di·men·sion

– noun
1. a. a property of space; extension in a given direction.
b. the generalization of this property to spaces with curvilinear extension, as the surface of a sphere.
c. the generalization of this property to vector spaces and to Hilbert space.
d. the generalization of this property to fractals, which can have dimensions that are noninteger real numbers.
e. extension in time.
2. a. measurement in length, width, and thickness.
b. scope; importance.
3. unit.
4. magnitude; size.
5. a. a magnitude that, independently or in conjunction with other such magnitudes, serves to define the location of an element within a given set, as of a point on a line, an object in a space, or an event in space-time.
b. the number of elements in a finite basis of a given vector space.
6. any of a set of basic kinds of quantity, as mass, length, and time, in terms of which all other kinds of quantity can be expressed; usually denoted by capital letters, with appropriate exponents, placed in brackets.

depth

–noun
1. a dimension taken through an object or body of material, usually downward from an upper surface, horizontally inward from an outer surface, or from top to bottom of something regarded as one of several layers.
2. the quality of being deep; deepness.
3. complexity or obscurity, as of a subject.
4. gravity; seriousness.
5. emotional profundity.
6. intensity, as of silence, color, etc.
7. lowness of tonal pitch.
8. the amount of knowledge, intelligence, wisdom, insight, feeling, etc., present in a person's mind or evident either in some product of the mind, as a learned paper, argument, work of art, etc., or in the person's behavior.
9. a high degree of such knowledge, insight, etc.
10. a deep part or place.
11. an unfathomable space; abyss.
12. the farthest, innermost, or extreme part or state.
13. a low intellectual or moral condition.
14. the part of greatest intensity, as of night or winter.