 A Scalar is a Zero Vector 
Now
let us look at the idea of a scalar.
A
"scalar" may in a general sense be considered as the sum of
the "absolute values" of the individual vector components of a
system of vectors whose observable resultant is zero. That is, it
represents the magnitude of the internal stress of a vector system, with
the absence of a single observable directionality of the system.
It also follows that every scalar is actually a stressed zero vector,
and every zero vector is a scalar.
Thus we have
four major types of scalars related to the four types of vectors:
(a)


(25)

(b)


(26)

(c)


(27)

(d)


(28)

where S stands for scalar,
for vector, and subscript s for spatial, m for mass, and c for charged.
For
example, comparing equations (25) and (26), it can easily be seen that
twice as many "pointmotions" is not at all the same thing as
twice as many "grammassmotions." The two resulting
vector systems are quite different.
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