Appendix B
The Network of Architectonic Signs

The apparent ‘duality’ of structure observed in the text—the ‘disjunction’ between ‘formal’ and ‘material’ structure in the architectonic code—is an artifact of our initial analytic stance, which focused sequentially upon the geometric and material invariants in the corpus examined. It does not correspond to a ‘duality of structure’ intrinsic to the network of signs itself.

Indeed, it has been implicit in our analyses of the invariant formal geometric properties of the matrix of cells comprising the ‘Minoan Hall System’ that a full picture of its organization necessarily incorporates certain invariant relationships among ‘material’ entities as well. Any given matrix is a tridimensionally-syntagmatic aggregation of cells, mass and space forms, certain materials in characteristic compositional relationships, patterns of color and texture, as well as relative size ratios among all of these entities. The organization of any such formation thus involves the syntagmatic copresence of a wide variety of sign types as these are defined by a given code.

In our analyses we made a case for the existence of two types of architectonic signs: those with direct signification and those whose signification was indirect or systemic. We also pointed to the evident fact that under certain conditions indirectly-significant signs may exhibit a tendency toward direct (sematectonic) signification. The same features employed as distinctive (sense-discriminative) in a given code may, under certain conditions, and for certain users, function in a directly-significative (sense-determinative) fashion: recall our discussion in Chapter II regarding distinctive, redundant, configurative, and expressive features.

The question is thereby raised concerning the nature of the minimal directly-significative signs in the architectonic code. We have noted that the ‘largest’ directly-significative sign encoded as much in the system is the cell (and we saw that ‘above’ the ‘level’ of the cell, signantia comprise patterns of syntagmatic aggregation—matrices, structures, settlements, etc.). What, then, are the ‘smallest’ or minimal sense-determinative sign units in a code?

The answer, from the point of view of the signans, is necessarily multiple: the minimally-(directly) significative units in the code may be features or bundles of features (forms), both of a ‘formal’ (geometric) or ‘material’ nature. Moreover, some such features may themselves also function in sense-discriminative ways. In other words, certain features may function, in a given code, in a sense-discriminative manner, while some of these, plus other features (i.e., redundant, configurative and expressive), will function in sense-determinative ways. The same will hold for forms (syntagmatically-simultaneous clusters of features).

We shall term such minimal signs figures, and note that their signantia may be quite various: geometric relationships or conformations, patterned relationships among spatial features, colors, textures, relationships of size and scale, as well as syntagmatic clusters of any of these.

Considered in this fashion, the figure, as the minimal directly-significative sign unit in the code, may be seen as systemically or operationally equivalent to the linguistic ‘morpheme’ if the latter is considered as a relational (rather than atomistic) entity.

It becomes increasingly evident that the architectonic and linguistic codes share correlativities of systemic organization at fundamental levels—that, in other words, they operate systemically according to equivalent design principles. This correlativity, which extends to the concept of ‘double articulation’—and, to a remarkable extent, to the dynamically patterned network or hierarchy of signs themselves—is based upon a relational rather than atomistic or formalistic picture of both codes. In other words, it is only through a consideration of either code as a system of relationships, in which meaningfulness implicates every level of organization, that such correlativities of design become patent. Moreover, it has become clear in our study that ‘form’ does not exist apart from ‘content’: both the built environment and verbal language are systems of signs at all scales of organization.

In the architectonic code there exists another structural design feature which is closely paralleled in verbal language. This is the syntagmatically-sequential arrangement of forms and form-clusters alternatively manifesting mass and space features. In other words, there exists an alternative patterning of mass and space forms, a necessary concomitant of the nature of an array’s sensory address. This property is patently correlative to the syntagmatic structural template involving the alternation of ‘consonantal’ and ‘vocalic’ phonemes or phoneme-clusters in language. This syllabic matrix upon which phonemes are necessarily arranged is a concomitant of the nature of acoustic perception. In both codes, this patterning is sense-discriminative in nature.

In the built environment, alternative patterning is considerably more complex, being tridimensionally (and spatiotemporally) syntagmatic, whereas in language alternative patterning is necessarily unilinear and temporal. In both cases, this structural property is a function of the mechanisms of sensory address, wherein disjunctions and gradiencies of formation exist as cues for the perception of distinctions in meaning.

While it is with a good deal of sensitivity and delicacy that any sketch of specific parallelisms among codes should be made, the results of our study, augmented by ongoing analyses parallel and subsequent to the present text, indicate forcefully that the architectonic and linguistic codes are designed along correlative lines. This is by no means to claim, however, that one is simply a cross-modal transform of the other, nor is it to assert that they are completely parallel codes in distinct media (see our remarks above in Appendix A).

The revealed correlativities of formative process, moreover, are not due to a derivative or genaeological relationship between the two systems, wherein either serves, phylogenetically or ontogenetically, as the model for the other: the architectonic code is no more built upon language than language is built upon architecture. Neither is a ‘secondary modelling system’ with respect to the other. Claims to this effect (in either direction) cannot be substantiated, nor forced by rhetorical fiat.

While it is patent that some semiotic systems in culture may in fact be deponent with respect to another or others, language and the built environment are panhuman sign systems which have evolved in close concert with each other from early palaeolithic times. Direct architectonic evidence—viz., evidence for architectonic formations essentially identical to our own—is at least a third of a million years old. While it remains unclear to what extent verbal language as we currently have it formed a necessary component of such environments, it is a reasonable assumption that the linguistic code in something like its known form should have been copresent. For a variety of reasons, each is unthinkable without the other, and it is patent that each is designed to operate in deictic and multimodal concert with the other.

At any rate, we should be wary of confusing their operant, profound and necessary interpermeability with genaeological evidence in either direction. Indeed, any equivalencies of organization are principally due to a shared semiotic and cognitive base in which each is deeply grounded.

* * * *

The foregoing observations, taken together with the results of our analyses in the text, suggest the following picture of the structure of the network of architectonic signs, as well as their systemic correlates in the hierarchical network of linguistic signs. What is presented below is a provisional sketch of such relationships seen by the writer as this book goes to press. Moreover, it should be borne in mind that the following chart is in part an artifact of the printed text: the relationships portrayed exist as figures in a complexly-multidimensional conceptual space. The ‘levels’ sketched represent in fact different perspectives on semiotic formation, and their edges are not as hard and fast as the diagram might suggest. The diagram attempts to portray the set of invariant relationships among entities in the code which have characteristic systemic functions, rather than a set of objects. Clearly, an architectonic figure in no way resembles a linguistic ‘morpheme’: but a figure bears a correlative relationship to other sign types in its code in the same systemic manner that a linguistic morpheme does in its. It is this nexus of relationships which the diagram below attempts, clumsily, to portray. The signs in any given code are a function of the systemic properties of the code as a whole: a code is not built up of signs any more than a house is built of bricks.

KEY TO DIAGRAM

A: Minimal sense-discriminative units, encoded as paradigmatic binary oppositions

B: Encoded as syntagmatically-simultaneous clusters of (A)

C: Maximal sense-discriminative units, encoded as syntagmatically-sequential arrays of (B), patterned alternations of (B) manifesting mass (consonantal) and space (vocalic) distinctive features

D: Minimal sense-determinative units, comprising one or more of (A), (B), or (C), either singly, simultaneously, or sequentially

E: Maximal sense-determinative units encoded as such in a system, comprising one or more of (D)

F: Minimal patterns of aggregation of sense-determinative units, comprising one or more of (E)

n: Maximal patterns of aggregation, comprising one or more of (F)

NOTE: the ‘boundary’ between sense-determinative units and patterns of aggregation of sense-determinative units is soft, and there may be considerable overlap between codal entities (E) and (F) in particular codes and contexts.