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Dualities

September 19, 2011

A late comment on this introductory post on dualities in the science2.0 alpha-meme blog  by Sascha Vongehr

When non-euclidean geometries came about through their euclidean models, Kant first dismissed them as obvious fakes or make-believes (lines not really lines, etc) not to be taken seriously. But nobody afaik (not that much) ever pointed at self-dual projective geometry as a form of refutation to Kant’s objection  – in the sense of a system symmetrically related to itself as non-euclidean geometries are asymmetrically related to euclidean geometries by modelling, so that the modelling relationship can’t be dismissed as foreign to the study’s main frame or even as incontrovertible stubble for the Razor (given also how the duality boosts local information economy inside the system, and how the symmetry denies a “side” to favor, duality is a theorem not an axiom, etc).

This is to hint that I find paradoxical or contradictory your insistence on a -fundamental- description embedding dualities, as long as you haven’t cleansed the taste for the foundational of  what (for instance) drove Kant to his attitude and further riddles it in more subtle ways. Just dismissing “Occam’s Razor” as an incompetent would-be philosopher’s buzzword doesn’t cut it imo.

To me, the first thing to do of dualities is to examine the possibility to describe theoretical (unification) physics as a process driven by somewhat confused (especially as regards its sociological side: physics is -taught-) over-greedy ideas on information economy. And in such a way that dualities fit the form of natural endpoints or fixed points for this process. In that frame I find it frustrating that most non-technical discussions of dualities fail to bring the spotlight on perturbative dualities, as if it was a foretold conclusion that this character was contingent (maybe it is, but I don’t see why).

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