Re: Comparing languages

From: Nathan Sanders (nsanders.DIE.SPAM_at_wso.williams.edu)
Date: 07/15/04 

Date: Thu, 15 Jul 2004 16:55:58 GMT

In article <xpak8hp6kqxv.m7eqg4ih9b03.dlg@40tude.net>,
 "Brian M. Scott" <b.scott@csuohio.edu> wrote:

> 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.

Thanks for taking the trouble to clarify the article, Brian! Your
version definitely made significantly more sense.

> I suspect that the author looked only at written languages
> and took words to be essentially those entities bounded by
> spaces.

I assumed as much, too...though I don't recall the author actually
saying this, so who knows what he actually looked at.

> >> 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
>
> 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

That's a possibility. This quote came at a point in the article where
the author was talking about clichés, which I took to be "invariant
paradigmatic meaning". I see now that the examples he chose could be
read as "invariant spelling" instead.

Unless I missed something (which is possible --- my German is almost
nonexistant, and he didn't give glosses for his examples), I don't
think the author makes it clear which one he is actually talking
about, but your interprepation is at least more workable, so I'll go
with that.

(I wonder how he intends to measure the learnability of languages with
no writing system?)

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

Arguably simpler in the case of isolating languages, since there's no
such thing as word-building (according to the author's definition of
word).

(Interesting side note: our most irregular forms tend to be high up on
the frequency list, and our least frequent irregular forms tend to be
regularized over time. I don't know if this is true for other
lannguages, but a cursory examination seems to show that it might be
the case. If so, then this seems to support a deeper connection in
language between frequency and irregularity that shouldn't necessarily
be treated as "complex".)

> > 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,

I didn't see anything in this article about actually testing
learnability, just a bunch of number-wanking. It's not clear to me
that a true, relevant pilot study was even undertaken, certainly
nothing to justify the following statement about "ease of learning"
(or "expressiveness"):

> >> 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.

> > 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.

To me, constants are...well, constant. Things like e, ¼, the
gravitational constant, the speed of light in a vacuum, etc., which
don't change (not intra-universally anyway). Your word "parameters"
would have been a better choice for what the author meant.

But this is a minor semantic point (which is why I originally put it
in parens).

> > 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,

This is what I was referring to. =) He asserts that Esperanto is
simple, then designs an experiment around that assumption, and voila,
Esperanto comes out simple! (Presumably...we didn't get to see the
results.)

> but not completely unmotivated nonsense, and there
> is a mildly interesting claim buried in this ill-written
> summary.

[snip excellent translation]

> 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,

Faintly, yes, I supppose. It completely ignores our abilities to
infer meaning from context and to recognize pattterns within sets of
irregular forms (such as the -al/-ar alternation and the vowel changes
in irregular verbs like sing/ring/drink).

> at least for languages
> with the same value of C. (Different values of C complicate
> the comparison significantly.)

Ah, oops. And since C isn't truly constant...

> 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.

Under the assumption that the difficulty inherent to missing out on
some vocabulary is independent of all other factors. Otherwise, the
formula he came up with tells us nothing, contary to his claims, about
how missing vocabulary affects learnability.

> 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.)

Given the similarity to Zipf's Law, I don't doubt that his formula, or
something like it, can describe the amount of unknown text in a given
block of text for a given language and a given prior knowledge.

I'm just not convinced that such a measure can say anything useful by
about the learnability of a language. "More tokens" isn't universally
harder to learn than "fewer tokens", since the structure of the tokens
can impede or facilitate learning. By analogy, learning (by which I
mean "memorizing") the long string 1357924680 is significantly easier
than learning the shorter string 94706215, and if you didn't know what
the symbol <2> meant before reading these strings, you would have a
much easier time figuring it out from the longer string than from the
shorter string.

Nathan 

-- 
Nathan Sanders
Linguistics Program       nsanders@wso.williams.edu                           
Williams College          http://wso.williams.edu/~nsanders
Williamstown, MA 01267

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