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Re: precedence for ReplaceAll?
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? 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 Mathematica". (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". ------------ VOCABULARY SIZE, TEXT COVERAGE AND WORD LISTS 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 Return to Main menu of papers