The Geometry of Consciousness add6-2
(Closing of 6.1)
... The dynamic equilibrium between these two modes, adjusting the Christoffel symbols ($\Gamma_{ij}^{k}$) or asserting normative inertia against the external force ($F^{k}$), is what continuously re-forms the boundary of the self. This boundary, however, is not a surface of zero thickness dividing an inside from an outside. It is a membrane of finite thickness, to which one thin layer is added with each collision against the external force.
6.2 The Immanent Emergence of Subjective Time
This formation of the self-boundary is fundamentally a temporal process. The time at issue here is not the parameter $t$ used to describe the trajectory. That parameter remains as a descriptive convenience; lived time is distinct from it, and is generated from within the membrane through the iterative steps of covariant differentiation. Husserl's tripartite structure of time-consciousness corresponds geometrically to the following:
Protention: The intentional tangent vector $X(t)$ projecting into the immediate future. It represents the normative inertia directed outward from the outermost layer of the membrane.
Urimpression: The instantaneous collision with the external force $F^{k}$ at point $p(t)$. It is the mismatch between anticipation and world, arising at the surface of the membrane.
Retention: The Christoffel symbols $\Gamma_{ij}^{k}$, updated at each collision and laid onto the membrane as a single thin layer. The past is preserved not as sediment that settles after agitation, but as lamination: layers folded upon one another with their order intact.
Subjective time is this membrane thickness itself: the thickness, measured by the metric, of the layers deposited each time consciousness resolves the mismatch between its internal normative field and the external force. The resolution of mismatch is not an event that occurs in time. Rather, the resolution produces a layer, and the accumulation of layers is time. The "thick present" of human experience is therefore not a metaphor. It is the thickness of the outermost, not yet consolidated layer, where the intentional trajectory (Protention) collides with the alterity of the world (Urimpression) and a new layer (Retention) is folded inward.
