[below is the draft text of a talk I will be delivering on March 16th, 2012, at Dumbarton Oaks. Usual caveats apply. If you spot anything odd, please let me know.]

Networks from Artefacts

 Trevor Hodge, a distinguished professor of classical archaeology and a former professor at Carleton University, passed away recently.[slide 2] I was supposed to attend a lecture of his in early February, but due to the regular rhythms of life at a university, meetings and duties conspired against me and I never heard him speak; and now I’ll never have the chance. I deeply regret this, because I wanted to tell him what an impact his book on Roman aqueducts and water supply had on me as a young graduate student.

Through Hodge’s book, I had a connection to Prof. Hodge that always felt personal. We understand that kind of social connection that can exist through the network of author – book – reader. That kind of relationship has influence, and matters: otherwise we would never publish anything [slide 3].  As a student, Hodge and the aqueducts led me to the construction industry of Rome, and thence to the brick industry more specifically. At first, it seemed a dry and sterile field. But then I encountered formal social network analysis, and suddenly, I had real people on my hands again, real people whose actions in the past I could dimly perceive.

In the same way that books can connect us, artefacts can become nodes in a network. [slide 4] 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, it becomes possible to draw a network. In which case, theories of evolving networks & social network analysis should concern us all. Tom Brughmans recently argued (2010) that the ‘social’ should be taken out of the analysis, that we should just be concerned with the networks themselves. I’m not sure I entirely agree. Fiona Coward (2010) wrote,

” … the archaeological record is not a passive by-product of social relationships: rather, it is social relationships (Gamble 1999, 2007; Barrett, 2000[1988]; Knappett 2005). 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:

“Methodology appropriation is dangerous. Even when the people designing a methodology for some specific purpose get it right – and they rarely do – there is often a score of theoretical and philosophical caveats that get lost when the methodology gets translated. In the more frequent case, when those caveats are not known to begin with, “borrowing” the methodology becomes even more dangerous.”

Demystifying Networks Parts 1 & 2 by Scott Weingart

In which case, let me show you how I draw networks out of the urban fabric of Rome and Constantinople trying to navigate the shoals of this dangerous method, and let us consider what these networks might mean for understanding the way Constantinople and her people worked. And then let’s push it a step further by reanimating those networks with agent based models. Let’s raise the dead.

—

We’ll start with Rome. This is a typical second century stamped brick from the industry centred on Rome. Other major cities all had their own industries (and occasionally, loads of stamped brick from places like Rome turn up in places like North Africa or Sardinia). The interpretation of stamped brick throughout the Roman world ultimately comes down to recasting the local version in light of what scholars believe was happening around the City of Rome.

Brick stamping at Rome began in the first century and ran, with some interruptions, until the 6th century. A typical second century brick looks like this [CIL XV.1 861][slide 5]

EX FIG ASINIAE QVADRATILLAE O D C NVN

NIDI FORTUNAT LVCIO

QVADRATO COS

Signum: pine nut.

The consensus is that these elements represents an abridged version of the contract between the officinator and the dominus. Locatio-conductio contracts were one of the usual means of letting out building contracts. In this context there are two varieties. Locatio rei refers to the plant and property used, while locatio operis refers to the finished product itself. Both types firmly involve the dominus in production. If the stamp is an abridged locatio operis contract, then the dominus paid the officinator to make a certain amount of bricks. If on the other hand, the stamp refers to locatio rei, then the entrepreneur is the officinator, contracting with the landowner to use his land for the officinator’s own profit.

These are, of course, social relationships, whatever kind of contract. Brick and brick stamps are ideal things for archaeological network analysis. To produce brick means having the ability to command resources, to control land, and to be tied into the webwork of patronage that physically creates humanity’s machine for living, the city.

In terms of how the stamps actually functioned in day-to-day life, one can imagine them serving multiple roles: distinguishing the output of different officinatores working side by side; for compensation or verification that the work has been carried out; to indicate the products of different figlinae belonging to one dominus; or different domini who used the same warehouse. From legal texts and other notices in the ancient literature, it seems likely that in Rome and in Constantinople, a certain proportion of bricks were levied annually for maintenance of public works. Brickstamps from Constantinople sometimes bear the phrase, ‘indiktionos’, ‘of the indiction’ without referring to the year in the cycle, which Bardill takes to mean that they were stamped to indicate that tax liabilities imposed by the annual indictio on the owners of clay lands had met their obligations.

***

So that’s a potted history of brick stamp ology. The practice of stamping bricks at Rome continues into the reigns of the Gothic kings, and so is contemporaneous with stamping practice at Constantinople. A typical stamped brick from Constantinople is more difficult to interpret, but again can contain names and years and other signs in various combination. The question is, what can we do with this information? What might it all actually mean, when put into perspective?

—

There is a lot of information in a typical stamped brick, even if we’re not always clear what it might mean, or what function, precisely, the stamps served. The most typical, and basic, use of brick stamp data by scholars is to help with dating built structures. However, it is also possible to do as Janet DeLaine has done, looking for patterning in the names on bricks from particular buildings, looking for interconnections and tying what she knows to the local prosopography. She is able to identify social patterns of patronage behind the provisioning of materials. In a sense, what she has done is a kind of network analysis without the formal network.

The strong version of Delaine’s approach is advocated by Irad Malkin. Malkin writes,

“Two-dimensional representations of connectivity mostly turn out to be messy “spaghetti monsters” with very long verbal explanations that are needed to accompany them”.

For Malkin, because we can’t have total knowledge of a network it is better to not try to draw out a network. It is as if he views the whole point of networks as the visualization of the network, and any accompanying statistics as suspect. This rhetorical dodge allows Malkin to avoid having to deal with the formal problems of methodology from the outset. Visualizations are simply maps, and maps necessarily simplify. We _necessarily_ put a boundary on a network when we focus on it. Nevertheless, it is better to have some knowledge that can be formally outlined, than to have a hand-waving description that turns out to be infinitely elastic. We can’t know every parameter of an ancient social network. But with brick, we can come pretty darn close.

When we start thinking in formal network terms, we can see that brick is a potentially very rich source. The relationships between the various kinds of data preserved in stamped brick make the stamped brick a rich multi-dimensional fossil of past social relationships. Let’s draw these out and that’s just the epigraphy! [slide 6] Formal network analysis is the most appropriate means to tease out what all these relationships might mean for individuals in the past.

In my PhD work, I began knitting these various dimensions together into various kinds of networks. I performed archaeometric analysis of the fabric of both stamped and unstamped brick, collected from across the Tiber Valley. I was able to cluster bricks into groups sharing the same clay sources, detecting patterns of usage underneath the epigraphic data. Because I had chronological information, I was able to observe how this network changed over time. Similarly, I could knit stamped bricks together on the basis of intersecting names, of estates, workshops, brick makers, and landowners, observing how these changed over time. I was able to calculate various statistics for particular periods, seeing that in some periods, these networks resembled small-worlds and hence, I argued, were self-organizing and emergent: no government control required (there’s a venerable argument that all brick making around Rome was directed by the state). At other times they appeared exceedingly fragile. It was a picture of constant flux and dynamism.

I built a beautiful and elegant argument which I recognize now could be fatally flawed. Is a network connecting landowners and brickmakers a one mode or a two mode network? That is, are all the nodes the same kind of thing, or are they different kinds of thing? If we imagine it to be a one mode network – these are all humans, after all – then all is well. But if it is a two mode network, if landowners and brickmakers are fundamentally different kinds of actors, then some of the statistics I calculated are flawed because the methodology behind the many of the various statistical algorithms I ran assume one-mode. Network analysis can be dangerous.

So, for today’s paper, I went back to the drawing board. I reformed a network of stamp types to findspots in the hinterland of Rome in the Tiber Valley. I have not tried to decompose the epigraphic multi-dimensionality to any great degree (though I probably should do that some day). I then reshaped this network into two one-mode networks: stamps connected to other stamps by virtue of being found at the same location, and locations to locations by virtue of using the same stamps.  Ideally, I would do this for the city of Rome itself, but that is a job of epic proportions; for my purposes today, the Tiber Valley is sufficient.

And this is what you find [slide 7 locations to locations]. What does it mean? There are any number of metrics which could be computed, but the right one depends, I think, on the nature of the data, of what human process could result in these physical traces, these fossils. That’s why we cannot divorce the social from archaeological network analysis.

Let’s begin by assuming that whatever we’re seeing in a network of locations connected by similar stamped brick, is related to the consumption of building materials and thus to ideologies of construction. In the Roman world, construction is a kind of show, a kind of costly signalling that the person having the structure built has access to resources. None of the structures that these bricks came from, if the accompanying assemblages are any indication (polychrome marble fragments, for instance), were simple basic farmsteads; they all appear to have been housing a notch above the ordinary.

Evidence from stamped brick at Rome, and from Cassiodorus, attest to the existence of brick depots along the Tiber – Portus Licini, portus Corneli(i), portus Neapolitanus, and portus Parrae. Evidence from for example the Baths of Caracalla in Rome point strongly to the warehousing of brick; the prosopography of individuals named in the brick seems to suggest a strong patronage element to what gets warehoused where. In which case, an appropriate metric to analyse a network based on locations joined by shared brick types would be community detection, which is also known as modularity.

Modularity, as implemented in the Gephi network visualization suite, depends on finding localized patterns of similar linkages or sub-networks which can then be aggregated at ever larger scales; when it can’t be scaled up it defines that collection of nodes and links as a ’module’ or ‘community’. This particular algorithm was developed looking at cellphone data from tens of thousands of European customers, and seems to work well when tested against networks with known subnetwork structures.

Modularity is a property of the network that no one person within the network could possibly perceive. We can imagine though that communities would tend to have access to the same kinds and amounts of information, or be subjected to the same influences, due to these particular network linkages. The visualization is coloured according to community. There are about X communities here, which perhaps can be interpreted as brick depots serving the Tiber valley (since some of these types are known in Rome too, these depots could well correspond to the named depots known from other evidence).

Some brick types appear to be part of two or more communities, suggesting that domini or officinators have some choice or option in where to ship their bricks. These bricks tend to have higher betweeness scores, too. Betweeness centrality is a measure to which a particular node sits atop the most shortest paths between every pair of nodes in a network. When we resize nodes (brick types) according to betweeness scores, we see that these are at the intersection of communities. Betweeness would seem to imply some sort of social relationship between the warehouses.

The Tiber Valley network shows results that make sense, both from what we know about the structure and organization of the Roman brick industr. Let us turn to the catalogue of stamped brick of Constantinople collected by Jonathan Bardill.[slide 8]

There are approximately 2100 individual stamp types recorded in the immediate environs of Constantinople. I sent an undergrad on a fruitless errand to see if any are recorded at Byzantine sites around the Eastern Mediterranean, but so far we’ve drawn a blank. Instead, I had her create a list of type according to findspot, which I then imported into Gephi. I collapsed this two-mode network [slide 9] into two one-mode networks. Let’s look at the location to location by brick type network . I ran the modularity routine, and determined 7 distinct communities, 4 of which are isolated from the rest. The remaining 3 interconnect, as in the figure. By this analysis, there were at least seven depots serving the city. I calculated betweeness centrality for locations – the larger the node, the more ‘between’ the site. The Great Palace Area, the Land Walls, and the Church of St. Polyeuktos appear most central. The Hagia Sophia is also quite central. In a way, nothing surprising there, that the largest or most complicated building projects should be drawing the most resources. Civil, military split?

If we turn this network inside out, and consider brick types connected to brick types by virtue of being found at the same site, we perhaps glean a more nuanced picture of the Constantinople brick industry. If the first network is a view of consumption, this can be imagined to be a view based on production. The large ‘balls’ on the graph correspond to a dense local network of brick types all at the same location. What are more interesting are the brick types that join these balls together, and places where the balls simply do not connect with the rest of the network. I ran both modularity (colours) and betweeness (size) again.

Modularity at first glance doesn’t seem to be as useful since there are a large number of unconnected bits and pieces; which perhaps indicates a combination of brick makers shipping to depots and directly to the site. (Total #=71). If we take the giant component, paring off the isolates, we end up with 11 communities  (47.56% of nodes are in the giant component; 64% of edges).  [Top 3 types w b/w central: 661.1a, 1394.1a 837.1a 966.1a, 730.1d]

There is a chronological question of resolution that needs to be addressed. These bricks range from the middle 5th century to the middle 6th century. Obviously, this network should be decomposed into sensible chronological chunks; brick demands it, I suppose. But, at the level of resolution we’re looking at here, I think that broad trends are preserved: modularity works, but betweeness should not be leaned on too much, other than implying a social connection between warehouses.

When you plot this network against the real-world geography of Constantinople , you see some interesting patterns there, too. Look at these long sweeping arcs. They connect sites along the coasts of both sides of the Bosporus to sites in the heart of the city. If modularity implies depot or warehouse, the distribution of bricks to these far flung places cannot have anything to do with economic rationality: there must be a social dimension. In point of fact, when I studied the Roman bricks from the perspective of archaeometry, there were very strong indications within the clay fabrics themselves. The patterns suggested that the use of brick was not bound by a purely cost-of-movement shortest-path type argument, like being consumed upriver from where they were likely made: such a movement was not ‘rational’ if we imagine brick to be a bulky, low-value and low significance product.

Obviously, this entire analysis represents a first pass on the data, highlighting some interesting trends that will need to be refined. But even at this rough level, when we reconsider these networks in light of my initial arguments for thinking of archaeological networks as social networks, we have the substrate for exploring ancient society in new, powerful ways. The static network analysis, which focuses on only two metrics, shows the brick industry of both Rome and Constantinople composed of communities and individuals balanced between multiple tensions. It holds the promise of a route into exploring the dynamic interplace between structure and agency.

I would like to conclude this piece by showing how we could reanimate these fossils of individual choices made in the past, preserved for us in brick, within the confines of a digital laboratory for simulation. Archaeologists and historians have had great success with this method explaining such complicated moments as the collapse of Anasazi settlement, the emergence of Bali water-temple networks, or the outcome of the Battle of Trafalgar. As far as I know, I’m the only Romanist playing this game at the moment, so please bear in mind the extremely tentative and provisional nature of this step!

The laboratory is the agent based (or individual based) modeling environment Netlogo . This is an open-source platform, with a relatively gentle learning curve and which has a strong track record in the social sciences. We use this laboratory not to raise the dead, not to simulate the past, but rather, to rigorously test the unintended or unpredictable outcomes of the interplay of our own understandings, our own mental models, of how life was lived in the past. If our understanding is correct, and our starting point is grounded in real data about the past (archaeology, literature, etc), then what emerges from the experiment must necessarily have truth value. On the other hand, if the results we generate are so counter-intuitive, so ‘out-there’, then we perhaps have learned that our initial understanding or data is flawed.

Let us create a population of artificial Romans or Byzantines, where each brick type stands for an individual person, and give that person the suite of connections preserved in the archaeology. [image slide 15, 16, 17 import routine] Let us then give them rules for behavior that are based on our understanding of how some phenomenon in the past worked – I would suggest patronage as the best choice. [slide 18] Each individual it should be noted is an individual: they might all have a capacity for remembering who they’ve interacted with, but some will have long memories, some will have short. It is a heterogeneous population. Then, we let these artificial individuals interact with each other according to their pattern of connections. I run this simulation in a world where we can imagine that the economic environment, an individual’s aversion to risk, and patterns of gift-giving matter in cementing patterns of patronage.

I haven’t done this yet for the Byzantine patterns [slide 19 represents a developing model], so my comments are limited to Rome. When we think of construction, especially public building, as a means by which a patron could make sure that economic benefits trickled down through his network of friends & clients, then a simulation of patronage based on patterns found in stamped brick makes a lot of sense. And what I seem to be finding is 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.

At least, in my simulation. It’s entirely possible that my understanding of how patronage works is ill-founded. But that’s the nice thing about doing these kinds of simulations. My simulation, my code, is completely available online for perusal, critic, and extension. I would be most pleased if you did so.

—

I’ve made the argument that archaeological networks are social networks. I’ve shown how I draw networks from archaeological materials, and discussed some of the appropriate metrics for understanding what these network topologies might imply for our understanding of the past. Modularity determines groupings of sites or artefacts that share some common social links. Betweeness can identify key sites or artefact types that act as linch pins for the entire system. I can see patterns of provisioning that seem to respond to social, rather than economic factors; in Constantinople, there looks like a clear civil, military split in the communities suggested by brick use. Then, I went out on a limb to show that once we’ve drawn these networks, the possibility exists that we can reanimate these fossils, and use them to explore questions about the past that previously only existed as thought experiments. They are a very particular kind of thought experiment, one that can be rigorously specified, shared, critiqued, and built upon.

In the same way I felt connected to Prof. Hodge through his book, these artefacts connected all levels of ancient society.  When I look at stamped brick, I see individuals, hard working folks enmeshed in a web of legal and social obligations. Computation & formal network analysis let me begin to untangle it.