Historical Metrology and a Reconsideration of the Toltec Module
By Gregory Vogel
Published in Southeastern Arcaeology 2006, Vol. 25, pp. 6-19
Archaeologists and other researchers have occasionally "discovered" measurement systems used by prehistoric people in North America and elsewhere. This paper demonstrates serious problems with many of these discoveries. Methodologically and theoretically, deriving prehistoric measurement systems from the evidence left to us today is difficult if not impossible in nearly all situations. The "Toltec Module" is one such fatally flawed measurement.
More than just debunking the Toltec Module, this paper also explores the methods and theories behind historical metrology (the study of past units of measurement), and more specifically, what I am calling cryptometrology (the search for past units of measurement).
(The Toltec Mounds site, by the way, has nothing to do with the Toltecs of ancient Mexico – it is a 1,000 year old Native American site in central Arkansas.)
Below is an additional introduction that wasn't part of the original article, it's a short piece I wrote just for fun. What's spatial statistical analysis for if not for fun?
The Toltec Module of 47.5 m has been proposed as a standardized unit of measurement employed in the layout of the Toltec Mounds site in central Arkansas (Sherrod and Rolingson 1987). Other researchers have hypothesized that this and other standardized measurements were employed in the construction of numerous late prehistoric mound sites throughout the Southeast. Many of these studies have not taken into account the methodological issues of an appropriate margin of error, the expected occurrence of the proposed measurements by chance, possible fractionations of the measurements in question, or the change in shape and size of the mounds through time. These studies have also lacked theoretical justification for inferring a prehistoric cognitive template (the unit of measurement) from distances measured at the sites today. I propose that as it is currently formulated, the Toltec Module is untenable as a prehistoric unit of measurement. Using GIS to measure all distances between features considered key locations in the Sherrod and Rolingson study reveals that the Toltec Module does not rise above the statistical background as significant. I also explore several theoretical issues concerning historical metrology (the study of past units of measurement), particularly as it applies to the prehistoric Southeast.
Figaro with a measure in his hand, Susanna at the mirror, trying on a hat decorated with flowers. Figaro: "Five...ten...twenty...thirty...thirty-six...forty-three..." So begins Mozart's comic opera The Marriage of Figaro, as Figaro measures a room to determine where a bed given to him by Count Almaviva will fit. We never learn what measure Figaro is holding (misura in the original Italian), or the reason for the odd increments he uses. And what possible misura could contain potential bed-length multiples that span all the way from five to forty-three? Figaro first debuted in 1786 though, four years before the French Revolution that spawned our modern metric system. Figaro's potential measures are numerous (although not completely immeasurable), and most pre-metric units were not standardized in any way we would consider precise today. Weights were measured by the stone, walnut, sack or kid. Distances were measured by the bodies of monarchs (nose to fingertip distance being the King's Yard ), and by travel times on foot or horse (half-a-day to get you there).
Precise or not, these measures worked well enough for those who used them. Well enough is still just fine for everyday use, and measures are easy to understand once you've been there. As Treebeard explained to Merry and Pippin, "I have brought you about seventy thousand Ent-strides, but what that comes to in the measurement of your land I do not know." Is seventy thousand a long distance? If you'd been carried from the heart of Fangorn Forest to Wellinghall in one day, clinging to the limbs of a walking tree, I'm sure you would have not doubt how far it is.
What about our measures today? Precise, of course. Consistent, reliable, legally defined invariant universals at last. We have standardized all creativity out of distances. The U.S. Bureau of Standards keeps foot-long brass rods as curios only these days. "One foot" is officially defined as 0.3048 of a meter. And a meter? It began as a unit one ten-millionth of the circumference around the earth. Not precise enough, it turns out, because there are many ways to measure the earth's circumference. One meter, today, is the distance traveled by a ray of electromagnetic energy through a vacuum in 0.00000000333564095 seconds (I hope I got the decimal place right).
How often do we take advantage of this precision, though, and how do we really use our measures? We play fast and free with lengths as if they didn't matter: three feet, a yard, a meter, one strong pace and about waist height are all the same for everyday use. Many of our "standardized" units even vary according to the occasion. A pint's a pound the world around but one mile on land is a little short of a nautical mile at sea. One tatami in Tokyo is close to 3/4 mat in Nagoya, where space (though still dear), is not sold at quite so high a premium.
And does all this matter? How does precision figure in our society today? Surely it is important, even necessary, for endeavors of science and technology. Or is it? Would we be where we are today as a technologically advanced civilization without highly precise and standardized units of measurement? If so, does that mean we can judge the technological advancement of a society by the precision of its measures? Precision: A Measure of Progress reads the title of a 1952 promotional pamphlet for General Motors. Stronger still is the Sangamo Electric Company's 1944 pamphlet On Measurement is Founded the Whole Progress of Man. (Unfortunately it doesn't tell us what the progress of Woman is founded on.)
These ideas make me slightly uncomfortable, because in some ways I believe them. I don't think we would be where we are today without highly precise and standardized units of measurement. I do believe that a society's technological advancement can be judged by the precision of its measures. Does this make me a cultural chauvinist? I'll leave that question open for now. At least I realize that measures, like all human constructs, are arbitrary, elastic, and only as useful as our creativity allows them to be.
In Mozart's opera we never learn where Figaro and Susanna's new bed fits within their room. Figaro's measuring is only a bagatelle, a sideways glance, a minor device of the operatic plot. The measure of his misura doesn't really matter. But what about our own measures? I'm convinced that they do matter. They are, I think, a key part of the framework of our rational (and irrational) thought. The more concrete, the more ingrained, the more a part of our daily lives our measures are, the more they work their way into our mental constructs not only of the physical world, but into our mental constructs of our personal and emotional worlds as well. Not that we think and feel in increments, but we sometimes communicate as if we do: emotional distance, near at hand, the depths of despair and the height of folly. How far did the short affair go? Give an inch and take a mile. The language of distance is less poetic than prosaic, but serves to communicate our deepest feelings anyway.
The paper that follows is a study in detail, focusing at first on a single prehistoric measure that doesn't even exist. From contemplations of this non-existent entity, I hope, come real ideas about measures, and how we interpret or misinterpret the past. Consider this a single Ent-stride towards understanding measures and the people who use them. Only 69,999 more to go.