Flatland, the above, e la quarta dimensione

Carl Sagan (Astronomo e scrittore di fantascienza) "spiega" la quarta dimensione partendo dalle due dimensioni, con una "buffa" digressione su Flatland.
(In inglese)


Have you ever considered how a four-dimensional being would appear to you if it suddenly came into your room?

Think of it this way. Consider a two-dimensional world resembling a sheet of paper. How would you appear to the inhabitants of such a world if you tried to interact with with them? The 2-D creatures would only see cross-sections of you as you intersected their universe. Your finger would look like a flat disc that grew in size as you pushed it through their world. Your five fingers might looked like five separate circles. They would just see irregular shapes with skin boundaries as you entered their world. Similarly, a hyperbeing who lived in the fourth dimension would have a cross-section in our space that looked liked a bunch of skin blobs.

A 4-D being would be a god to us. It would see everything in our world. It could even look inside your stomach and remove your breakfast without cutting through your skin, just like you could remove a dot inside a circle by moving it up into the third dimension, perpendicular to the circle, without breaking the circle.

A hyperbeing can effortlessly remove things before your very eyes, giving you the impression that the objects simply disappeared. The hyperbeing can also see inside any 3-D object or life form, and if necessary remove anything from inside. The being can look inside our intestines, or remove a tumor from our brain without ever cutting through the skin. A pair of gloves can be easily transformed into two left or two right gloves. And 3-D knots fall apart in the hands of a hyperbeing, much as a 2-D knot (a loop of string lying on a plane) can easily be undone by a 3-D being simply by lifting the end of the loop up into the third dimension.

Hypercube: is a Cube in four (or more) dimensions.