Visualising Four Dimensions

Need help in visualising four dimensions? Étienne Ghys has now created a series of videos for ‘teaching’ others how to visualise objects in the fourth dimension (the spatial, not temporal, fourth dimension).

How on earth can we visualize such a thing? [The] challenge in visualizing four dimensions is very similar to the one that would be faced by a perfectly flat creature who lived in two dimensions and tried to visualize three, like the inhabitants of Edwin Abbott’s Flatland or the lizards in the page in Escher’s Reptiles. A cube or a sphere would be nearly unimaginable for the two-dimensional lizards, since they are unable to rise out of the plane.