Choosing a programming language as a competitive tool

[David C. Ullrich]

On 8 May 2001 06:14:49 GMT, xdgobbi at irus.rri.on.ca wrote:

>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

This is _one_ _example_ of a vector in linear algebra - the concept is
much more general than that. A vector is an element of a vector space;
a vector space is an abstract structure with operations that satisfy
certain axioms (just like a group is an abstract structure with 
operations that satisfy other axioms.)

In particular the mathematical notion does not _depend_ on 
coordinates.

>Tensor Analysis:    a vector is a quantity that behaves in a particular
>                    manner under coordinate transformations 

And this flavor does not depend on coordinates either, in the sense
in which the phrase was used in "The abstract concept of a vector
does not depend on coordinates."

>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. 

This may be true.

> 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

David C. Ullrich
***********************
"Sometimes you can have access violations all the
time and the program still works." (Michael Caracena,
comp.lang.pascal.delphi.misc 5/1/01)