I imagine that, at the moment of first freezing, the pattern of frost is set. So should a mutant, winter-dwelling butterfly flap its wings near your windscreen, a different pattern would appear than if it had not. Dirt and debris on the screen, the micro-climate around the vehicle, the shapes of eddies: they must make for the variety of possibilities. It’s about turbulence.
In an October interview, Benoit Mandelbrot said this:-
The word turbulence is one which is actually common to physics and to social sciences–to economics. Everything that involves turbulence is enormously more complicated: not just a little bit more complicated, not just one year more schooling; it’s enormously more complicated….
The behaviour of economic phenomena is far more complicated than the behaviour of liquids or gases.”
In the same joint-interview, Nassim Taleb said this:-
Never in the history of the world have we faced so much complexity combined with so much incompetence in understanding its properties….
You may have chain reactions we never imagined before. These come from intricate relationships in a system we don’t understand.”
So I guess we should beware of those who tell us confidently to expect future economic events to follow a familiar pattern. They tend to be the same people who did not expect the current situation.
For those who did not catch the original video, here it is:-Donate and help me buy back my Fender ('About' tells you why) Tags: Benoit-Mandelbrot, friday_fractal, frost, Nassim-Taleb
It’s not Friday, nor Saturday, but this Christmas gingerbread dough (not paleo, nor mandelbrodt) cracked on its under side as it was rolled out. It struck me that the pattern was similar to the Wikipedia image below, formed by an electrical burn through a block of wood.
Whether this biscuit break is a genuine fractal, I’d happily invite comments. But fractal or not, in the Knackered House, that’s the way the cookie crumbles.
Donate and help me buy back my Fender ('About' tells you why) Tags: Benoit-Mandelbrot, fractal, 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
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