Re: Comparing languages

From: LEE Sau Dan (danlee_at_informatik.uni-freiburg.de)
Date: 07/16/04 

Date: 16 Jul 2004 09:38:43 +0200

>>>>> "Brian" == Brian M Scott <b.scott@csuohio.edu> writes:

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

So, given two atoms: Carbon-14 (atomic number: 6; mass number 14) and
Nitrogen-13 (atomic number:7; mass number 13). (Let's assume such
atoms exist.) Can you now tell me, using these pairs of number, which
atom is "more beautiful"? How do you define the *comparison
relation*? One person may consider the atomic number to be more
important for "beauty", and hence say Nitrogen-13 to be more
beautiful. Another person may consider the mass number to be more
important and hence say Carbon-14 to be more beautiful. A third
person is fond of diamond and hence would say Carbon-* to be the most
beautiful, irrespective of the atomic/mass numbers. A fourth person
hates graphite because it's dirty, and hence would say Carbon-* to be
the most ugly atom. So, who's right?

Just having 2 numbers is not enough. For n-dimensional quantities
(where n>1), there is no single canonical way of comparing them so
that you get a totally ordered set. It is like asking which of the 2D
vector (3,4) and (7,2) is "larger". Yes, you can use the magnitude,
but that's not the only way to compare 2 complex number concerning the
notion of "larger". In many situations, simply using the magnitude
results in weired results. To get meaningful results, you'd need to
perform a (not necessarily linear) coordinate transformation first.
But why that particular transformation and not another? That's often
a topic for debating.

    Brian> Of course most of us recognize that there's a great deal
    Brian> more to learning a language than learning vocabulary, but
    Brian> he has in fact provided a numerical measure of one small
    Brian> part of the difficulty of learning a language.

That's what I'm talking about. You get one number based on the
complexity of the vocabulary. You get another number based on the
complexity of the grammatical rules. Language A gets (100, 86) and
language B gets (73, 113). Now, tell me which is "easier to learn" or
"simpler". What formula would you use to make the comparison, and
more importantly, what WEIGHT would you use in combining each pair of
values? 

-- 
Lee Sau Dan                     +Z05biGVm-                          ~{@nJX6X~}
E-mail: danlee@informatik.uni-freiburg.de
Home page: http://www.informatik.uni-freiburg.de/~danlee

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