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Pataphor in Mechanism Design

[All art from Michael Nesbit’s Phlataphor series; view his portfolio here. LaTeX version here.]

Game theory analyzes extant strategic situations to identify their equilibrium properties. Conversely, mechanism design (‘reverse game theory’) creates auctions, markets, or games whose incentive structures bring about pre-specified equilibrium properties.[1] Mechanism design is typically billed as the ‘engineering’ branch of economics (Roth, 2002). In a very real sense, then, it’s a science of imaginary solutions.

The latter phrase is one of numerous definitions for ‘pataphysics, a rigorously nonsensical philosophy claiming to be as far from metaphysics as metaphysics is from physics. If science proceeds toward ever greater levels of generality, ‘pataphysics views each phenomenon as a singularity — and hence, “examine[s] the laws governing exceptions” (Jarry, 1911: 21). As for the prefix, one could do worse than to think of it as a mix of meta (beyond) and para (beside).

Here, I’ll focus on pataphor, a figure of speech that purports to be as far from metaphor as metaphor is from non-figurative language. Pataphor is a fairly recent idea in ‘pataphysics, often misunderstood as merely a hyperbolic metaphor or a derogatory term. By clarifying its structure, I hope to make pataphor more accessible both as a writing exercise & as a concept.

Part 1 schematically defines pataphor based on several examples, using a notation adopted from category theory. Part 2 frames mechanism design as ‘economic pataphorology’, showing how pataphor (as well as meta-metaphor) can be applied in settings beyond literature. Part 3 outlines how the notation for pataphor allows an analogous definition of patonymy (cf. metonymy). Part 4 considers chains of pataphors. Part 5 raises questions for future research.

Pataphor

Pataphor was invented by the American writer Paul Avion, under the pseudonym Pablo A. Lopez. Below, we’ll use his own examples as illustrations. His definition runs as follows:

Pataphor – 1. An extended metaphor that creates its own context; 2. That which occurs when a lizard’s tail grows so long it breaks off and grows a new lizard.

Pataphor is typically viewed as a fun, if contrived, writing exercise — it’s not at all clear how one might apply it outside of literature. Further, the concept is often muddled, due mainly to the phrase ‘extended metaphor’. What’s needed is a schematic definition, both to clarify the concept and show where it’s applicable. Using a kind of math fittingly nicknamed ‘abstract nonsense’, we can define pataphor by the following formula:

pataformula

where A is the state of affairs in a first ontology (world #1), C is a second ontology (world #2), B (the ‘hinge’) is an object that A and C have in common, f is a metaphorical statement where something in A is compared to B, and g is a non-figurative statement in which the object B is implicated in the state of affairs C.[2]

A pataphor combines a metaphor and non-figurative statement; it is NOT a kind of metaphor.

We can see this in the following ‘canonical’ example of pataphor:

Non-figurative: Tom and Alice stood side by side in the lunch line.

Metaphor: Tom and Alice stood side by side in the lunch line, two pieces positioned on a chessboard.

Pataphor: Tom took a step closer to Alice and made a date for Friday night, checkmating. Rudy was furious at losing to Margaret so easily and dumped the board on the rose-colored quilt, stomping downstairs.

Here, A is Tom & Alice’s world and C is Rudy & Margaret’s world. B is the chessboard — metaphorical (f) in A, non-figurative (g) in C. We say that in metaphor, Tom won the game; in pataphor, Rudy lost.

Next we’ll look at a flawed pataphor (or quasi-pataphor):

Non-figurative: The moon rose over the sea.

Metaphor: The yellow eye rose over the sea.

Flawed Pataphor: The yellow eye rose over the sea: in time, a tear fell, beading along a whisker to fall into the blue porcelain dish.

Here, A is the world containing the moon at nightfall, B is the yellow eye, and C is the world containing the cat. The reason this pataphor is flawed is because we can interpret all of it as occurring within the cat’s world (C) by reading ‘sea’ as a metaphor for the milk.

Last, we’ll look at a more prolix pataphor:

Jenny is eleven years old. She lives on a farm in Luxembourg, West Virginia. Today Jenny is collecting eggs from the henhouse. It is 10 a.m. She walks slowly down the rows of cages, feeling around carefully for eggs tucked beneath clucking hens. She finds the first egg in number 6. When she holds it to the light she sees it is the deep tan of boot leather, an old oil-rubbed cowboy boot, creased with microscopic branching lines, catching the light at the swelling above the scarred dusty heel, curled at the cuff, bending and creaking as the foot of the cowboy squirms to rediscover its fit, a leathery thumb and index prying at the scruff, the heel stomping the floor. Victor the hotel manager swings open the door and gives Cowboy a faint smile.

Here, A is the world inhabited by Jenny, notably the egg she finds. The egg, due to its brown color, is metaphorically compared to a cowboy boot. Here, the boot acts as the ‘hinge’ B, opening onto the world C inhabited by the cowboy and Victor. (Note that without the final sentence of the paragraph, this would just be an extended metaphor.)

Exercise: Why is the following not a pataphor? “The sweaters are hanging in the closet, their profiles the silhouettes of elephants at the Municipal Zoo before Mr. Bigby’s five o’ clock show.”

Answer: It’s only an extended metaphor (A—ᶠ→C), since it lacks a non-figurative statement (g) made within the second ontology.

It should be clear now that pataphor is truly a novel and rich idea, and that to view it only as an extended metaphor destroys its most interesting quality, namely: being trans-ontological (spanning multiple ‘worlds’).

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