which separates
one
homogeneous region from another, is called all
"isogloss." By tracing
the
isoglosses
of
many words, we notice that
most words display a unique pattern:
the
limits
of
pronunciation
eliffer for every word.
Where, then, is
the
region where a single and
eliscrete language
or
elialect is spoken?
The
representation
of
lan-
guages with a tree-like monolith, where languages are differentiated
from each
other
in a totally regular malmer without being influenced
by
other languages, is ollly
an
approximation.
Five years after Schleicher's work,
in
1872,
one
of
his students,
Johannes Schmidt, emphasized
the
importance
of
local linguis-
tic variation
and
proposed a theory
that
in some ways opposed
Schleicher's. According to Schmidt, each new fonn
of
a word spreads
over a geographic area like
the
waves spreading from a rock thrown
into a pond, influencing neighbOring speakers to various degrees.
This
metaphor
is particularly apt;
it
sets itself apart from
the
model
of
a tree, which presents completely isolated languages.
Can
these
two views
be
reconciled?
TIleories
of
biolOgical variation in space, developed in
the
mid-
dle
of
the
twentieth century by several different mathematicians,
resulted in very
sinlilar models. They have
the
generic
name
of
"iso-
lation
by distance"
and
show
that
genes vary randomly in geographiC
space, follOwing exact rules derived from statistics and probability.
TIle most
Significant regularity is
the
relation between genetic dis-
tance (calculated from averaging a
number
of
genes)
and
geographic
distance. We have seen
that
genetic distance increases regularly (but
always more slowly)
as
geographic distance increases, until it reaches
a maximum.
The
shape
of
the
theoretical and empirical
CUlves
is
determined by two measurable variables:
the
mutation rate, which
increases genetiC differences between two places, and
the
rate
of
genetiC exchange between neighbors
due
to
migration, which tends
to increase genetic similarity between
them-so
these forces are
opposed, to a certain extent,
and
balance each other.
The
same mathematical theory can
be
applied
to
linguistiC evo-
lution:
the
equivalent
of
mutation (which produces
new
forms
of
genes,
or
alleles) is innovation, which in linguistics is
the
generation
of
new sound, meaning,
or
grammar. Migration propagates
these
196