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Attractor States

A right-hand glove could be put on the left hand, if it could be turned around in four-dimensional space.

—Wittgenstein, Tractatus Logico-Philosophicus 6.36111

The difficulties: how do you imagine the process unfolding in time, where do you set the axis of rotation, and what in fact is the nature of the glove, this familiar object you’ve been pulling onto your right hand your entire life without ever suspecting it was other than what it seemed?

Assuming the axis of rotation transfixes the object: if the glove is in fact no more than it appears, a three-dimensional object with no extension along a fourth spatial degree, then the commencement of rotation will cause it to wink instantly out of apparent existence—except, theoretically, for a widthless line segment coinciding with the axis of rotation—until the transformation completes, at which time it will wink back into existence as its own mirror image, every point in its body affording a strict bijective correspondence to its former self but the geometric relations between those points now inverted.

If, on the other hand, the familiar glove turns out to be the three-dimensional tip of a four-dimensional iceberg, an object with previously unsuspected contours extending into hidden space, then before it attains its final transformed state—newly mirrored, but in every other respect the same old article—it will pass through warpings and deformations such that it ceases to resemble a glove at all, shrinking and distending, exhibiting unforeseeable prominences and depressions, splitting into multiple bodies before fusing back into one, and generally inducing nausea and fomenting outrage among church, state, academy, press and even those many private hearths that suppose, wrongly, they’ve already seen it all.

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