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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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| After tomorrow, entries will happen at weird and unpredictable times; they won't be my usual stuff, and I might even *gasp* miss a day. But meanwhile, here's another Cracked article that hits a little close to home. 4 Medical Myths We Got Thanks to Bad Reading Comprehension  A bunch of doctors exchanged jokes. People took them seriously and canceled Chinese food You donât need to spend your nights carrying out experiments or poring over data. Thatâs the job of scientists. Then scientists summarize their findings in papers. Then the media summarize those papers in articles. Then other outlets summarize those articles with their own articles. You might not even read those articles, but luckily, those are summarized as headlines. And that's as good a summary as any of lots of the science reporting I post here. 4. MSG Causing âChinese Restaurant Syndromeâ Was a Joke Not much worse than having a joke escape into the wild and be taken seriously. For decades, monosodium glutamate (MSG) has had a reputation for messing with peopleâs health. Some say it gives you headaches, while other people imagine various more serious long-term effects. In reality, MSG has the same effects on your body as salt does â except, it takes more MSG than salt to get that same effect. "But MSG really does give me headaches!" Yeah, look up the nocebo effect. The idea that MSG may be bad originated with one letter written to the New England Journal of Medicine in 1968 by a doctor named Robert Ho Man Kwok. One reader wrote demanding the original letterâs true identity, reasoning that Robert Ho Man Kwok had to be his troll name. It sounded like âHuman Crock,â didnât it? In reality, that was the guyâs actual name... I gotta be honest, I thought it was a troll name at first, too. Soon, newly informed members of the public reported feeling headaches and tingling after eating Chinese food. They didnât in clinical studies, but they did in the wild, and they blamed MSG. And this might be the best example ever on why clinical studies should carry more weight than personal anecdote. Of course, now that "MSG is bad" has permeated the public consciousness, no amount of fact-correcting is going to get people to change their minds. Some of you might feel baffled or even outraged that a scientific publication like the New England Journal of Medicine should act as a forum for comedy. No more baffled or outraged that a comedy publication like Cracked should act as a fact-checking source. Incidentally, I did a whole entry on the MSG bullshit last year: "Umami" 3. Medical Errors Arenât a Leading Cause of Death To come up with stats, the JHU analysis averaged results from a few previous studies, and it averaged them badly. One was a study of 12 deaths, while a second was of 14. You shouldnât use tiny numbers like that to extrapolate a total of 400,000 deaths nationwide. What have I been saying about small sample sizes? Yeah, I know I just said to trust studies over personal anecdotes, and I stand by that, but one must also remain skeptical of the study methods. Which this section of the article does, and better than most sources I've seen. The JHU analysis said 62 percent of all hospital deaths may be from medical errors. Other metanalyses come up a number more like 4 percent. Which is still a lot, but thatâs a big difference. Itâs the difference between âletâs go to the hospital and get that gaping wound looked atâ and âactually, with all the mistakes they do there, weâre better off just staying home and hoping for the best.â In fairness to everyone involved, "cause of death" can be tricky and complicated, and it's why we have professionals to make those determinations. And then you get the same sort of denial as I talked about above: for instance, when certain people refused to accept any "cause of death" that included COVID, because they held a strong (wrong) inner conviction that COVID couldn't possibly be fatal and because I don't know, some sort of conspiracy about funding and politics. Still, based entirely on what this section says, it's probably not the third-greatest cause of death. Which I have issues with, anyway, because every time we work on #1 and it gets pushed to #2, then we work on the new #1 and it gets pushed down the list... I guess what I'm saying is that there will always be a leading cause of death, even if we somehow cure cancer and heart disease and keep people from going out where there are snakes and cliffs, and personally, I think we should worry less about that and more about enjoying what life we have, because we're all going to die of something. 2. Men Arenât More Likely to Abandon a Sick Spouse No, but it's apparently okay to be sexist if the target is men. The researchers now did the right thing and issued a formal retraction. âWe conclude that there are not gender differences in the relationship between gender, pooled illness onset, and divorce,â they now said, and youâll today find only the corrected second paper they published, not the original. Some news sites even reported on the retraction. But those articles we linked to before are still up, with no corrections. And, just like with Wakefield's shameful connection of vaccinations to autism, there are, and always will be, stubborn people with primacy bias or confirmation bias, who will continue to believe the lie in spite of all the retractions. 1. Left-Handers Donât Die Younger Than Right-Handers Huh... I'd never heard this nonsense. Or maybe I did and dismissed it because I didn't care, being right-handed. Many articles that round up all the indignities lefties suffer mention a stat from a 1991 study, which says left-handed people on average die nine years younger than right-handers. Nah. If I'd seen that, even back then, the alarm bells in my head would have been heard for miles. Then, when we dig up the study, we see that it was based on just 19 car accidents by left-handed people and tried extending that rate to the population at large. oh for fucks sake In conclusion, science is great. Sometimes you get wrong conclusions, though, because people are involved and people are fallible (see also: death from medical mistakes). But it's generally self-correcting in the long run. Which hardly matters as long as there are people who only pay attention to what they want to believe, or to the first headline on any subject, ignoring the retractions and corrections. But hey, as long as there are bad studies, bad science articles, bad reading comprehension, and idiots, I'll never run out of blog fodder. |
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