A Ceramic Compositional Interpretation of Incense-Burner Trade in the

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21 A Ceramic Compositional Interpretation of Incense-Burner Trade in the Palenque Area, Mexico 1

RONALD L . BISHOP

Museum of Fine Arts, Research Laboratory, Boston, M A 02115 ROBERT L . RANDS Southern Illinois University—Carbondale, Department of Anthropology, Carbondale, IL 62901 G A R M A N HARBOTTLE Brookhaven National Laboratory, Department of Chemistry, Upton, N Y 11973

The Classic Maya culture of southern Mesoamerica had a strong theocratic orientation. Notable aspects of ceremonialism in the Palenque area include incense-burning, expressed archaeologically in ceramic supports and receptacles (incensarios). The supports are notable for their technological construction and ornate iconographic content. Incensarios form part of a much larger body of regional ceramics now being intensively studied. Objectives are to determine manufacturing centers and the directional flow of trading relationships; therefore paste composition is accorded special importance. Compositional data are derived through sampling that is successively less extensive but more intensive (binocular examination, petrography, and neutron activation). Focussing primarily on chemical composition, data reduction is achieved by a related set of vector manipulative techniques (iterative cluster analysis; discriminant functions; classification statistics). The resulting paste compositional reference units are evaluated by correlation with petrographic and archaeological information. Compositional data for incensarios are projected on the reference units for the Palenque region as a whole. Preliminary findings suggest that the ceremonial center of Palenque was the major focus of incensario manufacture. Apparently, exchange of incensarios to outlying communities, beyond the boundaries of intensive trace in other ceramics, helped to maintain Palenque's socio-religious primacy. The study o f ceramic t r a d e i s m u l t i d i m e n s i o n a l , r e l a t i n g t o c u l t u r a l and physiochemical v a r i a b l e s t h a t can o n l y be t r e a t e d s e l e c t i v e l y i n a progress r e p o r t . The major lowland Maya s i t e o f 1

Current address: Brookhaven National Laboratory, Department of Chemistry, Upton, N Y 11973. 0097-6156/82/0176-0411$07.50/0 © 1982 American Chemical Society

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Palenque, Mexico, i s the f o c a l p o i n t of such an i n v e s t i g a t i o n ( f i g u r e 1). Although problem o r i e n t a t i o n i s i n p a r t d i r e c t e d toward c h r o n o l o g i c a l refinement [ l ] , a primary goal has been the d e l i n e a t i o n of a " s u s t a i n i n g area" or other s p a t i a l u n i t s c h a r a c t e r i z e d by d i s t i n c t i v e p a t t e r n s of exchange [2,3,4,5]. In the present paper, a t t e n t i o n i s focussed on à p a r t i c u l a r c l a s s of ceramic o b j e c t s - i n c e n s a r i o s or p a r a p h e r n a l i a used i n the r i t u a l burning of incense. In attempting t o determine a manufacturing source f o r t h i s f u n c t i o n a l l y s p e c i a l i z e d c l a s s of p o t t e r y , i t has been necessary to make compositional c h a r a c t e r i z a t i o n s w i t h i n the broader context of the r e g i o n a l ceramics. In the absence of such an approach, i t would be f a r more d i f f i c u l t to assess r e l a t i v e p r o b a b i l i t i e s t h a t the incense burners were manufactured a t a s i n g l e center or i n m u l t i p l e centers and to e s t a b l i s h even the general l o c a t i o n of the zone or zones of production. In an e a r l i e r pétrographie study i t was noted t h a t one r e g i o n a l l y r e s t r i c t e d c l a s s of i n c e n s a r i o s - massive but e l a b o r a t e l y decorated flanged c y l i n d e r s t h a t apparently served as supports f o r f u n c t i o n a l censers - were so s i m i l a r m i n e r a l o g i c a l l y as t o suggest t h e i r manufacture a t a s i n g l e c e n t e r , perhaps Palenque [ 6 ] . I t was recognized t h a t patterned d i f f e r e n c e s i n symbolic content might i n d i c a t e the presence of d i f f e r e n t manu f a c t u r i n g centers or r e f l e c t temporal distinctions. As the s e n s i t i v i t y of neutron a c t i v a t i o n a n a l y s i s was brought to the i n v e s t i g a t i o n of trade i n the Palenque r e g i o n , the i n c e n s a r i o supports and other c l a s s e s of incense burners were analyzed as one aspect of the research. In previous s t u d i e s of Maya incen s a r i o s , i t had been suggested, a l t e r n a t i v e l y , t h a t these o b j e c t s formed p a r t of a f o l k c u l t [7] o r , a t l e a s t i n the case of the flanged c y l i n d e r s , f u n c t i o n e d on a h i e r a r c h a l l e v e l of Maya c i v i l i z a t i o n [8]. Demonstration of p a t t e r n s of exchange f o r these v a r i o u s ceramic o b j e c t s ( i n c e n s a r i o supports, f u n c t i o n a l censers, and other c l a s s e s of p o t t e r y ) should c o n t r i b u t e t o an understanding of t h i s and wider problems. In a d d i t i o n t o the o r n a t e l y decorated supports or stands; i n c e n s a r i o forms t h a t were analyzed i n c l u d e pedestal censers, l a d l e s ( o f t e n w i t h e f f i g y handles), bowls, and a c o n i c a l to trumpet-shaped c o n t a i n e r t h a t appears to have been u t i l i z e d i n c o n j u n c t i o n w i t h the supports, r e s t i n g i n the o r i f i c e of the c y l i n d e r ( f i g u r e 2). A l l form c l a s s e s except the supports show signs of i n t e r i o r burning; t r a c e s of r e s i n are o c c a s i o n a l l y present. Evidence l i n k i n g flanged c y l i n d e r s to incense burning a c t i v i t i e s i s d i s c u s s e d elsewhere [9,10,11]. Here we simply note t h a t the outcurved w a l l s of the trumpet-shaped censer provide a range i n diameter so as to f i t i n t o one or another or the t u b u l a r


1

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F i g u r e s i n brackets i n d i c a t e the l i t e r a t u r e references a t the end of t h i s paper.


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Figure 2. Incensario form classes. Key: a, cylindrical support; b, trumpet-shaped receptacle; c, pedestal; d, bowl; and e, ladle. Specimens not to scale. Also, b, base of specimen missing; and a, after Rands 1969 (courtesy, Instituto Nacional de Antropologia e Historia), not analyzed.


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supports, there being no n e c e s s i t y f o r a p a r t i c u l a r support and r e c e p t a c l e t o be matched i n diameter. These o b j e c t s could have been used interchangably, being manufactured a t d i f f e r e n t l o c a l i t i e s and s t i l l s e r v i n g e f f e c t i v e l y i n combination. The trumpet-shaped c o n t a i n e r i s found c o n s i s t e n t l y i n cave and pyramid contexts t h a t i n c l u d e t h e flanged c y l i n d r i c a l support, although t h e l a t t e r o f t e n occurs independently o f t h e removable containers. Specimens a r e o f Late C l a s s i c and perhaps Terminal C l a s s i c date (ca. A.D. 600-900). Information about ceramic pastes has been d e r i v e d through sampling t h a t was s u c c e s s i v e l y l e s s extensive but more i n t e n s i v e , i d e a l l y p r o g r e s s i n g from b i n o c u l a r examination t o petrography t o neutron a c t i v a t i o n as i l l u s t r a t e d i n f i g u r e 3 [12]. Chemical data were used f o r m u l t i v a r i a t e a n a l y s i s , o r d i n a l pétrographie data being p r o j e c t e d a g a i n s t t h e c h e m i c a l l y c h a r a c t e r i z e d ceramic specimens. Steps i n group formation a r e o u t l i n e d below; we wish to make two p o i n t s here. F i r s t , sharper i n f e r e n c e s may be drawn about l o c a l i t i e s f o r c l a y procurement when chemical data a r e viewed from a g e o l o g i c a l - m i n e r a l o g i c a l p e r s p e c t i v e . This approach has been u t i l i z e d i n t h e ongoing research but enters only m i n i mally i n t o d i s c u s s i o n i n the present paper. Second, the a n a l y t i c a l procedure enables m i n e r a l o g i c a l p a t t e r n s which have strong chemical c o r r e l a t e s t o be seen i n a body o f ceramics which i s much l a r g e r than t h e c h e m i c a l l y sampled p o t t e r y , broadening t h e a r c h a e o l o g i c a l a p p l i c a t i o n of the compositional i n f o r m a t i o n . The need f o r a broad compositional p e r s p e c t i v e was one f a c t o r i n our sampling, which had the o b j e c t i v e o f d i s t i n g u i s h i n g l o c a l l y made p o t t e r y on an i n t r a r e g i o n a l b a s i s . Incensarios are uncommon r e l a t i v e t o many other f u n c t i o n a l c l a s s e s o f ceramics and do not, t h e r e f o r e , comprise a r e l i a b l e body o f m a t e r i a l on which t o formulate groups t h a t may be indigenous t o a p a r t i c u l a r locality. S p e c i a l i z e d f u n c t i o n a l l y and i n d e p o s i t i o n a l context, i n c e n s a r i o s were not represented i n c o l l e c t i o n s from a number o f s i t e s and so would c o n t r i b u t e minimally t o our i n i t i a l under standing o f b a s i c compositional p r o f i l e s w i t h i n the Palenque region. Moreover, i n c e n s a r i o s excavated a t Palenque l a c k the time depth which i s one i n d i c a t i o n o f l o c a l i z e d production according t o t h e p o s t u l a t e o f s u s t a i n e d , l e a s t - e f f o r t procure ment o f l o c a l i z e d c l a y resources. In view o f these f a c t o r s , our i n i t i a l chemical groups were l a r g e l y based on j a r s , bowls, p l a t e s and other w e l l represented form c l a s s e s ; only a f t e r groups had been formulated on t h i s b a s i s were most o f t h e i n c e n s a r i o s analyzed. I t should a l s o be noted t h a t t h e c a p a c i t y o f our c l u s t e r i n g program, CLUS, would not permit simultaneous a n a l y s i s of a l l the i n c e n s a r i o and non-incensario specimens t h a t were c h e m i c a l l y analyzed. In r e c o g n i t i o n o f t h e formation o f groups t h a t permits the subsequent comparison o f a d d i t i o n a l specimens, w i t h t h e p o t e n t i a l o f i n c r e a s i n g group membership, t h e term reference u n i t i s employed.


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t SPECIAL PETROLOGICAL TECHNIQUES Figure 3. Starting with the binocular microscope, discriminatory power increases in a counterclockwise direction, as indicated by the circular background. Variations in flowline width reflect the differential sampling capabilities of the techniques. Special petrological techniques include X-ray diffraction, electron and proton microprobe, staining, and heavy mineral separation.


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A f u r t h e r p o i n t r e q u i r e s e x p l i c a t i o n . J u s t as a r c h a e o l o g i c a l problem o r i e n t a t i o n s d i f f e r , l e a d i n g t o "lumping" i n one case and " s p l i t t i n g " i n another, so i s i t p o s s i b l e t o use m u l t i v a r i a t e l y d e r i v e d groups on a r e l a t i v e l y broad o r r e f i n e d b a s i s . The more r e f i n e d groupings should tend t o p i n p o i n t microzonal d i f f e r e n c e s but, because o f sample s i z e o r other c o n s i d e r a t i o n s , may be l e s s robust s t a t i s t i c a l l y . Again, the i n v e s t i g a t o r may f i n d t h a t t h e broader groups r e l a t e more r e a d i l y t o independent v a r i a b l e s and thus have g r e a t e r p r a c t i c a l a p p l i c a t i o n t o h i s problem, o r t h e reverse may be t r u e . The formation o f paste compositional groups i s a h e u r i s t i c procedure. Neutron A c t i v a t i o n A n a l y s i s Incensario and non-incensario ceramics were prepared f o r instrumental chemical analysis, following usual Brookhaven National Laboratory procedures [13]. Samples and standards were bombarded f o r 18 hours a t a thermal neutron f l u x o f 1 χ 1 0 n/cm sec. A f t e r a 10-day c o o l i n g p e r i o d , a one-minute bombard ment a t t h e same f l u x l e v e l was used t o produce t h e s h o r t - l i v e d isotopes. The a c t i v a t e d samples were t r a n s f e r r e d t o counting v i a l s and p l a c e d i n an automatic sample changer. The counting c o n f i g u r a t i o n c o n s i s t e d o f a P r i n c e t o n Gammatech Ge-Li d e t e c t o r (35 cm c r y s t a l w i t h a b e t t e r than 1.8 keV r e s o l u t i o n on C o ) coupled t o an ND-2400 4096 channel a n a l y z e r and magnetic tape readout. The gamma s p e c t r a were processed by t h e BRUTAL program on t h e Brookhaven CDC 7600 computer. F i n a l elemental concentra t i o n s were obtained by use o f the "in-house" programs ELCALC and SAMPCALC. The present i n v e s t i g a t i o n u t i l i z e d t h e elements Na, K, Rb, Cs, Ba, Se, Ce, Eu, Hf, Th, C r , Mn, Fe, Co, and T i , t h e l a s t being determined by x-ray f l u o r e s c e n c e . The elemental data are on f i l e a t the Department o f Chemistry. 1 4

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F o l l o w i n g neutron a c t i v a t i o n a n a l y s i s , several steps were taken i n t h e i n v e s t i g a t i o n o f p o s s i b l e source areas f o r the Palenque-region incense burners. As has been seen, t h e i n v e s t i g a t i o n was p a r t o f a broader chemical c h a r a c t e r i z a t i o n , and t h e e f f e c t i v e compositional assignment o f i n c e n s a r i o s t o Palenque o r non-Palenque sources was n e c e s s a r i l y made i n r e l a t i o n s h i p t o other c l a s s e s o f ceramics. (1) The f i r s t s t e p , t h e r e f o r e , was t o f o r mulate p r o v i s i o n a l chemical groups o f non-censer ceramics f o r the region. Among these groups, some were comprised o f p o t t e r y which was s i m i l a r t o t h e i n c e n s a r i o s i n temper and t e x t u r e , being c h a r a c t e r i z e d by quartz sand i n t h e medium t o f i n e s i z e range. Only those chemical groups i n which t h e p o t t e r y i s p e t r o g r a p h i c a l l y s i m i l a r t o the incensarios are relevant t o the a n a l y t i c a l steps d i s c u s s e d here. (2) The p r o v i s i o n a l groups were subjected t o s t a t i s t i c a l e v a l u a t i o n and refinement. Divergent specimens


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were removed u n t i l i n t e r n a l taxonomic s t a b i l i t y r e s u l t e d . (3) I n t e r p r e t a t i o n of the groups f o l l o w e d . E s s e n t i a l l y , t h i s was based on t h e i r correspondences w i t h pétrographie and d i s t r i b u t i o n a l data. The l a t t e r took i n t o c o n s i d e r a t i o n a r c h a e o l o g i c a l provenience, s t r o n g d i s t r i b u t i o n a l p a t t e r n s being noted f o r l a t e r reference. As a c t u a l l y implemented, c o n s i d e r a b l e feedback between steps 2 and 3 took p l a c e . (4) Having s t a t i s t i c a l l y r e f i n e d the groups (step 2) and noted t h a t they possessed o v e r a l l pétro graphie p a t t e r n i n g and a r c h a e o l o g i c a l u t i l i t y (step 3 ) , we pro j e c t e d the compositional p r o f i l e s of the i n c e n s a r i o s a g a i n s t those of the reference u n i t s . The p r o b a b i l i t y of i n c e n s a r i o membership i n the v a r i o u s reference u n i t s was determined by standard m u l t i v a r i a t e s t a t i s t i c a l techniques. These steps are now considered in greater d e t a i l . Step 1. The i n i t i a l p a r t i t i o n i n g of the non-incensario data s e t was achieved through the use of the program CLUS - an i t e r a t i v e c l u s t e r i n g procedure [14]. CLUS seeks i n t e r n a l geometric evidence t o a r r i v e a t the "best" number of groups and t h e i r membership. The c l u s t e r i n g a l g o r i t h m r e f l e c t s the b a s i c p o s t u l a t e t h a t the t o t a l s c a t t e r or d i s p e r s i o n matrix Τ i s comprised of the matrices of within-group d i s p e r s i o n W and between-group d i s p e r s i o n B; e.g., Τ = W + Β [15,16]. For an " o p t i m a l " c l a s s i f i c a t i o n , s i n c e the t o t a l v a r i a t i o n i s held constant, one need only minimize W, thereby maximizing B. This i d e n t i f i e s the c l u s t e r s t h a t are the most i n t e r n a l l y homogeneous and e x t e r n a l l y i s o l a t e d . For a m u l t i v a r i a t e problem, the c l u s t e r i n g c r i t e r i o n t o be maximized becomes the r a t i o of the determinants Τ and W. This r a t i o w i l l change as the number of groups i s i n c r e a s e d , and i n s p e c t i o n of the

rate

of

increase

of

the

value

log

(max

^)

serves

as

an

informal i n d i c a t o r of the "best" number of groups [17,18]. The data s e t was standardized and transformed t o p r i n c i p a l component space. The 10 l a r g e s t components, r e t a i n e d to serve as the clustering v a r i a b l e s , represented 93 percent of the total variation. I t i s , however, d i f f i c u l t f o r any grouping procedure to deal s a t i s f a c t o r i l y w i t h the heterogeneity contained i n the o r i g i n a l data m a t r i x , as produced by n a t u r a l and c u l t u r a l f a c t o r s [19]. CLUS seeks a " g l o b a l " s o l u t i o n ; t h e r e f o r e , when the f u l l data s e t was i n p u t , CLUS determined t h a t three r a t h e r g e n e r a l i z e d groups were o p t i m a l , as evidenced by the c r i t e r i a d e s c r i b e d above. Geographic and pétrographie c o r r e l a t i o n s e x i s t e d w i t h the c h e m i c a l l y d e r i v e d groups but, as these were not s t r o n g , we attempted to see i f refinement would generate s t a t i s t i c a l l y robust u n i t s having g r e a t e r agreement w i t h the m i n e r a l o g i c a l and c u l t u r a l v a r i a b l e s . Experience has shown us t h a t to accept a f i n e r p a r t i t i o n of the whole data s e t a f t e r an " o p t i m a l " d i v i s i o n has been obtained by the computer o f t e n r e s u l t s i n a degenerative s o l u t i o n . Therefore, t o a s c e r t a i n i f g r e a t e r refinement was p o s s i b l e , each of the three groups was submitted s e p a r a t e l y t o CLUS, a l l o w ing the f u l l s e n s i t i v i t y of the c l u s t e r i n g a l g o r i t h m to be devoted

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to t h e r e s t r i c t e d matrix. Seven p a r t i t i o n s were s e l e c t e d , u n i t s 1 and 2 d e r i v i n g from one o f t h e o r i g i n a l c l u s t e r i n g s , u n i t s 3-6 from t h e second, and u n i t 7 from t h e t h i r d . The t e n t a t i v e groupings were u s u a l l y those c o n t a i n i n g t h e l a r g e s t number o f specimens w i t h i n an o p t i m a l p a r t i t i o n and having the s m a l l e s t i n t e r n a l elemental v a r i a t i o n . Each u n i t was then inspected f o r its homogeneity as based on s t a t i s t i c a l , pétrographie, and a r c h a e o l o g i c a l c o n s i d e r a t i o n s . B e t t e r p a t t e r n i n g w i t h non-chemical data - hence a more v i a b l e and useful c l a s s i f i c a t i o n - was obtained. Step 2. Operating i n a space d e f i n e d by l i n e a r d i s c r i m i n a n t f u n c t i o n s , and under t h e assumption o f a m u l t i v a r i a t e normal d i s t r i b u t i o n , Bayesian c l a s s i f i c a t i o n techniques were used as a h e u r i s t i c device t o evaluate group memberships [20]. D i f f e r e n t types o f i n f o r m a t i o n were sought; one c o n s i d e r a t i o n was t h e l i k e l i h o o d t h a t a given data p o i n t could e x i s t as f a r as i t d i d from t h e c e n t r o i d o f i t s group and y e t be a member o f t h a t group. Specimens were removed t h a t had group containment values so low as t o suggest t h a t t h e sherds might not belong t o any o f the groups under c o n s i d e r a t i o n . No absolute t h r e s h o l d was s e t ; r a t h e r each group was i n d i v i d u a l l y inspected f o r t h e general l e v e l o f compactness about t h e group c e n t r o i d . I t was found t h a t removal o f t h e specimens w i t h "lower" c o n d i t i o n a l p r o b a b i l i t i e s improved t h e i n t e r n a l pétrographie homogeneity. A second c o n s i d e r a t i o n r e l a t e d t o the p r o b a b i l i t y o f group membership. This i n v o l v e d t h e c a l c u l a t i o n o f p o s t e r i o r p r o b a b i l i t i e s , t h e samples n e c e s s a r i l y being assigned t o t h e group w i t h t h e highest p r o b a b i l i t y . The few specimens w i t h p o s t e r i o r p r o b a b i l i t i e s t h a t were s p l i t between two o r more groups were removed i n order t o provide more homogeneous and s t a b l e u n i t s . Group memberships were then reevaluated. In an e a r l i e r d r a f t [21] the assessment o f group membership was based, i n p a r t , on t h e p r o b a b i l i t i e s generated by SPSS, v e r s i o n 6, i n s t a l l e d on an IBM 370 computer. Subsequently, we have learned t h a t t h e IBM d i s c r i m i n a n t a n a l y s i s r o u t i n e was programmed i n s i n g l e p r e c i s i o n . The r e s u l t i n g l o s s o f p r e c i s i o n a t times created erroneous p r o b a b i l i t i e s and i n c o r r e c t group assignments. The p r o b a b i l i t i e s and percentages reported here were obtained by ADCORR o r SPSS ( v e r s i o n 7) implemented on a CDC 7600. These data update t h e above mentioned paper and t h a t o f Rands, Bishop and H a r b o t t l e [11]. The c l a s s i f i c a t i o n s t a t i s t i c s were based on a pooled c o v a r i ance m a t r i x ; t h i s has advantages but a l s o weaknesses. P a r t i t i o n ing o f a data s e t w i l l f r e q u e n t l y y i e l d groups having only a few members. These small c l u s t e r s - d i f f i c u l t t o evaluate s t a t i s t i c a l l y - may a r c h a e o l o g i c a l l y be as i l l u m i n a t i n g as t h e l a r g e r c l u s t e r s ; f o r example, long-distance trade may be i n d i c a t e d . Since d e r i v a t i o n o f d i s c r i m i n a n t f u n c t i o n s r e q u i r e s the i n v e r s i o n of t h e covariance m a t r i x , a group c o n t a i n i n g fewer samples than variâtes would n e c e s s a r i l y have a s i n g u l a r matrix and cannot be inverted. P o o l i n g allows t h e use o f d i s c r i m i n a n t f u n c t i o n s and ,,


419

M


420

N U C L E A R A N D C H E M I C A L DATING

TECHNIQUES

r e l a t e d s t a t i s t i c s t o d e s c r i b e group s e p a r a t i o n and the l i n e a r combinations o f v a r i a b l e s (chemical elements) r e s p o n s i b l e f o r t h a t s e p a r a t i o n . However, the unique c o n f i g u r a t i o n o f a small group's s c a t t e r matrix c o u l d be overshadowed by the i n f l u e n c e o f l a r g e r groups. I f a s p e c i f i e d l e v e l o f homogeneity i s found over a l l groups, a pooled matrix may be acceptable. I f s i g n i f i c a n t heterogeneity i s p r e s e n t , the a c t u a l p r o b a b i l i t i e s o f group mem b e r s h i p w i l l vary depending on whether the sample i s evaluated r e l a t i v e t o a pooled o r a separate covariance matrix. If covariance matrices o f unequal s i z e are used, there i s a g r e a t e r chance o f a specimen being assigned t o the group having the l a r g e s t o v e r a l l d i s p e r s i o n [ 2 2 ] . Therefore, i t i s important t o o b t a i n as much i n f o r m a t i o n as p o s s i b l e about the group d i s p e r s i o n s . The d i s p e r s i o n o r " g e n e r a l i z e d v a r i a n c e " o f a m a t r i x was measured by the determinant o f the group's covariance m a t r i x , and a t e s t f o r homogeneity o f the separate matrices was performed using the method o f Kendall and S t u a r t as programmed i n SAS.76 [23,24], Groups 2 and 7 were omitted from the homogeneity t e s t because o f i n s u f f i c i e n t members. The r e s u l t s f o r the remaining f i v e u n i t s are given i n Table 1, Column A, and i n d i c a t e t h a t the covariance matrices are not significantly heterogeneous (p Chi-square

0.0001

0.0001


21.

BISHOP ET AL.


421

Step 3. As i n d i c a t e d , e v a l u a t i o n s based on correspondences i n chemical, pétrographie and a r c h a e o l o g i c a l p a t t e r n i n g were made a t v a r i o u s p o i n t s i n the i n v e s t i g a t i o n . As these do not r e q u i r e a formal d e s c r i p t i o n o f s t a t i s t i c a l procedures, t h i s step i s not considered f u r t h e r a t the present time. Step 4. In order t o o b t a i n the p r o b a b i l i t i e s o f i n c e n s a r i o membership i n a l l the reference u n i t s , the program SPSS and a pooled covariance matrix were used. However, when the number o f group members was s u f f i c i e n t l y l a r g e , the p r o b a b i l i t i e s o f group containment were r e c a l c u l a t e d r e l a t i v e t o the c e n t r o i d and d i s p e r s i o n matrix o f t h a t s i n g l e group. This was accomplished by using the program ADCORR [25]. While i n p a r t complementary, several major d i f f e r e n c e s e x i s t i n the way SPSS and ADCORR deter mine group containment p r o b a b i l i t i e s . The b a s i s o f the SPSS c l a s s i f i c a t i o n s t a t i s t i c s i s the use o f d i s c r i m i n a n t f u n c t i o n s - weighted, l i n e a r combinations o f the o r i g i n a l standardized v a r i a b l e s s e l e c t e d t o d i f f e r e n t i a t e maxi mally among the groups. The maximum number o f f u n c t i o n s i s l i m i t e d t o the number o f groups minus 1. ADCORR, however, asses ses group containment q u i t e d i f f e r e n t l y . The o r i g i n a l v a r i a b l e s are f i r s t converted t o l o g c o n c e n t r a t i o n space ( f o r the r a t i o n a l e of t h i s t r a n s f o r m a t i o n , see Sayre [26].) The e i g e n v e c t o r s , equal i n number t o the rank o f the o r i g i n a l m a t r i x , are obtained from the variance-covariance matrix and are used t o determine t h e Mahalanobis d i s t a n c e o f a sample from i t s c e n t r o i d . The p r o b a b i l i t y o f a sample having a given Mahalanobis d i s t a n c e and y e t belonging t o the group i s based upon the d i s t r i b u t i o n o f H o t e l l i n g ' s T . Due t o the d i f f e r e n c e s between SPSS and ADCORR, only rough correspondences i n t h e i r r e s p e c t i v e c a l c u l a t i o n s o f group membership a r e t o be expected. However, i f the d e f i n e d groups a r e f a i r l y w e l l i s o l a t e d and homogeneous, the determination of p e r i p h e r a l o r intermediate specimens should be p o s s i b l e w i t h e i t h e r program. In e f f e c t , CLUS was used t o form the seven p r o v i s i o n a l groups (step 1). The c l a s s i f i c a t i o n options o f SPSS were p r i m a r i l y used to d e r i v e r e f i n e d u n i t s from these i n i t i a l groupings (step 2). A t approximately a 10 percent p r o b a b i l i t y o f group containment, ADCORR served t o support the SPSS c l a s s i f i c a t i o n . A t t h i s t h r e s h o l d , chemical, pétrographie, and a r c h a e o l o g i c a l data appeared t o converge i n an a r c h a e o l o g i c a l l y u s e f u l manner (step 3). There f o r e , the 10 percent ADCORR l e v e l was r e t a i n e d as the somewhat a r b i t r a r y lower l i m i t o f the acceptable c r i t e r i o n o f membership i n the p r o j e c t i o n o f i n c e n s a r i o data a g a i n s t the reference u n i t s (step 4 ) . 2

Data I n t e r p r e t a t i o n f o r the Reference U n i t s Out o f approximately 300 sandy-textured non-incensario ceramic samples, 194 were c l a s s i f i a b l e i n t o seven s t a b l e groups; mean c o n c e n t r a t i o n s f o r the f i f t e e n chemical elements a r e l i s t e d


422


i n Table 2. The other ceramics had s u f f i c i e n t l y low group c o n t a i n ment p r o b a b i l i t i e s t o suggest t h a t they were not c l a s s i f i a b l e i n t o any o f these reference u n i t s , as c u r r e n t l y defined. Each o f the seven groups proved on i n s p e c t i o n t o have i n t e r n a l pétro graphie as w e l l as chemical similarity. Based on sherd provenience ( t h e a r c h a e o l o g i c a l c r i t e r i o n o f abundance) two o f the reference u n i t s have a pronounced locus a t Palenque. This i s seen i n Palenque's s u s t a i n e d t r a d i t i o n o f red-brown p o t t e r y , s i m i l a r m i n e r a l o g i c a l l y t o u n i t s 1 and 2, as determined by e x t e n s i v e microscopic sampling. The r e l a t i v e l y long time span over which ceramics s i m i l a r t o those groups occurred i s i n c o n t r a s t t o low frequencies o r l a c k o f depth a t Palenque o f p o t t e r y resembling t h e other reference u n i t s . To minimize chance correspondences, a l l ceramics o f non-Palenque provenience [ 7 ] were removed from the "indigenous" appearing u n i t s 1 and 2, reducing the t o t a l o f the two groups t o 79 specimens. As a r e s u l t , s t i l l g r e a t e r pétrographie and chemical homogeneity was achieved w i t h i n these u n i t s . The goal o f o b t a i n i n g a chemical c h a r a c t e r i z a t i o n s u f f i c i e n t l y s e n s i t i v e t o d i f f e r e n t i a t e p o t t e r y made i n the immediate l o c a l i t y o f Palenque from other r e g i o n a l ceramics guided t h e s p l i t t e r ' s approach used i n the preceeding a n a l y t i c a l steps. I t i s recognized t h a t c h e m i c a l l y d i v e r g e n t c l a y resources might a l s o occur i n c l o s e geographical p r o x i m i t y t o Palenque and so e n t e r i n t o "indigenous" ceramic p r o d u c t i o n , c o n s t i t u t i n g an u n c o n t r o l l e d aspect o f the present research. We do not address t h i s problem here aside from n o t i n g the ambiguous s t a t u s o f approximately 100 quartz-tempered specimens which are u n c l a s s i f i e d according t o reference u n i t , some o f which would have been i n c l u d e d had boundaries been drawn l e s s c l o s e l y . We b e l i e v e , however, t h a t p o t t e r y has been i s o l a t e d which can be a s c r i b e d w i t h confidence to a microzone centered on Palenque. Although i n f o r m a t i o n regard ing many specimens has been t e m p o r a r i l y l o s t i n the process, t h e m u l t i p l e steps o f data r e d u c t i o n have been u s e f u l i n o b t a i n i n g a chemical p r o f i l e t h a t i s u n l i k e l y t o be d u p l i c a t e d a t manufactur ing centers l y i n g o u t s i d e the immediate l o c a l i t y o f Palenque. To a t t a i n t h i s was our o b j e c t i v e a t t h i s p a r t i c u l a r stage o f t h e research program. T o t a l specimens f o r the seven reference u n i t s are g i v e n , by s i t e provenience, i n Table 3. The u n i t s are represented i n f i v e dimensional d i s c r i m i n a n t space, the coordinates f o r the f i r s t two dimensions being shown i n f i g u r e 4. These two v e c t o r s account f o r 72 percent o f the t o t a l d i s c r i m i n a n t power. For convenience, approximate t e r r i t o r i a l l i n e s have been added t o the p l o t . Apparently r e p r e s e n t i n g the compositional p a t t e r n o f l o c a l l y made Palenque p o t t e r y , u n i t s 1 and 2 are enclosed w i t h i n a s i n g l e t e r r i t o r i a l boundary. Less w e l l represented but, as w i l l be seen, of c o n s i d e r a b l e i n t e r e s t f o r the i n c e s a r i o problem, i s u n i t 7, which r e l a t e s p r i m a r i l y t o the s i t e o f Xupa. Observable separa t i o n o f u n i t s 3, 4, and 5 i s p o s s i b l e o n l y when u t i l i z i n g a d d i t i o n a l d i s c r i m i n a n t f u n c t i o n s beyond the f i r s t and second. In

1.00

0.876

0.785

1.66

1.63

2

K 0

52.6

47.5

47.0

68.5

67.5

2

Rb 0

Chemical

2.30

2.22

3.12

3.52

2.99

2

Cs 0

436

423

448

647

608

BaO 3

18.6

16.8

19.3

17.8

17.0

2

Sc 0 2

108

a

1.61

1.24

1 .41

2.51

1.52

2

Eu 0 3

2

10.8

15.1

12.0

8.77

11.6

Hf0 2

12.6

11.8

12.0

13.8

11.5

Th0 3

1410

1600

1500

986

1190

2

Cr 0

Mean Elemental

330

251

328

360

325

MnO

4.20

3.68

3.89

5.52

4.64

2

Fe 0 3

2

1.09

0.899

0.968

T10

32.1

1.13

21.5 1.21

26.5

41.0

26.6

CoO

Concentrations.

2.22 9.58 11.4 1090 231 2.53 19.0 1.01 f i g u r e accuracy. Sodium, potassium, I r o n , and as p a r t s per m i l l i o n . Standard d e v i a t i o n s 5.26 f o9.22 1420 5.91Elements 35.5 0.953 2 t2.14 o 65 percent r sodium i n U 371 n i t 3. standard d e v i a t i o n s o f 10-15 percent.

79.4

93.2

138

93.2

Ce0

Paste Compositional Reference U n i t s :

0.150 0.962 47.0 2.77 455 15.5 131 Mean oxide c o n c e n t r a t i o n r e p o r t e d w i t h three U nt i t a 7 n i u m a r e given i n percent; others l i s t e d 0.991 from 1.48 62.2 2.44 516 22.0 ranged s i x percent f o r scandium i n U 106 nit o f lower m o b i l i t y ( e . g . , Se, Ce, Eu, Th) had

Unit 6

0.230

Unit 5

0.159

Unit 4

0.213

Unit 3

0.552

Unit 2

0.801

Unit 1

2

Na 0

Table 2.



424

NUCLEAR AND


g e n e r a l , sherds low on the x - a x i s r e l a t e t o the s i e r r a s ( t o the south i n f i g u r e 1) and tend t o be red-brown i n paste c o l o r . In c o n t r a s t , sherds e s p e c i a l l y high on the x - a x i s r e l a t e t o the Chiapas p l a i n s and have l i g h t e r brown t o b u f f pastes. Petrog r a p h i c a l l y , a decrease i n f e l d s p a r occurs i n the ceramics as one moves from s i e r r a s t o p l a i n s . A s i m i l a r but l e s s pronounced p a t t e r n i s observed f o r the micaceous nature of the ceramic matrix. Conversely, opal p h y t o l i t h s , present i n the c l a y as the r e s u l t of the decay of s i l i c a accumulator p l a n t s [ 2 7 ] , have a p l a i n s r a t h e r than P a l e n q u e - s i e r r a s o r i e n t a t i o n . The o b s e r v a t i o n s are constant w i t h e a r l i e r f i n d i n g s based on a Q-mode f a c t o r a n a l y s i s [28].

Table 3.

Provenience D i s t r i b u t i o n w i t h i n the Seven Reference U n i t s ( n o n - i n c e n s a r i o ceramics). 1

2

B e l i s a r i o Dominguez Nansal

3

4

5

1

1

1

Chancala

Bari

El

Retiro

1 1

1

Las Colmenas

3

Miraflores

1

4

Naranjo Nututum

2 68

11

14

6

6

Paso Nuevo San Manuel 2

Santa Isabel

1

Santo Tomas

2

3 8

1

1

1

4

1

6

2

2

9

11

9

3

117

11

1

12 1

1

3 3

2 4

4

Xupa

2

Yoxiha

8

Total

1 68

11

21

10 1

1

Zona S a l a

2 2

1

Santa Cruz

Total

1

8

Francisco V i l l a

Palenque

7

3

1

Chi n i k i h a El

6

1 20

22

39

13

194

1 1

11 1

12 1

2Γ

Λ

Ζ

1 11 «ιι

1 11 111 1 1 11111 1 111

-

\

\

3

5 _ 33 C 5 «#3 3

3

6 6 6 β 5 I 6666 6 61 66 6

1.27

3 5 6 | 6W66 3 5 4 4| 6 6 4 4 6 6 6 44 16 4 6|

3 5 5 54 4 6 M*t> 6

4 4 \ 5 \ \ 2\

\2 5 3 \ 3 \ 3

Figure 4. The seven reference units shown relative to the first two discriminant axes. Broken lines added to emphasize relative isolation of Groups 1 and 2 (Palenque), 6 (Rio Chacamax), and 7 (Xupa orientation).

- ζ ! 45

1

1

1

\

3 3 53 56 365 J



426


P a r t o f the evidence f o r the pétrographie p a t t e r n i n g sum marized above i s presented i n f i g u r e s 5 and 6. The coordinates are held constant i n the two-dimensional diagrams, p e r m i t t i n g t h e reference u n i t membership o f a given ceramic specimen ( f i g u r e 4) t o be compared w i t h t h e pétrographie v a r i a b l e s o f opal p h y t o l i t h s and feldspar. To f a c i l i t a t e r e c o g n i t i o n o f major p a t t e r n s , abundance o f t h e m i n e r a l o g i c a l v a r i a b l e s , as recorded i n the o r i g i n a l pétrographie a n a l y s i s , i s presented i n summary catego r i e s . The l a t t e r are expressed as rank ordered u n i t s f o r the opal p h y t o l i t h s ( f i g u r e 5) and as approximate mean percentages f o r f e l d s p a r ( f i g u r e 6 ) . The negative c o r r e l a t i o n observed between opal p h y t o l i t h s ( a t t r i b u t a b l e p r i m a r i l y t o g r a s s l a n d o r marsh environments o f the p l a i n s ) and high f e l d s p a r ( a t t r i b u t a b l e t o steep g r a d i e n t s o f the s i e r r a s , where e r o s i o n i s c o n s t a n t l y exposing f r e s h e r m a t e r i a l s ) i s e n t i r e l y l o g i c a l . General agreement of the combined pétrographie p a t t e r n s w i t h membership i n the r e f e r ence u n i t s , i n combination w i t h a r c h a e o l o g i c a l provenience o f the p o t t e r y , serves t o s e t o f f " S i e r r a s " and " P l a i n s " groupings on the f i r s t d i s c r i m i n a n t a x i s (see f i g u r e 4). Chemical data provide the major b a s i s f o r d i f f e r e n t i a t i n g ceramic pastes w i t h i n the P l a i n s and the S i e r r a s . Nevertheless, e x e m p l i f y i n g the c o n t r i b u t i o n o f petrography on t h i s more r e f i n e d l e v e l , e x c e p t i o n a l l y abundant p h y t o l i t h s c h a r a c t e r i z e Reference U n i t 6, high on t h e x - a x i s , and, w i t h i n the S i e r r a s , r e l a t i v e l y abundant mica c o r r e l a t e s w i t h the p o s i t i o n o f u n i t 7, high on the y - a x i s . The c o n t r i b u t i o n s o f the chemical v a r i a b l e s t o the SPSSd e r i v e d d i s c r i m i n a n t f u n c t i o n s are given i n Table 4. E s p e c i a l l y notable i s the very heavy l o a d i n g o f sodium on the f i r s t vector. Although sodium i s h i g h l y mobile i n most environments [ 2 9 ] , i t would nevertheless appear t o be a good i n d i c a t o r o f microgeographical d i f f e r e n c e s i n the Palenque region. I f sodium i s omitted from the data a n a l y s i s , potassium becomes the main c o n t r i butor t o group s e p a r a t i o n . The sodium and potassium concentra t i o n s apparently r e f l e c t t h e abundance o f a l k a l i o r p l a g i o c l a s e f e l d s p a r s i n t h e p o t t e r y ( f i g u r e 6 ) , as w e l l as q u a l i t a t i v e d i f f e r e n c e s i n c l a y mineralogy [30]. Suggested correspondences o f the numbered reference u n i t s t o t h e i r approximate geographical l o c a t i o n s are i n d i c a t e d i n f i g u r e 7. I t w i l l be r e c a l l e d t h a t approximately o n e - t h i r d o f the sandyt e x t u r e d p o t t e r y d i d not belong t o any o f the seven reference units. These unplaced specimens may have l o c i i n unworked o r p o o r l y sampled zones on t h e map, perhaps i n some cases r e f l e c t i n g r e l a t i v e l y long-distance trade. Some may y e t be a s c r i b e d t o new or e x i s t i n g reference u n i t s through a d d i t i o n a l data accumulation i n t h e on-going research.

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Figure 5. Abundance of opal phytoliths as summarized from original pétrographie data. Key 0 absent; R, rare; C, common; and A, abundant Sample coordinates same as in Figure 3. Note essential absence of phytoliths in the Sierra units 1 and 2 (Palenque), and 7 (Xupa orientation).

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Figure 6. Abundance of feldspar as summarized from original pétrographie data. Key: 1 < 3 percent; 2, 3-4 percent; 3, 4-6 percent; and 4, 6 percent. Feldspar abundance is expressed as percentage of grain (nonmatrix) fraction.

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1.68 --

A Ceramic Compositional Interpretation of Incense-Burner Trade in the

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