Circle, Point, Sphere

It might be argued that Circular motion, whether that of a celestial body, thought-thinking-itself, or entailed in Spinoza's definition of Circle, is still only an approximation to the idea of a Circle, so its imperfections, e. g. the directionality of the motion, are not that of the idea.  However, the definition that Spinoza rejects--a set of points equidistant from a point--has its own shortcomings, even if it does not entail directionality.  For one, the set of such points is infinite, which compromises clarity, and for another, the concept is dependent on a point that is not part of the set--the center point.  So, this definition comes no closer to an illuminating cognition of a self-sufficient perfection.  But, it does suggest a problem from a different direction.  For, plainly, this formulation is hindered by the attempt to define a Circle in terms of Points.  But, once a difference, and a possible incommensurability, in dimensionality is introduced, so, too, is, implicitly, another one--between Circle and Sphere.  Then, the challenge becomes to establish the independence of the former from the latter, which seems daunting, given that the Sphere, even if itself not in immediate evidence in Reality, is at least closer to it than a Circle is in terms of dimensionality.  Likewise, in general, for the Pythagorean-Euclidean tradition of Geometry--its elements diminish concrete Reality, a strong indication that it is abstract Knowledge, and not an object of esoteric cognition, rather the basis of useful human Technical Knowledge.