Thursday, December 15, 2011

Written in Stone: Epigraphy, the Codex Iustinianus, and the Geography of Roman Petition and Response

Quacunque enim ingredimur in aquila historia vestigum imponimus.
[Wherever we step, we tread on one or another scene of history]
--Cicero, De Finibus, 5.5

This project centers around the epigraphy of Roman land ownership and environmental law, such as agrarian and water rights, and their relationship to the Codex of Justinian. Although the Codex records many of the imperial rescripts relating to these subjects, it does not contain most of the petitions that these recripts were written in response to. To look closely at this one must turn to legal records that have not been edited, shortened on interpreted by late-antique and medieval scribes and jurists. The only documents of this type are found in legal inscriptions, most of which survive from North Africa and the Middle East.

These inscriptions, when looked at through a more geographic lense, show regional variations in legal practice and shed light on how the Romans adapted themselves to differences in environment and the agricultural practises of the native populations in the provinces.

My research will consist in looking through the vast and very understudied collections of inscriptions from museums in Libya, Tunisia, Algeria, and other collections, along with writing geographical commentaries on some of the more famous inscriptions like Henchir Mettich, (pictured above in a photo I took in the storeroom of the Bardo in Tunis), Lamasba (Ain Merawa) and Aga Bey Koyu from the Usak Museum, along with many more.

Sunday, November 27, 2011

Finding the Antipodes: Mathematical Constructivism and the Changing Logic of Cartographic Objects, 1960-1975

Abstract of my AAG 2012 Paper

In mathematics everything is algorithm and nothing is meaning; even when it doesn't look like that because we seem to be using words to talk about mathematical things.
Even these words are used to construct an algorithm. ---Ludwig Wittgenstein

...a proof of the existence of a magnitude can only be seen as completely rigorous if it contains a method by which the magnitude whose existence is being claimed can really be found. ---Leopold Kronecker

We look upon maps not only as stores of spatially ordered information, but also as a means for the graphical solution of certain problems for which the mathematics proves to be intractable. --William Warntz

In the early years of computer cartography new levels of abstraction entered into the field of geographical analysis through the algorithmic development of theorems from pure mathematics. In an attempt to answer previously intractable geographical questions, concepts from pure mathematics, like existence theorems, whose basic logical structure contains statements that confirm or deny the existence of particular sets of mathematical objects, were employed in various computer mapping schemes. The development of these programs injected high levels of topological and algebraic abstraction into geographical analysis and changed the basic ontology of geographic objects. Existence theorems, although they provide logical proof for whatever mathematical entity they are claiming existence for, do not however, necessarily provide a way to find or calculate those objects. In the field of pure mathematics existence theorems had long been objects of controversy from both a practical and philosophical perspective and their use sparked debates among many mathematicians. Mathematicians and philosophers, like Leopold Kronecker and Ludwig Wittgenstein, questioned the utility of a mathematical proof that provided no algorithmic way to find the mathematical object whose existence is claimed, while others such as David Hilbert and Richard Dedekind, saw no conceptual or philosophical difficulties with their use. This debate among the so-called constructivists, like Wittgenstein, who believed that in mathematics “everything is algorithm”, and the formalists like Hilbert, has left a large body of philosophical literature that has deeply analyzed the ontology of mathematical objects. [1]

In the fields of geography and cartography, these theorems entered into early computer systems through the construction of practical algorithms that calculated particular sets of objects useful in geographic analysis. Two important papers that can be seen as case studies in the use of constructivist forms of existence theorems in early computer cartography were published in the series Harvard Papers in Theoretical Geography by William Warntz and his associates at the Harvard Lab for Computer Graphics and Spatial Analysis in the late 1960s and early 1970s. This series of papers developed algorithmic constructions of many existence theorems and two of the most interesting, because of the sheer complexity of the mathematics, the Borsuk-Ulam Theorem and the Ham Sandwich Theorem, were applied to real world geographic problems [2].
Besides using existence theorems, mathematical cartographers would also begin to re-conceptualize on a more general level questions about the use of pure mathematics and its role in defining the diagrammatic logic of maps. In an early lecture, later written as a discussion paper for the Michigan Inter-University Community of Mathematical Geographers, Warntz says that, "More than ever before geographers are using the tools of calculus, probability, topology, symbolic logic, the various algebras, geometries, for example, are being taken more literally than ever before." He elaborates on these comments by explaining to the reader that something as abstract and foreign to geography as Venn diagrams are being taken, "in a far more literal sense than they were originally intended and by substituting real space and attendent phenonema for ideal space and by insisting on the utilization of all geometric properties involved as well as just the topological ones, geographers can reinterpret, add to, and refine the conventional concepts in the methodology of uniform regional geography and provide it with a basis in logic." [3]

Many geographers at the time would push the concept logic form and notions from set theory further into geographic analysis and not just in the sense of a useful analogy. In a paper written for one of the classic compilations texts from early years mathematical geography called, The Philosophy of Maps, Warntz and others like Waldo Tobler, and William Bunge, would change not only the vocabulary used in analysis but would also alter the very form of its expression. In an article in the collection, called Some Elementary and Literal Notions About Geographical Analysis and Extended Venn Diagrams, Warntz would say that, "Maps showing regional classification can be regarded as logic diagrams. Mapping of sets is a general mathematical concept. Geographical mapping is merely a special case of this." [4] Warntz here sees almost a mereological or mereotopological relationship between the spatial extent of Venn diagrams and their isomorphic counterparts of geographic regions.

John Venn

It is quite remarkable that the two systems of logic that Warntz draws on in this paper, Venn diagrams and existential graphs, are both visual and not symbolic logical systems. Most of the work done in logic during the 20th century has focused on symbolic systems with little research, at least until quite recently, on the heterogeneous reasoning of the type Warntz is advocating. He says that, "It is part of our purpose here to extend the use of such diagrams to the mapping of geographical regions by making use of properties already inherent in Venn diagrams but as yet unutilized... We intend to apply spatial properties literally to real spatial distributions on the earth's surface..."

Venn diagrams can grow to extremely complex forms depending on the number of sets one is dealing with and recent research on the use of logical diagrams has shown that Warntz was ahead of his time in thinking that the spatial and geometrical component of logical diagrams would be useful analogs for spatial maps. [5]
As stated above, Warntz' paper calls on the work of Charles Sanders Peirce (above) and his existential logic diagrams, which he sees as mappings from non-spatial sets to geographical maps. Looking at the complexity of Peirce's systems, there is both an alpha and beta form depending on the required complexity, one wonders how deeply Warntz explored the subject of existential graphs. An important aspect of these graphs that Warntz thought useful for regional geographic analysis was the fact that a logic diagram can be drawn as a two-dimensional figure with spatial relations that are isomorphic with the structure of some logical statement. This is very important if one is going to try to apply set theory of the type Warntz is envisioning here, simply because these spatial relations are usually of a topographic nature.Logic diagrams, especially the type developed by Peirce (simple examples shown above with a page frm Peirce's notebook below), stand in the same relation to the various logical algebras as maps of areas stand in relation to their particular algebraic functions; they are simply other ways of symbolizing the same basic structure. [6]

In much of what Warntz has to say here we are reminded of the long way we have come when talking about set theory, topology and the formal properties of spatial structures and their relationship to cartography. One only has to look at books like Varzi and Casati's, Parts and Places: the Structures of Spatial Representations (MIT, 1999) [7] to get a feel for how our language and conceptual grasp of these topics has improved since Warntz and others involved in the early development of computer cartography were experimenting with what at the time were radically new ideas.
The current project envisioned here, which grew out of my research for the 20th century volume of the History of Cartography, will provide a mathematical and philosophical analysis of both of the Harvard papers mentioned above, along with others from this formative period that apply set theory and logical analysis, in an effort to show not only how constructivist methods migrated from mathematics to geography, but also to show how these new levels of abstraction changed the foundational ontology of geographic and cartographic objects. Using the philosophical debates that took place over things like existence theorems in the mathematical literature as a basis, this study will show that a foundational shift in the ontology of geographical objects opened the door to new conceptualizations of geographic space and formed the theoretical basis for the development of spatial logics and the current use of topological and abstract algebraic methods in geographical analysis.

[1] It is interesting to note that many early mathematical geographers had an interest in Wittgenstein. Waldo Tobler, in a private communication, told me recently that he was persuaded by Peter Gould (1932-2000) to take up the reading of Wittgenstein.
[2] The two papers are; Geography and an Existence Theorem: A Cartographic computer solution to the localization on a sphere of sets of equal-valued antipodal points for two-continuous distributions with practical applications to the real earth (1968) and The Sandwich Theorem: A basic one for geography (1971).
[3] A Note on Surfaces and Paths and Applications, William Warntz, Discussion Paper Number 6, Michigan Inter-University Community of Mathematical Geographers, 1965.
[4] The Philosophy of Maps, edited by John Nystuen, Michigan Inter-University Community of Mathematical Geographers Discussion Paper 12, 1968.
[5] For recent research on the logical status of Venn diagrams and the nature of spatial logic see, Eric Hammer (1995), Logic and Visual Information, Stanford CA: Center for the Study of Logic and Information; Nathaniel Miller (2007), Euclid and His Twentieth Century Rivals: Diagrams in the Logic of Euclidean Geometry, Studies in the Theory and Applications of Diagrams, Stanford CA: Center for the Study of Logic and Information and Sun-Joo Shin (1994), The Logical Status of Diagrams, New York: Cambridge University Press.
[6] For more on Peirce's Existential Graphs see Sun-Jo Shin's seminal study, The Iconic Logic of Peirce's Graphs, MIT Press, 2002.
[7] Achille Varzi and Roberto Casati, Part and Places: The Structure of Spatial Representations, MIT Press. 1999.

Thursday, September 29, 2011

A Cartographic Commentary on the Henchir Mettich Inscription from Central Tunisa: Roman Surveying in the Medjerda Valley

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

As noted in my previous post, the inscription from Henchir Mettich in the Bagradas valley of Central Tunisia is important as a window on the landscape archaeology of the region and the history of agriculture during the Roman empire, but it is also important for the history of cartography as it relates to Roman law and the running of imperial estates in the second century AD. As one can see in the example of face one below, this coming from a series of photographs that I took last year in Tunisia, the inscription is badly damaged.

The inscription was published as CIL 25902 and very different transciptions of it can be found in Kehoe's, The Economics of Agriculture on Roman imperial Estates in North Africa and in van Nostrand's, The Imperial Domains of Africa Proconsularis: an epigraphical study.

The most important part of the inscription from a cartographic perspective is to be found on side one of the column shown below as published in the CIL and as a lithograph from Toutain's L'Inscription D'Henchir Mettich: un noveau document sur la propriete agricole dans L'Afrique Romaine.

The text on the first side of the column talks in some detail about the subject of subseciva or unallocated lands. The word is the subject of much discussion in the Corpus Agrimensorum and generally means lands unsuitable for allocation to settlers, either sirutated between the centuriae and the outer boundary of a communities territory or within centuriae. The word literally means "cut off" or "cut away below".

For example, Frontinus talks about the fact that he knows of fifteen different types of 'land dispute',
"...the position of boundary markers, a straight line boundary, boundary, site, area, ownership, possession, alluvial land, territorial juristdiction, subseciva, public places, places omitted and not enclosed, sacred and religious places, control of rain water and rights of way."

He continues later in his text on 'land disputes',
"A dispute over subseciva occurs when some or all of a centuria has not benn allocated and is possessed. Or if an adjacent landholder or someone else occupies any land from the edge of the allocated area, this also comes under disputes involving subseciva."

Hyginus also has much to say about subseciva. In his descritpion of categories of land he tells us that,
"Certain areas that protrude beyond the type of land which is curved or has angles, and are divided off by straight lines, are called subseciva, that is, pieces of land that remain when the boundary lines have cut them off and retain the character of peripheral areas."

The discussion of subseciva in the Henchir Mettich inscription begins after the dedication ends in line 6.

...qui eorum [i]ntra fundo Villae Mag-
[n](a)e Varian(a)e id est Mappalia Siga, eiseos agros qui su[b]-
[c]esiva sunt excolere permittitur lege Manciana
ita, ut eas qui excoluerit usum proprium habe-
at. [...]

The translation of this part of the column is not easy, but generally it says,

"To those coloni (who will have farmsteads) within the boundaries of the estate of Villae Magna or Mappalia Siga, who wish to cultivate more fields, permission is given to cultivate those fields which have not been alloted (subseciva) or have been classfied as unused, under the terms of the law of Mancia; namely that he who cultivates this lands shall have them for personal use."

One can infer from this that the land belonging to the Villa Magna was originally mapped and surveyed and then distributed to individuals, becoming some form of ager privatus. It certainly proves that this particluar area had boundaries drawn even though there are currently few physical remains of the Roman centuriation lines. Epigraphic evidence for Roman mapping has not been studied in a large scale fashion before and I hope to published my complete GIS of this information, at least from North Africa and Southern France, in the next year or so. For those who are interested I show the other four faces below...

Click on images to enlarge

Face II (above), Face III (below ), Face IV (below III)

Wednesday, September 07, 2011

Geometrical Problems from the Corpus Agrimensorum :
Mollweide meets Mommsen

A representation is made with a purpose or goal in mind, governed by criteria of adequacy pertaining to that goal, which guide its means, medium and selectivity.
--Bas Van Fraassen

The group of Roman surveying texts known as the Corpus Agrimensorum have provided a great deal of information regarding the actual practices of Roman surveyors in the field and given scholars insight into how the Romans allocated and measured land. My current project in locating and mapping the surviving remains of Roman surveying in North Africa takes its starting point from this 6th century compilation of surveying manuals. The texts themselves and the illustrations attached to them have attracted the attention of many scholars in past including historians of Roman law and agrarian practices such as Theodor Mommsen and Max Weber. In this sence the historiography associated with the texts is almost as interesting as the texts themselves.

What is less known about this historiography is the attraction the texts have held for more mathematically inclined historians of cartography such as C.B. Mollweide. Mollweide is best known as map projectionist, but also did fundamental research into some of the unsolved geometrical problems found in the Corpus.

One of the most interesting of these problems concerns the method for finding south. In the Corpus there are several methods given for this, but the one that interests us here is that given by the writer, Hyginus.

There is also another method of obtaining South, by marking three shadows. On level ground we shall set up a gnomon AB, and note any three of its shadows, CDE. These shadows we shall mark with the set square, to see their distances from each other. If we set them up before noon, the first shadow will be the longest; if after noon, the last. We shall then draw these shadows in proportion by a footrule... Let AB be a gnomon, B the ground. Let us take the longest shadow and mark it [i.e. its end opposite to B] on the ground as C; the second likewise D, the third E... Let us project hypotenuses from C on to A and from D on to A. Now with centre A and radius E let us draw a circle. Then let us project lines parallel to the base, i.e. ground, on to the perpendicular [AB] from the intersections of the hypotenuses and the circumference, from F on to G and from I on to K. Then we shall apply the longest line, GF, to the largest shadow, and from B we shall mark out [the length of] GF ; the second line to the second shadow, and we shall mark out [the length of] KI. Then from F and I we shall project a straight line, and likewise from C and D, the shadow ends. These two lines will meet at T. Join TE; this will be east-west.

The above text by Hyginus is accompanied in the Codex Arcerianus A by the figure shown below.

The figure as drawn by the scribe is however totally inadequate to explain the complexities of the method outlined by Hyginus and one has to question its purpose in the manuscript and whether it was in fact added to the text by a later copiest with less understanding of the method. Mollweide analyzes the text in an article 'Erlduterung einer in der Scriptoribus rei agrariae. . . gegebenen Vorschrift..' published in Zach's Monatliche Correspon-denz zur Beforderung der Erd- und Himmelkunde (Volume 28, 1813. p. 396-425).

Click on Figures to enlarge

The method that is being described in the text by Hyginus is extremely complicated and there are open questions concerning the level of mathematics and solid geometry involved.

Mollweide's solution is a complex affair and according to Dilke the method as described by Hyginus probably goes back to Alexandrian mathematical scholarship that has been lost but that must have been dependent on Apollonius' Conics.

The modern solution that Dilke adapted from Mollweide can be condensed to the following along with the figure below:

ABC, ABD, ABE are right-angled triangles. The lines CA, DA, EA go towards the centre of the sun. The arc EIF is part of a circle forming the base of a regular cone, parallel to the sun's daily round and so to the equator, and FI is a chord of this circle. Since GF is equal and parallel to BL, FL will be equal and parallel to GB; similarly IM to KB. As FL and IM are parallel to AB and so to each other, they lie in a plane in which FI and LM lie. But FI is also in the plane ACD, and LM is in the horizontal plane BCD; so FI is the intersection of the plane FIML with the plane ACD, and LM the intersection of the plane FIML with the horizontal plane BCD. As the plane ACD is cut by the horizontal plane at CD, which when produced meets LM produced at T, it follows that T is in the plane ACD and also in the plane FIML, and so is a point on the common intersection of both planes, i.e. of FI produced. Since the latter lies entirely on the plane of the circle through FIE, T is also in this plane, but likewise in the horizontal plane BCD, and so is a point on the common intersection of both planes. Since E is also such a point, it follows that ET is the intersection of a plane parallel to the equator plane with the horizontal plane, and so parallel to the east-west line.

One can see how different the figure which displays the actual construction as it described by Hyginus is from the original manuscript illustration.

Friday, May 20, 2011

The Morphology of the Early New England Landscape:
Searching for the Lost Maps of Henry David Thoreau

New York Times/Mattson Lecture
October 16th
Osher Map Library
University of Southern Maine

An article based on this lecture and intervening research will be pubished in the March 2011 issue of the Concord Saunterer: A Journal of Thoreau Studies.

The human organism has rarely been subjected to a severer test than the study of scientific problems, nor is there a truer hero than an investigator who never loses heart in a life-long grapple with the powers of the universe. It requires courage of the highest order to stand for years face to face with one of the enigmas of nature; to interrogate patiently, and hear no answers....
..................................................................................................................---Clarence King

Synopsis of the text of my lecture at the re-opening of the Osher Map Library and the "New Directions in the Study of Early American Cartographies" Conference...

In April of 1858, Ralph Waldo Emerson, in a letter to his friend H.S. Randall, wrote that, “Thoreau’s study seems at present to be equally shared between natural and civil history,” and that “he reads both with a keen and original eye.”

The civil history that Emerson refers to here is the history of the early exploration and discovery of the North American continent, especially the northeastern coast of New England and Canada. During the last 12 years of his life, from about 1850 thru 1862, Henry David Thoreau dedicated himself to historical and scientific studies that have either been ignored by or have puzzled generations of his commentators. What was the author of Walden and other works of transcendental literature doing out “in all weathers” as Emerson would say, counting tree rings, measuring the differences in the magnetic variation of compass needles, mapping the depths of streams or listing the blooming of plant species. Why was he borrowing the earliest exploration narratives of the New World from the Harvard Library, taking detailed notes on the names of places and the plants and animals mentioned, and making scaled copies of some of the earliest maps of North America?

During these last, but extremely productive, years of Thoreau’s life his interests turned sharply toward these types of more empirical and less transcendental studies—Thoreau being less influenced in his work at this time by Emerson than by the geographically oriented science of Humboldt and Darwin. Thoreau believed that the secrets of nature, and of humanities place within it, were ultimately revealed by identifying what was significant in the everyday world and that this in turn depended on meticulous attention to and an accounting of, the commonplace.

In this spirit Thoreau’s writings such as the Maine Woods, Cape Cod, Walden, A Yankee in Canada, his natural history essays, and of course his journals have occasionally been probed by humanist geographers and linked with the beginnings of modern environmental thought…this linkage stems mostly from Thoreau’s intense concern with the concept of place and his ability to see deep connections between historical process and environmental change.

Tonight I am going to talk to you about this linkage in a slightly different way than those geographers and historians who have probed Thoreau’s writings…for tonight rather than concentrate on his published works…I am going to speak with you about his cartography and how Thoreau’s cartographic explorations provided a link in his mind between natural and civil history… a link that led him to a very modern sense of man’s place in nature. To do this I am going to discuss, in more detail than perhaps has been done before, several important aspects of Thoreau’s mostly unknown and certainly understudied cartographic works
The first aspect, and perhaps the most important for his technical understanding of cartography and the process of mapmaking, was his work as a land surveyor. This work gave Thoreau the ability to look at maps critically and to understand not only their mathematical limits but also their broader cultural meaning. It also allowed him to wander the fields and woodlots of Concord and to observe nature closely in all seasons…in a way that his fellow transcendentalists certainly never would have.

The second aspect, and for the most part the driving reason for his engagement with early American cartography, was his interest in the history of the indigenous peoples of the north east. Thoreau would take nearly 4000 pages of notes on this subject…none of which has yet to be published and all of which are mostly unknown even to Thoreau specialists. In the course of this note taking Thoreau would copy and comment on many of the early maps of the northeastern United States and Canada by such seminal figures as Champlain, Ortelius, Smith, Verrazano and Wytfliet.

Finally, I am going to present to you two new maps that have recently been attributed by me to Thoreau and discuss my search for some of the other missing maps that he copied and annotated.

Some of what I am about to say might sound to some of you slightly academic, but really my talk tonight it is about something quite humble and speaks to the very heart and reason of why we are all here this evening. What am speaking about in the end is a story about a man in a Library, much like the one we celebrate this weekend, with a notebook, some old maps and his imagination on fire…

I am going to begin with one of those notebooks, namely Thoreau’s field notebook in which he kept the rough notes from his surveying activity. Even though we are talking tonight about Thoreau’s maps, it is with a pencil and a notebook that he truly found his way in the world…and we will have reason this evening to look at many of Thoreau’s notebooks.

The field notebook appears on the surface uninteresting as it is filled for the most part with measurements and locations…places around Concord, MA that Thoreau surveyed. But it provides a detailed record not only of how Thoreau worked but also how he approached the more technical aspects of cartography and we shall return to this notebook many times this evening. Thoreau surveyed many places around Concord and the list of his clients reads like a library of early American authors. Places like Bronson Alcott’s farm shown here.


Thoreau set himself up as a surveyor in late 1849 and by the end of 1851 was recognized as one of best and most accurate operating in the region. The question of exactly how Thoreau learned to survey is for the most part an open one but it does appear that he was mostly self taught. In early April of 1850 Thoreau would borrow from the Harvard Library a copy of Davies’ Elements of Surveying and navigation , [we will see a great deal of Library use by Thoreau this evening.] A copy of the 1847 edition of Davies was also owned by Thoreau. Davies was one of the most widely used books on surveying during the middle of the 19th century and with Galbraith’s mathematical tables, also borrowed from Harvard, represents a solid introduction to the principles of land measurement. Thoreau annotated his copy of Davies with notes from Galbraith on particular mathematical problems…this is Galbraith’s instructions on how to calculate the sine of an angle.

Thoreau took much more from Galbraith than mere mathematical instruction. In a journal entry dated June 9th of 1850 Thoreau lists nine books recommended by Galbraith’s text regarding the esoteric subject of the magnetic variation of compass needles. I am going to spend some time with this subject because I believe it shows how Thoreau thought through and imagined the complexities of mapmaking and his engagement with the subject can be used as a model for us to think through his transition from an Emersonian transcendentalist…to the more empirical view of the world that informed his readings and use of early American cartography

Thoreau’s interest in magnetic variation is first indicated on his advertising broadside where he explains the variation of the compass is noted so that the survey can be repeated.
Throughout the early 1850’s one finds references throughout his journals and field notebooks made to the books and articles Thoreau read on the subject and to the observations of compass needle variations that he made in and around Concord.

Magnetic declination for those of you who do not know is the variation that we see between magnetic north, or the north that a compass needle points to, and true north, the direction of the pole. The variation in the compass needle is caused by the earth’s magnetic field and was the subject of a great deal of scientific research in the mid-19th century. The exact direction that a compass needle points to is not constant even for a specific location, and although few people would notice these small changes, Thoreau, noted them quite explicitly…for example…in November of 1850, he made an entry in his journal that marks the beginning of what would be almost an obsession with the subject…

Thoreau writes,

“When I am considering the way which I walk, my needle is slow to settle, my compass varies by a few degrees and does not always point due southwest; and there is good authority for these variations in the heavens…”

Thoreau’s interest is more than just passing and he delves into the science of magnetic declination in a way that would become representative of his work not only in natural history but also in the way he approached cartography as well. In his field notebook he explains how he established the True meridian so he could continually check his surveys against the variation of his compass needle

True meridian slide

• Found the direction of the pole star at its western elongation (1,58-1/2) at 9h 26m PM (Feb 7th 1851).
• N coincides with a line drawn from the SE course of the stone post on the E side of our western small front gate, to the S side of the first door on the W side of the depot.

Thoreau has measured a reference line for the direction of true north… from the west gate of his home in Concord to the depot across the street.
By establishing a sight line for the True Meridian from his family’s house to the depot, Thoreau could easily check the declination of his compass before or after surveying. Thoreau would begin to include this information on his surveys even though it makes little difference to the purpose of the survey itself. For example we can see on his survey of Hosmer’s farm that Thoreau has added compass headings to each of the boundaries.

Thoreau would continue for some time to make detailed observations of magnetic declination and write them into in his field notebooks…
He would also go as far as to contact and correspond with William Cranch Bond, the director of the Harvard Observatory. Bond was conducting experiments in magnetic variation in Cambridge, and took thousands of measurements on magnetic declination in order to try to predict the changes that he and Thoreau saw in compass needles, a phenomenon that we now know to be chaotic. One can see just how chaotic by looking at one of the many graphs of Bond’s published measurements that Thoreau certainly read.

Thoreau soon found that Bond’s results were not applicable to Concord, even though it was just a few miles away.

One of the most amazing and important things about all this material is how it shows a change in Thoreau’s thought process and his turn away from the transcendentalist mode of thought that drove his early works. Among transcendentalists' core beliefs, at least as it was realized by Emerson, was an ideal spiritualstate that 'transcends' the physical and empirical and is only realized through the individual's intuition. In other words a real mind over matter philosophy. Emerson found little of higher worth in the empirical and downgraded most of science as “mere facts”. Thoreau would begin by the early 1850’s to leave these idealist tendencies behind and turn toward more realist studies of nature and history…to the point that by late 1852 he could write in his journal seemingly against Emerson, that “Mere facts & names & dates communicate to us much more than we suspect…”

This empirical turn toward a more scientific world view… would influence all of Thoreau’s thought from around 1852 onwards. Although we can never really call Thoreau a thinker who fully embraced the pure empiricism of late 19th century science, there is a change in his thought that effects all of his reading and observations even his interpretation of the early exploration narratives and the history of cartography… it is to his cartographic explorations that we will now turn…

In order to talk about Thoreau’s interactions with and interest in early American exploration and cartography we must look to what has become known as the “Canadian Notebook”. The notebook was begun shortly after Thoreau’s return from a trip to Canada and those few scholars who have actually read it….it remains unpublished… differ in their opinions of why it was composed. The notebook is divided into three parts… the second part is certainly the most intense interaction with cartography and cartographic literature that one will find in the entire Thoreau corpus.

This second part of the notebook contains notes from Thoreau’s reading of early exploration narratives and maps by such figures as Champlain, Lescarbot, John Smith, Ortelius and Wytfliet. Thoreau takes note of specific subjects like the changing of place names, the plants and animals that the explorers encountered, the size and flow of rivers, temperatures, snowfall, and the changing shape of the lakes and rivers shown on their maps. In other words facts, empirical data that describes the landscape and the conditions of place. This type of description is paralleled in his journal entries at the time where he is noting things like stream depths, tree ring counts, snowfall, and the blooming times of plants that he observed during his surveying of woodlots and farms around the Concord countryside.

Even as Thoreau was taking detailed notes on the maps and information found in these early exploration narratives he expressed his frustration with the study of human versus natural history. In his journal, on October 19, 1860, he writes,

“It is easier far to recover the history of the trees which stood here a century or more ago than it is to recover the history of the men who walked beneath them, How much do we know---how little more can we know—of these centuries of Concord life?”

It was to answer this question that Thoreau turned to early cartography and the texts that accompanied them. In the back of the Canadian notebook written in Thoreau’s hand, but in pencil, and in the wrong direction if one is reading from the front, Thoreau composes the following list of maps that he has copied…

On the back fly leaf written upside down in Thoreau’s hand:
“I have copied maps made ac. to…”
1.Verarzani’s plot in Hacklyts divers voyage 1582
2. Map made in forme sent from Seville in 1527 by Thorne
3. Map of Nova Francia etc. in Ramurio 3rd volume (1556) ac to discourse of a great sea captiane
4. Of America in Ortelius (1570 &e) who used Cabot and others
5. Of Norumbega and Virginia 1597 Wytfliet Lovanni
6. Nouvelle France Champlain 1612, 1632

The list, although there are 6 numbers, actually describes seven maps there being two by Champlain listed on the same line. I first encountered this list many years ago and became interested in determining if copies of the maps that Thoreau listed still survive, if he in fact drew them, and what they might have looked like.

Two of the maps on the list were quite easy to locate and are part of the Collection of Thoreau surveys and papers in the Concord Free Public Library. The one shown here was copied by Thoreau from Abraham Ortelius’ world atlas, the Theatrum Orbis Terrarum, published in 1570. Ortelius was the royal geographer to King Phillip II of Spain and a prolific atlas maker. Thoreau borrowed several different editions of the atlas from the Harvard Library over a period of years and I have not been able to determine when he made the sketch. Thoreau’s notes on Ortelius in the Canadian notebook are principally devoted to a commentary on this map…”a new description of America”…and they are very much concerned with place names…as is typical of these notebook entries that deal with maps Thoreau brings other sources in and makes comparisons…in the case of Ortelius Thoreau will ask about the antiquity of some of the place names the cartographer uses.

The second map found in the Concord Library is that of Cornelius Wytfleit. Wytfliet was a Flemish geographer who published an atlas called Descriptionis Ptolemaicae Augmentum in 1597. This sketch, which is cruder than the Ortelius, was made in 1855 again from a book borrowed many times from Harvard Library.

The other five maps have been more difficult to find and to identify. Three of them are very small and are found folded in the misc papers of Thoreau that are in the Morgan Library…they are unidentified and therefore do not appear in their catalog lists or finding aids. (an example shown below)

Of all of the notes in the Canadian notebook about cartography, by far the most extensive are associated with the narrative of Champlain’s voyages…time and time again Thoreau will borrow the 1613 and 1632 editions of this book from the Harvard Library…
Champlain made several voyages to the New World and explored the St. Lawerence River, along with most of the New England coast, at least as far south as Cape Cod. The narrative of his voyages is filled with maps and his reflections on the explorations.

Thoreau’s notes on Champlain’s texts are full of details on plants, animals, place names and especially the differences in the various editions of the maps Champlain made.…Thoreau writes praising Champlain’s accuracy as a geographer and he quotes in detail Champlain’s own commentary on the methods of his mapmaking.

But what about the two Champlain maps on Thoreau’s list of the maps he copied???…they appear in no inventory of any library, they are talked about in no scholarly articles and appeared to me to be lost.

Then one day, when I first came to the Library of Congress, almost ten years ago I happened to be doing some research on Thoreau and the depth of Walden Pond when Ron Grim…now of the Boston Public Library, mentioned to me that there were several maps in the Geography and Map Division thought to be by Thoreau but with no real attributions. Curious about this but not expecting much…for how could maps by Thoreau be sitting in the Library of Congress without firm attributions…I opened the folder and saw a manuscript…

Immediately I knew that I was looking at the missing Champlain maps. The manuscript that you see here is one of four pages that describes the two Champlain maps that Thoreau listed on the flyleaf of the Canadian notebook and copied, one from 1632,

This map was easy to identify as Thoreau’s because it is in his hand and fits the general form of his other map sketches. The second map however from 1612 was more difficult as it is a tracing and contains almost nothing that would directly link it with Thoreau. Thoreau does say in the manuscripts that accompany the maps that he annotated the 1612 map in red with later places names. This feature can be seen on the 1612 copy below.

While the finding of the two Champlain maps completes the list of the known cartographic copies that Thoreau made… it has opened up the question of how to understand Thoreau’s geographic explorations in relation to some of his larger projects and published works. For Thoreau’s relationship to cartography is a complicated one and has suffered from a lack of scholarly attention. In general Thoreau seems to have remained skeptical of maps even as he made constant use of them…in his journals he wrote,

How little there is on an ordinary map! ...between those lines indicating roads is a plain blank space in the form of a square or triangle or polygon or segment of a circle, and there is naught to distinguish this from another area…for on it are no moral lessons…

And in the Maine Woods he tells us that maps are “labyrinths of error.”

Thoreau’s true attitude toward cartography is not difficult to assess, if one takes the time to read through his extensive notes on the subject closely. The notes express an immediacy of experience that occurs when one is reading and observing directly…Thoreau did not think of historic maps from the past as obsolete, but rather as graphic and ideological documents that could help him understand what had been in a particular place before…In many ways we can consider Thoreau the first "modern" historian of cartography.

To conclude, I want to return to one of Thoreau’s surveys.


It is a simple drawing of a woodlot but I think it sums up Thoreau’s relationship to cartography and its influence on his work. The surveying of woodlots was very much part of Thoreau’s daily routine and it took him into areas of Concord seldom seen by his fellow citizens…surveying a woodlot generally meant the lumber it contained was up for sale and it was going to be cut down. Thoreau would return to the lots after they had been cut and in his journals noted in detail the succession of plants and trees that would follow…these notes would result in Thoreau’s most important work of natural history, “The Dispersion of Seeds”, which he composed shortly after reading Darwin in 1860…

Unfortunately, Thoreau did not live long enough to complete the great work on geography and the indigenous peoples of North America that his extensive notes in the Canadian and Indian notebooks would lead us to believe he was working on…all we have are the notes…more than 4000 pages of them unpublished

I have said that in what Thoreau wrote in these notebooks, as dry and factual as they are, we get a sense of a transition, an empirical turn, that not only occurs in his thought, but that would begin to lay the foundations of modern geography and environmental history…

Besides this however, we may also sense something more important…something deeper that you can all take pride in tonight… Thoreau used many books, articles and maps in these notes, most of which were read in libraries just like the one we celebrate this weekend. In his life and work we can see how something as humble and as common, as book or a map in a library…can spark the imagination and inspire great thoughts…without a library there would be no Henry David Thoreau, there would be no notes and drawings for us to wonder and marvel at this evening… like Thoreau’s notes, libraries, through their collections of books, manuscripts and maps teach us that…

“Mere facts & names & dates communicate to us more than we suspect…”

Thank you all for listening….

Wednesday, March 30, 2011

The Henchir Mettich Inscription from Central Tunisia:

Further Use of Epigraphy for the Study of Early Roman Property Law and Cadastral Cartography

...historians sometimes find much of what they are looking for when they step outside their rooms and look around in the landscape....

................................................................................................ --George Duby

The sociologist Max Weber, shown in the photograph below, wrote in his dissertation, Die Römische Agrargeschichte in ihrer Bedeutung für das Staats- und Privatrecht (Roman Agrarian History and its Significance for Public and Private Law), that Roman Surveyors distingushed three categories of land: ..



1. ager divisus et assignatus, land surveyed and assigned to owners which is further subdivided into two categories:

a. ager limitatus, that is land surveyed by centuriae and assigned to owners.

b. ager per scamna et striges land surveyed by scamna and striges and assigned to owners.


2. ager per extremitatem, land surveyed by boundaries.


3. ager arcifinius, land not surveyed. Weber completed the dissertation in 1891 and was greatly influenced by the work of great Roman historian, Theodor Mommsen.


Weber, in the dissertation, makes a case that the two broad categories of surveyed land, that of centuriae and that of scamna et striges are different systems of mapping based on land ownership laws. The centuriae surveys are more general and do not reflect the actual ownership boundaries of the land, while the scamna surveys follow actual property lines. Centuriation, the process of dividing the land into centuries, formed very regular patterns and, as is shown in the schematic below, had fixed sizes associated with it. Scamna and striges are different, in that the boundaries of the surveyed land form irregular rectangles of various sizes and extents.


Weber implies that this distinction has more than just structural meaning and cites the writings of the surveyor Hyginus from the Corpus Agrimensorum. Hyginus says that land surveyed per scamna et strigas was "subject to taxation" and for this reason "permanent property lines" had to be well defined. The question of the relationship of private property, taxation, and the role of surveying and cartography in the establishment of colonial tax and ownership rights in the Roman Empire is a very complex one and much more historical work needs to be accomplished in this area. One sourse of information regarding the interplay of these various bureacratic entities comes from epigraphic inscriptions. One important inscription regarding the role of ownership, rents and taxation that survives was found at Henchir Mettich near the village of Testour, Tunisa, west of Carthage. The inscription was originally part of the administrative documents associated with the estate or fundus of Villa Magna Variana. The section of the map below from the Barrington atlas shows the region to have been only lightly centuriated, yet the inscription, as I will show below implies that it was surveyed.



The inscription is currently part of the collections of the Bardo Museum in Tunis and is shown in the photograph below.

... ... The text found on the monument was first announced by M.R. Cagnat of the College du France and was published several times shortly after its discovery in 1896 by a Lieutenant Poulain, an officer in the French topographic corps.. The area around Henchir Mettich is currently a semi-arid district of mostly barren hills (approximately 400 mm-500mm rainfall per annum), some of which are currently cultivated with olive trees. The valley (modern Medjerda, Roman Babradas) is roughly sixty to eighty kilometers from the Mediterranean coast and is known as the Tell intérieur.

... ... While in Tunisia last year I took detailed photographs of the Henchir Mettich inscription at the Bardo (one of the series is shown in the above figure). The stone on which the inscription is written was in all probability moved from its original location to Henchir Mettich and is dedicated "to the safety of the Emperor Trajan" suggesting a date of around 115-117 AD. The test itself is quite long and is found on all four sides of the momument. Using edge dection algorithms I enhanced the inscription (figure to the left) so I could read it in its current condition, which appears degraded compared to some of the earlier publications of it. The inscription is addressed to the group of landowners and renters who are associated with the fundus. The actual boundaries of the fundus are not given in the inscription but it does tell us that the estate was large enough to have a wide variety of agricultural production. There are fields of wheat, barely and beans, along with orchards of olives and figs. This list is very much in line with the current agricultural output of the region. The inscription also mentions vineyards and pastures and home sites for workers. One of the most interesting parts of the inscription takes about the fact that some of the land is uncultivated and that a part of the land is leased to cultivators and also contains portions that are given over to the lessors for their own farms.

Those who worked the fields are described as coloni, of which the inscriptions defines two types: ...

1. those who lived on the fundus in their own homes (specifically homes they themselves built)

2. those who lived on the fundus but rented their buildings.


The inscription, whose entire contents I will translate in a future post, divides up in precise terms the rules associated with the various types of land associated with the fundus and talks about land renting and ownership rules and the terms under which things like unalloted farm lands may be occupied and cultivated. Much of the discussion of these rules implies a deep concern with boundary issues and surveying. For example the inscription states:

"To those coloni dwelling on the fundus of Villa Magna Variana, that is, of Mappalia Siga, who wish to cultivate the fields, permission is given to cultivate those fields which have not been alloted, under the terms of the Lex Manciana; namely that he who cultivates shall have personal use of the land. Of the crops which are raised on said land, the cultivators shall give to the owners, or lessors, or stewards of this fundus shares as fixed..."

The unalloted portions that are referred to resulted from the division of land for the purposes of distribution to private individuals. From this one can infer that the fundus was originally surveyed and distributed and therefore became ager privatus. If one believes the methodologies for such distribution as outlined in the Corpus Agrimensorum this implies the creation of a map at some time before 116-117 AD. There are other instances of this type of example. Mommsen in Volume X of CIL (pp 386) records an inscription from the ager Campanus, which settlers had begun to occupy without permission. The inscription says:

"He divided that territory into small farms (fundi) and leased them out at fixed rents. While in office he recovered more land than was expected, and he had the whole territory recorded on a surveyor's map (forma). This was then engraved on a bronze tablet..."

... The inscription's language is complex in a number of areas, especially in those referring to subseciva, or uncultivated, unalloted land. With the little evidence that survives however, regarding Roman surveying and cartography, epigraphy is just one more group of texts that need to be studied in a closer and more a critical way than historians of cartography have generally done...more on this inscription in later posts


The author practicing his epigraphy skills in the ruins of Carthage ...just outside of Tunis...

Tuesday, March 08, 2011

In Nietzsche's Shadow:
Cartography, Geohistory and the Changing Nature of Landscape would fancy him a madman when you see him walking along the most devious of paths...seeking for the traces of lost facts in rough woods and thickets...
--Cassiodorus on Roman Surveyors

My current work of searching for the remains of Roman mapping and cartography was born on the ancient paths and trails of Southern France. Hiking through these areas year after year continually brought me face to face with a type of historical research that I think has been missing from what has recently come to pass for the history of cartography. Wandering these paths and old Roman roads makes one consider the relationship that cartography has to landscape and with the kind of geohistory first imagined by members the French Annales School.

The village of Eze from Mont Bastide

The medieval historian Georges Duby said in his autobiography, History Continues, that,

"historians sometimes find much of what they are looking for when they step outside their rooms and look around."

I believe this to be especially true for the historian of cartography. Duby says that,

"What I was looking for in my wanderings through forests and fields was the reassurance of a concrete grasp on reality. The tattered, threadbare fabric that I was trying to mend stitch by stitch with the aid of my Latin texts needed solid support. I wanted to lay it down over a document of a very different kind: one just as rich...but without gaps and preserved not in the darkness of the archives but open to the sunlight and to life itself, namely, the landscape."

Duby talks at length about how,

"no technological revolution had yet radically transformed the agricultural system in my region, and forty years ago the network of paths was still much the same as it had been in the year 1000."

Today some things have changed but many of the old paths and field patterns survive and, as I have shown in my work on Tunisia, can be extremely useful when trying to reconstruct the Roman limits. This is especially true in places like Tunisia and Libya were a great deal survives in the way of field patterns and boundaries, but these same hints in the landscape can also be found in some areas on the continent. My own wanderings along the forgot paths of the moyenne and grande corniche, places like the Friedrich Nietzsche trail, which goes from the Mediterranean Sea up to the village of Eze (shown in the photo above) continuing to the summit of the Mount Bastide, have shown just how enlightening such an approach can be. Nietzsche himself used to walk this particular chemin daily while he was living in Eze, and composing parts of Thus Spake Zarathustra, but the history of the path goes back at least to the iron age. As Nietzsche said in Ecce Homo,

"The following winter [1883-84], under the halcyon skies of Nice, which glistened above me for the first time in my life, I discovered the third part of Zarathustra-and the book was finished. Scarcely a year for the composition of the whole. Many concealed spots and many heights in the landscape of Nice have become sacrosanct to me because of unforgettable moments there. That decisive part of the third book, 'Of Old and New Tablets,' was composed on the difficult and steep ascent from the railway station at Èze to the marvelous Moorish eagle's nest overhead.-My muscle tone was always greatest when my creative energies flowed most abundantly. The body is spirited-let us leave the 'soul' out of play. . . . One could often have spotted me dancing: at that time I could wander through the mountains for seven or eight hours at a time without tiring. I slept well. I laughed a lot-I was fit as I could be, and I was patient."

Along the trail one finds the remains of a large bastide or oppidum whose occupation dates back to neolithic times but that was also occupied and rebuilt by the Romans during the Julian-Claudian period. Many of the walls and some of the roads are still intact, as shown in the photo above. Ruins of this type, with parts of the road structure remaining, are useful in reconstructing how and where the Romans actually surveyed and mapped. Boundary stones and mile markers have also been found in this region and lend further help in producing accurate reconstructions of the type that I am engaged in.

Most of the theoretical foundation for these types of researches stem from the work of Fernand Braudel (1902-1985) and Marc Bloch (1866-1944), two of the founders of the Annales School. Braudelian landscape and geohistory can be reduced to a few basic assumptions.

1. geohistory has a specific concrete object that is 'tied to the soil', to elemental ecological the landscape and its historical modifications.
2. geohistorical process, because it develops so slowly, represents a relatively immobile history, whose characteristic patterns last for long periods, things like field patterns, paths and roads.
3. geohistory is fundamental to other kinds of historical process and underlies other forms of historiocity.

Braudel wrote that within the bonds of his technological capacity man is free to do what he will with the landscape in which he dwells. A very interesting Heideggarian parrallel could be written here using Heidegger's essay Building, Dwelling, Thinking but I will not go into that now.

According to Braudel, the very formative capacity of the human endeavor, the ability to bend the landscape and change it in ways that last beyond single human lifetimes, creates constraints that become determinants of later human history because they are relatively 'fixed' or 'permanent'. Hence paths and field patterns last much longer and have their origins in many places in the remote past. These things become fixed and although we do not recognize them at first sight, old paths and field patterns can tell us a great deal about the history of an area and can open up new areas of physical research that help in our cartographic researches.

One look at Marc Bloch's French Rural History will give some insight into what I am getting at here. Bloch's essay is very important for a number of reasons that are methodologically interesting for this particular project. Bloch, in this short book (it is only 200 pages long), is concerned ironically with a long span of time, beginning in the 13th century and ending in the early 18th century. His conception of rural history is broad, taking into account not only farming techniques, but customs and the development of social norms. What was for the time most revolutionary however, was Bloch's systematic use of non-documentary sources like estate maps and the layout of the physical environment itself.

French Rural History came to my attention because of it's use of the so-called 'regressive method'. Bloch read history backwards on the grounds that we know more about later periods and that it makes logical sense to proceed from the known to the unknown. There were others before him who used this method like the English historian Frederick Seebohm who, in 1883, published The English Village Community. The book begins with an important chapter entitled, 'The English Open Field System Examined in its Modern Remains". Seebohm uses the surviving clues in the landscape to work backwards to the foundations of early English village life much in the same way as Bloch does with his maps of remaining field patterns in France and as I am trying to do with Roman Surveying. More modern studies, like Alan Baker's, Studies of Field systems in the British Isles give one some sense of what the historian can achieve if one simply gets outside. All of this of course requires a certain rethinking of how we write and conceptualize cartographic history as something that as George Duby said, "is open to the sunshine".