Thursday, October 31, 2013

Test #5 North South East and West

Celestial phenomena form the basis for most cardinal and ordinal directional systems and the same was true anciently.

Fact #1. In temperate and tropical latitudes (south of the Arctic Circle, north of the Antarctic Circle), the sun rises in the east and sets in the west. On a flat horizon, sunrise will be due east and sunset due west twice a year, on the vernal equinox (near March 21) and the autumnal equinox (near September 21). The site of Dzibilchaltun in Yucatan is justifiably famous with tourists partly because of spectacular site alignments on equinox sunrise.
Equinox sunrise, Dzibilchaltun
This is the same structure on vernal equinox about 30 minutes after sunrise.
Equinox sunrise + 30, Dzibilchaltun near Merida
Even more renowned among tourists is the serpent of light that appears on the steps of the Temple of Kukulcan (El Castillo) at Chichen Itza on the afternoon of each equinox.
Serpent image created by the equinoctial afternoon sun
Fact #2. The earth's spin axis is tilted 23.5 degrees from the plane of the ecliptic, the hypothetical plane that intersects both the earth and the sun. This tilt causes the seasons as days in the northern hemisphere lengthen toward summer solstice (near June 21) and shorten toward winter solstice (near December 21).
Visual representation of earth's tilted axis
At the equator on a flat horizon, the sun will rise on the summer solstice at a point 23.5 degrees north of due east. On the winter solstice that point will be 23.5 degrees south of due east. So, at the equator throughout one solar year, the sunrise point will vary across 47 degrees of a 360 degree arc, with that variation centered on due east. As one moves north or south of the equator, variation in solstitial sunrise points increases according to the formula 23.5/cosign(latitude). So, for example, the solstitial variation between sunrise points at Guatemala City (15.5 degrees north latitude) is 48.76 degrees on a flat horizon, slightly more than at the equator. The solstitial variation between sunrise points at Mexico City (19 degrees north latitude) is 49.68 degrees on a flat horizon. Mexico City (Teotihuacan) is about the northern extreme of New World locations that could plausibly be referenced in the Book of Mormon text. So, when the Nephites observed sunrise or sunset, they were looking at points on the horizon within 24.84 degrees of due east or due west. As with the equinoxes, solstice sunrise points were important in ancient architectural layouts. This, for example, is the entrance to the  famous Temple of Karnak in Egypt on the winter solstice sunrise.
Entryway, Temple of Karnak, Winter Solstice
Moonrise and moonset points follow a more complex but ultimately similar pattern. The new moon rises due east and sets due west on the spring and fall equinoxes, just as the sun does. The full moon does the same. The waxing moon rises due east and sets due west on the summer and winter solstices, which is opposite the sun's behavior. The waning moon does the same. As the moon goes through its phases, it will rise and set at points on the horizon that vary (at the equator) by the 23.5 degrees of the earth's tilt + the 5 degrees of the moon's own tilt. Like sunrise and sunset points, the amount of moonrise/set variation north and south of due east/west increases as one moves from the equator to higher latitudes. This graph from Paul Middents of the Battle Point Astronomical Association shows lunar rise/set point variation on the horizon relative to solar rise/set point variation across the 18.6 years of a Draconic Cycle.
Variation in moonrise points on the horizon relative to sunrise points
As the graph shows, some years the variation in moonrise points will be up to 5 degrees smaller than the variation in corresponding sunrise points. Some years the variation in moonrise points will be up to 5 degrees greater. Like the sun, the apparent movement of the moon will always center on due east and due west.

Venus, the evening and morning star, exhibits similar predictable behavior in the sky rising and setting on the horizon at points in between the solar and lunar maximums. The apparent motion of Venus is  affected by its sidereal period (225 days), its synodic period (583.9 days), the tilt of its axis (2.7 degrees away from the plane of the ecliptic) and its interaction with earth's sidereal period (365.256 solar days). The ancient Assyrians were careful observers of the planet's movements as shown in the Venus Tablet of Ammisaduqa on display in the British Museum. This 7th century B.C. copy of a 17th century B.C. text was in the library at Nineveh.
Cuneiform Tablet Plotting the Heliacal
Risings and Settings of Venus
The Maya were even more precise in many of their Venus observations. The famous Dresden Codex calculates Venus cycles to within 1/100th of a day.
Dresden Codex with
Venus Calculations
In his outstanding new book Izapa Sacred Space: Sculpture Calendar Codex, 2nd Edition, 2013, V. Garth Norman shows how Izapa was laid out with clear site alignments to lunar, Venus and solar azimuths on the majestic horizon which includes 4,220 meter high Tajumulco, the highest mountain in Central America
Maximum Northern Venus Rise Point Between the Summer
Solstice and Lunar Maximum Rise Poiints
Throughout their various cycles and periods, the sun, the moon and the planet Venus all rise at azimuths centered on true east and set at azimuths centered on true west. The sun shows the smallest variation in maximum (solstitial) rise and set points on the horizon because it is only affected by the 23.5 degree tilt of the earth's spin axis. Venus shows slightly more variation in its maximum rise and set points on the horizon because it is affected by the 23.5 degrees of the earth's tilt + the additional 2.7 degrees of its own tilt. The moon, across the 18.6 years of a Draconic cycle, shows the most variation in its maximum rise and set points because it is affected by the 23.5 degrees of the earth's tilt + the additional 5 degrees of its own tilt. Ancient American skywatchers followed these patterns with great interest and based their calendars on immutable celestial phenomena.

Fact #3. The earth's rotational axis slowly changes orientation, moving in a circle that requires about 25,770 years to complete. This phenomenon, called axial precession, is illustrated in the graphic below.
Earth's Precession
Because of the earth's rotation, the sky at night seems to wheel in a huge circle around the pole star. This time lapsed image captures the essence of apparent star motion, noted by ancient sky watchers around the globe.
Stars in apparent rotation around the pole star
Today, the pole star in the northern hemisphere is Polaris, commonly called the north star. Because of the earth's axial precession, the faint star Gamma Cephei will replace Polaris as the pole star about 1,000 years from now. In 2,000 B.C., the pole star was the faint star Thuban in the constellation Draco. This chart shows the way the pole star changes through the 25,770 years of earth's axial precession cycle.
Precession Polar Star Chart
Sometimes in past ages the celestial pole was simply a void with no visible star at the center of the wheel. Nonetheless, ancient mariners and astronomers in the northern hemisphere oriented to this pole as an unerring indicator of true north at right angles with the eastern sunrise and western sunset. The Southern Hemisphere also has its celestial pole. The two stars forming the long leg of the famous Southern Cross point to the south celestial pole. This important navigational aid is emblazoned on the flag of Australia.

These celestial phenomena gave rise to systems of cardinal directionality broadly similar to the one we use today. Biblical authors, for example, called their cardinal points zaphon, negev, kedem and yam, words derived largely from their Levantine geography.
Biblical Cardinal Directions
The association of east with sunrise is well attested in the Biblical text. Numbers 2:3, Joshua 12:1, Isaiah 45:6, Isaiah 59:19Ezekiel 8:16,

In the New World scribal tradition, east was also the direction of sunrise. See "The Defeat of Cabracan" phrases 4, 14 in Popol Vuh Electronic Library, Allen J. Christenson translator and editor, Provo, UT: Brigham Young University, 2007. See the blog article "Water Fight on the River - Round Ten" for a number of other indications the ancient Mesoamericans knew and used an astral-based system of cardinal directionality similar to our own.   

The Aztec Calendar Stone served many purposes and illustrated many cosmological, chronological and geographic concepts among the ancient Nahuatl of central Mexico. Among other things, the Aztec Calendar Stone was a classic compass rose, dividing space into equal quadrants centered on the cardinal points we know today as north, south, east and west with ordinal points NE, SE, SW and NW.
Aztec Calendar Stone, National Museum of Anthropology, Mexico City
We commissioned Mexican graphics artist Fernando Vazquez to create a compass rose based on the Aztec Calendar Stone with cardinal, ordinal and intermediate points indicated. We will use this graphic to help us keep everything straight as we wander through the Book of Mormon text examining all occurrences of the words "north," "south," "east," and "west" with variants.
Aztec Calendar Stone as Compass Rose
North
Terms derived from the root "north" appear 83 times in the text:
  • north 36 instances, 33 in a specific geographic context that can be mapped
  • northward 45 instances, all in a specific context
  • northern 1 instance, in a context we can map
  • northernmost 1 instance, in a discrete context
Netting out duplicates, we have 39 from and to location pairs where we can calculate the azimuth of the vector between them. Azimuths could range from northwest (315 degrees) to northeast (45 degrees) and still be in the north quadrant. We plot all 39 vectors and calculate variance from true north. As with all images on this blog, click to enlarge.
Analysis of All Occurrences of the Term "North" with Variants
A summary of our results:
  • No variance exceeds 45 degrees which means all azimuths fall within the north quadrant. Our correlations conform to the text 100%.
  • The term "north" trends much more strongly toward true north than the term "northward," precisely as we would expect given the common usage of those terms in English.
  • "Northward" generally means in a northwest direction which is not surprising given the lay of the land and the flow of the rivers in southern Mesoamerica.
The data in text order:
Jerusalem North to Mount Zaphon
2 Nephi 24:31
Ashkelon North to Plain of Sharon
Omni 1:22Alma 22:33, 46:22, 50:29, 50:31, 50:33, 51:30, 52:2, 63:4; Helaman 3:3, 3:8, 3:9, 3:10, 3:11, 6:6, 7:1, 7:2; 3 Nephi 3:24, 6:2, 8:12; Ether 10:21
Land Southward to Land Northward - the fundamental axis
Mosiah 7:5, 7:16, 11:13
Land of Shilom to Hill North of Shilom
Mosiah 10:8
The North of the land of Shilom
Mosiah 27:6
Nephite culture core North to Bountiful line
Alma 2:36, 2:37
Local land of  Zarahemla Northwest to Wilderness of Hermounts
Alma 8:6
Land of Melek 3 days journey North to Ammonihah
Alma 22:27
Narrow Strip of Wilderness North to Wilderness ca. 90 B.C.
Alma 22:29
Narrow Strip of Wilderness to Northern Parts of the Land
Alma 22:29 (second time)
Narrow Strip of Wilderness North to Bountiful Line
Alma 22:30, 22:31
Land Bountiful Northward to Land Desolation including Cumorah
Alma 22:32, 63:5
Narrow (Small) Neck of Land to Land Northward
Alma 22:33
Land Bountiful North to Land Desolation across the East-West
Bountiful-Desolation Line
Alma 43:34
Lamanites North of Hill Riplah
Alma 46:17
Land on the North of Midpoint of Nephite Lands
Alma 50:9
East Wilderness North of Greater Land of Nephi
Alma 50:11
Southwest Corner of Nephite Lands to Land Northward of Bountiful 
Alma 50:15
Moroni North to Lehi
Alma 50:34, Alma 52:9
Narrow Pass to Land Northward
Alma 52:23
Mulek Northward along the Seashore
Alma 56:22
Judea Northward to other Nephite Cities
Alma 56:36
Antiparah and City Beyond Northward
Alma 63:6, 63:7, 63:9, 63:10
Proposed Hagoth Route Northward
Helaman 1:23
Local Land of Zarahemla to North Parts of the Land
Helaman 1:31
The Most Capital Parts of the Land North
Helaman 3:8
Sea South to Sea North
Helaman 4:7
East-West Fortified Line to North Country
Helaman 6:9, 6:10, 6:12; 3 Nephi 1:17

Greater Land of Zarahemla, Bountiful North of Narrow Strip of Wilderness
Helaman 11:20
Northward from Approximate Midpoint of Nephite Lands
3 Nephi 4:1, 6:2
Possible Land Vacated by the Nephites North of Refuge
3 Nephi 4:23
Land Southward to Furthermost Parts of Land Northward
3 Nephi 7:12
Land Southward to Northernmost Part of Land Northward
Mormon 2:3
Land Southward Toward North Countries
Mormon 2:20
Land of Jashon Northward to Land of Shem
Mormon 2:29
Narrow Passage into Land Northward
Ether 1:1
This North Country Land of Cumorah
Ether 1:42, 2:1
Tower of Babel (Shinar) Northward Down into Valley of Nimrod
Ether 9:35
North Countries from Perspective of Land Southward
South
Terms derived from the root "south" appear 57 times in the text:
  • south 36 instances, 34 in a specific geographic context that can be mapped
  • southward 20 instances, all in a specific context
  • south-southeast 1 instance, in a discrete context
Netting out duplicates, we have 36 from and to location pairs where we can calculate the azimuth of the vector between them. Azimuths could range from southwest (225 degrees) to southeast (135 degrees) and still be in the south quadrant. We plot all 36 vectors and calculate variance from true south, or in the case of the term south-southeast 1 Nephi 16:13, variance from true south-southeast (157.5 degrees).
Analysis of All Occurrences of the Term "South" with Variants
A summary of our results:
  • No variance exceeds 45 degrees which means all azimuths fall within the south quadrant. Our correlations conform to the text 100%.
  • The term "south" trends much more strongly toward true south than the term "southward," precisely as we would expect given the common usage of those terms in English.
  • "Southward" always means in a southeast direction which is not surprising given the lay of the land and the flow of the rivers in southern Mesoamerica.
The data in text order:
Valley of Lemuel nearly South-southeast to Shazer
Mosiah 9:14
The South of the land of Shilom
Mosiah 27:6
Nephite Culture Core Expansion South
Alma 8:18
South Entrance to City of Ammonihah from Wilderness Side
Alma 16:6, 16:7
Borders of Manti to South Wilderness East of Sidon
Alma 17:1
Gideon Southward to Manti
Alma 22:31
Multiple Mulek Landfalls up into South Wilderness
Alma 22:31 (second time); Helaman 3:8; 3 Nephi 3:24, 6:2, 8:11; Mormon 1:6; Ether 9:31, 9:32, 10:19, 10:21
Land Northward to Land Southward
Alma 22:32
Land Northward to Land Southward via Narrow (Small) Neck of Land
Alma 22:33
Lamanites Hemmed in South of Land Bountiful
Alma 27:22
Land of Jershon South of Land Bountiful
Alma 31:3
Land of Antionum South of Land of Jershon
Alma 31:3 (second time)
Wilderness Full of Lamanites South of Land of Antionum
Alma 43:31, 43:35
South of Hill Riplah
Alma 46:17
Land South of Desolation - Bountiful & Greater Land of Zarahemla
Alma 46:17 (second time)
South Portion of Nephite Lands in Land Southward
Alma 50:7
Lamanite Lands South of Narrow Strip of Wilderness Border
Alma 50:10
Fortified Southern Border in the Nephite East 
Alma 50:13
City of Moroni on the East Sea South by Narrow Strip of Wilderness
Alma 52:15
South and West Borders of Greater Land of Zarahemla
Alma 53:8
West Sea South
Alma 53:22
Melek to Judea on the South near the West Sea
Alma 62:34
Wilderness South of Land of Moroni
Helaman 1:31
South from the Most Capital Parts of the Land
Helaman 3:8
North Sea to South Sea
Helaman 4:8
All the Possession of the Nephites in the Land Southward in white overlay from
Land Bountiful on the North to the Narrow Strip of Wilderness on the South
Helaman 5:16
People of Nephi who were in the Northern Half
of the Greater Land of Zarahemla ca. 30 B.C.
Helaman 6:9, 6:10 (twice), 6:12 (twice), 3 Nephi 1:17
Lamanite Culture Core in Land South
Helaman 11:20
Southward Portion of Nephite Lands
3 Nephi 4:1, 4:26, 6:2
Deserted Nephite Lands South of Refuge
between Zarahemla and Bountiful
Mormon 2:29 (twice)
Land Northward to Narrow Passage in Land Southward
Mormon 3:5
Land Northward to Land Southward via Narrow Pass
Mormon 6:15, Mormon 8:2
Nephite Escapees from Cumorah into South Countries
Ether 15:10
Ogath Southward from Waters of Ripliancum
East
Terms derived from the root "east" appear 51 times in the text:
  • east 48 instances, 43 in a specific geographic context that can be mapped
  • eastward 3 instances, all in a specific context
Netting out duplicates, we have 30 from and to location pairs where we can calculate the azimuth of the vector between them. Azimuths could range from northeast (45 degrees) to southeast (135 degrees) and still be in the east quadrant. We plot all 30 vectors and calculate variance from true east.
Analysis of All Occurrences of the Term "East" with Variants
A summary of our results:
  • No variance exceeds 45 degrees which means all azimuths fall within the east quadrant. Our correlations conform to the text 100%.
  • Less variance occurs with east directions than with either north or south directions. This is due to the large number of east vectors that originate or terminate on the seacoast or river Sidon.
  • Our sample size for the term "eastward" is too small to support meaningful conclusions.
The data in text order:
1 Nephi 17:1
Nahom nearly Eastward to Old World Bountiful
2 Nephi 12:6
Israel East to Rabbath-Ammon, modern Amman
2 Nephi 21:14
Israel and Philistia together Spoil the Children of Ammon in the East
Expansion from Nephite Culture Core East ca. 100 B.C. 
Alma 2:15, 2:17
400 Meter Hill Amnihu East of Sidon
Alma 6:7
Valley of Gideon East of  Sidon
Alma 16:6, 16:7, 43:35, 43:52, 43:53, 49:16
Wilderness Valley East of Sidon, South of Manti
Alma 22:27
Greater Land of Nephi to East Sea
Alma 22:27 (second & third time), 3 Nephi 1:17
Narrow Strip of Wilderness to East Sea Terminus
Alma 22:29
Expansion from Nephite Culture Core to East Sea
Alma 22:29 (second time)
Northern Parts of the Land on the East, South of Bountiful
Alma 22:32, 22:33
Eastern Terminus of Bountiful Desolation Line to West Sea
Alma 25:5
Wilderness East of Sidon South of Manti to East Wilderness
Alma 25:8
East Wilderness Further into East Wilderness
Alma 27:22
Land of Jershon on the East by the Sea South of Bountiful
Alma 31:3
Land of Antionum East of Local Zarahemla South of Jershon
Alma 43:31
East of Hill Riplah
Alma 50:7 (twice), 50:9 (twice), 50:11
Central Sidon Corridor to East Wilderness
Alma 50:8
Greater Land of Nephi Northern Border East Sea to the West
Alma 50:13
City of Moroni by the East Sea on the South
Alma 50:34
Narrow Pass by Eastern Component of the West Sea
Alma 51:26, 52:13 (Note: "Nephihah" in Alma 51:26 is a scribal error that should read "Moroni.")
Nephite East Coast Cities
Alma 62:21
Proposed Entrance to City of Nephihah on the East
Alma 62:34
Wilderness East of Land of Moroni
Helaman 1:31
The Most Capital Parts of the Land East
Helaman 3:8, 11:20
Sea West to Sea East
Helaman 4:7
West Sea to Fortified Line Eastern Terminus
Ether 9:3
Hill Ramah-Cumorah Eastward to Ablom by the Sea
Ether 14:26
Shiz Pursuit Eastward to the Sea
West
The term "west" appears 41 times in the text with no variants. 38 of those instances appear in specific geographic contexts that can be mapped. Netting out duplicates, we have 28 from and to location pairs where we can calculate the azimuth of the vector between them. Azimuths could range from northwest (315 degrees) to southwest (225 degrees) and still be in the west quadrant. The phrase "west and north" occurs once in association with the phrase "on the west, and on the north" Alma 2:36-37. That variance we calculate from true northwest (315 degrees).
Analysis of All Occurrences of the Term "West" in the Text
A summary of our results:
  • No variance exceeds 45 degrees which means all azimuths fall within the west quadrant. Our correlations conform to the text 100%.
  • Less variance occurs with west directions than with north, south or east directions. This is due to the very large number of west vectors that originate or terminate on the seacoast or river Sidon.
The data in text order:
2 Nephi 21:14
Jerusalem to Ashkelon in Philistia
Mosiah 27:6
Expansion from Nephite Culture Core West ca. 100 B.C.

Four Quarters of the Land ca. 100 B.C.
Alma 2:34
Battlefield in Local Land of Zarahemla West of Sidon
Alma 2:36
Wilderness of Hermounts North and West of Local Zarahemla
Alma 8:3 (twice)
Melek West of Sidon, Wilderness West of Melek
Alma 22:27
Greater Land of Nephi South of Narrow Strip of Wilderness
Running from the East Sea to the West Sea
Alma 22:27 (second time)
Narrow Strip of Wilderness from East Sea to West Sea
Alma 22:27 (third time)
Narrow Strip of Wilderness from Head of Sidon to West Sea
Alma 22:28
Wilderness West in Greater Land of Ne phi
Alma 22:28 (second time)
Greater Land of Zarahemla to West Sea
Alma 22:28 (third time)
Greater Land of Nephi West to Land of First Inheritance
Alma 22:29
Nephite Culture Core Expansion to the West South of Bountiful
Alma 22:32, 22:33
Bountiful Desolation Line from the East to the West Sea
Alma 43:27, 43:32 (twice), 43:53
Valley West of Sidon, South of Manti
Alma 50:8
Greater Land of Nephi from East Sea to the West
Alma 50:11

On the West of Greater Zarahemla
Alma 50:11 (second time), 3 Nephi 1:17
Narrow Strip of Wilderness from West Sea to Head of Sidon
Alma 50:34
Narrow Pass by the Sea on the West
Alma 52:11, 52:12, 53:8
Borders of Greater Zarahemla by the West Sea
Alma 52:15, 53:22
Borders of Greater Zarahemla South by the West Sea
Alma 52:22
Wilderness West of City of Mulek with Battle Movements
Alma 62:22
Proposed West of City of Nephihah
Alma 63:5
Hagoth's Port in Land Bountiful on the West Sea
near the Narrow (Small) Neck of Land
Helaman 1:31
The Most Capital Parts of the Land West
Helaman 3:8, 11:20
Sea West to Sea East
Helaman 4:7
Fortified Line in Land Bountiful from the West Sea
to a Point One Days Journey East
Mormon 2:6
Land of Joshua in the Borders of Greater Zarahemla
by the West Sea
Conclusion
We have now analyzed all 232 occurrences of the terms "north," "south," "east," and "west" with variants in the text. We have identified 133 discrete from and to locations in both the Old World and the New where we can map a vector between them and calculate a directional azimuth. We have compared these 133 directional azimuths against the cardinal points of a traditional compass rose and calculated variance. In all 133 cases, the variance is less than 45 degrees which means our map fits the text precisely without discrepancy. We submit any viable Book of Mormon geographic correlation should pass this test.