Delineating the Boundaries of Qualitative Game Theory: A Case Study of an Antebellum Industrial...

Delineating the Boundaries of Qualitative Game Theory:

A Case Study of an Antebellum Industrial Homestead Site

Lindsey E. Cochran, University of West Florida

Abstract:

The Simpson Lot of Arcadia Mill is an antebellum industrial homestead site in Northwest Florida

that was inhabited by five population groups—none of which left particularly discernible

material traces. Visual based analyses using GPR results, 3-D GIS artifact density maps, and

Google SketchUp ultimately served as the foundation for the game theory interpretation to

determine social dynamics of the site. A multi-scalar data network identified the living quarters

of two female overseers at an antebellum textile mill; although specific information about their

lifestyle remains unseen, this previously untested approach successfully analyzes enigmatic and

faint patterns in the material record.

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Cochran SEAC Paper, 2013

In the summer of 2012, a UWF field school undertook excavations on the 3.1 acre

Simpson Lot at Arcadia Mill, 8SR384, an antebellum industrial site in Milton, Florida (Figures

1-2). Sawmill co-owner Ezekiel E. Simpson resided just south of the operational facilities’ area

in a Louisiana style mansion on top of a terrace that overlooked the saw and textile mills.

Alongside his home was a small cottage built on brick piers, shown in Figure 3, that was

presumably contemporaneous with the main house. This paper seeks to build upon previous

research of the Arcadia community (Beck and Lees 2008; Little et al. 1989; Phillips 1993, 1998;

Rucker 1988, 1990a, 1990b) to determine who was living in this smaller yet significant structure,

as results could help to facilitate future researchers’ understanding of slave-dependent societies

in the Gulf South region. This research has two objectives. The first, of course, is to attempt to

explain what happened at the site, and when. The second is to test if game theory, the study of

strategic and dynamic interactions, can be successfully applied in archaeological research.

The Simpson Lot is like many archaeological sites: it has been reused and repurposed

throughout its history. Due to dynamic post-depositional events, much of the existing material

culture was recycled or discarded by each subsequent population occupying or using the lot.

Even though Arcadia Mill was only functional for a short 38 years and was largely abandoned

after 1855, the Simpson Lot was subject to at least three additional occupations. As could be

expected with this level of contextual diversity coupled with dynamic site formation processes,

excavations yielded few diagnostic artifacts and only one sealed feature. Additionally, the main

house burned down in a fire, destroying the bulk of the known site-specific documents

concerning the lot (The Milton Gazette 1935; Kranc 2012). There is, however, an excellent oral

history record, and our neighbors at the site were gracious with sharing their recollections.

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Game theory has been called the Theory of Everything Social (Varofakis 2008:1255),

akin to physicists’ prestigious and enigmatic Theory of Everything, made of quantum worlds and

string theories. The title “Game Theory” is a bit of a misnomer, as it is a compilation of many

theories with many ways to actually “play” the game (von Neumann 1928, 1928a; von Neumann

and Morganstern 1944). The basic parameters of these games (discussed below) can be met by

typical archaeological projects.

It has yet to be widely proven, however, if game theory be used to address questions in

the historic realm and to determine why people made certain decisions. Can game theory be

applied retroactively to “predict,” with confidence, what actions created the material record--

when and by whom-- in situations where that material evidence is incomplete or missing

altogether? Modern day applications of game theory are excellent ways to predict, with great

confidence, why certain decisions are made. If we can successfully determine why historical

figures made specific decisions, then it may be possible to construct a series of hypotheses

concerning what materials would have been used and where. Using strict game theory, in the

sense of quantitative dilemmas and matrices, was too rigid to account for the uncertainty inherent

in anthropological questions. If this research were to apply quantities to each possible variable in

this test of the Simpson Lot, much of the essence of the data would be lost: materials are very

multi-faceted and cannot be easily quantified in only one meaningful dimension.

Each game is composed of four elements: the players, which are said to be inherently

rational beings; the types of information, be it perfect or imperfect, complete or incomplete, and

if all players know the same kind of information; the actions and strategies undertaken by each

player; and finally, the outcome of each game or set of games. There are a few standard ways to

display all of this information, the most common being a payoff matrix. This research, however,

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will employ a state vector game, also called a game against nature, or SONAT, in which the state

of affairs between two or more people, populations, or situations are listed. A SONAT vector

does not seek to find a state of equilibrium like many standard payoff matrices. Rather, this test

asks a series of questions about broad variables or attributes that can be answered with whatever

datasets are available (Gecil and Anderson 2010). Each test yields a list of plausible scenarios

that fit, to varying degrees, a suite of local, regional, and national historical trends, patterns,

information, and histories. To describe these principles and as a preview of analyses to come, a

SONAT vector diagram seeks to determine why Spaniard Juan de la Rua sold the original

Arcadia milling parcel and instead took up brickmaking in the 1820s (Figure 4).

The first step of a State Vector Game is to determine what “States” to test. In this game,

de la Rua is “playing” against six variables that determine if brickmaking or milling would be the

most profitable choice. A series of variables to test are listed, limited to those with sufficient data

to properly test both parties. Variables and attributes are short, simple phrases that can be further

defined according to the State that is being tested. Then, each State addresses what is listed, one

by one, essentially, “filling in the blank,” or “solving for X”.

Researchers at Monticello have used game theory with good results--most successfully in

studies of commodity exchanges, oftentimes paired with signaling theory or evolutionary game

theory (Neiman 2008). One advantage these researchers enjoy is a very complete material and

documentary record. Excavations and historical research of the Simpson Lot did not return a

robust network of data, so I engineered an alternative set of game theory methods.

To do so, I undertook a three tiered methodology: (1) use inter-disciplinary techniques to

complete a survey of the Simpson Lot; (2) analyze the recovered data using standard

archaeological techniques combined with GIS models and geophysical evidence; and (3)

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interpret those results using a game theory approach. Each dataset in this study builds upon the

information in the previous: historical and archaeological data are input into GIS maps, that are

then used to identify Target Zones and unanswered questions that can be addressed in game

theory tests.

This methodology differs from others in that it is based on SONAT vectors. This is the

first test of this method in anthropological studies, and seeks to reorganize data based upon an in-

depth construction of historical contexts and reevaluation of associations between material

culture, rather than conducting game theory tests that are based upon numerical matrices that are

very common in modern day economic applications. Game theory is typically used to determine

which option is best for the players involved, seeking to influence future decisions. Instead, this

application tests if game theory can be used to determine why past decisions were made.

The creation and occupation of Arcadia Mill and the Simpson Lot span seven major

historical eras. Each of these had major regional and local impacts that would have almost

positively been reflected in material refuse at the sites. Since this is the first intensive research

project at the Simpson Lot, much of the archaeological research was devoted to mapping the site

and determining its spatial and temporal parameters. Overall goals for the excavation phase were

to complete a systematic survey across the 3.1 acre land tract; execute a series of geophysical

tests and ground-truth those results; and finally, excavate larger test units in areas with high

artifact concentrations and potential to answer questions about the chronology and use of the

Simpson Lot.

There are three “Target Zones” used to interpret the site: (1) an unidentified cottage

(Structure 1, Figure 5); (2) the site of a former water tower (Structure 2, Figure 6); and (3) the

foundations of the Big House (Structure 3, Figure 7). All three structures are oriented 11 degrees

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east of north, implying some degree of contemporaneity as the earliest could have served as a

visual cue during the construction of the rest. Historic photographs were recovered for two of the

three buildings—the Big House and the cottage. The water tower at Simpson’s Bagdad Land and

Lumber Company was photographed in 1917 (Figure 8). Similar foundation configurations,

likely with contemporaneous construction dates and common ownership lead me to assume the

Bagdad tower resembled the one that once stood at the Simpson Lot.

The results from the shovel test survey revealed the location of three general areas that

may represent the expansion and subsequent collapse of several occupations on the site.

Materials were analyzed using a slightly modified Southian typology (South 1972, 1977),

concentrating on ceramics, glass, and functional artifact groups—all of which were categorized

in the lab according to standard UWF lab methods (Lloyd 2001) (Figures 9-13). Ceramics

recovered were quite diverse. Most of the assemblage, nearly eighty-two percent (81.2%)

consists of refined earthenwares, nearly three-quarters of which was whiteware.

Almost half of the entire assemblage consists of glass artifacts. Many of these (87.2%)

were too small to identify or lacking in diagnostic features, and were labeled as “indeterminate”

or “other”. Identifiable glass artifacts were as diverse as the ceramics. Datable decorations,

colors, and uses span the history of the Simpson Lot, although nearly all were recovered in

mixed contexts.

Next, a series of three geophysical techniques assisted in the identification of the shape of

Structure 1 and the location of auxiliary features or piers. We used ground penetrating radar,

electric resistivity, and gradiometry, but were only able to get results from the first technique due

to corrupt data and hardware issues. Three grids were surveyed (Figure 14), totaling 36m2.

Results were not groundtruthed over Grids A and B. The following radargram, in Figure 15,

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shows two cultural anomalies interpreted to be (1) a pipe and possible cistern or sewage tank and

(2) debris from the southeast corner pier of Structure 1.

The area of Grid C was the primary target of geophysical investigations as three brick

piers were visible on the surface (Figure 16). It was not initially apparent that Structure 1 was the

same building as shown in the historic photograph previously referenced. Although no refuse pits

were identified, a virtual field of cultural material and debris approximately 12-by-12 meters was

identified through the GPR testing. All cultural anomalies in Grid C were grountruthed after the

geophysical survey was completed.

The following artifact density maps were created in ArcGIS from an Access database.

These maps delineate the spatial and temporal boundaries of the site. I selected an inverse

distance (IDW) interpolation method, which uses an algorithm to interpret unexcavated areas in a

grid according to the weighted values of known points at varying distances from grid nodes. Four

comparative artifact density maps were used to guide my interpretation of the placement of

structures on site as well as the extent and state of the material debris around each major area of

use.

The first map shows the overall ceramic assemblage with concentrations around the

eastern side of the site, and moving around towards the northern central portion of the site

(Figure 17). The comparison between cut and wire nails (Figures 18-19) is one of the most

telling figures about the temporal associations of structures on the Simpson Lot. The material

debris field from each structure has an almost perfect inverse correlation, meaning that we found

artifacts where the structures were not and no artifacts where the structures were. Additionally,

most of the cut nails were recovered around Structure 1, while most wire nails were around

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Structure 3. This final image, is a map the full cultural material density, sorted by count, and

successfully delineates the expected material refuse field for all three structures (Figure 20).

Game theory methods are implemented because of a lack of substantial quantitatively

derivable data and the subsequent difficulties of using standard statistical techniques to

accurately test ideas about the site, and to look for patterns in the data. The State Against Nature

vector diagram begins by identifying four variables that can be addressed with the data at hand

on the Simpson Lot. The variables can be addressed or tempered with regional or local patterns,

generally following the “activity systems” model outlined by Rapoport (1993:13). Then, each

potential answer to the question or “state of affairs” will attempt to address the set of variables

by comparing what information and data are available to the individual constraints of each game.

This process will be repeated for each potential state of affairs.

Instead, State Against Nature diagrams will identify the game to be played by using a

series of testable variables that are necessarily tempered with regional or local historical and

archaeological landscape patterns since site-specific data is largely absent. In this game theory

SONAT diagram about the Simpson Lot (Figure 21), the variables include the architecture of

Structure 1, the location of the structure in relation to other features on the site like the Big

House and well, the number of people residing in Structure 1, and finally, expected levels of

autonomy. Next, three “States” are identified using site-specific data. Potential populations that

could have lived in Structure 1 are then listed, and more specific attributes that address each

overall variable are listed. Historical, archaeological, and remote sensing data have alluded to the

possibility that the antebellum resident(s) of Structure 1 could be: (1) a domestic slave serving

inhabitants in the Simpson Big House; (2) the female overseers of the antebellum industrial

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sawmill at Arcadia Mill; or (3) Structure 1 could be part of a line of slave cabins in which the

female textile workers resided.

As shown in the SONAT diagram, the first possible occupant (or “State”) of Structure 1

was a domestic slave. This person, typically a female, would have likely been materially

represented by a mid-to high range of architectural materials, such as brick piers and “comfort”

architectural amenities like a fireplace, or perhaps storage areas like a root cellar (Genovese

1968; Singleton 1992; 1995). Locally, the contrast between ironstone and brick building

materials at Area A and the Simpson Lot, respectively, is an excellent status marker. Residential

structures in Area A, where the Arcadia Mill working population resided, were built on ironstone

piers, a sturdy and readily available material at Arcadia Mill. Finally, the common requirement

of domestic slaves to care for the plantation owners’ family often necessitates a close spatial

relationship between slave and owner (Joseph 1993:57-73; Galle 2010:19-43).

The next potential occupant, an overseer to the late textile mill slaves, would have a

similar set of architectural status markers as the domestic slave. This degree of difference, of

course, would be partially dependent upon the race or gender of both the overseer and workers.

The location of the domicile would be dependent upon the responsibilities of the overseer. If s/he

was to supervise the slaves only at the industrial operations at Arcadia sawmill, then there is a

chance that the location of the living quarters is further from the location of the slaves’

residences. Further, there is a greater chance that the overseers are allowed to bring families with

them than slaves being allowed to stay with their families. There was a relatively high level of

autonomy for overseers across the southeast, especially compared to slaves in the later periods of

antebellum south (Genovese 1968).

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The third possible occupant, another class of slave, might have been housed in a series of

small domiciles reportedly located near the Big House. A clear separation exists between slave

and overseer style housing, and an even bigger difference exists between a “field slave” or

domestic slave domiciles, particularly architectural materials and spatial patterning. Finally, they

likely have low levels of personal and group autonomy, but were often allowed small garden

plots (Heath and Bennett 2000:41-42). Evidence for this might include areas with negative

archaeological evidence of use spaces adjacent to structures (Mintz 1974:231-232).

My analysis of the SONAT exercise leads me to hypothesize that female overseers

inhabited Structure 1 during the antebellum era. The architecture of Structure 1, in that it is

supported by bricks rather than ironstone, the relative closeness between Structure 1 and the Big

House, and the probable duplex configuration of the semi-autonomous house are all reflective of

probable characteristics of a house belonging to plantation overseers, and similarly, of overseers

to industrial operations.

The analysis of the Simpson Lot according to a game theory framework did not generate

any new hypotheses that were not able to be gleaned from the previously known historical

contexts. It did, however, facilitate pattern recognition by requiring the analyst to clearly deduce

what patterns or traces of peoples and cultures could exist. The appeal of a game theory approach

was its potential to overcome the nearly complete deconstruction of every element of the site by

the succeeding occupant. It is difficult, though, in antebellum enslaved communities or those of

low-wage workers because material “markers” are quite varied, and often indistinct. However, in

this and in other cases, employing a game theoretic approach enables the objective questioning

of the material culture and existing historical documentation as well as to generate hypotheses

concerning data that have not yet been found. Sometimes, deconstructing all evidence and

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recompiling it in another often less obvious and less intuitive manner brings about opportunities

to realize what specific data are missing from the network. This came into play at the Simpson

Lot with the hypothesis of the purpose of Structure 1.

Game theory was found to be most useful as a methodological tool, not as a theory or

mathematical model that can generate new information. The problem with trying to examine

historical processes in this manner is that all new information or conclusions are necessarily

circular—unless the test is engineered to have “0” or “1” binary style answers. Game theoretic

methods “forces” one to contextualize the issues from the era(s) in question in order to more

rigorously examine what would have been the optimal choice(s) for the players. It is a more

robust analysis than many because it doesn’t rely on a priori understandings of artifact markers

or analogy.

I propose that game theory has potential applications in archaeology if SONAT vectors

are used to influence research design. This method can be evaluated by playing the State Against

Nature game before investigations of the remainder of the Simpson Lot are undertaken. The

results can help inform what patterns or data may be present and should be used to guide field

methodologies to increase the likelihood of important information being recovered.

Game theory methods enhance our understanding of ephemeral sites like the Simpson Lot

by deconstructing and reorganizing data to incorporate broader, and perhaps better understood

historical or contextual patterns, and then predicting possible site-specific activities that

produced the material outcome recovered through excavations. Although more research is

necessary, the use of game theory methods has inspired a different hypothesis about the site’s

structure and lifeways of the inhabitants than originally deduced from standard methods, and is

thus an invaluable tool.

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CITATIONS

Beck, Monica L. and William B. Lees

2009 “As happy and contented with their vocation:” Shame and Pride Surrounding the

Industrial Slaves of the Arcadia Cotton Mill. Paper presented at the 20th

Conference on

Historical and Underwater Archaeology, Toronto, Ontario, Canada.

Galle, Jillian

2010 Costly Signatling and Gendered Social Strategies Among Slaces in the Eighteenth-

Century Chesapeake: An Archaeological Perspective. American Antiquity 75(1):19-43.

Gecil, Ilhamkubilay and Patrick L. Anderson

2010 Applied Game Theory and Strategic Behavior. CRC Press, Taylor and Francis Group:

Boca Raton.

Heath, Barbara A. and Amber Bennett

2000 “The little Spots allow’d them”: The Archaeological Study of African-American Yards.

Historical Archaeology 34(2):38-55.

Joseph, J.W.

1993 White Columns and Black Hands: Class and Classification in the Plantation Ideology of

the Georgia and South Carolina Lowcountry. Historical Archaeology 27(3):57-73.

Kranc, Suzanne Simpson Ripley

N.P. The Simpson Family at Arcadia. 2012.

Little, Keith J., Caleb Curren and Lee McKenzie

1989 Arcadia: An Archaeological Evaluation of a Nineteenth-Century Industrial Complex,

Santa Rosa County, Florida. The University of West Florida, Archaeology Institute,

Report of Investigations 21.

Lloyd, Janet

2001 Laboratory Procedures and Artifact Classification Manual. Manuscript on file at the

University of West Florida Archaeology Institute.

Mintz, Sidney

1974 Caribbean Transformations. Johns Hopkins University Press. Baltimore, MD

Neiman, Fraser D.

2008 The Lost World of Monticello: An Evolutionary Perspective. Journal of Anthropological

Research 64(2):161-193.

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Neumann, Jon von

1928 On the Theory of Games of Strategy in Contributions to the Theory of Games edited by

A.W. Tucker and R.D. Luce. 1959. Princeton University Press, Princeton.

1928a Sur la theorie des jeux. Comptes Rendus de l’Academie des Sciences 186(25).

Neumann, Jon von and Oskar Morganstern

1944 Theory of Games and Economic Behavior. Princeton University Press: Princeton.

Phillips, John C.

1993 Arcadia: An Early 19th Century Water-Powered Industrial Complex In Northwest

Florida. The University of West Florida, Archaeology Institute, Report of

Investigations 44.

1998 Flood Thy Neighbor: Colonial and American Water-Powered Mills in West Florida.

Gulf South Historical Review 14:143-162.

Rapoport, Amos

1993 Systems of Activities and Systems of Settings. In Domestic architecture and the Use of

Space, an Interdisciplinary Cross-Cultural Study, Susan Kent, editor, pp. 9-20.

Cambridge University Press: Cambridge.

Rucker, Brian

1988 Arcadia and Bagdad: Industrial Parks of Antebellum Florida. The Florida Historical

Quarterly 67(2):147-165.

1990a Blackwater and Yellow Pine: The Development of Santa Rosa County, 1821-1865.

Ph.D. dissertation, Florida State University.

1990b The Origins and Development of Arcadia and Bagdad. Manuscript on file at the

University of West Florida, Archaeology Institute.

Singleton, Theresa A.

1992 Preface to African-American Gardens and Yards in the Rural South, by Richard

Westmacott. University of Tennessee Press: Knoxville.

1995 The Archaeology of Slavery in North America. Annual Review of Anthropology 24:119-

140.

South, Stanley

1972 “ The Conference on Historic Site Archaeology Papers 1972—Volume 7”. Conference on

Historic Site Archaeology Papers. Book 8. http”//scholarcommons.sc.edu/archanth_

historic_site_arch_conf_papers/8. Accessed 19 August 2013.

1977 Method and Theory in Historical Archaeology. Clinton Corners, NY: Percheron Press.

The Milton Gazette

7 March 1935 Fire Destroys Arcadia, Home of C.H. Simpson: Santa Rosa Landmark is

Consumed by Flames Friday. In Santa Rosa Historical Society, Inc. Newsletter 30(4):1-2

6 June 1935 C.H. Simpson’s New Residence Most Completed: Attractive Bungalow Taking

Place of Home Burned. In Santa Rosa Historical Society, Inc. Newsletter 30(4):2

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Varofakis, Yanis

2008 Game Theory: Can it Unify the Social Sciences? Organization Studies 29:1255.

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FIGURES

FIGURE 1. Arcadia Mill Simpson Lot Site Boundary.

FIGURE 2. Simpson Lot Site Plan.

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FIGURE 3. Structure 1, Simpson Lot

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Variables:

Source of income

Labor force

Proximity to an economic core

Investment risk

Potential for political advancement

Safety

Game:

Sell land, timber, ironstone

Unstable labor due to Indian threat

Approximately twenty miles from economic core

High economic risk; uncertain revenue potential; high startup cost

Unknown potential for political advancement

Very unsafe

Sell bricks

Stable Spanish labor force

Approximately five miles from economic core

No economic risk; company already established and thriving

High potential for political advancement

Very safe

FIGURE 4. SONAT Vector, Juan de la Rua in 1819

SMILLLING=

S VARIABLES=

SBRICK=

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FIGURE 5. Structure 1 GIS with Block 8 and Block 9 Excavations

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FIGURE 6. Structure 2 Extant Foundations

FIGURE 7. East side of E.E. Simpson Residence

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FIGURE 8. Water Tower at Bagdad Land and Lumber Company, Taken in 1917 (photo courtesy

of Florida Digital Archives).

FIGURE 9. Top Row (L-R): Blue Shell-Edged Whiteware; Sponged Whiteware; Blue Transfer-

Printed Whiteware; Gilded Whiteware; Middle Row (L-R): Red Transfer Print Whiteware;

Brown Transfer-Print Whiteware; Broad Floral Hand-Painted Whiteware; Annularware; Bottom

Row (L-R): Hand-Painted Whiteware Rim.

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FIGURE 10. J. Noriega brick, Structure 2

FIGURE 11. Sample of Arms Artifacts. Top: Lead Bullets, Middle: (L-R) Lead Shot and Sprue,

Bottom: (L-R) Brass Bullet Casings.

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FIGURE 12. Sample of Clothing Artifacts. Top Row- Two Iron Buttons, Brass Button; Bottom

Row- Prosser Porcelain Button, Glass Button Fragment.

FIGURE 13. Plastic toy wheel; porcelain doll head fragments; red plastic toy wheel; glass

marbles.

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FIGURE 14. Geophysical Grid Layout.

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FIGURE 15. Grid A and Grid B GPR Radargrams, 0-253 cmbs.

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FIGURE 16. Grid C GPR Radargram, 0-161 cmbs.

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FIGURE 17. Arcadia Mill Simpson Lot Ceramics IDW Distribution.

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FIGURE 18. Arcadia Mill Simpson Lot Cut Nail IDW Distribution.

FIGURE 19. Arcadia Mill Simpson Lot Machine Made (Wire) Nail IDW Distribution.

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FIGURE 20. Arcadia Mill Simpson Lot All Artifacts, IDW Distribution.

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Variables:

S VARIBALES=

Architecture of Structure 1

Location in relation to other site features

# of persons residing in house

Expected level of autonomy

Game:

S DOMESTIC SLAVE=

Mid-to-high range of architectural status markers, mostly

due to visibility of structure

Resides close to the house, perhaps even inside big house

Unlikely to have family

Extremely low level of autonomy; expected to conform to white society

S INDUSTRIAL OVERSEER=

Mid-to-high range of architectural status markers, due to increased status within

community of laborers. May depend upon race or gender of enslaved person.

Close to workplace, but separate from wage workers and slaves

Often allowed families

Relatively high level of independence, but not necessarily political or economic autonomy

SONE OF MANY ASSOCIATED CABINS=

Low-to-mid range of architectural status markers

Clear separation between group of slave housing and owner residence

In-house population dependent upon region and time period;

unknown at Arcadia or NW FL

Low level of autonomy; may have garden or allowances to minimally modify structure

FIGURE 21. State Against Nature Vector Diagram, Occupants of Structure 1.

;

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