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Here we propose a two-dimensional chart, which is tentatively named the LLchart,
because the chart has the Local Language Ratio on the horizontal axis
and the LDI on the vertical axis.
The purpose of this chart is to solve a problem we encountered when
preparing an LDI chart based on data from cyberspace. It often happens that
languages used on the Web are completely different from languages spoken in
the real world. In many cases, the latter consists of local languages while the
former mainly consists of global languages like English, French or Russian.
And in those cases, the LDI of languages in cyberspace and that in the real
world are not considered to be the same. We have to take into account some
measurements about the presence of local languages, as presented in Figure 3.
Figure 3. Schematic diagram of the LL-chart
Notice that all countries with a local language ratio P fall within the area
between the two curves 1−[P 2 +(1−P) 2 ], Lieberson’s index in the case of two
languages, and 1−P 2 , which gives the maximum value of Lieberson‘s index 5 .
When P becomes larger than 0.5, the LDI becomes smaller and the plotted
point will move towards the bottom-right corner. When P is small, there are
two possibilities: either the vacancy of local language is filled by a dominant
foreign language, in which case the LDI shrinks and the point moves down
5
Two curves provide the upper and lower limits. The upper curve indicates the LDI of a two-language
community. As the addition of a third-language speaker to this community increases the average probability to
encounter different language speakers, this value is the minimum LDI of more than two language communities.
The lower curve indicates the LDI of a very special case, where each member, in addition to the local language,
speaks another language, or the maximum LDI.
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