In the world of reflections on wholeness, each of us encounters the puzzle of unity and division.

Unity in Wholeness: The Unbroken Circle

In the world of reflections on wholeness, each of us encounters the puzzle of unity and division. By considering the circle as an example of an integral object, it becomes clear that it is the integration of all constituent elements that creates the figure’s uniqueness. The key point here is the extraordinary unity: the even distribution of the distance from the center to any point on the circumference inexorably binds all elements together, transforming an arbitrary set of points into a singular whole.

The main idea is that when one attempts to isolate individual elements, such as points or segments, the very quality that defines the circle as a unified phenomenon is lost. Integration and the interconnection of the components play a decisive role because, without their unification, the essence of the object disappears. This is exemplified by the unchanging value of the radius in a circle, which not only establishes the formula of the figure but also symbolizes the continuity that unites the elements into one single entity. Separated parts cannot independently preserve this characteristic, which leads to the loss of the essence that, when fully integrated, reflects the complete whole.

In conclusion, it can be said that dividing an integral object damages its internal harmony. Attempts to restore completeness from disjointed fragments inevitably face the impossibility of recovering lost interconnections. This approach not only serves as a philosophical reflection but also reminds us of the importance of perceiving the whole through the lens of the interaction of its parts, a concept that is relevant in various aspects of our experience and knowledge.

What problems arise when attempting to divide an integral object, such as a circle, into separate parts?

When trying to divide an integral object like a circle into separate parts, the primary problem is the loss of that essential quality which unifies the object. In the case of the circle, its defining feature is its continuous, unbroken nature—for example, the radius, which equally determines the distance from the center to any point on the circumference, gives rise to the circle’s integral quality. Isolated individual points or segments do not, by themselves, possess the property that defines the circle as a whole. As emphasized in one of the sources:

"Thus, the radius of the circle is the same for the entire circumference, equally determining the distance from the center to any of its points, and therefore, it by itself forms the generative beginning of the circle, while the peripheral points can only form a circle when taken collectively. Outside of this collective, i.e., outside of the circle, taken individually, they have no definability, and the circle without them is invalid." (source: link txt)

Another source, referring to Aristotle’s reasoning, notes that the concept of a circle does not include the idea of its individual segments—the characteristics of the whole cannot be reduced merely to the characteristics of its parts. Such fragmentation deprives the notion of unity because the parts, once separated, do not retain the qualities of an integrated object:

"If the concept of a circle does not include the concept of its segments..." (source: link txt)

Thus, the primary problem of dividing an integral object is that its essence is defined precisely by the integration and interrelation of its constituent elements. Taken separately, the parts lack the inherent unity and therefore cannot fully capture the character of the object as a coherent whole. This leads to situations where attempts to reconstruct wholeness from divided fragments become conceptually impossible, as the internal connections and mutual dependencies are lost.

Supporting citation(s):
"Thus, the radius of the circle is the same for the entire circumference, equally determining the distance from the center to any of its points, and therefore, it by itself forms the generative beginning of the circle, while the peripheral points can only form a circle when taken collectively. Outside of this collective, i.e., outside of the circle, taken individually, they have no definability, and the circle without them is invalid." (source: link txt)

"And if the concept of a circle does not include the concept of its segments..." (source: link txt)