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Disc: Parameter Setting and the Garden of Eden

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Message 1: Parameter Setting and the Garden of Eden

Date: Sat, 5 Sep 1992 2:39:56 -0Parameter Setting and the Garden of Eden
From: <GIVENsbchm1.chem.sunysb.edu>
Subject: Parameter Setting and the Garden of Eden


Ultrametricity, the Garden of Eden, and Linguistic Typology

I joined Linguist too late to see a discussion of the recent works purporting
to show that the evolution of human languages paralleled the dispersion of
human genes, presumably leading back to a single "Ur-language" , just as the
study of genetic linkage has lead some to the conclusion that "a single
East-African woman" and her kin were forebears of us all.
While I didn't want to take a position on these studies,
I did wonder whether it is generally realized that such a "family tree"
structure follows from very minimal assumptions and need imply nothing about
the historical development either of languages or of populations.

Consider a "principles and parameters" description of the class of human
languages. Posit further that combinations of parameters tend to be favored if
they further "communicative efficiency". Of course, any such concept is very
complex - even commonsense elaboration of such a notion would reveal dozens
or hundreds of subtasks and subgoals that would be contributing factors. In
general, the settings of parameters which are
favorable for some subtasks are quite unfavorable for others. Economists, for
example are quite familiar with this property of interesting utility measures;
such competition between different subgoals is often termed {\it frustration}.

This minimal set of hypotheses already has rather dramatic consequences.
The set of points in parameter space, i.e., of possible human languages, that
maximize such an efficiency measure, do not in any sense regularly
fill a Euclidean domain. Rather, the set of such maxima have a natural tree
structure defined on them (in mathematicians' terms, they form an ultrametric
topology.) Thus, they have a natural "genetic" lineage, and will seem to
point "backwards" toward an orginial ancestor. The words in the last sentence
are in quotes because, again, no assumptions whatever about linguistic
evolution or influence of one language on another have been made.

Apart from "Garden of Eden" theories of evolution, the existence of tree-like
structures formed by the set of efficient languages would pose interesting
questions for a parameter-setting methodology. I am well aware of the danger
here: concepts like "communicative efficiency" may so annoy Formalists that
they refuse to deal with me. But perhaps not. There may be room in formal
linguistics for concepts of optimality, not so? One is free to replace
"communicative efficiency" with some other complex property to be optimized,
provided that it has the property described in the second paragraph as
"frustration".

Are these observations new or already well discussed? Are they interesting?