There is now a cloud appreciation society. You may have heard about it on the radio a few weeks ago. They have named a new cloud — undulus asperatus — from the Latin, which roughly translates as “agitated waves“. And the roughness is what matters. They are highly disturbed, heralding a storm, and yet tend to disperse without one. The pictures above are nothing of the sort: just cumulus or perhaps nearer cumulonimbus.
I’ve looked at clouds from both sides now, and it is true what they say: that some clouds do have a silver lining, though I’m hesitant to agree yet that every one does. More research is needed.
It was sports day when these photos were taken earlier this week, and for the first time in a while it was not rained off, not even just the once. So these clouds were silver-lined if you were the harassed head teacher. But the sun did not shine for the smaller Chip off the Hack who came away with no honours. Last year, if memory serves, he won the egg and spoon race. This year, although the video evidence is incomplete, it does look like he finished the course without dropping the egg once, compared with his fellow competitors who all seemed to have at least one upset. Had the eggs been real, this would have been a feat in itself, but that day it was not the one being measured. Shall I add that the spoons were not institutional dessert spoons of yore, but wooden spoons with barely any dish? Ah well. He is his father’s son.Donate and help me buy back my Fender ('About' tells you why) Tags: asperatus, cloud appreciation society, clouds, cumulonimbus, cumulus, egg and spoon race, fractals, Joni Mitchell, sports day
Renault Laguna seen from above on a cold and frosty morningDonate and help me buy back my Fender ('About' tells you why) Tags: fractals, friday_fractal
About a year ago I suggested I might post a fractal image each Friday. What was I thinking?
Well, a combination of guilty conscience about a commitment unkept and this sentence in Didier Sornette‘s cheerily entitled book Why Stock Markets Crash: Critical Events in Complex Financial Systems prompted me to revisit this partial promise:-
It turns out that many of the natural structures of the world are approximately fractal and that our aesthetic sense resonates with fractal forms.
Those who remember my misdirected concern about dangerous trees may appreciate that the oak has been safely pruned, and the only objects falling now are the autumn leaves and occasional acorn.
My recent routine interest in trees, and flora in general, seems closely correlated with a) the acquisition (for no financial outlay) of a Nokia N95 mobile phone containing a 5 megapixel digital camera and b) adherence to the paleo diet. The latter, you might think, is not seriously possible. But putting aside the confirmation bias, it has not been the only manifestation lately of a heightened sensitivity to fractal forms. Spooky.
More, if you can bear it, at my Flickr Photostream.
Donate and help me buy back my Fender ('About' tells you why) Tags: didier_sornette, fractals, friday_fractal
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(US DVD version). The narrative has been updated to account for a more contemporary sensibility and bring this geometrical allegory to life for a new generation, and one very easily turned off mathematics. So purists for the old story should get over themselves and help celebrate — if they were otherwise so inclined.
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.Donate and help me buy back my Fender ('About' tells you why) Tags: Benoit-Mandelbrot, Edwin Abbot, Flatland, fractals, geometry, Kristen Bell, mandelbrot, Martin Sheen, mathematics teaching, physics_teaching
Having 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 Redemptionwill know of its crucial contribution to geological and subsequent evolutionary theory. It floats my boat.
Donate and help me buy back my Fender ('About' tells you why) Tags: Claverton, fractals, iPhone, N95, Nokia, Simon Winchester, Steve-Jobs, William-Smith