Intuitive typology and automatic classification: Divergence or full circle?

JOURNAL

OF ANTHROPOLOGICAL

ARCHAEOLOGY

8, 1%188

(1989)

Intuitive Typology and Automatic Classification: Divergence or Full Circle?’ DWIGHT

W. READ

Department of Anthropology, University of California at Los Angeles, Los Angeles, California 90024 Received July 29, 1987 Classification is an assertion about how phenomena in some domain are structured. Artifact classification introduces the additional complexity that the domain is structured not only by material properties and morphological form, but by ideational properties as expressed through culture as well. It is argued that if artifact classifications are to be informative of cultural systems, class definitions need to be defined by criteria that are grounded in the properties of cultural systems. Inductive methods based on so-called objective, quantitative grouping techniques are found to be insufficient for this task. Alternative approaches are explored and it is concluded that there is as yet no general solution for the problem of partitioning an initially heterogeneous collection of artifacts into subgroups homogeneous with respect to underlying structuring processes in such a manner that the homogeneous groups can serve as the basis for formulating class definitiOIIS

With

cukurd

SdknCy.

0 1989 Academic

Fkss,

Inc.

I. INTRODUCTION

Classification, reduced to its minimum, consists of two basic, interrelated operations: (1) the definition of classes and (2) the assignment of entities to classes.The latter is primarily one of method and the former is guided by theory about the organization of a domain. Artifact classifkation, by the term “artifact,” carries with it the connotation of culturally grounded organization. More exactly, the domain of artifact classification is material culture and the theory encompassesmaterial culture as a product of behavior. But behavior is affected and regulated by culture in its capacity for providing the conceptual system which supplies meaning for action and behavior. In this sense artifact classification, as noted by Krieger (1944:272) four decades ago, should be judged by its ability to i This article was presented as the fifth annual lecture in the Albert C. Spaulding Lecture Series on Quantative Archaeology in the Department of Anthropology, Arizonia State University. The series honors Dr. Spaulding for his work on linking quantitative methods with archaeological and anthropological theory and using quantitative techniques as a language to think about anthropological issues. 158 0278-4165/89 $3.00 CopyriSbt 0 1989 by Academic Press. Inc. AU rights of reproduction in any form reserved.

INTUITIVE

TYF’OLOGY

AND

AUTOMATIC

CLASSIFICATION

159

reflect the structuring properties of culture as it gives meaning to and affects the actions of artisans and users of material products. It must be able to take into account, as Hodder (1982:7) has commented, “. . . material culture as the product of human categorization. . . .” Although other kinds of classifications for the same material are possible, such as the classification of bone material by species, the classification of lithics by mineral form, and so on, these are often grounded in other theories. To be informative of a cultural system, a classification must capture similitudes and differences relevant to the meanings provided through the cultural system. And it is emically oriented classifications of this kind that will be of concern here. By their nature, classes are an assertion of similitude and differences: entities take on similitude by virtue of membership in the same class; entities are different by virtue of belonging to distinct classes.In addition, but not necessarily, the similitude and differences may carry over to morphological properties and features. And herein lies the core methodological problem of artifact classification. The means for forming classes have generally been based on the material aspects of the objects (Dunnell 1986:158), yet the similitude of entities implied by common class membership need not be perfectly reflected in morphological and other physical measurements. Methods for grouping objects as an implicit, if not explicit, basis for defining classespresume an isomorphism between the similitude implied by common class membership and the similarity measured at the morphological level used for making the groupings. Without the isomorphism, the connection between measured morphological similarity and similitude as it relates to common membership in classes(which reflects an underlying cultural system) is undetermined. However, the presumed isomorphism is not necessary-objects may be conceptually similar but morphologically different. Hence the isomorphism must be demonstrated, not assumed, and failure to do so can, and has, caused obfuscation and confusion between means and ends: between groups and their properties as defined by morphological characteristics and classes and their properties as defined by cultural characteristics. Utilization of quantitative procedures such as discriminant analysis, principal component analysis, and cluster analysis as the means to provide a solution to the problem of reproducibly relating groups to classes (Clarke 1%8:518; Doran and Hodson 1975:158, among others) raises the analytically lower level, physical property to that of the distinguishing feature of classes. In the process, the idea of classification as a way to provide a measure of some aspect of the underlying cultural system becomes obscured and methods become a goal in themselves (Dunnell 1986:150), holding out the illusion of completely detached objectivity if

160

DWIGHT

W.

READ

based on appropriate statistical manipulations of data obtained according to the canons of sampling theory. The proposed methods have not and cannot work, except in an approximate sense, for they are based on a false premise of an isomorphism between morphological distinction and identity as measured by these manipulations, and cultural distinction and identity. To be sure, conceptual distinctions generally entail distinctions at the more concrete level as well; objects that are conceptually distinguished may show morphological distinctiveness. But the expression of these conceptual distinctions and their measurement and formulation through analytical manipulations have been inadequately considered. We have a panoply of analytical techniques which are powerful for separating and/or aggregating data viewed as points in some n dimensional space. But are the premises of these techniques the premises under which culturally based distinctions were made? Elsewhere Spaulding (1977) has argued in the negative. If the answer is negative, then serious questions must be raised about what archaeologists are trying to do with quantitative manipulations, and even whether these can escape the subjective aspect of classifications associated with classifications based on intuition about culturally relevant distinctions . The task undertaken here will be to examine whether there is agreement between the numerical methods that have been proposed and utilized, on the one hand, and the distinctions that seem to make cultural sense, on the other hand. As this discussion suggests, it will be argued that the quantitative analyses that have been made or proposed for formulating a culturally informative classification (e.g., Clarke 1968518) are deeply flawed. Further, correction of these flaws leads inexorably back to the issues raised by some of the early theoretical work on artifact typologies and classifications (e.g., Rouse 1939; Krieger 1944). But the return is not a circle. Rather, it is more like a spiral, leading back to the same position in one plane but extending outward in yet another dimension. II. GENERAL

FRAMEWORK FOR RELATING AND TYPES

ARTIFACTS

Implementing the linkage between class and artifact via group membership has proven to be diff’rcult in its execution (Doran and Hodson (1975: 158) and has not led to a commonly accepted set of analytical methods (Read 1982) for the task. Missing, I suggest, is adequate consideration of the relationship between the method of artifact analysis and the meaning of the classes that are inferred: Whose and what meaning is to be represented in the classification? One possibility is to take meaning as provided by the theoretical frame-

INTUITIVE

TYPOLOGY

AND

AUTOMATIC

CLASSIFICATION

161

work used to interpret the data at hand. Artifact classes, in this sense, have meaning according to the arguments and theory used to account for the order that is found in the data. For example, from this perspective projectile point classes might be asserted to have meaning as markers of time boundaries, not because of inherent properties of the objects, but because of a theoretical framework that purports to relate change in how objects are made to changes in the form and frequency of forms through time. The theoretical framework would posit the appearance and disappearance of types in a systematic temporal fashion and imply a corresponding methodology-seriation-for implementing the interpretive framework. Consider the argument more carefully. At first glance the posited interpretative framework does appear to delineate time sequences-at least over long time periods. But problems may arise when the group and the inferred types are considered on a time scale commensurate with the time scale of cultural processes and the changes that they entail. Temporal boundaries for cultures as a whole, which may “work” for time scales measured in hundreds of years, break down for time scales on the order of decades. That is, the broad trends break down when time scales that are relevant to the invention and diffusion of new or changed artifact forms are used. In lieu of tidy battleship shaped curves that show the long-term trends, the much messier processes of independent invention, diffusion, trade, differential occupation spans of sites, nonhomogeneous accumulation of material objects in a site during occupation, reutilization of material, unequal postdepositional processes, incomplete data recovery, and so on, must all be taken into account as potentially affecting the observed relationship between time and form (Flenniken and Raymond 1986) or time and frequency of artifacts of a given type (McNutt 1973; Doran and Hodson 1975:281-283; De Barros 1982). As one shifts from broad trends to their constituent, more local patterns, the matter of whose meaning is built into artifact classesbecomes more pressing. The initial, imposed meaning of artifact type class frequencies as measuring a temporal dimension becomes exposed for what it is: an association which is mainly the consequence of other processes more closely related to the factors that directly affect the cultural production and use (cf. Flenniken and Raymond 1986; Dibble 1987) of material objects. It is through these other processes that cultural meaning should be inferred. At finer levels of observation, meaning shifts from the interpretative framework imposed by the analyst to one aimed at discovering and recovering the system of processes and meanings which were part of the cultural system. For example, it is not time that causes change but, rather, it is events in time, such as change in the meanings that the artifact

162

DWIGHT

W.

READ

form may have had for the culture bearers, which lead to new production techniques and/or styles. Hence there is only an imperfect association between time and form. At this level meaning is still an integral part of an interpretive framework, but now the framework must explicitly allow for meaning as something already provided by the actors of a cultural system. As Spradley and Mann have phrased it, culture is a constructed reality (19755-7). Material objects are given meaning in the context of that constructed reahty, and hence are already part of a set of cultural meanings prior to the analyst’s constructions. How such meanings affect the production, usage, and discard of material objects thus necessarily becomes part of how pattemings discovered by the analyst are to be interpreted. The distinction I am making is not simply that of the analyst’s notion of style (“culture”) versus function (“objective meaning”), for that dichotomy presumes two aspects that may or may not be part of native conceptualization. Instead, I am referring to a concern expressed by Schneider (1984) in a different context, namely that of the analyst’s versus the native’s concepts. Schneider was referring to the study of so-called kinship systems, but the argument is applicable here as well. Schneider was concerned with the analytical distortion caused by using theoretical constructs such as residence type, descent system, and so on (and even kinship taken as genealogical connection) when these are not native conceptualizations. He has argued for the primacy of native concepts in analytical arguments and that the distinctions of concern are to be those of the native, not the analyst: “. . . of what block is this particular culture built? How do these people conceptualize their world?” (1984:197, emphasis in the original). To put it another way, there are inevitably two interpretative frameworks: the one of the native (emit) and the one of the analyst (etic). In so far as the actions taken and decisions made by the native are through one’s culture and the meaning it provides for external entities and actions, our interpretive framework must eventually come to grips with methods for at least partially incorporating such a framework as part of our understanding of the material objects we call artifacts. In some cases, the native’s interpretive framework is sufficiently constrained by external conditions so that the meanings may be little more than native justification for actions and decisions that must be taken if survival (at least in the short run) is to take place in the face of adverse environmental circumstances or of competing groups. For instance, regardless of the meanings that the Netsilik Eskimo associated with salmon fishing, caribou hunting, and sealing, it is clear that these activities had to be performed, roughly in the manner they were performed, if one were to exist on a year to year basis under the extreme arctic conditions with which they coped, given the technology available to them (Balikci 1970).

INTUITIVE

TYPOLOGY

AND

AUTOMATIC

CLASSIFICATION

163

Similarly, the !Kung San have had to regroup around the permanent waterholes during the dry season for them to live in this region. This is not to say that external conditions ensure that the “right” set of meanings are necessarily part of the constructed cultural reality, for nonoccupation of a region is also a viable alternative. When there are highly constrained conditions, it is possible to examine behavior in terms of etically defined frameworks such as optimal foraging, rational behavior, and the like and effectively account for the broad patterns. Yet in both examples, the actions that are taken, even if accountable solely through an etic framework, also have emit meanings which determine other aspects such as the composition and size of living groups. In turn these are formulated within a culturally constructed kinship universe. These other aspects are certainly part of understanding the manner in which the artifactual material articulates with the broader system and may also introduce other, nonmaterial constraints. An example is the constraining effects on social groupings induced through the limited kinship network for the individual in Netsilik society (Balikci 1970) in conjunction with their extreme fear of strangers (Rasmussen 1931; quoted in Balikci 1970: 1%59). Constraints of this kind may also have played a role in the transition from a primate-like to a foraging form of social organization (Read 1987a). Elsewhere I have presented a model based on rational choice that accounts both for the population stability of the !Kung San and why they (and other hunting gathering groups in arid conditions) are well below the maximum potential population density for the region given their method of resource procurement (Read 1986a). Central to that model is a claim about the meanings associated with time expenditure on child raising and child care versus gathering, with confhct in time expenditure resolved through increased spacing of children [see also Engelbrecht (1987) who suggests a similar mechanism for the low population density amongst the Iroquois]. Were these meanings to be changed, the model could also predict a growing, rather than a stable, population size. So even where behavior, in the broad sense, is predictable in terms of the analyst’s imposed meanings (e.g., density dependent growth leading to a stable population size), at a finer level understanding of behavior is contingent upon understanding the meanings associated with different choices of action and behavior. This being the case, it follows that classifications and methods of classification aimed at providing information on cultural systems must be justified ultimately in terms of their consonance with native meanings. At the level of methods, it follows that analytical distinctions that are made must have interpretation at the level of native meanings and not just at the level of meanings imposed by the analyst. For example, clustering pro-

164

DWIGHT

W.

READ

cedures are not justified as the basis for defining classes merely because they objectively partition a set of objects into more or less well-defined groups. Instead, grouping methods must be shown to produce distinctions that can be justified in terms of native meanings; that is, that etically defined analytical distinctions have emit saliency as well. This does not imply that distinctions must have had explicit, linguistic recognition as Gould (1980: 1 D-120) assumes erroneously; rather, only that the distinctions had cultural saliency in the sense of being acted upon by the artisans and users of material objects. For example, an etically defined distinction for pottery temper with the two attribute values, (1) sand and (2) sherd, has emit saliency if in fact pottery is tempered with one or the other and not via a random mixture of the two. Obviously, at a sufficiently fine level of analysis, the task of relating distinctions to an emit foundation may not be resolvable; nonetheless, I argue that much progress can be made before such a barrier is reached (e.g., Read 1987b). III. METHODOLOGY 1. Intuitive

versus Replicable

FOR GROUPING

and Objectively

DATA

Defined Methods

Two categories of methods will be considered: (1) intuitive and (2) replicable/objective. By the former is meant methods of grouping that have not yet been given algorithmic definition, such as sorting on the basis of the analyst’s perception of similarity and dissimilarity. By the latter is meant methods that have been given algorithmic definitions, such as statistical procedures. The distinction should not be construed as representing a difference either in analytical value or in degree of “correctness,” however. For example, intuitively defined classes may be more informative because they include subtle differences not captured in algorithmically defined methods, and algorithms might include assumptions that are invalid for the domain in question (Carr 1985; Read 1985). The distinction is better seen as a difference in replicability, and hence in suitability for a scientific methodology. Consider how the two methods compare to one another. Several virtues of intuitively defined classes include the following. (1) They are likely to be more sensitive to subtle patterning, particularly patterning that cannot be easily expressed in an algorithmic fashion. As is well known, the human visual system and brain are extremely effective for identifying and distinguishing patterns, though not without their own biases. Not all of these can be given exact expression in the form of analytical distinctions, for the basis upon which the visual system is able to determine pattern and coherence in external phenomena is still poorly

INTUITIVE

TYF’OLOGY

AND

AUTOMATIC

CLASSIFICATION

165

understood. (2) Intuitive groups can take into account varying relationships between local and global properties in a manner that is not yet duplicable by analytical techniques. (3) Both quantitative and qualitative aspects can be considered simultaneously by the visual system and differential weights can be made. (4) Tentative relationships and weightings can be modified as one continues to examine the objects. Trial attempts at forming groups can be explored and rejected or modified, with the information gained from these trial attempts used as part of continued, intuitive analysis. Convergence in this learning process upon distinctions that transcend the initial knowledge of the analyst suggests that these distinctions may be partially consonant with emically valid distinctions. Counterbalancing these virtues is the problem of replicability and verification. One person’s groups may not be replicable by another, raising the problem of whether the groups have any reality beyond an imposed ordering seen only by the intuitive typologist [but see Whallon (1972) for methods aimed at objective replication of an intuitive typology]. Acceptability depends heavily on the expertise of the analyst and the analyst’s expertise has an uncertain relationship to groups that would have cultural saliency to the producers and users of the objects. Repiicable procedures are virtually the opposite. They are sensitive primarily to differences expressed over most of the artifacts being analyzed. They can take into consideration the relationship between local and global properties (see below) only with difficulty, particularly when these relationships are not constant across the data set. Weighting of measures is notoriously difficult to achieve without introducing precisely the arbitrariness that the replicable procedures are supposed to circumvent (Gould 1974). Yet groups that are found, while replicable with the same technique, are not equally replicable across different techniques (Anderberg 1973:199; Christenson and Read 1977; Read and Christenson 1978; Aldenderfer and Blashfleld 1984, among others). There is an overabundance, in effect, of well-defined (i.e., analytically specified) algorithms but without an adequate theoretical framework for defining the grouping problem. As noted in a recent text “no one definition of a cluster will be suitable for all setsof data” (Dunn and Everitt 1982:103). In consequence, the relationship between the so-called objectively determined groups and emically meaningful groups is tenuous at best. More positively, the groupings that are defined can be replicated by other researchers and thus are more amenable to constructive criticism, discourse, and refinement. The expertise of the analyst at allegedly “understanding” the phenomena at hand is less critical as expertise is expressed in terms of analytical results and these are amenable to evaluation.

166

DWIGHT

W.

READ

Despite the drawbacks in linking the results of algorithmic procedures to emically meaningful groupings, replicable procedures are fundamental as part of scientific discourse. Nonetheless,it is equally important that these procedures be critically evaluated in terms of both their stated goals and their ability to provide distinctions which are meaningful in the framework discussed in the previous section. 2. Two Invalid

Assumptions

of Grouping

Procedures

So-called objective, or replicable, grouping procedures, despite differences in detail, are concerned with grouping objects on the basis of pairwise similarity of objects based on a set of measures made over the objects, with pairwise similarity measured by a suitable metric or norm in some n-dimensional space. The set of measures, or possibly a set of measures derived from the initial measures, defines the space. Groups are then defined using the measure of similarity (or dissimilarity for some algorithms) by a variety of techniques whose details need not concern us here. The general goal is to find groups that have “internal cohesion and external isolation” (Cormack 1971; quoted in Doran and Hodson 1975: 159). The fundamental assumption of the grouping procedures is that there will be convergence on a “correct” solution as the number of measured variables increases. Or, perhaps more accurately, it is assumed that if at least the underlying dimensions salient to definition of groups are measured, then “natural” groups will be found. Further, it is assumed that these dimensions will more likely be adequately measured as the variety of measures is increased. In effect, two assumptions-both erroneous-are being made, one explicitly and the other implicitly. First, it is explicitly assumed that the clustering algorithm will converge, in principle, onto the “correct” solution as the number and variety of measures increase (cf. Dunn and Everitt 1982: 13-14). Second, it is implicitly assumed that an inherent data structure is expressed in some fared subset of the n dimensions that have been measured. More specifically, suppose that the set of variables X = {x,, 3, - * - , x,} is measured over a collection of objects, C. The initial set of variables may need reduction, perhaps because some of the variables do not exhibit sufficient variability to warrant their inclusion, perhaps because of covariation amongst the variables. Let X’ = {x1’, x2’, . . . , x,‘} be this reduced set of variables, with m < n. The clustering will proceed with this reduced set of variables. The set of variables x’ defines a subspace S’ of the original space S defined by the set of variables X. Similarities will be measured in this space S’ and the implicit assumption is that it is with respect to the space S’ that groups will be defined, and that

INTUITIVE

TYPOLOGY

AND

AUTOMATIC

CLASSIFICATION

167

all groups can be defined in this same space. As we will see, the latter is an unrealistic, global assumption and thereby raises serious problems for numerical taxonomy approaches to subdividing a collection of objects into subgroups, each supposedly a set of representatives of some single process for which the class is to be a measure. IV. ASSUMPTIONS

OF NUMERICAL

TAXONOMY

APPROACH

Numerical taxonomy approaches, with their emphasis on replicable and objective grouping criteria (Sokal and Sneath 1963:49), have had a

salutary effect on classification and grouping methods. At the very least the numerically based procedures have made it clear that groups can be made in a replicable manner and thereby provide a firmer foundation for analysis. These procedures have also demanded that increasing attention be given to making one’s choice of measures and criteria for class and group definition explicit (Doran and Hodson 1975:186), hence more amenable to criticism, and through criticism, open to refinement. Refinement can be in two directions: expanding on the variety and range of measures or redefining what is to be measured. Of these two, the numerical taxonomy procedures have emphasized the former. Implicitly the philosophy behind numerical taxonomy assumes that as the variety of measures for the objects in some domain increases, there is greater assurance that the grouping procedures will recover a natural partition of the collection of objects being analyzed. From this viewpoint it follows that there should be emphasis on the number of variables used in the analysis as a proxy measure for variety in what is being measured. In principle, there is virtually no limit as to what might be included as no criteria are given for deciding when a variable should or should not be included. It is this theory-free aspect of the numerical procedures for formulating groups that has given them much appeal. If it truly is the case that the groups obtained will converge on some underlying natural grouping as the number and variety of measures increases, then no theory is needed, only the time for taking enough measures to ensure that all of the relevant data have been measured and included in the analysis. The assumption is not stated in this manner, but comes under the rubric of variable weighting. To include one variable and not include another is to use implicit weights of 1 and 0, respectively, hence to implicitly assert that one has a criterion for assigning weights. Sokal and Sneath have discussed the matter of variable weights at some length and concluded that in the absence of rational criteria for assigning weights, all variables should be weighted equally, for to do otherwise allows subjectivity to be reintroduced under a different guise (Sokal and Sneath 1963:119).

168

DWIGHT

W.

READ

Many advocates of quantitative procedures in archaeology have not been willing to take the numerical taxonomy argument to its logical conclusion and have instead argued that there needs to be some kind of variable weighting or redefinition of the kinds of variables that will be used (Voorrips 1982; Whallon 1982), but the basis for so doing is still seen as unclear (Dunnell 1986:193). This is unfortunate in that only the illusion of objectivity is created if criteria for variable selection cannot be given explicitly. But whether one is willing to accept equal weighting of variables or not, at least a consistent position is taken by the numerical taxonomists: the analytical method should be replicable and objective at all stages. Of course, weighting of variables inevitably enters in through the fact that not all possible measures are included in any analysis; hence, there has been an implicit weighting of variables. One might defend this position by arguing that one does not mean no variable should be weighted, only that once a collection of variables has been isolated for use in analysis, either all of these should be weighted equally or one must first state the basis upon which weights will be assigned. Yet the logic is still faulty since once it is recognized that some variables are properly excluded from the analysis, then there is agreement that for some variables there are, at least implicitly, rational criteria for weighting. These criteria are amenable to study aimed at making them explicit (e.g., Neff 1986), thereby allowing the criteria to be extended to other variables as well. If the fundamental assumption of numerical taxonomy, that the solution found will converge on some underlying natural set of groupings as the number and variety of measures increase, were true, then the matter of variable weights would largely be academic and could be ignored in practice. Unfortunately, that assumption is not true (see below). As the number and variety of variables increase, increasingly many variables are included that are uninformative about inherent groups in the data set, and with increasing number of irrelevant variables, the grouping procedures yield solutions that diverge from, rather than converge on, those groups. The key factor for the divergence is the potential discrepancy between the n-dimensional space that is measured by the total set of variables used in the analysis and the smaller, m-dimensional space defined by the dimensions through which groups should be distinguished and defined. There is no reason to expect that each measure selected by the analyst contains information on underlying groupings and, if not, it is measuring a dimension irrelevant for the definition of groupings. Thus, the ndimensional space defined by the original set of measures (or by a set of measures reduced in number by principal component methods) will have dimensions that are not needed for the definition of groupings. These “extra” dimensions have major impact on both the ability of clustering

INTUITIVE

TYPOLOGY

AND

AUTOMATIC

CLASSIFICATION

169

procedures to recover the underlying groupings and the ability of dimensionality reduction procedures to reduce the original, n-dimensional space to a smaller dimensional space which is constructed only of dimensions along which group differentiation is expressed. These extra dimensions have not been taken into account in assessing the ability of grouping techniques to recover groups that are inherent in the data: the implicit assumption of the numerical taxonomic philosophy is that there is an identity between the n-dimensional measurement space and the space defined by the dimensions in which group differentiation should be made. Were it the case that the two spaces are the same, then the numeric procedures would, most likely, be effective. Unfortunately the two spaces are unlikely to be the same-otherwise the whole problem of variable selection would already have been resolved-and if they are not the same there is decreasing likelihood of recovering underlying groupings as “extra” dimensions are included. V. LOCAL AND GLOBAL PROBLEMS WITH NUMERICAL IDENTIFICATION OF GROUPINGS

There are two kinds of problems that should be distinguished for the numerical procedures: local and global. By local problems I mean lack of concordance between models used for analysis and data measurement (Carr 1985) within the space defined by the variables being used for the analysis. By global problems I mean the problems associated with defining the space within which analysis should take place. In effect, the former addresses the question of what technique should be used, and the latter the matter of how variables are to be selected and the analytical space defined. 1. Local Problems

The kind of problems that arise at the local level are well exemplified by the variety of clustering algorithms for grouping data. The cautionary remarks that have been made (e.g., Aldenderfer and Blashfield 1984) concerning the different results that can be obtained for the same data with different algorithms are widely known and need no reiteration here. Each procedure has a different assumption about how similarity measures used for clustering relate to data structured as a union of several groups. Hence groupings that are found are linked to the assumptions of the procedure and may not be reasonable for the data in hand. At base, the problem stems from a lack of theoretical justification for anything but single linkage clustering (Jardine and Sibson 1971), yet single linkage clustering is unfortunately one of the least useful procedures due to chain-

170

DWIGHT

W.

READ

ing. For these reasons clustering procedures should be used in an exploratory and discovery, not definitive, manner (Dunn and Everitt 1982:105). 2. Global Problems While local problems arise through discordance between technique and the structure of the data being analyzed, these already presume that a satisfactory space has been defined within which analysis will take place. But if the space is incorrectly specified in the first place, then technique will not resolve the distortions that will arise. Specification of the space within which analysis will take place has two aspects: variable selection and construction of the analytical space based on these variables. A. Variable selection. Consider first variable selection as it relates to clustering algorithms. The central problem that arises in variable selection-one that occurs in other areas as well-is inadequate definition and/or understanding of the phenomena under investigation. If the groups to be recovered are to have saliency for constructing explanatory arguments that are grounded in the framework of meanings and uses for which the artifacts were a part, then the variables that are selected need to reflect the salient dimensions from the viewpoint of the makers and users of the artifacts. If pottery thickness, rim diameter, ratio of rim diameter to volume, and so on are relevant variables, it is not because of an etic, imposed framework of meanings expressed in the form of physical properties, but because the meanings in the etic framework do capture dimensions that had cultural saliency for the artisans and users. For example, it is possible to view pottery thickness and temper characteristics etically with regard to various physical properties such as the strength of the vessel, the size it could have and still withstand shock, etc. (Ericson et al. 1971; Braun 1983; Bronitsky 1986; Bronitsky and Hamer 1986; Carr 1986). Now merely because there is a direct translation of measurements such as pottery thickness, temper type, etc. into other physical properties which may then affect the uses to which the pot will be placed, it does not follow that these dimensions were necessarily acted upon. It requires additional bridging arguments along the lines of “through experience one learns about the properties of the objects when used in different contexts.” Further, the physical consequences need to have been important to the artisans and the users in the sense that they had to have been mapped into the “cultural knowledge” of the artisans. One claim about such a mapping and usually stated in a universal form is that of optimality-choices made by artisans and users were either directly optimal, or some sort of selection ensured that only optimal solutions were the long enduring ones. But there is no a priori reason to assume that at all times and places all persons work and act in an optimal

INTUITIVE

TYPOLOGY

AND

AUTOMATIC

CLASSIFICATION

171

fashion. Nor are there necessarily the internal dynamics that would lead to an optimal solution. Further, assertions of optimality require identification of the property, such as time efficiency or maintainability and reliability (Bleed 1986), that is being optimized, and that again leads back to the emit question of what properties define the dimensions along which decisions were made. For example, !Kung San arrows are certainly not optimal with respect to accurate shooting of an arrow at a distant animal. Yet they are effective for the task at hand of introducing sufftcient poison in the animal to ensure its death by poison. However, it is not clear that they are constructed in an optimal manner if for no other reason than it is not evident what would be the criterion for optimahty: e.g., time to make an arrow, cost of making a suitable bow, cost of materials, life span of arrows and bows, distance from animal for an accurate shot, aerodynamic stability, etc. A similar comment has been made by Bamforth (1986:39) with regard to tool curation: “. . . different aspects of ‘curation’ are adaptations to different circumstances, implying that no single measure of technological ‘efficiency’ can be universally applied . . . .” If dimensions relevant to physical optimality cannot be taken universally as the basis for variable selection, then it follows that variable selection must reflect emically relevant dimensions. However, these are not known in advance, hence analytical criteria-such as the pattern a frequency distribution might have when the dimension being measured had emit saliency (e.g., Read 1982)-to distinguish such measures are needed. Without such criteria it is difficult to define relevant dimensions without running the risk of circularity. B. Construction ofa space. As noted in the previous section, inclusion of variables that measure dimensions irrelevant to defining underlying groups is one major, global problem. A second, and related aspect, arises from the purported relationship of asserted classes to each other and how this bears on the definition of a space within which analysis is to take place. To see this, consider first the organization of classes into a structure. Two basic structures for classification have been distinguished (Conklin 1964): paradigmatic and taxonomic. The two are distinguished by whether the structure is independent of the order in which variables are considered. In a paradigmatic structure, the minimal classes are the intersection of the distinctions made along each dimension. For example, if one qualitative variable is Shape with two values, (a) triangular shape and (b) leaf shape, and two quantitative dimensions are Length and Width, with Length dichotomized into (a) short and (b) long, and Width dichotomized into (a) narrow and (b) wide, then a paradigmatic classification would have eight classes: (1) triangular/short/narrow, (2) triangular/ short/wide, (3) triangular/long/narrow, (4) triangular/narrow/wide, (5) leaf/

172

DWIGHT

W.

READ

short/narrow, (6) leaf/wide/narrow, (7) leaf/long/narrow, and (8) leaf/ long/wide. The order in which the variables enter into the definitions is immaterial to the class definitions because the distinctions made for one variable are realized regardless of the value of the other variable. For example, the distinction wide/narrow is made regardless of whether the value for Length is short or long. In contrast, a taxonomic structure has an ordering of the defining variables and the distinctions made for a variable do depend on the values of another variable. A taxonomic structure for the three variables Shape, Length, and Width (and which is used in the classification of projectile points from the California Paleo-indian site, 4-VEN39, that will be discussed below) could be (1) triangular/wide, (2) triangular/narrow, (3) leaf/ long, and (4) leaf/short. Here the Width distinction is used to subdivide only the triangular shape class, and the Length distinction is used to subdivide only the leaf shape class. In this case the definitions of the classes require that the variables be considered in the order (1) Shape, then (2) Width or Length. The Width and/or Length dimensions cannot be considered prior to the Shape dimensions. Of these two structures, the paradigmatic one most closely resembles the form assumed by dimensionality reduction and group formation, or object clustering, procedures (Read 1982). When data are measured multivariately, a paradigmatic form is implicitly assumed because each variable has a value for every case and the underlying distribution (such as multivariate normal) assumes that each variable is relevant for all cases. Hence groups based on subdivisions of a multivariate distribution will have, or can be put into, a paradigmatic form [see Read (1982) for an example using Scottsbluff points]. However, a paradigmatic analysis is not well suited to data having a taxonomic structure in which variables are included and groups are subdivided according to groupings made at a prior step. For instance, if the variable Length is not relevant for defining groups when one has first sorted the material according to the values of the Shape variable, then including Length as a variable to be measured for all objects in the data set introduces a false assumption. Including Length implies that a measure of similarity used for making groups should take this variable into account for the triangular shape objects when in fact this is not the case. Yet the variable Length cannot be deleted entirely since it is relevant for the shape class, leaf shape. In effect, the initial analysis needs to be able to include (in this example) the variable Length in a measure of similarity when comparing objects from the leaf shape class, but ignore the variable Length otherwise. But to do so presumes one already knows the underlying groups, in contradiction to the motivation for the analysis. Elsewhere I have argued, using a logical argument, that any clustering

INTUITIVE

TYPOLOGY

AND

AUTOMATIC

CLASSIFICATION

173

procedure based on a similarity measure which uses all variables in a similar manner for all pairs of points will tend to introduce “noise” in proportion to the number of variables which are not relevant for defining groups in the data (Read 1987~). The magnitude of the problem was illustrated with a simulated example based on three nonoverlapping groupings defined with respect to two variables (or dimensions). It was shown in the example that simply including two additional variables with distributions independent of the assignment of cases to the three groupings prevented a standard clustering procedure such as k-means from recovering the initial groups, even when the correct number of groups is specified in advance. As more variables with distributions independent of the three groups are added, the situation becomes worse (see Figs. 1A and B). Since one does not know in advance which variables are sensitive to the as yet unrecovered groupings, divergence from underlying groups in the data, rather than the convergence assumed in the philosophy of numerical taxonomy, is likely to occur as more, equally weighted variables are added. VI. POSSIBLE

RESOLUTION

OF THE DIVERGENCE

PROBLEM?

If numerical grouping methods fail to convergence on an appropriate solution because different groups require different sets of variables for their definition, then it may be possible to use instead a hierarchical approach where the relevant variables change at different stages in the analysis (Whallon 1972). In fact I (Read 1985, 1987b) have used a hierarchical approach to define the taxonomic structure for the 4-VEN39 projectile points mentioned earlier. Principal components were used to reduce the original nine variables, selected for their presumed saliency to the problem, to a set of three principal components (those with eigenvalues al) and then to examine the scores of items along the principal components for “breaks” -first univariately, then bivariately in a scatter plot. When a break was found, the data set was divided accordingly and the analysis was repeated on each of the subdivisions. For the 4-VEN39 points I found that none of the scores for the initial three principal components had bimodal distributions and of the three possible scatter plots, the plot of the first and second principal components unequivocally displayed two groups (which matches the results found in Christenson and Read (1977) where outliers were removed prior to the analysis) (see Fig. 2). These two groups corresponded precisely to the concave versus the convex based points. The data were then divided into these two groups and the principal component reduction was made again on each subgroup considered separately. The two new principal component solutions were examined univari-

174

DWIGHT

W.

READ

&

AA

Aa

A

“AA

A A A A A

A

A A

0 00

0 000

%o

8

*o

0

8*

1’1’1’1’1’1’1’1’1’1’1 -8

-10

-6

-4

-2

Boo

0

CANONICAL

2

0001

CLUSTER

4

VARIABLE A

A

6

8

10

1 2

A

0003

0 0 00 0

Oo

0

**oo

0

0 0 8

0

0 0 0

0

‘A

A A

A

A

AA

A

0 A

AA@

A A4 AA

A A -3

$

-4

A

* I

*

-3

I

’

I

’

-2

IT

-1 CANONICAL

CLUSTER

0001

A t

8

13

0

II

1

2

VARIABLE A

A

I

3

1 A

2

0003

’

I

4

INTUITIVE

TYPOLOGY

AND AUTOMATIC

CLASSIFICATION

175

ately, then in scatter plots. For the convex based points two clearly defined clusters were found in the plot of the second and third principal components, but not in the plot of the first two principal components (see Fig. 3). Discriminant analysis showed that these two groups were defined solely by the base-width dimension within the convex based points. Other variables had identical distributions for the two groups (i.e., the other variables had distributions that were independent of these two groups). Thus the two groups could be defined as (1) wide convex base points and (2) narrow convex base points. For the concave base points, inspection of the scatter plot of the first and second principal component (see Fig. 4) showed that a subdivision should be made into two groups which barely intersect in the form of two ellipses at right angles to one another. These corresponded to two different shape classes:(1) leaf shape and (2) needle/leaf shape. Separate analyses were run on each of these two shape classes. For the leaf shape points, two clusters were found in one plot of the first and third principal component. These two groups corresponded to a size difference (as measured by the variable, length) among the leaf shape points. All together, this led to the definition of five classes: (1) triangular shape/wide base, (2) triangular shape/narrow base, (3) leaf-needle shape, (4) leaf shape/short, and (5) leaf shape/long (see Fig. 5). Within a shape class, the contrasting classesare definable either by a dichotomized variable (hence reducing the class definitions to qualitative ones) or equivalently by the mean and standard error for the distinguishing variable (which yields a quantitative definition based on sample data used to estimate population parameters [see Read (1982, 1985, 1987a, 1987b)]. These classescan also be examined for additional structure as defined by the frequency counts of points per class. The two triangular classes had essentially identical frequencies (overall: 17 versus 18) regardless of the level in the site, and no clear functional differences. These facts suggest the possibility that the difference might reflect a moiety structure in Chumash society (Read 1987b). The argument is based on (1) historical data which suggest the Chumash did have a moiety type of social orgaFIG. 1. Plot of the two canonical variables for the three group means found using k-means clustering. (A) Plot showing the initial data with three groups defmed with respect to two dimensions. Each group has 30 points and independent, uniform distributions for the two dimensions. The canonical variable space is the same as the original, two-dimensional space. (B) Plot showing the groups found by k-means (three groups specified) when the original set of two variables has been augmented by six additional variables, each of which has a frequency distribution independent of the structure for the data shown in (A). The three groups that are found neither preserve the original data structure nor correctly assign cases to groups. Classification error rates are 7, 37, and 57%, for groups 1, 2, and 3, respectively. (See Read 1987d for more details.)

176

DWIGHT

W. READ

2 -

N 0”

1 .

4Y 0 .

-1 -

-2

-

-3

-

x

x

x I -2

-1

I 0

, 1

I 2 FACTOR

I 3 1

FIG. 2. Scatter plot of the fmt two “factors” for the 64 projectile points from 4-VEN39. In this, and in Figs. 3 and 4, the “factors” are the varimax rotated principal component solution using an eigenvalue of 1.O as a cutoff point for the number of principal components. The underlined symbols were- determined to be outhers in another analysis (Christenson and Read 1977). Symbols: x-convex base points; v-concave based points. Reproduced, by permission of the publisher, from Read (1985).

nization; (2) the apparent lack of differences that could be attributed to external constraints arising from usage of the points, thus suggesting that the difference is one of culturally imposed distinctions on an underlying continuum; (3) the essentially identical frequency distribution of the two kinds of points which would be consistent with a division of the village into two social groupings; and (4) the lack of variability in the different levels, again consistent with what is likely to have been an enduring aspect of social structure. Although the hierarchical procedure was effective in this instance, it does depend on two assumptions. (1) The m-dimensional space defined by culturally significant variables in which the groupings are expressed has in fact been measured by the ensemble of operational measures. (2) This space is represented directly either in the original variables or among the principal components so that the groups are clearly expressed univariately, bivariately, or possible in a three-dimensional plot so that there can be direct visual as well as analytical verification of the presence of subgroups in the data. Neither assumption is universally valid. Hence this hierarchical procedure is not a complete solution.

INTUITIVE

TYFQLOGY

AND AUTOMATIC

CLASSIFICATION

FACTOR

177

‘2

FIG. 3. Scatter plot of the second and third “factors” for the 36 concave base points from 4-VEN39. Symbols: n-narrow base; w-wide base. Reproduced, by permission of the publisher, from Read (1985).

VII. CLASS DEFINITIONS Up to this point in the argument it has been assumed that one “knows” what a projectile point is. The fact that, for the most part, one can distinguish a class of objects in a manner which has widespread agreement as to its reality has had the side effect of hiding a crucial aspect of how one goes about classification. What is the domain for which a classification is to be formed? Pragmatically, archaeologists have been able to proceed using “common sense” and have agreed upon domains with labels such as projectile points, scrapers, bruins, drills, jars, plates, hammerstones, etc. without feeling compelled to spend much effort on defining what these domains are. They are part of the “tools of the trade,” as it were, and “known” by all archaeologists. Now let us step away from the pragmatics and the common knowledge and ask how one might define a class such as projectile points. A rough definition might be that a projectile point is a stone artifact used to kill animals and hafted onto a spear, dart, or arrow shaft. This definition has a number of implicit aspects. First, let it be agreed that projectile points are made of stone and not pottery or wood. But why? The answer might be as follows. A projectile point, if it is to be effective, must be able to penetrate into an animal to a sufftcient depth and with consequent shock to the animal’s system so that the animal is either killed outright or sufficiently incapacitated to be killed by other means. This

178

DWIGHT

-2

-1

W.

READ

3

1

2 FACTOR

1

FIG. 4. Scatter plot of the first and third “factors” for the 28 convex base points from 4-VEN39. Outliers are underlined. Symbols: I-leaf shape; n-needleheaf shape. Reproduced, by permission of the publisher, from Read (1985).

implies that the projectile point must have imparted to it a substantial amount of force upon propulsion which will be virtually instantaneously imparted to the animal on impact. Hence the point is subjected to severe compressive forces at the time of impact. Stone has an excellent ability to withstand compressive forces and thus is a good choice for a projectile point. The inquiry can be pursued further, but the line of the argument should be clear. The attempt to define a class “projectile point” does not seem to lead to a morphological definition, but to an assertion about (in this case) a task to be performed and the means by which the task will be performed. Implicit in the above discussion has been the assumption that the animal is to be killed at a distance and the means for so doing shall be effective-otherwise the task has no rationale. It would seem from this example that to define a class, “projectile point,” several things are necessary. The first is to determine the task at hand. The second is to define the relationships and properties that will be invoked in the performance of the task. The third is to construct a model at the conceptual level which shows how these relationships and properties can be incorporated or realized through the material object. Fourth, it is necessary to show how this model of these relationships can be translated into a concrete object in which these relationships and prop-

INTUITIVE

TYPOLOGY

AND

AUTOMATIC

Projectile

Projectile

-$

7

a

Narrow

ngu<

Points

179

CLASSIFICATION

Points

at VEN39

Leaf/Needte

/of\

1 Wide

Small

Large

cont.

dist.

PHENOMENOLOGICAL

FIG. 5. Typology structure for the projectile points from 4-VEN39. The upper part of the figure shows the structure for the projectile point classes. The lower part of the figure shows archetypes from each of the classes. The ftith class (right side of the diagram) has a continuous size variation from small to large without any obvious cut points. Reproduced, by permission of the publisher, from Read (1987b).

erties are realized. Finally, while this is still an etic definition of a class, I have attempted to identify those properties and conceptual relationships that form the minimal external constraints that operate when the task in question is to be performed effectively. Whether a given kind of projectile point has a form that is effective now becomes an empirical question whose answer informs us as to whether these external constraints and relationships were emically realized as well. To pursue the argument further in this direction the notion of a class definition needs reconsideration. Implementing the fundamental definition of a class, namely that all of its members share some property in common, has been problematic. Many groups that seem to have coherence do not have this property. A strict monothetic criterion for groups has been too strong, whereas polythetic criteria give only the illusion of greater utility by introducing a vague definition of what, precisely, constitutes a polythetically defined class. The extreme of this trend-definitions that are allowed to be “fuzzy” at their boundaries-reduces the definition of the class to being synonymous with the group. It runs the risk of eliminating the distinction between group and class. All of these attempts to get good fit between a definition of a class and groups of objects that seem to “hang together” assume that the shared

180

DWIGHT

W.

READ

property of classes is a trait expressed by the object-width, thickness, color, curvature, etc. But with this assumption comes an inconsistency between the strict notion of a class as a collection of objects that share a property and the notion of a group as objects that are internally coherent. The inconsistency stems from assuming that measurable properties on entities should serve as the commonality of class membership, that is, of trying to use the consequence of class membership as the criterion for class membership. For example, with the points from 4-VEN39, concave based points may be easily distinguished from convex based points both at the level of classes and of groups. Here the class definition is monothetic and the points can be assigned unambiguously to one or the other of the two classes.But the analysis has shown that the concave based points are not internally homogeneous across other dimensions and can be subdivided into two classes, Narrow and Wide, according to the base width of the point. Here the definition of these latter two classes,and the assignment of an object to one or the other, is not based on a trait that the individual object possesses.Rather, it depends on the relurionship of the trait for the individual object to the same trait for other comparable instances (i.e., other concave base points from 4-VEN39). A projectile point from this site is not Narrow in the same way its base is concave or convex. Concavity or convexity of the base is a geometric property that can be assigned to a single point even when considered in isolation from other points. But a single point considered in isolation has only a particular base width, say 10 mm. The measurement of 10 mm is not “narrow” or “wide” as it stands. Further, it is not narrow even should it happen to fall at the lower end of the range of base widths. Rather, it can be classed as Narrow only because of the dichotomous form of the distribution of the base widths of points at 4-VEN39, hence it is Narrow only in relationship to these other points. At the level of the trait, where base width is measured as a value on a ratio scale variable, one cannot give a monothetic class definition, such as a range of values, without creating the problem addressed by Dunnell (1971) of having class definitions dependent on the particular properties of the members of the class used in the analysis. Thus, to assert that one group is distinguished, say, by a base width falling between 10 and 12 mm is merely a pragmatic devise for sorting data. It is not a class definition with cultural saliency because these upper and lower bounds are determined by vagaries of the data in hand. As argued elsewhere (Read 1982, 1985, 1987b), the statistical notion of a population parameter can circumvent this difficulty that Dunnell has seen with class definitions based on quantitative measurements. One needs only to assert that there wus some width that was deemed proper

INTUITIVE

TYF’OLOGY

AND

AUTOMATIC

CLASSIFICATION

181

for the projectile points and that artisans strived to make points with the desired width. In this framework the specific value for the individual point is a single datum from the distribution which characterizes the artisan’s manufacturing process. The class can be defined using the population mean p and standard deviation u for the base width dimension. These two parameters can be interpreted as representing both the width that was deemed proper (the mean value JL.)and the errors that arose in manufacturing when attempting to achieve that width (the standard deviation u). Such a class definition does not entail synonymity between units and empirical entities as Dunnell (1986:192) erroneoudy claims. Although this argument does preserve the use of a quantitative measurement as the basis for a class definition, it must be augmented by another feature of the measurements. Concave based points happen to include precisely two width classesat 4-VEN39 and it is the existence of these two classes that makes width a salient dimension for a class definition. Were there but one width deemed proper (i.e., a unimodal distribution of width values), there would be no reason to separate out base width as having more saliency for a class definition than other measures made on the same points. Yet there are two base widths, Narrow and Wide, and it is their juxtaposition that leads to a quantitative definition of the classes, not the converse. Further, there are two class widths not because artisans coincidentally happened to make two different widths; rather, they made two different widths because, I suggest, of their conceptual structuring of what we term the class of concave base points. To put it another way, there are not separately narrow/concave points and separately wide/ concave points, but a single super class, concave base points, divided into two subclasses via the opposition narrow/wide, hence forming a structure. If the argument is valid, it follows that criteria used for class dellnitions must also be capable of incorporating these structural relationships, or else they will be incomplete in the goal of having classes be as culturally informative as possible. One way to incorporate the structural information is through a classification system that begins with the relationships and ends with the morphological characteristics, rather than the reverse. For the projectile points, one could begin by identifying a task-killing an animal at a distance-and what the task entails for effective performance. A first approximation yields something like the following: an object must be transmitted from the hunter to the animal; to kill or incapacitate the animal it must either introduce a poisonous substance or physically incapacitate the animal; in the latter case it must penetrate sufficiently deeply or with sufficient force to stun or kill the animal. Further, whether the means is through introducing a substance or mechanically incapacitating the ani-

182

DWIGHT

W.

READ

ma1 will lead to different sets of relationships amongst the subparts of the projectile. Consider the latter. The object will need to be pointed, but will be constrained by at least two considerations: angularity of the tip for either (1) penetration through the skin or (2) shock introduced to the animal through making a massive wound (e.g., the difference between so-called clean bullets and dum-dum bullets). These constraints are ones of physics and are universal. Penetration requires a balance between sharpness of the point and momentum and the latter depends upon both the mass of the projectile point and the ability of the propulsion system to translate propulsive energy into velocity. For bows and atlatls the energy translation requires a point mounted on a relatively long shaft. This introduces the relationship between the shaft and the point as a basic relationship. Velocity introduces its own constraints (symmetry, weight, etc. of the point; length of shaft, feathering for aerodynamic stability, etc., of the shaft) as a result of the aerodynamic characteristics of a shaft with a relatively massive object mounted at one end (see Christenson 1986 and references therein). And all of these are affected by, and affect, the choice of material for the projectile point. Velocity and mass for heavy shock require hard, rigid materials that can withstand the forces introduced by sudden impact; hard rigid materials such as stone are heavy, thus substantially affecting aerodynamic characteristics, etc. In other words, the class, projectile points, is definable through the set of relations that are entailed in the task that has been identified. From this perspective, an object is not a projectile point because it has a certain shape; rather, it has a certain shape because it is a projectile point. The shape is constrained by the relations and is initially definable through a concrete model in which these relationships are realizable. Thus a projectile point must be made of a hard material capable of withstanding sudden shock; it must have a point within a fairly limited range, etc. Although the relationships that make an object a projectile point and not, say, a burin are quite well-defined (or definable); they also leave much room for variation when expressed in a concrete form. This indeterminacy in form gives room for other relationships that may or may not relate to material tasks. For instance, attempts by analysts to use projectile point forms and/or attributes as markers of social organizational units must assume the presence of such relationships, be they conscious expression or by-products of habitual behavior (Sackett 1982). The form is the material expression and follows from the totality of these kind of relationships. To define a class, as the measure of an underlying process, solely on the basis of form is to assume a one-to-one mapping between structuring process and morphological characteristic, hence implies the feasibility of defining classes monothetically on the basis of traits: i.e., via a qualitative definition. With quantitative measures

INTUITIVE

TYPOLOGY

AND

AUTOMATIC

CLASSIFICATION

183

the mapping from class to measurement is one-to-many. Thus, each point has a width but each width is not a class. Now suppose that there is a moiety organization as discussed above. Consider how this dichotomous distinction might be carried over into the morphology of points. One possibility is that there is a one-to-one relationship between the two structuring processes (manufacture of points either by members of one moiety or by the other moiety) and morphological traits observable on each individual tool. In this case, if all projectile points have a single shape (as is the case here) then the moiety distinction would be marked by a pair of traits, one of which is observable on each point. But the latter is not the case as, for example, there is a range of base widths. Hence there does not appear to be a one-to-one relationship between process and form/trait for these points. On the other hand, a one-to-many mapping of process to measured value would allow for a range of base widths to be associated with each part of the moiety distinction. The empirical result that the points have two distinct base width ranges suggeststhat there is a one-to-one mapping between process and a range of values. From this viewpoint, the measured value of the point’s base width is a marker of moiety membership only through its membership in a range of base widths. This possibility suggeststhat the common property shared by the members of a class such as “point made by members of one moiety” is not a specific morphological trait or measured value, but is definable through relationships amongst measurements. We can posit an underlying contrast between Narrow and Wide to serve as the markers of the moiety and through this contrast we can define one group of points as having the property, Narrow Base, in common and the other group as having the property, Wide Base, in common. The translation of the Narrow/Wide contrast or opposition into morphological form is via two modal values for base width, which in turn results in two unimodal distributions at the level of production of points as implied by the Central Limit Theorem of statistics. Note that the classes defined in this manner have members all of whom share a common property, but the property refers back to the process and not to the measurable traits that result from the process when a point is manufactured. The Central Limit Theorem in this argument serves to justify a pragmatic definition of a class based on ranges of values that can be used to define an object as belonging to one or the other of the two classes. The pragmatic definition is not truly a class definition, but a sorting device whose accuracy depends on the specifics of the particular situation. VIII. CONCLUSION

Numerical taxonomy procedures take as their beginning point morpho-

184

DWIGHT

W.

READ

logical similarity and dissimilarity. The argument given here is that 1120~ phological similarity is the consequence of, not the basis for, class and class structure definition. If so, numerical procedures provide at best a foundation for inductive inference, not deductive determination, of classes and class structure. This is a far cry from their original promise of providing an objective, replicable means for producing basic units. In retrospect, it is not surprising that a methodology which ignores the processes by which data are structured should fail to provide the fundamental groups that are generated by these structuring processes. It would be quite remarkable if one had such a procedure. If structuring processes are the beginning point of understanding the data in hand, then the initial goal becomes one of relating structuring process to measurable groups in the data and not the reverse. One might devise a sequence going from general process to material realization, but the difficulty arises that the sequence does not predict the particular form the objects should take. Hence it does not predict what will be appropriate measures, with the possible exception of those such as the tip of the point; that is, measures that are clearly constrained by the tasks for which the objects are to be used. If it is not possible to go from measures made over a collection of objects to classes via numerical methods, and if definition of the taxonomic structure does not lead to prediction of form, then it is necessary to devise a means to provide the missing part of the argument. In effect, one wants two kinds of information: (1) What are the emically relevant dimensions? and (2) What are the groups for which these dimensions are relevant when measuring similarity? Yet neither the numerical procedures nor the class structure definition approach can provide these two kinds of information. The first is strikingly reminiscent of Rouse’s notion of a mode (Rouse 1939, 1960) and the latter is a topic that has seen little consideration (but see Read 1985, 1987b). Though Rouse recognized the need to distinguish between artibrary attributes and attributes that had emit saliency, he did not provide any means for making the distinction other than the intuition of the researcher. Were it possible to determine the groups that reflected culturally salient differences, the problem of determining modes would reduce to an application of discriminant analysis techniques. Once the relevant groups were determined, discriminant analysis could be used to determine which attributes provide analytical distinction amongst these groups. Attributes which provide group distinctiveness would presumably have cultural meaning, whereas those that do not would be dimensions possibly without cultural distinctiveness. So the same problem keeps rearising; how to form homogeneous groups from heterogeneous data when dealing with incompletely understood structuring processes.

INTUITIVE

TYPOLOGY

AND AUTOMATIC

CLASSIFICATION

185

No simple solution appears to exist for forming a priori groupings. One method is to take advantage of the dimensions along which heterogeneity or homogeneity are likely to be displayed within an assemblageat the time of occupation. Generally, there will be greater homogeneity for shorter time periods and smaller geographic regions. From this it follows that individual assemblages-with subdivisions according to local stratigraphy-are the most likely to have internal cohesion. Hence the spatial unit of analysis should be, say, a single stratum from a multistrata site or local intrastratum concentrations of materials if the stratum is spatially heterogeneous. Further, the collection of material should be sorted initially by qualitative criteria (see Black and Weer 1936; Read 1982), including shape differences that are clearly distinct with respect to a quantitative dimension, e.g., jars with small openings versus large openings, if there is no gradation in orifice size. While these are etically stated criteria, the assumption is that both qualitative differences and breaks in what would otherwise be a continuum of values reflect underlying emically salient distinctions. In both cases the differences imply that only some choices amongst possible alternatives were actually made by the artisans and users, hence the discontinuities observed by the analyst have emit saliency . Taken together, these observations suggest that quantitative analysis should begin with a single qualitative shape class subdivided according to spatial units. The initial groups can be compared for the dimensions that distinguish them should there be heterogeneity in the data, or combined together if they are but arbitrary subdivisions of a larger whole (see Read 1974). Comparison between spatial units for objects qualitatively of the same kind provides a means for determining attributes with cultural saliency in a replicable manner. But, as argued above, choice of attributes needs to be formulated in terms of a model for how these data may be conceptually organized. The latter does not have a well-defined solution. Possibilities range from measures which are archival in the sensethat the shape may be recovered from the measurements (Read 1982)to a description in terms of how the object is produced (e.g., Krause 1984; Read 1986b). In effect, the challenge is to make objective what Rouse could not answer; namely, what are the emically relevant dimensions for the measurement of artifacts. There is return here to the ideas expressed by Rouse half a century ago, but the return is not in the same plane. Rather, it is at a different level, making the trajectory a spiral and not a circle. ACKNOWLEDGMENTS I thank Chris Cam, Andy Christenson, George Cowgill, and Bert Voorrips for their helpful

186

DWIGHT

W.

READ

criticisms and comments on this written version of the lecture that was given as part of the Albert Spaulding Lecture Series. Chris Carr and Bert Voorrips provided detailed comments that did much to soften the rough edges of the original paper. I wish to thank the Department of Anthropology, Arizona State University for funding this lecture in the Albert C. Spaulding Lecture Series. Funding for earlier lectures in this series were provided by the Fulbright College of Arts and Sciences, University of Arkansas.

REFERENCES

CITED

Aldenderfer, M., and R. Blashfield 1984 Cluster analysis. Sage, Newbury Park. Anderberg, M. 1973 Cluster analysis for applications. Academic Press, New York. Balikci, A. 1970 The Netsilik Eskimo. The Natural History Press, New York. Bamforth, D. 1986 Technological efficiency and tool curation. American Antiquity 51:38-50. Black, G., and P. Weer 1936 A proposed terminology for shape classifications of artifacts. American Antiquity 4:28&294. Bleed, P. 1986 The optimal design of hunting weapons: maintainability or reliability? American Antiquity 51:737-47. Braun, D. 1983 Pots as tools. In Archaeological hammers and theories, edited by A. Keene and J. Moore, pp. 107-134. Academic Press, New York. Bronitsky, G. 1986 The use of materials science techniques in the study of pottery construction and use. Advances in Archaeological Method and Theory 9:209-76. Bronitzky, G., and R. Hamer 1986 Experiments in ceramic technology: the effects of various tempering materials on impact and thermal-shock resistance. American Antiquity 51:89-101. can-, c. 1985 Getting into data: philosophy and tactics for the analysis of complex data structures. In For concordance in archaeological data analysis, edited by C. Carr, pp. 184% Westport, Kansas City. 1986 Radiographic analysis of ceramic technological variation for the absolute dating of archaeological assemblages: Woodland southern Ohio. National Science Foundation Proposal. Christenson, A. 1986 Projectile point size and projectile aerodynamics: an exploratory study. Plains Anthropologist 31:109-128. Clark, G. 1976 More on contingency table analysis, decision making criteria, and the use of log-linear models. American Antiquity 421163-79. Conklin, H. 1964 Ethnogenealogical method. In Explorations in cultural anthropology, edited by W. Goodenough, pp. 25-56. McGraw-Hill, New York. Cormack, R. 1971 A review of classification. Journal of the Royal Statistical Society A 134~321-53. De Barros, P. 1982 The effects of variable site occupation span on the results of frequency seriation. American Antiquity 47~291-302.

INTUITIVE

TYF’OLOGY

AND

AUTOMATIC

CLASSIFICATION

187

Dibble, H. 1987 The interpretation of middle Paleolithic scraper morphology. American Antiquity 52:109-17. Doran, J., and R. Hodson 1975 Murhematics and computers in archaeology. Harvard Univ. Press, Cambridge. Dunn, G., and B. Everitt 1982 An introduction to mathematical taxonomy. Cambridge Univ. Press, Cambridge. Dunnell, R. 1971 Systematics in prehistory. The Free Press, New York. 1986 Methodological issues in Americanist artifact classification. Advances in Archaeological Method and Theory 9:149-207. Engelbrecht, W. 1987 Factors maintaining low population density among the prehistoric Iroquois. American Antiquity 52~13-27. Ericson, J., D. Read, and C. Burke 1971 Research design: the relationships between the primary functions and the physical properties of ceramic vessels and their implications for ceramic distributions on an archaeological site. Anthropology UCLA 3234-95. Flenniken, J., and A. Raymond 1986 Morphological projectile point typology: replication experimentation and technological analysis. American Antiquity 51:603-14. Gould, R. 1980 Living archaeology. Cambridge Univ. Press, Cambridge. Gould, S. 1974 The fust decade of numerical taxonomy. Science 183373940. Hodder, I. 1982 Theoretical archaeology; a reactionary view. In Symbolic and structural archaeology, edited by I. Hodder, pp. l-16. Cambridge Univ. Press, Cambridge. Jardine, N., and R. Sibson 1971 Mathematical taxonomy. Wiley, New York. Krause, R. 1984 Modeling the making of pots: an ethnoarchaeological approach. In The many dimensions of pottery, edited by S. van der Leeuw and A. Pritchard, pp. 615699. Universiteit van Amsterdam, Amsterdam. Krieger, A. 1944 The typology concept. American Antiquity 3~271-88. Lewis, R. 1986 The analysis of contingency tables in archaeology. Advances in Archaeological Method and Theory 9277-310. McNutt, C. 1973 On the methodological validity of frequency seriation. American Antiquity 38454. Neff, N. 1986 A rational basis for a priori character weighting. Systematic Zoology 35:110-23. Phagan, C. 1985 Dolores archaeological program projectile point analysis. Part 1. Production of statistical types and subtypes. Dolores Archaeological Program Technical Reports, No. DAP-174. Rasmussen, K. 1931 The Netsilik Eskimos (Vol. VIII). Reports of the Fifth Thule Expedition, Copenhagen.

188 Read, D. 1974

DWIGHT

W. READ

Some comments on typologies in archaeology and an outline of a methodology. American Antiquity 39216-42. 1982 Toward a theory of archaeological classification. In Essays on archaeological typology, edited by R. Whallon and J. Brown, pp. 56-92. Center for American Archaeology Press, Evanston. 1985 The substance of archaeological analysis and the mold of statistical method: enlightenment out discordance? In For concordance in archaeological data analysis, edited by C. Carr, pp. 45-86. Westport, Kansas City. 1986a Mathematical schemata and archaeological phenomena: substantive representations or trivial formalism? Science and Archaeology 2&16-23. 1986b Shape grammar representation of projectile points: a bridge from material object to conceptual structure? Paper presented at the Slst Annual Meeting of the Society for American Archaeology. 1987a Foraging society organization: a simple model of a complex transition. European Journal of Operations Research 30:23&236. 1987b Archaeological theory and statistical methods: discordance, resolution and new directions. In Quantitative research in archaeology: progress and prospects, edited by M. Aldenderfer, pp. 151-184. Sage, Newbury Park. 1987~ Typology construction: an art or a science? Symposia Thracia, in press. Read, D., and A. Christenson 1978 Comments on “Cluster and archaeological classification.” American Antiquity 43:505-506. Rouse, I. 1939 Prehistory in Haiti: a study in method. Yale University Publications in Anthropology 21. Sackett, J. 1982 Approaches to style in lithic archaeology. Journal of Anthropological Archaeology 1:59-l 12. Schneider, D. 1984 A critique of the study of kinship. Univ. of Michigan Press, Ann Arbor. Sokal, R., and P. Sneath 1963 Numerical taxonomy. Freeman, London. Spaulding, A. 1977 On growth and form in archaeology: multivariate analysis. Journal of Anthropological Research 33:1-15. 1982 Structure in archaeological data: nominal variables. In Essays on archaeological typology, edited by R. Whallon and J. Brown, pp. l-20. Center for American Archeology Press, Evanston. Spradley, J., and B. Mann 1975 The cocktail waitress. Wiley, New York. Voonips, A. 1982 Mambrino’s helmet: a framework for structuring archaeological data. In Essays on archaeological typology, edited by R. Whallon and J. Brown, pp. 93-126. Center for American Archeology Press, Evanston. Whallon, R. 1972 A new approach to pottery typology. American Antiquity 3213-33. 1982 Variables and dimensions: the critical step in quantitative typology. In Essays on archaeological typology, edited by R. Whallon and J. Brown, pp. 127-161. Center for American Archeology Press, Evanston.