Authors: Gwen Dandridge
Tags: #history, #fantasy, #islam, #math, #geometry, #symmetry, #andalusia, #alhambra
“See, each one is the mirror of the one
before and they flip over a vertical line,” Ara said. “After it
changed, the thumping began.”
Tahirah pointed to the tile, “It repaired
itself, or did you repair it? The Alhambra must listen to you
indeed.” Tahirah was quiet as she stared at the wall. The tile was
now smooth and flat.
“How long ago did Suleiman make you this
promise?” the Sufi asked.
“It was about two days after you arrived.
Suleiman was angry with me for being outside the palace to watch
the parade.” Ara stopped, aghast at her unplanned confession.
“Yes, I felt you that day.” Tahirah closed
her eyes. “Your aura radiated excitement, fear and joy. Such a
strong presence you are, child. I remember being curious about a
girl so daring and bold. Much like me when I was your age,” she
said with a slow smile. “Now, let’s see, let me check my journal
for the exact date.” Pausing, she rose and walked over to a little
niche in her room. She picked up a small book and quickly flipped
through its pages. “Yes, as I thought. I arrived three weeks ago
today, so Suleiman was bound by his promise exactly twenty-one days
ago. How interesting,” she murmured, calculating numbers in her
head. “There are seven band symmetries, and Suleiman asked you to
find three examples of the first symmetry.” She glanced at the
girls. The snake wrapped about Ara’s arm and turned in agitated
circles.
“Promissssed, Arrrrra. You helpppp,” Suleiman
hissed, looking at Tahirah.
“Hmm. We have a two-fold problem,” she said
finally. “Both the Alhambra and Suleiman are affected. We all saw
what just happened. You found two examples of vertical symmetry,
but this third one was broken, tainted by the magic of the wazir.
When you saw it and noted its wrongness, it was able to heal
itself. Then Suleiman also changed from a lizard into a snake.
“This is encouraging. The bands of magic
holding him are more fragile than the wazir thinks. It is also
hopeful that Suleiman now speaks. He remembers being human and
fights the spells.” She looked off and gathered her thoughts.
“We need to continue your education in
symmetries,” she said, nodding her head emphatically. “Because of
his promise to teach you each of the band symmetries, I believe we
may have a way to restore Suleiman. The wazir’s magic was
incompletely drawn. A promise, especially one coupled with tribal
honor, is binding.” She stopped suddenly and considered.
“The wazir tied his evil magic to Suleiman.
That may yet be his undoing.” She looked intensely at Ara. “As the
palace heals, so does Suleiman. You are the catalyst: the daughter
of the Alhambra born of the line of the Nazrids. The Alhambra was
betrayed by one of its own, the wazir, and it is distrustful.
“You must continue finding the symmetries.
You need to seek out the damaged tiles for each symmetry. This
reminds the Alhambra of its strength. It fights the spell, just as
Suleiman does. If we are particularly fortunate, releasing Suleiman
from this binding should also undo the evil the wazir has twisted
into the Alhambra. Though whether Suleiman or the Alhambra will
fully heal, I cannot say.”
Ara sat unmoving, struck by the enormity of
the task placed before her, and laid her free hand on Suleiman.
Tahirah was silent for some time before
speaking. “Well, we must do what we can. Magic, as you know, is as
logical and ordered as mathematics. To reverse this spell, time is
halved and then halved again.”
She looked up at the two silent children,
their eyes wide in worry—and yet a touch of hope flickered there.
“The Alhambra’s magic is at risk. If this evil continues, the
Alhambra will fall.”
Layla turned even whiter. Ara looked down to
hide her fear and, seeing the snake on her arm, nodded,
remembering.
“Father has been really worried this spring,
but he said that the Alhambra protects its own. Is the symmetry
magic how it’s done?”
Tahirah smiled encouragingly at Ara. “It’s
more complicated than that, but yes, magic is buried in the
symmetries, and Suleiman is now tied to that magic.
“And now, we are also working against time.
If it took you twenty-one days from the time of Suleiman’s promise
till you found the symmetries, you have only half that time to find
the next and half again for the one after.” Tahirah spoke with
quiet certainty. “We are in a race to save both Suleiman and the
Alhambra. If we can pull Suleiman out of this enchantment, some of
the wazir’s evil may be broken and the Alhambra’s strength
regained.”
“I see,” said Layla, perking up. “Because Ara
completed the first task set by Suleiman in twenty-one days, then
the next task needs to be found in ten and one-half days, then five
and one-quarter days.” She looked worried. “I guess you have to
figure hours after that.” She wrinkled her nose.
“Yes, sixty-three hours, thirty-one and
one-half hours, lastly just under sixteen hours. Each time it
halves. That will mean the last symmetry must be found in under
eight hours.” Tahirah looked up gravely. “We are lucky it took you
so long to find all the examples of the first symmetry. A shorter
time would be almost impossible for us.” She stopped for a moment,
lost in thought as she gazed out her latticed window.
The responsibility dizzied Ara. “But it’s
still not enough time. I could never find them all. I don’t even
know the other symmetry patterns. How can I find broken ones if I
don’t even know what the correct ones look like?”
“Well, as it happens, I know those
symmetries,” Tahirah said with a quiet smile. “If Suleiman will
wrap himself around my wrist, I can act as his…assistant. We can do
this.” She looked at Layla. “And you will help as well, won’t
you?”
“I can’t. I’m not good at geometry like Ara,
and I’m not brave and…”
Tahirah squeezed Layla’s shoulders. “You are.
Everyone can do mathematics. It may be easier for some, but
everyone can master the principles. We need you. Suleiman is
counting on us. Both mathematics and bravery can be learned. You
must decide if it’s important to you. Suleiman needs all of us
now.”
Layla ducked her head. “But it’s so very hard
for me.”
“It’s going to be hard,” Tahirah said. “Hard
for Ara to keep her counsel about Suleiman and not to accidentally
betray herself before the wazir. Hard for me to admit I need the
help of two girls to solve a mathemagical problem—and very hard for
Suleiman to be a snake. He has placed his faith in us, and we hold
the key to his release. We can lean on each other for strength.
I’ll help you learn symmetry. Ara and you will help me learn about
teaching girls. Oath?” she held out her hand.
“Oath,” both girls replied, their voices
solemn, and grasped her hand in a three-way clasp.
Chapter 14
“But why did you bring us here in the first
place?” Ara asked, turning her head to the side. “We thought we
were being punished.”
Astonishment and hurt flashed in Tahirah’s
eyes. “Do you think me an evil djinn? I hoped you would prefer me
to the diet of bread and water that others suggested.”
Ara mouthed the word, “Oh.”
“I thought we could explore the Alhambra
together. I would teach you mathematics and Sufi mysticism.”
Tahirah tilted her head up at the ceiling’s
honeycombed recesses and winced. “The Alhambra is in pain—I can
feel it—I had a vision showing a key. I believe both of you are
part of that key.”
Ara reached one hand out, touching the
ceramic tiled wall as if to comfort the Alhambra.
“My visions are sometimes cloudy, but this
one was clear. I spoke with Suleiman not long before he was
transformed. He offered to go into town for me to retrieve a
scroll. He spoke with such pride about the two of you.” A sudden
memory made her shake her head. “I do think that you should begin
by removing the red stains from the lions’ chests. The color makes
them restless, hungering for a kill. They are lions, after all.
Your father wished them cleaned, and I agreed to see that it was
done,” she added. “I hope you don’t mind.”
“The stone lions? They have feelings?” Layla
said.
“Of course they do, though they are lions,
and their thoughts are not like yours and mine. They were created
long ago as defenders of the Palace of Lions, placed in its central
court facing out in twelve directions, so that none could approach
without their knowledge. Each lion was imbued with a trait to
support the sultan.”
“Do you talk to them?” asked Ara.
“I have tried,” she replied directly to Ara.
“But they have not responded. Nor is your father’s lion at his
side. I worry…perhaps it’s just that they don’t trust easily or
perhaps many things. We can’t know.”
“My father has his own lion?”
Tahirah looked thoughtful. “Yes, it is said
each lion trails the ruler of the Alhambra, though not every ruler
of the Alhambra is granted the ability to see this wonder.”
“But if you can see them, why won’t they talk
to you?” Ara asked.
“They are the guardians of the castle and are
wary of outside magic. I’m still not sure what the wazir is trying
to do. Why is he harming the Alhambra?” Tahirah mused, then shook
her slender shoulders. “Is he embroiled with the Castilians or with
the Saracens or the Aragons—or some other group entirely—or is he
on his own?” She closed her eyes. “All in good time, as Allah
wills. We have more pressing business. I need to teach you the next
symmetry. Here, Suleiman, come and wrap around my wrist so we can
do this together,” she said directly to the snake, extending her
arm.
Suleiman uncoiled himself from Ara’s wrist
and slithered across the floor to Tahirah. “Let’s see, Suleiman
taught you mirror symmetry across a vertical line, right?” The
snake rested unblinking in his new location. “My thought is that
the second one learned should be mirror symmetry over a horizontal
line. We should probably review both.” She pulled out a quill and
paper and launched into her lecture.
“You remember that symmetry is a relationship
of characteristic correspondence, equivalence, or identity among
constituents of a system. In mathematics it is a property that
generates repeated patterns. Band symmetry, which we are focusing
on here, runs in one direction like a frieze or border. Euclid
stated in his treatise that there is a connection between—”
“Actually no, I don’t remember what you’re
saying at all,” Ara interrupted, startled by the complicated words.
Layla sat beside her, looking despondent.
“No?” Tahirah asked, surprised. “That’s the
way my instructor presented it to me. How did Suleiman explain it
to you?”
“Well, a lot simpler. He did talk about
repeated patterns though,” Ara answered uncomfortably.
Suleiman raised his head, “Ssssymtry is
sssimple.”
“I see. Let’s start over, shall we?” Tahirah
took a deep breath and tried to recall herself as a young girl.
“I’ve got it. Symmetry is about two things, pattern and motion—in
particular, which motions a pattern can make and still remain the
same.
“Let’s draw some simple patterns. Ara, you
draw one, and Layla, you can draw the next. I’m going to explain
reflection or mirror symmetry across a horizontal line.”
“Suleiman called it a flip,” Ara
interjected.
“He did, did he?” Tahirah frowned at the
snake in her lap. “All right then, reflection, mirror or flip—all
three are names of this motion. Each of you draw something simple
on the parchment. Just one thing each!”
She smiled at them. “Lovely. Those are
excellent. Now we shall pretend there is a line below them that
they reflect…oh, sorry, flip over. Watch. I will draw the
horizontal mirror image, or flip, of each of your images. The
horizon is an imaginary line that stretches left to right across a
landscape,” she added by way of explanation. “See how these images
are now ‘flipped’ across the imaginary line below them. A perfect
match, if we were to see it in a mirror.” Tahirah hesitated as she
looked at each girl. Ara’s eyes were bright with comprehension as
she focused on the drawing. The dawning of understanding crept more
slowly across Layla’s face.