Boundaries, scale, and internal organization

JOURNAL

OF ANTHROPOLOGICAL

Boundaries,

2, 32-56 (19831

ARCHAEOLOGY

Scale, and internal

Organization’

STEPHEN A. KOWALEWSKI Department

of Anthropology,

University

of Georgia,

Athens,

Georgia

30602

RICHARD E. BLANTON Department

of Sociology and Anthropology, West Lafayette, Indiana

Purdue 47907

University,

Bloomsburg 17815

State

GARY FEINMAN" Department

of Philosophy and Anthropology, Bloomsburg, Pennsylvania

College,

AND LAURA FINSTEN Department

of Anthropology,

McMaster

University,

Hamilton,

Ontario,

Canada

Received September 1, 1982 The abstract systems properties of size, centralization, and boundary permeability are related in a theoretical model, wherein size and permeability are positively associated and these two properties are in turn negatively associated with centralization. The model is tested with regional archaeological survey data for 1500 B.C.-A.D. 1520 from the Valley of Oaxaca, Mexico. The results point out the conditions under which the model does and does not hold in the cultural evolution of this complex society. 1 We are grateful for the support given to the Valley of Oaxaca Settlement Pattern Project by the National Science Foundation, the City University of New York, Purdue University, the University of Arizona, the University of Georgia, and Arizona State University. Authority to carry out fieldwork and valuable assistance were granted by the Instituto National de Antropologla e Historia and the Centro Regional de Oaxaca, directed by Manuel Esparza and Rogelio Gonzalez. We thank the many members of our field and lab crews, and the Oaxacans whose land we walked over. Gregory Johnson, Scott Kleiner, David Hally, Charles Hudson, Arthur Murphy, Jackie Saindon, the editor, and two unusually helpful anonymous reviewers made valuable suggestions and criticisms of the several drafts of this manuscript, for which we are grateful, though we and not they are responsible for any errors. We also thank Linda Adams for typing the manuscript and Gisela Weis and Patricia DePratter for drawing the figures. * Present address: Department of Anthropology, University of Wisconsin, Madison, Wisconsin 53706. 32 0278-4165183 $3.00 CopYright 0 1983 by Academic Press. Inc. All rights of reproduction in any form reserved.

BOUNDARIES,

SCALE,

AND

INTERNAL

ORGANIZATION

33

If archaeologists were polled about which was their favorite ethnography, one that would probably come out near the top would be Edmund Leach’s Political Systems of Highland Burma (1954). Why this should be may not be obvious. The book has little to say about material culture and the theory is neither emphatically ecological nor economic, though there are thought-provoking implications for all those things and the materialism that Leach espoused at the time is comfortable enough. For the data-thirsty there are only a couple of sketchy maps and a few brief tables. But the attraction lies in the dynamic approach. Nothing-not a person’s community, status, culture, or even language--is assumed to stay the same, and everything has to be explained. Leach convinces us that there is no way to understand social structure without observing it over time. He is saying that anthropologists are, as in Heraclitus’s famous example, unable to step in the same river twice (one Heraclitic fragment says “we both step and do not step in the same rivers; we both are and are not.” (Barnes 1979:66)). Not being able to step in the same river twice and having to explain the existence of community or society instead of assuming them from the beginning are stringent requirements. We have to know not only how our people interacted, but what the limits of their interaction were in space and time, and why this network was limited to a particular size and duration. Our paper attempts to chart some of this flux, using the archaeology of the Valley of Oaxaca in southern Mexico. On one interpretive level we find fields of past interaction or organization and their boundaries in space and time. These fields of interaction were the ancient Valley of Oaxaca society (or societies). On another level we ask how some of the basic properties of these societies, as living systems, were related to each other. Specifically, was there any relation between how big the society was, how it was organized internally, and how open or closed it was to the outside? Given Leach’s point of view, one must be prepared for the possibility that all these things are subject to change-the society, the ways we have to measure and identify it, and even the “timeless’ relationship between general systems properties. And in the Valley of Oaxaca, they all did change, It may reasonably be objected that alteration of one’s measurements in midstream is a violation of proper method. In diachronic studies sensitive indices may simply disappear during a sequence, or take on a different meaning. The observer must then find another measure for the theoretical entity in question and justify that the new measure is essentially equivalent. As an example, imagine trying to map the boundaries of social territories as they change from preceramic to ceramic times. Projectile points might be used to define style zones for the first part of the sequence, but their frequency might be too low to be useful later on. Pottery

34

KOWALEWSKI

ET AL.

styles would be an obvious choice for territorial marking in ceramic times. But the possibility that point and pot styles functioned as boundary markers in the same way is not at all assured. A great deal can be learned from asking exactly what information such different stylistic channels convey, whether or not it turns out that the two are equivalent measures of social territories. The methodological issue of equivalent significance is difficult, but it is faced continually in many guises by researchers who observe events happening over time. The first section of the paper gives a few definitions and the background to the research. In the succeeding sections a theoretical model is developed and then evaluated with archaeological data from the Valley of Oaxaca, Mexico. Apart from method, there are three ways in which our present study may have potential significance. One is purely theoretical, emphasizing whether the abstract model we develop has a degree of heuristic or explanatory power anywhere in the world or at any time. At the opposite extreme, this study may be considered of value mainly for its exposition of certain characteristics in the cultural sequence of the Valley of Oaxaca. Our own objectives and preferences in this analysis lie between these two poles. We do not stress universal, lawlike relationships or a model for its own sake, but formulation and application of a set of theoretically interesting relationships to diachronic data. In the process one learns more about both theory and a particular sequence. THEORETICAL

EXPECTATIONS

Definitions. Before going any further, let us set out the necessary definitions to avoid terminological muddle, or at least to have the muddle be our own. By system we mean a set of interacting components. In this discussion we are specifically referring to concrete systems (Miller 1978:17) whose parts are physically real, distinguishable, and located in space and time. Examples of concrete systems are the households, barrios, communities, and regions of Flannery’s The Early Mesoamerican Village (1976), not the systems of variables constructed by the modelers of, for one famous case, the Classic Maya collapse (Hosler et al., 1977). The regional system is the total social system at the level of interacting communities. Interactions more often than not begin and end within the set of communities, hence the set of communities and the relationships between them constitute “the system.” Size of a system means the number of interacting parts. One must be careful to specify the type of interaction and the scale of the components. The size of the Iroquois confederacy (Morgan 1962) as a political organization was not the total population, but rather 5, the number of tribes

BOUNDARIES,

SCALE,

AND

INTERNAL

ORGANIZATION

35

making up the League. Size of the Iroquoian society might be measured by number of clans, or population as an approximation of participating members. In some instances spatial size might be pertinent, since the energy required for interactions increases with the distance between parts. Integration is the interdependence or interconnectedness between parts. A distinction can be made between interconnections and interdependence or interaction. The former refers to paths or linkages in a graph theoretic sense. It is proper to conceive of integration qua interconnectedness as the number of linkages between system components expressed as a proportion of the (finite) total possible. However, behavioral systems are unlike graphs and corporate organization charts because the actualization of potential links may be quite different from the form of the organization. Hence the second aspect of the distinction. Interdependence refers to the total amount of flow of matter, energy, or information between system components. Systems of similar size can then be compared vis-a-vis their amounts of flow between components. In settlement pattern studies it is usually easier to infer flow and interdependence than formal interconnectedness. In other realms, perhaps administrative hierarchies, it may be useful to consider interconnectedness as integration. The aspect of internal organization of interest to us here is centralization, defined as the relative amount of flow that is accounted for by a single node. Notice that centralization is not the same as integration. This point is very important, especially for studies of social evolution, but it is often overlooked. Integration is the relative amount of interconnectness or amount of interdependence. A system may be highly integrated but not exceptionally centralized (think of a tropical forest ecosystem); and a highly centralized system may be almost minimally integrated in the sense of connections (draw some dots on a piece of paper-the minimum number of lines that can connect them is the same n-l as the number of connecting lines in the most centralized arrangement). The crux is whether all paths lead to one door. Or in our case below, the proportion of the flows in the system accounted for by the leading center is considered the degree of centralization. This fairly strict definition of centralization may be helpful for anthropologists studying the evolution of hierarchical political systems, since it allows a clean separation of decision making in one place from decision making carried out at a variety of nodes in a conceivably more complex hierarchy. The permeability of a system’s boundary may vary from relatively closed to open and refers to the proportion of interaction that begins within the system and ends outside, or begins outside and ends within. Another way of saying this is that permeability is the proportion of flow (energy, materials, people, genes, information) across a system’s geo-

36

KOWALEWSKI

ET AL.

graphical limit. The direction of flow and the implication of amounts greater in one direction than another is an interesting topic. But directionality is beyond our present scope and we do not explicitly deal with it. The term “well-defined system” is sometimes used, especially in ranksize studies (see below), but as a technical concept it is vague, and in the social science literature it rarely refers to a system that has indeed been well defined by empirical observation. It is not hard to imagine situations in which a great deal of activity takes place on the edge of a system, but little actually flows across. Think of John Wayne’s camp preparing to defend itself against the enemy attack. Each side prepares itself, but not much goes back and forth between the two sides unless you count the “too quiet” stillness after the drums stop. Archaeologists in particular may need to speak of relative amounts of energy expenditure in frontier or boundary areas when they cannot observe or infer the amount of flow that actually crossed the boundary. For this situation we use the term boundary activity, which, though it does not specify very much, at least does not mislead. For an example, on the Ucayalli River of Amazonia, activity at the Last Shipibo-Conibo village before the tribal buffer zone was fairly high (DeBoer 1981:Fig. l), judging from its unusually large population. On the face of it one could not know whether this was an exceptionally large village because of considerable boundary permeability or because a large number of people were required to ensure closure. Previous research. Relationships between system size and complexity or integration were already well enough known in the nineteenth century for Herbert Spencer, hardly a leading-edge theoretician, to discuss the principles at length as they applied to biology and sociology (1895- 1897). Little argument is ever made over the fact that increasing scale is accompanied by increasingly complex organization (e.g., Barth 1978; Carneiro 1962, 1967; Gould 1978; Whyte 1977; McNab 1980). In what ways are large systems more complex than smaller ones? On this question there is less agreement. The general systems theorist James G. Miller advances as a hypothesis the proposition that growing systems develop greater decentralization and greater integration (1978: 108- 109). Rappaport (1977) agrees that centralization is a method of regulation distinct from integration, but says that progressive centralization is typical of human systems, unlike ecosystems, where the trend is toward greater elaboration of more redundant pathways. Basically the disagreement is whether, given size increase, central control per se is selected for, or merely increased integration in general. Conceptual advances along these lines have been made by organization theorists and archaeologists (e.g., Blau 1970; Webber 1979; Johnson 1978, 1981; Wright 1977; Braun and Plog 1982). The former are interested in

BOUNDARIES,

SCALE,

AND

INTERNAL

ORGANIZATION

37

firmalizing principles of management for the practical end of survival in competition, whereas the archaeologists wish to understand forms of human organization that were adaptive at least for a time. For both, the assumption of efficiency is essential. Johnson’s deductive model of decision-making organization (1978) held most other properties constant and increased size. Under those circumstances increments of vertical and then horizontal complexity in control functions were expected. In other words, centralization as defined here would increase with scale, but by no means uniformly, since both horizontal or vertical specializations, at different stages, were likely to develop. If integration were allowed to vary in Johnson’s model, however, centralization might increase or decrease with scale, depending on which connections between which components were modified. Hence the relationship between integration and centralization is not likely to be simple in real systems. For this reason we favor an analytic approach such as Johnson’s, wherein vertical and horizontal linkages and types of flow can be separated. It seems productive to imagine that, as scale changes, different contributions of horizontal and vertical integration will be optimally efficient, depending on such exogenous factors as the objectives of the participants and the matter of boundary maintenance, the factor we discuss below. Given the interplay or trade-offs between horizontal and vertical interconnections, we believe that increasing centralization has not in fact been documented for human social evolution, nor has a positive relationship between scale and centralization been demonstrated. What can be accepted is a regularity in the relationship between scale and integration if other factors such as objectives and boundary conditions are held constant. Thus, if a system remains a system and has a similar task (output) at f1 and fp, if efficiency is held constant, and if its size is sufficiently augmented, then its integration must increase between t1 and t,. Other possibilities of course include giving up the original objective or splitting into two systems. We wish to point out one further aspect of the size-integration problem not developed in the literature. Usually integration is thought of as the consequence, but logically this need not be so. Political leaders may attempt to increase their power, which may involve increasing integration, by increasing system size. Certain economic mechanisms achieve greater efficiency at larger scale, so that once instituted, new mechanisms may exert demand for increased scale. Of course whether demand for increased size by political authority or economic institution can always be met, by what processes, and with what time lag are interesting questions. In short, though the literature usually has one think of size as the cause, in some situations it is enlightening to conceive of it as the effect. The above discussion of previous research focused on the connection

38

KOWALEWSKI

ET AL.

between size and internal organization. Now we turn to boundary permeability and its relation to size and internal organization, which has received far less treatment. Larger systems are thought to have greater ratios of internal transactions to external transactions than smaller systems (see Miller (1978:193), where this is treated as a weak empirical generalization, and Platt (1969), who makes an analogy to surfacevolume ratios). This is related to the topic of rank-size relationships in systems of cities (e.g., Zipf 1949; Berry 1961). Studies of the significance of city size distributions must treat, implicitly or explicitly, which cities of all possible to include as members in a “system.” Boundaries are important for rank- size relationships because the rank- size rule itself is said to obtain when the constituent cities form a well-integrated, bounded system. Departures from rank-size are also thought to relate to boundary conditions. When one “primate center” is much larger than expected, a frequent explanation is that it serves as the connecting port to a wider, outside system (Vaptiarsky 1975). When the cities are all about the same size, it is believed to reflect the inclusion of more than one roughly equal system in the same rank-size graph (Johnson 1981) or an inherently open system (Kowalewski, 1982). Vapnarsky’s work (1975) most explicitly tries to relate degree of closure to internal organization. His ideas may be represented as in Fig. 1. Closed systems should be relatively decentralized (having log-normal rank- size characteristics) and highly integrated internally; and open systems, according to Vapnarsky, will be highly centralized (primate) and not well integrated. The negative relationship between centralization and integration we think is correct, following the definitions given above, and keeping in mind that these are relative quantities. When it comes to closure though, we believe the model is wrong. Vapnarsky made two mistakes. One was to use the nation-state as a “well-defined” system, and the other was to fail to measure the degree of closure. Argentina was the test case. Buenos Aires has been a notable case of extreme urban primacy, and Vapnarsky correctly points to its role as the country’s only major link to the world system. However, he then says that Argentina has a low degree of closure. This is empirically not true, at least compared to other countries. If closure has meaning independent of rank-size properties, it ought to refer to the amount of flow across the boundary relative to internal movements. The appopriate measure would be import and export

FIG. 1. The relationships between systems properties suggested in “The Argentine System of Cities.”

BOUNDARIES,

SCALE,

AND

INTERNAL

ORGANIZATION

39

trade as a proportion of the total economy. In a random sample of 24 countries, Argentina ranked third from the bottom in fraction of the Gross Domestic Product accounted for by foreign trade. Undoubtedly the position of Buenos Aires as a conduit to and from the outside is very important, and perhaps foreign trade to a large degree structures the Argentine economy, but that nation is a comparatively closed system, not an open one. Therefore, we cannot accept the proposed relationship between closure and centralization. Instead, as in Levine and Campbell’s observations on the formation of marked ethnic boundaries (1972:99), impermeability is typically a property of centralized systems. In the next section we propose a model wherein centralization is a property of relatively closed systems. A SIZE-BOUNDARY-CENTRALIZATION

MODEL

Theory in this realm is not, to our knowledge, developed enough to allow the construction of a deductive, formal model involving these variables. The justifications we offer for the following model are thus not as strong as they might be. Nevertheless, our aim is the application of these hypotheses so that new insights into past systems, as well as general theory, might be advanced. It is our hope that modifications of these hypotheses will be made. The model to be applied is depicted in Fig. 2. No assumption about causal directionality is made here, and none is tested. Under different circumstances the preponderance of causality could run either way. Instead we will look for associations. It is neither justifiable nor necessary to assume that the relationships between these properties are linear. For example, at very small scales, increments in size will affect “centralization” little, simply because small systems cannot afford the costs of centralization and there would be minimal benefit. Below a certain size, centralization is not expected at all. Similarly, great increases in permeability may upset the expected regularities. Thus the variable ranges within which the model should apply are not infinite. Range of applicability, the effects of great “qualitative” changes, and the nature of the relationships-whether linear or nonlinear-are theoretically relevant, but we cannot deal with them specifically . Why should size be inversely related to centralization? As the number of components or the physical distance over which they are dispersed increases, it becomes increasingly difficult and costly to maintain com-

FIG. 2. The size-centralization-permeability

model used in this study.

40

KOWALEWSKI

ET

AL.

munication in a centralized system. Integration may be achieved by specialization, increasing hierarchical depth, and by adding other kinds of paths of interaction that do not involve the central node. Both of the latter decrease centralization. Conversely the efficiency of centralized organizations comes into play as size decreases. Smaller systems are more easily integrated through a single place. Centralization and permeability are inversely related. In hierarchical systems, strong vertical connections may preclude the development of ties to other vertically organized components or systems. In fact communications between dominant and subordinate units are frequently encoded so that messages simultaneously display in-group membership and prevent leakage of information-except that which is intended-to the outside. Thus we think that while a (or probably the) primary function of primate centers in regional systems is the handling of boundary transactions, the overall amount of flow will be low compared to a less centralized organization. It is relatively cheaper to maintain a boundary as the size of a system increases. In biology this is seen in Allen’s and Bergmann’s rules (Luria et al. 19Sl), and it is easily understood as an expanding circle whose area increases at a faster rate than the perimeter. If the cost of boundary maintenance depends on the distance from center to edge, and if the productivity of the system varies with the area, then it is relatively cheaper to maintain the boundaries of a larger system, all other things being equal. However, it is very important to ask what boundary maintenance means in terms of closure. We suggest that in nonindustrial societies, boundary maintenance on the regional scale is usually directed toward encouraging regulated flows across the boundary, not closing the system, because such transactions are one of the better ways of increasing available energy in societies that do not invest in new technology. Expanding systems may thus acquire people and goods more cheaply through boundary transactions than by encouraging increased production at home. Therefore we are suggesting that systems increasing in size will also increase boundary transactions, and vice versa. This relationship should be the weakest of the three hypothesized, however, given the contradictory tendencies and the probable intervention of other variables. APPLYING

THE MODEL

The data used to examine this model came from archaeological settlement pattern surveys of the Valley of Oaxaca, in southern Mexico. One of the proposed goals of the survey was to examine the relationship between the region’s boundaries and its internal organization. With some qualifications, the survey information can be used for this purpose. In an

BOUNDARIES,

SCALE,

AND

INTERNAL

ORGANIZATION

41

article of this size we cannot describe the entire Valley of Oaxaca sequence or even those aspects that might conceivably be relevant to boundaries and internal organization. The reader should consult Blanton (1978), Blanton et al. (1982) and Kowalewski et al. (in prep.) for details. The testing of the model requires that measures of permeability, size, and centralization be made uniformly and have basically the same significance across time periods. We can do this for the urbanized part of the sequence, from Monte Alban Early I (500 B.C.) to the end of the Postclassic, but conditions prior to that were so different that the measures we used later in time had little meaning prior to the foundation of the first city. Thus initially for statistical purposes we use the seven phases from Early I through Monte Alban V. The pre-Monte Alban phases will be brought in separately. Variables. The values of each measure for the seven Monte Alban phases are given in Table 1. Three ways of measuring system size were used: total population, occupied area, and the area1 extent of the “core” or most intensively occupied area. We use total population as a proxy for regional system size, because we have no way at the present time of identifying appropriate and equivalent component units. Populations were estimated as a function of component size times a population density figure, usually lo-25 people per hectare. When actual houses or house lots could be discerned, they were counted and multiplied by 5- 10 people per house. For easier comparison the midpoint of the estimate’s range is used. The second measure, occupied area, was approximated by counting the number of our 4 x 4-km grid squares with at least one occupational component dating to the phase in question. The “core” for each phase was somewhat subjectively estimated by delimiting the area of the greatest buildup of population and sites with mounded architecture. The area is represented by an index value of the measured extent of these core areas on a map of the valley (Blanton et al. 1981). Centralization was measured by the region’s rank-size primacy, the proportion of the total population living in the largest center, and the demographic pull of the main center. Primacy, again, means that the leading center is abnormally large, more than twice the size of the second leading settlement. Rank-size graphs were drawn for the top 15 centers in each phase, and an index (Johnson 1980) calculated. The index measures deviation from the standard log-normal line drawn through the leading center. Negative numbers mean primacy, and positive values indicate a convex distribution. The demographic pull of the leading center refers to how the population outside the main center is distributed in terms of distance from it. A graphic illustration of this technique is given in Fig. 3, which shows profiles of population by distance from Monte Alban in Monte Alban Late I and II, in 4-km intervals. The median that is

Measures of Permeability Obsidian per 10,000 Population Percent population on edge Edge site size/ interior site size Percent of formal architecture on edge 28

24 .38 .40

18

.39

.35

.53

.47

0.5

35

0.2

34

36

22

- .47

41,290 115 239

II

0.7

16

-.60

50,922 130 288

LI

.63

1.10

50

19.6

14

21

.I0

115,223 142 346

IIIA

Phases

SO

44

38

5.3

31

13

-.20

78,739 78 187

IIIB

.64

1.37

58

10.7

23

20

-.Ol

70,074 80 160

IV

V

.68

1.04

59

63.7

t: 8

::

g m

8 E ‘: 26

.33

163,632 159 418

TABLE 1 BOUNDARYPERMEABILITY IN THE VALLEY OF OAXACA FROM 500 B.C. TO A.D. 1500

18

-.54

14,652 93 187

Measures of size Population Occupied grid squares Core area (index)

Measures of centralization Bank- size index Median distance from center for rural pop. (km) Percent population in center

EI

Variables

MEASURESOF SIZE,~ENTRALIZATION,AND

BOUNDARIES,

SCALE,

AND

MONTE

INTERNAL

ALBAN

ORGANIZATION

LATE

43

I

8070605040p 2

30zolo-

2

MONTE

80 70 60

0

8

DISTANCE

FIG. 3. Percent of population and II.

16

ALBAN

24

32

FROM THE (km)

II

40

MAIN

48

56

CENTER

by distance from Monte Alban in Monte Alban Late I

used to express the “pull” of the leading center is the distance at which half the population is accounted for, not counting the population of the leading center. These three measures were chosen to reflect centralization, the degree to which activities were concentrated in one place. For permeability four measures were devised. Obsidian frequency should be a good indication of the relative volume of importation, at least for the one commonly occurring good that we know had to come from outside the Valley of Oaxaca. Obsidian fragments were observed and counted in the field, but unless the observation was made in single component contexts, dating was not possible. Therefore we used only the single component sites for the measure, and in Table 1 obsidian is standardized as pieces per 10,000 persons in single component sites. The possible chronological associations, including the multicomponent sites, show the same pattern of relative frequencies between phases, but the numbers themselves undoubtedly disfavor the earlier phases. Nevertheless the relative amounts-Early I had less than IIIA or V-are probably accurate. The other three indications of permeability do not directly measure flows, but boundary activity. Hence our test results are actually limited to how size and centralization vary with relative amounts of activity on the physical edge of the region, not flows per se except for obsidian, which is only one item. We have defined the edge of the regional system as the set

44

KOWALEWSKI

ET AL.

of grid squares having at least half their area within 4 km of the survey boundary (see Fig. 4). This is worded as if the “edge” is an arbitrary or physiographic zone, but in this case the choice can be justified as an adequate representation of the edge of the actual behavioral system. First, every attempt was made in the field to carry the survey limit beyond the falloff of settlement density, and the cases where this could not be done represent only a minor fraction of the total perimeter. (Monte Alban V and IIIA, the phases we determined were most open (see below) not surprisingly had the most overflow). We are thus confident in having contained the regional system within the study area. On the interior side, the 4-km width of the edge includes the outermost sites of importance in all of the Monte Alban phases, so we are never measuring an empty zone. E2

E3

E4

E5

E8

.7

E

N20 N19 N18 N17

N3

-

Survey Limit

E2

E3

E4

EEi

E6

E7

E8

E9

El0

El1

El2

El3

Limit of Edge Area

El4

FIG. 4. The Valley of Oaxaca, showing the area considered the “edge”

of the region.

BOUNDARIES,

SCALE,

AND

INTERNAL

ORGANIZATION

45

Physiographically the edge zone is mostly Piedmont, though it contains significant alluvial tracts as well, and it ranges from the mountains to the valley floor. Though in most of the edge zone the kinds of irrigated land found in the interior do not exist, Piedmont streams can be tapped, so that while, overall, the edge has less agricultural potential than the interior, it is by no means an impossible desert. At first glance the Valley of Oaxaca appears to have only three or four main points of access to and from the outside. Were this the case we would need to give special weight to these natural gateways and attach less importance to other edge areas. However, an examination of the historical and recent paths of communication (forthcoming in Kowalewski et al., in prep.) convinces one that the Valley is more like a sieve than a bottle. Important trails are found all along the frontier. Therefore the best tactic is to treat the whole boundary equally. In terms of size, the edge is a little less than half the total regional area of 2100 km2. Notice that when we compare edge activity to centralized activity, it is not simply a matter of activity having to be at the primary center because it is not at the edge-the interior is a significantly large third possibility, amounting to a little over half the region. The first measure of boundary activity is the percentage of the total population living in the edge zone (it was calculated with and without the main center, with the same relative results). The second gives the average population size of edge sites compared to interior sites, not counting the main center. The idea is that site size reflects functional size, and thus degree of activity. The last row in Table 1 gives the proportion of edge sites with formal architecture to all sites with formal architecture. This kind of architecture refers to platform mounds arranged around plazas, usually in four-mound groups, but sometimes groups of three or more than four mounds. The function of these groupings is believed to be administrative-ceremonial, because of the regulation of public access. Results. Our method in applying the model to the Valley of Oaxaca sequence was to examine the strength and direction of the associations between the ten measures, where the observations or cases are the seven phases. The problem was viewed as one of correlation. Pearson’s r was generally chosen as the coefficient over Spearman’s rank order r because most variables are well distributed. The only variable with extreme or outlier values is obsidian, and for that variable all coefficients are Spearman’s r. Table 2 shows the resulting correlation matrix. As these kinds of analyses go, the matrix has a surprisingly high number of strong associations. All are in the direction predicted by the model. The average coefficients between measures of the same conceptual variable (within group) and between conceptual variables (between groups) are given in Fig. 5. The strongest connections are between permeability and centralization, and between scale and centralization. The scale/

.64

BETWEEN

.78 .97

MEASURES

Note: * indicates Spearman’s r. All others are Pearson’s r.

Population Occupied area Core area Rank- size Distance from center Center population Obsidian Edge population Edge site size Edge architecture

CORRELATIONS

.92 .39 .54

.55 .66 .64 S8

-.94 -.61 -.73 -.% -.67

.82* .32* .31* .96* .50* -.86*

TABLE 2 SIZE, CENTRALIZATION,ANDPERMEABILITY

OF

.83 .25 .38 .95 .52 -.88 .86*

.61 .18 .25 .82 .56 -.79 .75* .91

.82 .36 .46 .91 .66 -X6 .79* .95 .86

BOUNDARIES,

SCALE, AND INTERNAL ALL

cl

SCALE .80

47

ORGANIZATION

MEASURES

+

+ .47

WITHOUT

t

THE

TWO

AREA

MEASURES

AND

DISTANCE

FAOM

+

FIG. 5. Correlations between measures of size-centralization-permeability ley of Oaxaca between Monte Albsin Early I and V.

CENTER

t

for the Val-

permeability association is positive, but weaker, as we suggested it should be. Considerable improvement can be made in the strengths of the associations by dropping the two areal measures of scale (occupied area and core area). It has been thought that spatial size would be a good indication of system size, but apparently it is not. Perhaps the distances are immaterial when over half the region lies within a day’s walk from the center. The variable expressing the demographic pull of the main center on the rural population is also not as strongly associated as the others, perhaps for the same reason, as it too is a distance measure and the region may be too small. At this stage of our analysis of the settlement pattern data we still have little knowledge of just how many subregional units constituted the regional system. Presumably it is this that best reflects the size of the system that central authority had to deal with, but at the moment population size will have to stand in. Having established the credibility of the general model, at least for the particular case, let us see how it actually performs in each phase. Shown in Fig. 6 are the Monte Alban periods arranged on a scale of permeability ranging from relatively closed to more open. Smaller size and greater centralization also describe the left end of the scale, and larger size and decentralization the right. The phases were placed along the scale by summing their ranks for the ten variables in Table 1. Periods V and IIIA were the most open, followed by IV and then II. Early I, Late I, and IIIB scaled on the closed end. Notice that if one had expected an increase in centralization over time, these results would be a bit startling (see the sequence given in Table 3). The path through time is by no means steady, but the overall trend is toward less centralization. Now we compare across phases using a dynamic approach akin to the way the historian Braudel sees how models should be used (1970: 166).

48

KOWALEWSKI CLOSED

I

EI

1116

LI

ET AL.

II

IV

IIIA

V

OPEN

,

SMALL

LARGE

CENTRALIZED

DECENTRALIZED

FIG. 6. The Monte Alban periods arranged on a scale of size, centralization, ability.

and perme-

I have sometimes compared models to ships. What interests me, once the ship is built, is to launch it, to see ifit floats, then to make it sail wherever I please, up and down the currents of time. The moment of shipwreck is always the most meaningful.

As Table 3 shows, there are times when the size/centralization/ permeability model floats and times of shipwreck. The sequence has been expanded to include the Early and Middle Formative phases prior to Monte Alban. Since some of the measures used above are patently inapplicable in the early phases, they have been modified to be as consistent as possible with the conceptual variables and still reflect the nature of the social systems of Formative times. The signs in Table 3 indicate whether size, permeability, and centralization were increasing or decreasing compared to the previous phase, and those that are circled are values that are in the opposite direction of that predicted by the general model. The changes in scale, centralization, and permeability are exactly in accord with the expectations of the model in five of the eleven transitions in the sequence. The “shipwrecks,” of which there are two types, are enlightening. TABLE INCREASE

3

ORDECREASE IN SIZE,CENTRALIZATION,ANDPERMEABILITYOFTHE VALLEYOF~AXACA REGION FROM 1.5OOB.C. TO A.D.1500

Transitions s

Variables Size Centralization Permeability

-t

+

-

+

+

+

8”

+

-

e

+

+

+

-

+

+

Notes: For the pre-Monte Alban phases, size is measured by population, centralization by the size of San Jose Mogote compared to the next largest site, and permeability by an evaluation of the amount of foreign goods in the Valley, based on the published reports (Whalen 1981:30,60,74; Drennan 1976:75,86,112; Winter and Pires-Ferreira 1976:307; Pires-Ferreira 1976:325). Changes between the remaining phases are taken from the data in Table 1. a Circled signs indicate changes in a direction not predicted by the general model.

BOUNDARIES,

SCALE,

AND

INTERNAL

ORGANIZATION

49

One way the model does not hold is when permeability increased and centralization declined, as expected, but the size of the system became smaller rather than larger. This happened at two periods in the Valley of Oaxaca, Monte Alban II between 100 B.C. and A.D. 250, and again in Monte Alban IV between A.D. 650-850. These were the two periods when the Valley was to a degree a disintegrating region. In Monte Alban II the region consisted of five discrete clusters of settlements, separated by 4-8 km of unoccupied land. One cluster was the city of Monte Alban, with about 14,000 people living behind a massive wall. Because of its large size, traditional position as capital of the region, central location, wealth, and scale of public building, Monte Alban was the preeminent place of its time. But other centers in the Valley may have challenged Monte Alban, not only for autonomy in local administration, but for carrying on their own foreign relations. Symbols of military conquest in the form of carved stone monuments appear at several centers besides Monte Alban. Architectural buildings similar to monumental constructions on Monte Alban’s main plaza are found at outlying centers, and one outlying center even built a great plaza apparently duplicating Monte Alban’s. Monte Alban thus did not tightly integrate the Valley’s subareas as it had previously or would after A.D. 250. Pottery distributions show the same disunity. Ceramic styles were heterogeneously distributed. Each arm of the Valley had some pottery types largely distinctive to it alone. The phase from A.D. 650-850 was also a time of regional fragmentation. Monte Alban declined in population and political leadership, from 22,500 people and uncontested capital status in the previous four centuries to third largest city with only 4,000 people and no new public construction. Five to seven discrete clusters of settlement, separated from each other by 4-8km “shatter zones,” form the Valley “system.” As in the earlier period of fragmentation, these territorial entities may have had their own foreign connections, and they show a degree of ceramic style dissimilarity. The relationships between scale, centrality, and boundary permeability suggested in the general model obviously do not hold when the “system” under consideration is not a unified system, as in Monte Alban II and IV. In these phases population and centralization both declined somewhat, and more links were made with the outside. The other condition in which the model does not hold is when size, permeability, and centralization all increased. This happened in two instances lasting two archaeological phases each, from 1450 to 850 B.C. (from the Early into the Middle Formative) and from 500 to 100 B.C. (Rosario phase into Mone Alban Late I). These were the two occasions when the organization of the region underwent major transitions to entirely new, more complex forms. In the first case the transition was from a

50

KOWALEWSKI

ET AL.

barely sedentary, nonhierarchical society to sedentism and a ranked social hierarchy. Essentially this basic structure remained in place until 500 B.C. But after 500 B.C. a whole new order was built again, with another, much larger capital at Monte Alban, and a minimum of one to possibly three additional levels of vertical complexity in the administrative apparatus. We think this is the period of greatest political growth in the Valley of Oaxaca. While the previous transition established a two-tiered political structure, at least a three-tiered and perhaps even a more complex administrative apparatus was created in Period I. These two transitions also saw the greatest increases in system size in the Valley sequence. Population increased 27-fold from 500 to 100 B.C., and 6-fold in the first transition, compared to less than 3-fold for the next most significant increase. The general model called for decrease in centralization with system growth, but the phases just discussed had both growth and more centralization. Other studies of systems have demonstrated that integration increases with size. Our findings support this, because overall integration increased during these two transitions. But additional refinements can be hypothesized. We suggest that integration and centralization can both be augmented relative to previous states of the system when the growth in size is very great. In other words, with a sufficiently large increase in energy, which having more people would provide, the organization not only becomes more integrated than in the prior state, as we normally would expect, but can also afford to be more centralized. Note that these two times were occasions of hierarchy building, of increase in vertical complexity. Finally, the role of greater permeability in such episodes may be important as a means for growth and increased energy capture. DISCUSSION

Probably the weakest part of this formulation is the lack of specification of different kinds of flows and activities. There is evidence, though not conclusive, for a shift in emphasis in the location of boundary maintenance activities. Since full descriptions have been published elsewhere, only a brief sketch is in order here (see Flannery 1976; Flannery et al. 1981; Marcus 1976, 1980; Blanton et al. 1981; Spencer 1982). The nonsedentary and earliest sedentary communities have lithic, and then ceramic assemblages much like those in other parts of Mesoamerica, and a distinctively Valley or even a Oaxacan region was not yet defined. Obsidian was evidently obtained by individual households through their own trading partners, until about 1150 B.C. at San Jose Mogote and somewhat later in outlying villages, when central “pooling” replaced the

BOUNDARIES,

SCALE,

AND

INTERNAL

ORGANIZATION

51

simpler procurement system (Winter and Pires-Ferreira 1976:309). From the latter part of the Early Formative (the “Olmec horizon”) into the Classic, the highest level ideological trappings of the Zapotec polity were kept and displayed at the capitals, first San Jose Mogote, then Monte Alban. There is every reason to believe that in these periods San Jose Mogote was the scene of most extraregional transactions. At least until the Rosario phase, about 600 B.C., there is little inkling of specialized boundary activities at the small hamlets located on the actual edge of the system. In the early phases of Monte Alban the trend was to build more and more four-mound groups at sites on the edge of the system, though such architectural groups also are found in the interior. Period II, when the system experienced some decentralization, had the first good evidence for a distinctive type of activity on the region’s edge. The activity was ballplaying. Ballcourts in the Valley of Oaxaca originate in Monte Alban II, or at the end of Late I as far as we can tell. Sixteen Period II sites have them (Monte Alban might have had more than one). Of the 16,11 are on the outer edge of the Valley. Of the remaining five, three are the district or regional capitals, leaving only two in other interior locations. The ballcourts are also associated with formal, four-mound and plaza groups. Playing ball at administration sites on the frontier-why? For keeping a garrison in training and occupied? For competitive display? Whatever the reason, at least by Late I or II some kinds of transactions at the frontier were important enough to be regulated administratively. In the Early Classic (Monte Alban IIIA) the hilltop site with residential terraces and a small, formal mound group on top was the dominant kind of site, and more than a score of them were built, ringing the Valley’s southern and eastern sides (Elam 1981). They obviously had defensive advantages, and some had actual fortification walls. In several cases they were paired, a smaller one on the outside in sight of its partner, possibly to protect its larger neighbor as an outpost. These were densely populous settlements, not refuges, but most of their inhabitants do not seem to have been very wealthy by IIIA standards. The hilltop terrace sites certainly tell us that something important was going on on the frontier, including warfare but possibly other activities, such as the exchange of goods. In the Early Classic, Monte Alban seems to have surrendered most of its direct control over Valley affairs, including high-frequency, day-to-day boundary maintenance (cf. Rappaport 1977) to secondary, tertiary, and even lower ranking centers. But the capital kept to itself a monopoly on articulating the Valley region with the highest levels of Mesoamerican interregional contacts. After the Classic the trend was toward decreasing central administrative control over boundary flows. In many cases the outermost sites one finds in the Late Postclassic are tiny hamlets and isolated residences,

52

KOWALEWSKI

ET

AL.

indicating no great fear of attack. In a number of areas the sites dribble on and on into the mountains, and we were forced to draw our survey limit before they stopped. The regional frontier had no special kinds of sites, except for the forts put up by local lords fearful as much of each other as of attack from outside, and an occasional shrine. But more people lived on the edge of the Valley system in this phase than in any other. We think that a great deal of exchange took place, but it was so low level, permeating, and participated in by everyone that local lords, the only people with the authority to do anything about it, could not because the costs were too high. The general trend we have just described is simply this: boundary maintenance was one of the important reasons for the existence of the first centers in the Valley of Oaxaca. Early in the sequence, the small scale society concentrated almost all of its significant boundary activities in the center. The larger, more complex systems a millenium later differentiated between high level, ideologically enshrouded activities, which remained in the purview of the capital, and lower level exchanges, often carried out under administrative control, at the frontier. Decentralization of the regional system in the Postclassic meant that political regulation of frontier exchanges almost disappeared. SUMMARY

The evidence used in this study comes from regional scale archaeology, and it has the limitations and advantages of systematic surface survey. Methodologically the approach has been to take advantage of archaeology’s unique power and, in our opinion, its only reason for existence: understanding change over the long run. Thus we examined not one case, nor a sample of cases from different areas as in the comparative method, but instead 11 consecutive time intervals forming the trajectory of a society (or several, depending on the point of view) over a long sequence. As we see it, there is no way the comparative method can uncover this kind of societal dynamics, and no good reason why archaeology should only be done to provide cases as grist for the old comparative mill. The prehistoric regional system of the Valley of Oaxaca exhibits certain predictable relationships between changes in size, centralization, and the degree of boundary permeability, or at least activity on the boundary. A very simplified visual representation of our main conclusions is presented in Fig. 7. Increasing permeability is typically associated with increasing size and relatively low centralization. Closure is associated with smaller size and centralization. Under two circumstances this does not hold: (1) when the system is not a system (disintegration), and (2) when the increases in size and integration, especially vertical integration, are very

BOUNDARIES,

SCALE,

AND

INTERNAL

ORGANIZATION

CLOSED

OPEN

SMALL

LARGE

CENTRALIZED

DECENTRALIZED

SIMPLIFIED

53

REGIONAL SYSTEMS

FIG. 7. Simplified regional systems, showing the general relationships abstract properties of size, permeability, and centralization.

between the

great, in which case centralization also increases. The purpose of our model building, however, is not to propose iron laws, or even wishy-washy probabilistic ones, but to be able to apply ever better theory in learning more about the past. How far beyond the example of the Valley of Oaxaca can these propositions be extended-to all living systems, or only as far as the neighboring Valley of Nochixtlan? Not having studied this problem in other areas we have no basis for a claim, but is seems most logical to propose that an examination of societies of similar size and transportation technology would be the next step. REFERENCES CITED Barnes, Jonathan 1979 The Presocratic philosophers volume 1: Thales to Zeno. Routledge & Kegan Paul, London. Barth, Frederik (Editor) 1978 Scale and social organization. Universitetsforlaget, Oslo. Berry, Brian J. L. 1961 City size distribution and economic development. Economic Development and Culture

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Blanton, Richard E. 1978 Monte Albdn: settlement patterns at the ancient Zapotec capital. Academic Press, New York. Blanton, Richard E., Stephen A. Kowalewski, Gary Feinman, and Jill Appel 1981 Ancient Mesoamerica: a comparison of change in three regions. Cambridge University Press, Cambridge. 1982 Monte Alban’s hinterland, part 1: prehispanic settlement patterns of the central and southern parts of the Valley of Oaxaca, Mexico. Memoirs of the Museum of Anthropology, University of Michigan 15, Ann Arbor. Blanton, Richard E., Stephen A. Kowalewski, Gary Feinman, and Laura Finsten 1981 Patterns of regional inequality in the prehispanic Valley of Oaxaca. Invited paper presented at the symposium “Social systems, class, and regional inequality from urban formations to capitalism: the case of Oaxaca, Mexico,” at the Annual Meeting of the American Anthropological Association, Los Angeles. Blau, Peter M. 1970 A formal theory of differentiation in organizations. American Sociological Review 35(2):201-218.

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Braudel, Fernand 1970 History and the social sciences: the long term (translated by Sian France). Social Science Information 9(1):145- 174. Braun, David P., and Stephen Plog 1982 Evolution of “tribal” social networks: theory and prehistoric North American evidence. American Antiquity 47:504-525. Cameiro, Robert L. 1962 Scale analysis as an instrument for the study of cultural evolution. Southwestern Journal of Anthropology 18: 149- 169. 1967 On the relationship between size of population and complexity of social organization in human societies. Southwestern Journal of Anthropology 23:234-243. DeBoer, Warren R. 1981 Buffer zones in the cultural ecology of aboriginal Amazonia: an ethnohistorical approach. American Anfiquity 46(2):364-377. Drennan, Robert D. 1976 FAbrica San Jose and Middle Formative society in the Valley of Oaxaca. Memoirs of the Museum of Anthropology, University of Michigan 8, Ann Arbor. Elam, J. Michael 1981 Fortified sites and warfare in the prehispanic Valley of Oaxaca. Undergraduate thesis, Department of Anthropology, University of Georgia, Athens. Flannery, Kent V. (editor) 1976 The early Mesoamerican village. Academic Press, New York. Flannery, Kent V., Joyce Marcus, and Stephen A. Kowalewski 1981 The Preceramic and Formative of the Valley of Oaxaca. In Supplement to the handbook of Middle American Indians, volume 1: archaeology, Victoria Reifler Bricker, general editor, Jeremy A. Sabloff, volume editor, pp. 48-93. University of Texas Press, Austin. Gould, Stephen Jay 1978 Were dinosaurs dumb? Natural History 87(5):9- 16. Hosler, Dorothy, Jeremy A. Sabloff, and Dale Runge 1977 Simulation model development: a case study of the Classic Maya collapse. In Social processes in Maya prehistory: studies in honour of Sir Eric Thompson, edited by Norman Hammond, pp. 553-590. Academic Press, New York/ London. Johnson, Gregory A. 1978 Information sources and the development of decision-making organizations. In Social archaeology: beyond subsistence and dating, edited by Charles Redman et al., pp. 87-112. Academic Press, New York. 1980 Rank-size convexity and system integration: a view from archaeology. Economic

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1954 Political systems of Highland Burma: a study of Kachin social structure. Beacon Press, Boston. Levine, Robert A., and Donald T. Campbell 1972 Ethnocentrism: theories of confhct, ethnic attitudes, and group behavior. Wiley, New York. Luria, Salvador E., Stephen J. Gould, and Sam Singer 1981 A view of life. Benjamin/Cummings, Menlo Park, California. McNab, B. K. 1980 Food habits, energetics, and the population biology of mammals. American Naturalist 116: 106- 124. Marcus, Joyce 1976 The iconography of militarism at Monte Alban and neighboring sites in the Valley of Oaxaca. In The origins of religious art and iconography in Preclassic Mesoamerica, edited by H. B. Nicholson. Latin American Center, University of California, Los Angeles. 242:50-64. 1980 Zapotec writing. Scientific American Miller, James Grier New York. 1978 Living systems. McGraw-Hill, Morgan, Lewis Henry 1962 (orig. 1851) League of the Iroquois. Citadel Press, Secaucus, New Jersey. Pires-Ferreira, Jane W. 1976 Shell and iron-ore mirror exchange in Formative Mesoamerica, with comments on other commodities. In The early Mesoamerican village, edited by Kent V. Flannery, pp. 311-326. Academic Press, New York. Platt, John 1%9 Theorems on boundaries in hierarchical systems. In Hierarchical structures, edited by Lancelot Law Whyte, Albert G. Wilson, and Donna Wilson, pp. 201-214. Amer. Elsevier, New York. Rappaport, Roy A. 1977 Maladaptation in social systems. In The evolution of social systems, edited by J. Freedman and M. J. Rowlands, pp. 49-71. University of Pittsburgh, Pittsburgh. Spencer, Charles S. 1982

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evolution of social systems, edited by J. Friedman and M. J. Rowlands, pp. 73-78. University of Pittsburgh, Pittsburgh. Winter, Marcus C., and Jane W. Pires-Ferreira 1976 Distribution of obsidian among households in two Oaxacan villages. In The early Mesoamerican village, edited by Kent V. Flannery, pp. 306-311. Academic Press, New York. Wright, Henry T. 1977 Recent research on the origin of the state. Annual Review of Anthropology 6:379-397. Zipf, George Kingsley 1949

Human

behavior

ecology. Addison-

and

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of least

Wesley, Reading, Mass.

effort:

an introduction

to human