Saturday, December 27, 2014

Strahler Stream Order

In 1952 Arthur Newell Strahler (1918 - 2002), a professor of geoscience at Columbia, published an influential article entitled "Hypsometric (Area-Altitude) Analysis of Erosional Topography" in Geological Society of America Bulletin 63. Strahler introduced a numbering system he called "stream order" to quantify the hierarchical branching networks that typify watercourses in drainage basins. A 1st order stream is very small and has no tributaries. The confluence of 2 or more 1st order streams creates a 2nd order stream. If a 1st order stream flows into a 2nd order stream, the result remains a 2nd order stream. But, when 2 or more 2nd order streams converge they form a 3rd order stream. Obviously, as a stream increases in upstream network complexity its stream order number increases.

The Allegheny and Monongahela are both 7th order streams as they converge at Pittsburgh, Pennsylvania. The Ohio is an 8th order stream at its confluence with the Mississippi at Cairo, Illinois. The Columbia is a 9th order stream as it discharges into the Pacific downstream from Portland, Oregon. The Mississippi is a 10th order stream at its mouth below New Orleans. The Nile is an 11th order stream as it flows through Egypt into the Mediterranean. The Amazon, largest river on earth, is a 12th order stream by the time it reaches the Atlantic.
Strahler Stream Order Classification System
Stream order has proven so useful it has become a global standard among limnologists. In contemporary usage, 1st - 3rd order watercourses are called headwaters streams or small streams. 4th - 6th order streams are called medium streams. 7th - 12th order streams are considered significant rivers or large streams. The Usumacinta, our candidate for river Sidon, is a 7th order stream. Other 7th order streams of note include the Colorado, Hudson, James, Potomac, Rio Grande, Susquehanna, and Trinity, The Tennessee is an 8th order stream, as is the Rhone south of Lyon, France. The Missouri is a 9th order stream by the time it reaches St. Louis as is the Illinois which joins the Mississippi 37 kilometers upstream.

The journal of the International Society of Limnology (SIL from the Latin) is Inland Waters. An important article appeared in Inland Waters (2012) 2 entitled "Global Abundance and Size Distribution of Streams and Rivers." It was written by John A. Downing of Iowa State University and 9 other co-authors from 6 different countries. Depending heavily on satellite imagery, they have compiled data estimates from more than 36 million streams of water across the planet. Their results show startling consistency that will help us understand what to expect as we analyze the Sidon.

J.A. Downing, et al. Anaylsis of all Streams Worldwide
Going from left to right, the first column is the Strahler stream order number. The second column is the total number of streams of surface water on the planet. The third column is the mean stream length from the source in kilometers. The fourth column is the combined length of all streams in kilometers and the fifth column is the mean stream channel width in meters. There is only one 12th order stream on earth, the  Amazon, while there are an estimated 28.55 million 1st order streams. These tiny brooks average 1.6 km in length and .8 meters in width. It is important to note that only one of the five 11th order streams - the Nile - is an independent river flowing to the sea. The other four 11th order streams are all tributaries of the Amazon. And, only three of the 10th order streams are independent rivers flowing to the sea, the Mississippi being one of them and the Niger in western Africa another. The other twenty 10th order streams are all tributaries of either the Nile or the Amazon.

These columns demonstrate what the authors call "well-defined scaling laws" that apply to branching patterns "applicable across diverse geological and geographical regions." For example, column two in the chart shows generally a 1 to 5 relationship between main streams and lesser streams of a lower order. In other words, any given stream will have an average of five tributaries of the next lower order. Column three shows generally a 1 to 2 relationship between tributaries and the length of their main stream. In other words, as two streams of a lesser order join, the resulting higher order stream will be on average twice as long as the tributaries. The actual branching algorithms involve more elegant math, but you get the idea. Drainage basins, like many other kinds of networks with branches and nodes, follow the tenets of branching theory whose laws and coefficients are so consistent as to be "tautologous" and "statistically inevitable" (J.A. Downing, et al.). Trees and blood vessels also follow branching theory laws.

Any given river may vary considerably from the norm. This chart shows the relationship between stream order and width for 400+ well-documented main streams. The dotted line plots median stream channel width in meters with data points scattered in normal distribution patterns.
J.A. Downing, et al. Analysis of 400+ Well-Known Streams
The relatively narrow Nile, the only 11th order main stream on earth, is an obvious outlier. Wetter regions have wider streams. For example, one study of the River Tyne basin in NE England found 1st order streams with a mean channel width of 3.5 meters and 2nd order streams with a mean channel width of 6 meters.

So what does all this imply for the river Sidon in the Book of Mormon? We know that Almaand his converts traveled a distance of 21 Nephite "days" to get from the city of Nephi to the local land of Zarahemla Mosiah 23:3, Mosiah 24:20, Mosiah 24:25. Our best estimate of the distance they traveled in one day is 15 air (straight-line) kilometers (see the blog article Land Southward Travel Times). This makes the city of Nephi/local land of Zarahemla distance about 320 air kilometers. We know the head of Sidon was south of Manti in the narrow strip of wilderness that separated the greater lands of Nephi and Zarahemla Alma 22:27, Alma 22:29, Alma 43:22, Alma 50:11. So, the distance head of Sidon/local land of Zarahemla probably did not exceed about 250 air kilometers. How far was it from the local land of Zarahemla to the sea? The land Bountiful lay north of the local land of Zarahemla Alma 22:29 (see the blog article Downstream from Zarahemla). The distance local land of Zarahemla/seacoast probably did not exceed about 200 air kilometers. So, the entire length of the river from head of Sidon to the sea likely did not exceed about 450 air kilometers. According to the chart above, we would expect the river Sidon to be a 7th or 8th order stream. A 9th order stream (mean global length 1,256 kilometers) seems long, even taking sinuosity (the tendency of a river to meander) into account. A 10th order stream (mean global length 2,891 kilometers) is entirely out of the question. Keep in mind there are only 5 rivers on earth that are 10th, 11th or 12th order streams flowing to the sea. Conversely, a 6th order stream (mean global length 103 kilometers seems short. A 5th order stream (mean global length 45 kilometers) is  entirely out of the question.

The fact that our candidate for Sidon - the Usumacinta - is a 7th order stream puts it in the ballpark of reasonableness. From our head of Sidon (the Salama/Chixoy Negro confluence) to salt water at the mouth of the Palizada (distributary of the Usumacinta) on the Laguna de Terminos is 382 air kilometers and to the principal mouth of the Usumacinta at Frontera is 435 air kilometers or 936 river kilometers. Principal tributary, the Chixoy Negro, adds another 175 river kilometers for a total length source to mouth of 1,111 kilometers. The Usumacinta, among the 50 largest independent rivers on earth by annual average volume of water discharged (2,271 cubic meters per second), is a large 7th order river.
Usumacinta - Candidate for River Sidon
Geographers place the head of the Usumacinta at the Pasion Confluence which is 328 air kilometers or 590 river kilometers from the principal mouth at Frontera, Tabasco. The Mezcalapa-Grijalva since 1675 has been a tributary of the Usumacinta (See the blog article "Wandering River"). Their combined annual average streamflow is 3,664 cubic meters

Stream orders point out another important characteristic of water flow nomenclature. Headwaters streams (1st, 2nd & 3rd order) are generally not called rivers. They may be brooks, creeks, rivulets, forks, runs, burns or becks, but not rivers. The term "river" implies a certain size and a minimum level of upstream network complexity. Large streams (7th order or higher) are universally called rivers. Medium streams (4th - 6th order) are sometimes called rivers based on local custom. If a stream flows to the sea it is more likely to be called a river. If a stream is wide or carries a relatively high volume of water it is more likely to be called a river. These are the rivers of England. The noted Thames flowing past London is a 5th order stream, as are most English rivers. The Severn, longest river in the UK at 354 kilometers, is a 6th order stream.
The Rivers of England
The language of the Book of Mormon text that fell from the lips of the Prophet Joseph is now thought to be Early Modern English. See the article "Early Modern English." On the streets of London when Shakespeare was a child (ca. A.D. 1570) it is unlikely the term "river" would have referred to a stream smaller than 5th order.

The map above shows that many of England's rivers are longer than the 44.8 kilometers we would expect given the mean length of 5th order streams worldwide. The Thames, for example, is 346 kilometers long (7.7 X mean), the Trent measures 297 km (6.6 X mean) and the Great Ouse runs for 230 km (5.1 X mean). Compare that with our Sidon, which at 1,111 kilometers, is 4.7 X the global mean length of 7th order streams (237.4 km).

The following two images are from a spreadsheet listing well-known 7th order streams from 5 different countries.
Length of Selected 7th Order Streams a
56 rivers comprise our sample set.
Length of Selected 7th Order Streams b
8 7th order streams in our sample are longer than the Usumacinta, although none carries a greater volume of water.

Additional relevant information is in the article "OED on Rivers."

Monday, December 22, 2014

Sermon at the Temple

The Sermon on the Mount in Matthew 5 - 7 may be the single most influential religious text in all of recorded history. It defines the essence of Christianity for multitudes past and present. The fact that a very similar sermon appears in 3 Nephi 11 - 18 has provided fodder for critics of the Book of Mormon who contend that Joseph Smith simply lifted this iconic text from the King James Bible. Upon close examination it is now clear both the Matthew and 3 Nephi versions have significant dependencies on much earlier temple texts. Two key players in this unfolding exegetical drama are Margaret Barker who read theology at Cambridge and John W. (Jack) Welch who read Greek philosophy at Oxford.

Dr. Barker, an English Methodist preacher, is widely recognized as the founder of Temple Theology, a branch of inquiry within Biblical (primarily Old Testament) Studies.She was elected President of the Society for Old Testament Study (SOTS) in 1998 and edited the Society's second monograph series published by Ashgate. Barker is the author of 16 books. She was awarded the Doctor of Divinity degree in 2008 by the Archbishop of Canterbury "in recognition of her work on the Jerusalem Temple and the origins of Christian Liturgy, which has made a significantly new contribution to our understanding of the New Testament and opened up important new fields for resrearch." In 2008 she and others founded the Temple Studies Group which believes the Temple in Jerusalem had a formative influence on the development of Christianity. (One is reminded of Hugh W. Nibley's 1959 Jewish Quarterly Review article "Christian Envy of the Temple" published in Mormonism and Early Christianity, vol. 4 in The Collected Works of Hugh Nibley (Salt Lake City: Deseret Book and FARMS, 1987). The North American Academy for Temple Studies headquartered at Utah State University spun off from the UK-based Temple Studies Group. Jack Welch, Philip Barlow and Gary N. Anderson form the Academy for Temple Studies executive committee. For some intriguing Book of Mormon connections with ancient Temple lore, see the blog article "Temple Conference 2013."

Welch, Robert K. Thomas Professor of Law at the J. Reuben Clark Law School, BYU and Editor-in-Chief, BYU Studies, formed the Foundation for Ancient Research and Mormon Studies (FARMS, now the Neal A. Maxwell Institute for Religious Scholarship, BYU) in 1979. Jack studied history, philosophy, Latin and Greek at BYU, Greek philosophy at Oxford (St. Edmund Hall), then law at Duke where he edited the Law Journal. While at Duke, Welch studied with James H. Charlesworth, now George L. Collord Professor of New Testament Language and Literature at Princeton Theological Seminary. Welch is a member of the steering committee of the BYU New Testament Commentary.

Welch's book Illuminating the Sermon at the Temple & Sermon on the Mount: An Approach  to 3 Nephi 11-18 and Matthew 5-7 (Provo: Neal A. Maxwell Institute for Religious Scholarship, 1998) broke new ground as it compared the two texts and found many concepts, phrases and symbols clearly derived from earlier temple literature.
Reading the Sermon on the Mount as a Temple Text in Light of 3 Nephi 11
The Cover Painting is by Minerva Teichert
Margaret Barker has long been popular among LDS scholars because her Temple Theology bridges the Old and New Testament worlds just as the Book of Mormon and contemporary Mormonism do. Many Christian thinkers like to see the New Testament as a completely new and revolutionary worldview. Barker and most Jewish scholars view the New Testament as a late expression of pre-existing ideas, traditions, customs and symbolism from an earlier era. The Book of Mormon fits comfortably in the Barker - Jewish camp. Barker liked Welch's book and appreciated how beautifully the Book of Mormon elucidates and expands upon the Bible while dovetailing seamlessly with it. (For an Evangelical turned Catholic articulation of the same idea, see the blog article "Mormon Christianity" which discusses the work of Stephen H. Webb). This idea of Book of Mormon as extension of and reinforcement to the Bible is expressed powerfully in 1 Nephi 13 and 2 Nephi 29.

Barker asked Welch to do another treatment of his Sermon on the Mount material minus the Book of Mormon content for mainstream Old Testament scholars. At first Welch was hesitant. Leaving out the Nephite text would handicap him. After all, it was 3 Nephi that clarified many of the Old Testament - New Testament relationships in the first place. As he got into the project, though, Jack discovered rich new veins of material to work with in the Psalms as well as post-exilic Old Testament sources. In his 1998 analysis, he had limited his use of the Old Testament to texts that would have been on the brass plates of Laban spirited out of Jerusalem ca. 600 B.C. In 2009 Welch's The Sermon on the Mount in the Light of the Temple appeared in the Society for Old Testament Study Monograph Series edited by Margaret Barker and published by Ashgate.
Reading the Sermon on the Mount as a Temple Text
The Book of Mormon only appears once in this work, at the end of the final chapter as another example of the Sermon on the Mount in a Temple setting.

Welch's use of the terms 'illuminating' in 1998 and 'light' in 2009 are not coincidental. Temple liturgy as revealed by the Prophet Joseph in this the Dispensation of the Fullness of Times Ephesians 1:10, Doctrine & Covenants 128:18, etc. is a restoration of Temple worship in Old Testament times and the Temple clarifies and brightens our understanding of Matthew 5 - 7. Matthew, of course, was the Gospel writer who specifically targeted a Jewish audience. When Jack discovered chiasmus in the Book of Mormon on August 16, 1967 in Regensburg, Germany, the voice that startled him said "if it is evidence of Hebrew style in the Bible (referring specifically to the Book of Matthew), it must be evidence of Hebrew style in the Book of Mormon." John W. Welch, "The Discovery of Chiasmus in the Book of Mormon: Forty Years Later" in Journal of Book of Mormon Studies 16/2 (2007). A PDF of the article is available here.

As Neal Rappleye deftly observed in Welch's office on Friday, December 19, 2014 these two John W. Welch books are a formidable vindication of 1 Nephi 13:40. A work of Book of Mormon scholarship led directly to significant Biblical scholarship. We now understand the Bible better because of insights gleaned from the Book of Mormon.

Saturday, December 20, 2014

The Legal Cases in the Book of Mormon

Neal Rappleye and I spent the afternoon yesterday with Jack Welch in his office. He described his presentation in July to the Jewish Law Association Conference at the University of Antwerp. His paper was entitled "Narrating Homicide in the Hebrew Bible and the Book of Mormon." The Nephite text early on tells the story of a gripping homicide (1 Nephi 4) and many others are mentioned. The theme of the conference was "Judaism, Law and Literature." This snippet from the conference program helps put Jack's presentation in context.
Jewish Law Association Morning Conference Sessions
July 15, 2014, Antwerp, Belgium
From the time he left private practice in Los Angeles to join the BYU Law Faculty over thirty years ago, John W. Welch has been an avid student of Biblical Law in both Jewish and Nephite literature. Students in his ancient law classes through the years have authored hundreds of papers, many of which bear on aspects of Biblical Law evident in the Book of Mormon text.

Welch's important book The Legal Cases in the Book of Mormon (Provo: BYU Press and Neal A. Maxwell Institute for Religious Scholarship, 2008) is an accessible introduction to a major aspect of the Book of Mormon unfamiliar to most students. Written for a general audience and highly readable, it highlights just how much jurisprudence is in the Nephite text, and the astonishing degree to which Nephite legal process followed pre-exilic Jewish patterns.
Jack Welch's 2008 Book
I consider this hard-cover book so important - it pioneers an entirely new genre within Book of Mormon Studies - I will send a copy free of charge (while supplies last) to anyone who requests it via old-fashioned paper letter sent to Ancient America Foundation, PO Box 1538, American Fork, UT 84003-6538. Be sure to include your return postal address. If you prefer Amazon, click here. Before I read Welch's book, I had read the Book of Mormon dozens of times, often with considerable care. After reading The Legal Cases in the Book of Mormon, I will never read the Book of Mormon the same way again. It opened my eyes to many points of ancient judicial process that I had not previously recognized in the text because like most, I am not trained in Biblical Law.

Jack Welch is not only a student of Biblical Law in the Book of Mormon. He is a significant contributor to the global Biblical Law discipline generally and has been a member of the Jewish Law Association (JLA) for decades. He has served on the steering committee of the Society of Biblical Literature (SBL) Section on Biblical Law. Through his tireless efforts and the manpower provided by his students over decades, BYU is an important source of bibliographic reference materials in the field.

Apostolic Witness

One of the strongest testimonies of the Book of Mormon I have heard was given by Elder Jeffrey R. Holland in October, 2009 General Conference. His stirring witness was redacted into a powerful 4 1/2 minute 2010 Mormon Message. The image below is not interactive, even though it shows the video play symbol. Click on either of the two preceding text links to watch video.
Elder Holland Holding Hyrum Smith's Copy of the Book of Mormon
I appreciate Elder Holland's eloquence, reminiscent of Elder Neal A. Maxwell. I love his passion and respect his intellect. This phrase in particular caught my attention: "As one of a thousand elements of my own testimony of the divinity of the Book of Mormon, I submit this as yet one more evidence of its truthfulness." The context is the role the Book of Mormon played in the lives of Joseph and Hyrum Smith immediately preceding their martyrdom.

I was in Jack Welch's office yesterday. Since the late 1960's he has participated in the scholarly research, editing and publication of many of the "thousand elements" Elder Holland referred to. (The Apostle specifically mentioned "literary and Semitic complexity" in the text.) This resonates with me because my own experience has been a gradual increase in the depth of my understanding of and appreciation for the Nephite scripture. In my current calling as Bishop of a large and diverse ward, I have tried to help many members through faith crises. No matter if their doubts stem from Joseph Smith's plural wives, arcane episodes in Church history, Book of Abraham facsimiles, contemporary Church finances or their own moral turpitude, testimonies ultimately come back to the Book of Mormon. I bear unequivocal witness the Book of Mormon is an ancient record translated by the gift and power of God. The Book of Mormon is the safe harbor Elder Holland mentions that will help all find healing, hope and peace through Jesus Christ. In the Apostle's words, "for [184] years this book has been examined and attacked, denied and deconstructed, targeted and torn apart ...and still it stands." For decades I have heard alternative explanations for the Book of Mormon's origin and they all ring hollow. They are "frankly pathetic" as Elder Holland says compared with the grandeur, sophistication and subtlety of the text itself.

I find it vital to recognize both divine and human elements in the Church. If I infer humanity where there is divinity, I miss the awe. If I infer divinity where there is humanity, I have unrealistic expectations. The Book of Mormon is foundational. It is bedrock. It is in Elder Holland's articulation "one of the Lord's powerful keystones..." The Book of Mormon is the most divine object most of us will have the blessing to experience this side of the veil.

"I want it absolutely clear when I stand before the judgment bar of God that I declared to the world, in the most straightforward language I could summon, that the Book of Mormon is true, that it came forth the way Joseph said it came forth and was given to bring happiness and hope to the faithful in the travail of the latter days." Elder Jeffrey R. Holland, October 2009 General Conference address entitled "Safety for the Soul"

Thursday, December 18, 2014

Benjamin Cluff Expedition Route & Distances

While Benjamin Cluff (1858-1948) was President of Brigham Young Academy, later BYU, he led an audacious group of explorers on a hemispheric quest to find the city of Zarahemla which they thought was on the west bank of the north-flowing Magdalena in the modern nation of Colombia. Leaving Provo in 1900 and returning in 1902, the group traveled to northern South America on horseback, on foot and in small boats.
The Cluff Expedition Leaving Provo on April 15, 1900
The size of the group gradually dwindled as sickness, waning enthusiasm and meager finances all took a toll.
The Cluff Expedition on the Trail in 1902
The data below comes from the journal of expedition member Heber Lorenzo Magleby (1874-1941), my great-great uncle.
Heber Lorenzo Magleby in 1896
The original autograph of Magleby's journal is in the L. Tom Perry Special Collections of the Harold B. Lee Library at BYU. A typescript is in the J. Willard Marriott Library at the  U of U. Cluff and Magleby were among the stalwarts who made it the entire way from Utah to Colombia and back. The two of them later returned to Mexico and ran rubber plantations in Tabasco.

On February 17, 1901 the expedition left Tehuantepec, Oaxaca, Mexico and 67 days later on April 25, 1901 they arrived at Copan, Copan, Honduras. During this time they traveled 1,074 air kilometers in 22 legs of travel. They had 57 travel days and 10 rest or sight-seeing days during this period. Traversing much of the area we now identify as the Book of Mormon land southward, their journey helps establish a benchmark for pre-industrial travel rates in southern Mesoamerica.

Route of the Cluff Expedition through Southern Mexico and Guatemala
The northern legs of their route allowed them so see the impressive ruins of Palenque. These are the 22 legs of their travel.
Cluff Expedition Air (Straight Line) Distances Traveled
In the blog article "Land Southward Travel Times" we analyzed a number of pre-industrial journeys in southern Mesoamerica, the earliest dating from AD 378, in an attempt to deduce a likely value for the Nephite standard unit of distance measure "one day's travel." We concluded 15 air kilometers per day was a reasonable metric. The Cluff Expedition median of 16.70 and mean of 17.89 lend credibility to our derived value of 15 air kilometers per day.