Familiar, or common-sense space, is a world that is both volumetric and dynamic. This is the space we find ourselves in, and it is also the space in which our notion of distance arises as a primal temporary measurement. We live in and think in terms of dynamic volumetric space. Tools A review of scientific and mathematical literature will quickly reveal that we have very little equipment to help us to deal with dynamic volumetric space. Most descriptions begin by hacking away certain dimensions and hoping that the concepts become clear by dimensional analogy.
Tangibility is surrendered in favor of a series of abstractions.
The process depends completely on the notion of continuity and things that are infinitely small. Due to the apparent success of the calculus approach, we have come to accept the dimensional stepping as the only methodology and thereby teaching us to force the different levels of abstract dimension to be thought of as normal. Our world is volumetric and dynamic, and we seem to have an intuitive understanding of the notion of distance or span. The tool we need would have to be a dynamic volumetric entity whose characteristics are described purely in terms of span. The relationship between the voxel's six spans and its volume is of course perfectly definable.