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Re: Mathematica skill level snippet(s)

• To: mathgroup at smc.vnet.net
• Subject: [mg104778] Re: Mathematica skill level snippet(s)
• From: AES <siegman at stanford.edu>
• Date: Mon, 9 Nov 2009 05:47:04 -0500 (EST)
• Organization: Stanford University
• References: <hd0t9u$82o$1@smc.vnet.net> <hd3n4j$a2k$1@smc.vnet.net> <hd6bbm$odf$1@smc.vnet.net>

In article <hd6bbm$odf$1 at smc.vnet.net>,
 "Nasser M. Abbasi" <nma at 12000.org> wrote:

> > [Side question:  How many total words and symbols are there in the
> > **full** Mathematica vocabulary? 
> >
> > [I'm guessing maybe 3000 or 4000?  Or even more?]

> For version 7, Length[Names[?System`*?]] results in 3429
> 
> <http://12000.org/my_notes/compare_mathematica/index.htm>
> 
> My theory is this: A Mathematica expert is someone have used more than 50% 
> of these symbols. I am still working on my 5%  :)


Fascinating results -- I'm very impressed that you've done this.

Lurking behind my original question is, admittedly, my continuing 
concern that Wolfram, in its continuing attempt to make Mathematica into 
a single app that does absolutely everything for everyone, is instead 
creating a monster that has become increasing difficult for more and 
more of its potential audience to use.  

If you view Mathematica as a "second language" that its potential users 
must learn to use and communicate in, the vocabulary size of Mathematica 
then becomes one metric for measuring this.

I'm no expert on vocabulary sizes myself, and recognize that it's a 
complex subject; but one readable essay on the subject seems to be:

   <http://www1.harenet.ne.jp/~waring/papers/cup.html>

A few snippets from this essay (very heavily excerpted) are appended 
below.  There's a great deal more it; but I suggest that comparing it to 
Mathematica's vocabulary size, and thinking about Mathematica as a 
second language that users have to learn, ***and then use with absolute 
precision***, is an instructive exercise.

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VOCABULARY SIZE, TEXT COVERAGE AND WORD LISTS

Paul Nation and Robert Waring

How much vocabulary does a second language learner need?

There are three ways of answering this question. One way is to ask "How 
many words are there in the target language?" Another way is to ask "How 
many words do native speakers know?" A third way is to ask "How many 
words are needed to do the things that a language user needs to do?" We 
will look at answers to each of these questions.

How many words are there in English?

Webster's 3rd has a vocabulary of around 54,000 word families. This is a 
learning goal far beyond the reaches of second language learners and, as 
we shall see, most native speakers.

How many words do native speakers know?

At present the best conservative rule of thumb that we have is that up 
to a vocabulary size of around 20,000 word families, we should expect 
that native speakers will add roughly 1000 word families a year to their 
vocabulary size. That means that a five year old beginning school will 
have a vocabulary of around 4000 to 5000 word families. A university 
graduate will have a vocabulary of around 20,000 word families (Goulden, 
Nation and Read, 1990). These figures are very rough and there is likely 
to be very large variation between individuals.

For adult learners of English as a foreign language, the gap between 
their vocabulary size and that of native speakers is usually very large, 
with many adult foreign learners of English having a vocabulary size of 
much less than 5000 word families in spite of having studied English for 
several years. Large numbers of second language learners do achieve 
vocabulary sizes that are like those of educated native speakers, but 
they are not the norm.

How many words are needed to do the things a language user needs to do?

The significance of this information is that although there are well 
over 54,000 word families in English, and although educated adult native 
speakers know around 20,000 of these word families, a much smaller 
number of words, say between 3,000 to 5,000 word families is needed to 
provide a basis for comprehension. It is possible to make use of a 
smaller number, around 2,000 to 3,000 for productive use in speaking and 
writing. Hazenburg and Hulstijn (1996) however suggest a figure nearer 
to 10,000 for Dutch as a second language.

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