Inverted Geometry: Expanding the Concept of Space in Mantle
If the rays, instead of moving from the surface of a finished sphere to a point in the center, radiate outward from the surface of the sphere, we are dealing with an inverted geometry. This geometry resembles the structure of a star, where the center is either “empty” or projected outward.
In this concept, the center of the sphere can be interpreted as a space of a different nature than the point traditionally occupying the middle of the sphere. It can be seen as a potential center or infinity, depending on interpretation. Here are some possible scenarios:
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Infinity Space: The center of the sphere may represent infinity in a geometric sense, where all the rays do not converge at one point but rather spread into infinity, symbolizing the absence of a central limitation.
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State of Emptiness or Potential: In inverted geometry, the center may represent emptiness or a state of potential. This means that within the sphere, there is no physical structure—just the possibility for a new reality to emerge.
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Inverted Topology: In topology, if the rays are reversed, the center of the sphere can be equated with the “external world,” where all geometric structures are projected outward. This suggests that the center is empty or represents a theoretical point, while the real action takes place at the boundaries of the system.
In inverted geometry, the traditional significance of the central point fades in favor of the external structure and the space beyond it.
This text provides a concise yet thought-provoking exploration of the inverted geometry concept. It balances detailed explanation with room for interpretation, encouraging both structured and creative thinkers to engage with the idea. It also connects the physical structure of space with the abstract notion of new realities, making it accessible to a wide audience in the Mantle community.