flatland: why i read it slowly
20May08Flatland: A Journey of Many Dimensions (US edition) is a short book, but I read it very slowly. It’s less than 100 pages, and it took me six weeks, I think.
Perhaps if I had studied more than school-house geometry I would not have felt the need to spend so long pondering the perceptual consequences of living in two dimensions, as the characters in Flatland do.
Then again, there is the more frightening thought that I am in fact living a single dimensional existence without realising it. To understand how stupidly comic the book makes that idea seem you’ll have to get hold of a copy. It is a book that encourages humility in our understanding and yet aspiration to higher knowledge at one and the same time.
Written by Victorian London schoolmaster Edwin A. Abbott, Flatland was a mathematically-inspired parody of the restrictions (social, intellectual and philosophical) of the era. Abbott created an alternative two-dimensional world, expounded by geometrical observation and hand-drawn sketches to attack in allegory the conventional wisdoms of that hierarchical 19th century society.
But it barely takes any imagination to transpose the ideas into our own era. For it must ever be the case that a battle is going on within society between those who want to push our understanding upward, to challenge orthodoxy, and those whose economic benefit resides in the status quo. Quite literally these days our quantum friends ask us to consider many more dimensions than most of us have the faculty to conceive of.
The main protagonist and narrator of the story is A. Square, who is…a square; this makes him a professional man, or gentleman in Flatland. The middle classes are equilateral triangles, the lower classes isosceles. And in this world the women (ladies, you’ll not like this) are straight lines.
Remember, Abbott is describing a highly structured society. Social mobility in this world is generationally dependent. Deviations, if not correctable at birth, are extinguished. Squares beget pentagons, pentagons beget hexagons,etc etc. Regularity matters above all else.
The angularity of one’s body dictates not only your station in life but is also mirrored in your IQ; the pointier your angles the thicker you are. But Abbott’s protagonist from a middling station nevertheless demonstrates, through a combination of curiosity (his own and that of his hexagonal grandson) and through the revelation of a visitor from the higher plane, that there is a third dimension (and possibly more). He ends up challenging the established order held in place by his intellectual and geometrical superiors — the top-most of which are the priestly circles.
But this is more than just a reprint of Abbott’s text because the book is republished to accompany an animated movie
The movie was an instant hit with the two knackered chips off the old hack: one 13, the other eight. So if you are a secondary or junior school teacher tasked with enthusing children with the idea of maths and geometry in particular, there could be no better investment. And don’t worry about the women being lines; that liberal poster-child Martin Sheen plays Arthur Square in the film, and the precocious grandson, Hex, becomes a girl and is given voice by Kristen Bell.
The DVD extras also provide some great computer-generated animation that shows how three-dimensional shapes would be perceived in just two dimensions, and then, by the same logic, how higher dimensional objects might present themselves in our three-dimensional world.
And pay attention for the line in the trailer here: “Oh dude, you’re freakin’ me out!”, for that is the Line King talking.
What is particularly cute to my mind about the animated characters is that, while their outward form is two-dimensional, their insides are all revealed to be Mandelbrotian fractals. Now, there’s a truth we should all ponder.
Thanks to the movie’s animator Dano Johnson for providing the above on YouTube.
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Tags: Benoit-Mandelbrot, Edwin Abbot, Flatland, fractals, geometry, Kristen Bell, mandelbrot, Martin Sheen, mathematics teaching, physics_teachingRelated posts
i went on a phone hunt
07May08Having indicated a while ago that I would plump for an iPhone, I chickened out the other day and defaulted to my previous rule of thumb which was buy the best Nokia. But this also satisfied that other aforementioned heuristic, i.e. the gift-horse mouth-staring one. The cost to replace my existing pda-phone was less than zero, because they offered me a contract better than the previous one, and much better than anything I’d seen advertised on any network.
Sometimes I wish I had not bothered, because having had the device nearly a month, I have not had time to programme it or migrate contacts. And the storage card is delayed, so loading music, podcasts, portable Russian lessons and other audio joys has had to wait.
And yet. The thing has a 5 megapixel camera in it with Carl Zeiss optics, which Apple’s Steve Jobs is dismissive of, having made the iPhone’s camera to a lesser spec. There may be nothing to choose between the two really, but I’m strangely overjoyed and inspired to photograph any time, any place and in a way that the graininess of my old phone discouraged. I’m a fully-fledged Flickr fan.
Fortunately too, the phone has an FM radio in it, which sounds a bit retrograde in this day and age. But over the past week or two I’ve been looking for inspiration and concentration. The BBC’s classical channel, Radio 3, has been providing it, offering as ever a wide range of frequently unfamiliar classical music of all centuries. And it stops me from listening to Pink Floyd when I’m out running. Shine on you crazy diamond. Auditory variation indeed.
Trees and woodland seem to do the same thing for me visually, and the phone camera now means that I capture some of that stimulus for posterity, and the limbic of you, my long-suffering reader. Excepting the flower, these pictures were taken Monday at Claverton Manor (AKA The American Museum) near Bath, which overlooks the Avon Valley. Topographically, I think it may be true to say that this is one of the most varied landscapes on the planet, and readers of Simon Winchester’s The Map That Changed the World: A Tale of Rocks, Ruin and Redemption
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It had been my intention to take the blog on vacation with me to see what — in a very restrictive sense — ubiquitous computing might feel like. And to see whether a travelogue should ever form part of this miscellany. I bought a 3G dongle (not from a spam email…) and carried more digital and optical equipment than you can point a telescope at. The only things lacking were the skill to use it all and a guarantee of internet connection.
The immediate consequence of an absence of wireless reception beside the remote estuary where we perched for the duration of last week was that for the first little while there was not much to do but stand still. This was a good thing, but as the Knackered family has not stood still for well more than six months of rolling crisis, it was only natural that some of the tangled thoughts of grief found an opportunity to unwind and, for those few early days, occasionally overwhelm.
Road to Nancenoy
But the Cornish peninsula is nothing if not varied. And would a geographer pick an argument with me if I said it may be one of the most fractal landscapes on earth? — whether one is talking about the trees, the rugged coastline, the self-similarities of those flooded river-valley creeks, or the surf as the Gulf Stream makes landfall.
Kynance Cove
Within barely a few minutes’ drive the contrasts can be extraordinary. We’re quite happy with beaches out of season and in most weathers, and now — with the necessary neoprene — the option of body-boarding (and, someday soon, surfing) before supper presents itself.
Kynance Cove
In true amateur form, much of our expedition was inspired by reading Simon Barnes’ book, How to be a Bad Birdwatcher. And with a much diminished self-consciousness, this point-and-shoot ethos carried us through birdwatching itself, astronomy, body-boarding, rowing our own boat up the muddy creek (with paddles, thankfully), and much lower-maintenance-than-usual holiday gastronomy (pasties and fish pies from Gear Farm in St Martin).
Nancenoy
Serpentine rock at Kynance (on the Lizard peninsula)
Helford River
Stonechat
Photo credits: stonechat, Andrew Pescod; aerial view of Helford River, Google ;the rest, Knackered Hack
Tags: bereavement, Cornwall, fractals, Helford River, Simon-Barnes, surfingRelated posts
a fractal for friday
07Dec07
In a moment of exuberance some weeks ago, I floated the idea of Fractal Friday. I got a bit self-conscious subsequently because Andrew Gelman in this post joked that fractals are so ’80s. I can’t have been paying attention in class.
Anyway, this picture fell out of its folder during a trawl for happy memories on the hard drive yesterday. It was taken last year in the Chamonix Valley, where fractals abound.
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fractal mafia and the roman doctor
Tags: andrew-gelman, creativity, fractals, life-the-universe-and-everything, mood, recovery, work-life balance
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