Egypt Exploration Society
Automatic Analysis of Predynastic Cemeteries: A New Method for an Old Problem Author(s): Barry J. Kemp Reviewed work(s): Source: The Journal of Egyptian Archaeology, Vol. 68 (1982), pp. 5-15 Published by: Egypt Exploration Society Stable URL: http://www.jstor.org/stable/3821616 . Accessed: 08/02/2012 09:36 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact
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(5)
AUTOMATIC ANALYSIS OF PREDYNASTIC CEMETERIES: A NEW METHOD FOR AN OLD PROBLEM By BARRY J. KEMP
THEgreat expansion of interest during the last two decades in analytical method within archaeologyhas been essentially the province of the prehistoriansof Europe and North America. Yet one of the earliest initiatives in this direction is actually to be found within the covers of one of the Society's own excavation memoirs. This is Flinders Petrie's remarkable'sequence-dating' scheme for predynastic cultures, published in the report Diospolis Parva.I This centenary issue of the Journal of Egyptian Archaeologyoffers a fitting opportunity to exhibit a powerful modern analytical device for which Petrie and his 'sequencing' can be said to be distantly responsible. The problem and the form that the solution should take are disconcertingly simple. Given a number of graves containing selections of objects in fashion at the time of burial, what arrangementof them is likely to approximate most closely to the original order of burial? Petrie's answer, in effect, was that the arrangement to strive for is one where the histories, or life-spans, of individual types of object are the shortest. Thus, in Petrie's classic portrayalof the problem in which the contents of each grave are written on to a strip of cardboard,and all of the strips laid out in a line, the process of shufflingthe positions of the graves in orderto achieve the best order involves bunching together, as far as possible, all occurrences of the same type of object. The main difficulty is that the life-spans of different types overlap, and tend to be discontinuous because graves need not contain a full sample of all currently used types, and may also, in any case, have been robbed of some items. Bunching one type together may well have the effect of dispersing another. The practical difficulty is, in fact, immense, and Petrie was obliged to temper this method with intuition. His final act is part of the mythology of Egyptology. Having arrived at an arrangementof nine hundred predynastic Egyptian graves which satisfied him, he divided them into fifty-one arbitrarygroups, and numbered them from 30 to 80. Each of these numbered stages became a 'sequence-date'.2 The main difficulty remains. Its essence is the arithmetic of permutations. If one wishes to lay twenty-five cardsin a row, the number of possible different orders in which this can be done is in excess of fifteen quadrillion. To seek the best order within I W. M. F. Petrie, Diospolis Parva (London, 19OI; reprinted I973).
Apart from Diospolis Parva, Petrie published brief accounts of his method in an article entitled 'Sequences in Prehistoric Remains', J. AnthropologicalInst. NS 29 (1899), 295-301, and in his Prehistoric Egypt (London, I920), 3-4: cf. B. J. Kemp, MDAIK 31 (I975), 259-91. 2
6
BARRY J. KEMP
data from a cemetery of any realistic size from amongst all possible permutations is beyond the power even of modern computers. Computer science can, however, approach the problem in other ways. One way has been developed at the University of Cambridge, and now has the form of a programpackage which can be used by archaeologists without the necessity of mastering the esoteric mathematics which underlie it. The program-packagehas been developed by David Kendall, Professor of Mathematical Statistics at the University of Cambridge, utilizing a version of the Shepard-Kruskal multi-dimensional scaling routine devised by Robin Sibson. It has been nicknamedthe HORSHU-program, after the shape of an early type of configurationwhich it produced. Multi-dimensional scaling is a technique with applications in many fields of research. It creates automatically a visual display in two or three dimensions in which the differences between pairs of units-in our case they are graves-are represented as distances. The closer that two units are, the more similar they are, and vice versa. Identical units are over-printed. The automatic plotting begins from a random configuration,and the units are then moved to positions where the competing claims for correct placing of the various units are reduced to a level of minimum stress. Since each starting point is different, with most real data where a perfect solution is unlikely, a somewhat different plot is produced each time. It has become standard with the Cambridge HORSHU-program to create ten plots each time. These ten plots are then amalgamatedand reduced by the next step in the program to a single linear arrangementof units. The final step is the printing of the data in matrix form, in which the order of graves derived from the previous stages is printed vertically,with occurrencesof types markedagainstthe graves by a symbol. For clarity, the order of types is also automaticallyarrangedin two ways: one where the first occurrence of each type is given prority, and one where the ordering follows the midpoints in the 'life-spans' of the individual types, which are markedas dashes. Since the computer cannot decide which is the 'early' and which is the 'late' end of a sequence, the results are also printed with the order of graves reversed. The multi-dimensional scaling routine accomplishes the essential Petrie task: it groups together graves which are similar, and balances objectively the internal competition for the placings of individual graves which inevitably arises. It produces, in other words, a Petrie 'sequence', although the technical term that has come to replace 'sequence' is 'seriation'. Whether a particular result is chronologically 'true' or not is for the archaeologist to decide. The program should not be regarded as a replacement for archaeologicaljudgement, but as an analytical aid of great power which enables cemetery data to be handled and displayed to great effect. Indeed, the various parts of the program-packagecan be used separately. Thus the printing of the results in matrix form can be used to display an ordering of graves which the archaeologist may prefer for his own reasons. There is an element of flexibility. The principal limitation is that of cemetery size. A normal allocation of computing access provides the means for analysing a cemetery of up to about one hundred graves. However, by the time that one has eliminated graves containing only one useful type of object, a great many Egyptian cemeteries fall below this limit.
AUTOMATIC ANALYSIS OF PREDYNASTIC CEMETERIES
7
At the time of writing (December, I980) the program has been used to sort a number of cemeteries of the Dynastic Period,3and four from the Predynastic, namely: Armant 400-500, A and B at ElAmrah, and El-Mahasna; a fifth, from Salmani, near Abydos, is in the course of being processed. For this article I have chosen as the principal illustration of the method the results of the analysis of El-'Amrah cemetery B,4 with an analysis of the El-Mahasna predynastic cemetery as a supplement.5 Cemetery B at El-'Amrah was a relatively rich cemetery, located some six miles to the south-east of Abydos. The graves seemed to cover the entire Predynastic Period in the area, terminating with a group from the Early Dynastic Period. It also gave its name to the first of Petrie's subdivisions of the Predynastic Period, the Amratian (equivalent to sequence-dates 30-7). The principal excavator, Randall-MacIver, used the sequence-dating system with confidence, and felt that his own results worked out 'perfectly harmoniously' with it, with one insignificant exception.6 He also developed a typology of grave construction which reflected, to some degree, the sequencedating chronology. Some years later Petrie himself published his own list of sequencedates for many of the individual graves.7The cemetery offers, therefore, an interesting basis for comparison with any new form of analysis. The one important element missing from the excavation report is a detailed plan of the cemetery, so that it is not possible to carry out an analysis of how the various types of material were grouped in different areas. This gap in the record makes it difficult, in fact, to study the results in anything but a statistical way. The first step always is to create a series of types of objects. For this analysis only pottery was used, and the Petrie corpus was condensed to 43 types. Within cemetery B, a total of 70 graves contained combinations of two or more of these types. Of the ten multi-dimensional scaling plots produced, one is reproduced as an example in fig. i. It is the one with the lowest stress (9.842% after 75 iterations). Each cross represents one grave, accompanied by its label, and each grave is linked by straight lines to the three graves it most resembles in its contents. The plot suggests three groupings of graves on a similarity basis: at the top a fairly loosely assembled group containing one cluster of similar graves; a dense central area where many graves are very similar indeed and are partly overwritten; a dispersed group towards the bottom. The order of graves from the ten plots forms the basis of fig. 2, although the order has been reversed. In the first seriation, each small square symbol represents the occurrence of a particularpottery type, and, to make the diagram easier to read, the vertical columns of square symbols have been made continuous by inserting dots in the spaces. The order of types printed along top and bottom reflects a diagonal arrangementof the 3 Some outline results are given in Kemp and R. S. Merrillees, Minoan Pottery in Second Millennium Egypt (Mainz, 1980), 24-34; JEA 64 (1978), i66-8. 4 D. Randall-MacIver and A. C. Mace, El Amrah and Abydos (London, I902). In the preparation of the data for the analysis of this cemetery and of the cemetery at El-Mahasna much of the routine work was carried out by Mrs Moira Malfroy, to whose patience and care I am much indebted. 5 E. R. Ayrton and W. L. S. Loat, The Pre-dynastic Cemeteryat El Mahasna (London, I9I i). 6 Randall-MacIver, op. cit. 38. 7 Petrie, Prehistoric Egypt, pl. li.
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FORTRANMDSCAL 015 CREATED1 MAY 1975 DATA KMPAMR2SC IN MODE S ON 70 OBJECTS 'THISKMPAMR2NO TITLESET' 2 DIMENSIONS GLOBALSECONDARYSTART0.0 NOT OVERWRITTEN CONFIGURATIONKMPA2GSU HAS STRESS 9.842 PERCENTAFTER75 ITERATIONS LOADS 0.878 0.122 CIR--1 PLTKNFOF 23 SEP 1975 TRIADS FIG. I. Multi-dimensional
scaling plot for El-'Amrah cemetery B, one of ten used to generate the matrices in fig. 2
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PETRIE SEQUENCE-DATES
60 50 30 40 8212 8212 . 8136 8136 8163 8163 8143 8143 8132 8132 8215 B215 ....D..Qo3 8220 B 8220 ..o ......o 8144 8144 D........o B117 B117 .........D B 78 B 78 ...oo..n[...o S B 22 B 22 . a..o..D. ..Fn B 27 .. 27 ... ......... 75 B 75 ...mo...o.n.....o 0 8127 B127 o.........o...... 8199 .....[ 8199 F .......o B 49 B 49 ..o......F...... B 28 B 28 o.o ....oo .....ooo 0 8139 .n...ooo3.o..o0.m3 8139 B 68 0 ... ..c.........0 B 668 _ 8 35 ... o.o . B 35 m.....o. oo B 46 B 46 .... I....o ...I.cJo 8107 .c D.. .oo....o.o.o..ooX.. B107 B 21 B 21 C.....0......F] ....o.o..o B 88 . B 88 ....F..o.a ).o.o. ....o 0 B 37 o o0 . ..F . 13 ......F. 8 37 .. B210 ...IF.. .m . . .o.. 8210 __ 0 B166 .o. . oo. ..0.0 ....... 8166 . 0 B 17 .ED .n.o . .....o..... B 17 B154 ... . .O[] m .0... .. 8154 B104 ...............o.o 8104 . . 0 B 62 . o .o . o..oo. ..o .. B 62 .n. S B119 ... ... ...... . .... .1 8119 B106 .no . .. .. .o... . 8106 0 8232 . n.a .[ o .crn o.n..a .... 8232 8235 .o .o .. ...... .C) 0m a 8235 S 8227 . .. ... ...... 8227 0 8224 . .... .. m.o.. m 8224 B 87 .. .c ... ....T0 B 87 S B 40 o... . ... .C .0F .... B 40 B 43 ........ . .. io B 43 .... S . E. 8233 ..o .0 . .F..F ....o 8233 B 23 ...... .0C... B 23 .. ..o. B 65 .o.oo ...... m oF. .aco B 65 a B151 . ..... .... a. .o ..o 8151 8230 a a a. a.a) a. o.o .i3. a. 8230 S B189 ). .a C.... .. 00.) 8189 ... . a 8225 a. a .. mo. 8225 . . 8222 a a mmomO 8222 F .)a B172 a . 8172 B 12 . .... B 12a B131 . .... 8131 a ....c ] B142 B142 8146 a ...a. 8146 a .o..c B148 8148 a .o..c 1 8133 B133 B 33 a ...o. 8 33 B 32 a ...o. B 32 F .0.o. B 70 B 70 F) .0.0. 8140 8140 B 91 a .0.0. B 91 m.oc B185 8185 B 55 o]a. 8 55 0 .c 8B173 8173 8137 137]. 8137 0 a. B 81 B 81 0 0. B 57 B 57 B 80 a o. B 80 Fa a. 8180 8180 B 50 a o. B 50 C I B 54 B 54 3 3 3 1 22 31 231212222 121434281143133936 4 2 4 1 1312 32A61801821974370A8206315524A14A8329745A7A
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FIG. 2. Matrices for El-'Amrah cemetery B generated by the computer program, with sequence-dates and grave types
BARRY J. KEMP mid-points in the columns, depicted by dashes. In the second seriation, the order of types reflects the diagonal arrangementof the first occurrences of each type. To the right are Petrie's own sequence-date allocations, heavy dots being single. Further to the right there is a table, in similar format, showing the sequence-date range given to the graves by Randall-Maclver, using the same blocks of sequence-dates that he used. These do not represent an entirely consistent system, but reflect the extended range of sequence-dates which many tombs are given when Petrie's scheme is applied in practice. Further to the right still is a table of the different classes of grave construction, to which Randall-Maclver gave considerable attention. Down roughly to grave B222 the bulk of the seriation displays a strong element of continuity, exemplified by certain classes of pottery, such as nos.IO and 29. Amongst other classes, however, there is something of a separation into two groups, which takes place in a 'transitional' group of graves, say between B68 and B2io. In fig. 3 the pot types are drawn out, and arranged in three groups corresponding to three blocks of graves. From the top down to grave B68 is Group I; the 'transitional'graves B35 to B2IO are omitted; from Bi66 to B23 is Group II. A further 'transitional' group is then omitted; Group III comprises the graves from BI46 to the end. Between Groups II and III the separation is much more dramatic. The most obviously encouraging aspect of the seriations is that Petrie's class of 'Late' pottery is mostly grouped at one end, whilst the occurrences of 'White CrossLine' pottery (type 43) occur at the opposite end. Within Groups I and II, certain distinctive types are confined within Group II, namely all of Petrie's 'Decorated' and 'Wavy-handled' types. If we turn to the sequence-date table to the right, these three groups reappear. For Group III hardly any sequence-dates are given; both Petrie and Randall-MacIverregardedthis group as essentially Early Dynastic ('Protodynastic') in date. For the rest, the table of Petrie's own dates, particularlythe 'spot' dates, divides vis-a-vis Groups I and II around sequence-dates 47-8. Within Group I Petrie's table contains an element of 'drift' suggestive, perhaps, of two sub-phases, although these are not really apparent from the seriations; in Group II there is a marked degree of homogeneity. Randall-MacIver's table shows a division between a group with sequence-dates before 46, and a group with dates after 56. In writing in these terms, the seriation is being used as a standard against which to judge sequence-dating. If one were to arrange the graves according to the sequencedates, one would produce a seriation with less structure, with more dispersal of types. Within the difference between the computer seriation and the Petrie results is the element of Petrie's stylistic judgements. These were wrought upon finer points of classification than are present within the forty-three types used to construct this seriation. It would be an interesting experiment to divide the types into finer divisions and to proceed to another automatic seriation on this basis. One might expect from this a degree of local reordering of graves within the main groups, but no dramatic over-all changes of structure. Indeed, in view of the criticisms that have been levelled at the sequence-dating system, and the preliminary stage of work which the seriation represents, the degree of harmony between the two systems is encouraging. IO
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J. KEMP ~BARRY The evidence for dating Group III to the Early Dynastic Period is fairly sound, and includes brick-lined tombs placed by Reisner in his great study of tomb evolution at various points within the First and Second Dynasties.8 One tomb, no. B9I, also contained a cylinder seal, apparently to be dated to the first part of the First Dynasty.9 Thus, in cemetery B at El-'Amrah the First Dynasty seems to have been preceded by two predynastic periods. Yet there has been a persistent tendency to argue for three predynastic periods."IIs there a period missing at El-'Amrah? Randall-MacIver maintained that the cemetery showed continuous use. However, certain well-known classes of pottery are absent, including 'debased' Wavy-handled and cylinder jars, and pots with the final stages of decoration in the 'Decorated' redon-buff style. It is partly for this reason that a second seriation has been included in this article. The predynastic cemetery at El-Mahasna contains a representativeamount of pottery from these missing categories. Figs. 4 and 5 depict the results of an automatic seriation of this cemetery, based on 98 graves, and 38 classes of pottery. Onlythe 'mid-point' seriation is printed here. With a mechanical process such as this there is the opportunity, indeed the temptation, to experiment with the presentation of the data in order to judge the soundness of the method. In this case, the seven occurrences of 'White Cross-lined' pottery (type 43 in the El-'Amrah diagrams)were omitted from the data presented to the computer, but have been added afterwards to fig. 4, in the form of black-filled squares. As can be seen, they bunch satisfactorily towards the upper part of the seriation. If they had been included, the graves containing them would have been bunched even more tightly together, and this would also have had an improving effect on some of the 'spot' sequence-dates in the next column. For fig. 5, the seriation has again been divided into three main groups, with two blocks of 'transitional' graves omitted. Between Groups I and II, the El-Mahasna cemetery produces a clearer division of material than does El-'Amrah cemetery B. Group III is represented by many more types, some of them reaching back into Group II, and some of them being types missing from the El-'Amrah seriation. These 'missing' elements, however, do not form a separate group of material: they belong within a group which also contains elements from Group III at El-'Amrah. It is not the purpose of this article to develop a critique of schemes for subdividing and dating the predynasticsequence in Upper Egypt, merely to demonstratea particular method of analysis. Two cemeteries are, in any case, an insufficient base for broad generalizations. On their own, however, they do suggest certain hypotheses for further evaluation: that there are two principal divisions of predynastic material; that in II~~2
8 G. A. Reisner, The Developmentof the Egyptian Tomb(Cambridge, 1936), 34, 45, 49-52, 53, 67-8, 133-4,
192. 9
P. Kaplony, Die Inschriften der agyptischen Frilhzeit (Wiesbaden, I963-4), I, 6, 40;
Ill, Abb. 9.
II,
682-3 (n. I5);
10 Petrie, with his Semainean, see W. M. F. Petrie, The Making of Egypt (London, 1939), 55-8, pls. xxixxxxiii; Reisner, with his Late Predynastic, see his Development of the Egyptian Tomb, 346-7; Kaiser, with his Naqada III, see Archaeologia Geographica6 (I957), 69-77; cf. also the discussion and references in H. Kantor's important study in JNES 3 (1944), I10-36.
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n
GROUP III
0 0 S
0 0 0
98 ROWS 38 COLUMNS
EL-MAHASNA
FIG. 4. Matrices for the El-Mah asna predynastic cemetery generated by the computer program, with sequence-dates and grave types displayed for comparison
BARRY J. KEMP
I4
II1
II 12A
P
R
'35
L R
31
30
1 F
Q
I
\31A
R
25
16
P B
D
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p
,
10
0
23
D
39A
L
21A
W
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R
32 W;
r
AT 21B
R033 61
B
L
38A L --
C -<
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36
-43 /34
L P020
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W
21C
21 L
FR
R-26
FIG. 5. The pottery types of fig. 4 drawn out in the three groups marked on fig. 4
39B
42
AUTOMATIC ANALYSIS OF PREDYNASTIC CEMETERIES
15 Petrie's sequence-dating system this division is somewhat later than Petrie's own division between Amratian and Gerzean; and that certain forms of pottery, which, in effect, make up Petrie's 'Semainean' culture, belong to a sub-culture largely contained within the Early Dynastic Period, presumablythe First Dynasty.II But, whatever the outcome of future studies, this kind of approach should offer new life to old excavation reports. I Cf. the remarks on the Semainean in A. J. Arkell, The Prehistory of the Nile Valley (Leiden, I975), 46, citing a 1962 paper by H. Case.
