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.
I am a great fan of using units in physical calculations, 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').