Pattern 1: Multiplication of a scalar into the quantity and the result is of the same type as the original quantity.
is a magic square.
is also a magic square.Pattern 2: Add 2 of the quantity and the result is of the same type as the original quantities.
In the above statement, the sum is also a magic square.Any quantities that obey Pattern one and 2 are vectors, and hence unit vectors can be defined. The norm a.k.a the magnitude can be defined as the constant sum of magic square.
Since there are seven unit vectors we are dealing with a 7th dimensional space.