Dimension is a bi-directional pattern often taking the form of a straight line.  A dimension is normally a recognized pattern in a group of things, commonly called an attribute, and can be objective (by measuring it against a scale) or subjective (by using a relative label).   For instance, when referring to dogs objectively there may be a 100 pound dog, a 20 pound dog, and a 5 pound dog.  Subjectively there would be a large dog, an average dog, and a small dog.

A clarification between the difference of measuring objectively and subjectively can be gained by examining the well-known temperature dimension.  Notice the locational difference on the scale for the common words, cold, cool, warm, and hot, between someone who lives in an arctic environment and somebody who lives in a equatorial desert environment.  Context skews the meaning of subjective words.

See the discussion on adjectives & adverbs and conjunctions & prepositions for the universality of the impact of dimensionality on vocabulary.  (The author needs a reALITY check after that sentence.)

Focusing on the objective aspect of dimensionality requires the key concept of zero, subjectively called the middle or average, and often an enumeration extending in the opposite direction typically preceded by a negative sign. However, The discussion on order revealed that introducing symbols at too early of an age can cause confusion between quantity and order. Therefore, the adoption of the readily identifiable attribute of color is used instead of positive and negative signs. Red and green are used for dimensions going left and right, orange and blue are used for dimensions going down and out, and yellow and violet are used for dimensions going in and out.