The Drake Equation is familiar to students of exobiology and SETI (Search for Extraterrestrial Intelligence) as a means of stimulating thinking about the number N of communicating civilizations that might be expected to exist in a given volume of space. Drake conceived of N as a function of seven variables each one of which is subject to change with improvements in our knowledge of cosmology, stellar evolution, biology, and the development of civilization. As there has not been much non-fictional work recently in the area of "exolinguistics", it seemed that it would be an interesting problem to consider what might be some of the variables that, both at a given time and across time, contribute to determining the number of languages that are spoken on a planet which is, like ours, isolated.

For this conceptual exploration I am assuming normal physics and languages that operate through the oral-aural or manual-visual channels familiar to us here. I also assume that the emergence of language confers such enormous and immediate benefits on its "inventors" that there is no opportunity for it to become hard-wired: Wherever it emerges language is socially transmitted and hence unstable.

Like Drake's, this equation has seven terms: N = P R* T 1/I 1/M 1/Tr 1/SLA.

1. P = population. The number of languages cannot be larger than the total number of individuals capable of speech divided by the number in a stable band which is about twenty-five. While developing worlds soon cease to be hospitable to the existence of small self-sufficient groups, the figure twenty-five applied to an assumed total hunter-gatherer population of twenty-five million individuals implies a maximum number of coexistent languages of one million. This large number is a theoretical limit which is subject to reduction by other terms in the equation.

2. R* = rate of (irreversible) sound or gesture change (ie, phonological merger). If this factor creates barriers to mutual comprehension at a rate slower than the rate at which groups split into separate bands, then sets of bands will share languages even if they do not interact. For instance, if the cumulative effect of sound change is sufficient to prevent communication after 500 years and if the average band splits in two every 100 years, then N would have to be divided by 32.

3. T = topological scale-invariance. The basic idea is that certain geographies of habitat favor isolation of groups while others promote their interaction. At early epochs a high degree of inhomogeneity in the configuration and connectivity of planetary terrain would favor linguistic diversity. However, by also allowing the accumulation of technological and economic inequalities large-scale topological inhomogeneity may lead ultimately to sudden cultural expansions and colonial situations that reduce linguistic diversity.

4. I = intensity of interaction with foreigners. The more frequently individuals speaking different languages must interact, the smaller (over time) the number of languages they use becomes. In general, the more specialized and diverse an epoch's range of activities, the fewer the individuals involved in each of them and the more likely it is for them to need to communicate with foreigners.

5. M = multivalency. The more massive that communicative leverage becomes the fewer the languages that can support it. Economies of scale in evolving technologies of communication operate to favor audiences that are as large as possible, that is, audiences that have a language in common.

6. Tr = translation cost. If translation cost comes down over time this variable may counter and even cancel the effects of the two preceding. A world in which cheap and immediate translation is easily available is one in which a larger number of languages can coexist. (For a related discussion see "The Rosetta Hack" in Scientific American, Nov. 1996.)

7. SLA = second language acquisition cost. This is the flip-side of translation cost: The more cheaply accurate translations (or interpretation) can be made the less need for individuals to incur the costs of learning second and third languages. The largest component of SLA is the opportunity cost (= time lost) to the learner. Opportunity costs continue to rise as civilizations evolve.

Upshot. The value of N is highly dependent on a world's level of socio-economic and technological development. On worlds moving rapidly towards economic and technological homogeneity, all the parameters in this equation (except for Tr) should evolve in ways that favor a minimal value for N.

Question: Are there any economic, scinetific, or technological benefits in maintaining a value larger than 1 for N? A November 1996 article in Science (274:1479-80) by Van Alstyne and Brynjolfsson suggests that the ease of communication fostered by developments like the Internet may balkanize the scientific community by making it too easy for scientists to limit their interactions to small sets of like-minded colleagues and to ignore discourse in other fields. Assuming that a progressive reduction in the number of languages can be compared to the removal of geographical barriers to communication that is being effected by the Internet, we might expect a similar disadvantage to result. However, Van Alstyne and Brynjolfsson's views on the long-term effects of the Internet are hotly contested.

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