Friday, March 25, 2005

Resolving Duality

A fundamental 'cross-platform' concept in life is duality, the idea of the existence of opposites. A convenient way of representing this is a piece of string, each end being the opposite of the other, so good/evil, rational/irrational etc. This method then neatly suggests the existence of all in-between states in a spectrum. To fully extend the idea, consider each parameter to occupy one dimension in n-dimensional phase space, and you may 'plot' the position of any individual in that space (only, of course, as a hypothetical exercise).

Traditionally, the resolution has been to speak of, for want of a more precise phrase, a 'divine viewpoint' from which all dualities apparent from our 'mortal viewpoint' vanish. Now this has the feeling of a woolly get-out clause to me, so I needed a way to picture it. Cue return to the string model: the string is naturally pictured as occupying a single dimension, i.e. it's straight. Introduce a second dimension and the opposite ends may be bent round to touch each other - what were perceived in one dimension as being maximally separated may appear adjacent from a higher-dimensional viewpoint. Yet within the single dimension of the string, a hypothetical 1D observer would notice no difference.

Duality is resolved! I feel, though, that I'll have more to say on the subject soon...

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