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Geometry, a measurement unit and rectangular architecture at Early Neolithic Jerf el-Ahmar, Syria

Gil Haklay et Avi Gopher
p. 31-42

Résumés

L’analyse formelle architecturale des bâtiments EA30 et EA53 du site de Jerf el-Ahmar (Syrie) au Néolithique précéramique (vers 11600-10600 cal. BP) a permis d’identifier des régularités géométriques, impliquant notamment l’utilisation d'une unité de mesure. Ces caractéristiques nouvelles pour une architecture si ancienne suggèrent un processus dans lequel les notions d’espace et de planification architecturale (telles que les concepts de plan architectural et de mesure des distances) ont joué un rôle crucial dans l’apparition de la plus ancienne architecture rectangulaire attestée au Levant et dans le monde. De plus, l’utilisation de techniques de planification architecturale illustre le haut degré de réflexion cognitive dont pouvaient faire preuve les derniers chasseurs-cueilleurs de la région. Cette architecture soigneusement planifiée, qui ne laisse aucune place à l'improvisation, témoigne d’un état d’esprit visant à maximiser la maîtrise de l’homme sur son environnement.

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Acknowledgements

We thank Danielle Stordeur for her permission to use and reproduce the figures in this paper and the Dan David Foundation for the financial support.

Introduction

1The Pre-Pottery Neolithic A (PPNA; ca. 11,600-10,600 cal. BP) site of Jerf el-Ahmar, excavated under the direction of Danielle Stordeur in the 1990s, is situated on two hills, separated by a small gulley, on the bank of the Middle Euphrates in northern Syria (Stordeur et al. 1996; Stordeur et Margueron 1998; Stordeur 2000a). Both hills contain the remains of several successive levels of occupations (“villages” after Stordeur) during parts of the PPNA period (from the second part of the 12th millennium to the first half of the 11th millennium cal. BP; see table 1). The architectural remains uncovered at the site are of special interest for a number of reasons, among them, the “cigar-shape” dressed stone technology (Stordeur 2015: 52), the kiva-like communal structures (Stordeur et al. 2000), and the appearance of rectangular architecture (Stordeur and Abbès 2002; Stordeur 2015).

Table 1 – Stratigraphy

Table 1 – Stratigraphy

The eastern hill of Jerf el-Ahmar shows all four phases uncovered at the site (Early, Middle, Late and Transition) while the western hill revealed findings pertaining mainly to the Late Phase. The Early Phase comprises four villages (VII/E-IV/E) in which only curvilinear plan structures were uncovered. The onset of the Middle Phase (Villages III/E-I/E) is marked by the appearance of straight walls and right angles in Village III/E, while the successive Villages II/E and I/E include the communal Structure EA7 which is reminiscent of Structure EA30 (Village II/W) of the Late Phase—the subject of the current paper. The Late Phase is characterised by the appearance of rectangular-plan structures. It is known mainly from Village II/W in which structures are arranged with relation to the communal Structure EA30. The Transition Phase (from PPNA to PPNB), distinguished by its lithic technology, is known mainly from the eastern hill (Village -II/E) and includes the communal Structure EA53

Drawings G. Haklay; modified from Stordeur 2015

2The early villages at the site are located on the eastern hill, where the lowest four of ten villages superimposed one on top of the other yielded exclusively curvilinear structures (table 1). Rectangular structures were found only in the most recent three (or four) villages on both hills, dated to the final centuries of occupation at the site, i.e., after 11,000 cal. BP, possibly closer to 10,800-10,700 cal. BP, briefly before the onset of the early Pre-Pottery Neolithic B (EPPNB). Several villages were extensively excavated, exposing their spatial arrangements. In each village (from Level II/E onwards), a large, round communal structure was uncovered in addition to domestic structures (fig. 1).

Fig. 1 – The site of Jerf el-Ahmar, western hill

Fig. 1 – The site of Jerf el-Ahmar,                         western hill

Village II/W at Jerf el-Ahmar with the curvilinear Structure EA30 at the centre

Photo mission El-Kowm-Mureybet

3In this paper, we will focus on the most recent communal structures on both hills—Structure EA30 (Village II/west) and Structure EA53 (Village -II/east). After a brief description of these structures we will present our methodology and study of spatial forms (architectural formal analysis), and finally discuss the implications of the results with regard to the state of architectural planning towards the end of the PPNA and during the appearance of rectangular architecture, and as an example to the dynamics of cultural changes during this time.

Brief description of structures Ea53 and Ea30

4Communal Structure EA53 (fig. 2-5) is assigned to the latest occupational phase in the site (Village -II/E), defined as a PPNA-PPNB transitional phase. It is a circular, embedded in the ground structure, built against the perimeter wall of an older structure (Structure EA101, Village -I/E). The peripheral stone wall, about 2.40 m high, was built with slots to accommodate wooden posts, and was plastered. At the centre of the structure (at the lower elevation), a hexagonal floor is defined by decorated stone panels. Large posts were positioned at the corners and their imprints were preserved in a decorated clay coating. This central floor occupies most of the structure’s interior area and the space around was interpreted as a bench (Stordeur 2000a).

Fig 2 – Structure EA53 (Village -II/E)

Fig 2 – Structure EA53                             (Village -II/E)

Note the central polygonal floor defined by stone panels

Photo mission El-Kowm-Mureybet

5Communal Structure EA30 (fig. 1, 7-10) is located on the flat summit of the western hill (Village II/W; fig. 1). It is a curvilinear structure embedded in the ground, surrounded by open space as well as free-standing rectangular structures. The latter are among the oldest rectangular structures recorded thus far not only in the Levant but worldwide. The roof of EA30, probably above ground level, was supported by the perimeter wall and wooden posts embedded within it (see black dots; infra fig. 7-10).

6Two thick radial walls may have been load-bearing walls as well. The interior layout of the structure comprises a central, polygonal shaped floor at the lowest elevation, surrounded by elevated platforms and cell-like enclosures built against the perimeter wall. Stordeur accurately described the dividing walls as forming a geometric and radiating figure (Stordeur et al. 2000), and she noted that some walls are directed to a point in the perimeter wall that is also the point of intersection between the perimeter wall and the axis of symmetry (Stordeur 2015).

Methods

7The term architectural formal analysis denotes the analysis of architectural forms. It is applied by researchers and historians of architecture in order to reconstruct aspects of the architectural design processes reflected in monuments (e.g., Eisenman 1993; Eisenman and Roman 2015). It accomplishes this goal by discerning geometric regularities and identifying the spatial principles and compositional laws (design rules) governing the generation of the structure’s form. The archaeological application can also be understood as an attempt at reconstructing the initial stages of the chaîne opératoire of a structure’s construction.

8Within the scope of architectural formal analysis and to highlight spatial relations that may not be noticeable at first glance, we use an analytic tool based on standard deviation mapping to study spatial form and relative location of architectural features in space (Haklay and Gopher 2015). This method consists of a geometric and statistical calculation carried out by an algorithm. The input for the algorithm is coordinates (relative to an arbitrary origin) of physical points in space. For example, the points may trace the path of a wall, or mark the centres of postholes, or corners of an enclosure. A grid (e.g., of 5 cm spacing) is then superimposed over the detailed plan, and the algorithm proceeds by measuring the group of distances from each grid point to the set of input coordinates. Mean and standard deviation values are calculated for each group. The output is a statistical centre point in which the group of distances to the given input points has the lowest standard deviation value. Thus, relative to that centre point, the dispersion of the group of distances is minimal (it equals zero if the points all lie on a circumference of a circle). The next step of the analysis consists of examining whether the identified centre point could also refer to other spatial features than those tested, indicating a place of significance or highlighting architectural planning. For example, in the analysis of a succession of structures in the Natufian site of Eynan (Ain-Mallaha), we used this algorithm to identify an overlooked geometric connection between the peripheral wall of Shelter 51 and a series of concentric postholes which were previously assigned to the preceding Shelter 131. This led to a new understanding of the organisational schema of the structure and to insights regarding the principals and methods of the architectural planning involved (Haklay and Gopher 2015).

Architectural formal analysis

Structure EA53

9Danielle Stordeur noted that the bench forms a “perfect equilateral hexagon” (Stordeur 2000a: 3). This statement was confirmed by our analysis. We applied the standard deviation mapping algorithm (described above) to the five centres of post imprints (fig. 3). The results of the calculation are the centre point and radius of a fitted circle (the circle which passes through or the nearest to the centres of posts; fig. 4).

Fig. 3 – A. Original plan of Structure EA53; B. Visualisation of the centre finding calculation

Fig. 3 – A. Original plan of                             Structure EA53; B. Visualisation of the centre                             finding calculation

A. Stordeur et al. 2000: fig. 9; B. Drawing G. Haklay; modified from Stordeur et al. 2000: fig. 9

Fig. 4 – Structure EA53

Fig. 4 – Structure EA53

The resulted fitted circle

Drawing G. Haklay; modified from Stordeur et al. 2000: fig. 9

10The superposition over the plan (fig. 5) of a geometric hexagon inscribed in this circle, illustrates the overall exactness of the built form with respect to an ideal geometric form, as the sides of the hexagon align well with the stone panels (fig. 5). This rather precise geometric regularity suggests that the hexagonal form was measured and, most probably, was laid on the ground using ropes (fig. 6). This intrigued us to find out whether the central polygonal floor of Structure EA30 exhibits geometric regularities and forms a geometric pattern as well.

Fig. 5 – Structure EA53

Fig. 5 – Structure EA53

Superposition over the plan of a geometric hexagon inscribed inside the calculated fitted circle. Note that the western posthole and associated stone panels are marked (on the original plan) with dotted lines, indicating a reconstruction. Otherwise, the sides of the geometric hexagon fit the stone panels with an accuracy that suggests that this form was indeed geometrically constructed

Drawing G. Haklay; modified from Stordeur et al. 2000: fig. 9

Fig. 6 – The measuring of a hexagon by the construction of equilateral triangles

Fig. 6 – The measuring of a                             hexagon by the construction of equilateral triangles

Drawing G. Haklay

Structure EA30

  • 1 In the summary of Mureybet’s absolute chronology (Évin and Sto (...)

11According to the excavator, the history of Structure EA30 includes at least two major construction episodes. The earliest is the construction of Structure EA29 (Village III/W), which included the peripheral wall and the two massive radial walls embedded within it. Additional subdivision walls enclosed cells against the eastern sector of the peripheral wall (the four cells to the left and to the right of the radial walls, and the space between them). In the later construction episode (Village II/W), the massive walls were rebuilt and additional cells and platforms were added, defining the form of the polygonal central floor. Further alterations and renovations that transformed the structure and brought it to its final state took place in the southern part of the structure where the peripheral wall was made wider and the partition wall abutting it was removed, thereby merging two of the cells. However, the transformation of Structure EA29 into Structure EA30 should be regarded as an overall remodelling episode and not as an accumulation process in which cells and platforms were added over time. Since Structure 47 of Mureybet Stratum IIIA, as well as Structure EA7 of Jerf el-Ahmar, predate Structure EA30,1 yet these structures share a similar layout, the construction of Structure EA30 may represent an attempt to accommodate a pre-planned schema in the existing perimeter wall of its predecessor, Structure EA29. We therefore proceeded by analysing the interior layout, starting with the form of the polygonal central floor.

12For the purpose of the analysis presented below, we used Stordeur’s original drawing of Structure EA30 (Stordeur et al. 2000: 33, fig. 5), on which we marked a set of nine points representing the nine corners that define the polygonal central space (fig. 7, 1-9).

Fig. 7 – A. Plan of Structure EA30; B. Statistical centre point calculation

Fig. 7 – A. Plan of Structure EA30; B. Statistical                             centre point calculation

A. Note the polygonal central floor defined by a set of nine nodes. B. Using a set of points that mark the nine corners defining the polygonal central space as the initial data, a grid of a predefined precision (in this case 5 cm) was superimposed over the examined area as the infrastructure of a simple algorithm that followed these steps: 1. Measuring the distance from each grid point to each of the given set of points (in this case, the distances from each grid point to the nine polygon corners); 2. Calculating the standard deviation (SD) values of the group of distances associated which each grid point; 3. Identifying the grid point of the smallest SD value

A. Stordeur et al. 2000: fig. 5; B. Drawing G. Haklay; modified from Stordeur et al. 2000: fig. 5

13With reference to these points (the polygon nodes), a standard deviation mapping algorithm (e.g., Haklay and Gopher 2015) yielded a statistical centre point. A grid of a predefined precision of 5 cm was superimposed over the examined area. For each point of the grid, the standard deviation value of the group of distances to the nine polygon nodes was calculated (fig. 7). The topographic map converges onto a minimum value point which is the statistical centre (fig. 8A).

Fig. 8 – Structure EA30

Fig. 8 – Structure EA30

A. Visualisation of the centre calculation. B. Lines projecting from the identified centre point correspond to the faces of the interior walls separating the different area types: the platforms, the cell clusters, and the space between the two structural walls.

Modified from Stordeur et al. 2000: fig. 5

14In the next phase of analysis, we checked whether the resulting statistical centre point indicates a planned architectural geometric regularity when examined with reference to the entire assemblage of architectural remains of Structure EA30.

15We found that, indeed, the statistical centre point as noted above sheds light on the geometric architectural order in two respects. First, lines projecting from the (mathematically identified) centre point correspond to the faces of the interior walls that separate the different spatial element types—the platforms, the cell clusters and the space between the two massive structural walls (fig. 8B). Second, in relation to the centre point, the polygonal shape maps quite accurately onto a system of concentric circles of constant intervals that pass through its corners (fig. 9). This precision suggests that some unit of measure was used in the design and construction of the interior space as the distances from the centre point to all nine nodes of the polygon are multiplications of that unit, which measures approximately 0.54 m. This was most probably not a standardised unit of measure; it may have only been used in the planning and construction of this particular structure (and possibly Structure EA29 as well), yet it enabled the architectural planning and measuring on the ground of complex layouts (including pre-construction specified forms and proportions) and later their accurate construction.

Fig. 9 – Structure EA30

Fig. 9 – Structure EA30

Relative to the centre point, the polygonal form accurately maps onto a system of concentric circles of constant interval, suggesting that a unit of measure was used in the design and construction of the structure

Modified from Stordeur et al. 2000: fig. 5

16The proportions and form of the polygonal floor are further clarified by the observation that the radial projecting lines (the red lines in fig. 8B) tend to form two right angles (90° and 95°) at the centre point, which correspond to the right angles of the polygonal floor (in Nodes 3 and 8) and form two rectangles measuring 3 by 4 units of measure (fig. 10). We argue that the coherent and geometrically well-defined interior layout of Structure EA30 is a good indicator of architectural design and construction methods which involved the formulation of a floor plan and use of a unit of measure.

Fig. 10 – Geometric regularities in Structure EA30

Fig. 10 – Geometric regularities                             in Structure EA30

An idealised form of defined proportions describing the shape of the polygonal floor, superimposed over the original drawing. The 95º angle and the rounded platform edge in Node 2 may represent a slight deviation from the plan, possibly to enlarge the floor area

Drawing G. Haklay; modified from Stordeur et al. 2000: fig. 5

Discussion

  • 2 A floor plan is an abstraction and an orthogonal projection repres (...)

17The nearly perfect hexagonal shape of the floor of structure EA53 attests to an abstract planning process, since the decision to create a low hexagonal central floor and to place the posts at the hexagon nodes, was something that took place not only prior to construction but possibly away from the construction site as well. The precision of the hexagonal form suggests that it was laid on the ground by means of measurement. We have shown that the polygonal shape of the floor of Structure EA30 is a geometric construct of precise proportions, as well. Yet, in order to abstractly plan and build this more complicated form (the interior layout of Structure EA30) it was necessary to be acquainted with two architectural design concepts and methods: the concept of the architectural floor plan2 (Haklay and Gopher 2020), and the idea of distance measuring by a unit of measure. Distance measuring by a unit of measure enabled the reproduction of proportions predesigned in smaller (planning) scale.

18From a cognitive perspective, the “floor plan” as an exterior (out of the brain) planning device, is following Renfrew’s concept of fully “symbolic material culture” (Renfrew 2004) that preceded Donald’s “theoretic culture” mode, supported by the “ultimate” system of “external symbolic storage” which is writing (Donald 1991). Notations, calendars and other mnemonic devices are known in the Epipaleolithic and earlier, but there was an intensification of external symbolic storage systems during the PPNA (Watkins 2006), which is apparent in many aspects of symbolic behaviour (tokens, pebbles with patterns or pictograms, etc.). The floor plan, however, was different than other representations in that it was a tool which enabled, not only the communication of the design but the planning itself (including the specification of forms).

19It is plausible to assume a connection between two major spatial and architectural phenomena that appear, for the first time, side by side at late PPNA Jerf el-Ahmar (Village II/W):

  1. The use of distance measurements in construction which involved a new perception of space (the environment) as a measurable and quantifiable resource.
  2. The introduction of rectangular architecture, the hallmark of the subsequent PPNB period, which continues to dominate the spatial form of our current built environment.
  • 3 Floor plans could have been formulated with the use of small equal (...)

20Rectangular architecture may have thus been the result of advances in architectural planning methods. Distance measuring was an innovative application of an even deeper idea and practice—counting. We suggest that the application of measuring by counting to space was the fundamental platform for the appearance of rectangular architecture. With counting, (the proportions of) rectangular spaces could have been planned, described and laid out (measured). However, to do so without a concept of abstract numbers (and words that represented abstract numbers), the idea that a distance can be measured by smaller length units had to be combined with the use of a floor plan as an external planning device in the architectural planning process. Following Schmandt-Besserat, clay tokens were used to count and record quantities before the invention of writing, as early as the PPNA Mureybetian culture (defined by J. Cauvin after his work at Tell Mureybet in the Middle Euphrates, Syria) at sites such as Mureybet Stratum IIIA (Schmandt-Besserat 1982, 2010; Ibáñez 2008) dated by the excavators to ca. 11,500/11,400-10,700/10,600 cal. BP (see note 1). In a spatial and architectural application, the “tokens” may have been reeds of equal lengths, perhaps first used to delineate a small-scale plan, with each token representing a length unit, and eventually used as counters to measure the length of the walls (fig. 11).3

Fig. 11 – The planning and measuring of rectangular architecture

Fig. 11 – The planning and measuring                         of rectangular architecture

A form is specified by a floor plan composed of small units of equal length which are successively used as counters in the measuring process. A. Formulation of a plan (specification of the form) using reeds of equal length (7:3 length to width proportion in the example); B. Collecting by hand the reeds that mark the length to be measured (the seven reeds that mark the long side of the rectangle in the example); C. Each reed stands for one unit of measure (a “heel-to-toe” step in the example). Each time a unit is measured (after each step), a counter (a reed) is tossed. When the reeds run out, the dimension is measured (7 length units in the example). This is repeated for the other dimensions (the other rectangular sides) and the desired form is produced. This is done without abstract number concept and words representing numbers

Drawing G. Haklay

  • 4 Geometric construction is a sequence (chain) of operations with wh (...)
  • 5 At Jerf el-Ahmar, a top-down village planning is reflected in the (...)

21In summary, our assessment of the state of architectural planning during the appearance of rectangular architecture at the site indicates that this was accompanied by developments in architectural planning. We suggest that the appearance of rectangular architecture should be understood against the background of the advances in architectural planning methods, such as the use of floor plans, distance measuring and the geometric construction of polygons.4 It was, therefore, a top-down process that was initially derived from specialised fields of knowledge and methods, reflected in communal architecture.5

Conclusion

22In view of the geometric regularities identified in the communal Structure EA30 of Village II/W at Jerf el-Ahmar, we suggest that rectangular architecture may have originated from the attempt to confront one of the most basic problems of early architectural planning—how to plan, build and reproduce complex architectural designs which specify in advance forms and proportions? The solution required the conceptualisation of spatial and architectural planning notions, such as the architectural floor plan and proportional distance measurement using a unit of measure (which is essentially spatial counting). While the conceptualisation of these notions and their early application took place at the end of the PPNA (e.g., Structure EA30; see note 1 for Mureybet Structure 47), their utilisation became more frequent and commonplace at the beginning of the PPNB (e.g., sites such as Çayönü or Nevali Çori), when the change of perception of the environment (a new man-world relationship) became widespread and common and units of measurement were standardised (Stordeur 2000b: 38; Cauvin et al. 2011: 2; Haklay and Gopher 2019). For Cauvin, the appropriation of space was reflected by the imposition of the rectangular house form (Cauvin et al. 2001: 110).

23As a case study of Neolithic dynamics of change, the appearance of rectangular architecture as we suggested here may serve as another example of how an innovative idea (directly related to a new perception of space) finds expression in a material culture element. After its introduction, rectangular architecture continued to develop and proliferated in the architectural scene both for its recognised practical advantages (e.g., ease of expansion by adding rooms) and its acquired role in the organisation of space in Neolithic sites. This also relates to the social institutions that rectangular architecture came to house (e.g., Flannery 1972, 2002).

24It was only a few generations after the site of Jerf el-Ahmar was ultimately abandoned that plant (and possibly animal) domestication took place in the very same region (Lev-Yadun et al. 2000; Abbo et al. 2010) that has also been the centre of other cultural innovations since the PPNA (Gopher et al. 2001). It may very well be that the people responsible for plant and animal domestication (ca. 10,500 cal. BP) and the origins of agriculture were guided by a reflective attitude similar to that which characterised the inhabitants of Jerf el-Ahmar. Their desire to plan in advance and the level of architectural planning achieved (as we have shown above and in other places) attest to a new relationship with the world and a mind-set directed at maximising control of their own environment. This reflects a divorce from the “relational epistemology” that characterised pristine hunter-gatherer societies for a very long time (Naveh and Bird-David 2014) and a beginning of an objectified nature dominated by humans.

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Notes

1 In the summary of Mureybet’s absolute chronology (Évin and Stordeur 2008), the PPNA Stratum III was dated to 11,450-10,650 cal. BP—a range of some 800 years. This was based on 14C determinations (seven in each of the sub-strata) but no subdivision was made between Sub-stratum IIIA (to which Structure 47 was assigned) and the later Sub-stratum IIIB. Two of the seven dates of Sub-stratum IIIA originated in Structure 47 (from two 14C laboratories). Of the two dates, one is ca. 11,600 cal. BP (9950±150 [MC-734], charcoal, 10,174-9140 cal. BC) and the other ca. 10,800 cal. BP (9455±45 [Ly-11.626], charcoal, 9105-8615 cal. BC)—that is, a difference of some 800 years between the dates, which clearly poses a problem. If the older date, with its much larger range and larger error is rejected as aberrant, and we count on the younger date only, then Structure 47 of Mureybet Stratum IIIA would date to ca. 10,800 cal. BP, that is, towards the end of the PPNA, just a short while before the onset of the EPPNB at Mureybet Stratum IVA (dated to ca. 10,650-10,200 cal. BP). This would make Structure 47 practically contemporaneous with Structure EA30 of Jerf el-Ahmar or just slightly earlier.

2 A floor plan is an abstraction and an orthogonal projection representation of an architectural design. Despite the modern-sounding term, PPNA floor plans were quite different than modern architectural drawings and blueprints. The schematic floor plans consisted of geometric patterns that were regulated by modules. Linear units (such as reeds) could have been used to define the proportions of polygonal forms. Geometric construction methods were also used in the formulation of the plans, for example, the construction of an equilateral triangle in Göbekli Tepe (Haklay and Gopher 2020) and of a hexagon in Jerf el-Ahmar.

3 Floor plans could have been formulated with the use of small equal-length linear units, for example made of reeds all cut to the same length, indicating the relative lengths to be measured on the ground, for example, the length of a wall or the distance between two points. Figure 11a is a simple example of such floor plan. There, the reeds are used to specify the 7:3 proportion of a rectangular shape. To reproduce this proportion in the desired size on the ground, it was necessary to set a unit of measurement and to measure (count) seven and three units in perpendicular directions. In this example, the polygon is a rectangle, but in this method, many forms and proportions can be planned (specified) in advance and executed with accuracy This could have taken place also without an abstract number concept, using the reeds as counters (fig. 11B-C).

4 Geometric construction is a sequence (chain) of operations with which one can produce the exact same forms in any size. This knowledge of geometry is not reflected in any other aspect of material culture and thus, should not be taken for granted.

5 At Jerf el-Ahmar, a top-down village planning is reflected in the built terraces in Village II/E and the arrangement of dwellings with respect to the communal structure of this village and Village II/W. While there is a diversity in the type of dwellings, there is an intra-site standardisation in the model/layout of communal structures. The communal structures were planned in detail and executed with precision. Methods of architectural planning already became specific and specialised. It was not common knowledge. Not everyone could plan a detailed design that can be accurately executed. It is clear in the case of PPNA Göbekli Tepe that the planner (architect) was not the leader (Haklay and Gopher 2020).

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Table des illustrations

Titre Table 1 – Stratigraphy
Légende The eastern hill of Jerf el-Ahmar shows all four phases uncovered at the site (Early, Middle, Late and Transition) while the western hill revealed findings pertaining mainly to the Late Phase. The Early Phase comprises four villages (VII/E-IV/E) in which only curvilinear plan structures were uncovered. The onset of the Middle Phase (Villages III/E-I/E) is marked by the appearance of straight walls and right angles in Village III/E, while the successive Villages II/E and I/E include the communal Structure EA7 which is reminiscent of Structure EA30 (Village II/W) of the Late Phase—the subject of the current paper. The Late Phase is characterised by the appearance of rectangular-plan structures. It is known mainly from Village II/W in which structures are arranged with relation to the communal Structure EA30. The Transition Phase (from PPNA to PPNB), distinguished by its lithic technology, is known mainly from the eastern hill (Village -II/E) and includes the communal Structure EA53
Crédits Drawings G. Haklay; modified from Stordeur 2015
URL http://0-journals-openedition-org.catalogue.libraries.london.ac.uk/paleorient/docannexe/image/297/img-1.jpg
Fichier image/jpeg, 258k
Titre Fig. 1 – The site of Jerf el-Ahmar, western hill
Légende Village II/W at Jerf el-Ahmar with the curvilinear Structure EA30 at the centre
Crédits Photo mission El-Kowm-Mureybet
URL http://0-journals-openedition-org.catalogue.libraries.london.ac.uk/paleorient/docannexe/image/297/img-2.jpg
Fichier image/jpeg, 985k
Titre Fig 2 – Structure EA53 (Village -II/E)
Légende Note the central polygonal floor defined by stone panels
Crédits Photo mission El-Kowm-Mureybet
URL http://0-journals-openedition-org.catalogue.libraries.london.ac.uk/paleorient/docannexe/image/297/img-3.jpg
Fichier image/jpeg, 1,2M
Titre Fig. 3 – A. Original plan of Structure EA53; B. Visualisation of the centre finding calculation
Crédits A. Stordeur et al. 2000: fig. 9; B. Drawing G. Haklay; modified from Stordeur et al. 2000: fig. 9
URL http://0-journals-openedition-org.catalogue.libraries.london.ac.uk/paleorient/docannexe/image/297/img-4.jpg
Fichier image/jpeg, 1,2M
Titre Fig. 4 – Structure EA53
Légende The resulted fitted circle
Crédits Drawing G. Haklay; modified from Stordeur et al. 2000: fig. 9
URL http://0-journals-openedition-org.catalogue.libraries.london.ac.uk/paleorient/docannexe/image/297/img-5.jpg
Fichier image/jpeg, 250k
Titre Fig. 5 – Structure EA53
Légende Superposition over the plan of a geometric hexagon inscribed inside the calculated fitted circle. Note that the western posthole and associated stone panels are marked (on the original plan) with dotted lines, indicating a reconstruction. Otherwise, the sides of the geometric hexagon fit the stone panels with an accuracy that suggests that this form was indeed geometrically constructed
Crédits Drawing G. Haklay; modified from Stordeur et al. 2000: fig. 9
URL http://0-journals-openedition-org.catalogue.libraries.london.ac.uk/paleorient/docannexe/image/297/img-6.jpg
Fichier image/jpeg, 262k
Titre Fig. 6 – The measuring of a hexagon by the construction of equilateral triangles
Crédits Drawing G. Haklay
URL http://0-journals-openedition-org.catalogue.libraries.london.ac.uk/paleorient/docannexe/image/297/img-7.jpg
Fichier image/jpeg, 85k
Titre Fig. 7 – A. Plan of Structure EA30; B. Statistical centre point calculation
Légende A. Note the polygonal central floor defined by a set of nine nodes. B. Using a set of points that mark the nine corners defining the polygonal central space as the initial data, a grid of a predefined precision (in this case 5 cm) was superimposed over the examined area as the infrastructure of a simple algorithm that followed these steps: 1. Measuring the distance from each grid point to each of the given set of points (in this case, the distances from each grid point to the nine polygon corners); 2. Calculating the standard deviation (SD) values of the group of distances associated which each grid point; 3. Identifying the grid point of the smallest SD value
URL http://0-journals-openedition-org.catalogue.libraries.london.ac.uk/paleorient/docannexe/image/297/img-8.jpg
Fichier image/jpeg, 736k
Titre Fig. 8 – Structure EA30
Légende A. Visualisation of the centre calculation. B. Lines projecting from the identified centre point correspond to the faces of the interior walls separating the different area types: the platforms, the cell clusters, and the space between the two structural walls.
Crédits Modified from Stordeur et al. 2000: fig. 5
URL http://0-journals-openedition-org.catalogue.libraries.london.ac.uk/paleorient/docannexe/image/297/img-9.jpg
Fichier image/jpeg, 1,2M
Titre Fig. 9 – Structure EA30
Légende Relative to the centre point, the polygonal form accurately maps onto a system of concentric circles of constant interval, suggesting that a unit of measure was used in the design and construction of the structure
Crédits Modified from Stordeur et al. 2000: fig. 5
URL http://0-journals-openedition-org.catalogue.libraries.london.ac.uk/paleorient/docannexe/image/297/img-10.jpg
Fichier image/jpeg, 366k
Titre Fig. 10 – Geometric regularities in Structure EA30
Légende An idealised form of defined proportions describing the shape of the polygonal floor, superimposed over the original drawing. The 95º angle and the rounded platform edge in Node 2 may represent a slight deviation from the plan, possibly to enlarge the floor area
Crédits Drawing G. Haklay; modified from Stordeur et al. 2000: fig. 5
URL http://0-journals-openedition-org.catalogue.libraries.london.ac.uk/paleorient/docannexe/image/297/img-11.jpg
Fichier image/jpeg, 420k
Titre Fig. 11 – The planning and measuring of rectangular architecture
Légende A form is specified by a floor plan composed of small units of equal length which are successively used as counters in the measuring process. A. Formulation of a plan (specification of the form) using reeds of equal length (7:3 length to width proportion in the example); B. Collecting by hand the reeds that mark the length to be measured (the seven reeds that mark the long side of the rectangle in the example); C. Each reed stands for one unit of measure (a “heel-to-toe” step in the example). Each time a unit is measured (after each step), a counter (a reed) is tossed. When the reeds run out, the dimension is measured (7 length units in the example). This is repeated for the other dimensions (the other rectangular sides) and the desired form is produced. This is done without abstract number concept and words representing numbers
URL http://0-journals-openedition-org.catalogue.libraries.london.ac.uk/paleorient/docannexe/image/297/img-12.jpg
Fichier image/jpeg, 95k
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Référence papier

Gil Haklay et Avi Gopher, « Geometry, a measurement unit and rectangular architecture at Early Neolithic Jerf el-Ahmar, Syria »Paléorient, 46 1-2 | 2020, 31-42.

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Gil Haklay et Avi Gopher, « Geometry, a measurement unit and rectangular architecture at Early Neolithic Jerf el-Ahmar, Syria »Paléorient [En ligne], 46 1-2 | 2020, mis en ligne le 01 décembre 2021, consulté le 12 janvier 2025. URL : http://0-journals-openedition-org.catalogue.libraries.london.ac.uk/paleorient/297 ; DOI : https://0-doi-org.catalogue.libraries.london.ac.uk/10.4000/paleorient.297

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Auteurs

Gil Haklay

Sonia and Marco Nadler Institute of Archaeology, Tel Aviv University, P.O.B. 39040, Ramat Aviv, Tel Aviv 69978 – Israel

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Avi Gopher

Sonia and Marco Nadler Institute of Archaeology, Tel Aviv University, P.O.B. 39040, Ramat Aviv, Tel Aviv 69978 – Israel

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