Temporal Topologies of Becoming: 1 Time as Emergent Topology

Time emerges from relational differentiation, not as an external dimension.

Time is commonly treated as a background against which events unfold — a linear, uniform metric through which the world moves. Yet from a relational ontological perspective, this is a fiction: there is no pre-given temporal container. Instead, temporality emerges from the interplay of gradients, cuts, and reflexive coherence — from the very dynamics that constitute becoming itself.

1. Temporality as Relational Patterning

Gradients of readiness generate local inclinations; cuts produce actualisations; reflexive coherence sustains continuity. Each of these dynamics contributes to what we experience as temporal ordering:

• Successive cuts along a gradient create the sense of sequence.

• Differential steepness produces variability in “felt duration.”

• Reflexive modulation maintains continuity without collapsing openness.

Time, therefore, is the pattern of becoming, not the stage on which becoming occurs. To describe temporal succession is to describe the topology of relational differentiation.

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2. Linear Illusion and Continuous Differentiation

The sense of linear time arises from perspectival slicing of continuous gradience:

• When an observer notes events sequentially, the underlying gradient is discretised into points.

• This discretisation produces the appearance of a flow from past to future.

• Yet ontologically, these events are local inflections within a continuous slope, not marks on a pre-existing line.

Linear time is thus epistemic, not ontic: a convenient perspective on continuous relational processes. The actual field remains a seamless topology of inclinations, intensifications, and modulations.

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3. Event Density and Temporal Topology

Not all regions of a field produce actualisations at the same rate. Some areas are steep, others shallow:

• Steep regions produce frequent cuts, creating high “event density.”

• Shallow regions produce sparse cuts, creating apparent temporal elongation.

• Variability in local slopes shapes the felt rhythm and thickness of duration.

Temporal topology is therefore heterogeneous: duration is a function of relational intensity and gradient modulation, not a uniform metric.

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4. Temporality Across Domains

This relational account of time applies across scales and modalities:

• Physical systems: the flow of energy or matter reflects local gradients and actualisations.

• Biological systems: metabolic cycles, neural firing, and organismic rhythms emerge from differential readiness and local rebalancing.

• Semiotic systems: discourse unfolds along interpretive gradients, producing sequences of construal and symbolic time.

In each domain, time is emergent, distributed, and scale-sensitive — a topology rather than a universal, homogeneous measure.

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Next: Rhythms of Gradient Interaction

Having established that temporality emerges from relational differentiation, the next part will explore how rhythmic patterns arise. We will see that oscillations, resonances, and regularities are not imposed externally, but emerge from the interplay of local gradients and reflexive coherence, generating the patterns we perceive as rhythm and temporal structure.