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Mar 118 min read

An Exercise in Middle Woodland Geometry I


Circleville Work [Anderson 2011]


"Good people of old

Looked oft at Mount Yoshino

And said that it was good.

Good people of our time,

Take a good look

At the good mountain of Yoshino!

Good people,

Take a good look!"

Emperor Temmu (672-686 AD)

Nara, Japan [Higuchi 1988]


Disclaimer


Original ideas are rare and dangerous because often they are wrong. Building a narrative about the past is always a speculative venture, no matter what tools of science and intellect have been applied to it. Science is about mistakes or misconceptions followed by discoveries which can often lead to insight, but rarely a complete picture. Isaac Newton was not the first to use the term "standing on the shoulders of giants," but he is the most famous because he forever related this phrase with science. Perhaps someday I can see a little further, perhaps not. These shoulders include not just archaeologists but a wider group of people from different professions, all sharing a single obsession. Then there are the people of this remarkable culture, the real giants.


Part I - What is Hopewell?


Hopewell Interaction Sphere [Roe 2010]


Hopewell is the name for an inflorescence of an Eastern North American indigenous mound-building culture during an archeological category of the past called the Middle Woodland. The practice of mound building has existed for thousands of years in the Eastern Woodlands. The culture represents a particular mortuary practice or cult spreading over the Eastern Woodlands. Bayesian analysis of radiocarbon data from six of the major Hopewell centers results in dates from 90-120 C.E. to 395-430 C.E. [Seeman 2023] Thus the culture spanned at least a period close to that of the history of the contemporary United States. The culture is centered in what is now southern Ohio along the Scioto River Valley and influenced much of the woodlands of eastern North America. They were named after a landowner of one of their mounds, the first excavated. (1) Besides mounds, they are famous for building earthworks. These are large open enclosures some 2 meters high. Many of these are built to form geometric shapes such as square, circle, and sometimes octagon. These earthworks are extensive, with the largest being mostly under the current town of Newark, Ohio, covering some four square miles. [Romain 2007] There is evidence that a ceremonial road was built from the Newark complex to the main centers near Chillicothe, Ohio, a distance of around 60 miles. [Schwarz 2016] Newark and other earthworks are believed to be aligned astronomically with the solar equinoxes and a more complicated 18.6-year moon cycle. [Hively and Horn 1982] [Hively and Horn 2013] [Hively and Horn 2020a] In addition, there is speculation that Hopewell culture used a common system of measurement for all their built structures [Marshall 1987] [Marshall 1996] and that their geometric forms were not only multiples and fractions of this common measurement system but they constructed circles and squares having common areas. [Volker 2005]


It should be noted that this was a hunter-gatherer culture with the start of the domestication of local plants, called the Eastern Agricultural Complex. This was before "three sisters" agriculture (corn, beans, and squash) became dominant. [Wymer 1996] There were no towns as such, the population was scattered around the ceremonial centers in small family units. They had no writing system although their mother culture, the Adena, had left inscribed stone tablets at several locations. [Penney 1980] Southern Ohio was an important pilgrimage center with exotic goods: flint, copper, silver, obsidian, mica, meteorites, soapstone, and seashells carried in from all over the continent.


Hopewell culture had a rich material technology as shown by the amount and quality of non-perishable artifacts that have been found. This is not the whole story. Using estimates from places where perishables survived, artifacts, such as basketry, fabric, clothing, footwear, wooden tools, hides, and cordage represent some 20 times the number of materials compared to non-perishables. [Hardy 2008] Cordage marks on pottery, the impression of a fine fabric on a copper breastplate, wooden tools, wooden objects wrapped with copper sheets, copper-wrapped reed pan pipes, pieces of painted and carved hide, and bits of undated coarse fabric found in a dry cave are some of the only objects found. [Carr and Maslowski 1995] [Shetrone 1928] The beauty and intricacy of surviving non-perishable objects suggest that Hopewell culture could also produce quality baskets and fabrics.


Paulus Gerdes (1952-2014) was a Dutch mathematician who lived most of his life in Mozambique, Africa. He was on the mathematics faculty of the Eduardo Mondlane University in Maputo and Rector of the Pedagogical University of Mozambique. In 2006 he was President of the Founding Commission of the Lúrio University in Nampula. He promoted an Afro-centric mathematics curriculum for all levels of teaching. Gerdes specialized in ethnomathematics, which studies how a culture creates and uses mathematics. [Wallencamp 2022]


The spread of mathematical ideas has always been considered a diffusion model. Mathematics defuses from some central source. A similar model has been used for the spread of agriculture. Humans do move about and ideas and methods do spread, but this model is too simple, agriculture started in myriad places all over the planet, other forms of agriculture supplanted older ones, and some methods spread to other lands. Gerdes suggests that mathematics, like agriculture, started in many different places from what humans discovered in their everyday lives of feeding themselves and making objects. Most importantly, they created a geometry from weaving fabrics and baskets. [Gerdes 2003]


This is called empirical geometry because it came from everyday life rather than Greek logic. One can already see a bias in this definition because where did Greek geometry come from? A better term for this would be embodied mathematics. [Lakoff and Núñez 2000] There is a philosophical divide regarding whether mathematics is embodied or exists outside of ourselves. Is math discovered or created? This is the religious connection to math which is strong in not only Greek thought but in almost all cultures, ancient and modern. A great many mathematicians today would hold the view that math is discovered. I think that perhaps one possible answer is the way humans are psychologically wired. [O’Keefe and Nadel 1978] In any case, the builders could have created an embodied geometry and then used it to fulfill a complex religious and social purpose.


In his book, Awakening of Geometrical Thought in Early Culture, [Gerdes 2003] Gerde shows how weaving could develop some fundamental concepts that might have set the foundations of Hopewell geometry. Some of his examples are:




Seneca Basket - Unknown date [National Museum of the American Indian]


The history of the various surveys of Hopewell earthworks is a story by itself. Since many sites have been permanently destroyed, old surveys are the only information on some works. The earliest description of the earthworks was in 1820 and titled Description of the Antiquities Discovered in the State of Ohio and Other Western States by Caleb Atwater. [Atwater 1820] Atwater had a career as a minister in Massachusetts. After his first wife died, he remarried and moved to Circleville, Ohio in 1815 where he started a legal profession. He founded Ohio's public education system. [U.S. National Park Service 2024] Circleville was built inside a large double circle of earthworks connected to a large square enclosure. The town was originally laid out to conform to this pattern with part of it within the circular enclosures. Starting in 1837, both circular embankments were removed and the circular pattern of the town was turned into rectangular parcels. By 1857 the circles had been squared. [Reps 1955] Atwater is important because his descriptions include features lost before the first surveys.


In 1847, the Smithsonian Institution published: Ancient Monuments of the Mississippi Valley, [Squier and Davis 1847] a compilation of surveys by E. G. Squier and E. H. Davis between 1837 and 1847. It is important because this was done just after the canals were built and before the railroads, which changed the landscape of Ohio forever. Unfortunately, these surveys turned out to be inaccurate, yet they are still important as the surveys and their descriptions of the earthworks include features that have been lost. In 1862, James Salisbury, a doctor from Cleveland, and his brother, Charles Salisbury, amateur archeologists, surveyed the Newark Earthworks. Their results are unpublished but exist in a collection at the American Antiquarian Society. [Salisbury and Salisbury 1862] In 1881, the new Bureau of Ethnology at the Smithsonian Institution sent expeditions all over the country under the supervision of Cyrus Thomas. In Ohio, the surveyor was James D. Middleton. A report was published in 1894 as Report on the Mound Explorations of the Bureau of Ethnology. [Thomas 1894] Middleton's work is considered the most accurate, but all show different features that have been lost.


James A. Marshall (1932-2006) was a civil engineer from Illinois. Since 1965, he devoted much of his spare time surveying various earthworks in Ohio and other places. [Marshall, W 2006] In one of his papers, he mentions trying to get funding for a book that would include his plats. [Marshall 1987] I don't believe this happened. After his death, his siblings donated all his documents, some 7,445 cataloged items, to the Ohio History Connection [Ohio History Connection 2009]. Marshall is important not only for his accurate surveys but also for the idea that the builders had a consistent sense of geometry, a standard unit of measure, and used these concepts to build their earthworks.


During the last 20 years, a growing trend in archaeology has been to use non-invasive methods. Satellite imagery, aerial photography, new imaging techniques like LIDAR, and geophysical 'imagery' like magnetometry, ground penetrating radar, and others have transformed the field.  [Ohio History Connection 2022] [Burks 2014] This has expanded a view often limited to a single site to include a whole landscape. All these methods create data that can be fed into GIS. GIS in archaeology has become a computational tool not only for visualization but also for geospatial analysis. [Wheatley and Gillings 2022]

In 2020, Encountering Hopewell in the Twenty-first Century, Ohio and Beyond was published. [Redmond 2022 I] [Redmond 2022 II] It contains papers given at a conference in Chillicothe, Ohio in two volumes. Three articles in the first volume give results using imaging technologies. One explores earthworks outside of Ohio, in central Indiana. [Davis and Burks 2020] Using LIDAR and GIS visualization techniques they found extensive new features including squares with circular corners, called 'squircles'. Another article describes the excavation of Moorehead Circle, which found a circle of post holes inside the large hilltop earthwork at Fort Ancient, [Riordan 2020] This could be termed a 'woodhenge,' a circular arrangement of poles having astronomical significance. The woodhenge had been replaced by a dirt embankment. They also found remains of a large building and extensive paving and modification of the inner part of the circle. A final article gives the results of a magnetometric survey of the Seip Works in the Paint Creek Valley near Chillicothe. [Komp and Lul 2020] They found extensive activity within one of the circles. Some features labeled as squares were squircles like those found in Indiana. These studies suggest the extensive use of wooden poles set in the ground in their building techniques and more transitory shapes including the intermingling of squares and circles instead of being separate. Posts were not found, just the post holes. There are several possible uses. Post holes were used to hold up structures, as a placeholder for later earthworks, in some cases stockades, as a woodhenge, and other unknown single or grouped uses. Some holes have ashes at the bottom. A way to remove a stump from a felled tree is to burn it. Perhaps some of these post-holes were just from trees that were removed as they modified their landscape, This is important to note when trying to find patterns in the placement of these features.


Possible household [Pacheco 2022] (2)


N’omi Greber was Curator of Archaeology at the Cleveland Museum of Natural History until her death last year. Among other discoveries, she coined the term "Great House." Many of what were thought to be Hopewell mounds were originally large structures that were later decommissioned, burned, and buried. In the following quote, she is talking about assemblages of artifacts found near or in graves. Her comments could refer not only to the earthworks but to many of the current unknowns about Hopewell culture.


“As usual, any estimate of Ohio Hopewell activities is hampered by the lack of even a relative chronological yard stick. For example, do the known large deposits represent the entirety of the Hopewell era? Certainly they do not represent the entirety of the ceremonial/ritual/political/economic activities. What is the relative chronology of these deposits, particularly compared with those of Tremper and Seip? Are great artifact deposits and monumental structures coeval or spaced through time? What is the relative chronology of the construction of major mounds and large enclosures, especially at sites where both appear? Until there is a well documented time line for Ohio Hopewell, we will need to continue constructing our hypothetical cultural interpretations on very shifting sands of time.” [Greber 1996]


In archaeology, there is a term called seriation. This is placing artifacts in some order based on similarities and differences of features with the idea that this order can be matched to a temporal order. This has become a high art with ceramic pottery. [Read 2007] Perhaps the different forms of these earthworks present a progression of styles and skills of the builders. The archaeologist Christopher Carr sees the different forms as showing alliances between different geographic settlements and sees evidence in the burial practices and ethnographic studies. [Carr and Smyth 2020] Marshall categorized the earthworks he studied into hilltop (nongeometric), nongeometric, geometric, and crypto-geometric. [Marshall 1996] The archaeologist William Romain has attempted to match sites to shape types and sizes. [Romain 1996] His categorization matched some sites that are believed to be over one hundred years apart. How could this be? He also calculated a second possible Hopewell unit of measure. Another possibility is not similarity but that each site was designed to the local landscape and the astronomical markers along a horizon. The earthworks themselves create an artificial horizon allowing the builders to isolate astronomical features and prominent landform features.


Copper mine tailings form an artificial horizon. Serrita Mts behind them are hidden. Sahuarita, AZ [Dahl 2014]


A. Martin Byers was an anthropologist and archaeologist first at Vanier College and later at McGill University in Montreal, Canada. He uses a social-structural approach to study Hopewell culture. He emphasized the spatial relationship between the geometric shapes as a code, a circle connected to a square by a walled passageway would be C=S. With this, he has attempted to create a grammar of the social space. [Byers 1996] This spatial approach to spatial relationships suggests Hillier's spatial logic, [Hillier 1976] a British school of spatial theory that doesn’t seem too popular in the US.


Bob Hively and Ray Horn are professors at Earnhardt College in Richmond, Indiana. Hively is an astrophysicist and Horn is a philosopher. In 1974 they were asked to co-teach a year-long History of the Cosmos course. At the time it was just speculation that Stonehenge in Britain and other sites in Europe used the rising and setting points of the sun and moon as a calendar. Finding no published maps of Stonehenge, they first looked at nearby Fort Ancient and then the Octagon at Newark. [Hively and Horn 2020b] Worship of both the sun and the moon can be found worldwide. How their repeated motions across the sky relate to a slice of time, a calendar, is a major focus of many cultures. It is believed that the Olmec culture in Mexico was the first to invent the long count calendar. [Coe and Houston 2021] The Olmec were at the height of their power during the Hopewell period. It is known that the culture obtained obsidian from a formation called Obsidian Mountain in what is currently Yellowstone National Park. [U.S. National Park Service Hopewell Culture Obsidian] A quick check on Google Maps shows that it takes 25 days of walking to get from Chillicothe to Yellowstone, and from Chillicothe to Villahermosa, Mexico is 36 days. There is no evidence of any contact between the two cultures and the Chihuahuan Desert is a formidable obstacle but it could be possible.


The sun rises and sets at different horizon points each day moving north or south. Twice during the year the sun pauses and reverses direction. These are what we now call the Solstices. In the middle of this cycle is the equinox. The two solstices and the two equinoxes divide the year into four parts. The moon also has a cyclical motion across the sky but this motion is longer and more complicated. The moon has two sets of solstices, a major and a minor, completing a cycle every 18.6 years. Thus there are 8 points on a lunar calendar.


Lunar Cycle [Young 2010]


Solar and lunar alignments, and alignments to planets or stars, have been found at hundreds of sites worldwide. [Wikipedia - List of Archaeoastronomical Sites by Country] So many that one criticism of what is now called archaeoastronomy is that the practitioners see alignments everywhere, even when they may be just random coincidences. The other criticism is that there is little attention to the why of this phenomenon. It would seem to me that for any culture to exist it must supply some control over time, a way for the culture to organize the daily lives of the people participating in it.


In 1997 the astrophysicist Judith Young started building a stone circle observatory based on both lunar and solar alignments, called Sunwheel on the campus of the University of Massachusetts in Amherst, MA. [Young 2010] During 2024-2025, the moon will reach a major standstill. Sunwheel is planning events and is open to the public.


What Hively and Horn found in Newark is important to Hopewell studies and the ongoing preservation of the Newark earthworks. [Ohio Archaeological Council 2023] Among their findings: [Hively and Horn 1982] [Hively and Horn 2006] [Hively and Horn 2013] [Hively and Horn 2020a]


  • Newark contains two separate systems of alignment, one for the lunar calendar, and the other for the solar.

  • A third standard of measurement that they call the OCD for Observatory Circle Diameter.

  • Newark was laid out using the baselines of prominent land features.

  • Other Hopewell earthworks have been laid out using similar alignments


At the end of the 1996 conference book A View From the Core, the editors conclude with commentary and critique by the archaeologist Olaf H. Prufer. [Prufer 1996] He represents an 'old guard' of Ohio archaeology. He has nothing good to say about archaeoastronomy or Marshall's theories and makes a good point about the need for empirical evidence. This was written before the ubiquity of computational statistics, now called data science.


Concluding Remarks


What we know of a culture, especially of a culture without writing, can only be gleaned from its artifacts. This article is an introduction to Middle Woodland culture, emphasizing its most famous artifact, geometric earthworks. The problems of measurement, geometry, structure, landscape, and cognition will be considered in subsequent articles.






Part VI - Landscape


Part VII - Memory


 

Notes:


(1) The name "Hopewell" is unfortunate as it has nothing to do with the culture or anyone who participated in it. The term "Hopewell people" is particularly offensive to native people. Perhaps the tribes currently involved in the preservation of the earthworks will someday give a proper name to this magnificent culture.

(2) "Martin Byers disputes Pacheco’s notion that the huge wooden structures he found are habitation sites. Based on their size and what sorts of things were found there, Byers thinks they are ancillary ceremonial buildings associated with the nearby earthworks." [Brad Lepper. personal correspondence]


 

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