Choosing a programming language as a competitive tool

[xdgobbi at irus.rri.on.ca]

Greg Ewing <see at my.signature> wrote:
> "Isaac To Kar Keung" <kkto at csis.hku.hk> wrote in message
> news:7iitjdren1.fsf at enark.csis.hku.hk...
>> Right, vector really has its mathematical meaning.  If you can understand
>> that vectors are not meant to be just 2D or 3D vector, you can understand
>> why vector means an array.

> But a collection of coordinates are just one way of
> representing a vector. The abstract concept of a
> vector doesn't depend on coordinates.

Be careful here.  The definition of 'vector' varies according to
application (or by which branch of math, physics, or engineering,
or biology you are dealing with).

Linear Algebra:     a vector is a 1D array of real or complex numbers
Tensor Analysis:    a vector is a quantity that behaves in a particular
                    manner under coordinate transformations 

Classical physics:  same definition as tensor analysis, though often
                    watered down to 'magnitude + direction' which is
                    an adequate definition for many applications
Quantum physics:    same definition as linear algebra (in general)

Engineering:        whatever suits the problem, but this almost always
                    means the definition given by tensor analysis

Biology:            a intermediate organism which carries an infectious
                    agent between the source and the host organism
                    (sorry, this is a bad joke)

Computer Science:   a vector is a 1D array of just about anything -- the
                    elements are often all of the same type (homogeneous)
                    or at least are all derived from the same base type,
                    though heterogeneous vectors are also common

Um, just a minute --  what exactly is my point here?  Oh yes...
for a general purpose computing language to define a vector as anything
other than a 1D array is a little silly.  There is no single, true
definition of a vector, and it's best to stick to the definition that
programmers (and computers) are most comfortable with.

 - David