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I’m presenting next week at the Society for American Archaeology Annual Meeting. I’m giving two papers. One argues for parsimonious models when we do agent based modeling. The other reverses the flow of archaeological network analysis and instead of finding nets in the archaeology, I use agent based models to generate networks that help me understand the archaeology. (The session is ‘Connected Past’.) Here is the draft of my talk, with all the usual caveats that that entails. Parts of it have been drawn from an unpublished piece that discusses this methodology and the results in much greater detail. It will appear…. eventually.
Scott Weingart has been an enormous help in all of this. You should follow his work.
My interests lie in the social networks surrounding primary resource extraction in the Roman world. The Roman epigraphy of stamped brick easily lends itself to network analysis. One string together, like pearls, individual landowners, estate names, individual brick makers, signa, brick fabrics, and locations. This leads to very complicated, multi-dimensional networks.
When I first started working with this material, I reduced this complexity by looking only at the humans, whom I tied together based on appearing in the same stamp type together. I called these ‘producer’ networks. I then looked at the ties implied by the shared use of fabrics, or the co-location of brick stamp types at various findspots, and called these ‘manufacturing’ networks.
I then sliced these networks up by reigning dynasty, and developed a story to account for their changing shapes over time.
This was in the late 1990s, and in terms of network theorists I had largely only Granovetter, Hanneman & Riddle, and Strogatz & Watts to go on. The story I told was little more than a just-so story, like how the Camel got its Hump.
I had the shape, I had points where I could hang the story, but I couldn’t account for how I got from the shape of the network in the Julio-Claudian period, to that of the Flavian, to that of the Antonines. I’ve done a lot of work on networks since then; now I want to know what generates these networks that we see archaeologically, in the first place.
In this talk today, I want to reverse the direction of my inquiry. We are all agreed that we can find networks in our archaeological materials. The problem, I think, for us, is to explain the network processes that produce these patterns, and then to use our understanding of those processes to narrow down the possible entangled human & thing interactions that could give rise to these possible processes.
We need to be able to understand the possible behaviour-spaces that could produce the networks we see, to tease out the inevitable from the contingent. We need to be able to rigorously explore the emergent or unintended consequences of the stories we tell. The only way I know how to do that systematically, is to encode those stories as computer code, to turn them from normal, archaeological storytelling rhetoric, to computational procedural rhetoric.
So this is what we did.
One story we tell about the Roman world, that might be useful for understanding things like the exploitation of land for building materials, is that its social economy functioned like a ‘bazaar’.
According to Peter Bang, the Roman economic system is best understood as a complex, agrarian tributary empire, of a kind similar to the Ottoman or Mughal (Bang 2006; 2008). Bang (2006: 72-9) draws attention to the concept of the bazaar. The bazaar was a complete social system that incorporated the small peddler with larger merchants, long distance trade, with a smearing of categories of role and scale. The bazaar emerged from the interplay of instability and fragmentation. The mechanisms developed to cope with these reproduced that same instability and fragmentation. Bang identifies four key mechanisms that did this: small parcels of capital (to combat risk, cf Skydsgaard 1976); little homogenization of products (agricultural output and quality varied year by year, and region by region as Pliny discusses in Naturalis Historia 12 and 18); opportunism; and social networks (80-4). As Bang demonstrates, these characteristics correspond well with the archaeology of the Roman economy and the picture we know from legal and other text.
Bang’s model of the bazaar (2008; 2006), and the role of social networks within that model, can be simulated computationally. What follows is a speculative attempt to do so, and should be couched in all appropriate caveats and warnings. The model simulates the extraction of various natural resources, where social connections may emerge between individuals as a consequence of the interplay of the environment, transaction costs, and the agent’s knowledge of the world. If the networks generated from the computational simulation of our models for the ancient economy correspond to those we see in the ancient evidence , we have a powerful tool for exploring antiquity, for playing with different ideas about how the ancient world worked (cf. Dibble 2006). Computation might be able to bridge our models and our evidence. In particular, I mean, ‘agent based modeling’.
Agent based modelling is an approach to simulation that focuses on the individual. In an agent based model, the agents or individuals are autonomous computing objects. They are their own programmes. They are allowed to interact within an environment (which frequently represents some real-world physical environment). Every agent has the same suite of variables but each agent’s individual combination of variables is unique (if it was a simulation of an ice-hockey game, every agent would have a ‘speed’ variable, and an ‘ability’ variable, and so the nature of every game would be unique). Agents can be aware of each other and the state of the world (or their location within it), depending on the needs of the simulation. It is a tool to simulate how we believe a particular phenomenon worked in the past. When we simulate, we are interrogating our own understandings and beliefs.
The model imagines a ‘world’ (‘gameboard’ would not be an inappropriate term) in which help is necessary to find and consume resources. The agents do not know when or where resources will appear or become exhausted. By accumulating resources, and ‘investing’ in improvements to make extraction easier, agents can accrue prestige. When agents get into ‘trouble’ (they run out of resources) they can examine their local area and become a ‘client’ of someone with more prestige than themselves. It is an exceedingly simple simulation, and a necessary simplification of Bang’s ‘Bazaar’ model, but one that captures the essence and exhibits subtle complexity in its results. The resulting networks can be imported into social network analysis software like Gephi.
It is always better to start with a simple simulation, even at the expense of fidelity to the phenomenon under consideration, on the grounds that it is easier to understand and interpret outputs. A simple model can always be made more complex when we understand what it is doing and why; a complex model is rather the inverse, its outcomes difficult to isolate and understand.
A criticism of computational simulation is that one only gets out of it what one puts in; that its results are tautological. This is to misunderstand what an agent based simulation does. In the model developed here, I put no information into the model about the ‘real world’, the archaeological information against which I measure the results. The model is meant to simulate my understanding of key elements of Bang’s formulation of the ‘Imperial Bazaar’. We measure whether or not this formulation is useful by matching its results against archaeological information which was never incorporated into the agents’ rules, procedures, or starting points. I never pre-specify the shape of the social networks that the agents will employ; rather, I allow them to generate their own social networks which I then measure against those known from archaeology. In this way, I start with the dynamic to produce static snapshots.
We sweep the ‘parameter space’ to understand how the simulation behaves; ie, the simulation is set to run multiple times with different variable settings. In this case, there are only two agent variables that we are interested in (having already pre-set the environment to reflect different kinds of resources), ‘transaction costs’ and ‘knowledge of the world’. Because we are ultimately interested in comparing the social networks produced by the model against a known network, the number of agents is set at 235, a number that reflects the networks known from archaeometric and epigraphic analysis of the South Etruria Collection of stamped Roman bricks (Graham 2006a).
What is particularly exciting about this kind of approach, to my mind, is that if you disagree with it, with my assumptions, with my encoded representation of how we as archaeologists believed the ancient world to have worked, you can simply download the code, make your own changes, and see for yourself. If you are presented with the results of a simulation that you cannot open the hood and examine its inner workings for yourself, you have no reason to believe those findings. Thus agent based modeling plays into open access issues as well.
So let us consider then some of the results of this model, this computational petri dish for generating social networks.For my archaeological networks, I looked at clustering coefficient and average path length as indicator metrics, (key elements of Watts’ small world formulation). We can tentatively identify a small-world then as one with a short average path length and a strong clustering coefficient, compared to a randomly connected network with the same number of actors and connections. Watts suggests that a small-world exists when the path lengths are similar but the clustering coefficient is an order of magnitude greater than in the equivalent random network (Watts 1999: 114).
In Roman economic history, discussions of the degree of market integration within and across the regions of the Empire could usefully be recast as a discussion of small-worlds. If small-worlds could be identified in the archaeology (or emerge as a consequence of a simulation of the economy), then we would have a powerful tool for exploring flows of power, information, and materials. Perhaps Rome’s structural growth – or lack thereof – could be understood in terms of the degree to which the imperial economy resembles a small-world (cf the papers in Manning and Morris 2005)?
The networks generated from the study of brick stamps are of course a proxy indicator at best. Not everyone (presumably) who made brick stamped it. That said, there are some combinations of settings that produce results broadly similar to those observed in stamp networks, in terms of their internal structure and the average path length between any two agents.
One such mimics a world where transaction costs are significant (but not prohibitive), and knowledge of the world is limited . The clustering coefficient and average path length observed for stamped bricks during the second century fall within the range of results for multiple runs with these settings. In the simulation, the rate at which individuals linked together into a network suggests that there was a constant demand for help and support. The world described by the model doesn’t sound quite like the world of the second century, the height of Rome’s power, that we think we know, suggesting something isn’t quite right, in either the model or our understandings. But how much of the world did brickmakers actually know, remembering that ‘knowledge of the world’ in the model is here limited to the location of new resources to exploit?
Agent based modeling also allow us to explore the consequences of things that didn’t happen. There were a number of simulated worlds that did not produce any clustering at all (and very little social network growth). Most of those runs occurred when the resource being simulated was coppiced woodland. This would suggest that the nature of the resource is such that social networks do not need to emerge to any great degree (for the most part, they are all dyadic pairs, as small groups of agents exploit the same patch of land over and over again). The implication is that some kinds of resources do not need to be tied into social networks to any great degree in order for them to be exploited successfully (these were also some of the longest model runs, another indicator of stability).
What are some of the implications of computationally searching for the networks characteristic of the Roman economy-as-bazaar? If, despite its flaws, this model correctly encapsulates something of the way the Roman economy worked, we have an idea of, and the ability to explore, some of the circumstances that promoted economic stability. It depends on the nature of the resource and the interplay with the degree of transaction costs and the agents’ knowledge of the world. In some situations, ‘patronage’ (as instantiated in the model) serves as a system for enabling continual extraction; in other situations, patronage does not seem to be a factor.
However, with that said, none of the model runs produced networks that had the classical signals of a small-world. This is rather interesting. If we have correctly modeled the way patronage works in the Roman world, and patronage is the key to understanding Rome (cf Verboven 2002), we should have expected that small-worlds would naturally emerge. This suggests that something is missing from the model – or our thinking about patronage is incorrect. We can begin to explore the conundrum by examining the argument made in the code of the simulation, especially in the way agents search for patrons. In the model, it is a local search. There is no way of creating those occasionally long-distance ties. We had initially imagined that the differences in the individual agents’ ‘vision’ would allow some agents to have a greater ability to know more about the world and thus choose from a wider range. In practice, those with greater ‘vision’ were able to find the best patches of resources, indeed, the variability in the distribution of resources allowed these individuals to squat on what was locally best. My ‘competition’ and prestige mechanisms seem to have promoted a kind of path dependence. Perhaps we should have instead included something like a ‘salutatio’, a way for the agents to assess patrons’ fitness or change patrons (cf Graham 2009; Garnsey and Woolf 1989: 154; Drummond 1989: 101; Wallace-Hadrill 1989b: 72-3). Even when models fail, their failures still throw useful light. This failure of my model suggests that we should focus on markets and fairs as not just economic mechanisms, but as social mechanisms that allow individuals to make the long distance links. A subsequent iteration of the model will include just this.
This model will come into its own once there is more and better network data drawn from archaeological, epigraphic, historical sources. This will allow the refining of both the set-up of the model and comparanda for the results. The model presented here is a very simple model, with obvious faults and limitations. Nevertheless, it does have the virtue of forcing us to think about how patronage, resource extraction, and social networks intersected in the Roman economy. It produces output that can be directly measured against archaeological data, unlike most models of the Roman economy. When one finds fault with the model (since every model is a simplification), and with the assumptions coded therein, he or she is invited to download the model and to modify it to better reflect his or her understandings. In this way, we develop a laboratory, a petri-dish, to test our beliefs about the Roman economy. We offer this model in that spirit.
[edited April 4th to make it less clumsy, and to fit in the 15 minute time frame]
I am reading Ian Hodder’s book, ‘Entangled: An Archaeology of the Relationship between Humans and Things’ Hodder writes that the tanglegram cannot be represented as a network, since a network doesn’t consider the nature of the relationships or nodes. This is not in fact the case. Representing these complex relationships as a network is quite possible, and allows the ‘tanglegram’ to actually become a object to query in its own right, rather than a suggestive illustration. I’ve uploaded the network data to Figshare:
I used NodeXL to enter the data. If there was a bidirectional tie, I made two entries: A -> B, B -> A. If it was only one way, I entered it with the directionality of the original tanglegram. I saved it as a .net file, opened it in gephi, and ran gephi’s statistics.
This was all rather rough and ready; because I was working from a blown-up photocopy of the original figure, and I’m trying to get ready for a trip, there could be errors. One would need Hodder’s original data to do this properly, but I offer it up here to show that it’s possible, and indeed worthwhile: why else would you bother drawing a tanglegram, if not to use it to help your analysis?
In the image below, I resize the nodes to represent betweenness centrality (which elements of the tanglegram are doing the heavy lifting?) and recolour it according to modularity. Modularity finds five groups (nodes listed in descending order of betweenness centrality):
Group 0: house, groundstone, burial, plaster, figurines, pigment, skins, painting, personal artefacts, animal heads, food storage, human heads, special food, human body parts, burials, storage rooms, bins
Group 1: hoard, chipped stone, sheep, mats, dung, wild animals, fields, bone, cereals, wooden object, weeds.
Group 2: food, hearth, fuel, ash, clay balls, oven, traps, wood
Group 3: clay, baskets, extraction pits, wetland, reeds, birds, dryland, marl, ditches, fish, clean water, landscape, field, eggs
Group 4: midden, dogs, colluvium, mortar, pen, mudbrick
Seems quite suggestive! For the files for yourself, please see:
I had a conversation with Scott Weingart the other day, prompted by this plaintive cry:
Brain is broken this AM. Need suggestions for inclass exercises to teach SNA. Can't depend on there being computers: must be analog. Help?—
Shawn Graham (@electricarchaeo) October 15, 2012
Backstory: I’m teaching a class where we are looking at maps and networks and archaeological data, as ways of understanding how cities and countryside blur into one another in the ancient world. Last week, we played iterated Prisoner’s Dilemma’s with playing cards (thanks to this site by Alannah Morrison) as part of a discussion about Agent Based Modeling.
Which brings me to the conversation with Scott. Today, we’re playing with Gephi and making network models of the character relationships in our favourite TV shows. The next step is to combine the two lessons to address the question: what flows over networks? What do different network shapes imply, and what kinds of metrics answer what kinds of questions? So I think I’ll set up two different networks with the students – literally, I’ll arrange students in a line, a star, etc – and have them play iterated Prisoner’s Dilemmas with the people to whom they’re connected. We’ll use playing cards to represent payoffs… and hopefully we’ll see the cards flow over the network.
I thank Scott for his suggestions!
Then we’ll turn to Netlogo’s community models of network dynamics. That is, they will. The classroom computer is so locked down that I can’t run a freaking java applet in the classroom.
Anyway, that’s the plan for today.
Interested in networks, and looking for an exemplar that I could do in my class, I turned to the Portable Antiquities Scheme database, and extracted coins known to have originated from the mint at Sirmium (modern Sremska Mitrovica, Serbia). You can find the list here. I downloaded the data as a CSV. Looking at it, it seemed to me that a multimodal graph of coin to findspot, to material, to date, and to ruling house might be useful (and of course could be transformed into single mode graphs as necessary). So I made a list, where the 21 coins were marked ‘source’ and the other data were marked ‘target’ (which means that I repeated the coins four times in my list).
Here is the resulting network in a zoomable pdf: coins from Sirmium in the UK – PAS. I ran modularity and betweeness centrality. Most central nodes were ‘copper’ as a material, Constantine I and II, and then coins 283287 and 433211 and the date, AD324. If you revisualize the graph so that the communities are grouped into single nodes, the most ‘between’ of these communities is group 3, which has the following data: coins 410195, 272397, 451670, 474164, 283287, silver as a material, Constantius II and Valentinian I, and Bedford, Isle of Wight, North Kesteven, and the Vale of White Horse.
I’m no numismatist, but perhaps the coin folks out there can take a look at this small experiment, and tell me if these patterns are meaningful to them… my csv files & gephi files are here:
What follows is a process of me thinking out loud whilst working with data related to the Tiber Valley Brick Industry.
If we look at the distribution of stamped bricks across the Tiber Valley (as collected by the BSR), we can work out some of the implications for production and consumption by considering the way location, stamp type, and fabric of the brick intersect. I looked at every combination for every site in the South Etruria Survey, having done archaeometric analysis on the same collection to the point where I could say that ‘these two bricks share the same fabric’.
Here is the table (where 1 implies same, 0 implies different):
Which we may collapse, as some of these become functionally the same.
1. A&G: imply a common origin and distribution
2. B&H: imply a geographically dispersed production
3. D&F: imply a single clay source exploited by different figlinae.
Finally, there is situation ‘C’, which suggests that builders at a site had access to a variety of sources.
Since we can closely date many of the bricks, we can look at how these modes play out over time (remembering that this is a tally of relationships):
|Mode 1 (A/G)||10||2||2||6||2||22|
|Mode 2 (B/H)||54||14||4||4||6||82|
|Mode 3 (D/F)||13||13||7||7||2||42|
|Combination C (“Consumer Choice”)||17||7||6||2||1||2||35|
We can graph that:
Thus, by simply categorizing the relationships and graphing their evolution over time, we develop a complex view of the changing dynamics of production and consumption in the Tiber Valley.
However, we can also represent these relationships as a multi-modal network graph. The nodes in this graph are bricks and locations. Some of those locations, like the findspots, are known in space. Other locations, like the precise x,y, of the clay bodies is unknown or can be suggested to be roughly in a particular area. I create a directed graph where clay sources are ‘source’ and bricks are ‘target’, and where bricks are ‘source’ to findspots. I also categorize the linkages according to the relationships determined above. The result is below (Fig 1), where colours = communities and size = betweeness:
all relationships in tv-bricks (zoomable pdf of the png image)
One can then filter this graph, looking for instance for relationships of type B (Fig 2). What I would really like is to be able to lay these graphs out so that my findspots and claysources can be pinned to geographic space, while allowing the bricks themselves and their relationships to float freely. This would require a layout plugin that understood how to apply a different layout algorithm to nodes with null latitude/longitude values. That at the moment is rather beyond me.
Finally, one can collapse this graph into its component communities, and look at those relationships. In this PDF you can zoom in and see not just the bricks, but also the kinds of relationships, and the clay body that seems to go with this group (B6, somewhere in the neiborhood of Fiano Romano-ish).
Here we collapse the communities into single nodes, and run betweeness on this graph (fig 4). We end up with community 6 being ‘most between’; this community seems to source its clay from somewhere in the upper Sabina in the Forum Novum area (see chapter 3 of Ex Figlinis). Next most between is community 1, which sources in South Etruria in the Fiano Romano area and in the lower Sabina. Then we have community 8, which is pulling from either side of the Tiber in the lower reaches of South Etruria and the Sabina.
Community 6 has within it two sites and six bricks -TVP3592 and TVP2304; bricks se18, se13, se116, se104, se156, and se152. These bricks are first century bricks from the Tonneiana/Viccianae, PL (which might mean ‘Portus Licini’), someone named CASPR and a Q. Sulpicius Sabinus. What does ‘betweeness’ mean in this context here? Obviously, a question with a lot riding on it, but off the top of my head, if the association of PL with Portus Licini, which was a known brick warehouse is suggestive.
Community 1 is a much more complicated group with six sites and 15 brickstamps. Figlinae mentioned are Tonneina/Viccianae again, some Domitianae Veteres, an explicit Portus Licini stamp, a few tied to the Domitiana family, some late ‘officinae’ stamps (including ‘Boconiana’, which implicitly suggests the town of Bocignano).
There is directionality implicit in this diagram, but I’m not entirely sure yet what to make of it.
From the first to third centuries AD, the brick manufactories in the Tiber Valley around Rome made millions of bricks. A proportion of these carry makers’ marks, with many different dimensions of information – the brick maker; the estate; the landowner; the year; and various decorative features which may or may not be signficant. I worked on this material for my PhD thesis (which these days makes me cringe when I look at it). I’ve been reconsidering that work lately, especially in light of recent work by Malkin, Knappet, Brughmans, and of course the interest in digital humanities in networks more generally.
I discovered on an old and nearly defunct laptop a file I’d created as part of my PhD work, which listed the text of every stamp in the CIL XV.1, and gave the original neo-latin description of the figurative device on these stamps. (CIL is written in 19th century academic Latin). So, I decided to see what I could find if I translated this into a Gephi two-mode network, and ran some descriptive statistics on it – how I wish I’d had these tools a decade ago!
As I wrote in 2002 there are 46 different types of signa, across 428 types of stamp, totalling about 3000 examples listed in CIL. The file I’m working here is a bit more messy, with many variants of the typical motifs. So, what do we have? It’s a two mode network, which can be filtered into a single giant component of 570 nodes and 608 edges connecting it. For the brick afficonados amongst you, you can pick out the big name figlinae like Terentianae or Domitianae, and see how they interconnect based on shared useage of signa. If you calculate modularity on this network, you get 18 very strong sub-communities. That jives very nicely with the archaeometry I did on the brick, finding about 12 groups in a cluster analysis using Ward’s Method on the XRD results from the South Etruria Survey collection of bricks.
Next thing: split this graph up by time, space, clay sources, and usage patterns at sites.
Here’s the pdf version with labels. Keep in mind, this is rather rough.
I’m contributing to a volume on ‘Land and Natural Resources in the Roman World’. Below is my draft, on which I welcome comments and questions.
Towards the computational study of the Roman economy
Shawn Graham, Carleton University, Ottawa Canada
“Economies are complicated systems encompassing micro behaviours, interaction patterns, and global regularities. Whether partial or general in scope, studies of economic systems must consider how to handle difficult real-world aspects such as asymmetric information, imperfect competition, strategic interaction, collective learning, and the possibility of multiple equilibria. Recent advances in analytical and computational tools are permitting new approaches to the quantitative study of these aspects. One such approach is Agent-based Computational Economics (ACE), the computational study of economic processes modelled as dynamic systems of interacting agents.”
Most models of the Roman economy do not take into account this idea that micro-behaviours, feedback, and local interaction provide the circumstances out of which emerge those larger issues about which we are typically concerned. Before we can ask questions about growth, or market integration, or the degree to which Rome was ‘primitive’ versus ‘modern’, we have to focus on individual decision making. In this paper, I outline an agenda for how we might be able to do this. It comes down to this: we have to draw out and understand networks of individuals at all geographical scales and then use those networks as the substrate for computationally simulating individuals’ economic activities. Thus, archaeology and ancient literature become united through computation.
It is not necessary, I think, to rehash the historiography of studies of the Roman economy; the broad outlines of the debate are well known. What I find exciting though is the emergence of the New Institutional Economics of Douglass North. These works all draw attention to ideas around the consequences of individual decision making from incomplete knowledge, of how ‘good enough’ or satisficing decisions push actors and economics towards path-dependence (where because of past decisions one is locked into a particular mode). The idea that network relationships (and the institutions that emerge to promote these) are the mechanism through which ancient economies deal with incomplete knowledge is a powerful one because we can find and outline the traces of these networks through archaeology.
Bang takes this idea further and through cross-cultural comparison with Mughal India pushes our attention to the bazaar: “a stable and complex business environment characterised by uncertainty, unpredictability and local segmentation of markets’. Bang shows how the bazaar helped shield the individual from (while at the same time encouraging) fragmented information and instability. For Bang, one of the key mechanisms for exploring and understanding a bazaar-like economy is social networks, the way they form, and how information flows through them. We need to focus on the social differences between actors in a market situation.
Even the Emperor can be incorporated into such a perspective. In considering the Emperor as both the embodiment of the state and a private person intervening in its economy as one more player amongst other private citizens, Lo Cascio draws attention to the interplay between the Emperor’s euergetism and private markets, that he solved the problem of feeding Rome “by leaving unchanged the market mechanisms at work” and by “establishing and enforcing the rules of the game”. He does so to ensure that individuals neither engage in rampant speculation to force up prices, but also to ensure that prices do not become set to low, that is, to ensure an adequate profit. The success or failure of the Emperor to do this should depend on his position in the network.
This is a very complex view, too complex for any one individual to hold in one’s head and to be able to understand the non-linear outcomes of so many interacting parts. We need the computer. To understand the Roman economy, we need to simulate it. The best way to do this is to ground our simulation in what our evidence actually gives us: the actions of individuals in the past, whether we find that evidence in the archaeology or the ancient literature. We have to build up from individuals before we can begin to understand what ‘the Roman economy’ might actually mean.
Roman Economics Needs to be Networked
Networks and network analysis are currently in vogue in many areas of research. Tom Brughmans has neatly summarised the historiography and main issues surrounding networks and network analyses as applied to archaeological research. In essence, he argues that all of the varied approaches to network analyses are united by the idea that networks are ubiquitous and influence decision making; through networks both tangible objects and intangible influences spread (and in turn, promote or hinder network growth). Through studying networks, we are able to bridge the study of parts through reductionism to the emergent whole. The methodological advantages enumerated by Carl Knappett can be tied explicitly to the advantages that the New Institutional Economics bring. A network perspective forces one to consider relations between entities; they are spatial whether considered in social or physical terms; they work across scales; they can incorporate people, objects, and time.
Schortman and Ashmore make the argument that a by-product of social networks is the emergence of power, through collaborative or cooperative action. Debates around structure and agency in the social sciences revolve around questions related to the concentration of power and the generation of hierarchies across multiple spatial scales. It is from this contending for assets that politics becomes necessary and structures for the same emerge. 
Achieving power over others involves monopolizing some aspect of the production, distribution or use of materials. On the other hand, others can contest this by using their own social networks to gather resources (whether material or social). In this way, action through social networks results in political structures which are themselves the aggregate of flows of materials and ideas through social networks.
Perhaps the most well-known term in network studies is the idea of the ‘small-world’, first coined by Stanley Milgram. A small-world is not just a metaphor, but rather a precise concept in network terms, where a randomly connected network with mostly local connections has a few long distance connections which allow the entire network to be spanned in only a few steps. This is a crucial concept and one we should look for archaeologically or as a by-product of our models. Brughmans writes
“ … Such a specific topology has direct implications for the processes underlying it, like the transportation of materials, the spread of religious ideas or the enforcement of political power. These processes would largely take place between the highly connected nodes [actors of whatever kind] and they would only reach the larger number of less connected nodes through these [linkages]. In a small-world network, on the other hand, nodes within the same small-world are more often directly connected to each other, while only processes involving other small-worlds (e.g. long-distance trade) would go over the bridging nodes.”
How can we draw out networks from archaeological materials? Objects carry the resonances of who make them. They mark out membership and social identity. “Exchanging these items thereby manifests and extends crucial social linkages… Networks, therefore, come alive, in part, through the transfer of items that partake of their members’ social essences”. Objects therefore could be taken as proxies for social actors. Artefacts are the result of human, individual, decisions. They influenced other individuals at the time through their complex resonances of thing and place and object life-history. By considering artefacts and their relationships explicitly in terms of social network analysis, we reconnect with the individual in the past, and we obtain a perspective that allows us to see what kinds of actions were possible in the past, patterns of agency and structure, that those actors themselves could not see.
Anytime one can discern a relationship, a network is possible. Fiona Coward reminds us that the archaeological record is not a passive by-product but rather is in fact social relationships: “The patterning of material culture is a direct result of the social relationships between individuals and groups in which these objects were caught up. A network perspective provides a much more realistic picture, not only of objective sociality, but also potentially of individuals’ subjective experience of their worlds”.
But as Scott Weingart warns us, we also have to take into account the dangers of methodology appropriation. Network analysis comes to us from graph theory, from statistics, from computer science. The methods, philosophies and concerns of those disciplines are not necessarily congruent with archaeology. Brughman’s recent work will go a long way to addressing the potentials and perils of drawing out networks from archaeological materials.
If we can draw out networks from the ancient literature or the archaeological record, what then? We re-animate these networks using agent based (or ‘individual based’) modelling. This is a technique where a population of autonomous, heterogeneous ‘agents’ are created within a computerized environment. They are given rules of behaviour which they implement given a particular situation (whether when interacting with other agents, or with the environment). They are goal-oriented and to a degree, self-aware. That is, if we are interested in something called ‘the Roman economy’, we simulate the agents that compose that economy and their behaviours: not the economy itself (in contrast to traditional economic models with their equations and ‘rationalizing’ assumptions; we simulate at one level of complexity below our ‘target’.
Lea Tesfatsion discusses a number of ways in which ‘agent-based computational economics’ can be used, and classifies different studies according to their objectives. The one which should concern us here is what she calls, ‘qualitative insight and theory generation’: “how can economic systems be more fully understood through a systematic examination of their potential dynamical behaviours under alternatively specified initial conditions?” A key feature of agent modelling that differentiates it from other approaches is that once the starting conditions are specified, all subsequent events are driven by agent interactions. The researcher then is not so concerned with the final results of the simulation as its evolution over time, its history. Thus, the focus is on the process. That is to say, we study the model’s history to generate insight into real history.
Research into agent based models of economies has found that the topology of interactions matters. It is not just the pattern of social ties that matters, but also the environment in which these actions take place. We can explore the environmental aspect by setting the simulation on top of a cellular-automaton, a chess-board like arrangement of squares, where each square represents a unit of land and its holdings, and which responds to rules about growth, climate, geology, and so on. In many ways, a cellular automaton represents a dynamic geographic information system and which could obviously be drawn from archaeological GIS. Combined with an agent-based model representing the decision making agents, we then have a powerful tool.
A number of researchers have applied ABM and cellular automata to studying problems of structural change in agricultural societies, exploring everything from government intervention, to the diffusion of innovation in agriculture, to the beginning of European-style agriculture in Indiana in the early 1800s. These studies point to ways in which economic path-dependence emerges, under what circumstances innovation may diffuse, and decision making processes at different spatial scales.
Archaeology and Simulation
Simulation has a long history in archaeology. Agent based modelling is an outgrowth from several different fields, primarily game theory and complex systems studies. John Barret, in considering the relationship between agents and society, drew attention to how agents both form and are constrained by, the social structures that emerge from their interactions. He argued therefore that the level of ‘society’ should not form the basic unit of archaeological analysis, but rather the individual. It is social learning that creates a society (or an economy, for that matter).
There are now many agent-based models of past societies. Many of these are quite complicated, with many moving parts, which can make it difficult to understand what the model results may actually be telling us. I advocate instead for extremely simple models, exploring only a limited aspect of the phenomena in which we are interested in. After building a series of these, we can consider their results in aggregate.
Building a Simulation
How do we translate our arguments over the Roman economy into an agent framework? Tesfatsion suggests a four-step method for recasting that understanding in a way that can be modelled and explored:
“• Select as your benchmark case an equilibrium modelling of an economy from the economic literature that is clearly and completely presented and that addresses some issue you care about.
• Remove from this economic model every assumption that entails the external imposition of an equilibrium condition (e.g., market clearing assumptions, correct expectations assumptions, and so forth).
• Dynamically complete the economic model by the introduction of production, pricing, and trade processes driven solely by interactions among the agents actually residing within the model. These procurement processes should be both feasible for the agents to carry out under realistic information limitations and appropriate for the types of goods, services, and financial assets that the agents produce and exchange.
• Define an “equilibrium” for the resulting dynamically complete economic model.”
Tesfatsion remarks that when she tries this exercise with economics students, they find it difficult to understand the economy at this level working with individual agents. The challenge of this method is that it foregrounds survival: that the needs of subsistence, of surviving over time (death is always a possibility in these models) are the bedrock on which everything else is based.
Thus, we build our rule-sets that our computational agents will follow from our understanding of how an individual [Roman; collegium; military unit; family; city] acts in particular situations. While every agent might have the same suite of variables, each agent is heterogeneous. Its particular combination of variables is unique. We might all be playing basketball by the same rules, but my abilities are different than yours. We model the appropriate underlying environment. We specify the initial starting conditions, and then set the simulation in motion. We run the simulation over and over again to explore the complete behaviour space for all of the particular starting conditions, to see what emerges when and how.
To know that we have found something new about the Roman economy from such a process, I would suggest that we ground one of the model’s behaviours in social networks. There are various ways this might be accomplished. We might draw from an understanding of how patronage worked in the Roman world. Or, we could draw from Bang’s arguments about Rome-as-bazaar. Then, when the simulation has run its course, we can measure the emergent network and compare its features to real networks known from the archaeology. When the two correspond, then the model settings for that particular run have something important to tell us about ancient society. Alternatively, we could reverse that and specify networks found in the archaeology as our starting point. Do the model outcomes, when set from a starting point known archaeologically, make any sense according to what we believe to have been true about the Roman economy? If not, then perhaps our rule sets are flawed.
Doran underlines some of the main impediments to simulation building amongst archaeologists, limitations in computing power, and the disciplinary boundaries that create barriers to knowledge building. As Doran points out, the computing power issue is largely no longer an issue. Quite complicated simulations may be built on a desktop computer without too much trouble in terms of hardware. The second problem is more difficult. One way we can break those boundaries down may lie in the choice of simulation environment: the simpler and more intuitive the framework, the easier to use, develop, and communicate results. In my own work, I use the open-source Netlogo modelling environment, which I recommend to anyone interested in exploring the possibilities of this approach. While Netlogo has its genesis in efforts to educated school children in complex systems thinking, it is now in its fifth major release and is quite powerful. The learning curve is not overly steep, and much can be accomplished through tweaking the many models that come pre-packaged with the software (more on this below).
A simulation is an argument in computer code about the way the world works, and so represents a kind of ‘procedural rhetoric’. It is object-oriented, meaning that each individual behaviour exists as its own object. One then arranges the objects (which can be conditional) in the order the agents should carry them out, given a particular position in the environment or social position vis-à-vis other agents. One can have quite sophisticated simulations running after a day of working through the included tutorials. This should not be taken as a sign that Netlogo is simplistic. Quite powerful models have been built in it, including modelling the emergence of cities in the third millennium BC.
An excellent place to begin is with the included model, ‘Wealth Distribution’. In this model, a ‘world’ is simulated where grain is distributed randomly. In some places it grows thick on the ground; in other places it is sparse. A population of agents are introduced to this world. Their goal is to find enough grain to keep living, and to reproduce when conditions are right. The agents have ‘vision’ or knowledge of the world, to differing degrees. They have ‘metabolism’, or a preset amount of food they must consume with each time-step or they shall die (which again varies by individual). The amount of food collected above this metabolic rate becomes ‘wealth’. When this simulation is run, it becomes apparent that the differential distribution of resources in this world is sufficient in itself to create a partition of the world into classes where there are a few extremely wealthy individuals and a vast mass of others who are in constant danger of ‘dying’ from not having enough food.
We could then extend this model to represent something of the Roman world. We could give the agents a way of looking for help, of becoming a client of someone a bit wealthier than themselves. In return we could imagine that these ‘clients’ could offer support to their patron in turn. Perhaps the number of followers, and their relative ‘wealth’, could be translated into a score for ‘prestige’ which in turn affects the ‘patron’s’ ability to extract wealth from the world. What kind of artificial society results? In my ‘Patronworld’ model, which had its inspiration in the Wealth Distribution model, chains of connected individuals (that is, networks) do emerge from this dynamic, but they are fragile. One result seems to be that extremely high levels of gift-giving seem to go hand in hand with network collapse. It seems to do this by destabilizing the networks: too many people outside particular chains of patrons-clients are shut out of the system. Given the competitive building that characterizes the late Republic, this result is intriguing. It is a very simple model, to be sure, but one that foregrounds an important element of new models of the Roman economy: networks and social life. This kind of modelling also has the virtue that if one disagrees with the assumptions of the model, the code can be easily modified and adapted. In this way, model building is not an end point of research but rather a first step of a larger conversation (my own models may be found at the digital data repository Figshare.com and I welcome their use, adaptation, and improvement).
We need more and better networks drawn from historical and archaeological data. It is not enough, in contrast to Malkin, to use ‘networks’ as simple metaphor. Particular network topologies have different implications for the actors which make them up. If we are to make progress on the Roman economy, we need to explore the multiple networks of individuals and objects at multiple social and spatial scales. We need to turn our archaeological geographic information systems into computing environments in which agents can interact: at a stroke, we will have unified landscape archaeology, ancient history, and the study of ancient economics. Once we have this data, we can take our current understandings of the ancient economy, whether ’consumer city’, ‘primitive’; ‘modernising’, ‘bazaar’, NIE, or something else and translate them into an agent based simulation. If we can generate analogous networks to the ones we know archaeologically, then we might just have the wherewithal to argue that we have a model that tells us something useful, something new, about the past.
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 Tesfatsion 2006: 832.
 Indeed, many economic models fail to recognize that the spatial context of economic action undermines many of the basic assumptions of economic theory, Dibble 2006: 1515.
 The discussion is usefully treated in for example Scheidel 2010, Manning and Morris 2005, and Scheidel and von Reden 2002.
 North 1990, and its application to the ancient world in Frier and Kehoe 2007; Bang 2009; the various papers in Manning and Morris 2005; Scheidel’s forthcoming Cambridge Companion to the Roman Economy
 Frier and Kehoe 2007.
 Frier and Kehoe 2007: 119.
 Bang 2006: 79.
 Bang 2006: 80-4.
 Bang 2008: 197.
 Lo Cascio 2006: 225.
 Lo Cascio 2006: 231.
 Graham 2006b: 111-113.
 cf. Davis’ diagrams in 2005; 1998.
 Brughmans 2012; 2010.
 Brughmans 2012; Bentley and Maschner 2003:1.
 Knappett 2011: 10.
 Schortman and Ashmore 2012: 3.
 Schortman and Ashmore 2012: 2-3 citing Barrett 2000, Bourdieu 1977, Dobres and Robb 2000; Dornan 2002; Garnder 2007; Giddens 1984.
 Schortman and Ashmore 2012: 3-4.
 Milgram 1967.
 Buchanan 2002; Watts and Strogatz 1998; Watts 1999.
 Brughmans 2010.
 Shortman and Ashmore 2012: 4.
 Graham and Ruffini 2007: 325-331.
 Coward 2010.
 Weingart 2012.
 Brughmans 2012; 2010.
 cf. Wilensky and Resnick 1998: 4; Agar 2003; Gilbert and Troitzsch 2005: 199-202. Gilbert and Troitzsch is an excellent resource for learning how to build simulations.
 Tesfatsion 2006: 840.
 Tesfatsion 2006:843.
 Watts and Strogatz 1998; Barabasi and Albert 1999.
 Janssen and Ostrom 2005: 1496 citing Dibble 2006; Wilhite 2006; Vriend 2006.
 Berger 2001.
 Deffuant et al., 2002.
 Hoffmann et al 2002; Evans and Kelley 2004.
 Some of the earliest work being in Clarke 1968, 1972; see Graham 2006a: 53-4.
 The premier journal is the Journal of Artificial Societies and Social Simulation, jasss.soc.surrey.ac.uk.
 Barrett 2001:155.
 for instance Lehner 2000; Kohler, Gumerman and Reynolds 2005; Dean et al 2006; Graham 2006a; Premo 2006; Graham and Steiner 2008; Symons and Raine 2008; Graham 2009; Costopoulos and Lake 2010.
 Tesfatsion 2006: 852-3.
 cf. Wallace-Hadrill 1989.
 Bang 2006; 2008
 Doran 2011.
 Wilensky 1999.
 Bogost, 2007: 28-44.
 Ourednik and Dessemontet 2007.
 Wilensky, 1998.
 Published in Graham 2009.
 Graham 2009: 11.
 cf. DeLaine 2002 on patronage in building projects at Ostia.
 Malkin 2011: 18-9.
This plugin allows multimode networks projection. For example: you can project your bipartite (2-mode) graph to monopartite (one-mode) graph. The projection/transformation is based on the matrix multiplication approach and allows different types of transformations. Not only bipartite graphs. The limitation is matrix multiplication – large matrix multiplication takes time and memory.
After some playing around, and some emails & tweets with Scott, we determined that it does not seem to work at the moment for directed graphs. But if you’ve got a bimodal undirected graph, it works very well indeed! It does require some massaging though. I assume you can already download and install the plugin.
1. Make sure your initial csv file with your data has a column called ‘type’. Fill that column with ‘undirected’. The plugin doesn’t work correctly with directed graphs.
2. Then, once your csv file is imported, create a new column on the nodes table, call it ‘node-type’ – here you specify what the thing is. Fill it up accordingly. (cheese, crackers, for instance).
3. I thank Scott for talking me through this step. First, save your network; this next step will irrevocably change your data. Click ‘load attributes’. Under attribute type, select your column you created for step 2. Then, for left matrix, select select Cheese – Crackers; for right matrix, select Crackers – Cheese. Hit ‘run’. This gets you a new Cheese-Cheese network (select the inverse to get a crackers – crackers network). You can then remove any isolates or dangly bits by ticking ‘remove edges’ or ‘remove nodes’ as appropriate.
4. Save your new 1 mode network. Go back to the beginning to create the other 1 mode network.
A Small Greek World
Networks in the Ancient Mediterranean
304 pages | 21 illustrations | 235x156mm
978-0-19-973481-8 | Hardback | 24 November 2011
I was excited to obtain this book.
Unfortunately, this is a book about social network analysis in antiquity that does not, in point of fact, contain any social network analysis. Rather, Malkin uses concepts drawn from networks and theories of evolving networks as metaphors to reframe centre-periphery arguments about the emergence of the Greek world around the Mediterranean as a ‘small world’.
There is much that is good with this book, in terms of its description of colonization and the emergence of the Greek world. He offers up a theory of ‘backwards-propagation’ to explain how the colonies could often be more Greek than Greece. As a Canadian educated in the UK, I know that this is a very real – and timeless- phenomenon; it is indeed a useful concept to bring into the discussion. However, Malkin need never have invoked any network theories in order to use that concept. Peregrine Horden and Nicholas Purcell’s The Corrupting Sea achieved much by focusing on the idea of connectivity of micro-regions without invoking social network analysis; this work is essentially a deeper exploration of that idea.
The broad strokes of Greek colonization are well known; there is ample material there for network studies of many different kinds (including work that seeks to generate likely networks, for example as in Rihll & Wilson 1991, the work of Tim Evans, Ray Rivers, and Carl Knappett, my own Travellersim). Malkin lays out the groundwork of the relevant concepts in chapter 1. But on p18 and 19 one reads,
Graphic illustrations of wide-ranging Mediterranean networks in the form of connective graphs usually prove to be unhelpful. Two-dimensional representations of connectivity mostly turn out to be messy “spaghetti monsters” with very long verbal explanations that are needed to accompany them… I have opted for the larger canvass of what seems to me highly probable at the risk of not presenting statistics and formulae that I am incapable of offering due to the state of our sources of knowledge”
Malkin takes pains on p16 to distinguish between ordinary (whatever that may mean) ‘networks’ and the ‘networks’ of network analysis, as if the two were distinguishable. They are not. The only difference is that in one we are using a metaphor, and in the other, we have taken pains to try to outline as fully as possible the connections relevant to the question we are asking, to understand the implications of the topology (yes, the statistics) for what they might mean for history. To invoke a small-world (a precise concept in network terms) without actually measuring to see if small world conditions are fulfilled does damage to the concept and to the analysis.
Elijah Meeks has recently written about developing conventions for the representation of network data, drawing on the long history of cartographic literacy. As far as Malkin’s critique of the visualization of networks go, it’s well founded: but the visualization has never been the endpoint, the raison d’etre, for the exercise. It’s the statistics. If you don’t know the shape of the thing, the important nodes (cities, individuals, extra-urban sanctuaries, what have you), how can you claim to be doing any sort of network analysis?
Scott Weingart has written about ‘halting conditions’, about knowing where to draw the linewhen your data are necessarily complex and in practice, infinite:
The humanities, well… we’re used to a tradition that involves very deep and particular reading. The tiniest stones of our studied objects do not go unturned. The idea that a first pass, an incomplete pass, can lead to anything at all, let alone analysis and release, is almost anathema to the traditional humanistic mindset.
Herein lies the problem of humanities big data. We’re trying to measure the length of a coastline by sitting on the beach with a ruler, rather flying over with a helicopter and a camera. And humanists know that, like the sandy coastline shifting with the tides, our data are constantly changing with each new context or interpretation. Cartographers are aware of this problem, too, but they’re still able to make fairly accurate maps.
It is not acceptable for ancient historians to bemoan the incompleteness of our sources – to use that as a crutch for not doing something – and then to go on and write another 224 pages. We’ve been studying the ancient world for several centuries now. Surely we’ve got enough material to be able to draw a line, to map something out, yes?
Should you buy this book? By all means, yes. Its roundup of the major themes and ideas in network studies in chapter 1 is valuable, and will no doubt be useful for those wishing to do formal network analysis, insofar as it establishes network theory in the broader classicist conversation. I’ve focused primarily on the first chapter in this review, since much of my teaching and research at the moment explicitly concerns network analysis in antiquity. The materials presented in subsequent chapters (Island Networking and Hellenic Convergence; Sicily and the Greeks; Herakles and Melqart; Networks and Middle Grounds in the Western Mediterranean; Cult and Identity in the Far West) do indeed move the conversation on from stale center-periphery models, and should be lauded. It would perhaps have been better though if it had not been framed in terms of a theoretical/methodological framework that is not, in fact, used.
[disclosure: I asked Oxford UP for a review copy when I saw it in the catalogue, in the hopes that I could use it as a text in an upcoming course on digital antiquity. I do not think I will be doing so, given my issues indicated here.]