Sunday, July 31, 2016

geometry

The words "a one inch cube" define a Universe, but, to get back to that particular universe we need to attach some sort of name, so that we can ask to be returned to that particular universe.

Also, in a sense "a one inch cube", even with a name attached, is not really a complete definition of a Universe, it's rather a framework, within which a universe can be described. A Universe comes into existence when we describe things as being in specific place in or around a one inch cube.

But now let's note some virtues of a one inch cube as a framework within which to describe a universe. As noted, it is completely definite, and, additionally, it is very simple.


Now, we can put things in the universe defined by our one inch cube by describing their locations relative to that cube.

It's interesting to me that this seems like an incomplete formula. Don't we need to also describe the shapes of things we want to put in this universe? But, in fact, shape is a form of location. Let's say we now want to place another one inch cube somewhere in our universe. Well, a cube is an infinite number of points, but not just any points - points that conform, in their locations, to certain rules. The rules are defined by the term "a cube", and, if we want to be more specific, and describe a particular cube, we can add that a corner of this cube is defined by three specified points.

In other words, the word "location" really refers to a point, and then a "thing" can be a point, or a set of points, and then there are "things" we call lines, and surfaces, which are infinitely large sets of points, but out of all possible points, these sets are strictly limited by terms that include points and distances and shape names. And this means that, if we describe a thing, we are describing a set of points. We can even somewhat arbitrarily but not illogically redefine the word "location". We can say that it refers to a point or to a set of points.