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As we have seen, analogical thinking offers us an gateway to understand the mutual functional relationships between elements within a system. A system may consist of an apple and its tree, an (polair-)axis and its plane, or any other interconnected system. Within it, functional identities can be assigned to elements that are in themselves value-free or neutral.
In other words, analogical thinking offers a key for understanding interdependent systems as well as a springboard for gathering knowledge along the line of a known lawfull connection. We will now further elaborate on the leap we just took.
Form and content
Let us start by looking at the relationships within a purely abstract system, such as a circle. The universal character of the circle makes it a suitable candidate for identifying general basic relationships which then may be recognized in other, more specific situations as well. So in this figure with its center, radius and circumference we can recognize the functional relationship between these three elements. Now their distinguished functions result in an added intrinsic value for each of these elements.
In principle, a geometrical point is dimensionless; it has no proportions whatsoever. If not it would not have gathered itself totaly inward yet. It would still be a spot with some dimension. It is infinitely small and lacks in a geometrical sense any intrinsic properties. The same goes for the center of a circle.
Similarly, in a purely geometrical sense, the circumference of a circle does not possess any qualifying properties either.
Still, the circumference is a product of the center, as it may be considered to have been ejected outwards by it. Actually, the circumference could not even exist without a center having been pin-pointed first. Therefore both, the center and the circumference are in a functional relationship with each other.
So a point is beyond proportions. If it would have any proportions, it would not have ‘collected’ itself completely yet. It would still be a tiny spot with a measurable size, not an absolute point. A true point, being infinitely small, can be seen as the expression of the indeterminacy of infinity.
By contrast, the circumference of a circle does have a specific, limited size. Still, we cannot pin-point any starting point or end point on the circle’s circumference. So in a sense, its circumference, too, is a reflection of infinity. One might say that the essence of the center, infinity, is coming to the fore or revealing itself through its circumference.
Thus a circle’s circumference can be viewed as a form of manifestation of its center.