Space dimension estimation

3D? 2D? 5D?

Within the sensorimotor paradigm, the question of space is a primary tremendous issue. While space seems like a kind of universal, homogeneous and isotropic 3D container shared by all of us and our environment, discovering that space actually exists only on the basis on what is actually available “from the inside” (i.e. the sensorimotor flow) is far from being intuitive. Especially since the sensorimotor flow isn’t homogeneous, isotropic and 3D…

In particular, is it possible to rediscover that space out there is a 3D space (at least from our point of view!), and that it can be characterize by 6 independent spatial variables corresponding to the 3 translations and 3 rotations we all know? This important question has already been raised by Henri Poincaré at the end of the 19th century. Philipona showed in 2008 it was possible to recover space dimensionality from the sensorimotor flow, but only from infinitesimal movements. By using non-linear dimensional estimation techniques, we have shown in this paper that, while using realistic movements magnitudes, it was still possible to correctly estimate space dimension.

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This article was updated on February 20, 2022