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Re: What is @@@?

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  • Subject: [mg87540] Re: What is @@@?
  • From: Bill Rowe <readnews at>
  • Date: Sat, 12 Apr 2008 07:01:34 -0400 (EDT)

On 4/11/08 at 1:45 AM, siegman at (AES) wrote:

>Look, after using Mathematica extensively since, literally, version
>1.0, I know full well that "3" is not an operator!

That was not apparent to me from what you wrote.

>But, it sure seems to me that the quote given above unambiguously
>implies that it is -- otherwise the sentence would have (and could
>have, and should have) said something like

Taken by itself, I can see how you would interpret this way. But
no part of the documentation should ever be considered in
isolation from other parts of the documentation.

>Characters that are not letters, NUMBERS, letter-like forms, or
>structural elements are treated by Mathematica as operators.

Certainly, it could have been written that way. But if you "know
full well" numbers are not operators where is the problem?

>This branch of this thread started with my query about where in the
>documentation I could learn about all the non-alphameric operators
>that are so ubiquitous, and confusing, in Mathematica.

>I use and understand some of these; I know that I don't know all of
>them; I would like to have a brief overview (3 or 4 pages max)
>giving a quick list of all of them (or least the most important of
>them) and a brief (few sentence), so that I might learn what the
>rest of them are, and perhaps improve my skills.

>I was pointed to Section A 2.7.  It doesn't really do what I want --
>and seems to be inaccurate (or at least imprecise) to boot.

If the point of your post was Section A 2.7 is confusing to you,
it would have been far more effective to say so rather than pose
a question about whether "3" could be seen as an operator.

>Finally, you mention "precedence" for Mathematica's documentation.
>Precedence implies _precedence rules_ (otherwise it's meaningless).
>So, if you'll pardon a little sarcasm:  Where in the Mathematica
>documentation are these precedence rules for the Mathematica
>documentation itself given?

Perhaps this was poor wording on my part. My point is none of
the documentation should be expected to stand in isolation from
other parts of the documentation. It is reasonable to expect
later parts of the documentation assume an understanding of
earlier parts of the documentation. This is particularly true of
an appendix.

Earlier parts of the documentation make it clear "3" is a
number. It should not be necessary to repeat this. And the
documentation should be consistent. Hence the lack of an
explicit exclusion of numbers from the set of operators in an
appendix should not be necessary.

You say above you have been using Mathematica since version 1.0.
If so, how can you take this portion of the documentation as
implying numbers can be operators?

>1)  Writing totally precise, complete, detailed, absolutely accurate
>_reference_ documentation, of the sort needed by experts, for any
>system as massive and complex as Mathematica, is very hard -- a very
>difficult task.

This is certainly true.

>Wolfram works hard, I believe, at providing this kind of reference
>documentation -- as they more or less have to -- but don't do a
>perfect job, as the opening sentence of A 2.7 illustrates in an
>admittedly pretty minor way.

>2)  Writing less precise, less complete, much shorter, simpler, less
>detailed, and very differently organized and structured _user_
>documentation, for  the benefit of beginners and/or ordinary
>non-expert users of a system like Mathematica is at least equally
>hard -- in fact, perhaps an even more difficult task.

This is also true.

>Wofram has thus far, at least in my view, _totally_ failed at
>performing this task and providing this kind of _user-oriented_
>documentation for version 6.0; and deserves severe criticism for
>this failure.

This is a rather extreme overstatement and is clearly not true.
You are using version 6 successfully aren't you? If so, the
documentation cannot be considered a total failure. This type of
criticism is neither productive nor warranted.

Can the documentation be improved? Certainly, it can be. And I
am equally certain Wolfram is open to suggestion as to how that
might be done. But labeling the documentation as a "failure"
offers no ideas for improvement and serves no useful purpose.

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