Re: [Phys-l] Equations

[John Denker <jsd@av8n.com>]

Edmiston, Mike wrote:
> I don't disagree with John's listing of four distinct ideas.  Indeed, I
> find his description helpful.

:-)

>  I am stating what my incomming
> students think, and I am always trying to find ways to get through to
> them.  

That's commendable.

Here's a possibly constructive suggestions:

A) Enlarge their repertoire of concepts.  Make explicit the distinctions:
  Equation
  Causation
  Definition
  Calculation

B) Rather than attempting to distinguish
      F = ma                     (1)
versus
      a = F/m                    (2)
it would be better to use a different notation.  One possibility is to
write it as a chemical reaction:
      F <-- ma                   (3)
versus
      a <-- F/m                  (4)
That is, statement (3) says we can react m and a to produce F, while
statement (4) says we can react F and m to produce a.

The *symmetric* statement (1) implies both of the non-symmetric statements
(3) and (4).
            (1) ==> (3)
            (1) ==> (4)
In the converse direction we have
     (3) && (4) ==> (1)

And of course (1) and (2) are exactly equivalent, for nonzero m:
           (1) <==> (2)


This upholds the principle of say what you mean, and mean what you say.
If you want to talk about the symmetric relationship between F and ma,
that's cool.  If you want to talk about the non-symmetric relationship
between finding F and finding ma, that's also cool.

Different relationships need to be expressed differently.  Do not say
"=" when you mean "<--".