Müller tries to use Kantian philosophy to support his theory, arguing that by the "manifold accessible to pure intuition" Kant meant, or could have meant, the a priori possible manifold of physical points that could be perceived by the retina.
Müller explained stereoscopic vision by arguing that each retina is able to perceive itself, that is, to perceive a priori the manifold, or grid, of points that can be projected onto the retina.
To this end, we replace Euclidian distance with geodesic one – the length of the shortest curve between two points that lies on the manifold.
Given a timelike orientation, a quasi-Cauchy surface unproblematically divides the manifold into its past (i.e., all points that can be reached by past-directed timelike curves from S) and its future (ditto mutatis mutandis).
The Bullet source can be modified to add a user data member to the persistent manifold structure that owns the manifold points.
He distinguished macroscopic coincidences in the field of our sense experience, to which he does accord a privileged and foundational epistemic status, from the microscopic point coincidences that define an ontology of spacetime manifold points.
What Einstein realized in 1915 was that, in 1913, he was wrongly assuming that a coordinate chart sufficed to fix the identity of spacetime manifold points.
In the tangent space of manifold points on a Riemannian manifold, linear operations may be performed.
The great-circle distance between two manifold points is unique.
It is a form of Riemannian geometry in which space and time are linked in a four-dimensional manifold, and it is the curvature at each point that is responsible for the gravitational "force" at that point.
