In the field of basic physics, a dimension was described as one of the three basic directions an individual could travel from a specific point, namely height, width, and length, with the fourth dimension being time. (TNG: "Where Silence Has Lease") These four dimensions make up the realm of space, or "space-time", as scientists came to refer to this dimensional existence. ( TNG: "Tapestry"; ENT: "Storm Front")

It was believed that beyond the universe itself, few things, like other dimensions and higher levels of being, exist. Unfortunately, during the 23rd century, the existence of these concepts could not be proven logically. (Star Trek: The Motion Picture)

The androids of planet Mudd had an advanced understanding of dimensions, having formulated computations that inevitably lead to a total description of the parabolic intersection of dimension with dimension. (TOS: "I, Mudd")

Other universes, such as the mirror universe, coexist with our universe by occupying the same physical space but on different dimensional planes. (TOS: "Mirror, Mirror") It was later determined that the dimensional structure of each alternate universe was totally dissimilar, and that any use of power would disturb its structure. (TOS: "The Tholian Web")

The galactic creation point extended through space and time into another dimension where the logic of things was totally different, where magic, the ability to control reality with thoughts, was part of the laws of nature. (TAS: "The Magicks of Megas-Tu")

According to Spock, the antimatter universe – as well as the negative universe – occupy the same space as our universe, but in different dimensions. ( TOS: "The Alternative Factor"; TAS: "The Counter-Clock Incident")

The planet Meridian had a dual existence, appearing in both the Gamma Quadrant of our universe and another dimension that intersected with this one at that point. (DS9: "Meridian")

Fluidic space, along with the Q Continuum, both lay in an extra-dimensional realm. (VOY: "Scorpion"; TNG: "Hide and Q")

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