African languages and descriptional density

I have recently been having some fun with bibliographical data. Specifically, I have tried to determine a simple way to calculate the "descriptional density" for various African languages, especially with regard to grammar descriptions.

Descriptional density (a concept I’ve invented myself, I think) aims to determine how well-described any given language is in terms of existing grammar books and dictionaries. For instance, if a given language has only one grammar book written about it, and another language has fourteen grammar books written about it, then obviously the latter language is more well-described than the former. In other words, it’s descriptional density is higher.

There are no doubt many factors that should be taken into account when calculating something like descriptional density, such as number of publications or titles, size of description, number of authors involved, number of varieties described, availability of the grammar(s), and so on. However, many such factors are difficult to operationalize in simple ways. For instance, the size of a grammar book is not always related to its inherent usefulness, quality or even comprehensiveness. The availability of an item is difficult to determine easily (at least as a numerical value). Indeed, there are seemingly only two factors that can be handled without stumblig onto major difficulties, and still get a reasonably informative result: number of titles or works and time span (T). These can be worked into a formula as follows:

In general, one grammar book equals a W value of 1. However, many grammar books appear in second, third, fourth, etc., editions. It seems unintuitive to give a second edition the same weight as a first edition. After all, it is still essentially the same book, albeit with some minor or major revisions. Hence it seems convenient to distinguish primary works (W1) from secondary works (W2). While primary works are given a value of 1, secondary works are given a value of 1/3 (a third).

T (time span) represents the number of years spanning between the publication of the first and the latest grammar. For instance, my bibliography includes 135 primary works (grammar books) for Swahili. The earliest of these was published in 1850, and the latest in 2006. This gives a time span of 156 years. In order for this number not to inflate the calculations unnecessarily, it needs to be whittled down a bit, which is why I use the square root of the actual time span in the formula.

By adding the total number of primary works (W1), with a third of the total number of secondary works (W2), and the square root of the time span (T), we get a total index value representing the descriptional density (DD) for any given particular language.

Here, then, is a list of fifteen of the largest Bantu languages spoken in Africa, ranked according to their DD (descriptional density) values:

	LANGUAGE	DD VALUE	W1 + W2	T
	Swahili	173.49	135 + 78	156
	Zulu	70.53	42 + 48	157
	Kikongo	67.29	45 + 11	347
	Chewa/Nyanja	51.11	31 + 26	131
	Xhosa	42.15	20 + 27	173
	Shona	41.63	26 + 15	113
	Setswana	39.08	20 + 18	171
	Lingala	37.29	23 + 11	113
	Sesotho	31.45	16 + 9	155
	North Sotho	25.91	14 + 3	119
	Luba-Kasai	25.82	13 + 7	110
	Kirundi	24.23	12 + 7	98
	Kinyarwanda	21.54	9 + 9	91
	Sukuma	20.87	11 + 1	91
	Kikuyu	17.31	7 + 2	93

Notice how the ranking only roughly corresponds to the actual number of grammar descriptions (whether we look at primary works only or primary and secondary works jointly). By taking time span into account, we get a bit more sophisticated picture of how well-described any given language is. As already mentioned, I have only looked at grammar descriptions. For a more comprehensive look, I need to look also at dictionaries, but that is a project for another sleepless night.

You can read more details about this here.