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Introduction

In Mesoamerica, obsidian is found in the transverse volcanic axis that extends east to west across central Mexico, and in the highlands of Guatemala (Figure 1).Obsidian from different sources vary in quality (in regards to tool making ability), luster, chemistry, and color. A number of these attributes have been used to identify the sources used in the past using analytical approaches. Two of the most important source identification methods are x-ray fluorescence and neutron activation (Pires-Ferreira 1976:292). There were two important investigations in sourcing material from San Lorenzo in the 1970s. These were carried out by Jane W. Pires-Ferreira (1976) and Cobean et al. (1971). In this project I use this information in combination with geographical data sets to calculate possible least cost paths between the obsidian sources and San Lorenzo. The intention of this is to examine the possible paths of different trade routes in regards to time and distance. While euclidean distances have been indirectly applied before, this project is the first to examine anthropomorphic distances, which have potential to change the current perception of perceived marginal costs between sites.

Background

The Material

Obsidian is an igneous glass formed from the rapid cooling of extrusive lava (Pires-Ferreira 1976:292). The homogeneity of obsidian glass and its lack of crystalline structure, give it excellent properties that allow for shaping flaked stone tools. The properties of obsidian enable it to be fashioned into tools that are far sharper then modern surgical blades (Cotterell and Kamminga 1990:127-128). Obsidian was not available to all native cultures and alternatives such as chert were exploited. Although obsidian was widely used in Mesoamerica, it is located in only a few areas and varies greatly in quality. This made certain sources more and less desirable for different technologies. Due to this factor there was incentive to acquire obsidian from many different sources.

Previous Source Studies

Pires-Ferrerira

The study by Jane W. Pires-Ferreira used neutron activation to identify obsidian sources. This method determined the composition of the rock by examining the percentage of sodium (Na) and manganese (Mn) in the material (Pires-Ferreira 1976:292). Original source locales are established by comparing geological samples to obsidian tools found at archaeological sites. However, it is important to remember that sourcing alone cannot identify anything about the procurement method by which obsidian was obtained. Despite this, knowing the source is still useful for determining which cultures had contact with each other, as well as relative costs of moving raw material over space.

                               Figure 1: The volcanic systems of Mesoamerica used by the Olmecs

Pires-Ferreira established three different exchange networks for the Early Formative period that contributed the majority of the obsidian found at San Lorenzo. The first is the “Guadalupe Victoria Exchange Network” which provided 62.2% of the obsidian material (in the sample) for San Lorenzo (Pires-Ferreira 1976). Though Guadalupe Victoria is located 300 km away from San Lorenzo, distance alone does not define a radius for trade since the Las Bocas, Puebla located 100 km to the west of Guadalupe Victoria contains no obsidian from this site. At San Lorenzo, the Guadalupe Victoria source provided a lot of the low quality obsidian which was inappropriate for the manufacturing of pressure blades (Pires-Ferreira 1976:301-302). Instead this obsidian was used for the production of simple percussion flake tools. High quality blade obsidian was available from an alternative network: the “Barranca de los Estetes Exchange Network”. Barranca de los Estetes only supplied about 4.8% of the total obsidian in the sample.  It is likely that San Lorenzo was only indirectly incorporated into this network during the Initial Formative period, accounting for the low number of pressure blades in its assemblage (Pires-Ferreira 1976:303-304). The third system is the “El Chayal Exchange Network”, with obsidian originating from El Chayal region in the highlands of Guatemala. This source contributed 21.7% of the sample at San Lorenzo and is located even further away from the site (580 km) than the “Guadalupe Victoria Exchange Network” (Pires-Ferreira 1976:302-303). This site was the source of higher quality obsidian then Guadalupe Victoria and was appropriate for the manufacture of pressure blades (Hammond 1972). 

Cobean et al.

Cobean and others (1971) examined the obsidian recovered at San Lorenzo in much greater detail. They used a method of x-ray emission spectroscopy to determine major elements and then used neutron activation to examine their analytical samples. From this they confirmed the reliance on obsidian from the Guadalupe Victoria source and other sources that originate from Orizaba Volcano throughout the early Formative period. They also identified several other sources that contributed heavily to the assemblage. These include: Altotonga, Veracruz; Teotihucan, Mexico; Pachuca, Hidalgo; El Paraiso, Querétaro; as well as El Chayal and Ixtepeque, Guatemala. It was not that the obsidian came from specific sources that interested them, but that the Olmec expanded had their procurement network to include new sources. The Olmec of San Lorenzo developed new sources of obsidian supply, during the San Lorenzo A and San Lorenzo B phases, expanding the number to a total of eleven. This increase corresponds to a substantial increase in the occurrence of pressure blades in their sample (Cobean et al. 1971). Whether it was demand for prismatic blades that caused an expansion in the number of sources recovered or vice versa is not clear.  What is evident, however, is that there is a substantial increase in blades during the San Lorenzo B phase.

The Cost of Obsidian Tools

Sanders and Santley conducted a detailed energetic study of the cost of creating and distributing obsidian blades (1983). Although their approach discusses a later period than the occupation at San Lorenzo, the costs that they propose for transportation and production would not have been greatly different. The first part the analysis was to determine the cost of producing blades. In one day, a specialist could produce approximately 125 blades, which represents a maximum potential of 37,500 blades a year. Given their estimates for the use of approximately 21 obsidian tools per household per year, in a year one specialist could produce enough to supply an estimated 5,600 consumers. Using even a generous population of 10,000, as proposed by Clark (2007:15), it is clear that San Lorenzo would have needed no more than a couple of specialists to fulfill their needs. If this is true the people of San Lorenzo collectively would have needed to provide each specialist with 1,650 kg of maize per year in order to support the specialists’ families. The cost to each consumer in the sites total population would not have exceeded between 1.47-2.5 kg of grain a year. This makes the production costs relatively inexpensive.

The other main cost of obsidian is the transportation of the blades. Since beasts of burden were unavailable in Mesoamerica, products were transported by human porters. Though not accounted for here, access to river transport at San Lorenzo could have greatly reduced some of the costs that are about to be described. Sanders and Santley created three assumptions for the calculation of costs. The first assumption is that the further away you are from the site, the greater the cost, since the transporter will be able to make fewer trips per year. The second assumption is the average transporter will need about 1,837 kg of maize to support his family every year. The third assumption is an adult male can carry about 23 kg over a distance of 30 km each day. These 23 kg of obsidian are enough to provide for 216 families. Distance will have a logarithmic effect on people who can be provided. Every time distance from a source is doubled, only half as many people can be provisioned. Despite these conclusions, even at 1,200 km away, the costs would only be 2.64 kg of corn for transportation for 21 obsidian tools that is required for a household in a year (see Table 2). Though Sanders and Santley do not account for quarrying costs, they perceive the total cost of obsidian tools needed to support a household to be only 5.04 kg of corn per year even at the 1,200 km range.

Methods and Results

Data

The first part of the experiment was to collect all the necessary for the project analysis. This would include finding an appropriate Digital Elevation Model (DEM) for a large area of Mesoamerica. Another part of the data collection process was finding all the areas of interest (AOI) and plotting them on the map. 

Transforming the DEM

The DEM that was used came from a previous experiment that was conducted at The Pennsylvania State University. The data was represented as one large detailed raster in a predefined projected. The problem with this current projection was that it did not serve the intentions of this project. Being a Transverse Mercator coordinate system it measured distance in terms of degrees. For this project however a metric measurement was required that would preserve distance and give metric measurements. Therefore the raster was transformed (using the Project Raster Tool) into a Lambert Conformal Conic and the parallels were adjusted to fit the AOI (figure 2). The resultant data was used for all elevation and distance calculations in this experiment.





                             Figure 2: Demonstrating the data transformation in the DEM and Shapefile
 

Collecting the Locations

In order to find the locations in this experiment several shapefiles containing relevant data were accessed. These were combined into a single shapefile that contained all the requisite points. This had to be projected into the same coordinate system as the DEM in order that later cost paths could be created. The result of this was that locations were found for each of the following sites: San Lorenzo, Pico de Orizaba, Guadalupe Victoria, Zaragoza, El Paredón, Santa Elena, Tulancingo, Otumba, Zacualtipán, El Chayal, Ixtepeque, Ucareo, and Zinpecuaro.

Running Experiments

Now that the data had all been imported into compatible data type for the ArcGIS software the next step was to now calculate information from this data. The first step was to run Euclidian distances to each of the locations from San Lorenzo. This information represents the absolute minimum distance that could be traveled. This will be useful later in later discussion because it can serve as a means of comparison. The information was represented in terms of meters; from this approximate costs can be determined in terms of food consumed by a porter to transport one household’s yearly needed obsidian. To calculate Sanders’ and Santley’s cost table was used to create an exponential regression of transportation costs (1983) (See table 3 for results). 


                                                                                                            Table 3: Euclidian Costs of transporting a yearly assemblage of obsidian for one household in terms of Kg of Corn

Once finished with Euclidean distances the next step was to run the ansiomorphic distances. These distances serve to provide costs to differential topography. Basically the principle is that walking up hill is more time consuming then walking downhill to a point, therefore giving relative costs to every pixel of the DEM.  This is accomplished by using Tobler’s Hiking Function (See Tobler 1993).

Specifically in this experiment Tobler’s Hiking Function was applied to the DEM that was earlier discussed. This created a new raster map that when queried provided costs in terms of time from San Lorenzo to each location. However; for this experiment the interest was not time so a conversion to distance must take place. This is appropriate since a porter would have been the primary interest in time to minimize his costs. Therefore to calculate cost path distances from time cost vectors were used. Using these vectors costs in terms of kilograms of corn needed to be exchanged to a porter by one household to provide yearly obsidian assemblage was used (See table 4).


  Table 4: Ansiomorphic costs of transporting a yearly assemblage of obsidian for one household in terms of Kg of Corn

Results and conclusion

From the experiment performed above very different costs from Euclidian and Ansiomorphic distances were calculated. For example sites such as El Chayal went up an astounding 15% in cost, while other sites such as Guadalupe Victoria went up in cost as little as 1% in cost. There seems to be a general tendency for sites that are further away to increase more significantly in costs then those sites close by (see table 5). This information is very useful because it increases the perceived costs of trade with distant areas. For example trade with El Chayal from San Lorenzo would have been 15% more expensive then what would be expected from straight line distances. The effect of this may compound the effect that distance is having in trade than previously expected. This could be confirmed by a new assemblage analysis which when published can see if these expectation hold true.

In conclusion though the results from this experiment are very specific they provide another piece to the puzzle of trade at San Lorenzo. This principle can be accessed to many different products (as long as costs can be established) that may enlighten us to other aspects of the economy. Eventually from the combination of this information an analysis of possible different trade networks in the Olmec world could be established .


 

 Percent change in costs from Obsidian Sources in terms of Euclidian and Ansiomorphic distances in order of distance from San Lorenzo

Bibliography

Clark, John E.

2007

Mesoamerica’s First State. In The Political Economy of Ancient Mesoamerica: Transformations during the Formative and Classic Periods, edited by Vernon L. Scarborough and John E. Clark, pp. 11-46. University of New Mexico Press, Albuquerque.

 

 

 

 

 

 

Cobean, Robert H., Michael D. Coe, E. Perry, Jr., K.T. Turekian, and D.P. Kharjar

1971

Obsidian Trade at San Lorenzo Tenochtitlan, Mexico. Science 174(4010):666-671.

 

 

 

 

Cotterell, Brian  and Johan Kamminga

1990

Mechanics of Pre-Industrial Technology. University of Cambridge, Cambridge.

 

 

 

 

Cowgill, G. L.

1975

On Causes and Consequences of Ancient and Modern Population Change. American Anthropologist 77:505-525.

 

 

 

 

 

Hammond, N.

1989

Cultura Hermana: Reappraising the Olmec. Quarterly Review of Archaeology 9(4)1-4.

 

 

 

 

 

Pires-Ferreira, Jane W.

1976

Obsidian Exchange in Formative Mesoamerica. In The Early Mesoamerican Village, edited by Kent V. Flannery, pp. 292-306. Museum of Anthropology, University of Michigan, Ann Arbor.

 

 

 

Sanders, William T., and Robert S. Santley

1983

A Tale of Three Cities: Energetics and Urbanization in Pre-Hispanic Central Mexico. In Prehistoric Settlement Patterns: Essays in Honor of Gordon R. Willey, edited by Evon Vogt and Richard Leventhal, pp. 243-291. University of New Mexico Press and Harvard University Press, Albuquerque and Cambridge.

 

 

 

Tobler, Waldo

1993

Three Presentations on Geographical Analysis and Modeling. In Technical Report 93-1. National Center for Geographic Information and Analysis, Washington D.C.

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