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**DEAN
HARTLEY**Science
and Speculative Science in Folded Universe Series |

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## Addendum:

### This novel is science fiction. That means it is a story with some connection to science, particularly speculative science.

## Physics

We experience three directional dimensions and one time
dimension. However, there is another dimension that effects us - it is an
imaginary dimension. This dimension is useful in describing
electromagnetic radiation, which travels through space over time, yet requires
this extra dimension.

We also have proof that space has a local curvature; light
is bent as it passes through gravity wells.

## Mathematics

Mathematically, curvature can be positive, zero, or
negative. By convention, the surface of a sphere has positive curvature.
A saddle point has negative curvature. You can think of the surface not
having enough stuff to lie flat as you get further from your reference point.
The constant pi is the ratio of the diameter of a circle and its circumference.
On a sphere, this ratio is not constant and is less than pi. For negative
curvature, there is too much stuff for the surface to lie flat. A circle
drawn around a point on the inside of a torus would have a ratio greater than
pi. The brim of a typical cowboy hat has this feature.

## Fiction

The fictional assumption is that our universe has generally
negative curvature and thus has many folds. In the one-dimensional view
below, the universe is folded back and forth to fit into a small area. The
observed directional dimension follows the curve and the extra dimension is the
imaginary dimension. Thus, if you could travel along the imaginary
dimension, you could skip lots of conventional space and get to a distant
location more quickly. The book assumes a method of doing this that
matches a disk at our location with a disk at a distant location. The math
uses Dehn's lemma and the substitution of axes. The physics is fictional.

The figure below shows how two different starts (four-pointed objects) might be
easily accessible from the Sun (five-pointed object).

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