying this is bad advice, though buy vs. rent needs to be evaluated on an individual basis (if you're only going to be somewhere for a year or two, renting might make sense). What I am saying is that, well, how many people can actually take this advice seriously? 5. Owning a home can reduce longevity risk. Here’s another reason it’s better to own instead of rent. Let’s say you’re 70 and have found your dream location... Again, not arguing, but who's his target audience here? He starts with college applicants, moves on to presumably working-age consumers, and now we're in senior territory. People need money advice at all ages, sure, but it's going to be different for different life points. 8. Don’t worry about career and job hopping. How can you not shop around when there are so many options? I thought this was pretty much the norm these days. Why even bring it up? 9. Consider working for yourself. I tell this to my students often. If you start the right business the right way, it will raise your remaining future earnings and provide unmatched job security. And if you start the wrong business, or the right business the wrong way, or the wrong business the right way, or the wrong business the wrong way, you're boned. Way more businesses fail than succeed. We usually only hear the success stories (in contrast with lottery winner stories, where we disproportionately hear the sob stories), so there's significant survivorship bias. 11. Your living standard is your bottom line. Simulate its potential paths based on alternative investment and spending strategies to see where these strategies can land you. I'll be sure to put a pin in this and circle back later; I'm sure we can leverage the optimal outcome here. 12. Marriage beats partnering long-term. It may mean somewhat higher net taxes, but it comes with an array of valuable implicit insurance arrangements... 13. If you do get married, count on getting divorced. Why am I even still reading? 18. The Social Security Administration’s Program Operations Manual System has thousands of rules, which its staff can get wrong, in part or in full. Talk to multiple offices and do your own research. Leaving aside for the moment that it's clear that people who "do [their] own research" these days are basically just scrolling Facebook looking for things to confirm what they already think (and are wrong about)... "talk to multiple offices?" How much time does this guy think people have to sit on hold with a government agency, even in retirement? 21. If you’re worried about downside risk, play the stock market like a casino. Think of the investment in stocks as cash you take to the casino: Don’t spend a penny of your winnings, if you make any, until you’ve left the building. Wow. Just. Wow. This has got to be, hands-down, the worst piece of advice I've ever seen anyone give anybody apart from, maybe, just maybe, "Hey, you should spend a stormy night in this Victorian mansion built on an orphanage graveyard." No. If you want to gamble, gamble. That's fine. It can be fun. Try not to overdo it. The house will win in the end, but at least you've had some good times. The stock market is the one place where you can bet with the house, and enjoy at least some of their advantage. To do so, you need to buy and hold for several years. With proper diversification, you get minimal downside risk over a long enough time frame. And if you're afraid of the stock market, just keep your money in a mattress where it's guaranteed to lose value over the long term. Or, you know, buy Dunning-Krugerrands with it. That's no worse advice than some of the stuff here.   I keep forgetting to do this for a movie I saw on Sunday because my brain keeps skittering away from the experience. One-Sentence Movie Review: Everything Everywhere All at Once: Whatever everyone involved in the making of this movie was smoking, snorting, shooting and/or swallowing... I need it. Rating: 4.5/5 |
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