Negative Numbers of Dimensions

[anderscolingustafson]

In 3 dimensions if you increase the diameter of an object N times in all directions the object will take up N³ times more space. In 2 dimensions if you increase the diameter of an object N times in all directions the object will take up N² times more space. In d dimensions if you increase the diameter of an object N times in all directions the object will take up N^d times more space.

This trend can be extended even when the number of dimensions is a negative number. If for instance the number of dimensions was -1 then increasing the diameter of an object N times in all directions would "increase" the amount of space the object takes up by N^-1. So in a negative number of dimensions increasing the diameter of an object in all directions would actually decrease the amount of space the object takes up.

In any number of dimensions the number of sides the equivalent of a cube will have is twice the number of dimensions so in a negative number of dimensions the equivalent of a cube would actually have a negative number of sides. This also means that in a negative number of dimensions the equivalent of a cube would have negative surface area because the surface area.

In any number of dimensions the equivalent of a triangle has one more side than the number of dimensions so in -1 dimensions the equivalent of a triangle would have 0 sides as -1+1=0 while in a number of dimensions less than -1 the equivalent of a triangle would have a negative number of sides. The equivalent of an octahedron in any number of dimensions is 2 raised to the number of dimensions so in a negative number of dimensions the number of sides that the equivalent of an octahedron would have would be a fraction between 0 and 1.

[wendy]

Negative dimensions do exist, but they have no measurement. The namon or nulloid lives in a space of -1 dimensions, and represents the unit of product for several real products.