32 Dirk Geeraerts and Dirk Speelman
We can then think of each of the dots as places - towns and villages - in
that area. A black dot indicates a place where we find an attestation for a
given concept, and a white dot indicates a place where we get a null obser-
vation for the concept, i.e. where the concept is represented by no lexical
item. The situation on the left hand side of the figure is intuitively more
dispersed than the situation on the right, but how can we turn that intuition
into a quantitative measurement? We express dispersion as a proportion
between average distances.
First, we take the distance from one observation of a term to the imme-
diately neighboring observation, i.e. the closest other observation of that
term. The distances are geographical distances, based on the latitude and
altitude of the places. We do this for all other observations of the term and
calculate the average distance to the immediately neighboring term obser-
vation. Informally, this is the average distance between a black dot and
another black dot representing the same lexical item.
Second, we take the distance from one observation of a term to the im-
mediately neighboring observation of the concept, i.e. the closest other
observation of that concept, regardless of whether the nearest neighbor
appears with the same lexical item or not. We do this for all other observa-
tions of the term and calculate the average distance to the immediately
neighboring concept observation.
Third, for each term, we take the proportion of the two averages that we
just described. This measure yields the dispersion for a single term in the
onomasiological range of a concept, but we are obviously interested in the
overall dispersion for the concept. That is why we calculate a weighed av-
erage of the measures of dispersion of the individual terms: we average
over the dispersion of the terms, but we use a weight factor that corres-
ponds to the relative frequency of the term in the onomasiological profile of
the concept.
- The range of a concept is illustrated by Figure 2. Each of the solid boxes
indicates the maximal geographical range of a given term for a given con-
cept, regardless of the dispersion within that maximal area of occurrence.
The situation on the left hand side of the figure is more fragmented than the
situation to the right: the average area covered by the various terms is
smaller to the left than the average area covered to the right. In practical
terms, range is calculated in the following steps. First, we calculate the
surface that is covered by the attestations of one term. Second, we calculate
the proportion of that surface to the surface that is covered by the concept