Sunday, July 17, 2011

Flatland: A Romance of Many Dimensions

Flatland: A Romance of Many Dimensions is an 1884 satirical novella by the English schoolmaster Edwin Abbott Abbott. I´ve read it some years ago, after attending a course of fractality and hyper dimensions in art. The professor read us a paragraph after showing Dalís´ hypercube in his Crucifixion (Corpus Hypercubus) from 1954.

Dali´s Crucifixion (Corpus Hypercubus)

At this time, I didn´t thought that the author, writing with the pseudonym of ¨a square¨ would use this fictional flat-two dimensional world of Flatland to criticize the social hierarchy of Victorian times. He considers the circle as the perfect figure.
My reflection, since then, and based on my research about fractal urban morphology, is that figures are not always what we think they are, sometimes, it depends on the point of view. For example, an aspirin is a cylinder, but, under a microscope it turns into a multicolored fractal; seen from above, in a flat representation, we see a circle.

An aspirin, seen under a microscope. From

But, coming back to the society, Abbot was very strict ¨a Flatlander, seeing a Line, sees something that must be THICK¨ and he was rather mocked than understood, because of his metaphoras.
So, I found it interesting to copy some paragraphs from the editor´s prologue to the second edition of 1884, where he is explaining Abbott´s opinions, in behalf of him:
¨If my poor Flatland friend retained the vigour of mind which he enjoyed when he began to compose these Memoirs, I should not now need to represent him in this preface, in which he desires, firstly, to return his thanks to his readers and critics in Spaceland, whose appreciation has, with unexpected celerity, required a second edition of his work (...) But he is not the Square he once was. Years of imprisonment, and the still heavier burden of general incredulity and mockery, have combined with the natural decay of old age to erase from his mind many of the thoughts and notions, and much also of the terminology, which he acquired during his short stay in Spaceland.He has, therefore, requested me to reply in his behalf to two special objections, one of an intellectual, the other of a moral nature.
The first objection is, that a Flatlander, seeing a Line, sees something that must be THICK to the eye as well as LONG to the eye (otherwise it would not be visible, if it had not some thickness); and consequently he ought (it is argued) to acknowledge that his countrymen are not only long and broad, but also (though doubtless in a very slight degree) THICK or HIGH. This objection is plausible, and, to Spacelanders, almost irresistible, so that, I confess, when I first heard it, I knew not what to reply. But my poor old friend's answer appears to me completely to meet it.
"I admit," said he—when I mentioned to him this objection—"I admit the truth of your critic's facts, but I deny his conclusions. It is true that we have really in Flatland a Third unrecognized Dimension called 'height', just as it is also true that you have really in Spaceland a Fourth unrecognized Dimension, called by no name at present, but which I will call 'extra-height'. But we can no more take cognizance of our 'height' than you can of your 'extra-height'. Even I—who have been in Spaceland, and have had the privilege of understanding for twenty-four hours the meaning of 'height'—even I cannot now comprehend it, nor realize it by the sense of sight or by any process of reason; I can but apprehend it by faith.¨
It´s worth to keep on reading....
The book also inspired the plots for animated films.

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