Figure 1 The distribution of the game of twenty squares.
Related Figures (19)
Fig. 2. Example of a game of twenty squares with the numbering system that indicates the route of play. (Samal, Staatliche Museen, Vorderasiatisches Museum, Berlin, S 3688, after May, 1991, Fig. 143). The board has a rectilinear shape, 12 squares on the main axis, eight additional squares, and no special squares. “The game of ‘Hounds and Jackals’ originated in Egypt in approximately 2100 BC, and soon spread into the Near East, Fig. 4. Style A of the game of 58 holes. Note the links between the holes. The depiction of the eyes on this example may have indicated a starting point. (Egypt, Cairo Museum no. 68128, after Meyer, 1982, pl. 6.1). the entire data set). IQV varies between 0, when all observations aré in a single category (i.e., an attribute fixed at one particular attri. bute state within a time period), to 1, when observations are evenl} split between all categories (i.e., boards are evenly split for ar attribute between all possible attribute states). IQV is not affectec by sample size and should be comparable across different data sets though as with most statistics, estimates of IQV for small sample sizes are less precise. Fig. 3. The distribution of the game of fifty-eight holes. one board from the Southern Levant, dated to between the fourth and second century BC, was much younger than the remaining boards and was also dropped from the analysis. Thus, 90 boards grouped into five temporal categories were used for the analyses presented below. Fig. 5. Style B of the game of 58 holes. Note the marked holes. The upper end in the illustration shows a labyrinth that is mainly found with style B. (Megiddo, Rockefeller Museum, Jerusalem, no. 38826, after Loud, 1939, pl. 46). Fig. 6. Style C of the game of 58 holes. Note the links that cross from one player to the other. The numbers indicate the route of play. (Tepe Sialk, Musée du Louvre, AO19438, after Meyer, 1982, pl. 6.2). Overview of the game of twenty squares as found in the archaeological record. None = no square is marked. One marked square = one square is marked but its position is unknown. Unknown = description/illustration not available or surface was damaged 4? = it is probably square 4 that is marked. * This is a double board where the markings are as follows (see figure) > According to Hoerth or ca. 13—12 following Meyer. Overview of the game of fifty-eight holes as found in the archaeological record. Table 2 Notes: Brds. = Boards; Innov. = Innovations/Innovative; Addit. = Additional; Mrkd. = Marked; Lab. = Labyrinth; Number of innovations and innovative boards not calculated for 2000—1700 BC. Innovation frequency represen the total number of innovations divided by the number of chances for an innovation (i.e., number of observations). Innovations and variation over time for attributes of the game of fifty-eight holes. Samples studied, innovations and variation over time for attributes of the game of twenty-squares. Notes: No. region = Number of regions in which the boards have been found; Brds. = Boards; Innov. = Innovations/Innovative; Freq. = Frequency; Sqrs. = Squares; Addit. = Additional; Mrkd. = Marked. Number of innovations and innovative boards not calculated for 2150—1900 BC because there is no preceding period. Innovation frequency represents the total number of innovations divided by the number of chances for an innovation (i.e., number of observations). Fig. 9. Number of additional squares off the main axis, over time, for the game of twenty squares, showing the original configuration (#8), and the timing and geographic location of four innovations (#5, 10, 12, 16). Innovations are indicated by black circles. As a second comparison, we turn to Neiman’s (1995) study of pottery innovation rates (uw). Shennan and Wilkinson (2001) and Kohler et al. (2004) have estimated wu for different temporal phases for pottery of the Linear Bandkeramik (LBK) of Neolithic Europe Fig. 8. Historical contact and the transmission of the game of fifty-eight holes. Fig. 7. Historical contact and the transmission of the game of twenty squares. The oldest twenty squares boards, those dating before 1600 BC, are nearly homogenous. Several attributes are standardized across all boards within a time period (e.g., number of extra squares off main axis), while other attributes show just two different states (e.g., number of central squares). For example, Fig. 9 plots the number of extra squares off the main axis over time. As seen, prior to 1600 BC, all boards have 8 extra squares. Four innovations are evident after 1600 BC, with some boards containing 5, 10, 12, and 16 extra squares. The earliest of these innovations (16 extra squares) appears just after 1600 BC in Egypt and seems to have been successfully transmitted over time and space, continuing to appear Strength of association (Cramer’s V) statistics for attributes of twenty square: boards. Table 5 Fig. 10. Average IQV for twenty squares and fifty-eight holes by time period. Variation in fifty-eight holes boards also began high, but never witnessed a period of winnowing. Instead, variation in board form remained high compared to twenty squares and, if anything, seems to have decreased slightly over time. This is not consistent with our hypothesis. As shown in Table 4, the innovation frequency was higher than twenty squares, but a larger fraction of the innovations that appeared were not retained in the larger pool (i.e., appear only once in our sample). Thus, of the 9 innovations that occur before the latest time period (i.e., before 700 BC), only 57% (n = 5) appear to have been retained, and appear in the pool of younger boards. The Strength of association (Cramer’s V) statistics for attributes of fifty-eight hole: boards. Notes: * — Sample size is too small and test value cannot be calculated. Fig. 11. Average IQV against the number of regions in which at least one board wa recorded. In support of Hypothesis 2b, Fig. 11 shows a positive relationship between the average IQV statistic for a period against the number of regions in which at least one board was recorded (r = 0.35; p = 0.09). This suggests a link between board variation and the
