In Praise of Fractals and Poetry
In 2002, Grosholz appeared with Benoit Mandelbrot, father of fractal geometry, at an Entertaining Science event in New York. She wrote “In Praise of Fractals,” one of my favorite poems from her book, for the occasion.
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> Nor Apollonius
Which one is being referred to? Apollonius of Tyana or Apollonius ot Perga? and why?
> Clouds are never spheres, Nor mountains cones, nor Ponderosa pines
They’re not fractals either, but fractals gives a better approximation. The “mountains never cones” is what inspired Mandelbrot to invent fractals in the first place.
> But rather of an altogether different. Level of complexity
The definition of complexity is a tricky one, but one accepted definition is that something geometrically simple can be described by a small number of mathematical symbols. In that context, fractals are really extremely simple, so ar pseudo-random numbers, but they look complicated.
> The number of the scales of distances Describing her is almost infinite.
We’ve had debates on the forum about “almost infinite”. When it comes to how well fractals describe nature, the number of scales actually present seldom exceeds 5.
> How shall we study the morphology of the amorphous?
Nice poetry.
> A lineage of shapes fretted by chance, whose regularities are all statistical
No, that’s exactly what fractals isn’t.
> Some fractal sets are curves (space-filling curves!) or complex surfaces; others are wholly disconnected ‘dusts’; others are just too odd to have a name.
Yes.
To be admired power to interpret nature’s coiffure of molecules and mountains.
Not molecules, fractals fails miserably to interpret nature in the quantum domain.
> What gentle revolution of ideas disjoins the nineteenth century from ours! Cantor, Peano, Mandelbrot
That’s right. Along with catastrophe theory and a mathematics of computing, fractals are one of the very few new branches of mathematics invented in the 20th century. Of course, the poem is wrong in that we live in the 21st century.
> The masters of infinity, Cantor, Peano, Hausdorff, and Lebesgue
That’s the popular view. For a correct view, see my monographs on infinite numbers. The real masters include Aristotle, De-Bois Reymond, Hahn, Robinson and Conway.
> Spinoza’s darling Cause.
Huh? “Spinoza begins by noting that he has stated various truths about God in Book I”.
> Imagination shoots the breeze with Nature
Poetry needs improvement. Why would one ever want to shoot a breeze?
mollwollfumble said:
> Imagination shoots the breeze with Nature
Poetry needs improvement. Why would one ever want to shoot a breeze?
Not, shoots a breeze, shoots the breeze…..
you know, catch up with a friend or family member and talk about random shit, get the latest news and whatnot.
I think the kids today call it Facebook.
In this case though, Imagination and Nature are kickin’ back with a cold one, solving life’s problems as they watch the world unfold, and maybe they are discussing some ideas for an event to annoy someone, or inspire us, or cause us to observe in awe and wonder.
mollwollfumble said:
> Nor Apollonius
Which one is being referred to? Apollonius of Tyana or Apollonius ot Perga? and why?
Here’s a less symmetrical, coloured-in one:
