Re: [boost] [Review][PQS] Review deadline

From: John Phillips (phillips_at_[hidden])
Date: 2006-06-12 17:29:49

Andy Little wrote:

> 
> AFAIK a vector classically represents a magnitude and direction without more
> information though, so the vector would be a position vector

   Yes, anything that is a representation of a magnitude and a direction 
is, in the math and physics senses of the word, a vector. Then there are 
different representations of that vector, and that is where it is 
possible for mixed units to appear.
   In general, the only representation that has no concerns about mixed 
units is cartesian coordinates in a space where the sense of scale in 
all directions has the same units. The x, y and z positions in cartesian 
3 space is an example. However, that same vector is represented by a 
magnitude and 2 direction angles in spherical 3 space, and there is no a 
priori reason to prefer one representation to another. The choice of 
representation is always current application dependent.
   Thus, for some not explicitly defined potential vector library it is 
possible to have mixed units in even the simplest of applications.

   There are also spaces where the units (or more accurately, the 
dimensions) are not the same in all directions, so any vectors in those 
spaces will have mixed units in any coordinate system. A commonly used 
one is called "phase space" and it includes the position and momentum 
variables for a system all in the same space. Thinking of them together 
turns out to be quite important in some applications, so the example can 
be quite meaningful for some people.

                        John Phillips

> 
> 
> 
> regards
> Andy Little
> 
> 
> 
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