Fibonaccing Aya
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One day Aya was getting ready for her usual walk around the reservoir.
There was a strange fog outside.
She could see the path.
But she could not count the carps hidden in the fog.
So Aya had an idea.
She would count her own self.
Aya already had her friend Oura, who counted her steps.
But Oura could not count her thoughts.
Thoughts changed Aya.
She could feel it.
“How can I count what happens to me while I walk?”
“Every step I make, a little I makes a new step.
“Little i.
“Iota.
“Little I moving forward.”
Aya stood still.
“Before I move, I need a beginning.”
“I have not moved yet.
“I am in Zero.
“Today I am counting myself from the very beginning.”
Aya took her first step.
“I am Aya.
“I am one Aya.”
“But I must remember what I was.
“I am One now.
“Before this, I was Zero.
“To find my next self, I will add who I was to who I am.”
0 + 1 = 1
Aya took her next step.
“Oh!
“I stayed the same!
“Just One.
“I am Aya and I do not change.
“What a relief!”
“Ready for the next step.
“I am One now.
“And one step ago, I was One.”
1 + 1 = 2
“Two?
“Oh.”
“I am Two, remembering that I was One.
“If I bring them together...”
1 + 2 = 3
“Three?”
“Yes. Plus does not lie.
“I am now Three.”
“Now I am Three.
“One step ago, I was Two.
“My next step will be...”
2 + 3 = 5
“Five!”
“Five, remembering Three.”
3 + 5 = 8
“Eight!”
“I am already Eight!”
“How many steps did Oura count?”
Aya looked back.
0 1 1 2 3 5 8
“Six steps.
“And there are already Eight of me!”
“I always knew Oura was not reading me correctly.
“Good thing I am now in charge of it.”
Aya made another step.
“I am Eight.
“I remember Five.”
5 + 8 = 13
“Thirteen.”
“Now I am Thirteen, remembering Eight.”
8 + 13 = 21
“Twenty-One!”
“Wow.
“I am growing very fast.”
“I will soon become tired of counting.
“I am just Bunny Aya, not a scientist.
“I have to make someone count for me.”
She thought about Oura.
“No. Oura counts the steps of little i.”
“Who holds the changes in my thoughts best?
“The journal.
“Yes!
“I should write him a letter.
“Very clear directions.
“A journal can become chaotic without some order.”
Dear Journal,
Begin with no Aya: 0.
Then write the first Aya: 1.
At the next place, look at how many Ayas there are now.
Look at how many there were one step before.
Use + to bring the present Aya and the remembered Aya together.
Write the new number.
Move to the next place offered by Iota.
Repeat.
Each time, use the newest number and the one just before it.
Keep your record as long as Aya keeps walking.
Oura will count the steps of little i.
You will count what happens to Aya while she takes them.
Please watch one another.
Sincere Aya
Aya always signed “Sincere Aya.”
She thought “Sincerely, Aya” might suggest that at other times she was not sincere.
And Aya always felt sincere.
“Okay. Now Journal understands.”
Aya looked at him again.
“But I have given you a task.
“I have not given you a name.
“For some reason, having a name makes understanding easier.”
Liber Abaci“Let’s see...
“Liber Abaci.”
The Book of Calculation.
“Sounds very scientific.
“Yes. This is a scientific journal.”
The name reminded Aya of a mathematician who had written a problem about rabbits.
“Of course!
“Fibonacci!”
Her journal was in very good company.
“Oura can count my steps.
“Journal can keep track of my changing self.
“And I can keep walking.”
Aya smiled.
“I am so lucky to have great thinking friends.”
Aya looked at the path disappearing into the fog.
There was still a long way to walk.
“I wonder how many of me will come home?”
Aya left Journal with these numbers:
01123581321
Which two will he bring together next?