Re: displacement and graphs

["John S. Denker" <jsd@MONMOUTH.COM>]

At 08:59 AM 10/10/01 -0500, Rick Tarara wrote:
> 'Location' also implies (at least to me) a location
> relative to some reference.

OK.

>   Therefore I'm not sure it is any better than
> 'position' in removing the implied vector nature of the beast.  It would
> seem that 'displacement' is the term we've created to explicitly contain the
> vector nature.  To get away from your first objection (if P is not a vector
> how can delta-P be one) then we probably should ONLY talk about
> displacement, but students are going to think in 'location' or 'position'.

Whaaaaaaat?

What is "implied" about the vector nature?  The beast in question is a
vector, always was a vector, and always will be a vector.  Fiddling with
the nomenclature isn't going to change this.

If you want to get really, really technical, you can draw a distinction
between the space of points P and the space of position-vectors from the
origin to P.  But the two spaces are isomorphic, so who cares?  Anybody who
is sophisticated to understand the distinction should be sophisticated to
understand that it doesn't matter.  For everybody else, just tell them P
"is" a vector, end of story.

=============

There exist a few non-vector quantities.  Surprisingly, nobody has
mentioned them yet.  These include
  distance := (scalar) norm of (vector) separation
  speed    := (scalar) norm of (vector) velocity

But these quantities are of very limited use;  "removing" the "vector
nature" does not make things "better" -- just the opposite.  There are some
fundamental laws involving position and/or velocity, and (as we saw a
couple of weeks ago in another thread) trying to re-express these laws in
terms of non-vector quantities produces all sorts of ugly singularities and
other problems.