Re: vector notation

[John Denker <jsd@AV8N.COM>]

Larry Smith wrote:

> I always thought the vector arrow over the letter (or the squiggly
> under it) was employed in handwritten work precisely because it is
> hard to do boldface by hand.

I'm of two minds on this topic.
  a) There's something to be said for using the best formalism
 available in any given situation.
  b) On the other hand, a textbook should teach people how to
 think for themselves, and a formalism that cannot be carried
 out by hand leaves a lot to be desired.

When I speak of formalism, I don't just mean vectors.  Another
example concerns graphing inequalities.  Textbooks typically
use halftones to shade one side of the inequality ... but
that is well-nigh impossible to do by hand.  It would be
nice if the books would present at least some of the examples
(maybe all of them?) using cross-hatching of the sort that can
be done by hand.

OTOH I do draw a line that excludes unduly-primitive formalism.
I hate the fact that email discussion groups like this cannot
process text with subscripts, superscripts, math operators, etc.
These are things that can be typeset and can be drawn by hand,
just not expressed in 7-bit ascii.  To work around this
problem, often I cobble up an HTML page and send the URL to
the list.

Returning to the discussion restricted to vectors, let me
point out that it may be possible to duck the question
entirely.  When I'm doing calculations by hand, I don't
bother to decorate vectors at all:  no squiggles, no arrows
on top, no font tricks, no nuthin.  I'm happy to write F=ma
just like that, undecorated.  I know what's a vector and
what's not.  (When I am _presenting_ a calculation, I
might decorate the vectors ... but that's to suit the
audience, not to suit me.)  I'm not alone in using
undecorated vectors, and I suspect the trend is in this
direction.  Note that the folks who do Geometric Algebra
(Clifford Algebra) don't decorate their multivectors.
Their scalars, vectors, bivectors, et cetera are all
written the same.

In the field of computer science, there are analogous
issues.  There are some who argue that the _type_ and
_scope_ of a variable should be apparent from the name
of the variable.  An extreme manifestation of this is
Hungarian Notation
  http://www.google.com/search?q=hungarian-notation
  http://wombat.doc.ic.ac.uk/foldoc/foldoc.cgi?Hungarian+Notation
but others find this ridiculous.