Re: Equation or Formula

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

Tim O'Donnell wrote:
> F = ma
> Is this an equation of Formula?
> I get the most interesting discussions in class.
> It probably doesn't matter, but is there a difference?

The difference, if any, is so small that it doesn't matter.

We've discussed this before.  See e.g.
  http://mailgate.nau.edu/cgi-bin/wa?A2=ind0110&L=phys-l&P=R21716

which says in part:   We have
   -- Einstein's theory
   -- Newton's laws
   -- Maxwell's equation
   -- Bianchi's identities
   -- Simpson's rule
   -- Shannon's formula
   -- Bell's theorem
   -- Zorn's lemma

 I don't see any significant metaphysical distinction between Newton's
"law"
 of gravitation and Einstein's "theory" of gravitation.  Both give
 mathematical formulas that purport to predict how Nature behaves.
 Maxwell's "equations" are in the same category.

Steven T. Ratliff wrote:
> Based on the definitions in Tim's message, it appears that F=ma is both an
> equation and a formula.

I would agree with that.

John Barrer wrote:
> I always tell my students that formula is someting
> they stopped using many years ago.

Really?  I've never heard the quadratic formula called
anything else.

> I want them to think
> about mathematical relationships between variables
> that are expressed in equation form.

That's commendable, but it's not inconsistent with
the existence of formulas and/or recipes.

Joseph Bellina wrote:
> How about, it is neither, since we really don't know what a force is,
> and don't independently know what mass is, the best we can do is say
> that it is an organizing principle for seeing the relation among these
> interdependent quantities.

I wouldn't have said that.  We know quite a lot about what
mass is, and quite a lot about what force is, and what acceleration
is.  F=ma is _not_ the definition of force, mass, or acceleration.

Larry Cartwright wrote:
> I believe it depends on who you ask.

Certainly it depends on context.

> In my experience, most physicists
> and physics teachers don't bother with the distinction.

Right.

> Chemists and
> mathematicians are more like to make the following distinction:
>
> If it is a complete statement with the verb "=" (or in chemistry, the
> "arrow" symbol), then it is an equation.  If it is an incomplete
> expression with no verb, then it is a formula.

Agreed as to chemists, but not as to mathematicians.
To my ears, a chemical formula is completely different
from a mathematical formula.

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

If you really want to fuss over small points (and I don't
recommend it) I would say that "formula" is slightly
broader than "equation", in the way that "vehicle" is
broader than "car".

In particular, I would include near-equalities among the
formulas.  I would speak of a formula for estimating XYZ;
if it's only an estimate it doesn't really qualify as an
equation.