Brown University

The Mathematical Theory of Big-^{2} Nevertheless, the fact remains that Pétard was the first to treat any aspect of the field with full mathematical rigor mortis.

By now, however, it has become clear to all survivors that Pétard’s formalism was excessively narrow, being based entirely upon quantitative mathematics, and the deployment of qualitative mathematics in the field would bring about as great an advance as has already been found to be the case in several other sciences, e.g. linguistics.^{3} I have therefore undertaken to supplement Pétard’s paper with a brief survey of methods inspired by modern linguistic theory and practice, in the hope that I and my professional colleagues may eventually be able to arrive at a Unified Formal Theory of Big-^{4}

In order not to complicate unnecessarily what follows, I shall confine my attention to the special case of lions (as did Pétard); application of the same methods to other species of big game I take to be obvious.

1. The Yale School Method. It is a well-

2. The Prague School Method. This school has correctly seen the central role played by distinctive oppositions and their neutralization in the workings of language. Now, lions are distinctively opposed to big-

3. The Copenhagen School Method. A central tenet of Hjelmslevian linguistics is that language is form, not substance, so that a manifestation of linguistic form in, say, writing is in principle neither more nor less irrelevant to the glossematicist than its manifestation in speech. Similarly, it is immaterial to the glossematic big game hunter whether his lion is manifested in flesh and blood (not to mention teeth and claws) or in, say, glazed tiles on an Assyrian mudbrick wall: his true quarry is the leonine form. He may hunt his lions with impunity in museums and art galleries, leaving the deserts to the adherents of other schools.

4. The M.I.T. School Method. This school employs a powerful arsenal of transformations in its work. These transformations operate upon structured concatenations, or equivalently upon trees, converting them into other structures closer to the surface. We thus have, on the one hand, surface structures, and on the other hand, deep structured concatenations or trees. These latter we shall term bathycats and bathytrees, from Greek *bathýs* ‘deep’. (We need not consider here the special apparatus by which bathycats sometimes ascend bathytrees.) A big-^{5} (2) Alternatively, a set of appropriate transformations may be applied in a cyclical manner to a set of bathytrees in order to transform them into a circular stockade around the lion. A third possibility remains as yet untried, viz. to transform a bathycat under the appropriate conditions (e.g. a strong collar and chain) into a surface lion. It appears to be harder to constrain deep structures than surface structures, at least in the case under discussion. (Editor’s note: It should be understood that this article was prepared well in advance of a later change in the theory, which replaced individual deletion transformations with “omega movement,” usually phrased as “kill them all and let the semantics sort them out.”)

5. The Method of Machine Translation. This is essentially an empirical rather than a theoretical endeavour, but it has its peculiar merits. There is a well-*‘nevidimyj idiot’* (which another, less interesting class of algorithms might have obtained as translation of English ‘invisible idiot’). The power possessed by the former class of algorithms is very great indeed, and never fails to astonish the novice machine translator. Using a well-*ležat’ na šapke* NOT into English ‘lie on a cap’, but into ‘a captive lion’, thereby achieving our goal.

6. The Method of Generative Phonology. Construct a suitable rule of accent shift able to shift the accent in an English disyllable from the initial to the final syllable, and apply it to the last word of “a lion in the desert,” to obtain “a lion in the dessert.” Given a sufficiently large and sticky dessert, one may then capture one’s lion by an elegant disregard of quotation marks (useful also in the method of machine translation). Although the method of generative phonology is much favored by the more diplomatic members of the big-

7. The Method of Internal Reconstruction. Although historical linguistics has been rather neglected by the profession of late, its methods may prove of value to the task at hand. The method of internal reconstruction would seem to be especially valuable, because almost any conceivable reconstruction of a lion’s internals would greatly increase the animal’s tractability. One might even venture to reconstruct at random (like a surgeon wearing a blind-

^{1}The author is indebted to his colleagues at Brown University, who have shown a sympathetic*Journal of Irreproducible Results* and the *Worm Runner’s Digest,* who have not allowed themselves to be unduly influenced by the fact that this paper was not submitted to their journals for publication. The research herein was funded by grants from the Department of Wealth, Miseducation, and Hellfare (no. 000000-

^{2}All major works on elephantology are reviewed by von Slonowitz (1938) or Verbljudov (1979). Unfortunately, they are all hard to come by. In general, one may observe (with Zonker, 1968) that the availability of even the best works on the subject is chaotic.

^{3}It is probably unnecessary to remind the reader of the names of linguists who have made major contributions to this line of research, so we shall not bother to.

^{4}Note carefully that this theory has only a sportive connection with the hunt for a Big Formal Theory of Games (see Von Neumann and Morgenstern 1953).

^{5}The existence of mammoths prehistorically embedded in the arctic tundra is well established, and may serve as evidence that primitive big-

(The asterisk * has the meaning now customary in linguistics)

Pétard, H. 1938. A Contribution to the Mathematical Theory of Big-*The American Mathematical Monthly* 46.446-447.

*Verbljudov, V. V. 1979. *Slony: istorija teoretičeskogo slonovedenija* [= *Elephants: A History of Theoretical Elephantology*]. Irkutsk.

Von Neumann, John, & Oskar Morgenstern. 1953. *The Theory of Games and Economic Behavior.* 3rd ed. Princeton.

*von Slonowitz, E. L. E. 1938. *Kurza Einführung in die Elephantologie* [= *A Brief Introduction to Elephantology*]. 6,345 vols. Baden-

*Zonker, Gary. 1968. *The Tao of Elephants.* Iona.

* * * * * * * *

*Old Linguists never die, they just undergo Over- the-Hill Movement.*

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