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Dec 27, 2009
Apollonian gasket, a fractal with interesting properties. Its dimension is about 1.3; the Sierpinski triangle has dimension 1.585. There’s a wiki list, naturally.
Dec 27, 2009
How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension (pdf)
The dimension of the British coastline is 1.25, more than a straight line but less than the plane. Huh? Let’s back up a bit.
The coastline paradox is this: the length of a coastline depends on the scale you measure it. If you choose to measure only rough features, the measured length will be shorter than if you started measuring small variations on the scale of a few meters. Therefore, a coastline doesn’t have a well-defined length: to be exact, you need to specify the scale you’re measuring on. Empirical results show that real coastlines have the property of statistical self-similarity: at various scales, the same features repeat (but not on every scale, of course). Furthermore, the length function L(G), where L is measured length and G is the scale, is approximately L(G) = MG1-D.
Now, the mathematician Benoit Mandelbrot (yes, that Mandelbrot) connected this with a previously obscure mathematical concept called the Hausdorff dimension of a curve. It’s easy to imagine what it means for a line to be of dimension 1 and a plane of dimension 2, but what about a dimension like 1.25? The Hausdorff dimension is sort of like a regular dimension — it resembles regular dimensions in certain ways, so for example a regular line has Hausdorff dimension 1 and a plane has dimension 2. But Hausdorff dimensions can take on fractional values. When they’re applied to curves, they measure in some sense just how complicated the curve is (or: how much space it fills in the limit, as you zoom in on a fractal). So, for example, a straight line has dimension one. But there is a kind of curve called a Peano curve that fills the plane; its dimension is 2. Mandelbrot interprets the D in the equation for L(G) above as a coastline’s Hausdorff dimension. Curvier coastlines will have higher D’s and therefore higher Hausdorff dimensions; Britain’s D is approximately 1.25, because the British coastline is curvy; South Africa’s is about 1.02, because the South African coastline is pretty straight.
This stuff makes my head spin in a wonderful way, and I wish I understood it better, but at the same time, there is so much uninteresting theory to learn in order to get to the good stuff that I don’t see myself really getting into it anytime soon.
Dec 27, 2009
Paresthesia
Paresthesia is a sensation of tingling, pricking, or numbness of a person’s skin with no apparent long-term physical effect. It is more generally known as the feeling of “pins and needles” or of a limb “falling asleep” (although this is not directly related to the phenomenon of sleep). The manifestation of paresthesia may be transient or chronic.
Dec 25, 2009
Infallible Man Falls
I have a hard time imagining him as anything more than a harmless old man, diabolical eyes notwithstanding. Though I don’t condone violence, it’s certainly a lot easier to feel satisfied about Berlusconi getting punched in the face (or for that matter someone narrowly missing Bush jr. with a shoe) than it is when someone’s toppling the pope. But if you think about it, that silly old man is responsible for his share of, dare I say it, evil policy.
Dec 24, 2009
This is starting to become a tradition. By Rob Sheridan.
Dec 22, 2009
Monterroso
After I wrote about microfiction I discovered Augusto Monterroso, who just might be its uncrowned master. Unfortunately (for me, personally), he wrote in Spanish. I’ve been trying to find The Black Sheep and Other Fables, one of his books that’s actually available in English — I’m kind of impatient, don’t want to wait until long into 2010 to get it, so I was looking for an ebook, but the only versions I’ve found are in Spanish. Fuck.
Anyway, here are a few of his really short short stories that I’ve found on the web:
The Dinosaur:
When he woke up, the dinosaur was still there.
The Lightning That Struck In The Same Place Twice:
Once there was a Flash of Lightning that struck in the same place twice. But it found that it had done enough damage the first time round and was no longer necessary, and it got very depressed.
Once there was a Cockroach called Gregor Samsa who dreamt he was a Cockroach called Franz Kafka who dreamt he was a writer who wrote about a clerk called Gregor Samsa who dreamt he was a Cockroach.
The black sheep:
In a distant country many years ago there existed a black sheep. It was shot. A century afterwards, the repentant flock raised an equestrian statue to it, which looked very good in the park. So it came about that thereafter, whenever any black sheep appeared, they were quickly executed so that future generations of ordinary sheep might also be able to practise the art of sculpture.
Finally, according to the cable, last week the Tortoise arrived at the finish line. At the press conference he declared modestly that all along he had feared that he was going to lose, since his competitor was right on his heels. As it happened, one ten thousand trillionth of a second later, like an arrow and cursing Zeno of Elea, Achilles crossed the line.
Apparently he’s somewhat well-known in the Spanish-speaking world and comparatively little known in the English-speaking world. I might write more about him when I get a hold of any of his books. This is wonderful stuff, what little I’ve seen of it, anyway. Bonus: comes with the approval of Italo Calvino, García Márquez, and others.
Dec 21, 2009
We live in a spectacular society, that is, our whole life is surrounded by an immense accumulation of spectacles. Things that were once directly lived are now lived by proxy. Once an experience is taken out of the real world it becomes a commodity. As a commodity the spectacular is developed to the detriment of the real. It becomes a substitute for experience.Larry Law.
Dec 21, 2009
Happy Winter solstice! (The exact moment when the Earth’s axial tilt is farthest away from the Sun is due in a little less than two hours.) Because although I have yet to feel Christ’s warmth fill my being, I sure as hell am looking forward to feeling the warmth of the Sun lengthening every day.
Dec 20, 2009
50
I can’t imagine any logical reason why, but somehow it feels scarier to publish fiction than nonfiction. I mean, when you write nonfiction, at least if you’re being honest and non-ironic, you’re putting your real opinions and feelings out there. Your personality is sort of on the line, even if only in a highly metaphorical way that only matters to the thin-skinned among us. Yet somehow fiction, where you can put on any kind of personality and where you don’t have to pour out anything that you truly believe or actually feel, feels more personal. Perhaps it’s simply that I have more practice putting out nonfiction for others to see.
Anyway, I’ve become interested in microfiction. When it’s good, it’s fun to read, even when it’s bad you only waste a few seconds, minutes at most to read it, and it’s fun to write. Microfiction (defined as fiction that stays under some arbitrary word limit, whether it’s a thousand, five hundred or a hundred words) seems particularly well suited to the web. Not because I’m concerned about diminishing attention spans or interested in finding “a voice for the digital generation” or anything of the sort. It just fits.
There’s history in this, of course. No one ever tires of the six-word “For sale: baby shoes, never worn”, which is attributed to Hemingway. All sorts of authors, including Borges and Kafka, wrote short short stories only a few hundred words long. Jumping forward in time, lots of people are doing that sort of thing online. I’ve previously linked to Scientific Facts, sadly no longer updated, which tends to stay somewhere around 150 - 400 words. On Twitter, there are all sorts of people doing it. There’s Arjun Basu, who writes short stories that are exactly 140 characters. There’s thaumatrope, a zine that actually pays authors to write tweet-sized stories in the horror, fantasy and science fiction genres. On Tumblr, there was Fifty Words, no longer updated. While I can’t say I loved all or even most of Sam’s stories, I admire his dedication: not only did he publish one every weekday for a year, but he stuck to exactly fifty words, no more but also no less.
See also: Nanoism, Espresso Stories, 6-word scifi, Six word stories (like “Confessed anonymously. Forgot about e-mail signature.”), genre microfiction (how many words do you need to put a story in a specific genre?).
I think these <=50-word-stories are fun to write. They allow me to explore ideas that are best explored in fiction, but I don’t have to write up a whole thing, the idea can stay small. I know I can be verbose, but microfiction is all about paring down to the essentials. (It’s not about “point[ing] beyond meaning, to a kind of emptiness.”) It’s also all about clever ambiguity and suggestion. Not “show, don’t tell”, but “suggest, don’t show”. You have to do this, if the story is to be any good. You can’t have 3-dimensional characters, complex plots, character development, subtly, well-drawn mileus, lyrical metaphors (well, maybe you can squeeze in one or two) and so on in fifty words. If you want the story to be a real story, you must give the reader something to work with and trust them to imagine the rest. That’s why I’ve chosen fifty words, no more, but possibly less. You wouldn’t think it possible, but I’ve seen these tweet-sized stories and fifty-word stories and so on that contain redundancy and purple prose, simply to fill up those 140 characters or fifty words — which is why I feel an exact word or character count is not an enabling limit but a disabling one. You should allot a twenty-five word story twenty-five words, exactly.
Those were many words on brevity. Anyway: I decided to put some fifty-words-or-less stories out there. Currently at the rate of one per day. This may fizzle out quickly like my attempt at blogging Nietzsche’s The Gay Science, but I feel reasonably confident I can keep this up for some time. Technically, some of these may not be “stories” so much as “vignettes”, but who cares. They are what they are.
I don’t know why I gravitate towards the tragic. I’m not depressed, honestly. Anyway, this thing allows me to take on perspectives I don’t agree with; I do not, for instance, really believe that if only depressed people could manage to make themselves a little sadder, they would turn around and suddenly become euphoric, nor that too much happiness, per se, is a bad thing. But I can see how that could be a comforting fiction for someone to believe.
Dec 18, 2009
Ted was the rebel android, operating solely by an utter refusal to dream of electric sheep.thaumatrope.
Dec 17, 2009
Dimensions is a series of videos visualizing and explaining mathematics. It covers, among other things, visualizing fourth dimensional objects (as purely mathematical objects, with no pseudoscience to anchor it to the “real world”) and fibrations. This chapter visually explains the Julia and Mandelbrot sets (which produce all sorts of wonderful fractals). I haven’t seen anyone try to give an elementary explanation of just what these sets are, but I think this video does so beautifully. Don’t be scared by the French title — the voiceover is in English.
All the chapters are online. This is number six, which builds on chapter five, which introduces complex numbers. There’s also more detailed explanation in text. You should just watch the video, but what it says is this: consider a transformation T(z) = z2 + c, where c is an arbitrary complex number. For instance, when c = 0, the transformation is T(z) = z2. Consider what happens when you start putting numbers into the transformation. You can build a series of such numbers: z1, z2 = T(z1), z3 = T(z2) etc. This series is called called the orbit of the point z under the transformation T. If you consider it, you’ll find that for T(z) = z2, values for z that are less than 1 will stay inside a bounded area of the plane no matter how many times you transform it (in fact the points will move around inside the unit circle). All other values for z will tend towards infinity, moving further and further away from the origin under this transformation. The set of values for z that stay bounded throughout their orbits for a given transformation is called its filled-in Julia set, and the Julia set is that set’s border. They make pretty fractals. If you keep varying c, you’ll find that the filled-in Julia set morphs. For many values, the set is in one piece (connected), but for some values, the whole thing explodes into an infinity of unconnected parts — you can no longer see a connected figure on the plane. There is a set of values for c such that the filled-in Julia set of the transformation T(z) = z2 + c is connected. That set is the Mandelbrot set, whose border also makes pretty fractals.
That I find strangely beautiful.
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Daily Meh is written and edited by Simen (contact me). I live in Norway. This blog is about whatever interests me. Here are some of my favorite posts from the archives.
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