Bob Sciamanda sent three interesting e-mails to the list earlier today.
I have a problem with his definition of a one-dimensional vector as a
component of a three-dimensional vector, carrying a sign for direction.
As I understand it a component is obtained by a vector dot product and is a
scalar, not a vector. the sign is not the direction of a vector but a
consequence of whether the angle involved in obtaining the component is less
or greater than pi/2. In particular, vectors do not have signs, they have
directions; they are intrinsically positive.
What we can do (and this was the line that Tim Folkerts took as along) is to
associate the components with a unit vector along the special one-dimension
line.
I agree that "mathematical models are our own constructs, subject to our own
definition and use" but
it's preferable if we have common definitions and use.