​Interlude: Limits of Modality, Dark Matter and Black Holes

As previously stated, space and time are not external parameters but modalities through which differentiation becomes stable and distinguishable. Space retains differentiation in extension, while time retains it through change, allowing differentiation to manifest dynamically, as an event. However, differentiation need not always be structured simultaneously in both modalities. It is possible to conceive structures retaining differentiation in only one modality, becoming limiting forms—beyond the ordinary scenario wherein space and time coexist.

Dark matter is a structure distinguishable through gravitational interaction: it shapes galaxy clusters and bends space but remains indistinguishable in temporal modality. We observe no changes, responses, or events such as emission or collisions, typical for ordinary matter. For example, in the Bullet Cluster, dark matter manifests through gravitational lensing but neither emits nor participates in detectable interactions. It is distinguishable only spatially—as a stable topology lacking internal dynamics. This could be interpreted as the reversed unfolding of its temporal differentiation: the temporal modality capable of manifesting dynamics seems "collapsed," leaving only a spatial imprint. It forms a background, structuring the scene for other differentiations while remaining invisible in temporal flow.

A black hole, by contrast, is a structure continuously active temporally. It absorbs matter, distorts the temporal continuum, emits radiation (e.g., Hawking radiation), yet becomes inaccessible in spatial modality. Inside the event horizon, differentiation loses localization—the form disappears, spatial modality ceases and only change remains. For an external observer, a black hole is distinguished through temporal dilation near the event horizon and quantum emission, yet its internal structure cannot be localized: space "collapses." It is a process without scene, an event without extension. Moreover, through Hawking radiation, a black hole gradually loses mass and ultimately vanishes, which can be understood as the dissolution of temporal differentiation, its reversed unfolding.

At the quantum level, time need not be unidirectional; it may allow differentiation to unfold both forward and backward. Differentiation in temporal modality thus can not only structure as event sequences but also return to an unstructured state. Quantum particles can exist in superposition, simultaneously moving forward and backward in time, as recent photon experiments illustrate. Dark matter, deprived of temporal modality, can be seen as a structure whose differentiation has entirely unfolded backward, leaving only spatial stability. Black holes demonstrate how temporal differentiation gradually dissolves—but during radiation emission, they may manifest bidirectionality, returning information to the universe.

Hypothetical particles, such as tachyons, moving faster than light, could exemplify another "reversed" modality. Yet their existence remains speculative; they may be fundamentally impossible due to phase space constraints, lacking experimental support thus far. Nevertheless, even absent tachyons, bidirectional temporality at the quantum level demonstrates time’s flexibility. It permits differentiation states that transcend linear causality.

Hence, we identify two asymmetric modalities of differentiation:

Dark matter: distinguishable spatially, devoid of temporal modality.

Black holes: distinguishable temporally, devoid of spatial modality.

These forms represent not anomalies but boundary cases of modal differentiation. They illustrate that differentiation need not be simultaneously structured in both directions but may appear partially—in a single mode of retention. This broadens the very notion of a node of differentiation: nodes need not always be structured concurrently in both space and time.

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