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Thanks, Chen. Perhaps the greatest ancient astronomers were the Mayans, who lived right

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here where I'm standing. The Mayans inhabited the Yucatan Peninsula in Mexico and Guatemala.

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These people made astronomical and seasonal observations which rivaled anything seen in

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Europe during the Roman Empire or the Dark Ages. These amazing people mapped the heavens,

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they evolved the only true writing system native to the Americans, and they were masters

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of mathematics. They invented calendars that are still accurate today. And without metal

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tools, beasts of burden, or even the wheel, they were able to construct vast cities with

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an amazing degree of architectural perfection and variety. The largest structure at this

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site is El Castillo, the Castle. That these temple builders were mathematically precise

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in their architectural designs is borne out by the natural phenomena which occurred during

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the fall and spring equinoxes. In the spring, as the sun rises, the shadow cast on the steps

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appear to form the body of a serpent which slithers down the stairs. Here at Chichen

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Itza, there is a structure unlike anything else ever created by the ancient Mayans. It's

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called El Caracol, and it actually looks like a modern observatory. Its design didn't function

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the same way as our modern observatories. Instead, its walls contain many windows. Inside

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the dome, stones could be removed, enabling the Mayan astronomers to observe different

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parts of the sky. The Mayans looked at the sky differently from any other civilization.

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Being near the equator, the equinox passages were easier and more accurate to determine

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because the sun cast no shadow at local noon during this time. They also had great veneration

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for the Milky Way. They called it the World Tree. The star clouds that formed the Milky

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Way were seen as the Tree of Life, from which all life came. The Mayans also had their unique

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constellations. Like today's zodiac, they had their scorpion. Gemini, which appears

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to us as twins, however, was seen as a peccary, a nocturnal animal in the pig family. Other

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zodiac symbols were a jaguar, a bat, a turtle, the tail of a rattlesnake, and a sea monster.

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Because they looked at things differently, perhaps it's not surprising that the Mayans

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had a different mathematics as well. We use a numbering system based on 10 digits, but

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the Mayans used a system based on the number 20. Sounds a little bit complicated, but in

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fact it was more efficient for counting than some of the older systems used in Europe a

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long time ago. The Mayan counting system required only three symbols, a shell representing zero,

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a dot representing a value of 1, a bar representing 5, and a shell with a dot representing the

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base number 20. There are two advantages to the Mayan counting system. The first of these

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is the idea of zero, which many civilizations at that time did not have. Second, they only

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used three symbols to represent lower and higher numbers. In Rome, multiple symbols

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were used. I for 1, V for 5, X for 10, L for 50, C for 100, and M for 1000. Mayan numbers

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were written from bottom to top, so the number 19 becomes bars of 5, 5, 5, with four dots

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above the bars. To complete the first set of 20, a dot was raised over a shell-like

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symbol. To get 21, the elevated placement of the dot remained to represent 20, and a

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dot was added underneath to represent 21. Then the counting cycle for the next 20 began

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again. So what do you think the number 40 or 41 would look like? In Europe at this time,

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people still struggled with the Roman numeral system. That system suffered from two serious

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defects. First, there was no zero. And second, Roman numbers were entirely symbolic, having

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no direct connection to the number of items represented. So, are you ready for a challenge?

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Okay. Working together, try adding 21 and 33 using the Mayan system. Then try adding

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21 and 33 using Roman numerals. This is a good time to pause the program. So how did

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you do? Let's check your work. In Mayan, the number 21 is represented as dot, dot. 33 is

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two bars equaling 10, three dots for units, and an elevated dot representing 20. Adding

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together, you get 54, which is two bars, four dots, and two elevated dots. Easy to decipher.

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In Roman, you have XXI plus XXXIII equals LIV. Unless you actually know what the Roman

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symbols stand for, you have no idea what you are seeing. In Mayan, you can actually add

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up the dots, bars, and shells. Mayan merchants often used cocoa beans, sticks, and shells

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to do these calculations. From these three symbols, the Mayans could do everything from

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the simplest arithmetic needed for trade to keeping track of astronomical events, both

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past and future. Speaking of astronomy, remember how I said the Earth's axis was tilted at

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23.5 degrees? If you round that to 24, how would you write that in Mayan? The Mayan system

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of counting using dots, bars, and shells can be compared with the ones and zeros used

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by modern computers, and it was all done 1,500 years ago. With all the advances that the

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Mayans made, it's interesting to speculate what would have happened if the Mayans had

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sailed east to discover Europe instead of the Europeans sailing west to discover the

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Americas. To learn more about Mayan mathematics, go to the following websites. Back to you,

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Stan. Thanks, Stan. Well, guys, that wraps up another episode of NASA Connect. We'd like

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to thank everyone who helped make this program possible. Got a comment, question, or suggestion?

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Well, then email them to connect at lark.nasa.gov. I'd like to leave you guys with a thought

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and a challenge. What is impressive about these sites is the accuracy of their observations

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and the time and effort they put into building these observatories. Looking back at these

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buildings and places, we see that the ancients had a natural connection to their environments

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and that they were also capable of high-tech accomplishments in their own times. So now,

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here's my challenge. How do you think people 300 or even 1,000 years from now will see

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us through the artifacts that we leave behind? Until next time, stay connected to math, science,

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technology, and NASA. Goodbye for now.

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The evening stars, they will tell us it's in the west direction. It's almost nighttime.

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Deliberated more like the dipper and all that. It revolves in different position. It will

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tell us if it's fall, spring, or summertime, wintertime.