Expectations of humans and math
He expected her to be on time and she expected him to understand when she showed up late. By understand, she meant accept her lateness without showing her the slightest trace of annoyance. But while he tried to understand the reasons she was late, he could never accept what he saw as such blatant disrespect. He didn’t feel it would be truthful or fair to her to act as if nothing was the matter. He knew however if he expressed displeasure at the lateness, she would become disappointed and angry with him. He did not wish this, because overall he liked her and wanted to please her. The unfairness of this circumstance and his own powerlessness to do anything about it would give rise to a burning fire in his gut, a species of rage that frightened both of them, as soon as the clock read 5pm when they were supposed to meet and he could not see her car in the distance. When she arrived half an hour later and found him in this condition, she would then retaliate with a stinging retort exposing one of his shortcomings, infuriating him even more. There would be an awkward silence and then they would begin the tutoring session.
As he was waiting for her to show up, sitting glumly in the dilapidated Tim Hortons coffee shop in the centre of the town, with cigarette butts littered across the sidewalk crossing it, he would often think of the reasons why she showed up late. He knew that a lot of it simply due to the fact that she’d picked up a bad habit, just like he was prone to nail biting and playing violent video games when he was stressed out. And he knew that it wasn’t something that she had learned on her own; her whole family had a tendency to show up late, a habit that the largely Protestant community was not accustomed to; it reinforced the family’s outsider status. But he noticed that while her sister felt remorseful about being late and was taking steps to change it, she was almost defiant in her lateness.
“It’s part of my culture,” she would laugh airily. And she would tell herself she was whimsical and creative and this was why she was always late. And he would tell himself that she was selfish and entitled and that was why she didn’t even try to show up on time.
He couldn’t understand why a girl who was so caring of those around her, who inquired about the health of the workers at Tim Hortons, who conscientiously threw out her garbage and kept her table as clean as possible, who took such pains to understand mathematics, would have such a blind spot when it came to appreciating the importance of showing up on time.
One damp May day, it was again 5:30pm when she was supposed to show up at 5 pm. He sighed and decided to use the gross Tim Hortons bathroom even though he didn’t particularly need to, in the hope that she would arrive while he was there and she would get a taste of her own medicine. In order to waste more time, he even flattened his hair that was sticking up from behind the Toronto baseball cap he usually wore.
When he left the bathroom, she was waiting for him at their usual table left of the door.
“Hi Byron!” she said brightly. “Now for once I’m the one who has to wait for you!” She smiled impishly and took out her math textbook.
Byron again felt that alien and unwelcome species of rage begin to attack him after her airy comment that showed a complete lack of consideration for the fact that he had been waiting for her for the past 45 minutes. He breathed deeply and went through the square roots of various numbers in his mind; this was another tactic he had for putting out the fire in his gut when there were no video games nearby and his nails were already bitten down. Byron wasn’t yet at a place where he could begin to analyze the cause of his outrage, he could only deal with the effects.
“Square root of 1 is 1, square root of 4 is 4, square root of 9 is 3, square root of 16 is 4, ,” he murmured to himself, taking solace in the predictable order of the numbers, which always helped him ground himself in a strangely disordered world.
Elaheh, although she thought Byron was looking a bit peculiar, continued smiling innocently and turned the page to the lesson for the week.
Byron ignored his anger and threw himself into exploring the concept of imaginary numbers with Elaheh. As usual at the beginning of the study she was very sarcastic about the material and her ability to understand it.
“As if real numbers were not enough, they now have to throw imaginary numbers at us,” Elaheh groaned. In the space of a few months, she had tried to learn to graph precisely, to solve problems using the sine, cosine and tangent laws, to do business math and to calculate rates of change. She felt that her brain couldn’t absorb any more, she felt she was just beginning to understand how to do the math from last week, and didn’t see how she could now begin to learn something new.
“Well Elaheh, no numbers are real, numbers are something that humans made up to help us understand our world just like words,” Byron says. “You know sometimes you want to say something, but there just don’t seem to be the words to say it?” He asked, “Like when you think of the universe and how large it is or try to describe Creation?”
“Yes,” Elaheh replied with more interest.
“Well it sort of works that way with numbers too. If you think of numbers as a language, just as there is always a point where words break down where we need to formulate new words or come up with new arrangements for words, there comes a point when we need to invent new ways of thinking about numbers in order to more accurately convey reality. Like if you need to analyze electrical waves in order to calculate the speed of the electricity going to the homes in our town, but the electrical waves cannot be contained with the so-called real numbers.”
Again, Byron could see from the eager way she had turned to face him that Elaheh’s interest was piqued. After about half an hour, Elaheh would typically become thoroughly engaged and he would see her eyes light up with a flicker of understanding. It was really for the flicker of understanding that Byron would continue to tutor her. He always marveled at how she would arrive at the session dragging her feet with a heavy heart and so convinced she would be unable to understand and would leave lighter and more confident. Suddenly the thought occurred to him that maybe that was why Elaheh showed up late, because she subconsciously didn’t want to do the math.
Byron had stopped tutoring some of the spoiled grade nines who would show up late and whose parents forced them to come to him. He was well aware that he was one of the only good math tutors in town and could afford to be choosy. But he never quite had the heart to stop tutoring Elaheh, although he would often think about doing so. In his angrier moments he would plan the conversation he would have with her to tell her their tutoring arrangement would no longer work.
“I have decided that I can no longer tutor you anymore,” he would say sternly. “It is disrespectful of you to not show up on time every single week,” he would add, pointing his finger at her in an exaggerated way that he would never have the audacity to do in real life. In another imaginary conversation, Byron would stand up in front of a chalkboard and give Elaheh a lecture about all the other things in life that would become difficult for her because she couldn’t show up on time, with appropriate diagrams showing cause and effect. But in his imaginary conversations he could never quite sound decisive enough. He always felt as if Elaheh’s crestfallen face would convince him to change his mind, so he would never bring it up.
A few friends in school would tease Byron about Elaheh.
“I think you like her,” they would say, snickering. But he wasn’t the type of guy who “liked” girls in the high school sense. He had never dated a girl before and had never really wanted to. He didn’t like to look at girls cheekily or watch romantic comedies, nor did he tell girls they were beautiful in certain colours. He didn’t know how to have a conversation with a girl who expected him to interact with her sex, rather than with her mind, to engage in confusing flirtatious banter with her; to send sweet, yet cryptic text and facebook messages to her; Byron was very straightforward.
And he had a certain confidence from being the eldest brother and very good at math, that he didn’t need to follow the unspoken codes of the idiots he attended high school with, who thought that by virtue of being a man he should have a certain way of speaking and dealing with females. He didn’t find that these types of relationships followed any sort of logic.
As they began to work through the negative square root imaginary number problems in between nibbling on the timbits, Byron began to smile as he felt he had helped Elaheh see that imaginary numbers were not really difficult after all, that they were just another facet of the language of math.
“Do you think you’re understanding it?” Byron asked eagerly. He had never asked this question before, as he knew her attitude towards math was so negative that she would give him a melodramatic answer, but hoped that maybe today it would be different.
Elaheh looked up from her textbook, tossed her thick mane of black hair back and looked at him, rolling her eyes in exasperation. “It’s always easy to say that I understand it here, but then when it comes to the test I don’t get good marks.”
As she said this, Sandy, one of the Tim Hortons employees, clucked her tongue sympathetically. “You’ll get your good marks darling,” she said encouragingly.
Elaheh smiled wanly. “Thanks Sandy,” she said.
“Well are you doing better than before?” Byron ventured timidly. He knew what it was like to be frustrated about not understanding something, but had never cared so much about his grades, although to be fair, he had never been in a position where he felt pressure to perform in school.
“Yes,” Elaheh said, “but not well enough for the universities.”
Byron didn’t know what to say next. He thought it was a little too much for her to expect him to help her go from a failing math grade to being able to get into university in the space of a few months. He was disappointed in her disappointment, especially because he had thought, or perhaps hoped, she was feeling as good about the learning process as he was.
“I think it’s my teacher,” Elahah said spitefully. “He doesn’t like me and marks me harder.”
“Why doesn’t he like you?” Byron asked. He was starting to connect certain dots in his mind.
“I don’t know, he just always gets angry with me,” she said. “He doesn’t understand my personality.”
“He doesn’t understand your personality or he doesn’t understand why you always show up late?” Byron replied with some venom in his words. He instantly sensed in Elaheh’s recoiling demeanor that it wasn’t the right time to bring this up, but at the same time there was a burning desire in him to address this question. This desire was fueled by approximately five hours spent waiting for her when he added up all the time he had spent hanging aimlessly around Tim Hortons from 5:00 to 5:30 pm, sometimes 5:45, in the past three months. He wondered had she not shown up late for the tutoring sessions how these five extra hours of study time would have affected her mark.
“Yes yes, I get it, you think being late is the source of all my problems in the world, if I would just show up on time everything would be fine!!” Elahah burst out. She breathed heavily after trembling with rage. “Somehow stupid me would even understand math,” she said sarcastically, glaring at him.
“Well, being on time does have to do with math as it has to do with your ability to measure time,” Brian said smiling. He was determined to be calm. “And I don’t think being on time is the only thing is life, but at the same time I think it’s easy to forget the importance of it.”
“Well, I would be on time, but sometimes my father needs the car and comes back late,” Elaheh said defiantly. “I’m sorry but being respectful of my parents is important to me, unlike a lot of people in this town.”
“How many times has this happened?” Byron asked.
“Maybe five?” Elaheh said, averting Byron’s eyes.
“Really?” Byron pressed.
“Okay, maybe once or twice,” Elaheh admitted. “But there are other things that come up too,” she said. She was frustrated that she couldn’t think of anything else. She felt trapped in the conversation, often as she felt on a math exam, when she felt there was no way she could come up with the right answer.
“And do you think that nothing comes up with me?” Byron asked. “That I don’t have to plan to make sure that I show up on time? That my parents don’t ever need the car?”
“Your life is different from mine,” Elaheh said. “Just because it’s possible for you to show up on time, doesn’t mean you have the right to expect it from everyone else,” she said.
Byron began to think about whether it was fair to expect everyone to show up in time in the same way that he could expect a certain result from a simple mathematical formula. But he couldn’t see how there was anything wrong with expecting people to arrive at the time they both agreed previously to arrive.
“You haven’t given me a good reason as to why you have to arrive late every single week,” Byron said matter-of-factly.
“I don’t have to give you a reason, it’s really none of your business,” Elahah spluttered. “If you want, you can charge me extra for how much of your ‘precious time’ I’ve wasted and then I think I’ve had enough of this conversation, thank you very much.” Elaheh closed her math book and put it in her bag.
Byron shivered and drew his breath in. Just as he shuddered at the thought of leaving a math problem without finding a satisfactory answer, he disliked ending a conversation before coming to a logical conclusion. But he could see that this conversation had entered a low point and thought maybe it was the type of conversation you left for a while and returned back to at a later date, just like some of his more complex math problems.
“Okay, let’s change the subject,” he said, smiling brightly. “What do you want to study in university?”
Elaheh was still breathing heavily from rage and was visibly upset. She had been trying to keep her voice down to avoid attracting the attention of the customers and employees in the coffee shop, but noticed that the elderly couple a few tables down were listening in. She decided to follow the thread in the conversation he had introduced to save face. “I’m really not sure,” she said. “But I have to take math to keep my options open.”
“Well, is there anything you like to do and could see yourself doing in the future?” Byron asked gently.
“Well, it’s very unlikely I’ll do anything with math,” Elaheh responded, shrugging her shoulders. “My parents want me to go into medicine though, which I think might require me to understand math.”
Byron began to think about Elaheh’s situation and how difficult it must be to study math and struggle with it, without a clear vision of how it was going to help her in the future. He realized that although he didn’t know quite where it was going to take him, he had the advantage of knowing that math was in his future, that it was something he could do.
“Maybe you show up late because you are not sure why you are coming here,” he suggested sympathetically.
Again Elaheh felt irritated with Byron’s poking. “Like I’ve explained before, I just show up late because I do. It’s a part of my culture, most Iranians tend to show up late, it’s just part of who I am,” she explained. “Some people even like it or think it’s funny.” Elaheh thought with a smile how her friends in school teased her in a good-natured way about her lateness.
“OK, fair enough,” Byron said. “That’s what my good friend Cyrus says about Jamaicans too, and I’ve heard that being late is also part of Italian culture,” he said.
“But just because something is part of our culture, does this mean we just accept it without trying to change it?” Byron inquired. “Like if it’s part of my culture to be a big jerk that yells at everyone, I just accept it and that’s it?”
Again Elaheh felt annoyed with Byron and his implication that being late was in the same category as being a jerk. “Like I’ve made clear, I’ve had enough of this conversation,” she said. “You seem to think that you’re this perfect person that knows what everyone should do and how everyone should act just because you happen to be good at math.”
“I’ve never said anything else about how you should act beyond suggesting that you should try to be on time,” Byron said, raising his voice a little. “I’m not even saying that you need to show up on time, I’m just suggesting that it’s possible for you to show up on time.”
“But you say it or hint it every week, like you think somehow you are going to make me change,” Elaheh persisted.
“Square root of one is one…” Byron began to murmur to himself as he felt his face flushing.
“Life isn’t just about math,” Elaheh said. “People aren’t just like numbers that you put in order.”
“That’s not what I think,” Byron said automatically. But as he said it he began to think about why she might think that about him and he felt a little uncomfortable.
“All I’m asking you is just to consider what I’m saying, just like I’m going to consider what you’re saying,” Byron said in a soft pleading voice.
“Okay, I’ll think about it,” Elaheh said quickly, responding to his peace offering.
Byron then stood up and shook Elaheh’s hand formally. “And now I think we’re done for the day.” Byron expected that because of her anger, Elaheh wouldn’t walk outside with him, but to his surprise, Elaheh joined him as he walked out the Tim Hortons door to the parking lot a block down the street.
Upon going outside, both looked up at the burgeoning rain clouds and Byron realized that he and Elaheh had just experienced their own rainstorm after three months of build up. Although he wished the storm had been gentler, there was a sense of relief that it had finally rained down after months of threatening to do so.
Byron felt that the air had cleared, giving him a certain space to think about what had just taken place in a way that he couldn’t while he was still engaged in it.
Byron first began to think about what he could expect from a conversation with a complex human being and what he could expect from a complex math problem. He decided that he could expect to perceive certain logic and a pattern to the way both progressed. It was largely predictable how there would be different ideas as to why Elaheh showed up late and varying opinions about the acceptability of this. It was also possible to see based on past conversations that both Elaheh and Byron would react negatively to what they perceived as criticism.
Yet Byron could see that while much of what took place in the conversation seemed inevitable, there was also much that couldn’t be predicted. At the beginning of the conversation, he would never have expected that Elaheh would be as ready to consider his point of view as she was by the end of the conversation. Byron could see that, while in math it was easier to be in control of the problem, conversations had an organic quality that couldn’t be stifled.
Byron could tell that in conversations, just as in math, there are right answers and wrong answers, but there are also more than three dimensions to consider when he was dealing with multifaceted human nature. He noticed that he could say the right words and say them with the wrong spirit—or even what was perceived as the wrong spirit—and the conversation could go nowhere. He saw how easy it was for both Elaheh and him to pick up the slightest attitude of superiority in each other and how violently each reacted to perceived feelings of superiority, Byron’s to what he perceived as Elaheh’s feeling of entitlement to show up late, and Elaheh’s to what she perceived as his desire to control her and force her to act in a certain way. He could see that both had high expectations—which were really desperate, longing hopes—of how they wanted to be treated by the other, but at the same time were annoyed to see that their expectations usually went unmet. It was also irritating for both to realize that ignoring the unmet expectations would not make them go away, and that a healthy relationship between two people often involves a conversation around one’s expectations of each other, with the idea that these will evolve overtime.
Although this didn’t mean that both had equally valid expectations. Byron still felt that his expectation that Elaheh would show up on time was more reasonable than Elahah’s expectation that he shouldn’t be upset when he showed up late. Still as Elaheh had pointed out, the fact that she showed up late every single week did not mean she had nothing to offer the world or that he couldn’t learn anything from her. Or that he shouldn’t try to understand why she showed up late. It was a complex equation. Nevertheless, he wasn’t powerless as he previously imagined. He could think much more carefully about the situation than he had thought before. And he could even think about the way that he felt about it.
Byron then thought about his feeling about the situation and how the previous conversation engaged both his mind and his heart in different ways than mathematics did. When he was involved in a complex math problem, his heart was motivated by a desire to create order, to understand the inner workings of a complex system. After his conversation with Elaheh, he also had a desire to better understand the complex system of human relations, as he could see that a conversation between two hearts was living, multi-dimensional and multi-faceted in a way that he hadn’t yet experienced with math. Just as in math, in human relations there are norms and standards of behavior that need to be respected, but what happens when they are not? What is a helpful way to respond? He found that his extensive experience with math couldn’t prepare him adequately on this front, although his approach to problem solving that he learned in math was useful in certain ways.
As Elaheh and Byron reached their cars, they parted with another handshake, a little less crisp than the previous one.
“I think it’s good for both of us to talk about other things aside from math from time to time,” Elaheh said.