The straight line, circle, segment
The two forms of knowledge - discursive and intuitive - are in a simplified geometric definitions. The circumference can not be conceived discursively, however, the segment can not be thought of intuitively. Two segments appropriately compounds are still a segment, the circumference will not tolerate itself. To define the circumference of one concept is needed, the distance (a notion that is closely related to the time). Once it is defined in some way the distance in a set of objects for convenience of representation called "point", the circumference as the figure rises easier than you might think (according to some criterion of simple algorithms). The definition of a circle is implicit and intuitive, it is not discursive reasoning that acts but the pure intuition, there are steps to follow, not a building nor put a point after another. He objected that the compass is "speech" which expresses the circumference, but in fact the compass is already in the circle essence: it is already all contained within the compass to draw the circle action is only a manifestation of something that still has its being already full. How it's different to the discourse segment. Once the two points are given nothing is yet said of the segment. How many different lines can in fact draw between one and the other points? What makes a certain line segment be? Perhaps because it is the shortest? But this would imply the consideration of the totality in the act of all possible lines from one of the two points, in the ordinary a topical non-viable infinite space. The definition of Euclidean straight line is completely unintelligible. It may be related to the direction but the direction is exactly what the lines define. It could also mean that the segment is the only line that joins the two points having a length equal to the distance between two points, but in this case the definition is misplaced: what is that in fact the length of a line? Perhaps the sum of an infinite number of infinitesimal segments of length?
short, straight line and circle are two examples of the different ways of thinking. In developing a circle I can see the form that made so many times I've seen in nature but also turn my attention the pure concept of points equidistant from a center in a collection that may have nothing to do with the usual space, a set in which there is a certain dynamism, at least an embryonic concept of "time" so that you can define a distance. To the right is not so. Only the geometric visualization can help me, but if I try to imagine the sheer idea of \u200b\u200b"right" here is that I lose myself in an extremely structured, with many properties (eg direction) and always lies in the view.