There are several definitions of the noun dimension:

  1. as a measurable extent of a particular kind, such as length, time, weight, color, surface, volume, capacity;
  2. in physics and mathematics, the dimension of a mathematical space is informally defined as the minimum number of coordinates needed to specify any point within it; thus a line has a dimension of one because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line;
  3. as an aspect or feature of a situation.

The Wikipedia article about dimension elaborates much more the meaning of the term in mathematics, physics and other disciplines.

Multi-dimensional thinking in mathematics and physics has much advanced since the invention of the Cartesian coordinate system by the French mathematician and philosopher René Descartes: cartesian coordinates support a straightforward progression from a line to a plane, from a plane to a space, and so forth. An attractive property of these coordinates is that they provide a set of numerical values for every point in (multi-dimensional) spaces, and thus allow the study of phenomena via mathematical formulations.

In the notion of a Topic dimension we combine the third definition (dimension as an aspect or feature of a situation) with the property of coordinates that they exist for every point in a "space" of interest.

In our society, the space of interest comprises all possible situations for which comparable features have been defined or named, the topics. All topics that can be related to one another are grouped in one dimension, and the group of topics is such that for every possible situation, the topic dimensions includes a term, or topic.