Re: Comparing languages

From: Brian M. Scott (b.scott_at_csuohio.edu)
Date: 07/15/04 

Date: Thu, 15 Jul 2004 05:10:14 -0400

On Wed, 14 Jul 2004 04:17:22 GMT Nathan Sanders
<nsanders.DIE.SPAM@wso.williams.edu> wrote in
<news:nsanders.DIE.SPAM-E23BFF.00171914072004@news.verizon.net>
in sci.lang:

> In article <ccshds$7fp$1@news-reader4.wanadoo.fr>,
> "pierre.levy" <pierre.levy11@wanadoo.fr> wrote:

[...]

> Comments on the article you quoted:

The thing's so poorly written that it took me a while to
figure out what was going on. It's actually pretty
simple-minded, but there is some substance, and a few of
your criticisms aren't actually justified.

[...]

>> vorto (word, as composed of certain sounds or letters without regard to its
>> meaning, e. g. child, children, give, gives, gave and given are six
>> different words),

> I'd like to know how they scientifically define "word" in a usable,
> cross-linguistic sense. Professional linguists have a hard enough
> time doing this. Somehow I doubt that a non-linguist with an agenda
> has managed to do it.

I suspect that the author looked only at written languages
and took words to be essentially those entities bounded by
spaces. Of course this runs into the problem of differing
conventions (German <Versicherungsvertreter>, one 'word',
versus English <insurance agent>, two 'words') even without
getting into languages like Chukchi.

>> As all the
>> words in Esperanto are only combinations of invariable elements, the study
>> of the international language is the most simple case to begin with.

> ?!?!? This is certainly not true. You only need to look at the
> prepositions to know this: <de> can mean "of", "from", or "possessed
> by" (and lord knows what else!), while <al> can mean "at", "to", or
> "towards", or can act as a marker for "indirect objects".

The objection is irrelevant, because you've misunderstood
what he's saying. He's not talking about semantics at all;
he's talking only about the sequences of letters (or, if
he's being just a little more sophisticated, phonemes, but
I'd take no bets on that). He's merely noting that
Esperanto has nothing like the English plural morphophoneme
with its several shapes, some completely irregular, or like
German strong verbs.

He does not, however, appear to recognize that Chinese or
some of the polysynthetic languages might be equally simple
in this respect.

[...]

>> aforementioned table does not give definitive values to these constants,
>> because the material of the different languages studied is not adequate
>> in the sense mentioned above and needs additional research.

> Oh. So the research hasn't even been done yet?

This isn't a fair objection. There is nothing wrong in
principle with doing what amounts to a pilot study,
estimating theoretical parameters using small samples to get
an idea of what to look for (and to determine whether the
proposed model actually fits the data at all well in the
first place).

>> 1) The new method of statistical research is much superior to the previous
>> ones in speed and gives results with remarkably less effort than these.

> "Gives results"? They don't have any yet! (see previous quote and
> comment)

Not true. The author apparently presents some genuine
results in Figs. 1 - 4, which we haven't seen.

>> 3) The mathematical expression of this law holds two constants, which
>> vary from language to language, and are indicators of the ease of learning
>> the considered language, or of the expressiveness of the same.

> "Or"? So, for some languages the connstants indicate ease of
> learning, and for others it represents expressiveness? How do we know
> which constants go with which indication? Is this pre-determined by
> the theory, or do we find out after the fact?

> And how do they know this? Have they tested it? Have they defined
> "easy to learn" and "expressiveness" and compared them with these
> magical "constants" (which, by the way, aren't actually constant,
> since they vary from language to language!)?

Here again you go too far. The claim is that associated
with each language is a pair of numerical parameters. For
each language it's a fixed pair. They are claimed to be
constants in much the same sense that atomic weight is a
constant: different isotopes have different atomic weights,
but for each isotope the atomic weight is a constant.

[...]

> It only shows this because the author asserts it! There's no
> conclusion, just an assertation, a bunch of intermediate mumbo-jumbo
> that's wrong and/or just plain stupid, and then a restatement of the
> intial assertion under the guise of a proved conclusion.

This isn't quite correct. The claims about simplicity are
nonsense, but not completely unmotivated nonsense, and there
is a mildly interesting claim buried in this ill-written
summary. I'm going to try to explain a slight variation of
what he claims to have done, simply to avoid his notion of
'cliché', but the idea should become clear enough.

Imagine that you have a list of all English words arranged
in order of decreasing frequency. (To be definite, take
'word' here to correspond more or less to his 'paradigm': a
dictionary entry together with all inflexional variants.)
For each positive integer n let L(n) be the set consisting
of the n most frequent words. (In his example his set I
corresponds to L(200), his set II to L(350), and so on, if
you change my 'words' to his 'clichés'.)

Now take as a dataset a large sample, T, of text; say T
contains N word tokens. For each positive integer n let
d(n) be the number of tokens not in L(n), and let x(n) =
d(n)/N, the fraction of tokens in T that are not in L(n).
Clearly x(n) decreases as n increases.

His y is my n, and for a given value of y (and hence of my
n) his x is the percentage corresponding to my fraction
x(n), i.e., 100*x(n).

His claim is that for any given language log(x) is a linear
function of y. The corresponding claim in my setting would
be that there are constants a > 0 and b > 0 such that to a
decent approximation log(x(n)) = -an + b, and that any other
substantial English text T' would yield approximately the
same constants a and b. Equivalently, there are positive
constants k and C such that x(n) = C*2^(-kn). (He writes
his version a bit differently, but it boils down to the same
thing. His D is my 1/k, and his B can be calculated from my
C and k.)

If k is large, x(n) falls off rapidly with increasing n; if
k is small, the decay is less rapid. Recall that x(n) is
the fraction of tokens in T that aren't in L(n); if your
working vocabulary is limited to L(n), x(n) is the fraction
of tokens that you don't know. If this decreases rapidly
with increasing n, knowledge of a relatively small lexicon
will suffice to recognize most tokens, so there is some
faint connection with simplicity, at least for languages
with the same value of C. (Different values of C complicate
the comparison significantly.)

Of course most of us recognize that there's a great deal
more to learning a language than learning vocabulary, but he
has in fact provided a numerical measure of one small part
of the difficulty of learning a language. Or rather, he's
done so *if* his empirical observation that log(x(n)) is
approximately a linear function of n actually holds up. And
it may do so, because all of this turns out (after a little
mathematical analysis) to be nothing more than a minor
variation on Zipf's Law. (Of course that also means that
it's pretty much old hat.)

Brian

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