Re: apples and oranges

[Ludwik Kowalski <kowalskiL@Mail.Montclair.edu>]

Ed Eckel wrote:

> Kind folks:
>
> In a recent discussion on mathematically representing the
> relationship between mass and acceleration for a given
> force, the following issue arose.  We have been taught from
> early grades that we can't add apples and oranges.   And we
> have been taught that multiplication is a shorthand for
> repetitive addition.  How come we can multiply apples and
> oranges and get something reasonable?  That is, why is it
> that mass times acceleration yields something useful when
> addition of mass and acceleration does not?

Good question, Ed.  Here is my tentative answer. It makes no
sense to add mass to acceleration but their multiplication is OK.
In cases like this multiplication is no longer a shorthand for
repetitive addition, as it is when one of the multipliers (or
both) is a pure number.




> I am at a bit of a loss on this one and would appreciate
> some suggestions on how to deal with this (interesting)
> issue constructively.
>
> Ed Eckel
> Georgetown Day School