Course Schedule
Monday, February 18th, Presidents’ Day, Independence Day in Gambia, National Democracy day in Nepal: Foreshadowing of modern complications: when is George Washington’s birthday, anyway, and why are we celebrating it today? General discussion of the “natural units” that make up a calendar: day, month, year. How long are they? How could ancient or modern non-industrial societies determine these? Handout outlining the GW discussion; the Handout from Marking Time, by Duncan Steel. Some historical details about Presidents’ day on Wikipedia.
Homework Assignment Number One: Write a one-page summary of the cues a traditional pre-industrial civilization might use to determine when one year has elapsed. This is not intended as a serious ‘scholarly’ essay, but only as a snapshot of your understanding of our discussion in class. Do pay attention to crafting good sentences and paragraphs, though!
Reading: Read the Handout from Marking Time – it includes a piquant introduction to many of the issues we will encounter throughout the block (regrettably, this book is out of print too). Also read pp. 39-46 from the Ascher Handout, about the calendars of the Trobriand Islanders and the Kodi; you might find some of this discussion useful for your Homework essay.
Tuesday, February 19th, Battle of Iowa Jima (1945): The astronomical background: the modern version and the traditional interpretation. The motion of the sun and the moon across the celestial sphere, and how those motions determine days, months and years.
Homework Assignment Number Two: Write down brief definitions in your own words of the following important terms: Celestial Sphere, Ecliptic, Solstice and Equinox. You can of course “cheat” and try to lift language out of the Richards handout, or else off the Internet. The real point of this exercise is for you to carefully think through and internalize these complicated ideas yourself!
Reading: Handout from Richards, pages 17-41; Handout from Holford-Stevens. Much of what we do in class will carefully follow Richards. The Holford-Stevens extract is a delightfully British brief version of a lot of what we will be discussing in the next several days; it is worth revisiting as the days pass (see references below). There are more interesting facts herein than we’ll ever have a chance to discuss – lots of good paper topics, though!
Wednesday, February 20th, my mother’s birthday (93 today!), Total Lunar Eclipse today: More about astronomy: different definitions of the year. How do we measure time: Sundials, stars and clocks.
Homework Assignment Number Three: Some homework problems on the accuracy of year estimates, as compared to astronomical values.
Reading: Handout from Richards, pages 42-63; also Holford-Stevens.
Thursday, February 21st , International Mother Language Day, W. H. Auden’s Birthday: Modular arithmetic. This will be a purely mathematical discussion, introducing you to the ideas of modular arithmetic. There will be a Handout summarizing what we learn.
Homework Assignment Number Four: A set of problems to practice what we’ve learned. You will want to use and play with the small Excel program I will demonstrate in class, so that you do not have to compute all multiplicative inverses by hand. You can find this program Euclid.xls on the Course Drive, in the subdirectory Math, in the subdirectory Anderson. You should copy this file to your H: drive, or else to a hard drive on your own computer. You will need Microsoft Excel to run this program. As we discussed in class, you will need to log on to the CC network with a machine with the Course Drive mapped. Any school machine will have that – there are instructions at the Help Desk website to do this for your own machine (which might be a good idea in the long run).
Friday, February 22nd, World Thinking Day, George Washington’s History Book Birthday, Edna St. Vincent Millay’s birthday: More practice with modular arithmetic. Numeration and positional number systems. What is the difference between base 10, base 20 and base 60?
Reading: Handout on numeration and Mayan computations – you actually only need to read the numeration part. We will cover the Mayans on Monday.
Homework Assignment Number Five: Some homework problems on positional numbers, and changing from one base to another. These problems are included in the Handout.
Saturday, February 23rd, Red Army day in the
Soviet days, W. E. B. DuBois’s birthday, my friend Kaylyn’s birthday.
Sunday, February 24th, The Academy Awards!
Monday, February 25th, National Day for Kuwait: Discussion of the readings on days, hours and clocks. An example of a non-Western calendar: the Mayans. Mayan numeration. The haab, the tzolkin and the Long Count, and how to move from one to another.
Reading: Read pp. 59-74 from the Ascher. Handout.
Homework Assignment Number Six: More problems from the Handout about the Mayan calendars.
Tuesday, February 26th, Jeremy Bentham’s birthday, intercalary days in the Baha’i calendar: Finish up on the Mayan calendar – the Calendar Round. Discussion of the various types of calendars: lunar, solar, lunisolar, wandering year. Empirical, Arithmetic and Astronomical calendars. Intercalary days and months. An important special case: The Roman calendar. The lunar beginnings and the reforms of Julius and Augustus Caesar. Inclusive counting and days of the week.
Reading: Handout: an outline and a table to help understand the Roman calendar, and how the Romans described the days of the month. Look back at Holford-Stevens.
Homework Assignment Number Seven: Some practical counting and labeling problems related to the Roman calendar.
Wednesday, February 27th, Dominican Republic
Independence Day, Approximate Pi Day, Reichstag fire in Germany (1933): The Hebrew Calendar. This is a lunisolar calendar designed to
keep in synchronization with a “theoretical moon”. We will learn how to compute the structure of a given year in
this calendar, using modular arithmetic.
Reading: Ascher, pp. 46-57. Handout on the calendar computations.
Homework Assignment Number Eight: Discover how many days there are in the Jewish year 5426 (this is the year 1665 in our calendar), and the day of the week for Tishri 1. Then choose an AD year of your choice in the Gregorian calendar. Translate this to the appropriate Jewish year, and then compute the year type and day for Tishri 1.
Thursday, February 28th, Florian Cajori’s Birthday: Finish up the Hebrew Calendar; review for the midterm. I will hand out a study guide for the exam. In addition to morning class, we will have an option problem workshop from 1:30 to 2:30.
Homework: Study for the exam!
Friday, February 29th, Jimmy Dorsey’s birthday, Harold Pinter Birthday Party on campus today, LEAP DAY!!: Midterm Exam, 9-noon. Closed book, notes and colleagues – I will supply you with some needed charts and information as part of the exam. There is a student-oriented math talk at noon in Tutt Science 122, about regular polyhedra, a topic first considered by Plato. There is free pizza at this talk!
Reading: Next week we will be grappling with the major problem of the Christian calendar: determining the date of Easter. Read Handout from Duncan’s book: Chapter Five; please note Homework Number Ten below.
Homework Number Nine: Look at the algorithm for computing the date of Easter, given on page 73 of Duncan’s book. Please run through this algorithm for year 2008. Your write-up should give all the intermediate values for the variables a, b, c etc. You will undoubtedly not understand why you are doing the arithmetic you are doing – that’s exactly the attitude of most medieval monks doing Easter calculations. Please note that Duncan writes year%19, while we would write year (mod 19). When Duncan writes year/100, he really means the quotient we obtain, without the remainder. Last minute advice: please distinguish between ells and ones in this formula. They both appear! L
Saturday, March 1st, St. David’s Day.
Sunday, March 2nd, Lou Reed’s birthday.
Monday, March 3th, Jean Harlow’s Birthday: For this morning only, we will begin class at 10:30 a.m. The perpetual Julian calendar. History of the calculation of Easter: Dionysius. What are the desiderata for this calculation? Critics and early suggestions for reform: Grosseteste, Bacon, et al.
Homework Number Ten: In the chapter you read from Duncan’s book Calendar, we encounter a tension between the Christian (and Augustinian) idea of sacred time on the one hand, and the spiritually and practically important task of determining the date of Easter on the other. Write a 1000 word essay exploring this tension, and how Augustine might have resolved it. This assignment could of course turn into a major research project, and I am not asking for that; instead, I am looking for a more personal report on your understanding of this issue. However, you should consult at least one or two outside (cited) sources, in addition to Duncan’s chapter.
Tuesday, March 4th, before FDR, this was Inauguration Day: Building the Paschal table. Golden Numbers, Dominical Letters. How do we determine the date of the (Julian) Easter? Handout on computing the Julian Easter.
Wednesday, March 5th, Boston Massacre, 1770: Calculating Easter using modular arithmetic, instead of the tables. Handout on the modular version of Easter.
Reading: Handout from Duncan, Chapter 13.
Homework Number Twelve: Some problems about Julian Easter.
Thursday, March 6th, Ghana’s Independence Day: The Gregorian reform; the perpetual Gregorian calendar. What did Gregory do about the moon? Translating from Julian to Gregorian. Introduction to the Scaliger chronology system.
Homework Number Thirteen: Problems on the Julian vs. Gregorian Easter, the Alfonsine estimate, and a little about Scaliger.
Friday, March 7th: (International Women’s Day is on Saturday): More about Scaliger. How to count days. Handout on them. The Zeller congruence. Assignment of Project spots. Review for Final Exam.
Homework Number Fourteen: Problems about the Scaliger day count.
Monday, March 10th, Tibet rises up against the Chinese (1959), Lent begins this year for Orthodox Christians: Please note that your Final Paper is due this morning at class time. Final Project Presentations, Part One, starting at 9 AM.
Tuesday, March 11th: Final Project Presentations, Part Two, starting at 9AM.
Wednesday, March 12th: Final Exam.