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Re: precedence for ReplaceAll?

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  • Subject: [mg110689] Re: precedence for ReplaceAll?
  • From: AES <siegman at>
  • Date: Fri, 2 Jul 2010 02:57:04 -0400 (EDT)
  • Organization: Stanford University
  • References: <i0i1lh$hqv$>

In article <i0i1lh$hqv$1 at>,
 Bill Rowe <readnews at> 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?

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"!)

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 

(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.)

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".



Paul Nation and Robert Waring

How many words are there in English?

Two separate studies (Dupuy, 1974; Goulden, Nation and Read, 1990) have 
looked at the vocabulary of Webster's Third International Dictionary 
(1963), the largest non-historical dictionary of English when it was 
published. When compound words, archaic words, abbreviations, proper 
names, alternative spellings and dialect forms are excluded, and when 
words are classified into word families consisting of a base word, 
inflected forms, and transparent derivations, 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  . . .

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. 

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

The good news for second language learners and second language teachers 
is that a small number of the words of English occur very frequently and 
if a learner knows these words, that learner will know a very large 
proportion of the running words in a written or spoken text. 

With a vocabulary size of 2,000 words, a learner knows 80% of the words 
in a text 

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.i

How much vocabulary and how should it be learned?

We are now ready to answer the question "How much vocabulary does a 
second language learner need?" Clearly the learner needs to know the 
3,000 or so high frequency words of the language. These are an immediate 
high priority and there is little sense in focusing on other vocabulary 
until these are well learned. 

Contact Info:
Rob Waring
Notre Dame Seishin University, 2-16-9 Ifuku-cho, Okayama, Japan 700
Tel 086 252 1155 Fax 255 7663 Home 086 223 0341
Email:Rob Waring 

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