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March 08, 2008

Broadening the Scope of Symmetry

David Wade’s Symmetry: The Ordering Principal, explores the notion of symmetry as it is seen in science, mathematics, art, and culture. The idea of symmetry seems to be applicable to almost anything: “there is nowhere that its principals do not penetrate,” he says. To contain symmetry means to contain balance and proportion. Wade suggests these things cannot exist without “transformation, or disturbance, or movement,” or in a sense — asymmetry. This is a fascinating paradox.

This book led me to ponder the consequences of asymmetry. Can the things that are deemed asymmetric exist just as fully and endure in the same way that symmetric things can? And can what seems to be symmetric actually be asymmetric? (Like the design on the cover of the book, for instance). This is something I discovered last week in class with the paper folding experiment. I began with one diagonal fold, having no intention of maintaining evenness on each side. I folded in no particular pattern, but what I ended up with was a shape that looked like a perfectly structured cone. With its folds, it appeared symmetric. It was only with the unfolding, when the paper became flat again, that the creased lines appeared to have no symmetry at all. So perhaps what we see as containing equality and perfect harmony is only playing tricks on us.

It seems that almost all things may start out being symmetric, but later deviate towards something else, a different pattern. Is it possible for the same thing to be both symmetric and asymmetric? If so, what do we identify it as? Consider the shape of a fork. If this object is cut horizontally and folded over, we have asymmetry. The opposite is true if we divide it vertically.


Five interlocking tetahedra. Is this symmetric?

Posted by pbali at March 8, 2008 05:17 PM

Comments

A fascinating paradox indeed.
It is as if there is a seeking of symmetrical circumstance, as if such seeking could be used, especially by the mind whose use participates in transformative gestures, as explanation for motion when motion is understood as being toward a destination or, less planned, when understood as arriving at a destination.

The imposing --for to some extent, meaning tends to be imposed-- of meaning itself transforms, disrupts, resets the frame so as to assist the imposed meaning seem more resolved, more certain,

certainty being yet another agent of transformation, one that repositions and reconfigures so that the particular certainty seems correct and substantiated.

So the erroneous can frame as effectively as other options.

--OH YES, YES ,YES --how delightful this contemplation of the symmetric/asymmetric hoax? hope? You've identified (one of the) possible relationships between the sym/asym --matters of how they're frmaed, circumstances of the encounter, the angle of consideration, the configuration of what is being considered,

and a model relying on flux (hoax of flux? hope of flux? facts of flux? errors of flux?); in a model relying on flux, generally there is denial of permanence, so at least perception of components of existence move through cycles that more stable and less stable, more symmetrical, less symmetrical, no one form being the only, or even necessarily the primary form, depending on what is determined based on apparently prevailing circumstances at the time of consideration/interaction on some scale.

That a particular entity may manifest in symmetrical or asymmetrical forms suggests what? Is feedback from the movement through forms establishing biases within certain sets of conditions? As more of the allness of considered, is symmetry or asymmetry being approached, assuming a leaning, an emerging bias? As more is subtracted from an "allness of allnes," is symmetry or asymmetry generally being approached, assuming a leaning, an emerging bias?

Fascinating, fascinating; thanks.

Posted by: thyliasm at March 11, 2008 11:38 AM

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