Physical Dimensionality

All matter exists in four dimensions—roughly characterized as left-right, toward-away, up-down, and time. The first three are conceptually clumped together and called “spatial dimensions.” Time is treated as a dimension here because we want to talk about “position” in space and time.18

Any physical object occupies space and persists in time. This is true of the largest object in the universe and the smallest atom. However, when the measure of one or more dimensions of an object is small, or insignificant, with respect to the measure of others or is tiny with respect to its environment, it is useful to describe and represent objects by pretending that they occupy fewer than three spatial dimensions. For example, a sheet of paper can be considered a pseudo-two-dimensional object; it has thickness (up-down), but that dimension is miniscule compared with left-right and toward-away. A parking meter in a city could be considered a pseudo zero-dimensional object, because the measures of all its dimensions are insignificant with respect to its environment. (The parking meter would certainly not be considered a spatially zero-dimensional object by its designer, manufacturer, or the driver who uses it. Therefore, the pseudo-dimensionality of an object depends on its context.)

It is important to consider the pseudo-dimensionality of both an object and the field (the space) in which it resides. A point on a line is a zero-dimensional object in one-dimensional space. ...

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