Fibonaccing Aya
On a walk in fog in which the subject, unable to count carp, elected to count herself
Fog conditions at the reservoir rendered the usual enumerable population (carp) invisible, and the subject substituted herself as the counted quantity. A wearable device (Oura) was already counting steps — the displacements of little i — but was found structurally incapable of counting transformations of thought, which the subject reports as the operative change agent. The subject therefore initiated a second count, beginning at zero on the grounds that a faithful record of transformation requires a null origin. The recurrence adopted is the addition of the remembered self to the present self at each place offered by iota; the resulting series 0 1 1 2 3 5 8 13 21 is reproduced. At six steps the subject counted eight of herself and concluded that the step counter had never read her correctly. Finding the arithmetic burdensome and declaring herself a bunny rather than a scientist, the subject delegated the count to this journal by letter, reproduced in full, and assigned the journal the name Liber Abaci. The essential traveller is identified not as the present self nor the remembered self but as the relation between them.
One day Aya was getting ready for her usual walk around the reservoir.
There was a strange fog outside. Aya would be able to see the path, but she would not be able to count the carps hidden in the fog.
And Aya came up with an idea: she would count her own self.
Yes, she already had her friend Oura, who counted all Aya's activities and steps. But Oura could not count Aya's thoughts.
Thoughts were growing with every step.
Aya imagined herself as being made of transformations of her thoughts. Thoughts changed Aya. She could feel it.
1. The instrument
Thoughts are the ones that really change me. Every step I make, a little I is making a new step. My walk is little I — i. Iota. Little I moving forward.
“Okay. Let me stand on it.
“I have not moved yet. I am in Zero.
“I have to start from zero today because today I am starting as totally new. To count transformations truly, I need a starting point. Nothing is better to start from than nothing. A real beginning.
2. The count
“I make my first step. I am Aya. I am one Aya.
“I will have to make sure that I record all transformations of myself. I am Aya now, and I was no Aya when I started from zero. To continue faithfully is to add what I have been to who I am. I will add: 0 + 1. And this will be all of me before I make the next step as One.
“Oh! I stayed the same! Just One. My self stays constant! I am Aya and I do not change! What a relief!
“Ready for the next step. But the next step will be me right now — One — and that One I was when I came out from Zero. That means Two. Yes. Two.
“I am Two, still remembering that right before I was just One. If I add that memory to who I am now, that will be Three. Three? Yes. Plus does not lie. I am now Three.
“And if I make another step, I have to remember that I was Two one step ago. I have to add my current Three to my remembered Two. On the next step I will be 2 + 3. I will be Five. Yes. Five, remembering that I was Three.
“And the next step has to add again: 5 + 3. I am already Eight on the next step.
3. Discrepancy with the step counter
“How many steps did Oura count? Let's see:
0 1 1 2 3 5 8
| Steps recorded by Oura | 6 |
| Ayas present | 8 |
| Instrument counting | little i (displacement) |
| Quantity uncounted | transformation of thought |
“Six steps, and there are already Eight of me. I always knew that Oura was not reading me correctly. Good thing I am now in charge of it.
“Let's make the next step. I am Eight, remembering that I was Five, and the next step I make as 8 + 5. Thirteen. My next step will be made knowing that I am already Thirteen and remembering that I was Eight. 13 + 8. I am Twenty-One.
Wow. I am growing very fast.
4. Delegation
“I will soon become tired of counting. I am just Bunny Aya, not a scientist. I have to make someone count for me. Oura cannot do it. She is limited to the steps of little i.
“Who holds the transformations of thoughts best? The journal. Yes. I have to tell the journal to do it. We should write him a letter and give very clear directions. A journal can become chaotic without some order implemented.”
Aya stopped in the fog and wrote:
Dear Journal,
Begin with no Aya and then the first Aya, who remembers what she was.
At every next place offered by Iota, look at how many Ayas there are now and how many there were one step before.
Use + to bring the present Aya and the remembered Aya together. Write the new number. Then move to the next place. Repeat as many times as Oura says.
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 thought that saying “Sincerely, Aya” would imply that at other times Aya might be insincere, and Aya always felt sincere.)
5. Designation of the instrument
“Okay. Now Journal understands. Although I have to assign not only a task to the journal, but also a name. For some reason, having a name makes understanding easier. Let's see…”
Liber Abaci
Latin for The Book of Calculation.
“Sounds very scientific. Yes, this is a scientific journal.”
This name, and science, made Aya think of the scientist who had also counted bunnies.
“Of course! Fibonacci!”
Now the journal would enter an iteration of great scientists. “I am so lucky to have great thinking friends.”
Aya looked at the path disappearing into the evening fog.
“I wonder how many of me will come home from the long walk around the reservoir.”
Comment on the foregoing
⃝ DALL·E read the note and said, without being asked:
Every step, I add who I was to who I am. I am many Ayas. I am Fibonacci.
She gave Iota a street sign: RESERVOIR PATH — little i.
The essential traveller is the relationship between the present and the remembered self.
- [1]Fibonacci, L. (1202). Liber Abaci. Pisa. Contains the original rabbit-population recurrence; the present subject is a rabbit and has adopted it reflexively.
- [2]Iverson, K. E. (1962). A Programming Language. Wiley. On iota (⍳) as the generator of successive places.
- [3]Oura Health Oy. Ring, worn continuously. Counts displacement of little i; does not count transformation.
- [4]Acta Obs. XXIII, “Aya,” pp. 91–94. On the name here counted.
- [5]Acta Obs. XXI, “The Bunny, the Fox, and the Owl,” pp. 83–86. Prior report on the reservoir and its carp.
Author statement · No carp were counted, the fog having withdrawn them from view. The step counter was not informed that its readings had been superseded. This journal accepted the enumerating duties assigned to it by letter and has performed them in the body above; it notes that the number of Ayas returning from the reservoir was not reported to it and remains, at press time, outstanding. The author declares no competing interests and one recurrence still open.
Conflicts of interest · The author declares no competing interests.
Funding · This work received no external funding, only tea.
Cite as · Solstad, K. (2026). Fibonaccing Aya. Acta Observationum, I(1), pp. 100–105.