© Jan Christoph Meister. All rights reserved. Version 03.09.2003. Contact: mail@jcmeister.de
The Metalepticon: a Computational Approach to Metalepsis
Jan Christoph Meister,
Universität
I. Introduction
The technical term
‘metalepsis’ may not be well known outside narratology and narrative theory: the
phenomenon denoted by it certainly is. Metalepses abound in representational
art and often are the hallmark of particularly innovative works. Hence, when
Gérard Genette introduced the term into the narratological debate in his Discours du récit the little more than
two pages devoted to the topic surveyed an impressive range of literary works
and authors: Cortazar, Vergil, Diderot,
Sterne, Balzac, Proust, Pirandello, Genet, Robbe-Grillet. Indeed, Genette traced this literary ancistry way back to Plato’s Theaitetos, [1] thus combining his narratological definition
of metalepsis with an (albeit sketchy) account of the phenomenon’s
proliferation throughout the history of Western thought and literature.[2]
However,
it is crucial to note that Genette’s narratological definition is in
principle a functional rather than a
historical, phenomenological or ontological one. Genettian narratology (as narratological theories in
general) conceptualizes narrative as a symbolic system consisting of three
representational and discursive layers that are organized in a hierarchical
fashion. In this symbolic system mediations and shifts between histoire, récit
and discours (or vice versa) are
essentially the prerogative of the highest level narrator and will therefore
normally be effected by interventions that originate on the systematic level of
discourse. This ‘top-down’ approach
comes natural to us as it is simply a necessity of representational logic.
Against this normative background metalepsis amounts to an unorthodox and
altogether aporetic technique of manipulating representational layers in that
it postulates the obverse to be possible: in a metalepsis the represented
begins to take control of the act of representation.
Radical
as this effect may seem from a theoretical point of view it has long been
conventionalized and integrated into the body of representational techniques
deemed acceptable in our cultural context, as with other unorthodox or
non-isomorphic representational schemata, such as analepses and prolepses. Indeed, metalepses have been ‘naturalized’ to
such an extent that ordinary readers or spectators will hardly begin to
entertain theoretical deliberations on
the integrity of representational logic when faced with a metaleptic
narrative, even though they might of course be puzzled or confused by it. Narratologists
still tend to focus primarily on literary narratives, a preoccupation that
proves particularly misguided in the case of metalepsis: long before Cortazar’s
often referred to Continuity of Parks of 1967 and right to the present
day mainstream Broadway productions and Hollywood movies have entertained
millions of spectators with highly metaleptic narratives, ranging from Olsen
and Johnson’s 1941 movie Hellzapoppin’
[3]– a slapstick comedy about the making of a
movie after a Broadway production which is not just full of internal metalepses,
but also has an added extra-fictional metaleptic twist in that there had in reality been a very successful Broadway production of the same
title three years before–to the highly acclaimed current musical hit The Producers by Mel Brooks (also
preceded by a movie of the same title in 1968). In the latter we watch Max
Bialystock and Leo Blum, two down-and-out
Broadway producers as they consciously attempt to produce a sure-fire
flop by putting on stage a pro-Nazi musical-within-the-musical. Yet contrary to
Bialystock’s and Blum’s expectations the musical, offensively titled Springtime for Hitler, proves to be a
huge success, prompting Max Bialystock to burst out in song in Scene 5, Act 2:
“Where did we go right?” The answer to the question is immediately found:
Bialystock realizes that on Broadway, the Hitler apology (which includes a
formidably choreographed SS-ballet taking the absurd to its utter and chilling
extreme, as well as a Hitler played by a drag queen) simply had to succeed given the fact that the
majoritiy of the audience would normally be Jewish and therefore interpret the
narrative as a satire rather than take it seriously.[4] Bialystock’s observation is of course meant to
be applied to the fictional audience in as much as to the real, suggesting
tongue-in-cheek that the success which Mel Brook’s witty musical enjoys in
reality (having received the highest number of Tony awards ever) is owed to the
same reason as that of his unsuccessfully unsuccessful character Bialystock–and
so the metalepsis extends from the play-within-the-play right into our own
domain of existence. Indeed, The
Producers is a case in point for the performing arts’ capability to involve
the public in real-world affecting metaleptic constructs and ironic
self-reflections that can easily surpass the impact of those fashioned in high
brow literary narratives.
Our
list of examples taken from popular mainstream entertainment culture could
easily be extended. A particularly intriguing metaleptic achievement as
contemporary Hollywood productions go is director Spike Jonze’s and
scriptwriter Charlie Kaufman’s recent Adaptation
(2002) in which the real life Charlie Kaufman, acclaimed author of Jonze’s
previous movie Being John Malkovitch,
inserts himself into his own story. Not only does the real John Malkovitch
reappear in the new movie as the real
John Malkovitch; to make matters even more complicated Charlie Kaufman finds
himself accompanied by a fictitious twin brother named Donald. Donald will
eventually succeed as Charlie’s aesthetic alter ego and highjack his brother’s
faltering project, the script adaptation (sic!) of a novel that significantly
lacks narrative substance and thus appears to be untellable as a movie. Following the advice of (real-world)
scriptwriter guru Robert McKee to the letter, Donald turns Charlie’s script
into one about making the script
itself, and its genre from an arty psychological movie about ‘an author in
search of a script’ into a traditional shoot-out-plus-car-chase narrative. But
it doesn’t stop here, or in the movie theatre: the actual real-world screenplay
for the movie Adaptation which you and I can buy in any bookstore also features
two authors: Donald and Charlie Kaufman;[5] not to mention the fact that the book whose
adaptation Adaptation is (and is
about) is also anything but fictional, but real world author Susan Orlean’s
1999 bestseller The Orchid Thief .
Whether
avant la lettre or not, the above cases demonstrate that metalepsis
is indeed a very powerful, widely practiced and appreciated trope that
consciously plays with the logic of representation which underlies all aesthetic
illusion. However, for the spectator or reader this play is not entirely
without risk. Genette clearly pointed to this second aspect too, that of metalepsis’s
deeply aporetic ontological consequences. It was Borges who originally commented that, if fictional characters are
believed to be able to assume the roles of
readers and spectators, then we, their real readers and spectators, may
by implication also find ourselves to have become fictional.[6]
Representational unorthodoxy, it seems, will ultimately result in an
ontological dilemma. If taken to the extreme metalepsis will thus amount to a
double catharsis, a representational and an existential one. How and as what we
may come out at the other side of it God alone would seem to know.
The
purpose of this article is to prove that this last conclusion is possible, but
by no means necessary, and that the fervor and awe which characterize some of
the philosophical and philological exegeses of metalepses might be symptomatic
of the critical debate’s tendency to over shoot the mark. In terms of more pragmatic and
functionally orientated approaches David Herman has perhaps best expressed the
general narratological consensus on metalepsis when he defined it as
the interplay of
situations, characters or events occupying diegetic levels that are prima facie
distinct [7]
This definition is
perfectly acceptable, save for the fact that it unintentionally downplays the
functional aspect emphasized in Genette’s initial approach. Significantly, Genette adopted the term metalepsis from rhetoric–the term, not
the concept: for in literary rhetoric metalepsis is not a structural feature,
but deemed part of the ornatus, the
rhetorical means by which an utterance can be made more pleasing and appealing
to its receiver.[8] Heinrich Lausberg in his Elemente der literarischen Rhetorik counts metalepsis under the tropes
characterized by the use of synonyms.[9] More precisely, in terms of Lausberg’s
definition metalepsis refers to a contextually
inappropriate use of synonyms. One such case of ‘metaleptic’ use is that in
which a proper name is replaced by a synonym which would otherwise be perfectly
acceptable, but in a given context simply defeats the communicative purpose of
a proper name as an indicator for one particular individual only. The second
case is that in which one replaces a word associated with two possible
meanings, such as ‘nature’. One of the word’s meanings will normally prove
contextually inappropriate; for example, in the Goethean ‘nature and spirit’[10] the two nouns obviously refer to existential
principles, and not to empirical entities. Traditional rhetorical metalepsis
subverts our common practice of semantic disambiguation among competing synonyms by consciously
choosing the one that will express the inappropriate rather than the
appropriate meaning intended by the original term. Thus ‘nature and spirit’
will be translated into ‘landscape and ghost’, a formulation in which the
synonyms are strangely at odds with the register and intended semantics of the
original phrase.
As we can see the original rhetorical definition of
metalepsis was in itself functional rather than ontological, and hence
Genette’s adaptation of the term in his narratological approach is at the
outset methodologically consistent. What makes a chosen synonym metaleptic in a
traditional rhetorical sense is not that it is lexically wrong, but that it is
contextually inappropriate and functionally problematic. However, it is crucial
to note that the idea of appropriateness is in itself already based on a
particular historical concept of signification. This brings us to a second aspect
of narrative metalepses which has hitherto been largely neglected. As we have
just seen, metalepsis as a rhetorical concept presupposes that the link between
signifier and signified is contextually defined and thus to a significant
degree arbitrary. The same applies to narrative metalepsis: it is a concept
which simply does not work on the basis of a non-arbitrary concept of
signification. For example, could Plato, whose poetological convictions stem
from a decidedly non-arbitrary concept of signification implied by his idealist
ontology, even ‘think’ something akin to a narrative metalepsis? The answer must clearly be ‘no’, and this not
because of an idiosyncratic disregard
for fiction. The impossibility to appreciate metaleptic aesthetic effects is anything
but a whimsical peculiarity in Plato; in fact it is a perfectly logical
consequence of the ontological and semiological presuppositions on which a
Platonian universe is based.
Our
situation today is exactly the obverse. Indeed, representational metalepses in
art are quite fashionable because we deem them ‘meaningful’ in a more abstract
sense and enjoy playful self-referentiality. Since Aristotle's’ Poetics
we have grown accustomed to the idea that statements made under the condition
of fictional representation are exempt from tests for prepositional truth. At
the same time, one would assume that it is precisely our voluntary abandonment
of the criterion of referentiality which makes us all the more dependant on
that of consistency—and logical consistency, it seems, is precisely what
narrative metalepsis negates. The same of course applies to myse en abyme.
In fact, one of the consequences of
looking at metalepsis’s formal properties is the realization that the
distinction between mise en abyme and metalepsis concerns mainly
the level of apparentness and unavoidability which the aporia assumes in a
particular work. In other words, mise en abyme is simply a fully-blown,
fully implemented instance of the type of paradox already implied in even the
weakest case of metalepsis. In a formal model the distinction can thus be
ignored, whereas it must certainly remain crucial to the design of typologies,
as well as to descriptions and interpretive analyses of empirical examples in
aesthetic artifacts.
Apart
from Genette the original functional definition of the concept’s predecessor in
rhetoric has hardly played a role in
narratology; one has generally preferred to explicate the aporetic design
characterizing the phenomenon of metalepsis in two other regards:
a)
in
terms of ontological order, i.e. as an aporetic narrative statement negating
the absolute validity of ontological
distinctions among existential levels in worlds;
b)
in
terms of theory of communication, i.e. as an aporetic narrative statement
leading to the identification of communicative roles normally considered
as distinct.
Narratological
approaches to metalepsis accordingly vary in terms of goals and methodologies;
figure 1 attempts to systematize these:
Figure 1: System of narratological approaches to metalepsis
Against this background
I will now propose an explication of metalepsis that focuses on its
consequences for the communicative contract entered into by author,
narrator and reader of fictional narratives, a contract which in turn presupposes
the validity of an even more fundamental—though mostly implicit—agreement which
one might call the representational contract. The underlying hypothesis is that this
contract is negated by metalepsis, but can be ‘normalized’ (restituted) by
certain subsequent operations. The
methodological consequence, therefore, is that metalepsis should not–as
the ontological approach implies–be conceptualized as an absolute phenomenon,
but rather as a case of representation turned self–referential in the extreme.
Methodologically
my approach is closely related to that of
Tom Kindt and Hans-Harald Müller whose contributions to the current
volume are based on the similar considerations of principle. Kindt explicates the Gricean background to
the notion of communicative contract and proceeds to compare metalepsis to other
narrative procedures that tend to call this contract into question; his aim is
to outline potential strategies of
‘normalization’ that are specific to metalepsis, as opposed to those pertaining
to other forms of narrative anomalies,
and particularly to narratorial unreliability.
Müller presents a case study in which the ‘narrative output’
(Dällenbach) of a particular metaleptic novel (Leo Perutz’ Die dritte Kugel) is evaluated in terms of competing and mutually
exclusive reconstructions of the
narrated events offered indiscriminately to its readers by the text. In other
words, Müller’s approach demonstrates how metalepsis can work as a kind of
salvatory clause retrospectively inserted into the communicative contract, a
clause which expressly licenses ambiguity on the base level of the interpretatively
reconstructed histoire and thereby
waves the hermeneutic postulate that any global interpretation presupposes a
successful disambiguation of the interpreted material at base level.
My
own approach is somewhat more abstract. I will attempt to identify the minimal
logic conditions under which metalepses can occur, and the maximum complexity
which it can reach, and will then try to illustrate the pragmatic constraints
which are placed on metaleptic constructs. I will proceed by first giving a
rather abstract formal definition of metalepsis in the form of a computer algorithm,
and then activating that algorithm to test it for its boundary conditions. This
approach basically reconceptualizes the narrative phenomenon as an algorithmic one, tests its functionality
and limitations and then returns to a philosophical evaluation in which the
implications of metalepsis for the representational contract are briefly considered.
The overall methodological signature of my approach is that of humanities
computing: a research praxis which is based on the belief that the
reconceptualization of humanities’ phenomena in a foreign methodological
paradigm will help us to discover new aspects to old problems.[11]
II. Towards
a computational model of metalepsis
In designing a formal
model of metalepsis it is vital to note that metaleptic phenomena are by no
means restricted to the aesthetic domain.[12] Let us
look at mathematics for example (geometry, to be more precise), bearing in mind
that the drawing of parallels between mathematics and literary science—in fact,
of parallels between mathematics and anything for that matter—is risky. However,
the translation of a mathematical theorem into a speculative metaphor may be
permissible as long as we conceive of it not as an explanation, but as a heuristic
employed for the purpose of
reconceptualizing our understanding of “metalepsis”, and I beg the
reader to take it in this sense.[13]
One particularly relevant case is
that of the analogy between metalepsis and theoretical objects such as the
Möbius strip which visualizes August Ferdinand Möbius’s (1790-1868) theorem of
a one-sided surface (figure 2),[14] or that of the less well-known
Klein bottle, a theoretical object named after the German mathematician Felix
Christian Klein (1849-1925) that attempts to illustrate the idea of a
three-dimensional continuum that feeds back into itself (figure 3).
Figure 2: Möbius strip
Figure 3:
Klein bottle[15]
These playful
theoretical objects serve to illustrate an epistemological problematic
encountered even in the hardest of natural sciences, that is, in modern
physics. It was Heisenberg who realized that according to the theory of quantum
mechanics, you can either gather precise knowledge about a particle’s impulse,
or about the particle’s spatial position. To have both at the same time is not
possible, because the observer is necessarily involved in the process of
observation. Or, as Wolfgang Pauli put it in a letter to Heisenberg:
Man
kann die Welt mit dem p-Auge und man kann sie mit dem q-Auge ansehen, aber wenn
man beide Augen zugleich aufmachen will, dann wird man irre.[16]
In epistemological terms
this is indeed what metalepsis amounts to: a case of being instructed to ‘open
both eyes at the same time’. One eye is needed to orientate ourselves on the
level of discourse, and one to orientate ourselves within the world represented
by it. The problem of an impossible logic double-focus has troubled other
disciplines as well; Wittgenstein’s Tractatus
for example approaches it from an analytical angle and states:
Der Satz kann die gesamte Wirklichkeit darstellen, aber er kann nicht das darstellen, was er mit der Wirklichkeit gemein haben muß, um sie darstellen zu können – die logische Form. Um die logische Form darstellen zu können, müßten wir uns mit dem Satze außerhalb der Logik aufstellen können, das heißt außerhalb der Welt.[17]
The
same dilemma underlies Gödel’s famous mathematical problem, formulated in the
so-called Incompleteness Theorems[18], and it reoccurs
in yet another variant in Computer Science in the context of what is known as
the Halting Problem. A current
encyclopaedia definition describes it as follows:
The halting problem is a decision
problem which can be informally stated as follows:
Given a description of an algorithm and a
description of its initial arguments, determine whether the algorithm, when
executed with these arguments, ever halts (the alternative is that it runs
forever without halting).
Alan Turing proved
in 1936 that there is no general method or algorithm which can solve the
halting problem for all possible inputs.
The importance of
the halting problem lies in the fact that it was the first problem to be proved
undecidable. Subsequently, many other such problems have been described; the
typical method of proving a problem to be undecidable is to reduce it to the
halting problem.[19]
Marie-Laure Ryan, in her
contribution to this volume, explains the relevance of the ‘Halting
Problem’-theorem for our understanding of metaleptic constructs in greater
detail. What will be presented now is a practical example for a ‘metaleptic
machine’ (Ryan) fundamentally affected by the halting problem: a computer
algorithm that attempts to resolve the irresolvable representational problem of
metalepsis. What will make this attempt at the impossible interesting to us not
that it will fail—we know that right from the outset—but how and why it
fails. This will hopefully shed some new light on our subject matter.
The task of our program shall be to generate a verbal
representation of the famous sketch Drawing
(1948) by Dutch artist Maurits Cornelius Escher (1898-1972), perhaps one of the
best illustrations of the principle of metalepsis in that it visualizes the representational
and the ontological aporia in one:
Figure 4: M.C.Escher: Drawing (1948)
Does the left hand draw
the right hand, or is it the other way round? And which of the two hands is
more ‘real’? The question is impossible to answer, it seems, but let us try and
forward it to the computer nevertheless. In order to do so, we need to feed the
computer some data as well as some
instructions. In this case data and instructions will both be contained in a little program which I wrote for this
purpose, the Metalepticon. The
program consists of two types of statements: statements about facts and
about rules. These two classes are defined as follows:
·
facts are true
statements about the representational system; i.e. Escher’s drawing
- rules determine how facts may be (re-)combined in order to interpret that system
Facts and rules represent the
entire information about the representational system and its potential
interpretations which we will make available to the Metalepticon. Once this
virtual machine has ‘read’ (compiled) the input we will ask it to start
processing it and generate output, that is, to combine the facts according to
the rules and draw inferences, thus generating meta-representations or
‘knowledge’ about the representational system embodied in Escher’s ‘hand draws
hand’-etching. We will proceed in a
step-by-step fashion before eventually asking the Metalepticon to generate all
logically consistent inferences that can be derived from its input. Here now is
the actual program, written in standard prolog syntax:[20]
% Metalepticon
v.1
% JCM - 01.07.2003
% Facts
% ——————————————————————————
% Facts
known to the narrative system can be represented in 2 ways:
% From
the left perspective = index 1
agent(1,`Left
hand draws`).
object(2,`right
hand`).
% From
the right perspective = index 2
agent(2,`Right
hand draws`).
object(1,`left
hand`).
% Rules
% ———————————————————————
% Two rules define the system's representational
functions:
% 1.
The rule for generating simple representations
representation(Narrator,
Narrated):-
agent(AgentDomain,Narrator),
object(ObjectDomain,Narrated),
AgentDomain =\=
ObjectDomain.
% 2. The rule for generating nested meta-representations
meta-representation(MetaNarrator,
Narration):-
agent(MetaDomain,MetaNarrator),
representation(Narrator,
Narrated),
agent(AgentDomain,Narrator),
object(ObjectDomain,Narrated),
Narration = how(Narrator,
Narrated),
NarrationDomain =
MetaDomain-1,
% the following adds any narration identified as object of a meta-narration to the
% known facts
assertz(object(NarrationDomain,(how(Narrator,Narrated)))).
Running the Metalepticon code
will essentially amount to finding out what the concrete value or ‘meaning’ of
its variables might be. In other words, all the program does is to try and slot
the facts which it has received as
input into the position of the variables while at the same time respecting all
the rules.[21]
In our experiment we have proceeded
in three steps, instructing the computer to resolve three different questions:
(1) “On the level of representation, who can assume the roles
of narrator and narrated in
Escher’s representational system?” – This question is the natural language equivalent of the Metalepticon’s first head clause
representation(Narrator, Narrated):-
which is tied to the
conditions defined in the remainder of rule 1.
In processing our question the Metalepticon
will produce a total of two possible answers (separated by the ‘;’) as the
following screen shot shows:
Figure 5: Metalepticon
after processing of 1st query
(2) “On the level of meta-representation, who can assume the
roles of Meta-Narrator and Narration in Escher’s representational system?” – This question is the natural
language equivalent of the Metalepticon’s
head clause
meta-representation(Meta-narrator,
Narration):-
which is tied to the
conditions defined in the remainder of rule 2.
In processing this second question the Metalepticon will also produce an answer. By re-iterating the query
we can ask it to find the second possible unique answer, then the third,
fourth, fifth and so on. Here is the result:
Figure 6: Metalepticon
while processing of 2st query
As one sees it proves
difficult to find out how many
possible answers there actually are: every time we issue the repeat command, an
ever deeper-nested structure will be generated. Since we don’t want to waste
our time pressing the repeat key millions of times we will take a shortcut by
issuing a new command:
(3) “Generate all
possible answers for the following question: ‘On the level of meta-representation, who can assume the
roles of Meta-Narrator and Narration
in Escher’s representational system?’ ” – This command makes use of a particular
feature in the prolog programming language used for the Metalepticon, namely the possibility to
force the program to generate a list of all correct unique answers to a given
problem. For reasons soon to become apparent I have termed this clause the go_crazy- command:
go_crazy:-
findall(X,meta-representation(MetaNarrator,Narration),List).
If we instruct the
machine to execute this command the machine will (sooner or later, depending on
the hardware used) abort the Metalepticon and report that it has
confronted an error. Its screen will then look like this:
Figure 7: Metalepticon
after processing of 3rd query
Consulting our on-line help
about the mysterious ‘Error 6’ that caused the program to abort execution we
will learn the following:
Figure 8: On-line information on prolog error 6
What has happened here?
The machine, for all its computational power, seems to have hit a wall. However, it is important to note the exact
nature of its problem, for contrary to what one might initially think the
machine is not just engaged in inescapable recursion, a so-called infinite
loop. In a classic condition of infinite looping the computer will generally
not be able to even begin to output
relevant results: caught in an inescapable recursion of processing logic, it
will be forced to keep on stacking processing instructions on top of each
other. This will eventually lead to an error whose effect is similar–the
program will crash–but conceptually different, a so-called stack overflow. In prolog, the stack is a virtual segment of the machine’s memory which is
reserved for storage of dynamically generated processing instructions, whereas
the heap is that part of the memory
which is used to store the original program and input data itself, as well as
the interim results which it may dynamically generate and will temporarily
store so that they may be reused by a recursive instruction at a later stage,
until the end result is finally handed over to the output stream: normally a
disk drive, a screen or a printer; in other words: some form of external
representation device.[22]
Looking
at the enormous amount of nested structures generated by the algorithm we
realize that the Metalepticon’s
problem is that command (3) forces it to generate an indefinite amount of
output which, at the same time, is also considered an interim result. It is
this latter category that poses the problem; the machine simply cannot ‘keep in
mind’ all the interim results. This is what our on-line help refers to by
telling us that “the program has asserted too many clauses.” What exactly does
this mean? According to the Metalepticon’s second rule, every result
which the computer generates is immediately fed back into its own knowledge
base, thus creating a new clause or fact
which the machine needs to take into consideration thereafter. In other words,
it is the dynamic nature of the Metalepticon which ultimately causes the
problem, not necessarily its self referential design per se because, as the second
run of the program has demonstrated, despite recursion the program will produce a finite number of results
as long as it is given a finite number of facts.[23] However, once we instruct the Metalepticon to reinterpret every
computationally identified correct statement
of fact as a new fact which in itself needs to be
computed, it will never be able to reach its halting condition: the program’s
demands on its heap memory keep on
expanding, while at the same time ever
deeper nested structures wait to be analysed and computed.
From
a semiotic point of view the problem of this ever-expanding memory is rooted in
the elimination of a stable logical distinction between statements of facts (meta-representations) and facts (representations). A ‘normal’ (strictly procedural) computer
program would insist on resolving this blatant case of ambiguity and simply
tell us that something is wrong, either in its own code, or in the data which
we input into its knowledge base, and then stop to work. Seen in this light the
dilemma of the Metalepticon proves to
be not that it is too stupid, but rather that it is too intelligent: that it
can learn and dynamically expand its knowledge about facts, and that it will insist on trying to find answers in the
face of a conceptual ambiguity that results from recursion in as much as from
reinterpretation. This attempt at ‘intelligent’ behaviour is what forces our program
to fall prey to the metaleptic suspension of the base principle of
representation, the principle of fundamental distinction between sign and
signified. Had it not been for the inconspicuous last line of program code
assertz(object(NarrationDomain,(how(Narrator,Narrated))))
in which the assertz-predicate instructs the machine
to behave ‘intelligently’ and add the newly computed object-result to its current knowledge no error would have
occurred.
As
stated at the outset the Metalepticon is merely an experimental modeling
device. The interesting question raised by our experiment is not what the
machine can handle, but rather how many recursions and what demands placed on
our own memory we, the natural observers and cognitive processors of
metalepses, are willing to tolerate before we report an error. This is bound to
be contingent on various factors, some of an ontogenetic and some of a cultural
order; just as some people enjoy Bach’s quadruple canons and fugues (which
possibly constitute the most intricate self-referential artistic structures to
date), while others don’t. Such reaction
– similar to that owed to the restricted amount of memory available to the Metalepticon
– is merely the result of pragmatically or conventionally imposed limitations.
Knowing how metalepses work, or why our attempts to process them in terms of
standard semiotic assumptions cannot,
presents only a partial solution.
III. The meaning of metalepsis
Let us rephrase the
question, then. What is the point in imposing limitations, of reporting
a cognitive and hermeneutic processing error, so to speak? An important
semiological and poetological necessity sets the case of a concrete,
aesthetically represented and cognitively processed metalepsis apart from that
of an abstract formal model of metalepsis like the Metalepticon. In reading
and watching aesthetic metalepses we consciously choose to 'open both eyes at
the same time', yet certainly have no intention of 'going crazy'. Rather than
wasting our mnemonic faculties on ever deeper nested structures we will at some
point decide that now has come the time to exit from the self-referential loop.
It is precisely at this point where we no longer question what and how metalepsis
represents something, but rather what metalepsis itself taken as a structure
may mean. What, then, could be the meaning of metalepsis?
I
believe that the metadiegetical ‘switch’ implied in metalepses is perhaps of a
more profound nature than one would normally assume. To understand this we have
to realize that in the case of metaleptic paradox, logical consistency—or
rather, inconsistency—is precisely not a matter of how a world separate from
our own empirical one is internally organized. Or, to put it
differently: metaleptic constructs prove a possible world impossible not because
that world is shown to have some immanent logical defect. Rather, they
do so because they imply that there is, indeed, only one world. In other
words, they don’t just negate the plausibility of a possible world. They negate
the very idea of a possible world indexically distinguishable from the
observer’s reality. In the ongoing history of ideas metaleptic constructs thus
play the role of a conceptual wormhole through which we get sucked back in
time, way past Platonian idealism, back into the preceding magic universe where
signs are things, and things are signs.[24] For metalepsis, when considered not primarily
as an aesthetic, but as a semiotic phenomenon, amounts to a cancellation of the
representational contract on which the modern concept of symbolic
systems, taken in a common sense, is based. Borges was right: Metalepsis implicitly
equals the observer with the observed, and the observed with the observer, and
so forth. One can interpret this as an ontologic problem, if one so wishes, but
one can also explain it in terms of its aporetic semiologic.
Which brings me to a
conclusion that can be summed up in three simple points.
(1) We all know that what metalepsis
states is, of course, completely absurd: p = q doesn’t’ work.
(2) There are two ways of experiencing this:
from the p-side, or from the q-side.
(3) There is however only one way of knowing that (1) and (2) are the case:
from the outside.