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Re: precedence for ReplaceAll?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg110711] Re: precedence for ReplaceAll?
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Sat, 3 Jul 2010 08:16:47 -0400 (EDT)

On 7/2/10 at 2:57 AM, siegman at stanford.edu (AES) wrote:

>In article <i0i1lh$hqv$1 at smc.vnet.net>,
>Bill Rowe <readnews at sbcglobal.net> wrote:

>>>Mathematica has, what, about 5000 commands in its vocabulary?

>>Less. Using a tool documented in one of Roman Maeder's books, I get
>>a total of 3442 symbols in the System context of version 7.0 for
>>Mac OS X x86 (64-bit) (February 19, 2009). Some of these of course
>>are constants such as E. Additionally, 580 of these currently have
>>no documentation that is returned by doing ?symbol. So, it seems
>>there is much closer to 3000 things to be covered in the
>>documentation.

>Interesting data.   Does this include all the named Options (or any
>other "reserved words") that are defined or used with commands?

Yes.

>Mathematica is of course, among other things, a "second language",
>with a vocabulary that has to be learned.  The vocabulary size that
>one has to learn to be fluent, or even minimally productive in
>Mathematica seems to me a topic worth considering.

>(And, for an engineer like me, having at least 3442 identified
>symbols IS "about 5000"!)

=46ine. But I would have expected even as an engineer "about 5000"
would mean something more than 4000, that is accuracy to at
least the first digit when rounded.

>A special aspect of Mathematica as a language is that just knowing
>its vocabulary is a long way from enough.  That vocabulary has to be
>used or "spoken" with absolute accuracy: absolutely perfect
>spelling, absolutely perfect perfect word order, absolutely perfect
>punctuation (defined by some very complex and arcane rules),
>absolutely perfect choice of words used -- to be of any use at
>all. There's no such thing as "pidgin Mathematica".

True.

>(And to illustrate this point, for purists the first word in your
>quoted excerpt above would have to be "fewer" rather than "less" --
>right? "Fewer" for countables, "less" for uncountables.)

The language for my response is English. And it seems to me if I
had written a complete sentence, either

There are fewer than 5000 things

or

There are less than 5000 things

would be equally correct.

>I'm no expert on vocabulary science, but the excerpts from an online
>article given below (very heavily trimmed, lots of cautionary text
>and discussion removed) give some interesting data on that topic,
>and how Mathematica might compare to other "second languages".

I deleted your excerpt. Part of the point seems to be there is a
limit to how large a vocabulary can be before it becomes too
large to be understood by most people. And since some of the
numbers cited in the excerpt are around the same as the number
of things in Mathematica, the implication that you might be
attempting to draw is the vocabulary of Mathematica is too large.

But despite there being a fairly large number of things in
Mathematica, this isn't a good measure of what has to be learned
to use Mathematica effectively. My *guess* is there is far less
than 1000 things that constitute new learning for someone who is
familiar with mathematics that need to be learned to use
Mathematica effectively.

Most of the things in Mathematica are familiar mathematical
operators or functions such as Gamma or Sqrt that should already
be well understood by someone familiar with mathematics. So, it
is really the things unique to Mathematica that need to be
learned rather than every thing in Mathematica. And this is a
fairly small subset of what is in Mathematica by design.



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