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.