Subject Index

• What the index measures.
• The formula
• The case for nonlinearity
  
• What the index does not measure.
  
• Dialects are not languages.
  
• Managing diversity.
  
• Tolerance, understanding, and separation.
  
• Language and understanding.
  
• Footnotes.

What the Index Measures

The formula
Greenberg's Diversity Index is given by the following equation

DI = 1 - $\Sigma (P$_i)²

where
$P$_i = the percent fraction of the total population which comprises the ith language group
i = 1 to n, where n is the number of languages that comprise the society
$$Σ = is the summation of (P_i)² for all i

The value P_i² tells us the probability of any two people of the same language sub-population accidentally meeting in the society as a whole. The value Σ(P_i)² tells us the probability of any two people of the same sub-population for all sub-populations accidentally meeting. Thus, the value 1 - $\Sigma (P$_i)² tells us the probably of any two people of any sub-population not meeting. In a perfectly diverse society the value P_i becomes increasingly small as the size of the population becomes large. This is because P_i in such a society is defined as 1/N where N is the size of the population. As P_i becomes smaller, (P_i)² becomes smaller still, and the value $\Sigma (P$_i)² rapidly shrinks toward zero. Thus, a perfectly diverse population yields a Greenberg index very close to 1 -- namely,

DI = 1 - $\Sigma (P$_i)²
= 1 - 0
= 1

where 1 is the limit of 1 - Σ(P_i)² as P_i approaches zero. Obviously, in a perfectly homogeneous society the value of P_i is one, because the percent fraction of the total population speaking that language is 100% or 1. Thus,

DI = 1 - $\Sigma (P$_i)²
= 1 - 1
= 0

In summary, then

(less diverse, more homogeneous) 0 ≤ DI ≤ 1 (more heterogeneous, more diverse)

The case for non-linearity

The progression from a perfectly homogeneous society (DI = 0) to a perfectly heterogeneous society and vice versa, although mathematically smooth, is not linear.

Consider graphs 74a and 75a (new windows) in which two artificially constructed scenarios can be observed. In the first graph we examine how the index behaves with respect to a two-language population in which the two language subgroups are represented in different proportions. In the second graph we look to see how the index behaves with regard to a multi-language population in which each language subgroup is represented equally as a fraction of the entire population. Graphs 74b and 75b (new windows) are pie graphs illustrating the diverse make-up of each population indicated by the different values of the index provided in graphs 74a and 75a (new windows), respectively.

In particular, graph 74a (new window) shows us that in a two-language population the highest level of diversity possible is 0.5. Reading the graph from right to left we also observe that most of the change in the index occurs, after one of the language groups is subordinated by the other by a ratio of less than 30/70. What we learn from this is that larger language subgroups have a larger affect on the behavior of the index than smaller subgroups. Graph 75a (new window) provides us with a similar, but more dramatic story with regard to the number of languages represented in a single population. Reading the graph from left to right we learn that most of the diversity indicated by Greenberg's index is accounted for by the first four languages.

In summary, small, but numerous language subgroups add little to the overall diversity of a society as measured by Greenberg's diversity index, but several major subgroups contribute significantly to high values of the index.

index

What the index does not measure

As with any mathematical index the Greenberg index can measure no more than what is contained in the data provided by the variables that define the function. In this case the fractional representation of each language subgroup in the population.

Dialects are not languages

As was indicated in our discussion about Switzerland and Singapore, how one defines language is a crucial determinant of the number of languages included in the index and each language's relative proportion in the total population. Dialects represent different spoken and sometimes written forms of the same language. Speakers of different dialects of the same language can largely understand one another. Speakers of dialects of different languages cannot. In todays world there are few languages that do not comprise different dialects. British, Canadian, USAmerican, Austrialian, and the English of New Zealand are all dialects of the English language. To this list one might add some of the English spoken in Hong Kong, Singapore, India, Nigeria, and a whole host of other countries that may or may not belong to the British commonwealth and have designated English as their principal national language. Moreover, within each of these nations there are often additional variations of what might be considered a standard national dialect. A person born and raised in the central southern state of Oklahoma, for example, speaks very differently from someone born and raised in Rhode Island. The same can likely be said of various regional differences in most or all other nations where English is the primary language.

In short, it is extremely misleading on the part of the Singapore national government to refer to the many Chinese languages spoken in Singapore as Chinese dialects. Although it is not wrong to call them dialects, because few languages in today's world are not, they are dialects of completely different languages. This misunderstanding is further compounded when the government has the audacity to call the Mandarin taught in Singapore's primary and secondary school system the mother tongue of all ethnic Chinese living in Singapore. To believe the Singapore government in this light would mean ignoring all of the differences represented in graph 72 (new window) and redrawing the entire graph with only four colors (see graph 51a - new window) -- one for those who speak school English in the home, and one additional color for those who speak school Tamil, school Mandarin, or school Malay.¹ By this time one can pretty well bet that if the value of Greenberg's Diversity Index were calculated by the Singapore government, it would appear much lower than what a less nationally motivated language expert would determine. Alternatively, the value would simply not be published!

Indeed, just because two people speaking different languages originate from the same country does not automatically turn their languages into dialects of the same language after immigration. Surely in the case of Chinese Singaporeans they both speak a language of China and are both ethnic Chinese. Upon closer examination, however, their cultural and language habits are very different and each constitutes a very different ethnic and linguistic subgroup in Singapore. As a large group they may be more similar to one another than they are different from South Asians or Malays, but when viewing themselves these smaller differences likely appear just as large.

In conclusion the index is only as good as the data and the analyst used to calculate it.

index

Managing diversity

How one interprets the Greenberg index is of course another problem. For example, is diversity a good thing or a bad thing? Obviously in the eyes of the Singapore government it is not nearly as good as the US English Foundation would have us believe, but then not nearly so bad that the Singapore government fails to acknowledge that important differences exist. Certainly Singaporeans themselves are unwilling to put these differences aside simply to make it easier for Singpore's illustrious bureaucrats to govern them. Obviously ethnic and linguistic diversity can be troublesome for a large number of reasons. On the other hand, it can also be very rewarding for those who are willing to take the time and effort to understand the origin, maintenance, and functioning of ethnic differences.

Tolerance, understanding, and separation

For many people in the United States ethnic, racial, religious, and linguistic diversity is both desired and celebrated. For many others it is resented and the cause of important social conflict. This is because an important social function of culture is the provision of order and stability in human relationships. The more diverse a society, the more difficult it is to know how to behave in public. This is because one can no longer anticipate the reaction of others to one's own acts.

When everyone grows up in the same culture speaking the same language, each acquires certain thought and behavioral patterns that everyone knows and respects. As deviations from these accepted patterns are considered disruptive, one is careful not to engage in them. Thus, cultural, ethnic, religious, linguistic, and even racial diversity are natural antagonists to established ethnic and linguistic orders already in place. In short, individuals from different cultures bring with them different accepted modes of behavior and thought. What is acceptable to one is not likely to be acceptable to others.

Accordingly, depending on the level of tolerance toward, the understanding of, and the degree of separation between members of different groups of the same society an enormous amount of social friction can arise or be avoided. In other words, the Greenberg diversity index is not a measure of social stability or instability, Neither is it a measure of communicability or incommunicability;  rather it is a measure of the potential for conflict and disorder in the absence of tolerance, understanding, and/or separation.

index

Language and understanding

Although tolerance and separation can be achieved in the absence of understanding, it is far easier to show tolerance when understanding is present. Moreover, complete separation is rarely complete and ever less likely into today's world.

In diverse societies there are necessarily many standards by which to judge individual behavior. In fact, there are as many standards as there are groups to which individuals belongs. As no individual lives in a social vacuum, the notions of right and wrong of each individual are necessarily determined by the groups to which the individual belongs, including the group into which the individual is born, the one or one's in which he or she is raised, and those to which the individual belongs as a matter of personal choice and mutual acceptance. Thus, in order to judge an individual's thought and behavior one must view it from as many perpectives as there are groups that are affected by it.

In societies where group differences are largely accentuated by linguistic barriers, the only way to achieve understanding and thus clear judgement is through a common language. Common in this sense does not necessarily mean one language shared by all in a society of many different languages; rather, it means one language shared by all those who are affected. Thus, in a society with three principal languages bilingualism is sufficient to achieve understanding between two individuals of two groups, and any two bilingual people, who share one language in common and one not, are capable of providing a bridge across all three of the society's different groups. Of course, understanding another's language and understanding what another is seeking to communicate are unlikely to be the same, unless the listener truly understands the cultural setting associated with the linquistic medium of the speaker.

In the end, it is possible to achieve understanding across cultural and linguistic boundaries in a highly diverse society without everyone speaking the same language, but that understanding can only be achieved in so far as both the language and the culture associated with the language are fully understood. In this regard partial knowledge can be just as damaging to a communication as no knowledge at all, because partial knowledge can lead one to believe that full knowledge is present when in fact it is not. One can only know what a person truly knows insofar as his or her knowledge is displayed. Everything else with regard to what that person knows or does not know is a matter of speculation based upon known standards of assessment and a large number of stereotypes that may or may not be applicable. In short, partial knowledge of another's language, in any but the most superficial of contexts, can just as easily lead to misunderstanding as it does understanding. Where knowledge of another's language and standards of behavior are unknown, we are hesitant to venture. Where partial knowledge is present our inhibitions are reduced, but the underlying dangers are ever present.

Thus, it is far better to have few speakers who know each other's language and culture well, and who can act as go-betweens for those who do not, than to cultivate a high-risk medium of communication where both the likelihood of miscommunication and contact are high. In short the lingua francas of our world are only as useful as the underlying commercial transactions are solid. They are neither necessary, nor sufficient for overcoming the potential dangers associated with diversity.

In conclusion, the Greenberg index tells us nothing about the ability of a society's members to communicate across diverse linguistic boundaries and thus nothing about the true level of social friction arising from linguistic diversity.

index

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¹ Obviously the Singapore government recognizes these differences, for it was from their data base that the data for graph 72 (new window) was obtained. Thus, one is left to conclude that the Singapore Ministry of Education either does not know what a mother tongue is, or has redefined the term for the purpose of educational propaganda in its effort to homogenize Singaporean society. Certainly the wrong signal is being sent to the rest of the world about Singapore's underlying language and ethnic diversity. Surely Singaporean parents and their children know the difference, if only in their own respective languages. (text)