It's Elemental

Tag: Linearity

  • Notes on the roots of epistemology in recursion

    Notes on the roots of epistemology in recursion

    threefold recursive spiral of knowing
    Unity in distinction, distinction in unity.

    There is a necessary recursion at the very heart of epistemology. Epistemology can never be founded upon a principle of linearity, where thinking traces its origin to something that lies before thinking, and somehow emerges or grows out of it, because the very existence of this “before”, whatever its nature, must always be assumed BY THINKING itself, as a distinction within thinking.

    Therefore, the only proper starting point for an epistemology is the fundamental distinction OF distinction itself, by thinking FOR thinking, which constitutes the basis of all further distinction, and is implicit in it. The fundament of epistemology must be the recursive distinction of distinction. The nature of this self-distinction (distinction of distinction by distiction) is implicitly infinitely recursive, and identifies the very nature of thinking to be at its root one of distinction. Its implicit infinitude is a key aspect of thinking’s foundation, with definite consequences. It means that thinking is fundamentally (not secondarily) FREE: its potential to distinguish is unlimited. There is nothing that lies outside of thinking’s potential.

    The consequences of this are more than epistemological, they are ontological. Thinking, infinite in its potential, is (more…)

  • Why every line is a circle… and vice versa: a projective geometric exercise.

    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…)