PELION. QUEERQUEG TAVERN.
As a growing crowd of the curious watched, Non plotted variable star data on a chalkboard. He then drew two thick diagonals.
“Those are lines, and sometimes, a line is all it takes to change the world. Meet my friend Cepheid. She made this plot. On Earth, she worked as the Harvard curator of astronomical photographs and made a groundbreaking discovery. She noticed that brighter Cepheid variable stars had longer periods. By plotting apparent magnitude against the log of the period for variable stars in the Magellanic Clouds, she drew these lines and uncovered the period-luminosity relation—Leavitt’s Law.”
[https://i.imgur.com/6UvQldL.png]
“Isn’t it just a plot?” asked Nagappaloosa.
“This law finds the distances to stars. With these lines, Cepheid figured out how to measure the universe! If you know the brightness, you know the distance.” With that, several offered accolades to Cepheid, who acknowledged the crowd with a smile.
Non followed with a screen showing a Clifford torus animation.
Clifford Torus [https://i.imgur.com/2BdpAyX.png]
“This is a Clifford torus, also called a square torus. A weird object from the fourth dimension. You can think of it as a simple 2D square with opposite edges connected. Link two of these together for a 4D sphere. The four-dimensional sphere dissects into two identical square tori. Isn’t that neat?”
Non Sequitur held Icosian in the air and let it float there, cycling through markings.
[https://i.imgur.com/smmkIYl.png]
“Observe this line in space. In its simplest form, a wormhole or portal connects two 3D spheres, creating a bridge between distant points. It’s a fascinating concept—worthy of a book, don’t you think? Now, watch as my staff uses a wormhole to defy gravity itself.”
Near Gravitation, Misner-Thorne-Wheeler, Cepheid put Wormholes, Leavitt-Ramanujan-Schwarzschild.
Non flipped through the heavy, much-annotated book, amazed. ‘She worked with Ramanujan?’
“What’s a vector?” asked a child covered with needles. Non initially thought of a sea urchin street urchin, but it was a porcupine, with a satchel of for-sale scarves suggesting a tailoring apprenticeship.
“An excellent question. Let’s circle back to vectors in a moment.”
“Gravity crushes wormholes,” corrected Cepheid. “Relative to Icarus, the staff has a fixed positional tensor. Your staff utilizes an antigram of exotic matter Sagittario acquires for us.”
║ I HELPED SAGITTARIO CAPTURE EXOTIC MATTER IN A VEXING BILLION YEAR EXERCISE.
Ñ̰ REALLY? NEAT! BUT I AM SO OUTCLASSED. I SHOULD STOP BEFORE I EMBARRASS MYSELF MORE.
Cepheid saw Non’s pep wane. “You’re doing fine, Non. Please go on. What do the numbers mean with the red markings?”
“It’s a difference set. A smaller difference set has 1, 2, 6 and 4 in a circle. Add up neighbors in all ways to get values 1 to 13, nothing missed or repeated. For example, 4+1 is 5, and 4+1+2 is seven. My staff Icosian has a difference set of length 183 between two portals.” Non moved the central part. “The ends of this staff attach to each other.”
Difference set [https://i.imgur.com/xFRhlr1.png]
Grassleaf moved the central part himself. “Wait. Out of all the things you could have requested, you wanted a portal-assisted staff just so you could show a modulus function using 4D nonsense?”
“I didn’t know! Also, a rolling cycle via folded space is folderol, obviously. The portals allow levitation and vectors. They've already saved my life today.”
Non let Icosian drop to his hand with different markings.
[https://i.imgur.com/smmkIYl.png]
“Without cycles, you have options. The first option in blue is a Golomb ruler, which misses some lengths but has no repeats. Take this one—it’s 216 units long with 18 marks. Except for six small cases, every known Golomb ruler is constructible by a Fibonacci sequence method developed in 1938 by Singer.”
“The other choice in yellow, a sparse ruler, repeats items but misses nothing. My 1-meter-gap sparse ruler measures all lengths up to 214 with 26 marks. Length L needs 「sqrt(3 L + 9/4)」+ 0|1 marks. Length 214 needs 26 marks. For my proof, I added one mark to Brian Wichmann’s approach and addressed complexities, such as the case of 1792.”
“There are other nice sequences. The Fibonacci rabbit problem of 1202 leads to 1, 2, 3, 5, 8, 13 with limiting ratio 1.61803, the golden ratio, phi, φ2=φ+1. The Narayana cow problem of 1356 gives 1, 2, 3, 4, 6, 9, 13, 19, 28 with limiting ratio 1.46557, the supergolden ratio, psi, 𝜓3=𝜓2+1, giving fractal dimension 1.03. That equation leads directly to my psiquad tiling pattern.”
Cepheid interjected skeptically, “That equation alone isn’t enough.”
“You’re right, there’s more to it. The equation 𝜓3=𝜓2+1 has one real and two complex solutions. By taking powers 0, 1, 2, and 3 of a complex root, we get a quadrilateral—let’s mark the origin with a dot. Adding powers 4 and the negative of power 2 creates splitting lines, dividing the quadrilateral into two similar shapes, both exhibiting supergolden ratios. By drawing additional splitting lines, we achieve a fractal triangle through a smooth substitution system. It’s all about adding the right lines. Here's a picture.”
Psi-quad [https://i.imgur.com/0Qj5A7Z.png]
“Scaling that one shape cannot make the needed spiral manifold,” said Cepheid.
“It’s easy,” said Non, showing a spiral of the fractal triangles.
Psi-quad Nautilus [https://i.imgur.com/ezygk6K.png]
Cepheid stared at the sudden surprise nautiloid. “How is that possible? You took 𝜓3=𝜓2+1, used a complex root, the simple powers gave you the coordinates of a new substitution system. And then ... it solves the portal spiral equation? This is borderline magic, Non, but I'm looking right at it. How did you find it?”
"Millions of failed math experiments. With a computer, it's easy to try things." Non moved to finish up. "Behold the power of adding a line! For a portal tiling, I bet psi-quad works better than anything.”
♫ WOULD YOU LIKE TO TRY THE PSI-QUAD SYSTEM ON YOUR STAFF?
║ WHAT? YLEM, THAT WAS THE–
Ñ̰ SURE?
║ WAIT! NO! NO! DANGER! UNDO! YOU CHANGED THE FRACTAL DIMENSION OF ICOSIAN’S PORTALS!
Ñ̰ DO I HAVE UNDO NOW? IS EVERYTHING OKAY?
║ I DIDN’T SHATTER. TALK TO VECTOR BOY WHILE I CHECK.
Non turned to the spikey lad. “May I borrow one of your scarves? The one with a hex grid, thank you. You asked a question. What is a vector?”
Non set Icosian in the air with a slight drift.
“Let me answer with a joke: An equitaur walks into a bar.” He walked away while wrapping the scarf around his eyes.
“A displacement vector is a change of position. I used to be there, now I’m here. On this map of the tavern, we can show an arrow between the two places. The arrow has a direction and a length, also called the magnitude. That arrow is a vector.” He put a screen with a map up.
“Next, I’m stopped. My velocity vector is zero, just a dot on the map. But if I start moving, like this, I’m moving in a certain direction and at a certain speed. The bar also has a vector. See the map.”
“You’re going to miss the bar,” said the spikey lad.
“I am? Let me change my vector. How about now?”
“Your bar is moving, too. You need to go faster or you’ll miss it.”
Non sped up, then blindly bonked into the bar. Several chuckled.
“This smart lad solved the Boat Collision problem. Will two ships moving in straight lines collide? A navigator on one of the vessels finds the relative angle at two different times. If angles are equal, the boats will collide. It’s a property of similar triangles. Let’s try that again, but this time with some angle readings. Watch the map.”
Twelve clops ended with a bonk. With the scarf on, Non couldn’t see who spoke.
“I bring fish up here from Larissa. Been fishing for years. I do that every day. The avoiding crashes thing, not walking into bars. Actually, I do that, too. I didn’t know it was math and vectors.”
“We all use math every day,” said Non, quoting the byline of a show he’d advised for, Numb3rs. “Catch the scarf.” He twirled his head, making one end swing around in a growing spiral, until it slipped off and landed in the lad’s hands. A few cheers.
This story has been taken without authorization. Report any sightings.
Non updated the diagram. “There, we had an initial Archimedean spiral with vectors for angular velocity, angular acceleration, torque and friction. When the friction failed to keep it on my head, we added vectors for tangency, gravitation, momentum, air resistance, acceleration and velocity. Congratulations, you solved all that and caught it. And those scarves look excellent.” He closed out his talk.
“Son, that was beautiful,” said his engineer father. “I’m glad you know vectors now.”
Cepheid joined in. “Non, could you accompany me to the telegram office? I need to send pictures.”
“Sure! Walk or ride? I’m fine with either.” A glance from Lagen disapproved of the riding option.
Later, with Cepheid holding around his torso and riding sidesaddle, Non wrote down file names on a card. “My black staff Icosian is semi sentient. Ask it for these.”
║ SEMI-SENTIENT. THANKS.
Ñ̰ YOU ASKED FOR SECRECY. RAMANUJAN IS HERE? HOW ABOUT HAWKING? EULER? CURIE? SHELLEY? ASIMOV?
║ I’M A SEMI-SENTIENT PICOID, REMEMBER? ONE TRILLIONTH OF A CAGY MIND. I DON’T KNOW. MANY MASK THEMSELVES INSIDE CHARACTERS. TO FIND ASIMOV, YOU MIGHT NEED TO TRY SARAH TOPPS.
On the mountaintop, Non reached his limit for social interactions as Cepheid, Gridwork, and a centauress exchanged pleasantries. He set his staff near a computer and stepped outside for solitude.
Later, near his parents’ cabin, Non used a privacy wall.
║ CEPHEID HAS THE FILES SHE NEEDS. NAGA SET UP FIREWALLS. DID I SCARE YOU?
“Yes.” As he finished, he saw manure bags and a shovel. He filled a sack as Patch and Pachinko arrived in a cart, the unicorn pulling.
“Load ‘em up, please. I like how you drew lines,” said the unicorn.
“Thanks, Pachinko.” Non stacked sacks and took empties.
“May we examine your bullet wound?” asked Patch. “We’re bacters. We sort good and bad bacteria. A few jabs might help.” With assent, the rabbit and unicorn examined Non’s healing wound.
“Want details? Every injury gets infected, but this may need help,” said the rabbit, looking into a case with many tiny vials, all labeled. He selected four of them and 4 tiny needles.
“Go ahead. Some sort of antibiotic?”
“Phages,” said the unicorn. “They outnumber all other living creatures combined.”
Four tiny jabs later, he took in the mountain scene as they trotted off, looking over the windmills, roads, and verdancy. As the Sun (S38) hid behind the mountain across the valley (‘Cave of Chiron over there’), he washed his hands in a rain barrel marked for washing. He obeyed the mats “Clean Your” and “Hooves Here,” then summoned Icosian and headed inside, leaning the staff against the wall.
Ñ̰ THERE YOU GO.
║ THANKS. I’LL BE OVERSEEING YOUR MIND MESH.
“Non! Dinner’s ready,” said Nagappaloosa.
His father Lagen knelt before a drafting table with a blueprint for a zeppelin, an oil lamp providing light as he spun through a calculation on a Curta calculator.
“This is the Erymanthia. I’m one of the engineers. She’s in Athens, but security just went up for anything Hercules-related. Sorry about Lernea. And you died, too, right before we both got shot. Bad day.”
“I lost my dog. But it’s gotten better.” ‘The zeppelin is a giant flying pig.’
“I remember my bad day, May 6, 1937. As a young engineer, I designed and built a mooring mast. The morning paper had an article about me. Then the Hindenburg came up and burst into flames! Worst catastrophe in the world. I felt guilty for years until the mast got ruled out.”
‘I’m glad this zeppelin isn’t manatee-shaped. Shut your mind off. Say nothing.’
“Dear, don’t reuse stories just because Non doesn’t remember them.”
Nagappaloosa set the table, a speedy task with all the snakes helping her. A massive salad of different greens with olive oil, vinegar, garlic and salt formed the main course, which the snakes mixed merrily with nuts and fruit slices. One snake ladled a rich gazpacho soup for him with a big dipper.
“I think I’m supposed to avoid garlic?” Non loaded up his bowl anyways.
“Ten bulbs, avoid. A minced clove doesn’t matter,” said Nagappaloosa, before digging in.
Non watched his equine-headed parents eat, just to be sure he’d not be breaking any social norms of the house, then dug in. At the tavern, he’d held back from stuffing himself. His grazer lips could do a lot of the work. He could swallow more. Equine parents didn’t mind him eating like a horse. ‘4 kg grain, 8 kg forage daily, mostly low-cal foods. Six times my high-cal human diet. But I can eat faster?’
Nagappaloosa finished. “Would you like a marshmallow now or a good breakfast in the morning?”
“Breakfast. I passed the Mischel test as a kid,” said Non. “It was the one treat I didn’t like.”
A clip-clop and knock. “Telegrams.” Naga let in the centauress from earlier.
“Onex P. Goblin sends a note that Swee wants his stuff back,” said Naga before handing the note back for recycling. “I’ll keep this other one for now. Non, this is Violent Reset.”
“A pleasure, once again,” said Non, recalling the centauress on the mountaintop.
“You must have met my twin, Constance. Good to meet you. Any replies?”
“Who would go?” asked Lagen. “Swee and Onex are both dangerous. Onex only talks to Middy and Naga. Middy doesn’t want to go meet her ex-husband. Mama Naga is due to give birth at any hour. But someone should go. I’ve looked the items over and they’re not worth a skirmish.”
“I could go in the morning,” Non Sequitur volunteered.
♫ QUEST ACCEPTED, SWEE AND ONEX P. GOBLIN. YLEM. THAT WAS THE GAMING INTERFACE. NOT ME.
“Risky move, son. Be ready to run away if things turn sour,” said Lagen.
‘I’m Brave Sir Robin.’ “We’re doing what they’ve asked. Shouldn’t get complicated.”
“Reset, relay Non will bring Swee’s gear in the morning.” Reset sped off as Non held the door for her.
“I’ll set up a sleeping mat for you. The stars are out. You can take the telescope. If you do, don’t dally too long, you need a good mind mesh,” said Lagen Cruciger.
Lagen Cruciger [https://i.imgur.com/W88m1I4.png]
“I’d love to look at the stars.” Non watched Dad take down a box, noting the hourglass dolphin swoosh in his pelt. Black hands, whereas Non’s hands stayed white despite a changing pattern. Dad looked powerful, letting Non predict his own health two decades hence.
Ñ̰ ONEX P IS ONE XP? ONE EXPERIENCE POINT? IS CAVE OF CHIRON 𝜒𝜌, CHI-RHO?
║ DON’T READ THAT MUCH INTO IT. YOU KNOW MORE ABOUT GAMING THAN THIS PICOID KNOWS.
Non stood at the door, the telescope on his shoulder.
“You’re letting in bugs and staring into space, son. Didn’t you give up on notifications? If you get back from the Swee stuff early, that’s when a ship sails from Larissa to Athens. We can catch up on things. I could get you a security job on the Erymanthia,” said Lagen.
♫ ACCEPT QUEST, WHEN PIGS FLY, Y/N?
║ HOW VERY ANNOYING. I’M BEING SCHEHERAZADED INTO STAYING WITH YOU. ACCEPT IF YOU WISH. IF YOU WANT A TRUE LITRPG, A FAUX POWER REGION LIKE OLYMPUS CAN LET YOU GRIND LEVELS.
“My item gave me messages. Sorry, I tried to keep up. See you in a bit,” said Non.
“Enjoy the stars. Just remember.” Dad pointed to a worn wall plaque: It’s Pasture Bedtime.
Outside, Non looked at the spectacular starscape. On Earth, the Centauri system was about 4 light years away, the closest stellar neighbors to the Sun. Here at the galactic center, over 10 million stars were closer than that. Sagittario visibly warped the stellar background. Non equipped a lens rated as safe for the black hole. But then he wanted to check “his” journal.
Book fair planning. Book collectors. Books collected. Maps. Some of his own math figures. Memories of his Earth self. Innocent doodles. All innocent.
He opened private screens, then looked to see what he had on file in his mind. Mission: Copy Birds of America. Other tasks for Lernea. Floor plans. Espionage. Contacts. Memory snapshots.
At the top of the book scans, The Learning Hydra, a journal.
“I’ve pushed over the book from my recent memory that you wanted to look at.”
║ THANK YOU. I HELD THAT BOOK WHEN I DIED AS RUMBLER. I’VE ANXIOUSLY WONDERED ABOUT IT. CURIOUS. THERE’S ALSO A COPY OF THIS IN YOUR PERSONAL LIBRARY.
Non opened the memory snapshots and saw his home on Earth, his old self and his dog at peace in the backyard. Then to the crime scene in Lernea’s library lair, which he closed.
“I shouldn’t have opened that. I bet that will be dream material. Time to look at the stars.”
A few opaque screens in key spots kept annoyingly bright stars like S2 from ruining his night vision. He then marveled at the glory of the galactic core.
“Would you like to see yourself through my eyes?”
║ YES, PLEASE. I APOLOGIZE FOR THE STELLAR CLUTTER.
Non Sequitur felt a mild presence in his mind as he looked at a sky with ten thousand times as many visible stars. Many within a few light days away, including the supermassive black hole. The excessive number of stars almost overwhelmed him, like galaxies in the Webb telescope pictures.
“It’s magnificent. And you’re beautiful. I’ll listen if you want to discuss anything. Or be an optimist if you’re worried. Or I can try to bring things into focus as I learn a whole new set of constellations here. But I’ve also seen many items representing Earth constellations today. Let me adjust the Reticulum on this Telescopium.” The accretion disk image sharpened through the eyepiece.
♫ YOU HAVE GAINED INFORMATION OVERLOAD. FAREWELL, SWEET SIMPLICITY, AND HELLO, ENDLESS INTRICACY.
📚 INFORMATION OVERLOAD: POP-UP DETAILS FOR LANDMARKS, FAUNA, FLORA, AND PERSONS IN A GIVEN LOCALE.
♫ PLEASE GIVE SUPPLY MORE EXAMPLES FOR A FURTHER REWARD.
║ ME AGAIN. THIS GAME INTERFACE KEEPS CATCHING ME BY SURPRISE.
Non pulled up a Wikipedia page for reference, then started.
“An air pump was put on that cart. Antlia. I was offered a chance to haul water. Aquarius. You called Officer Song eagle beak. Aquila. I saw a herd of sheep and their herder. Aries and Boötes. He sent hunting dogs at Swee, one big, one little. Canes Venatici, Canis Major, Canis Minor. Henrietta Swan Leavitt talked to me. Cygnus. I might find Asimov if I try Sarah Topps. Triceratops, Lacerta. I’ve seen sextants, triangles, chisels, easels, rulers, microscopes, scales, clocks and a furnace. The rabbit and unicorn are Lepus and Monoceros. The Nemean Lion is mentioned in the book by the Hydra you held. Leo. I’ve met twins. Gemini. My Dad is an equitaur and my grandma’s a pegasus. Dad’s name is Lagen Cruciger, he styled himself after the hourglass dolphin. Grassleaf recommended swordfish and crab. I just got served soup with a big dipper. Ursa Major. Should I keep going?”
♫ HIDDEN QUEST DETECTED: WELL LEARNT CLUB. CHECK YOUR NOTIFICATIONS.
║ INTERESTING. I WAS UNAWARE OF THIS. WANT TO START ON NOTIFICATIONS?
“Tomorrow. I’m tired and eager to be my full self.” He noticed thousands of info dots in the Icarus night sky, offering an encyclopedia of info on all the nearby stars, gas clouds, lenses and filaments.
A kobold ran towards Non as he packed the telescope back in the box.
The kobold held a list of the 88 constellations. “Non Sequitur, you finished it! You made it so hard, running up and down the mountain. Twelve of us couldn’t keep track! Bint will be happy.”
Non tiredly regarded the kobold. “Bint set up this hidden thing?”
The kobold shook its head. “No, Lernea set it up with Icosian and Bint. Thank you for solving it! Agresa would be up all night helping paint pictures of constellations for you to find tomorrow. Can go sleep now!”
Non nodded to the kobold. “Sleep sounds like a good plan. Thanks, Agresa, and thank Bint for me.” He walked back to the cabin and put away the telescope. He shuffled about items on his person and in the area set aside for his stuff.
Non glanced at the 2D blueprints at his Dad’s desk. Someone murdered his boss, the Lernaean Hydra. The Erymanthia boar zeppelin blueprints were right here. Maybe important? He found he could memorize each blueprint. Then he found postcards from his equitaur uncle, with the last from the previous year.
Dear Lagen,
As I’m sure you know, Equitaurs lost their protected status. I shouldn’t have relied on having a home provided for me. My retirement is suddenly over. I should have been nicer. I’m now in Eastport, Italy, but no reliable address. I hope to travel to Greece so I can see you again.
With love, your brother, Psykter
Non laid on the sleeping mat and sighed as his thoughts shuffled around. His uncle had a house and an assistant given to him, just for being rare. Then Psykter went from royalty to dirt in a day. His uncle had been unpleasant to people while living in retirement?
When prompted to record a message for himself, he turned off the “Press the Button” wake-up game.
♫ YOU HAVE EARNED A FAVOR FROM SAGITTARIO. PORTAL ENERGY REDUCED 7%! SEE NOTIFICATIONS FOR OPTIONS.
Non fell asleep before he could appreciate it.