Limited DIMENSIONS

13 04 2014

[A dedication to my dear friend Dagny]

Dagny: And who can remember what Decartes said?
Children: I THINK therefore I am!
Dagny: And what is the name of this shape again?
Children: A SPHERE!
Dagny: And this one?
Children: a KLEIN BOTTLE!
Dagny: And this?
Children: a TORUS!
Dagny: And this?
Children: a HYPERBOLA!

From (the extraordinary classic) FLATLAND – Edwin A. Abbott

I devoted several months in privacy to the composition of a treatise on the mysteries of Three Dimesions…. I spoke not of a physical Dimension, but of a Thoughtland whence, in theory, a Figure could look down upon Flatland and see simultaneously the insides of all things…But in writing this book I found myself sadly hampered by the impossibility of drawing such diagrams as were necessary for my purpose; for of course, in our country of Flatland, there are no tablets but Lines, all in one straight Line and only distinguishable by difference of size and brightness; so that, when I had finished my treatise (which I entitled, “Through Flatland to Thoughtland”) I could not feel certain that many would understand my meaning…
 
Meanwhile, my life was under a cloud. All pleasures palled upon me; all sights tantalized and tempted me to outspoken treason, because I could not compare what I saw in Two Dimensions with what it really was if seen in Three, and could hardly refrain from making my comparisons aloud. I neglected my clients and my own business to give myself to the contemplation of the mysteries which I had once beheld, yet which I could impart to no one, and found daily more difficult to reproduce even before my own mental vision…
 
One day, about eleven months after my return from Spaceland, I tried to see a Cube with my eye closed, but failed; and though I succeeded afterwards, I was not then quite certain (nor have I been ever afterwards) that I had exactly realised the original… And yet at times my spirit was too strong for me, and I gave vent to dangerous utterances… even among the highest Polygonal and Circular society. When for, example, the question arose about the treatment of those lunatics who said that they had received the power of seeing the insides of things, I would quote the saying of an ancient Circle, who declared that prophets and inspired people are always considered by the majority to be mad…
 
… I exist in the hope that these memoirs, in some manner, I know not how, may find their way to the minds of humanity in Some Dimension, and may stir up a race of rebels who shall refuse to be confined to limited Dimensionality.
 
flatland
 
 

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