Palladius and Horizontal Sundials - How 36 numbers and astronomy help us understand the ancient world

ORAL

Abstract

Palladius was a Roman aristocrat ``gentleman farmer.'' He wrote the only surviving farmer's almanac from the Roman period. It includes advice on how to take care of grapes, olives, wheat, and manage a farm. Farming chores need to be done in season and in the right time of the day. For describing when things should be done, he used a sundial. That's why Palladius left a table of the length of the shadow of a pole - a GNOMON - for 11 hours in the first day of every month for 12 months, hence 132 numbers. Palladius presumed symmetries that cut this to 36 useful numbers, the only useful such table from Roman times That is a treasure trove for both historians and astronomers! Unfortunately we know little else about Palladius, except that his farm was probably in Sardinia, and his family had property somewhere in Gaul, present day France. Its not clear when and where he wrote this, and that could be one question answered by those numbers. In trying to answer that specific question using spherical trigonometry and (as calibration) a recipes for building a sundial from the first century BC, we discovered discrepancies. Those could indicate great error in assembling this table, great progress by assuming that Ptolemi's greatest ``discoveries'' were taken into account, or a combination of several minor factors.

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Authors

  • Ran Sivron

    Baker University

  • John Richards

    Baker University

  • Jatinder Kumar

    Harvard U., Baker University, Bejing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Northrop Grumman, Baltimore, MD, University of Kansas Dept. of Physics \& Astronomy, Kansas State University, Department of Chemistry, College of Materials Science \& Engineering, Sichuan University, China, Illinois State University, Mullard Space Science Laboratory, University College of London, Holmbury St. Mary, United Kingdom, Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO, United States, Weizmann Institute of Science, Rehovot, Israel, Monmouth College, Missouri State University, Birla Institute of Technology and Science, University of Illinois at Urbana Champaign, Ames Laboratory. Department of Physics and Astronomy, Iowa State University, Siena College, \'Ecole Polytechnique F\'ed\'erale de Lausanne, Switzerland, Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Kansas State University, Purdue University, Princeton University, Oklahoma State University, University of Chicago, University of Iowa, University of Kansas, University of Kansas and University of Iowa