Wednesday, December 31, 2008

Sketching the Unknown:
A Phenomenological and Computational Study

of the Rossi “Map With Ship”

The actual maps that exist are but a tiny subset
of the theoretical maps that could exist. These
real maps are products of a very small number
of trajectories through cartographic space...each
with its own unique place in this mathematical
construction. Every real map is surrounded by a
tiny cluster of real or unreal neighbors
who are its ancestors and descendents...

The motivation for this investigation stems from the problem of trying to identify the possible sources and the overall chronological similarity of the Rossi “Map With Ship” to other maps that may be contemporary with it. The history and origin of “Map With Ship” has been a problem for historians of cartography almost since its discovery and it has never been adequately studied from an analytic perspective. A recent C-14 dating of the vellum yielded two age distributions both after 1475.The map purportedly shows the coast of Asia, including Japan, and the coast of North America in the area of Alaska and the Aleutian Islands. Scholars have drawn attention to the fact that the strait shown on the map is depicted in a form that recalls several European maps of the region from the late sixteenth century and later. In particular the maps of Zaltieri of 1566 and that of Forlani of 1574 have been discussed in recent studies[1]. The date of the map has been variously claimed to be from the time of Marco Polo’s journeys, to be a fifteenth or sixteenth century copy of a map from the time of Polo, or to be an outright fake or forgery. Although there have been several studies of the Rossi materials in the past no real conclusions have been reached as to the veracity of any of the above claims[2]. The “Map With Ship” is a strange mixture of elements that graphically do not seem to fit the style of any particular cartographic time frame. It is closely related to other maps in the Rossi corpus such as the “Map of the New World” and the “Sirdomap Map” and it appears to be a palimpsest in several areas on both the verso and recto. The map also contains script in three languages: Venician, Chinese and Arabic[3].
Marcian Rossi, the original owner of the collection of maps and documents, corresponded in the early 1930’s with Leo Bagrow who wrote the first study of the corpus[4]. In this study Bagrow reproduces part of Rossi’s letter:

“Marco Polo entrusted the maps to Admiral Rujerus Sanseverinus who had graduated the Nautical School at Amalfi. A number of centuries later his descendent Ruberth Sanseverinus married Elizabeth Feltro Dell Rovere, Duchess of Urbino. In the year 1539 Julius Cesare de Rossi, count of Bergeto married Maddalena Feltro Rovere Sanseverinus…”

Rossi continues this genealogical tree down to his great-grandfather Marciano de Rossi from whom he received the group of map and documents. None of this has however been verified by scholarship.
The following paper will attempt to shed some light on the date of “Map with Ship” by taking a more phenomenological approach to the information actually shown on the map through the use of several mathematical models. By modeling the projection of the Map with Ship, assuming that there is one, and by looking closely at the scale error displayed in the coastal outlines, this study shows that the information on the map is consistent with the geometric methods that would have been available to cartographers in the late medieval period or to a fifteenth or sixteenth century copyist. This is not to say in any way that the map dates from this early period but rather to more conservatively conclude that there is nothing in its geometrical makeup that would exclude such a dating. The calculations for the Rossi map contained several sources of error most especially in the selection of homologies. The final selected points required experimentation and trail and error as the map is somewhat devoid of specific geographic details. The calculated transformational grid overlaid on the Rossi map is shown in the Figure.

The transformational grid shows that we have induced a scale error change from north to south and east to west that is consistent with the family of pseudo-conic projections. Almost all of the error in the Rossi Map is located in angular scale deviations in the Alaskan region, the very region whose existence on the map is the most suspect. The variation in the transformational grid is extremely interesting in that it implies that the information on the map was probably not copied verbatim from a Portolan chart (there is scale deviation and there is little rotation) but rather from a projected map. The pseudo-conic projection scale variation shown on the Rossi map is however nearly indistinguishable at this large level of error from the only other small scale map projections that would have been available to someone before 1550, that of Ptolemy's first and second projections. Hence although the map is projected, and could not have been derived from nautical charts, it is consistent with the geometrical tools that were available to cartographers before the discovery of the information that the map shows. Based on the results of the spline and warping calculations we also calculated the two-dimensional the similarity coefficients of the Rossi map compared to other possible projections[5].
These coefficients yield a measure of how similar or dissimilar a map is to different projections using distance functions and calculating least-square norms. We attempted this calculation in order to show that the Rossi map was not similar to any other commonly used modern projections and to determine how far it was geometrically from the family of conic projections that characterize those of Ptolemy. This calculation, the results of which are shown in the graph, confirm the results of the spline calculations and show that the Rossi map is most similar to the conic projections of Ptolemy and has little in common with more modern forms.
One can easily see in the diagram below that the Rossi map’s coefficients place it in the location of the two conic Ptolemaic models and far from the cylindrical Sinusoidal and Mercator projections.

(Click on image to enlarge)

There are spaces in which the determination of position requires not a finite number, but either an endless series or a continuous manifold of determinations of quantity. Such manifolds are, for example, the possible determinations of a function for a given region, the possible shapes of a figure, and so on.
-Bernhard Riemann
In conclusion we have shown that the Rossi “Map With Ship” has no internal or geometric inconsistencies that would lead us to believe that it was definitively copied from a modern map. However, the models employed in coming to this conclusion unfortunately do not totally rule out this possibility. For although we have suggested that the map was not copied verbatim from a Portolan chart we have no way of narrowing down the possible geographic sources more precisely at the present time. All we can say based on this study is that it is still possible that the Rossi map was copied from or based on geographic sources that are consistent in their construction, geometry and scale error with those that COULD have been produced or copied from late medieval and early modern sources. The question of the date of the map and its authenticity must however await further studies.

[1] Benjamin B Olshin, “The Mystery of the ‘Marco Polo’ Maps: An Introduction to a Privately-Held Collection of Cartographic Materials Relating to the Polo Family”, Terrae Incognitae, 39 (2007): 1-23

[2] Leo Bagrow, “The Maps from the Home Archives of the Descendants of a friend of Marco Polo,” Imago Mundi 5 (1948): 3 –13.
[3] The Chinese symbols on the map are unreadable and appear to be either nonsensical or copied by someone who did not know the language as is some of the Arabic script.

[4] Bagrow, (1948)

[5] Waldo Tobler, “Measuring the Similarity of Map Projections,” American Cartographer 13 (1986) 135-39.