An Exercise in Middle Woodland Geometry VIII

Last Wyandots leave Ohio on the Miami and Erie Canal [Ohio History Collection 1843]

Memory

Being But Men

Being but men, we walked into the trees

Afraid, letting our syllables be soft

For fear of waking the rooks,

For fear of coming

Noiselessly into a world of wings and cries.

If we were children we might climb,

Catch the rooks sleeping, and break no twig,

And, after the soft ascent,

Thrust out our heads above the branches

To wonder at the unfailing stars.

Out of confusion, as the way is,

And the wonder, that man knows,

Out of the chaos would come bliss.

That, then, is loveliness, we said,

Children in wonder watching the stars,

Is the aim and the end.

Being but men, we walked into the trees.

Dylan Thomas 1939

Out of the chalice of this spiritual kingdom

foams forth the mind's infinity.

Friedrich Schiller, 'Friendship' 1782 - translation by Hannah Arendt

Introduction

The archaeologist William Romain published several articles [Romain 1991] [Romain 1995] [Romain 1996] and a major part of a book [Romain 2000] dealing with the relationships between the intra-site elements of the Middle Woodland (Hopewell) geometric earthworks, namely circles, polygons, parallel walls, and gateway mounds. He also looked at inter-site relationships. In a chapter from the book, A View From The Core [Pacheco 1996], he makes the following comment:

"... the way each earthwork neatly fits within other design shapes that may be miles and miles away is unique. And, the whole phenomenon is even more intriguing when we consider that many of these inter-nesting earthworks were built at different times over a period of hundreds of years."

[Romain 1996, p. 205]

Additionally, he is one of three researchers who have proposed a standard system of measurement for constructing these earthworks. [Marshall 1987] [Hively & Horn 1982]. For this to persist for hundreds of years, the phenomenon must be studied within the context of a 'culture'.

What is a culture? The Merriam-Webster Dictionary gives four versions:

• the customary beliefs, social forms, and material traits of a racial, religious, or social group
  

• the set of shared attitudes, values, goals, and practices that characterizes an institution or organization
  

• the set of values, conventions, or social practices associated with a particular field, activity, or societal characteristic
  

• the integrated pattern of human knowledge, belief, and behavior that depends upon the capacity for learning and transmitting knowledge to succeeding generations

[Merriam-Webster 2024]

The building of geometric earthworks took place mainly in a region defined by the current state of Ohio. However, other aspects of this culture influenced much of eastern North America at this time. [Caldwell 1964] There is speculation and evidence that these earthworks were pilgrimage sites for all the Woodlands. [Lepper 2024] The culture had no system of writing; it was egalitarian, and its elites were religious and intellectual. It was a transitory system between hunter-gatherer subsistence and full-blown agriculture. The region is one of the eight in the world where humans independently domesticated plants. The duration of the culture's existence is controversial, but the dates range from approximately 100 BCE to 700 CE. The most conservative estimate is 350 years, slightly longer than the current lifespan of the United States. [Seeman & Nolan 2023]

The question posed by Romain's comment is: How does a culture with no written language keep a sophisticated mathematics and building style alive for hundreds of years? Notice the final definition of culture, which is a pattern of transmission between generations. A culture exists in space and time; it can have a discrete beginning and end, or elements can blend or combine into one type or another. For instance, the cultural practice of building mounds and earthworks lasted until Contact in the Mississippi south [National Park Service 2023], the extreme north [Howey 2012], and the northwest Woodlands [Wisconsin Historical Society 2012]. However, the actual practices associated with these structures may have changed greatly. This is an important point; the styles can change, and the meanings associated with these styles can change, but they are not always in sync. Stylistic change is the bread and butter of archaeology, but understanding meaning is much more difficult and fraught with Western ideologies and biases. [Coolidge 2015]

Indigenous societies have been remarkably resilient in the face of plagues, war, starvation, forced displacement, and 150 years of forced assimilation. The study of non-writing societies through interviews and recordings is called ethnography. This study is also fraught with Western ideologies and biases. In addition, the person interviewed will often tell the interviewer what they want to hear. For instance, there is little ethnographic evidence of knowledge of earthworks; participants usually reiterated the colonial belief that they were forts for defense. [Romain 2000] Often, the participant will lie or deliberately hide information. The coping strategy of a conquered subject. The royal physician to the Spanish crown in Mexico, Francisco Hernamdez, who was studying native botanical knowledge, wrote the following complaint in a letter to the King of Spain:

"Nor will I speak of all their fraudulence or terrible lies, which caught me off guard more than once; how they played tricks on me, which I took care to avoid with all the tact at my disposal; and how often did I get the properties and even the names of the plants wrong because I depended on false information from an interpreter."

[Hildago 2014, p. 64]

Aboriginal societies in Western Australia have largely survived assimilation. During the 60 thousand years of human occupation, there have been many large meteor strikes to the continent, but no reference to these events exists in conversations with native speakers. [Hamacher & Norris 2009] In some cases, ethnographic texts become the only means by which a group can connect with its past. [Hunter 2016] [Howell 2018] Ethnographic information cannot be dismissed given these problems. The analysis of texts and stories using statistical data techniques, known as digital humanities, is one way to uncover hidden patterns. [Bol 2019]

Culture and human evolution

Cultures are human constructions. Elements of cultural activities have been found in chimps, crows, and even fish. [Boesch 2020] [Bayern 2018] [Tariel-Adam et al. 2025] Humans can be said to be defined by culture. Culture is a historical process; a change over time that can occur at a slow or rapid pace. Thus, culture is an evolutionary process, evolutionary in an older sense of change over time, not the modern sense of Darwinian evolution (DE).

DE is defined as the change in a population's genetic makeup over time, called population genetics. [Okasha 2024] As the theoretical underpinning of a theory of evolution, it has been thought that culture could be defined similarly. Populations contain discrete entities called alleles or genes. Frequencies of genes define phenotypes, how a population looks and acts. This was the basic premise when Darwin's theories were combined with genetics in the 1930s to create a full theory of evolution. The discovery of DNA and the resulting field of molecular biology created many nuances, but didn't change the basic premises. DNA is a code, a symbolic system in which new living creatures are built and built again through a process called replication and transmission.

Cultural ecology

The attempts to shoehorn cultural evolution into DE with memes and such are a Procrustean attempt at best. [Lewens & Buskell 2023] However, humans are biological creatures, so culture at least arose out of a Darwinian framework. Culture is a dynamic system like DE, but it is quite different in the form and structures of transmission, replication, and selection. As one example, culture is encoded twice, once in a human mind and second in the artifacts created by these minds. [Bohannan et al. 1973] This requires a more generalized model of evolution, which includes DE and other possibilities. [Currie & Killin 2024] Without this model, it is not possible to understand how culture affects human evolution. Evolution is occurring at some level in all humans, and genetic changes such as lactose tolerance or the ability to live at high altitudes are relatively recent. Also, population genetics assumes random mating, and all cultures impose some limits on who can mate and when. Cognitively, there is little difference between humans now and 2 thousand years ago. The beginnings of Imperial Rome occurred during the construction of the geometric earthworks. We recognize Romans easily, why not the Woodlands people? They did not have a written language, but there is no evidence that the invention of writing has caused either genetic or cognitive change. Writing does cause cultural change, and the invention of writing does affect memory.[Jensen 2023]

Culture and artifact

Most of what we know of a past culture comes from studying material remains; its artifacts. Anthropologists study modern cultures by examining what they produce, not just utilitarian objects, but what we call media: writings, voice recordings, still and moving pictures, etc. Media is a symbolic expression of language. Anthropological fieldwork has consisted of a researcher entering a culture as an outsider, learning the language and customs, recording the words of willing participants, and then creating a report, a media object. [Howell 2018] Utilitarian objects can also have symbolic meaning. The object can have purely symbolic writing or evidence of the beginnings of writing, called 'proto-writing,' on its surface. [Jackson 2002] In addition, an object has a quality called 'style':

• a particular manner or technique by which something is done, created, or performed
  

• a distinctive manner or custom of behaving or conducting oneself
  

• a distinctive quality, form, or type of something

  [Merriam-Webster 2024]

Defining what styles an object possesses, defining a measure of a style, creating typologies of sets of styles associated with an object, and creating categories of similar typologies is a major problem in Archaeology. [Sanz & Fiore 2014] Stylistic change can be gradual or abrupt and is one tool in attempts to build a timeline, a history of an object. Attempts to relate stylistic change to cultural change are called 'bridging theories.' [Haidle 2014]

An example of a utilitarian object is a chair. A common object, but defining what it is exactly is difficult. It has to do with sitting, but humans, until recently, sat on the ground or their heels. Chairs, which raise a sitter above the ground, originally symbolized hierarchy, the throne. Chairs were also associated with certain occupations and extreme wealth. Mass production made chairs more available. Today, much human work is done in a chair. The human back is not designed to sit for years in a chair, so stylistic change has gone into ergonomics, making a chair designed for the human form. I am writing this now while sitting on an ergonomic chair. Next to me in my workspace is a carved wooden African 'chief's seat.' I rarely sit in it; presently, it is piled with books. [What is a Chair? 2023]

Modern chair [Author photo 2025]

African seat [Author photo 2025]

Notice that the office chair has no decorations or ornaments, while the carved seat is covered with rectangular designs. The overall design of the seat probably had some meaning at one time, although this one has no provenance and was manufactured for the tourist trade. There is no way to decode the cultural meaning of the work by just looking at the object itself; it must be placed into a range of contextual relationships.]

What people eat affects their fitness and thus directly affects DE. What one eats and how one prepares it is cultural. Frequencies of faunal and botanical remains, evidence of feasting or malnutrition, relate a culture to Darwinian results better than sherd frequencies alone. An example is in a book compiling the archaeological results of a specific region, the Falls of the Ohio River. [Pollack 2021] This region is the only major crossing point of the Ohio River and thus was used by groups moving from the north to the south. It has a rich archaeological history going back thousands of years. This region is now the city of Louisville, Kentucky.

When Europeans first contacted the peoples of what became North America, corn dominated their agriculture. In particular, what is called 'Three Sisters Agriculture', the companion planting of corn, beans, and squash. When planted together, yields are greater because of the bean plant's ability to trap nitrogen in the soil. In addition, the protein in beans and corn, when eaten together, has all the amino acids of a complete protein. Squash provides important vitamin A. When corn is cooked in limewater (Calcium hydroxide) [Wikipedia Calcium Hydroxide], there is additional nutritional content. The process is called nixtamalization, which comes from the Aztec word for limewater, nixtli. Corn agriculture moved north from Mesoamerica from a tropical beginning to the American Southwest, the Woodlands South, the Woodlands Midwest, and the East. The complex of practices and ideologies created around corn in Mesoamerica didn't move north as a package; elements arrived at different times and locations. Corn and perhaps squash have been found in the Woodlands Archaic, although in minute quantities. Beans seem to have come later, at the start of Woodland corn agriculture. [Mt. Pleasant 2016]

The people who lived around the rich resources of the Falls region gathered wetland plants and nuts from the forest. Wetland plants gradually changed to dryland plants, oil-rich grasses. This was the beginning of the Eastern Agricultural Complex and sedentary lifestyles. There is evidence that nut forests were being actively managed. The Falls were a crossing place, but around 1000 CE, it became a border between the Mississippian polities and an egalitarian culture in Ohio and Kentucky called 'Fort Ancient,' believed to be ancestors of the Shawnee. [Lepper 2018] Corn kernels found exclusively in the Falls area have 12 lateral rows and come from a midwestern variety, while corn kernels found further east in Kentucky have 8 lateral rows and are an eastern variety. This suggests that each culture used a different variety of corn, but that the Falls region formed a boundary between the two. The cultures ate a different combination of plant foods. Mississippian still ate a mixed diet of Eastern Agricultural Complex seeds and gathered nuts, while Fort Ancient ate mostly corn and beans. The article does not provide data on squash. The most important difference is that while Mississippian culture grew corn, they didn't grow beans, and thus were missing an important 3 Sisters feature, a way to boost nitrogen in the soil, and a major source of protein. This changed after 1300 CE and the collapse of Cahokia, after which Fort Ancient corn started showing up in the Falls region. This sequence of first a boundary and then mixed contact also shows up in distinctive Mississippian and Fort Ancient pottery styles. [Rosen &Turner 2021]

Corn agriculture in Mesoamerica consisted of specific technologies for planting, growing, harvesting, and processing, plus ideological and religious structures built around these technologies. These didn't all spring up at once. On the Pacific coast of Chiapas and Guatemala, in a region called Socorone, an early culture called Mokaya, meaning "people of maize" (1900 BCE), used corn as a drink and for competitive feasting among emerging elites, rather than a nutritional staple. [Pool 2007, p. 181]

To move north, corn had to be adapted to the dry and cold American Southwest or the wet and cold American Midwest. This was helped by corn duplicating large chunks of its genome 10 times during domestication. It is estimated that 1/10th to 1/3rd of the corn genome has been duplicated. [Gaut 2001] By Contact, corn agriculture had dominated the continent. However, not all of the religious and ideological beliefs followed. Studies like those at the Falls show that the diffusion north was complex and spotty, and cultural acceptance was Situational; local groups used what they needed, even to the point of being detrimental. [Crawford et al. 1997] The same can be said about another Late Woodland technological innovation, the bow and arrow. [Nassaney & Pyle 1999]

Art and Archaeology

Art has traditionally been a Western concept that has been recently expanded. [Fiore 2014] The Stanford Encyclopedia of Philosophy states that any definition of art must include ten criteria. These are just criteria; definitions are so prolific and conflicting that it is perhaps best to think in terms of archaeology. Of the ten, four are important to this article:

• entities (artifacts or performances) intentionally endowed by their makers with a significant degree of aesthetic interest, often greatly surpassing that of most everyday objects, first appeared hundreds of thousands of years ago and exist in virtually every known human culture;
  

• such entities are partially comprehensible to cultural outsiders – they are neither opaque nor completely transparent;
  

• such entities sometimes have non-aesthetic – ceremonial or religious or propagandistic – functions, and sometimes do not;
  

• traditionally, artworks are intentionally endowed by their makers with properties, often sensory, having a significant degree of aesthetic interest, usually surpassing that of most everyday objects;

[Adajian 2024]

Art is included in a wider concept called aesthetics. The word comes from the Greek word for visual perception. Aesthetics is personal; it is how one feels about objects in the world and how these feelings modify choice. This meaning of the word came from 18th-century European discussions of the term 'taste.' [Shelley 2022] Aesthetics has a broader meaning in that it is how one is supposed to choose and interact with objects, be they art or everyday objects. Thus, a culture has an aesthetic, how one is supposed to act, and the objects and motions needed to make and use these actions. This is a common theme in many non-Western cultures, and it can become a set of rules governing a lifetime. [Saito 2024] This is the meaning that applies to archaeology; it is hoped that by studying the artifacts of a culture, by understanding where they were placed, how they got there, and how they were made, an aesthetic can be determined. [Coreby et al. 2004]

I am not an art critic by any means, but many Hopewell artifacts have moved me deeply. One in particular is the amazing Shaman of Newark, a carved pipe of a shaman transforming into a bear. He is holding a human head.

Shaman of Newark [Ohio History Connection 2014, Hopewell Headhunters? ]

Another that gives me chills every time I look at it is a carved mica cutout of a long-fingered human hand.

Mica cutout  [Ohio History Connection 2025]

The pipe is a stand-alone object. This scene, but the substance that was smoked (perhaps a form of tobacco in addition to other psychotropic agents), the act of smoking while looking at this object, and the whole context and meaning of the act, are unknown. The mica cutout is totally out of context as it is part of a larger structure consisting of other pieces of mica, human bones, conch shell horns, human ashes, various colors of sand and clay, and other features forming a tableau. This scene may have been viewed after creation or may have been immediately covered up. [Carr 2021]

In 2012, the French anthropologist Pierre Lemonnier published Mundane Objects: Materiality and Non-Verbal Communication. [Lemonnier 2012] The book is based on fieldwork in New Guinea and among French racing car enthusiasts. The artifacts include garden fencing, eel traps, hand drums, and model racing cars. They share four anthropological characteristics:

• their making and using relate to different domains of social life that are thus brought together in the actor's mind in a unique way;
  

• they are part of some kind of non-verbal communication;
  

• that special communication concerns key values or key characteristics of particular social relations that are usually hidden, although they pervade everyday life;
  

• the very physicality of the artefacts in question is involved in that process and is not equated to a vague and putative link with their “materiality,” but it can be precisely shown.

[Lemonnier 2012, p. 119]

Lemonnier calls these types of artifacts 'resonators' in that they represent clouds of social relationships, social rules, stories, and supernatural myths. He makes a point of this process being unspoken, but what I find more interesting is how this relates to how a culture does or doesn't change. New Guinea is an important place for anthropological study because, for some of these groups, Western contact was as late as the 1960s. Christian missionaries made people give up their objects as a means to convert them. Some did and lost contact with their culture, some replaced lost objects with like ones, while others stopped using the object but continued the chain of ritual. If archaeology is to learn anything from ethnography, there is a need to discover not only the global aspects of human cultures, but also how cultures react to the forces of history.

In October of 2023, we took a tour of Rock Art Canyon on a ranch east of Winslow, Arizona. The rancher's granddaughter gave a tour. They were related to the original Mormon settlers in the region. The family got along well with their Diné neighbors; there was a recent men's and women's sweat lodge on their property. We were shown a room crammed with artifacts, including over 100 complete pots. As the 86-year-old rancher put it:

"You go out every morning on an old horse; you are bound to find something interesting."

Our hostess made an interesting comment. These pots have round bottoms because if they were square, they would be hard to clean. Food could get stuck in the corners, spoil, and cause disease. This got me thinking about some Ohio ceramics, round pots with square bottoms and four pegs for supports. Called tetrapods, these were of fine quality, much better than the normal pottery. They were found in funerary settings. My interest is in finding artifacts that relate stylistically to the geometry of the earthworks. I initially looked for baskets that had round tops and square bottoms. Baskets are perishable, and I have found few examples past Contact in the Woodlands. Two complete tetrapods were found at Mound City:

Tetrapod Pot [Ohio History Connection 2025]

Bird Design [Ohio History Connection 2025]

The bird pot is unusual, besides the motif. The image doesn't show this, but an analysis by Olaf Prufer has a more oblique photograph. The pot has four lobes and a rounded square rim, a squircle rather than a circle. Prufer puts these and other sherds in a Southeastern series. A tetrapod bottom was found at Seip, and other fragments were found at Turner and Tremper. He doesn't say this, but he suggests that tetrapod pots can be found in all three of his stylistic categories for the Southeastern series. Also, it is unclear at times whether he is talking about the number of known tetrapods or the number of fragments, but at one point he mentions 15. [Prufer 1968]

In the book The Adena People, James B. Griffin devotes a chapter to Adena pottery. He spends a great deal of time on tetrapods, and he concludes that they are later Hopewellian finds. He mentions tetrapods being found in Southeast Indiana, Wright Mound in Kentucky, Rutherford Mound in Illinois [Stoltman 2015], and the Pinson complex in Tennessee. [Mainfort 1989] He concludes that the source of this pottery is the Gulf Coast. [Webb & Snow 1974]

Ceramics is categorized by clay, temper, color, thickness, shape of rim, type of decoration, the instruments used to make the decorations, and many others. I am interested in pots with square bottoms and those four little legs. From what I've found so far, pottery of this type is rare. In Teotihuacan [Cowgill 2015], in Olmec culture [Pool 2007] [Pommereau 2024], and in Chinese ritual vessels [Rawson 1998], I found only round bottoms and tripodal legs; only a few figurines had square bottoms, and some seated figures were seated on a four-legged chair. However, there was a series of tetrapod jars from the Mayan period from 200 BCE to 100 CE. Called Usulután, this series came from southeastern Guatemala, western Honduras, and El Salvador, but they were widely dispersed in Mesoamerica. It was first believed that this dispersal was from human migration, but current thought is that they were a popular trade item. [The Metropolitan Museum of Art 1982]

Mayan tetrapod pot [The Metropolitan Museum of Art 1982]

These pots started with tiny feet, but as time went on, the feet became more spherical and much larger.

The culture around the Northern Florida Gulf of Mexico region, West to the Mississippi River, during the Middle Woodland period is called Swift Creek. Swift Creek pottery has been found in many places. It is typed by the designs, materials, and construction rather than the shapes.  At the Pinson Mounds site in western Tennessee, cremated remains of multiple individuals were found along with artifacts, including broken pottery from several southern regions, including Swift Creek. [Sears 1962] [Keith 2020] Christopher Carr speculates that they might be offerings or urns transporting cremated remains to be mixed. [Carr & Case 2005] Southeastern style pottery was found at the Mann site in southwestern Indiana, including dozens of tetrapod supports. A sample of this pottery was studied using petrography, X-ray Diffraction Analysis, and Scanning Electron Microscope Analysis. The results show that most of the ceramics, no matter what style, were made locally, except for some found to be from the Appalachian Summit, which was a major source of mica. [Ruby & Shriner 2005]

It can be seen that not only could the pots be transported to a location, but the knowledge of how to make such a pot could also be transmitted. Tetrapods are a rarity in a rare assemblage, made even worse by the structural style, the only way to identify it is by the base. If the base doesn't exist, there is no way to tell by looking at the rest of the pot. The Swift Creek complex design style can be assigned to even small sherds and has been found over an extensive region:

Extent of the Swift Creek design style [Brock and Moore 2019]

Tetrapods were common

Swift Creek Culture tetrapods found in Florida [Sears 1962, p. 10, fig. 3]

3D model of a tetrapod pot [University of South Florida Libraries 2016]

There have been attempts to find contacts with Mesoamerica in the Swift Creek culture. Usulután pottery has the same tetrapod form as Swift Creek, and they are similar in time; however, nothing else about the pottery matches except for being a tetrapod. A pot found in northern Florida, dated from 1300 BCE, the Fort Walton culture, shows that this shape is ancient in the Gulf of Mexico region. So perhaps this form came from the Gulf Coast and was adopted by someone in the Mayan area.

Tetrapod found at Fort Walton, Florida [Dean 2022]

Below is an unusual square-bottomed pot without tetrapods found in North Carolina. It is believed to be Middle Woodland:

Square bottom pot [Research Laboratories of Archaeology 2025]

A series of articles by Brad Lepper and Benjamin Barnes suggests that tetrapod pots were used as water drums. [Barnes & Lepper 2018] [Lepper & Barnes 2018] [Lepper 2018] Five small carved steatite (soapstone) spheres were found at Seip earthworks. Christopher Carr calls these marbles and labels them as "Shamanic Paraphernalia." [Carr 2008, p 155] Lepper and Barnes suggest that these spheres were part of a water drum still used by the Shawnee tribe and in rituals of the Native American Church. The head of the drum is made of hide that has been softened and stretched over the top. The head is wrapped around small spheres placed along the rim and tied in place with rawhide. A video of the construction explains it better:

Tying up a water drum [King 2011]

Notice that the iron base of the drum has tiny tetrapod feet, and the spheres around the rim are connected to the feet by strips. The Native American Church started in the 1890s [Wikipedia Native American Church], but the usage of water drums can be traced back even further to groups such as the Shawnee. In this case, a charcoal chunk was added to the water inside the drum:

" ... charcoal stands for fire; fire and water will make anything move. But man must guide it. A drum with water alone inside it wouldn't sound good. The fire in the drum lights everything up; the spirits and the Creator can see it."

[Voegelin 1942, p. 471]

In their second paper, Barnes and Lepper suggest that the tetrapod pots found at the earthworks could be water drums. Lepper also cites an unpublished study by Richard Zurel [Zurel 2004] who found wear patterns around the feet of tetrapod vessels in the University of Michigan collection, near the rim, where the spheres would be, and along the side where the straps would cross.

The designs on the spheres are shown here:

Drawing of teatite spheres and their complete designs [Barnes & Lepper 2018, p. 70, fig. 6]

One question that comes up is, why would such intricately carved spheres be used when they are covered up by rawhide? There is no historic president; all modern spheres for water drums are plain. Plain spheres could have escaped notice by early archaeologists. Finding more plain or carved spheres would help answer this question.

The design styles on Swift Creek pottery are intricate and unique. If the designs on the Seip spheres and the Seip ceramics also have Swift Creek type designs, then this would confirm a link to tetrapod pots and possibly water drums. A project at the University of South Carolina called Snowvision, after the archaeologist Frankie Snow, created a database of Swift Creek design motifs and a machine learning technique to relate sherds to design motifs and locations. [Lu et al. 2022] [Smith 2020] [Wilder et al. 2020] [Smith 2016]

Typical Hopewell Square with gateway mounds, Plate XXIV [Squier & Davis 1847]

Small mounds called 'gateway mounds' are found inside square and octagonal earthworks. These are part of the earthwork plan and are usually arranged in front of entrances. Many alternate placements exist for both entrances and gateway mounds. Still, the most popular theme seems to be a square with four sections separated by entrances blocked from the inside by gateway mounds. This is perhaps a 'structural saliency', a global structural property that has been modified into many forms. When I see these mounds, I can see lines of people dancing around the gateway mounds in patterns like the wrappings around the base pegs of a water drum.

Water Drum [Fields 2025]

Water drums are used because they create a sound that carries. It is interesting to think about the acoustic properties of the earthworks. Brad Lepper sent me this vignette:

"After the Civil War, there was a grand reunion of the soldiers and sailors from Ohio who had served in the Civil War held at the Great Circle. The Cincinnati newspaper reported that 20-30,000 people gathered within the Great Circle to listen to orations by President Hayes, Generals Garfield and Sherman, and other dignitaries, but nowhere is there any mention of people being unable to hear the speakers."

[Lepper 2025 personal communication]

There is a subdiscipline of archaeology called Archaeological Acoustics. [Navas-Reascos et al. 2023] There is also software that takes 3D models and models of instruments and allows for the exploration of the acoustic properties. [Dalenbäck 2021] [Dalenbäck 2025]

The possibility of continuous water drum use going back thousands of years from today is exciting, as is the addition of a new component to landscape studies, that of sound.

Cognitive Archaeology

Cognitive Archaeology (CA) tries to match human cognitive skills with the material artifacts of a past culture. The information gathered from artifacts is called 'etic,' and past humans' actual thoughts and ideas are called 'emic.' The mappings of etic, knowledge of artifacts, to emic, how the participants thought and acted, are called 'bridging theories.' CA is an attempt to bridge both directions.

Bridging arguments  [Haidle 2014, p. 2, fig. 1]

CA has always been influenced by biology and the analogy of culture being like Darwinian evolution. I have already mentioned some issues with this.

One idea taken from biology is that of transitions. This is exemplified in Maynard Smith and E. Szathmary's book, The Major Transitions in Evolution, first published in 1997. [Smith & Szathmáry 2010] The final transition in the book is human language. In 1991, the cognitive neuroscientist Merlin Donald published the book Origins of the Modern Mind. [Donald 1991] His major thesis is that:

"... the human mind co-evolved in close interaction with mind and culture."

[Donald 1993, p. 1]

He outlines three major transitions:

• The development of fine motor skills and the ability to transmit these skills to others through 'memesis', imitation. Donald calls this "memetics action, using the whole body as a communication device" [Donald 1993, p. 5]
  

• The development of language through what he calls 'lexical invention,' the mapping of meaning to symbol, he calls it metaphor, but I prefer the term "analogy.'
  

• The externalization of memory. This is where CA enters the picture. I would say that the extended ability of long-term memory in humans is a preliminary to this, an internal externalization, if you will.
  

Donald goes into great detail about the limitations of working memory. He gives short shift to long-term memory:

"The contents of our long-term store were accessible only by means of the limited associative strategies available to biological memory, such as similarity and contiguity; thus the need for oral mnemonics, extensive literal oral recitation, and a dependence on specialized individuals, like shamans, to preserve particularly important memory material."

[Donald 1993, p. 14]

I don't agree with him on this as it represents a view of long-term memory in the modern world, not the ancient. [Eskritt et al. 2001] In particular. I think of the 'memory palace' or 'method of loci' first mentioned in the Roman text, Rhetorica ad Herennium, in 89 BCE and attributed first to the Greek poet Simonides of Ceos in the 5th and 6th centuries BCE. [Wikipedia Method of Loci] This memorization method uses spatial memory to build a palace or house of associated landmarks. In 1991, the first World Memory Championships started. The participants, from 21 countries, use the method of loci extensively. The 2024 winner is from Mongolia. [The World Memory Championships 2024]

Memory in Australian Aboriginal societies is believed to go back at least 7,000 years, with memory of the inundation of the land bridge between New Guinea and northern Australia. Notice again the stress on landscape and location:

"In Aboriginal society, great store is still placed on the learning of traditional knowledge while the geography of the land is taught systematically to new generations, locally through stories about country and totems held within patrilines, and on a larger scale through songs that describe songlines—records of ancestral beings crossing the land performing creative acts that placed totemic sites and language and people into the landscape ..."

[Nunn & Reid 2016]

Donald states that during the Upper Paleolithic, modern humans started downloading, or rather offloading, symbolic memory to their material objects. This later became purely symbolic in the form of writing, where a set of symbols represents a spoken language.

One criticism of Donald, a popular critique of cognitive science, is that human minds are not computers and that downloading memory to a passive storage confirms a false duality between mind and the world. [Thomas 1998] I don't think this is fair to what Donald is saying. Lemonnier and others have shown that the relationship between even everyday objects and memory is dynamic and complex. Memory resides not just in objects but in the actions and social relationships between people. Dynamic networks of groups can hold memory outside the sum of individual memories of the group. The group itself becomes a computational device. This is believed to be how an ant hive works. [Neumann et al. 2009]

In [Time], I mention that many non-Western cultures have a very different concept of time. Time is not linear but circular, and the past, including a distant mythic past, is close by and considered real. Cultures use seasons, stages of human development, and develop calendars to lock people into a perpetual cyclic past by ritual and rules. Autonoesis is the human ability to mentally place oneself in the past and future. In addition, humans are constantly creating scenarios and plans for future actions based on current and past conditions. Autonoesis uses what is called episodic memory. This type of memory has not been mapped directly to brain function like long or short-term memory [Najenson 2024], but seems a combination of both, along with the human ability to abstract, symbolize, and understand a sense of place. This psychological state is an important driver of human behavior and, as a result, human culture. [Sant’Anna et al. 2024] [Tulving 2002]

The first two of Donald's transitions are considered genetic, but the third is due to brain plasticity and tradeoffs with internal long-term memory. A fine-grain study of human evolution over the last two thousand years has shown some genetic changes, lactose tolerance in Europeans, high altitude tolerance in Tibetans, immunity changes, etc. [Field et al. 2016] Recent cognitive evolution, the genetics of cognition, is an open question.

A challenge to transitions in cognitive evolution states that the major transitions had to do more with changes in neural structure, and that these changes opened up new spaces for the exploration of cognitive possibilities. Cognitive traits are evolvable or plastic, meaning they can be turned off or on according to circumstances. [Barron et al. 2023] For instance, memory feats have not been lost because of writing; they can be restored if necessary. So culture does not so much evolve cognition as explore the possibilities of our current neural wiring. Another example is the modern computer. All computers use the same design, created by John Von Neumann. For the last seventy-five years, we have been exploring the possibilities of this design, the cognitive space of this design. This cognitive space has been very useful, but a computer is a very different design from the human brain. Yes, computation is universal, but brains and present computers carve out different, only slightly overlapping niches in a vaster space.

Genetic changes affecting development are seen as the most heritable. [Miller et al. 2020] [Mollon et al. 2021] Time and growth from childhood to adulthood must be considered. We are born with a certain set of cognitive tools, like mimetics and analogy, but the mind is constructed by culture.

Cultural Transmission

I have already mentioned the linkages and problems associated with using Darwinian evolution as a model for cultural evolution. Using the tools of population genetics and statistical mechanics to study cultural evolution adds a quantitative component. [Smith et al. 2008] This is done by modelling, simple formal models are built through rigorous mathematics, but with minimal parameters. Also, any population of elements, 'agents', has internal computational powers; they can make decisions based on knowledge of their current state and past states. Models can be analytical, but are often stochastic as results diverge as populations get smaller, and often an analytical model is too complicated or doesn't exist. [Mesoudi & Whiten 2008] [Mesoudi 2025] [Rorabaugh 2014]

Genetic transmission is either vertical, sexual, or through duplication of a cell, or horizontal, DNA elements entering from outside sources. Even in groups like mammals that are mostly vertical transmitters, DNA from viruses can be transmitted horizontally. Single-cell creatures like bacteria have a much larger percentage of horizontal transmission. In 1991, two biologists, L. L. Cavalli-Sforza and M. L. Feldman, published Cultural transmission and evolution: a quantitative approach. [Cavalli-Sforza & Feldman 1991] They defined vertical transmission as cultural knowledge directly acquired from one's parents. They also defined five other methods, including a new category of 'oblique' transmission:

• Intrafamilial Oblique—closely related adult family members other than parents in the parental generation.
  

• Extrafamilial Oblique—distantly related adult members of the social group in the parental generation.
  

• Remote Generations—grandparents, great-grandparents, or strong oral traditions left by elders.
  

• Intrafamilial Horizontal—siblings and other closely related family members in the same generation.
  

• Extrafamilial Horizontal—contact with unrelated individuals of the same generation (includes peers).

[Hewlett et al. 2024, p 4]

In biology, Kimura's Neutral Theory was first posed as a challenge to selection. Random mutations were what caused biological diversity. What happened is that neutral theory became a null hypothesis from which the signal of selection could be measured. A stochastic simple model shows that after a long period of mutation, called 'genetic drift' over many individuals, the distribution of types is log-linear, also called a 'power law' or 'scale-free.' A 2004 paper by Bentley et al. tests this null hypothesis against lists of baby names, patents, and pottery motifs from the 400 year-old history of a German Valley. baby names showed a greater variety of names for females than males, patents were neutral, and pottery motifs followed the population of the whole valley rather than individual villages. [Bentley et al, 2004]

In 2024, Hewlett et al. published a survey of cultural transmission usage by hunter-gatherer groups in the Congo. In addition to Cavalli-Sforza and Feldman's six types, they added three 'group' types:

• conformist bias - cultural beliefs and practices of members of an entire group can impact the individual
  

• concerted transmission - ridicule
  

• cumulative transmission - initiation ceremonies

"Cumulative transmission is how cultural knowledge or skills become 'embodied' in a child. Daily physical movements, social-emotional, and cognitive actions and interactions shape the child’s neuromuscular, endocrine, nervous, and other bodily systems. The skills and knowledge become part of an individual’s embodied capital. Repeated actions and interactions contribute to establishing cultural habits or customs, such as where and how to urinate and defecate, using utensils or hands to eat, and brushing or washing one’s teeth. Embodied cultural traits are highly conserved unless substantial changes occur in the social–ecological setting."

[Hewlett et al. 2024, p 4]

There is a drop in parental transmission after early childhood, followed by more interactions among diverse members of the group. [Eerkens et al. 2014]

Information Packaging

Shannon's Information Theory deals with the transmission of a message between a sender and a receiver, how to deal with a noisy channel, and a measure of how structured the message is, the amount of 'surprise' in a message. The theory says nothing about what these structures are or how the message is packaged. A concept from fluid mechanics helps. This is the idea of a 'coherent structure.' An example is turbulence and the various complex structures formed by turbulence, like vortices, hurricanes, tornadoes, and special cloud formations like the Morning Glory Clouds in Australia. [Beaver 2022] A coherent structure is a set of relationships held together logically in time. As a circular logic, coherent structures exist because we humans see them as such. A culture can be thought of as a coherent structure, as it is a set of relationships represented in time. Artifacts of a culture are coherent structures within the culture, as they can represent a set of complex relationships between people and their behaviors. Cultural transmission is how a person learns. Since humans are mimetic, much learning is done by doing. Learning is embodied. In a culture without writing, memory is crucial. So, what are the coherent structures of cultural transmission?

Stories and Songs

The game of telephone is an example of how bad humans are at transmitting factual information to each other. As shown in court testimony, factual evidence is hard for humans to remember. Humans tell stories, but these stories transmit affective information, surprise, but not factual information. Surprise can stabilize a story; the surprise remains even when the facts change. This is best explained in the 2108 paper below:

'Story retelling is a process whereby cultural information is transmitted horizontally across social networks and vertically down generations. For the most part, retelling research has focused on the relevance and stability of factual information, “who did what, where, when, and why”; comparatively little is known about the transmission of affective information. We suggest that affect can serve as a second axis of stability for retelling, partially independent from factual information. In serial reproduction tasks modeled after the telephone game, we find that surprisingness of stories is well preserved across retellings – even when the facts and events of the story are not. The findings are significant for the communication of information, and thereby also the stability and transformation of culture in general.'

[Breithaupt et al. 2018]

Besides speech, another form of human communication is music. It perhaps seems strange that music is thought of as communication, but all cultures sing. Song is often a form of speech in which words are sung. The musical part of the song is highly structured and, although sometimes complex, is made up of a discrete number of tonal elements. A recent study has shown how a song can evolve. [Anglada-Tort et al. 2023] This was done over the internet, using crowdsourcing to create a statistically large population. Two populations, one from India and the other from the USA, were randomly divided into social learners and individual learners. Using a technique called 'iterative learning,' participants listened to and then sang a random melody. This was recorded. The next time, they either heard their version of the melody or their melody was played to a different person to learn.

Oral transmission effects on short melodies [Anglada-Tort et al. 2023, p. 1475, fig. 3]

What the study found is that, over time, the melody evolved to be more structured and to be made up of simpler elements. Also, there were significant differences between individual learners and social learners, and between the two cultural groups. With the cultural groups, the melodies evolved into melodies using the tonal elements of the culture. As the melodies evolved, social learners evolved towards structure more slowly, having more noise, while individual learners tended to innovate more.

Stories packaged as songs seem to be optimal for human memory. Music, especially music learned in youth, is remembered into old age. [Schulkind et al. 1999] Stories linked to local places and events in these places seem to evoke memory. Keith Basso collected stories among the Western Apache. All places have names, and many places have stories associated with them. When someone is doing something that others think is socially wrong, a story linked to a familiar place is told to them. They see this place all the time, and whenever they see this place, they are reminded of the story and the need for them to change their behavior. [Basso 1996] Cultural transmission is not by discrete memes but by informational structures packaged specifically for human-to-human transmission and to optimise memory, often by relating it to physical space. [Skelton 2024] With proper use, these structures can last a human lifetime and can be transmitted across generations.

A concept of measurement

So, how did so many Ohio earthworks get built over a period of hundreds of years, according to a set of design principles relating circles and squares of a standard size? The Great Circle at Newark has a diameter of around 1,200 feet. This is a huge distance. When I was there in 2023, I don't think I comprehended the sheer size, maybe because there are several large trees now growing in the circle. Last fall, I paced the diameter of a street near my house, and it is an impressively long distance. How did the builders measure this distance? They could have used a rope, but did they have the technology to make a 600-foot rope? How much would this weigh? How would you keep it from stretching in the wet Ohio climate? Could the rope last for three or four hundred years? Humans measure things based on their bodies. So, how does one measure 600 feet? One way to do this is by using pacing. Pacing is a two-step process and has been used by the Romans for surveying and for marching by Roman legions. [Hill 1990] [Open Access Surveying Library 2020] The variability of a pace averages out over long distances. Paces can be counted, and multiple sets of counts can be counted. So a 600-foot distance can be packaged as n times m number of paces. A standard pace can be learned as a leader can train a group of marchers to pace the standard distance. Stories, songs, and the embodied skills of each generation could be handed down.

Conclusion

Just defining what a culture is can be difficult, and especially difficult given our Western biases. Groups having the same language can have different cultures, and a culture can encompass different language groups. Culture can have a local element over a small region, yet be part of a larger regional or global culture. Trying to understand a culture through a few scattered, broken artifacts is even more difficult. The main hope is that these people are humans, and that there are certain sets of behaviors and ways a culture forms and evolves, that somehow are part of all of us. Imagine landing on a distant planet and finding a 'lost' alien civilization? How could we understand it at all? The only constant is that them and we are perhaps sentient. Not much to go on. Another problem is that cultural evolution, although created through a biological process, is not like biological evolution. Understanding a culture of the past through cultures close to it or even having fragments of the original culture is also difficult. Can a memory last thousands of years? What is lost in translation, in retelling? The answers are difficult and spread over a myriad of disciplines, but they are being answered.

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Part I - What is Hopewell?

Part II - Measurement

Part III - Geometry

Part IV - Newark, the Core, and Beyond

Part V - Time

Part VI - Landscape

Part VII - Sky

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