hypcontinued

The following is a brief excerpt from ‘Geometry, Relativity & the 4th Dimension’ by Rudy v.b. Rucker (Dover books, N.Y. 1977) Referenced with permission by Rudy Rucker...check out his new book SPACELAND...a trip through 4D.

...”If you take a regular sphere and crush its northern and southern hemispheres into the plane of the equator, you get a disk, or solid circle. Similarly, we can imagine crushing the heavenly and infernal hemihyperspheres into the space of the hypersphere’s largest component sphere to get a solid sphere. The solid sphere can be turned back into a hypersphere if we can some how pull its insides in 2 directions perpendicular to all of our space directions.”

Diagrams A & B are from ‘Geometry,Relativity & the 4th Dimension’by Rudy Rucker (pg.9)

(Pg.12)”...it would seem that a 4D being could turn us into our own mirror image by rotating us, in the 4th dimension, around a plane that cuts through our body...”, (pg13.) “There is actually a model of how a rotation of a 3D object through 4D space might actually appear”...”If you look at a Necker cube (diagram above) for a while it spontaneously turns into its mirror image and back agin. If you watch it ‘do’ this often enough, the twinkling sort of motion from one state to the other begins to seem like a continuous motion, But this motion can only be continuous if it is a rotation in 4D space. So perhaps we can actually produce a 4D phenomenon in our minds!”

A visual hypershift is achieved by ‘movement’ of our perceptions (eg:Necker cube, where front reverses with back).