Mathematics of the Calendar Final Paper

 

You will be writing a 6-8 page paper on some aspect of the calendar; in addition to the written paper you submit to me, you will also give a 15-20 minute oral presentation to the class on your paper.  The paper/presentation will count for 20% of your grade.  We have 25 students this block, and I’d like to have no more than 16 presentations (8 or fewer on each of the two presentation days).  Consequently, I invite some of you at least to do your project in pairs.  I will expect a single essay and a single presentation from the two of you.  Under ordinary circumstances, each member of a pair will receive the same grade for the project.

 

There are many possible topics!  You might report on a calendar used by a culture not discussed in class, or research the details of some important historical development.  Some good topics have a more cultural slant, and some are more mathematical.  In all cases this paper will involve some independent library research on your part.   There will inevitably be a little bit of mathematical content in any acceptable topic, but you do have a lot of leeway to make your own choices!  I give below a list of interesting topics you might consider. 

 

The final version of your paper is due at the beginning of class on the 4th Monday of the block (March 10th).  The oral presentations will take place on Monday and Tuesday of that week.  Part of your responsibility in this assignment is to attend and listen to the presentations of your colleagues!

 

Here is some advice and general guidelines: 

 

1.      As a research paper, you will need to provide a complete bibliography, with citations inside your text as appropriate.  I am not overly concerned about the exact format of your bibliography and internal citations (footnotes, or whatever you use), but I do want you to take care to let me know where your information and ideas have come from.  Don’t plagiarize! 

  1. Some Internet sources are fine, but beware!  There is a lot of “junk” on the Internet about the calendar, especially about astrology and related matters.  Take care to evaluate how reputable your sources are.
  2. You should also include at least three hard-copy sources --- journal articles or books. 
  3. Since we will be listening to oral presentations on these papers, each student or student-oair will need an individual topic.  First come, first served.  I’ll be keeping track, and let you know which topics are fair game. You and I may need to have a conversation over a day or two to refine or modify your subject of interest, to get a topic that is feasible, not already spoken for, and related to the course material.  Choosing a topic sooner rather than later is obviously a good idea!  But in any case, you need to have me approve your topic by Thursday afternoon, March 6th. 

5.      Despite item 4, there may still be some overlap in topics chosen.  Please try to be helpful in sharing library resources if this happens.

  1. I will certainly use the quality of your writing as a factor in evaluating your paper.  Please visit the Writing Center if you need help.  I will also be happy to look at an extract or draft during the latter part of the third week, if you would like me to provide you with some preliminary feedback.
  2. Your oral presentation should last no more than 15-20 minutes.  To allow for adequate time for all reports on Monday and Tuesday morning, we should plan on meeting at 9 a.m. on those two days.  We will negotiate time slots for the oral presentations on the Friday before.  But note that the written paper is due in all cases on Monday.
  3. You should not just read your paper to your classmates, but instead look for some way to enliven and energize it.  Powerpoint (or other visual aids) would be great, but is not necessary.  If you are unused to public speaking, you might want to practice your presentation on an unsuspecting friend or roommate.  Please let me know if you have any technical needs.  We can of course log you on to the CC network and Internet, and put your work on the computer projector.

 

Here are some potential paper topics.  Paper topics that are already spoken for are highlighted in the list below.  If I’ve forgotten you, or attached you to the wrong topic, please let me know!

 

1.      Stonehenge (and other megaliths in Britain).  Why was it built and when?  What are the astronomical alignments of the stones?   There is a lot of controversy among scholars about these questions – you should give some notion of that in your paper.  Beware of junk sources on the Internet!

2.      Possible astronomical and calendric structures among Anasazai structures in the American Southwest (especially Chaco Canyon in New Mexico).

3.      Possible astronomical and calendric structures among the Incas in Peru (especially at Cuszco and Macchu Pichu) -- Greg.

4.       Possible astronomical and calendric structures among the Mayans in Mexico and Central America. – Mary & Lise

5.      The pantheon – Clara & Emily S.

6.      The Chinese calendar.  You should give some insight into the history and cultural significance of the calendar in China, and also some detail about how it functions mathematically.  Guillermo and Ashley

7.      The calendar of the French Revolution. – Sam L. and Sam Y.  You should put the proposed reforms both in a mathematical context, and also in a political one.  Alternatively, you could focus more generally on the impact of revolutionary politics and the calendar, and include the Soviet Union and President Niyazov’s cult of personality in recent-day Turkmenistan.

8.      Empirically based calendars among traditional peoples.  The Trobriand islanders are the ones who used the spawning of the sea worms.  There is probably not enough information about this single case, but you could probably find more anthropological information about empirical calendars.

9.      Calendars in India.  The Indians used a lunar unit of time called the tithi.  It raises many astronomical and mathematical questions. 

10.  Marshak and the conjectural Paleolithic moon calendars.  This is a matter of hot scholarly debate.

11.  The history of the apparent early Christian policy of co-opting pagan holidays with Christian feasts.  -- Caty

12.  The Javanese-Balinese calendar.  This calendar involves a lot of abstract cycles, like the Mayan tzolkin.  You can find some information about this in Mathematics Elsewhere, by Marcia Ascher. 

13.  African calendars.  There is a little bit about calendars used by some African cultures in Africa Counts, by Claudia Zaskavsky.  There is probably not enough information there for a paper, but I expect a literature search would turn up a lot more!  There are a few references cited in Mathematics Elsewhere.

14.  The precession of the equinoxes.  The locations of the equinoxes on the ecliptic are actually changing very slowly, on a cycle of about 25,800 years.  Why does this happen?  What are the astronomical and calendric consequences?

15.  The cultural history and background of the seven-day week.  There’s a book about this called The Seven Day Circle, by Eviatar Zerubavel.  I’ve not read it, but Marcia Ascher recommends it.

16.  The Bahai calendar.  It’s all about 19! – Ashley

17.  The history and politics of adopting the Gregorian calendar in Great Britain.  There’s quite a bit about this in Duncan’s book.   Davian and Matt

18.  Religious implications of the Gregorian reform -- Paige

19.  Celtic calendar practices and cross-quarter days.  You can find a lot in Michael Judge’s book Dance of Time – but Judge is unfortunately not a scholarly work, and so it lacks references.  There is a rich literature here – but beware junk sources. Tracy is doing the Wiccan calendar, which is related to this topic, but there might be room here for a second project.

20.  Modern (19th and 20th century) proposals for calendar reform.  

21.  The Block Plan as a calendar-- Max

22.  Something else you’d like to learn about!  I’d encourage you to think about a calendar topic that relates to your major, or some other interest you might have!  Graham is working on the library and school of Alexandria, and its relationship to calendars.  Kaleb and Adam are exploring calendars created by Tolkien.  Lylya and Julie are working on the history of clocks and time measurement.  Becca and Emily H. may be working scientology and the calendar.