Re: _Verum Et Factum Convertuntur_ (or: Surprised By Syntax)

In article <d7ld9j$na5$1$830fa7a5@xxxxxxxxxxxxxxxx>,
Colin Fine <news@xxxxxxxxxx> wrote:
>Herman Rubin wrote:
>> In article <3g6b70Fas7rlU1@xxxxxxxxxxxxxx>,
>> Harlan Messinger <hmessinger.removethis@xxxxxxxxxxx> wrote:


..................


[snip]

>> <> On the first day of my freshman writing class I give the students this
>> <> assignment: You will be divided into groups and by the end of the
>> <> semester each group will be expected to have created its own language,
>> <> complete with a syntax, a lexicon, a text, rules for translating the
>> <> text and strategies for teaching your language to fellow students. The
>> <> language you create cannot be English or a slightly coded version of
>> <> English, but it must be capable of indicating the distinctions -
>> <> between tense, number, manner, mood, agency and the like - that English
>> <> enables us to make.


>>>Why must it be capable of indicating the distinctions that English in
>>>particular enables us to make?


>> Otherwise, it would not be an adequate substitute for English.
>> Languages are not that great as it is, and lowering the level
>> does not make them any better.

>Who said anything about 'lower'? Anyway, what do you mean by 'level'?
>You seem to be implying (or assuming) that if language A cannot make a
>distinction that language B makes, then it is 'worse' or 'at a lower level'.

These are college students, supposedly writing English. To
understand a language, one must look at it LOGICALLY; this
seems to run against the feelings of many. The purpose of
a language is communication, not just babbling.

>> For many of them, it is unclear what language they speak.
>> It is not the Queen's English, or as well structured as
>> Ebonics, which really is not that hard to understand, if
>> spoken slowly, or written. The sequence of words they
>> utter is so poorly structured that one often cannot tell
>> the doer and the doee; the meaning of the words, and even
>> more the meaning of their order, is ala Humpty Dumpty.

>Apparently you are concerned that you don't know how to label the
>language they speak. Don't worry, I'll do it for you: it will be English
>(or in some cases another language). It will of course be some dialect
>of English, and the implication from what Mr Fish was saying is that it
>will not be a standard or high-prestige dialect.

If everyone has his own dialect, how much communication can
there be? It is not the words which matter, but the ideas.

>It is almost certain that 'the sequence of words they utter' will be
>perfectly well structured, and the meaning clear to those who speak the
>same dialect.

This is by no means clear. Many, if not most, are so used to
imprecise language that nobody, including themselves, knows
what they mean.

Indeed, if you will drop your preconceptions you will
>probably find that, apart possibly from some vocabulary, it will be
>quite adequately clear to you. The meanings of some words may be
>unfamiliar to you, but they will be no more (and no less)
>Humpty-Dumpty-like than those you use.

You are quite incorrect here.

<snip>

>> <> In English, for example, most plurals are formed by adding an "s" to
>> <> nouns. Is that the only way to indicate the difference between singular
>> <> and plural? Obviously not. But the language you create, I tell them,
>> <> must have some regular and abstract way of conveying that distinction.


>>>Again, why?


>> You do not see the importance of syntax, and even precise
>> semantics. I believe the greatest hindrance to the development
>> of mathematics among the Greeks was the lack of what is usually
>> called "algebraic notation", and which should be added to all
>> "natural" languages. It is pure syntax, with little semantics,
>> and highly precise, and does apply to ordinary language.

>Apparently for you syntax requires an ability to express plurality in
>some regular manner. So Chinese and Japanese (to take just two examples)
>do not have syntax?

Chinese and Japanese have their ways of expressing it.

>The question was why the new language must ape the characteristics of
>English as opposed to any other language.

This was not required, although as the course was supposed to
help develop writing English, that emphasis was reasonable.

>As for algebraic notation (or any other kind of logical system) this has
>very little to do with language. Simple algebraic (or logical, or for
>that matter chemical) expressions can be conveyed in ordinary language;

Nonsense.

>once they get beyond a certain limit of complexity, even where there is
>a way of rendering them verbally,

Here is a quote (from memory) that a bright girl made:

Algebra is like cheating. It makes complicated word problems
trivial to solve.

Now algebra does not in any way simplify the arithmetic
operations needed to solve the problems. What it does is
to translate the clumsy word problems into a concise
language, so the problem is no longer obscure, but
transparent.

it is useless (I seem to recall some
>edition of the Guinness Book of Records contained a 'word' which was the
>'formula' of a protein. It just consisted of the names of all its
>amino-acids in sequence, with some magic to join them together. This is
>not a 'word' in any useful sense).

No, but it is a sentence in a useful sense. German has
many cases where words, or particles, are joined together
to form long strings, and one understands them by breaking
them up into the component pieces. This is also syntax.

>It is at that point that a notation comes into its own - but a notation
>does not necessarily have anything to do with language. A numeral such
>as 1478655231 means the same thing all over the world (wherever our
>numerals are used) but will be spoken very differently.

And it is not numerals which are important, but numbers.
This is something which the school teachers of mathematics
do not seem to understand. The Sumerians and Babylonians
wrote the number represented by that string of numerals as
'1'54'5'37'33'51', or however they would represent that
string in their characters, with different characters in
the 1's place and in the 10's place. Or it could be
represented base 16 as 58227CFF. It is the meaning, not
the words, which matters.

And as for
>structural formulae in organic chemistry, I don't know of any
>satisfactory verbal representation in the general case.

There are fair ones.

>> Why do you think we have computer languages? Machine language,
>> or assembler language, are adequate for anything.

>This is nonsense. Computer languages are designed for expressing
>algorithms, data structures and the like.

They do far more than that. They certainly can process written
languages.

They have no semantics in the
>sense that a linguist would mean the term. (They have something called
>semantics, but it is an analogy or a metaphor: you can talk about the
>semantics of an operator or a function, but this means a specification
>of the operation, not a 'meaning' in the linguistic sense.

I suggest the linguists are being overly restrictive. Also,
the mathematical CONCEPTS involve semantics, and these are
typically not understood by most people.

And variables
>(atoms, constants, etc) have no semantics.).

Constants have semantics, or they would not be constants.
I do not know what you mean by atoms. Variables have no
semantics, which is why they are that useful, but their
syntax is very important, and it is this simple and precise
syntax which makes "mathematical notation" such a powerful
means of communication.

>The difference
>> is syntax; in my opinion, the syntax is not flexible enough.
>This is back to front. The syntax is the part of computer languages
>which does have some resemblance to that of natural languages (a distant
>resemblance, but it's the same kind of process, which isn't true for the
>semantics).

>> But if the language takes two pages to convey what could be clearly
>> done in one line, how well will something be understood?

What I am saying is that the designers of that particular
computer language were only concerned with whether the
computer could handle it. A computer is a super-fast
sub-imbecile; it can take those two pages and wade through
it with complete patience, filing items and erasing them
as appropriate, without error. It has perfect recall and
lots of short-term memory, and lots of speed.

For example, take the binomial theorem. In mathematical
notation,

(a+b)^n = sum_{k <= n} (n!/(k!*(n-k)!))*a^k*b^(n-k)

Consider the following verbal expression of this:

The product of a non-negative integer number of terms, each
the sum of two quantities, is the sum over all non-negative
integers at most the given integer of the product of all
integers up to the given integer divided by the product of
all integers up to the index of summation multiplied by the
product of all integers up to the difference of the given
integer and the index of summation, multiplied by the
product of the first quantity the number of times equal to
the index of summation and by the second quantity the
number of times equal to the difference of the given
integer and the index of summation.

Now I have not put this into assembler language; it would
be much longer. Syntax matters.

>I don't know what you're on about here. If it can be clearly conveyed in
>one line, it is clearly conveyed. If it takes two pages then it takes
>two pages. ?

The difference between the easily understood one-line formula
and the verbal statement is the point. Syntax can take a
difficult to understand expression and make it easy.

>Colin


--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

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