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Re: Re: Mathematica skill level snippet(s)

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  • Subject: [mg104814] Re: [mg104778] Re: Mathematica skill level snippet(s)
  • From: DrMajorBob <btreat1 at>
  • Date: Tue, 10 Nov 2009 06:03:33 -0500 (EST)
  • References: <hd0t9u$82o$> <hd3n4j$a2k$>
  • Reply-to: drmajorbob at

As your own quotations from the reference show, it's not necessary to know  
even 10% of the word families in a second language. Even native speakers  
typically don't know half.

That likely applies (approximately) to Mathematica as well, so you haven't  
demonstrated a problem with the size of Mathematica.

It's also MUCH smaller than any spoken language... although admittedly,  
the meaning of a Mathematica "word" can be quite involved.

We learn whatever subset we need, and that's a continual but manageable  


On Mon, 09 Nov 2009 04:47:04 -0600, AES <siegman at> wrote:

> In article <hd6bbm$odf$1 at>,
>  "Nasser M. Abbasi" <nma at> 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[â??System`*â??]] results in 3429
>> <>
>> 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:
>    <>
> 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.
> ----------
> 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.
> ---------------

DrMajorBob at

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