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The Arithmetic of Distance: A Module

Curricular materials created for the 2013 SAIL seminar:

Mediterranean Trivium: Earth, Sea, & Culture in Italy

This module invites students to consider the relativity of distance. How big is the Mediterranean? It can, of course, be measured and the size rendered in numbers. But size also depends on perception and experience. This is especially true before the development of sophisticated tools for measuring distance.

Even now, but especially in the past, people measured the sea relative to other bodies of water they knew or heard about. They also calculated its size in terms of the time it took to travel from one point to another. To understand distance as travel time, the module asked students to use Orbis: The Stanford Geospatial Network Model of the Ancient World. The exercise involved calculating distances in order to imagine how the ancients experienced the size of the Mediterranean.

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Context of the Module

  1. I used this module in two courses: Culture, Society, and History: The Mediterranean, a course for first- year students, and Senior Seminar: Nature in History, for senior history majors.
  2. In each course, the module happened early in the course after students had read introductory material on the geography of the Mediterranean. (Fernand Braudel, The Mediterranean and the Mediterranean World in the Age of Philip II, trans. Siân Reynolds, vol. 1 (New York: Harper: 1972). They read the prefaces, a section of Part 1, and they summarized and reported back on the sections.
  3. In the first-year iteration, it served as one activity in a six-hour unit on Geology, Ecology, and Society, and in the Senior Seminar it illustrated one method, among others, of doing environmental history, specifically, in this case, of the Mediterranean region.


Updated May 02, 2016

Learning Goals

Content/concepts: Using Orbis, measure and compare travel times between Rome and four other cities, in summer and winter. Experiment with other variables including cost and speed. Compare to modern figures for air and sea transport. Work with an historical data base.

Higher order thinking skills: Figure out the meaning of the results. In some cases, they do not correspond with expectations. For example, it takes longer to reach some destinations in the summer than the winter. Why?

Multidisciplinary analysis: The database students used reconstructed routes and times based on archaeological, historical, and literary evidence. They did this exercise in the context of a study of ancient cartography.

Other skills: Students worked with partners in order to develop collaborative techniques useful for discussion and, in the case of the seniors, for class discussion and for collaborative research workshops.


Updated May 02, 2016

Teaching Materials and Activities

  • Orbis: The Stanford Geospatial Network Model of the Ancient World:
  • Braudel, Fernand, The Mediterranean and the Mediterranean World in the Age of Philip II, trans. Siân Reynolds, vol. 1 (New York: Harper: 1972).

Instructions: Go to; click on Orbis; Mapping Orbis; Interactive distance cartogram

Students received a work sheet (Arithmetic of Distance-Appendix, #1) asking them to calculate the fastest travel time, in number of days, in winter and summer to and from the cities of Rome, Antioch, Constantinople, and London.

  • Another hand-out (Arithmetic of Distance-Appendix, #2) compared travel times from Rome to Constantinople, Alexandria, Verona, and Carthage in the ancient world and now by air and by sea.
  • Results led to a discussion of the impact of weather, winds, and currents on sea travel in the ancient period and to the implications of the large distances (measured in time traveled) for trade, control of the Empire, and the exchange of people and ideas.
  • For the first-year class, the Orbis exercise accompanied a study of descriptions of the earth and the place of the Mediterranean in it including those of Hecateus (550-480 BCE); Strabo (18 CE), Claudius Ptolemy (90-168 CE), Christian T-O maps; Piri Reis (c1470-1553/4), the Mercator (1569), Google Earth globe. (See Resources section.)

Teaching Notes

I used a PowerPoint supported lecture/discussion for the maps. It took about an hour. Reserve at least one hour for the Orbis exercise and another hour for the discussion. I allotted less and found that it took students more time than I anticipated to figure out the program and to calculate the distances.

Having students work in pairs is a good idea because they can share computers, technical expertise, and talk some about what they find. Orbis is reasonably easy to use, but it generated some frustrations. For example, it is hard to calculate the distances to London, because they fall off the screen. Next time, I would omit London.

I should also have allotted more time to the discussion, particularly to the comparison of how ancients understood the geography of the Mediterranean and how they experienced it.

Consider adding time or a complementary homework assignment to allow them to explore some of the other features of the site, including calculating overland trade routes for goods and for military maneuvers. The site also offers studies based on the data which could have been useful either for content or for research methodologies.


Post-exercise discussion determined how well students used the results to identify patterns and how well they identified the variables most useful in explaining them.

Resources and Materials


Lead Partner
Susan Ashley
Professor of History, Colorado College
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