The Mathematical Theory of Big-Game Hunting must surely be ranked among the major scientific achievements of the twentieth century. That this is so is largely the work of one man, H. Pétard, in whose fundamental paper (1938) certain recent advances in mathematics and physics were employed with great skill to create a theory of unmatched—not to say unmatchable!—power and elegance. One must not, of course, dismiss Pétard’s predecessors totally out of hand: the field had a long and distinguished history as a technology, was raised to the rank of a science by the Mysore and Nairobi schools during the nineteenth century, and finally achieved the exalted status of a professional discipline at the seminal First International Congress of Elephantology (held at London in 1910), where delegates from many nations discovered that they shared not only a common set of goals, aims, and targets, but also a common set of methods, theoretical predispositions and indispositions, and preferences in hard drink.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-Game Hunting.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-known law of physics that no two bodies can occupy the same space at the same time. Moreover, it is obvious that every lion is a body. Therefore, no two lions can ever occupy the same space at the same time, i.e. can never occur in the exact same environment. Disregarding the pathological case of overlapping lions, every lion is thus in complementary distribution with every other lion, and all non-overlapping lions are also allo-lions of a single lion-eme. Now, emic units are never physical entities, whereas every body is a physical entity. Thus, the lion-eme is not a body, and it is harmless. The capture of the lion-eme can therefore be effected without risk. Whether one has thereby sufficiently captured the allo-lions is a disputed question. In practice, the capture of allo-lions is usually left as an exercise for graduate students or for field workers.

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-game hunters in most environments. (This opposition, although naturally tending toward equipollency, may be regarded as privative so long as either the hunter or the lion remains unmarked.) But in certain appropriate environments, such as a large patch of catnip or a cloud of species-specific tranquilizing gas (specific to lions but not to hunters), the opposition between the lion and the hunter is fully neutralized, and the lion may be captured without difficulty.

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-game hunter of this school may proceed in either of two ways. (1) Since a lion is without a doubt a structured concatenation, it may be operated on by appropriate transformations, e.g. an embedding transformation which embeds it in a large block of ice, or a deletion transformation which deletes its teeth and claws.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-known class of algorithms able to translate e.g. English ‘out of sight, out of mind’ into Russian ‘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-designed algorithm of this sort, we translate Russian 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-game hunting profession, in our opinion it is an example of argument in a viscous circle, particularly when the dessert in question is a semi-cooked angelfood cake.

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-fold) and still expect to obtain the desired result in tractability. No doubt the ease with which this method leads to results has resulted in its recent popularity among younger members of the profession.

Footnotes

¹The author is indebted to his colleagues at Brown University, who have shown a sympathetic—even compassionate—interest in his work on this paper over the last ten years. He is also obliged to the members of The Society for Useless Research, to whom he has given no account of his work, and to the editors of the 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. 000000-000-001/2) and the Disunited Nations Secretariat for Trivial Information (grant number mislaid). Any errors in this paper, apart from those due to Edsel Murphy’s Prime Law (“If anything can go wrong, it will; if anything can’t go wrong, it will anyway”), are therefore entirely their fault.

²All 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.

³It 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.

⁴Note 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).

⁵The existence of mammoths prehistorically embedded in the arctic tundra is well established, and may serve as evidence that primitive big-game hunters were already tacitly aware of the underlying principles of transformational elephantology. I trust that this observation will enable professional historians of the discipline to reach as yet unattained heights in the exercise of their expertise.

Bibliography

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

Pétard, H. 1938. A Contribution to the Mathematical Theory of Big-Game Hunting. 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-Baden.

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

* * * * * * * *

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

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