Re: i,j,k, units, vectors, etc.

[John Denker <jsd@MONMOUTH.COM>]

At 11:36 PM 9/17/99 -0400, Ludwik Kowalski wrote:
> I am not proposing to change anything. Only to
> recognize that the word "unit" means a different
> thing here.

Surely we all recognize that common English words have multiple meanings.
These meanings are sometimes related, and sometimes unrelated.

If the two meanings of a word are very different, it's not confusing.  We
don't think of accountants when somebody says "Tally ho!".

But in the more common case, the meanings have a common thread, for a good
reason.

> What would be a better name for i, j and k?

Let's not look for a better word -- but rather a better multi-word phrase.

The appliance in my kitchen isn't really a "microwave";  that word is just
shorthand.  The usual rule is:  when in doubt, spell it out.
  the appliance is a "microwave oven"
  the meter is a "unit of measurement"
  i or j or k is a "unit vector"

When spelled out like that, it seems unlikely that anybody would be
seriously confused.

The word "unit" has ancient roots.  It has to do with one-ness.  This could be
  * having a length of one, as in a unit vector, or
  * representing one of something, as in a unit of measurement.

... and in the same vein note that we have unitary matrices.  These are all
fine uses of the concept of one-ness.  So I would say that these meanings
are closely related for a good reason.

==============================

BTW I don't buy the argument that says in effect "i,j,k are not vectors
because their length and direction are already specified."  Hmmmm.  The
fact that we know their length and direction proves that they *are*
vectors.  For homework:  write down the components of the vector k.