The Primordial Point: Foundation of Relationality

 

The Primordial Point: Foundation of Relationality

At the very core of any system lies a single point, which represents the most fundamental unit of existence. Initially, this point exists in isolation, incapable of relating to anything else. However, the very fact that it exists implies the potential for relationality—its existence hints at the possibility of interaction and connection.

The point begins to relate when it differentiates itself, extending or projecting into two new points. This marks the first step towards multiplicity, transitioning from unity to duality, and introducing the concept of asymmetry into the system.

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Dimensional Growth and Emergent Symmetry

As the process of relationality unfolds, each new point created does not merely connect back to the original point, but also establishes connections with other new points that form its neighborhood. This leads to a triadic relationship: the original point and two emergent points, representing the minimal geometric interaction.

As this process continues, the system evolves in a fractal manner: each new point further extends the web of relational connections, and over time, this fractality leads to increasingly complex structures. Despite the growing complexity, all points remain traceable back to the original, preserving a sense of unity and connectedness throughout the system.

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The Speed of Light as a Relational Constraint

One of the key consequences of relationality is the emergence of speed constraints, particularly the speed of light. The speed of light, $c$, emerges as a natural reflection of the foundational point’s ability to relate to others. In the context of our system, each point can only "relate" to a finite number of other points within a single "tick" of time. This reflects the core concept of causality—there are limits to how quickly relationships can form and propagate through the system.

The relational speed defines how efficiently a point can interact with others, and it is bounded by the constant $c$. The speed of light sets the upper limit for how time and information can flow through the system. In essence, $c$ acts as a measure of how the relational capacity of the original point propagates through the expanding network of points.

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Infinite Reduction and the Relational Limit

As we approach infinitely smaller scales, the system begins to collapse back into its most fundamental form: the original point. At this scale, the relational structure breaks down, much like how space-time behaves at the Planck scale in physics, where conventional concepts of space, time, and causality cease to apply.

The relational ability of the original point sets a limit to how small the divisions of the system can be. This is a fundamental constraint that governs how space and time manifest at all scales. Ultimately, the point’s finite relational capacity regulates how interactions unfold in the system.

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Fractal Rule as Symmetry

The rule governing the creation of new points, where each point generates two additional points, is inherently fractal. This process leads to a self-similar geometry, where the structure of the system remains consistent across different scales. However, the introduction of dimensionality—in the form of time and space—introduces asymmetry.

• Time flows directionally, establishing a sequence of events and interactions.
• Space expands radially, creating a network of points that radiate outward from the original point.

These asymmetries are fundamental to the structure of the system, with time providing a directional flow and space organizing the interactions in a radial manner.

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Connection to Temporal Flows

In this model, the concept of speed of light is a direct result of the point’s relational dynamics. Temporal flows depend on how quickly the original point can relate to others, defining how time progresses. This relational ability underpins both the emergence of time (as a sequence of interactions) and space (as a measure of the distances between relational points).

The interplay between temporal and spatial flows, and their constraints, governs the behavior of the system at all levels. Both time and space are not independent, but rather emergent properties of the relational rules of the foundational point.

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A Unified Perspective

In my model, time and space are not separate entities; they are deeply interwoven, emerging from the same relational dynamics. The speed of light and time are both expressions of the fundamental relational structure defined by the original point’s capacity to relate.

The rate at which time progresses (the “speed of time”) and the maximum rate at which information or causality propagates (the speed of light) are both determined by the geometry of interaction between points and the constraints on these relational flows.

At the quantum level, the distinctions between space and time blur. What we perceive as space and time are not independent dimensions but rather interconnected flows that reflect each other. The way we measure these flows ultimately shapes our understanding of both space and time, which are simply two aspects of the same underlying system.

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Initial Symmetry and Relational Geometry

At the outset, the system begins symmetrically: all points relate to one another with equal relational capacity (αi​=constant). At this stage, spatial distances (r) are not yet influenced by the speed of light, and interactions occur without any directional or spatial bias.

As the system progresses, the interactions evolve, and we begin to incorporate the effects of both spatial and temporal geometries. This can be captured in the following equation:

$$c_{\text{eff}} = c \cdot \left( 1 - \frac{\alpha_i(r)}{\text{max}(\alpha_i)} \right) \cdot \left( 1 - \frac{\tau(t)}{\text{max}(\tau)} \right)$$

This equation represents the effective speed of light, which is influenced by two key factors:

1. Spatial Geometry: The first term, $\left( 1 - \frac{\alpha_i(r)}{\text{max}(\alpha_i)} \right)$, adjusts the spatial interactions. As the interaction strength weakens (e.g., as $r$ increases or $\alpha_i(r)$decreases), the effective geometry is reduced, making interactions more constrained.

2. Temporal Geometry: The second term, $\left( 1 - \frac{\tau(t)}{\text{max}(\tau)} \right)$, adjusts the temporal evolution of the system. As the system approaches its maximum temporal flow, interactions become slower, reflecting the dilatory effects of time.

Both terms effectively reduce the system’s capacity to interact, illustrating how both space and time shape the system’s dynamics.

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Conclusion: Space as Emergent from Time

Ultimately, space and time are two expressions of the same fundamental system. The emergence of space is not an independent phenomenon but a consequence of how relational dynamics unfold over time. As interactions evolve, the fractal nature of these relationships leads to the creation of multi-dimensionality. Space, therefore, is not pre-existing; it emerges from the interplay of time and relational dynamics.

This unified view connects space and time in a way that reflects their interdependence, showing how both dimensions are manifestations of deeper relational properties of the system.