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# Complex Numbers

Rated: 18+ · Book · Personal · #1196512
Not for the faint of art.
 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.
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April 1, 2021 at 12:02am
April 1, 2021 at 12:02am
#1007417
 No Fooling As it is April Fools' Day, how about an article that actually fits with the plain (as opposed to metaphorical) theme of the blog? Imaginary Numbers May Be Essential for Describing Reality   A new thought experiment indicates that quantum mechanics doesn’t work without strange numbers that turn negative when squared. Sure, you can skip this if you want; it won't break my heart. But for anyone who's ever laughed at the idea of "imaginary numbers," this one's for you. After all... all numbers are imaginary, in a sense; there's just a subset with the official name of "imaginary." Mathematicians were disturbed, centuries ago, to find that calculating the properties of certain curves demanded the seemingly impossible: numbers that, when multiplied by themselves, turn negative. They weren't as disturbed as non-mathematicians, I'm pretty sure of that. Want to disturb a mathematician? Ask one how to divide by zero. All the numbers on the number line, when squared, yield a positive number; 22 = 4, and (-2)2 = 4. Mathematicians started calling those familiar numbers “real” and the apparently impossible breed of numbers “imaginary.” As I've noted, all numbers are already abstractions. These are just... I guess... more abstract? Yet physicists may have just shown for the first time that imaginary numbers are, in a sense, real. Okay, fine; I still say the opposite is true. “These complex numbers, usually they’re just a convenient tool, but here it turns out that they really have some physical meaning,” said Tamás Vértesi, a physicist at the Institute for Nuclear Research at the Hungarian Academy of Sciences who, years ago, argued the opposite. “The world is such that it really requires these complex” numbers, he said. Even my own surface exploration of math and physics has led me to the conclusion that if the math exists, eventually some physicist will find an application for it. I may be wrong, but it's happened too many times to count (see what I did there?) The earlier research led people to conclude that “in quantum theory complex numbers are only convenient, but not necessary,” wrote the authors, who include Marc-Olivier Renou of the Institute of Photonic Sciences in Spain and Nicolas Gisin of the University of Geneva. “Here we prove this conclusion wrong.” Now, I've always heard that complex numbers also show up in, say, electrical engineering. I wouldn't know. Electricity might as well be magic, as far as I'm concerned. I got somewhat familiar with the math involved because the Mandelbrot set   is just plain fascinating. Anyway, the article goes on to describe the experiment in question, whereupon it quickly loses me. What does this all mean? Well, nothing much to everyday life. Maybe it adds another layer of flavor to this blog's title knowing that what is imaginary possesses a kind of reality. Like I said, I just find it interesting, so y'all get to read about it here.
March 31, 2021 at 12:02am
March 31, 2021 at 12:02am
#1007361
 The Cure Going back to Scientific American for this one. The Power of Psychedelics   They worked for my depression. Could they be the future of psychiatry? Just to be clear, here, I haven't used psychedelics. Some people I know have. What I have had is depression, and meds that never worked for it. In 2012, I had my first psychedelic experiences, as a subject in a clinical trial at Johns Hopkins University School of Medicine’s Behavioral Pharmacology Research Unit. Pretty sure you don't have to go to Johns Hopkins to find shrooms in Baltimore. Prior to their 1971 prohibition, psilocybin and LSD were administered to approximately 40,000 patients, among them people with terminal cancer, alcoholics and those suffering from depression and obsessive-compulsive disorder. The results of the early clinical studies were promising, and more recent research has been as well. Some drugs are legitimately dangerous. Some are only dangerous in context; I wouldn't want to encounter a tripper (or a drunk) driving on the road. Many are considered dangerous but probably have medicinal benefits; I've always seen shrooms as one of those. The main reason for prohibition in their case is we can't have people thinking for themselves, making their own decisions, or exploring alternative mental states; if people did all that, where would capitalism find its wage slaves? Eight years after my sessions, researchers continue to prove the same point again and again in an ongoing effort to turn psychedelic drug therapy into FDA-sanctioned medical treatment. To be fair, "prove" is a bad word here. Research supports (or doesn't); it can disprove, but it can't "prove." Psychedelic drug therapy subverts the timeworn patriarchal hierarchy by creating an atmosphere of cooperation and trust rather than competition and domination. Gender-Studies-like-typing detected. Doesn't mean it's wrong, though. MDMA (3,4-methylenedioxymethamphetamine) is rapidly proving effective in treating PTSD. Chemical names can sound scary (if, that is, one can pronounce them at all). They shouldn't. As I've harped on too many times already, everything we ingest is made up of chemicals, and I guarantee you a lot of them have long names. Granted, this one includes "methamphetamine," but it's important to note that MDMA (aka Ecstasy or Molly) is not meth. The success of the cancer studies has led to investigational treatment for patients suffering from intractable depression, early-stage Alzheimer’s, anorexia nervosa and smoking addiction. On the other foot, there's a long history of Puritanical pearl-clutching in the US, and any medicine that alters one's mental state is frowned upon (including alcohol, which in fairness is probably way more dangerous than cannabis or psychedelics). This alone is probably what's been stalling approval of effective therapies. There's also this persistent idea that we should be self-sufficient, and not turn to altered states of consciousness to relieve the pain of everyday life. That's pernicious. Clearly, abuse of any drug (or any substance in general) has its dangers, but personally, I'd like to see a follow-up on these studies of psychedelics. I still have little desire to use them recreationally, but this is one thing science is for: to get closer and closer to the truth. Some say psychedelics help with that on a personal level; why not combine the two? Anyway, check out the article, if you can get past the gender-studies lingo involved.
March 30, 2021 at 12:01am
March 30, 2021 at 12:01am
#1007295
March 29, 2021 at 12:01am
March 29, 2021 at 12:01am
#1007228
March 28, 2021 at 12:03am
March 28, 2021 at 12:03am
#1007169
March 27, 2021 at 12:03am
March 27, 2021 at 12:03am
#1007113
March 26, 2021 at 12:02am
March 26, 2021 at 12:02am
#1007070
March 25, 2021 at 12:01am
March 25, 2021 at 12:01am
#1007019
March 24, 2021 at 12:01am
March 24, 2021 at 12:01am
#1006963
 What's a Wonk? Look, sometimes I just like to trace a word's etymology. The preoccupation of ‘wonks’   But I often get more than I bargained for. After all, no word exists by itself. If you’re looking for evidence on how language can change, look no further than William Safire’s 1980 “On Language” column in the New York Times discussing collegiate slang—or, as Safire puts it, “campusese.” I have a vague memory of that, but I couldn't recall the contents if you paid me. According to that column, easy courses were called “guts,” and people who would do anything for an A were called “throats,” short for “cutthroats.” “Throats” was a replacement for “grinds,” itself a replacement for “bookworm.” I have an alternative idea for why people who would do anything for an A were called "throats," but let's leave that alone for now. And when I went to college just a few years later, the word "gut" was absolutely still in use for easy courses. The course I took in film, for example, was officially titled "Cinema as an Art Form," which we changed to "Cinema as a Gut Form," often shortened to "Cinema-gut." “At Yale, the grind is a ‘weenie,’ ” and “at Harvard, the excessively studious student is derided as a ‘wonk,’ which Amy Berman, Harvard ’79, fancifully suggests may be ‘know’ spelled backward. (In British slang, ‘wonky’ means ‘unsteady.’)” As I had no contact with Ivy League people -- well, except my cousin who had gone to MIT, but we didn't speak much -- this is all news to me. Merriam-Webster defines “wonk” as “a person preoccupied with arcane details or procedures in a specialized field” or, broadly, a “nerd.” Meanwhile, the distinction between "nerd" and "geek" is still hazy to me. If pressed, I'd say a nerd is someone who likes to learn stuff, while a geek has more of a math/science focus. Everyone is a nerd about something, but not everyone can claim geekitude. Webster’s New World College Dictionary, the one favored by the Associated Press, calls “wonk” slang. And though its synonyms are slightly insulting terms like “nerd,” “geek,” and “dweeb,” “wonk” is worn as a badge of honor by many people who are specialists in their field (or claim to be). Yeah, look, "nerd" and "geek" haven't been insulting for many years now. We reclaimed them long ago. As for "dweeb," well, that's just a nerd in a bowtie. Turns out, the word “wonk” has had many (unconnected) meanings over the years. This is why I'm a nerd about etymology. We are still not any closer to the etymology of “wonk.” The OED has a clue, in its entry for “wonky,” which it traces to 1919: “Of a person: shaky, groggy; unstable,” the British definition Safire cited. “Of a thing: faulty, unsound; unreliable.” The OED says its etymology is “Obscure: the German element wankel- has similar force.” I am forced to assume that "wonk" and "wonky" have entirely different etymologies, like "candle" and "candy." Just because words sound or are spelled similarly doesn't mean they come from the same place. The article doesn't, however, make a connection with Willy Wonka, which is a terrible oversight; seems to me that fictional character's name would have connections to both "wonk" and "wonky." You know, because he was an expert on candymaking, and more than a little eccentric. In the end, words mean what we collectively decide they mean, and only the most passionate grammar wonk won't admit that language itself is wonky as hell.
March 23, 2021 at 12:08am
March 23, 2021 at 12:08am
#1006902
March 22, 2021 at 12:02am
March 22, 2021 at 12:02am
#1006850
March 21, 2021 at 12:02am
March 21, 2021 at 12:02am
#1006785
 Put a Pin in This Synergy I thought about writing this entry in ironic corporatespeak, but I can't bring myself to do it. Forgive Me, For I Have Sinned ... Against The English Language   Look, the English language isn't exactly pure as driven snow. They're unavoidable — corporate buzzwords and gobbledygook. Oh, they're avoidable, alright - you just have to be old enough to retire. Belittled and unloved, corporate jargon endures, even thrives. There is no movement to rip down the wallpaper. And let's be honest fellow desk jockeys. Not only have we heard these words and phrases. We've probably used them ourselves. Even worse than the author's use of corporate jargon are the atrocities committed against the English language in that paragraph. The use of jargon is often tied to where people stand in a social hierarchy, according to a new paper from three social scientists... People with less prestige in an organization are more likely to use buzzwords. Like interns, new hires and first-year students. Oh, it was in a paper; it must be true. She makes a distinction between useful jargon in specialized fields such as medicine, science and law — and the workplace language so prevalent today, a hybrid of business school lingo and Silicon Valley hype. The latter, she says, is littered with "BS words — like orientate or guesstimate, or omnichannel or core competency." To be fair, "orientate" is probably just fine in Britain, and "core competency" might actually have real meaning. The word "guesstimate" has been around for at least 45 years, and I have hated it for 50 of those years. Make a guess. Or an estimate. Pick one. Okay, so apparently "guesstimate" has actually been around since the 1930s. That doesn't mean we can't make it stop if we really wanted to. Let's take a word that suddenly became popular a few years ago: efforting. On the surface it sounds ridiculous. Let's dig a little deeper... nope, it sounds ridiculous below the surface, too. But we English speakers love to verb nouns, and then gerundize the resulting verb. I remember when "parent" was strictly a noun, for example. To quote the great sage Calvin, "Verbing weirds language."   On a more consequential scale of slippery is the word "synergy," a longtime favorite of corporate executives extolling the benefits of mergers. And this really pisses me off, because "synergy" is a great word with a specific meaning. But like many other words, it's been beaten into oblivion by oblivious idiots. Being able to complain about language changes is one of the many perks of getting older, along with joint pain and ragging on "kids these days." But I've always hated corporate jargon, and did my best not to practice it when I was running a company. I should have had a swear jar, except it'd be called a jargon jar. While swearing in a professional setting is generally frowned upon, buzzwords are far, far worse offenses.
March 20, 2021 at 12:01am
March 20, 2021 at 12:01am
#1006689
 Fish and Ships Just some fun historical trivia today. How Fish and Chips Migrated to Great Britain   The fried fish was introduced by Jews fleeing religious persecution. I could list a few dishes that became generally popular due to Jews fleeing religious persecution. The Irish-American penchant for corned beef and cabbage on St. Partick's Day, for starters. The powerful pairing of fish and chips has long been considered a British staple. Dubbed “the undisputed national dish of Great Britain” by the National Federation of Fish Friers, it’s been enjoyed on the island for over a century, with an estimated 35,000 chip shops in business by 1935. I made sure to eat plenty of fish&chips when I was in England, though I was unaware of its historical origins. The best I had was in this little town on the east coast called Whitby, where they go out and catch the fish in the morning so it's all ready for lunch. From the 8th to the 12th century, Jews, Muslims, and Christians lived in relative peace in Portugal, known as Al-Andalus under Moorish rule. I'm guessing that was the first and last time. As religious violence worsened, many fled Portugal and resettled in England, bringing with them culinary treasures founded in Sephardic cuisine—including fish. There were two main branches of European Judaism: the Ashkenazim in the east, and the Sephardim in the west. Culturally, they were quite different. It was mostly Ashkenazim who immigrated to the US, bringing with them such things as corned beef, bagels, and latkes. The dish of white fish, typically cod or haddock, fried in a thin coat of flour, was a favorite particularly among Sephardic Jews, who fried it on Fridays to prepare for the Sabbath, as the Mosaic laws prohibited cooking. Hence why it's called "FRY day." That's a joke. Friday was named after a Norse god, like most of our days of the week. But the Friday-night tradition was likely chipless until the late-19th century. The general popularity of the potato bloomed late in Europe, and it wasn’t until the late 1800s that the tuber was accepted, due especially to the promotional efforts of a French scientist. And yet what we call French fries and the British called chips were, if my sources haven't failed me, a Belgian invention. There are also competing theories about who created the pairing of, as Churchill called them, “good companions.” Most trace it back to the early 1860s, when Joseph Malins, a Jewish immigrant, opened up a fish and chips shop in London. Others point to John Lee, a man living outside of Manchester, who ran a “chipped potato” restaurant that sold the beloved pairing. Because London and Manchester need another excuse for a rivalry. British natives and immigrants alike began slathering their cod in batter and frying up husky chips. Industrialization in the 19th and early 20th centuries launched the fish dish to even greater heights, as it became a favorite for factory and mill workers in London and beyond. One of the great things about food, besides being necessary for continued existence, is how different cultures adapt and expand on other cultures' cuisines. Some call this cultural appropriation. While that's not impossible, for the most part, I see it mostly as a beneficial thing. I've mentioned in here before that certain Italian cuisines, based off of pasta and tomatoes, couldn't exist without noodles from Asia and tomatoes from the Americas. The potato itself, of course, was a New World plant as well. We live in a time when we can sample foods (and booze) from all over the world, and as far as I'm concerned, that's a wonderful thing. What really matters with food is not where it came from, but how delicious it is. And it's hard to get more delicious than fish and chips.
March 19, 2021 at 12:03am
March 19, 2021 at 12:03am
#1006640
March 18, 2021 at 12:01am
March 18, 2021 at 12:01am
#1006580
March 17, 2021 at 12:03am
March 17, 2021 at 12:03am
#1006536
March 16, 2021 at 12:02am
March 16, 2021 at 12:02am
#1006473
March 15, 2021 at 12:01am
March 15, 2021 at 12:01am
#1006406
 The Ideas of March Oh, wait, that's supposed to be "Ides," not "Ideas." Here's the thing: I've been up way longer than usual at the moment; I've had a couple of beers, and I've been busy doing stuff all day. So I'm a little burned out. I pick articles at random to feature here. As luck would have it, just now, my usually friendly random number generator had a good laugh at my expense, and came up with this ponderous pondering: The mathematics of mind-time   The special trick of consciousness is being able to project action and time into a range of possible futures By the way: If you're put off by the word "mathematics," don't be; there's not a single equation in the article. As far as I can tell, it could just as well have been titled "The philosophy of mind-time." This was fascinating when I first found it, for some reason, and it continued to stretch my brain today. The only problem is, today, my brain is already stretched as far as it can get right now. So... I'm just going to leave this here. I hope someone else will be interested. I neither agree nor disagree with the article, incidentally; I just like the way the author presents their case. This stuff is seriously above my pay grade, but at the moment I can't even think of ways to riff off of it for humorous effect. Yeah... I know... I'm cheating today. I'll give myself this one. Hopefully, I won't make a habit of it. I'm going to go turn off my consciousness now. Tomorrow we'll see if I can make jokes, or at least be coherent.
March 14, 2021 at 12:01am
March 14, 2021 at 12:01am
#1006352
 Make It So I don't know if I can do this one without offending someone. But I'm going to try. TV’s first interracial kiss launched a lifelong career in activism   On Nov. 22, 1968, an episode of “Star Trek” titled “Plato’s Stepchildren” broadcast the first interracial kiss on American television. So, that would be five years to the day after the JFK assassination, well into the civil rights / desegregation era. Laws changed. Lots of peoples' minds did not. I was too young to watch it when it came out, but of course when I got old enough to catch reruns, I saw that and all the other episodes of Trek. I don't think it ever occurred to me to note the "interracial" aspect, and I was certainly ignorant of the history behind it. Kid Me was too busy being bothered by other aspects of that particular episode, as we'll see in a bit. The episode’s plot is bizarre: Aliens who worship the Greek philosopher Plato use telekinetic powers to force the Enterprise crew to sing, dance and kiss. You know, as far as Trek episode summaries go, that's pretty tame. I'm trying to imagine being Roddenberry or Coon or whichever producer was responsible for hearing all the elevator pitches (yes, there were elevators back then), and having to go, "No... weirder." Anyway, that was the part that I recall being scarred by as a child: the idea of aliens using mind powers to force others to do their bidding. Dance, my puppets! DANCE! (The episode, by the way, is worth watching just to see Nimoy doing his "I'm being forced to do this" dance.) It was only later that the cultural significance of the Shatner/Nichols scene was pointed out to me. I mean, I lived in the South, not far from where the "Loving" in "Loving v. Virginia" came from, so I wasn't exactly sheltered from racism; I just thought of it as something only ignorant people believed in. I guess I still do. The smooch is not a romantic one. But in 1968 to show a black woman kissing a white man was a daring move. As I see it, one of the main purposes of science fiction is not to show how things will be, but how they could be. This includes social change. But just as significant is Nichols’s off-screen activism. She leveraged her role on “Star Trek” to become a recruiter for NASA, where she pushed for change in the space program. Her career arc shows how diverse casting on the screen can have a profound impact in the real world, too. The rest of the article pretty much focuses on Nichelle Nichols, which as far as I'm concerned is a good thing. But it's impossible to talk about Nichols without mentioning Uhura, and especially that episode of Star Trek. So it's good to get that bit out of the way. Nichols’ controversial kiss took place at the end of the third season. Flag on the play: it was the middle of the third (and final) season. It's worth taking a look at the bits I'm not quoting here; the article is pretty short and details Nichols' efforts to advocate for inclusion. Star Trek is, of course, fiction, but the stories we're told influence the way we see the world. The show was far from perfect, but it tried to demonstrate the benefits of diversity at a time of great social change. And who knows; maybe someday life will imitate art.
March 13, 2021 at 12:01am
March 13, 2021 at 12:01am
#1006274