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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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| So... I've seen every episode of Doctor Who. I mean, as much as I could, anyway. A great deal of the early material has been lost, probably forever. But a few years ago, before the 50th anniversary, I went and found every episode, including the lost ones that were re-created from stills and audio tracks (and a few that were redone in animation), and watched them. Old Who, new Who, all of them. Didn't get to the 90s movie until later, but eventually watched it (almost wish I hadn't). Well, I haven't gotten around to watching the recreated 4th Doctor episode Shada yet, but as it never aired when it was made, it doesn't really count. Still, I'm going to watch it at some point, because Tom Baker will always be "my" Doctor. There's been a lot of hype about the most recent incarnation, which premiered Sunday. New Doctor, new companions, new composer, new showrunner... lots of new stuff there. In a way, that's good - it's accessible to viewers who haven't gotten into it before and don't want all that baggage. I was, I suppose, cautiously optimistic (because far be it from me to be completely optimistic about anything). Don't be scared. All of this is new to you, and new can be scary. Well, I'm here to tell you that the 13th Doctor *is* The Doctor. Thoroughly, completely, without a doubt. She nailed it. The other actors nailed it. The writers nailed it. The composer... well, jury's still out on that, but no complaints. We're all capable of the most incredible change. We can evolve while still staying true to who we are. We can honor who we've been and choose who we want to be next. Now's your chance. How about it? I would say that if science fiction / fantasy / horror / adventure aren't your thing, you probably still won't like it. But if they are, and you haven't seen Doctor Who yet, and have been intimidated by the weight of 55 years of history attached to it... now's your chance. Of course, now that I've posted this, the rest of the season might very well suck. Many episodes do. You can't be a show like that and not sometimes have your experiments fail. But that doesn't take away from this first episode, which, as I said... nailed it. |
| The local supermarket sells prepackaged pizza. "So what? Every supermarket sells prepackaged pizza." Yeah, I know. Shut up. That's not the point. This particular pizza has the usual pizza toppings - several different varieties; I get the pepperoni kind - but its crust is... naan. That despairing scream you just heard was every Italian and Indian currently reading this. It is delicious. Feel free to complain about cultural appropriation... once no one ever sells another bacon, egg and cheese bagel. Until then, I'll just keep enjoying multiculturalism. |
KĂĄre Enga in Montana  : I do write fantasy and mostly fiction. It's my way of exploring humanity, a very irrational animal if there ever was one.Humans are both rational and irrational. What a lot of people miss in discussing the dichotomy is that the opposite of rationality is not emotion (I blame Spock). Emotions are there for a reason, which makes them rational. I'd argue that irrationality can be best defined as acting against our own self-interest - but then we have to get into defining self-interest, which is problematic. A mother protecting her baby can appear to be irrational, but if her actions preserve her legacy (genetic or otherwise - this applies to adoptive parents as well), it can be a successful strategy. People have died or put themselves in harm's way for ideals, as well; standing up for what someone believes in is not necessarily irrational. Harlow Flick, Right Fielder  : I would add that the burden of proof falls on the person making the claim.This is absolutely true, in my worldview. It is not possible to prove a negative. Perhaps the most well-known formulation of this is Russell's Teapot  . If you tell me there's an Invisible Hello Kitty guiding my every action, but there's no way for me to sense the presence of said mouthless feline, I'll need something more than your assertion. And yet, I can't prove that the IHK is not there. And I shouldn't have to. (I really hope she's not.)Which brings me to my original point about reality. Some philosophies claim that there's another reality "beyond" this one, or something similar, and that the world we know is the illusion while this other reality is the "true" reality. Hell, entire religions have been built on such nonsense. Lately, this has manifested itself in the pernicious idea that we're living in a large, complex computer simulation. Even Elon Musk has asserted such, and since he's rather charismatic, people have taken that ball and run with it. It's unreasonable, irrational, and, most importantly, unverifiable (quantum mechanics is, in contrast, irrational but verifiable). Moreover, it's immaterial (pun intended); it has no bearing on how we treat each other and the very real, verifiable, complex, and sometimes mysterious world around us. Are there things we don't understand? Of course. Perhaps there always will be. Actually, I hope there always will be, because I don't care to think about what we might do if there were nothing to point our curiosity toward. But that doesn't mean you get to fill in the gaps of your understanding with outrageous claims. And yes, I consider the idea that there's a supernatural entity who created the universe and takes an interest in who we have sex with to be outrageous. I've no problem with people believing that if it brings them comfort, but when they start trying to make us all believe that way, I start to push back. I used to work with a devout Mennonite. That's fine; I can get along with just about anybody as long as I avoid the subjects of religion, politics, and whether Kirk or Picard was the better captain. (It was Kirk. Just saying.) One day he (the Mennonite, not Captain Kirk) started showing me optical illusions. You know the ones - some squiggly lines that appear to move; gray dots that aren't really there, but you can see them because of some trick of how the image is arranged; colors that appear different depending on what other colors are around them. You can find examples of all these and more online; I can't be arsed to look them up to link them right now. Anyway, it turns out that what he was trying to tell me was that we can't trust our senses, so we have to trust in God. As revealed through the Bible and interpreted by a particular sect of Shenandoah Valley Christians, in his case. I looked at these optical illusions and came up with an entirely different conclusion - that since our perceptions are sometimes limited or skewed, we have to seek the reasons why we're seeing stuff that isn't there. Usually it has to do with how our brains interpret the data they're given. And to do this, it requires study, hypotheses, testing, conclusions, and more testing. In other words, science. As a result, we've actually learned stuff about our eyes and brains, which is pretty cool when you think about it - the human brain starting to figure itself out. And that is what I meant when I said, a few days ago, that what's real is what I can sense; I'd only add the phrase "subject to scientific investigation." Science is specifically designed to overcome the limitations of our senses - telescopes, microscopes, mathematical models, and other tools of science are there to help to reveal the reality that's already there but we can't quite see. Many things that science has discovered are far beyond the perceptions of our common lives, especially when you get into the very big (cosmology), very small (quantum mechanics) or very fast (relativity). And yet they've been tested, and they work. But sometimes it's wrong and we have to start over. That's okay. I'm comfortable with saying "I don't know." Some people aren't, and they search for, or claim to have found, some Ultimate Truth. And that, in many cases, is what I'd call irrational. |
Brandiwyn🎶  : Science points to all kinds of things that we CANNOT sense as being real, proven indirectly by empirical data and math.*points to black holes* *points to the infinity of the universe* So who's to say aliens / demons / monsters / zeitgeists (Zeitgeister?) / (insert the inimical presence of your choice) aren't real? Just because we don't yet have quantifiable evidence (direct or indirect) doesn't mean they don't exist. (As a reminder, Earth is round and circles the sun, and molecules are made of atoms are made of subatomic particles.) I'm just trying to help you get over your nightmares by pointing out that they may be physically real, not just real in the sense that synapses are really firing. Just because we haven't proven it yet doesn't mean we won't eventually. So don't worry, you may not actually have a sleep disorder. This is exactly what I'm talking about when I wrote: The more you try to define "reality" and "illusion" as they relate to each other, the more slippery it gets. Incidentally, B, what you said doesn't frighten me in the slightest or change my worldview. You did a much better job of that with one picture of a Hello Kitty food truck. (shudder) I also wrote: Can I sense it? Yes? Then it's real. It does not logically follow from this that if I can't sense it, it's not real. I'm pretty sure black holes exist because a) science predicted them and b) we can see their effects on other matter and infer that there is, in fact, a black hole there. It's like sitting nice and comfy inside your house and seeing, through the window, trees swaying - even if you can't hear the wind, the swaying trees are a dead giveaway. But one must beware of taking even science at face value. Consider, especially, nutritional science. Over my lifetime, for example, eggs have gone from bad to good to bad to good to bad to... I think they're supposed to be good again? Or, after several studies that seem to indicate that moderate alcohol consumption is good for you, another study came out flatly against any amount of alcohol. There are good reasons for this sort of thing - nutritional studies are, probably more than any other branch of science, subject to confirmation bias, problems with small sample sizes, and extraneous factors. To use the egg thing as an example, you can't exactly get 10,000 people together and have half of them eat nothing but eggs, and the other half eating nothing but egg placebos. There are other factors involved in any nutritional study results. As for the alcohol thing, what that particular study failed to take into account was that if you take away one of the primary things that makes life worth living (booze), there's simply no point in living longer. This sort of thing erodes trust in science and the scientific method, to everyone's detriment. So, at this point, we have a good half the population believing that climate change is a hoax, and a not-insignificant number of people insisting that the Earth is flat. Science works. It's the best way we have of understanding the universe. It's not always right, and it's subject to changes and even reversals, but once something has been tested and observed enough, there's a high level of confidence in the result. There's a very high level of confidence that the Earth is roughly spherical. There's a very low level of confidence that drinking is always bad (and we need to be careful how we define "bad.") Incidentally, the science is still split on the "infinity" of the universe. Could be finite but huge. Could go either way. What is known to a very high level of confidence is that the universe is bigger than we can possibly see. Infinity strikes me as a mathematical construct, though, not something with any sort of physical equivalent - but then we're getting into speculation and philosophy, not hard facts. I am certain, however, that given our short lifetimes, the cosmic speed limit, and the size of even the observable universe, it might as bloody well be infinite for all practical purposes. Hell, even if we could live a billion years, we couldn't closely observe more than a small fraction of the universe. Anyway, if you want to get into things we can't directly observe but are pretty sure about, try dark matter and dark energy. Science shows that they make up the vast majority of the stuff in the universe. They're called "dark" specifically because we can't see them. We don't even know what they are, though there are guesses that are being tested right now - without much success. Might be it'll turn out to be something that turns all of physics on its head, the way Einstein's insights into the speed of light destroyed the idea of the "luminiferous ether." At the same time, there are things that are claimed to exist that there's flimsy to no evidence for, or even evidence against: Bigfoot, space aliens, the Illuminati, ghosts, unicorns, and honest politicians, for example. That doesn't - and shouldn't - stop speculation about them, or imaginative writing. Some of these things might actually exist - especially space aliens (because see above discussion about the enormously, mind-boggling, effectively infinite, vast size of the universe) - but until we have real, hard evidence, it's speculation and guesswork. That is not to say that these things aren't real. To wax Platonic (or Kabbalistic), anything you can think of has a reality of sorts. But again, my worldview is mostly practical, so I'll stick with what I can sense directly - or what science has shown to a high level of confidence has a material reality. (The title of this blog entry is a reference to the title of a book found in The Elder Scrolls series of games. I find it amusing.) |
| Thought that might get your attention. I can't think of any science fiction or fantasy authors who have been adapted to successful movies/TV more than Philip K. Dick. Tolkien, maybe, but given that his output was basically two stories and some background, it didn't take long to exhaust the source material. Stephen King, certainly, but I wouldn't put him in either of those genres, though his stories often contain elements of both. There might be some author I'm overlooking; if so, I'm sure someone will tell me. The thing is, I'm not sure why there's so much Dick in the entertainment world. Sure, his stories were often edgy and provocative, but the same could be said for any number of authors. And the original stories didn't really lend themselves to action/adventure fare; they had to be adapted. They were more along the lines of thought-provoking, a feature often attributed to the author's use of mind-expanding substances - which is yet another reason their popularity is a bit surprising. Some of you might know that my favorite movie of all time is Blade Runner (The Director's Cut version), which, of course, is an adaptation of one of Dick's stories. Off the top of my head, let's not forget Total Recall, A Scanner Darkly, and Minority Report. Just now, I looked it up, and there were a lot more as well - probably not all falling into the "successful" category. There's even a Black Mirror / Twilight Zone - like series on Amazon called Philip K. Dick's Electric Dreams. I confess I haven't seen many of those, but the ones I watched were pretty true to Dick. I also discovered once that there is a such thing as too much Dick. I once watched Blade Runner, A Scanner Darkly, and Minority Report back-to-back, and it took me weeks to recover. Somehow, I think, his drug-fueled themes bleed through to the adaptations, giving us a contact high. Oh, and let me reiterate that the remake of Total Recall sucked ass. The "sequel" to Blade Runner didn't, but it wasn't great, either. It also wasn't a true adaptation, but basically fanfiction. Anyway, this is my roundabout way of noting that Amazon's Dick adaptation The Man in the High Castle Season 3 has just come out, all episodes at once; so if I miss tomorrow's entry, it's because I'm still bingeing on Dick. No need to call 911 to report an overdose, though. |
| https://www.theatlantic.com/health/archive/2018/10/hallucinations-hearing-voices... There’s a good chance you’ve hallucinated before. If you’ve ever felt the buzz of your phone against your thigh only to realize the sensation was entirely in your head, you’ve had a sensory perception of something that isn’t real. And that, according to the psychologist Philip Corlett, is what makes a hallucination. The more you try to define "reality" and "illusion" as they relate to each other, the more slippery it gets. I find it easier to stop trying to do so; I'm an engineer, not a philosopher, and therefore my worldview is largely practical. Can I sense it? Yes? Then it's real. But hang on - I can sense these hallucinations as well. I swiftly know them for what they are, but at the time they seem real. And what about dreams? I'm a bit disappointed that the article doesn't mention that phenomenon, which is known to happen to the vast majority of people (and other animals as well). I got to wondering if maybe the biochemical mechanism that prompts hallucinations is somehow related to the one producing dreams. Most of the time when I get sensory hallucinations as described in the linked article, it happens when I'm about to fall asleep. Maybe I'll hear my name called, as plain as if someone were speaking directly to me. Sometimes it's related to other senses, such as the shaking of a minor earthquake, or a sudden, unbidden visualization. And dreams themselves are sensory - I don't know about other people, but sometimes I'll get smell or taste or touch in a dream. During a dream, things seem real enough, until the logical mind takes over and you realize that you wouldn't really have gone to class without pants. Or whatever. (I've rarely had that one, but I keep getting dreams about being back in college and there's this one class that I've spent most of the semester having forgotten that I signed up for it.) Dreams are real, in a sense. That is, they can affect a person emotionally. Sometimes they can even present a solution to a problem you've been thinking of, and so they spill over into everyday reality. Confession time: I've experienced sleep paralysis way more than I'd like. Of course, once is way more than I would have liked, but it's been significantly more than once. The way it presents with me is a very vivid sequence that, at the time, I think is actually happening. Usually there's someone else in the room, someone who's not supposed to be there (these days, no one is supposed to be there, but this started when I was married). The presence is never benign. At some point I think I might be dreaming, which for a regular dream is about when I wake up, go "okay, that was weird," and get on with my day - but in an episode of sleep paralysis, I desperately try to wake up and can't for a subjectively long time; meanwhile, the presence becomes more and more inimical. This is the classic "night mare" of historic description. But even that isn't the worst part about it. The worst part is that when I do wake up, the feelings are still with me - and I. Can't. Move. I can breathe, and my heart is still beating (fast), but no voluntary muscles will so much as twitch, not even my eyelids. I know, logically, what is happening: when we go into dream/REM sleep, the brain shuts off motor functions so that, in the dream, one can walk or fly or swim, or pick something up, or bite into a cheeseburger, or whatever, without these things translating to physical body actions. Other people have the opposite problem, in that the brain doesn't fully shut off those pathways, and so they get their legs all tangled up in the sheets or whatever. I've had that too, but it's not even close to as scary as a sleep paralysis episode. Anyway, like I said, I know this logically, but the back of my mind - especially active at the edge of sleep - still thinks there's someone or something else in the room and I'm utterly unable to kick in the basic animal flight-or-fight reflexes. I'm just as stuck as if someone's wrapped me in duct tape (don't even think about it). I'm pretty sure that many of the stories of alien abduction (those that aren't hoaxes, anyway) are the result of sleep paralysis, or something very similar. Their descriptions match. Now, I've never had Grays probing my ass, but the stories are otherwise consistent - being unable to do anything, inimical presence, sometimes physical displacement, extreme limbic reactions. In the old days before we really conceived of aliens as such, people would describe demons, or a demonic presence. People in other cultures probably experienced whatever monsters their particular cultural zeitgeist (pun intended) presented them with. Eventually, it wears off, and once I concentrate on moving just one muscle, and do so successfully, it breaks me out of the paralysis. Nightmares suck at the time, but despite the scary description, once it's over, I find the experience intellectually fascinating. In other words, it makes me think and be curious about the process. So in that sense, they're real. |
| As a kind of follow-up from yesterday's post, I thought I'd talk about money. Sometimes I'm reminded that most humans don't have the same kind of thoughts about money that I do. The word "millionaire" still conjures up thoughts of a carefree lifestyle, but consider this: Assuming a fairly modest middle-class budget of $50,000 a year, a million dollars will last (assuming interest basically keeps up with inflation) about 20 years. If you're 80, great. If you're 50, it's a crap shoot. If you're 20, forget it. Now, there are ways to stretch that. Lots of people get by on less, but to have the kind of discipline it would take to, say, live on $40K a year while knowing that there's a lot more money sitting in some account somewhere is rare. Also, with decent investments, your return would be higher. Lots of retirement planners use a 4% rule of thumb - basically, invest the lump sum, live on 4% a year. With a $1M windfall, say from a lottery win or an inheritance, you could invest it in an index fund (average annual return of about 6%), and live off 4% (40K) a year - with the difference allowing for inflation and the inevitable bear markets. Either way, we're left with $40K being not a whole lot to live off of, depending on where you're doing the living of course. The expectation of "millionaires" is a somewhat more comfortable lifestyle, even now. It's even worse if your net worth is $1M but half that is tied up in your house - which is probably an asset, but it's not a productive one; it tends to appreciate, but the only ways to get at that money are to a) sell the house (where are you going to live?) or take out home-equity loans (and get eaten by the interest charges). (Of course, $40K a year would usually let someone work a job they actually like, regardless of salary, so it certainly wouldn't suck - but we're not talking about being able to jet off to Belgium on a moment's notice.) But time and again I run into people who insist on thinking of money as something to spend, rather than something to build on. That's when you get into the lottery winners who blow through their fortunes in a few years. Or, locally, we had a semi-famous ex-wife of a billionaire who somehow couldn't live on only $1M a month and ended up selling a bunch of assets to some orange-faced guy. Popular "wisdom" doesn't help, either. "Money isn't everything." Okay, but it's pretty damn important if you like to sleep indoors and eat. "It's better to be poor and happy than rich and unhappy." No, it's better to be rich and happy - which you can't do if you're not rich, which is what happens when you spend all your money; furthermore, I'll take being rich and unhappy over being poor and any emotional state. "Money can't buy happiness." Well, okay; but only because "buying" implies spending the money, not using it as a tool to get more money. "Money won't keep you warm at night." Um... it literally does. "The best things in life are free." Never had single-malt Scotch, have you? These are things they tell poor people so they don't revolt, not Great Truths of Life. And then there's debt. I knew a girl who was impressed by men with fancy cars. "He must be wealthy," she'd say. Well, maybe - or maybe he's hundreds of thousands of dollars in debt so he can impress shallow girls. They talk about "good debt" and "bad debt," and there's some truth to that, but it's not as cut-and-dried as "a mortgage loan is always good debt." Sometimes, it's a trap. (Though credit-card debt is almost always bad.) Anyway, point is, the outward trappings of wealth are not the same thing as wealth. I won't even go into the problems with thinking about spending some amount per month as being "affordable," as opposed to paying the whole amount up front. Or the absolutely fucked-up system we have regarding health-care delivery. "But the US has some of the best health care on the planet!" Okay, arguably true, but that's only if you can find a way to pay for it. I don't have health insurance because the best plan I could find would cost me enough for me to take a cruse every month (not steerage, either), were I so inclined - with absolutely no guarantee that they'd pay the bills. At least with the cruise I'd maybe see some whales. Anyway, the point is, I could be wrong about all of this - but I've thought about these things, which a lot of people don't. Which I think is why you get the so-called "lottery curse." Again, not a curse, but unproductive attitudes about money in general. |
| https://www.thedailybeast.com/he-won-dollar19-million-in-the-lotteryand-became-a... Jim Hayes won the jackpot of a lifetime and spent big on Lamborghinis and Vegas gambling trips. Then his life went south and he turned to crime. “Having money enabled me to live my wildest dreams,” he said. “But there’s a flip side. It’s the lottery curse.” Okay, I'm just going to come out and say it: There is no fucking "lottery curse." The Venn diagram of "people who play the lottery" and "people who make bad financial decisions" has significant overlap. That's all. It's been said that the lottery is a tax on people who can't do math. Well, that's not the whole story - it's not a question of being bad at math, exactly, but being bad with money in general. Yeah, from a return-on-spending point of view, it's a fool's game, but at some point, someone does win big. It's not a retirement plan, but it's also not exactly like burning the cash you'd spend on lottery tickets in a firepit. Now, I'm not saying that lotteries are evil (or good) or that people who play the lottery are stupid (or smart). Those are not the issues, either. Again, it's about making good financial decisions, and that doesn't take intelligence so much as knowledge and the discipline to apply that knowlege. The guy in this article strikes me as being of somewhat normal intelligence, definitely not a moron, but not about to crack the Unified Field Theory either. “Common sense tells you that if you win millions, your life is made—but it doesn’t always end up like that.” No, common sense tells me that if you win millions, you need to not blow it all. “Right before he won, he was dealing with depression and some pretty severe problems,” said Stephen Demik, a criminal defense attorney who represented Hayes on the robbery case. “But when you win $19 million, your first stop isn’t going to be a psychologist— it’s going to be a new car lot.” And we start to see the problem right here. Not even his words - his attorney's. No, if I won the lottery (unlikely, as I don't buy tickets), my first stop wouldn't be a psychologist OR a new car lot, but a lawyer. A financial lawyer, not a defense attorney. Just going by the article, though, I'd say it was a combination of bad rolls of the dice, and him having no financial discipline. Not a curse, unless "being unable to deal with what life throws at you" is a curse. I've seen a bunch of articles like this lately, and they all seemed geared toward convincing us all that if you win the lottery, your life is going to be in ruins. Well, yeah, it could be. Or it could not be. You don't hear about the people who win a lottery and spend wisely, because they don't end up living in garages and robbing banks; they're on a beach somewhere in Belize or quietly going on with their lives without worrying too much about how they're going to afford their next month's groceries. They do exist. There's selection bias there on the part of reporters, and it's pernicious. So to sum up: go into the lottery with lousy financial acumen, and you're boned. Go into it with some amount of sensibility about money, and you'll probably do okay. Not that you're going to win it, anyway. But someone will. |
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