[Puzzles in Language Change] reading for Sep 16: Reali & Griffiths (2010)

[Igor Yanovich]

Dear everyone,

The reading for this week is Reali & Griffiths (2010), attached. I
apologize for sending it so late - I didn't feel well over the weekend.
Also attached is a supplemental reading Bentley et al. (2010), which is a
published reply to Reali and Griffiths, providing a bit more perspective
to their paper.

Reali & Griffiths (2010) is only 7 pages long, but it is mathematically
and conceptually dense. Please try to read all of it in one quick pass,
without dwelling on the parts you do not understand, and specifically on
the math - if you are not already familiar with such stuff, it may be
faster for you to understand what is going on during the reading group
than on your own. As you skim through, please concentrate on Sections 3a,
4a and 5 (the conclusion). Together, they are just 1.5 pages of text.


There is a broad and a narrow reasons why I selected this paper. The broad
reason is that it introduces several lines of formal thinking about
language evolution and language change which form quite a literature on
their own, but are not well-known among linguists (and often, in turn, are
themselves not very well-informed about what's going on in linguistics).

The main research sequence this type of approach is that we make
particular modeling assumptions, then study the behavior of our model, and
then decide whether it's a useful model for how language change works. Of
course, we may often build the model in the first place because we want to
model a particular linguistic phenomenon. Then we will have a hunch about
what our model should and should not capture. But the general focus is on
understanding how the model works, and testing the model often does not
involve any _specific_ linguistic dataset.

In particular, Reali & Griffiths's contribution in this paper is building
a connection between TWO possible ways to model language change and
language maintenance. One approach is to try to import machinery from
population genetics, and from studies of evolution in general, into
linguistics. On the linguistic side, Croft (2000) builds an abstract
framework along those lines, and he has some subsequent papers with
collaborators where they actually do modeling - we will look at one of
those papers in a few weeks. On the "formal", non-linguistic side, there
have been several people trying to apply mathematical methods from
evolution studies to language. One example is the book Niyogi (2006).

Another research tradition may be called the Iterated Learning paradigm.
The basic idea there is to model language transmission through a chain of
agents (=speakers) who infer a grammar from the observed data, and then
generate a new sample of data which is used by the next generation
learner. In other words, this paradigm formalizes the kind of assumptions
linguists usually make when thinking about transmitting language through
language acquisition. On the bright side, the formal model allows us to
see what predictions we can derive. On the less bright side, the actual
models that people built and tested are all quite simplistic, not getting
near the complexity of real languages. However, studying such simplistic
models is a necessary step if we want to eventually figure out the
dynamics of learning for more complex grammars. An important reference if
you want to understand Iterated Learning better is Griffiths & Kalish
(2007), available online at
https://cocosci.berkeley.edu/tom/papers/iteratedcogsci.pdf

What Reali & Griffiths (2010) do, is to show that the behavior induced by
iterated learning actually amounts to the behavior induced by a very
simple and common population-genetics model. In this way, they connect two
traditions, which allows for transfer of results between them. Also,
importantly, they provide one possible basis why population-genetics
techniques might be applicable to language: if population-genetics-style
behavior arises as the result of iterated learning, this provides us with
a kind of basis for evolutionary analyses that knowledge about DNA and
mutations gives us for biological evolution.


The narrow reason I wanted to discuss Reali & Griffiths is in their
section 4a. There, they try to show that their techniques lead to the
emergence of S-curves of change. But there is actually a problem with
their argument, as we will discuss. I think that identifying this problem
may be, among other things, a good example of how to approach modeling
papers if one has linguistic interests.


Also at the meeting, we will do a quick follow-up on Labov's model for the
adolescent peak and the S-curve. It turns out that his particular model,
which was also assumed by Tagliamonte & D'Arcy, actually does not work as
intended. (There is no big substantial problem - the data are still the
data. But the model cannot be as Labov defines it.)


See (some of) you on Wednesday!
 -Igor
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