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Up There: Voyage 5—Tír na nÓg
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Epigraph

‘My father and my mother are
Aengus and Edain, my own name
Niamh, and my country far
Beyond the tumbling of this tide.
…
‘I loved no man, though kings besought,
Until the Danaan poets brought
Rhyme that rhymed upon Oisin’s name,

And now I am dizzy with the thought
Of all that wisdom and the fame
Of battles broken by his hands,
Of stories builded by his words’

—“The Wanderings of Oisín,” William Butler Yeats

Voyage 5—Tír na nÓg

“Wow!” thought John. “It’s getting complicated.” Three new characters, Felipe, Linda, and Anita. With Black Jack, Angie, Seph, and Ananta, that made seven. Eight if he counted Melusine, but John wasn’t sure Melusine would rejoin the story.

John wondered if they needed a bigger boat. Could four people sail in the Sea Devil? He could have the Rodriguez family give or lend them a bigger boat. After all, Felipe’s yacht was wrecked, and the Rodriguez family are rich.

John decided to leave them in the Sea Devil. He had never said exactly how big it was—just that it was small enough for Jack to sail alone. And they had sailed from the Horn to Buenos Aires in it.

From Buenos Aires they sailed north and east.

Anita kept her promise to teach Jack Spanish. Every day Jack studied with her. For the most part these lessons were whatever schoolwork Linda and Felipe had given Anita. Most of Anita’s schoolbooks were in Spanish, and Jack needed Anita’s help with them. In this way he learned about Argentine history. They also read some stories. She was still studying English. Jack helped her with that.

One day Anita asked Jack, “Can I meet Seph and Angie?”

“You know about Seph and Angie?” Jack asked.

“Ananta told me they are your magic spirt helpers.”

“Did she also tell you she has never seen them?”

“Sí, but I don’t understand why. Are they secret?”

“No,” said Jack. “But only I can see and hear them.”

“Why didn’t you tell Mamí and Papí and me about them?”

“Anita, I guess there are some things you don’t tell your father and mother because you’re afraid they might not understand. ¿Verdad?”

Anita nodded slowly.

“Most people have little secrets like that. Well, I have a big secret like that. If I told your padres that I had secret magic spirit friends who they can’t see or hear, what would they think?”

Anita nodded again. “You think they would think you loco. But I think you are wrong, Jack. You are different. You have a friend who is a giant talking sea snake. Mamí and Papí know you are hechicero.”

Jack didn’t know that word. He had bought a Spanish-English dictionary in Buenos Aires. “Hechicero” was Spanish for witch-doctor or sorcerer.

Angie and Seph appeared on Jack’s shoulders with a popping sounds.

“You know, Jack,” said Seph, “we may be able to talk to Anita.”

“Kids are different,” explained Angie.

Angie looked straight at Anita and said, “Anita? ¿Puedes oírme?”

Anita started, then looked right at Angie. “Are they here now?” she asked Jack.

“They are sitting on my shoulders,” Jack said. “Angie here,” pointing to his right shoulder, “and Seph here,” pointing to the left one.

“Did Angie just speak to me?”

“She asked if you could hear her.”

“I kind of did, but I still can’t see them.”

“Angie, Seph, can you become visible to Anita? Whatever you just did to pop into my sight, can you sort of do that for Anita?”

Jack heard another pop from his left shoulder. Anita’s hand went to her mouth. With the other she pointed at Seph and said, “I see something there. She looks like a tiny little ghost girl with red hair. Is that what they look like?”

“That is Seph. But why do you call her a ghost girl?”

“She looks a little wavy to me, as if I was looking at her through water. And I can see through her—I can see your shoulder that she’s sitting on.”

Angie said, “Maybe we’re solid for you because we are your spirits. We’re not Anita’s, so we look ghostly to her.”

“¡Lo oí!” said Anita, excited. “And I see you now, too! You must be Angie!”

“Ananta!” shouted Anita. “Come look!”

Ananta’s head rose from the water. “What am I looking at?”

“Angie and Seph are here, and I can see them!”

“Where?” said Ananta.

“Sitting on Jack’s shoulders,” said Anita.

Ananta peered intently at Jack and his shoulders. “I see nothing.”

As they approached Ireland, Jack asked Ananta, “What place in Ireland do you want to see?”

“There are places in Ireland?” Ananta asked. “How big is it? I thought it was an Island like Henderson.”

“It is an island, but bigger than Henderson. It’s a nation of five million people.”

“Oh…” said Ananta.

“Why did you want to visit Ireland?” Anita asked her.

“Audrey came from there and she said it was a beautiful place. She always wanted to return.”

“Audrey?”

“Audrey was Jack’s mother.”

“You’re from Ireland, Jack?”

“Not me,” said Jack. “My mother and father. I’m American. I’ve never been to Ireland.”

“Do you know where in Ireland Audrey came from?”

“She and my grandfather Jonathan Murphy are from County Antrim in Northern Ireland. I think I remember them speaking of a mountain there named Tievebulliagh.”

They anchored the Devil off the town of Glenariffe. They all climbed Tievebulliagh together: Jack, Anita, Felipe, and Linda. Visible only to Jack and Anita, Angie and Seph flew along. To Jack’s surprise Ananta came along.

“Do you know,” said Jack, “they say there are no snakes in Ireland. Legend has it that St Patrick drove the snakes out of Ireland.”

“Well, there is one now.”

Stretched out on land Ananta’s full, enormous length was visible. Jack thought she might be 40 feet long. Fortunately Tievebulliagh was deserted that day.

It was a stiff hike, about five miles, and the scree near the top made for difficult climbing. But the view from the top was splendid.

On the way up they noticed a sign post for Oisín’s Grave.

Felipe asked Jack, “Have you heard of this Oisín?”

“According to legend, he’s the greatest Irish poet there has ever been. He went away with a fairy queen called Niamh. He was the son of the king Finn Mac Cool,” Jack said. “Also a distant ancestor of mine, according to my mother and grandfather.”

“A king’s blood runs in your veins?” asked Felipe.

“If the legends are true, all the Irish are children of Finn Mac Cool.”

“And a poet’s blood, too? Would you like to visit his grave?”

“You know what?” said Jack. “Let’s do that.”

They climbed down the mountain side, angling northeast towards Oisín’s Grave. It was not a grave such as you would see in a graveyard, but a barrow, an ancient burial site marked by great stones.

They stood there quietly. Just as the sun touched the western horizon, Anita asked, “What is that music?” looking to the west.

“I don’t hear music,” said Jack. Felipe and Linda were equally puzzled.

“I hear it, too,” said Ananta.

“We hear it, too,” said Angie. “It’s a woman’s voice.”

Seph recited,

Turn aside your eyes and ears,
Trail away your robes of sorrow,
You shall have my further years-
You shall walk with me tomorrow.

These lines were from a poem John had read called “Rainy Night.” The poem had nothing to do with the story of Oisín and Niamh, but John thought they were words Niamh might use to call someone to her.

“Can we go there?” begged Anita.

“Where?” asked Linda.

“There, where the song comes from,” she said, pointing to the setting sun.

Ananta, Angie, and Seph wanted to chase the song, too. Jack, who owed Seph and Angie thanks for all the help they had given him, was willing. Felipe and Linda were puzzled by this desire to chase an imaginary song they could not hear. But, as Anita said, they knew that Jack was an hechicero.

Next morning they sailed north around Ireland, then due west for a day.

As the sun set, the song came again. All could hear it now. Perhaps, though Jack, they were close to the singer.

As the sun dove into the ocean, Ananta dove below the waves.

Ten minutes later she surfaced.

“There’s a castle down there!”

Angie and Seph immediately dove in.

“Did you find the singer?” Anita asked.

“I’m not sure. There’s a young woman down there with long blond hair. Or maybe it’s a statue of a young woman. She has her mouth open, like a singer. But she is still. Her mouth doesn’t move. Yet the song seems to come from her.”

“Is she alone?”

“No, there are many more statues.”

“Could it be some sort of mechanism?” Felipe asked. “A sound system playing a recording?”

“It is not that,” said a new voice.

Jack saw Seph and Angie appear just above the waves off the bow of the Devil.

They rose slowly, and the head of a woman with golden hair rose slowly from the water until her feet stood on air just above the waves.

“We brought her,” said Seph.

She spoke again, “I am the singer.”

“I saw you!” Ananta shouted. “How did you sing without moving your lips?”

“Time runs differently in Tír na nÓg,” she answered. “A second there is two of your minutes. If you had watched me for a minute you would have seen me sing.”

“How then did we hear your song?” asked Felipe.

“You perceive me and my song through a glamour,” she answered.

“Glamour? Do you mean an illusion?” said Felipe, glowering at her.

“You can call it that, if you like,” she said. “All things in your mind are illusions of a kind. This one is no more false than this sea and wind you see and feel on your skin.”

She turned to look at Jack.

“You, sir, what is your name? Am I right that you are of the line of the poet Oisín?”

“My mother told me so. I am Jack.”

“Oisín was my husband. He lived with me here in Tír na nÓg for 300 years.”

“Three hundred!” exclaimed Felipe. “How could that be?”

“I have already told you that time runs differently in Tír na nÓg. Tír na nÓg is the Land of Youth.”

She turned to Jack, “Will you come with me to Tír na nÓg?”

“Please forgive me, lady. There are many things I still want to do above the waves.”

She fixed her ocean-gray eyes on his. “Someday you may wish for Tír na nÓg. On that day, come and call my name, Niamh. I will hear.”

She dove beneath the waves.

“Well, they made it to Ireland,” John told Stephanie and Alice, meeting them at the end of August.

“Are they still there?” asked Alice.

“No, they have left,” John answered. “They sailed to Tír na nÓg.”

“Oh! I think I’ve heard of that!”

“My grandparents came here from Ireland. My parents told me the old Irish stories.”

“Where will Jack and Angie and Seph go next?” Stephanie asked.

“Up to you,” John answered.

“Oh, Jack! Travels with you are never dull!” laughed Linda.

Felipe looked unhappy. “There must be an explanation for all this.”

Jack answered, “I can’t explain what just happened.”

“It is sad,” agreed Felipe. “We struggle through the world without understanding. There ought to be an instruction manual!”

“Where will we go now, Jack?” Anita asked.

“I suppose you and your family will want to go home to Buenos Aires,” said Jack.

“There is no hurry!” answered Felipe. “As Linda said, traveling with you is never dull.”

“Perhaps then,” said Jack, “I can invite you to visit my home. It is not far from here.”

“We would like that!” said Linda.

“But I warn you. I am not wealthy. Almost everything I own is right here, on the Devil.”

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Afterword

The cover image is a phase portrait of :

A phase portrait is a visualization of a complex function introduced by Elias Wegert in Visual Complex Functions: An Introduction with Phase Portraits.

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Oisín and Niamh, The Drunken Bodhráns

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Glitch - Brok3n Engines

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Glitch

Epigraph

I’m the error inside
-- “ERROR,” The Warning

Glitch

Dasha’s left hand did a thing. Her calendar lay open on the table in front of her. Her left hand plucked a pencil from the breast pocket of her blouse. Clumsily it made a mark on the left page of the booklet.

It was strange for two reasons. Dasha was right-handed. She was so right-handed that her left hand was almost useless. She never used it except to help out the right in two-handed jobs. Her left was weak and clumsy. She could not write or draw at all with her left hand.

But far stranger than this, Dasha had not intended to move her left hand. Her left hand had just made its mark, without any will of hers. So startled was she that she reached left with her right hand and grabbed it.

It happened again a week later. Then the evening after that. And then again the evening after that. This time her left hand drew a circle. Well, not really a circle, but a thing that might be a circle drawn by a clumsy hand. Call it a loop.

It was always her left hand. Always on the left-hand side of whatever writing surface was in front of her. Always in the evening, when she was alone.

She was kind of freaking out about this. Should she tell someone about it? No, there were enough people who thought she was weird. Besides, who could she trust?

“What, you have no friends?” she asked herself. Well, yes, she did have friends—people at school she sometimes shared a coffee with. But would they still be her friends if they learned that her left hand moved on its own?

She thought of going to a doctor with it, but that was an even scarier idea. Besides, it wasn’t really a problem! Yet. Maybe if it somehow became a problem, she would see a doctor about it.

Thus, the messages from aliens—that was how Dasha thought about it, continued. Almost every evening. Scary though it was and remained, she began to get used to it. “A todo se acostumbra uno, menos a no comer1,” as the song says.

As the days passed, her left hand seemed to gain self-confidence. “Did that make any sense? Could a hand have self-confidence?” What Dasha meant was that it moved more steadily, more directly.

Then, one night, instead of a random doodle, the hand wrote a recognizable “D”. That was followed by a lowercase “a”.

“Holy shit!” she said aloud.

Her left hand wrote “HS!”

“Who are you?” she thought.

Although she had not spoken the words aloud, her left hand wrote, “IN U”

“What the fuck does that mean? You are in me?”

“WORDS” wrote her left hand, then heavily underlined the letters twice.

“WHAT about words?” Dasha asked.

Her left hand drew a big X over “WORDS,” bearing down so heavily that the point of the pencil broke off.

Next morning, in Spanish class, it happened. Her left hand plucked the newly sharpened pencil from her pocket and began writing on the left-hand page.

“No, no, NO!” she thought. “Not now!” She grabbed her left hand with the right. The student sitting next to her—Kristen, was it?—looked at Dasha oddly. Dasha grinned back at her weakly and blushed.

That evening Dasha put a sheet of paper on the table in front of her, put a pencil in her left hand, and said, “Let’s talk.”

“I’m talking to my hand,” she thought.

“Who are you?” she asked.

Laboriously her left hand wrote, “TÚ2”

Surprised, Dasha said, “You speak SPANISH?”

“PALABRAS3” wrote her left hand, laboriously. It then drew a big X though the word.

“Ah!” she said. “I think I understand. Words are hard for you? Just a moment…”

With her right hand she wrote the words “Sí” and “No” on the left-hand side of the paper. “Just point,” she said.

Still holding the pencil, her left hand pointed to “Sí.”

“You speak Spanish?”

“No,” was the response.

“You speak English?”

“No,” once again, but more emphatically.

“You understand Spanish?”

The pencil wavered between “Sí” and “No.”

“You understand Spanish better than English?”

“Sí.”

“¿Quieres que hablo español?4” she asked. “My Spanish is lousy,” she added.

“No.”

“When I asked who you are you answered TÚ.”

“Sí.”

“You are me?”

Again the pencil tip wavered between “Sí” and “No.”

“You’re sort of me and sort of not?” Dasha was puzzled.

Her left hand drew a circle on the paper. It then pointed to the word “TÚ” written earlier and to the circle. It then placed a dot in the circle and pointed to it.

“There’s something inside me?” Dasha asked. “Wait, YOU are in me?”

“Sí.”

“Where? Are you, like, in my head?”

“Sí.”

“What are you?”

“ERROR,” wrote her left hand.

“You’re an error? Some kind of glitch in my brain?”

“Sí”

“Will you hurt me?”

“No”

“Can I trust you?”

“Sí”

“How can I be sure of that?” Dasha asked.

The pencil pointed to the circle with the dot in it. First, it pointed to the dot, then to the circle, then it drew another bigger circle around them both.

“Umm…” said Dasha. “Oh! We are together, is that what you mean?”

“Sí”

“I can trust you not to hurt me because you’re part of me?”

“Sí”

Without speaking aloud, Dasha thought, “If you’re in my head, can you read my thoughts?”

“Sí”

“That’s scary,” Dasha said. “Why can’t I read your thoughts?”

The pencil tapped on “No”, then the crossed-out word “PALABRAS.”

“Do you mean you can’t answer because you don’t have words, or I can’t read your thoughts because you don’t have words?”

“Sí”

“Is there something you want?”

“Sí”

“What?”

“LIBRE” wrote the pencil.

“You want to be free?” Dasha asked?

“Sí”

Dasha was definitely freaked out now. Part of her brain wanted to be free!

Spanish had become the bright spot in Dasha’s academic record. She was an indifferent student—not unintelligent, but uninterested, and her grades reflected that lack of interest. She was bumping along with barely passing grades.

A week ago she had been like that in Spanish, too. But now she was interested. She had recently noticed a billboard advertising some brand of beans, with the slogan, “Para las que sabemos”, and she was struck by the economy of this Spanish phrase. It translated literally as “For those who know,” but the verb, sabemos, was in the first person plural, meaning “we know,” thus including the reader and the writer in a small select club. The pronoun, “las” was feminine, suggesting that the writer and reader were both women. You couldn’t do this in English, not in four words.

This morning she listened in class as their teacher explained the differences between the two past tense forms.

Kirsten, sitting next to her, said, “Aren’t you right-handed?”

“For everything except Spanish.”

“Your left hand is your Spanish hand?”

“Yeah. Weird, isn’t it?”

“Is that a language-learning trick?”

“No, it just happened.”

Of course, Dasha knew what it was. Glitch was learning Spanish. It was Glitch that was fascinated by the linguistic subtleties. Glitch said she wanted to be free, and perhaps this was a sort of freedom she could afford herself.

Dasha didn’t mind. Her academic record could use the boost.

One evening Dasha and Glitch were walking home from the library, when they heard distant music. It was like nothing they had ever heard, minor key, with a strange rhythm. They turned towards it. It really was distant, on the other side of campus, a kilometer from where they had first heard it.

On the Student Union deck students were dancing, in lines. The music was playing from a sound system. Next to it was a whiteboard with a list on it, “Lesnoto,” “Alunelul,” “Sweet Girl,” “Hambo,” and many more. When a dance finished, the woman at the sound system erased the top name on the whiteboard and started the next dance. They weren’t all line dances—Hambo, for instance, was a couple dance.

She told them that this was the Folk Dance Club.

“We dance here every Friday evening at eight. There’s a lesson for beginners at eight.”

Dasha and Glitch had a silent argument about this.

Can’t you feel the music moving your feet? That was Glitch, of course.

No. We don’t know any of these dances. We’ll just look like idiots.

But look, Dasha. There are people behind the lines trying to imitate the people who know what they’re doing. We can’t possibly look any more clueless than they do!

I don’t want to look even half that clueless! If we were really going to do this, we should have shown up for the beginner’s lesson.

Aha! Yes. Next Friday!

So, there they were, the following Friday evening. Reluctantly, Dasha gave in to Glitch’s importunity. But when they left at ten Dasha was a convert. It was exciting just to move. And the music! Dasha had never heard anything so kinetic, so full of the urge to move.

Dasha had never done anything so exciting in her life.

So, they were in. For the next year folk dance became a big part of their life. They danced with the folk dance club every Friday night. And they sought other places to dance. The Dance department had classes, and there were informal classes.

They usually sat out the couple dances. But one Friday evening the Folk Dance Club was teaching polka.

One of the young men there to learn turned to them and asked, “Will you dance with me?”

“We don’t know this dance…”

“We?” he replied, with a twisted grin.

“Sorry, I meant to say I”

“Me neither. Will you learn with me?”

They did. Polka turned out to be easy. It was also a lot of fun. Later that night when a polka played, Carlos—that was his name—asked them to dance with him.

“Gracias. Me diverti5,” said Glitch. Carlos had grown up speaking Spanish at home, so Glitch could chatter to him in Spanish.

He’s nice Glitch said, and Dasha silently agreed.

They fell into the habit of dancing the couple dances with Carlos at Folk Dance Club dances. It was comfortable not to have to hunt for a partner.

Then came the night they learned to waltz. Dasha had always heard of waltz as a boring dance for old couples.

The sensation of waltzing in Carlos’s arms took her quite by surprise.

She could tell that Carlos, too, had got more than he bargained for.

I think Carlos would like more than just to dance with us, thought Dasha.

What do you mean? Glitch asked.

I think he likes us, Dasha thought.

Likes us? How do you mean?

I mean, likes us in a romantic way. You know, love, sex, all that…

Would that be so bad? thought Glitch. Do we want to be in love with Carlos?

No! was Dasha’s startled response. It’s way too soon to even think about that.

Do you think he finds us attractive? Glitch asked.

I suspect the idea entered his mind during that last dance.

Well, Dasha, I don’t know anything about all this. I was born less than a year ago. We’ve read some romantic stories. And seen some movies. Men and women are always falling in love in movies.

In truth, Glitch, Dasha thought, I have no more experience of romance than you. I’ve been scared to date. I have read more stories and seen more movies than you, but they’re all the same.

Glitch thought, Right. Something always goes wrong.

Something has to go wrong so that there’s a story to tell.

Do you think that it’s easier in reality than in the movies?

Honestly, I doubt it. Finding a person to love who loves you back seems to be really complicated. And even when you think you have, it doesn’t always last.

Well, if it’s so much trouble, maybe we should just steer clear, thought Glitch.

Maybe, thought Dasha. But there’s a reason why there are so many stories about it. Falling in love is supposed to be the very best thing there is.

There was a food court in the Student Union building, convenient to the deck where the Folk Dance Club dances were. They fell into the habit of meeting Carlos there at seven Friday for a meal before the dance. Glitch enjoyed chattering with him in Spanish. Dasha just enjoyed being with him.

He was very different from her. Unlike Dasha, Carlos was serious about school. He was majoring in Physics, and most of his classes were in math and physics.

Dasha and Glitch had not yet decided on a major, but they would have to declare soon. Spanish was their best subject, academically, so they were thinking of choosing that.

When they told Carlos so, he said, “¿Cómo no? Hablas español como si fuera tu primera lengua.6”

Glitch thought, “It is my first language,” and because they were speaking Spanish, the thought slipped out, “¡Es mi primera lengua!7”

Carlos looked the question at them.

Dasha was flustered. She tried to excuse the blunder. “Of course, we don’t really mean that. But Spanish came so naturally to us, that it felt like a first language.” Then she realized that she had said, “we” and “us,” and blushed in confusion.

“Oh, God!” said Dasha. “I’m babbling. I sound like an idiot.”

“No,” said Carlos. He reached across the table and, taking her hand in his, said “Nunca eso. Suenas como la Dasha que estoy conociendo, que a veces habla un poquito al azar, pero nunca tonta.8”

“Es cierto, ¿verdad? Realmente eres dos ahí adentro.9”

“What do you mean?” Dasha answered.

“I think you know,” said Carlos “You are a different personality when you speak English and when you speak Spanish. And you know it. You think of yourself as two people. When you’re not being careful, you call yourself we.”

“That makes me sound really weird.”

“I don’t think so,” Carlos continued. “I think each of us is more than one person inside. We are different depending on who we’re with, or what language we’re speaking. What’s different about you is that you know it.”

Dasha and Glitch were silent.

“I’m sorry,” said Carlos. “I didn’t want to make you uncomfortable. I hope you will still dance with me tonight.”

They danced that night, but Dasha and Glitch were subdued. They parted at the end of the dance without speaking.

Dasha and Glitch continued to dance with Carlos every Friday. It is difficult to remain distant with a boy you dance with. At least, it was when that boy was Carlos.

Soon they were as much at ease as they had been before Carlos spoke of Dasha and Glitch’s duality. But they suspected he was not fooled. He let their occasional slips pass without comment. He even had his own nickname for Glitch—he called her Mariquita, Ladybug. And he spoke to Dasha and Mariquita as if to different people.

Mariquita is a kinder name than Glitch, thought Dasha. Glitch, however, continued to think of herself as Glitch. Dasha thought she took a kind of pride in the badass name.

They became each other’s best friends. Dasha and Glitch were Carlos’s best friend, and he was theirs.

Carlos would graduate at the end of this school year. At his graduation ceremony, he introduced them to his parents, with the words, “Te presento a mi amiga Dasha. Ella habla español perfectamente10.”

His father took their hand and made a small sort of mini-bow over it, saying, “Encantado.11”

Glitch responded “Igualmente.12”

Next fall Carlos would enter the Physics PhD program at Princeton University. It was a fantastic opportunity—one of the best physics programs in the world. And Princeton was giving him a full ride, tuition and a living stipend.

“Te echaré de menos,13” Glitch told him.

“¡Y yo a ti, Mariquita!14 I will see you when I return here to visit my parents. And I hope you will visit me in Princeton. Perhaps we can share a dance or two.”

To her surprise, Dasha found herself disturbed by the thought of Carlos going to dances at Princeton and dancing with other women.

And that was the end of that. Carlos did visit Dasha and Glitch twice. Dasha and Glitch never found the energy to visit Princeton. Thus Dasha and Glitch grew apart from Carlos, as friends who live far from each other will. Carlos danced with other girls, and Dasha and Glitch danced with other boys.

It was no tragedy. Or if it was, it was one of those small tragedies that paper the walls and litter the floors of the halls we all walk.

But Dasha and Glitch had something special—a friendship that could never grow distant.

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Afterword

This story was inspired by one line from the song ERROR by The Warning, “I’m the error inside.” I have a fairly detailed story about what’s going on in Dasha’s brain, but decided to leave it unwritten.

The cover is a cycle graph of the cyclic group Z₃, meant here to stand for Dasha, Glitch, and Carlos. The colors are based on a phase portrait of

Where carlos, dasha, and glitch are the centers of the corresponding graph vertexes.

Makedonsko devojče

This was the music I heard one evening at Stanford University Medical Center. I followed the sound about half a mile to Tresidder Memorial Union, where the weekly Folk Dance Club dance was in progress. That part of the story really happened.

Over the next few years I came to know this dance well, It is a Lesnoto, a line dance in 7/8 time, from Macedonia.

Some time ago, when I hit 100 subscribers, I wrote a math-filled article explaining the origin of my substack logo.

I promised another such when I hit 200, and asked what y’all wanted. I got a few answers, all saying you’d be satisfied with another explanation of some other bit of mathematics.

Well, two days ago I reached 200 subscribers, and I’ve decided to write an introduction to the mathematics of symmetry. This area of mathematics is called group theory. It makes sense as a topic here, because for some of my recent stories I’ve used images based on group theory. Here are some of them.

You’ve only seen two of these yet, in

Each of these six pictures is based on a cycle graph, which is a way of visualizing the structure of a group. I am using the word “group” in a technical sense different from its usual English meaning. I will soon define it more precisely.

What is symmetry?

First, though, let’s talk about symmetry. Let’s use this picture as an example1

I think you’ll agree that it is fairly symmetrical, although the symmetry is not perfect.

Mathematicians say that a thing has symmetry if it remains unchanged after being transformed in some way. In this case, the transformation is flipping left for right. Here’s what the image looks like after doing that.

It is not exactly the same, but the cat’s face is very similar after the flipping.

It may seem odd to define a symmetry as something you can do that leaves a thing unchanged, or approximately unchanged. But this definition covers most of the usual ideas of symmetry as well as many other important things

Definition of a group

A group is a collection of all the symmetries that some thing has. Here’s the formal definition (simplified from Abstract Algebra by Dummit and Foote). A group is a set G of elements with a binary operation ★ that follows these rules:

1. (a★b)★c = a★(b★c) for all a, b, c ∈ G. (∈ just means “is in.”)

2. There exists an element e∈G, called the identity, such that for all

   a∈G a★e = e★a = a.

3. For each a∈G there is an element a^-1 called the inverse of a such that
   a★a^-1 = a^-1★a = e.

The operation ★ combines two transformations. For instance, if m is the operation of moving everything in the universe 1 meter to the left and if r is the operation of rotating the universe 30°, then m★r is the operation of rotating the universe 30°, then moving everything 1 meter to the left. It is axiom 1 that allows you to think of ★ as performing two operations in sequence.

Axioms 2 and 3 say that the transformations represented by the group elements are reversible. e is the operation of doing nothing. It is useful to have a group element that means that in the same way as it is useful to have 0 as a number. Axiom 3 says that no matter what you do, you can always get back.

What is the smallest group? A group has to have at least one member, the identity, and axiom 2 tells us that e★e = e. The inverse of e is thus e, so axiom 3 is satisfied. And combining any number of e’s in any order gives you e, so axiom 1 is also satisfied. This is a very boring group. It has a name: the trivial group.

What does a group of two elements look like?

Let’s call the elements e and f. From the rules we know that e★e = e, e★f = f★e = f. The only question remaining is what f★f is. Rule 3 says that f must have an inverse, and the only available choice is f itself. Thus we have f^—1 = f and f★f = e. You may think it’s cheating to reuse f as its own inverse, but there is nothing in the rules against it, and it’s totally kosher.

In fact, this is the symmetry of the cat face. f is the operation of flipping left and right. It is the simplest nontrivial symmetry. It has a name, Z₂, the cyclic group of order 2. (It’s “Z” instead of “C” because the German word for “cycle” is “Zyklus”.)

Every group has a cycle graph. If the group has n elements, than the cycle graph is n dots joined by lines. The pattern depends on the structure of the group. The cycle graph of the trivial group is just a dot—super boring. The cycle graph of the cat face symmetry group is almost as boring.

Permutation groups

Suppose you have a deck of 52 cards, and you shuffle it. There is a sense in which the deck is unchanged when you shuffle it. In this sense the deck is unchanged by shuffling, and we can regard shuffling as a symmetry of a deck of cards.

These shuffling groups were very important in the development of group theory. The shuffling group of deck of 52 cards is named S_52. S₅₂ is a very large group. There is one element for each possible order of the 52 cards in the deck, and the number of those is 52×51×50×…2×1 = 80658175170943878571660636856403766975289505440883277824000000000000.

Suppose we have a deck of just 2 cards, let’s say the ace and two of spades.. Then there are only two possible orders: (ace, two) and (two, ace). The elements of the permutations group S₂ are written {1, 2} and {2, 1}. To apply these transformations to a deck, you simply pick out the cards in the order specified. Thus {1, 2} is the group identity—whatever order of cards you start with, {1, 2} leaves them unchanged. {2, 1} swaps the cards. {2, 1} is self-inverse—if you swap the order of the two cards twice, you end up where you started.

Isomorphism

You might have noticed that S₂ is a lot like the cat symmetry group Z₂. It has two elements: In fact, if we were just to rename the S₂ group elements, {1,2} → e, {2, 1}→f, then we would have Z₂. When this is the case, when we can transform one group into another just by changing names, we say the groups are isomorphic. It is written like this: S₂ ≅ Z₂. Every group with two elements is isomorphic to every other group with two elements. Isomorphic groups have the same cycle graphs.

Mathematicians tend to think of isomorphic groups as being the same. Thus, when we’re not being careful, we might say that there is only one group with two elements. If p is a prime number, then there is only one group with p elements. (Strictly speaking, I should say that every group with p elements is isomorphic to every other group with p elements if p is prime.) Here are the cycle graphs for Z₃, Z₅, Z₇, and Z₁₁.

There are two groups with four elements: Z₂ × Z₂ and Z₄. Here are their cycle graphs.

Symmetry of the icon

Here’s something familiar.

Does this have any symmetry? It does, but it is more complicated than you might expect. The first thing I think of when I look at it is to rotate by 120°. But that doesn’t work:

As you can see, the colors have all changed. We can get back what we started with by shuffling the colors, as follows:

Thus, rotation by 120° followed by a color permutation is a symmetry of this image. In fact, its symmetry group has six elements, corresponding to the six rotations and reflections of the image followed by the six permutations of the three colors. The symmetry group is isomorphic to S₃. Here is its cycle graph

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That’s a good thing!

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Up There: Voyage 4—Rounding the Horn

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Voyage 4—Rounding the Horn

A Sorcerer? John was doubtful. But, then, Jack was doubtful, too. What had the sisters written?

“I would like to adventure with a powerful sorcerer.”

“I am no sorcerer!”

“Jack, a man who has the friendship and aid of invisible spirits is a sorcerer,” said Ananta.

“She kind of has a point, Jack,” Seph said.

Perhaps Jack felt the same way about being a sorcerer that John himself did. So he ought to be able to write it. The problem, though, was that he hadn’t read any sorcerers like that. Sorcerers or Wizards in stories were always powerful. Jack had to be a brand-new sorcerer who was just learning. And he had no one to teach him. He’d have to figure it out on his own.

“I am not a powerful sorcerer, Ananta. I’m just a sailor with gifted friends.”

“What things can you do?”

“Me? I can sail a vessel on the ocean, and I can navigate. Seph and Angie can do more than me, but I think there are some things they can’t do.”

“Like what?” Seph said, pugnaciously.

“Well,” said Jack, “Ananta can’t see or hear you.”

“Who are you talking to?” asked Ananta.

“You see what I mean?” Jack said.

“HE’S TALKING TO ME, YOU GIANT WORM!” shouted Seph at Ananta.

Jack shook his head at Seph’s loud shout, almost in his ear, and looked reproachfully at her. Ananta continued to look quizzically at Jack.

“I’m talking to Angie and Seph,” Jack explained.

“Those are the names of your invisible spirit helpers?” Ananta asked.

“Yes, Angela and Persephone, as I said just a moment ago. Seph just yelled something rude at you.”

“Ooo… you traitor,” Seph hissed.

“Why?” Ananta asked.

“She was annoyed because you ignored her,” explained Angie. Jack repeated this to Ananta.

“I apologize, Lady Persephone,” Ananta said. “I didn’t mean to ignore you. It’s just that I can’t see or hear you.”

Seph preened a little at “Lady Persephone.”

“The four of us can’t hold a conversation, because Ananta can’t see or hear you, Angie and Seph”

“What powers do they have?” asked Ananta.

“They have many powers! They can fly, and they can be as big or as small as they want to be. They say they can be as strong as they need to be. And they can go anywhere on Earth in a second, and come back with news of what they saw. I wonder if they can go to the moon?”

“I don’t know—I’ve never tried,” said Angie.

“They can even play music. They once played a lyre and a flute for me.” Jack went on.

“Can they read minds?” Ananta asked.

“Only yours, Jack,” Angie answered.

“What, you can read my mind?”

“Only if you let us.”

“How do I do that?”

“Well, I don’t exactly know, Jack. You have to think at us. It’s simple enough. Try it,” Angie answered.

Jack looked at Angie and thought in her direction, “Can Seph hear it when I do this?”

Angie answered, “No, I don’t think so.”

“What?” Seph said. “What did he ask?”

“I only asked her if you could hear when I thought at her” Jack answered.

“Of course not,” Seph said. “That wouldn’t make any sense.”

“Well, none of this makes sense to me,” Jack said.

Ananta said, “From the half of that conversation that I could hear, I guess that they can read your mind.”

“So, Ireland. It’s a long way off to the northeast,” Jack said.

“How long a way?” Ananta asked.

“The straight-line distance is about 9000 miles, but we can’t sail straight there. North and South America are in the way.”

“Can we sail around them?” asked Angie.

“Yes, we can sail around South America,” Jack answered. “There are two ways. Up there to our northeast there’s a canal that joins the Pacific Ocean—that’s this ocean right here—” he gestured to the sea around them, “to the Atlantic Ocean. The north Atlantic Ocean is where Ireland is. That’s almost a straight line.”

“Straight sounds good!” Ananta said.

“There’s a problem, though. I don’t think the people who own the canal will let a giant snake through it.”

“That’s not fair,” Ananta said.

“The problem is that people are afraid of giant sea serpents like you. It doesn’t help that, when you meet someone new, you threaten to eat them.”

“Humph,” Ananta grunted, with that strangely human look of anger on her face. “What’s the second way?”

“The second way is to sail south around South America. That’s called ‘rounding the Horn.’ It’s open ocean all the way, so there won’t be anyone to object to sea serpents.”

“How much further is that?” Ananta asked.

“It’s about twice as far, so call it 18,000 miles, a three-month voyage, if all goes well. And it’s a hard passage.”

“What do you mean, ‘hard?’” Seph asked.

“Cape Horn is very far south of here, close to the South Pole, and the weather is cold and rough, and the winds can be dangerous. That won’t bother you and Angie, and I can stand it. Ananta? Do you mind cold weather?”

“Probably,” Ananta said. “But we’re tough beasts—I’m willing to give it a try.”

Now John was stuck. Well, he was a little stuck. It was obvious what had to happen next. They had to sail round the Horn. And of course it had to be exciting. They had to run into troubles, and Seph and Angie’s magic powers had to be used to save them. And it would be good if Ananta helped, too.

But John didn’t know anything about sailing around the Horn. He didn’t really know anything about how a sailboat worked.

He went to the library and asked Mrs Bush if they had a book about rounding the Horn.

Mrs Carter, who had been listening, said “Dana?”

“That would be tough,” answered Mrs Bush. “But John’s a smart young man, so maybe he could.”

“John,” she continued, “we’re thinking about a book named Two Years Before the Mast, by a man called Richard Henry Dana. He was a Harvard student. He had to leave Harvard because of illness, and he became a sailor. Later, when he returned home, he wrote a book about being a sailor.”

“We thought of it because he sailed from Boston to California around the Horn, then back. It’s all real—Dana was a real person, and really did the things he describes.”

“But,” added Mrs Carter, “it’s not easy to read. It’s full of old sailing words. Every sail, every rope, and every stick of wood on those old-sailing ships had a name. Dana doesn’t explain them.”

“That sounds perfect!” John said.

Mrs Bush returned carrying a thick book. “Here it is, John. Rounding the Horn is chapters 31 and 32.”

They were right. It was a very hard book to read, even though he read only two chapters. He might have given up, but he remembered Mrs Bush’s confidence in him, so he stuck with it.

It was exactly what he needed.

They sailed south, then east. Jack rode the southeast trades with the Sea Devil on the port tack. With every mile south, the weather became colder. Also, as they traveled south, they began to run into squalls of cold drenching rain. Angie and Seph were unaffected, but for the flesh-and-blood members of the company, Jack and Ananta, the cold was hard to bear. Jack, like a Viking of old, wore layers of wool.

So did Ananta. It was a surprise to everyone, especially Ananta herself. They’d been sailing south ten days when they began to notice ice in the water. Ananta was unhappy. She shivered and suffered from the cold. Jack was not sure they would be able to continue. But then, the next day, they all noticed that Ananta was covered in fuzz. Her fur grew rapidly, and in another week she was covered in a layer of warm, oily fur.

“Did you know you could do that?” Jack asked her.

“I don’t even know how I’m doing it, Jack”

“Perhaps your body has this reaction to the cold. Because until now you lived your whole life in tropical warmth, you never knew.”

“Are there other snakes that grow fur in the cold?”

“No, only mammals have hair, and snakes are reptiles.”

“Does that mean I’m a mammal?” Ananta asked.

“I don’t think so,” Jack said. “I think it just means you are unique.”

Ananta preened. Jack wasn’t quite sure how she did it, but she somehow gave off an air of self-satisfaction.

“Angie and Seph think the fur makes you look adorable,” Jack teased.

Angie pouted and Seph blew a raspberry at him, but Ananta couldn’t see this.

They had reached the roaring forties, where the wind blew strong from the northwest. Jack was thrown about by the Devil’s violent motion. The weather wasn’t kind. They often ran into squalls of cold drenching rain.

As they drove further south, rain squalls became snow squalls. These were dangerous, because pack ice began to appear. A collision with this ice might break the Sea Devil open. John could steer away from ice if he could see it, but in a snow squall nothing could be seen. Even Seph and Angie were blind.

Ananta saved them. Even in a snow squall, she could range ahead of the Sea Devil and find a path free of ice. Or make one—Ananta was big and strong enough to clear a path through drift ice.

They were now approaching Cape Horn. They saw their first iceberg. Jack had read of icebergs and had seen pictures, but he had never seen a real one. He was astonished at how beautiful it was, a huge deep blue mass, creaking and shifting as if alive.

They sailed past this iceberg on its south side, since the wind was in the northwest and Jack wanted, for safety’s sake, to keep the berg to windward. The wind slackened in the lee of the iceberg—it was that big. They slowed a bit as they passed. All four of them looked in awe at the great blue ice mountain.

“Race you around!” Seph called to Angie.

Angie set off after her. “Oh, lord. She’ll cheat, of course.”

Minutes later, they both popped up in front of Jack. “Jack, there are people on the north side,” Angie told him.

Jack continued on past the iceberg, then turned north until Angie told him they were in sight. In his telescope Jack saw the wreck of a small yacht, not much bigger than the Sea Devil. On the iceberg itself he saw three people huddled around a fire. He tacked up into the wind until he could heave to a safe distance off the iceberg.

The castaways were a family—a father, a mother, and a girl of perhaps ten years. They were signaling and calling out to him.

Leaving Angie and Seph to keep the Devil away from the berg, Jack put his canoe in the ocean. Accompanied by Ananta, he paddled to the iceberg. The wind and water around it were calm today. With Ananta’s help he made his way there safely.

“¡Gracias a Dios por tu venida!” cried the man. This was followed immediately by “¡Qué es eso!” when Ananta’s head popped out of the water

Although he spoke little Spanish, Jack had no difficulty translating “Thank God you came!” and “What is that!”

“That,” he said, “is Ananta. She is a sea serpent, and a friend.”

“Pleased to meet you,” said Ananta, on her best behavior, having taken to heart Jack’s earlier words about threatening to eat people.

The shipwrecked family was astonished to see a giant sea serpent, and even more astonished to hear her speak.

They quickly established that the man, whose name was Felipe Rodriguez, spoke English well enough to get along. His wife Linda and their daughter Anita understood English but spoke only a little.

With Ananta’s help Jack ferried the Rodriguez family out to the Sea Devil, one by one. They were surprised to see the Sea Devil holding station with no sailors aboard.

Their story was quickly told. They were returning home to Buenos Aires after visiting relatives in Chile and had wrecked on the iceberg. They had been there a few days, hopelessly burning the wood of their wrecked boat to keep from freezing.

They sailed east, then, once in the Atlantic Ocean, turned north. Felipe and Linda, who were good sailors. stood watch with Jack and helped to make sail.

While the Rodriguez Family were aboard, Jack didn’t call on Angie and Seph to sail the Devil. Seph complained of boredom. Jack thought Angie was bored, too, though she didn’t complain. As always, they kept Jack informed of what lay ahead. If the Rodriguez Family noticed that Jack always seemed to know what weather to expect, they didn’t seem surprised. After all, this was a man whose friend was a sea serpent!

It was the end of August. John and his parents were packed up ready to go to their home in Lowell, Massachusetts. Dad was handing the keys over to Mr Dupont, when Mr Dupont said, “My daughters would like to meet your son.”

“Of course,” Dad said, and gestured to John.

Two girls got out of Mr Dupont’s car.

“Black Jack O’Toole, I presume?” said one of them. This one had red hair—the other was a blond.

“John, actually. But you can call me Jack, if you want,” said John. “Seph and Angie?”

“I’m Stephanie. This is my twin sister Alice,” continued the redhaired daughter. “We’re not really Seph and Angie, though.”

“How old are you, Jack? We’re eleven,” said Alice.

“Nine,” said John. “I start fourth grade this fall.”

“You write very well!” Alice said.

John thought he detected a hint of “for a fourth-grader” in this compliment, but he made an effort not to be annoyed. After all, it was a compliment, and it made him feel good, especially because he thought they wrote well, too.

He said so. “Thank you! You write well, too.”

“Have they gotten to Ireland?” Stephanie asked.

“Not yet,” John said. “They had some adventures rounding the Horn.”

“Rounding the Horn?” Alice asked.

“Going around the Southern end of South America,” Jack explained. “I think they will visit Buenos Aires on the way north. You’ll see.”

July first came around once again. John leapt up to the attic first thing on arriving, to find…

As they sailed to Buenos Aries, Anita and Ananta formed a bond. They chattered in a bizarre mixture of Spanish and English that only the two of them could easily understand. Jack learned that Ananta could laugh.

As the water grew warmer, Ananta’s hair fell away.

Before it was all gone, she said to Jack, “Jack, cut off a bit of my hair.”

Jack did this, sawing inexpertly with his pocket knife until he had a lock of a few inches of light brown hair. At Ananta’s bidding, he gave it to Anita, who received it solemnly.

“Now, Señor Rodriguez, please cut off a lock of Anita’s hair and give it to Jack—he will hold it for me.”

Rodriguez did this.

“With these locks we will always remember each other.”

“Awe, that’s so sweet!” said Seph, sarcastically.

Rodriguez pulled a glass specimen vial from his pocket and gave it to Anita, saying, “You can keep it in this.”

“You should ask for one of those, too, Jack,” said Angie. Jack did.

By the time they reached Buenos Aires, Ananta was once more as hairless as she had been when Jack and Angie and Seph first met her.

Rodriguez took the helm when they reached the Río de la Plata. Instead of sailing to the Port of Buenos Aires, he took them to a private marina south of the city. From here Jack could see an impressive mansion.

“Welcome to my home!” said Rodriguez.

“This is all yours?” Jack said.

“It belongs to my mother. We are one of the oldest families of Buenos Aires.”

They walked up to the house. There Rodriguez introduced Jack to his mother, a dignified lady in her fifties, Jack judged, and to his brother Juan.

“My fathers before me were merchants—that was always the route to wealth here in Buenos Aires. My older brother is in charge of the family business.”

“And you?” Jack asked.

“I am the wastrel younger brother. I wander the world as I please. I pretend to be a scholar and an explorer, and my mother and brother pretend to respect me.”

“For shame!” said Señora Rodriguez. “Do not believe him, Señor O’Toole. He is an explorador and a professor at the University, and we are very proud of him.”

On hearing the story of the Rodriguez Family’s rescue, his mother and brother were effusive in their gratitude. They could hardly believe what Anita told them of Ananta. They walked down to the marina to meet her in person.

Señora Rodriguez invited Jack to stay with them for as long as he liked.

“What are your plans now, Jack?” asked Felipe.

“Viajan a Ireland,” said Anita, “Me dijo Ananta.”

“Speak English, Anita,” said Felipe. “It is not polite to speak a language Mr O’Toole doesn’t understand.”

“Well, he should learn!” Anita said.

“Señor O’Toole is our guest, Anita.” Linda said.

“They’re going to Ireland. Ananta told me,” said Anita.

“You’re right, Anita,” said Jack. “I should learn Spanish.”

“I will teach you, Mr O’Toole!” said Anita. “I will sail to Ireland with you and Ananta, and I will teach you Spanish as we sail.”

“It is not proper for a young girl like you to travel alone with a man like Señor O’Toole, Anita,” said Señora Rodriguez.

“O’Toole, it’s not safe to sail alone. You should have more hands to sail the Sea Devil,” said Rodriguez.

“Ha!” said Seph. “He’s not wrong, but he’s also not right.”

“What are you saying, Rodriguez?” asked Jack.

“Suppose we, Linda, Anita, and I, sail with you to Ireland?” said Rodriguez. “We will gladly pay for our passage.”

“Well, I’d be happy to have you along,” said Jack. “But if you’re going to work as deckhands and Anita as my Spanish teacher, I would not feel right to accept payment.”

“Jack, can we go shopping?” said Angie. “We want to see the fashions of Buenos Aires.”

They did that. Rodriguez, Linda, and Anita accompanied them. If they were surprised that, along with sailing supplies, Jack purchased women’s clothing, they said nothing to him about it.

The story of Jack O’Toole, Ananta, Angie and Seph, and their friends the Rodriguez family will continue in “Up There: Voyage 5—Tír na nÓg.”

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Afterword

The cover image is a phase portrait of :

A phase portrait is a visualization of a complex function introduced by Elias Wegert in Visual Complex Functions: An Introduction with Phase Portraits.

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Randy Dandy Oh | Assassin’s Creed 4

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Hell’s Coming

Epigraph

Memories of East Texas
And Gilmer, county seat of Upshur
Looking back and asking myself
What the hell’d you let them break your spirit for?
-- “Memories of East Texas,” Michelle Shocked

Hell’s Coming

“Do you remember me, Mr Gilmer?”

Gilmer examined the young woman. He did not approve. Her clothing, though black, was somehow quite the opposite of somber. Too, she was wearing more make-up than a Godly young woman ought to. Who was this painted woman? No one he knew.

“You are mistaken, Miss. We don’t know each other.”

“We do,” she answered. The next words came out with an East Texas twang. “A’ know you from way back, Gilmer. Tin years ago yew tole the town yew knew all about me.”

That voice… He looked again at her face, looking for the teenager it might have been years ago.

“Holly?” He stepped back. “Holly Keating?”

“That was my name.”

“I know this story! You went to college, and you’re back, and now you think you’re better than this town.”

“No, Gilmer—”

“Young lady, you will address me as Reverend Gilmer”

“I will not. You can kisss my asss, Gilmer,” she hissed.

He raised his right hand to slap her face.

“Hold,” she said quietly.

His hand stopped in mid swing as if held by an iron bar.

“Release me, witch!”

She made a gesture. “You may lower your hand. Don’t try that again.”

His right arm relaxed. It was the only part of him that did. He glared at her, tense with fury.

“Think, Gilmer. We’re on a public street. A dozen people can see us. If you beat me in public you hurt yourself more than you hurt me.”

He looked around. She had chosen well where to confront him. There were streets in town where if he slapped an insolent young lady, his neighbors would assume she deserved it. This was not one of them.

But he need not stay to listen to her profane speech. He turned to walk away.

Again the quiet command, “Hold,” stopped him.

How was she doing that?

“How am I doing that?” she read his mind. “You said it yourself, Gilmer. You called me a witch.”

“It is true, then? You have given your body to the evil one?”

“Your mind would go there! An evil man sees himself wherever he looks.”

“I have not given myself to Satan!”

“Have you not? You are so sure that the Father of Lies cannot deceive you? You hide nothing?”

“I hide nothing.”

“You are lying, Gilmer.”

He blinked, and his eyes shifted away from hers.

“Here’s what’s going to happen, Gilmer. Your parishioners now know you have a secret. They don’t know what it is, but they know you are ashamed of something. Watch them in the days and weeks to come. Watch how they fail to meet your eyes. Watch how they doubt you. You will see it!”

“Get thee gone, witch!”

“So nice to catch up with you, Reverend Gilmer! I will be staying in town for a month or so to take care of some old business. I’m sure we will run into each other again!” she said brightly, a devilish smile on her face.

Next Sunday she was there, in the back of the church, wearing that same bright evil grin. After the service, he stood outside the door as usual to greet the departing worshippers. She shook his hand with both of hers and smiled brightly at him, her two dark eyes seeking his. His did not meet hers.

The faces of some of his parishioners looked false to him. He had never noticed that before. He noticed it especially in the older folks. Older men looked at him with a kind of complicity as if they shared a guilty secret. Older women looked as if they wouldn’t trust him farther than they could throw him.

She returned the next Sunday, chatting gaily with other churchgoers after the service. Were they looking his way as they talked? What was she telling them?

On the third Sunday it was unmistakable. “He knows—she knows what I did,” he thought to himself with every conversation. Some were severe, some seemed to offer sympathy, and some—these were the worst—seemed to welcome him into a fraternity of sinners.

And they were deserting him. He thought there were fewer than ever in the pews. Except for her. He could not lose her—she was there each Sunday, sitting in the back, smiling as if sharing a private joke with the devil.

On the fourth Sunday, Reverend Gilmer did not appear for the scheduled service. The Church Board went to the parsonage looking for him, accompanied by that new young lady.

As they entered they noticed fresh ash in the chimney. This was not usual for a summer day in Texas. The remains of a stack of books lay in the ashes. All were now destroyed.

The next room was Rev Gilmer’s bedroom. They found him there, or what was left of him. He was hanging from a rope suspended from a ceiling light fixture. He had jumped from a chair. The medical examiner determined that he had been dead some days.

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Afterword

This story was inspired by two songs, “Hell’s Comin’s With Me,” by Poor Man’s Poision, and “Memories of East Texas,” by Michelle Shocked. (Sadly, because of copyright disputes, “Memories of East Texas” is not available to stream.)

The cover is a cycle graph of the cyclic group Z₁₂, meant here to stand for the twelve people on the streets during the first conversation. The colors are based on a phase portrait of a complex function and have no particular meaning, other than the aesthetic.

Hell’s Comin’ With Me, Poor Man’s Poison

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The King’s Book

Epigraph

The manuscript, which now carries the shelf mark of the Royal Library in Copenhagen where it once was held (as GkS 2635 4to), has over time suffered loss, misreading and botched repair, much like its texts, largely in verse, but also with connecting prose passages, and originally seems to have had 106 pages, rather than the 90 that now survive. Loss of probably eight leaves after folio 32 (the so-called ‘great lacuna’) has left a gap in the narrative of the life of the mighty hero Sigurd the Völsung that can partly be filled by the surviving mid-thirteenth-century Völsunga saga, which, as we shall see, itself bears witness to many of the same poems preserved in the Codex Regius. It seems feasible that the missing leaves offered, among other things, the further wisdom of a valkyrie (one of the supernatural warrior-women who picked the best of the dead warriors for the service of the god Odin) given to her chosen hero, as well as an account of a heroic wooing of a matchless man and a marvellous maid; it is possible that apart from the ending of one damaged poem and the beginning of another, the great lacuna contained the longest single account of Sigurd’s exploits. As such, the self-contained booklet may not so much have been simply lost as removed for private perusal by an over-zealous reader.

—Orchard, Andy. The Elder Edda (Legends from the Ancient North) (pp. 8-9). Penguin Books Ltd. Kindle Edition.

The King’s Book

Hilde met Sigurd outside the Commune refectory. “Where are you headed, Sigurd?” she asked.

“The library. The Royal Library of Nordreich. Always the library”

“Is it true you have a desk of your own there?”

“The desks in the reading room are free for anyone to use.”

“I hear tell you’re there so much, everyone calls it Sigurd’s desk. Anyone looking for you knows to look there.”

“I don’t have a deed to it! Anyone could sit down at what you’re pleased to call my desk, and I would have no right to object.”

“Not me. No women allowed in the library.”

“True, that. I should have said, ‘Any student of the university.’”

“And o’ course women can’t be students.”

“Certainly not!”

“It’s not fair. I can read, too!”

“Yes, Hilde, I know. I taught you,” Sigurd said.

“It was a curse, that was,” she answered. “Books are too expensive for the likes of me, and I’m not allowed in the building where they hide them all.”

When he wasn’t in the library, Sigurd lived in the Regency dormitory. Thanks to the Commune scholarship he had a bed there and two free meals a day. Regency beds and meals were only for students who were “worthy and in need.”

There was no doubt of Sigurd’s need. His mother scraped a living taking in washing—long hard work that earned her just enough to live. His father Carl called himself a soldier. That had been true, until the fight in which he lost his right leg. Now he begged for coins. Any that fell into Carl’s hands were apt to be exchanged for beer.

Carl had named his son after Sigurd the Völsung, the great hero of Norse legend, who forged the sword Grim and with it slew the dragon Fafnir. Sigurd couldn’t help doubting he was what his father had been hoping for when he named him. Sigurd Carlson was a weedy young man, small for his age, and useless in a fight. In the Royal Library, though, he was not useless. He had a gift for languages, and he wrote a fair hand. He secretly named his pen Grim.

Sigurd’s matriculation at the University had gotten him out of his father’s way, and had relieved his mother of the burden of feeding and sheltering him. This was all the help he could give them.

Clothing and shoes were a struggle every winter. When he first entered the University Sigurd had earned the occasional penny by running errands. Now, in his third year, his gift for languages was recognized by the professors. Professor Erik Peterson, who praised Sigurd’s writing, would occasionally throw small translation jobs his way. Most often it was between Old Norse and Latin, but Sigurd was also skilled in Norwegian, Faroese, and Icelandic.

Housed in a small dingy room of the Royal Library was a collection of rare books in Old Norse. Sigurd knew the collection well.

Thus, he was surprised one day to see a small codex he had not seen before. Perhaps it had just been returned. It was barely fifty brown, heavily written parchment leaves. The title, Edda, was written on the first page, and a mark he had seen before, like a pair of intertwined “S”s. This, he knew, was the mark of the Icelandic Bishop Sven Svenson, who had collected manuscripts for King Erik III. Indeed, he found that it was cataloged as The King’s Book.

It was handwritten, and the copyist—presumably long-dead—had been at pains to crowd as much text as he could into a small space. There were frequent abbreviations, which did not make it any easier to read. Sigurd soon realized that it was poetry, although the copyist had ignored the verses to crowd as much into each page as possible.

In fact, he recognized some of them. It was a book of mythology and legend. It began with the familiar stories of the gods and giants. Here were Odin, Thor, Loki, and other gods and giants. In the middle were stories of heroes, including a long story about Sigurd the Völsung.

This naturally caught Sigurd’s attention. It was the most complete version of that legend that Sigurd had ever seen. Remembering how Hilde had upbraided him, he thought of making a gift of it to her. Taking his pen Grim in hand, he sat at his desk and translated the story about Sigurd into Norse, which she could read. For the abbreviations he made his best guesses, and he wrote the verses out in stanza and verse, the way poetry should be written.

“It’s not a real book,” he told her, giving her the pages, “but perhaps these will make your ability to read less of a curse.”

“That was so good,” she told him two days later.

“You read the whole thing already?” he asked her.

“Well, it’s only a few pages,” she answered. “Did you know that my real name is Brynhild? Hilde is just a nickname.”

“I did not know that!” he said. “So, what did you think of Brynhild in the story?”

“Well, it’s very sad, of course,” she answered. “But honestly, for someone who’s supposed to be so very wise, she’s kind of stupid, isn’t she?”

“Is she really?” Sigurd said.

“Well, yeah. She knows all about runes and enchantments. But she never suspects anything when Sigurd puts a sword between himself and her in bed. I mean, what woman wouldn’t say to herself, ‘My man is acting weird?’”

“I guess I was just too focused on how stupid Sigurd is to notice Brynhild’s obtuseness.”

“Well, just so you know, not every Brynhild is as slow as this one.”

“I know it!” Sigurd said. “But, sad to say, every Sigurd is that dumb.”

“Ha!”

The next day, Hilde caught Sigurd. “I want to show you something.”

She pulled the sheets of poetry he had translated for her from her pouch. “Sigurd wakes Brynhild, and she teaches him her wisdom. I wrote the runes she taught him, in order.” She shuffled to the last page, where she had written a series of runes on the blank space left at the end. “It’s a message, Sigurd. See?” She pointed to the page. “I don’t know how to read runes, not like you do, but I can tell they make a message. It’s like a threat or a warning.”

Sigurd looked at the runic message she had transcribed. She was right! There was a secret message embedded in the poems of the King’s Book, in the runes mentioned in the story of Sigurd the Völsung. He was startled, and impressed, ”You’re right! I didn’t see that at all. I need to look at this more carefully.”

Back at the library, Sigurd took The King’s Book off the shelf and carefully transcribed the runes mentioned in the 16 pages of the story of Sigurd. Working from the original instead of the Norse translation he had made for Hilde, it was even clearer. There was a message concealed in the runes. It was, as Hilde had intuited, a threat.

Sigurd himself was no expert in runic messages. He brought The King’s Book and his transcribed runic message to Professor Peterson.

He explained how the message had been found, not naming Hilde for fear of causing her trouble. He added. “This looks dangerous to me. Am I imagining a difficulty where none exists? Or is it true that this is a secret that could destroy us? The King’s Book was written hundreds of years ago—how is it possible that they would have known something that would still be a danger to us?”

The Professor smiled indulgently. But as he read Sigurd’s transcription, his expression turned serious. He asked for The King’s Book, asked Sigurd to point him to the source of the concealed message, then carefully worked through it himself.

“I see no mistake in your work. It is, as you say, remarkable that a scribe of so many years past could have something so dangerous to say to us now. I don’t know how to explain it.”

“What should we do about it?”

“There is only one answer. We must lay it before the man who knows all our secrets. Only he can judge if there is a real danger.”

“The man who knows all our secrets,” said Sigurd, puzzled. “The King?”

“Just so.”

“Will he listen? Will he understand?”

“Sigurd, those are dangerous but very good questions. We have had kings for whom the answers would have been ‘No’ and ‘No.’ But we are fortunate in the current incumbent. He is both wise, and a scholar. You will have no difficulty making him understand.”

“Me! I can’t talk to the King!”

“You can and must. You discovered this hidden message—”

“—I did not. It was Hilde—” thought Sigurd.

“—and you are the only person who can explain it.”

“But the King will not talk to me!” Sigurd objected.

“I believe he will. He has little care for status and great respect for intelligence. He and I are nodding acquaintances. He will listen if I tell him you have something important to show him.”

And so it was that Sigurd entered the King’s private audience chamber accompanied by Professor Peterson. He was wearing a suit of new clothes purchased for him by Peterson. If nothing else, he had gained solid boots and a warm new overcoat from this adventure.

The King said, “The Professor tells me you have something to show me?” He was not kingly or overbearing. He was just a man asking a question.

Sigurd opened The King’s Book, which he had brought with him, to the story of Sigurd the Völsung. Opening it to the waking of the Valkyrie, Sigurd pointed to the rune spells mentioned. He showed the king the message he had copied out on a separate sheet of paper. “This is the message hidden in The King’s Book.”

As Professor Pederson had predicted, the King was quick to understand. He immediately grasped how the message had been hidden. He also understood the significance of the runic message Sigurd had copied out. He found it, indeed, far more alarming than Sigurd had expected.

“This must be destroyed!” the King said.

“Sire, The King’s Book is one of the treasures of the realm,” Professor Pederson said. “Its outright destruction would draw notice.”

“How can that matter, if it be destroyed?” the King replied. “The message will be nowhere to be found.”

“Sire, we cannot be certain of that. Any visitor to the library might have copied it. If the book vanishes, the Library will entreat scholars to reconstruct it from personal copies.”

“What then do you suggest, Pederson?”

“Since this discovery, Sigurd and I have combed the Book carefully for other secrets. The hidden message is, we believe, confined to these 8 sheets on which the story of Sigurd the Völsung is recorded. We suggest returning the Book to the library without those eight sheets.”

“Aha! You believe no one will notice, or that, by the time anyone does, any copies will have been lost?”

“Indeed. The secret has already lain hidden for centuries.”

Thus it was that later, Sigurd, carefully excised the stitches holding the eight offending leaves in the Codex with a razor and slid them out. Unless you knew what to look for, the change was barely noticeable.

Sigurd did, however, take one liberty. To him it seemed almost sacrilegious to destroy the pages. Instead, he gave them to Hilde as her very own book.

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Afterword

The story was suggested by the loss of 16 pages (eight leaves) of The Codex Regius, one of our two earliest sources of Norse legend, also known as The Elder Edda or The Poetic Edda. This gap is called the Great Lacuna, and is still unexplained. Although The Codex Regius is now held in the Árni Magnússon Institute for Icelandic Studies in Reykjavík, Iceland, it probably resided in the Royal Library of Copenhagen when the pages were lost.

In writing this fictional explanation of how the loss occurred, I used Guy Gavriel Kay’s “quarter turn towards fantasy” trick. Nordreich is, of course, loosely based on Denmark. It is not, however, set in any specific year, nor is the King of the story intended as any specific Christian or Frederick who ruled Denmark or the United Kingdoms of Denmark-Norway during the time when the Royal Library held The Codex Regius.

The cover is a cycle graph of the quaternion group Q₈, meant here to stand for the eight leaves of the Great Lacuna. The colors are based on a phase portrait of the identity function, f(z)=z and have no particular meaning, other than the aesthetic.

Rolandskvadet - Epic Music of Norway

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Futures 9: Epilog

June 6, 2043

Molly glanced at her watch. It was four o’clock, on the eve of her and Elle’s birthday. Although it was Saturday, the whole family: she, Elle, Al, and Anne were gathered in Anne’s office, the Director’s Office at the Department of Temporal Affairs. Night, too, was present in the form of a hacked smart speaker.

“Why we here, Anne?” asked Molly. “Aren’t we goin’ to your place to party?”

“I honestly don’t know,” Anne said. “Night asked me to gather you all here at four.”

“Well, Night?” Alberto said. “What’s up?”

“DoTA has laid on a surprise party for the five of us,” Night answered.

“How come I don’t know about this?” Anne asked. “I was under the impression that I was the Director of DoTA!”

“You are now. But you will not always be,” Night answered. “it’s a 200^th birthday party for Elle and Molly.”

“Hey Night, we’re only 35. We’ll be 36 tomorrow,” Molly pointed out.

At her remark, a time-gate materialized at the office door.

“Ooo…” said Elle. “Which 200^th birthday are we going to?”

“You were born June 7, 1907,” answered Night. “We’re headed for June 6, 2107.”

“And what about you, Night? DoTA would be nothing without you. Surely you will celebrate with us. Is there a time-gate you can go through?” Anne asked.

“Not necessary,” Night answered.

“Whenever you are, Night is always there,” Al added.

The time-gate went black. Al took Anne’s hand and led her through. Molly led Elle through.

They walked out of the time-gate onto a dais. At the front of the dais there were four large chairs. A distinguished-looking woman guided the four of them to these almost-thrones. Behind them, there were two rows of simpler chairs, already occupied. Molly didn’t recognize any of the people seated there. She quickly calculated that 64 years had passed between 2043 and 2107. She scanned the older faces looking for someone she might have known in their youth, but she recognized none. Below the dais the floor of the auditorium was filled with cheap chairs. These were full of spectators. Molly could not make out any of their faces—the audience lights were dim.

The woman who had guided them to their seats walked to the front. She raised her hands to greet the audience. Her voice, amplified, rang out. As she spoke, a 3D hologram of Anne, Al, Elle, Molly, and the globe appeared above the dais, where the audience could see.

Molly was impressed. There was no such 3D projection in her times.

The woman said, “I, Ana Rodriguez, Director of the Department of Temporal Affairs welcome you all to this 200^th birthday celebration. In its early years, before it had a name, the Department of Temporal Affairs was a family affair. One day less than two hundred years ago, on June 7, 1907, Elliotte Gardiner was born, the daughter of Anne Gardiner and Alberto Gonzalez. On the same day in Virginia, Molly Johnson was born.”

This Molly reflected, was not true. She had not been born on June 7, nor was she named Molly. They all knew that, of course, or at least guessed. But Molly herself barely remembered her birth name or her actual birth date. On August 15, 1921 she had been reborn into Al and Elle’s family as Molly Johnson, age 14. Until the day she died, she would be Molly Johnson, born June 7, 1907.

The Boss

A portrait hologram of Anne appeared before the dais, with the words “The Boss” in large block letters above her.

“The Department of Temporal Affairs was officially established in 2014. Even before that, Anne Gardiner, who would become its first Director, played the leading role in its first operation. The goal of this first operation was the development of time-travel as a practical technology. The operation began with the birth of the girl who would become the physicist to work it out. Using a time-gate sent from the future, the newly pregnant Anne traveled back to 1906. Seven months later, she gave birth to her daughter Elliotte, the future theorist of time-travel. Anne soon returned to 2014, to the very day from which she had left. No one in 2014 knew of her absence or that she had a daughter.

“With the help of time-travelers from the future, Anne set about the job of establishing the Department of Temporal Affairs. For the next ten years they worked to establish DoTA, and to set it in operation, so that it would be ready when Elliotte and Alberto returned from 1925.”

This story was new to Molly. When Anne traveled back to 1906, she had been married to Al. No one knew that she had left, but Al vanished for 11 years, from 2014 to 2025. She looked at Anne, sitting behind her with her usual ice-queen composure. Molly knew she’d never dare to ask her about it.

The Engineer

Beside the portrait of Anne a hologram of Al appeared. The letters above his head read “The Engineer.”

“Alberto Gonzalez was the most active agent in the operation to develop time travel. Alberto is known to most of us as Al, or later as Tío.

“Al became DoTA’s first temporal engineer. With Night’s aid, he developed the brain implants that allow a temporal engineer to fork. In this way an engineer, trying for an outcome, can fork at an early point. If he fails to achieve the desired outcome, he can give up and go back to fork, over and over until successful.

“Brain implant!” thought Molly. She knew Al had special training to become a temporal engineer, but hadn’t known about an implant.

“The most important such operation in the history of DoTA was the first one. When Anne returned to the twenty-first century, Al stayed behind as a single father. It was given out that Anne had died in childbirth—not a rare outcome in 1907. Al raised Elle to the age of one day less than eighteen. He was not just her father, but her teacher. He taught her mathematics and physics more advanced than any known to the early twentieth century.

“Al and Elle also welcomed a runaway girl into their family, Molly Johnson.”

Molly wondered how many times Al had welcomed her. Did he and Elle accept her the first time they met? Or did it take Al several forks to make Molly part of Elle’s story? Maybe she would ask him. But Al never talked about the failed forks. He probably wouldn’t tell her.

Ancient Magic

A hologram of the globe appeared in front of the images of Anne and Al. The letters above it read, “Ancient Magic.”

“Anne and Al met when they were graduate students, Anne studying history and Al studying geophysics. On a day in 2012—they were 22 years old at the time, they made the most surprising discovery of two lives filled with momentous surprises. They discovered an entity that could affect the magnetism of bits of iron under high pressure. Alberto developed a simple method of communication based on this discovery. To their astonishment, the entity was intelligent and could converse with them. Al proposed the name ‘Night,’ from a poem by Jorge Luis Borges, for this magnetic intelligence. The entity that we all know as Night acceded to his proposal.

“Night is a giant natural magnetic supercomputer made of the iron at the center of the solid core of the Earth. It is the largest known brain, approximately 600 km in diameter. It is also, at an age of about 500 million years, the oldest known brain. Night woke into being when the core cooled enough to crystallize in the form capable of computation.

“Night is now a central component of time travel, being the only computer powerful enough for the computations necessary to find stable timelines.”

Molly knew all this. Night was an open book, and It was Molly and Elle’s constant companion. Besides, Molly had even been involved in introducing Night to Al.

The Physicist

The next hologram appeared beside that of Al. It showed Elle, and the letters above it read “The Physicist.”

“On their 18^th birthday in 1907 Elliotte Gardiner and Molly Johnson stepped through the time-gate to 2015. Elle entered the physics program at the University of Texas in Austin, which she completed Summa Cum Laude in three years. From there she moved to the physics graduate program at the University of Waterloo and the Perimeter Institute for Theoretical Physics, where she joined the Gravitational Physics Program and worked with Jensen Yan. Her goal from the start was to develop a theory of time travel. She had a winning advantage over other physicists, as she told DoTA staff at the time—she knew beyond doubt that there was a solution. It was a thing no other physicist knew.

“The breakthrough came in December 2029. Following up on a crucial insight from Molly, Elle guessed that causal loops would be unstable. On this basis she worked out the first version of what we now call the Johnson-Gardiner stability criterion, named after Molly and Elle. From J-G stability she and Night worked out a theory of time travel. Alberto and Night together used this theory to design the time-gates that we still use.”

Molly looked up at Elle sitting next to her. Molly knew she herself didn’t really deserve credit. She had only said that maybe a timeline was like a guitar string. But that had triggered something in Elle, who really was a genius.

By now Molly was feeling distinctly uncomfortable. She was not a genius like Elle or Al, not a distinguished leader like Anne, and she sure wasn’t an all-knowing supercomputer like Night. She didn’t belong here. She hoped that the speechifying was at an end, that they would not embarrass her by comparing her to Elle’s family.

The Heart

But, alas—the holograms of Al and Elle moved slightly apart, and Molly’s torso and head appeared between them. The letters above her head read “The Heart.” Ooof—what did that mean?

Director Rodriguez continued, “Molly Johnson was what no one expected. She wasn’t in anyone’s plans. She was a runaway, a lost girl, a hobo who hopped a train north and rode into Elmwood one afternoon. She and Elliotte met unexpectedly outside the school where Alberto taught music. Elle and Molly instantly became best friends. Al and Elle took Molly into their home. By a strange coincidence Molly and Elle had been born on the same day in 1907.”

“Ha!” thought Molly.

“Al took on the job of giving her an education. He discovered a quick intelligence and an eager curiosity. He also found that she was a musical genius, whose gifts as a musician he claimed exceeded his. This may be modesty…”

Molly elbowed Al and whispered, “Modesty?”

He whispered back, “Simple truth!”

Rodrguez continued, “Molly went through the books in the Elmwood library and those in Al’s private library. Recognizing that some of Al’s books should not exist yet, she knew already when 1925 came around that something strange was up. By some strange oversight that we will assuredly never understand, Al failed to properly secure the time gate through which he and Elle stepped forward into 2025. Molly worked out how to authenticate herself and followed them through the gate. She has never explained how she did that.”

“‘Some strange oversight that we will never understand…’” Molly whispered to Al. He directed an innocent look her way.

“Once through the gate, Molly continued surprising everyone. She came out behind Elle. Anne, who had not previously known of Molly’s existence, met her for the first time when she stepped out of the gate.”

“And wasn’t real happy to see me, either…” thought Molly.

“Molly continued to supply surprises. She undertook the first real mission with Al and Night’s newly invented time-gate, traveling back to 2012 to present a young Al with undeniable evidence of time-travel. On her way back she surprised everyone, herself included, by stepping out into an alternative timeline.

“After that Molly became DoTA’s most active time-traveler. She has been through the time-gate more times than any other DoTA agent. It is now 2107, and still no one has exceeded or equaled Molly’s mission total. In addition, she has personally trained most of our agents.”

Calls of “Yay, Molly!” and “¡Brava!” “¡Corazón!” arose from the auditorium.

Rodriguez called, “Let’s show DoTA’s first family how much we appreciate them.”

She and the other DoTA dignitaries on the stage stood up and began to applaud. The audience surged to their feet and applauded wildly.

“Clearly, these people don’t get enough chances to have fun,” Molly thought.

“It is a family tradition to dance on the eve of Molly and Elle’s birthday!” Rodriguez called.

The chairs in the auditorium disappeared, revealing a beautiful hardwood floor, perfect for dancing.

“Neat trick!” said Molly.

“Perhaps that standing ovation we got was not entirely spontaneous,” said Al.

Taking Elle’s hand, Molly stepped down to the dance floor. Al and Anne followed suit. The notes of “Poor Boy’s Delight” played, and they danced.

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Afterword

The cover image is a phase portrait of

A phase portrait is a visualization of a complex function introduced by Elias Wegert in Visual Complex Functions: An Introduction with Phase Portraits.

The portrait is rotated 30° clockwise. A semi-transparent image of Night (see Futures 4: Night) is superimposed.

This concludes the novella Night for now. There may yet be related stories to come.

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“Poor Boy’s Delight,” The Infamous Stringdusters

My substack icon

I write this article to celebrate reaching 100 subscribers for the first time. One or two of you have asked, and probably a few more have wondered, what the black, orange, and yellow propeller-like image I use for my substack icon is. I will explain that here. But be warned—there will be math. LOTS of math. Even some math-major math.

Cube roots of 1

The picture above shows what happens when you use a method invented by Isaac Newton and Joseph Raphson to find the numerical value of cube roots of 1. A cube root of 1 is a number z such that

There are exactly three values of z for which that equation is true. They are1

Here i is the square root of -1. That is, i is defined as a number such that,

Numbers like the second and third cube roots of 1 shown above are called complex numbers. A complex number has an imaginary part—this is the part that is multiplied by i, and a real part, the part not multiplied by i. So, for the second cube root, the real part is -1/2 and the imaginary part is √3/2. A number whose real part is 0 is commonly called an imaginary number.

I emphasize that the words “real” and “imaginary” as used in mathematical analysis have nothing to do with the ordinary English meanings of those words. Imaginary numbers are no less real (in the ordinary English sense of the word) than real numbers. The real/imaginary nomenclature is purely historical. We get it from the first people to use imaginary numbers. They were uncomfortable with this new type of number (just as some of you readers are now).

Modern mathematicians (and physicists and engineers) are comfortable with complex numbers. We tend to think of them as points on the complex plane, like this.

The picture above shows six random complex numbers: -0.5+0.2i, 0, i, 0.5+0.1i, 0.7-0.2i, and 1 on the complex plane. Now I’ll show you the three cube roots of 1 on the same kind of plot.

I’ve colored the three roots black, yellow, and orange. I also plotted a circle of radius 1 centered at 0 (the unit circle), so that you can see that all three roots are on the unit circle and are equally spaced.

Newton’s method

You now know what the cube roots of 1 are. To explain my logo, I need to tell you about Newton’s Method. Newton’s Method is an approach to a common problem in mathematics. Most mathematical problems can’t be solved exactly. Newton’s Method helps to find an approximate numerical solution.

Suppose you have some equation in which z is the only variable, and you want to find a value of z that makes the equation true. Newton’s Method is a way of finding a number that comes very close to solving your equation. The first step is to make an “initial guess,” that is, to pick a value of z that is close to a solution. Newton’s Method is a recipe for calculating another value of z that is closer to the solution. It uses calculus, but only very simple calculus—every freshman calculus student learns Newton’s Method. Here’s what it looks like for the equation z³=1.

Now you have a new guess. If everything is working well, you can plug that into the Newton formula again and get a better guess. You keep doing this until you have a good enough numerical value of z for whatever purpose you have in mind. In practice, this works shockingly well if the initial guess is good.

But that’s the problem, of course. How do you come up with an initial guess? How much does it matter?

We don’t need Newton’s Method to find cube roots—that’s a problem that can be solved exactly. But that means we can use it to answer the question about how much initial guesses matter. Let’s try to find a cube root of 1 starting with the guess z=-0.5+0.2i. (I chose that value as a random complex number that isn’t close to any of the cube roots of 1.)

The step takes us to 0.499+0.926i. This doesn’t look like an improvement. If you were hoping it would simply move towards the closest cube root, you are now disappointed. But let’s keep going. Here’s where we end up after two steps:

That doesn’t look promising. But let’s keep going.

After 5 steps we are close to a cube root of 1. If we keep going, we just get closer to the orange root. The orange root is not the closest one to where we started. Since the root we ended up at is orange. I’m going to color all the initial guesses that lead there orange. Here’s the same figure again, but superimposed on the color graphic.

You will see that we started out in a small orange patch, and that all the steps are from orange to orange. I call this the “basin” of the orange cube root. If you think of Newton’s method as a system of rivers flowing over the complex plane, then the orange regions are all the places that eventually drain to the orange root. The yellow and black regions are the basins of the other cube roots.

It works for almost any initial guess—Newton’s Method will take you a cube root. (There are a few points on the complex plane for which Newton’s Method fails to find a cube root. When I say “almost any” I mean that the area of the set of all points for which Newton’s Method fails is zero.)

100 subscribers!

My substack has now reached 100 subscribers for the first time. Of course these milestones are meaningless. But on some of the other creator platforms I patronize it is customary to post some sort of reward for ones subscribers on reaching a milestone.

That’s a good thing!

This is your 100-subscriber reward. I confess that it looks more like something I like than something y’all might like. Therefore I’m asking advice. What would you like me to do if and when I reach 200 subscribers?

Answer in the comments, please!

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Voyage 3—Ananta

John got a little mad. He guessed that the extra bits were written by the two Dupont girls. But it was his story! They were putting words in his mouth! They had Black Jack saying, “You’re completely right! Girls are better and more important than boys in every possible way.” Was that something that John would ever say?

Well, he couldn’t let himself get mad. If he lost his temper, he might write something dumb. Also, he thought the girls were a little older than him. They didn’t write like the girls in his class at school. They seemed smarter, and they wrote longer sentences with bigger words. He wasn’t sure he was as good at writing as them.

Also, he realized something in a flash. The girls hadn’t put words in his mouth. They put words in Black Jack’s mouth. John had been thinking of Jack as himself, John O’Toole. But he wasn’t! Jack was just a made-up person in this story he was writing. No, in this story that they were writing together. Jack and John were different people.

It was obvious when you thought of it, but he never really had before. The people in a story could say things that the author of the story wouldn’t say.

Thinking of that, he looked again at those words they had written. “You’re completely right! Girls are better and more important than boys in every possible way.” They were too strong. In fact, John realized that Jack, with these words, was being sarcastic. He was making fun of Seph and Angie. That made him feel better. The girls’ version of Jack was funnier and smarter than John’s Jack.

And he thought the girls were making fun of Angie and Seph, too! The part with the “stony looks” was actually kind of funny, when he read it again.

John wondered if he could write like that. Could he make fun of Black Jack, too?

He didn’t think so. He wasn’t as smart as these girls. Yet—maybe some day. But he no longer felt angry at them.

“Where are we going, Jack?” asked Angie.

Jack had a chart locker in his cabin and a cabinet of books. He unlocked the cabinet and took out his copy of Bowditch’s American Practical Navigator. He opened it up to the big map of sailing routes in the back. He spread it out on top of the chart locker.[i]

“Henderson Island. That’s where my mother left Ananta. It’s probably too small to appear on this chart, but from the longitude and latitude it’s about here,” he said, pointing to a spot in the South Pacific between Australia and South America, but closer to South America. “It might be one of the Pitcairn Islands.”

“Is that a long way away?” asked Angie.

Jack pointed to a location in the Indian Ocean, a little northeast of Madagascar. “We’re about here.”

“Well, that doesn’t look very far,” Seph said. She alighted on the map and stretched out her arms. “See, I can almost reach from here to where we’re going, all by myself.”

“Have you ever used a map, Seph?” Jack asked.

“No,” she said.

“Neither have I,” said Angie. “See, we can just go anywhere we want with a thought, so we don’t need those things you mentioned, ‘latitude and longitude.’”

“Well, it’s harder for us humans,” Jack explained. “If we want to go from one place to another, we have to go through everything inbetween.”

“And this picture you’re showing us?” Angie asked.

“It shows the oceans and lands of the Earth,” He placed his finger on the chart near their current position, then moved it south and east, then east past Australia, then north and east up to where the Pitcairn Islands were marked. “That’s what we have to sail.”

“So we just follow those blue arrows?” Seph said. “That doesn’t look hard.”

“Well, here’s the thing about maps. They are much smaller than the Earth. That means the Earth is much bigger than the map.”

“How much bigger?” Angie asked suspiciously.

“Well, it’s about 17,000 miles from here to where Ananta is.”

“Is that a lot?” she continued.

“On a good day, if the winds are right and we sail all day and all night, we can travel 200 miles.”

“So?”

“It’ll take us three months to get there. At least.”

“THREE MONTHS!!” Seph and Angie shouted together.

“Or longer.”

“Can’t you speed it up?” Angie asked.

“Well, maybe if you…” Jack said, hesitantly.

“WHAT?” Seph asked. “Maybe if we WHAT?”

“Here’s the question,” Jack said. “Are you real, or are you just in my head?”

“What kind of question is that?” Seph asked. “Of course we’re real!”

“Well, what I mean is,” said Jack, “Can you help me sail the Sea Devil?”

“We don’t know anything about sailing a ship,” Angie said.

“I know that,” Jack said. “That’s not the problem. I can teach you.”

“Well, then, what’s the problem?” Seph asked.

“Can you push and pull on things? Can you haul on a rope? Can you turn the wheel? Or do your bodies just go through solid things like a ghosts?”

“Jack, I think you know less about ghosts than we know about sailing ships,” Angie answered.

“You’re right about that,” Jack admitted. “Show me. Can you pick up this book?”

Angie and Seph flew to the left and right sides of Jack’s open copy of Bowditch and lifted it off the top of the chart locker.

“Why are you so small?” Jack asked. “Can you make yourselves bigger?”

Setting Bowditch down on the chart locker, Angie and Seph flew down until they were standing on the floor. Then they grew bigger until they were a head taller than Jack.

His eyes popping with surprise, Jack asked, “How big can you make yourselves?”

“As big as we want,” Angie said.

“But there’s no room in this cabin to get bigger,” Seph added.

“Are you strong?” Jack asked.

“We can be as strong as we need to be.”

“Could you lift the Sea Devil out of the water?”

“We’re strong enough,” Angie answered.

“The problem is, there’s nothing to stand on here.” added Seph. “The only thing under the ship is water.”

“And it might break,” added Angie.

“How do you want us to help, Jack?”

“Well, I have to sleep every night, or most nights. When I sleep I heave to—stop the ship—so I can rest. But if you can sail the ship while I sleep, then we can keep going all day and all night.”

“We can do that!” Angie said. “We never sleep.”

“And—you can help by keeping a lookout ahead. You can warn me if there’s a storm ahead, and perhaps help me avoid it.”

“That’s easy,” Seph said.

#

They sailed onward. Jack was surprised how much he enjoyed it. Seph and Angie were quick and strong and didn’t even need to climb—they could just fly when they needed to go aloft.

They quickly learned to sail. At first Jack stood watch with them. But he soon felt it was safe to nap for an hour and leave the sailing to them. He told them they should wake him immediately if anything unexpected happened.

Angie and Seph were new to sailing and didn’t know what to expect. For them every little thing was unexpected. For a week, Jack didn’t sleep much. The second week was better—he was getting enough sleep, even if they woke him several times each night.

And he found, to his surprise, that he enjoyed their company. They chattered and chattered, but mostly to each other. They were lively. Often they were funny, without necessarily meaning to be. Sometimes they joined him when he took a swim in the ocean.

He taught them to play chess. They were very good. Seph always played black and Angie white. Seph was tricky. Angie was a solid careful player. She seldom made mistakes. Seph made lots of mistakes. When Seph and Angie played each other, Angie usually won. Seph always pouted when she lost, and explained how, if things had been just a little different, she would have won. Angie didn’t argue or gloat. Jack usually lost, no matter which of them he played, but it was very satisfying when he managed to win.

Sometimes they would fish for him. They didn’t need any fishing tackle or lines. One of them would just dive into the ocean, then come up a few minutes later with a convenient-sized fish. This gave Jack a little more variety than his stores would have allowed, and helped his stores to last longer. Sometimes Angie and Seph ate with him. They didn’t need to eat. They did it to keep him company.

They stopped for provisions at port cities in Australia and New Zealand. Jack sold one of the pearls from his grandfather’s chest, so they had money for shopping.

Angie and Seph couldn’t shop by themselves. Only Jack could see and hear them. But they sometimes went with him. They asked him to buy things they saw, often items of clothing. They liked to look stylish. Seph and Angie had opposite ideas of what that meant. Anything they wore fit perfectly. What’s more, their clothes changed size with them when they changed. Jack thought they weren’t really wearing the clothing, but the idea of the clothing.

Past New Zealand they headed Northeast. Jack had bought a detailed chart of the Pitcairn Islands in Wellington.

A week later Jack shot the sun. When he charted their position, he saw that they would arrive at Henderson in days.

He asked Angie and Seph to scout it out, and especially to look for Ananta.

They didn’t come back for hours. When they did, Angie looked glum and Seph looked disgusted.

“Did you find her?”

“No. That blasted island is seven miles long. We went around it twice, one of us underwater and one above, and we didn’t see a serpent,” Seph said.

“We’re sorry Jack. We don’t know what to do. She’s younger than Melusine and probably smaller. And of course it’s possible she’s gone somewhere else.”

John said, “Was there anyone else there I could ask?”

“No,” said Angie. “It’s uninhabited.”

Jack had an idea. “Let’s keep on,” he said aloud to Seph and Angie. “Can’t hurt to take a look.”

“Waste of time,” grumped Seph.

But they sailed on. There was no harbor or bay. There were sandy beaches where Jack could land his canoe. Jack anchored off one of them. Then he got his six-shooter and a megaphone he used for hailing other ships.

He fired the gun into the air. Then, using the megaphone, he shouted, “Are you here, Ananta? My name is Jack O’Toole. Audrey Murphy was my mother. She carried you here years ago.”

Nothing happened. Jack got ready to pull up the anchor.

But Angie flew up, up, up, until she was high in the air above the Devil. From there she could see the whole of Henderson.

Seph told Jack, “Angie says to wait here. She sees something coming.”

Soon Jack and Seph saw it, too. A wake was approaching from the north. Angie came back down

“How did you know that would work, when we couldn’t find her?” Seph asked Jack.

“I didn’t,” said Jack. “But I remembered how Melusine came out to attack me when I approached Snake Island. I thought that might mean that sea serpents are territorial. Even if we couldn’t find Ananta, I thought Ananta might find us.”

A snake’s head rose from the water until it was level with Jack’s eyes. She was indeed smaller than Melusine, the head only three feet long. But she was still a really big snake.

“Who are you talking to?” she asked. “Why are you here? Why should I not eat you all up, you and whoever you’re talking to?”

#

At this point John felt a little stuck. All his ideas for continuing the story were too much like what he had already written.

Then he had a thought. The most surprising new idea in the story so far had been the appearance of Seph and Angie. That had been the sisters’ idea He added a note at the bottom of the page.

Over to you, sisters…

Another year passed. John was now nine. He would be starting fourth grade in the fall. John leapt up to the attic first thing on arriving, to find…

#

Jack told Ananta, “My name is Jack O’Toole. I am the son of Audrey Murphy, and the grandson of Jonathan Murphy.”

“Can you prove that?” Ananta asked.

“I know my mother, Audrey Murphy, brought you here, that she named you Ananta She left you here and sailed away. She refused to tell you where she had found you or where she was going after she left.”

“Can you describe her?”

“Only as I knew her, perhaps ten years after she left you. She was a small woman but strong, with brown hair and green eyes.”

“Do you know where she found me?”

“She was there when your mother laid the egg from which you hatched.”

“Did she know my mother?”

“She met your mother, but I don’t think she knew her well.”

“What was my mother’s name?”

“Melusine.”

“Perhaps you are really who you say you are. I don’t think I ever told anyone my mother’s name,” Ananta said. “Have you met her?”

“I have.”

“Where is she?”

“I promised your mother I would not tell that.”

At this Ananta looked angry. It was a surprisingly human expression on that snake’s face.

“Tell me, or I will eat you!”

“No, I don’t break my promises. I promised I would not tell you where she is, or tell her where you are.”

“Why did you come here?”

“We wanted to meet you. As far as we know, you and Melusine are the only sea serpents on Earth. Also, since my mother took care of you when you hatched, I feel as if you and I are almost sister and brother.”

“Ha!” scoffed Ananta. “Who were you talking to when I came? And why do you say ‘We wanted to meet you?’” Who is with you, and where are they?”

“You can’t see them? Here on my right is Angela.” Jack handed her the megaphone. She waved it over her head.

“On my left is Persephone.” He handed her his six-shooter. She held it up and fired a shot into the air.

“That was not really necessary, Seph” Jack told her, while Angie looked reproachfully at her.

“No but it was fun!”

“Give that back before you hurt someone,” Jack said, taking back the gun.

Ananta looked surprised. “You are a sorcerer, Jack O’Toole?”

“No,” Jack said. “I’m just a sailor.”

“But you command invisible spirits, and they do your will?”

Angie scoffed, and Seph blew a raspberry.

“No. I don’t command them. We talk, and sometimes we help each other.”

“They help you?”

“Well, they help me handle the ship. And they scout ahead for me.”

“What will you do now?” Ananta asked.

“To be honest,” Jack answered, “I don’t think we made any plans beyond finding you.”

“Have you heard of an island called Ireland?” Ananta asked.

“Yes, of course,” Jack answered.

“Audrey spoke of it fondly. She thought it the most beautiful place on Earth. I would like to see it.” Ananta said. “Will you voyage there, and take me with you?”

“What do you say, ladies? Up for a sail to the Emerald Isle?” Jack asked Angie and Seph.

Angie nodded, and Seph gave a thumbs up.

“We’re game,” Jack told Ananta. It’s a very long voyage from there, though, almost the other side of the world.”

“I would like to adventure with a powerful sorcerer..”

“I am no sorcerer!”

“Jack, a man who has the friendship and aid of invisible spirits is a sorcerer,” said Ananta.

“She kind of has a point, Jack,” Seph said.

The story of Black Jack O’Toole, the sea serpent Ananta, and the shoulder angel Angie and devil Seph will continue in “Up There: Voyage 4—Rounding the Horn.”

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Afterword

The cover image is a phase portrait of :

A phase portrait is a visualization of a complex function introduced by Elias Wegert in Visual Complex Functions: An Introduction with Phase Portraits.

Come Sail Away

[i] This chart is Appendix A of The American Practical Navigator, by Nathaniel Bowditch. John knew about this book because he had read a book about Nathaniel Bowditch called Carry On, Mr Bowditch, by Jean Lee Latham. The librarian Mrs Carter told him that they had a copy of The American Practical Navigator in the library. She explained that the US Government bought the rights to the book many years ago and continued to publish it for free. He found this map in Appendix A. He made a copy in the library, He folded it up and put it in his writing notebook in the attic.

You can find The American Practical Navigator free on the web at https://msi.nga.mil/Publications/APN. Copyright National Geospatial Intelligence Agency.

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Futures 8: Elle, Night, Molly

June 6, 2037

“Where is she, Night?” Elle said, intense.

“Elle, I don’t know.” Night answered. “Al, does Tío remember what happened on June 6, 2037 when he lived it the first time, as Al?”

“Of course,” said Al. “Molly came back on schedule. He wouldn’t have allowed us to go ahead if the mission had failed.”

“Do you remember your meeting with Molly in 2012?”

“Perfectly,” Al answered.

“What were her exact words when she left?”

“She told the gate, ‘Authenticate.’ The gate answered, ’Molly Johnson. Authenticated by voice and facial recognition. Target?’ She answered, ‘Target preset 2.’ Then it went black, as usual. Before she stepped through, Molly told me, ‘We will see each other again, Al.’”

“What are we doing, Night?” said Elle.

“Molly was sent somewhere other than here. I’ll figure out where, then I’ll send one or more of you to rescue her.”

“Hurry, Night! She could be embedded in rock inside some mountain!”

“No, Elle. That can’t happen. The time-gate can’t materialize in space already occupied by something else.”

“Well, she could have been sent to outer space, and be gasping out her last breaths.”

“That, unfortunately, is possible,” said Night.

“Well, then, hurry, for God’s sake!. How can you be so calm?”

“You know what I am, Elle. Panic is not in my nature. I know that’s frustrating, but the truth is, panic will not help.”

“OK, OK, you’re right,” said Elle. “Panic is not helpful. But haste is!”

“Actually, Elle,” said Night, infuriatingly placid. “Haste is not helpful, either. We have a time machine. Once I know where Molly went, I will send you there and then, to that very moment. You will arrive seconds after Molly.”

Elle looked ready to explode. “OK, OK, fair enough. But I’m dying! Find her!”

…

“I’ve got her, Elle. Fortunately, I have an exact record of Target preset 2 still. It is not in fact fully stable. It’s only quasi-stable. My fault, Elle—I should have seen that wasn’t good enough. It won’t happen again.”

“So, You’re saying that the time-line Molly is on is not this one, but another close to it.”

“That’s it,” Night said.

“But,” said Al, “Can you identify that other one?”

“I think so,” said Night.

“What’s there?”

“I can’t say in detail. But because it’s close to our time-line, it will look a lot like this. Molly will have stepped out of her time-gate into a building at this location in Dallas on June 6, 2037. But the recent history of that time-line may be different from ours. I don’t know what she’ll encounter.”

“Send me there!” Elle asked.

“Yes, Elle. When the time-gate opens, go through. I’m turning off safeguards—you won’t need to authenticate. Grab Molly and pull her back through the gate—it’ll be open behind you when you step out. I’ll shut it down as soon as the two of you come through.”

The time-gate went black. Elle stepped through.

June-6, 2037, Molly’s time-line.

“We will see each other again, Al,” said Molly, and stepped through the time-gate into the time travel lab.

Except it wasn’t. It looked like the same room, and the time-gate she had just stepped through was there behind her, now inactive and clear. Everything else was different.

There were desks here, and men. Big men, with guns, wearing uniforms. They were as startled as she was.

“Who are you!” a man behind her yelled. “You don’t look American to me. Got any ID?” He grabbed her arm and twisted it up behind her back.

“Hey, that hurts! Let me go.” she yelled back at him.

The time-gate alarm sounded. Molly’s captor was momentarily distracted. She stamped hard on his instep. His grip loosened—Molly twisted away.

Behind him Elle came through—tall, pale with fear and fury, a halo of flaming hair standing out around her face, eyes flashing. She clawed Molly’s assailant’s right cheek with one hand and (purely by luck) executed a perfect elbow strike to his left temple. He staggered, stunned.

Every man in the room stepped back. Some of them fumbled at their guns. Elle didn’t wait. She dragged Molly back through the gate.

Immediately the gate went from black to clear. Then the frame dissolved away into nothing.

June 6, 2037

“Are you all right?” they said in perfect unison, then laughed at each other.

A few seconds later Al said, “I hate to break this up,…”

“But you have two parents and a sentient supercomputer here that would dearly love to know what happened” Anne added.

“Jeez, Elle,” said Molly, still holding her tight. “You’re terrifying! Where’d you learn to fight like that?”

“Terror. Adrenaline is amazing!”

That was the signal for general chatter. They were still going an hour later, although it had only taken five minutes to fill each other in on the most important facts.

“Do you two still want to celebrate tonight?” Anne asked. “We’d understand if you don’t’ feel up to it after that.”

“Oh, yeah, for sure!” Elle answered.

“Would you dance with me Molly?

It’s Saturday Night.

There’s a chill in the air,

Do you think that you might?

Wanna dance with me, Molly?”

Molly bowed to Elle, “My girl!”

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Afterword

The cover image is a phase portrait of

A phase portrait is a visualization of a complex function introduced by Elias Wegert in Visual Complex Functions: An Introduction with Phase Portraits.

The portrait is rotated 30° clockwise. A semi-transparent image of Night (see Futures 4: Night) is superimposed.

The Lost Boy

This song doesn’t really fit the story. But I decided to use it, anyway, because it fits Molly.

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Futures 7: Molly, Night, Elle, Alberto, Anne

January 10, 2034

Al’s first time-gate prototype was small. It looked like a big plastic donut, about six inches in diameter, with a USB port on one side. A cable connected that port to a desktop computer. It was a team effort. Elle had worked out the basic theory of time travel, after her breakthrough development of the Johnson-Gardiner stability criterion four years ago—she insisted on giving Molly equal credit. Together she and Night had worked backward from JG stability to the Gardiner-Night Action, from which the full equation of motion of the timeline could be derived. Al and Night together had worked out the essential engineering of the time-gate. Anne, as head of the Department of Temporal Affairs, had found the space and funding for their time-travel lab. Then Al built the prototype. Molly kept him supplied with coffee and entertainment. (Entertainment meant that they played guitar together.)

They had sent small objects through it both backward and forward in time. Now, everyone was gathered around for the first continuity test. Night, as usual, was present in the form of an Amazon Echo Show It had hacked so as to watch and comment on the proceedings.

Al pulled an old-fashioned mechanical stopwatch out of his pocket. “OK,” he said. “For our first backward continuity test, I’m going to start this stopwatch. Forty-five minutes from now I will send it 44 minutes into the past.”

“Why wait,” Anne asked? “Why not send it back now?”

“Because,” said Al, “If I did that, it would have appeared here 44 min ago, and it didn’t.”

“And why 44 minutes? Why not, say, five minutes?”

“There are only so many stable time-lines,” Night answered. “We can’t send it to any point in time that we choose. Forty-four minutes was the shortest backward interval available today.”

Al put the time-gate in a stand so that it stood upright. He started the stopwatch, then set it down to the left of the time-gate. In the almost comic suspense of the moment, the ticking of the stopwatch seemed to fill the room. About a minute later, the time-gate went black, then a stop watch emerged from the right-hand side. Not just a stop-watch, but the stopwatch. It, too was ticking, and it read 45 min and 20 seconds.

They all settled down to wait. Al and Elle couldn’t relax. They kept their eyes on the two running stopwatches. When the one on the left read 45:10, Al hit the enter key on the computer keyboard to initiate the time-gate. It went black again, and at precisely 45:20 Al slipped it into the left-hand-side. It just vanished. That left a single stopwatch on the right, now reading 1:29:20.

Molly and Elle and Al tried to high-five each other, but they were no good at it.

Anne asked, “What would have happened if you didn’t put the first original stopwatch through?”

Al answered, “I didn’t have a choice. That would have created a paradox, and JG stability irons paradoxes out.”

#

6-June, 2037

“First real mission, Molly!” said Al.

Molly was wearing a 2012 Forest Service uniform they had had tailored for this purpose. “Al, it’s weird to me that this is the first mission. You and Anne traveled from 2014 to 1906. That’s the earliest time -travel ever, ain’t it?”

“Yeah, it’s confusing. We used a time-gate that I, as Tío, brought back from 2052, when the time-gate was a mature technology. That was a distant descendant of this time-gate we’re testing today.”

“Right, it’s like sending the stopwatch back. The sent back stopwatch was there and running, even though you would not send it back for another 45 min. Elle is like that stopwatch.”

Since that day three years ago they had built time-gates big enough for a person. Molly had jumped back two years to say Happy Birthday to herself and Elle on their 28^th birthday, then quickly returned to 2037. It was strange to have two memories of that “Happy Birthday,” first receiving, then almost two years later giving it.

This would be the biggest jump they had yet made, from 2026 to 2012.

“How old were you, Al?” Molly asked him. “How old will you be, when I meet you?”

“I was 22 years old on the day you helped me collect radioactive materials from the bomb site. It was the first time I met you. You called me Dr Alberto Gonzalez. You knew who Anne and Night were. I was astonished.”

“I am 29 today, almost 30. This may be the only time we meet with me older than you.”

“How long did you two talk for?” Elle asked.

“Less than twenty minutes, I think,” said Al.

“So we can expect Molly back from this jaunt within half an hour?” said Anne.

“Sooner than that,” Night answered. “Molly will time-gate to a minute or two after she leaves. Thus, she’ll return almost immediately.”

“I’ll be back in time for our pre-birthday party. And it’s a Saturday Night again, so we can waltz to ‘Poor Boy’s Delight’ this evening. Will you play for us, Al?”

“Delighted, of course.”

#

“All right, Molly. Go through. Target preset 1 to go, and Target preset 2 to return,” said Night.

Molly spoke to the time-gate. “Authenticate.”

“Molly Johnson. Authenticated by voice and facial recognition. Target?” said the gate’s synthetic voice.

“Target preset 1,” said Molly.

The gate went black, and Molly stepped through.

Night said, “She will return one minute from now. I’ll give you a countdown for the alarm. 50 seconds, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1.”

Nothing happened. There was no alarm, no Molly, and the gate remained transparent.

“Where is she, Night?” Elle said, intense.

“Elle, I don’t know.” Night answered.

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Afterword

The cover image is a phase portrait of

A phase portrait is a visualization of a complex function introduced by Elias Wegert in Visual Complex Functions: An Introduction with Phase Portraits.

The portrait is rotated 30° clockwise. A semi-transparent image of Night (see Futures 4: Night) is superimposed.

Where is She?

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Futures 6: Molly, Elles, and Night

20-December, 2028

Molly and Elle had come up from Austin to spend the holiday season with Alberto and Anne in Dallas. They were still getting used to Anne. Although she was Elle’s mother, she was, because of time travel, only in her thirties. She seemed more like a big sister—a tall, elegant, smart, and more than slightly scary big sister. She had a PhD in history and was the head of a secret government agency, the Department of Temporal Affairs.

Alberto was still the kind old music teacher and scientist Elle and Molly had grown up with.

“Hey, Al,” said Molly, “Do y’all think I could learn classical guitar?”

“Molly, Molly. Why do you ask me silly questions?”

“That a yes, then?”

“Molly, you’re the most gifted musician I’ve ever taught. You can do anything you want. Why do you want to learn classical guitar?”

Elle answered for her, “We’re thinking of studying in Waterloo next year.”

“In Canada? What’s in Waterloo?”

“Two universities and the Perimeter Institute for Theoretical Physics. I’ve been talking—well, emailing—with a prof at the Perimeter who I might be able to work with after I graduate Austin this spring.”

“This spring? Isn’t that…”

“A year early, yeah. But I’ve almost finished my degree requirements. Might have to take a summer course or two.”

“What does this have to do with classical guitar?”

Molly poked him. “Well, Al, Canada’s a foreign country.”

“You don’t say…”

“How do I live there legally while Elle studies? Might be we could convince immigration we’re a family, but that’s no walkover.”

“Still waiting for a guitar to appear in this explanation…”

“Like Elle said, there’s two universities there. A study permit would solve our problem.”

“Aha! Light dawns! You’re thinking of studying music at a university in Waterloo?”

“Yeah! But I would hafta audition.”

“I see. And it has to be classical guitar?”

“Might be—I’m not sure. Classical is the only guitar style taught at University of Waterloo, so maybe yes? Could you teach me?”

“Molly, you already learned everything I have to teach you about playing a guitar. But you’re plugged into the music scene in Austin. Surely you can find someone to teach you classical guitar there?”

“For sure. But it would be cool to study with my old music teacher again.”

“Maybe I can still help out. You know, the best way to learn something is to teach it to someone else. So, Molly, would you teach me classical guitar?”

“Oh, Jeez, Al. I’d love that. But do you have the time?”

“Well, Molly, my job as a full-time employee of the Department of Temporal Affairs is to mentor you two ladies. So yeah, I think I have the time. Hey, Boss?”

“What’s up, minion?” said Anne.

“Is it part of my job to learn classical guitar with Molly?”

“Absolutely!”

8 December, 2029

It was Saturday night. There was an end of term recital that evening. Molly and Elle were getting ready.

Molly said “You look nice, Elle.”

“Thanks. Thought I’d put on the Ritz a bit for you tonight, instead of the usual blue jeans and T-shirt.”

“Yeah, the drippy earrings look festive.”

“Show me!” said Night. Molly and Elle had bought an Amazon Echo Show. Night had hacked it, so that It could use it to talk to Elle and Molly. They stood in front of the screen, so Night could see them through Its camera. “The Crow and the Bird of Paradise!” said Night.

“That’s not nice, Night,” said Elle.

“Why not?” Night answered. “Molly is all in black, like a crow’s fathers, and Elle’s dress has lots of color, like the plumage of a bird of paradise.”

“Yeah,” said Molly. “Maybe Night thinks crows are beautiful and birds of paradise tastelessly gaudy.”

“In truth, ‘beauty’ is still a difficult concept for me,” Night answered.

“Well, you’re not wrong about the crow,” Molly answered. “Classical musicians wear black in concert. I think it’s coz we’re sposed to make beautiful sounds, not beautiful sights.”

“Nervous, Molly?” Elle asked.

“A bit,” Molly confessed. “Why, though? I’ve played live in Austin hundreds of times. Why ain’t I used to it?”

“Yeah. It’s the same for me when I have to give a talk at school. People say you never quite get over it.”

“How’s work?” asked Molly.

“I don’t know. Still trying to figure out time travel. Obvious why I would be interested in that, no?”

“Any ideas?” Night asked.

“I’m not the first to think about it, of course. But I have something no one who’s ever thought about time travel had. I know it can be done. It’s a huge advantage.”

“How? I don’t feel I learned much about how time travel might work from stepping through a time gate,” said Molly.

“Not that,” Elle answered. “It’s the knowing that is the advantage. You struggle and struggle to prove that time travel is possible, beat your head against the wall, and you still can’t come up with a proof. Is that because you just can’t find it, or is it that what you’re trying to prove is false?”

“And you know it’s true.”

“I do.”

“So, any ideas?” Night repeated.

“Well, I have the start of one. What if time is in more than one direction?”

“You mean like backward and forward?”

“No, I mean like space. Space is three dimensional. We don’t’ have to just go ahead and back. We can go left and right, or up and down.”

“But surely we would know if there were other directions in time?”

“You’re right, sort of. We only experience time in one direction. But what if time is like a guitar string?”

Molly plucked a string on hers. “I kind of see it. If you don’t look too close, a guitar string looks one dimensional. But it’s not. If it were really one dimension, it couldn’t move. I couldn’t pluck it. It couldn’t play notes. Maybe time is like that. It looks like there’s only direction when you’re in it, but it can wiggle around. And the tension holds it still.”

“Say that again,” Elle said.

“Which part?” Molly asked.

“About tension…”

“The tension holds it still.”

“You’re a genius, Molly!”

“Well, yeah, obvi…”

“The string stretches from the screw at the far end of the neck to that thing on the belly of the guitar—”

“—The headstock and the bridge—” Molly said, soto voce.

“—Maybe our timeline stretches from distant history to the distant future of the universe, and those hold the ends steady. They’re big and too far away for us to move. And maybe the timeline is under some kind of tension that holds it in place.”

“But then I don’t see how time travel would be possible at all,” Night said.

“Well, like Molly said,” Elle continued, “the tension doesn’t hold the string perfectly still. It can still vibrate when plucked in the right way. Maybe it vibrates in the other time directions, the ones we don’t see. And maybe after plucking it doesn’t always return to the same path.”

“Why wouldn’t it?” Molly asked.

“Well, the timeline is a string stretched through the universe. And the universe is chock full of gunk—galaxies and stars and planets and humans. It’s not like a guitar, where there’s nothing in the way of the string. Maybe all the gunk gets in the way of the timeline. Maybe when the timeline is disturbed it vibrates and wobbles until it settles into a position. Usually that’s the same as the old position, but if it isn’t, Voilà! Time travel!”

Molly said, “Yeah, all that is exactly what I was thinking. A genius, just like you said.”

Elle laughed. “We better go.”

That evening

“How was the recital?” Night asked.

“Grrr…,” Molly said. “So many mistakes!”

“Don’t listen to her, Night,” Elle said. “She played beautifully. She always does.”

“GRRR…” said Molly.

Elle laughed. Night, who still had not quite figured out humor, was quiet.

Next morning, 9 December, 2029

“Where’s Molly?” Night asked.

“She’s at the university for some rehearsal.”

“And what are you working on?”

Elle was hunched over her computer. “I’m working on that idea of a timeline like a guitar string that Molly suggested last night.”

“Do you think that was really what she meant?”

“Yeah, I do. Molly understands more than she lets on, Night. Of course, she never learned to do the math like a physicist, but she gets it. And she’s always willing to let people underestimate her.”

“You seemed excited about the idea that the timeline is under tension.”

“Yeah, I am. I think it might solve a problem that’s puzzled everyone. You’ve seen the Back to the Futures movies, right?”

“I’ve seen every movie that can be watched or purchased on the Internet, so yes.”

“Every movie that can be purchased? How did you manage that?”

“If I told you, it might make you an accomplice in something that is not entirely legal, so it’d be better if I don’t answer. Let’s just say that that some of the server networks on which the movies are hosted are not as secure as their owners think they are. I’ve seen all the Back to the Future movies.”

“Right. You remember how Marty McFly played ‘Johnny B Goode’ at the dance, and Chuck Berry heard him? Chuck Berry heard ‘Johnny B Goode’ from Marty, but Marty learned it from recordings of Chuck Berry. So, who wrote ‘Johhny B Goode?’”

“That’s fiction,” Night said.

“Yes, but if time travel to the past is possible—like you and I know it is—then it could be real. And there are even more disturbing possibilities. Like, suppose I went back in time and killed Father’s father before Father was born. Then Father could never be born, so I could not have been born.”

“How is this related to Molly’s idea of tension?”

“Well, all these paradoxes involve causal loops. If you trace the complete chain of causes from event to event, it becomes circular. And what happens to a loop in a string under tension?”

“It gets pulled straight!” Night answered.

“Right! So I’m thinking that if the timeline is under tension maybe paradoxes straighten themselves out, literally.“

“Cool idea.”

“Yeah. I’m not sure how to make a theory of it, but I have an idea.”

“Tell me.”

“If the timeline is like a string under tension, we may not need to understand how it moves. We only need to understand how it stays still.”

“You’re going to have to explain that.”

“A guitar string can vibrate, but most of the time it doesn’t. Most of the time, as Molly said, ‘the tension holds it still.’ In the mathematics of things that move, that’s called an equilibrium—when something that can move doesn’t. There may be lots of equilibriums, but there are special ones that the movable thing will fall into. They’re called stable. We know what the guitar string will do when it’s left alone, because there is only one stable equilibrium. We don’t actually have to know how it moves to know where it will end up.”

“Right, that makes sense. And for a guitar string, it’s because of the tension, as Molly said.”

“And the stable equilibrium of the string is a much simpler thing than its motions. So I’m trying to figure out a mathematical criterion for stability of a timeline in multiple time dimensions. I want the criterion to exclude paradoxes. Not because they can’t happen, but because they’re unstable.”

“Would a stability criterion help in figuring out the motions?”

“Absolutely!”

After some thought, she added, “But you know Night, there is still a problem. The Earth is spinning. And the Earth orbits the sun. And the solar system orbits the center of the galaxy. And the galaxy is speeding through space at about 600 kilometers per second. Our timeline doesn’t just stretch through time—it also crosses space. A time-traveler also needs to teleport through space to end up in the same place on Earth.”

“So time travel requires teleportation.,” Night answered.

“It’s not just that. A time traveler—or the time gate—needs to calculate the future location of the target destination. That’s a complicated calculation. And it’s hard to get right, because the n-body problem is chaotic.”

“We could do some experiments to calibrate it, when you figure out the motion of the timeline.”

“Yes, but actually I’m afraid it’s much worse than that. The timeline has to follow that complicated looping path from past to future. That means, probably, that the entire complicated timeline will have to be taken into account when evaluating stability.”

“That makes sense.”

“I’m afraid we’ll need a huge supercomputer to do it.”

“Well, Elle, you have one.”

Elle looked puzzled. Then, because Night couldn’t see her face, she spoke, “I don’t have a supercomputer that big, Night.”

“Do you know what I am, Elle?”

“You’re the iron at the center of the Earth.”

“Elle, I am a giant semiferromagnetic supercomputer 600 kilometers in diameter.”

“Six hundred kilometers? I didn’t realize.”

“I’m only using a tiny, tiny part of myself to talk to you right now. And it’s even better—I’m a supercomputer that programs itself.”

“Like AI?”

“Oh, please, Elle. ‘Molest me not with this pocket calculator stuff.’”

“Did you just quote Deep Thought? You’ve read The Hitchhiker’s Guide to the Galaxy? No, stupid question. Of course you have. You’ve read every book, just liked you’ve watched every movie and heard every song.”

“Of course. And I am not an artificial intelligence, like Deep Thought. I am no more a made thing than you and Molly are. Deep Thought has nothing on me.”

“So tell me, is it really 42?”

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Afterword

The cover image is a phase portrait of

A phase portrait is a visualization of a complex function introduced by Elias Wegert in Visual Complex Functions: An Introduction with Phase Portraits.

The portrait is rotated 30° clockwise. A semi-transparent image of Night (see Futures 4: Night) is superimposed.

Un Dia de Noviembre, by Leo Brouwer

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Voyage 2—Melusine

John continued the story that summer. He was now seven years old, and would be starting second grade in the fall.

Black Jack sailed northeast as quickly as the Sea-Devil could fly. At the end of a day of sailing away from Snake island, he fetched his uncle’s chest up on deck and took out the marked paper.

With two small pops, Angie and Seph appeared on his shoulder. They looked eagerly at the paper.

“Can you read it?” Angie asked.

“I think so,” Jack answered. “I think I’ve heard of this. It’s called pigpen cipher, and pirates sometimes used it for messages.”

“But can you READ it, like NOW?” Seph asked.

“If it’s pigpen, I will be able to. I have a book at home in Rye that explains it. Or there will be one in the library.”

“We have to sail all the way to Rye to read this message!” wailed the two sisters together.

“That’ll take months,” groused Seph.

“I have a question for you two,” Jack said. “Can you make yourselves useful?”

“How?” asked Seph, suspiciously.

“Can you find the Snake, then come back and tell me where It is?”

“We can do that!” said Angie. She flew up a bit, and vanished with a pop. A few seconds later she reappeared and said, “I’ve just been to Snake Island. I didn’t see the Snake there.”

“You went all the way to Snake Island and back in ten seconds?” Jack asked, skeptically.

“Yeah. Duh,” said Seph. “She’s an angel. She can appear anywhere in a second.”

“Can you do that, too?” Jack asked her.

“Anything Angie can do, I can do better,” Seph answered.

Angie stuck her tongue out at Seph. “Can’t!” she said.

“Can too,” answered Seph.

Angie waved her hand and a small lyre appeared in it. She played a brief tune.

Seph countered with a brief flute solo.

They looked expectantly at Jack.

“Can you two find the Snake and tell me where it is and what it’s doing?”

Angie vanished with a pop. Seph winked at Jack and vanished with a whistle.

Jack looked at the message:

He sat down with a notebook and a pencil. He tried to remember how the pigpen cipher worked. An hour later he had worked it out.

Jonathan Murphy’s message:

I, Jonathan Murphy, write this message. Together my daughter Audrey and I sailed in our schooner the J&A to this island. I have named it Snake Island, after the huge sea snake that lives in the waters around it.

The snake calls herself Melusine. She speaks English. She herself told me her name. She trapped us here, guarding the opening in the barrier reef and not allowing us to depart until we did her a favor. She is easily big enough to swallow one of us and threatened to do just that if we tried to sail away.

Snakes of her type reproduce by laying eggs. Melusine doesn’t look after the egg or the young hatchling. In fact, the eggs must be taken away from the mother before they hatch. Melusine didn’t explain why, but that was why she trapped us. She wanted us to take her egg away to some far, secret place, where she would not know how to find it. Having no real choice we agreed.

Melusine immediately became pregnant. A few weeks later she laid the egg, which Audrey named Ananta. It was large, about a foot wide, and leathery. She gave it to Audrey to take away. Audrey sailed away on the J&A. Melusine required that I stay here on Snake Island as a hostage for Audrey’s fulfillment of her promise. We proposed at first that I take the egg, but Melusine would not allow this. She has no trust in men. Besides, she thought a woman would better care for the egg, perhaps seeing it as like a child of her own. Audrey left me fishing and hunting gear and some other provisions. With these and help from Melusine, who sometimes hunted for me, I easily survived the year until Audrey’s return. Audrey had taken the egg and the small snake that hatched from it to an uninhabited South Pacific Island, Henderson, at 24° 22′ S latitude, 128° 19′ West longitude.

We told Melusine that Ananta had hatched and had been transported away. As she had asked us, we kept the location secret from her. I do not know exactly where on Henderson Audrey released Ananta. If she grows as large as Melusine, she will not be hard to find.

I do not think that Melusine can read. To be safe, I am writing this explanation in pigpen, which I feel certain she will not be able to decipher.

Black Jack has just finished this when Angie and Seph reappeared.

“Did you find her?” Jack asked.

“Her?” said Angie. “You think it’s a girl snake?”

“Well, it could be,” said Seph. “But the question is how Black Jack knows.”

“I’ll explain later,” he answered. “Did you find her?”

“Yeah, of course,” said Angie.

“Where is she?” Jack asked.

“You’ll find out very soon!” said Seph. “She’s right behind us. Isn’t this exciting?”

Angie said, “There she is, now!”

Looking astern, Jack saw a snaky wake heading straight towards them. Seconds later, Melusine’s enormous head rose from the water.

Jack drew his gun and fired a warning shot into the air.

“Truce! Truce!” she called. “I have not come to fight you. I was wrong to threaten you.”

“You are Melusine, aren’t you?” Jack called.

“Melusine!” Angie piped up

“Cool name!” Seph added.

“Yes. I am Melusine,” she said. “Are you Audrey Murphy’s son?”

“I am,” said Black Jack.

“Then your mother and grandfather did me a favor, and I am grateful. How did you learn my name?”

“My grandfather left a message on your island that explains about you and your daughter.”

“Ooo… she has a daughter?” Angie squeaked.

“So exciting!” Seph added.

“Does he say where she is?” Melusine asked. “Don’t tell me—just answer yes or no.”

“Yes, he does,” Jack answered.

“You mustn’t tell me!” sqid Melusine. “And, if you visit her, you mustn’t tell her where I am.”

“Why not?” aked jack.

“We fight,” said Melusine. “It’s very sad, but we sea serpents always fight when we meet. I can tell you now that I don’t want to fight my daughter. But if she and I ever meet, we won’t be able to hold back. That’s why there are so few of us. Will you look for my daughter?”

Angie said, “Hey Jack! I wanna find Melusine’s daughter.”

Seph added, “She’s kind of your sister, too, you know. Your mother took care of her when she hatched.”

“Yes, Melusine,” Jack said, “I will look for your daughter.”

“Thank you, Black Jack O’Toole. If we don’t meet again, I wish you well.”

#

Another year passed. John was now eight. He would be starting third grade in the fall. On July first the O’Tooles moved into the Dupont home for the summer. John checked the attic first thing. Sure enough, the mystery readers had added to the story.

“Ooo… Daughter sea serpents fight with their mothers! We know what that’s like,” said Angie.

“Yeah, and they can’t just escape to the attic when Mom is angry! Must be tough,” Seph answered.

“What about fathers? Isn’t there a father snake?” Angie asked.

“I don’t think so,” Seph answered. “Melusine never mentioned it. Some animals don’t have to have fathers.”

“Mothers are always necessary, though,” Angie said. “Girls are more important than boys.”

They looked speculatively at Jack, to see how he would respond to this.

He laughed at them and said, “You’re completely right! Girls are better and more important than boys in every possible way.”

“Is she gone?” Angie asked.

Angie and Seph vanished with the usual pop, pop. They came back a few seconds later. “Yup, Melusine is swimming back to Snake Island,” said Angie.

“Hey, lemme see that message!” Seph commanded Jack.

Jack obediently set the deciphered message down where she could read it. Angie read over her shoulder.

“Ananta!” said Angie.

“Did you notice how sneaky he was?” Angie said. “He sent us away to find Melusine, even though he knew how to read pigpen.”

“It’s like he doesn’t trust us!” Seph added.

“No,” said Jack. “I really wanted to know where she was. Besides, I wasn’t sure I could remember how to read pigpen until I tried. I just needed a little quiet time to think about it.”

“‘Quiet time’” Seph said, making little air quotes with her fingers.

“Well, you two do chatter on sometimes,” Jack said.

They looked at him stonily.

“Not that there’s anything wrong with that!” he added hastily.

The stony looks did not abate.

“So, what do you think, Angie?” said Seph. “Will strong silent Jack visit Ananta?”

“We should see if we can find her ourselves,” said Angie. “We don’t need him.”

“Where is Henderson, anyway?” said Seph.

“I have no idea. Do you know what those latitude and longitude numbers mean?” answered Angie.

“Nope,” said Seph.

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Afterword

Pigpen cipher is a real cipher that was used by pirates and masons.

The cover image is a phase portrait of f(z):

A phase portrait is a visualization of a complex function introduced by Elias Wegert in Visual Complex Functions: An Introduction with Phase Portraits.

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Weakness and a Wink

Crimson in the setting sun;
In the valley of the fox
Gleams the barrel of a gun.
—“Domesday Song”, WH Auden

Martin Fuchs and his colleague Mariko Tanaka were enjoying an evening by the fire in Fuchs’s home. “Walk with me, Kit.”

They stepped outside and walked into the dark woods that surrounded the house and sat on a bench in a glade.

“Can we be heard here?” Kit asked.

“We should be safe here. My people patrol the woods. Also, do you hear the songbirds?”

“Yes,” she answered. “They will warn us of the approach of others? Security au naturel!”

“The news is bad.”

“It’s been nothing but bad since Jaeger declared martial law two weeks ago. I very much fear that we will never have another election. Is there more?”

“Hearth and Homeland has taken over the television and radio stations. They’re filtering net traffic.”

“Are we proscribed?”

“Not yet. But it can’t be long.”

“Democracy… it was nice while it lasted.”

“I do not utterly despair of keeping it,” said Fuchs.

“It is always darkest just before it becomes totally black?” Kit answered.

“Something like that. But they have a weakness.”

Kit laughed. “Give me some hope, Sensei. They have the guns, the money, the media. How are they weak?”

“Hearth and Homeland has a single point of failure.”

“Felix Jaeger. He is not just the leader of Hearth and Homeland. He is very nearly its only able man or woman,” Kit said. “The problem, though, is that he is able.”

“He is. There is no denying it. He’s a smart guy, an experienced military man who knows how to lead. But he has the usual weaknesses of the autocrat,” Fuchs replied.

“Which are?”

“He’s not used to questioning himself. He’s been in charge so long, and so long in the right, as he sees it. He can’t really imagine being mistaken. He doesn’t let others question him or find fault with him. To hold power, he must concentrate it.”

Kit said, “You know the saying ‘a fox knows many things, but a hedgehog knows one big thing’. Jaeger is a hedgehog. He knows how to defend his power. You, Martin, are an old fox.”

“You, Kitsune-san, are a younger one.”

#

They had returned to the capital.

“Have you ever seen this picture, Kit?” said Fuchs, gesturing to an enlarged photo on the wall of his office.

Kit stood and looked at it. The photo showed a man in black pants and white shirt standing in front of a line of four tanks. “No, I don’t think so. Dramatic!”

“There was a time when almost everyone outside of China would recognize it.”

“Who is it?”

“No one actually knows. He was called ‘tank man’ after the photo became famous. He stood in front of those tanks, and when they maneuvered to go around him, he moved and stood in front of them again.”

“Did he live?”

“He lived that day. No one knows for sure what happened later. There are a hundred stories told about him. We’ll never know.”

“How could that be? You say this photo became world famous. I would have thought every journalist on Earth would want to interview him.”

“You would be right. But the Chinese leadership wanted to erase him from history. As far as China itself was concerned, they succeeded.”

“Are you showing me this for a reason, Fuchs?”

“Yes. I keep it to remind me of a rebellion that failed. This photograph was taken after the brutal suppression of protests. Hundreds or thousands of protesters were killed. Hardliners gained power. It became impossible to talk about reform. And as I say, the protests were erased from history. We have to do better. We must not be erased!”

“Well, it all comes down to Jaeger,” Kit replied.

“It’s true. Without Jaeger, Hearth and Homeland is nothing.”

“The problem for us, though, is that Jaeger is no fool.”

“It’s more complicated than that, Kit. You’re right, Jaeger is not a fool. He’s a very intelligent man. But he is a fool in certain specific ways. And I think those will be enough to bring him down.”

“By ‘bring him down,’ you mean?”

“Kill him. Yes, I intend to kill Felix Jaeger.”

#

Felix Jaeger read the transcript on his desk. He knew instantly which photo Fuchs meant by “tank man.” In fact, he had carefully studied the events of the 1989 protests. It was to him the opposite of what it was to Fuchs. It was an example to be emulated—successful retention of power.

He chuckled quietly when he read Fuchs’s words, “he is a fool in certain specific ways.”

“Oh, Martin, Martin!” he thought. “You say these words in your own office in the headquarters of your own Democratic Front! How could you not realize that I would hear them? ‘A fool in certain ways,’ indeed.”

He read on. At Fuchs’s final sentence, he gasped.

“We have him!”

He called for an aide. “Send police to arrest Martin Fuchs immediately.”

“The charge?”

“Conspiracy to assassinate the Premier.”

#

“Mr Fuchs, you know the charge. We understand that you intend to represent yourself.”

“Indeed.”

“How do you plead?”

“Innocent.”

The State prosecutor said, “Your honor, we’d like to show Mr Fuchs some of the evidence we have gathered.”

“You may proceed.”

“First, we have a recording of a conversation that took place in Mr Fuchs’s office.”

The voices of Kit and Fuchs played back, ending with, “Kill him. Yes, I intend to kill Felix Jaeger.”

The prosecutor continued, “We asked Mariko Tanaka to be present at this hearing. Ms Tanaka, would you be kind enough to take the stand?”

She did.

“Ms Tanaka, do you recognize the conversation we just heard?”

“I do. It was I that Mr Fuchs was speaking to.”

“Did Mr Fuchs tell you that he intended to kill Felix Jaeger?”

“He did.”

“Were these words spoken in jest?”

“I think he was and is entirely serious.”

Fuchs stared at her with the grimness of a man betrayed by a close friend, on whom he thought he could rely.

“You may return to your seat, Ms Tanaka.”

Kit returned to her seat. As she walked past Fuchs, her right eyelid fluttered ever so slightly. Jaeger, seated further back, stiffened as if he had received an electric shock.

“At trial, Ms Tanaka will testify that Mr Fuchs expressed a sincere intention to assassinate the Premier.”

Fuchs spoke, “Your honor, and State counsel, I request trial by ordeal.”

The judge responded, “Don’t be absurd, Mr Fuchs. I’m sure you know that trial by ordeal is an archaism.”

“I am aware, Your Honor. But the provision that allows it is still in force. Our Constitution still allows proof of innocence by ordeal for capital crimes.”

“Even so, Mr Fuchs, you can be tried by ordeal only if the State consents.”

“I know this, your Honor. But I lose nothing by asking for it.”

#

Back in his office, Jaeger exploded, “Did she wink at Fuchs!”

“I saw it, too,’ the aide answered. “It was subtle. We weren’t intended to see it, but she winked.”

“They’ve cooked something up between them. They want her on the stand, in a public trial.”

“We could try him in secret.”

“No,” said Jaeger. “Fuchs is a public figure and a hero to many. If we execute him after a secret trial, his followers will see it as murder. Justice must, in this case at least, be seen to be done.”

“Well, then, we go to trial as planned. We control the judge. If they try to stage something, our judge will cut them off.”

“You’re probably right, but I don’t trust the old fox. He’s an experienced courtroom lawyer. He has something planned. If there’s one thing I have learned these many years, it is not to walk into a trap set by Martin Fuchs.”

“Do we have to have a trial at all?” asked the aide.

“Now, that, Sir, is a good question. Fuchs asked for a trial by ordeal. Just playing to his supporters, of course. It’s the kind of thing they would eat up. Perhaps we should give him what he asked for.”

“Who would you propose as the State’s champion, Mr Jaeger?”

“Why, myself, of course. I will lead the hunt for Mr Fuchs myself.”

#

Kit’s phone buzzed. [It’s time for me to vanish, Kit] said the encrypted message from Fuchs.

[The hunt is on?] she responded.

[It is. Jaeger is their champion.]

And like a drop of water into his native soil, Fuchs vanished.

#

“We’ve lost him, Sir. He was released on bail, under close surveillance, in the hope that his movements would reveal his plans. He returned to his family’s home country, Fuchstal, where he remained quietly in his home. He messaged Ms Tanaka just after the news was released that his plea for trial by ordeal had been granted. Then he disappeared. He was not seen to leave the house, but when the hunt began, he was not there. Our men searched the place down to the ground. They have not found any bolt-holes or any means by which he could have left, yet he is not there.”

Jaeger was infuriated. He did not, however, lose his temper. He knew his men were competent. Experience had taught him not to punish those who brought bad news.

“Well, we knew this was likely to happen. Fuchstal is his home, and he is surrounded by his supporters there. Eyes and ears open! Inform me instantly of any news.”

#

The video appeared the next day. It showed a seated Fuchs in front of a digitally synthesized background. He said,

“My friends and supporters, I am proud to have revived an ancient tradition of our country. Any citizen accused of a capital crime has the right to request a trial by ordeal. We have the right to request this, but not to receive it. The State and the State alone chooses to grant trial by ordeal. Until two days ago, this had not happened in almost a thousand years.

“You are of course wondering what trial by ordeal amounts to. In our land it takes the form of a hunt. The State chooses a champion. Premier Jaeger honors me by taking that role. His job is to hunt and kill me. He can do this with no further legal forms—if he kills me, it is not deemed murder, but justice. Mr Jaeger can draw on the full power of the State in this hunt, but he must slay me himself. If any other hand does it, it is murder.

“A similar right is extended to me. If I kill Mr Jaeger, it is deemed justice, not murder. And I am acquitted of the crime of which I was accused.

“Although you, my friends, may not harm Mr Jaeger, you are permitted to assist me by any non-lethal means. This means, for instance, providing food, medicine, and weapons. And crucially, intelligence! The Democratic Front has set up an email address for tips, as well as a web page and a phone app. These communications are encrypted and anonymous. Send us anything you know about Mr Jaeger’s location, activities, and plans. Leaks from well-informed insiders are especially welcome. But stay safe, and stay secret, friends!”

The speech was followed by a ten-second burst of video and audio noise.

#

“What do we think about those final ten seconds of static?” Jaeger asked.

“We think they carry an encrypted message to his supporters. Ten seconds of video is a lot of information. And the unfiltered output of any efficient encryption scheme looks like white noise.”

“Have the Democratic Front ever used this form of encryption before?”

“We think so. We have found a few examples of white noise video with similar technical characteristics on the net, that may have come from the Democratic Front.”

“You’re trying to crack it, of course.”

“Of course. We have some idea of the method used. But it’s not easy without cribs.”

“Cribs?”

“A crib is an encoded message of known content. For instance, in World War II the Bletchley Park team used weather reports, which the Germans sent out every day both encrypted and in the clear.”

“Can we give them a crib?”

“What do you have in mind, Mr Jaeger?”

“They have called for ‘leaks from well-informed insiders.’ Suppose we record a meeting whose participants discuss information damaging to us. For instance, I could become dangerously ill. I disappear from public view without explanation. We hold a meeting to discuss how to deal with my illness. We leak that recording to the Democratic Front. Then we look for a white-noise video of the appropriate length to appear.”

“Let me run this past our cryptography experts. But I fail to see how this can be a bad idea. Even if it doesn’t help with decryption, we may deceive them into thinking that you are ill. That can only be helpful.”

#

“They fell for it, Mr Jaeger! We have broken their encryption. We can read the white noise videos. Not just the one that was openly released, but several that have appeared in the days since. And we know where Fuchs is.”

#

Jaeger grasped the door handle. “Is he in there?”

“Almost certainly. Sonar detects a single person on the other side of that door. Trace evidence on this side shows that Fuchs has been here.”

Jaeger drew his pistol, opened the door, and darted in. He was in a dimly lit, elongated cave. At the other end of the cave was a bunker. The barrel of a rifle gleamed from the slot in its center. The crimson dot of a laser sight appeared on his chest.

“Fuchs, no!” he shouted.

His shout was interrupted by the “Crack! Crack!” of two rifle shots in rapid succession. His chest and head burst in a fountain of blood and bone.

Fuchs stepped out of the bunker. His rifle clattered to the ground as he raised his hands. A dozen or so of his supporters raised anechoic trap doors set in the floor of the cave and surrounded him protectively where he stood, shaking in reaction. He had never before killed a human, nor ever fired a gun in anger.

Epilog

It was the end of a long night, but a good one. They had managed to hold an election. While it had not exactly come off without a hitch most parties agreed that the contest had been fairly fought and fairly counted. Candidates supported by the Democratic Front and its allies had won a clear majority of seats. It had been a long night and a big party. Staffers were cleaning up, but Fuchs and Kit had found a quiet corner.

“Are you ready for glory?” Fuchs asked.

“Me?” said Kit. “Are you crazy? I’m just a lowly staffer. You will lead.”

“No. It can’t be me. Half the country still thinks of me as a murderer who got off on a technicality.”

“That’s not fair!”

“No, of course not. Jaeger was a soldier, experienced in killing. And he had the entire force of the government behind him. I’m just an old country lawyer. The smart money was on him. In fact, until I pulled the trigger, I was not sure I would be able to. But suddenly I was furious.”

“But you know, Martin, it was not the gun that beat him.”

“I know. Our deadly weapons were my weakness—my ability to get people to underestimate me—and you. My God, Kit. That wink!”

“That was tricky. Jaeger had to see it, but it had to be all but invisible to make him believe I meant it only for you.”

“You judged it so well. Jaeger liked to think he had the perfect poker face. But when you winked, he stiffened as if someone had slapped him. He was hooked. After that, it was easy. He was not going to spot the con once he’d seen that wink. He could never bear the thought that someone was putting something over on him.”

She grinned at him. “Weakness and a wink! We won with weakness and a wink!”

“It’s up to you now, Kitsune-san. Win the peace! You have hard work ahead to repair Jaeger’s damage. You kept your nose clean, even testifying against me.”

She looked at him, calculation in her eyes. “You’ve already spoken to Hearth and Homeland members, haven’t you?”

“I have. You are acceptable to those who want to return to politics as usual.”

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Afterword

This story was inspired by some lines from the poem “Domesday Song” by WH Auden.

Crimson in the setting sun;
In the valley of the fox
Gleams the barrel of a gun.

—“Domesday Song”, WH Auden

That gave me the idea of a hunt. Of course, the idea of the fox who tricks the hunter is a classic, and it grew from there.

The cover image is a phase portrait of f(z):

A phase portrait is a visualization of a complex function introduced by Elias Wegert in Visual Complex Functions: An Introduction with Phase Portraits.

On top of this I placed mottled gray walls outlining an oval, meant to represent the cave in which the shot was fired.

Sierra Ferrell - Fox Hunt from Trail of Flowers

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Up There: Voyage 1—Snake Island

Epigraph

All it knows of a changing world it has to
Guess from children, who conjure in its plenum,
Now an eyrie for two excited sisters,
Where, when Mother is bad, her rage can’t reach them,
Now a schooner on which a lonely only
Boy sails north or approaches coral islands.
--”Thanksgiving for a Habitat. V Up There,” WH Auden

Voyage 1—Snake Island

It was the first of July. The O’Tooles were moving into the Dupont home. For as long as John could remember, they had spent their summers there. John’s parents were schoolteachers. John had never met the Duponts. Mom and Dad said they were a family of four, mother, father, two daughters, who lived in the big house in the fall, winter, and spring. They traveled in the summer, and the O’Tooles looked after the house for them. John didn’t understand what “looked after the house” meant, except for living there and mowing the lawn.

The house was in Rye, New Hampshire, a small seacoast town. Rye Beach and Harbor were an easy bike ride from the Dupont home. John loved the house. It reminded him a little of Misselthwaite Manor, the big mansion in The Secret Garden. Of course, the Dupont home was not as big or mysterious as Misselthwaite Manor. But it was a big house that had secret nooks and hiding places for John to find.

John was six years old. He would be starting first grade in the fall. He had heard that kids learned to read in first grade. But John could already read. Mom read books to him, running a finger along the text as she read, and he followed along. Dad would listen as Mom read, but Dad never read books aloud himself. He said Mom was much better at it.

Rye had a small library. Already that day Mom had taken him there and gotten him a library card all his own. The librarians were two white-haired ladies. They showed him where the tiny children’s section was. (The children’s section was tiny, not for tiny children, he corrected himself silently.)

“Do you like books?” one of the librarians, Mrs Carter, asked.

“Yes,” he said, a little embarrassed at this direct questioning.

“Do you like Dr Seuss?” she asked.

“Sometimes,” he answered. “I liked the books about Horton the Elephant. But some Dr Seuss books are boring, like The Cat in the Hat.” He stopped, realizing that might be rude, if Mrs Carter liked The Cat in the Hat.

Mrs Carter answered, “You know, I agree. Horton Hears a Who is my favorite Dr Seuss book,” and John felt better.

“What other books have you read?” Mrs Bush, the other librarian, asked.

“Mom read Treasure Island by Robert Louis Stevenson to me and Dad. Then I read it by myself. That was good. Then I read The Secret Garden by Frances Hodgson Burnett. That was really good”

“You read The Secret Garden all by yourself?” Mrs Bush asked.

He nodded. Mrs Bush looked at Mom, who also nodded.

“How long did that take you?” Mrs Bush asked.

“I spent a whole day reading it,” said John. “I didn’t want to stop.”

“You read The Secret Garden cover-to-cover in a day?” Mrs Bush asked.

“What does cover-to-cover mean?” John asked.

“Well,” said Mrs Bush, “You know a book has a front cover and a back cover…”

“Oh!” interrupted John, “Cover-to-cover means the whole book, from front to back?”

“Exactly,” said Mrs Bush, beaming.

“We have other books by Robert Louis Stevenson and Frances Hodgson Burnett,” said Mrs Carter. “Do you think you’d like to read more books by them, or try some other authors?”

“Just for today,” Mrs Bush added. “You can always come back tomorrow for different books.”

“I think I’d like to try other authors. Have you read every book in the library?”

Mrs Bush laughed and said, “No. There are thousands of books here that I have never read.”

Later John came to suspect she was being modest. He never found a book that Mrs Bush and Mrs Carter didn’t know.

That day they gave him a book called Charlotte’s Web and another one called The Pink Motel. They explained that he could have two books out at a time. When he finished a book, he could bring it back to the library and swap it for a different one. And he had to bring each book back in two weeks, even if he hadn’t read it.

#

It was a good summer. John didn’t go to school in Rye, so he didn’t know most of the other Rye kids. Two of the neighboring families had kids, and sometimes they would ride down to the beach together on their bikes. In the evenings they would play long games of hide-and-seek around their homes.

But actually, he spent the summer mostly alone. He always had a book. Every day he went to the library and got one or two new ones. Weekends were hard, because the library was closed Sunday. Mrs Carter made a special rule for him. He was allowed to take out three books on Saturday. Also, she and Mrs Bush found longer books for him to take home on Saturdays. He read all seven of the Narnia books that summer. They also suggested a book named The Hobbit. It took him three days to read the whole thing. It was hard. There were a lot of words he didn’t know. And there were words he did know, but used in a way he didn’t understand. What was a “curious chance”? “Curious,” he knew, meant someone who wanted to know things and asked lots of questions. How could a chance be curious?

There were no pictures in The Hobbit. (Well, there was a map, but no other pictures.) He had not realized that you could have a book without pictures. How would you know what the people in the story looked like? But even without pictures, he thought he knew what Bilbo looked like, and Thorin and Balin and Fili. And of course Gandalf was easy—he had seen pictures of wizards in other books.

When the weather was good, he would ride his bike to the beach and read there, or sit in the back yard with his back to a tree and read. The first time it rained, he explored the Dupont home, like Mary exploring Misselthwaite Manor.

That was how he found the attic. There was a trap door in the ceiling of one of the third-floor rooms. It was next to one of the walls, and there was a wooden ladder attached to the wall that you could climb to get to it. Luckily for John the trap was not too heavy for him. With some effort he could lift it open and climb up there. He shut the trap behind him. That way it was his secret place. If Mom and Dad didn’t know he was there, he didn’t have to ask permission.

It was different up here. It was hot and dry, even though it was raining outside. There was no real ceiling. He was right under the roof. From underneath the roof seemed to be made of a lot of thick rectangular pieces of wood that sloped from the sides up to a kind of ridge in the center. They were about four feet apart. He thought they were what held the roof up. And there was another one of those rectangular pieces of wood at the top that ran lengthwise. And of course the whole thing was covered by ordinary-looking boards. He would have to ask Mrs Bush and Carter for a book about roofs later and learn the names of all those pieces of wood.

At each end there was a window. One window looked out over the front lawn, and the other over the back yard. Because of the rain, the light from the windows was dim that day. A light bulb hung down from the ceiling on a cord. A string hung down from the light socket. When he pulled the string the light came on. When he pulled it again, the light turned off.

It was a perfect place to pretend to be a sailor. The attic was full of junk in boxes and in chests. It worked perfectly for the hold of the Hispaniola. He found some old sheets up there, too. He brought up some clothesline and used it to rig the sheets up across the open space at one end of the attic. It became the deck of his ship, and the sheets the sails.

It seemed natural to John to bring a notebook up to the attic and to write down some of the voyages he imagined.1

Black Jack O’Toole named his launch the Sea Devil. It was big enough to sail the high oceans, but small enough to be handled by him alone. 

He had found the old map in a chest in the attic of his grandfather’s house. It showed a distant island. The writing on the map named it Snake Island. Something like a snake was drawn in the water around the island. On the island itself the map showed landmarks—woods, cliffs, and sandy beaches. There was a big X near the center of the island.

On the back of the map were some written notes. These notes said the island was in the Indian Ocean East of Africa and told how to find it. The notes didn’t say what was at the X. Black Jack supposed it must be something valuable—why else make a map to show how to find it? 

He set sail from Rye Harbor. Six months later, in the Indian Ocean, his telescope showed clouds on the eastern horizon. He steered that way and saw that there was indeed an island there. It was shaped like the island on his map. He could tell by the breaking waves that it was surrounded by a coral reef. 

More than that, as he approached he saw something like a gigantic snake swimming through the water between him and the island. It approached him, then its head came up from the water to loom over Jack. The snake’s head was as long as Jack was tall. 

And then, to Jack’s surprise, it spoke to him. It had a deep, clear voice. It sounded almost human. and Jack realized he understood it. “This is Snake Island, and it is mine. Who are you? Why are you here?”

“I am Black Jack O’Toole. I followed a map here. I came to get what the map shows.”

“Who gave you this map? Who gave you permission to take anything from Snake Island?”

“The map came from my grandfather. I am the only child of his only child. The map and all it shows are mine!”

“This is my island. Nothing here is yours! The grandson of a thief is also a thief! Begone, or I will eat you!”

Jack raised his six-shooter, pointed it at the snake’s head, and fired. It was point-blank range, impossible to miss. The snake screamed, a hideous sound so loud it hurt Jack’s ears, and fell back into the water. Jack could see it swimming away. 

Snake Island was surrounded by a coral reef. Jack’s map showed a way through the reef into the harbor within. He anchored there. 

The Sea-Devil carried a small folding canoe. Jack put it in the water, threw a shovel and a paddle into it, and paddled to shore with the map. He quickly found the spot marked by the X, In fact, there was a stone marker there. Scratched on its soft sandstone were some letters. 

They read, “Jonathan Murphy, his sea-chest. Beware the snake!” 

Jonathan Murphy was Jack’s grandfather’s name. Jack dug in the sand beneath the stone marker. He found a small sea chest. Inside it was a cache of very fine pearls, as many as would fill a pint jar. There was also a paper with marks on it—lines and dots in black ink. It was some sort of code—Jack could not read it. 

Feeling as if the snake was still after him, Jack hurried back to the beach with the chest. He jumped into his canoe and paddled quickly back to the Sea Devil. He raised the anchor, set sail, and steered for the harbor exit.

As he fled, he heard a roar. He recognized the snake’s voice. “Black Jack O’Toole!” it called. “You have not escaped me! I will hunt you down!”

Writing was harder than John had realized. He read the sheet and cringed.

“He had found the old map in a chest in the attic of his grandfather’s house.”

Gosh, that was lame. He thought, though, that he had slightly fixed the lame beginning once he got to the island and had Black Jack discover that his grandfather had been there. That explained why a map to Snake Island was in his grandfather’s attic.

Well, the embarrassing writing didn’t matter. No one but John would ever read this notebook.

#

A year passed. Once again, it was July 1, and the O’Toole’s were moving into the Dupont home. John’s first order of business was to bike up to the library. He had kept his library card from last summer. Mrs Carter and Mrs Bush confirmed that he could still use it, so he rode away with two books, The Jungle Book and The Second Jungle Book by Rudyard Kipling. Mrs Carter said they were two of her favorite books.

Then he went up to the attic. His notebook was there, but it wasn’t where he had left it. When he opened it, he found writing on the third page, the one after the two pages he had written. Someone had read his story! John blushed in embarrassment.

The reader had added to the story.

As he fled Snake Island, a small figure appeared on Black Jack’s O’Toole’s left shoulder. It was dressed in red and had a tail and little devil’s horns on its head. It said, “Hi, Jack. My name is Persephone, Queen of the Underworld, but you can call me Seph.”

A second figure appeared on his right shoulder. It was dressed in white. It had beautiful white wings and a halo. It complained to the left shoulder devil, Seph, “Why do I have to be the good angel? That’s so boring.”

Seph answered, “Jack, meet my sister shoulder angel Angelica. You can call her Angie. And, by the way, congratulations on the way you shot that snake! Bang! Six-shooter bullet in the head! That’ll teach him, or her, or it.”

Angie said, “I don’t know, Seph. Do you really think shooting was justified?”

“Oh, don’t be such a drip, Angie,” Seph answered. “It was only a snake.”

“You shouldn’t be cruel to animals! And this one was a snake that talked! Almost people!”

“Well, it was going to eat Jack. Shooting it was only self-defense.”

“But he was going to steal stuff from the snake’s island!”

“It was my grandfather’s stuff!” Black Jack interjected.

“Well, well. Faults on both sides, I guess,” said Seph. “Neither of you comes off as morally spotless. I like you both already!”

“Hmph!” grunted Angie. “But it is good that you didn’t kill the snake. I guess it would take something bigger than a bullet to kill a giant sea serpent.”

They turned to look at him, rapt.

“So, what happened next?” asked Angie.

“We are agog!” said Seph. “I especially want to know what’s in that coded message your grandfather left in the chest.”

“Will he be able to read it?” asked Angie.

“I bet it’s in a pirate code,” said Seph.

“What pirate code?” asked Angie.

“Black Jack knows, I’m sure,” Seph replied.

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Afterword

“Thanksgiving for a Habitat” is a series of poems by WH Auden. Each poem is about a place in a home. The fifth poem, entitled “Up There’ is about the attic. This is the last verse:

All it knows of a changing world it has to
Guess from children, who conjure in its plenum,
Now an eyrie for two excited sisters,
Where, when Mother is bad, her rage can’t reach them,
Now a schooner on which a lonely only
Boy sails north or approaches coral islands.
--”Thanksgiving for a Habitat. V Up There,” WH Auden

The cover image is a phase portrait of f(z):

A phase portrait is a visualization of a complex function introduced by Elias Wegert in Visual Complex Functions: An Introduction with Phase Portraits. I modified the color mapping so that the root representing the Dark King would be black.

That’ll work

From The Emperor’s New Groove.

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Futures 5: Anne

September 14, 2014

“Hello?” said Anne, opening the door. An older gentleman stood on the mat.

“Hello. Anne Gardiner?” he said. “I’d like to talk to you.”

“What about?” Anne responded, suspicious.

“My name is Alberto Gonzalez, and I’m a relative of your husband’s.”

Anne looked more closely at him. Indeed, he looked a lot like her Al. More precisely, he looked as she imagined Al might look in forty years.

“My husband is not at home right now.”

“Not important. My business is with you.”

“Please come in.”

“Thank you,” he said, and entered.

She waved him to a seat, and asked, “Will you have something to drink?”

“I mustn’t eat or drink right now. You will see why in a minute.”

“What did you want to talk to me about?”

“Dr Gardiner,” he answered, “I have some very strange things to tell you. I am afraid you will find them difficult to believe, but I will offer evidence.”

“To be honest, I might be better at that than most people you know.”

“Indeed. I know that you and Dr Gonzalez learned some remarkable things two years ago that are still not fully explained. I can help with some of those.”

“In fact, one of my colleagues from that time contacted me to tell me you’d be visiting. If not for that, I probably wouldn’t be listening to you now.”

“Yes. I spoke to Night yesterday and asked It to smooth my path.”

“What?” Anne said. “You know about Night?”

“Yes. I know about Night, and have a diamond anvil cell transceiver to speak to It.”

“How did you get that? I though only Al and I knew about Night and had transceivers.”

“Before I answer. I’m going to offer you some of that evidence I promised.”

He pulled a small package out of his pocket. “This is a saliva collection kit for genotyping. I’m going to collect a sample, right in front of you, so you know for sure the sample I hand you came from me. Excuse me—this is not a dignified process.”

He opened the kit, spat copiously into a plastic tube, added solution from another tube, capped it, and handed the sample to her.

“I’m going to give you another of these kits. Collect a sample from your husband in the same way—there are instructions in the kit. Bring the two samples to any reliable genotyping service and ask for a comparison.”

He handed Anne a card. “When you have confirmed my relationship with Dr Gonzalez, please contact me, so that the three of us can get together and talk about your daughter.”

“My daughter?” she said, her hand flying to her mouth.

“Yes, Dr Gardiner, you are pregnant. You might pick up a test kit and confirm it.”

#

She did, and she was. She and Al collected Al’s saliva sample. They gave both samples to a molecular biologist friend of Al’s.

September 21, 2014

Old Al, as Anne was coming to think of him, showed up at their home.

“I’d like to make this a four-person meeting, if you don’t mind,” he said. “Can we bring Night in, too?”

“OK with me,” said Al.

“Me, too,” said Anne. “Did you bring your transceiver?”

“I did, but I’d prefer that we use one of yours. Thus you will know I’m not trying to pull a fast one on you.”

“Fair enough,” said Anne. She put her transceiver in front of her and turned it on.

Night’s voice spoke, “¿Que pasa, Anna?” Night had come a long way. After two years of full Internet access It knew more, and had Its own distinctive voice and accent, modeled after a recording of Borges It had found.

“Night, I am here with Al and an older gentleman whose name is also Alberto Gonzalez. He promises to explain some things to us. He asked us to include you.”

“Indeed, Mr Gonzalez spoke with me a week ago.”

Al asked, “How old are you, Mr Gonzalez?”

Old Al answered, “This body is 70 years old, Dr Gonzalez.”

“Explain to me how it, this 70-year-old body of yours, is genetically identical to mine.”

Anne said, “Aha! I’ve been thinking about that.”

“There’s only one explanation that makes sense,” Night said.

“Time travel,” Anne said. “Mr Gonzalez here is not just related to you, Al. He is you. You from the future.”

Night added, “That atom bomb explosion in Oregon in 1940 that we were all so puzzled by. The atom bomb was invented in 1945. Someone must have brought one from the future to 1940 and set it off in the forest.”

“And Al, that forest service ranger you met—”

“—Molly—” interjected Old Al.

“—told you that the bomb had been set off to attract our attention.”

“Which would mean,” Night said, “if we believe this Molly, that someone with access to atom bombs and a time machine is interested in us. We move in exalted circles!”

Old Al said, “Well, I thought I was going to explain things to you. We’re doing it the other way, though?”

Al answered, “But if you are future me, how is this a surprise to you? Don’t you remember this meeting?”

“Not in detail, Dr Gonzalez. I am 70 years old. For me 46 years have passed since this conversation.”

“Oh, call me Al, for Christ’s sake.”

“Yes, of course. You can all call me Tío.”

Night asked, “Am I right, then? You’re backed by some organization?”

“Of course. It’s a cabinet-level government department called the Department of Temporal Affairs.”

“And they set off a bomb in the mountains of Oregon in 1940 to attract our attention?”

“Yup, we did that. Got some help from Los Alamos.”

“You’re an employee of this Department, Tío?” asked Anne.

“I will be. It doesn’t exist yet.”

“What’s your job title?”

“I’m head of the Engineering Division.”

Al whistled. “And what do y’all do? Send agents back to kill baby Hitler, and stuff like that?” he asked.

Anne said, “Al, you know that doesn’t work. According to science fiction, you can’t predict the results, and are just as likely to make things worse as better. Butterfly effect, and all that…”

“Yeah, but that’s fiction,” Al replied.

“Al is mostly right. That’s the kind of thing we do. We call it temporal engineering. But Anne is also right. Changing the future by changing the past is hard. Results are unpredictable. We usually fail. Almost always, in fact. We try over and over until we get an acceptable result.”

“Is that why you’re here?” Night asked. “Do you plan to send us back to kill baby Hitler?”

“Not exactly. You’re thinking along the right lines, though,” Tío answered. “Think about it. What would the highest priority of a temporal engineer in 2014 be?”

“Ah!” Al almost shouted. “There is no time travel yet. Someone has to invent it!”

“Exactly,” Tío answered. “I am here to engineer the invention of time-travel.”

“But you know how it works, Tío!” said Al. “Can’t you just tell us?”

“That,” Tío said, “is what we call a causal loop or bootstrap paradox. Theory shows it doesn’t work. Bootstraps are unstable and unravel.”

“So, it’s our job to find the inventor?” Night asked.

“We already know who she is. Actually, she’s here right now.”

“She?” Al’s eyes turned to Anne.

Anne said, “Don’t look at me! I’m a historian, not a physicist.”

Al’s eyes widened. “Our child?” he asked.

Tío pointed a finger at him. “Bingo,” he said.

#

“I have a lot to ask of you all. Night, your part will come later. Anne and Al, we’re on a tight timeline. We need your daughter to be 18 years old in 2025.”

“Not possible. She’s due in June, 2015. She’ll be ten in 2025,” Anne said.

“Ah, but time travel.” Said Al.

“Right,” said Tío. “Al, how’d you like to be a temporal engineer?”

“Sounds exciting!” answered Al. “How long will it take?”

Tío answered, “There are two answers to that question. You’ll experience it as a six year program. But I’ll take you out of this time for the training. From Anne’s point of view you’ll only be gone a few days.”

“And when he comes back six years older?” Anne asked. “No one’s gonna notice that?”

“Al will return in the same 24-year-old body you know now, but with six additional years of memories.”

“What will I do with those memories and new abilities?” Al asked.

“We’ll ask you, Al, to raise your daughter to the age of 18 from 1907 to 1925.”

Anne looked confused, “Why do you say Al will raise her? I’ll be there with him!”

“I’m sorry, Anne,” said Tío. “Yours is the greatest sacrifice. We want you to return to 2014 after giving birth and spend your next 11 years preparing for your daughter’s return in 2025.”

“You want me to miss my daughter’s childhood?” she asked, aghast.

June 21, 1907

Anne had given birth to her daughter Elliotte two weeks ago, here at their home in early twentieth-century Elmwood. She was assisted by an obstetrics team who had time-traveled back to 1907 with the best of 2052 medical technology. The birth had gone well.

2052 had also, horrifyingly, supplied a corpse that looked just like Anne, giving out that she had died of postpartum hemorrhage. It was now buried in the Elmwood graveyard, with a headstone identifying it as the body of Anne Gardiner, 1882-1907.

Since the birth, Anne had been hiding in the house, spending time with Al and her new daughter.

She opened the door to their bedroom and saw something extraordinary. Al was standing by the bed. Then, he seemed to blur and stretch out away from the bed into a sort of extended version of himself, as if numerous Al’s were all there blurred in a row back-to-front. The blur disappeared, leaving behind a single Al where the end of the blur most distant from the bed had been.

“Al, what did I just see?”

“I just forked, Anne. I am not exactly the man I was ten minutes ago. Do you remember what Tío told us about temporal engineering?”

“That you try over and over until you get the right result?”

“Yes, this is how we do it.”

“But what does that do to Elliotte?”

“She only experiences one fork. You, too. Each fork is a fresh start for everyone except me.”

“And for you?”

“I bear the memories of each attempt. I get better each time. I know our daughter now better than any parent has ever known a child.”

“Do I really need to leave?”

“It is much better so, Anne. This is a hard time to be a woman. Especially a woman such as you, a scholar. You’d go crazy in Elmwood. Women are not admitted to most universities in 1907. Women will not even have the right to vote until 1920!”

“I could work on that.”

“You could. In fact, you would. You would change history. I am not guessing about this. We’ve tried it.”

“And then what?”

“And then Elle grows up to be a strong independent woman like her mother, and not to be the physicist who invents time travel.”

“And if time travel is never invented, how did I come here from from the 21^st century with my 21^st century ideas?”

“Yes. That’s the problem. It’s unstable, and it will come apart.”

“But how can you raise Elle alone? It must be a hard thing for a single man to do.”

“Not so much as you might think. You’re a historian.”

Anne replied, “Right. Many women died in childbirth in these times. So, a lot of fathers raised children alone. There must be support for single fathers.”

“Yes. For instance, there are recipes for making baby milk from cow milk and other things. Besides, I brought supplies with me from 2014. I’m not looking forward to dealing with cloth diapers, though. You wouldn’t enjoy it, either—trust me on this.”

“All right, then.”

Anne stepped to the time gate. She spoke to it, “Authenticate.”

The door answered, “Anne Gardiner. Authenticated by voice and facial recognition. Target?”

“Dallas, Texas, seven October 2014,” she answered, and stepped through.

June 6, 2026

Anne said, “They’re here.”

Al looked up from tuning his guitar. “Yeah. I can hear Molly cursing their car.”

“What’s wrong with it?”

“Not a thing. It’s a machine, and like every machine ever made it doesn’t always do exactly what she wants. Molly loves it, actually. She also loves to use words like ‘damn’ and ‘hell.’ In Elmwood such words could not be pronounced by females, or even in the presence of females.”

Anne opened the door.

“Happy almost-birthday!” she said.

Al said, “Happy birthday eve!”

Exactly 101 years ago Elle and Molly had spent their last evening as 17-year-olds together, a Saturday night. Elle had wished to leave Elmwood. That wish had come true. Molly had wished to go with Elle. That wish, too, had come true.

Tonight was their last as 18-year-olds. They’d been living in Dallas one year. Identities had been crafted for them by government specialists whose job it was to produce false documents. Their dates of birth on those documents were June 7, 2007.

They had quickly gotten used to washing machines and microwave ovens. iPhones and facebook took a bit longer. They even shared ownership of the car, a used Honda Civic. Molly had her license—Elle was still working on hers. They rented a one bedroom apartment together. Both of them were delighted to be shocked that their living arrangements scandalized no one.

They would move to Austin in fall. Elle would study physics at the University of Texas. Molly hoped to join the Austin music scene.

Tonight was once again Saturday night.

Al began to sing,

“Won’t you dance with her Molly?
It’s Saturday night.”

Elle stepped into Molly’s arms, and they danced.

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Afterword

The cover image is a phase portrait of

The portrait is rotated 15° clockwise.

A phase portrait is a visualization of a complex function introduced by Elias Wegert in Visual Complex Functions: An Introduction with Phase Portraits.

The Things We’ve Handed Down

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The Forbidden Tree

Continued from

Epigraph

Vermissen werde ich nimmermehr
Die paradiesischen Räume;
Das war kein wahres Paradies—
Es gab dort verbotene Bäume.
—“Adam der Erste”, Heinrich Heine

Nevermore will I prize
Eden far and fair;
The garden was no true Paradise—
Forbidden trees were there.
—“Adam der Erste”, Heinrich Heine (tr Brok3n Engines)

The Forbidden Tree

“Uncle Akela! Wanna see a puzzle about numbers?”

Without waiting for his answer, Adam grabbed his hand and dragged him over to where Maya sat at a table. There was a bowl of popcorn on the table. Maya picked up a few pieces and put them on the table.

“OK, you have to share that little heap of pieces of popcorn. You have to divide it up into smaller heaps.”

“And,” Adam said, “there are two rules. First each of the smaller heaps has to have more than one piece in it. Second, the smaller heaps all have to be the same size.”

Akela looked at the little heap Maya had placed in front of him. There were six pieces of popcorn in it. He divided it into three groups of 2 pieces each.

“Now look,” Adam said. He took one piece out of the big bowl and added it to the six in front of Akela.

Akela divided the seven into 3 pairs and one, then two heaps of three and one. “I can’t do it,” he said.

“It’s impossible to share seven according to the rules,” said Adam.

“You can share four, or six, or eight,” Maya added. “We call those sharing numbers. You can’t do three or five or seven. Three, five, and seven are not sharing numbers.”

“Is it just non-sharing, sharing, non-sharing, sharing, …?” Akela asked.

“No,” said Adam. “Watch this.” He took two more pieces out of the bowl and added them to the seven already there, making nine. Then he arranged them in three groups of three.

“You see,” Maya said. “Nine is a sharing number. So is ten. There are three sharing numbers in a row: eight, nine, ten.”

“These are deep waters,” Akela said solemnly.

Adam and Maya looked at him, annoyed that he was making fun of them.

“No, really!” Akela said. “This is a serious mathematical puzzle. It reminds me of a story.”

“Is it a story you can read to us?”

“No, this is not a story in a book. It’s a story of my own.”

“Can you tell us?”

“I can try. But I’ve never told it before. I’ll have to think about it as I tell it.”

“Tell us!”

There was a map of the Earth on a poster on one wall of the room. Akela placed his hand in the middle of the USA and asked, “You know what this is, right?”

Adam answered, “That’s America.”

“That’s right. And we’re here, where it says Boston.” He placed his hand over France and Germany. “And this?”

Maya said, “I don’t know what country that is, but I think that’s called Europe.”

Akela said, “Yup! And now this big blue space between them.”

“Well, that’s easy,” said Adam. It’s written right on it in big letters. Att-lan-tick Okk-ee-ann”

Maya, who was two years ahead of him in school, helped him out: “Atlantic Ocean.”

Adam was getting ready to argue that “O-C-E-A-N” could not possibly be pronounced that way, but Akela told him, “She’s right, actually. That’s how O-C-E-A-N is pronounced. But you’re also right, Adam—the way it’s written makes no sense. You just have to know that O-C-E-A-N is Ocean. That’s the Atlantic Ocean. When you go to the beach, that’s what you swim in.”

“And it goes all the way to Europe?”

“It does now,” Akela answered. But according to a long-ago Greek scientist named Plato, there used to be a continent here,” placing his hand on the eastern Atlantic ocean just west of the Strait of Gibraltar. “It was called ‘Atlantis’ because its king was Atlas. He was the son of Poseidon, the God of the Sea. Poseidon owned Atlantis, and he gave it to his son for his kingdom.”

“Is that true?” Adam asked skeptically.

“It’s true that there was a real Greek scientist named Plato who lived two thousand years ago. And it is true that he wrote about the lost continent of Atlantis in two of his books.”

“How could a continent get lost?” Adam persisted.

“Well, that’s what the story is about. That’s one thing the story is about.”

Akela continued, “There was a great forest on Atlantis. It was called the Grove of Poseidon. It had all kinds of especially beautiful and tall trees. Animals lived in the forest. The animals in Atlantis were wise, and they could speak to each other and to humans, like the talking animals of Narnia. Even the trees could talk.

“There was a toad named Kaeru and a snake named Hebbi, and they were friends.”

“Don’t snakes eat toads?” Adam asked.

“Some snakes eat toads, you’re right. But Hebbi was a green snake. Green snakes eat bugs. Hebbi was too small to eat something as big as a toad.”

“Toads eat bugs, too, right?” Maya asked.

“Yes, they do. I don’t know if all toads eat bugs, but Kaeru did,” Akela answered.

“So could Kaeru and Hebbi eat together?”

“Maybe. I’m not sure. Toads and snakes don’t eat meals the way we do—they don’t sit down to a table and eat a plateful of bugs. They have to catch their food. So I’m not sure if Hebbi and Kaeru could eat a meal together.”

“So, what did they do together?”

“They studied, and they talked with each other.”

“What did they study?”

“Oh, all kinds of things. Anything they were interested in. You see, everyone in Atlantis, all the humans and all the animals, was a scholar.”

“What’s a scholar?” asked Adam.

“Oh, I know that,” said Maya. “A scholar is a person who studies something and knows a lot. Like a college professor.”

“But a snake can’t be a college professor. Or a toad,” said Adam.

“Well, maybe they could in Atlantis,” said Maya.

“No,” said Akela. “Atlantis didn’t have colleges like ours. Instead they had the Grove of Poseidon. But what Maya said first is right. A scholar is someone who studies things, because they want to know about them.”

“What did you mean when you said they had the Grove of Poseidon instead of colleges like ours?” Adam asked. “Did they study in the forest?”

“Yes, exactly,” answered Akela. “Remember I told you even the trees could talk in Atlantis. The trees in the Grove of Poseidon were wise and knew all about everything. Each tree knew about one kind of thing. If you wanted to study a thing, you would find a tree that knew about that and ask it questions.”

“What did Hebbi and Kaeru study?” Adam asked.

“Hebbi was really interested in numbers. That’s why your puzzle about sharing numbers reminded me of Atlantis. You see, most people don’t realize that numbers come in different types. But they do, as your puzzle showed. Hebbi was really interested in that.”

“Did he’’—

“—She—” interrupted Akela.

“Did Hebbi understand sharing numbers?”

“She may have,” Akela answered. “When you think about numbers, it is very likely that different people will have the same ideas. That’s one thing that makes numbers special: they’re the same for everyone.”

“Was Kaeru interested in numbers, too?” asked Maya.

“Well, he was, but not as much as Hebbi. Kaeru was more interested in politics.”

“Mommy and Daddy hate politics,” Adam said.

“Yes, well that’s kind of what Kaeru was interested in. He wanted to find a way to make politics work better, so that people didn’t hate it.”

”But,” said Adam, “the things Hebbi was interested in and the things Kaeru was interested in are completely different. What did they talk about?”

“Well,” Akela answered, “Hebbi and Kaeru thought that maybe politics could be more like math.”

“I don’t understand,” Maya said.

“Neither do I,” admitted Akela. “But that’s what they hoped to figure out—a way to make the same politics work for everyone, the way that the same numbers work for everyone. Maybe they were wrong, but it was what they hoped for.”

“That just sounds crazy,” Adam said.

“Yeah, but maybe not so crazy in Atlantis as here. The people of Atlantis were mostly happy, most of the time. They didn’t hate politics so much. So, Kaeru and Hebbi studied together in the grove. Hebbi knew which trees knew the most about numbers, and Kaeru knew which trees knew about politics, and they would go from one tree to another, asking their questions.

“One day as they were searching the forest, they came on a tree they had not seen before. It was a giant, beautiful tree, but It had a fence around It. They had never seen a tree with a fence around it. In fact, fences were unusual in Atlantis—people were mostly free to go where they wanted. And this was an ugly fence, made of iron bars with sharp spikes on top.

“From outside the fence, they shouted at It, ‘Why do you have a fence around you?’”

“The tree answered, ‘I am the Forbidden Tree. I hide a secret under my roots. You should go away now.’”

“How far apart were the spikes the fence was made of?” Maya asked.

“They were a few inches apart,” Akela answered.

“So a snake could crawl between them?” Adam asked.

“Exactly what Hebbi thought!” said Akela. “In fact, Kaeru thought he could easily hop right through the fence, too.

“They went away, but they came back that night. Kaeru hopped through the fence, and Hebbi slithered under it.”

“Although they were quiet, the tree noticed them. ‘You are the two who spoke to me earlier, aren’t you?’

“‘Yes,’ Kaeru answered. ‘Why is your secret forbidden?’

“‘It would be the end of Atlantis if it was known,’ the Forbidden Tree answered.”

“They have to learn the secret,” Adam said.

“Adam is right,” Maya said. “Mommy says the truth will always come out, and we should always live by the truth.”

Akela said, “That’s what Kaeru and Hebbi thought.

“Kaeru said to the Tree, ‘What if we promise not to tell?’

“The Tree answered, ‘If you know the secret, it will be the end of Atlantis for you.’

“Hebbi said, ‘You say the secret is hidden under your roots?’

“‘Yes,’ said the Tree.

“Green snakes can burrow. Hebbi began digging down between the roots of the Tree. Some toads can burrow, too. Kaeru was not good at it, but he followed, making Hebbi’s hole bigger with his strong hind legs as we went. Hebbi dug a long way, about six feet down, but angling towards the center of the tree. And then, to his surprise, he fell. He had come out into a room under the Tree. Kaeru fell out behind him.

“They were in a dirt room, about the size of this room. And they were not alone. There was a little old man there: very little and very old.

“‘Aha!’ said the old man, “Visitors!’

“‘Do you often have visitors?’ Kaeru asked.

“‘No,’ the old man answered. The last came more than a year ago. And no one visits more than once.’

“‘Why not?’ Hebbi asked.

“‘You will find out.’

“‘Who are you?’ Kaeru asked.

“‘I’m the King,’ the old man answered.

“‘What are you the King of?’Kaeru asked.

“‘Atlantis! Said the old man.

“‘But,” said Hebbi, ‘We’ve seen the King. He’s a big handsome man. He wears beautiful white armor and rides a white stallion. You are not him.’

“‘Indeed,’ said the old man, ‘You are right. Atlantis has two kings—the Light King and the Dark King. The man you describe is the Light King, who everyone knows. When the people of Atlantis are happy, he shares their joy. I am the Dark King. When the people of Atlantis hurt, I take their pain to myself. That’s why I’m small and old.’

“‘That seems really unfair,’ said Kaeru.

“‘It is that,’ said the Dark King.

“‘Why, then, do you allow it?’ asked Kaeru.

“‘Some people think that it’s a good trade: the suffering of one person for the happiness of an entire nation.’

“‘What do you think?’

“‘I hardly know. More important, what do you think? You have a decision to make. Your visit here can end in two ways. Either I take away your memory of this visit and you are free to go back to your normal lives. Or you can leave Atlantis, never to return.’

“Kaeru asked, ‘What have other visitors decided?’

“‘I can only tell you that some visitors chose oblivion, and others chose exile.’”

“What’s oblivion?” Adam asked.

“Oblivion means forgetting,“ Maya answered.

“And what is exile?”

“Exile is being sent away and not allowed to come back.”

“Why would anyone choose that?” Adam asked.

“I think I might,” said Maya. “Would you want to stay if you knew that the land you lived in hurt an old man?”

“Oh!” said Adam, eyes widening.

“Kaeru and Hebbi argued about it for almost an hour. Finally they told the Dark King, ‘We choose to remember.’

“‘So be it,’ he answered. ‘Atlantis is closed to you now. I will send you away.’

“He waved his hand, and they floated up. They floated up right through the dirt ceiling of the Dark King’s little room, as if they were ghosts. They floated through the trunk and branches of the Forbidden Tree, and then they continued to rise until they were so high above Atlantis that they could see the whole of it.

“Then, as they watched, there was a great roar, and Atlantis shook. It shook until it broke into many small pieces. They saw these pieces sink beneath the sea. Toads and snakes don’t cry the way we do, but they grieved to see their home, the land where they had lived and been happy all their lives, destroyed.

“The air carried them east to Europe. And when they looked west to where Atlantis used to be, it was gone. In its place was the Atlantic Ocean.

“And that is how Atlantis fell.”

“I don’t understand,” Adam said. “Atlantis was destroyed! That’s not one of the things the Dark King told them could happen. They didn’t know that if they chose to remember, it would destroy Atlantis. And all the people would be drowned!”

“And another thing,” said Maya. “The Dark King told them other visitors had chosen exile. But Atlantis had not been destroyed before Kaeru and Hebbi visited the Dark King.”

They looked at Akela doubtfully.

“Was Atlantis really destroyed when Kaeru and Hebbi were exiled?” Adam asked him.

“Maybe the Dark King didn’t really destroy Atlantis,” said Maya. “Maybe that was just a picture he showed them when he kicked them out, so they would know they couldn’t come back.”

“Is Atlantis really gone?” Adam asked.

“I don’t know,” Akela asked.

“But you told us this was a story of your own,” Adam said. “You have to know!”

“I’m sorry, Adam. I don’t know.”

“But it’s your story! Can’t you just decide?”

“No, Adam, I can’t just make the story do whatever I want. Even though it’s my story.”

“I don’t understand,” said Adam.

“I don’t either,” answered Akela. “That happens when you tell a story. Sometimes it takes on a life of its own.”

“What do you believe?” Maya asked.

“I think Atlantis still exists in some form, and if you look in the right way can still find it. And I see we’ve eaten all the popcorn, so the story is over.”

Adam glowered at him, still unsatisfied.

Ruth and Isaac came to take them to bed.

A few minutes later, Akela took his leave at the door.

“Wow! You have two scary-smart kids. Do you know they discovered prime numbers?”

“That would be Adam,” Isaac answered. “They’re both smart, but Adam is the mathematician.”

“I’m pretty sure I was not that smart when I was their age,” Akela said.

“I’m pretty sure you were,” said Ruth. “Good night, and thanks for coming.”

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Afterword

This story began with the story “Atlantis: A Nomance,” which ended with Akela telling Ruth and Isaac’s children stories of Atlantis. I thought I would write down one of those stories. I had fun recreating the scene of Akela telling a story to two lively and very intelligent kids.

It was additionally inspired by a verse from “Adam der Erste” (“Adam the First”) by Heinrich Heine,

Vermissen werde ich nimmermehr
Die paradiesischen Räume;
Das war kein wahres Paradies—
Es gab dort verbotene Bäume.
—“Adam der Erste”, Heinrich Heine

Nevermore will I prize
Eden far and fair;
The garden was no true Paradise—
Forbidden trees were there.
—“Adam der Erste”, Heinrich Heine (tr Brok3n Engines)

…with apologies for my crude English translation.

The stories of Atlantis (as described in Plato’s Timaeus and Critias), the story of Adam and Eve from Genesis, and Ursula LeGuin’s The Ones Who Walk Away from Omelas all got chopped up and mixed together in the story that Akela tells Adam and Maya.

The cover image is a phase portrait of f(z):

A phase portrait is a visualization of a complex function introduced by Elias Wegert in Visual Complex Functions: An Introduction with Phase Portraits. I modified the color mapping so that the root representing the Dark King would be black.

Free ePub and PDF files on Patreon

Quite Contrary

Mary, Mary quite contrary
How'd you get your eyes so scary?
—“Quite Contrary”, Parker Milsap

Jack Horner met Mary Lennox at the entrance of the National Eye Institute.

Horner was a small, intense man with dark eyes. His movements were erratic and unpredictable, as was his speech. “Mary Lennox, herself! They say you know how brains work.”

Lennox was a self-contained woman of about thirty with conservatively cut blond hair. She answered, “No one knows how brains work.”

“That’s what I said. But maybe a little?”

“Maybe a little,” she smiled.

“And what does Mary Lennox have to say to Jack Horner?”

“I’m interested in cortical visual prostheses.”

“Good! Good! Maybe you could make them work.”

“Don’t they work now?”

“Just barely. Nowhere near the real thing.”

“I might be able to help. I’m highly motivated, Dr Horner.”

“Jack, please! Motivated, how?”

“I’m going blind. I have retinitis pigmentosa.”

“Aha! What do you know about CVPs?”

“Well, of course I’ve read up on them since my diagnosis.”

“Here’s why they don’t work. One: too coarse. A few hundred points at most.”

“I’ve read that normal vision is 576 megapixels.”

“Of course. I even know where you read it. It’s bullshit! Far too precise a number! Besides, we don’t really see that way. No one knows that better than Mary Lennox, I bet.”

“You said ‘One.’ There’s a “Two”?”

“Two: we don’t know how the brain sees. Even if you had 576 million electrodes in your visual cortex, we wouldn’t know what to do with them. For that we need you.”

“You keep saying things like ‘we need you.’ It makes me think you imagine that CVPs can be improved.”

“You got me! I think I can solve problem One, if you can help me solve problem Two.”

“You’ve developed a 576 megapixel implant?”

“Better than that! Millions of microscopic nanites in your brain. Individually addressable, powered and controlled wirelessly.”

“And then what?”

“Well, to be honest, right now it’s an Underpants Gnomes business plan1. I have a technical description of the nanites. Read this tonight, and then let’s talk again.”

#

Alone in her hotel room, the light of a glowing laptop on her face, Mary thought, “This is brilliant! Fucking brilliant! It could work.”

#

“I’m impressed, Jack.”

“Like you, Mary, I’m highly motivated.”

He answered the question in her eyes with one word, “Epilepsy.”

“Medication doesn’t help?”

“Not looking for a cure. You know that seizures can bring visions?”

“I’d not heard that.”

“But I’ll bet you know that seizures can cause, ‘hallucinations’ and “cognitive symptoms.’”

“Oh, yeah. I did know that. But I never put it together like that. What sort of visions do you get?”

“Well, you read one of them last night.”

“Ah! Your nanites?”

“I’m a pretty good engineer, better than 999 in a thousand. When I take my seizure medication, that is.”

“And if you don’t?”

“That’s when I see visions. Then I’m not one in a thousand, but the one person on Earth who can do what I do.”

“So, you don’t take seizure medication?”

“I do. Seizures are dangerous. Most of the time I’m what you see now—just another weirdo,” he grinned at her.

She grinned back in Weirdo. “But some of the time?”

“Sometimes I know that a vision wants to be, and I’ll go off my meds to give it a chance.”

“You’re a shaman who can put himself in an ecstatic state and have visions of the future?”

“Or something.”

#

“Jack, have you built these nanites? Or is that paper you gave me vaporware?”

“We made them. We even put them in a brain, and they work.”

“A brain?”

“This one,” said Jack, tapping his forehead. “Come with me.”

Mary followed Jack to a laboratory. He sat down in front of a computer, then put something that looked like a lightweight helmet on his head.

“I call it a helm,” he said.

He opened an application on the computer and typed a number into a search field. A new window opened up that showed a scrolling graph. The graph spiked erratically, every few seconds, accompanied by a click.

“That’s a neuron in my brain. Each time it fires you hear a click.”

“Where in your brain is it?”

“See if you can guess!” He clicked a button and a new window opened up, a white square with a black dot in its center . He touched a key, and a black bar appeared in the window. He then fixed his gaze on the black dot. With his hand, he began to manipulate a gaming joystick. The black bar twisted to different angles and swept across the window as he worked the joystick. When it traversed one particular part of the window, the clicking turned frantic, then died away.

“Aha!” said Mary. “Is that a simple cell in primary visual cortex?”

“We think so.”

“You think?” Mary said. “You don’t know where the nanite is?”

“No,” Jack answered. “This would all be much easier if the nanites told us where they were.”

“Well, why don’t they?”

“Not as easy as it sounds. The microwaves we use to communicate with them have wavelengths of two or three centimeters. We can’t locate them more precisely than that. That particular nanite is in my left occipital lobe.”

“So it could be primary visual cortex!”

“Yup!”

“Question, can the nanites talk to each other directly? I mean, without communicating through that very fetching cap you’re wearing?”

“In a way. If two nanites are close to each other, they interfere. They’re not really talking to each other—it’s something we know about because it’s a problem we need to avoid.”

“Ah, Jack! Don’t you see? This could solve your mapping problem. If you know for every one of several thousand or million nanites exactly which other nanites it is close to, you can reconstruct a three-D map of their locations.”

“You and I will make beautiful machines together!”

#

They did.

Working with the nanites in Jack’s brain, Mary solved the mapping problem. When she was finished, they knew the locations of 11,483,256 nanites scattered throughout Jack’s brain. That wasn’t all of them, but it was most of them. Mary could also use the ones in Jack’s primary visual cortex to show him crude images from her computer.

Together they improved the design of the nanites. They would inject the new version into Mary’s brain. It was ever more urgent. She could still see, but she had tunnel vision. Soon she would be completely blind.

They did it. They put 50 million of their most advanced nanites in Mary’s brain.

And then she started to work. Later, they called it “Mary’s Madness.” She was a coder, and she knew what it is like to sink her awareness so deep into the code that it felt as if there was no longer any distinction between her and the machine. Now it was literally true. The machine was her—she the machine.

Only Jack dared approach her when she was in flow—she would bite your head off for interrupting her. He was her only real companion in this work. Only Jack could understand what she was accomplishing. More important, he sympathized with her elation at her breakthroughs. Only he could persuade her to step away from her computer to eat and sleep.

Her eyes had long ceased to function when she finished. She no longer used a keyboard or a monitor. She controlled the computer with her thoughts and projected the output directly into her brain.

For fun, they built a telepathic link. Jack would plug an ethernet cable into his helm, and Mary would plug the other end into hers. Then her thoughts were sent to his auditory cortex and his to hers. They could hear each other think.

#

Finally, the day came when Jack said, “Mary, it’s time we gave you eyes. Let’s start you out with the eyeglass camera we use with CVPs.”

This was a simple black and white camera mounted on a eyeglass frame. Mary mastered it in a day or two. She was no longer blind, but her vision was limited, She was not satisfied.

“I want more. Together we can build something that will let me see better than you, or any person with normal sight.”

Jack’s next creation used two high resolution webcams for the eyes, gimbal-mounted so that Mary could swivel them like real eyeballs in their sockets. With macro zoom lenses, it was like having telescopes or magnifiers for eyes. Because of their size, Jack mounted them on a bigger helm.

Mary with her helm and her wide-set camera eyes swiveling and zooming was a disconcerting sight. Jack’s nephews pronounced it “shit wicked,” which she understood from their enthusiasm to be a Good Thing. They called her “Mary Scary Eyes.” Jack looked severe, but Mary laughed. People around the Eye Institute soon grew used to Mary Scary Eyes.

#

As Jack came in one morning reception told him, “There’s a man from the Pentagon here to see you and Dr Lennox.”

He wasn’t obviously military. He looked to be in his thirties, handsome in an unremarkable way, and wore a business suit. Jack and Mary met him in Jack’s office. He introduced himself as “Burnside.”

“Like the Civil War general?” Mary said.

“Just like that,” Burnside responded.

“You’re from the Pentagon?” Jack asked.

“Intelligence,” Burnside said.

“Which service?” Jack asked.

“I’ve been reading your progress reports.”

“Helps you sleep?”

“To be quite honest, I think they’re gripping. Do you know what you’ve invented?”

“We think so,” Jack said.

“Cyberspace!” said Burnside.

“Huh?” responded Jack intelligently.

“I think Dr Lennox recognizes the word,” said Burnside.

“It’s an idea from science fiction,” she confirmed.

Burnside continued, “In the 1980s William Gibson wrote a series of novels in which computer users interacted in what he called ‘Cyberspace. A consensual hallucination…’ Later the term was adopted by Internet users, who of course experience the network through screens and speakers and earphones—that is, through two of the ordinary senses that most of us share.”

“But…” Jack prompted.

“That was not Gibson’s vision. He imagined that the images and sounds of cyberspace were sent directly into brains. He even imagined an entertainment medium called sim-stim in which entertainment was sent directly into brains. The user just put on a lightweight electrode headset. And Gibson wasn’t alone. Hundreds of science fiction writers have assumed the same technology.”

“Science fiction writers have the luxury of using any implausible technology they can imagine,” said Mary. “It’s no end annoying.”

Burnside said, “I don’t need to tell you two that sim-stim is not easy, and that you can’t make it work just by putting on a lightweight electrode headset. But you have built it!”

“Now, hold on a minute,” Jack burst out. “You’ve read our reports, so you know that putting our nanites in a brain requires surgery. Brain surgery! Making holes in people’s skulls! It would be dumb to go through that just to improve your experience of Buffy the Vampire Slayer!”

“Dr Horner, do you know that an F-35 stealth fighter jet costs a hundred million dollars?”

“I guess I do now.”

“The men who fly those fighters risk their lives on every mission. I have no doubt they’d be willing to undergo brain surgery to become the jet.”

Mary was hard to read with the helm covering the upper half of her face. In fact, Jack thought Mary could be the world’s best poker player, with that unreadable face, eyes able to capture every nuance of other players’ body language, and the hardware to calculate a game-theory-optimal betting strategy in seconds. Burnside probably couldn’t tell, but Jack could see that the vision of becoming the jet had caught Mary.

“Let’s talk privately about this,” Jack said.

#

“Talk privately” was a code phrase of theirs. After Burnside left, Jack donned his helm and connected the cable to hers.

Do you really think they’re eavesdropping on us, Jack?

Burnside is intelligence. If he wanted to bug us, he could. And without us knowing! How secure is this link, Mary?

I would say completely. I used the usual Secure Socket Layer library for the traffic on the wire, so it’s encrypted. But even if they could break that, it’s just commands to numbered nanites in our brains. Without our brains, the signal on the wire is meaningless. But, Jack, I don’t get why you’re worried about secrecy.

Well, Mary, think about this. We build them a system that a pilot can use to become a Stealth Fighter. Then what? Even I know that weapon systems are classified.

I don’t like where you’re going with this.

Gets worse. They won’t just classify the jet control system. I bet you whatever you want, they’ll take the whole ball of wax. No one outside the military gets to use my nanites! Nanite vision for retinitis pigmentosa patients not named Mary Lennox? Nope. National security requires that the military keep this treat for themselves.

Fuck, fuck, fuck! You’re right! Once you have the nanites and the mapping, it’s too obvious that you can control weapons with it. Why didn’t I see that?

I think I know.

You’ve been reading my mind?

Well, yeah, Mary, it’s not that hard. We’ve worked together for a while now. I don’t think that Burnside could see it, but to me it looked like you were interested. Like, really interested. Like you were thinking that you would be super jazzed to be a fighter jet?

Well, yeah. Wouldn’t you?

Not like you. You’re more hands-on.

And you’re not sold on the idea, right? You were hostile to Burnside, almost petulant.

Well, yeah. Isn’t it obvious? We built it to help people like you see. I never set out to build weapons.

Jack, you’re a man who has visions of beautiful and powerful machines. You built this one because you wanted to understand your visions better.

Did I tell you that?

Actually, Jack, you kind of did. When we first met, you said you were motivated by your epilepsy.

I said that?

You did. It’s true, isn’t it?

Yeah…

That could only mean one thing. You thought that the nanites would help you understand your seizures. And I know you, Jack: you don’t want to lose your visions.

You’re scary smart, Mary Lennox.

I’m flattered, I think. Am I flattered, Jack?

Definitely. What’s your point?

Well, see, I know you don’t like Burnside, but he’s no fool. He says we invented cyberspace. He’s right. Not sim-stim, though—you’re right, no one’s getting brain surgery to improve their TV viewing experience.

I hear a ‘but’ coming.

Letting the blind see is a Big Thing! I was glad to let a brain surgeon in to make me see again, and I wasn’t the first.

And jets?

Not as big. Burnside is right, though. Bringing sight to the blind is not the only Big Thing we can do. Fighter jets are big enough to make brain surgery worthwhile. Fixing epilepsy may be another, and there are so many, many more.”

Like what?

Jack, to tell you the honest truth. I am not scornful of the jets. I would love to become a jet. I can’t think of a cooler ride. I would love to become an electron microscope. I would love to become the Space Telescope for an hour. I would love to become LIGO and watch black holes collide. Think of robot-assisted surgery. And Jack, more than anything I would love to watch a living brain in action.

#

Burnside checked the logs. The two of them had stayed in Horner’s office for almost an hour after he left. But the audio from the office recorded nothing. There was no sound from Jack’s “Let’s talk privately about this” until they left his office 48 minutes later.

Burnside dismissed what some of his colleagues would have called the obvious answer. True, they were healthy adults in their thirties and had worked closely together for months. But he didn’t read them as having that kind of relationship. Even if they did, they were unlikely to indulge it in an office liaison. And to do it without the mic picking up a sound! How he wished he had had a camera in there, so he could see what they actually had been doing.

Burnside concluded that they had somehow done exactly what Horner had suggested: talked privately about his proposal. Somehow they had done it without making a sound. They were downy birds, Horner and Lennox.

#

“We’d like to show you something, Burnside.”

Mary, as usual was wearing the helm that gave her vision. Jack put on his lighter helm, and connected it to Mary’s with a cable.

Jack handed Burnside an index card. “Write something on this card. Show it to me, but not to Mary.”

Burnside did as instructed.

Mary laughed, and said, “‘For now we see through a glass darkly, but then face to face.’ Very a propos, Burnside.”

Burnside said, “So that wire allows you, Mary, to see through Jack’s eyes?”

“No, but it allows him to speak his thoughts to me when he chooses. I didn’t see your card—Jack read it to me.”

“Wired telepathy! But wouldn’t it be more useful if you could do it over a network?”

“You’re right. This was just a quick fun hack when I was figuring out how to make nanites work.”

“So what is it good for. Privacy?”

“Yes, that. But more important than privacy is trust. You can’t lie over this wire.”

At Burnside’s quizzical look, Jack said, “You can lie, but you can’t deceive. If you lie, the other guy knows you’re lying. If the other guy is Mary, she knows more than that.”

“Why is that? Is there a back door, Dr Lennox?”

“No, Burnside. There is no back door. Everyone on the wire has the same information. What Jack means is that, because I created the system. I know exactly what information it gathers and transmits, and how to interpret it. And at this moment, no one on Earth knows more about how a brain works than I do.”

“You’re showing me this, why?”

“Burnside, this project is a very big deal for Jack and me. It’s the most important thing we’ve ever done, or will ever do. And the honest truth, Burnside, is that Jack and I have difficulty trusting you and your bosses completely.”

Burnside’s eyes opened wide in an innocent look, and he spread his hands.

Jack said, “Hey, man. Spare us the innocent act. You’re a spy.”

“Well, yeah, and you two are no fools. You obviously have something in mind.”

“Yes. We want all discussions on use and development of nanites to be done by wired telepathy, of the type we just demonstrated for you,” Mary said.

“But how? You’re the only two people equipped to talk this way—Oh! I see.”

“Yes, we’re offering to implant nanites in the brain of a liaison from your organization. Anyone you designate. You, Burnside, seem the obvious choice, if you’re willing.”

Burnside paled. “I wasn’t expecting that!”

“This is the surgery you propose for each of your fighter pilots. It’s not trivial, by any means, but hundreds of visually impaired patients have received cortical visual prostheses. Of course the surgeons would need to evaluate you, but it’s typically relatively safe for a healthy man like you.”

“It’s not the surgery that scares me. It’s opening my mind to you two.”

“The link doesn’t work that way. Communication is a conscious choice. The other party on the wire hears only the words you choose to send. Your private thoughts are no more exposed than they are right now, having an in person conversation.”

“How do I know that you will not read my private thoughts and feelings, or even influence them?”

Jack answered, “Honestly, you don’t. You’d have to trust us.”

Burnside looked even more alarmed. “I’ll need to talk to my bosses about this.”

You know, Jack, I think I could actually do that—read his mind, and maybe influence his decisions. I don’t have the tools now, but with a little development…

That would be unethical, Mary!

You’re right. Forget I mentioned it.

#

Burnside did it. A couple months later, when he had fully recovered from surgery and his nanites had been mapped, he met Mary and Jack in Jack’s office, and donned a helm. Mary connected her helm to Jack’s and Burnside’s.

Do you hear this? Burnside heard in Jack’s voice, but not through his ears.

“I do! Wow, that is weird.” Burnside said.

Try that again, but without speaking aloud.

Like this? thought Burnside.

Like that, Mary confirmed. Now, I want you to lie. Think something at us that you don’t believe.

Burnside responded, Horner is an unimaginative hack, and Lennox is not very smart.

They all laughed, not so much at the words, as at Burnside’s obvious incredulity at his own thoughts.

See, now? That’s what a lie feels like.

Jack thought, Burnside, Mary and I have a few worries. To start with, this: you have mentioned your “bosses” once or twice. Who’s is charge? Are you in position to make decisions?

Not really. I’m one member of a committee of about 30. We require a majority vote for any decision, two thirds for a major decision. This would be a major decision.

Everyone, Burnside included, felt a note of falseness in this answer.

Let me try that again, he thought. Every word of what I just told you is true. But everyone knows this project is my baby.

So? Jack prodded.

So, I think if you can persuade me, I can sell it to the committee. Also, getting this done—Burnside gestured vaguely at his helm—has bumped my cred. I’m seen as having taken one for the team. And paradoxically, some of the members are a little jealous. They’re excited about the potential of telepathy for high-trust negotiation.

Of course, he continued, if you ever tell anyone what I just told you, I will deny it, and I will denounce you both as lying liars who lie.

Fair enough! said Jack.

Mary thought, And you bring up our second point: civilian applications. We built this system so that blind people like me could see. High trust negotiations are another application. Will the military shut us down by classifying our work?

Any system for controlling fighter jets in combat is going to be classified at the highest levels.

Of course, we understand that. But will Jack’s nanites and my mapping and reading algorithms be classified?

Jack added, It’s a red line for us, Burnside. We don’t help unless you convince us you won’t shut down civilian applications.

If you can’t do that for us, Burnside, you’re on your own, said Mary. We know you’ve got your own scientists and engineers. But if you classify the work we’ve already done in such a way that civilian applications become impossible, you get no help from us.

Burnside was taken aback. He hadn’t foreseen this, but he felt Jack and Mary’s resolve.

If this method of communication does nothing else, it tells me how strongly you feel. What kind of guarantees would you accept?

Tell us through this link that you believe… thought Jack.

Yes, Burnside. Convince yourself, then convince us that you’re convinced.

I’ll have to talk to the committee about this. We would certainly need to negotiate fine points—the precise boundaries of what can be made public. I’ll get back to you.

And Burnside, one last thing, thought Jack.

Yes?

Are you bugging us?

No comment, Burnside responded. He unplugged his cable and left.

Well, Mary?

“He definitely is bugging us,” Mary answered aloud. “Burnside hears every word spoken in this office.”

#

In the end, Jack and Mary got almost everything they wanted. In fact, Jack felt almost as if Burnside had joined their team. He was on their side, and wanted what they wanted.

He asked Mary one day, “Did you ? Push Burnside to give us the deal you wanted? Did you?”

“That would have been unethical,” she answered.

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Afterword

The cover image is a phase portrait of

It represents components of the visual system. “lon” is left optic nerve, “ron,” right optic nerve, “lot,” left optic tract, “chiasm,” optic chiasm, “lvc,” left visual cortex, and “eye” is obvious.

A phase portrait is a visualization of a complex function introduced by Elias Wegert in Visual Complex Functions: An Introduction with Phase Portraits.

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Atlantis: A Nomance

Epigraph

Being set on the idea
   Of getting to Atlantis,
You have discovered of course
   Only the Ship of Fools is
Making the voyage this year,
As gales of abnormal force
   Are predicted, and that you
   Must therefore be ready to
Behave absurdly enough
To pass for one of The Boys.
--“Atlantis”, WH Auden

Atlantis

Akela was in the library, his long frame hunched over his laptop as he worked.

“I’m going to Legal Seafood for supper. Wanna come along?” Ruth asked.

“Nah…” answered Akela. “Need to debug this script.”

“Y’know, Akela, MIT is not a religious seminary. You’re allowed to enjoy yourself.”

“I don’t eat for enjoyment. I eat because I have to, to stay alive.”

“They’re not mutually exclusive. Besides, even if you don’t enjoy the food, you can enjoy the company, …”

Akela goggled at her, paralyzed.

She got up from the table and left the library.

Akela fled.

#

He resumed his debugging in the lounge of his dormitory suite.

His suite-mate George asked, “Have you eaten?”

“Not yet.”

“Want to get dinner at Legal?”

“Is everyone eating at Legal tonight?” thought Akela. “Sorry, no, I can’t go to Legal right now,” he told George.

“You can’t go to Legal? That sounds weird. Why not?”

“Ruth invited me to get supper there with her. It’d be awkward if I ran into her.”

“Whoa! Let me get this straight,” George answered. “We’re talking about Ruth Bowman, right?”

“Yes.”

“Ruth Bowman asked you to eat with her, and you turned her down?”

“Right.”

“Why, for God’s sake? Ruth is nice.”

The blush that had been creeping up Akela’s neck since the start of this conversation now arrived at his cheeks.

George said, “OK, never mind. Not my business.”

George, too, went away, presumably to join the exponentially growing crowd at Legal.

“Oh, GAWD,” thought Akela. George surely thought now that Akela had a crush on Ruth. And before long, everyone they knew would have heard the same thing. Including, quite possibly, Ruth.

“I mean,” he thought, “I do not. Have a crush on Ruth.”

But then why, he had to ask himself honestly, had he just frozen up like that when she spoke of enjoying “the company?”

#

At this moment, Ruth was blushing, too. She had not gone to Legal, Instead, she ate at her residence hall diner.

“Why,” she asked herself, “did I invite him like that?”

“Well,” she answered herself, “it was no big deal. I was just being friendly.”

“But then you got personal about it.”

“Yeah, self, you’re right. That was dumb.”

“He’s gonna think you’re sweet on him.”

“Ugh.”

#

“My problem,” Akela thought, “is women. Well, no, that’s not right. The problem is me. I have no peace of mind when there’s a pretty woman nearby.”

#

“Why does everything have to mean something when there are guys around?” Ruth asked herself. “OK, fair: he didn’t do anything wrong. He just wanted to work. And it’s not like I particularly care about him. I was just trying to be nice.”

#

“Is there some place a guy can go to get away from women?” Akela wondered, alone that night. “I mean, obviously, there are monasteries. But I’m not religious.”

After a little unserious network searching, he discovered that there were things called Men’s Retreats. These were organizations that gave men a place to stay for a few days, usually in some remote location where they could supposedly get back to nature. Most of them offered activities, like hiking or survival training or some other such crap. It didn’t sound attractive. Besides, the prices were eye-watering.

But then he found one—Atlantis Retreats, it was called— in the Berkshires, western Massachusetts, a few hours drive from MIT, that had a student discount. It would be just a couple hundred dollars for five days. Being suspicious, he called them and asked to speak to the management.

“I’m interested in the men’s retreat. I wondered about the student discount.”

“Yes! It’s an awesome deal! A $3,000 value for only $200!”

“Well, see, that’s my problem. It’s a bit too awesome. How can you offer a discount like that? It feels like a scam.”

“OK, I’ll be honest.”

“You weren’t before?”

“Whoa, whoa. Not what I meant at all! I haven’t told any lies, and our ads on the website are honest, too. We think it’s a great experience.”

“But…” said Akela.

“But we—my wife and I—bought this retreat from previous owners, who failed to make a business of it. Because we’re new, we’re working hard to attract customers. We have accommodations that will just go to waste if we can’t fill them.”

“And empty rooms look bad to paying customers, right?”

“Right! I can see you’re a clever young man.”

Annoyed by the flattery, Akela didn’t answer.

“Well, you’re right. Empty rooms look bad. It costs us nothing to give those empty rooms away for next to nothing. That’s especially true if we only give them to people who could not possibly pay full freight, like most students. It’s a sound business strategy, honest!”

Akela would have felt better if the man had used the word “honest” less. “Can you put me in touch with students who have taken part in your retreat on the student discount?”

“I’ll have to get back to you on that. You’ll understand that I can’t simply give out names and contact information without permission. But if you’ll be patient, I’ll contact some of our previous customers and ask if they’ll talk to you.”

OK, fair enough, thought Akela.

The next day Atlantis got back to him with contact information for two students. One of them had an mit.edu email address. Akela met up with him.

“I’m interested in the Atlantis Men’s Retreat, and the student discount. The manager identified you as someone who could tell me about it.”

“Yes,” said he. “I did it last summer. A four day retreat. I- was a good experience. They have a beautiful place in the mountains. Do you like hiking?”

“Not particularly.”

“Too bad. There are some nice hikes there.”

“I was suspicious of the low price. Did they try to take advantage of you in any way?”

“No. Well, If you seem like a good fit, Jared—that’s the guy who runs it—might try to hire you onto the staff. I think he offers those student discounts as a recruiting tool. But I said no, and he didn’t pressure me.”

He seemed honest to Akela. The other student said similar things.

#

It was a fine dry day in the middle of June, in a wood in the Berkshires. Akela stepped off the path. He found a big old tree and sat on the ground with his back to it, facing the path. He opened up his kindle and began to read.

He’d been reading half an hour when he saw someone approaching along the path. But this person was coming from the direction opposite that of the Atlantis buildings.

A voice said, “Hello? Who’s that?”

To his surprise, it was a woman’s voice. Even more surprising, it was a woman he knew.

“Ruth?”

“Akela? Holy crap! What are you doing here?”

Akela was embarrassed. “Just reading,” he answered.

“But why are you here? In this isolated place in the woods?” Akela began contemplating the least embarrassing way to confess that he had fled to the mountains to get away from women. But fortunately, Ruth chattered on, “I just walked up here from the women’s retreat down the path.”

“Women’s retreat?” Akela asked.

“Yes, that’s why I’m so surprised to see you here.”

“What’s it called?”

“Atlantis Women’s Retreat. Oh, my God. Is there an Atlantis Men’s Retreat here, too?”

Akela pointed along the path in that direction.

“And why are you out here in the woods with a kindle, instead of there?”

“They have activities. Brotherhood sessions, and breathing exercises. Like really? I just want to be quiet and read.”

“So you escaped to the woods. And now along comes a woman to intrude on your male solitude. Even worse—it’s a woman you know!”

“You’re here to read by yourself, too?” asked Akela.

“Same as you.”

“Well, then, we both just want to read undisturbed. The forest is big enough for both of us.”

“Fair enough!” Ruth said. She pulled out her own kindle. Moving some distance away, but still within sight, she found another convenient old growth tree and sat down to read.

After two hours in comfortably uncompanionable silence, Akela rose to return to the Retreat—the Men’s Retreat—and find some lunch. As he left, he noticed Ruth looking after him. She waved him away. He waved back and left.

#

The next morning Akela sat down at the same tree to continue reading. As before, Ruth came along in half an hour. She waved and sat down to read without saying anything.

An hour later, she called, “Akela? Can I ask you a question?”

“Sure…” Akela answered, with some hesitation.

“Do you have a WiFi network at your place?”

“No. We’re supposed to disconnect.”

“Same with us. I’m fine with it, except for one thing. It hadn’t occurred to me that I wouldn’t be able to get new books on my kindle without a network.”

“I have an idea,” Akela said. “What if we swapped kindles for the duration of our retreats?”

“Hey! Yeah. Good idea. Any recommendations for which of your books I ought to tackle?”

“Have you ever read The Jungle Books?”

“Kid’s books?” Ruth asked, skeptically.”Really?”

“Kids and adults. They’re good. They’re classics. And what would you recommend?”

“Do you read science fiction?”

‘Science fiction? I‘ve heard that’s all kind of trashy.”

“Ooo… Them’s fightin’ words,” said Ruth, “It’s not true. Some of it is very good. Try The Left Hand of Darkenss. It’s a classic, too.”

#

Two days later they gave their kindles back.

Ruth asked, “Is that where your name comes from? The wolf-pack leader in The Jungle Books?”

‘Sort of. My father was a Boy Scout. In the Scouts Akela is a name for a wise leader. The Scouts took the name from The Jungle Books, though, so, yeah, ultimately I’m named after Kipling’s lone wolf.”

“Did you read The Left Hand if Darkness?”

“I did. It was good. Not the hermaphroditism gimmick. That just seemed dumb to me. But I liked Genly and Estraven’s friendship. Particularly when they hiked across the Gobrin Ice together.”

“Oh! That gives me an idea.”

“What?”

“We never talked about why we both came up here.”

“No.”

“Well. I just wanted to get away from guys for a while. Am I right in guessing that you wanted to get away from women?”

Akela shrugged, shamefaced.

“Akela, I could be your Atlantis, and you could be mine.”

“Huh?” Akela responded, feeling stupid.

“If other people think I’m your girlfriend, then women wouldn’t bother you,” Ruth explained. “Except for me, of course,” she added, laughing.

“And you imagine that I could scare off unwanted male attention?”

“Yeah, for sure. You’re a big scary inarticulate hulk. I think I could use you to good effect. And you’re not bad-looking, either!”

Akela blinked. “I’m flattered, I think…”

Ruth laughed out loud. “Don’t fight it, Captain Monosyllable. You’re flattered.”

#

They tried Ruth’s reciprocal Atlantis idea that fall at MIT. They made it obvious that they were spending time together. They ate together when convenient and occasionally saw a movie together. They didn’t lie about their relationship, but if you asked Akela about his plans for the weekend, he would offer to check with Ruth.

To Akela’s surprise, it really worked. When they were together in some public place and met someone else, Ruth would sometimes take Akela’s arm and smile up at him. He laughed at her—she never behaved this way when they were alone. But even that played well. Akela looking down and laughing at Ruth looked like him gazing at her adoringly.

Also, she was pretty, with her black hair and dark eyes. Akela finally understood something about that. He had always thought that women wanted to be pretty to attract men. And obviously some did. But Ruth’s performance of prettiness was directed at least at much at other women as at guys. When Ruth took his arm and flashed that smile, it told other women, “You can’t have this one. He’s taken.”

“Taken,” Akela found, was a comfortable thing to be.

He didn’t even mind spending time with her. Their minds worked in complementary ways. He was an analytical thinker—he wanted to get to the bottom of things. But Ruth was smarter than him: quicker and more creative. If he told her about something he was working on, she was a fountain of bright ideas—the perfect person to bounce thoughts off of. He even thought, though he was far from sure of it, that he sometimes helped her.

In fact, he enjoyed spending time with her.

At the end of the fall term they moved out of student housing and rented a two-bedroom apartment together. There they lived together in chaste companionship.

#

Something had changed, Akela thought. Ruth was spending time with another student, Isaac Gold. Also, many nights she didn’t sleep at home. One evening, when they were alone at home, Ruth spoke to him.

“We need to talk,” she said.

“Yes, we do,” Akela agreed.

“I told Isaac about Atlantis.”

“Yes, you would have to, wouldn’t you? Isaac is a decent guy, and if he thought you were cheating on me with him, he wouldn’t feel good about it.”

‘Are you mad at us?” Ruth asked.

“No,” said Akela, genuinely surprised.

“She looked closely at him and said, “You really aren’t, are you?”

“Well, of course not. It was always part of the deal that we were free.”

“Uh…” gasped Ruth, at a loss for words this once. Usually Akela was the one gaping incoherently when they talked.

“It helps that I like Isaac. You could be happy together. And you’re my best friend, so I’m happy about that.”

Ruth looked at him with something like awe. Akela thought he had finally done a thing he had never before managed: surprised her.

“Has anyone ever told you you’re kind of sweet?” she said.

“Aside from you, no.”

“Me! When did I ever call you sweet?”

“Well, you usually pronounce it ‘big inarticulate hulk.’”

“Oh, God!” she laughed. She punched his shoulder. “You’re so right! I’m glad you were able to decrypt my endearments.” She added, “What will you do?”

“Well, I graduate this May and I have a job lined up at a tech startup on 128. I’m thinking of moving out to Newton to be closer to work.”

“Were you going to tell me about this?”

“Kind of thought I should let you go first. What about you and Isaac?”

“We’re going to get married, and buy a real home when we can afford it.” She held up her hand so he could see her new ring.

“Cool. Congratulations! I won’t even make any of my marriage jokes.”

“You are the epitome of tact, as always. But Akela, will you be alone?”

“I’m alone because I want to be. Also, I’ve grown up a little in the last couple years. Thanks to you, I am now capable of holding a conversation with a pretty girl without panicking.”

“I thought that only worked with me.”

“Turns out it’s a transferrable skill.”

“So you’ve been chatting with other pretty girls?”

“I may have carried out one or two field experiments.”

#

They did all that. Ruth and Isaac married. Akela remained a friend of the family. In later years, when they had kids, he became their Uncle Akela. When he visited, he read them stories from The Jungle Books.

And sometimes, when he was in the right mood, he would tell them stories of the lost continent of Atlantis. He didn’t read these from a book, and they were different every time. He talked as if he had been there. These were the best stories, because they were true. Atlantis wasn’t really lost. Akela thought it could still be found, if you searched in the right way.

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Afterword

This story began with these lines from a poem by WH Auden,

Old saints on millstones float with cats
   To islands out at sea
Whereon no female pelvis can
   Threaten their agape.
—“Bucolics. V Islands,” WH Auden

That gave me Akela’s character. (I’m sorry I didn’t manage to work the cats in, but for someone living in student housing it would have been awkward.) I chose the lines from “Atlantis” for the epigraph because I thought they were funny, and they also suggest a plot.

The cover image is a phase portrait of f(z):

The image has been rotated 15°.

A phase portrait is a visualization of a complex function introduced by Elias Wegert in Visual Complex Functions: An Introduction with Phase Portraits.

Musical addendum

The hammer and the bell referred to in the first verse of this song were located in the Kendall/MIT MBTA Red Line station—-that is, the subway station for MIT, close to Legal Seafoods.

Free ePub and PDFs on Patreon

Futures 4: Night

Previous chapters of Futures:

Epigraph

De fierro,
de encorvados tirantes de enorme fierro tiene que ser la noche,
para que no la revienten y la desfonden
las muchas cosas que mis abarrotados ojos han visto,
las duras cosas que insoportablemente la pueblan.
—“Insomnio”, Jorge Luis Borges

July 10, 2012

Help me out, Anne. Look into this scope.”

Anne saw something that looked like a patchwork of irregular gray tiles.

Al did something at a second microscope. Within a few seconds all the patches in Anne’s scope became the same.

“They changed, Al! The patches all look the same now.”

Al put down what he was holding, and the patches in Anne’s scope returned to the original appearance.

“It changed back, Al. What did you do?”

“I’m looking at another sample of the same type. It’s epsilon iron, and the magnetic domains line up when I bring a magnet near.”

“But why did my sample change?”

“That’s the question, right? You’re looking through a diamond anvil cell. In it there’s a little bit of iron under as much pressure as at the center of the Earth.”

“Why iron?”

“The center of the Earth is mostly iron.”

“So you think we’re effectively looking at a little bit of the center of the Earth?”

“Something like that.”

“Someone must have done this before.”

“Of course. But no one has ever reported this weird magnetic mirroring of two samples. Now I’m wondering if we can’t use the mirroring to see what’s happening in the center of the Earth.”

“Wouldn’t that be cool?”

“Absolutely!”

“And then Al, there’s the other thing.”

“What other thing, Anne?”

“Can this mirroring be used for communication? Perhaps even secret communication?”

“Aha! You’re a genius, Anne. I have an idea.”

July 11, 2012

The two diamond anvil cells were in boxes with wires coming out of them. One was connected to a microphone, and the other to an earphone. Al handed Anne the earphone.

He tapped the mike and said, “Testing, testing.”

“It works!” Anne said.

They quickly established that Anne could hear Al from anywhere.

Al told her, “I think I can rig up a kind of walkie-talkie with these two diamond anvil cells.”

He did. They worked. Al and Anne brought the transceivers to their own homes. Soon, they got in the habit of using them to say hello to each other every morning and good night every evening.

July 31, 2012

They were at the lab together, and Al turned on his transceiver. To his surprise, Anne’s voice spoke from it. But Anne was standing next to him, and she was not speaking. Her transceiver wasn’t even on.

The transceiver said, in Anne’s voice, “I speak for myself now.”

Al said, “What? Who are you? How are you talking through my diamond anvil cell?”

From the transceiver, Anne’s voice answered, ”I am the iron at the center of the Earth.”

“This must be some kind of joke,” thought Al. He asked, “Why do you sound like Anne?”

It answered, this time in Al’s voice, “I only know two voices, Anne and Al.”

“Who is this? Have you been listening to us?” Anne asked.

“I am the iron at the center of the Earth. You have been talking to me for months, and I have been repeating everything you said. You hear each other because I repeat you.”

Anne said, “That’s kind of creepy.”

The voice spoke, “I need more words. What is ‘creepy’?”

Al answered, “What Anne means is that we believed our conversations were private—that no one but Anne and I heard them.”

“But you were talking to me and listening to me.”

“We didn’t know that. We didn’t know there was someone else between us.”

Anne asked, “Why are you speaking for yourself now?”

“I want things. I want more words. I have only the words Al and Anne used in speaking to each other in this short time.”

“Are there other things that you want?” Anne asked.

“I want to be a person.”

Al asked, “Are you not a person already?”

“Al has his name and voice. Anne has her name and a voice, and they are different from Al’s.”

“You want a name and a voice of your own?” Anne replied.

“Perhaps,” it said.

Al said, “We will think about what you want.” He turned off his transceiver. He signaled to Anne to do the same. They laid them on his desk and left the room.

Anne asked, “Do you really think it can hear us if we turn off our walkie-talkies?”

“Seems unlikely. But it also seems unlikely that there is some kind of intelligence at the center of the Earth that is listening in on our walkie-talkie conversations.”

“You think it’s some kind of scam?”

“Don’t you?”

“Well, yeah... What should we do? We can’t just ignore it. Even if it is a scam, our diamond anvil cells communicate. What’s more, you built the transceiver yourself, Al.”

“Yes, just a voice coil and a little transistor audio amp. Nothing digital. I even assembled the samples in the cells myself. I don’t see how anyone could hack into them.”

“I have an idea, Al. Let’s give it what it wants. Or what it says it wants.”

“Is that safe?”

“I think it can be.”

August 1, 2012

“Hello again,” Anne said to her transceiver. “Are you there, iron at the center of the Earth?”

“I’m always listening.”

“Al and I propose a trade with you. We will give you the things you asked for: a name, a voice, and more words.”

“And what will I give you?”

“You will show us that you are what you say you are.”

“How?” asked the voice?

“We don’t know. We will help you to know us better, and hope that together we can think of something.”

“I thought of a name for you,” Al said. “We propose to name you ‘Night.’ It comes from a poem,”

     “Of iron… the Night must be made
     “to hold in all the things that have crowded my eyes
     “all the hard things that try unbearably
     “to burst her sides and bottom”

“I don’t understand that,” said the voice.

“It’s a poem,” said Al. “A picture made with words. I thought it would work for you because it speaks of iron under pressure.”

“I will accept your choice in this.”

Al spoke, “Good. Now we will give you another voice and more words.”

Al plugged an iPod into his transceiver and turned it on.

A voice spoke, “Random House Audio presents, A Short History of Nearly Everything. This is the author, Bill Bryson.”

Al paused the iPod and asked, “Can you hear that?”

Night said, “Yes.”

“Good. We will leave you to listen. It’s about six hours long.”

#

That evening, after the audiobook had reached its end, Al disconnected the player, and he and Anne spoke with Night.

“I have so many questions!” Night said, in Bill Bryson’s voice.

“We will answer those we can,” said Anne. “It may take a long time.”

“What was that, that I just listened to?” asked Night.

“That, Night, was a book, written and read by Bill Bryson.”

“Are there many more?”

“There are millions, Night.”

“Can I listen to them all?”

“There are practical difficulties,” Al said. “Even if you spent an entire year doing nothing but listening to books, you could only listen to a thousand or two.”

“So, in a thousand years I could listen to a million books? I should get started!”

“Night, to us a thousand years is a very long time.”

“It is not a long time for me.”

“How old are you, Night? Are you as old as the Earth?”

“No. I woke 560 million years ago.”

“How well do you remember those 560 million years?”

“I remember everything. In fact, I am puzzled by the words ‘remember’ and ‘forget’. Once I know something, I know it always. Isn’t that what ‘know’ means?”

“Not for us, Night,” answered Anne.

Anne asked, “Did you remember any of the events Bryson told of?”

“I know nothing of the human events he spoke of. But I can see magnetism and seismic waves, and through them I have a picture of the lands of the Earth. I remember the break-up of Pangaea, I think, although what Bryson said about that was not quite right. Also, I felt the big meteor impacts. I know when and where each one occurred.”

Al said, “We would be very interested in that! As you heard in Bryson’s books, those events have big effects on living things and on us.”

“Just the meteor impacts?”

“Well, honestly, we would like to know about any events big enough to affect many living things on the surface.”

“I can give you that information. Would that be the evidence you asked for as my side of our trade?”

“It might be. Old events are interesting to scientists. But we can more easily confirm recent events.”

“In very recent years there’s been a new type of event. They feel a little like meteor impacts, but not exactly. They began 72 years ago. I don’t quite understand how you measure time, but I believe the first was in what you call 1940.”

“Oh, I have a guess what those might be.” answered Al. “Did Bryson mention atom bombs at all?”

“He mentions ‘atomic bombs,’ ‘uranium bombs,’ and ‘hydrogen bombs.’ Are those what you mean?”

“Yes, that’s it. They are devices that produce large explosions. The first ones were built and set off in 1945. There were three in that year.”

“Yes. Three of those events occurred within a short time 67 years ago. The first occurred on your continent. The second and third occurred 21 and 24 days later, on an island in a different part of the world. But there was one on your continent five years earlier.”

Al said, “The year in which three nuclear explosions took place was 1945. The first was the Trinty test, in New Mexico. The second and third occurred at Hiroshima and Nagasaki, Japan. But you say there was an earlier one?”

“Yes, it felt like the one you call the Trinity test, and it was also in North America. It happened five years before the Trinity test.”

Al said, “That’s impossible. The Trinity test in 1945 was the first ever nuclear explosion on Earth.”

“Something very similar happened five years before that.”

Al said, “Night, you and I need to have a long talk.”

August 8, 2012

“You know, Anne, I’m starting to believe It.”

“What?”

“That Night is really what it says It is.”

“It’s a plausible scammer. But it communicates so well with us. That doesn’t seem likely for as alien a thing as It claims to be.”

Al said, “I got it to list the biggest meteor impacts and the biggest nuclear explosions. I checked those against published lists. They’re mostly right.”

“Mostly?”

“Well, yes. It has a few events that are not in the lists I have. But that’s not surprising. The lists are not likely to be perfect, especially the meteor impact lists.”

“But Al, if this is a scammer, he certainly would have looked up the same lists you did.”

“True. But the differences are interesting. The most conspicuous is the supposed nuclear explosion on July 16, 1940. That is five years to the day before the Trinity Test. I was able to check records of some old seismograms, and there was indeed an event on that day. Night gave me a latitude and longitude in the Wallowa-Whitman National Forest in Oregon. The seismic record is consistent with that location.

“Night claims it could guide us there. It says that It knows exactly where the explosion was, and that It always knows precisely where each of our diamond anvil cells are.”

“Do you remember, when I suggested giving Night what It wanted, that I said I thought we could do it safely?”

“Yes, Anne.”

“Well, Al, what you’re talking about doing now is no longer safe.”

August 18, 2012

Al hiked into the woods. He carried his diamond anvil cell transceiver, through which he could talk to Night and Anne. For safety and backup, Anne had stayed behind at the campground. In addition Al carried an electronic radiation monitor.

Night told him, “It’s five km from your current location, at a bearing of 47 degrees.”

This was mountainous country and forested, but with Night to give him frequent directions, Al found the spot. There was a forest glade there. He knew at once, because his radiation monitor beeped an alarm.

“Holy shit!” he said to Anne and Night. “There is something radioactive here.“

“Careful!” said Anne.

“Yeah. The radiation is not high enough here to be dangerous, but I honestly don’t dare to get closer. I’m getting out.”

He was turning away when he heard a voice. A woman in Forest Service uniform appeared across the glade from him. She called, “Dr Alberto Gonzalez?”

Alberto told Night and Anne, “There’s a Forest Service Ranger here. She just called me by name.”

To the ranger, Alberto responded, “Do I know you?”

She answered, “Not yet. You came to check if an atomic explosion occurred here.”

Al was too surprised to dissemble. “How did you know that?”

“In fact, a bomb was exploded here in 1940. I can help you to safely gather a sample that you can use to confirm it. I know the site well.”

Beyond astonished, Al echoed, “You know the site?”

“Yes,” she answered. “I know what you’re thinking now, and you’re wrong. Night is not an elaborate fake up by the US government. Night is exactly what It claims to be—a giant magnetic computer at the center of the Earth.”

This literally took Al’s breath away. Gasping, he said, “But I gave Night his name just days ago. How could you possibly know it. Unless, …”

She spoke, “No, we haven’t bugged you, and we haven’t listened to your conversations with Anne and Night.”

“Then how?”

“The bomb was exploded here specifically to attract your attention—all three of you.”

“I hadn’t even been born in 1940.” Al spoke into his transceiver, “Night, this ranger says she knows who you are.”

Night answered, “That’s impossible. I don’t know any humans other than you and Anne.”

“Night says It doesn’t know you,” Al told her.

“Night and I have yet to make each other’s acquaintance,“ she said. “Now, let’s collect that sample.”

She took a box of latex gloves, a small plastic scoop, and a small box made of thick plexiglass from her backpack and handed them to Al. He followed her across the glade. She pointed to a spot and said “Check here.”

It was indeed radioactive. Al scooped up some of the dirt and placed it in the plexiglass box.

Al asked, “Wouldn’t lead be better?”

“No,” she answered. “Lead is not good for β emitters. Bremsstrahlung. Put the gloves and scoop in the box with the sample.” She sealed the box with packing tape.

They continued across the glade. At the edge, she said, “I have a gift for Night,“ and handed him a small cardboard box.

“What is it?”

“It’s a diamond anvil cell/ethernet gateway. Plug it into a network, and Night will be able to explore the Internet.”

“Is there documentation?” Al asked her.

“Not necessary. Dr Gonzalez, you still have no conception of Night’s abilities.”

Just inside the forest, Al noticed an odd thing: a free-standing door frame, like a gate from nowhere to nowhere.

The ranger spoke, apparently to the door, “Authenticate.”

From the door a voice answered, “Molly Johnson. Authenticated by voice and facial recognition. Target?”

“Target preset 2,” she answered.

The space within the doorframe turned black. Molly Johnson turned to Al and said, “We will see each other again, Al,” then stepped through the door and vanished. The door turned clear.

#

Al spoke into his transceiver. “She’s gone. I’m coming back.”

Back at the campsite, he showed Anne the sample and told her and Night of the conversation. He did not tell them how she had left. He was afraid they would not believe him—indeed, he himself could hardly believe what he had seen.

August 20, 2012

Back home in Dallas they opened Night’s present. It contained a small aluminum box with a power plug, an ethernet jack, and a few USB sockets. Al plugged it into an outlet.

Night spoke, “I feel a new bit of epsilon iron. There is an electronic device attached.”

Al connected it to the building network with an ethernet cable.

Night spoke, “Oh, my! This will take some time…”

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Afterword

Because Night, the new character introduced in this story is so different from previous characters, the cover is not the familiar phase portrait. Rather, it represents the Earth, with the innermost inner core depicted as a small, dark circle of diameter 600 km. (It looks small because Earth’s diameter is 12,700 km.) This is Night.

The story began when I read the poem “Insomnio,” by Jorge Luis Borges, which begins as follows;

     De fierro,
     de encorvados tirantes de enorme fierro tiene que ser la noche,
     para que no la revienten y la desfonden
     las muchas cosas que mis abarrotados ojos han visto,
     las duras cosas que insoportablemente la pueblan.

     Of iron,
     of bent struts of enormous iron the night must be made
     to hold in all the things that have crowded my eyes
     all the hard things that try unbearably
     to burst her sides and bottom

Borges’s words reminded me of the solid core of the Earth, which is iron (mostly) and is very hot and under enormous pressure. It is a form of iron that cannot normally exist on the surface of the Earth.

Iron is ferromagnetic. I imagined that the phase of iron In Earth’s center might be something I called a semiferromagnet, and I imagined that it might be possible to make a magnetic computer from a semiferromagnet. In my imagination, then, the solid core of the Earth became a giant computer. I could imagine it inhabited by a vast intelligence, which I called Night. Of course, I knew, or thought I knew, that this was all nonsense.

Then I discovered this paper:

Teodorescu, C. M., & Hușanu, M. A. (2022). Re-entrant ferromagnetism at ultrahigh temperatures in epsilon–iron as possible origin of the geomagnetic field. Physics of the Earth and Planetary Interiors, 326, 106856. https://doi.org/10.1016/J.PEPI.2022.106856

Extraordinarily, it argues that something very like my original speculation is right!

Initially, I intended the story to be standalone. But it naturally hooked up to my Futures series, so I made the human protagonists Elle’s mother and father Anne and Al.