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 |    Not for the faint of art. |
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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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| The article I'm featuring today is old in internet terms: nearly six years. It only popped up on my radar recently, and I have to admit, when I saw the headline, my knee-jerk reaction was close to rage. Men Have No Friends and Women Bear the Burden  Toxic masculinity—and the persistent idea that feelings are a "female thing"—has left a generation of straight men stranded on emotionally-stunted island, unable to forge intimate relationships with other men. It's women who are paying the price. I guess "rage" is one of the emotions we're allowed to feel. In this case, it was mainly for two reasons: the overgeneralized headline and subhead; and how a "man" problem is turned around to be a "woman" problem. Then I remembered that the target audience for Harper's Bazaar is chicks, and my rage subsided somewhat. The goal, I figured, wasn't to fix men, but to commiserate with women. Which brought my rage back to a simmer. But okay. Okay. Being a man and all, I choked back all emotion, as we must always do or face social ridicule, and tried to give the article a fair chance. Kylie-Anne Kelly can’t remember the exact moment she became her boyfriend’s one and only, his what would I do without you, but she does remember neglecting her own needs to the point of hospitalization. Starting an article with an anecdote is a time-tested way of grabbing a reader's attention. That's fine. What I have an issue with is that, coming as it does immediately after that headline, it makes it sound like Kylie-Anne's problem (and it is, obviously, her problem, not that of her nameless and ultimately irrelevant boyfriend) is just an ordinary relationship scenario, ho-hum, this is what we're all facing, isn't it, girls? Can't you relate? Kelly’s boyfriend refused to talk to other men or a therapist about his feelings, so he’d often get into “funks,” picking pointless fights when something was bothering him. I don't mean to sidestep the issue or pretend that this sort of thing isn't a problem. It absolutely is, and it's one reason I don't conform to that version of masculinity. But, and I'll just point this out and leave it here, this guy had a girlfriend and I don't. So, clearly, it works, at least at first. After three years together, when exhaustion and anxiety landed her in the hospital and her boyfriend claimed he was “too busy” to visit, they broke up. I've been considering getting a t-shirt with a giant waving red flag on it to wear in public. That way I can skip the small talk and have people avoid me before starting a conversation that reveals whatever internal red flags I project. Saves time and energy that way. Kelly’s story, though extreme, is a common example of modern American relationships. Oh, now they admit it's extreme. Women continue to bear the burden of men’s emotional lives, and why wouldn’t they? For generations, men have been taught to reject traits like gentleness and sensitivity, leaving them without the tools to deal with internalized anger and frustration. Hey, look at that sneaky use of the passive voice! I suppose the implication is that men are taught exclusively and only by other men: fathers, uncles, brothers, male peers. Meanwhile, the female savior trope continues to be romanticized on the silver screen (thanks Disney!), making it seem totally normal—even ideal—to find the man within the beast. Yeah, you know, if it didn't resonate with viewers, they wouldn't keep depicting it. The Mouse has many faults, but this looks to me like another dodging of responsibility. They also, classically, depicted male heroes saving helpless damsels in distress, but that trope, at least, seems to be fading, or at least morphing, because people demand that women save themselves, instead. Incidentally, though, I do sometimes wonder about a gender-swapped Beauty and the Beast. I'm nowhere near good enough to write something like that, and besides, if I can think of it, it's already been done. The article continues to describe the problem, and, I'll grant, it's not unjustified. After a while, it finally names an actual man: So Shepherd turned to the internet, downloaded a men’s group manual, and invited a few guy friends who he knew would be receptive. He capped the membership at eight and set up a structure with very clear boundaries; the most important being what’s talked about in men’s group stays in men’s group. I'm not saying it's a bad idea by itself. But are we sure that downloading instructions from some site on the internet is really the way to go? At that point, you might as well use the movie Fight Club as an instructional guide. Not to rag on that film; it's still one of my favorites. But it's fiction. Lots more at the link. My gender-role-approved rage has settled down to a dull feeling of numbness, which is also gender-role-approved. Now to order that giant red flag T-shirt. |
| Today, instead of picking an article at random, I decided to go with this one from Lifehacker, which plans for the year that's (mostly) still ahead of us. Considering the source, though, you might want to double-check any of these that you might care about. The few that I did check out didn't really track, so I don't trust the rest of it without verification. Mark These 2025 Celestial Events on Your Calendar Here's when to look up for full moons, meteor showers, and planetary parades. No, I'm not going to repeat all of them. That's what the link is for. Jan. 3–4: Quadrantid meteor shower. The Quadrantids are active from Dec. 28 to Jan. 12 but are expected to peak around 4 a.m. EST on Jan. 4. Yeah, this is the main reason I jumped this one out of the queue. I've never had much luck with meteor showers—it's always cloudy when the good ones happen, and every time I travel to a darker place to see one, it ends up being a dud—but your experience may vary. Jan. 13: Wolf Moon. The first full moon of 2025 has extra appeal, as it will pass close to (almost in front of) Mars. If I had one wish, like from a genie or whatever, I could, of course, wish for world peace. Or an end to homelessness. Or, to be selfish, a billion dollars. But no, if I had one wish, it would be to end this bogus association of moon names with Gregorian calendar months. That's the crusade I'd choose (mainly because I can see how all those other wishes could be twisted to horrific effect, like ending homelessness by disappearing all the homeless). The Wolf Moon is not defined as the full moon in January, no matter how many websites and "authoritative" sources say it is. It is the first full moon after the northern hemisphere winter solstice. Yes, this year, those happen to be the same thing. But they are not always. This, as usual, maddened me so much that I almost missed the cool part about Mars. And I also almost missed this: The red planet will appear to disappear behind the moon at 9:16 p.m. EST and reappear at 10:31 p.m. EST. I'll give "appear to disappear" a pass, but the last sentence was "close to (almost in front of) Mars" and this one implies it would occult Mars entirely. This. This is why people don't trust Lifehacker. So, to break this down a bit: A Moon/Mars conjunction occurs just about every lunar month. Because most solar system bodies orbit at a slight tilt to each other, eclipses don't happen at every conjunction. This is true for the Sun/Moon conjunction, which is why we don't get a solar eclipse every month, but also for when the Moon appears closest to any given planet. Plus, sometimes, it happens when Mars is in the daytime sky and we can't see it. Additionally, as with solar eclipses, the timing of the event varies with location, because of parallax. So if you're going to say "9:16 pm EST to 10:31 pm EST," you also have to note the location on Earth where that's true, and it's not "the entirety of places that observe Eastern Time." Now, a quick glance tells me that other sources give different timings for the eclipse (I guess it should be considered a Martian eclipse), but the January 13 date appears to be correct for both Full Moon and Martian Eclipse. Remember when I said eclipses don't happen at every conjunction? Well, one happening at a Full Moon is remarkable, both for its rarity and spectacle. Of course, it's not happening precisely at the Full Moon (5:27pm EST), but close enough for spectacle. One wonders if Mars will even be visible against the glare of a Full Moon. I guess we'll find out. Well, other people will find out; something this rare and mars-velous (I couldn't resist) practically guarantees that, wherever I am, the sky will be covered in a thick blanket of clouds. Nevertheless, I've noted it on my calendar. I've been known to beat the odds before, including during two solar eclipses, and I would very much like to see this. Well, that took up way more space (pun also intended) than I expected. I'll just throw in some highlights from the rest of the calendar year 2025 skywatch forecast: February's main event is a planetary parade, when the planets appear to be in one line in Earth's sky. The parade actually begins on Jan. 10 when the Moon joins up with Jupiter and continues through February. See, again, misleading. The planets will appear to line up, sure, but halfway through that period, the Moon will be on the other side of the sky. There were a few consecutive nights maybe 30 or so years ago when all the visible planets lined up in one quadrant of the sky. Or at least most of them; it's been 30 years and I barely remember the details. What I do remember is going up to the Blue Ridge Parkway on one of those nights, with some friends and a telescope. It wasn't cloudy. But it was colder than my ex-wife's lawyer's heart. As this is happening in January and February, well, it'll be cold again here. Saturn will drop off mid-month, but tiny Mercury will be barely visible in the parade on Feb. 28. And maybe, just maybe, I'll finally be able to see Mercury and know that it's Mercury. I've bitched about that before. I might have seen it at some point in the past, but it's only ever visible just after sunset or just before sunrise, and at those times, the twilight washes out a lot of contextual stars. So I don't know if I've ever actually seen Mercury in the sky. As a side note, last night, I got treated to a post-sunset very bright crescent Moon not far from a very bight Venus. It was cool. But I expect tonight, the Moon will appear even closer to Venus and it'll look even more awesome. Provided the clouds don't roll in. March 14: Total lunar eclipse... Though the total lunar eclipse will be visible around the world, the full 65-minute totality will only happen in the Americas and Antarctica. Nice for our continent. Unless it's cloudy. I fully expect it to be clear everywhere but Virginia that night, unless I go to, say, Wyoming to see it, in which case it'll be clear everywhere but Wyoming. Saturn will be at opposition on the night of Sept. 21. Just like Mars in January, this event will show Saturn at its brightest, visible to the naked eye. To clarify, if Saturn and Earth are in the right alignment such that Saturn appears at night, that planet is always visible to the naked eye. Doubt we'll be able to see the rings without aid, but even binoculars might be enough to make out that distinctive feature of the planet... provided, of course, that the rings aren't edge-on, which I don't know. And if it's not cloudy. The rest is mostly meteor showers, which, as I said, are cool, but I've never had much luck viewing them. Maybe this year will be different, but I say that every year. And there's a few "supermoons," too, toward the end of the year. Again, though, that just describes a Full Moon near perigee, which happens every year and I think it doesn't deserve all the hype attached to it. Still, if it gets people to look up, I'll allow it. Just stop with the association of Full Moon names with Gregorian calendar months. |
| From aeon, an article aged over seven years: Oh, a new word, eh? Cool, cool. This is an essay first published in 2017, so surely that word's been spread to the farthest reaches of the travel community by now, right? One thing I’ve noticed over the years of bringing my students to Ireland – my homeland – is that they pay rapt attention to the little things. This heightened and delighted attention to the ordinary, which manifests in someone new to a place, does not seem to have a name. So I have given it one: allokataplixis (from the Greek allo meaning ‘other’, and katapliktiko meaning ‘wonder’). I'm not really mocking. I've invented dozens of words that never caught on (and one that did in ways I could never have anticipated). Okay, but I'm also mocking, a little, because there's no fucking way a word like allokataplixis would ever go viral, except maybe if it were the name of a new penis-enlarging drug. Even then, we'd shorten it to allo, which could get confusing. For the past five years, I have travelled around Ireland each summer with a bunch of allokataplixic American kids. And there it is: the adjective form. Marvellous to them also is the slight smell of salt in the air when you arrive in Dublin, the raucousness of seagulls crying overhead... [loads of poetic imagery] ...the sun setting on the Atlantic viewed from the beaches of the west, the melancholy slopes in County Kerry that were abandoned during the famine. Well, yeah. What's ordinary to locals is often fresh and exciting to visitors. It's not just Dublin (never been, but want to go), but almost any place you're not used to. Like how millions of New Yorkers pass by the Empire State Building without admiring its art-deco grandeur. This is why some of us travel: to find the beauty in the mundane, to see it with new eyes and, maybe, pass along some of that newness to those jaded by familiarity with it. Yet over the years that I’ve been bringing students to Ireland I’ve observed that their thirst for fresh experience is contagious. It oftentimes brings out the best in people. A tourist generally has an eye for the things that, through repetitive familiarity, have become almost invisible to the resident. It can also bring out the worst in people. One does not need, however, to be an outsider or a tourist to be allokataplixic. Is it not the task of most writers to awaken us from the dull, the flat and the average sentiments that can dominate our lives? Many of the Irish writers that my students read before travelling have a knack for noticing the marvellous in the everyday, and of making the quotidian seem wholly other and amazing. Just in case you were wondering if this had anything to do with writing. I don't take issue with the general ideas in the article (there's even a foray into the fractal, which is always like candy to me). It's just... that word. You'd think we could come up with something better, something with fewer syllables, something less pretentious than an obscure phrase from Ancient Greek. You'd think so, but I'm stumped. |
| Well, now that that's over, let's get back to it. What better way is there to start a new calendar year than by pointing out a mistake made in the previous calendar year? A bit from Ars Technica: Journal that published faulty black plastic study removed from science index Chemosphere cut from Web of Science, which calculates impact factors. Some people might not have noticed the black plastic crisis. I didn't see anything about it until the retraction, myself, so I was less prone to primacy bias. This article goes beyond one single retraction, but I'll point this out anyway: usually, people hear about the study, usually through some breathlessly urgent reporting by someone trying to be first out of the gate, and then the retraction happens... and radio silence ensues, leaving people believing the first report. Worse, some people (exhibiting the aforementioned primacy bias) do hear about the retraction, but the falsified original stays in their brain. Rarer is the case where an entire journal faces consequences for publishing shoddy studies. The publisher of a high-profile, now-corrected study on black plastics has been removed from a critical index of academic journals after failing to meet quality criteria, according to a report by Retraction Watch. If you've been lucky enough to avoid the whole made-up controversy, this article does a fair job explaining the events timeline. It's there if you want to read it. However, it gets worse. It appears that the people responsible for the original, retracted study on black plastic kitchenware did make a math error. This is bad enough, as it contributes to primacy bias, though anyone can make math errors or other mistakes (which is one reason you have peer review in science). But the worst part is, it looks like the authors of the original study had an Agenda: The statement says that, regardless of the math error, the study still found unnecessary flame retardants in some products and that the compounds can "significantly contaminate" those products. That is not science. That is opinion contaminating science. It's like if the Committee for Bug-Free Food found that 1% of the contents of canned tomatoes was bugs (there is, as I understand it, a maximum allowable bug level in food, as attempting to remove all insect parts reaches a point of diminishing returns, but I can't be arsed to research what it is), but then said they misplaced a decimal and it's actually 0.01%—and then still insisted that there's still bugs in the food and so canned food should be avoided at all costs. Usually, the next thing you find out is that the Committee for Bug-Free Food is in the employ of someone with a vested interest in selling their own line of (more expensive) bug-free food. Now, I'm not weighing in on whether you "should" use these plastic utensils or not. It's not an issue of grand global importance, the way the Wakefield disaster was, and still is. I just think any such decision should at least take the science into account. The actual science, not the one with math errors and strongly-held opinions. |
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