Authors: Gwen Dandridge
Tags: #history, #fantasy, #islam, #math, #geometry, #symmetry, #andalusia, #alhambra
“Yes,” the girls chorused.
Tahirah moved more tiles from the stacks in
front of them.
“The simplest symmetry is called a
translation. The design or object moves one space across the row.
It does not reflect. It looks different upside down and right side
up, so there is neither horizontal nor vertical symmetry. In fact,
it is unchanged in every way but for the fact that it is moved
along the row one space. Note that you can tell it’s not reflected
because the flower stem points in one direction only. If it
reflected vertically, the stem would alternate pointing to the left
and to the right.”
“But that’s boring,” Ara said, baffled,
looking at the simple flower buds. “How can that be anything? It’s
too easy.”
Tahirah smiled. “Not quite as easy as it may
seem. Here, look at this one.” She collected six other tiles.
“It’s a double reflection—wait,” Ara frowned.
“It isn’t.”
“That right, it isn’t. Now explain why.”
Layla peered over her shoulder as Ara frowned
at the tiles. “Well, the red line that goes up the middle—it isn’t
the same on both sides. It doesn’t reflect. In fact,” Ara said,
looking at it critically, “it doesn’t reflect horizontally either.
But that’s strange. It almost does.”
Tahirah settled in a bit more. “Good, you see
the difference. Symmetry must obey rules, and this one does not
follow those rules for reflection. This is a simple translation.
Another word for this symmetry’s motion is slide.”
“Oh,” Layla said, showing more interest, “a
slide, like in dance, a stepping to the side?”
Tahirah laughed. “Yes, very much like dance.
The only way this symmetry group can move is by stepping to the
side.” She looked out the window. “It is nearing dark. I’ll walk
you into the harem where you will be safe. The wazir cannot go
there, nor can any man. Remember, be careful. I’ve done what I can
to confuse the wazir. Keep Suleiman away from him, but most
important, do not put yourselves in danger.”
Chapter 28
Sleep didn’t come easily to the girls that
night. Ara wanted to go back to the fountain to attempt a
conversation with her lion. Maybe now he would show himself to her
and speak.
Layla, terrified of the wazir, argued long
and hard that if the lion wanted to talk to them, he knew where
they were. Suleiman, after thoroughly investigating the room,
selected a soft pillow and, purring blissfully, kneaded it with his
front paws before falling asleep.
“Girls, it is almost dawn and soon time for
prayers. Why are you not up and about?” To Ara, lost in restless
sleep, Su’ah’s voice seemed far away. Something soft flicked across
her nose. She opened her eyes slightly.
The tail swept across her face again.
“Achoo,” she sneezed. Suleiman pushed the covers up a bit to poke
his nose outside the blanket. He’d crawled under last night
complaining of a draft.
“Are you coming down with a cold?” Su’ah
asked.
Ara shoved Suleiman back under the covers.
“No, something just tickled my nose. I’m fine.”
Su’ah stood gazing out the window at the
brightening sky. “Looks like another beautiful morning.” She stood
watching for a moment, and then said. “Why, there’s the wazir.
What’s he doing?”
Ara jumped up and ran to the window to look
through the honeycombed slats. “Where?” she breathed, leaning
against the sill. Layla opened her eyes wide.
Su’ah pointed to a shadowy figure standing
backlit by a flickering torchlight from the palace. “See, it’s him
all right. What’s he doing with that cat?”
The sky was rosy with light illuminating the
scene as the sun began it’s climb: a tortoise-shell cat crouched in
a corner, spitting furiously. The wazir, looking disgusted, kicked
at it, but it darted between his legs, escaping as the voice of the
muezzin rang out. The call to prayer, Fajr. The wazir slammed his
fist against the wall and then hurried away. Ara and Layla quickly
got their prayer rugs and, facing Mecca, began to pray.
Praise be to God, Lord of the worlds!
The compassionate, the merciful!
King on the day of reckoning!
Thee only do we worship, and to Thee do we cry for
help.
Guide Thou us on the straight path,
The path of those to whom Thou hast been gracious;
with
Whom thou art not angry, and who go not astray.
From under the tousled bedcovers, Ara heard
Suleiman perform his devotions.
Washed and scrubbed after their baths, the
girls returned to their sleeping quarters. Su’ah had left earlier
to watch over Dananir’s small son. Layla went directly to the bed,
wanting to collect Suleiman before they left for breakfast.
“He’s gone,” Layla whispered. Panic lurked in
her voice.
“He can’t have disappeared.” Ara grabbed the
covers, looked under them, and then started searching the room. “He
knows we need him to be with us when he changes, and half a day has
already gone by. He’s a very smart cat. Or, at least, he was a
smart tutor,” she amended.
Layla ran to the window to scan the yard
below. “Where could he be?”
“I’m here,” Suleiman announced, slinking into
the room. The fur on his neck stood out.
Layla rushed over to him and cradled him in
her arms. “Where did you go? We were worried.”
Suleiman shivered. “I went to speak with the
Lions, feline to feline. We have much in common. They are magical
lions, and I am a cat transformed through magic. I hoped they might
advise me on how to break this spell faster.”
“What happened?” Layla asked. “Didn’t they
help?”
He wriggled, wanting to get down. “The power
they hold is overwhelming. Being near them is like staring at the
sun too long. Even partially bound by the wazir’s magic, they
radiate. They pulse with power. They knew, of course, that I had
been transformed.” He leapt to the floor and paced.
“They scolded me for wanting to change back
to my human self. Me, a Turk of the tribe of Qizilbash! The lions,
Wisdom and Reason, said I should take the opportunity to learn from
each transformation. I was too prideful, they said.” He flashed the
girls a look of indignation before twitching his tail.
Neither girl spoke, uncertain what to say.
Suleiman continued pacing. Both recalled him in his human form:
smart, competent but very pompous.
“What are you supposed to learn?” Ara
asked.
“They said that I was wasting valuable magic
by not using the time wisely, that each animal shape I turn into
had lessons to teach. They were not sympathetic.” He bristled.
Suleiman continued to pace while the girls
snuck quick looks at each other.
“Did they hint at what they thought you
should learn?”
“Humility,” Suleiman spat. “I believe that
was the first lesson.”
Ara winced. Layla considered that for a
moment, then said, “What about sympathy for those who are
powerless?”
“What about it?” the cat snapped.
“That was something you learned as a lizard.
Maybe that’s what they meant.”
Ara looked at her cousin in amazement.
Suleiman’s tail flicked in annoyance and Ara
thought he was going to dismiss Layla’s suggestion. He reached up
to the weaving hanging on the loom and sharpened his claws.
“Perhaps that’s true. Maybe the lions are right. There is something
to learn here. I need to think on this.”
“Please, could you think about it without
destroying Su’ah’s weaving?” Ara implored.
“Your pardon,” he apologized,
self-consciously removing his claws from the material. “I need to
go for a walk and consider Wisdom’s words.”
“But we need you here!” Ara protested. “You
need to help us find the translation symmetry.” The cat stared at
her and flattened his ears. Ara grasped at a thought. “Was Wisdom
my lion’s name? Was he the one you spoke to?”
“Your lion didn’t stoop to introducing
himself,” Suleiman huffed. “Yes, a walk is just what I need.”
“You can’t leave. It’s not safe,” Layla said,
a plea in her voice.
Suleiman gave her a look that would curdle
milk. “I’m a cat—I come and go as I please. I escaped through
cunning yesterday—I can do it again.” He arched his back in what
seemed a casual stretch before trotting toward the door. “Don’t
worry, you won’t have trouble finding translation symmetries. There
are too many to count in the Alhambra,” he said. “If I see the
broken one, I’ll let you know.”
And he was gone.
Ara was the first to recover. “I might guess
his
lesson is independence,” she said.
“Now what?” Layla asked.
Ara picked up her lute and headed for the
door. “We have classes to attend. I guess we continue on. We have
until Asr, three hours before sunset the day after tomorrow to find
this symmetry. We must wait for his return, otherwise we won’t know
what he changes into.”
After an unhappy look at the door, Layla
grabbed her dance clothes and calligraphy stylus and followed
Ara.
Neither could look at the other. Unspoken was
the fear—what if he never returned?
Chapter 29
By early the next morning both girls were
beside themselves with worry. Suleiman had not returned, and only a
few hours remained. Ara had found a translation right outside their
room. But it was whole, not broken.