“Where is Suleiman?” Layla asked as Ara struggled to remove her caftan.
“He’s in here somewhere. He moved up my sleeve and won’t stay still.” Angrily, Ara reached behind her head. “I’m going to grab him by his tail and…” A loud, prolonged squeak came from behind her.
“You’re squooshing me,” the mouse shrieked, wriggling deeper into her hair. Layla gently tried to remove the mouse from the tangle.
“Stop being a baby,” Ara yelled back, flapping her hands at the back of her head. “You should have stayed where I put you—ouch, that hurt!”
“Ara, be still,” Layla said as she disentangled the upset mouse from the equally upset girl. “He keeps wiggling and you keep wiggling. Stop it. You’re both making it worse.” Ara held her hands at her side while Layla worked.
“There!” Layla triumphantly cupped the mouse in her hand. “He’s free.”
“Girls, what’s all that racket?” Su’ah called as she shambled into the room. Her eyes widened in disbelief. “Ara, what did you do to your hair? I had it so neatly braided. I don’t understand how you get messy so quickly.” She went over to the girls, hairbrush in hand. “It looks like a rat’s nest. What have you done this time?” Evaluating the devastation, she added, “Even for you, this is remarkable.”
Layla and Ara looked at one another. Layla placed the palmed mouse in her sleeve and, smiling sheepishly, began, “We were in a hurry and Ara, um, Ara—” she began.
“I thought I felt a bee in my hair,” Ara finished.
“You were in a hurry, and you felt a bee in your hair,” Su’ah repeated, slowly looking from girl to girl. There was silence while she mulled over their story, a frown on her face while she tugged the brush through Ara’s long black hair with well-practiced strokes, stopping to unsnarl each knot. “Well, I suppose that’s as believable as many of your stories. Tahirah wants you in her rooms. You’d better get a move on. Her servants are waiting outside for you.”
“Allah be praised,” Ara muttered and started to pull away, but Su’ah pulled back.
“Not this moment,” she amended. “Let me finish braiding your hair. At least you’ll start out tidy. Bees, hmm.” She yanked Ara’s braid a bit harder than seemed necessary.
As soon as Su’ah was satisfied that Ara was presentable once again, the girls rushed out of the room. Tahirah’s servants were hard put to keep up with them in their eagerness to tell her of Suleiman’s latest transformation.
“We only have five and one-quarter days from when he changed into a mouse,” whispered Layla. “What is the next pattern of symmetry we have to find?”
Tahirah was crouched, working with something on the floor when they entered. A servant followed behind them bringing in steaming lemon tea. “Thank you,” Tahirah said to the woman, who bowed and left.
“We have much work to do,” Tahirah said over her shoulder to the girls, “and little time. I felt a healing in the fabric of the Alhambra this morning. You must have found a horizontal symmetry, the broken one.”
Ara nodded and came closer, saying excitedly, “Look, Suleiman’s changed into a mouse.” Layla carefully set the rodent on Tahirah’s shoulder.
The mathemagician tensed and slowly turned her head to stare as the mouse busily cleaned his whiskers and smoothed down his fur. “I am grateful the spell is unraveling,” she said slowly, “but there are other animals I would have been more pleased to see.” There was a long pause before Tahirah finished flatly, “Mice bring back very bad memories for me.”
“But I thought you weren’t afraid of anything,” Layla burst out and quickly cupped the mouse into her hand.
“Everyone is afraid of something. Some more than others,” Tahirah said slowly, still watching the mouse. “Most of my family died from the Black Death. The plague came, and whole villages died.” Her eyes had a faraway look. “It isn’t a pleasant death. Some said it was Allah’s will, but I knew it was not. Allah is joy and beauty. There was neither joy nor beauty in this.
“I was very young, a year or so younger than the two of you, and just learning the power of mathemagics. The plague passed me by, but I was unable to save my family.
“Thousands of people died that year. No one was safe, from the lowest of the low to sultans in their walled palaces. All died. And always, the rats and mice were there, hundreds and thousands of them, crawling over everything. They died too. Everything died.” She shuddered and took a breath.
The girls stood transfixed, unsure how to react, while Tahirah continued to wrestle her memories.
Suleiman looked up from polishing his whiskers. “What?” he asked. His sharp black eyes alighted on the tray of flat bread, fruit and olives. “Is that bread? I’m very hungry.”
Tahirah rubbed her hand across her forehead, and slowly her expression changed. “Suleiman, I say to you what I say to others, ‘whithersoever ye turn, there is the Face of God.’ Once again, Allah shows me the folly of my ways. I accept and learn. Food you may have and the support of my hand and heart, may I ever be Allah’s vessel, inshallah.”
Ara leapt in. “He’s really little, and he won’t hurt anyone. I’m sorry about your family, truly I am, Tahirah.”
“Child, that was ages ago. I thought I had put it far behind me. This has reminded me that goodness comes in all shapes, not just the ones I like.” She took one last calming breath. “Time for us to continue. Suleiman, please sup. You must be hungry. Then you and I will teach the next symmetry pattern,” she added firmly, pulling herself together.
The mouse leapt off Layla’s arm and scampered over to the bread. Tahirah and the girls sat down to their tea. The girls sipped from their cups, quieter than usual, afraid to disturb their friend and teacher. Suleiman, after muttering a polite bismillah, ate some bread, then exclaimed in delight upon finding a ripe fig. He devoured a large mouse-mouthful and then several more.
“Tea is calming, is it not?” Tahirah said, smiling at the girls. “I believe it is time, perhaps even past time, for our next lesson. Suleiman, I hope you are now full and ready.”
The mouse looked up, cheeks stuffed with food. After what appeared some internal debate, he mumbled, “Uff courshh,” and swallowing, joined the group.
Tahirah pointed behind her to a stack of ceramic tiles on the floor. “I searched out some tiles for our lesson. This will make it easier to explain and not use expensive paper. As you remember, your last symmetry was a horizontal reflection. And the one before that was a vertical reflection.” She paused. Suleiman scurried over to the tiles and ran around each one. “I instructed you to find the horizontal symmetry, making absolutely sure that it did not also have a vertical symmetry.”
“Yes, we were very careful about that. You said it was important,” Ara recalled. Layla nodded.
“This third symmetry has both a vertical and a horizontal reflection. Both symmetries exist in one design. That’s why it was important not to find a vertical symmetry with the horizontal one last time. Let us put together some of the tiles to make this pattern.”
Suleiman, who had been carefully examining the tiles, placed a paw on some. “Here, this is the first example I showed you, a triangle,” he squeaked. “Take these four tiles and make a design that has both vertical and horizontal reflections.”
Ara and Layla sat down near the tiles. This didn’t look too hard. Layla reached to pick up a tile and then looked at Ara, who nodded encouragement.
Layla left the first tile alone and slid the second directly below it and turned it until the blue was on the bottom. The next two tiles she placed on the right side. One she placed white edges matching with the top one, and the other she slid under to match.
She looked up at Tahirah when finished. “Is this correct?” she sounded, uncertain.
“Perfect, though there are other answers. Now explain why it is correct,” Tahirah encouraged, obviously pleased that shy Layla solved the problem.
The girl lay on her stomach, studying the tiles. “Well, the two on the top are the flips of each other…and the tiles below look exactly like a mirror reflection of the ones above.” She hesitated then, less confident. “But mathematics isn’t really this easy, is it? It’s always been hard for me. Ara is the one who likes math.”
Tahirah thought before responding. “It can be simple. Mathematics is a human way of explaining the world. It gives us some insight into the wonders that Allah created. Part of the world is very simple, and part is more complex.
“The basics of mathematics are very easy. Complex mathematics is only the basics added together, step by step. Each step is not complex, though the whole may seem that way.
“It’s as dance is for you, Layla, or playing the lute for Ara. Placing your finger on a string and plucking a note is not hard, but playing a tune takes much practice. Playing many tunes well takes again more practice. Mathematics also takes practice. You are learning to think in different ways and, as you do, it becomes easier.” She smiled down at the girls. Suleiman climbed upon Layla’s back and surveyed the scene with the air of a miniature ruler.
Tahirah, though still appearing uncomfortable with the mouse, pressed on and, from another small, stack set a new tile on the floor. “Here is a more complex example of the double reflection we are studying.”
Ara touched the tile. “I’ve seen this. It’s in the Hall of the Two Sisters. I never noticed the symmetry of it before.”
“Yes, it’s a copy of the one on the far left wall as you enter. It is very lovely, is it not?” Tahirah said, admiring the tile maker’s work. “One more point I need to make with this symmetry is that it looks the same right-side up or upside down.”
Layla screwed up her nose. Ara also looked unsure. “You mean if you turn the tile upside down, it still looks the same?” Ara said, turning the piece around. “Oh. It is the same. How odd.”
“That’s it?” Layla’s smile was hesitant. “Just if it’s the same when it’s upside down as right side up?”
“Yes.” Tahirah agreed, smiling, as she took out more tiles. “Now make this pattern into a band or row.”
Ara took two more identical tiles and lined them up edge to edge with the first.
“Good. If you look you can see that the reflections in the row are a bit different from the single tile. The row has only one horizontal flip but there are multiple places within the row where there is a vertical flip. You could put a mirror between each tile and it would reflect, or you could put a mirror straight down the exact center of a tile and it would also reflect.”
“Yes,” Ara exclaimed, understanding. “There are many places where it could be folded in half and match exactly.”
“I have said that you two almost teach yourselves, and it is very true,” Tahirah said looking very pleased. “You remind me of your mother.”
Ara straightened. “You remember my mother?”
“Certainly. I was fortunate to have her in my classes. She was such a bright light. As are both of you. I am Allah blessed to have served two generations of clever girls.”
They stood, grinning at the praise, and prepared to leave, Suleiman hidden again in the folds of Layla’s sleeve.
Ara suddenly leaned forward and said in a near whisper. “The wazir. We heard the wazir talking. He knows his evil spells are unraveling, and he searches for Suleiman.”
“We heard he still believes that Suleiman is a lizard,” Layla said, “but he thinks Suleiman is somehow undoing his magic.”
Tahirah frowned. “We have been fortunate, have we not? The wazir searches for the one who thwarts him in his magic. He is arrogant and blind and hasn’t yet turned his eye toward the harem. I have placed spells about the palace to avert his interest from us. How long they will last, I cannot say.” There was silence in the room except for Suleiman’s anxious breathing. “Allah forbid that he learn of your involvement.
“Every day that he is unaware of your connection to the magic is a day we rejoice. I count each as a blessing from Allah.” She bowed her head. Many heartbeats passed while Tahirah regained her composure.
“You have less time yet again, only five and one-quarter days, and much of this day has vanished with our Christian guests. But all is not lost. The People of the Book are gone, and no more beet juice must be cleaned from the lion fountain.” She smiled wryly.
Ara shook herself out of her fear. “Wait, before we leave. Can we use this same symmetry? The one from the Hall of the Two Sisters? Does it count?”
“The magic works as long as you see a broken symmetry, one that in your heart you are seeking. Be very careful who you ask for help. A secret is no longer a secret when two people know,” she warned. “This lesson is over, so off with you. Remember, courage outweighs fear.” Opening the door, she waved them out of the room.