Re: Being careful with dimensions

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Wed, 22 Sep 1999, Joel Rauber wrote:

> The way I write it [i.e., (2N)i - (3N)j] is "F = (2i - 3j) N"
> Which of course begs the question;  unless you interpret my style as meaning
> the units go with the vector and the components or the unit vectors; (I
> don't make such an interpretation, I have a more live-and-let-live
> philosophy until I decide to get positively pedantic).  Any comments on the
> above style of writing the vector?

I prefer the above as well simply because it is more economical.  And I
don't see any issues wrt what the units "go with"; both forms are 100%
identical in meaning.

I tell students--especially in lab where units tend to become a *very*
serious barrier for many--that the beautiful thing about units is that
they *completely* take care of themselves as long as you simply *let*
them, that the *only* way to get in trouble with units is to get sloppy
and make algebraic mistakes.  And let's be clear: Leaving units out is an
algebraic mistake; units obey precisely the same rules of algebra as
numbers and variables.

IMO students have problems with units primarily because of a blind
overreliance on calculators.  Unlike slide rules, calculators *do* keep
track of powers of ten.  Students get used to thinking that calculators
"do it all" because they *do* in math and because math is overwhelmingly
where students have previously used calculators.  But like slide rules
calculators do *not* generally keep track of units even though they are
algebraically identical to powers of ten and *no* less critical in
physics.

One way to fix all of this would be to demand calculators that *do* keep
track of units, but I suspect that students would be better served by
calculators that do *not* keep track of powers of ten!

John Mallinckrodt      mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm