AST201L.Lab8.Word

NAME & USERNAME: SECTION: LAB 8 MAYA AND THE WANDERING STARS, II INTRODUCTION Following Lab 7, in this lab you will examine some Maya astronomical records in order to gain a better understanding of how Maya astronomical knowledge has been recorded and interpreted through time. Finally, apply your knowledge of Maya numerals to understand dates in the Long Count calendar. LEARNING GOALS The points below are the expected topics to understand by the end of this lab period. Remember to review these points before completing the lab. If you do not understand one, review the steps that cover it and discuss with your instructor.  Understand the physical origins of numbers in Maya astronomical records  Learn how Maya people record numbers and dates to make astronomical observations and track the passage of time LAB8-1

NAME & USERNAME: SECTION: STEP 1: MAYA ASTRONOMICAL RECORDS In this step, you will examine a portion of the Dresden Codex, a surviving example of written Maya records. 1 These records were recorded on painted fig bark and contain both numbers and words. Each symbol is called a glyph and can represent either phonetic sounds or symbolic ideas. Some of the glyphs here represent numbers— you will learn how to read the numbers and relate them to astronomical events. First, we will need to determine the base system used to record numbers in these observations. The base system of a number system defines its place values. As an example, the base system used in science is base 10 , meaning that as you look at a large number, e.g., the number 111, each “1” increases in value by ten as you move to the left: the rightmost 1 signifies 1 (= 10 0 ), the middle 1 signifies 10 (= 10 1 ), and the leftmost 1 signifies 100 (= 10 2 ), meaning that in total, this number is 100 + 10 + 1. In a different base system, such as base 2 (or the binary system, the base system used for most computers), the rightmost number again signifies the 1’s (=2 0 ) place, but the second signifies the 2’s (= 2 1 ) place, then the 4’s (= 2 2 ) place, and so on. 1. [1pt] Let’s do some practice about the base system and find out how to represent the number 111 in base 2. First, find out how the number 111 is made up of the numbers from powers of 2 by filling out the following blanks: 111 = 1 × 2 6 + 1 × 2 5 + 0 × 2 4 + 1 × 2 3 + 1 × 2 2 + 1 × 2 1 + 1 × 2 0 And so, in the base system of 2, we would write the number of “111” as 1101111. 2. [1pt] Now, try the numbers of 23 and 32: 23 = 0 × 2 5 + 1 × 2 4 + 0 × 2 3 + 1 × 2 2 + 1 × 2 1 + 1 × 2 0 And so, in the base system of 2, we would write the number of “23” as 10111 . (Note that just like in base 10, we don’t need to write more zeros to the left of the first non-zero digit at the highest place value in the number.) 32 = 1 × 2 5 + 0 × 2 4 + 0 × 2 3 + 0 × 2 2 + 0 × 2 1 + 0 × 2 0 And so, in the base system of 2, we would write the number of “32” as 100000. One thing to notice about the different base systems is that the number of glyphs that are used to represent numbers is equal to the base of that system . For instance, in base ten, we have ten different number glyphs (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9), while in base two, only two different number glyphs (0 and 1) are needed. Notice also that the value of the largest glyph (e.g., 9 in base 10, 1 in base 2) is one less than the base of that system . Using this knowledge, let’s try to determine which base the Maya records are in by identifying the numeral glyphs. Examine the glyphs in the next page first (pages 54 to 56 in the Dresden Codex) and answer the questions below. 1 To gain more practice with doing mathematical calculations using Maya numerals, visit maya.nmai.si.edu/maya-sun/maya-math-game . LAB8-2

NAME & USERNAME: SECTION: Given the value of this glyph, what base system are the numbers in the Maya text? The base system is Base 20. 5. [3pt] Now that we have determined the base system of the numerals in the Maya text, we need to determine which direction the numbers should be read (i.e., recall numbers “23” and “32” in Step 1). The glyph on the left below appears multiple times in the Maya text. There are two possible ways to interpret this number: one, where the digit with a higher place value is above the digit with a lower place value; and the second, where the digit with a lower place value is above the digit with a higher place value. What number would this glyph represent if the digit with the higher place value was above the digit with the lower place value? The number is 177. What number would this glyph represent if the digit with the lower place value was above the digit with the higher place value? The number would be 340. Examine the two numbers you obtained. Given that these records represent astronomical observations, which number do you think is the intended meaning of the glyph? (Hint: an average lunar month is 29.5 days long). The number would be 345. Based on the previous answer, can you interpret what the astronomical significance of this glyph would be? Again, given the answer to the last question, which way should the numeral glyphs be read? LAB8-4

NAME & USERNAME: SECTION: 6. [1pt] Reading along the bottom of the codex pages, most of the glyphs are the same as the glyph you examined in part 5. However, another glyph appears in this sequence. Draw this glyph below. What number does this glyph represent? The number is 148. The combination of this number and the one in part 5 represents a sophisticated relation of sidereal astronomical cycles and intervals, lunar orbits, solar orbits, full moon periods, and lunar synodic periods. 2 In fact, 65% of the pages in the Dresden Codex contain richly illustrated astronomical tables focused on eclipses, equinoxes and solstices, the sidereal cycle of Mars, and the synodic cycles of Mars and Venus. These observations allowed the Mayans to plan the calendar year, agriculture, and religious ceremonies around the stars. Between 1800 and 1900, the Maya numerals and the Maya calendar were successfully deciphered by German librarian Ernst Förstemann. He realized that the Dresden Codex is an ephemeris. Subsequent studies have decoded these astronomical almanacs, which include records of the cycles of the Sun and Moon, including eclipse tables, and all of the naked-eye planets. For example, the eclipse tables in the Dresden Codex accurately predicted solar eclipses for 33 years in the 8 th century. Icons of serpents devouring the sun symbolize eclipses throughout the book (Figure 1). You can view the entire Dresden Codex at the Library of Congress website here: https://www.loc.gov/item/2021667917/ . 2 You can read more about the Dresden Codes Lunar Series and Sidereal Astronomy here: http://www.jqjacobs.net/archaeology/maya_astronomy.html . LAB8-5 Figure 1: The depiction of a solar eclipse— two “wings” (one dark and one light) on either side of a smaller sun glyph and a serpent at the bottom. This image is from Page 59 of the Dresden Codex.

NAME & USERNAME: SECTION: The date is January 27,2005. 3. Use the converter to determine the Maya date corresponding to this event. Fill out the date in Baktun, Katun, Tun, Uinal, and K’in in the table above. 4. Note the Maya numeral glyphs are vertical and put next to the calendar glyphs. The combined glyphs then read from top left to bottom right in the webpage. Record/draw the combined glyphs corresponding to the time periods in the final column of the table above. You might notice that there are three more glyphs that are not listed in the table above. You can learn more about them at the end of this lab. 5. Using the table above, determine how many total days have passed from the start of the Maya calendar to your chosen event. 12 baktun 12 X 144,000 days = 1,728,000 days 19 katun 19 X 7,200 days = 136,800 days 11 tun 11 X 360 days = 3,960 days 17 uinal 17 X 20 days = 340 days 15 k'in 15 X 1 day = 15 days If you are interested, you can learn so much more about Maya Calendar from the National Museum of American Indians website at https://maya.nmai.si.edu/calendar/calendar-system . 6. [Bonus] In addition to the Long Count calendars, the Maya use two shorter cyclical calendars, the Tzolk’in and Haab. The Haab calendar tracks the solar year, and consists of 18 months made of 20 days, and one month made of 5 days (so a total of 365 days). The Tzolk’in calendar cycles through the numerals 1-13 in addition to 20 successive glyphs, generating a 260-day long cycle. The date also includes a glyph corresponding to one of 9 deities of the Maya underworld. The last three glyphs from the website shows these three calendars. Record/draw your glyphs below and write down what they are: LAB8-7