Transcript for NASA Connect - Ancient Observatories: Timeless Knowledge

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In this episode of NASA Connect,

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learn how ancient cultures
observed seasonal cycles

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and how the Sun played a
part in their observations.

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We'll also conduct a cool hands-on
activity measuring shadows created

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by the Sun and a gnomon.

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Stay tuned for another exciting
episode of NASA Connect:

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Ancient Observatories.

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[Music]

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Cama'i tawow, or welcome,
to NASA Connect.

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I'm Jennifer Pulley, and
this is the National Museum

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of the American Indian.

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And I'm Dr. Sten Odenwald at an
archaeological site in Mexico.

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Hola, this is NASA Connect, the
show that connects you to math,

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science, technology -- and NASA.

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On today's program, you will
see how ancient cultures found a

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connection to the stars.

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You will also learn how many

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of these societies
were very sophisticated

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when making celestial observations.

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You'll also learn about the
mathematics and geometry used

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by these ancient peoples
to make their observations.

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What you will learn today
will absolutely astound you.

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But first, Jennifer, tell us about
that building that you're in.

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Sten, this is the newest
museum in our nation's capital.

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As you enter the museum, hundreds
of written and spoken words meaning

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"Welcome" in native languages
throughout the Americas are

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projected onto this wall.

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These people -- not only
here in the Americas,

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but also their brothers and
sisters in Africa, Asia, Europe,

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and the Pacific -- looked
at our starry skies.

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All of these people had
a connection to the Sun.

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In the museum, this
room celebrates the Sun.

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From this circle, the four cardinal
directions -- north, south, east,

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and west -- extend
out of the building.

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The angles of solstices and
equinoxes are mapped on the floor.

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A light spectrum is
cast by the Sun,

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which shines through the prisms
set into the south-facing wall.

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Each prism is sighted to the Sun

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for a particular time
of day and season.

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The dramatic designs in this
modern museum show the connection

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between astronomy,
nature, and people.

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That connection is the key

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to understanding how the
ancients looked at our universe,

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which is the theme
of today's program.

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Today we will talk to
Native American astronomers.

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Dr. Sten Odenwald will treat us
to the foundations of astronomy

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as we know it today,
and he will fill us

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in on the celestial
accomplishments of the Mayans.

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Throughout the program,
you will be asked

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to answer several
inquiry-based questions.

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After the questions
appear on the screen,

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your teacher will pause the
program to allow you time to answer

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and discuss the questions.

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This is your time to explore
and become critical thinkers.

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Now let's learn more about
ancient observatories.

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The science of interpreting the
relationship between the Sun

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and the daily lives of primitive
people is called archeoastronomy --

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"archeo" meaning "archeology,"

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and "astronomy" meaning
"the study of stars."

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Observing celestial
phenomena is the one constant

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that unifies humankind
throughout space and time.

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Ancient man knew celestial events
followed cycles -- circles --

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and these events could be recorded.

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Approximately 5,000 years ago,
they devised a way to place stones

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in certain positions to align
for lunar and solar events.

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Events like seasons were noted
and found to recur regularly

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with certain positions
of the Sun and stars.

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The earth spins on its
axis once every day

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and gives us the familiar
experience

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of daytime and nighttime.

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For thousands of years, humans
have used this cosmic cycle

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to regulate their workday,
their meals, and their sleep.

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The earth orbits the
Sun once every year,

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and from this we get the
familiar 365 day cycle.

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Earth's orbit around
the Sun is an ellipse --

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basically, that means an
oval with the Sun offset

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from the center of the ellipse.

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Does this mean that we have
summer when the earth is closest

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to the Sun and winter when the
earth is farthest from the Sun?

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The surprising fact is that
the distance from the earth

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to the Sun has absolutely nothing
to do with the changing seasons.

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Our northern hemisphere is
closest to the Sun in January

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and farthest from the Sun in July.

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So what is causing the
change in temperature?

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Earth's axis is tilted
by 23 1/2 degrees

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from a line perpendicular
to Earth's orbit.

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What does this mean?

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To understand this tilt, we have
to use a bit of basic geometry.

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An angle has two sides
and a vertex.

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The sides are rays that share a
common endpoint called the vertex.

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The angle formed by two rays can
be named in a variety of ways.

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For example, the angle
formed by ray AB

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and ray AC can be named angle BAC,
angle CAB, or angle A for short.

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Notice that A must be the middle
letter in both three-letter names

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because it's the vertex.

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You can measure angles
using a protractor.

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The unit of measure is degrees.

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Angles can be classified
by their measures as acute,

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right, obtuse, and straight.

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If the earth rotated on
its axis perpendicular to,

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or at a right angle to the orbit,

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there would be no
changes in temperature.

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The earth rotates at
an angle 23 1/2 degrees

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from this perpendicular line.

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It's a very small tilt, but enough

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to affect the Sun's
rays hitting the earth.

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This is a great time to
pause the program and think

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about the following questions:

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Why is the area near
earth's equator hotter

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than the areas near the poles?

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If the tilt of earth's axis
measured 33 degrees rather

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than 23 1/2, how might
seasonal changes

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and temperature ranges differ?

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Teachers, it's now time
to pause the program.

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The tilt of the earth's
axis gives us our seasons,

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and because of the extremes in
heat and cold, it's very important

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to keep track of the changing
seasons if you're growing food.

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This seasonal cycle is important
to ancients and even modern people.

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In some parts of the world,
like the arid climates

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of the southwest states of the
USA, the growing season was

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so short that people could not
waste much time getting the seeds

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in the ground at the
start of spring.

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But how do we predict when
the growing season will begin

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in the spring?

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For that matter, how can we tell

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when the other seasons
begin and end?

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It turns out that just by keeping
track of how high up the Sun gets

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over the horizon at noon,
you can determine the start

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of the seasons exactly.

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Almost all ancient
people that relied

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on planting times discovered
this little relationship.

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The start of the four seasons --
summer, fall, winter, and spring --

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are noted by what astronomers
call the summer solstice,

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the fall equinox, the winter
solstice, and the spring equinox.

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At the start of summer --

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around June 21 in the
northern hemisphere --

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the Sun is at its highest point
above the horizon at noon.

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As the Sun begins its movement
back away from its maximum height,

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the number of daylight hours
has declined to an equal number

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of daylight and nighttime hours.

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This is the fall equinox,
near September 21.

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A few months later, the
path of the Sun arrives

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at its lowest point at noon.

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The Sun spends very little
time above the horizon

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of the northern hemisphere, and
the night is much longer than day.

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Welcome to the winter solstice,

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or start of winter,
around December 21.

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After a few more months, the path
of the Sun works its way higher

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in the sky, eventually
arriving at a path

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where day and night are equal.

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This happens March 21
at the spring equinox,

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a vital time for planting crops.

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Archeoastronomers have found three
types of early observatories:

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simple markers, circles of
stone and wood, and temples.

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Early on, markers were used to
create sight lines to the horizon

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so that during the equinox or
solstice, the Sun would appear

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to rise exactly on the sight line.

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Stonehenge, in England, was set
up this way, as were a number

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of ancient Native American
buildings, such as the ones

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at Chaco Canyon in New
Mexico, and Hovenweep in Utah.

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England's Stonehenge is one
of the earliest examples

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of an observatory in Europe.

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Stonehenge is a large
calendar capable

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of predicting the
equinoxes and the solstice.

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Before Stonehenge in 3,000 BC,

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the ancient Egyptians had devised
a solar calendar of 365 days,

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the starting point of which
hinged on the helical rising

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of the star Sirius, which
also happened to coincide

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with the summer solstice and
the annual flooding of the Nile.

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By being in touch with
celestial phenomenon

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and their natural surroundings,
the ancient Egyptians were able

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to predict events of
great significance

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in their desert environment.

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At Abu Simbel, massively
carved statues

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of Ramses the Great face east

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to greet the Sun god Ra,
the bringer of light.

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As the Sun rises each day, the
statues are illuminated again,

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perhaps a sign of
rebirth for Ramses.

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But the most compelling
is a passage

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to the temple's inner sanctuary,
which is aligned so that

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on October 18, the Sun
filters into the sanctuary,

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illuminating a statue of Ramses.

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While October 18th doesn't mean
much to us in the Western world,

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this October date
corresponds to the beginning

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of the Egyptian civil
year and the celebration

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that occurred during the
time in which Ramses lived.

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It was the Greeks, however,

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that created the first portable
cosmological tool for keeping track

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of these motions -- a stick.

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The Greeks actually called
it a gnomon, and it was used

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to keep track of the
shadow of the Sun.

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Actually, it's a little bit
more difficult than that,

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because the shadow
depends on your latitude.

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Again, if you were
not near the equator,

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the shadow will be shortest
during the summer solstice

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and longest during
the winter solstice.

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For the spring equinox and fall
equinox, the shadow will be halfway

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between the shadow
lengths at the solstices.

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In the southern hemisphere,
the shadows will be reversed,

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just as you all know the
seasons are reversed.

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When it's summer in the United
States, it's winter in Argentina.

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This all works pretty well
if you're not at the equator.

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At the equator, the summer
solstice Sun casts a shadow

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in a southerly direction, and the
winter solstice Sun casts a shadow

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in the northerly direction.

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During the equinox, at the
equator, the shadow disappears.

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Oh, and another thing that
they were used for is sundials.

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And it looks to me like it's
time to go back to Jennifer.

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Okay, guys, let's take a
look at how a gnomon works

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and see the angle of the Sun at
certain times during the day.

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Students from Newcomb Elementary
School in Newcomb, New Mexico,

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will preview this
show's hands-on activity.

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Ya'e'teeh.

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Hello. We are students from
Newcomb Elementary School.

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We are located on the
Navajo Reservation

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in the Four Corners
Region of New Mexico.

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Tracking the passage of the
Sun in the sky continues

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to play a very important role in
the life of our Navajo culture.

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Traditional Navajos
still use this system

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of tracking the Sun's
shadows to tell time

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and to tell the changing
of the seasons.

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For example, when my
grandfather herds sheep,

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he does not wear a watch like this.

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He uses the Sun's
shadow to tell time.

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It also helps him to tell when
to take the sheep back home

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in their corral.

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It also helps him to
tell when to plant corn

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and watermelon on his farm.

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NASA Connect asked us to show you
this program's hands-on activity.

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In this activity, the students will
make Sun shadow plots every half

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hour, marking the ends
of the shadows made

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by the Sun and a gnomon.

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You can download a copy
of the educator guide

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from the NASA Connect website for
directions and a list of materials.

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Turn a cardboard box upside down.

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Tape a large piece of
paper to the cardboard box.

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Draw two lines that are
perpendicular to each other:

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from top to bottom,
and the other from left

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to right across the paper.

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Mark its center with a dot,
and make a very small hole

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in the center of the box
using the point of a scissors.

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Stick the gnomon through the dot
and the hole in the cardboard.

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Secure it with tape so that 10
centimeters is sticking straight

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up out of the box.

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Use a protractor to make sure the
gnomon is perpendicular to the box.

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On a clear, sunny day,
find a large, flat area.

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Tape the box to the
ground on all four sides.

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Starting as early in
the morning as possible,

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mark the end of the gnomon's
shadow every half hour

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until the end of the day.

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Next to the dot, label the
time of the day it was marked.

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You will analyze the
data you collect

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by measuring angles and length.

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Remove the gnomon and draw a
straight line from each dot

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to the hole that the
gnomon was placed in.

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Measure and record the angle
between the horizontal line drawn

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through the center of the
paper and each marked shadow.

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Then measure and record
the length of each shadow.

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Using geometry, find and label
true north on your Sun shadow plot.

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Verify local solar noon
using shadow length times

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and sunrise/sunset times.

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How do the lengths, positions,
and angles of the shadows change?

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What do the changes tell
you about the position

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of the Sun throughout the day?

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Would the curve change if you
used a different sized gnomon

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to cast the shadow?

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And don't forget to check out this
cool web activity for this program.

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You can download it from
the NASA Connect website.

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Great job, you guys.

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All right.

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Let's review.

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We've seen how ancient cultures
used the Sun/Earth connection

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to mark the season.

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And you've seen an activity which
uses the placement of shadows

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to record the movement of
the Sun across the sky.

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Research regarding Native American
astronomy has recently begun

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to gain headway in archeoastronomy.

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Let's look at the
ways native cultures

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in the Americas used the
Sun/Earth connection.

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Nancy Maryboy and David Begay
are two indigenous astronomers

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from the Navajo Nation.

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Ya'e'teeh.

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Hello. We're in Hovenweep
National Park in southern Utah.

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I'm a Cherokee Navajo, I
live not far from here,

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and I'm an educator
on the Navajo Nation.

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A "cultural astronomer" means
you deal with the astronomy

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of your own culture, and we
put things within the context

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of a Native worldview.

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Right behind me, on the boulder,

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you can see an indication
of a solar phenomena.

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On the boulder, there's two images:

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one's a concentric
circle, one's a spiral.

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As the Sun begins to
rise, shafts of light come

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in from each direction, and
as the Sun continues to rise,

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the lights meet in the center.

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This only happens once a year.

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This phenomenon occurs on
the longest day of the year

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and is a very appropriate
way to mark time.

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This can be a very harsh
environment to live in.

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It can be hot, it can be
cold, and it can be very dry.

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In order to survive, people
had to live in accordance

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with the natural environment,

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and that meant the natural
cosmic environment: the Sun,

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the Moon, and the stars.

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It was very important to track
the path of the Sun and the Moon

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and certain constellations,
and to do that,

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people used natural
markers like petroglyphs

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and Sun and Moon alignments.

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Remember, there was no watches,
there was no timekeepers,

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there was no calendars.

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My name is David Begay.

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I am a cultural astronomer.

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I've been living out
here for many years.

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My clan is Midishkisinee.

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This clan is a descendant
from the Jemez Pueblo people.

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And here is one of the structures
at Hovenweep National Monument.

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This structure had many purposes,
one of which was an observatory.

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The ancient had a profound
respect for the movement

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of the Sun and the stars.

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On the longest day of the year,
the Sun shines through an opening,

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and the light falls on a marker.

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What people experience here is
really a cultural experience.

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It's a whole life experience.

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People felt the movement
of the Sun.

[00:18:11.108]
People felt the movement
of the Moon.

[00:18:14.318]
It was a daily experience.

[00:18:17.348]
Among the Navajo people,
for the Sun,

[00:18:19.538]
when it reaches summer solstice,
it's a total life experience.

[00:18:25.028]
People used to talk about
the solstice being a

[00:18:27.988]
four-day phenomenon.

[00:18:29.658]
People used to say,

[00:18:31.168]
[speaking Native], the sun spent
four days before it starts moving

[00:18:36.188]
back the other way.

[00:18:37.218]
So it's really something
that was experienced.

[00:18:40.328]
It was talked about.

[00:18:41.168]
It was a part of the
culture that's been passed

[00:18:42.928]
down through the generations.

[00:18:44.468]
I think people talk about these
movements in terms of days.

[00:18:50.088]
I'm not really sure if you can
really call it "special" math.

[00:18:53.478]
I don't think tracking the Sun

[00:18:55.558]
down to the second was
important at that time.

[00:19:00.398]
These buildings and boulders are
remnants of ancient civilizations,

[00:19:03.748]
much like the ruins in Rome,
the ruins in Greece, and today,

[00:19:07.968]
they're still very relevant to
us out here in the Southwest.

[00:19:11.588]
We still see the same sky, and
we're in awe of the technology

[00:19:15.348]
that was employed to
build these buildings

[00:19:17.578]
and capture these solar
and lunar alignments.

[00:19:20.568]
Today we look in the sky.

[00:19:22.468]
We use some of the same knowledge
that the ancestral Pueblans used.

[00:19:26.918]
We use it for planting, we
use it for setting ceremonies,

[00:19:29.918]
and we use it to keep
the earth in order.

[00:19:32.978]
The balance between earth and
sky is still very important

[00:19:36.078]
to Native peoples.

[00:19:38.428]
Thanks, Nancy.

[00:19:41.708]
And thanks, David.

[00:19:43.138]
You know, guys, one of the
earliest Native American structures

[00:19:46.518]
to observe the Sun and the
stars is Casa Rinconada.

[00:19:50.258]
Located in the Chaco Cultural
National Historical Park,

[00:19:54.308]
Casa Rinconada is a large kiva.

[00:19:57.538]
Kivas are large circular
rooms used for ceremonies

[00:20:01.478]
by Native American cultures.

[00:20:03.848]
Like Hovenweep, on the day of the
summer solstice, a beam of light

[00:20:08.518]
from an opening in the kiva
precisely illuminates a niche

[00:20:12.588]
in the far wall.

[00:20:14.668]
For years, Chaco Canyon was
primarily seen as a trade center,

[00:20:19.078]
but with the advent of
archeoastronomy, Chaco is beginning

[00:20:23.318]
to be seen as a center of
astronomy and cosmology.

[00:20:27.318]
So far on today's program, we
have seen how the relationship

[00:20:30.438]
between the Sun and the
earth weaved a connection

[00:20:33.298]
between all ancient cultures.

[00:20:34.978]
Now, much of the information from
those cultures has been lost to us.

[00:20:38.658]
However, other cultures have
recorded that information,

[00:20:41.898]
and now that information
is being interpreted.

[00:20:45.018]
For a look at one of
these ancient cultures,

[00:20:47.188]
let's return to Dr. Sten Odenwald.

[00:20:50.528]
Thanks, Jen.

[00:20:54.298]
Perhaps the greatest ancient
astronomers were the Mayans,

[00:20:57.018]
who lived right here
where I'm standing.

[00:20:59.788]
The Mayans inhabited the Yucatan
Peninsula in Mexico and Guatemala.

[00:21:04.118]
These people made astronomical
and seasonal observations,

[00:21:07.048]
which rivaled anything seen

[00:21:08.468]
in Europe during the Roman
Empire or the Dark Ages.

[00:21:12.228]
These amazing people
mapped the heavens,

[00:21:14.728]
they evolved the only true writing
system native to the Americas,

[00:21:18.498]
and they were masters
of mathematics.

[00:21:21.578]
They invented calendars that
are still accurate today,

[00:21:24.508]
and without metal tools, beasts
of burden, or even the wheel,

[00:21:28.898]
they were able to construct vast
cities with an amazing degree

[00:21:32.058]
of architectural perfection
and variety.

[00:21:34.218]
The largest structure at this site
is El Castillo -- "the castle."

[00:21:38.898]
That these temple builders
were mathematically precise

[00:21:41.798]
in their architectural designs is
borne out by the natural phenomena

[00:21:46.228]
which occur during the
fall and spring equinoxes.

[00:21:49.518]
In the spring, as the Sun rises,
the shadow cast on the steps appear

[00:21:54.608]
to form the body of a serpent
which slithers down the stairs.

[00:21:58.678]
Here at Chichen Itza, there is a
structure unlike anything else ever

[00:22:01.858]
created by the ancient Mayans.

[00:22:03.698]
It's called El Caracol,

[00:22:05.108]
and it actually looks
like a modern observatory.

[00:22:08.948]
Its design didn't function the same
way as our modern observatories.

[00:22:12.808]
Instead, its walls
contain many windows.

[00:22:16.008]
Inside the dome, stones
could be removed,

[00:22:18.918]
enabling the Mayan astronomers to
observe different parts of the sky.

[00:22:23.058]
The Mayans looked at
the sky differently

[00:22:25.058]
from any other civilization.

[00:22:27.128]
Being near the equator, the
equinox passages were easier

[00:22:30.888]
and more accurate to determine
because the Sun casts no shadow

[00:22:34.628]
at local noon during this time.

[00:22:36.688]
They also had great
veneration for the Milky Way.

[00:22:39.978]
They called it "the world tree."

[00:22:42.698]
The star clouds that form the Milky
Way were seen as the tree of life,

[00:22:46.648]
from which all life came.

[00:22:49.418]
The Mayans also had their
unique constellations.

[00:22:52.578]
Like today's zodiac,
they had their scorpion.

[00:22:55.558]
Gemini, which appears
to us as twins, however,

[00:22:58.148]
was seen as a peccary, a
nocturnal animal in the pig family.

[00:23:02.348]
Other zodiac symbols were
a jaguar, a bat, a turtle,

[00:23:07.228]
the tail of a rattlesnake,
and a sea monster.

[00:23:10.748]
Because they looked
at things differently,

[00:23:12.578]
perhaps it's not surprising

[00:23:13.788]
that the Mayans had a
different mathematics as well.

[00:23:16.788]
We use a numbering system
based on ten digits,

[00:23:19.758]
but the Mayans used a system
based on the number 20.

[00:23:22.748]
Sounds a little bit complicated,
but in fact, it was more efficient

[00:23:26.078]
for counting than some
of the older systems used

[00:23:28.098]
in Europe a long time ago.

[00:23:29.498]
The Mayan counting system
required only three symbols:

[00:23:33.628]
a shell representing 0, a dot
representing a value of 1,

[00:23:39.018]
a bar representing 5, and a shell

[00:23:42.188]
with a dot representing
the base number 20.

[00:23:45.538]
There are two advantages to
the Mayan counting system.

[00:23:48.178]
The first of these is the idea
of zero, which many civilizations

[00:23:51.618]
at that time did not have.

[00:23:53.488]
Second, they only
used three symbols

[00:23:55.588]
to represent lower
and higher numbers.

[00:23:57.768]
In Rome, multiple
symbols were used.

[00:24:00.338]
I is for 1, V for 5, X for 10, L
for 50, C for 100, and M for 1,000.

[00:24:08.308]
Mayan numbers were
written from bottom to top,

[00:24:10.638]
so the number 19 becomes
bars of 5, 5, 5,

[00:24:15.358]
with four dots above the bars.

[00:24:18.268]
To complete the first set
of 20, a dot was raised

[00:24:21.278]
over a shell-like symbol.

[00:24:22.908]
To get 21, the elevated
placement of the dot remained

[00:24:27.138]
to represent 20, and a dot was
added underneath to represent 21.

[00:24:32.178]
Then the counting cycle for
the next 20 began again.

[00:24:35.978]
So what do you think the number
40 or 41 would look like?

[00:24:39.558]
In Europe at this time,
people still struggled

[00:24:42.248]
with the Roman numeral system.

[00:24:44.148]
That system suffered
from two serious defects.

[00:24:47.218]
First, there was no zero.

[00:24:49.558]
And second, Roman numbers
were entirely symbolic,

[00:24:52.908]
having no direct connection to
the number of items represented.

[00:24:56.388]
So are you ready for a challenge?

[00:24:58.468]
Okay, working together, try adding
21 and 33 using the Mayan system.

[00:25:04.368]
Then try adding 21 and
33 using Roman numerals.

[00:25:08.388]
This is a good time
to pause the program.

[00:25:10.978]
So how did you do?

[00:25:12.268]
Let's check your work.

[00:25:14.438]
In Mayan, the number 21 is
represented as dot, dot.

[00:25:19.618]
33 is two bars, equalling
10, three dots, for units,

[00:25:25.438]
and an elevated dot
representing 20.

[00:25:27.818]
Adding together, you get 54,
which is two bars, four dots,

[00:25:33.138]
and two elevated dots.

[00:25:34.998]
Easy to decipher.

[00:25:37.198]
In Roman, you have XXI
plus XXXIII equals LIV.

[00:25:42.808]
Unless you actually know what
the Roman symbols stand for,

[00:25:48.168]
you have no idea what
you are seeing.

[00:25:50.868]
In Mayan, you can actually add
up the dots, bars, and shells.

[00:25:55.228]
Mayan merchants often
used cocoa beans, sticks,

[00:25:57.998]
and shells to do these
calculations.

[00:26:00.478]
From these three symbols, the
Mayans could do everything

[00:26:03.208]
from the simplest arithmetic
needed for trade to keeping track

[00:26:06.668]
of astronomical events
both past and future.

[00:26:09.558]
Speaking of astronomy, remember how
I said the earth's axis was tilted

[00:26:13.008]
at 23 1/2 degrees?

[00:26:14.978]
If you round that to 24, how
would you write that in Mayan?

[00:26:18.698]
The Mayan system of
counting using dots, bars,

[00:26:21.408]
and shells can be compared
with the ones and zeroes used

[00:26:24.058]
by modern computers, and it
was all done 1,500 years ago.

[00:26:29.138]
With all the advances that the
Mayans made, it's interesting

[00:26:32.168]
to speculate what
would have happened

[00:26:33.748]
if the Mayans had sailed east
to discover Europe instead

[00:26:36.628]
of the Europeans sailing west
to the discover the Americas.

[00:26:39.598]
To learn more about
Mayan mathematics,

[00:26:42.378]
go to the following websites.

[00:26:44.358]
Back to you, Jennifer.

[00:26:46.768]
Thanks, Sten.

[00:26:49.398]
Well, guys, that wraps up
another episode of NASA Connect.

[00:26:53.628]
We'd like to thank everyone who
helped make this program possible.

[00:26:56.838]
Got a comment, question,
or suggestion?

[00:26:59.918]
Then email them to
"connect at larc.nasa.gov."

[00:27:05.138]
I'd like to leave you guys
with a thought and a challenge.

[00:27:09.358]
What is impressive about
these sites is the accuracy

[00:27:13.268]
of their observations and
the time and effort they put

[00:27:17.178]
into building these observatories.

[00:27:19.458]
Looking back at these
buildings and places,

[00:27:22.168]
we see that the ancients
had a natural connection

[00:27:25.078]
to their environments, and
that they were also capable

[00:27:28.468]
of high-tech accomplishments
in their own times.

[00:27:32.108]
So now, here's my challenge.

[00:27:34.688]
How do you think people
300, or even 1,000 years

[00:27:39.258]
from now will see us through the
artifacts that we leave behind?

[00:27:45.128]
Until next time, stay
connected to math,

[00:27:47.678]
science, technology, and NASA.

[00:27:51.208]
Good-bye for now.

[00:27:57.988]
Finally, they picked
one star out and said,

[00:28:00.158]
"this one will be the morning
stars, it will give us direction

[00:28:03.338]
that the daylight is coming,
it will give us direction

[00:28:06.668]
that it's in the east."

[00:28:08.888]
And the next one is
the evening stars.

[00:28:13.148]
They will tell us it's
in the west direction.

[00:28:15.898]
It's almost nighttime.

[00:28:18.778]
They liberated more, like
the Dipper and all that.

[00:28:22.338]
It revolves in different positions.

[00:28:24.748]
It will tell us if it's fall,
spring, or summertime, wintertime.

[00:28:29.468]