Puzzling Through the Repetitions in Life
February 20, 2018
Mathematics Department Chair
Jackie Nygaard is a faculty member and the chair of the mathematics department.
Jackie has earned bachelors, masters, and doctorate degrees in mathematics and education from the University of Utah, Southern Utah University, and Utah State University. He worked in public education as a mathematics and science teacher, technology specialist, and administrator. He developed a passion for serving middle school students in St. George, Utah for 13 years before coming to BYU-Idaho in 2007.
Jackie joined the United States Marine Corps right out of high school and met Heather while serving in Hawaii. They were married in 1988 and have been blessed with 2 amazing sons, Kaleb and Joshua, who have both graduated from BYU-Idaho and moved on to climates just as cold as Rexburg.
Jackie has served in many capacities in the church and currently serves as an assistant area auditor (which is as obscure of a calling as it sounds, but yes it is a real thing).
It is often puzzling how much repetition there is in life and the Gospel. Think of all the things that you need to repeat daily, weekly, monthly, and even more or less frequently. Whether it is the daily battle with the razor or starting every morning with prayer; studying for our classes, posting on discussion boards, or studying the scriptures; attending school, going to work, or worshiping in church and the temple-repetition is a fundamental part of our lives. President Hinckley taught that "repetition is a law of learning (Hinckley, 2000)," yet looking up repetition in the scriptures, you will find that repetition is almost always associated with a warning against "vain repetition."
What are some things that you find yourself repeating? Do they bring you joy or do you find them monotonous? What makes the difference to you? How do you avoid "vain repetition?" Share your thoughts on the discussion board and engage in the conversation.
Devotional is a fantastic place to be on a Tuesday afternoon. Thank you for participating, and whether you are here or tuning in from elsewhere, it is an honor to be with you. Over the course of the past 10 years, I have missed very few devotionals. I make the weekly walk down from the Ricks Building and am uplifted as speakers share a piece of themselves as they powerfully teach the gospel. As much as I love devotionals, sometimes devotionals may seem a bit repetitive; but even with the repetition, I have been blessed by my attendance and have been blessed to have two sons attend BYU-Idaho. I was always grateful that they were willing to join me, even if, I must confess, dozing did occur more than once or twice (as the photo evidence cannot be denied).
I often wonder why, when I'm enjoying a talk, I may fall asleep. Is it because after 50 years of Church activity, it sometimes feels as if I've heard it before? Is it because devotional follows a particular cadence that just lulls me to sleep? Is it just a nice, comfortable seat? Is it because I'm simply tired? Or does it have something to do with how I listen? And does how I listen have something to do with an attitude regarding the repetitive nature of devotionals? Whether we're talking about devotionals, church, school, work, or the gospel, life is full of repetition. Have you ever wondered why there is so much repetition? It can be a real puzzle.
I like puzzles. I haven't always liked puzzles, but I have grown to love them in all different forms. As a child, I enjoyed a tradition in our home of doing a jigsaw puzzle on New Year's Eve. As a boy, I would put in a few pieces, but it seemed to require more patience than I possessed. As I grew older, I began to find a little more enjoyment in the puzzles, and as an adult with a family of my own, I carried on the tradition of doing a puzzle every New Year's Eve. A few years ago, after a long New Year's Eve, my kids observed, "You're a lot more fun when you're working on a puzzle." I wasn't really sure how to take that, but the main point was that when I'm working on a puzzle, I'm awake and I'm engaged, whereas if I just sit down to read or watch a show, I am often asleep within a few minutes.
Much like life, puzzles are full of repetition. Any puzzle will do. It doesn't much matter what the picture is. I dump the pieces and quickly put the box away where it can't be seen, for I prefer the picture from a puzzle to emerge through the puzzling.
At the beginning, it is common to spend time doing nothing but turn pieces over--repetitively. The pieces are sorted and organized--sometimes by color, sometimes by shape. Sometimes they aren't sorted at all, but just spread out on the table. The beauty of a puzzle is that there is never one sure way to approach the puzzling.
It can be overwhelming at first, but beginning with the most obvious parts of the puzzle--edges, writing, people, or prominent figures--it becomes something new with each assembled piece. Once you find one piece, you have to turn around and find another piece. With all this repetition, why am I still awake? Could it just be the puzzling?
Sometimes I'll see a spot and look for the piece that will fit the spot, but other times I will find a piece and look for the spot it will fit. But most often, through repeated attempts, the different pieces come together through recognition of the patterns and their relationship to each other. When one area isn't coming together, I'll leave it and start in another area. I can jump all over and not worry, because in the end it will all come together. The picture will emerge, and satisfaction will settle in as a result of all the puzzling.
To some, a puzzle may seem boring and not worth the time; after all, it is pretty repetitive. I have heard the same said of reading, writing, history, mathematics, accounting, economics, anatomy, or just about any topic we need to learn. I've heard it said of running, golf, music, or just about any activity in which we participate. I have heard it said of family home evening, Sunday School, scripture study, the temple, or sacrament meeting. One thing that fascinates me is how something can give one person such enjoyment, peace, or satisfaction while another person finds the very same thing boring, burdensome, and unsatisfying. To me, that is an interesting puzzle. What makes the difference? Perhaps it is simple differences in preference, and isn't it a blessing that we are not all the same? Perhaps it extends beyond mere preference; perhaps it is our willingness to exercise our agency to think and puzzle.
As members of this church, we believe in obedience, sacrifice, consecration, sustaining leaders, bearing one another's burdens, and making covenants with God to remember Him and obey these commandments. Which, quite frankly, requires a lot of repetition. In return the Lord promises us His Spirit. I propose that in keeping our covenants and puzzling through this life in a spirit of obedience, there are two important elements that need to come together--repetition and thinking.
President Gordon B. Hinckley taught, "I remind you that repetition is a law of learning."[i] Yet Elder Marvin J. Ashton referred to "avoiding vain repetition" as a spiritual gift.[ii] So as we puzzle our way through life, how do we make sure the repetition in our lives serves us as a law of learning rather than merely being vain repetition?
Last semester, Elder Dale G. Renlund taught us about the doctrine of Christ. Let's listen again: "The doctrine of Christ--faith, repentance, baptism, and receiving the Holy Ghost--is not intended to be experienced as a one-time event. Our theology teaches us that we become perfected by repeatedly and iteratively 'relying wholly upon' the doctrine of Christ. This means that we repeat the steps in the doctrine of Christ throughout our lives. Each step builds on the preceding step, and the sequence is intended to be experienced over and over again." They went on to teach that as we are only baptized once, we must substitute "the ordinance of the sacrament for the step of baptism."[iii]
So exercising faith, repenting, partaking of the sacrament, and receiving the gift of the Holy Ghost is repetitive by divine design. But how we approach the repetition seems to be important. So, again, how do we make sure the repetition in our lives serves us as a law of learning rather than merely being vain repetition?
I think this was what Elder and Sister Renlund were trying to teach us. Did you notice that Elder Renlund used another word? He said "repeatedly and iteratively." Although many things just require repeating, it may be that word iteratively that makes the difference between repetition for learning and vain repetition. Let's compare and contrast repetition with iteration. Since I am a math professor, I will use three different examples from mathematics, for in mathematics, iteration has an important meaning and yields important results. Listen carefully, and see if you can pick out how iteration is different from mere repetition.
Iteration Accelerates Growth
The first example to help us compare and contrast repetition with iteration is the growth of money through simple versus compound interest. An investment of $100 growing by simple interest of 10 percent will grow $10 the first year. The next year, the same $100 will be used to grow by $10 again. Each year, interest is determined by going back to the original amount invested and calculating 10 percent. With this process of repetition, steady growth is achieved. In 10 years, the amount of money has doubled, and in another 20 doubles again. In the case of simple interest, the interest earned is simply repeated in the exact same amount year after year.
If we look at the same $100 investment but this time with interest compounded annually, the first year, $10 is earned; but the interest earned is not ignored, and the new amount of $110 is what earns interest the next year, so $11 interest is earned. As time goes on, that difference continues to grow, and in 50 years, the interest in a single year has surpassed $1,000.
In the case of simple interest, we see repetition that causes steady constant growth, but in the case of compound interest, everything that comes out of the equation is rolled back in when the process is repeated. This is iteration, and you could see it made an enormous difference.
Can you think of anything in your living of the gospel that repeats daily? You shared some fantastic insights on the discussion board this week. Ben Brown shared, "Telling my wife I love her every day."[iv] A repetition that causes that love to grow. There is definitely growth occurring in Indira's family as she shared their repetitive routine: "We kneel down every night to pray. [It] is a repetitious exercise and we all know that in 5 nights it will be our turn again, but maybe because I'm the mother or because [it] is a moment when we are all together, I love this kind of repetition."[v]
Hopefully, you are seeing growth as a result of your faithful repetition, but is that growth repetitive, or is it iterative?
When I was a young man getting ready to graduate from high school, President Ezra Taft Benson challenged the members of the Church. He said, "There is a book we need to study daily, both as individuals and as families, namely the Book of Mormon."[vi]
Although I may not have responded immediately, within a few months, as a young Marine, I began reading in earnest, and when Heather and I married in 1988, we made a commitment that we would read it together every day. When our children came along, we included them and taught them a nightly routine that included reading the Book of Mormon. Sometimes we would get home late at night, and we'd want to get the kids right to bed, but they would quickly remind us that we hadn't read scriptures yet. As a result of following through on that commitment to read the Book of Mormon every day, we have been blessed. We have been through the Book of Mormon together at least 30 times, and we stand as a witness to the blessings President Marion G. Romney promised when he said:
"I feel certain that if, in our homes, parents will read from the Book of Mormon prayerfully and regularly, both by themselves and with their children, the spirit of that great book will come to permeate our homes and all who dwell therein. The spirit of reverence will increase; mutual respect and consideration for each other will grow. The spirit of contention will depart. Parents will counsel their children in greater love and wisdom. Children will be more responsive and submissive to the counsel of their parents. Righteousness will increase. Faith, hope, and charity--the pure love of Christ--will abound in our homes and lives, bringing in their wake peace, joy, and happiness."[vii]
Our two sons are grown now, beginning families of their own. Upon reflection, I have been concerned that perhaps our reading together may have been more repetitive than it was iterative. The repetition did help us grow, but did we get the full iterative power that we could have? I asked my sons for their thoughts, and Kaleb shared: "Each time through there are new adventures, new sermons, new lessons to experience. The beauty of reading the Book of Mormon as a family was experiencing those new experiences together each time we read.... The Book of Mormon never felt repetitive. The characters were familiar to me, but they were always teaching something new."[viii] So I'm confident steady growth was achieved through our repetition, and as our individual and family experiences continually informed our reading, perhaps at times it was more iterative, delivering accelerated growth.
Iteration Puts Failure to Good Use
A second example from mathematics is a method that the ancients used for calculating square roots. They would begin with a number and a guess for the square root. They would take half of the sum of the number divided by the guess and the guess itself. As an example, if you were looking for the square root of 100 and guess that the square root is 1, then you calculate. The answer is 50.5, which is completely wrong, but we use that failure, and it goes back into the process as our new guess. And we get 26.24. 26.24 yields 15.03, and we calculate again. 10.84--another failure that leads to 10.03, which then yields 10. When we put 10 back in, 10 comes back out. So we have arrived at the correct solution. Even though we started with a terrible guess, in five iterations we had arrived at the correct value.
Notice this case helps us understand that iteration is not just about growth but about learning from failure and increasing precision. If we turn to the scriptures, we have an example of this type of iteration in 1 Nephi. We all know that before the trip back to Jerusalem to retrieve the plates, Nephi said, "I will go and do the things the Lord hath commanded me."[ix] But as robotic as that may sometimes sound, to keep that commitment, Nephi and his brothers were required to think. And their best thinking led to failure. Let's look at their process.
I and my brethren did consult one with another....
... We cast lots[;] ... Laman went[;] ... he talked...
... Laban was angry, and thrust him out....
... Laman fled.[x]
Failure! The brothers' desired response: "Return unto my father in the wilderness."[xi] Nephi's response: "As the Lord liveth, and as we live, we will not go down unto our father in the wilderness until we have accomplished the thing which the Lord hath commanded us."[xii]
Now, it's easy to say we'll do what the Lord commands when we're back at home with Dad and the task seems simple enough, but to say it again after the first failure and the magnitude of the task looms large is what makes Nephi Nephi.
I persuade my brethren....
... We went down to the land of our inheritance, and we did gather together ... our precious things....
... We went up again unto the house of Laban....
... Laban saw[;] ... he did lust after it[;]...he thrust us out, and sent his servants to slay us....
... We did flee[,] ... obliged to leave behind our property.[xiii]
Failure! After the second failure, Laman and Lemuel were not just ready to go home; they were scared, frustrated, and angry. They began taking it out on Sam and Nephi. The angel intervened, and afterwards, Nephi, trusting in the Lord, took matters into his own hands.
I caused that they should hide themselves without the walls[;] ... I, Nephi, crept into the city....
... I was led by the Spirit....
... I beheld a man ... drunken with wine....
... I found that it was Laban....
... I beheld his sword....
... I was constrained by the Spirit that I should kill Laban; but I said in my heart: Never at any time have I shed the blood of man. And I shrunk and would that I might not slay him.[xiv]
Take note of this reasoning with the Lord. Nephi is committed to keeping the Lord's commandments, but that does not mean he abandons all reasoning. Instead, he thinks. And because he is thinking, he receives greater understanding through the gift of the Holy Ghost. "Behold the Lord slayeth the wicked to bring forth his righteous purposes."[xv]
I ... heard[;] ... I remembered....
... I also thought....
And I also knew....
And again, I knew....
... I did obey ... , and I smote....
I did gird on his armor....
... I went forth unto the treasury...
... I should carry ... the plates of brass...
... I went forth unto my brethren.[xvi]
Success! The beauty of Nephi's story is not just that he was so obedient but that to fulfill the Lord's command, he had to think about how it could be done and what its consequences would be. He failed, then used that failure to develop another idea. Just like with the square root method, each iteration had the same objective. In Nephi's case, to get the plates. But the prize was not immediately realized; it required failure, thought, learning, and moving forward in faith iteratively. It was not vain repetition; it was working through multiple iterations, learning from each subsequent failure.
Iteration Creates Beauty
The final comparison comes from basic fractal geometry. A fractal is defined as "a geometric pattern that is repeated at ever smaller scales."[xvii] One of the earliest and simplest descriptions of a fractal was published in 1904 by the Swedish mathematician Niels Helge von Koch and is called the Koch curve.
The Koch curve is produced by starting with a line segment, dividing it in thirds, and then rotating the middle third 60 degrees, maintaining the connection and giving the impression of a bottomless triangle sitting in the middle of the original line. If we continually repeat this process by repeatedly returning to the original line segment, you quickly see that although pretty cool the first time, by the fourth or fifth repetition, it doesn't seem there is much to it. Perhaps this could be considered "vain repetition."
On the other hand, if we iterate the process rather than merely repeat it, the repetition still happens, but what happens before is not ignored. Rather than repeating on the original segment, the iteration recognizes that after the first process, we now have something new, and what was one segment is now four segments. If we repeat the process on each of the new segments, we have something different and a little more complex. If we repeat it again and then again, we end up with something that many consider beautiful. When this curve begins with three segments in an equilateral triangle rather than a single segment, you end up with the Koch snowflake.
With this image in mind, let's think about our experience with the doctrine of Christ and especially the sacrament. Are we starting from the same point every week--going back to the beginning and repeating the process, going through the motions but not realizing any real change? Or are we transforming into the greater disciple we might become as a result of the fact that who we were coming out of the process last week is going into the process this week? We are not starting from scratch. What do you do to make the repetitive experience of the sacrament an iterative and transformative experience?
All of the things we are taught to do during the sacrament are important. To those great ideas, I recommend one additional bit of thinking. I would like to share an idea that has had a profound impact on my weekly sacrament experience. I heard the theologian Don Saliers say concerning communion, "God is remembering my life in its entirety and remembering the whole of humanity. So my finitude, my inability to love, the string of broken promises which is my life to this point suddenly is going to be mended by God remembering me."[xviii] Upon hearing this, I began to think about the words of the sacrament and the fact that it is a covenant between me and the Lord. A covenant that God keeps much better than I do and honored it even before I entered the covenant. I covenant to remember, and so does He. He remembers me, and as I have taken time during the sacrament to recognize the evidence that surrounds me that God loves me and remembers me, I know that His promise, "I will not leave you comfortless,"[xix] is a promise kept. I have been surprised at the thoughts that come to mind. Little things that have happened during the week that I had all but forgotten remind me that I am not alone. God remembers me, even in my weakness. Like the Koch curve, when I approach the sacrament with an understanding of it being an iterative rather than merely repetitive process, I begin to witness something truly beautiful.
Elder Renlund, in his closing testimony in that devotional address last semester, said:
The time will come, in each of your lives, when there will be a hesitation to go to church and partake of the sacrament. If it hasn't happened yet, it will. But know this: if you follow the Savior's direction and go and partake of the sacrament, with a broken heart and a contrite spirit, blessings will pour upon you that will keep you firm, that will keep you solid, that will keep you established on that firm foundation that is Jesus Christ. Your decision to do so will affect eternity. You will establish yourself upon Jesus Christ, the author and finisher of our faith.[xx]
Life is full of repetition. Last week, Brother Burgener challenged each of us to do something to serve someone else. He taught us how we could do that with greater empathy. That is a practice we need to engage in repeatedly and iteratively.
All this repetition is a puzzle. How we approach the repetition matters for the disciples of Jesus Christ we aim to become. Simple repetition is important, but iteration can accelerate growth, help us continually learn, and produce greater beauty and understanding.
So my challenge to each of you is this: Choose one thing you are currently working with that involves repetition of some kind. It could be in your studies, your relationships, your church service, or your personal worship. Ask yourself, "What can I do to make this repetition more iterative?" Anticipate the results. Will it bring increased growth and learning--greater precision that may involve learning from failure--or will it increase the beauty in your life and relationships? Once you think about it, do something about it.
I testify that as we all take action, we will move closer to becoming the disciples of Jesus Christ we hope to become.
In the name of Jesus Christ, amen.
[i] Gordon B. Hinckley, "Great Shall Be the Peace of Thy Children," Ensign, Nov. 2000, https://www.lds.org/ensign/2000/11/great-shall-be-the-peace-of-thy-children?lang=eng. [ii] Marvin J. Ashton, "There Are Many Gifts," Ensign, Nov. 1987, https://www.lds.org/ensign/1987/11/there-are-many-gifts?lang=eng. [iii] Dale G. Renlund, "Come unto Christ," BYU-Idaho Devotional address, Sept. 26, 2017, http://www.byui.edu/devotionals/elder-and-sister-dale-g-renlund#transcript. [iv] Ben Brown, discussion board post. [v] Indira Estrada, discussion board post. [vi] Ezra Taft Benson, "A Sacred Responsibility," Ensign, May 1986, https://www.lds.org/ensign/1986/05/a-sacred-responsibility?lang=eng. [vii] Marion G. Romney, "The Book of Mormon," Ensign, May 1980, https://www.lds.org/ensign/1980/05/the-book-of-mormon?lang=eng. [viii] Kaleb Nygaard, personal communication to speaker. [ix] See 1 Nephi 3:7. [x] 1 Nephi 3:10-14. [xi] 1 Nephi 3:14. [xii] 1 Nephi 3:15. [xiii] 1 Nephi 3:21-26. [xiv] 1 Nephi 4:5-10. [xv] 1 Nephi 4:13. [xvi] 1 Nephi 4:14-20, 24, 27. [xvii] American Heritage Dictionary (2000), s.v. "fractal." [xviii] Don Salier, in "The Meaning of Communion: At the Table," On Being, radio broadcast transcript, Nov. 18, 2004, https://onbeing.org/programs/don-saliers-edward-foley-meaning-communion-table. [xix] John 14:18. [xx] Renlund, "Come unto Christ."