The next day I went over to Alice’s house with a calculator, some pencils and a textbook in my arms. As usual, Alice was waiting for me at the front door and greeted me with an excited smile. “I can’t believe you’re here so early; I barely had time to get dressed.”
“You’ve being saying that for as long as I’ve known you.”
“Sorry, I didn’t mean to insult you, if you happened to be taking it that way. This is something I like about you; the earlier you come, the more time we have to play together. I can’t wait for us to do more of Mozart’s sonatas.”
“Sure, we’ll play the piano, but only after you’re finished with your math homework.”
Suddenly the cheerfulness on Alice’s face disappeared, her mouth was half-open in shock, her left hand suspended in mid-air and remained frozen. “When you said you were going to tutor me in math, you were being serious?”
“Yeah, I promised to do something and then I go ahead and fulfill the promise. Is this a totally new concept to you?”
Her eyes fluttered, then said, “When you put it that way, then no.” She opened the door for me to enter. I have seen Alice happy, I have seen her sad, but never before have I seen her afraid; it was slightly disturbing.
Alice’s room was so cluttered that we had to go to the kitchen to do her homework. She laid out all her educational accoutrements on the table. Her textbook was covered with pictures of cupcakes and donuts, her pencil box was made by Skittles, and all her pens and pencils were covered with colorful designs that looked like sprinkles. I was overwhelmed by the excessively diabetic nature of her stationery, but reminded myself of my purpose and quickly turned my attention to her. “Let’s do this, you do your homework, and when you encounter a problem you can’t solve I’ll help.”
“Okay,” she said, looking down at her textbook with an extremely serious face, “This is a problem that have been giving me trouble, I’ll read it aloud, ‘You are a bartender. You need to make a drink that is 38% alcohol. However, you only have two different liquors, one 27% and the other 95% alcohol. How much of each liquor should you use to make 100mL of the drink?’”
I stroked my chin and said, “The first thing that strikes me about this problem is this: What kind of a math textbook would teach teenagers how to mix drinks?”
Alice shrugged and smiled.
“Okay, I’ll completely ignore that, let’s solve this problem. First, draw a whiskey glass which has a capacity of 100mL.”
“Can you draw a small umbrella in the glass?”
I looked at Alice with a funny look, then said, “Yes, if that’s what you want, although it wouldn’t help us solve the problem. But aren’t umbrellas usually in drinks like margaritas, which are served in martini glasses?”
“I don’t know these things; I don’t drink.”
“Me neither, but I know this because my dad drinks; he does this to cope with living with mom. Anyway…” I said, then drew a glass with the umbrella, then labeling it “100mL”. “We know the total volume of the final drink, 100mL, so we write that on the glass. We also write 38% alcohol. Now, we don’t know how much of the 95% to pour in, so we label it as ‘x’.” I drew a horizontal line breaking the glass into two unequal halves, and wrote “x mL, 95%” “We also don’t know how much of the 27% we should put in, but it should be 100mL – x mL.” I then wrote “100mL – x mL”on the upper half. “Now, this picture is a little cluttered, so let me erase the umbrella so it will look neater. Sorry umbrella, having you around is too much trouble.” After redrawing the diagram I said, I said, “Now, we can write down the equation x + 100 – x = 100, but that doesn’t solve anything because that comes out to 100 = 100. What we need is to make use of the concentration of the liquors. We take advantage of the obvious fact that the amount of alcohol from the two liquors equals the amount of alcohol in the final mixture. You do that by multiplying the volume by the concentration. For the final mixture, that’s .38 X 100…”
“Wait, why did you do that?” Alice asked.
“Why did you turn 38% into .38?”
I thought for a while, then said, “when you see %, what it means is divide by 100. So 38% is 38 divided by 100. Now, there’s a trick to dividing by a hundred, and that is all you have to do is move the decimal point two places to the left.”
Alice looked surprised, she said, “Really? But why would moving the decimal point divide a number by 100?” I thought for a while, then said, “Well, because…” From this point on I went on a long tangent explaining the base-10 number system, scientific notation, powers of 10, multiplying and dividing by powers of 10, and numbers in bases other than 10. I wasn’t aware of how far off-course I was until I looked at the clock and noticed that an hour has passed.
“Sorry, we can’t continue further wasting time talking about things that will not help with the homework.”
“Aww,” Alice said in the same tone with which she speaks to her cat, “but I want to learn more about exponentiation. And in truth, we weren’t wasting time, I was still learning about math.”
“That’s true, but it wasn’t a part of this assignment.”
I set up the equation for Alice to solve and said, “Here, can you solve this?” Alice gingerly picked up her pencil, examined the equation carefully, then slowly solved the equation. It was like watching a snail crossing the patio, but she was taking a lot of time carefully punching the numbers into her calculator and writing the intermediates steps down. But she did finish in the end.
“Did I do it right?” Alice asked shyly, her eyes avoiding mine.
“Yeah, that’s correct,” I said.
Her eyebrows pinched together as she said, “How can you tell?”
“I solved that equation in my head while you were halfway through solving it on paper.”
“Wow, you must be some sort of super-genius.”
“No, you were just incredibly slow.”
Alice glowered at me with bulging eyes and shouted, “What do you mean slow?”
I twitched in fright in reaction and said, “You really weren’t that slow, I was being ridiculously fast.”
Alice calmed down and said, “No, you are right, I am slow. My last tutor said I solved equations at a pace that made sloths yawn.” She buried her dejected face in her hands.
“Oh, don’t feel too bad. I’m sure with practice you’ll do better.”
“You’re just saying that to make me feel better.”
I held her hand, looked deeply into her eyes and said, “No, I’m being serious. Remember how terrible I was at piano, but then I played with you for a year got much better?”
Alice smiled and said, “Yeah, I was a good teacher wasn’t I?”
“See? All you have to do is practice, and not feel ashamed of being bad at it.”
Alice’s face immediately brightened, and we continued on to the next set of math problems. But she continued holding my hand as though it were a security blanket. I didn’t mind it at first but after a while it felt awkward. I’ve always dreamed of Alice holding my hand, but in a more romantic setting instead of doing math. But she looked happy, so I didn’t dare disturb her.
To be truthful, I didn’t know if her math skills would improve with practice, but I couldn’t stand to see her sad and angry. Her mathphobia was quite strong, and I needed to constantly hold her hand, both literally and metaphorically. Sometimes keeping her happy was emotionally draining, but I wanted to win her affections so I put up with her neediness. There was a lot I had to teach her, unfortunately a large portion of things she wanted to know wasn’t a part of the curriculum, but I had to cover them because she was very curious; I also had to constantly keep her interest because the material the school was teaching wasn’t all that interesting. This meant I was spending hours each day with Alice, which was a very pleasant experience. Even though dealing with her emotional problems sometimes left me feeling frustrated, being together with such a beautiful creature more than made up for it.