I’d like to make a contribution with regards to circularity/linearity, from a geometrical standpoint. If you don’t like geometry, stop reading, or better yet, read with increased intensity.
The polarity between circle/line is one that is fundamental to many geometries – they are taken to be quite different logical entities. Primarily this arises because of (in a move parallel to Russel’s need to introduce the Theory of Types to avoid paradox) a limited way of dealing with infinity. Cybernetics shows us, by providing a wider view (attention to relations, recursions, and thus relations of relations, etc.) that the Theory of Types is unnecessary and points towards a more flexible and mysterious understanding of paradox. In the same way, projective geometry provides a way of dealing with infinity that encompasses, expands, and re-frames the conventional geometric view. (more…)