Re: apples and oranges

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

Just for the fun of it. Suppose we discover that a new vitamin,
very important to our well being, exists only in apples and in
oranges. And that each orange has 5 times more of it than one
apple. We can not extract it and express the amount in grams.
Then we invent a dose unit GEM, the amount present in 1
orange or in 5 apples. An individual is expected to consume
10 GEMS per week to be healthy. For example, two oranges,
ten apples, one orange plus five apples, 0.5*O+7.5*A, etc.
We would be forced to perform operations of additions on
fractions of apples and oranges.


Normand Beaudoin wrote:

> We have to think to the problem geometrically or cartesianly.
> In case of oranges and apples, we have two different and
> independent axis (or vectors) in the field of fruits...
> Addind 2 apples with 3 apples gives 5 apples on the axis of apples.
> In other words, a length of 2 apples plus a length 3 apples give a
> length of 5 apples on the axis of apples.
> .......
> But there is a problem which still bugs me: are apples and oranges
> orthogonal !!!???