Chapter III

The Hierarchy of Signs

CELLS, MATRICES AND FORMS

The foregoing analyses, which comprise a portion of an ongoing analysis of architectonic codes by the writer and others, have served to illustrate the evident fact that the question of signification in the built environment is a function of the level of organization of a code. We have thus far noted the existence of at least two major levels of signification, or two types of architectonic signs: the space-cell and matrices of cellular aggregation.

The space-cell comprises a fundamental meaningful unity in a code, a sign type which moreover achieves distinctive modifications depending upon its association with sequences of cells. In the case of the Minoan corpus, the individual cell types (labelled above (a,b,c)) occur both singly and in the a-b-c sequence comprising the so-called Hall System. In these two cases, each cell functions in a different manner—i.e., cell type (a) is differently significative according to its occurrence as a single item (or in other cellular aggregates) or as a component in the a-b-c system.

The space-cell^a enters into a variety of higher-level formations which are significative in various ways. Cells (in a corpus such as the two just looked at) aggregate into patterned sequences of cells or cell -matrices (such as a domestic hall-system). Larger units or structures may comprise separate buildings—i.e., sets of cells or matrices governed by controlled points of juncture or intersection, standing in opposition to other equivalent formations. Separate structures may (to continue our discussion in the context of the Minoan corpus) be either isolated or contiguous to other structures (sharing common mass-boundaries or party walls).

Above the level of the individual structure, characteristic formations may comprise neighborhoods of structures organized into patterned grids or blocks of varying types of configuration. Each corpus may exhibit one or more grid types with contrastive geometric configurations, often within the boundaries of a single urban fabric or settlement. Each corpus, and each settlement within a corpus, may reveal characteristic properties of formation including particular patterns of segregation of formative or functional types; neighborhoods may be walled off from each other (as in traditional Chinese or Peruvian cities; Hardoy, 1973, 380 ff.),¹ or may be distinguished on the basis of disjunctions in the size of structures, the existence of concentric barriers of structures of different function (residential, commercial, etc.), changes in grid orientation, size and manners of approach to individual units, height of structures, and so forth.

In short, the amount of variation above the level of the cell, matrix and structure may be very great both within a corpus and between corpora. In other words, architectonic codes are highly creative in terms of the amount of variation in the arrangement of significative units, even within the same settlement. Nevertheless, characteristic patterns of arrangement of units appear to occur for each code, and we may say that there evidently exist various kinds of rules of formation which prescribe formative organizations recognizable to members of a society as belonging to that code as permissable variations on a theme.

In certain cases, large-scale formative patterns may achieve canonical “idiomaticization” in a manner analogous to the rules of formation which prescribe the organization of the type of architectonic sign termed above a matrix^a of cells. A grid of streets is essentially a diagram of relational organization of structures and groups of structures (blocks, neighborhoods), a prescription of significantly-appropriate relationships.

In other words, the architectonic sign is an increasingly more abstract or diagrammatic entity the “higher” one goes “above” the level of the space-cell, consisting of sets of syntactic rules of combination of significative entities like cells or more or less “fixed” cell-patterns or matrices. If we take an “architectonic code” as meaning, among other things, sets of elemental units, relationships among those units, and rules governing relationships, then a code may be considered as storing certain kinds of information both overtly (as in the case of the range of permissable space-cells) and implicitly (as in the case of larger-scale entities such as matrices, structures, neighborhoods, grids, and so forth).

But there will most likely be a kind of overlap between overt and implicitly-coded information—as in the case of certain characteristic cell-matrices, which (to make a direct analogy with language) are partially reminiscent of idiomatic phrasings in speech. It would appear to be the case, as our Minoan and Egyptian examples illustrate, that idiomaticization is a characteristic feature of formative organization: it is the case both with a verbal idiom (“he blew his stack”) and an architectonic matrix (a Hall System) that the constitutive elements in each occur singly in other contexts with varying significance—“he blew his stack”: “he blew his nose” :: Minoan cell (a)+(b)+(c): (a) in another context (where it serves simply as a light well in any number of other contextual sequences).

What is “stored” as such in an architectonic code, then, are (1) entities which are directly significative, such as space-cells, which are associated with certain parameters of meaning or function, and (2) entities which comprise diagrams of interrelationship among significative elements—our matrices, structures, grids and so forth. It will be clear that “idiomaticization” or pattern-fixing may occur at various levels of organization above the level of the space-cell. In a given corpus, for example, matrices and structures may be more or less permanently “fixed” so that only one or two or several building-types recur constantly with a more or less fixed format. In some corpora, as for example the Minoan, the format of structures of residential function exhibit a wide degree of variation: no two Minoan houses are identical in formation.

The systematic collation of formations across corpora has barely begun, despite a plethora of impressionistic accounts, and we have a great deal to learn about the apparent “universality” of formative types. Nevertheless, architectonic universals only exist in code-specific situations, and are consequently subject to a wide range of contextual variation.

If it is in fact the case that the space-cell occupies a privileged position in a corpus by being coded or stored as such, what of its constituent “parts”? We are accustomed to consider cellular formations as made up of component entities such as walls, floors, ceilings, doors, stairwells, windows, and the like. But is it the case that the space-cell, as an architectonic sign, is “made up of” other signs?

We will be concerned here with several issues: first, the question of the singularity of reference of such entities; secondly, the question of the contrastive identity of these entities (i.e., do such entities all “blend into” one another or are they discrete elements in a code?); thirdly, with the relationship of such items with aspects of material realization and its evident variability; and fourthly, with the specific roles of such items in the definition and delimitation of space-cells themselves.

Clearly, these issues are closely interrelated and cannot be neatly separated, so that a conclusion proposed for one question will have important ramifications for each of the others.

Preliminary to a consideration of these issues is the question of the recognition and identity of subcellular entities. On this score there is a good deal of confusion introduced by the problem of the material variability of formations. Are a blue wall and a red wall which are formally identical on other counts (size, shape, material composition, position in a space-cell, etc.) in fact “different” entities?

The question cannot be answered properly outside the context of a given corpus. It may be the case that in corpus (Q) such a material difference is associated with different signata (e.g., contrasts in social status or function, aesthetic associations, etc.), whereas in corpus (Q’) no such significative difference is evident—i.e., the choice of wall coloration may be dependent upon arbitrary and dynamically-changing extra-architectonic factors.

It is evident that such significative distinctions as suggested for corpus (Q) comprise a realm of signification categorically different from that suggested above for formal (geometric) signification; we will return to this issue below.

In concert with our discussion above, it is proposed that an architectonic array achieves definition and identity by means of perceptually palpable disjunctions in formation (e.g., boundary conditions described, through edges, by changes in orientation and alignment within the array. It was suggested that disjunctions in formation will generally be considered as being correlative (in various senses, as is now apparent) to disjunctive contrasts in signification.

Subcellular entities achieve discriminative identity through contrastive opposition to other such entities. A wall is distinguished from a floor, or a doorway, on the basis of the presence or absence of certain features of formation. Thus, a given item such as (a) (below) contrasts with (b) on the basis of contrastive features of relative height, length and width. Indeed, it is clearly the case that such formations are distinguishable on the basis of the application to an array of a generalized analytic reference frame with three coordinate parameters so that in a general sense, (a): (b): : (h = 1 >> w): (h << 1 = w). (“>> “= very much greater than).

The situation is compounded, however, by the obvious fact that items such as either (a) or (b) may exhibit a great deal of variation in relative proportions, or at least apparently so. Thus, compare (a) and (a’) below:

Such a situation would appear to throw the issue of formative organization into the bottomless bin of non-discrete, gradient formation in which the analyst would seem to have to choose between admitting into a typology of formations a large set of form-classes with a few ranges of proportional variation in each, or a single set within which there occur a wide variety of gradient transformations.

But the problem is in fact one of focus and perspective, and it will be clear that we can speak of such “entities” in a very limited sense out of context.

If we understand such formations as being purposeful principally in the sense of their role as discriminators of space-cells, then much of the aforementioned problem dissolves, since it will be primarily their relational aspect as elements in an array which will distinguish them in a code. From such a perspective, variations in internal relative proportions within formations (a) and (b), including the kind of variation suggested by the last example ((a) vs. (a’)), will be patently secondary to their opposition to each other.

Consequently, a range or parameter of variation in items of the type (a) will be contrastively opposed to an equivalent situation in (b).

In other words, the significance of such subcellular entities lies in their opposition to other equivalent entities; as architectonic signs they have a principal function in discriminating one space-cell from another. They comprise, in effect, tools to make tools, the latter being directly significative, the former being indirectly significative (or rather significative in the sense of cueing perception of directly-significative formations).

Thus, in the following example, space-cells (A) and (B) are distinguished on the basis of a perceptually-palpable opposition between two subcellular entities (x) and (y):

Similarly, the following space-cells (C) and (D) are distinguished on the basis of another binary opposition, in this case between formations (v) and (w):

The space-cell is composed of sense-discriminative formations which as signs are primarily significative in terms of their contrastive oppositions to other such signs. In and of themselves, they lack singularity of reference; they are arbitrary, conventional, and code-specific units which are significant in terms of the architectonic code itself: they are systemically significant.

The situation, however, is complicated by the fact that in a given code, certain formal configurations may in fact have a singularity of reference in addition to their systemic function. This phenomenon, termed elsewhere by the writer sematectonic^a meaning, will be discussed below,²touching as it does on the important problem of architectonic symbolism. For the moment we are concerned with their primary role as systemic sign-formations.

We have now in a sense come full circle to the issue addressed at the beginning of Chapter 11 above, namely the question of the generalized array. It should now be apparent that the process of defining and identifying systemic signs in a particular code is an inevitable correlate of such a process.

We will make a stronger claim, however: namely that because of their role as discriminators of cellular formation, only those entities which participate in contrastive oppositions to other such entities in equivalent contexts will be admitted to the repertory of systemic signs in a given corpus. Such a criterion will allow us to differentiate systemic signs from their contextual variants.^a

A given item will be admitted as a constituent systemic unit in a given corpus insofar as it stands in opposition to other such units in a space-cell. Thus, item (a) below will be opposed to items (b), (c), (d), (e), etc.:

just as item (f) in the following will be successively opposed to (g) and (h):

The identity of systemic signs will be code-specific, and will provide us with yet another means for the comparison of architectonic corpora. In corpus (R), for example, the system of such signs may comprise the following:

which will contrast with that of corpus (R’):

The system of subcellular formations will vary from one corpus to another, often to a very great degree (note that we are not considering material variation, which will add yet another dimension of potential contrast). Some systems will be relatively “simple” in comparison with others—i.e., in the sense of having fewer systemic signs.

Clearly, however, there is no justification for distinguishing one corpus from another in a qualitative sense, if that distinction is based on the number of systemic items in a subcellular system (i.e., “simpler” systems are not more “primitive” than those which have a larger number of such units). It should be apparent that simplicity or complexity is a function of perspective on the code or the level of organization being addressed: code (S), with a relatively small number of systemic units, may exhibit a wide and rich range of contextual variation both materially and syntactically (i.e., in terms of the parameters of cell-matrix aggregation), while code (S’), with a relatively large number of such units, may exhibit fewer material and syntactic variations.³

Nor is there the slightest justification for equating formal simplicity or complexity with level of complexity of culture in general. This point has been made strongly and adequately by others in other areas of inquiry, and needs no additional comment here.⁴

The following chart illustrates the set of systemic forms established on the basis of contrastive oppositions observable in the exemplary corpus of formations discussed above.

Figure 4

The chart exhibits a number of salient features which deserve comment here. The first is that these units (let us henceforth refer to them as systemic forms)^a are specified materially as belonging to two distinctive classes (viz., those occurring as mass-formations, and those occurring in the corpus as spatial or volumnar formations). In addition, several forms occur both in space and in mass (D, E, G, H), depending upon their contextual position in a space-cell.

Secondly, the number of forms is quite limited, about a score. In other words, the number of forms is not wwlimited: the enormous variation in cellular and material formation in the corpus arises out of the interactive and contextual combination, reduplication, embedding, and transformation of these few units in the code. The productivity or creativity of an architectonic code, and its seemingly transfinite possible formations, rests upon the interactive relationship of such forms.

Two additional points are worthy of note in this regard. First, the rules of combination of forms are corpus-specific. Thus, the above corpus admits (1) below, but does not permit (2):

On the other hand, the corpus does not admit (3) above, but does permit (4). Evidently, a corpus will reveal, in its structural oppositions, certain asymmetries of realization: homologies which might be expected by the analyst may not form part of a given code.

Consequently an analysis will seek to establish not only what may occur (be realized) in a corpus, but also what it appears to forbid at a given time and place. In addition, it may be found that in certain contrastive oppositions, one term of the opposition may occur with great frequency whereas the other term may occur relatively rarely. Thus the latter may be seen as a highly “marked” formation in the sense that its occurrence is a special, or focused-upon event, calling attention to itself by its unusual occurrence. In the case of (3) above, it may be unattested as a formation because of the accidents of survival in the archaeological record. Should this be the case, then the latter type of marked-unmarked opposition would be present.

In other words, just as a corpus will specify certain formations as canonical or acceptable, it will proscribe others. There exist, in other words, semiotic constraints^a in an architectonic code.

The second point of interest, in a sense correlative to the previous, is the fact that not all possible ranges of formal variation will occur in a given corpus. This may be seen by referring to the chart in Figure 4 above, where, for example, form /C/ only occurs as a space-formation and not as a mass-formation; there will be corpora where the latter possibility is fulfilled.

Clearly, architectonic masses and spaces are in no way analogous to the sounds and silences of language, for example; architectonic spaces are not “empty” of signification (even though masses may carry more highly articulated information, this is not a “presence/absence” situation but a “more vs. less” situation). The system is highly marked and asymmetrical.

The point cannot be overly stressed that architectonic spaces are significant in systemic (and in some cases sematectonic) ways independently of the presence or absence of correlative lexico-semantic items in the language of members of a given society.

There may, however, be a salient homology between the architectonic and linguistic codes with respect to a trait of “alternative patterning,” comprising in the former the universally-employed framework of mass/space sequencing, and, in the latter, the consonantal/vocalic alternative sequencing (similarly universal) or “syllabic” framework.

This alternative patterning is realized differently in the two codes in the sense that in language it is unilinearly syntagmatic or sequential, whereas in architecture it is tridimensionally syntagmatic, involving both linear sequencing and consecutive embeddings.

The existence of the mass/space alternation in the architectonic code points up the evident fact that forms are themselves classifiable in terms of certain manifest features: the set of forms is thereby bifurcated into two subsets. In addition, it has been noted that several forms may function either spatially or massively, depending upon the cellular context and, consequently, upon their positional contiguity or separation from one another.

Note that in an architectonic system, a contiguity of two space-forms yields a larger space of compounded configuration: the contrast between two such forms, then, would appear to be “neutralized” and the forms merged or blended. While it is evidently the case that such a “neutralization” may remain unmarked in a given array, it is clear that corpora in general tend to preserve the contrastive opposition in some way—for example by distinctions in material articulation (framing of a doorway or window, for example, or with a variety of other articulations).⁵

The situation, in other words, tends toward the preservation of discrete oppositions where the syntagmatic patterning of forms is concerned, and this is noticeable not only in the case of alternative (mass/space) patterning, but also in the case of form sequencing involving juxtapositions of mass/mass or space/space. Once again it is important to recall that an architectonic code is addressed to the mechanisms of human visual perception, which serve to distinguish entities on the basis of formational disjunctions cued by boundary conditions (edges), contrastive oppositions in textural medium or in color, size, and so forth. An architectonic system uses any means at its disposal to get its messages across.

The existence of two overlapping subsets in the set of forms specific to our corpus raises the question as to the extent that we may be dealing with not merely a taxonomy of individual forms, but rather a system of forms.

In the list of forms given in Figure 4 above, it will be seen that such entities are distinguished from one another on the basis of their geometric properties. Thus, form /D/ is opposed to /E/ in the following way:

/D/: /E/ :: (h<< 1, w): (h, 1 >> w)

Similarly,

/A/: /B/ :: (h >> (1=w)): (h >> diam.)

Also,

/C/: /J/ :: (h=1=w): (1h:21:3w)

/C/: /I/ :: (h=1=w): ((h=1)< w)

and so forth.

In other words, the differences among forms in a system of forms comprise relative ratios in internal proportion, and all such units can be compared on a common set of tridimensional coordinates. In this way, the various forms specific to a corpus will be seen to occupy relative contrastive positions in a coordinate space. This, of course, is code-specific: not all contrasts may be significative in the same ways.

It would appear that we have two different ways of classifying forms— one, on the basis of their inherent or internal geometric features, and a second, on the basis of a bipartite categorization according to medium-type (not specific materials). The question arises, however, as to the extent to which the latter classification is ambiguous.

It has already been noted that the mass/space opposition appears to be related to certain properties of geometric formation itself—namely, some aspect of relative positioning of forms. Looked at in this manner, it will become evident that the media opposition is in some way secondary, for some forms occupy positions peripheral to others, while some occupy infixed or embedded positions within others. The following subsystems are revealed:

Some forms may be both peripheral and central, viz., /A/B/F/G/H/, while others may be both central and embedded, viz., /A/B/. The frame of reference of these relational terms, of course, is the space-cell itself.

In other words, it is the case that certain forms may have more than one distinguishing geometric feature. Thus, /A/ has a property of embeddedness, peripherality and centrality, whereas form /F/ has centrality and peripherality. /A/ is distinguished from /B/ in context /C/ in that only the former has centrality. This is illustrated in the following:

(The corpus manifests an asymmetry of realizations; even though /B/→ /c/ looks as thought it might be a simple homology to /A/ → /C/, it does not occur.)

Form /B/, however, does manifest a property of centrality, but only as infixed in forms /I/ and /J/, and then only when reduplicated (in which case it may alternate with /A/) .

The property of peripherality, however, is ambiguous, and we need to distinguish between lateral peripherality (right/left/front/back) and vertical peripherality (up/down), since the two properties will be associated with different forms.

Thus, /D/, /H/, IKI have a property of lateral peripherality, which serves to distinguish them from /E/, /F/, /G/, and /L/. In the case of /L/, however, any contrast between the axes of lateral peripherality (right/left/front/back) is in a sense “neutralized”; /L/ is consequently one single surface. With form /M/, however, a further degree of “neutralization” occurs: /M/ = /L/ minus one vertical peripheral axis (up or “above”).

It will be evident that the sextuply-contrastive “axes” referred to here are isomorphic to the generalized frame of reference employed here and elsewhere, as well as to the tripartite binary contrastive axes of the human form, conceived as projecting, through its bilateral symmetries and contrasts, “front” vs. “back,” “right” vs. “left,” “above” vs. “below,” and, generically, “center” vs. “periphery.” Of these contrastive somatic axes, only “right” and “left” are mirror-reversals; in the other cases, the two terms of the opposition are formatively different.

This situation has many cultural resonances, notably in the culture-specific semantic “weightings” or markings given the various opposed terms (cf. the generically positive weighting of up/above, front, and right vs. the negative weighting of down/below, back, and left in many societies).

Ultimately, it would seem, both our generalized reference frame and, perhaps, the generic structure of the components of built environments themselves are founded on palpable constancies of human somatotopy^a.⁶ It may be tempting to regard the structure of the architectonic code, in its fundamental “logic,” as a generalization of the inherent relationships of the human body as an instrument in the measurement of the world.

Such would hold whether or not corpora were predominantly rectilinear or curvilinear in realization, for obvious transformational reasons. It might appear to be the case that there is an inherent “six-sidedness” in our (geometric) perception of objects of any kind (i.e., a tripartite set of binary contrasts), if we were to follow the suggestions of G. A. Miller and P. N. Johnson-Laird (1976) in their recent provocative study.⁷

But of course such a geometric logic of formation is necessarily equilibrated in the mature adult, as studies by Piaget and many others have demonstrated, with topological and perspectival reference systems in perception.⁸ The three sets of spatial concepts appear to be acquired sequentially in early childhood (topological, perspectival, geometric).

Hence it is evident that a space-cell is to be understood as a complex formation in three space-manifolds:^a (1) as a topological ‘unicum’ or bounded region with some kind of closure; (2) as a projective or perspectival array with projected and contrasted planes or surfaces relative to a (shiftable) centrality; (3) and as a geometric formation with inherent tripartite binary contrasts as specified above. Necessarily, since it is the case even in predominantly “curvilinear” corpora that objects are aligned and oriented relative to each other as well as internally, we would be justified in speaking of a perceptual “neutralization” of certain geometric distinctions or disjunctions.⁹

The result is a concise and systematic picture of the organization of architectonic forms as composed of bundles of relationally-defined features whose function is to discriminate one form from another.

The nature of the architectonic form, then, is not that of a primitive or ultimate constituent in a code, but of a formal systemic unit itself composed of simultaneously-occurring distinctive features. Each form manifests two or more such relational features.

In a sense this situation is analogous to that obtaining in the relationship between forms and space-cells, wherein forms have a systemic significance in distinguishing cells from each other: geometric features^a are similarly significant in a systemic sense in serving to distinguish one form from another.

In contrast to forms, which occur (except for situations of “neutralization” described above) in contiguity and tridimensional sequence, distinctive features occur simultaneously, serving, in their interactive copresence, to define and delimit individual forms with respect to one another. The situation is apparently homologous to that in language codes, wherein phonemic units occur on a sequential or syntagmatic axis, or axis of copresent combinations, while the bundles of distinctive features (which as signs serve to distinguish one phoneme from another) occupy a paradigmatic axis, or axis of simultaneity.

The system of distinctive features in the architectonic code reveals a series of increasingly finer distinctions. Thus, the system exhibits a contrast between what we may term “inherent” and “compositional” features. The former involves “internal” relationships of forms, whereas the latter involve “external” relationships between forms (within the overall framework of the cell). Bifurcating both subsystems is the distinction between mass and space realization: several forms (/D/E/F/G/H/) have alternative realization depending on context. Form /G/ may be realized spatially (as a central-infixing in peripheral form /E/) or massively (as a central-embedding in itself-in-space).

Consequently, each form comprises a bundle of at least two features. Geometric features, as noted above, serve principally to discriminate architectonic forms, and are thereby systemically significant. They are, in other words, sense-discriminative in nature (as are forms themselves with respect to cells) .

This situation is compounded by the fact that in certain instances both forms and features may simultaneously serve in a sense-determinative^a fashion—i.e., with singularity of denotation^a(vs. their other role in “double articulation”). Forms /G/ and /H/, for example, are not only systemically significant, they are also metonymically indicative of juncture or connection or intersection between cells. Others (e.g., /D/, /F/, as spatially-realized) signify visual connectivity among cells.

Note that a necessary property common to all these forms is peripherality. Hence, from a feature point of view, peripherality is singularly denotative of juncture or intersection. But different peripheral forms provide distinctive information. For example, /E/ provides information about intersection with another or other cells, but is not indicative of connection (only contiguity). /E/ with /G/ infixed provides information about both contiguity and connectivity. Some corpora will provide a further distinction between a form of the type /G/ → /E/ which provides information about connectivity within a structure in contrast to connectivity between structures, and so forth. In such a case, the latter may not be distinctive formally but rather materially (as when a doorway is heavily articulated in outline).¹⁰

Singularity of denotation among systemic signs such as forms and features, what we termed before “sematectonic” signification, involves a number of different functions.

For example, a feature may function con figuratively in signalling divisions of a formation into formal units of varying complexity. Peripherality, then, is both systemic and configurative.

A form may function redundantly, as when it focuses upon another distinct form so as to enhance or augment its occurrence (for example the use of engaged columns adjacent to a certain doorway in a structure, contrasting with other doorways without engaged columns, or doorways with smaller engaged columns, etc.; in such a case, the form serves to enhance the perceptual attention to that door). A feature may function redundantly in the case of the aforementioned, where a given formation is augmented or perceptually enhanced by a scalar emphasis on one or more dimensions (e.g., the doorway is taller than the others, or wider, or deeper).

Forms and features may also be used expressively in exhibiting the “trademark” of a certain builder through certain distortions of scale, etc., or in the emphasis of certain significative formations at the expense of the diminution of others.

In contrast to systemic significance, sematectonic significance (particularly with respect to its expressive functions) is not necessarily organized in binary fashion but may be scalar or graded in some way such that distinctions in expressive content are associated or correlated with gradations in formation.

The functions listed above clearly do not exhaust the possibilities (see below, Chapter IV); they are intended to be illustrative of some of the multiplicity of functions exhibited by architectonic signs. The nature of architectonic semiosis is only beginning to be understood in a systematic way, and an enormous amount of work on large bodies of synchronic data awaits our attention.

Before passing on to our final, concluding section, another point regarding architectonic distinctive features is worthy of comment. It may in fact be the case that a comparison with language here is even more apt than suggested above, for it is becoming apparent that both the existence and internal ordering of the system of distinctive features finds independent confirmation in certain behavioral properties of the human perceptual system, particularly regarding the manner whereby the child gradually comes to assimilate and acquire spatial and object concepts. Work in perceptual and cognitive psychology in recent years has found increasing evidence for the sequential acquisition of various classes of spatial features which achieve systematic and equilibrated relative oppositions in the architectonic code.¹¹

In other words, what is distinguished in the set of copresent features in the code is acquired separately, in tandem.

Understanding of the relationship between the acquisition of architectonic and linguistic distinctive features is still largely in its infancy. But there is some indication of homologous processes in the acquisition of features of both codes; it is not clear to what extent it may be possible to speak of equivalent formations in both systems. Certainly the latter is not required by the theory of architectonic systems elaborated here.

Our primary point here is that just as the existence of the code-specific system of linguistic distinctive features,—proposed by N. Troubetzkoy to, and brought to its full picture by R. Jakobson and others (Jakobson and Waugh, 1978)¹²—is confirmed by the study of language acquisition in children (and its reversed, piecemeal formational loss through aphasia), so the existence of the system of architectonic features may now find independent confirmation in comparable study of spatial and object concept-acquisition and representation.

For a fuller discussion of this complicated issue the reader is referred to the work of Bower, and Moore (1976) confirming the acquisition of “compositional” features of object-arrays separately and prior to the acquisition of internal or “inherent” features of forms themselves; and the studies by J. Goodnow and others (Goodnow, 1977) indicating that children, in acquiring drawing skills, progress through the assimilation of one feature to another, incorporating and equilibrating features into a systematic whole.¹³

Our description of architectonic forms has focused principally on geometric or tridimensional signs. Generations of analysts have been accustomed to speak of surfaces, planes, facades, elevations, and so forth, as significant formations in their own right. The question which arises here concerns the systemic position of such “entities” in the system of formations elaborated here.

The question is pertinent in the present framework for it would appear to be the case that in some sense, planes or surfaces “coexist” with (tridimensional) forms as similarly serving to discriminate one space-cell from another, or one matrix or structure from others. Looked at from this perspective, it seems to be the case that cellular forms can be simultaneously two-dimensional planes and near surfaces of three-dimensional forms (or sets of forms).

Consider that the interior “surface” of a rectilinear cell consists of six planes, corresponding to the set of six planar intersections of the binary-contrasted axes of front vs. back, right vs. left, and top vs. bottom; in other words:

Consider further that such planes are copresent with the tridimensional forms which serve to distinguish one cell from another, and that in fact they provide additional information (or, rather, information of a different kind) regarding such discriminations not provided by the set of forms —namely, perspectival and directional position.

Forms /D/ and /E/, for example, carry only configurative or geometric information, and are not specified in terms of their direction or orientation. That is, /D/ is unspecified as to whether it occupies either the “top” or “bottom” of a cell space (i.e., of central form /C/, etc.), it is only specified as to its generic vertical peripherality. Is it necessary, then, to propose the existence of two /D/s? Or to propose, by analogy, four /E/s? Clearly not, since we are concerned principally with geometric or formal information.

Conversely, a plane^a can be conceived as carrying no unambiguous specific information regarding the kinds of/orw-relationships evident, say, in the following:

where one or more forms are relationally-embedded in another one. Here we are dealing with two different forms; from a planar perspective, however, such compound formations are identical or equivalent. On the other hand, in the following case:

we are dealing with three different planes but three identical forms.

In addition, it will be the case that planes are not necessarily coterminous with single peripheral forms, as in the case of a uniform facade of a multicellular structure:¹⁴

Hence it is clear that with planes and forms we are dealing with two different perspectives on cellular and architectonic formation, both of which may be seen as contributing to the sense-discrimination of cells, and of cell-aggregates (matrices, structures, etc.). It will be evident that planes also serve sense-determinative roles in a code—as, for example in corpora where different types of facades are indicative of differently-functional aggregations of cells: e.g., highly articulated planar facades = public buildings, etc.

It appears to be the case that planes and forms, as signs, carry partly-complementary and partly-redundant systemic information regarding the distinction of one cell from another. If we picture the various perspectives on significant formations in an architectonic code as outlined above (viz., features, forms, cells, matrices, etc.), as hierarchical “levels” of organization, then a planar perspective cannot be admitted into such a conceptual space “between,” say, features and forms, or “between” forms and cells, but must be admitted as a “parallel” level of organization to that of forms. In other words,

(1) ....................features

(2) ............ forms........planes

(3) ............(alt. patterning)

(4) ....................cells

(5) .................matrices

(6) ..................structures

(n) ......................(etc.)

It need not be emphasized that just as forms are code-specific in their detailed properties or features, so also will planes be specific to a given corpus. Corpus (T), with a rectilinear organization, may distinguish planar formation by means of a sextuple system of features, whereas corpus (T’), with a curvilinear organization, may distinguish planar formation by means of a binary system of features, as suggested by the following:

From the point of view of corpus (T), however, corpus (T’) may be said to manifest a “neutralization” of portions of a six-fold distinctive contrast (and vice-versa).

Many corpora are, from this point of view, “mixed”—for example the Minoan, with sextuple, ternary’and binary subsystems of planar formation:

If the forms of a code are organized into a system on the basis of composite realization of bundles of features, then it will be evident that planes similarly reveal a parallel and complementary system of features:

Consequently, the system of features defining forms is modified from what was presented above to the following:

which, moreover, is in line with our initial proposals. It will be clear that our “finer distinctions” (see above) properly belong to the system of planar features.

Hence our portrayal of the various “levels” of organization of the significant formations of a code will be modified on the first two “levels”:

Regarding the situation where a plane serves to define and delimit an aggregate of cells, as in a uniform “facade” of a structure:

from the perspective elaborated here such a situation may be seen as a process of neutralization of the following:

Architectonic systems, as noted above in another context, tend toward the preservation of contrastive oppositions in a variety of ways—indeed, in any way possible—so that it will normally be the case that cellular discriminations are cued in some way, whether through material articulation:

which in various ways will either (or also) be signalled by the presence of peripheral/embedded

forms:

The latter situation appears to be generally the case in corpora, whereas situations where a single, blank plane serves to define an entire cell-aggregate vertically-stacked tend to be rarer (and hence, in a given corpus, perhaps more highly “marked”).

In a parallel fashion, it is necessary to incorporate the third space-manifold into our picture of formal organization, namely topological features. Once again, the notion of the space-cell as a topological unicum has been implicit in our description from the outset (see above, Chapter 11). From a topological point of view, the cell is defined as a formation with a property of boundedness; it is, in other words, a domain. Our picture of the organization of an architectonic code necessarily requires the incorporation of topological signs, which serve a sense-discriminative function vis-a-vis cells. As an entity in the code, domain is itself composed of copresent features which serve to distinguish domains.

Topologically, we recognize the existence of binary contrastive oppositions between boundedness vs. unboundedness, and inside vs. outside, both (again) relative terms.

Similar to the situation of planes above, boundary conditions may delimit or distinguish cells, matrices (as with functionally-distinct “zones” of a structure), neighborhoods and settlements. An entire settlement may comprise a topological unicum in contrast to other settlements; once again we may conceive of such a unicum as resulting from various kinds of neutralization of multiple bounded unicums, parallel to the processes described above for forms and planes.

From a topological perspective, distinctions in either planar or formal formation become neutralized or non-relevant, just as from a planar perspective various disjunctions inform will be non-relevant.

Such a picture is in accord with the general notion of invariance behind variability, or relational invariance, seen above as constituting one of the fundamental principles of architectonic organization.

The resultant picture of the organization of the architectonic code, if that is portrayed by means of “levels,” is as follows:

It will be clear that the multidimensional nature of built environments requires a multiple contribution to the definition of cells and other directly significant formations or patterns of formation, a situation in obvious and necessary contrast to what obtains in other semiotic systems (e.g., language and language-based codes). Once again, the nature of the processes of perceptual address, and their resultant mechanisms, serve to contrast architectonic and linguistic semiosis.

A word of caution is required here regarding the nature of the representation of architectonic organization biased by the limitations of the written word. It cannot be emphasized strongly enough that we are dealing here with a multidimensional, relational organization which is not reducible to the graphic “levels” in the model shown above. Such “levels” should not be taken too literally as hard-and-fast and strongly-disjunctive plateaux in a hierarchy. We are dealing in fact with a variety of different perspectives on synchronous objects such that the identity and delimitation of any one “entity” is modified by the copresence of all others in a network of relations, in the variety of ways suggested in our account. This has been implicit from the outset of our discussion. It should be clear also that the nature of architectonic signification is itself highly complex and multidimensional: our example of the Minoan Hall System has suggested that a complex architectonic sign is a composite realization of a variety of significant formations whose code-specific interrelationships do not at all resemble an aggregate of building blocks, but rather describe a multidimensional semantic domain whose “component parts” are drawn from a highly disparate set of entities, some of which are redundant, complementary, and even in certain instances contradictory.

Moreover, such a formation is itself a modal component in a multimodal behavioral situation whose various component formations are interactively equilibrated in extremely complex ways, beyond our present abilities to characterize systematically. Although any semiotic system has its own coherences and internally-consistent (albeit asymmetrical and highly marked) formations, in daily life everything is intertwined like galaxies passing through each other: what we weave in the ordering of our dynamically-unfolding personal and societal realities is composed of highly disparate and continually changing materials, and we are continually changing instruments, sometimes using one alone, but mostly balancing several in parallel or in tandem. What is begun in one thread (language) is completed in another (spatial relations), only to be modified by other considerations at a moment’s notice.¹⁶ A boundary between two settlements may be a city wall or a piece of legislation, a disjunction in building materials or in dialect, a river or a proscription on who may marry whom, a difference in religion or a railway line.