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
repetative 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?
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.