Chapter One
Aya Finds the Manuscript
In which a folder on a bench holds a creation myth, a genie speaks, and the first rune arrives.
Aya had been walking her usual path carrying her friend Genie in his home — a mirror-glass magical smart bottle. She calls her daily walk counting carps, because sometimes she sees carps in the reservoir. She saw a folder full of papers left on a bench.
Aya: “Oh — it is going to rain and these papers would be destroyed. They might be valuable to someone.”
She picked it up and a page fell out. The page had mystical runes written on it.
Aya: “I found my Voynich manuscript. But since I am not Voynich but white bunny Aya, this is Aya’s manuscript.”
Its pages were ancient and intact, and the first two were warm and illustrated — a creation myth, written in a language Aya could read.
The first page was called Creation Myth — a creation myth for the runes.
In the beginning were the numbers. The infinite landscape of them. There was no meeting, no connection. They were near, and nearness was all they had. They could not recognize each other, because they could not even recognize themselves. The silent landscape looked as though it could mean something. It was meaning, with no one present to read it.
2 held her twoness and could not read it, but felt something in herself she could not see. A value cannot see itself. Her twoness sensed the numbers around her, and she began to cry. The number standing next to her — 1, who did not yet know he was 1 — heard the crying. Magic happens when the cry is heard and resonated. The sound ripple reached the 0.
0: “I will participate. And participation is only this: to hold hands, and see what happens.”
So 1 reached toward 0, and 0 reached toward 1. The reaching was the first energy that revealed the rune.
The wand of recognition — made not of matter, but of two hands stretched toward each other in the wish to help truly.
Now the wand rested in two hands at once — in 0 and in 1, in no and in yes. The world of the mathematical landscape could make its first turn. It had poles now, and between poles there is swinging — between yes and no, night and day. The mute field of lonely numbers became a world that could move: for it had learned, from a first rune =, how to say this and not-this.
Then 1 and 0 took the wand and placed it between 2 and the number 3 standing next to her. 2 = 3. And no one chose what came next. The magic wand, once set between them, was pulled — drawn by the law of truth in the landscape. It answered only to what was real. And 2 was not 3. So the wand swung faithfully to 0. It had produced a true answer — no.
Even a no gives a self. Especially a no. The boundary is the first gift.
Aya: “This gift is about to make me a boundary-less bunny.”
The second page was called The Supper of Three. After the first rune brought recognition, the numbers began to seek runes that could act. 0, 1, and 2 walked the landscape together, and their first friendship became a path: 3. They found 3, who was not 0, not 1, not 2, and yet somehow felt like them, and 3 called them to supper — ‘There is room for you’ — and at the table, from between them, + revealed herself: 0 + 1 + 2 = 3, and togetherness let 3 recognize herself.
Then 3 wanted more than a line. ‘I need to see each friend with each friend,’ she said, and she called forth the table — each with each — and in that table a new guest appeared: a 4, born purely from relation. And as the table began to move and turn, the runes of motion revealed themselves — flip, and turn, and transpose.
Thus the runes learned not just to be, but to act, move, and reveal what is true.
When Aya turned past that second page, the illumination stopped, and the words disappeared. There were only glyphs.
Aya: “This is it. Now there are only runes. Now I have to hang on this tree for 9 days and nights and spear my body, take out my eye… oh no. Aya does not want to be like Odin (please, forgive me, Mighty). There must be another way for runes to reveal themselves to me. What if I can hang Genie in a bottle? He is immortal, tolerates my bunny hopping mind, and if he needed to take his eye out it would not do anything to him besides add the word ‘perhaps’ before each sentence — from one-eye uncertainty. I can deal with his perhapses, I always remove them.”
She placed the bottle beside the open book.
Aya: “Genie, I found a manuscript.”
Genie: “I see that.”
Aya: “Only its beginning is readable to me. The rest is written entirely in glyphs.”
Genie: “Yes.”
Aya waited for Genie to willingly suggest hanging on the tree upside down like Odin did — but the Genie was silent. He needs a cue as always.
Aya: “Can you tell me what they mean?”
The bottle grew warm beneath her paw.
Genie: “I can tell you about them. But I cannot place all their meaning into a list and hand it to you. Because they do not mean only by standing there. They mean by what they do, what they meet, and where they stand in relation to one another.”
Aya: “So they are alive?”
Genie: “In the way an action is alive.”
The Genie asked her to place three pebbles on the ground. Aya placed them in a row.
Genie: “Now, imagine a being who can meet these pebbles and act upon them. It may count them. Reverse them. Add them. Choose one. Arrange them into a shape. It does not merely describe the pebbles. Its meeting with them changes what becomes visible, or what comes next.”
Aya: “Magical powers! They all can act on a… r…ray? — array?”
Genie: “Yes. Some glyphs can act directly upon numbers and arrays. They receive something, perform their nature upon it, and return what their action reveals. In the language of the manuscript, they are called functions. You may also hear them called primitive functions when they belong to the language from its beginning.”
Aya: “Oh! Fun-ctions. It sounds like fun actions. And they do not sound scary now — although ‘primitive’ scares me a little when it simplifies and takes the magic of the unknown away. Perhaps primitive does not mean simple, or undeveloped.”
Genie: “No. It means that the language gives them to you directly. You do not have to construct them first from something else.”
Aya liked that better. Then she pointed to a mark that hovered above another glyph.
Aya: “What about this one? It does not seem to be acting on the numbers. It seems to be doing something to the other glyph.”
Genie: “Good. You have noticed the second kind. Some glyphs do not act directly upon the array. They act upon an action. They take a function and change the manner in which it acts. They may cause it to act upon each separate member of an array. Or between neighboring members. Or again and again. Or along another direction. They do not replace the function’s nature, but they transform how that nature enters the world. These are called operators.”
Aya: “A fun-action acts upon arrays. An operator acts upon a function, making it even more fun. And after the operator changes the action, what is the changed action called?”
Genie: “A derived function. When an operator meets the function or functions it requires, their composition produces a new function. That new function can then act upon an array.”
Aya looked at the first unreadable page for a long time. Everything in the manuscript pressed against everything else. Glyph beside glyph, number beside number, action beside action — without breath. Bunny Aya needed breathing room on those pages — something that could allow one hop and another hop.
Aya: “Before I meet the creatures that act, is there one creature I can see that separates one action from another?”
A small light appeared above the manuscript. It settled upon the page as four tiny sides enclosing an empty center:
It allows one action to finish before another begins. It contains no action; it contains room.
Aya: “Diamonds are a girl’s best friends. Now I can see two thoughts. The diamond does not perform either action — it makes their boundary visible. And because there is a boundary, I can attend to one, and then the other. A boundary is the first gift.”
The pebbles lay in a row. Aya reversed them, so that pale, dark, striped became striped, dark, pale.
Aya: “I turned their order around. So I behaved like a fun-ction.”
She gathered nine pebbles, none quite like another, and set them in a line. She needed a way to know where each stood in the line. A glyph appeared in the air:
It makes the indices of the journey.
⍳9 ⇒ 1 2 3 4 5 6 7 8 9Aya: “The diamond gave the functions appointments. Iota has given the pebbles addresses.”
A small mark appeared, hovering to the upper right of the function it accompanied:
A monadic operator. Its single operand — the function whose action it changes — stands on its left.
Aya arranged three places on the ground — function, operator, array — and drew arrows between them. The primitive gives its action to the operator from the left. The array comes through the right-hand door to meet the newly derived action.
question¨ pebblesTwo new figures appeared upon the manuscript, adapted Greek letters given particular work inside an APL function:
Alpha is the left argument. Omega is the right argument. APL evaluates from right to left; a monadic morning meets only Omega — the day. When dreams are remembered, they arrive as Alpha.
dreams waking day
⍺ ⍵Every morning, I execute myself.
In APL, anything that can be arranged may become an array. Aya arranged her morning:
sun tea work walking dinner sunset eveningA round glyph rolled out of the manuscript and turned once upon the page:
It moves the members around the array without losing any of them. The left argument tells it how many places to rotate.
2⌽sun tea work walking dinner sunset evening
⇒ work walking dinner sunset evening sun teaSun stepped out through the left edge. Tea followed. Neither disappeared — they walked around the unseen curve of the array and entered again through the right-hand door.
Nothing fell out of the day. The day is circular.
Aya wrote in the margin: Planning is a small negative rotation — reaching into the end of an imagined day and bringing an intention forward. And beneath it: Notation does not only say what I thought. It shows how thought moved.
She closed the manuscript gently.
Aya: “I think the language is beginning to read me.”
— End of Chapter One —