Prev: Export 3D graphics to Web page (a la LiveGraphics3D)
Next: ContourStyle Question
From: Bill Rowe on 3 Jul 2010 08:17
On 7/2/10 at 2:57 AM, siegman(a)stanford.edu (AES) wrote:

>In article <i0i1lh$hqv$1(a)smc.vnet.net>,
>Bill Rowe <readnews(a)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.


From: Murray Eisenberg on 4 Jul 2010 03:09
Except that Wolfram Alpha is often more forgiving than Mathematica
itself with respect to word order, punctuation, and choice of words.

On 7/2/2010 2:57 AM, AES wrote:

>
> 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".

--
Murray Eisenberg murray(a)math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower phone 413 549-1020 (H)
University of Massachusetts 413 545-2859 (W)
710 North Pleasant Street fax 413 545-1801
Amherst, MA 01003-9305

From: David Park on 4 Jul 2010 03:10
I seem to recall that many years ago when I attended MIT there were two
supermarkets. One was close to Harvard Square and its speed checkout counter
had a sign saying "10 or fewer items". The second was closer to MIT and its
speed checkout sign said "10 items or less".

But both counters were always crammed with customers with many more that 10
items. Upon investigation it turned out that the MIT students couldn't read
and the Harvard students couldn't count.

(Of course, I was told that story. I didn't actually read the signs myself!)


David Park
djmpark(a)comcast.net
http://home.comcast.net/~djmpark/


From: Bill Rowe [mailto:readnews(a)sbcglobal.net]


>(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.



From: AES on 5 Jul 2010 06:03
Well, just so both Harvard and MIT graduates can do right in the future,
here's what the dictionary that comes with Mac OS X says:

USAGE Fewer versus less:

Strictly speaking, the rule is that fewer, the comparative form of few,
is used with words denoting people or countable things (: fewer members;
| fewer books; | fewer than ten contestants).

Less, on the other hand, is used with mass nouns, denoting things that
cannot be counted ( | less money; | less music). In addition, less is
normally used with numbers ( | less than 10,000) and with expressions of
measurement or time ( | less than two weeks; | less than four miles
away).

But to use less with count nouns, as in | less people or | less words,
is incorrect in standard English.


[The rules of correct English are apparently nearly as complex, arcane,
and inconsistent as those of correct Mathematica.]

From: Bill Rowe on 5 Jul 2010 21:15
On 7/5/10 at 6:03 AM, siegman(a)stanford.edu (AES) wrote:

>Well, just so both Harvard and MIT graduates can do right in the
>future, here's what the dictionary that comes with Mac OS X says:

>USAGE Fewer versus less:

>Strictly speaking, the rule is that fewer, the comparative form of
>few, is used with words denoting people or countable things (: fewer
>members; |fewer books; | fewer than ten contestants).

>Less, on the other hand, is used with mass nouns, denoting things
>that cannot be counted ( | less money; | less music). In addition,
>less is normally used with numbers ( | less than 10,000) and with
>expressions of measurement or time ( | less than two weeks; | less
>than four miles away).

>But to use less with count nouns, as in | less people or | less
>words, is incorrect in standard English.

I would be willing to bet you could find another reference which
would not make this distinction without a great deal of
difficulty. There are really not that many cases in English
where words have really precise meaning.

>[The rules of correct English are apparently nearly as complex,
>arcane, and inconsistent as those of correct Mathematica.]

I strongly believe the rules for correct English are more arcane
than the rules for Mathematica. But, a large amount of meaning
in English is context which allows useful communication to take
place when strict rules aren't followed. In fact, the lack of
precision in English is what makes it difficult to create
something like Wolfram Alpha and makes Wolfram Alpha so impressive.


First  |  Prev  |  Next  |  Last
Pages: 1 2 3 4 5
Prev: Export 3D graphics to Web page (a la LiveGraphics3D)
Next: ContourStyle Question