Number Qualities (story cont’)
Day three: What is TWO?
The time had come once again for the two girls to ponder an ancient question. What is TWO? Adira had some ideas.
“Two is a pair. A pair of shoes. A pair of earrings. A pair of gloves. Mama and Daddy. They make a pair.”
“Yes,” Phaedra said “Mama and Daddy are quite a pair! And we are a pair. A pair of sisters! Speaking of Mama, that reminds me of something she always tells us when we are quarrelling. She says ‘There are two sides to everything.”
“She is right, isn’t she Phaedra?” Adira said. “There are two sides to a coin. Two sides to a playing card. Two sides to every arguement!” And the two girls began to laugh.
“When I think of two,” said Phaedra “I think of opposites. . . the sun and the moon, dark and light, boy and girl, day and night, hot and cold, black and white, little and big. Opposites come in twos! “
“And our bodies!” said Adira “There are lots of twos that make up our bodies. . . two eyes to see, two ears to hear, two feet to walk, two hands to work.”
“Ah, but we only have one nose!” laughed Phaedra.
“But two nostrils!” said Adira and the two girls laughed and laughed.
Phaedra thought for a moment and made up the following verse which she recited to her sister:
Two are my eyes, ears, hands, and feet,
Dark and Light at sunset meet.
As they continued talking the sun began to set in the west and the two sisters began to yawn. “I think it is time to rest now.” Said Phaedra.
“Yes,“ said Adira “The sun is setting in the west. But soon it will be rising in the east and a new day will begin. Let us be rested for Cipher’s visit.”
And so it happened that when the lovely lady in the gossamer gown appeared the next morning, the two girls recounted all that they had discussed about the number two. And as before, Cipher smiled at the sisters, and was pleased. Then she bent down and rubbed the sandy dirt from a nearby rock to reveal two new symbols [2, II].
The girls had a feeling what the next ancient question would be, and as they suspected Cipher said “Your question for tomorrow is “What is THREE?” Phaedra and Adira bid goodbye to Cipher and immediately set to the task of discussing this new question.
Day four: What is THREE?
The two girls were feeling more comfortable now. Knowing how to begin to think about the question made it easier for them. “Well, where should we begin?” said Phaedra.
“I know,” said Adira, “Let’s try to name things that come in threes.”
The girls gave this serious consideration. “There are three leaves on a clover.” said Phaedra. “Unless you find a lucky one!” She smiled.
“There are three sides to a triangle!” said Adira “And a triangle can look so many different ways.” The girls stopped to ponder this thought. They found some sticks lying on the ground and began to break them into different sizes, joining them to make interesting triangles with different shapes.
When they finished this activity, they continued to think of things that come in threes.
“What about fairy tales?” said Adira “Mama has told us many stories with threes, like the Three Bears, the Three Billy Goats Gruff, the Three Little Pigs.”
“Yes,” Phaedra chimed in “Remember in the story of the Three Bears, many things happened in threes. Little bear had a little bowl, a little chair, a little bed. Mama bear had a medium-sized bowl and chair and bed, and Papa bear had a big bowl, chair and bed. Little . . . medium . . . big. Remember their porridge? Hot, cold and warm. The warm one was just right for Goldilocks.”
“What about our bodies?” said Adira “Yesterday we found many things on our bodies that come in twos. Are there things about us that come in threes?”
Phaedra thought about this for a moment. “Well,” she said with a chuckle, “Once when our teeth were newly emerging we only had three teeth!” The sisters laughed at Phaedra’s joke. They both enjoyed making jokes, and had the same sense of humor.
“But in seriousness,” said Phaedra to her sister “We are three in one. For you see we have thinking in our heads, feeling in our hearts and in our hands we have the ability to do work. In nature we can also see three.” Phaedra continued, her younger sister listening with great interest. “First there are the minerals, stones and shining crystals which we walk upon. Then there are all the marvelous plants which grow up out of the earth towards the sun. Finally there are the animals which live and move about on the land, in the air and in the sea.” And again as she had done the two previous days she created a verse which she recited.
Stone, Plant and Beast,
Earth Air and Sea,
With my head, heart and hands
The world do I meet.
The day passed quickly as the girls talked and looked around them for more signs of the number three. When they fell asleep they had lovely and restful dreams. In the morning they were once again visited by Cipher. She listened to their answer and rewarded them with the knowledge of the third symbols [3, III] and their next question, ‘What is FOUR?’
When Cipher departed the girls turned to each other and Phaedra said to her sister “We are a fourth of the way to answering the twelve ancient questions. Let us get right to our next question. I am eager to see what is behind that door!”
Day five: What is FOUR?
The sisters spent the day in discussion about the number four. Their daily talks about numbers were beginning to feel like a wonderful game. What insights could they come up with today? How could they impress Cipher with their observations?
Phaedra began. “Four reminds me of tables and chairs. It’s their four legs that make them sturdy and strong. Remember the three-legged stool that Daddy had for milking the cows?”
“I remember how wobbly it was!” said Adira “I fell off of it once or twice. I always wished that it had been built with four legs.”
“Yes,” Phaedra replied “The milking stool! How much more sturdy it would have been had it been built with four legs!”
“What ever happened to Daddy’s stool?” said Adira
“Oh, it was broken one day when our black and white jersey cow kicked it. Remember?”
“Hmm,” said Adira with a wry smile on her face. “I wonder which of her four legs she used to kick it?”
The girls laughed, and then began to make a list of all the four-legged animals they could think of . . . cows, horses, pigs, sheep, dogs, cats, rabbits, goats, camels, lions, zebras, lizards. . .
The list went on and on.
“Ah,” said Phaedra “Here’s a riddle for you!” Phaedra was very clever and enjoyed making jokes and telling riddles.
“From the North, from the West,
From the South, from the East’
We whistle and blow,
Our number you know
But what are we?”
Adira thought for a moment, and before she could answer Phaedra said “The Four Winds!”
Adira smiled “Yes,” she said “The winds come from the four directions—north, south, east and west. There are also four seasons! “ And then Adira recited a verse.
Winter, Spring, Summer, Fall
There are seasons, four in all.
Weather changes, sun and rain and snow,
Leaves fall down and flowers grow.
“Brillant!” said Phaedra “I hadn’t thought of the four seasons! What about the four elements?”
Adira looked perplexed. She had never heard of the four elements. “What are the four elements?” Adira asked.
“Earth, water, fire and air.” Said Phaedra “Everything in nature is made up of one or more of these elements. Take bread for instance, bread requires all four elements – wheat from the earth to grind into flour, water to make it wet, yeast to create the air needed to make it rise, and fire to bake it.”
“Speaking of bread,” said Adira “It’s been a while since we have eaten. Let’s have a meal.” And just as she said these words the girls turned around to find a lovely dinner laid out for them on a nearby rock. They were becoming accustomed to the convenience of this strange but beautiful land. After they ate the two girls retired for the night.
Cipher came in the morning and the girls gave her their answer. Cipher then revealed the next symbols [4, IIII] to them and gave them their next already-anticipated question “What is FIVE?”
Day six: What is FIVE?
It was time to discuss Cipher’s next question “What is FIVE?”
Phaedra and Adira started their discussion right away. “What do you think Adira?” said Phaedra.
“Well,” said Adira “I have five fingers on this hand” and she held up her right hand. “Oh and I have five fingers on this hand!”
“Don’t forget your toes!” laughed Phaedra.
“Yes!” said Adira “Five toes on each foot!”
“Do you know what I think of when I think of five?” said Phaedra “I think of a star. You know the five-pointed kind.” Phaedra picked up a stick and began to draw a star in the sand. “Stars are difficult to draw.” Said Adira. “I have a hard time with them.”
“Here,” said Phaedra “try this.” and Phaedra drew five dots in the sand. Try to make a star using these dots to help you.” Adira did her best to draw a star. “It will become easier if you practice a bit.” “And watch this.” Phaedra said. Instead of drawing a star, this time Phaedra connected the dots so that it formed a shape with five sides. “This is called a pentagon.”
“Oh yes, I see” said Adira “A triangle has three sides. A square has four sides and a pentagon has five sides.”
“Now look,” said Phaedra. “We can draw a person in the pentagon. The head, two hands and two feet are like the points of a five-pointed star.”
“How interesting!” said Adira.
The two girls talked for a bit longer. They remembered the apple blossoms in the spring with five petals that hung from the apple tree in their backyard, the five armed starfish that they had seen when visiting the ocean with their grandparents, the wonderful story of the “Five Little Peppers” that was one of Phaedra’s favorite books. But in the morning when it was time to tell Cipher their answer, they mentioned the star. It seemed the most beautiful example of five they had come up with. And Cipher rewarded them with the next symbols in helping to decipher the code [5, V]. And of course their visit with her ended with the next question “What is SIX?”
Day seven: What is SIX?
Phaedra and Adira had a new number to consider. Six. What would they come up with?
Adira immediately thought about the hexagon. In the days previous, they had discussed the pentagon, the square, the triangle. “A hexagon has six sides.” said Adira. “Yes,” said Phaedra “It is a beautiful shape. Honeybees use it to create the comb in their hive, a series of beautiful interlocking forms.”
Phaedra continued. “There is another place in nature where the number six is always
found. The snowflake. Most snowflakes have a six-fold symmetry. That means that they are the same on the left and the right sides and have six points.” “I have heard that no two snowflakes are exactly alike.” said Adira “That’s right” said Phaedra. “Just like people, I suppose. But just like people are shaped like a five-pointed star, snowflakes are shaped like a six-pointed one!”
“Is there such a thing as a six-pointed star?” asked Adira. “Yes,” said Phaedra “It is called the Star of David. It is a sacred symbol for the Jewish people.”
“Oh, I know!” said Adira “I know another place in nature where you can find the number six! The legs of an insect. All insects have three legs on each side of their body. Six in all.”
“Some people think centipedes are insects.” Said Phaedra. “But they’re not. They have too many legs!”
“Six is a magical number, isn’t it?” said Adira “It’s found in nature in so many places. Insects, snowflakes, honeycomb. . . oh, and lilies. Easter lilies, starburst lilies, tiger lilies. Like the lily that the angel Gabriel held in his hand on the day that he told Mary she would be the mother of Jesus.”
“Yes,” said Phaedra “The lily became a symbol of Mary.”
Adira yawned. “Phaedra, I’m getting tired. These last six days of discussion about the numbers have been fun, but tiring. I am so curious to know what lies beyond that door.”
“Well,” said Phaedra “When we give Cipher our answer tomorrow we will be half way to finishing the twelve ancient questions. Take heart! We will know the secret code soon!”
The two girls fell asleep after eating a hearty meal and in the morning they told Cipher their answer. The symbols were shown to them – five plus one is six as the Roman numeral revealed [6, VI].
It was exactly a week since the first day they had come to this strange and mysterious land. Would their parents be worried asked Adira. “No,” said Cipher “Time is not the same here. When you return, as indeed you will, your parents will not even know you have been gone.” The girls were relieved that their parents would not be concerned about where they were and were excited to hear Cipher say that they would indeed be returning to their home. They liked the time they were spending in this world and wanted to stay longer but all the time had been thinking how delightful it would be to tell their parents of all they had learned. Would they ever believe it?
Well, there was little time to think about that. They were given the next ancient question, “What is SEVEN?” Cipher promised them that the answer would be like no other and a special gift would be bestowed on them should they answer it correctly. “Let us get right to our answer.” Said Phaedra.
Day eight: What is SEVEN?
The number Cipher had asked them about was seven. The girls thought the answer would be easy. Cipher had said their answer would be like no other, so why couldn’t they think of a single thing that was made of the number seven. The girls thought and thought and after a long silence Adira spoke up. “I know!” she said “The seven dwarves. You know that story we read about Snow White and the seven dwarves – Dopey, Sleepy, Grumpy, Bashful, Happy, Sneezy and Doc.”
Phaedra laughed. Adira was always thinking about the stories she had heard. It was true that there were seven dwarves in the story of Snow White but Phaedra was certain that this was not the answer Cipher was looking for.
“Well, yes,” Phaedra said “The seven dwarves. Can we think of anything else?”
“Why would Cipher promise us a special gift now after a week of answering questions? Why now?” said Adira. Then a thought occurred to her. Perhaps it was because they had come to the end of their first week with Cipher. One week, SEVEN days!” “That must be it,” Adira said. We have been asked about a number that matches the amount of days we have been answering Cipher’s questions!” She felt as if she had solved a puzzle and was proud of herself.
“Well, I thought of something.” said Phaedra. “There are seven stars in the Big Dipper.” As she said this she looked up at the darkening sky and squinted in an attempt to find the Big Dipper.
“Oh, you know so much about the stars Phaedra!” said Adira. “What else can you tell me about them?“
“Well, I can tell you that another name for the Big Dipper is “the Drinking Gourd”, and that the two stars at the end of the bowl on the Big Dipper are called the pointer stars. If you draw a line through the two pointer stars and keep going it will lead you right to the North Star, one of the brightest stars in the sky.”
And then it was as if a light bulb had gone on in Phaedra’s head. When she said the word ‘sky’ it made her think of the day last summer when her family was driving in the car after a rainstorm. The sun had come out from behind the clouds and stretching from one side of the horizon to the other was the most magnificent rainbow Phaedra and Adira had ever seen! “A rainbow! That must be what Cipher was talking about. A rainbow is made up of seven colors – red, orange, yellow, green, blue, indigo and violet.”
“Yes! A rainbow’s colors! Of course! Do you know how I remember the colors of the rainbow? I say the sentence “Richard of York Gained Battles in Vain” The first letter of each word in that sentence is the first letter of each color in the rainbow. Richard – red, Of – orange, York—yellow, Gained – green, Battles—blue, In—indigo, Vain—violet.”
“What a clever way of remembering.” said Phaedra and she covered a yawn with her hand. Darkness had fallen on the land.
“I sure am glad that you thought of a rainbow.” said Adira “That must be the answer! Let’s get some sleep!”
In the morning when Cipher appeared to the girls, Phaedra said “Well, we know that there are other possible answers to the question ‘What is seven?”, but the one we like the best is ‘Seven is the colors of the rainbow.”
Cipher smiled and said to the girls “Once again, you have done well.” And as she said those words a remarkable change began to occur — the sky in the once grey land turned blue, bright blue. The sun sent golden streaks of color across the blue sky and kissed the blades of green grass that sparkled with drops of morning dew. The hilltop where the girls stood which had previously been shades of tan and grey took on all the colors of the rainbow as every sort of flower, butterfly and tree was filled with a shimmering quality of light. The girls stood in amazement and laughed with joy at the beauty of this place. If this land could be so dazzling, imagine what lay behind the door! They were eager to receive their symbols [7, VII] and confirmation of the next question “What is EIGHT?”
Day nine: What is EIGHT?
The girls were considering the number eight.
A few things came to mind right away. Phaedra said to her sister “Eight makes me think of a spider. Did you know that spiders have eight legs and most of them have eight eyes?”
“Really?” said Adira. “I didn’t know that spiders could have that many eyes! Imagine, they can keep one eye on each leg! Now, that’s what I call watching your step!”
The girls laughed at Adira’s joke, and pondered the mysterious and intriguing qualities of spiders. Then Phaedra said, “There is a creature that lives in the sea that also has eight legs. Do you know what it is?” Adira thought for a moment and then said “I believe it is an octopus. Is that right?” “Yes,” said Phaedra, “an octopus. It’s name helps us to know that it is associated with eight. Octopus begins with the prefix ‘oct’ and that means eight. For instance, we’ve been talking about shapes in the last days — a triangle has three sides, a square, four, a pentagon, five, a hexagon, six. What do you think an eight-sided shape is called?”
“An octagon!” Adira said and smiled at all she had learned. “That’s right, an octagon.” said Phaedra. “There are other words that begin with the prefix ‘oct’ like octet, that is a musical group composed of eight players, or octagenarian, that means a person in their eighties.”
“Octa-ge-nar-ian,” Adira said slowly. “That’s not easy to say! But Phaedra, what about the month October? It isn’t the eighth month of the year, it is the tenth.”
“Oh yes, that’s a very good question! The name October comes from Roman times when the yearly calendar was different. At that time, October was the eighth month. A lot has changed since Roman times, but the influences are still apparent.”
“Yes, like the Roman numerals that Cipher has been showing us. They are much different from the way we write numbers now, but the older Roman way is still in use.”
The girls felt satisfied that they had explored the number eight thoroughly and decided to turn in for the evening. In the morning they told Cipher all they had discovered during the course of their conversation. They were not surprised when she revealed the next two symbols. Truth be told, they were now figuring out the symbols themselves even before Cipher uncovered them, but seeing the forms carved into the rock confirmed their efforts. And then without a moment’s hesitation, they set to their next task of answering the next ancient question, ‘What is NINE?’
Day ten: What is NINE?
Phaedra and Adira were eager to discuss the number nine. They remembered many sayings that contained the number nine and began to say them to each other. “A stitch in time saves nine!” Phaedra said “Remember Mama always says this to us when we are rushing through something?” “Yes,” said Adira “I never did understand it really.” “Well,” said Phaedra “it means if you take your time with something and do it right the first time, in the long run it will save you time . . .or something like that!” The girls began to laugh.
“How about the saying “She is dressed to the nines” Adira said. “That’s another one I don’t fully understand. I know it means that a person is dressed really fancy, but I don’t understand what ‘to the nines’ really means.”
“I think it’s funny when a person says a cat has nine lives.” Phaedra added “Why not ten lives, or eleven?” Both girls shrugged their shoulders at the same time.
The number nine was proving somewhat more difficult than the rest. The girls were having a hard time coming up with an answer. “I’ve heard of nine pins” said Adira “That was the name for bowling when only nine pins were used instead of ten.”
Then Phaedra thought about the number itself. “Nine is three, three times. One, two, three then four, five, six, then seven, eight, nine. I suppose nine could be represented by three triangles.”
“Well,” said Adira “I keep thinking about Mama and the nine months she carried us in her belly before we were born.” “Yes!” said Phaedra “Pregnancy last nine months. That makes it a very important number indeed.”
The girls were tired. They hoped that the few ideas they had come up with would be enough for Cipher and would afford them the chance to see the next symbols. They were getting very anxious now to solve the code to the padlock. The morning came quickly and with it came the good news that Cipher would indeed reveal the symbols. [9, IX] She gave them their next question, “What is TEN?” They knew this would be a big one and got right to work.
Day eleven: What is TEN?
Ten! Phaedra and Adira had reached the number ten! They were excited to have come so far, knowing that in a few short days they would have all the clues to solve the code. What a fun journey they were on and how much they had already learned!
Phaedra and Adira took a moment to gather their thoughts, then in a flurry of words they both began to explore possible answers. “Ten is ten fingers and ten toes!” said Adira.
“And the Roman numerals have shown us that counting can easily be done on our fingers. Our number system is based on ten. Think about it, you have one to ten then ten to twenty, twenty to thirty and so on.”
“It’s the same with money.” Said Adira “A dime is worth ten cents. Ten dimes makes a dollar.”
“Yes,” said Phaedra “ and it’s that way with years. Ten years make a decade. Ten decades makes a century.”
“So what about a ten-sided form? What is that called?” said Adira
“A decagon.” Phaedra replied.
“A decagon.”Adira repeated “So ten years is a decade. And a ten-sided shape is a decagon. Does that mean ‘dec’ is the prefix for ten?”
“That’s right.” said Phaedra
“Do we know of any other words that begin with ‘dec’?” said Adira “That may help us to find more things associated with the number ten.”
“Well, let me think. I know crabs, lobsters, crayfish and shrimp are called decapods. That must mean they have ten legs.”
“Ah, and let me guess. Although December is the twelfth month of the year now. It was the tenth month of the old Roman calendar!” Adira added.
“Yes, you must be right.” Said Phaedra “You’re clever to think of that!”
As the sun was setting the girls continued talking about their experiences in the beautiful land. They were looking forward to seeing Cipher, the lovely lady whose company they enjoyed every morning. After eating a meal they retired for the night and in the morning they shared with Cipher all of the ideas they had about the number ten. Cipher was proud of how hard they worked and was impressed by their thoroughness. She revealed the secret symbols to them [10, X] and then gave them their next question. “What is the number ELEVEN?”
Day twelve: What is ELEVEN?
Phaedra and Adira were ready to answer their next question “What is ELEVEN?” They began to collect their thoughts. The problem was they couldn’t think of anything.
Phaedra told Adira that she had always liked the number eleven because it was made up of two ones – one right beside the other – and she liked the balance of that. Phaedra said “I especially like it when the digital clock at home reads eleven minutes past eleven o’clock. Twice a day the clock is filled with ones!”
Adira said that she liked the number eleven because it was the first number after the number ten, it was the first number starting on the path to twenty.
But these observations did nothing to help the girls answer the question. The girls sat quietly on the ground and each propped up her chin with her hand. Certainly there had to be something. They thought and they thought. And as they did the hours passed. They watched the morning turn to afternoon, and the afternoon turn to evening, and still the girls didn’t have a good answer. Eleven was one of those numbers that was used to count, but they couldn’t think of anything that was made up of eleven. The girls were beginning to get worried. “What if we can’t think of an answer,” said Adira “We won’t receive the symbols! Then we won’t be able to solve the code!”
Phaedra hid her own worry. “We’ll think of something!” Phaedra reassured her sister. “We’ve got to!” But the hours continued to pass. The girls thought and thought. The thinking was making them tired. They both began to yawn. Then just when they thought they could not keep their eyes open another moment Phaedra said “I know! I know! I have thought of something that contains eleven. There are eleven players on a soccer team!”
“You did it Phaedra!” Adira said. “You thought of something in the eleventh hour!” And the girls looked at each other in surprise. Adira too had thought of something.
“In the eleventh hour – that’s a saying that means “at the last moment”! You’re right,” said Phaedra “I thought of something at the last moment, and now so have you!”
“But will it be enough for Cipher?” Adira asked.
“It will have to be.” Said Phaedra.
The girls yawned again and soon fell into a deep sleep. In the morning they presented Cipher with the only two answers they could come up with. And in response she smiled. “That was a hard question!” said Cipher “You girls have proven that you can be persistent in your quest for answers. That will serve you well when you go through the doorway.” The girls were excited to hear Cipher talk about them going through the doorway. They were anxious to get to the last question! Cipher revealed the symbols [11, XI] and asked the twelfth and final question, “What is TWELVE?” The girls were confident they would find the answer.
Day thirteen: What is TWELVE?
The final question had been asked! The girls were up to the challenge. They began to think of all the things that were made up of twelve.
“Well,” said Phaedra “The first thing that comes to mind is that there are twelve months in every year! January, February, March, April, May, June, July, August, September, October, November, December.”
“And there are twelve hours of the day and twelve hours of the night—twenty four hours all together!” said Adira
“Oh yes,” said Phaedra “One can see that on a clock. The hands of the clock go around twice in one day. At twelve noon both hands point to the twelve on the clock and they do that again at midnight. Then a new day begins at the stroke of midnight.”
“The stroke of midnight.” said Adira “That is the moment when Cinderella’s stagecoach turned back into a pumpkin.” Phaedra laughed. She loved how her sister was always thinking about stories.
“Twelve is a dozen.” Said Phaedra “A dozen eggs. A dozen doughnuts.”
“Umm, doughnuts. I wish we had some doughnuts.” said Adira. And as she said this a dozen doughnuts appeared on the ground next to her. The girls looked at each other with delight. “I will miss this place!” said Adira
“What else has twelve?” said Phaedra.
“Oh, I know!” said Adira. “The best of all! There are twelve days of Christmas!”
“Yes!” said Phaedra “How does the song go?” And the girls began to sing. “Twelve drummers drumming, eleven pipers piping, ten lords a leaping, nine ladies dancing, eight maids a milking, seven swans a swimming, six geese a laying, five golden rings! four calling birds, three French hens, two turtle doves and a partridge in a pear tree!”
The girls were so happy. They had found the answer to the last question. Tomorrow they would receive the last symbols. In honor of the event Phaedra made up a verse. She said:
Twelve is the number
That charts space and time
Twelve inches make one foot
Twelve months the year’s signs
Twelve hours of day
Twelve hours of night
When we think of twelve
All the world’s made right.
The next morning they could hardly wait to give Cipher the answer. When they were finished telling her everything they had discussed, Cipher gave them the last symbols [12, XII].
Then she handed them a golden scroll. “You have done well.” said Cipher “Because of your diligence, because of your patience, because of your intelligence, you have received the honor of deciphering the code. What lies beyond this door is the key to all understanding about the magical world of numbers. Once you have entered you will gain the power to return to your home whenever you desire. And likewise you will always have access to the Land of Numeria – just speak the words “I desire to know the mystery of numbers.” and you will be able to return to the Land of Numeria whenever you wish. Congratulations and godspeed!”
The girls each gave Cipher a hug. “Thank you,” they said, “We have learned so much!”. Then they turned to each other. “Let us see what the scroll can tell us!”