By Small and Simple Numbers Part 2: Agency

Continued from "By Small and Simple Numbers Part 1".

Introduction

In his BYU Devotional called "Where Will It Lead?", Elder Dallin H. Oaks said the following:

The direction in which we are headed is critically important, especially at the beginning of our journey. I have a friend who concluded his career as a pilot flying long routes across the Pacific for a major airline. He told me that an error of only two degrees in the course set on the 4,500-mile, direct-line flight from Chicago to Hilo, Hawaii, would cause the plane to miss that island by more than 145 miles to the south. If it were not a clear day, the pilot could not even see the island, and there would be nothing but ocean until you got to Australia. But of course you wouldn’t get to Australia, because you wouldn’t have that much fuel. Small errors in direction can cause large tragedies in destination.

The concept that small numerical differences can lead to large differences over time can be applied to the decisions we make in this life.

The Math of Agency

Those of you who read my first post might remember a little bit about the gospel relationship I discussed. Here is what I said:

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.)

 

 

This post is the one in which I will explain the math behind the principle of moral agency. (Agency is more commonly known outside of the LDS faith as free will). First, let's consider why the quality of our decisions today determines our ability to make decisions in the future. Here is a quote from the Gospel Principles Sunday School Manual:

When we follow the temptations of Satan, we limit our choices. The following example suggests how this works. Imagine seeing a sign on the seashore that reads: “Danger—whirlpool. No swimming allowed here.” We might think that is a restriction. But is it? We still have many choices. We are free to swim somewhere else. We are free to walk along the beach and pick up seashells. We are free to watch the sunset. We are free to go home. We are also free to ignore the sign and swim in the dangerous place. But once the whirlpool has us in its grasp and we are pulled under, we have very few choices. We can try to escape, or we can call for help, but we may drown.

There are many more examples of this principle. When someone makes the decision to start using drugs, it becomes much harder for him or her to choose to not use drugs again. When a teenage pregnancy results from a couple choosing to violate the law of chastity, the possibilities for the couple's future are severely restricted. The list goes on and on.

 

The following equation can model this principle. In this equation, "A" is the amount of agency, "C" is the quality of an individual's choices, and a "d" before a variable means "a change in":

 

 

Using calculus, we can see that the above equation is equivalent to the following equation where "A₀" is the amount of agency we start out with and "e" is Euler's number (approximately 2.718):
 

 

If we make only positive choices, our agency over time will look something like the following:

 

 

If we make only negative choices, our agency over time will look something like the following. (As can be seen, we lose that which we had.):

 

 

A little difference in the quality of our choices can make an enormous difference in our future agency. Here is what a 20% difference in the quality of our choices can do:

 

 

Conclusion

 

As is clearly displayed by these visuals, "by small and simple [numbers] are great things brought to pass (Book of Mormon, Alma 37:6)." To again quote from the BYU Devotional by Elder Oaks:

All of us—and especially young people—need to be very careful about the paths we choose and the directions in which we set our lives. What seem to be only small deviations in direction or small detours from the straight and narrow path can result in huge differences in position down the road of life.

It can be hard at times to make the best decisions rather than just good decisions. I discovered this math while I was serving a full-time proselytizing mission for the Church of Jesus Christ of Latter-day Saints. As a missionary, I saw people trying to change their lives for the better every day. I could tell how hard it was. I want to provide people with assistance in following their Savior. When I discovered this math, any desire I had to take the easier route vanished and was replaced by a desire to take the optimum route. For me, these equations and graphs are powerful motivation to do good continually. I hope this blog post is able to do the same for you. I know that as we follow the plan the Lord has set for us, we will be eternally blessed.

 

To be continued.

The Math of Christ's Birth Part 3: The Wise Men and Star

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

Each Christmas, millions of people around the world read the Bible story of Christ's birth from the Gospels of St. Matthew and St. Luke. The Gospel of Matthew teaches:

"Now when Jesus was born in Bethlehem of Judæa in the days of Herod the king, behold, there came wise men from the east to Jerusalem, Saying, Where is he that is born King of the Jews? for we have seen his star in the east, and are come to worship him (KJV Holy Bible, Matthew 2:1-2)."

Who were these "wise men from the east"? How did the wise men know that the appearance of a new star signified the birth of the Jewish Messiah? What can astronomy and mathematics teach us about the new star that appeared? These are questions that will be discussed in this blog post.

 

Although we do not possess the New Testament in its original form, the earliest New Testament manuscripts we have are written in Koine Greek (See Note 1 to learn more). Where the King James Version of the Bible says "wise men", these Greek transcripts say "magi". The magi were royal priests and scholars in Persia, Babylon, India, and Arabia. The magi were literate and studied religious texts. They also had great knowledge of astronomy.

 

In the Old Testament, we read about Jerusalem being conquered by Babylon shortly after 600 B.C. (The Book of Mormon teaches that 600 BC is when Lehi and his family left Jerusalem after Lehi had received a vision that Jerusalem would be destroyed due to its wickedness.) The Jews were taken captive into Babylon. Daniel, a righteous Jew, became a personal adviser to the Babylonian King Nebuchadnezzar. When the Persians conquered the Babylonians, they freed the Jews and gave them the option to return to Jerusalem and rebuild their temple. A righteous Jew named Esther became a Persian queen. Due to this history, both the Babylonian and Persian magi were well acquainted with Jewish sacred literature. Although most of the magi were Zoroastrians, some of the magi likely were Jewish.

 

When the wise men arrived in Jerusalem and told Herod that they had seen the Messiah's star and were come to worship Him, Herod "was troubled, and all Jerusalem with him (KJV Holy Bible, Matthew 2:3)." The fact that all of Jerusalem was troubled suggests that the Jews did not recognize the new star as a sign of their Messiah's birth. This can be partially explained by the wicked condition of most of the Jews at the time. However, there were some Jews who were still righteous. Why didn't the righteous Jews recognize the new star as a sign of their Messiah's birth? The only Old Testament prophecy regarding a new star appearing at the time of the Messiah's birth is the following: 

"I shall see him, but not now: I shall behold him, but not nigh: there shall come a Star out of Jacob, and a Sceptre shall rise out of Israel, and shall smite the corners of Moab, and destroy all the children of Sheth (KJV Holy Bible, Numbers 24:17)."

 

As can be seen, the prophecy regarding the new star was rather vague.  Let us assume for a minute that this scripture alone could allow people to recognize the new star as a sign of Christ's birth. Most estimates of the population of Jerusalem at the time of Christ range from 15,000 to 100,000 people. Even if the population was only 15,000 and only 1 percent of the people in Jerusalem were looking for the signs of Christ's birth, 150 people should have recognized the new star as such a sign. Yet, no one did. Math makes it apparent that the Jewish scriptures alone were not enough to recognize the star as a sign of Christ's birth.

How, then, did the wise men know that the Savior had been born? LDS Apostle Bruce R. McConkie said of the wise men, "Rather, it would appear they were true prophets, righteous persons like Simeon, Anna, and the shepherds, to whom Deity revealed that the promised Messiah had been born among men (Doctrinal New Testament Commentary)." This view is consistent with mathematics.

Matthew's account of the wise men continues:

"And when [Herod] had gathered all the chief priests and scribes of the people together, he demanded of them where Christ should be born. And they said unto him, In Bethlehem of Judæa: for thus it is written by the prophet, And thou Bethlehem, in the land of Juda, art not the least among the princes of Juda: for out of thee shall come a Governor, that shall rule my people Israel. Then Herod, when he had privily called the wise men, inquired of them diligently what time the star appeared. And he sent them to Bethlehem, and said, Go and search diligently for the young child; and when ye have found him, bring me word again, that I may come and worship him also. When they had heard the king, they departed; and, lo, the star, which they saw in the east, went before them, till it came and stood over where the young child was. When they saw the star, they rejoiced with exceeding great joy. And when they were come into the house, they saw the young child with Mary his mother, and fell down, and worshipped him: and when they had opened their treasures, they presented unto him gifts; gold, and frankincense, and myrrh (KJV Holy Bible, Matthew 2:4-11)."

What was this new star that appeared to signify Christ's birth and guided the wise men to the home of Mary and Joseph? A variety of early Christian writings by such prominent church leaders and scholars as Ignatius, St. James, and Eusebius teach us that the new star was different from the other stars in the sky; the new star was indescribably bright, thereby preventing the other stars in the sky from being seen. Korean and Chinese astronomers from the time of Christ's birth also recorded an incredibly bright star appearing. We read in the Book of Mormon that, when the new star appeared, "there was no darkness in all that night, but it was as light as though it was mid-day (Book of Mormon, 3 Nephi 1:19)."

There is only one known astronomical object that can accomplish such a feat; the most likely explanation is that the new star was a supernova. A supernova occurs when a star explodes suddenly. At its peak, a supernova can release more light than the rest of the stars in the galaxy combined. Thus, a supernova can make it light outside during the night time. Supernovas are rare. There have only been five clearly documented supernovas that have been visible without the aid of large telescopes. These occurred in 1006, 1054, 1181, 1572, and 1604 A.D. The ones in 1006 A.D. and 1054 A.D. were so bright that they cast shadows and could be seen during the day time. Each of these five supernovas faded away within six months to three years. By some simple math, it can be estimated that there have probably been fewer than ten supernovas such as the one seen when Christ was born that have occurred since the time of Adam and Eve (See note 2). Although Christ was born in a humble stable, his birth was displayed in the heavens with incredible grandeur.

One lesson that math and astronomy allow us learn from the new star's appearance is the level of planning that God has put into His Plan of Salvation. As Elder Neal A Maxwell once said, "Recall the new star that announced the birth at Bethlehem? It was in its precise orbit long before it so shone (Encircled in the Arms of His Love)." Earth and the supernova had an enormous gap of space and time. Yet, God's plan was so well-orchestrated that the star appeared on the exact night that the Son of God entered this world. Using math and astronomy, we can estimate how long before Christ's birth the Star of Bethlehem was placed in orbit. We get an estimate of about one million years or longer (See note 3 to see how I calculated this).

Mathematics can also help us better understand the role the Star of Bethlehem played in guiding the wise men to the Christ child. Some people have incorrectly assumed that the star guided the wise men to the specific house Joseph, Mary, and Jesus lived in. This is a reasonable assumption when only verses 9 through 11 of Matthew 2 are considered. However, math shows this to be a completely unreasonable assumption. The nearest star to earth, named Proxima Centauri, is approximately 4.25 light years (25 trillion miles) away. Even if the star the wise men followed was as close as Proxima Centauri and Mary and Joseph lived a full mile away from their nearest neighbor, trigonometry tells us that the angle of the star in the sky would only be 1/4,300,000,000 degrees different for someone standing at Mary and Joseph's house and someone standing at their nearest neighbor's house. Since the human eye can only see angular differences of 0.02 degrees and bigger, the wise men could not have seen a change in the star's position as they walked around the streets of Bethlehem. The far more likely scenario is that the wise men started asking citizens of the small town of Bethlehem where the Messiah was. Since the shepherds had already told the people of Bethlehem about Jesus' birth (See Luke 2:15-18), someone was likely able to lead the wise men to the house of Mary and Joseph.

A final thing math can teach us about the wise men is how long it took them to get to Jerusalem. Babylon has a straight-line distance from Jerusalem of 520 miles. However, the path most people took from Babylon to Jerusalem was about 900 miles. Persia was over 1000 miles away. Although it may be a shock to some people, cars weren't available back then. When groups made long journeys by foot, donkey, or camel, about 20 miles were covered per day. Thus, it probably took the wise men about two months to get to Jerusalem. Bethlehem is only about 5 miles away from Jerusalem, so the wise men could have made it to Bethlehem in a couple hours. Some people have assumed that it took the wise men about two years to get to Jerusalem. This assumption is derived from the fact that Herod killed all of the children that had been born within the past two years. There are two possible explanations for the two year time frame. The first possibility is that it could have taken the wise men a while to get their group ready to travel to Jerusalem with their gifts. The second possibility is that Herod was trying to be extremely sure that the Messiah was killed.
 

Note 1: Koine Greek is the Grecian dialect that was spoken throughout the Mediterranean and Middle Eastern regions following the conquest of much of the Old World by Alexander the Great over 300 years before Christ's birth.

Note 2: According to the Biblical chronology, it has been approximately 6000 years since Adam and Eve were exiled from the Garden of Eden. Adam died at the age of 930 (Holy Bible, Genesis 5:5). Thus, it has been about 5000 years since the time of Adam and Eve. Since the only three known occurrences of supernovas that made it light at night occurred about 1000 (two of them) and about 2000 years ago, it can be estimated that such a supernova occurs less frequently than once every 500 years. 5000 divided by 500 yields an estimate of fewer than ten such supernova.

Note 3: Using the stellar mass-luminosity formula, it can be found that a star about 40 times the mass of the sun will have a lifetime of around one million years. 40 times the mass of the sun is about the upper limit for the mass of a star that will explode as a supernova. Smaller stars will live longer before exploding. Thus, the Star of Bethlehem was probably in its orbit for about one million years or longer. Taking into account the time the light took to travel from the supernova to the earth does not change this estimate. Most of the stars we can see with our naked eye are within a few hundred light years of the earth. Even though a supernova at its peak can give off as much light as a few hundred billion stars, the fact that the Star of Bethlehem made it light outside at night suggests that it was within ten thousand light years of the earth. Ten thousand additional years is insignificant compared to a rough estimate of at least one million years.

The Math of Christ's Birth Part 2: Messianic Prophecies

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



 

Mathematics provides compelling evidence that Jesus is the Christ. Jesus fulfilled the Old Testament prophecies regarding the coming of the Messiah. Using mathematics, we can approximate the percentage of people throughout history who will fulfill each of these prophecies. The results are astounding! Keep reading to learn more!

Since the days of Adam and Eve, prophets have been called to testify of Jesus Christ. In response to Mary conceiving the Savior, Zacharias (the father of John the Baptist and Mary's cousin-in-law according to Luke 1:36) "was filled with the Holy Ghost, and prophesied, saying,"

"Blessed be the Lord God of Israel; for he hath visited and redeemed his people, And hath raised up an horn of salvation for us in the house of his servant David; As he spake by the mouth of his holy prophets, which have been since the world began (Luke 1:67-70)."  

The so-called "prophecies" of most religions throughout history have been rather vague. This vagueness has allowed their "prophecies" to be easily fulfilled. However, due to their lack of specificity, the fulfillment of these "prophecies" has lent little scholarly support to the authenticity of these religions. For an example of what I mean, consider fortune cookies. Fortune cookies often say something to the effect of "You will have an important experience in the near future." People have important experiences all the time. Therefore, having an important experience soon after getting this fortune does not imply that the fortune cookie manufacturer is the true religion of God.


On the other hand, Old Testament prophets gave very detailed and specific prophecies regarding the coming of the Messiah. For example, 700 years before Jesus' birth, the prophet Micah prophesied that the Messiah would be born in the relatively small city of Bethlehem (See Micah 5:2). The prophet Isaiah prophesied that the Messiah would be born of a virgin (See Isaiah 7:14). Long before crucifixion had ever been invented by the Romans, David prophesied that the wicked would pierce the Messiah's hands and feet (See Psalms 22:16). There are many, many more specific prophecies like these. Jesus Christ fulfilled these prophecies.



Peter Stoner, an emeritus professor of science at Westmont College, calculated the probability of someone fulfilling these prophecies. For example he took a liberal estimate of the number of people who have lived in Bethlehem since the time of Micah and divided it by a conservative estimate for how many people have lived on the earth since the time of Micah. This yielded the result that 1 in 300,000 people have been born in Bethlehem. After considering only eight prophecies, Stoner showed that only 1 in 10^17 (a 1 with 17 zeros after it) people will fulfill all eight of them. After considering 48 prophecies, Stoner showed that only 1 in 10^157 (a 1 with 157 zeros after it) people will fulfill all 48 of them. The American Scientific Affiliation confirmed the accuracy of Stoner's calculations.

 

To illustrate just how unlikely it is for someone to fulfill all 48 of these Messianic prophecies by chance, imagine that the entire universe was completely filled with an enormous number of pennies and one quarter. Now, imagine that all of these coins got mixed up, and you drew one coin from the universe at random. It is estimated that the universe has a volume of about 3.58 x 10^80 (358 with 78 zeros after it) cubic meters. Thus, it is far more likely for you to draw the one quarter from the universe than it is for someone to fulfill all 48 of these prophecies.

 

The math so far leaves us with only two reasonable possibilities: Either every single one of Jesus Christ's Apostles lied about the events that occurred in Jesus' life, or Jesus is the Messiah. Let us consider the likelihood that all of Jesus's Apostles lied about the events that occurred in Jesus' life.

 

In the Book of the Acts of the Apostles, we read about how the Apostles succeeded in getting many thousands of people to convert to Christianity. In Acts 2, we read that the Apostles had the Spirit poured out upon them on the day of Pentecost. They were able to speak to a large multitude of people from a variety of nations in their own tongues. Due to the Apostles' ability to speak in any language, the multitude became willing to listen. As Peter spoke, the multitude felt the Spirit, and three thousand people were baptized. In Acts 3, we read that Peter and John healed a man lame from birth. Due to this miracle, the congregation listened to what Peter had to say. My point is that there were many more people who had witnessed great works performed by Christ's power than just the Apostles.

 



 

The Early Christian Church suffered immense persecution. The Apostles spent much of their ministries in prison for not denouncing their stories about Christ. Peter was crucified upside down for sticking to his story. Thousands and thousands of early Christians suffered poverty, political abuse, murder, and/or being sold into slavery. All of this occurred because the Christians would not deny their testimonies before the Jews and Romans. They knew what they had seen, heard, and (most importantly) felt in their hearts. The likelihood that an individual will continue lying about his or her experiences in the face of tremendous persecution and/or death is low. The likelihood that many thousands of people will do so is astronomically low. Thus, mathematics can rule out lying as a legitimate explanation.

 

When we consider the math, we are left with only one reasonable explanation: Jesus is "the Christ, the Son of the living God (Matthew 16:16)." I can testify of this. My testimony is strengthened as I engage in scholarly research, but it primarily comes from an even surer source of knowledge, "my Father which is in heaven (Matthew 16:17)," I know from the Holy Spirit that Jesus is my Lord and my God, my Savior from my sins and sorrows. You can gain this witness too as you read, ponder, and pray about the Holy Scriptures. I say these things in the name of Jesus Christ. Amen.

Continued in The Math of Christ's Birth Part 3: The Wise Men and Star



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/

By Small And Simple Numbers Part 1

Introduction

I have promised for the last couple blog posts that I would talk about the math behind some gospel relationships found in the scriptures. For those of you who have been anxiously awaiting the fulfillment of this promise, you're in luck; that's what this post is all about. However, I will first share a little background on this discovery.

One morning, I was studying the topic of knowledge and intelligence. I noticed an interesting pattern: the scriptures teach that if we increase our knowledge and intelligence, we will be able to continue to increase them at a faster rate. This can be compared to financial investment: the more money you currently have, the quicker you can gain more money.

Those of you who know me really well know that my two favorite things are the Gospel of Christ and math. Seeing a scriptural example of quantities changing in a specific way allowed me to recognize that my two favorite things can be combined. This was the birth of theometry. Within a few minutes, I was coming up with equations to model increases in knowledge and intelligence. Within a few more minutes, I was drawing graphs of the equations and showing them to my missionary companion. (I had been on a proselyting mission for the LDS Church for about six months at the time.) I was ecstatic.

Before long, I had come up with equations for knowledge and intelligence, faith and works, agency, diligence, et cetera. As I began to see the implications of these equations, the words of an ancient prophet named Alma kept coming to my mind. (I will explain why later in this blog post.)

By Small and Simple Things

Near the end of his mortal ministry, the great prophet Alma gathered together his sons Helaman, Shiblon, and Corianton to give them words of counsel. He spoke to Helaman first, and told him that he was going to entrust the spiritual and historical records of the Nephites and Jaredites into his hands. During Alma's explanation to his son of the great importance of these records, Alma said:

"behold I say unto you, that by small and simple things are great things brought to pass; and small means in many instances doth confound the wise. And the Lord God doth work by means to bring about his great and eternal purposes; and by very small means the Lord doth confound the wise and bringeth about the salvation of many souls."

Alma's words were surely fulfilled. Some of the recorded material given to Helaman later became part of what we know today as "The Book of  Mormon: Another Testament of Jesus Christ". This is a book of sacred scripture that members of the Church of Jesus Christ of Latter-day Saints (commonly referred to as "Mormons") read alongside the Holy Bible. From this book, millions of people around the world have gained a testimony of the gospel of Jesus Christ and a knowledge that God still speaks to His children today through a living prophet. This small and simple book has confounded the wise and brought about the salvation of many souls.



Through small and simple miracles, records of ancient prophets were preserved and became the Book of Mormon.

The doctrine that God brings about immense results through very small means is applicable to so many aspects of Christ's gospel. I have gained a testimony of this as I have involved myself with theometry. The rest of this blog post will show a few gospel relationships that teach the impact of small and simple numbers. If you don't want to learn all the math involved, you can still learn from what I will share by reading the rest of the text and looking at the graphs.

Knowledge and Intelligence

Since I have already talked a little bit about knowledge and intelligence, we will investigate this gospel relationship first. We can easily learn how these two attributes are related by looking in a dictionary. The Google dictionary defines intelligence as "the ability to acquire and apply knowledge and skills." In other words, the greater your intelligence, the faster you can learn.

Intelligence = Rate at which you can increase your knowledge

We can learn even more about the relation between these attributes by reading the scriptures. Doctrine and Covenants 88:40 teaches:

"For intelligence cleaveth unto intelligence; wisdom receiveth wisdom; truth embraceth truth; virtue loveth virtue; light cleaveth unto light"

The more intelligence, wisdom, truth, or light we have, the faster we can improve at these attributes. Since we can gain knowledge faster by having more knowledge, and since intelligence is our ability to acquire knowledge, an increase in knowledge results in an increase in intelligence.

Increase in knowledge = Increase in intelligence

Now it's time for some math. I will represent knowledge with the letter "K", intelligence with the letter "I", amount of effort being put into studying with the letter "S", and time with the letter "t". For notation, I will have "∝" mean "is proportional to", and adding a "d" before a variable will mean "a change in". For example, if I said "dK ∝ 2", that would mean "a change in knowledge proportional to two".

In order for someone to have an increase in knowledge of a certain amount (dK), they need to have some level of intelligence (I), some amount of effort being put into studying (S), and some time to have elapsed (dt). A formula to model this concept is:

 

We can model the fact that an increase in knowledge naturally leads to an increase in intelligence with the equation:

 

Substituting this equation into the one preceding it, we get:

I will now use calculus to solve for "I" (It's okay if you don't know calculus. Feel free to skip down to the graph of the function I will derive.) I will assume the rate of study is constant over time and will introduce arbitrary constants (c₁, c₂, c₃, c₄, & c₅):

 

Now, since a gain in knowledge yields a gain in intelligence, we can solve for "K"

 

Shown below is a graph of how knowledge or intelligence might change over time assuming a constant rate of studying:

 

Knowledge or Intelligence as a Function of Time



Why is mathematically modeling knowledge and intelligence useful? For me at least, visually seeing the enormous difference that putting forward the effort to gain knowledge can make is motivational. Seeing this graph helps me better understand my divine nature and scriptures such as Doctrine & Covenants 130:18-19:

"Whatever principle of intelligence we attain unto in this life, it will rise with us in the resurrection. And if a person gains more knowledge and intelligence in this life through his diligence and obedience than another, he will have so much the advantage in the world to come."

Increasing doctrinal understanding is crucial because, as Boyd K. Packer taught:

"True doctrine, understood, changes attitudes and behavior (Ensign, "Little Children")."

I can bear my testimony that God's hand is found in everything. As we seek for Him in all that we do, He will reveal Himself in ways we may not have expected. Stay tuned for my future blog posts!

"By Small and Simple Numbers" is to be continued.

Check out my other blog that gives Mormon answers for life's great questions at 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/