## Episode 1: Melinda

Melinda Mirreme was curled up behind the backmost table in Kasper’s Koffee Bar, sipping from a mug of Kasper’s finest brew as she slowly sketched out a design in her notebook. “Calculate the area when I add this extra layer to the snowflake, Poly,” she instructed her canary-like mech, Polynomial Time. “There’s got to be a fairly obvious pattern to how it changes.”

Poly floated down from the charging point above the table and perched on the edge of Melinda’s mug to peer at the sketch and accompanying equations. “One and eleven twenty-sevenths the original size, Melinda.”

“Huh.” Melinda wrote that down. “What else? Oh, Poly work out the change in the area from the last time.” She didn’t hear the answer, being distracted by the arrival of a messenger mech, not unlike the one she’d modified to create Poly. The mech itself was a common enough sight, but nobody should need to send her a message by mech now. She checked her watch — still hours before she was expected back home. Metal clanged and she looked up to see the mech collapsed on the table. “That’s odd.” Melinda squinted at the table. “A quality bronze mech like that shouldn’t run out of charge halfway through an errand.” But when she lifted the mech to the charging port Poly had been using it remained inert.

“Does it work for you, Poly?”

The little tin mech obligingly flew up. “It works, Melinda. Mmm, tastes good.”

“Alright, then there must be something wrong with this mech. I wonder whose it is.” Melinda found the clip at the back of the creature’s neck to pop open the head and remove its memory tape. She unrolled the top of the long paper ribbon and ran her finger over the series of ridges that had been scored into it. “Poly, check my transcription, please. I’ll write ones for the ridges and zeroes for the gaps that have been left untouched. And we’ll group them by eights. Got that?”

Poly drifted back down to perch on the coffee mug. “I”ve got it, Melinda.”

“Zero, one, zero, zero, zero, one, one, one; and zero, one, zero, one, zero, zero, one, zero, and; zero, one, zero, zero, zero, one, zero, one. Well, they all start with zero so far, which is hopeful. Pity it doesn’t fit in your head for you to translate it directly, isn’t it?”

“I am not unhappy to maintain these memory tapes, Melinda.” Poly twitched its wings.

“There there, I’m not going to switch anything out. Not that you’d know the difference anyway. Now let’s see how quickly I can get the rest of this tape down before you dredge up the Ascii codes from wherever I left them in your memory.”

* * *

Melinda dropped her pen and stretched, inspecting her double page of ones and zeroes. “I think I need more coffee before we carry on.”

“Coffee is the elixir of life,” Poly replied solemnly.

Melinda laughed. “Do I say it that often?”

“My natural language learning algorithms think so.”

“You spend too much time with wannabe mathematicians.” Melinda fished in her jeans pocket for another coin and spun the dials at the side of the table, selecting black with sugar. “Hop off the cup Poly, or you’ll get coffee in your circuits,” Melinda said just before the dark, steaming liquid came hissing out of one of the pipes that ran from the kitchen all over the coffee bar.

“Now,” Melinda said, sipping her coffee left-handed, “be a dear, Poly, and tell me what these Ascii codes translate to as ordinary letters.”

“Gee,” Poly said, and Melinda noted down the letter. “Arr, Ee, Ee.”

Greetings, student. This message serves as an offer of a place at the Mechatropolis Academy for Mathematical Sciences. We await your response with the return of this mech.

Melinda squealed loudly enough that a number of other patrons turned and stared. A dreadlock-shrouded face appeared from the kitchen to ask “Is everything alright out here?”

“I’m going to the Academy, Kasper!”

Kasper grinned widely. “Well, that’s exciting enough, to be sure, but no need to go shrieking your head off.”

“Sorry.” Melinda poured the rest of her coffee down her throat. “I have to go up and tell them I’m coming!” She looked around at the rest of the coffee bar. “Sorry,” she repeated.

“Ah, that’s alright.” The man at the next table smiled at her. “Can’t say most of us wouldn’t have done the same. Good luck!” He nodded respectfully.

Melinda contemplated this as she walked out to the lift shafts. This didn’t make her a mathematician — there was so much more she needed to learn — but her neighbour in the coffee bar had almost treated her like one. Life was going to be different. Different, but exciting, she decided as she waited for the big brass lift that would take her to Mechatropolis upper echelon. A politician she recognised from the newspapers pushed past her as the lift platform arrived. She wondered if he would have been more careful had she been wearing a mathematician’s gown. Probably not if it was just a student’s gown, she decided. Not that it mattered. She would take Analysis classes and have proper Mechatronics lessons and study Algorithm Design. “This is going to be epic, Poly,” she said as the lift’s huge bronze gears turned and glinted in the gaslight.

Where the middle echelon was a network of gaslit streets, the upper echelon stretched out open and seemingly unconstrained. Huge light tubes attached to the ceiling illuminated the lift shafts and the signpost indicating the Academy, the City Hall and the Space Port. Closer to the Academy, the shadows changed; there were more structural pillars here, with gentler light tubes snaking around them. She paused at the front to take it all in. The Academy building stretched up right to the roof — the surface, really, since nothing else lay between the upper echelon and open space. She’d heard that the ceilings of the Academy’s top floor were all made of glass, to allow for better study of space. Pipes and gears crept up the walls, occasionally sneaking in through a window or terminating in a complicated contraption. Messenger mechs fluttered past, into the building or the narrow mech vents leading to middle echelon. Melinda sighed. It was glorious, and she was going to be part of it. She strode forward and greeted the doorkeeper.

“Hello, my name is Melinda Mirreme. I came to return the messenger mech and accept the place at the Academy.”

“Good afternoon, Miss.” The doorkeeper looked at the mech in her outstretched hand. “Heh. You got the message out without repairing the mech? Don’t see that often. Well, congratulations. You can expect a letter by tomorrow’s evening post latest, which will tell you all about your induction and so on.”

Melinda peered past him into the hallway with its rows of doors and occasional desks piled with documents.

He smiled. “Now, I know you’d like to look around, but I’m afraid I’m under instructions to send all of you lot back home for now once I have your names. Melinda, yes?” He pulled a list out of his pocket and made a tick. “Looking forward to seeing you at induction, Miss Mirreme!”

Find it on Wikipedia:

## Prologue

After Earth burned, the remnant of humanity was contained in the self-sustaining asteroid mining colonies. Carey Atkinson declared asteroid DZ-74316 the city-state Mechatropolis and herself its first mayor. The rest of the asteroid belt ultimately followed suit and the diversity of humanity became embodied in the dozen asteroid city-states, from Arthaign’s flowing drapery and elegant suits, through Khaya’s spacious, efficient corridors to the gaslit streets and polished wood of Mechatropolis.

In the prestigious upper echelon of the Mechatropolis delvings, together with the City Hall and the spaceport, stands the Academy for Mathematical Sciences, founded in Atkinson’s time and still delivering new and fascinating innovations. A selected few youngsters are invited into the Academy’s lecture theatres and teaching laboratories to uncover some of the universe’s deepest secrets.