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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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| And so it came to pass that during the 30DBC I collected an even thicker backlog of blog fodder links. Too many, in fact, to get to all of them before the end of the year, especially considering that I'm going to be traveling again (I'm back home now, but only for a few days). So, back to picking from the list at random. Today we're going to talk about two of my favorite subjects: money. https://www.vox.com/future-perfect/2019/9/23/20870762/money-can-buy-happiness-lo... It turns out money can kind of buy happiness after all A new paper argues that, actually, winning the lottery totally does make you happy. Oh, dis gon be gud. Does winning the lottery even make you happier? For a long time, researchers said no. Research hadn’t found any conclusive evidence that people who won large sums of money were happier afterward. There was even some evidence they were worse off. Gosh, when your sample set includes a significant number of people who are, by definition, not good with money, maybe there's some implicit bias going on? Look, I'm not ragging on people who play the lottery in general. I've done it. I also gamble in Vegas. Gambling by itself doesn't make someone bad with money or other decisions, but it does attract people who are. For many people, the lottery represents hope that they can break out of their economic situation, and that's not a bad thing in and of itself. This fact became widely known, partially because it’s so appealing to many people. It’s nice to think that life satisfaction isn’t just about how much money you have, that other things matter more, that we can’t solve all our problems with a sudden infusion of cash. There are certain sayings about money that like to float around. "Money doesn't buy happiness." "Money isn't everything." There might be grains of truth in such sayings, but mostly these homilies and others like them are designed to appeal to people who don't have a lot of money, and to keep them from rising up in revolt against the rich. We'll see how long that'll work. But there’s a problem with that research: It’s probably wrong. This is my shocked face:  Their chapter in the book makes the case that past research about the lottery was badly designed, which is why it found the counterintuitive conclusion that lottery winnings don’t make us happy, instead of the much more boring truth: They totally do. Yeah, look, I can't be arsed to follow every link in every article I come across, but from what I recall from such studies, some people handle the influx well and others, not so much. If more than 50% of the people fall into the "not so much" category, it gets reported as "money can't buy happiness" or some such - ignoring the minority, and the circumstances that might separate the "good" stories from the bad. It's also important to reiterate that in life, unlike in stories, there's no such thing as a happy ending; there are only choices about when to end your story. Lottery winners are selected at random, so they can help answer this question for us: Does money cause happiness? Again, I take issue with this premise. Lottery winners are selected at random, yes, but they are selected from a group that is largely predisposed to spend money on lottery tickets - already a biased sample. The first paper to take a serious look at the happiness of lottery winnings was a 1978 paper... Old data is old. My home state, for example, didn't have a lottery in 1978. Unlike many of the previous studies, they find, “All effects of interest are statistically significant.” Winning the lottery does make you happier. Winning more money has a more pronounced effect on your happiness. There’s certainly a lot more work to do in this vein, from testing non-German data sets to exploring how life satisfaction from a lotto win sticks around five or 10 years out. But if these results hold up, then the mysterious paradox that puzzled economists — why doesn’t winning money make people more happy? — might be solved. Winning money does actually make people more happy. I'm not arguing with the results, here. And I'm sure everyone has heard at least one story about a lottery win that went bad. Those play well in the news. It serves as a source of confirmation bias to the anti-lottery crowd, and it makes non-winners feel better about losing. "Sure, I've spent over $100 on the lottery this year with nothing to show for it, but at least I didn't ruin my life by winning $37 million!" You don't hear stories about people who won the lottery and went on to live a relatively easy life free of money worries - because those are, simply, boring and don't fit into anyone's preferred narrative. It's just not exciting to report on Jane Smith from Poughkeepsie who was able to quit her soul-crushing telemarketing job and knit doilies for sale on Etsy without having to worry about selling enough to keep living in Poughkeepsie. Jane might or might not be happy, but she's probably less stressed, and to me that's a better outcome than some nebulous concept of "happiness." A surprising share of published studies are underpowered, meaning they collect so little data they wouldn’t find a result even if one was real. This can lead to false negatives — like the result that lottery winnings don’t make people happy — and false positives, when the small sample size produces noise that is interpreted as a positive result. Making studies bigger tends to solve this, but it’s expensive — so underpowered studies are likely to plague research for some time. And I shouldn't have to note that this is a big problem in research in general. I've ranted on this sort of thing before (mostly in regards to nutritional "science"), so I'm not going to belabor the point. But on the whole, it looks like the obvious is usually true — having more money makes people less stressed and more satisfied with their life. Money might not buy happiness, but it buys a lot of things that make the pursuit of happiness easier. And I maintain that anyone who seriously thinks that money doesn't buy happiness hasn't experienced the joys of drinking really good whiskey. That shit is not cheap, but it is a font of happiness. Seriously, though, I personally think - without any scientific studies to back it up, mind you - that life is what you make of it. Happiness is, by nature, ephemeral, and I don't agree with the mindset of "happiness is all that really matters," but whether a particular individual will be liberated or enslaved by a sudden influx of a lot of cash - well, I'm not sure that can be predicted with any kind of accuracy. I am going to stop short of asserting that "happiness is a choice." It's not, always, and to say so is like a slap in the face to a lot of people. Lots of things in life are beyond our control, though we do have some choices about how we react to things. I do know that I wouldn't mind being a test case. You know. Just to be sure. I just can't bring myself to play the lottery with any kind of regularity (it's been many years since I actually bought a ticket), so I'll never find out. |
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