Prehistoric units of measurement, or quanta, have been suggested as existing at many prehistoric archaeological sites throughout the world.  Perhaps most famous are those postulated for megalithic sites in Europe (summarized in Heggie 1981), including the Megalithic Yard of 0.829 m (Thom 1971; see Baxter 2003:228-235 for a recent summary of research into the Megalithic Yard).  Such quanta have been proposed for sites in North America as well, including a unit of 57 m at numerous Hopewell earthworks (Marshall 1979, 1987), a measurement of 5 m at Cahokia (Smith 1969), the Archaic Standard Unit of 1.666 m and Standard Macro-Unit of 86.63 m (Clark 2004), a measure of 48 m at Kolomoki Mounds (Pluckhahn 2004), and the Toltec Module of 47.5 m at the Toltec Mounds site in central Arkansas (Sherrod and Rolingson 1987).  These studies are examples of historical metrology – the study of past units of measurement.  Few such reports in North America acknowledge this field, however, or refer to the literature for theory and methodology (see Kula [1986] for an outline and history of historical metrology).  Deciphering prehistoric quanta in the Southeast would of course hold important implications for the societies who employed them.  It is not at all clear, however, that any such units of measurement exist.  I propose that the Toltec Module, as it is currently formulated, is theoretically and methodologically untenable.  Many of the arguments presented here apply to other studies of historical metrology throughout the Southeast in general.

            Sherrod and Rolingson (1987) proposed the Toltec Module (TM) of 47.5 m as a unit of measurement employed by the builders of Toltec Mounds and 26 other late prehistoric sites (including Cahokia and Spiro), used in the construction of the sites and still expressed in mound layout and patterning.  Toltec Mounds is a late Woodland civic ceremonial center, and the type site for Plum Bayou culture.  Archaeomagnetic and calibrated radiocarbon dates show the site to have been occupied from about A.D. 700 to 1050, although this may not reflect the full extent of the occupation (Rolingson 1998:24-25).  There are at least 19 mounds known to have been present, within a core site area defined by a backwater pond on the northwest, and an embankment and accompanying ditch surrounding the rest (Figure 1).  The area surrounded by the embankment measures roughly 900 m northeast to southwest and 450 m northwest to southeast.  The mounds surround two open plaza areas, one near the north end of the site and one near the south.  The TM quanta was based on the apparent ubiquity of multiples of this distance between what were considered significant 'target' points at the sites.  Understanding exactly how a distance of 47.5 m was first derived is instructive in understanding how it was determined to be significant:

            A module of measurement at the Toltec Mounds site was first recognized as a 95 m value.  This was found by discovering that the major axis dimension of the base of Mound A, 95 m, was present in that dimension, or multiples of it, between Mound A and other mounds on the south plaza.  Since some mounds were spaced on one-half of this increment, or 47.5 m, it was thought that this smaller unit would be a more useful one, even though the larger was more common. (Sherrod and Rolingson 1987:36)

Figure 1. Sherrod and Rolingson's (1987:37, Figure 9) map of the Toltec Mounds site, showing the location of mounds, the embankment, and Toltec Module distances radiating from the center of Mound A.  Tick marks on lines are 95 m (2 x the Toltec Module). 

            It thus appears that Sherrod and Rolingson tested only for multiples of 47.5 m, and not other potential distances.  The target points that were used to search for the module included the centers, edges, and 'midslopes' of the mounds, the edges and openings in the surrounding embankment, and the ditch accompanying the embankment.  Their method consisted of straight-line measurements between target points (some measured on the ground and at other sites apparently measured from maps), and calculations of how closely these distances approximated multiples of the TM.  Figure 1 shows several of Sherrod and Rolingson's (1987) measurements from the center of Mound A.  Exactly how many such measurements were made at this and other sites, and how key target points were chosen for inclusion is not explained in the original study.  Sherrod and Rolingson suggest that the TM may be expressed in the heights of some of the mounds as well (as fractions of 47.5 m), but the heart of their argument lies in horizontal distances between certain target points.  Those they posit as corresponding to the TM at the Toltec Mounds site are presented in Table 1 (Table 3 from Sherrod and Rolingson 1987:39).  These represent "all module data" (1987:36) from a transit survey of the site.

Table 1.  Distances presented by Sherrod and Rolingson as corresponding to
Toltec Module distances (Sherrod and Rolingson 1987:39, Table 3).

            Although 42 occurrences of the TM are presented in the table, it is important to note that 16 of these were derived from a stake set in the location of Mound H, which had previously been leveled.  Mound H was proposed as being in line with the equinox, directly east of Mound A.  The stake was placed exactly 9 TM (427.5 m) east of the center point of Mound A, on an exact 90 degree azimuth, not necessarily in the geographic center of Mound H.  In addition, 16 occurrences presented in the table were based on other mounds no longer present.  The locations of most of these mounds were estimated from earlier sketch maps and artifact concentrations on the surface (of a field which had been plowed for several decades).  Only 19 of the 42 distances posited as significant were based on existing mounds. 

            Sherrod and Rolingson's conclusion of the TM as a unit of measurement was based on its common occurrence between the chosen target points.  The apparent ubiquity of the TM convinced other researchers as well, and one review of the original study noted, "The 'Toltec Module' fails to hit the mark in enough cases that the authors must posit both local variations of the base unit and also considerable imprecision on the part of the ancient surveyors.  Nevertheless, the occurrences of both alignments and the module are so frequent that there seems little doubt of their reality" (Webb 1989:439).  The TM has since been accepted in several summaries of archaeoastronomy and related fields (e.g. Brown 1997:478-479; Haag 1993:105-106), and other researchers have applied the TM directly to other sites.  With appropriate caveats, Young and Fowler (2000:277) speculate on possible sub-divisions of the TM used in the construction of woodhenges and other features at Cahokia.  In a popular summary of the site, Kitt Chappell (2002:53) states 47.5 m as a significant distance in the layout of Cahokia.  Most recently, Pluckhahn (2004) has proposed the limited use of a 48 m module for the Kolomoki site in Georgia, which he suggests may be related to the TM.

            In this paper I outline several problems with interpreting the TM as a unit of measurement employed in the construction of its type site, the Toltec Mounds.  Many of these arguments are also directly applicable to any study of historical metrology conducted on mound sites in the Southeast.  I argue that the margin of error used by Sherrod and Rolingson is so great that most apparent TM measurements at the site are spurious.  In fact, the margin of error inherent in all Southeastern mound sites, due to the nature of the archaeological evidence, makes any attempt to derive a unit of measurement as short as the TM suspect.  I then use geographic information systems (GIS) modeling of the Toltec Mounds site to demonstrate that multiples of 47.5 m do not stand out as significant against the statistical background.  Multiples of the TM appear to be common not because of the specific layout of the site, but because 47.5 m is a short distance compared to the numerous targets that are relatively close together.  Any similarly short distance would be nearly ubiquitous, and the shorter the distance, the more common its occurrence.  Taking another approach with GIS, I use statistical time-series analysis (applied to spatial instead of temporal data) in an attempt to determine which distances occur most commonly between Sherrod and Rolingson's target points.  While somewhat speculative, this time-series analysis demonstrates that there are many distances at the site which occur more commonly that the proposed TM.  Finally, I discuss theoretical issues concerning the search for a prehistoric unit of measurement, particularly in light of what we know about mounds and mound centers in the prehistoric Southeast.

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