Re:apples and oranges

[Zach Wolff <zachary_wolff@yahoo.com>]

I'm only a freshman physics student, but I remember being taught
dimensional analysis in high school chemistry and treating units as
something analgous to a quantity by which a pure number is multiplied.
 4 kg * 2 m/s^2 is saying (pure number)4 * (idea) kg * (pure number)2
* (idea)m/s^2.  The answer is only the simplification of as many of
these different quantities as possible.  Math tells us that
multiplying the pure number 2 and 4 gives us the pure number 8. 
Physics tells us that multiplying the ideas kg and m/s^2 gives us the
idea newtons.  Physics is disovering the relationships of these ideas.
 Without the concept of force kg * m/s^2 = kgm/s^2.  The nonphysical
examples like apples * oranges seem meaningless because we do not have
a concept appleoranges.  kgm/s^2 is meaningless without the concept of
force.  This seems to come up as students first learn the relations
between units, and the compound units they create.  Meters are easily
understood.  Newtons may be somewhat more abstract, but an amount of
push is still something we can feel and conceptualize fairly easily. 
A Newton meter is usually regarded as a foreign and meaningless
concept when it is first introduced.  It takes some new understanding
to really grasp that a newton meter does have a physical meaning and
to then be able to discuss work an energy.

These views are in disagreement with Sarma's earlier statement in it's
treatment of conversion factors.

---DEVARAKONDA VENKATA NARAYANA SARMA <narayana@hd1.vsnl.net.in> wrote:
> You can multiply apples and oranges. It all depends on the situation.
>
> Let us suppose that in a country apples are very scarce and oranges
are
> abundent. Suppose two farmers want to barter apples and oranges.If
> the exchange rate is 5 oranges for an apple, the farmer who wants
> 10 apples has to give
>
> 	10 apples X 5 oranges = 50 oranges !

The unit for the exchange rate is not oranges.  It is oranges/apples
as Sarma expressed in his words above, but not in his equation.  10 *
apples * 5 * oranges/apples = 50 (apples * oranges)/apples 
apples/apples=1, so the final answer is 50 oranges.

> Whenever we want purchase an American book in India we have to 
> multiply the cost of the book in dollars with exchange rate in rupees
> to get an answer in rupees.

The same idea is present in this example.  The exchange rate is not
(or should not be) expressed in rupees, but in rupees/dollar.
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