From the Tree to the Labyrinth (10 page)

We must first reach a consensus on the concept of labyrinth, because labyrinths come in three varieties (cf. Santarcangeli 1967; Bord 1976; Kern 1981). The classic labyrinth of Cnossos is
unicursal:
there is only one path. Once one enters one cannot help reaching the center (and from the center one cannot help finding the way out). If the unicursal labyrinth were to be “unrolled,” we would find we had a single thread in our hands—the thread of Ariadne which the legend presents as the means (alien to the labyrinth) of extricating oneself from the labyrinth, whereas in fact all it is is the labyrinth itself.
³¹
The unicursal labyrinth, then, does not represent a model for an encyclopedia (
Figure 1.15
)

The second type is the Mannerist labyrinth or
Irrweg.
The
Irrweg
proposes alternative choices, but all the paths lead to a dead point—all but one, that is, which leads to the way out (
Figure 1.16
). If it were “unrolled,” the
Irrweg
would assume the form of a tree, of a structure of blind alleys (except for one).
³²
One can take the wrong path, in which case one is obliged to retrace one’s steps (in a certain sense the
Irrweg
works like a
flowchart
).

Figure 1.15

Figure 1.16

The third kind of labyrinth is a
network,
in which every point may be connected with any other point (
Figure 1.17
).

Figure 1.17

A network cannot be “unrolled.” One reason for this is because, whereas the first two kinds of labyrinth have an inside and an outside, from which one enters and toward which one exits, the third kind of labyrinth, infinitely extendible, has no inside and no outside.

Since every one of its points can be connected with any other, and since the process of connection is also a continual process of correction of the connections, its structure will always be different from what it was a moment ago, and it can be traversed by taking a different route each time. Those who travel in it, then, must also learn to correct constantly the image they have of it, whether this be a concrete (local) image of one of its sections, or the hypothetical regulatory image concerning its global structure (which cannot be known, for reasons both synchronic and diachronic).

A network is a tree plus an infinite number of corridors that connect its nodes. The tree may become (multidimensionally) a polygon, a system of interconnected polygons, an immense megahedron. But even this comparison is misleading: a polygon has outside limits, whereas the abstract model of the network has none.

In Eco (1984b: ch. 2), as a metaphor for the network model, I chose the
rhizome
(Deleuze and Guattari 1976). Every point of the rhizome can be connected to any other point; it is said that in the rhizome there are no points or positions, only lines; this characteristic, however, is doubtful, because every intersection of two lines makes it possible to identify a point; the rhizome can be broken and reconnected at any point; the rhizome is anti-genealogical (it is not an hierarchized tree); if the rhizome had an outside, with that outside it could produce another rhizome, therefore it has neither an inside nor an outside; the rhizome can be taken to pieces and inverted; it is susceptible to modification; a multidimensional network of trees, open in all directions, creates rhizomes, which means that every local section of the rhizome can be represented as a tree, as long as we bear in mind that this is a fiction that we indulge in for the sake of our temporary convenience; a global description of the rhizome is not possible, either in time or in space; the rhizome justifies and encourages contradictions; if every one of its nodes can be connected with every other node, from every node we can reach all the other nodes, but
loops
can also occur; only local descriptions of the rhizome are possible; in a rhizomic structure without an outside, every perspective (every point of view on the rhizome) is always obtained from an internal point, and, as Rosenstiehl (1979) suggests, it is a short-sighted algorithm in the sense that every local description tends to be a mere hypothesis about the network as a whole. Within the rhizome, thinking means feeling one’s way, in other words,
by conjecture.

Naturally it is legitimate to inquire whether we are entitled to deduce this idea of an
open-ended
encyclopedia from a few allusions in Leibniz and an elegant metaphor in the
Encyclopédie,
or whether instead we are attributing to our ancestors ideas that were only developed considerably later. But the fact that, starting from the medieval dogmatics of the
Arbor Porphyriana
and by way of the last attempts at classification of the Renaissance, we slowly evolved toward an open-ended conception of knowledge, has its roots in the Copernican revolution. The model of the tree, in the sense of a supposedly closed catalogue, reflected the notion of an ordered and self-contained cosmos with a finite and unalterable number of concentric spheres. With the Copernican revolution the Earth was first moved to the periphery, encouraging changing perspectives on the universe, then the circular orbits of the planets became elliptical, putting yet another criterion of perfect symmetry in crisis, and finally—first at the dawn of the modern world, with Nicholas of Cusa’s idea of a universe with its center everywhere and its circumference nowhere, and then with Giordano Bruno’s vision of an infinity of worlds, the universe of knowledge too strives little by little to imitate the model of the planetary universe.

Whether or not this was the unconscious model for a new ideal of encyclopedic knowledge, it must be said that the first real efforts at creating semantic representations in encyclopedic form did not get underway until the second half of the twentieth century and only after a fierce debate regarding the shortcomings of any dictionary representation.
³³

Clearly, although the idea of the encyclopedia as postulate and ideal model is infinite, all that could be attempted were limited and
local
representations, which however did not exclude the possibility of their progressive and potentially limitless enrichment.

The new encyclopedic models assumed a number of formats, among them:

(i) Matrices representing the presence or absence of traits chosen ad hoc to account for the differences among items belonging to the same semantic subset, such as
chair, armchair, sofa,
etc. (cf. Pottier 1965).

(ii) Contextual selection models (specifying the various meanings a given lexeme may take on in different contexts) (cf. Eco 1975, 1984a).

(iii) Models by Cases that include Agents, Objects, Instruments, Purposes (the verb “to accuse,” for example, is defined as an action in which a human Agent communicates to a human Object by means of a verbal Instrument with the Purpose of revealing to him that the action of another human Object is evil; whereas “to criticize” is explained as the action of a human Agent who by means of a verbal Instrument speaks to a human Object with the Purpose of demonstrating that the action of another human Object is open to censure; or else the verb “to kill” is analyzed as the action of a human Agent which causes a change of state, from living to dead, of an animated X—further specifying, by the use of the English verb “to assassinate,” that the X in question must be a political figure) (cf. Fillmore 1968, 1969, 1977).

(iv) Representations that take into account, in the case, for instance, of a term like “water,” the properties that determine its extension or its referent (its being H
₂
O); labels of a quasi-dictionary variety, such as being Natural and Liquid; as well as stereotypical notions like Colorless, Transparent, Tasteless, Odorless, Thirst-Quenching (cf. Putnam 1975, 12).

(v) Representations that take into account all possible properties of a term and specify, for a chemical element for example, odor, color, natural state, atomic number, effects, history, etc. (cf. Neubauer and Petöfi 1981).

None of these proposals, however, had had recourse to network structures. It is in the field of artificial intelligence that frame-, script- or scenario-type representations appear, registering each stage of a sequence of typical events (for instance, what does “going out to a restaurant” mean: entering, sitting down at a table, ordering from the menu, eating, requesting the bill, etc.)—all models that have proved successful in the field of artificial intelligence, where, in order for a computer to understand a text and draw conclusions from it, it must first be provided with all of the competences with which (even without their being aware of it) the average human being is endowed (cf. Schank and Abelson 1977; Schank and Childers 1984).

But it is with Quillian (1968) that the notion of a
semantic network,
structured as a labyrinth of interconnected nodes, first appears. To simplify things, all we have to do is take another look at
Figure 1.17
. Any node can be taken as the point of departure or
type
of a series of other nodes
(tokens)
that define it (let’s say the point of departure is
dog
and that this node is defined by its links with
animal, quadruped, able to bark, faithful,
etc.). Each of the defining terms may in its turn become the
type
of another series of
tokens.
For instance,
animal
could be exemplified by
dog,
but also by
cat,
and would include
quadruped
but also
biped;
or, if a node
cat
were to be identified, it would be defined by a number of nodes it shared with the definition of
dog,
such as
animal
and
quadruped,
but it would also refer to nodes like
feline,
which it shares with
tiger,
and so on.

A network model implies the definition of every concept (represented by a term) through its interconnection with the universe of all the concepts that interpret it, each of them ready to become the concept interpreted by all the others.

If we were to expand the network of linked nodes ad infinitum, from a concept assumed as
type
it would be possible to retrace, from the center to the outermost periphery, the entire universe of the other concepts, each of which may in its turn become the center, thereby generating infinite peripheries.

Such a model is also susceptible of a two-dimensional graphic configuration when we examine a local portion of it (and in a computer simulation, in which the number of
tokens
chosen is limited, it is possible to give it a describable structure). But it is not in fact possible to represent it in all its complexity. It would have to be shown as a kind of polydimensional network, endowed with topological properties, in which the paths become longer or shorter, and every term gains in proximity with the others, by way of shortcuts and immediate contacts, while remaining at the same time linked to all the others according to historically mutable relationships.