What is Chiasmus and Why Does it Matter?

In this blog post, I hope to answer three questions: What is chiasmus, how does it relate to math and religion, and why does it matter? Maybe you have never heard of chiasmus before, or maybe you know all about it. Regardless, you can likely gain new knowledge and insights by reading this blog post.

When you were in grade school, you likely learned how to write a one page essay. You were probably taught that your first paragraph should present your paper's main idea. You probably learned that one of the sentences in your first paragraph should be your thesis statement, and that it should clearly state your paper's primary arguments. The following three or so paragraphs should give reasons why your thesis statement is true. Finally, your last paragraph should pull the rest of your paper together to convince the reader of your arguments.

Now imagine that you have to start going back to grade school (kind of like what happened in the movie "Seventeen Again".) However, imagine that this time your writing class is very, very different. Envision you are sitting at a desk, pencil in hand, and you are being instructed by your teacher that you are going to spend class today writing a one page essay. You think that this will be easy; you are thinking, "I already know how to write a one page essay! Why do I have to be here again! This is torture!" However, you are about to be surprised. Your teacher is now telling you that you should always start a one-page essay by writing down the main point (or thesis statement) in the center of the page. "Now," she says, "you need to make a list of at least a couple points that support or build upon your main idea. We will call each point in the list you make an 'element'. Once you have a list of elements, you will need to use them in your essay one at a time. For each element, put part of your point just above what you have written so far in the middle of the page and part of your point just below what you have written so far. Once you have used all of the elements, your essay is done." You are extremely confused. You blurt out, "Excuse me teacher, this is not how to write a proper one page essay." With a smile on her face, she calmly replies, "That may not be how people normally write one-page essays nowadays, but what you learned today is how people wrote back in ancient Israel." All you can think is, "I just don't get it! Why would anyone write a paper that way! That is just plain weird!"

I hope that theoretical example helped you to understand just how different writing was in ancient Israel from how it is in western civilizations today. The writing style you imagined being taught is called 'chiasmus' and was thought of by the Hebrews (Hebrews is another way of saying ancient Israelites) as a beautiful form of poetry. (If you are still a little confused about what chiasmus is, don't worry. I'll explain it more in the next paragraph.) If you were to read a book written by an ancient Israelite, you could reasonably expect to find chiasmus in it. Likewise, if you read a book that contained strong chiasmus in it, you could reasonably assume that it was influenced by a Hebrew. One well-known book that was written by ancient Israelites is the Holy Bible. The Bible is packed full of plenty of chiasmus.

Basically, chiasmus is a literary style in which a list of elements (or points) are written down and then repeated in reverse order. This makes it so that you end up with an ABCCBA type pattern. The word 'chiasmus' was derived from the name of the Greek letter '𝞆' (commonly transliterated into English as 'chi'). This is because simple chiasmus can be illustrated with an 'X' (see the example below).

Do you see how, in the example above, the order of 'first' and 'last' is reversed? That is what makes it a chiasmus. Simple chiasmus can even be found in western literature. For example, President John F. Kennedy said the following:

Even though writing from much of the world contains simple, one or two sentence long chiasmus, chiasmus that fill entire blocks of text are unique to ancient Israel (and the surrounding countries).

The Bible, which was written by ancient Israelites, contains extended (long) chiasmus. For example, the following chiasmus is found in the Bible:

a	There died on the earth
	b	all birds,
		c	cattle,
			d	beasts and creeping things,
				e	man;
					f	all life
						g	died
						g	and was destroyed.
					f	Every living thing
				e	both man,
			d	creeping things,
		c	cattle,
	b	birds,
a	were destroyed from the earth.

- Genesis 7:21-23 (when translated literally from the Hebrew)

Notice that the first 'a' matches up with the other 'a', the first 'b' matches up with the other 'b', etc. Some chiasmus are the length of an entire chapter. A few are even longer than that.

So why does this even matter? How will knowing about chiasmus affect your life? There are two fundamental reasons: First, the Book of Mormon is either a book of scripture from God that will bless your life more than any other book and set you on the path towards exaltation, or it is a complete and utter fraud that will set you on the path towards Hell. Either way, it is extremely important to find out if the Book of Mormon is true. Is it a book written by Joseph Smith and/or other early LDS Church leaders, or is it exactly what it claims to be: a book of scripture written by prophets of a group of ancient Israelites who were led by God out of Jerusalem and to the Americas? A good test of this is whether or not there is intentional chiasmus in the Book of Mormon.

At the time the Book of Mormon was published, almost nobody in America knew about chiasmus. After extensive research, scholars have concluded that, at the time, there was only one book in the U.S. that even mentioned chiasmus. (See footnote 1.) Moreover, the section on chiasmus was only a short excerpt in the middle of this long book. To further complicate things, this book was kept in Philadelphia, Pennsylvania while Joseph Smith lived in Palmyra, New York. Remember, cars and airplanes didn't exist as a mode of transportation back then. It is EXTREMELY unlikely that Joseph Smith (or any of the other early Church leaders) could have known about chiasmus before the Book of Mormon's publication.

Thus, if the Book of Mormon contains intentional chiasmus, then the Book of Mormon is not a fraud. Rather, it is the word of God! It is a book that will change your life if you apply yourself to a daily study of its pages and ask God in earnest prayer each day what He wants you to learn from it.

There is a second reason why knowing about chiasmus matters. The center of a chiasmus is called the 'chiastic turning point'. The chiastic turning point is usually the main idea that the author is trying to convey. It is comparable to a thesis statement. All of the other elements are meant to build upon and explain the chiastic turning point. So, if you know that a section in the Book of Mormon or Bible is a chiasmus, you can first look and see what the main idea that the author was trying to convey is by looking at the chiastic turning point. Then, you can see how the other elements are meant to build upon and explain the chiastic turning point. This will allow you to understand the passage of scripture better, and it will allow you to gain new spiritual insights. It has definitely done that for me.

Let me show you an example. Alma 36 is an entire chapter long chiasmus. In Alma 36, Alma the younger is telling his son Helaman about his conversion story before he gives Helaman the Nephite records. For the first half of the chapter, Alma tells all about his wickedness and the negative consequences that came from his actions before his conversion. In the second half of the chapter, Alma tells all about his righteousness and the blessings that followed after his conversion. The chiastic turning point is the point at which he was converted. If you look, you will see that it was when he remembered the words of his father about Jesus Christ, the Son of God, and cried unto Christ for mercy that he was converted. At the moment that he yielded his heart unto Christ, everything turned from bad to good. There are profound lessons to be learned from this. I know of no passage of scripture that provides a stronger testimony of Christ's saving grace than this beautiful chiasmus does.

a

My son, give ear to my words (Alma 36:1)

b

Keep the commandments [and] ye shall prosper in the land (Alma 36:1)

c

Captivity of our fathers—bondage (Alma 36:2)

d

Surely God did deliver them (Alma 36:2)

e

Trust in God (Alma 36:3)

f

Support in trials, trouble, and afflictions (Alma 36:3)

g

I know this not of myself but of God (Alma 36:4)

h

Born of God (Alma 36:5)

i

Seek no more to destroy the church of God (Alma 36:9)

j

Fell to the earth (Alma 36:10)

k

Limbs paralyzed (Alma 36:10)

l

The agony of conversion (Alma 36:11–16) destroyed, torment, harrowed up, racked, the pains of hell, inexpressible horror, banished and extinct, the pains of a damned soul

m

I remember … the coming of one Jesus Christ, a Son of God, to atone for the sins of the world

m

I cried within my heart: O Jesus, thou Son of God, have mercy on me (Alma 36:17–18)

l

The joy of conversion (Alma 36:19–22) no more pain, what joy, marvelous light, exquisite, nothing as sweet, singing and praising God, longing to be with God

k

Limbs received their strength again (Alma 36:23)

j

Stood upon my feet (Alma 36:23)

i

Labored without ceasing to bring souls unto repentance (Alma 36:24)

h

Many have been born of God (Alma 36:26)

g

Knowledge is of God (Alma 36:26)

f

Supported under trials and troubles, yea afflictions (Alma 36:27)

e

Trust in him (Alma 36:27)

d

He will still deliver me (Alma 36:27)

c

Egypt—captivity (Alma 36:28–29)

b

Keep the commandments and ye shall prosper in the land (Alma 36:30)

a

This according to his word (Alma 36:30)

And now we get to math. Some people have claimed in the past that the chiasmus in the Book of Mormon occurred by chance and were not intentional. This was an important question to settle, for the authenticity of the Book of Mormon was at stake. Two physics professors at Utah State University, named Boyd and Farrell Edwards, made a statistics program that was capable of calculating a rigorous lower bound on the statistical likelihood that the chiasmus in the Book of Mormon were intentional. For Alma 36, they found that there is less than a one in 150,000 chance that the chiastic structure could have occurred accidentally. In science, if something is shown to have greater than a 95% chance of being the case, it is assumed to be true until evidence comes along that suggests otherwise. For Alma 36, we can be more than 99.999% sure that it was an intentional chiasmus. So, it is almost indisputable that it was intentional. There are many other strong chiasmus in the Book of Mormon.

Thanks to math, it has been confirmed that the Book of Mormon is exactly what it claims to be: It is the word of God! It is a book of Divine revelation! We should heed its every word! We should value its teachings over the teachings of man! However, even though the math tells a clear story, we should not stop there in gaining a testimony of the Book of Mormon. I invite you to read the Book of Mormon, ponder in your heart the message it contains, and pray to Heavenly Father in the name of Jesus Christ to ask Him if the Book of Mormon is the word of God. If you do so, the Holy Spirit will confirm its truthfulness to your heart. Numbers on a page can change your beliefs. However, a conversion by the power of the Holy Ghost is far more likely to change your actions and character. Together, learning by study and learning by faith can provide an unshakable testimony of the truth that will not be affected by the very jaws of Hell.

I invite you to ponder and pray about who you can share this message with. Then, follow through on the inspiration you receive. Every person around you is a child of our Loving Father in Heaven. He or she has Divine potential inside of him or her. By sharing this glorious message of truth with him or her, you are providing an opportunity for him or her to latch ahold of that potential and bloom into that beautiful son or daughter of God he or she is capable of becoming. I testify of this message in the name of Jesus Christ. Amen.

Footnote 1: In case you are wondering, the only book in the U.S. that mentioned chiasmus at the time the Book of Mormon was published was "Introduction to the Critical Study and Knowledge of the Holy Scriptures" by Thomas Hartwell Horne. It was first published in 1825.

The Math of Christ's Birth Part 1: The Shepherds

 

Much of the world is acquainted with the timeless tale of Christ's birth. As the Bible teaches us, Joseph and the virgin Mary went to Bethlehem to be taxed. The time came for Mary to deliver the Christ child. There was no room for them in the inn, so Mary wrapped her baby in swaddling clothes and laid him in a manger. A new star appeared at the time of Christ's birth. Shepherds were visited by angels and told of the glorious birth of their long-awaited Messiah. Wise men came from the east to give gifts to the baby Jesus and worship Him.

Each Christmas season, hundreds of millions of people remember the birth of our Savior. However, far fewer people consider the mathematics relating to the Nativity story. This blog post (and ones that will be published later this month) are intended to help people learn more about the math of Christ's birth. In this blog post, I will consider the shepherds. In blog posts later this month, I plan to consider (from a mathematical perspective) the Messianic prophecies, the wise men from the East, the new star that appeared, and the commercialization of Christmas. I sincerely hope these blog posts will be thought-provoking and faith-promoting for all who read them.

 

St. Luke recorded the following regarding Jesus' birth:

"And there were in the same country shepherds abiding in the field, keeping watch over their flock by night. And, lo, the angel of the Lord came upon them, and the glory of the Lord shone round about them: and they were sore afraid. And the angel said unto them, Fear not: for, behold, I bring you good tidings of great joy, which shall be to all people. For unto you is born this day in the city of David a Saviour, which is Christ the Lord. And this shall be a sign unto you; Ye shall find the babe wrapped in swaddling clothes, lying in a manger. And suddenly there was with the angel a multitude of the heavenly host praising God, and saying, Glory to God in the highest, and on earth peace, good will toward men. And it came to pass, as the angels were gone away from them into heaven, the shepherds said one to another, Let us now go even unto Bethlehem, and see this thing which is come to pass, which the Lord hath made known unto us. And they came with haste, and found Mary, and Joseph, and the babe lying in a manger (Holy Bible KJV, Luke 2:8-16)."

Up until the time that Joseph was sold into Egypt, shepherding was considered by the Hebrews to be a noble occupation. The Egyptians, however, considered shepherds to be the scum of the earth. By the time Moses led the Israelites out of Egypt, the Israelites possessed the Egyptian view of shepherds. When David, a shepherd, was anointed by Samuel, defeated Goliath, and became a powerful Israelite King, the Israelites' view toward shepherds improved. However, this did not last long. By the time Christ was born, shepherds belonged to Israel's lowest social status. The Jewish religious leaders had officially given shepherds the title of "sinners". (With this in mind, it is interesting to consider the fact that Christ referred to himself as a shepherd.)

From, a mathematical perspective, it is quite profound that Angels visited the shepherds. When Christ was born, an enormous number of people were less than 10 miles away. We read in Luke:

"And it came to pass in those days, that there went out a decree from Cæsar Augustus, that all the world should be taxed. (And this taxing was first made when Cyrenius was governor of Syria.) And all went to be taxed, every one into his own city. And Joseph also went up from Galilee, out of the city of Nazareth, into Judæa, unto the city of David, which is called Bethlehem; (because he was of the house and lineage of David) (Holy Bible KJV, Luke 2:1-4)."

There is also considerable evidence suggesting that Christ was born on 15 Nisan (See Note 1 to learn more). This would correspond to the Jewish Passover. Because people were gathering to be taxed and for the Passover, Jerusalem and its suburbs (including Bethlehem which is only 5 miles away from Jerusalem) would have been packed. This is why there was no room for Mary and Joseph in the inn. A famous Jewish historian, Josephus, wrote that approximately 1,197,000 people were gathered together in Jerusalem for the Passover in 70 A.D. (See Note 2 to learn more.) We can assume that a similar number of people were within walking distance of the Christ child when he was born.

 

The Bible does not state how many shepherds were visited by angels. However, the text suggests that it was not a very large number. If we make the liberal guess that there were 30 shepherds who visited Christ the night of His birth, that is still only about 0.000025 percent of the people who could have visited Him that night. The angels visited an extremely small number of people at the very bottom of the culture's caste system!

Why did angels come to a small group of social outcasts? Why didn't they announce Christ's birth to the kings and priests? Why did Luke choose to record something about shepherds? We may never know all of the specific reasons during our earth life. However, there are clear lessons to be drawn from the shepherds; the numbers vividly show that God loves all of His children regardless of economic or social status. As St. John beautifully expressed:

"For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life (Holy Bible KJV, John 3:16)."

 

Continued at Math of Christ's Birth Part 2: Messianic Prophecies

 

Note 1: Nisan was the first month of the Hebrews' religious calendar and the seventh month of their political calendar. 15 Nisan corresponds to the beginning of April. Christmas is celebrated on December 25, but it is unlikely that Christ was actually born on that day. For example, the shepherds were spending their night outside. Most shepherds in Judea did not spend their nights outside with their flocks during the cold and rainy winter. Furthermore, the Romans typically did not have people gather to be taxed during the winter. Most scholars believe that early Christians picked December 25 for Christmas to correspond with the timing of Pagan festivals for the birth of the sun. Doctrine & Covenants 20:1 says, "The rise of the Church of Christ in these last days, being one thousand eight hundred and thirty years since the coming of our Lord and Savior Jesus Christ in the flesh, it being regularly organized and established agreeable to the laws of our country, by the will and commandments of God, in the fourth month, and on the sixth day of the month which is called April." Many LDS Church leaders and scholars have understood this verse to mean that Christ was born on April 6. Other Church leaders and scholars disagree. Regardless, 15 Nisan does happen to correspond well with Messianic prophecies and Jewish traditions regarding the Messiah.

 

Note 2: Josephus was born in Jerusalem, but later became a Roman. He was commissioned by the Roman Emperor to write a comprehensive history of the Jews. His writings are commonly quoted in Biblical commentaries. The Passover in 70 A.D. was when the Roman Emperor, Nero, destroyed Jerusalem. According to Josephus, most of the people who had gathered for the Passover were slain, and the rest were sold into slavery. That event (known as the Siege of Jerusalem) played a major role in the Apostasy of the Early Christian Church, but that's a different topic for a different blog post.

 

Feel free to comment with any questions you may have.

The Knowledge, Power, and Priesthoods of God

CAUTION: This blog post has the potential to forever transform your understanding of the knowledge, power, and priesthoods of God. Do not continue reading past this point unless you are prepared to have your mind blown!

 

For nearly two centuries, leaders of the Church of Jesus Christ of Latter-day Saints have taught a large quantity of information regarding the omniscience, omnipotence, and priesthood authority

of God the Father and His Son Jesus Christ. Yet, studies show that there remains confusion among the Church members regarding a noteworthy doctrine: Is God still increasing in knowledge, power, and priesthoods? If so, what is the current scope of his knowledge, power, and priesthoods?

These are questions that have long troubled me as I have diligently studied the writings of the Prophets and Apostles of present and past dispensations. Finally, a couple months ago, I considered this question from mathematical perspective. When I did so, my understanding was enlarged and I saw that some supposed contradictions can actually be harmonized. Now, I am not saying that I definitively know that I am right; I am merely saying that I came to an understanding that seems to me to be consistent with the scriptures and teachings of modern-day Church leaders.

 

As Mormon fundamentalists repeatedly point out, there seems (at least at a first glance) to be two sets of teachings in the Church regarding the extent of God's knowledge and power and whether or not He is progressing in these attributes.

 

In the early Restored Church, basically all of the major church leaders (with the clear exception of the Pratt's) taught that God is still progressing; they argued that, although God is an omnipotent, omniscient Being, He is still gaining more knowledge and power with every passing day. For example, here are quotes by two of the early Presidents of the Church, Brigham Young and Wilford Woodruff:

 

"Brother Orson Pratt has, in theory, bounded the capacity of God. According to his theory, God can progress no further in knowledge and power; but the God that I serve is progressing eternally, and so are his children: they will increase to all eternity, if they are faithful (Brigham Young, Journal of Discourses)."

 

"If there was a point where man in his progression could not proceed any further, the very idea would throw a gloom over every intelligent and reflecting mind. God himself is increasing and progressing in knowledge, power, and dominion, and will do so, worlds without end. It is just so with us. We are in a probation, which is a school of experience (Wilford Woodruff, Blessings of the Saints—Condemnatory State and Conduct of the Christian World, Etc., Journal of Discourses)."

On the other hand, most of the Church leaders since the early 1900s have taught that God's omniscience and omnipotence have necessarily caused Him to become stagnant in His learning. For example, here are quotes by a past President of the Church, Joseph Fielding Smith, and a former Apostle (who was also Joseph Fielding Smith's son-in-law), Bruce R. McConkie:

"It seems very strange to me that members of the Church will hold to the doctrine, 'God increases in knowledge as time goes on.'...But how does anyone know? Where has the Lord ever revealed to us that he is lacking in knowledge? That he is still learning new truth; discovering new laws that are unknown to him? I think this kind of doctrine is very dangerous. I don’t know where the Lord has ever declared such a thing. It is not contained in any revelation that I have read. Man’s opinion unaided by the revelations of the Lord, does not make it so (Joseph Fielding Smith, Doctrines of Salvation)." 

"There are those who say that God is progressing in knowledge and is learning new truths. This is false—utterly, totally, and completely. There is not one sliver of truth in it. It grows out of a wholly twisted and incorrect view of the King Follett Sermon and of what is meant by eternal progression. 

"God progresses in the sense that his kingdoms increase and his dominions multiply—not in the sense that he learns new truths and discovers new laws. God is not a student. He is not a laboratory technician. He is not postulating new theories on the basis of past experiences. He has indeed graduated to that state of exaltation that consists of knowing all things and having all power. 

"Will he one day learn something that will destroy the plan of salvation and turn man and the universe into an uncreated nothingness? Will he discover a better plan of salvation than the one he has already given to men in worlds without number?...If God is just dabbling with a few truths he has already chanced to learn or experimenting with a few facts he has already discovered, we have no idea as to the real end and purpose of creation (Bruce R. McConkie, Seven Deadly Heresies)."

There appears to be a contradiction. Which school of thought is true doctrine? How can we tell? Bruce R. McConkie gave us the answer. He said:

"Nonetheless, as Joseph Smith so pointedly taught, a prophet is not always a prophet, only when he is acting as such. Prophets are men and they make mistakes. Sometimes they err in doctrine. This is one of the reasons the Lord has given us the Standard Works. They become the standards and rules that govern where doctrine and philosophy are concerned. If this were not so, we would believe one thing when one man was president of the Church and another thing in the days of his successors. Truth is eternal and does not vary. Sometimes even wise and good men fall short in the accurate presentation of what is truth. Sometimes a prophet gives personal views which are not endorsed and approved by the Lord (Bruce R. McConkie, Letter to Eugene England)."

Thus, the key to identifying the truth is to carefully consider a variety of statements made by General Authorities of the past and present against the backdrop of the Holy Scriptures. Although the Standard Works and Holy Spirit definitely take priority, I would argue that math can also assist us in this process. I believe, along with such wise men of history as Pythagoras and Plato, that all truth can be expressed through mathematics.

Before we delve into the scriptures, I would like to consider the mathematical relationship between knowledge, power, and priesthoods. Power is defined as "the capacity or ability to direct or influence the behavior of others or the course of events (Oxford Dictionary)." In order for an individual to have any amount of power, there are at least two requirements: he or she must have sufficient knowledge, and he or she must have adequate resources. Clearly one cannot perform a task when he or she doesn't know how. Furthermore, even when one does know how to accomplish a task, he or she cannot do so without adequate resources. The term "resources" encapsulates such things as time, physical materials, and authority.

Thus, power (P) is a multiplicative function of knowledge (K) and resources (R). However, if you double the amount of available resources while maintaining a constant amount of knowledge or vice versa, the amount of power will not actually double; progression in power can begin to be limited by a lack of progression in either of these two values. Since knowledge and resources can be measured according to any system of measurement we desire, we can pick a system of measurement such that the following equation becomes an approximate model (at least for a given interval):

 

What resources does God need to govern the Universe? We know that time is not a factor, for Alma 40:8 teaches "all is as one day with God, and time only is measured unto men." Physical materials is not a factor either, for "even the winds and the sea obey him (Matthew 8:27)!" The only resource we really need to consider in this equation is authority over the elements.

As the LDS Gospel Topics section on priesthood explains, "priesthood is the power and authority of God. It has always existed and will continue to exist without end (see Alma 13:7–8; D&C 84:17–18). Through the priesthood, God created and governs the heavens and the earth. Through this power, He exalts His obedient children, bringing to pass “the immortality and eternal life of man” Therefore, Deity's fundamental resource is priesthood. The equation above for power can be rewritten as follows where "p" represents the quantity of priesthood authority that is worthily possessed:

An important thing to notice is that this equation shows that, if God progresses in priesthoods or knowledge, He progresses in power as well. With that in mind, we're ready to look at what the scriptures have to say. First, let's consider two verses from the fourth Lecture on Faith. (The Lectures on Faith are the seven doctrinal discourses that made up the doctrinal portion of the 1835 edition of the Doctrine and Covenants.)

"without the knowledge of all things, God would not be able to save any portion of his creatures; for it is by reason of the knowledge which he has of all things, from the beginning to the end, that enables him to give that understanding to his creatures, by which they are made partakers of eternal life; and if it were not for the idea existing in the minds of men, that God had all knowledge, it would be impossible for them to exercise faith in him. 

"And it is not less necessary that men should have the idea of the existence of the attribute power in the Deity. For, unless God had power over all things, and was able, by his power, to control all things, and thereby deliver his creatures who put their trust in him, from the power of all beings that might seek their destruction, whether in heaven, on earth, or in hell, men could not be saved; but with the idea of the existence of this attribute, planted in the mind, men feel as though they had nothing to fear, who put their trust in God, believing that he has power to save all who come to him, to the very uttermost (Lectures on Faith 4:11-12)."

As can be seen, Joseph Smith the Prophet clearly taught that God has all knowledge and all power. This principle is explicitly taught dozens of times throughout the Standard Works. This is the grounds on which many Church leaders have argued that God is not progressing in knowledge and power. After all, how can someone gain more knowledge if they already have all knowledge? The answer to this question depends on what is meant by "all knowledge". The word "all" is very context-specific. For example, if a child were to say that they own all of the toys (and was telling the truth,) the listener would be able to safely assume that the word "all" was used in reference to all toys that were in the room, not in reference to all toys that have ever existed or ever will exist. One instance in which the scope of God's knowledge is given context in Moses chapter one:

"And the Lord God spake unto Moses, saying: The heavens, they are many, and they cannot be numbered unto man; but they are numbered unto me, for they are mine. And as one earth shall pass away, and the heavens thereof even so shall another come; and there is no end to my works, neither to my words. For behold, this is my work and my glory—to bring to pass the immortality and eternal life of man (Moses 1:37-39)."

In this chapter, the Lord God appeared unto Moses in the mountaintop, and Moses was shown all of God's creations and was taught about the Plan of Salvation. God continually referenced His omniscience in this chapter. In the quote above, God said that all things in the heavens "are numbered unto me, for they are mine." In other words, He has intimate knowledge of all things in the Universe because they are part of His dominion. God emphasized that all things He showed unto Moses are His multiple times. We may therefore conclude that, when the scripture state that God has "all knowledge", it may mean that God has knowledge about all of His creations. If this is the case, then God will increase in knowledge (and consequently power) if He forms another creation. In the quote above, God clearly stated that He never stops making more creations. Thus, if God's knowledge is limited to His creations, He does increase in knowledge and power.

 

The Doctrine and Covenants teaches us that "All truth is independent in that sphere in which God has placed it, to act for itself, as all intelligence also; otherwise there is no existence (Doctrine and Covenants 93:30)." In this section, the term "intelligence" was used in reference to an intelligent being (We can see clearly that humans, angels, and the Savior are all intelligences in Abraham 3, especially verse 19.) In other words, this section was teaching that all intelligent beings are given truth and the ability to act within a given "sphere". Since God is an intelligence, it is completely plausible that His knowledge and power are confined to the sphere of His creations.

This new perspective addresses Bruce R. McConkie's concern that a lack of all knowledge could lead to a failure in the Plan of Salvation. In order to be confident of His plan for His creations' exaltation, God would only need to know all things pertaining to His creations. Thus, He can still be learning new truths while maintaining complete confidence in His Great Plan of Happiness.

A final scripture that can give some additional insight into the extent of God's omnipotence is in Psalms: "[The Lord] telleth the number of the stars; he calleth them all by their names. Great is our Lord, and of great power: his understanding is infinite (Psalms 147:4-5)." This scripture invites two questions: Is God's knowledge really infinite, and, if His knowledge really is infinite, is it possible for Him to still be learning?

First, does this scripture really mean what it says; is God's knowledge really infinite? To start, we need to understand that the Old Testament was written in Hebrew, not English. Information can get lost in translation and transcription. In the Wentworth Letter, Joseph Smith wrote "We believe the Bible to be the word of God as far as it is translated correctly (Articles of Faith 1:8)." I can't read Hebrew, but I do know that the NIV translation for Psalms 147:5 reads "his understanding has no limit." This can either mean that God's knowledge is currently infinite, or it can mean that there is no limit to how much He can learn. Next, we need to understand that the Hebrew people were far more concerned with concepts than precise numerical values. For example, different accounts give different heights for Goliath the giant, but they all state that he was really tall. In fact, the Hebrews did not even have precise units of distance, area, or weight. Distance, for example, was measured in cubits. A cubit was the length of the forearm which varied from person to person. In most Hebraic literature, hyperbole was abundant. The point is, we can't assume based on this scripture alone that God's knowledge is actually infinite.

Second, if God's knowledge actually is infinite, is it possible for Him to still be learning? In my last blog post, I showed that knowledge tends to increase in an exponential fashion. The simplest exponential function is (where is K is Knowledge, t is time, and e is Euler's Number which is approximately 2.718):

 

This function's graph looks like this:

 

How fast someone is increasing in knowledge at any given time is equal to the slope of the graph at that time. As can be clearly seen, as the time goes to infinity, the amount of knowledge goes to infinity. Also, as time increases, the slope also increases. Calculus can be used to figure out the slope as time goes to infinity. It turns out that, for this function, the rate of knowledge increase is infinite when the time goes to infinity. Thus, at an infinite time, someone who already possesses infinite knowledge can be gaining more knowledge at an infinite rate. But, how can someone still be increasing in knowledge if their knowledge is already infinite? I admit, this seems a little nonsensical from a purely philosophical perspective, but I can understand this using mathematics.

Consider every number from 0 to 1. You can put any series of decimal place digits you want after a 0 and a decimal point (such as 0.32819... or 0.69275...) and you will get some number between 0 and 1. There are an infinite number of possibilities. Thus, between any two integers, there is an infinite amount of numbers. We also have the number set of all integers (...-1, 0, 1, 2, 3,...) There are an infinite number of integers between 0 and infinity. Although you have an infinite amount of numbers in a certain interval, that doesn't mean there are no numbers outside of that interval. Similarly, you can have all knowledge and still be learning.

Before I conclude, I would like to give a clear scriptural example of the Savior progressing in power. Joseph Smith even used this as an example for how the Savior progresses in his King Follett Sermon. When the Savior was resurrected, he gained the power to resurrect all mankind (See 1 Corinthians 15:20-22). After He had ascended to His Father, He appeared to His Apostles and explained to them how things were different now. During this sermon, Christ told them, "All power is given unto me in heaven and in earth (Matthew 28:18)."

Check out my other blog at https://mormonanswersforlife.blogspot.com/

Constants - The Fingerprint of God

God's Fingerprint is Everywhere
Every time I look at the world around us, I see a lot of parallels to the stories found in the Holy Scriptures. Today I was reading some Pew Research survey results on religious affiliation in the United States. It was devastating to see a staggering drop over the last decade in the number of people that identify themselves as Christians. Meanwhile, the number of people that claim to be atheist or agnostic has approximately doubled.

This reminds me of a scriptural story found in the Book of Mormon (a book of scripture used alongside with the Holy Bible) about a man named Korihor.
Korihor traveled throughout the land, preaching there is no God to the citizens of each city. He contended that "every man fared in this life according to the management of the creature; therefore every man prospered according to his genius, and that every man conquered according to his strength; and whatsoever a man did was no crime... [and] when a man was dead, that was the end thereof (Book of Mormon, Alma 30:17-18)."

Korihor ended up in a conversation with Alma, the leader of Christ's church in the land. Their dialogue went as follows:

"And now Korihor said unto Alma: If thou wilt show me a sign, that I may be convinced that there is a God, yea, show unto me that he hath power, and then will I be convinced of the truth of thy words. But Alma said unto him: Thou hast had signs enough; will ye tempt your God? Will ye say, Show unto me a sign, when ye have the testimony of all these thy brethren, and also all the holy prophets? The scriptures are laid before thee, yea, and all things denote there is a God; yea, even the earth, and all things that are upon the face of it, yea, and its motion, yea, and also all the planets which move in their regular form do witness that there is a Supreme Creator (Book of Mormon, Alma 30:43-44)."

I have encountered many modern-day Korihors. Alma's counter-argument is full of wisdom. "All things denote there is a God." In this blog post I want to show how numerical constants denote there is a God. I will only discuss a few examples. I am sure there are many, many more valuable examples.

Phi
The first constant I want to talk about is called "Phi" (pronounced "fee"), is represented by the Greek letter "Φ", and is approximately 1.618. Phi is also commonly known as the "Golden Ratio". Personally, I think it should be called the "God Number" because it is an almost unparalleled evidence of God's hand at work.

Φ = 1.618...

Phi has a variety of cool mathematical properties. It is closely related to a mathematical series called the Fibonacci Sequence where each number is the sum of the two previous numbers.

Fibonacci Sequence:

1, 1, 2, 3, 5, 8, 13, 21, 34...



Phi can be approximated by taking any number in the Fibonacci sequence and dividing it by the previous number. The further along in the series you go, the closer the number is to Phi.

1 ÷ 1 = 1

2 ÷ 1 = 2

3 ÷ 2 = 1.5

5 ÷ 3 = 1.67

8 ÷ 5 = 1.6

13 ÷ 8 = 1.625

21 ÷ 13 = 1.615

34 ÷ 21 = 1.619

 



Here is a another fascinating relationship between Phi and the Fibonacci sequence (The Fibonacci sequence is found going downwards in both of the columns of blue numbers):

 Φ^1 = 1 × Φ + 0

Φ^2 = 1 × Φ + 1

Φ^3 = 2 × Φ + 1

Φ^4 = 3 × Φ + 2

Φ^5 = 5 × Φ + 3

Φ^6 = 8 × Φ + 5

Φ^7 = 13 × Φ + 8

Φ^8 = 21 × Φ +13

In addition to creating these (and many more) cool math relationships that are clearly not coincidence, Phi is found all throughout nature. It is found in ratios between many parts of the human body, honey bee breeding habits, planetary orbits, and the spirals of DNA, sunflowers, pineapples, snail shells, etc.
Below is a drawing of a Nautilus shell with vertical and horizontal lines following the spiral. If you start at the center of the spiral and work your way outwards, each straight line increases in length by a ratio of Phi:

 

How amazing is that? Phi is found everywhere in mathematics and nature. Science offers no explanation for why this constant keeps popping up in so many seemingly unrelated things. However, if all things were made by a Divine Creator, then an explanation is clear; Phi is part of the fingerprint of God.

The Speed of Light
Another constant that is a powerful manifestation of God's fingerprint is the speed of light. The speed of light is represented by the letter "c" and is 299,792,458 meters per second. (That is just over 670 million miles per hour!)



c = 299,792,458 m/s

In the early 1900's Albert Einstein came forth with his groundbreaking theory of Special Relativity. He proposed the radical idea that matter and energy can be converted back and forth into each other. (This has since been demonstrated very clearly with the atomic bomb.) For this conversion, he put forward his most famous equation:

E=mc^2

 

Energy equals mass (similar to weight) times the speed of light squared. The idea that the speed of light determines how much energy you get for a certain amount of mass is truly amazing! The speed of light is such an arbitrary value, yet it is the same constant used for this and many other important equations in physics about things other than light. Why is this? Once again, God's hand is at work.
 

Another thing that shows the speed of light is a value determined by God is merely the fact that it is a constant. Why does light travel at the same speed in every part of the universe at all times? If this universe was created by chance as many people claim, wouldn't we expect the speed of light to have been randomly determined? If it was randomly determined, why doesn't light change speeds at random as it moves from place to place? Science does not provide any explanation for how constants are determined and enforced throughout all space and time. On the other hand, revealed religion does.

A revelation from God to one of His modern-day prophets teaches that something called the Light of Christ "proceedeth forth from the presence of God to fill the immensity of space. [It's] the light which is in all things, which giveth life to all things, which is the law by which all things are governed, even the power of God who sitteth upon his throne, who is in the bosom of eternity, who is in the midst of all things (Doctrine and Covenants 88:12-13)." The Light of Christ is the mechanism by which God implements constants throughout all space and time.

 

Pi

The final constant I want to talk about is Pi. Pi is represented by the Greek letter "π" and is approximately 3.14.

 

π = 3.14...

 

 Pi is defined as the ratio between the circumference and diameter of a circle.

 

 

The amazing thing about Pi is the fact that it never changes; the circumference of a circle divided by the diameter always equals 3.14... Some might ask "Why is that so incredible? Isn't it obvious that the circumference and diameter always maintain the same ratio?" However the issue is actually not that simple.

Einstein's General Theory of Relativity, which has been consistent with observed data up to this point, posits that space is not flat but curved. It is true that we can't see this curvature, but, according to Einstein, we can feel it. Einstein's theory says that gravity is the result of spacetime being curved. Once we accept that space can be curved, Pi being a constant is truly a miracle.
 

To demonstrate this, imagine that a circle is drawn on a flat surface. The ratio between the circumference and diameter will be about 3.14.

 

 

Now imagine that a circle with the same circumference is drawn on a spherical surface. If we measure the distance from one side of the circle to the other, traveling along the surface of the sphere, we will get a larger number than we did on the flat surface. Since the diameter is longer than before, the ratio between the circumference and diameter will be less than 3.14. We can see that the value for Pi changed.

 

Finally, imagine that a circle with the same diameter as the circle on the flat surface is drawn on a saddle-shaped surface. If we measure the perimeter of the circle, traveling along the saddle, we will get a larger number than we did on the flat surface. Since the circumference is longer, the ratio between the circumference and diameter will be greater than 3.14. Once again, we can see that the value for Pi changed.

 

 

The physics equations for spatial curvature state that the density of mass in a region of space determine its shape. If the universe really did spontaneously create itself in a Big Bang (as so many people claim,) we could expect to see a random mass distribution throughout the universe. Consequently, space would be curved like crazy all over the place with no apparent pattern. It would therefore not be unreasonable to expect to see Pi varying at different locations. However, we don't see this. Rather, there appears to be a definite order and uniformity to all things throughout the universe.

Again, math allows us to see Divine Providence in action. Apart from spiritual impressions, what better testimony-builder is there than theometry? Perhaps there is none. Check back in a couple weeks to see my next blog post on mathematical relationships in the scriptures.

Check out my other blog that gives answers to some of life's great questions at mormonanswersforlife.blogspot.com/

What in the World is Theometry?!

Theometry's Story
I grew up learning that math existed on one side of an imaginary fence and religion was on the other. I honestly thought of them as distinct subjects that were completely separate from each other and were not to be mixed. I knew they didn't contradict and were both useful to know. In fact, I felt strongly that they filled in each other's gaps. Yet, I never once thought during calculus class, "Wow, I wonder how this relates to God!" Nor did I ever think in Sunday School, "I wonder what Christ's Atonement can teach me about mathematics."

 

 

Not too long ago, I was serving a proselytizing mission for the Church of Jesus Christ of Latter-day Saints (commonly nicknamed "the Mormons".) During my mission, I came to a stunning realization: God is a God of math! My lifelong mental separation of math and religion was merely a lack of understanding! I am quite the math nerd, and I am especially fond of mathematical modeling. (Mathematical modeling is making equations that describe real-life phenomena.) So, I quickly got to work making equations that describe gospel principles. I got a couple friends to help out. Since I had just discovered a new branch of mathematics, I just had to give it a classy name. After months of spinning the gears in my head, the perfect name came to me: THEOMETRY. "Theos" is Greek for god, and "-metry" is a Greek-derived suffix that means "to measure". Thus, "theometry" would be defined as the branch of mathematics that deals with measuring the things of God. (Not to mention, there is just a special ring about the word! It sounds like a mix between the words geometry and theology.)

I am learning so much great stuff from theometry, so I have wanted to share it with the world for over a year. A few nights ago, I had the brilliant idea of giving theometry its very own blog. I just know this blog is going to be revolutionary, so be sure to become a blog follower.

What in the World is Theometry?
I know your curiosity is now peaked. What in the world is theometry?! How do math and God go together? Is God really a God of math?
Theometry is everywhere. There are many different ways that math and God relate. To see what I mean, let's take a look at the holy scriptures.
The scriptures are packed full of relationships between different things. An equation is defined as a relationship between 2 or more things. Therefore, every time a relationship is established, it can be described with a math equation. Since religion and math are being blended, these equations fall under the scope of theometry.
As a simple example, the Book of Mormon (a book of LDS scripture that goes alongside the Holy Bible) states:
"Wherefore, men are free according to the flesh; and all things are given them which are expedient unto man. And they are free to choose liberty and eternal life, through the great Mediator of all men, or to choose captivity and death, according to the captivity and power of the devil (2 Nephi 2:27)."
This verse teaches that we have the freedom to make choices. If we use our freedom wisely, our freedom will increase. Otherwise, our freedom will decrease. There is a clear relationship between our choices and our freedom. Thus, there must be an equation to describe how our choices and freedom relate. (In a later post, I will discuss the actual math behind this verse, but for now I just want to demonstrate that it contains math.)

I have figured out equations that model a significant number of gospel relationships. As I have done so, my testimony of the gospel's self-consistency and interrelatedness has grown significantly. More importantly, I have gained a greater understanding of how the gospel works. As I have made graphs for equations I have developed, I have been able to visually see the long-term effects of short-term choices. Viewing these results has drastically increased my drive to improve my actions. I have seen first-hand just how much good theometry can bring about.
Modeling gospel relationships is only the tip of the iceberg. As will be discussed in future blog posts, math can be used to analyze the scriptures' and modern-day prophets' literary structures, self-consistency, progression of civilizations, name derivations, and so on. Looking at scriptural writings from a mathematical perspective enables us to test their plausibility. Math can be used to determine the likelihood that life on this planet occurred by chance rather than having been created intentionally by a Divine Power. The possibilities are truly endless.

Is Theometry of the Devil?
As I have worked to develop theometry and have told some of my close friends about it, I have met a lot of resistance. As an example, one person told me that theometry is in complete opposition to the will of God. He argued that God wants us to live according to faith, not according to mathematical formulas. He further contended that it is a sin to try and measure God.
Is theometry really a sin? I do not believe it is. The scriptures teach us that "God created all things (Book of Mormon, Mosiah 4:9)." If this is true, did not God create math? The scriptures also teach that "all things...are made for the benefit and the use of man (Doctrine and Covenants 59:18)." We must conclude that God made math for our use and benefit. Any time that math is used to solve a real-world problem, one or more of God's creations are being measured. So, in a sense, one is measuring the things of God. If theometry really was a sin, then no math should be engaged in. However, as I already showed, God made math for our use and benefit. Furthermore, the scriptures teach that "all things which are good cometh of God (Book of Mormon, Moroni 7:12)." Engaging in theometry has done nothing but build my faith (contrary to what my one friend said would happen.) Is it not then of God?

Many incorrectly think that faith is completely blind. That notion is completely contrary to the Lord's teachings on faith found in Alma 32 and Hebrews 11. Yes, we need to take a step into the darkness, trusting that the Lord will take care of us if we follow Him. But, where does this trust come from? We gain the trust to follow God from the evidences we have seen up to that point. Faith is evidence-based belief that motivates us to act even when it is difficult. Therefore, seeing mathematical support for God will increase our faith if we are yielding our heart unto Him.

Stay Tuned
As I previously stated, I know this blog's future content will cause a paradigm shift. No reader of it will ever think about math and religion in the same way again. So, I am once again petitioning you to become a blog follower.

Be sure to check out my other blog that gives answers to life's tough questions at mormonanswersforlife.blogspot.com