Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: apples and oranges





Maybe the clue to handle this problem reside in the word "dimension"!
IMHO there is a slight difference between adding apples and oranges and
multiplying them.
We have to think to the problem geometrically or cartesianly.
In case of oranges and apples, we have two different and independant 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.
Multiplying 2 apples with 3 apples gives 6 apples on the axis of apples.
When we remain on the same axis, multiplication can be considered as a
shorthand for repetative addition. But when we use elements on
independent axis, we cannot say that multiplication is a shorthand for
repetative addition.
Multiplying 2 apples with 3 oranges gives an area of 6 apples-oranges in
the plane of apples-oranges. This time, multiplication is no more a
shorthand for repetative addition. It is a different operation or at least an
operation differently conceived. We can mix the units but not the
independent axis.
It does not means that defining a particular kind of operation whith wich
for example 1 apple + 1 orange = sqrt(2) (apple+orange) is not possible. It
is just that we (the whole hymanity) have not yet find sufficient uses for
that. But maybe somedays...

But there is a problem which still bugs me: are apples and oranges
orthogonal !!!???

Normand Beaudoin