Author Climbing in the Queyras, Summer 2013

Saturday, September 15, 2012

Fourier Finds Caesar:

A Study in the Physical Evidence of Roman Surveying and Land Usage Using Image Analysis and Periodic Functions

Landscapes are dynamic constructions, with each community and each generation imposing its own cognitive map on an anthropogenic world of interconnected morphology, arrangement, and coherent meaning.

--Kurt Anschuetz, An Archaeology of Landscapes

Finding the physical and epigraphical remains of Roman surveying and centuriation throughout the Roman world remains an area of research that currently engages only a few historians of cartography. In the past the practice of Roman surveying was studied by many important Roman historians like Theodore Mommsen and Max Weber[1]. There remain however, many difficult and unanswered questions about Roman cartography, and the lack of actual extant maps has made me begin to look elsewhere for information that might shed light on its origins and methods. My current research on this problem employs GIS and image analysis to historical aerial photography and remote sensing imagery. It is my hope that in the near future it will produce the first complete map of North African sites that shows both the extent and orientation of Roman mapping. Several authors, such as Rita Compatangelo [2], J.W.M. Peterson [3], D.J. Bescoby [4] have pioneered the use of various mathematical transforms in the analysis of remote sensing imagery for the purpose of finding new sites and orientations. I have started to apply these methods in combination with edge detection algorithms in order to calculate the extent of Roman surveyng and the various types of orientations associated with the physical remains of limites.

The physical remains of Roman centuriation take on a number of sizes and orientations, but are typically discovered through the outlines of the limites that seperated the various regions from one another. Limites or Limes (singular) can be defined as a man-made boundary or balk, that is uncultivated and wide enough to form a road or pathway, which divided centuriae or other land division units from one another. These can take many forms from simple paths all the way to larger structures like the main roads of the decumanus and kardo maximus that were centrally located in a surveyed region. The feature that makes these remains discoverable through the use of transformational techniques is the fact that they appear on the landscape as periodic phenomena. This simply means that the pattern of centuration repeats itself over areas of the landscape, showing up as linear freatures that appear in remote sensing imagery as periodic pattern of grids over fixed distances. One of the most useful ways to study periodic phenomenon, at least from a mathematical perspective, is through the use of Fourier Series and transforms [5]. These transforms model any periodic phenomenon that we might be ineterested in as a infintie series of cosine and sine functions of varying frequencies.

This sum can be expressed more conviently through the use of complex exponentials which are easier to work with algebraically. Using a discrete and algorithmic version of the Fourier transform, known as the fast Fourier transform (FFT), Peterson and Compatangelo, in truely ground breaking papers, showed that one could calculate the most common period found in a group of periodic linear features found on more modern maps. I say the most common period, because many of the linear features found on the landscape today are subdivisions of modern and medieval origin, and it is sometimes extremely difficult to determine the date of the features whose period the transforms are measuring. As an illustrative example, one can think of the linear features found in the landscape as a more complex superposition of the images in the figure shown below. In the figure we see that there are linear features that repeat themselves and that in each of the figures they have different periods of repetition. One of the figures also has a different orientation than the other two. What we see in the landscape is typically a combination of all of these in the same region and on the same remotely sensed image. Peterson used the FFT to generate periodograms that produced the most common harmonics in a series of regions dislaying linear features that he took from 19th Century Ordnance Survey Maps of Scole-Dickleburgh area in South Norfolk. What the periodogram does is allow one to pick out the frequency of the linear features and the larger harmonics. An simple example of this is shown in the figure below. The periodograms not only show the most common distances between the linear features found on the map or on the satellite image, but they also yield a series of harmonics that might have the physical meaning. Larger harmonics beyond the most common one may show subdivisions in the original survey or different grid patterns from the type one is looking for. Because we are not only interested in the distances between linear features in the landscape buy also in their orientation, we have employed a second technique known as a Radon transform. This technique has been used by Bescoby to detect Roman boundaries in aerial photographs in Albania. The strength of this method is that it allows for the calculation of the angle and hence the orientation of the series of linear features. When combined with the two-dimensional version of the Fourier transform, this allows a complete characterization of the grid formed by the limites of Roman surveying. The Radon transform can be expressed by the equation below and its operation can be seen in the graph shown in the figure. Finding the size and orientation of linear features in a landscape lets us compare what we have calculated with known patterns of centriation found in literary and epigraphical evidence, such as that found in the 5th or 6th century Corpus Argimensorum. According to Hyginus, one of the authors found in this compilation of Roman surveying texts, the typical layout for an area of surveyed land is shown below. The letters and numbers define the parcel of land and very often appear as eppigraphic inscriptions on surviving boundary stones. The main intersection shown in the figure is that of the kardo and decumanus maximus which are the beginning points of any Roman survey. A typical kardo or decumanus can be seen in the photograph below that I took in a heavily centuriated area around Carthage just north of Tunis. The distances that the Romans typically used and their various names are shown in the schematic, with a century measuring 2400 Roman feet or about 705 meters. Many of these grids would however have been further subdivided in a variety of schemes that are not easily dated using physical evidence. The research that I have been doing has concentrated its efforts on the non-coastal regions of North Africa, taking in parts of Tunisia, Algeria and Libya. Below are two satellite images of the areas around Dougga and El Jem in Tunisia both of which are the sites of important Roman towns and ruins.

In both of these photographs one can see a variety of linear features that may or may not be associated with Roman activity.

It would be interesting to know the extent to which the Romans actually produced maps of these areas considering their overall importance to the history of Roman colonization and occupation in the region. El Jem for example contains one of the best preserved Roman colesseums in all of Africa.

To apply these algorithms to remote sensgin imagery it was necessary to clean them up and enhance the linear features using edge detection algorithms. An example of this is shown in the figure below.

Once this is accomplished and the various transforms have been applied we can begin to compare the results with known grids based on our knowledge of Roman practice derived from the epigraphic and literary evidence.

Using ArcGIS I have generated maps with overlays showing the orientation and extent of the surveyed region under study. The map below shows a single division into centuriae around Enfida, Tunisia. The map below shows both a division into centuriae and into a second subdivison which probably dates from a later time. [1] There are many studies of Roman surveying. For a modern bibliography see Brian Campbell, The Writings of the Roman Land Surveyors, Society for the Promotion of Roman Studies, 2000.

[2] Rita Compatangelo, Un Cadastre De Peirre Le Salento Romain, Annales Litteraires de l'Universite de Besancon, 1989

[3] John Peterson, Fourier Analysis of Field Boundaries, in G. Lock and J. Moffet, CAA91: Computer Applications and Quantitative Methods in Archaeology 1991. BAR International Series s577. Oxford, 149-156.
[4] D.J. Bescoby, Detecting Roman land Boundaries in aerial photgraphs using Randon transforms, Journal of Archaeological Science (2006) 33, 735-743. See also, J. S. Bailly et'al "Agarian Landscapes linear features detection: application to artificial drainage networks" International Journal of Remote Sensing 29 (2008) 3489-3508 and E. Magli, Pattern Recognotion by means of the Radon transofrm and the continuous wavelet transform, Signal Processing 73 (9990 277-289.

[5] See any of the recommended books on Fourier Analysis on this blog or for a good introduction to the subject see L. Solymar, Lectures on Fourier Series, Oxford University Press, 1988.

Monday, September 03, 2012

His aqueducts and his cartography:
Frontinus, Roman law and the missing maps of the waters of Rome
The foundations of the science of land measurement lies in practical experience, since the truth about sites or area cannot be expressed without lines that can be geometrically measured.
--Frontinus, De arte mensoria

According to R.H.Rodgers, 'obscurity veils the early career of Julius Frontinus,' who in the year 97 was appointed curator aquarum of the city of Rome. Frontinus wrote two groups of texts that are important to us here in our study of Roman cartography; those being De Aquaeductu urbis Romae and a series of texts on Roman surveying. The work that remains extant on Roman surveying is found in the Corpus Agrimensorum and is very fragmentary. Karl Lachmann (shown below), who worked on the first edited edition of the text, believed that the full work comprised two books, the first consisting of De Agrorum Qualitate and De Controversiis, the second work containing De Limitibus, De arte Mensoria and some other more fragmentary texts from Urbicus, another writer on Roman surveying who may have copied his work from the now missing parts of Frontinus.

Besides his interest land surveying however, Frontinus is more well-known for his text on the aqueducts of Rome. (For more on this see the website run by Katherine Rinne) In the text of De Aquaeductu urbis Romae he discusses the fact that he made maps used in the administration of the aqueducts. In the prologue to the book Frontinus refers to his work as a commentarius, and explains that it is a collection of data and other materials that he made primary for 'himself'. The contents of the book are quite technical and numerical, pertaining to sizes of individual aqueducts, the dates they were built, pipes and their sizes, the quantities of water delivered and legal matters relating to the right of private individuals to the use of public water. Although most of the material serves an adminstrative aim some of the text deals with methodological issues and it is these that are of interest for historians of cartography. In Chapter 17 of his book on aqueducts Frontinus writes:

Non alienum mihi visum est longitudines quoque rivorum cuiusque ductus etiam per species operum complecti. nam cum maxima huius officii pars in tutela eorum sit, scire praeposiutum oportet quae maiora impendia exigant. nostrae quidem sollicitudini non sufficit singula oculis subiecisse; formas quoque ductuum facere curavimus ex quibus adpareret ubi valles quantaeque, ubi flumina traicerentur, ubi montium lateribus specus adpliciti maiorem adsiduamque petendi ac muniendi vi exigerent curam[1].

Which translates as:

It has seemed to me not unfitting to include as well as description of the lengths and courses of each aqueduct, according to the classifications of construction. Because the greatest part of the duties of this position lies in the maintenance of the lines, the man in charge must know what thongs demand greater outlays. My sense of responsibility has not been satified with personal examination of particular items. I have also taken care to prepare maps of the lines, from which it is clear where there are valleys and how great they are, where rivers are crossed, and where channels attached to the sides of mountains demand greater and constant attention...for their repair.

Hence we learn here that Frontinus had detailed maps made of the aqueducts describing not only the lines themselves but also the topography of the surrounding countryside that they traversed. According to Harry B. Evans, in his Water Distributon in Ancient Rome, (Michigan, 1994), "Frontinus' mapmaking merits closer attention." Evans postulates that Frontinus' data, which he gives in the text on aqueducts, is in fact derived from the maps that he had made and that those sections of the text describing the actual lines are commentaries on the maps themselves. There are other indications in the text that Frontinus is using maps as he pinpoints some of the sources of the aqueducts by using exact spatial references to the existing road system outside of Rome.

Although none of Frontinus maps survive there are maps on inscriptions that show what aqueducts maps may have looked like. An example shown here (CIL 6.1261) displays in graphic form the lines of an aqueduct and the epigraphy gives indications of water flow and on what legal terms individuals may draw water from particular lines. The inscription contains the names of the people who shared the channel that came off the aqueduct, the volume of water that they where alloted, and the scheduled times that they could take that allotment.

The inscriptions translates as:

a. for Thyrsis, freedman of Augustus, two pipes from the second to
the...hour, on the fourth day before... b. for the freedman of C. Julius
Caeser, C. Bicoleus Rufus Squaterianus, one pipe... c. to the Aufidianum of Julius Hymetus, two pipes from the second
to the sixth hour... d. To Vibius...pipes, to C. Bicoleus, Freedman of C. Julius
Caesar,... pipes from the sixth hour until sunset...

There are several known examples of this type of inscription and another is shown below (CIL 14.3676). This inscription describes a shared channel related to the supply of water at Tibur, a rural area outside Rome. The stone containing the inscription is found built into the side of the Church of Saint Peter at Tivoli and it preserves a fragment of a map showing two channels. The inscription itself lists the people to whom the water is to go to, the amount of water they have been alloted, and the time of day when it may be taken. (for more on water rights see Cynthia Jordan Bannon, Gardens and Neighbors: Private Water Rights in Roman Italy, Michigan, 2009). As Evans says, all of this deserves further work....and can help us understand some of the lesser known aspects of Roman cartography and its application.

[1] I have used the new edition of Frontinus by R.H. Rodgers, "De Aquaeductu urbis romae", Cambridge Classical Texts and Commentaries 42, 2004.