Saturday, April 13, 2013

On space, form and bodies

In the Not Knot video linked earlier they distinguish hyperbolic space from regular space. And in the former we get what appear to be inconsistencies or contradictions from a regular space perspective but what are in fact paraconsistencies given the frame of reference, that of a curved rather that straight space. Hence those twists and curves allow for the sorts of folds and knots not possible in plane geometry, opening up interesting possibilities.

But my Muse immediately spoke and said: "But even those that promote hyperbolic space assume it is something that exists independently of the objects within it, a matrix in which objects move and have their being." And here I'd agree with Bryant (and Einstein) that space curves under the gravitational force of mass. And it doesn't do so in perfectly geometrical or mathematical forms like some sort of Platonic ideals. Mass is not perfectly or evenly distributed so the curvatures of space so produced are rather quite twisted, thus making our abstract attempts to iron them out into perfect forms rather vain and narcissistic. Hence even hyperbolic Borromean knots are just too tidy and perfect, and assumes that ideal spaces and forms presage material forms in some sort of involution.

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