The Gift of Uncertainty
Associate Professor of Mathematics Education
July 9, 2019
Associate Professor of Mathematics Education
July 9, 2019
It took me a very long time to write this devotional address. Sometimes when I have the opportunity to give a talk or teach a lesson, I know immediately what I want to talk about. This happened a few months ago in my ward. The bishop came to my door and asked if I would be willing to speak the following Sunday, and I instantly knew what I wanted to talk about. When I sat down to write that talk, it felt as if the talk wrote itself.
This devotional was very different. I was plagued with uncertainty about what to say from the moment I was asked to speak. Two months later, I had written and discarded pages and pages of drafts and half-formed thoughts. I did not know what the Lord wanted me to say to you today. I did not know what I wanted to say to you today.
And so finally, one week before I was required to submit the text of my address, I accepted that perhaps what I needed to talk about today was not knowing.
Perhaps this will be strange to say, since I have grown up in a church that encourages members from a very young age to say the words “I know,” but the thing I am most certain of in this life is that we do not know all things. In fact, on the grand scale of all truth, it is quite possible that, statistically speaking, we don’t know anything. And by that I mean that because God and truth are so vast and so big, the things we know are so small in comparison as to render that knowledge essentially nonexistent. So today I want to talk about this idea of not knowing and about finding God in our uncertainty.
I want to add this caveat: I am speaking from my own perception and experience. Paul, in his epistle to the Corinthians, talked about spiritual gifts—the gifts of wisdom, of knowledge, of faith, and of healing.1 I will openly confess that I was probably not given the gift of knowledge. At times in my life I have had faith and I have had hope, but, in general, my knowledge has often felt a little tenuous. However, I have come to believe that uncertainty can be a gift every bit as much as knowledge is, so I will approach you today in this spirit of uncertainty.
I would like to discuss several aspects of not knowing. My hope is that in at least one of them you find something helpful for or of value to living your life, attending school, developing your testimony, building relationships, and going out into the world to do whatever it is you will do on this earth.
First, I think it is helpful to talk a little bit about knowledge itself. We use the phrase “I know” in many ways, but they are not all the same. Consider the following statements:
1. I know that 2 + 3 = 5.
2. I know that on a clear day, the sky is blue.
3. I know that I love my parents.
All of these statements use the phrase “I know,” but the way I know each of these things is not the same. Take the first statement. This one is easy for me as a math teacher. If I take two distinct objects, say M&M’s, and combine them with three more M&M’s, I will have five M&M’s. Although I have come to recognize that truth in mathematics is far more complex than we usually imagine, it is nevertheless very difficult to dispute the statement that 2 + 3 = 5.
But now consider the second statement: the sky is blue. On the surface it seems equally indisputable. I believe that all of you will agree with me that on a clear day, the sky is blue. But I do not know if when we look at the sky that we all see the same thing. And if a person is unable to see the sky at all, what does it mean that the sky is blue? Scientifically we can speak about light and wavelengths, but this does not reflect my experience of seeing blue. In fact, I recently learned that ancient languages did not have a word for blue and that in lacking a word to describe the color, people who spoke these languages may have been incapable of even seeing the color blue. To explore this possibility, researcher Guy Deutscher decided to do what countless researchers have done: he experimented on his own child. When his daughter was very young, he was careful to never describe the color of the sky to her. Finally, one day he asked her to look up and describe the color, but she had no idea how to describe it. The sky at first did not fit any ideas of color to her.2
This complicates the truth of my statement that the sky is blue.
When I consider the third statement, that I know I love my parents, I have to concede that there is no objective way to measure this. In fact, I have failed embarrassingly on a few simple measures of love. Last year, when my dad called me on his birthday, I didn’t even say happy birthday to him! Still, I can say that I know with 100 percent certainty that I love my parents, and I truly believe they know the same. It is just a different kind of knowledge than the knowledge that 2 + 3 = 5.
When it comes to matters of the Spirit, we frequently hear the words “I know”:
I think we sometimes assume that any “I know” needs to mean “I know” in the same way that I know that 2 + 3 = 5. But we can’t know these things in the same way, because they are different types of truth and they are accessible to us in different ways. What I think we usually mean is that we are equally confident in those things. Even then, some of us are and some of us are not. Not all of us have been given the gift of knowledge.
I believe it is important to understand the kind of knowledge we should be seeking. Knowledge that 2 + 3 = 5 is fairly set, but knowledge about the color of the sky is born of our experience with the sky. Not only is the color of the sky ever changing, but, as we gain experience, our ability to describe what we are seeing and even our very ability to see can change and grow—just as our ability to know God can change and grow throughout our lives. If I assume that knowing God is like knowing that 2 + 3 = 5 and then I experience something that conflicts with my understanding, I have to go back to the drawing board with all of arithmetic. But if knowing God is more like knowing the color of the sky, apparent conflicts with my current understanding have the potential to expand rather than shatter my view.
Knowledge of spiritual things is also manifested in how this knowledge drives our actions. It is far less important that I know I love my parents than it is that I show this love to them and continue to try even when my expressions are imperfect. Knowledge that the Church is true or that God lives or that Jesus loves us is less important than what our faith and hope compel us to do. Knowledge of God’s love is important, but how I take that love and allow it to change myself and the world around me, even when my efforts are imperfect, is far more important.
Knowledge that is complete and certain can also be limiting and, quite honestly, not all that interesting. A living knowledge that changes, grows, adapts, and motivates us to action is a knowledge that embraces states of uncertainty and not knowing. These states lead us toward change and growth. In fact, as humans, we tend to move on quickly from simple facts like 2 + 3 = 5 to complex questions of what we can do with these facts and then to questions that stretch our understanding past its apparent limits. Math is much bigger and much more open than 2 + 3 = 5, just as God is much bigger than we imagine.
I want to turn in another direction now and address another side of not knowing. I would like to begin with a story.
One day while I was working on this devotional address at home, my four-year-old daughter was playing on the couch next to me. Our dog Jin barked at the back door, wanting to be let into the house.
“Can you let Jin inside?” I asked my daughter. Because what are children for except to do the small tasks you don’t feel like doing yourself?
But instead of jumping up happily to help, my daughter informed me, “Jin did not bark.”
“Well, I just heard him,” I told her.
“Jin is not outside,” she responded.
“Well,” I said, “I am actually looking at the door, and I see him standing outside.”
“He is not outside,” she insisted.
Because I was working on a devotional address about knowledge, I decided to do that “experiment on your own children” thing and asked, “Do you know that Jin is not outside?”
With great confidence she looked at me and said, “I know that Jin is not outside.”
At this point I got up myself and let our dog inside, and my daughter exclaimed, “Oh, Mommy, Jin was outside!”
Her apparent genuine surprise convinced me that she had not been lying when, in the face of visual and aural evidence, she had informed me that our dog was not actually outside barking to be let in. I believe she really knew that the dog was not outside because she wanted him to not be outside. It would have been inconvenient for her if he were outside because she would have had to stop playing and go let him in.
It makes for a funny little anecdote when it is about my determined, headstrong little daughter, but we do this all the time. When we know something, we are likely to hold on to that knowledge as tightly as we can, even when we are mistaken. We usually don’t realize we are doing this. Of course we don’t, because we know!
Our human minds are built to make sense of the world around us, to categorize, to evaluate, and to put our experiences and observations into simple boxes. The ability to create order and organization out of the chaos that surrounds us is incredibly important to our survival and well-being. But a consequence of this well-developed human ability is that we all think we know and understand far more than we actually do.
One of my favorite stories from the history of mathematics is the story of the parallel postulate. Around 300 BC, Euclid of Alexandria wrote a book called Elements in which he essentially built geometry on the foundation of five postulates or statements that are accepted as truth without needing additional reasoning or argument. Four of his five postulates are pretty straightforward. One, for example, was that with two given points, we can draw a straight line connecting those two points. But the fifth postulate has given mathematicians grief for the last two millennia. This postulate reads:
If a straight line intersecting two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than two right angles.3
It is a mouthful, but essentially this postulate allows us to believe some things about parallel lines, or lines that never intersect, that intuitively seem like they must be true about parallel lines.
The problem is that mathematicians weren’t convinced that this concept was conclusive. The fifth postulate seemed like an idea about geometric space that needed to be argued, rather than a conclusion that could be put forth without argument. For centuries, mathematicians attempted to find a way to make this argument using just the first four postulates and perhaps a new, more self-evident postulate.
One person who worked on this problem in the early eighteenth century was Giovanni Girolamo Saccheri. He attacked the problem using quadrilaterals and thought he had succeeded. In his Proposition XXXIII he stated that a particular counter result would be “repugnant to the nature of the straight line.”4 Basically, Saccheri knew what a straight line should do and knew what parallel lines should do. Ultimately his argument for the truth of the parallel postulate hinged on the fact that without it, straight lines ended up behaving in ways that were “repugnant” to their nature.
But a century later and more than two thousand years after Euclid wrote his book Elements, a handful of mathematicians finally asked, “What if we are wrong about the nature of straight lines? What if in some spaces lines behave one way, but in other spaces they behave in a completely different way?”
By letting go of their knowledge, they discovered something fascinating: if they reconsidered the way parallel lines work, geometry did not fall apart. In fact, by tweaking this one condition, they managed to create or perhaps discover a strange, new, wonderful geometry that we now call hyperbolic geometry, which is every bit as mathematically valid as the Euclidean geometry you learned in high school, although it is much harder for humans to wrap their heads around.
Mathematics, when you spend time with it, has a particular kind of beauty that is not always conveyed well in our school experiences. Hyperbolic geometry has its own beauty, both mathematically and visually. But opening the door to this beauty required humans to admit that what they thought they knew could actually be wrong.
I think it is important for us to question what we think we know and to open ourselves to the idea that it might be wrong, even (and perhaps especially) when being wrong would be inconvenient or uncomfortable for us. I might ask myself some of the following questions:
Accepting that we may not know what we think we know does not mean we need to let go of all certainty or conviction. Rather, openness to being wrong can be a humble position of faith in which “hope for things which are not seen”5 can flourish as we allow ourselves to accept that there are things that are not seen to us.
Finally, it would be easy for me to frame the topic of uncertainty as “uncertainty until,” with the expectation that not knowing is just a step in the process to knowing. But while we might gain greater understanding throughout our lives, there is also no end to not knowing in mortality. In fact, there will be many times in our lives when answers do not come and when not knowing is a seemingly permanent state.
One of the things I have always loved about the gospel is the promise of answers and assurance to those who diligently seek. The story of our Church in the latter days could be said to begin with James 1:5: “If any of you lack wisdom, let him ask of God, that giveth to all men liberally, and upbraideth not; and it shall be given him.” I myself have experienced times in my life when I have felt guidance and answers flow to me from heaven. As we hunger and thirst after answers, we can come to see the entire purpose of the gospel as providing answers, and we can overlook the mystery of God and the importance of questions.
When I was young, I believed in the God of Lost Things. I have several memories of frantically praying to Heavenly Father that we could find that one last library book, the one that was due today, because we couldn’t go to the library until we had found every book, and I was sure that I had literally looked everywhere. In retrospect, it is easy to look at the low stakes of the situation and see silliness in my frantic pleas. It is easy to explain away the fact that the book was always found eventually. Still, I have had a small handful of specific experiences in which I felt that an inconsequential prayer was answered in a way that was difficult for me to explain away. Not long ago, I watched my young son experience this for the first time himself when, after his simple prayer, we immediately located the keys we had been searching for for days. I do not know if these are answers to prayers, but at the times that they happened, it felt like God was reaching out to me in love.
A difficulty most of us face as we grow from childhood faith to adult faith is the question of why God would answer a prayer for lost keys but not answer prayers that are far more consequential: prayers about major life decisions, prayers for answers to perplexing questions, prayers for healing and recovery from terrible illness, or prayers for peace in a world beset by tragedy.
In spite of this, I still personally believe in a God of Lost Things. I believe that God sometimes answers those prayers not in spite of their inconsequence but because of it. I believe that an answer to a prayer about lost keys can be a message of love from our Heavenly Parents, who know that when it comes to matters of more consequence, we will struggle to see Their hands in our lives. This life is not the time for us to receive all answers, nor is it the time for everything to be made right. Sometimes God will reveal His will to us, but many times we are required to move forward in uncertainty.
This time in your life is a time of decision-making. I know from experience and from my work as an academic advisor that sometimes it can feel overwhelming. When I was in my mid- to late twenties, I remember looking back over the previous decade and realizing that I had made a major, life-changing decision every single year of that decade. It felt exhausting. The pace of major decision-making has slowed down for me, but it has not stopped. It turns out that making potentially life-changing decisions is just a part of adulthood.
The role God plays in making these decisions, however, is not always constant. Sometimes you will just know on your own what you want to do, and God is there to play a supporting role. This is how I felt about my decision to come to BYU as an undergraduate. I had no grand revelation; it was just where I wanted to come. At other times you may feel that God leads you in a very specific direction, maybe even a direction that you wouldn’t have chosen for yourself. When I was deciding where to go for my doctoral program, I knew where I wanted to go, but I had several powerful spiritual experiences that sent me in another direction. To this day I have great certainty that, in spite of the challenges, it was exactly where I needed to be for those five years.
But at other times you won’t have certainty. You won’t be certain about what God wants you to do and you won’t be certain about what you want to do. When I finished my doctoral program, I felt lost in both of those areas. I thought that eleven years of higher education should have left me with a clear sense of what I wanted to be when I grew up, but instead those waters felt muddier than they had ever felt. I thought that, by that point of my life, I should have felt more confident that I could hear and know the will of the Lord, but right then it seemed that the heavens were silent.
In that moment, the only thing I could do was move forward. I wanted to move forward along the right path, but the only thing I could do at that time was move forward along a path. I wanted to know that everything was going to work out for the best, but that was not something I could know. Embracing uncertainty is hard, but at some points in our lives it is the only thing we can do.
I have long loved the story of the brother of Jared. He experienced plenty of guidance from the Lord as he and his family and friends were led toward the promised land. But the part of the story I love most is when the Lord made him answer his own question. The brother of Jared had followed the Lord’s instructions to build barges, but there was a problem. The vessels were sealed and windowless; as a result, there was no light within the vessels. When the brother of Jared approached the Lord, he appeared to expect an answer:
O Lord, behold I have done even as thou hast commanded me; and I have prepared the vessels for my people, and behold there is no light in them. Behold, O Lord, wilt thou suffer that we shall cross this great water in darkness?6
But instead of providing the brother of Jared with a solution, the Lord told him what he probably already knew: You can’t make windows and you can’t have fire.7 And then the Lord turned it back to the brother of Jared and essentially asked, “What do you think?”8
Most of the time, when I truly don’t know what to do, I would just rather have God tell me what to do, because I am pretty sure that I might make a mess of things and that God could keep me from making a mess of things. When left to our own devices—as we so often are—and when left to press forward in the face of uncertainty—as we so often are—eventually we will all make a decision we regret, hurt someone we intended to help, follow a path to a dead end, or find ourselves at the wrong place at the wrong time.
The brother of Jared thought about the Lord’s question and decided to produce sixteen stones from molten rock for the Lord to touch so that they might shine:
Do not be angry with thy servant because of his weakness . . . ; nevertheless, O Lord, thou hast given us a commandment that we must call upon thee, that from thee we may receive according to our desires.9
And the Lord granted the brother of Jared his desire and reached His hand out to touch the stones and made them shine.10
In embracing the uncertainties of life and moving forward in spite of knowing that all might not turn out as we would hope or like, we create our own stones for the Lord to touch and turn to light. Maybe something good will happen when we move forward in darkness. Maybe something bad will happen. Probably it will be a little of both. But God can touch all of those stones. If we make our decision and offer our decision up to the Lord, He can turn all of our stones to light. He can give us opportunities to do good, build relationships, find faith, change, and grow, even with the stoniest of stones that we offer him.
As a teacher, I have spent a lot of time carefully planning lessons. I articulate learning goals and then create assignments, activities, and discussion questions aimed at meeting those learning goals. I try to anticipate student thinking and figure out how to respond to student thinking. But my best lessons are often those that invite an element of uncertainty, lessons in which I don’t know exactly what students will say or how they will approach a particular problem—and they don’t either. And the truly transcendent lessons—the ones after which I come home and can’t stop telling my husband about the amazing thing that happened in class—are always the ones in which something happened that I could not predict or plan. It is at the cusp of uncertainty that the real magic happens. As the Master Teacher, God would certainly allow for that uncertainty in His lesson plans for our lives. And it is as we let go of our need for knowledge and certainty that God can step into our lives in His expansiveness and work true miracles.
A few weeks ago, my husband and I took a trip to Boston. There are many beautiful, old churches in Boston, and on Sunday morning we decided to take advantage of the opportunity and attend a church service in the Old South Church in downtown.
The service, the rituals, and the music were all unfamiliar to me. Stepping outside of the familiar helped me to pay a different kind of attention than I often do in my familiar, comfortable Sunday church experiences. One hymn particularly struck me with its psalm-like sentiment. It opened with an expression of uncertainty: “O God, my God, O gracious God, why do you seem so far from me?”11 And as we sang through the four verses, I found myself expecting a turning point that never came, expecting the hymn to conclude with something along the lines of “God, you may feel far from me, but I know you are there.” Instead, each verse continued its questioning. Why is there pain and suffering in the world? Is God even there and does God care? There was no resolution, only questions, and for days I could not stop thinking about the hymn.
For all the scriptures and talks that exist about certainty and knowledge, we can miss the mystery and wonder that come at the edges of our certainty, the times when we do not know. Nephi confessed, “I know that [God] loveth his children; nevertheless, I do not know the meaning of all things.”12 In Alma we are reminded that “faith is not to have a perfect knowledge of things”13 and that “there are many mysteries which are kept, that no one knoweth them save God himself.”14 Jacob expressed this wonder at the mystery of God:
Behold, great and marvelous are the works of the Lord. How unsearchable are the depths of the mysteries of him; and it is impossible that man should find out all his ways.15
To me, it is a beautiful mystery that I can fail to fully comprehend God but that, nevertheless, in my own incomprehension I can feel that I have some understanding of God’s infinite love for me. I am not always comfortable with uncertainty, but I now recognize that certainty can be a constraint. When we are able to make space for uncertainty in our lives and for the possibility of things that lie beyond our comprehension, we can come closer to our God, who knows us intimately, even if our human state prevents us from fully knowing God. As Paul said so beautifully, “For now we see through a glass, darkly; but then face to face: now I know in part; but then shall I know even as also I am known.”16
In this life we know only in part, and, in fact, the more I learn, the more I see that I do not know. But I also believe that God knows us completely and that in our uncertainty we can accept God’s love for us as certain and constant. We may not know how God will turn our stones to light, but we can have hope that God will turn our stones to light.
I say these things in the name of Jesus Christ, amen.
© Brigham Young University. All rights reserved.
1. See 1 Corinthians 12:8–10.
2. See Jad Abumrad, Robert Krulwich, and Tim Howard, “Why Isn’t the Sky Blue?” Radiolab, 21 May 2012, produced by Tim Howard and WNYC Studios, 14:23–17:10, wnycstudios.org/story/211213-sky-isnt-blue.
3. Euclid, Elements (c. 300 BC); quoted in Victor J. Katz, A History of Mathematics: An Introduction, 3rd. ed. (Boston: Addison-Wesley, 2009), 53.
4. Giovanni Girolamo Saccheri, Euclid Freed of Every Flaw (1733); quoted in Katz, History of Mathematics, 693.
5. Alma 32:21.
6. Ether 2:22.
7. See Ether 2:23
8. See Ether 2:25.
9. Ether 3:2.
10. See Ether 3:6; see also Ether 6:2–3.
11. John Bell, “O God, My God,” Iona Community hymn, 1988, in Arthur G. Clyde, ed., The New Century Hymnal (Cleveland: Pilgrim Press, 1995), no. 515.
12. 1 Nephi 11:17.
13. Alma 32:21.
14. Alma 40:3.
15. Jacob 4:8.
16. 1 Corinthians 13:12.
Amy Tanner, undergraduate coordinator for the BYU Department of Mathematics Education, delivered this devotional address on July 9, 2019.