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An Exercise in Middle Woodland Geometry V

Nov 2, 202422 min read

Seip Earthworks [Squier & Davis 1847, Plate XI, n. 2]

Structure of the Mayan Calendar Round [Atwell 2024]


Time


"For us believing physicists, the separation between past, present and future has only the meaning of an illusion, albeit a tenacious one." [Albert Einstein, letter to the family of Michele Angelo Besso, March 21, 1955]


“How can we live without our lives? How will we know it’s us without our past?” [John Steinbeck, The Grapes of Wrath]


“We haven’t re-created the past here. The past is gone. It can never be re-created. What we’ve done is reconstruct the past—or at least a version of the past. And I’m saying we can make a better version.” [Michael Crichton, Jurrasic Park]


“Who will lay hold on the human heart to make it still, so that I can see how eternity, in which there is neither future nor past, stands still and dictates future and past times? Can my mind have the strength for this?” [St. Augustine, Confessions]


"... the Power of the World always works in circles, and everything tries to be round… The Sky is round, and I have heard that the earth is round like a ball, and so are all the stars. The wind, in its greatest power, whirls. Birds make their nest in circles, for theirs is the same religion as ours… Even the seasons form a great circle in their changing, and always come back again to where they were. The life of a man is a circle from childhood to childhood, and so it is in everything where power moves." [Black Ek]


Introduction

The concept of time is so full of ambiguities and paradoxes that it is no wonder that many societies worship time and its mysteries. Time at the human level is one-way, there is no going back, ever. At the quantum level though, time has no direction although the Universe has a history like everything else. Scratch a physicist, and you will get a different explanation of why. [Carroll 2010] Human time has a past, a present, and a future. The present repeats in a circle, dawn and dusk, seasons repeat themselves, birth follows growth, follows new birth, follows death and decay. A great human achievement is that we have figured out ways to measure time. No actual clock has been found in the brain. [Wittmann 2009] Our sense of time is distributed differently depending on the duration.


Archaeological Time

One cannot go back in time but the past leaves traces because everything has a history. Any collection of objects first needs to be ordered somehow in time. Human artifacts are created, used, and often broken or entombed. Traces can be rediscovered, physically removed, or completely erased. Ordering and dating traces of the past requires a diverse set of methods and technologies.


stratification


Most sites are buried in the earth. Over the ages, artifacts left by older usage get covered up by those of more recent usage. Things get stratified, as one digs down objects become older than those above. [Hirst 2024] This does not work in all instances and often a site has been plundered by 'collectors' mixing levels or placing things out of context.


seriation


It was the British archaeologist Sir Flinders Petrie who during the 1880s [Poole 1998] came up with the idea that artifacts could be ordered based on certain attributes that change over time. Seriation orders a set of objects along a line which hopefully can represent time. The method belongs to a set of problems called 'combinational optimization problems' and is related to the Traveling Salesman Problem. [Hahsler et al. 2008] Problems of this type take longer to solve, on the order of O(sum(n)!) to O(sum(n!)) where n is the number of objects to be ordered and sum() is the sum of the number of objects in each k classification. Because of this, a set of objects is first clustered into classes. Also, some dimensional reduction schemes must be used. An R language package, called 'Seriation', exists with a whole set of routines for clustering, dimensional reduction, ordering, and visualizing data. [Hahsler 2015]


Seriation data usually takes two forms abundance or presence-absence. Abundance is generally measured as a percent or ratio while presence-absence is a binary 1-0. [Marquardt 1978] For geometric earthworks the abundance of artifacts found inside might not work because in many, few artifacts have been found. [Lepper 2016] Viewing the earthworks as artifacts with a presence or absence of attributes might be useful. Absence can have two forms, an attribute is absent because it does not exist or an attribute is absent because it is unknown whether it existed or not. This different type of absence changes the nature of the statistical model [Hahsler 2023] If a binary variable is part of a hierarchy, meaning that another variable has meaning only if the first variable is true, also changing the statistical model. In [Newark, the Core, and Beyond] I argue that presence-absence data should be probabilities, not binary values.


In 1998 Katharine C. Ruhl and Mark F. Seeman published a paper on the temporal ordering of copper ear spools in Ohio. The spools created a visible ring that was either red (copper) or white (a sheet of meteoric iron.) They concluded that over time the diameter of the spools got bigger and the angle where the inside of the ring turned inward got less rounded and more abrupt. This made the ring more pronounced, both changes making the ring more visible at a distance.  [Ruhl & Seeman 1998] One of the features of these earthworks is their size. The Great Circle at Newark is quite visible in any GIS imagery. I did a crowd count using some web software. The most sparse setting is one person every 10 square meters. This allows almost 10,000 people to be inside. [Catel 2024] It is believed that wearing these large copper ear spools was an elite practice. Women shaved one side of their heads to make the spool more visible.


Female figurine [Ruggeri 2024]


Ruhl & Seeman use their study to test a theoretical model by Christopher Carr about the relationships between artifacts and temporal order in 'middle range' cultures: These are hunter-gatherer societies that have shown a high degree of complexity but are not what we think of as the standard village and city civilizations. [Carr 1995]


"The theory maps a hierarchy of formal attributes to a hierarchy of behavioral and other processes and constraints in a partially determinant, partially indeterminant, and context-dependent manner. The hierarchy of formal attributes is defined by largely objective criteria, including the relative visibility of the attributes, their relative placement in a hierarchy of manufacturing decisions, and their relative position in a sequence of production steps. The processes and constraints that are considered include technological (procedural and material), sociocultural, social-psychological, personal psychological, depth-psychological, and physiological-level factors, which pertain to varying spatial scales." [Carr 1995, p. 171]


This forms a hierarchy of temporal importance:


  1. "the visibility of the attributes relative to each other;

  2. the relative order of the attributes in a hierarchy of manufacturing decisions involved in planning the design and attributes of the artifact; and

  3. the relative order of the attributes in a sequence of production steps involved in manufacturing the artifact and manifesting its attributes." [Carr 1995, p. 173]


This point about visibility relates to how the earthworks were viewed. Modern science uses the ortho map, looking directly down. This view exposes the geometry. It is a view that was never possible for the builders except in the minds of the designers or drawn on some surface. It has been shown that some geometric earthworks were built in relation to various higher points on the horizon [Hively & Horn 2016] so some people had access to an oblique view of the construction. Visibility for people visiting the earthworks would be completely different:


  • Entrances are of great importance as they set the tone for what comes after.

  • Entrances control flow and an initial view seen through a human cone of vision.

  • Horizon is controlled so what appears above this horizon could be important.

  • Geometric features show up as straight lines or curves and angles where they meet.

  • Walled lanes that are parallel converge towards a vanishing point. Lanes that diverge could look parallel in a distance. Lanes that converge create a greater sense of distance.


James Marshall [Marshall 1996], William Romain [Romain 1996], A. Martin Byers [Byers 2005], and Warren DeBoer [DeBoer 2010] have all attempted seriations of the earthworks based on mostly geometric properties. With mixed results. Marshall based his on the mathematical knowledge needed to build each earthwork, Romain on similarities to a standard of measure developed by Marshall and others, and by shape, and Byers and DeBoer did a more formal seriation each based on their own sets of categories. The trick is to find out what in a myriad of features changes or doesn't change with time.


Seriation has a one-dimensional result. Other methods using network analysis give the same timeline but add a second dimension. This dimension is often Euclidean distance but it can be statistical distance or any other distance measure. [Östborn & Gerding 2014]


paleoclimate data


Paleoclimate refers to climate changes and fluctuations before historic time. A host of methods are used. These include data from tree rings, packrat middens, lake sediments, ice cores, and many others. This data is collected in national and international databases. [National Centers for Environmental Information 2024] A 2017 study using sediment data from a lake in Indiana went back 2100 years. The study is about the Medieval Climate Anomaly (950–1250 CE) and how it affected Mississippian cultures during and after. [Bird et al. 2017] It does cover at least the latter part of the Middle Woodland period. The most that can be said is that this period was wetter and slightly cooler than historic times. Because of the wet climate, tree ring data is pretty useless as only a few fragments of wood have survived. Post holes show the diameter of the tree and if the post hole has been excavated, the depth and angle of the post.


radiocarbon dating


Carbon-14 is the longest-decaying isotope of carbon. It is formed in the atmosphere due to cosmic ray interaction. Living creatures take up carbon continuously so the amount of C14 stays the same. When it dies this amount starts to decay. With a half-life of 5,730 ± 40 years, it decays at a constant rate. By measuring the amount of C14 in a specimen its age can be determined. The physicist Willard F. Libby first proposed using this method as an absolute dating technique in the mid-1940s. It is accurate between 500 and 55,000 years. Radiocarbon dates are measured in years BP (Before Present.) Present is 1950, the year atomic bomb testing changed the composition of carbon in the atmosphere. Because a radiocarbon date is a statistical number there is always a range of accuracy. Over the years the amount of material needed to get a date has been reduced, as well as the time needed to date a specimen. The amount of C14 in the atmosphere is considered at equilibrium but there are fluctuations, due to the Earth's magnetic field, differences depending on what continent, and differences in the ocean. This requires a calibration curve that is an ongoing project, all sorts of data from tree ring data to fluctuations in solar activity help calibrate the curve. Thus, radiocarbon dates are more accurate. Most of the problems with radiocarbon dates come from contamination of the sample and a lack of understanding of the context in which a sample was taken. This can seriously skew the results. Of course, the sample must have a biological origin. [Hajdas et al. 2021]


The term 'Adena' stands for a set of cultural similarities that began to appear around 400 years before the cultural similarities termed 'Hopewell.' Adena comes from the name of the Chillicothe estate of Thomas Worthington, a two-time senator and governor of Ohio. The Curator of Archaeology for the Ohio Archaeological and Historical Society (now the Ohio History Connection), W. C. Mills excavated a large conical mound on the estate in 1901. He found 33 bodies buried during two stages of construction and a large subfloor tomb at the base made out of logs. The mound had a circular enclosure. I have been unable to find the status of a ditch. The mound was destroyed and may today exist as a slight rise of a road in a Chillicothe subdivision. [Ward 2020] The Adena mound became a cultural template from which other mounds were typed. In particular, the structure of the log tombs and the artifacts found within. Several researchers devised trait lists that grew rather large, became typologies, and were then grouped into temporal categories. With the advent of radiocarbon dating a set of dates began to be assembled. In 2014 Brad Lepper and colleagues dated the Adena Mound for the first time. Mills was unusual for his time in that he collected perishable items, pieces of bark and fabric used to wrap the bodies, which were believed to have come from the main tomb. These were found in old cigar boxes at the Ohio History Connection. [Lepper et al. 2014] Lepper placed his findings with other known Adena radiocarbon dates and some Hopewell dates from Mound City.


[Lepper et al. 2014, fig. 6, p. 217]

Here is his conclusion:


'The similarity of the textiles from the Adena Mound to those from the Hopewell mounds, coupled with the results of the radiocarbon dating of the bark and textile samples from the Adena Mound, fully corroborate an important conclusion of Webb and Baby (1957:109) based on the small number of radiocarbon dates available to them: “Adena is older than Hopewell and culturally ancestral to it.”


The Adena Mound, therefore, as well as the circular enclosure that once surrounded it, may have served as a center of mortuary activity for the ancestors of the builders of Mound City. Certainly, the Adena Mound would have constituted an important element of the ceremonial landscape of the Scioto River valley for all subsequent peoples, and the construction of the Mound City–Hopeton complex, among the earliest of Hopewellian monumental earthworks, within sight of the Adena Mound may not be coincidental...'


Notice that Adena Mound is linked to Mound City by time, location (visibility), and similarity of textile types, not just time alone. Notice also that individual mounds have multiple results, little smears across time. Some authors use the raw distributions of the radiocarbon results instead of box and whisker plots, these do look like little smears. Sometimes these smears can form a scaffolding, with enough supporting data, from which a biography can be created. [Henry 2021]


Log tombs have been designated as a defining trait of Adena culture. An honors thesis by Allegra Ward shows that log tomb 'types' have persisted well into Middle Woodland times. [Ward 2020]


The concepts of 'Adena' and 'Hopewell' differ depending on the region as they are both regional and pan-regional phenomena. In 2011 N'omi Greber wrote a short article honoring a colleague, R. Berle Clay. She quotes Clay and herself. [Greber 2011]


'“Now it may be best to move ahead, minus Adena as an integrating concept, although it may have local applications. Perhaps started with the best of intentions to order local archaeological matters in conceptual space, it has been hopelessly confused by conflicting interests.” (Clay 2005: 95-96).

...

“We might find a new naming system that recognizes both the diversity and the unity of the archaeological cultural remains that overlap in space, time or both across the Central Ohio Valley, although such a scenario is unlikely. An elegant single word name that combines space and time could complicate cross-region comparisons. Because knowledge of space is more readily available, for many purposes longer phrases would at least define a local region (for example): Middle Muskingum Adena, Middle Muskingum Hopewell.” ( Greber 2005: 39).'

[Greber 2011, p. 65]


Archaeological time is a local phenomenon that is intimately bound to a location, a landscape, and perhaps a region. Things get fuzzier the larger the physical space and the longer the time. Part of a continent, fuzzier yet. Time and space share the statistical properties that autocorrelation increases as both time and distance decrease. Events close in time are more related than events far away in time. Places close together are more related than places far apart. These are simple concepts yet they form the theoretical structure that allows for the ability to measure relationships between the two. [Cressie & Wilke 2011]


I have talked about this before [Newark, the Core, and Beyond] but Serpent Mound is an example where a radiocarbon date has sparked a controversy. William Romain and colleagues have published a date for the construction of Serpent Mound in the Early Woodland. Brad Lepper supports a Late Woodland date based on ethnographic and other evidence. [Romain et al. 2017] [Lepper et al. 2019] The early date is based on soil samples which may have issues for this type of method as soil can be a reservoir for storing old carbon. [Hajdas et al. 2021, p. 62]


optically stimulated luminescence


Rock and earth contain trace amounts of natural radioactive materials that have a constant rate of decay. Quartz and felspar crystals will trap the energy when exposed to this radiation due to their structure's nature. This energy is released when a surface is exposed to sunlight or heat. Optically stimulated luminescence is a procedure for dating the last time a slice of an earth or rock core was exposed to sunlight or high heat. [Feathers & Muller 2020] [Vervust et al. 2019]


There are many methods to date one artifact or site. Multiple ordering methods can be combined with absolute dating and archaeological context using a technique called 'Bayesian Chronological Modeling.' [Hamilton & Krus 2018] [Newark, the Core, and Beyond] An example is a Middle Woodland mound complex with two squircular [Geometry] enclosures in the Appalachian Summit on the Tennessee-North Carolina border called Garden Creek. [Wright 2019] Here Alice P. Wright used artifact assemblages from different layers of one mound to trim date ranges from radiocarbon dates of these layers using Bayesian methods. This mound is a platform mound, a common mound type in the South although at least one has been found in Ohio at Marietta. [Greber 1990] This is a burial mound with six main burials and a cache of mixed bones of perhaps two individuals believed to have been interned by a later culture. The mound was first dug out, then the first level was added. Finally, a second level. It was a platform because each stage was flat on top and slightly smaller in area than the latter. Looking at the many post-hole patterns she found the outlines of nine overlapping structures built during three mound-building episodes.


The site was thought to have 3 mounds but a geomagnetic survey found a fourth mound and two enclosures. The enclosures had a rounded square (squircle) shape with a single entrance. No mounds were inside. The evacuation of one enclosure uncovered a ditch. There was no evidence of an earthwork. This could be that the earthwork had been erased as ditches alone are rare. Or it could be a local expression. The ditch had been partially filled three different times with a layer of single-colored soil. Fortunately, the soil contained charcoal for dating and artifacts for stratigraphy so a similar analysis was done. The soil contained pieces of mica and quartz crystal but no finished products. This suggests that manufacturing was going on. Later posts were placed along the path of the filled ditch including the entrance, walling off the enclosure. Even later the posts were removed and the post holes were filled with cobblestones and loose artifacts, effectively erasing the enclosure.


Wright created a list of structural characteristics of this type of enclosure which she called 'morpho memes.' She also looked at orientation. A few years later Edward R. Henry completed a study in central Kentucky using a similar biographical perspective. He found a similar squircular enclosure with a similar history of use. The main difference was that in this case, an earthwork was discovered outside the ditch. The ditch was later filled with layers of colored soil and the enclosure was surrounded by a ring of posts like at Garden Creek. {Henry et al. 2021] These two biographical studies along with evidence from a smaller circular enclosure inside the large hilltop enclosure called Fort Ancient in Southwestern Ohio [Riordan 2020] show that these small enclosures have complex and long histories with many changes.


Human Time

Human time is variable and relative. There are regularities. Day follows night and season follows season. In the middle latitudes, daylight is much longer in summer than in winter, and the onset of spring can span several weeks. Likewise, a human lifespan is highly variable, and human perception of time changes as one ages. One exception to this is ovulation and to some extent gestation. To measure time one needs a time slice that can be repeated—for example, the time to boil a regular-sized egg at a certain altitude. When asked how long it takes to walk between villages one could say 5 egg boils. Human beings are obsessed with time. It may be because we realize our time as individuals is so short.


Modern research on the human brain has failed to find a biological pacemaker or clock. rather different sets of cognitive structures lead to a perception of time at intervals from a few hundred microseconds to several minutes. This is very much like the Western concept that time is created by the self. The duration here is short, the next level is the much older rhythm of waking and sleeping. [Wittmann 2009] [Ashcroft 2022] Another Western concept of time is that of a one-way line with past present and future. This has been challenged by modern physics. The representation of biological change over time has gone from a line of ascension to a tree, a bush, a network, and the Now is visualized as a circle with the first common ancestor in the center and the circle itself as the current biome. This is more like the non-Western view of time as a circle. Indigenous cultures also have a view that the past is a place outside of time that can be accessed through song, ritual, memory, and places. This access moves human time around the circle. This concept has been called 'world renewal' in the Woodlands [Brown & Cousins 2001], 'flower worlds' in Mesoamerica and the Southwest US, [Hays-Gilpin & Hill 2008] and 'Dreamtime' in Australia. [Goddard & Wierzbicka 2015] These terms are an attempt by Western researchers to name extremely complex concepts. A recent Australian attempt to translate accurately the concept of Dreamtime into English has resulted in this:


 George Kubler was an art historian and an expert on Aztec ceramics. In 1971 he published The Shape of Time: Remarks on the History of Things. [Kubler 1971] This book is a splash of different ideas. One was that ordinary objects and art objects share a similarity and can be studied as such. This idea not only has implications for archaeology [Lepper personal communication] but is said to have influenced artists in the 1960s and 70s. [Bard Graduate Center 2023] He has a view of time that is distinctly human-centric, the productive lifetime of a maker of things.


Dynamic Time

Dynamic time is the periodic regularities of the Sun, the Moon, the planets, and the stars. Changes over the ages are so slight as to be invisible. This gives a perceived timelessness to these movements. In addition, the motion of the heavens is deterministic., one can calculate the exact configuration of the sky at any moment in the past. The waxing and waning of the moon mark out a time as does the position of the sun about the horizon. This gives days, months, seasons, and years. The rising and setting of the moon proceeds along the horizon in a longer cycle of 18.5 years. The stars rise and fall at similar angles according to the latitude with a single star in the northern hemisphere pointing North. The planets follow more complicated but also periodic paths. The relationship between an observer, the horizon, and the sky is called 'positional astronomy' [Iwaniszewski 2015] [Ruggles 2015]


The Mayan Calendar System is four interlocking calendars. Haab is a solar calendar. It comprises 18 months of 20 days plus a final month, Wayeb, which is 5 days long. Tzolk’in is a lunar and ritual calendar. The ritual year is 260 days; nine phases of the moon, around the human gestation period, and the life cycle of corn, from planting to harvest. This calendar is still in use today. The Calendar Round is a linking together of the solar and lunar calendars, this creates a 52-year cycle, the age in which a person is considered an elder. The Long Count extends time into the distant past and the distant future. It is still cyclical, but each cycle is 5,125 1/3 years. This system matches the human conception of time with dynamic time. Long Count dates can be converted into modern dates. It more rightly should be called the Mesoamerican Calendar System because evidence of these calendars has been found as far back as 1100 to 1400 B.C.E. This puts this system as Olmec, considered a mother culture of this region. Whether the Olmec had writing is still an open question as not enough evidence is presently available but it is believed that they did. The Middle Woodland period in North America corresponds to the decline of the Olmec on the Gulf of Mexico and an et-Olmec culture along the Pacific Coast. [Closs 2000] [Coe & Houston 2021] [Šprajc et al. 2023] [Smithsonian National Museum of the American Indian 2024]


Societies that control time can set the seasons and anticipate the future. The lunar procession of 18.5 years carves a human life span into three to five stages. Three of these cycles correspond to 55.5 years, quite close to the Mayan 52-year cycle. Elites who have discovered this knowledge have tremendous power. Time links the sky to the landscape, the sky becomes part of the landscape.


 






Part VII - Sky


Part VIII - Memory


Part IX - Quidnunc


 

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