Comment by xeonmc

Represents high-dimensional objects in terms of "how many dimensions required to describe them (n-vector).

Then also adds the notion of describing them in terms of "how many dimensions are excluded from your embedding dimension to describe them (m-pseudovector)

Example in 3D:

scale: requires no vector dimensions <-> quantity (pseudovolume)

line: requires one vector dimension <-> plane family (pseudoplane)

plane: requires two vector dimensions <-> plane normal (pseudovector)

volume: requires three vector dimension <-> metric (pseudoscalar)

    Two Dimensions (n+1=3):
    scalar = pseudobivector
    vector = pseudovector
    bivector = pseudoscalar

    Three Dimensions (n+1=4):
    scalar = pseudotrivector 
    vector = pseudobivector 
    bivector = pseudovector 
    trivector = pseudoscalar

    Four Dimensions (n+1=5):
    scalar = pseudotetravector
    vector = pseudotrivector
    bivector = pseudobivector
    trivector = pseudovector
    tetravector = pseudoscalar