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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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Congratulations on winning an honorable mention for Best Blog at the 2018 Quill Awards for [Link To Item #1196512] . *^*Smile*^* This award was sponsored by the blogging consortium including [Link To Item #30dbc] , [Link To Item #blogcity] , [Link To Item #bcof] and [Link To Item #1953629] . For more details, see [Link To Item #quills] .](https://images.Writing.Com/imgs/writing.com/writers/badges/type-Blogging-2180.gif) ![Merit Badge in Highly Recommended
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PROMPT November 10th What do you find yourself insecure about? Are you able to overcome your insecurities? If so, how? If I had any insecurities - and, mind you, I'm not saying I do - but if I had any, I think chief among them would be a reluctance to share any insecurities in an open forum online. People can use that shit against you - mock you, take advantage, that sort of thing. Not that I ever worry about it. Such an insecurity would, I think, be very difficult to overcome, if it were real. I mean, hypothetically, there might be some things you can share with trusted friends, but casual acquaintances, backstabbing co-workers, fickle family members? Yeah, no, it would be too easy for bad actors to get a handle on you and crush your psyche. It's like - you don't leave your doors unlocked when you park your car on a city street, right? Not because everyone will steal from it - most people wouldn't - but because the one or two who would do such a thing can ruin your day. So, rest assured, it wouldn't be you , the one reading this right now, that I wouldn't trust in this purely theoretical situation, but some other passer-by. Consequently, it's a good thing I'm not insecure about anything or I'd have to worry about not being completely forthright in my own blog, and that would be a shame, wouldn't it? |
PROMPT November 9th Write a stream of conscious entry starting with the words “I wish...” I wish... you know what? No, I don't. It never ends well. It's cold, so you wish it were warm. But then it gets hot so you wish things would cool off. It's dry, so you wish for rain and then you wish for the rain to stop. It never ends. "Be careful what you wish for," they told me. "You just might get it." So I learned not to wish. But sometimes... sometimes it might be good to imagine something better coming along. On the other hand, nothing comes without a price, and nothing can come into your life unless something else leaves it, and who's to say which is better? I think that's why I like to write fiction. I can think of things happening and work through the consequences without actually experiencing them. It's why I try to expect - or at least anticipate - the worst. And yet, on occasion... I wish I could wish. |
PROMPT November 8th Besides music, what are some of your favorite sounds?  A while back, I vaguely recall, there was a 30DBC prompt that asked the old question: would you rather be deaf or blind? And I said something like, I despise 75% of all sounds, but the other 25% is music, and I wouldn't want to live without music. If someone has the dedication to swing back and look at what I actually wrote, and finds that it's something different from that, and calls me on it, well, congratulations. I don't really mind the little sounds that accompany everyday existence: the hooting birds, the rustling leaves, that sort of thing, but I can't say they're my favorite sounds. Almost everything else that I can call a "favorite" (that isn't music) is defined by when it stops. Neighbor leaf-blowing? Oh, good, it stopped. Jet fighters flying in formation overhead? Oh, good, it stopped. Dog barking its fucking head off across the street? Oh, good, it stopped. Cat meowing for dinner? Oh, good, it stopped. Now that I mention that, though, I'm rather partial to cat purrs, but the great thing about those is they're more felt than heard. I've been known to reject potential romantic partners if they're the kind of people who leave the TV on all day for "background noise." (I don't even have a TV anyway.) Not to mention that a non-trivial reason why I never wanted kids is because children noises make me meshuggah. If I can't listen to music, I prefer silence, or as close to it as I can get. Not that I'd want to be deaf; not just because of music but because I like to have some advance warning that someone is trying to sneak up on me - less likely to have such warning if there were a lot of background noise. So, between yesterday's prompt and today's, I suppose I've been outed as someone who prefers both silence and darkness. Make of that what you will. |
PROMPT November 7th What is your favorite color? Do you have a favorite color pairing? What’s something in your life that you picture when you think of your favorite color? Do you choose to wear clothing that is your favorite color? Has your favorite color changed over your life? Use these questions to explore how your favorite color has influenced you. What is your favorite color? Black. Do you have a favorite color pairing? Black with More Black What’s something in your life that you picture when you think of your favorite color? The Void. Do you choose to wear clothing that is your favorite color? Almost all the time. Has your favorite color changed over your life? For a while in high school, I thought my favorite color was blue, but no, it was still black. "But Waltz, black isn't a color! It's the absence of color!" Black is a color. It's technically an achromatic color, a color without hue. An object that is black doesn't radiate much in the visual spectrum (in the case of black holes, not at all), and it absorbs all visible light that impacts it. It probably generates or reflects other frequencies on the EM spectrum, though; we just can't see those. Some scientists a while back came up with a material that's nearly 100% black; it's so black it's hard to look at. Sadly, they didn't make me a t-shirt out of this material, but licensed it to some idiot artist. I'm a lot of fun at weddings, let me tell you. My affinity for black has little to do with its cultural associations, though. Mostly, I just think it looks good. Partly, it has to do with science, in some sort of metaphorical sense - as a black object absorbs light, so I absorb knowledge, however imperfectly. It's not the only color I wear, but its primary sartorial advantage is that it pairs with almost anything, which is useful when you don't want to ever think the sentence: "What color shirt will work with these pants?" So my traveling outfit consists of black shoes, black jeans, a black t-shirt, and the loudest Hawaiian shirt I can find. People should sigh in relief that at least I don't pair the Hawaiian shirt with striped pants. |
PROMPT November 6th I have another link for you all today: http://www.wmfc.org/uploads/GenerationalDifferencesChart.pdf What parts of the chart did you find to be accurate and which did you find issue with? Anything you related strongly to? Is a chart like this useful, or does it rely too heavily on stereotypes? I've said this before and I haven't run into anything that has changed my opinion: "generations" are utter bullshit; people are born, live and die on a continuum; and attempts to pigeonhole us are about as useful and accurate as star charts and Facebook quizzes. Also, as Barack Obama (misspelled on the chart) is listed as a GenXer when by its own reckoning he's a Boomer, having been born (IN THE US FOR FUCK'S SAKE) in 1961. Given that simple error (compounded by the typo), I can't trust anything the chart says. And further yet, by my calculations it's a good 11-12 years out of date now. And what the hell is it with the two date ranges for Millennials? Can't that generation do anything right? (KIDDING I'M KIDDING JEEZE) Again, I've run through this argument before, but for newcomers: I was born in 1966. That would put me in GenX, along with people born (per the chart) in 1980. So they'd lump me in with someone from 1980, 14 years distant, but not from 1964, 2 years separated? How about twins born on the cusp of 1964-65? Theoretically, one could be a Boomer and his or her little sibling (by all of three minutes) could be an Xer. That could make Thanksgivings way fun as the older sibling could throw "kids these days" shade at the younger one. It's really remarkable how much work has gone into the preparation of this nonsense chart, without even the fun math involved in astrology, or the years of college needed to come up with a Myers-Briggs analysis. The whole "generations" thing was developed, I'm pretty sure, as a tool for marketers as a way to target people for manipulation. This is seen nakedly in the stuff at the very bottom of the chart, which admittedly I skimmed down to. I'm not saying everything in it is wrong, of course - after all, Xers are "skeptical" and "cynical." Hey, spot on there. Stopped clock and all that. So of course I tried to track down where the pdf came from. The webpage corresponding to the domain in the pdf's URL (try telling THAT to someone from 1965) is the West Midland Family Center, out of Michigan - hence, one supposes, the focus on the various cohorts' work ethics and "fundraising tips." But that gives me the opportunity to point out a rule that has never led me astray in all the years I've followed it. To wit: Never trust an organization with the word "Family" in the name. Inevitably, they are run by people who are appalled at the idea that someone, somewhere, who is not a child, is having fun, and will work very, very hard to stop that nonsense immediately. Now, I don't know... I haven't clicked around that particular organization's website very much. Could be they're an exception. I wouldn't bet the farm on it, though. (I actually do own a farm, by the way. That's not just an expression for me.) |
PROMPT November 5th Write your entry today inspired by one of the emotions listed on the webpage below: https://soulspottv.com/15-words-youve-never-heard-describe-emotions-we-all-feel-... Just one? Damn. Usually I'd snark on most of them. 2. Liberosis: (n) The desire to care less about things. To loosen your grip on your life, to stop glancing behind you every few steps, afraid that someone will snatch it from you before you reach the end zone—rather to hold your life loosely and playfully, like a volleyball, keeping it in the air, with only quick fleeting interventions, bouncing freely in the hands of trusted friends, always in play. I've been working toward this for most of my life. I mean, not the playful volleyball metaphor - I hate sports - but caring gets you nowhere, so I actively try not to. You know how pedants are always like "It's not 'I could care less' but 'I couldn't care less,' because 'I could care less' means you do care somewhat?" (Okay, I'm one of those pedants.) Well, I could care less. No, really, it is theoretically possible for me to care less. It's like one of those mathematical functions that approach but never quite reach zero and you're skipping this sentence, aren't you? I actively try to care less. It helps to know that no matter what we do, no matter what we as individuals or a species or the greater community of living things achieve, no matter how we spread into the universe, no matter to what heights of art, science, engineering, or something we currently have no word for we reach... regardless of any of that, the universe continues to race in the direction of higher entropy, and eventually, it will fade into oblivion. All of the energy transfer that could have taken place will have taken place, and every point in the universe will have reached an equilibrium, the same temperature. This is known as the "heat death of the universe," and "temperature" will have no meaning because there's no way to measure it, no one to measure it. Spacetime itself will cease to have any meaning. No process of life or anything else will be able to proceed, because any such process requires energy transfer, and I just said that that will wind down to nothing. This is absolutely inevitable, and not only is there no way to stop it, but any attempt to do so will only hasten it because that's how entropy works. In fact, I've come to the realization that the purpose of life is to accelerate entropy, almost as if the Universe itself wants to end its own pointless existence. In short, nothing matters and that's the big cosmic joke. I'm aware that this sort of thing could cause an existential crisis for some people. At the very least, it can trigger the classic Five Stages of Grief, starting with denial. Deny all you want; that doesn't change the Second Law of Thermodynamics. But remember, the solution is to stop caring and laugh in the face of Fate. In that vein, then, as per the linked article, I, too, can propose made-up words for emotions that don't really exist and it wouldn't matter if they did: 1. Zeppelinalgia That feeling you get when you look to the west and your spirit is crying for leaving. 2. Grinchestia The sadistic joy that can only be achieved through ruining someone's winter holiday. 3. Wonkanastia The satisfaction of providing children with important life lessons by fitting their punishments to their misdeeds. 4. Johnwickitude When someone wrongs you and you retaliate utterly disproportionately to the situation, and damn but it feels great. 5. Entropoeia Per the above discussion, the moment of absolute darkness that envelops you when you realize that, in the end, nothing matters at all, followed by the relief you feel when snatch yourself back from the abyss in time to laugh about it. I mean, you did do that, right? Right? Hello?... |
PROMPT November 4th Would you rather be surprised or surprise someone else? Write about it! Confession time: I always wanted a surprise party. I've been to other peoples' surprise parties, even though they never seem all that surprised to me. It's always been on their birthdays, though, so I'd expect it wouldn't have been all that surprising. "Hm, it's my birthday and my friends are all acting weird around me. I bet I'm getting a surprise party!" I never arranged one, because I suck at that sort of thing, so that might explain why no one has ever done it for me. But that's being pleasantly surprised. Clearly, if it's a negative surprise, I don't want to be the target of that. On the other hand, I'm not a big fan of giving people an unpleasant surprise, either. I mean, I think pranks can be funny if they're played on anyone who is not me, but a prank is one of those things that's funnier in theory than in practice. With my philosophy of "always expect the worst," I try to avoid getting myself into situations where I'm surprised in a bad way. I was just thinking today, before I saw the prompt, of all the things that could go wrong if - I mean when - I go to Belgium and/or France. That is, after all, why I'm trying to learn French. Stranded in the Pyrenees (there are worse places to be stranded, I suppose), money stolen, trapped in the Eiffel Tower, that sort of thing. That's why I want to learn French - so I can say "help!" in the local language. Turns out I've already learned many useful phrases. For example (keeping in mind that some of these might be wrong because, like I said, still learning): Je veux une bière. I want a beer. Je voudrais plus bière, s'il vous plaît. I would like more beer, please. Je veux un verre de vin. I want a glass of wine. La bouteille de vin pour moi maintenant. The bottle of wine for me now. Je dois rentrer à l'hôtel. I have to go back to the hotel. J'ai besoin de dormir maintenant. I need to sleep now. C'est le matin. It's morning. Où sont mes vêtements?! Where are my clothes?! So you see, I want to be ready for surprises, even in France. |
PROMPT November 3rd Write about a time when you waited a long time for something. Did you end up getting what you wanted? Was it worth it? Well, there was the time I went to the DMV one morning, and left three years later with a driver's license... Okay, I'm exaggerating a bit, but it felt like three years. There's a brewery in Richmond, VA called Hardywood. They've since expanded into other locations, including one right here in my town, but at one point they just had the one location in an industrial park about an hour's drive from me. Now, there are breweries all over Virginia, but this particular brewery made a gingerbread stout that was, at the time, the only beer to ever get a perfect 10/10 score on a popular beer rating site. Not only that, but I'd had the opportunity to sample it and it was, indeed, delicious. So, naturally, I had to have some. Also naturally, so did every other drunk in Virginia, and let me tell you, we are fucking legion. To further set the scene, this particular beer is a seasonal offering, not available year-round. As you might be able to tell from the name, it's winter-holiday-themed. That means it came out in November. If you don't know anything about November in Virginia, I can sum it up in two words: it sucks. Cold, but usually not cold enough to snow. Often rainy. Rainy is fine. Cold is fine, to a certain extent; at least, I'm used to it. Cold and rainy... it sucks. So it was that on the cold and rainy November release day for Gingerbread Stout one year - I dunno, maybe 2013? It's been a while - I found myself and a friend standing in line outside the enormous Hardywood brewery in Richmond, waiting to claim my allotment of just two bottles (albeit 1L bottles) of sweet nectar of the winter gods. Along with every other drunk in Virginia. The line snaked from the brewery door, out to the street, and around the block. As a reminder, this is an industrial park block. In the rain. In the cold rain. In the nasty Virginia November cold goddamn rain. We waited. The line inched forward. It rained. It colded. The line inched forward. The day stretched on into eternity. (insert elevator musak here) (pause for effect) Finally we got our bottles and booked out of there. Was it worth it? Oh, definitely. Since then they've increased production and one can often find this paragon of beer in local stores, so there's no need to go through that again. At the same time, however, it's not quite as good as it was the first few years. Delicious, yes, worth buying, certainly, but I wouldn't wait in the - did I mention cold rain yet? Because it was cold and rainy - cold rain in an industrial park for it again. Now, it may seem strange that when prompted for something I had to wait a "long time" for, I pick something that I had to wait, max, a few hours for. This is because I don't wait. I'm not a patient person. If I do find myself waiting for something, I distract myself - games, reading a book, whatever. Can't do that in a cold, rainy, outdoors queue. So, say, waiting for my passport or tax refund or the latest Brandon Sanderson book that I preordered from Amazon months before it's due to come out - well, I don't count those as waiting, because I'm doing other stuff. Also, beer is important. |
PROMPT November 2nd Write about jouska. From Psychology Today, jouska is defined as “a hypothetical conversation that you play out over and over in your head. For example, replaying an argument in your head where you say all the right things and “win” the argument, or practicing asking your boss for a raise and playing out his or her responses and your comebacks.” Jouska is why I'm single. Doesn't everybody do this? It's basic self-programming. In the "replay" scenario you're practicing for similar situations in the future, and in the other scenario you're training yourself to deal with different responses. The trick to being a jerkface asshole is when someone comes to you having practiced the conversation in jouska, you say something that they could not possibly have thought of in their practice. Example: (Employee slinks in, hat in hand) "Um, boss, sir, may I have a raise?" Boss: (pause for effect, then) "Tell me, Widders, what do you think of pomegranates?" There's absolutely no reason you should allow yourself to play to their jouska script. If you do this, though, you have to practice jouska yourself just so you can come up with off-the-wall, non-sequitur responses to any rehearsed conversation. I mean, in the above scenario, presumably the peon has practiced this with the boss giving different levels of "yes" "no" "maybe" and "why" responses, and they've got all kinds of data backing up why they should get a raise, including having come to work on time even with measles, securing a multi-million-dollar contract for the company, and their kid has cancer. None of this matters; your job as boss is to make sure they don't get a raise. They're not expecting a conversation about pre-Raphaelite paint mixing techniques, so give 'em one. On the peon's side, even though you know this could happen, you practice jouska anyway, right? Like I said, everyone does it. Sometimes you lie awake at night, staring into your old friend the dark abyss, replaying a conversation until you've convinced you monkey brain that it went your way, after all. Or you're worried about the meeting tomorrow so you play out different scenarios, remembering to be ready for loops thrown at you involving pomegranates or paint. But not me. No, I don't run variations on the script until things go my way, because I know things won't go my way. I run scenarios until they involve the worst possible outcome for me. There's a good reason for that: I only like to be pleasantly surprised. It's the same reason I'm pessimistic about everything. If I go into a situation expecting, or even hoping for, a good outcome, I can be disappointed. If, on the other hand, I go into, say, the doctor's office expecting a cancer diagnosis, then if it is not cancer I can feel the pleasure of relief; whereas, if it is cancer, I can feel the euphoria of having been right. Which brings me to why I'm single. Every time I think about meeting someone, the jouska goes something like this: Me: "Hi, my name is-" Her: *PEPPER SPRAY* Or this: Me: "Let me buy you a drink." Her: "I was just leaving. With my husband. The pro boxer." Or this: Me: "Hey, let's talk about pre-Raphaelite paint mixing techniques." Her: "Zzzzzzzzzz..." I think some guys, they go into potential relationships, and they like to skip ahead in their minds to the part where they're both naked. Maybe some chicks to that, too; I don't know. Point is, some people just kind of wing the whole "get to know you" part and rush to the "let's get the lube" part. In other words, their jouska involves playing out the clothes-on scenes in such a way as to get to the R-rated movie as quickly as possible. But not me. No, whenever I meet someone I think I might be interested in dating, my mind doesn't skip ahead to the date, or to the sex, or to the breakfast afterward, or to the trip to the Paint History Museum. It skips right to the part where she's had enough of my bullshit and storms out the door for the last time. Knowing she'll leave me for some Australian dingo-fucker is enough to keep me single. Now, look, I know this might come across as me having a low opinion of women. Think about it, though - if I had a low opinion of women, I could probably convince myself that I could attract one and keep a relationship going. It's myself that I'm certain is unworthy, not anyone else. Proof? Well, what's the one thing women say they look for in a partner? Looks? No. Money? No. Muscles? Gimme a break. Six-pack abs? N-well, maybe. Probably it helps. Cats? Definitely not. No, it's a sense of humor. You may not like my sense of humor, but I think we can all agree that I have one, yes? Yes? Okay. Good. And yet I'm still single. Q.E.D. I have the one trait that heterosexual women claim to be looking for in a male partner, and still can't stop being single. Consequently, it's me. Therefore, my jouska will continue to justify this to myself. |
PROMPT November 1st I’m sending this prompt in between princesses and spidermen begging at my door for free candy.  If you celebrate Halloween in your part of the world, what are your family’s traditions? What were the popular Halloween costumes in your childhood? Which candy was the most coveted?   Of course, when I was a kid, it was called Samhain and we'd load our pack asses with sacrificial chickens and make the week-long trek over muddy roads to the nearest henge. Okay, fine, I'm exaggerating. The roads had some rocks on them. I've lived in the same house for over 23 years now, which is longer than I lived in the house where I grew upspent my childhood. In that quarter of a century, we've had years where greedy, grubbing spooks have shown up for socialist handouts, and years where I got to eat all the candy myself. This year I'm losing weight, so I didn't buy any candy. If I have to diet, so do the zombies, goddammit. Hey, at least I didn't print up a bunch of "The True Meaning Of Halloween" pamphlets to hand out to convert the little bastards to Paganism. I'm absolutely boring when it comes to seasonal decorations. Other people on my street put up halfhearted carved gourds for Halloween or a few desultory lights for Yule, and maybe a limp flag for the Fourth of July. But that all seems like w*rk to me, and w*rk is something I go to a lot of trouble to avoid. Especially w*rk that has no functional purpose. Engineer, remember? If it doesn't hold something up or tie something down, it's not worth doing. My ex liked to decorate, and sometimes I'd even help her in the interest of marital harmony. That worked out so well that she's my ex. So, my family's traditions (hey, my cats count) are to turn off the lights on Halloween evening, take a nap, and pretend to ignore the knocking and the sounds of splattered eggs and thrown toilet paper. This Halloween, though, I didn't have to bother: they issued a tornado watch, it rained, and the winds got up to 50 miles an hour, enough to blow trick-or-treaters right into the next county. So no beggars. Peace. Well, peace except for expecting a gust-blown tree limb to come crashing through my roof (spoiler: it didn't). As for my childhood? I don't remember. I suppose the usual standbys: ghosts, vampires, cartoon witches. I can't say I remember any particular costume that I or my friends ever wore. Maybe my mom cut holes in a white sheet once in an attempt at a ghost but then thought better of the optics. And then we come to the biggest advantage of having been an only child: I got to eat ALL the candy. Well, all except for the candy corn. I may not remember a single costume, but I distinctly remember the first time I stuck one of those disgusting lumps of earwax into my unsuspecting gobhole. I think I was four or five. "What the shitting fuck is this piss?" I believe were my exact words after I spit the abomination onto the good carpet. Even my dog wouldn't touch it. So, "which candy was the most coveted?" Anything that wasn't candy corn. |
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