Re: [Groff] Why does tty-char.tmac not represent meaning?

[Ingo Schwarze]

Hi Doug,

thanks for commenting, also showing that you are not opposed to the
general idea.


Doug McIlroy wrote on Sat, Jun 24, 2017 at 07:22:11PM -0400:

> Please change "gradient" to a generic name.
> It is usually read "del"

Using that designation would be unfortunate because "del" is also
commonly used for the partial derivative symbol, round d, \(pd.

> or "nabla"

I'm certainly fine with "nabla"!

> and it is often symbolized "grad" or "div"

I wouldn't like "div"; in tensor analysis, "div" == \(gr\(pc
is not the same as "grad" == \(gr; the latter is a vector
operator taking a scalar argument (or increasing the order
of the tensor it operates on when using the tensor product),
while the former is a linear form (or decreasing the order
of the tensor it operates on).

> But "gradient", by picking out one meaning of several
> (gradient, divergence, laplacian)

I have never seen the "nabla" symbol used for "laplacian".
The Laplacian is the scalar product of the gradient with
itself, or equivalently, the divergence of the gradient.
The Laplacian is a scalar, while both "grad" and "div" are
first order tensors.

So, for the Laplacian, we have

  \(*D = \(gr \(pc \(gr

but the "nabla" symbol itself is never called "laplacian"
as far as i can tell.

> can obscure, rather than reveal, the meaning.

Indeed, arguably, pronouncing

  grad s = \(gr s
  div  v = \(gr \(pc v
  curl v = \(gr \(mu v
  lapl s = \(gr \(pc \(gr s

as

  grad s = nabla s
  div  v = nabla dot v
  curl v = nabla cross v
  lapl s = nabla dot nabla s

can be considered more natural and less likely
to cause misunderstandings than

  grad s = gradient s
  div  v = gradient dot v
  curl v = gradient cross v
  lapl s = gradient dot gradient s

though i did certainly hear both in spoken language.


Anyway, it would be nice to get the patch in!

Individual characters can always be reviewed and tweaked on a
case-by-case basis once the general policy is established.

Yours,
  Ingo