One of the more obscure facts concerning the Polish astronomer-mathematician known as Copernicus is that in 1526, almost three quarters of a century before Gresham proposed his “law” regarding the replacement in the marketplace of good (i.e., undebased) coinage by bad (debased), Copernicus presented a similar theory in his book Monetae cudendae ratio, which was not published in his lifetime. (This was fortunate for the renown of the Elizabethan Gresham, whose theory also apparently was never published, and may, in fact, never have been written down.)

Gresham’s Law is applicable, of course, not merely to coinage, nor even to money in general, but to any elements of a closed system which are exchanged. A process involving the displacement of one class of items by another, mediated by a privative feature possessed by the displacing class of object relative to the class it is displacing (e.g., non-“goodness”), if allowed to function indefinitely and in the absence of extrinsic factors, must eventually achieve stasis. So long as there are “bad coins” (which need not, of course, literally be coins) available, and so long as other factors do not intrude, there must eventually come a point where all “good coins” have been driven from the marketplace (i.e., circulation), and nothing but “bad coins” are left: “bad coins” (henceforth “b-coins”) no longer drive “good coins” (henceforth “g-coins”) out of circulation, for the simple reason that there are no more g-coins in circulation to be driven out. At this point the process of displacement ceases and stasis is achieved; we might call this the heat death of the marketplace.

In the real world, this is, of course, an ideal situation, since inevitably extrinsic factors either put g-coins back into circulation or lead to further debasement of the coinage, which begins the process anew. In this latter case, we may speak of equilibrium: displacement is constant. The coins in circulation that formerly were “bad” are now “good”, relative to the newly debased currency. In the real world, such processes are common enough, but even they must eventually achieve stasis when debasement can go no further. Although in theory such a process can renew itself endlessly, the experiences of Germany, Hungary, and (recently) Zimbabwe with hyper-inflation suggest that in practical terms there is in fact a limit to the process, namely when the value of money becomes asymptotic to zero. However, the result is neither equilibrium nor stasis, at least not in the short term. What happens is that the Gresham process reverses: g-coins drive “bad” ones out of the marketplace. This is exemplified by cases of informal dollarization, in which the nominal currency of the jurisdiction in question simply no longer circulates.

One condition, and perhaps the only one, under which equilibrium in such processes can be achieved is by feeding g-coins into the system. This will occur when the marketplace is expanded through the exploitation of an external source, so that at the same time that b-coins are replacing the “good” ones, g-coins are constantly entering the system, and the proportion of “good” to “bad” coins is kept roughly constant. An example is the rape of the New World by the Spaniards in the 1500s. All other things being equal, such a process could be considered to be in a stable equilibrium: so long as there is gold and silver to be extracted from places like Mexico, the process can continue forever. In the real world, of course, the marketplace eventually stops expanding when the sources of g-coins are exhausted (i.e., when the resources are finite). At that point Gresham’s Law operates once more and... (see above regarding Zimbabwe).

So what has all this got to do with linguistics, let alone Mongolian vowel harmony? Let us consider the process of assimilation by which harmonic vowel systems arise in the first place. The net effect of such harmonization is, of course, vowel harmony, though vowel harmony is in itself neither a phonetic nor a phonological process, but rather a morphophonological constraint. Let us assume that at some point in the ancestry of the Mongolian language there was a non-harmonic system; any vowel could co-occur with any other. The allowable types of vowel adjacencies include, in theory, all of the vowel sequences available, though extrinsic factors may put constraints on the types that in fact did occur. Let us call the member vowel sequences of this system “good” sequences, by which we mean sequences containing both harmonizing and non-harmonizing pairs of vowels. We can only assume that such a liberal state of affairs once obtained, since we have no evidence for a pre-vowel-harmonic stage in the ancestry of Mongolian.

Over time, some process or processes of assimilation presumably reduced the possibilities of co-occurrence, so that in a particular context certain “good” vowel sequences were no longer available, and only a restricted class of sequences, which we might term “bad” sequences, could occur. This is no mere terminological trick. Over time, the effect of assimilatory processes is to constrain the possibilities of co-occurrence in a language. If allowed to continue unhindered, such a process must eventually achieve stasis, that is, vowel harmony. No more assimilation is possible, because no more disharmonic sequences occur. The “bad” sequences have driven all the “good” sequences out of morphophonological circulation and none remain to be displaced.

As it happens, vowel harmonic systems are prone to decay, that is, are unstable, and inherently so. It is often thought that the borrowing of disharmonic forms such as professor and monetize is the major engine that drives the development of neutral vowels and subsequently the collapse of the harmonic system. But this is incorrect; vowel harmony systems are inherently unstable and require no foreign influence to develop neutral vowels and, subsequently, collapse into disharmony.

For Gresham’s Law to operate, it must be the case that both g-coins and b-coins are mandated to be equivalent. Since b-coins are by definition worth less than g-coins, the difference in value is retained by withdrawal of the g-coins from circulation. When no such equality is mandated, Gresham’s Law reverses, and it is the g-coins that drive the b-coins out of circulation, since the real value of the b-coins, which is less than that of the “good” ones, is now their value in the marketplace as well.

The same effect obtains in vowel harmonic systems. But what “mandates” the “value” of the “coins”? In the case of language, it is the markedness (naturalness) of the vowels. Some vowels are simply less natural (more marked) than others. For example, front rounded non-low vowels (like the vowel in French un ‘a, one’) and back unrounded non-low vowels (like that in Russian byt’ ‘to be’) are marked, that is, less “natural” than front unrounded and back rounded non-low vowels. Over time such vowels tend to disappear from the phonological systems of languages; they are “driven out of the marketplace”. This is precisely what happened to the high back unrounded /ɨ/ of Mongolian, which has survived amongst Mongolic languages only in Moghol, a Mongolic language spoken until recently in Afghanistan, and there only in one context (namely immediately following the back velar /q/). The unmarkedization (normalization, we might say) of this vowel in other Mongolic languages involved merger of the vowel /ɨ/ with its front counterpart, /i/. This created a quasi-neutral vowel. I say quasi-neutral, because words in which this vowel occurs in the initial syllable count as front-vocalic words. Hence, while there are forms like Khalkha идэх /idexe/ ‘to eat’, there can be no such forms as */idaxa/ (*идах), though forms like both унших /unšixa/ ‘to read’ and хүжис /xüžis/ ‘sticks of incense’ can, and do, occur.

The effect of replacing such “unnatural”, hence “bad” (unnatural) vowels as /ɨ/ by “good” (natural) ones like /i/ is to increase the possibilities for vowel sequences, that is, to replace “good” sequences by “bad” ones. This is a process that operates in opposition to Gresham’s Law. The eventual effect of this process of disharmonization is the breakdown of vowel harmony: the “bad” sequences have been completely displaced and only “good” ones remain. Further change is no longer possible. This does not, of course, preclude the possibility of the expansion of the system through a massive influx of harmonic foreign vowel sequences. We can imagine that something of the kind happened when French phonology affected the phonological system of Old English, resulting in the apparent equilibrium of the modern English system, in which “b-coins” (native English phonemic sequences) co-exist with “g-coins” (Franco-Latinate sequences).

In the course of this article, I have to some extent been “cheating” by deliberately adopting rather simplified concepts of stasis and equilibrium, which (I suspect) no ecologist, economist, statistician, or engineer would accept (though in my defense, I point out that Gresham and Copernicus themselves were making a number of implicit assumptions which are unrealistic at best and illogical at worst). A more adequate analysis of the ecology of vowel systems such as that of Mongolian vowel harmony must await an analysis in terms of entropic equilibrium, or at the very least a better analysis of the dynamics (including the equilibrium) of such systems. What Galileo did for physics remains, centuries later, to be done for morphophonology.

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