Non-Euclidean Perceptual Space

It always amazed me that there has scarcely been a distinct characterisation of the geometry of human perception – how points and distances vary in space as perceived by us. There’s often talk about the vanishing point – the convergence of parallel lines in our visual field. This straightforwardly contradicts Playfair’s axiom, equivalent to Euclid’s 5th axiom in his description of geometry. Parallel lines cannot intersect in Euclidean geometry, essentially. Yet roads and train tracks pointing away shrink, until they vanish; is the far-away world unimportant and shallow to an ego-point capable of only seeing its own local environment, its neighbourhood? This is a feature of hyperbolic geometry: for a given point, everything is smaller the further one moves away from it, but this is true for any point. The centre of the universe is everywhere; seems so gratifying. But also lonely… with a prodigious unknown stretching out in every direction. Something is out-there, but I intrinsically have no idea what, and if any attempts are made to move elsewhere, one loses sight of another spatial subset; dynamic reconfigurations. Not only is every point different, but at each point everything else seems different.

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