Mapping The Book Of Mormon

[charity]

I have a question. The land divisions of 1800's America were based on people owning specific parcels. Kings granted great tracts of land to individuals. Surveyors were actively describing land parcels. George Washington was a surveyor.

Do we know if this was the case in Central American culture? Did inviduals own set parcels? If they didn't, the directions would not need to be extremely precise.

[Tarski]

(And shhhhhh, don't tell anyone, but the people who bring these things up are not the brightest bulbs in the chandelier.) 

What utter insulting nonsense (and a bit ironic). I find the exact opposite to be true. In fact, the usual attack on the doubters is that they are just too intellectual for their own good and are just trusting in the "learning of man". Which is it? Are we too dumb or too smart?

I notice three types of people in this regard:

1. Those who don't notice things like given in the list (dim bulbs?)

2. Those who sort of see them if pointed out but feel that thinking about it too much is a sin and a sign of unfaithfulness.

3. Those who become experts at rationalizing away good simple observations that cast reasonable doubt on religion. These folks are often into arcane minutia but can't see the forest for the trees. These folk use their brain power to rationalize ways to keep on believing because that is the singular motivation under it all.

[charity]

tarski, asked "too dumb or too smart?" The answer is "unwise." See 2 Nephi 9:28. "Too dumb or too smart" might make a topic of its own. If you would care to do it, I will participate in it.

But I apologize for a post which takes away from this topic. This is a great and productive thread, and I will stay with it. Thanks, Larry.

[poulsenll]

Do we know if this was the case in Central American culture?  Did inviduals own set parcels?  If they didn't, the directions would not need to be extremely precise.

Charity

As far as we know, and the archeological evidence is preetty good, the common man practiced the same type of agriculture as they do now. This is either "milpa" or "slash and burn" agriculture. Milpa was practiced where shallow lakes or waterways existed and involved dredging up soil from under water to form small islands where they could plant and harvest agricultural products. This type of agriculture is still practiced at Xochimilco in Mexico City.

With this type of agriculture there was a type of ownership, in that the same groups and/or families maintained a given "milpa' over extended periods of time.

The majority, however, practiced "slash and burn" which is a form of dry land farming and depends on rainfall for irrigation. In order to be productive, they had to have a means to determine the time of the rainy seasons and they also had to continuously prepare new plots of ground as the old ones became infertile after only a few seasons of use.

With this type of agriculture, there was no real ownership of land. When the land became infertile, the family simply looked for an area that had not been used long enough for trees and brush to have grown up and proceeded to prepare it for use again. They did this by cutting down the growth and then burning it. The ashes then served to fertilize the ground and the new plot was then usable for another few years.

The manner in which they determined the boundaries of the plot reflects their relationship with their environment and their concept of their location in the cosmos. Sorry for the big words. They would go to a likely location and place a stone on the ground to mark the place where they intended to establish ther new hearth and around which they would build their dwelling. They would then look for a particular landmark that marked where the sun rose at either the summer or the winter solstice and pace off the distance of roughly half the land they wanted to clear. Placing a rock at that location, they would then return past the first rock and pace off the same distance in the opposite direction and place a rock there. Returning to the center, they located the landmark that marked the location of sunrise at the remaining solstice and followed the same procedure. This resulted in a rectangular plot of ground with the corners indicating the limits of the suns movements during the course of the year. The position of the sun as it rose on the eastern border of their land each morning provided a built in calendar of the passing seasons and a means to estimate the coming of the rains. And unlike many of us today, they were up every morning to see the sun rise.

It was very important for them to feel that their hearth was in the center of their land, as they were more interested in where they were located in the cosmos rather than where everything else was located.

Larry P

[charity]

Since they marked the solstices, but knew that the sun did not come up in the same place every day, would lend to them using the words "eastward," "westward" instead of "east," "west?"

[poulsenll]

Since they marked the solstices, but knew that the sun did not come up in the same place every day, would lend to them using the words  "eastward,"  "westward" instead of "east,"  "west?"

Charity

You almost have the right idea, however, westward is not found in the Book of Mormon text and eastward is hardly found at all except in the Book of Ether. They were more interested in where the sun was rather than where east was located. Not that they did not know when the sun was at the equinox that it rose due east. Or for that matter, they probably knew that the North star was nearly stationary and marked the midpoint in the norfthern sky between where the sun rose and where it set. They were dependent on the sun for their sustenance and therefore were more interested in where it was relative to where they were. It was more important where the sun was and except to some priests and astronomers where due east was located was of little importance in their lives. We translate there words for "where the sun rises " as east but east, indicating a cardinal point of the compass, is our concept not theirs.

What this indicates is that when translating their term to ours we must realize that it does not have the same precise meaning which, in our day, we attribute to the word "east".

However, in Joseph Smith's day, the terms eastward, westward, northward and southward were, as you suggest, imprecise terms used to indicate any direction within a given quarter.

Note the following definition of occidental in the 1828 Webster

OCCIDENT'AL, a. [L. occidentalis.] Western; opposed to oriental; pertaining to the western quarter of the hemisphere, or to some part of the earth westward of the speaker or spectator; as occidental climates; occidental pearl; occidental gold.

Keep up the good work. Understanding the cultures of the Americas prior to the introduction of European influence is crucial to our interpretation of geographic directions found in the text of The Book of Mormon.

Larry P

[charity]

Then if the sun is used for directions, it would make a difference that meso-America is located between the Tropic of Cancer and the Equator. The sun traces a different path across the sky, than what we see (in the US) since we are mostly between 30-50 degree N. Correct?

[poulsenll]

Then if the sun is used for directions, it would make a difference that meso-America is located between the Tropic of Cancer and the Equator.  The sun traces a different path across the sky, than what we see (in the US) since we are mostly between 30-50 degree N.  Correct?

Charity

Right on. The big question is, Can we find any evidence of this difference in the text of the Book of Mormon.

Larry P

[poulsenll]

For those of you doing your homework, there is a new installment in the pundit thread and a new homework assignment.

Larry P

[SolarPowered]

Clue, the rectangle can not be divided into equal areas by drawing diagonals.

Actually, drawing the diagonals of a rectangle does in fact divide it into four precisely equal areas.

[JarMan]

Actually, drawing the diagonals of a rectangle does in fact divide it into four precisely equal areas.

width (long side) = w; height (short side) = h

Area (north or south) = 1/2 * w * h/2 = hw/4

Area (east or west) = 1/2 * h * w/2 = hw/4

Right you are SolarPowered.

[poulsenll]

Actually, drawing the diagonals of a rectangle does in fact divide it into four precisely equal areas.

width (long side) = w; height (short side) = h

Area (north or south) = 1/2 * w * h/2 = hw/4

Area (east or west) = 1/2 * h * w/2 = hw/4

Right you are SolarPowered.

Jarman

Wrong formulas, your formula is for a right triangle. The triangles produced by drawing diagonals are only right triangles for a square. The areas of the triangles when the rectangle is divided by diagonals are proportional to the angles at the intersection at the center. A simple visual inspection shows that they are not equal. A simple way to get the relative areas is to cut them out and weigh them.

In addition the short side for both the square and the rectangle is not the height of either the rectangle or the square. The short side is 1/2 the diagonal . Your formula will give the wrong value for the square and is not applicable to the rectangle.

Larry P

[charity]

Larry, the words in the 1828 are fascinating.

I particularly noticed the following:

1. hills and mountains are fairly interchangeable. The definitions noted that hills are generally smaller than mountains, but hills can be called mountains, and mountains can be called hills.

2. While north, south, east, west are generally defined as cardinal points, in the definition of "south" it says that is any point between horizon and zenith. Which means you can be pointing up and say "south." I think.

3. Down can mean toward the mouth of a river.

4. A sea is a large body of water nearly enclosed by land, a branch of an ocean. There was no interchangability between ocean and sea in the definition.

5. Wilderness in the United States means a forest, but in more common usage means a desert.

6. Nortward, southward, etc. In a direction more nearly north in the quadrant, so it could really be a very wide difference directinally.

Very interesting. Thanks.

[SolarPowered]

Actually, drawing the diagonals of a rectangle does in fact divide it into four precisely equal areas.

width (long side) = w; height (short side) = h

Area (north or south) = 1/2 * w * h/2 = hw/4

Area (east or west) = 1/2 * h * w/2 = hw/4

Right you are SolarPowered.

Jarman

Wrong formulas, your formula is for a right triangle. The triangles produced by drawing diagonals are only right triangles for a square. The areas of the triangles when the rectangle is divided by diagonals are proportional to the angles at the intersection at the center. A simple visual inspection shows that they are not equal. A simple way to get the relative areas is to cut them out and weigh them.

In addition the short side for both the square and the rectangle is not the height of either the rectangle or the square. The short side is 1/2 the diagonal . Your formula will give the wrong value for the square and is not applicable to the rectangle.

Larry P

Actually, his formula is correct for all triangles: Area is always one-half the base times the height, no matter what the angles.

You can convince yourself visually by drawing the diagonals, then also drawing the vertical and horizontal lines that connect the midpoints of the sides. You will then see that there are eight congruent triangles, two in each of the previous "wedges".

[Calm]

Actually, drawing the diagonals of a rectangle does in fact divide it into four precisely equal areas.

width (long side) = w; height (short side) = h

Area (north or south) = 1/2 * w * h/2 = hw/4

Area (east or west) = 1/2 * h * w/2 = hw/4

Right you are SolarPowered.

Jarman

Wrong formulas, your formula is for a right triangle. The triangles produced by drawing diagonals are only right triangles for a square. The areas of the triangles when the rectangle is divided by diagonals are proportional to the angles at the intersection at the center. A simple visual inspection shows that they are not equal. A simple way to get the relative areas is to cut them out and weigh them.

In addition the short side for both the square and the rectangle is not the height of either the rectangle or the square. The short side is 1/2 the diagonal . Your formula will give the wrong value for the square and is not applicable to the rectangle.

Larry P

Hmmm...

each triangle created by the diagonals can be divided into two right angle triangles.

Each of those triangles is identical, just rotated. Add any two together and you either get identical rectangles or equal in area triangles.

At least that is how it appears in my mind. I'll have to draw it up to see.

add-on: sorry I dont' know how to draw this up, but using the Vertical angle therom and the Rectangle Diagonals Conjecture (a rectangle's diagonals are congruent and bisect each other) plus the SSS congruence theorem (if three sides of a triangle are congruent to the three sides of another triangle, the triangles are congruent), you end up with the areas being the same.

Imagine the rectangle being divided by both diagonals and bisectors. You have eight triangles. The shortest sides are all congruent, the hypotenuses are all congruent and the longer sides are all congruent, thus making all the triangles congruent and thus making the sum of any two of the triangles congruent as well.

Hope this makes sense. Draw it out for yourself and match the length of the sides to see (using slash marks makes this easy for those not used to geometry).

Is my brain asleep or not?

===

add-add-on: looks like solarpowered beat me to it.

This is not the case for all quadrilaterals as you can see here: http://mathforum.org/pow/solution24.html#problem.5.23.94

[solomarineris]

Poulsnell

lets not have any arguments based on the abscence of data.

Ok, Poulsnell, just tell me first if there's any credible data about BoM mappping or locality, then we can discuss which ones are credible or not.

sdovis

May I suggest that the most interesting and a critical question is: where is the narrow neck of land?

I think Uncle Dave's map fits the description best but the trouble is we have absolutely no archeological evidences backing it up.

If you don't like that one there's probably more than a million "narrow neck of lands" from Panama to our most picturesque "Dead Horse Point", Utah.

[Moksha]

Has anyone ever considered the North and South islands of New Zealand as a possible setting for the Book of Mormon? Do any of the Maori war chants sound vaguely like Hava Nagila?

Edit to add content link for theory:

Sounds of Israel - Maori possible Kinship

[poulsenll]

Actually, drawing the diagonals of a rectangle does in fact divide it into four precisely equal areas.

width (long side) = w; height (short side) = h

Area (north or south) = 1/2 * w * h/2 = hw/4

Area (east or west) = 1/2 * h * w/2 = hw/4

Right you are SolarPowered.

JarMan

My apologies You are right. I did not check my geometry. I was thinking of the possible directions available in each quarter.

However when considering directions it is not the area of the enclosed triangles which is important but the magnitude of the angles at the point where the lines intersect. The greater the angle towards the long side of the triangle relative to the short side, the greater the possible directions available in that quarter relative to the quarter with the smaller angle. If you draw a circle with its center at the intersection and radius equal tho 1/2 the diagonal, the length of the arcs for south and north are greater than those for east and west. In other words there are more possible directions in the northern or southern quarters versus the eastern and western quarters.

This would suggest that a system of directions based on a rectangular view of the land would result in more references to north and south than to east and west.

Hope this makes sense.

Larry P

[poulsenll]

May I suggest that the most interesting and a critical question is: where is the narrow neck of land?

I think Uncle Dave's map fits the description best but the trouble is we have absolutely no archeological evidences backing it up.

If you don't like that one there's probably more than a million "narrow neck of lands" from Panama to our most picturesque "Dead Horse Point", Utah.

solomarineris

That is the problem with putting undo emphasis on the narrow neck. As you point out, there are just too many possibilities. Dave's map, actually Holley's map, revolves around the possibility that this narrow neck is the one described in the Book of Mormon and that the Hill Cumorah in New York is the same as that mentioned in the Book of Mormon. He ignores the fact that the Book of Mormon Hill Cumorah was north of the narrow neck, not east of it. He also ignores the description of the river Sidon where it describes its source as located in the Narrow strip of wilderness. Zarahemla is also described as being north of the narrow strip and south of the Land of Bountiful.

In his attempt to show that Joseph Smith used the area of the Great lakes to create the geography of the Book of Mormon, he ingnores the more explicite descriptions of geography found in Alma in favor of placing emphasis on a single feature which is only mentioned a few times in the text.

[JarMan]

If south and north are mentioned much more often than east and west, to me that indicates that the land is relatively long and narrow in the north/south direction. Take California, for instance. We've all heard of Southern California and Northern California but we typically don't refer to Eastern or Western California. I grew up in Washington State which is a bit longer east to west than north to south. We always referred to Eastern Washington and Western Washington, but rarely to Northern or Southern Washington. (Now that I think of it, though, this may have had more to do with the fact that the Cascades divide the state into somewhat distinct east/west zones.) So maybe there can be geographic features that divide the land into "zones" (like a narrow neck, for instance) which affect how we talk and think about it directionally.

I'm not sure that I understand the explanation of directions based on the description of the "south forty." In New York I understand they would have been using the metes and bounds system rather than the PLSS. As different as these two systems are, the one thing they do have in common is the reliance on the cardinal directions of north, south, east, and west. The difference between the two systems is the starting point for a survey. The PLSS uses standard monuments that are placed in the ground for the purpose of surveying. The metes and bounds system, on the other hand, uses any landmark or geographic feature for a starting point. In both systems north is north and east is east. I suppose that you could use the terminology "northward" when giving the direction from, say, a fencepost to another physical marker in the metes and bounds system. But I think it would be understood that "northward" is something different than "north."

[poulsenll]

If south and north are mentioned much more often than east and west, to me that indicates that the land is relatively long and narrow in the north/south direction.  Take California, for instance.  We've all heard of Southern California and Northern California but we typically don't refer to Eastern or Western California.  I grew up in Washington State which is a bit longer east to west than north to south.  We always referred to Eastern Washington and Western Washington, but rarely to Northern or Southern Washington.  (Now that I think of it, though, this may have had more to do with the fact that the Cascades divide the state into somewhat distinct east/west zones.)  So maybe there can be geographic features that divide the land into "zones" (like a narrow neck, for instance) which affect how we talk and think about it directionally.

JarMan

From a global point of view, which is typical of our culture's view of geography, you are right. When I first started thinking of this problem, I thought of shape or geographic features that limited the number of locations to the east and west. However as I began to understand how ancient cultures viewed geography, I realized they had a more local view of geography. They thought of themselves at the center of the land with everything distributed around themselves rather than a fixed map where they were located at some point on the map. I distinguish these two types of geography by the terms "geocentric", map based, and "anthrocentric", man based. In the anthrocentric point of view features are located in vectorial directions from the center of a circle. The distribution of directional terms used should be proportional to the angle of the compass circle which they considered to be north or south. The greater the angle which they included in there concept of north, the greater the number of references to this direction will occur in their description of geography. Mesoamerican cultures included every thing between where the sun rose and where it set at the summer solstice in their concept of north. Their word, which we translate as "north" was more correctly translated as "to the right of where the sun rises", from the point of view of the rising sun rather than their own point of view.

Using this concept, one can calculate the expected ratio of directional references and compare it to that found in the text of the Book of Mormon. The actual ratio comes out surprizingly similar to the theoretical ratio.

I'm not sure that I understand the explanation of directions based on the description of the "south forty."  In New York I understand they would have been using the metes and bounds system rather than the PLSS.  As different as these two systems are, the one thing they do have in common is the reliance on the cardinal directions of north, south, east, and west.  The difference between the two systems is the starting point for a survey.  The PLSS uses standard monuments that are placed in the ground for the purpose of surveying.  The metes and bounds system, on the other hand, uses any landmark or geographic feature for a starting point.  In both systems north is north and east is east.  I suppose that you could use the terminology "northward" when giving the direction from, say, a fencepost to another physical marker in the metes and bounds system.  But I think it would be understood that "northward" is something different than "north."

The "south forty" has to do with how we divide the compass circle into quarters and then reference them as north, south, east and west. Just as we can divide a square into quarters in two different ways, so we can divide the compass circle into four quarters in many different ways. Anciently it was divided by drawing lines from northeast to southwest and from northwest to southeast. This places the cardinal directions at the midpoint of each quarter and the cardinal points are used to name the quarters and not to form the boundaries of the quarters. Thus we have a south quarter just as we have a "south forty" when we use an x rather than a + to form the quarters.

I want to thank you for calling my attention to my error in geometry. It has helped me to clarify my thinking and hopefully to do a better job of explaining it.

Larry P

[SolarPowered]

If south and north are mentioned much more often than east and west, to me that indicates that the land is relatively long and narrow in the north/south direction.  Take California, for instance.  We've all heard of Southern California and Northern California but we typically don't refer to Eastern or Western California.  I grew up in Washington State which is a bit longer east to west than north to south.  We always referred to Eastern Washington and Western Washington, but rarely to Northern or Southern Washington.  (Now that I think of it, though, this may have had more to do with the fact that the Cascades divide the state into somewhat distinct east/west zones.)  So maybe there can be geographic features that divide the land into "zones" (like a narrow neck, for instance) which affect how we talk and think about it directionally.

Relevant question: What's the largest U.S. city east of Reno, Nevada?

[poulsenll]

Larry, the words in the 1828 are fascinating. 

2. While north, south, east, west are generally defined as cardinal points, in the definition of "south" it says that is any point between horizon and zenith.  Which means you can be pointing up and say "south."  I think.

Charity

Here is another definition from 1828 Webster related to the use and meaning of directions.

OCCIDENT'AL, a. [L. occidentalis.] Western; opposed to oriental; pertaining to the western quarter of the hemisphere, or to some part of the earth westward of the speaker or spectator; as occidental climates; occidental pearl; occidental gold.

The phrase "pertaining to the western quarter" implies that a hemisphere can be divided into quarters, one of which is the western quarter. The following figure shows this division based on both a square and a rectangle. The angle of the eastern and western quarters using a rectangular division is based on the angle between sunrise at the summer solstice and sunrise at the winter solstice.

Larry P

[JarMan]

I understand the explanation of the south forty. But what I don't understand is how that would make Joseph Smith's concept of directions or language related to directions significantly different than ours today.

The explanation of directions based on the solstices is interesting. But do we really know that ancient Meso-Americans used that concept when describing direction or location? I wonder what written records we have that are related to describing direction or location and how confident we are in their translation.

However as I began to understand how ancient cultures viewed geography, I realized they had a more local view of geography. They thought of themselves at the center of the land with everything distributed around themselves rather than a fixed map where they were located at some point on the map.

This is also an interesting analysis. But how does it apply to the Book of Mormon? Is Mormon really taking a anthrocentric view of geography and not a geocentric view. When he talks of a narrow neck of land separating the land northward from the land southward, as long as he thought of the narrow neck as being "home", then I suppose that could be an anthrocentric view.

It would be an interesting exercise to look at all of the geographic references in the Book of Mormon and try to justify an anthrocentric view of things. Along with that I think it would also be interesting to try to determine what Mormon's idea of "home" was and see if that seemed to fit into the "center of a circle." The most interesting thing, though, would be to determine if that concept offered a significantly different geographical layout than most scholars have offered today and whether that different layout better lends itsself to determining a real-world location for Book of Mormon cities and events. Finally, I wonder if an anthrocentric explanation of geography would resolve some of the apparent ambiguities.

[poulsenll]

  Finally, I wonder if an anthrocentric explanation of geography would resolve some of the apparent ambiguities.

Jarman

It did for me.

Brant Gardner used one of my convergences in his talk at the FAIR meetings to point out the ability of geography to resolve how otherwise unexplainable questions such as "Why did King Limhi's search party get lost in the wilderness? can be answered by a more anthrocentric point of view concerning geography.

Larry P