In the history of Western cartography, a distinction was made between maps and charts. Charts referred to the depictions used by mariners that contained varied types of information based on their experience and specific to their purposes. Maps, however, were largely academic, concerned with the world as a whole. Early cartographers, such as Ptolemy of Alexandria, Greece (ca. 120 CE) defined what they did as geography―"a representation in pictures of the whole known world together with the phenomena that are contained therein." He distinguished that from chorography, which he deemed regional and selective, "even dealing with the smallest conceivable localities, such as harbors, farms, villages, river courses, and the like." Our broader definition of maps is in keeping with more modern writers who view world-wide maps and local maps simply as different streams, which have an underlying conceptual unity and which eventually merged. Differences in terminology, however, have persisted. Hence, maps specifically for mariners are still called charts, and so the unique objects created by Marshall Islanders are commonly referred to as stick charts.
That's an excerpt from Mathematics Elsewhere: An Exploration of Ideas Across Cultures by Marcia Ascher. Ascher is―or rather was, since she died in 2013―a Professor Emerita of Mathematics at Ithaca College. She's an accomplished mathematician. I'm really not, although I can add, subtract, multiply, and divide in my head. So when she goes into detail on some things, it can sail over my head.
No matter. It's a great book. While mathematics is her academic subject, she also provides some interesting anthropological studies here. And what she realizes is that mathematics reaches in various forms across the globe, but it never exists in isolation. There are algorithms used in divination rituals. There are calendars. The Jewish, Gregorian, and Muslim calendars are respectively luni-solar, solar, and lunar. There are other calendars that are none of these things, and their purpose isn't to measure time in the natural world. And of course, maps. The purposes cause math to take different forms in different cultures.
1 comment:
The most I've ever known about charts is their use in navigation at sea, an essential requirement for professional sailors throughout history. As well as describing seas, rivers, and coasts they also included maps of man made and natural features. Equally necessary were the charts of water depths, navigational hazards such as reefs and wrecks and anything else that might help or hinder ships near shore or distant from it. Naturally, what I'm describing are western charts that evolved over the course of hundreds of years.
Professor Ascher must have been an extraordinary teacher in her time and it was very good of her to write such a detailed history of indigenous methods of using math without those people having any basis in western approaches to the subject. The article about stick charts was especially interesting particularly in consideration of the fact that Pacific islanders used them to discover not just Australia but all the other widely separated islands. I'm not sure I'd want to be left in the bottom of a canoe expected to find land. Humans really are amazing.
I did know about math involved in astrology and the i-ching but not any of the others or just how important they are in other cultures. Thanks for the introduction to such a fascinating subject - thanks too for the link to Sapiens.
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