Flatland was totally wrong about infinitely thin planes | GEOMETRY: Dimensions, Hypercubes and Hyperspheres, Polytopes, SpaceTime Curvature, etc | Sacred Geometry Web | Forum

“Flatland – a Romance of Many Dimensions” by Edwin Abbott is a quite famous and influential little book about understanding the fourth spacial dimension. Yet it makes a mistake that is found almsot everywhere that the analogy to a 2D person trying to conceptualize a 3D universe is used.

A 2D world is INFINITELY thin. 
This means that it is not only thinner than our atoms, quarks, planck units – it is INFINITELY thin.Therefore there is ZERO possibility of a 3D creature interacting with a 2D world.

It is conceivable that a 2D creature might see cross sections of some planck unit spheres as we passed through its universe, but if these spheres are zero dimensional singularities as suggested by Nassim Haramein
then the chances of a ZERO dimensional universe intersecting them for more than an infinitesimal amount of time as the 3D object passed through the plane are infinitesimally small.

You can download the text of Flatland from here
an updated politically more correct version here

and watch a popluarizations of it here