On 11/11/2012 08:52 AM, Dan wrote:
> On Sat, 10 Nov 2012, Thorsten Bonow wrote:
>
>> Therefore solving it symbolically first and inserting the units
>> afterwards is exactly what the students shouldn't be doing.
>
> I think the "elegant" answer to this would be that dimensions are not
> the same thing as units. The dimensions don't go away just because
> the equation is written symbolically, and the optimal time to check
> the dimensions are correct is probably while the equation is still in
> symbols, before substituting in numbers and units.
Units in physical calculations are useful for practical as well as
fundamental reasons. The former have to do with debugging calculations,
and Maxima paradoxically makes them less useful---it simply does not
make mistakes, so there is no point in checking the resulting units if
the initial equation was correct. Of course it is still useful to
cross-check the initial equations for dimensional consistency.
The more important reason to use dimensioned variables is subtler---it's
the idea of dimensional analysis, i.e. deriving physical laws just from
the dimensional analysis of problem variables:
http://www.av8n.com/physics/dimensional-analysis.htm
This may be too deep to explain in detail to but the most advanced high
school kids, but a simple example like Leo Butler provided might be
appropriate ('is time equal to distance times velocity or time divided
by velocity').