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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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| From the BBC, we have a non-boring article about boring people. Why we snap-judge some people as 'boring'  Why do people with certain professions and interests make us yawn – even before we get to know them? Imagine you are at a party, and your friend calls you over to meet their cousin Barbara. Your friend peppers his introduction with a few facts: Barbara lives in a small town and works as a data analyst for an insurance agency. Her favourite pastime is watching television. You may find yourself groaning at the mere thought of the meeting – and that reaction may say as much about you as it does about data analysts who enjoy a bit of trash TV. No, all I want to know is: Is Barbara single and heterosexual? Because she sounds like the perfect partner, someone not inclined to pester me to go hiking in (shudder) the outdoors, or demand we go out dancing or whatever it is the kids do these days. That is, unless her TV tastes include "reality" shows. That's a hard pass. I guess that makes me boring, too. According to recent research, people have many preconceptions of what features make up a stereotypical bore. Mine is "slow-speaking math professor" (or, since this is the BBC, "maths professor"). This may be because of personal experience. People judge those who match ‘boring’ stereotypes harshly, considering them less competent and warm than the average person, and unfairly shunning them in social interactions – before they have even opened their mouths. Yeah, no, I'd rather wait until someone actually starts speaking to decide whether they're boring or not. And even if they are, so what? Van Tilburg’s research builds on more than two decades of scientific interest in people’s experiences of boredom. You want to know what's boring? Studying boredom for twenty years. Twenty goddamned years. In 2014, for instance, researchers at the University of Virginia, Charlottesville asked participants to spend 15 minutes in a sparsely-furnished room. Oh, great, as if my hometown needed more negative publicity. The participants did not have their mobile phones, computers or any reading materials – but there was a device that delivered a small electric shock at the press of a button. Despite the obvious pain that this would bring, 18 of the 42 participants decided to do this at least once to break up their boredom. I'm guessing this study involved students, like most university psychology studies. It tends to skew the results. Students, used to a hectic, fast-paced lifestyle, don't know what the hell to do with themselves when confronted with nothing to do. Me, I'd just treat it as a novelty. For an hour, maybe. Still, I'd probably hit the button just once, more out of curiosity than boredom. Speaking of curiosity, I was wondering how long this exile lasted for. An hour? A day? A week? So I clicked through to the actual study. From the abstract: "In 11 studies, we found that participants typically did not enjoy spending 6 to 15 minutes in a room by themselves with nothing to do but think, that they enjoyed doing mundane external activities much more, and that many preferred to administer electric shocks to themselves instead of being left alone with their thoughts." Six to 15 minutes? What the idling fuck is wrong with people? I've spent way more than that sitting in dentists' waiting rooms or train stations, without even using my phone. You may wonder whether this reaction was peculiar to the set-up of the experiment – but it has now been replicated in other situations. Okay, good to know. In one later study, participants were forced to watch a tedious film that played the same 85-second scene on repeat for an hour. When given the opportunity, many participants chose to play with a device that delivered an uncomfortable zap of electricity. That's an entirely different scenario, in my opinion. If I had to watch a boring 85-second scene on repeat, I'd try to find a way to up the amperage (not the voltage—it's the current that'll kill you). No, I'd rather have no stimulation than a crappy video. This may explain why it is so insufferable to be stuck with a bore at a party, while we can hear all the other excited conversations around us. While we are obliged to hear about the minutest details of our new acquaintance’s job, we are missing the chance to make a deeper social connection to someone who would be much better suited to our personality. Yeah, but what if a boring person is better suited to your personality? The article goes on to note how people pre-judge other people as boring or not. Working with Eric Igou at the University of Limerick and Mehr Panjwani at the London School of Economics and Politics, Van Tilburg first asked a group of 115 US residents to describe the most typical qualities that they associated with boring people. I'd be like, "Being a professor at a British or Irish school." Because I'm a troll. These results were, in themselves, highly revealing. According to Van Tilburg’s participants, data-entry workers, accountants and tax officers were considered to be the most boring professionals. I mean, okay, tax officers are a lot of things, but "boring" isn't a word I'd use. Hobbies seen as boring included going to church, watching TV and sleeping. Sleeping is not a hobby. In terms of personality, bores were thought to be closed-minded with a narrow range of interests, and to lack a sense of humour or strong opinions on any issue. They were also thought to be overly negative complainers, whinging about every issue. Lacking a sense of humour (or even humor) would certainly be a deal-breaker for me. I mean, come on, you know me. But how can you complain about every issue if you don't have strong opinions about them? How to be interesting I'd say "Write a daily blog about stuff you find on the internet," but I may be biased. His first is to consider whether you can reframe your job description. Data analysis might, at first glance, be seen as a boring profession – but perhaps you are contributing to a bigger endeavour, such as scientific research. In general, scientists were thought to be much less boring than data workers – so emphasising the scientific element of your job could help to bypass people’s biases. These people obviously haven't met actual scientists (apart from the ones conducting the study). While we hear about exciting scientific breakthroughs all the time—some of them right here in this blog—they're almost always the result of years or decades of plodding and meticulous research. In other words, actually doing science is boring as hell unless that's something you want to dedicate your life to. Remember that bores, in general, were considered to be closed-minded with few passions. Almost everyone enjoys TV, after all, and if you list that as your only hobby you are inevitably going to seem bland. But what are your more individual obsessions? Things like gardening, journaling, fishing and knitting were all viewed relatively positively. About the only pastime I'd consider more boring than fishing is watching golf. Or maybe watching fishing. Van Tilburg points out that people are much more likely to apply negative stereotypes to others when they feel threatened. By judging you unfairly harshly for your job or your hobbies, someone may just be covering up their insecurities. Exactly how one can feel threatened by a boring person is beyond me. And I'll just leave you today with this.  (From this delightful book ). |
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