## Dimensionality

Dimensionality is a measure of complexity. This section introduces the notion of dimensionality. Hopefully it will not increase your dementia. Dimensions are used to describe physical or topological things. The use of dimensions in algebra and geometry offer a frame of reference to think about the dimensionality in system information.

In geometry, if you have a mass less point in space, it has no dimensions.

If you drag the point some distance then you have a line which is a one dimensional object. If you drag the line some distance you create a plane. If you drag the plane then you have a solid or 3 dimensional object. Three dimensions are all we have to work with in space unless you would like to include time as another dimension.

We can carry this idea a little further in algebra by creating multi-dimensional arrays.

A three dimensional array is like a cubic box full of cubic boxes, each containing some useful information about a problem domain.
After 3 dimensions, dimensionality is hard to visualize but a few more dimensions have practical applications. Maxwell envisioned that the natural laws of motion, energy, electromagnetism and gravity could be reconciled in a mathematical system using 10 dimensions.

What if, we are a projection of just a few of God's dimensions such that we can sense a similarity but not comprehend His complexity.
When considering systems in general each of its attributes can be considered a dimension if it is orthogonal to the others. For example; color and texture and chest circumference could be attributes of a suit jacket system. If sufficient values of each is available then the range of configurations for this 3 dimensional system can be large but manageable. Imagine configuration as; (brown, tweed, 42)... now begin adding more attributes to our system and the possible configurations can very quickly become staggering.

The number of orthogonal attributes of a system determines its dimensionality. As you can see, dimensionality is related to configurability and complexity. The more dimensions you add, the more complex a system becomes and the more confiurable it is.