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Egypt
Journal of Archaeological Science 32 (2005) 59–67 http://www.elsevier.com/locate/jas
From mess to matrix and beyond: estimating the size of settlements in the Ptolemaic Fayum/Egypt Katja Muellera,*, William Leeb a KU Leuven, Afdeling Oude Geschiedenis, Blijde-Inkomststraat 21, B-3000 Leuven, Belgium Universita¨t Hamburg, Mineralogisch-Petrographisches Institut, Grindelallee 48, D-20146 Hamburg, Germany
b
Received 27 January 2003; received in revised form 3 June 2004
Abstract This article seeks to introduce a new methodological approach to estimate population size of settlements in the Graeco-Roman Fayum/Egypt (330 BC–400 AD). The aim is to represent and analyse the relationship of settlements and the facilities they provide. We suggest turning the information commonly contained in traditional site gazetteers into presence–absence matrices of selected facilities. We then use these facility matrices to estimate the size of ancient settlements through linear regression. The equation is initially tested on medieval settlements in Norwich and East Anglia (England) and later applied to a settlement-facility matrix for the Ptolemaic period (330–30 BC). The results from the medieval data show the validity of the approach with a complete data set. The circumstance that the Ptolemaic data is fragmented and incomplete naturally adds a small, but acceptable error to the estimates. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Ptolemaic–Roman Egypt; Fayum; Medieval cities; Settlement size; Facilities; Regression analysis; Presence–absence matrix
1. Introduction Spatial geography, the analysis of data on its spatial relationships, has recently attracted an increasing interest by ancient historians and archaeologists alike. The spread of intensive survey archaeology throughout the Eastern Mediterranean has clearly contributed a major impulse to this development. Regional survey and local surveys attached to excavations have also become frequent in Egypt. In particular, the Fayum region has seen its fair share of survey activities ([4]: pp. 233–235, [32,33,35]). The Fayum is a unique and interesting region. It has preserved a large number of ancient settlements [1]. In addition, several thousand Greek and Demotic-Egyptian papyri inform us in often minute
* Corresponding author. Tel.: C32 16 324922; fax: C32 16 324909. E-mail address: [email protected] (K. Mueller), [email protected] (W. Lee). 0305-4403/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jas.2004.06.007
detail about anything from the rural administration and land use to the religion of the these settlements [14,15]. As a region, it can clearly be defined both geographically and administratively. The desert encloses it almost completely. The Ptolemies and Romans continued to conceive of and to administrate the Fayum as an entity, the Arsinoite Nome. More than any other region in Egypt, the Graeco-Roman Fayum offers a good opportunity for a comprehensive regional study of its settlement pattern. Preceding work on the Graeco-Roman settlement pattern in the Fayum has so far taken the shape of site gazetteers, either archaeological [19] or papyrological [8,17]. Several years ago, KU Leuven initiated a project to create a similar gazetteer of ancient Fayumic settlements, this time, in an online format and by surveying all available evidence relating to each settlement [13]. Different sections discuss the location, population, land use, economy and religion for individual settlements.
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These are clearly important and vital measures. But we think, on the basis of such gazetteers, it is possible to abandon this ‘one-site-at-a-time’ approach. This article is intended to provide an initial methodological advance towards a detailed spatial study of the Graeco-Roman Fayum. It seeks to clarify the relationship of Fayumic settlements between one another and throughout the Fayum. There are a multitude of relationshipsdeconomic, social, cultural, physical and institutionald which can bind one settlement to another and shape a complex settlement network. We shall confine ourselves here to two features: the size and facilities of Fayumic settlements. How do settlements throughout the Fayum relate to each other in settlement size? How did settlement facilities spread through this area and which of these are present in a particular settlement? These two questions can be answered separately. But, as we shall see below, size and facilities can have a close correlation. The presence or absence of a particular facility in a settlement may depend on its population size.
2. Assembling a database An initial task was to select and generate a database of the facilities and size of ancient Fayumic settlements. Although a considerable number of Greek and Demotic-Egyptian papyri have survived (ca. 10,000), and provide us with an enormous quantity of information, not all of which is applicable here. Only information on facilities which could conceivably correlate with the size and set-up of a settlement were selected. We excluded all artificial hydrological and communicative features such as dykes, canals, roads and bridges. We assumed that, in general, public institutions, officials and professional occupations promise a good correlation. Resurveying 10,000 papyri for this purpose would clearly have been an extremely time-consuming task. However, our venture was eased by several publications, tools and existing databases [8,17]; Prosopographia Ptolemaica online at http://prosptol.arts.kuleuven.ac.be/; the KU Leuven Fayum Project with an online gazetteer of Fayum settlements at http://fayum.arts.kuleuven.ac.be/. To generate our data sheet for both the Ptolemaic (330–30 BC) and Roman (30 BC–300 AD) facilities, we relied mainly upon these works. The data sets, matrices and final estimates can be downloaded from http://fayum. arts.kuleuven.ac.be/stat_fayum/Stat_Fayum.html. A second issue was how to represent our data. Papyri supply us with a sheer mass of information, as a result of which conventional ways of representing this informationde.g. alphabetical site indexdno longer suffice. Such site gazetteers can be extremely useful. But for assessing and processing facilities common to all, or to only a few settlements, such gazetteers are irksome.
Modern urban geographers employ a reasonably simple, but effective method for grasping the distribution of facilities, institutions and occupations throughout a particular settlement patternda presence–absence matrix or scalogram analysis. Settlements and facilities are set against each other, with the facilities marked as present or absent in a settlement. Some facilities are base functions, common to all settlements. Other facilities are present in only a few larger settlements. Settlements are sorted successively by identifying the most common and the least common facility ultimately to assess the largest single source of variation among all facilities ([29]: p. 254; [9]: pp. 88–89). A preliminary collection of occupations yielded insufficient results. We had to exclude these from the present study. We finally settled for the following facilities (Table 1). In the Roman period, the archiphylakites seems to have been replaced by the office of archephodos. The office of praktor, here mainly praktor agyrikon (money tax-collector) became of increasing importance only in the Roman period. Therefore, this office will only figure in the Roman matrix. In contrast, the central grain registry office is an institution only attested for the Ptolemaic period, between 205 and 105 BC. 2.1. Ptolemaic and Roman facilities matrices The two matricesdfor the Ptolemaic and Roman periods, respectively (Figs. 1 and 2)dlist horizontally these 13/12 facilities and vertically 111 Fayumic settlements. The facilities were marked as either present with ‘1’ or absent indicated by ‘0’. The facilities were then sorted vertically in order of their frequency. Facilities are thus ranked from 1 to 12/13. The settlements were ranked according to a classification based on adding together the ranks of the facilities present within the settlement. The two matrices give us a first glimpse into the distribution of facilities. Despite the fragmentary state, several settlements contain a large number of facilities, others had only a few. Both matrices appear similar, the Roman matrix being slightly denser than the Ptolemaic matrix. But this is misleading. Many settlements and facilities have shifted in rank from the Ptolemaic to the Roman period. And although the majority of settlements continued to be inhabited and the same facilities were being used throughout the Graeco-Roman period, the continuity of the rank distribution and thus of the absence/presence of facilities is relatively low. If those facilities which entered or dropped from either matrix in the Ptolemaic or Roman period are ignored, the most noticeable shift occurred for the office of the grain collector and the public registry office. In the Roman period, both the grain collectors and the public registry offices became far more widespread than
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K. Mueller, W. Lee / Journal of Archaeological Science 32 (2005) 59–67 Table 1 Selected Graeco-Roman facilities and matrix ranking Facility (Greek)
Facilities (Translation)
Ptolemaic matrix rank
Roman matrix rank
References
Officials komogrammateus komarches epistates archiphylakites phylakites archephodos praktor sitologos
village scribe villages elder superintendent head of police policeman chief guard tax-collector grain collector
1 6 2 7 4 – – 9
2 6 – – 9 8 3 1
[16] [23] [22] [21] [21] [8] [8] P. Erasm II; [3]
bath prison public registry office gymnasium local granary public bank central grain registry office
10 13 12 11 3 8 5
10 12 4 11 5 7 –
[8] [8] [17]: 180–196 [37]: 488–489; [17]: 178 [8] [7]: 175–183; [6] [11, 20]
Institution bath desmoterion grapheion gymnasion thesaurus trapeze ergasterion
earlier. Each larger village seems to provide a registry office, whereas in the Ptolemaic period these were spread very thinly throughout the Arsinoites Nome. To judge from the facility ranking, the settlement pattern was even less settled than the world of institutions and officials (Fig. 3). The highest ranking Ptolemaic settle-
ments were: Krokodilonpolis, Philadelpheia, Oxyrhyncha, Euhemereia, Theogonis, Theadelpheia, Tebtynis, Kerkeosiris, Soknopaiou Nesos, Arsinoe in the Themistou Meris. Towards the Roman period half of these dropped, frequently quite dramatically, in rank. Several previously minor settlements emerge in the Roman
Fig. 1. Distribution of Ptolemaic facility.
Fig. 2. Distribution of Roman facility.
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Fig. 3. Changes in the Rank of Graeco-Roman settlements.
period with a significant number of facilities, which boosted their rank. These two matrices would clearly allow us to address a number of historical issues on the survival and death of settlements, facilities and institutions. Since our focus here lies with the size of settlements, such a discussion must be continued elsewhere. However, no research into papyrological issues can ignore the question of sources. Some papyrologists insist that with more papyri we would know more about all kinds of issues. In addition, so they say, the distribution of papyri would skew and distort our perception of issues. For many ancient topics this may hold some truth, but not for all [27]. More papyri result not necessarily in more facilities attested for a particular settlement. We can only continue to be cautious and aware that there exist gaps in both, our evidence for facilities and in the actual provision of facilities. There can never be absolute certainty on whether the absence of a facility indicates a lack of evidence or the actual absence of that facility. 2.2. Settlement size Above we have analysed settlements primarily according to their facilities. This has allowed us to rank these. Let us now assume that all higher ranking settlements are by default the largest settlements in the area. A high rank in the facility matrix can equal a large settlement population size. But not always and exclusively is this case. Only ancient figure for the population size of settlements can help to verify such an assumption. Estimates for ancient population sizes have a long tradition. The current trend is probably to view such estimates as a mere sport and, in any case with some suspicion. This distrust is founded upon two issues, the scarcity of actual population figures and the shear disparity of earlier estimates. Estimates are pursued through several main approaches: archaeological
remains, literary texts, papyrological evidence and lastly ‘guesstimates’. A common approach is to multiply the spatial extent of an archaeological site by a constantdanything from 100 to 600 persons per ha ([36]: table 1). Papyrologists have worked with a similar method, multiplying adult males preserved in ancient tax registers by a constant of 2.909 ([5]: p. 103 n.35) or of 3.1 ([30]: p. 131). For the size of Graeco-Roman settlements in the Fayum, both papyrological sources and archaeological evidence are available. Davoli [19] has compiled an archaeological gazetteer of Fayumic sites. For some 19 sites, she gives the archaeological size (Table 2). The size of Magdola is probably wrong and should be excluded. Philoteris was recently surveyed by C. Ro¨mer [33a]. For a discussion on the location of these and other settlements see Mu¨ller [25–27]. Another set of data for population size papyrological will soon be available with the publication of new Ptolemaic tax registers from the mid to end third century BC. These papyri attest the population size of 23 ancient settlements ([12]: chapter 4, table 4.4; [24]: table 3; [34]). For the Roman period, rather scarce information on the population size has survived ([2,30]: p. 134). In the rare case in which both types of sourcedpapyrological and archaeological, are available, large discrepancies result in the traditionally estimated population size. For example, for Roman Philadelpheia, papyri suggest a population size of 3000 persons. With an archaeological size of 50 ha, the site might have accommodated not less than 7500 inhabitants (Table 3). Similarly, for Roman Theadelpheia, papyri suggest 2300 inhabitants ([30]: p. 134). The site covered some 25 ha, which would result in a population figure of 3750. The different data source for the population size are not without problems and difficult to bring into convergence. The archaeological record is admittedly the more complex. The site size commonly represents several layers of accumulated habitation. Hence, when the site continued to be inhabited from the Ptolemaic to the Late Roman period, there is little chance to derive accurate measures for the extent of habitation individually for each period. For this reason, we have decided to use only one set of data: the early Ptolemaic tax registers. This automatically restricts all further estimates which will now follow to Ptolemaic settlements. Estimates for the Roman Fayum do not concern us here.
3. Multiple regression estimates To estimate the population sizes of settlements, we suggest using the method of linear regression. This method is based on the idea that the presence or absence
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Table 2 Archaeological Size of Graeco-Roman settlements in the Fayum (H = Herakleides, P = Polemon, T = Themistos. *Identification or information doubtful) No
Site
Ancient identification
Meris
Size in ha
Population size (150 persons/ha)
1 2 3 4 5 6 7 8 9 10 11 12 13
Kiman Fares Kom Medinet el-Nihas Kom Aushim Kom Umm el Boreigat Kom el Kharaba el Kebir Qasr Qarun M. Watfa Kom Umm el Atl Kharabet Ihrit Dimai Kom Nicola Qasr el-Banat Kom el-Khamsin
– P H P H T T H T H P T P
288 *200 79 57 50 40 36 34 25 23 19 19 18
43,200 – 11,850 8550 7500 6000 5400 5400 3750 3450 2850 2850 2700
14 15 16 17 18 18 19
Kom Medinet Madi Kom Madi Kom Talit Medinet Quta Kom Medinet Ghoran Tell el-Maraka Kom Shalaui
Krokodilonpolis Magdola Karanis Tebtynis Philadelpheia Dionysias Philoteris Bacchias Theadelpheia Soknopaiou Nesos * Euhemereia Kerkethoeris/Berenikis Thesmophorou, ([31]: p. 54) Narmouthis Ibion Eikosipentaurouron Talei * Ghoran * *
P P P T P P P
17 12 12 5 4 3 3
of some facilities is strongly correlated to settlement size. Mathematically, we express this correlation by assigning numbers to each facility. To calculate the estimated size of the settlement we add together the numbers associated with the facilities known to be present in the settlement. In addition, we choose to add another number to the estimate. This number is not associated with any facilities but may be considered the estimate of the population of a settlement which has none of the facilities. This may be written as Pa ¼ bC
X
ð1Þ
An ana
n
where Pa is the estimated population size of settlement a (the overbar indicates that it is an estimate not the actual quantity), ana is 1 if the facility n is present in Table 3 Settlement sizes and error of estimates Region
Average size of settlement
Absolute error of estimates
Error in % of average
East Anglia 1500–1599 East Anglia 1600–1649 East Anglia 1650–1699 BaberghSuffolk 1522 Ptolemaic Fayum
1046.35
351.91
33.63
1540.10
528.52
34.31
2093.08
484.09
23.13
330.62
108.23
32.73
661.91/ (530.01)
311.28
47.02/ (58.73)
2550 1800 1800 750 600 450 450
settlement a and 0 if the facility is absent, An are the numbers associated with each facility, b is the number not associated with any settlement. The way in which the numbers An and b are calculated is described in Section 3.2. In the following sections, we demonstrate that the method described above produces reasonable estimates of population figures by applying it to medieval settlements in Norwich and East Anglia (England), see Section 3.1. We made this choice because reliable data both for populations and facilities were available. In Section 3.2, we shall apply the method to settlements in the Ptolemaic Fayum and generate estimates for the population of settlements for which the facilities are known, but not the population. 3.1. Taxing and testing medieval cities sizes In order to demonstrate that the idea of multilinear regression works, we apply it to a matrix for medieval settlements in the vicinity of Norwich and East Anglia (England). More correctly, there exist three matricesdfor the years 1500–1599, 1600–1649, and 1650– 1699 ([29]: 254 table 11, 273 table 16, 283 table 20). Each matrix lists vertically the settlements of East Anglia. Instead of facilities, here the occupations of the inhabitants are listed horizontally in the order of frequency of occurrence. These matrices can be combined with figures for settlement sizes for years 1524, 1603 and 1670 listed elsewhere in Patten’s monograph ([29]: 251 table 12). Every matrix lists roughly 70 different occupations for each of the 48 settlements.
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Another, contemporary occupation matrix is based on the data from the Muster of Harness of 1522 for the region of Babergh Hundred in Suffolk. It lists some 30 occupations for 32 settlements. Combined with the settlement sizes as estimated from the number of names attested between 1522 and 1524, this provides us with a fourth matrix ([28]: 6 table 1, 9 table 2). The method of multilinear regression requires that the number of variables (facilities) must be less than the number of data points (settlements). This is not the case for the medieval data. Therefore, we have to choose a set of occupations (= facilities) to work with. The Ptolemaic data have less evidence for facilities and thus this problem does not arise for the Ptolemaic estimates. To select which facilities should be included in the calculation here, we use the matrix mai, with elements 1 or 0, depending on whether facility i is available at settlement a. The rows of the matrix are sorted in order of size of the settlement a. For the method to succeed, it is important that the facilities chosen strongly correlate with population size. In the matrix of numbers mai described above, this would correspond to the numbers mai for the given i being all 1 below some critical value of a and 0 above it. This would indicate that the facility was always present in cities above a certain population size, and always absent in cities below that size. To find out which facility in the list corresponded most closely to the ideal case we calculated the quantities of facilities ti by the following formula: X 2 ð2Þ ti ¼ maC1;i ma;i a
The form of the equation above means that 1 is added to the value of ti whenever a 1 is succeeded by a 0, or a 0 is succeeded by a 1 in the column corresponding to a single facility. This means that the smaller the value of ti the more strongly correlated the facility i is with settlement size. The minimum value of ti possible is 1 (unless the facility is always present or always absent, in which case ti will be zero). Once the values of ti are calculated we then select facilities with the smallest values of ti within certain ranges of i to form set of facilities for which the next stage of the calculation can be performed. Once the facilities to use have been chosen, we calculate the quantities An and b (described above). This is done by the least squares method. To apply this, we form the quantity X 2 Pa Pa ð3Þ S¼ a
where Pa is the actual population of settlement a, and Pa is the estimated population, calculated using Eq. (1). The quantity S has the property that it is zero when the
predicted populations of the cities are equal to their actual values. Any deviations cause S to take a positive value. Starting with some guess values of An and b the values are adjusted to make S as small as possible subject to the condition that they must be positive or zero (this constraint prevents the method from predicting negative populations sizes). The average valuepof theffi ffiffiffiffiffiffiffiffiffi error involved in using this method is given by S=N, where N is the total number of cities. The results of our tests on the four matrices are encouraging. The error of our estimates dropped when seen percentile to the average size of the settlements (Table 3). This table also includes, for comparison the results of the calculation for the Ptolemaic Fayum, described in Section 3.2. In conclusion, reasonable estimates of the populations of settlements can be obtained from a regression formula of the form of Eq. (1). It now remains to apply this method to estimating the sizes of settlements in the Ptolemaic Fayum.
3.2. Estimating Ptolemaic settlement sizes The Ptolemaic matrix of the facilities and settlement size data for the Ptolemaic Fayum is rather fragmentary. For some settlements, there is a good set of facilities, for others no facilities are attested. For very few settlements, we have a population size. But, in 18 cases, both population size and some facilities are attested (Table 4). This circumstance allows us to use the same multilinear regression analysis as applied above. To test how facilities relate to population size and finally to estimate the population size for all settlements in the Ptolemaic facility matrix, we used the data for these 18 settlements (Table 4). We assume that the population size was linearly related to the presence or absence of the following 12 facilities: village scribe (komogrammateus), village elder (komarches), superintendent (epistates), head of police (archiphylakites), policeman ( phylakites), local grain store (thesaurus), central grain office (ergasterion), grain collector (sitologos), public bank (trapeze), gymnasion, bath and prison (desmoterion). No public registry office (grapheion) was present among the 18 settlements. This facility was discarded. Eq. (1) was used to estimate the population sizes. We calculated the numbers An and b using the least squares method under the constraint that the numbers must be positive or zero. The facilities and corresponding values of the coefficients are given in Table 5. It should be noted that the largest city in the Fayum, Krokodilonpolis has not been included in Table 4 or the subsequent calculations, although data on population and facilities exist. Krokodilonpolis had facilities that no other settlement in the Fayum accommodated. Including Krokodilonpolis in the calculation would
65
6 2 5 7 1 3 7 2 2 2 4 3 1 3 2 4 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 3
Table 5 Facilities coefficients n
Facilities
An
1 2 3 4 5 6 7 8 9 10 11 12
Village scribe Village elder Head of police Policeman Public bank Grain collector Central grain office Superintendent Local grain store Baths Gymnasion Prison
0 0 0 0 92.0 114.5 119.5 192.8 220.7 363.5 364.5 1038.0
merely have added more coefficients for these facilities unique to Krokodilonpolis. It would have increased the complexity of the calculation without actually affecting any of the other coefficients and without increasing the accuracy of the results. The constant b = 216.2. The average error is 310. Fig. 4 shows the estimated population plotted against the actual population. The solid line indicates where the points would lie if the estimated populations were equal to the actual populations. The dotted line is the regression line (R2 = 0.59). Compared to the error in the medieval data analysis (Table 3), the error for the Ptolemaic data set is higher. One important factor in causing this comparatively higher error is the incompleteness of our data set. However, our methodology allows us to refine the estimates of the coefficients in the light of new discoveries. Although at present, not very precise, this method has the potential to make valuable quantitative estimates of ancient population sizes. To judge from the coefficients, several facilitiesd village scribe, village elder, head of police and policemandrelate only marginally to population size. Their
T H T P T T T T H T T T H T T T T T Arsinoe Psenyris Dionysias Kerkeosiris Philoteris Magais Trikomia Lagis Persea Theoxenis Anoubias Athenas kome Helioupolis Hermoupolis Polydeukeia Lysimachis Philagris Krotou Ibion Total
1681 1361 1137 1106 1076 *783 497 474 396 *337 300 227 154 *134 130 122 *99 *96
1 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 0 0 9
1 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 0 0 9
1 0 0 0 0 1 1 1 0 1 1 1 0 1 0 1 0 0 9
0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 5
0 0 1 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 5
0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 4
1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 3
1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 3
Public bank Village elder Head of police Local grain store Policeman Superintendent Village scribe Ptolemaic population size (Papyri) Meris Place
Table 4 Population size and facilities for selected settlements, Ptolemaic Fayum (*association possible, but not certain)
Central grain office
Grain collector
Baths
Gymnasion
Prison
Total
K. Mueller, W. Lee / Journal of Archaeological Science 32 (2005) 59–67
Fig. 4. Error of settlement size estimates.
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presence or absence from a settlement is largely independent from the size of that settlement. In the case of the policeman, this situation is caused by their relative frequency. They are present in almost all settlements from the smallest hamlets to larger settlements. In theory, larger settlements would have had a higher number of policemen than smaller ones. The equation used here is insensitive to the frequency of each facility within a settlement. In terms of size–facility correlation, the absence or presence of a policeman, for instance, is the decisive, not the actual number of policemen in each settlement. Despite the wealth of papyri, it appears unrealistic that a similar and, more importantly, a somewhat complete facility matrix with absolute frequencies for each facility, could be generated. It may, however, be feasible to consider such an approach for a small selection of facilities. In this case, modern geographers have proposed the calculation of centrality values for different settlements and regions based on the frequency of particular facilities. The equation used is: C¼
t ! 100 T
ð4Þ
where C is the location coefficient of facility t, t is one outlet of facility t and T the total number of those outlets in the region. If the location coefficient is multiplied by the number of outlets of that facility in a settlement, a centrality value is derived for that settlement. This can be repeated for all selected facilities and the individual centrality values of a settlement derived ([18]: p. 61; [9]: pp. 88–89; [10]).
4. Conclusions The question, which we set out to answer before embarking on research for this article, was whether, despite all the common limitations and disparity of evidence, it would be possible to write both, a spatial and population geography of the Graeco-Roman Fayum. Would it be feasible to reconstruct the institutions of ancient Fayumic settlements, not settlement by settlement, but as a regional network? This article is a contribution to this topic. We have focused on two issues, the methodological presentation of data (here facilities) and the correlation between facilities and settlement size. The latter led us to estimate the size of over hundred Ptolemaic settlements. A presence– absence matrix was constructed for both Ptolemaic and Roman settlements. The resulting ranking exposed a high continuity of settlements and facilities. But it is important to note that nonetheless, facilities and settlements underwent significant shifts in their respective ranking. The Graeco-Roman settlement pattern of the Fayum was everything but static. Possible reasons
and explanations for these changes have only been touched upon superficially. It remains to exploit these matrices for advancing new perspectives on the internal structure of ancient settlement.
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K. Mueller, W. Lee / Journal of Archaeological Science 32 (2005) 59–67 [23] H.E.L. Mißler, Der komarch. Ein Beitrag zur Dorfverwaltung im ptolema¨ischen, ro¨mischen und byzantinischen A¨gypten, Ph.D. thesis, Philipps University of Marburg, 1970. [24] K. Mu¨ller, Ptolemaic settlements in space. Settlement size and hierarchy in the Fayum, Archiv fu¨r Papyrusforschung 48 (1) (2002) 107–125. [25] K. Mu¨ller, The cities of the Ptolemies, On aspects of Ptolemaic settlement, Ph.D. thesis, University of Cambridge, 2002. [26] K. Mu¨ller, Places and spaces in the Themistou Meris (Fayum/ Graeco-Roman Egypt), Locating settlements by Multidimensional Scaling of papyri, Ancient Society 33 (2003) 103–125. [27] K. Mu¨ller, Mastering matrices and clusters. Locating GraecoRoman settlements in the Meris of Herakleides (Fayum/Egypt) by Monte-Carlo-Simulation, Archiv fu¨r Papyrusforschung 49 (2) (2003) 218–252. [28] J. Patten, Village and town: an occupational study, The Agricultural History Review 20 (1972) 1–16. [29] J. Patten, English Towns 1500–1700, Folkestone, Kent, 1978. [30] D.W. Rathbone, Villages, land and population in GraecoRoman Egypt, Proceedings of the Cambridge Philological Society 36 (1990) 103–142. [31] D.W. Rathbone, Towards a historical topography of the Fayum, in: D.M. Bailey (Ed.), Archaeological research in Roman Egypt, The Proceedings of the Seventeenth Classical Colloqium of the Department of Greek and Roman Antiquities,
[32]
[33]
[33a]
[34]
[35]
[36]
[37]
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British Museum, held on 1–4 December 1993, Ann Arbor, 1996, pp. 50–56. D.W. Rathbone, Surface survey and the settlement history of the ancient Fayum, in: Archeologia e papiri nel Fayum, Storia della ricerca, problemi e prospettive, Atti del convegno internazionale Siracusa, 24–25 maggio 1996, Siracusa, 1997, pp. 7–20. D.W. Rathbone, Mapping the south-west Fayum: sites and textes, in: Atti del XXII congresso internazionale di Papirologia Firenze, 23–29 agosto 1998, Firenze, 2001, pp. 1109–1117. C.E. Ro¨mer, Philoteris in the Themiston Meris. Report on the archaeological survey carried out as port of the Fayum Survey Project, Zeitschrift fu¨r Papyrologie und Epigraphik 147 (2004) 281–305. D.J. Thompson, The infrastructure of splendour: census and taxes in Ptolemaic Egypt, in: P. Cartledge, P. Garnsey, E. Gruen (Eds.), Hellenistic constructs, Essays in Culture, History, and Historiography, Berkeley, 1997, pp. 242–257. I. Uytterhoeven, Hawara (Fayum): tombs and houses on the surface. A preliminary report of the K.U. Leuven Site Survey, Ricerche di Egittologia e di Antichita` Copte 3 (2001) 45–83. J.R. Zorn, Estimating the population size of ancient settlements: methods, problems, solutions and a case study, Bulletin of the American School of Oriental Research 295 (1994) 31–48. F. Zucker, Gymnasiarchos komes, Aegyptus 11 (1931) 485–496.
From mess to matrix and beyond: estimating the size of settlements in the Ptolemaic Fayum/Egypt Katja Muellera,*, William Leeb a KU Leuven, Afdeling Oude Geschiedenis, Blijde-Inkomststraat 21, B-3000 Leuven, Belgium Universita¨t Hamburg, Mineralogisch-Petrographisches Institut, Grindelallee 48, D-20146 Hamburg, Germany
b
Received 27 January 2003; received in revised form 3 June 2004
Abstract This article seeks to introduce a new methodological approach to estimate population size of settlements in the Graeco-Roman Fayum/Egypt (330 BC–400 AD). The aim is to represent and analyse the relationship of settlements and the facilities they provide. We suggest turning the information commonly contained in traditional site gazetteers into presence–absence matrices of selected facilities. We then use these facility matrices to estimate the size of ancient settlements through linear regression. The equation is initially tested on medieval settlements in Norwich and East Anglia (England) and later applied to a settlement-facility matrix for the Ptolemaic period (330–30 BC). The results from the medieval data show the validity of the approach with a complete data set. The circumstance that the Ptolemaic data is fragmented and incomplete naturally adds a small, but acceptable error to the estimates. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Ptolemaic–Roman Egypt; Fayum; Medieval cities; Settlement size; Facilities; Regression analysis; Presence–absence matrix
1. Introduction Spatial geography, the analysis of data on its spatial relationships, has recently attracted an increasing interest by ancient historians and archaeologists alike. The spread of intensive survey archaeology throughout the Eastern Mediterranean has clearly contributed a major impulse to this development. Regional survey and local surveys attached to excavations have also become frequent in Egypt. In particular, the Fayum region has seen its fair share of survey activities ([4]: pp. 233–235, [32,33,35]). The Fayum is a unique and interesting region. It has preserved a large number of ancient settlements [1]. In addition, several thousand Greek and Demotic-Egyptian papyri inform us in often minute
* Corresponding author. Tel.: C32 16 324922; fax: C32 16 324909. E-mail address: [email protected] (K. Mueller), [email protected] (W. Lee). 0305-4403/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jas.2004.06.007
detail about anything from the rural administration and land use to the religion of the these settlements [14,15]. As a region, it can clearly be defined both geographically and administratively. The desert encloses it almost completely. The Ptolemies and Romans continued to conceive of and to administrate the Fayum as an entity, the Arsinoite Nome. More than any other region in Egypt, the Graeco-Roman Fayum offers a good opportunity for a comprehensive regional study of its settlement pattern. Preceding work on the Graeco-Roman settlement pattern in the Fayum has so far taken the shape of site gazetteers, either archaeological [19] or papyrological [8,17]. Several years ago, KU Leuven initiated a project to create a similar gazetteer of ancient Fayumic settlements, this time, in an online format and by surveying all available evidence relating to each settlement [13]. Different sections discuss the location, population, land use, economy and religion for individual settlements.
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These are clearly important and vital measures. But we think, on the basis of such gazetteers, it is possible to abandon this ‘one-site-at-a-time’ approach. This article is intended to provide an initial methodological advance towards a detailed spatial study of the Graeco-Roman Fayum. It seeks to clarify the relationship of Fayumic settlements between one another and throughout the Fayum. There are a multitude of relationshipsdeconomic, social, cultural, physical and institutionald which can bind one settlement to another and shape a complex settlement network. We shall confine ourselves here to two features: the size and facilities of Fayumic settlements. How do settlements throughout the Fayum relate to each other in settlement size? How did settlement facilities spread through this area and which of these are present in a particular settlement? These two questions can be answered separately. But, as we shall see below, size and facilities can have a close correlation. The presence or absence of a particular facility in a settlement may depend on its population size.
2. Assembling a database An initial task was to select and generate a database of the facilities and size of ancient Fayumic settlements. Although a considerable number of Greek and Demotic-Egyptian papyri have survived (ca. 10,000), and provide us with an enormous quantity of information, not all of which is applicable here. Only information on facilities which could conceivably correlate with the size and set-up of a settlement were selected. We excluded all artificial hydrological and communicative features such as dykes, canals, roads and bridges. We assumed that, in general, public institutions, officials and professional occupations promise a good correlation. Resurveying 10,000 papyri for this purpose would clearly have been an extremely time-consuming task. However, our venture was eased by several publications, tools and existing databases [8,17]; Prosopographia Ptolemaica online at http://prosptol.arts.kuleuven.ac.be/; the KU Leuven Fayum Project with an online gazetteer of Fayum settlements at http://fayum.arts.kuleuven.ac.be/. To generate our data sheet for both the Ptolemaic (330–30 BC) and Roman (30 BC–300 AD) facilities, we relied mainly upon these works. The data sets, matrices and final estimates can be downloaded from http://fayum. arts.kuleuven.ac.be/stat_fayum/Stat_Fayum.html. A second issue was how to represent our data. Papyri supply us with a sheer mass of information, as a result of which conventional ways of representing this informationde.g. alphabetical site indexdno longer suffice. Such site gazetteers can be extremely useful. But for assessing and processing facilities common to all, or to only a few settlements, such gazetteers are irksome.
Modern urban geographers employ a reasonably simple, but effective method for grasping the distribution of facilities, institutions and occupations throughout a particular settlement patternda presence–absence matrix or scalogram analysis. Settlements and facilities are set against each other, with the facilities marked as present or absent in a settlement. Some facilities are base functions, common to all settlements. Other facilities are present in only a few larger settlements. Settlements are sorted successively by identifying the most common and the least common facility ultimately to assess the largest single source of variation among all facilities ([29]: p. 254; [9]: pp. 88–89). A preliminary collection of occupations yielded insufficient results. We had to exclude these from the present study. We finally settled for the following facilities (Table 1). In the Roman period, the archiphylakites seems to have been replaced by the office of archephodos. The office of praktor, here mainly praktor agyrikon (money tax-collector) became of increasing importance only in the Roman period. Therefore, this office will only figure in the Roman matrix. In contrast, the central grain registry office is an institution only attested for the Ptolemaic period, between 205 and 105 BC. 2.1. Ptolemaic and Roman facilities matrices The two matricesdfor the Ptolemaic and Roman periods, respectively (Figs. 1 and 2)dlist horizontally these 13/12 facilities and vertically 111 Fayumic settlements. The facilities were marked as either present with ‘1’ or absent indicated by ‘0’. The facilities were then sorted vertically in order of their frequency. Facilities are thus ranked from 1 to 12/13. The settlements were ranked according to a classification based on adding together the ranks of the facilities present within the settlement. The two matrices give us a first glimpse into the distribution of facilities. Despite the fragmentary state, several settlements contain a large number of facilities, others had only a few. Both matrices appear similar, the Roman matrix being slightly denser than the Ptolemaic matrix. But this is misleading. Many settlements and facilities have shifted in rank from the Ptolemaic to the Roman period. And although the majority of settlements continued to be inhabited and the same facilities were being used throughout the Graeco-Roman period, the continuity of the rank distribution and thus of the absence/presence of facilities is relatively low. If those facilities which entered or dropped from either matrix in the Ptolemaic or Roman period are ignored, the most noticeable shift occurred for the office of the grain collector and the public registry office. In the Roman period, both the grain collectors and the public registry offices became far more widespread than
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K. Mueller, W. Lee / Journal of Archaeological Science 32 (2005) 59–67 Table 1 Selected Graeco-Roman facilities and matrix ranking Facility (Greek)
Facilities (Translation)
Ptolemaic matrix rank
Roman matrix rank
References
Officials komogrammateus komarches epistates archiphylakites phylakites archephodos praktor sitologos
village scribe villages elder superintendent head of police policeman chief guard tax-collector grain collector
1 6 2 7 4 – – 9
2 6 – – 9 8 3 1
[16] [23] [22] [21] [21] [8] [8] P. Erasm II; [3]
bath prison public registry office gymnasium local granary public bank central grain registry office
10 13 12 11 3 8 5
10 12 4 11 5 7 –
[8] [8] [17]: 180–196 [37]: 488–489; [17]: 178 [8] [7]: 175–183; [6] [11, 20]
Institution bath desmoterion grapheion gymnasion thesaurus trapeze ergasterion
earlier. Each larger village seems to provide a registry office, whereas in the Ptolemaic period these were spread very thinly throughout the Arsinoites Nome. To judge from the facility ranking, the settlement pattern was even less settled than the world of institutions and officials (Fig. 3). The highest ranking Ptolemaic settle-
ments were: Krokodilonpolis, Philadelpheia, Oxyrhyncha, Euhemereia, Theogonis, Theadelpheia, Tebtynis, Kerkeosiris, Soknopaiou Nesos, Arsinoe in the Themistou Meris. Towards the Roman period half of these dropped, frequently quite dramatically, in rank. Several previously minor settlements emerge in the Roman
Fig. 1. Distribution of Ptolemaic facility.
Fig. 2. Distribution of Roman facility.
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K. Mueller, W. Lee / Journal of Archaeological Science 32 (2005) 59–67
Fig. 3. Changes in the Rank of Graeco-Roman settlements.
period with a significant number of facilities, which boosted their rank. These two matrices would clearly allow us to address a number of historical issues on the survival and death of settlements, facilities and institutions. Since our focus here lies with the size of settlements, such a discussion must be continued elsewhere. However, no research into papyrological issues can ignore the question of sources. Some papyrologists insist that with more papyri we would know more about all kinds of issues. In addition, so they say, the distribution of papyri would skew and distort our perception of issues. For many ancient topics this may hold some truth, but not for all [27]. More papyri result not necessarily in more facilities attested for a particular settlement. We can only continue to be cautious and aware that there exist gaps in both, our evidence for facilities and in the actual provision of facilities. There can never be absolute certainty on whether the absence of a facility indicates a lack of evidence or the actual absence of that facility. 2.2. Settlement size Above we have analysed settlements primarily according to their facilities. This has allowed us to rank these. Let us now assume that all higher ranking settlements are by default the largest settlements in the area. A high rank in the facility matrix can equal a large settlement population size. But not always and exclusively is this case. Only ancient figure for the population size of settlements can help to verify such an assumption. Estimates for ancient population sizes have a long tradition. The current trend is probably to view such estimates as a mere sport and, in any case with some suspicion. This distrust is founded upon two issues, the scarcity of actual population figures and the shear disparity of earlier estimates. Estimates are pursued through several main approaches: archaeological
remains, literary texts, papyrological evidence and lastly ‘guesstimates’. A common approach is to multiply the spatial extent of an archaeological site by a constantdanything from 100 to 600 persons per ha ([36]: table 1). Papyrologists have worked with a similar method, multiplying adult males preserved in ancient tax registers by a constant of 2.909 ([5]: p. 103 n.35) or of 3.1 ([30]: p. 131). For the size of Graeco-Roman settlements in the Fayum, both papyrological sources and archaeological evidence are available. Davoli [19] has compiled an archaeological gazetteer of Fayumic sites. For some 19 sites, she gives the archaeological size (Table 2). The size of Magdola is probably wrong and should be excluded. Philoteris was recently surveyed by C. Ro¨mer [33a]. For a discussion on the location of these and other settlements see Mu¨ller [25–27]. Another set of data for population size papyrological will soon be available with the publication of new Ptolemaic tax registers from the mid to end third century BC. These papyri attest the population size of 23 ancient settlements ([12]: chapter 4, table 4.4; [24]: table 3; [34]). For the Roman period, rather scarce information on the population size has survived ([2,30]: p. 134). In the rare case in which both types of sourcedpapyrological and archaeological, are available, large discrepancies result in the traditionally estimated population size. For example, for Roman Philadelpheia, papyri suggest a population size of 3000 persons. With an archaeological size of 50 ha, the site might have accommodated not less than 7500 inhabitants (Table 3). Similarly, for Roman Theadelpheia, papyri suggest 2300 inhabitants ([30]: p. 134). The site covered some 25 ha, which would result in a population figure of 3750. The different data source for the population size are not without problems and difficult to bring into convergence. The archaeological record is admittedly the more complex. The site size commonly represents several layers of accumulated habitation. Hence, when the site continued to be inhabited from the Ptolemaic to the Late Roman period, there is little chance to derive accurate measures for the extent of habitation individually for each period. For this reason, we have decided to use only one set of data: the early Ptolemaic tax registers. This automatically restricts all further estimates which will now follow to Ptolemaic settlements. Estimates for the Roman Fayum do not concern us here.
3. Multiple regression estimates To estimate the population sizes of settlements, we suggest using the method of linear regression. This method is based on the idea that the presence or absence
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K. Mueller, W. Lee / Journal of Archaeological Science 32 (2005) 59–67
Table 2 Archaeological Size of Graeco-Roman settlements in the Fayum (H = Herakleides, P = Polemon, T = Themistos. *Identification or information doubtful) No
Site
Ancient identification
Meris
Size in ha
Population size (150 persons/ha)
1 2 3 4 5 6 7 8 9 10 11 12 13
Kiman Fares Kom Medinet el-Nihas Kom Aushim Kom Umm el Boreigat Kom el Kharaba el Kebir Qasr Qarun M. Watfa Kom Umm el Atl Kharabet Ihrit Dimai Kom Nicola Qasr el-Banat Kom el-Khamsin
– P H P H T T H T H P T P
288 *200 79 57 50 40 36 34 25 23 19 19 18
43,200 – 11,850 8550 7500 6000 5400 5400 3750 3450 2850 2850 2700
14 15 16 17 18 18 19
Kom Medinet Madi Kom Madi Kom Talit Medinet Quta Kom Medinet Ghoran Tell el-Maraka Kom Shalaui
Krokodilonpolis Magdola Karanis Tebtynis Philadelpheia Dionysias Philoteris Bacchias Theadelpheia Soknopaiou Nesos * Euhemereia Kerkethoeris/Berenikis Thesmophorou, ([31]: p. 54) Narmouthis Ibion Eikosipentaurouron Talei * Ghoran * *
P P P T P P P
17 12 12 5 4 3 3
of some facilities is strongly correlated to settlement size. Mathematically, we express this correlation by assigning numbers to each facility. To calculate the estimated size of the settlement we add together the numbers associated with the facilities known to be present in the settlement. In addition, we choose to add another number to the estimate. This number is not associated with any facilities but may be considered the estimate of the population of a settlement which has none of the facilities. This may be written as Pa ¼ bC
X
ð1Þ
An ana
n
where Pa is the estimated population size of settlement a (the overbar indicates that it is an estimate not the actual quantity), ana is 1 if the facility n is present in Table 3 Settlement sizes and error of estimates Region
Average size of settlement
Absolute error of estimates
Error in % of average
East Anglia 1500–1599 East Anglia 1600–1649 East Anglia 1650–1699 BaberghSuffolk 1522 Ptolemaic Fayum
1046.35
351.91
33.63
1540.10
528.52
34.31
2093.08
484.09
23.13
330.62
108.23
32.73
661.91/ (530.01)
311.28
47.02/ (58.73)
2550 1800 1800 750 600 450 450
settlement a and 0 if the facility is absent, An are the numbers associated with each facility, b is the number not associated with any settlement. The way in which the numbers An and b are calculated is described in Section 3.2. In the following sections, we demonstrate that the method described above produces reasonable estimates of population figures by applying it to medieval settlements in Norwich and East Anglia (England), see Section 3.1. We made this choice because reliable data both for populations and facilities were available. In Section 3.2, we shall apply the method to settlements in the Ptolemaic Fayum and generate estimates for the population of settlements for which the facilities are known, but not the population. 3.1. Taxing and testing medieval cities sizes In order to demonstrate that the idea of multilinear regression works, we apply it to a matrix for medieval settlements in the vicinity of Norwich and East Anglia (England). More correctly, there exist three matricesdfor the years 1500–1599, 1600–1649, and 1650– 1699 ([29]: 254 table 11, 273 table 16, 283 table 20). Each matrix lists vertically the settlements of East Anglia. Instead of facilities, here the occupations of the inhabitants are listed horizontally in the order of frequency of occurrence. These matrices can be combined with figures for settlement sizes for years 1524, 1603 and 1670 listed elsewhere in Patten’s monograph ([29]: 251 table 12). Every matrix lists roughly 70 different occupations for each of the 48 settlements.
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Another, contemporary occupation matrix is based on the data from the Muster of Harness of 1522 for the region of Babergh Hundred in Suffolk. It lists some 30 occupations for 32 settlements. Combined with the settlement sizes as estimated from the number of names attested between 1522 and 1524, this provides us with a fourth matrix ([28]: 6 table 1, 9 table 2). The method of multilinear regression requires that the number of variables (facilities) must be less than the number of data points (settlements). This is not the case for the medieval data. Therefore, we have to choose a set of occupations (= facilities) to work with. The Ptolemaic data have less evidence for facilities and thus this problem does not arise for the Ptolemaic estimates. To select which facilities should be included in the calculation here, we use the matrix mai, with elements 1 or 0, depending on whether facility i is available at settlement a. The rows of the matrix are sorted in order of size of the settlement a. For the method to succeed, it is important that the facilities chosen strongly correlate with population size. In the matrix of numbers mai described above, this would correspond to the numbers mai for the given i being all 1 below some critical value of a and 0 above it. This would indicate that the facility was always present in cities above a certain population size, and always absent in cities below that size. To find out which facility in the list corresponded most closely to the ideal case we calculated the quantities of facilities ti by the following formula: X 2 ð2Þ ti ¼ maC1;i ma;i a
The form of the equation above means that 1 is added to the value of ti whenever a 1 is succeeded by a 0, or a 0 is succeeded by a 1 in the column corresponding to a single facility. This means that the smaller the value of ti the more strongly correlated the facility i is with settlement size. The minimum value of ti possible is 1 (unless the facility is always present or always absent, in which case ti will be zero). Once the values of ti are calculated we then select facilities with the smallest values of ti within certain ranges of i to form set of facilities for which the next stage of the calculation can be performed. Once the facilities to use have been chosen, we calculate the quantities An and b (described above). This is done by the least squares method. To apply this, we form the quantity X 2 Pa Pa ð3Þ S¼ a
where Pa is the actual population of settlement a, and Pa is the estimated population, calculated using Eq. (1). The quantity S has the property that it is zero when the
predicted populations of the cities are equal to their actual values. Any deviations cause S to take a positive value. Starting with some guess values of An and b the values are adjusted to make S as small as possible subject to the condition that they must be positive or zero (this constraint prevents the method from predicting negative populations sizes). The average valuepof theffi ffiffiffiffiffiffiffiffiffi error involved in using this method is given by S=N, where N is the total number of cities. The results of our tests on the four matrices are encouraging. The error of our estimates dropped when seen percentile to the average size of the settlements (Table 3). This table also includes, for comparison the results of the calculation for the Ptolemaic Fayum, described in Section 3.2. In conclusion, reasonable estimates of the populations of settlements can be obtained from a regression formula of the form of Eq. (1). It now remains to apply this method to estimating the sizes of settlements in the Ptolemaic Fayum.
3.2. Estimating Ptolemaic settlement sizes The Ptolemaic matrix of the facilities and settlement size data for the Ptolemaic Fayum is rather fragmentary. For some settlements, there is a good set of facilities, for others no facilities are attested. For very few settlements, we have a population size. But, in 18 cases, both population size and some facilities are attested (Table 4). This circumstance allows us to use the same multilinear regression analysis as applied above. To test how facilities relate to population size and finally to estimate the population size for all settlements in the Ptolemaic facility matrix, we used the data for these 18 settlements (Table 4). We assume that the population size was linearly related to the presence or absence of the following 12 facilities: village scribe (komogrammateus), village elder (komarches), superintendent (epistates), head of police (archiphylakites), policeman ( phylakites), local grain store (thesaurus), central grain office (ergasterion), grain collector (sitologos), public bank (trapeze), gymnasion, bath and prison (desmoterion). No public registry office (grapheion) was present among the 18 settlements. This facility was discarded. Eq. (1) was used to estimate the population sizes. We calculated the numbers An and b using the least squares method under the constraint that the numbers must be positive or zero. The facilities and corresponding values of the coefficients are given in Table 5. It should be noted that the largest city in the Fayum, Krokodilonpolis has not been included in Table 4 or the subsequent calculations, although data on population and facilities exist. Krokodilonpolis had facilities that no other settlement in the Fayum accommodated. Including Krokodilonpolis in the calculation would
65
6 2 5 7 1 3 7 2 2 2 4 3 1 3 2 4 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 3
Table 5 Facilities coefficients n
Facilities
An
1 2 3 4 5 6 7 8 9 10 11 12
Village scribe Village elder Head of police Policeman Public bank Grain collector Central grain office Superintendent Local grain store Baths Gymnasion Prison
0 0 0 0 92.0 114.5 119.5 192.8 220.7 363.5 364.5 1038.0
merely have added more coefficients for these facilities unique to Krokodilonpolis. It would have increased the complexity of the calculation without actually affecting any of the other coefficients and without increasing the accuracy of the results. The constant b = 216.2. The average error is 310. Fig. 4 shows the estimated population plotted against the actual population. The solid line indicates where the points would lie if the estimated populations were equal to the actual populations. The dotted line is the regression line (R2 = 0.59). Compared to the error in the medieval data analysis (Table 3), the error for the Ptolemaic data set is higher. One important factor in causing this comparatively higher error is the incompleteness of our data set. However, our methodology allows us to refine the estimates of the coefficients in the light of new discoveries. Although at present, not very precise, this method has the potential to make valuable quantitative estimates of ancient population sizes. To judge from the coefficients, several facilitiesd village scribe, village elder, head of police and policemandrelate only marginally to population size. Their
T H T P T T T T H T T T H T T T T T Arsinoe Psenyris Dionysias Kerkeosiris Philoteris Magais Trikomia Lagis Persea Theoxenis Anoubias Athenas kome Helioupolis Hermoupolis Polydeukeia Lysimachis Philagris Krotou Ibion Total
1681 1361 1137 1106 1076 *783 497 474 396 *337 300 227 154 *134 130 122 *99 *96
1 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 0 0 9
1 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 0 0 9
1 0 0 0 0 1 1 1 0 1 1 1 0 1 0 1 0 0 9
0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 5
0 0 1 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 5
0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 4
1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 3
1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 3
Public bank Village elder Head of police Local grain store Policeman Superintendent Village scribe Ptolemaic population size (Papyri) Meris Place
Table 4 Population size and facilities for selected settlements, Ptolemaic Fayum (*association possible, but not certain)
Central grain office
Grain collector
Baths
Gymnasion
Prison
Total
K. Mueller, W. Lee / Journal of Archaeological Science 32 (2005) 59–67
Fig. 4. Error of settlement size estimates.
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K. Mueller, W. Lee / Journal of Archaeological Science 32 (2005) 59–67
presence or absence from a settlement is largely independent from the size of that settlement. In the case of the policeman, this situation is caused by their relative frequency. They are present in almost all settlements from the smallest hamlets to larger settlements. In theory, larger settlements would have had a higher number of policemen than smaller ones. The equation used here is insensitive to the frequency of each facility within a settlement. In terms of size–facility correlation, the absence or presence of a policeman, for instance, is the decisive, not the actual number of policemen in each settlement. Despite the wealth of papyri, it appears unrealistic that a similar and, more importantly, a somewhat complete facility matrix with absolute frequencies for each facility, could be generated. It may, however, be feasible to consider such an approach for a small selection of facilities. In this case, modern geographers have proposed the calculation of centrality values for different settlements and regions based on the frequency of particular facilities. The equation used is: C¼
t ! 100 T
ð4Þ
where C is the location coefficient of facility t, t is one outlet of facility t and T the total number of those outlets in the region. If the location coefficient is multiplied by the number of outlets of that facility in a settlement, a centrality value is derived for that settlement. This can be repeated for all selected facilities and the individual centrality values of a settlement derived ([18]: p. 61; [9]: pp. 88–89; [10]).
4. Conclusions The question, which we set out to answer before embarking on research for this article, was whether, despite all the common limitations and disparity of evidence, it would be possible to write both, a spatial and population geography of the Graeco-Roman Fayum. Would it be feasible to reconstruct the institutions of ancient Fayumic settlements, not settlement by settlement, but as a regional network? This article is a contribution to this topic. We have focused on two issues, the methodological presentation of data (here facilities) and the correlation between facilities and settlement size. The latter led us to estimate the size of over hundred Ptolemaic settlements. A presence– absence matrix was constructed for both Ptolemaic and Roman settlements. The resulting ranking exposed a high continuity of settlements and facilities. But it is important to note that nonetheless, facilities and settlements underwent significant shifts in their respective ranking. The Graeco-Roman settlement pattern of the Fayum was everything but static. Possible reasons
and explanations for these changes have only been touched upon superficially. It remains to exploit these matrices for advancing new perspectives on the internal structure of ancient settlement.
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