Friday, May 19, 2017

Direction and Radiality

The concept of Spatial Direction is derived from that of Radiality, and, more precisely, from that of the distinction between Center and what can be called Exocenter.  Now, while a Center is a Point, Exocenter is not; rather, it is a general Elsewhere, only subsequent differentiation within which yields points, which can be termed Exo-Points. Spatial Direction is thus defined in terms of the relation between a Center and an Exo-Point, and can be made more precise by the quantification of the differention, e. g. expressed as an Angle.  This concept of Direction is also implicit in non-quantified versions, e. g. it is entailed in the distinction between 'following the North Star' and 'going in the direction of the North Sea'.  So, while Newton presents Direction as a primitive notion, it is a derivative one, and it cannot be derived from his concept of Absolute Space, which has no privileged Points, i. e. no Centers.

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