Open Vulpinsula & Surroundings The Docks The Age of Machining

[Cryle]

Cryle had practically guzzled the water. So caught up in the spycraft and machining-learning, she realized she hadn't eaten* or drank anything since early last evening, shortly before making her attempt at getting inside the quarter. The coolness in her throat and stomach felt nauseating at first, but as she stood and breathed, a little pinkness returned.

She was, after all, still fumingly embarrassed. The last time she had let herself babble like that...

She handed the flask back to Kaii and mumbled something vaguely appreciative and respectful, but altogether entirely unintelligible. She wasn't sure her tongue or lips could do words for a while after that deluge. Buffer overflow was reading into garbage syllable data.

She distracted her mind, briefly, with the putting away of lenses and eyepieces, and the slipping of her telescope back to her baldric. Taking up position at the corner of the desk, she drew out her own notebook and pencil from her toolkit, and began scanning the design. For each gear in the schematic, she marked down the size, relative size, number of teeth, followed by all the depths and pitches as Kaii had provided. Then she wrote down a second list on another page, arranging them by size, and tore it out of the notebook to show to Swifttail. She had drawn a thick line dividing the smallest from the largest, and all the information was there, his own miniature schematic to work from.

On the first page, she simply crossed out the gears she would not be working on. Then, resting her pencil atop the opposite page of her notebook once more, the numbers began to flow.

She was vaguely aware of Swifttail's nervousness, and had she been less embarrassed about her outburst, she would have slowed to show him why certain numbers were manipulated so. It had been her own hurdle as a kit, watching someone trying to explain long division. They had shown how, but without the why, it was total nonsense. Why put that number there, why that number, why add or subtract this and that? It was all part of a method - one she had ditched in favor of her own, once she'd understood the concept at a later age. Correct calculations made sense, but for the calculations to be correct, the calculations themselves had to be sensible.

Cryle worked in silence, save for the scritching of pencil on paper, and a quiet grinding of teeth. Her eyes boggled slightly. For all her embarrassment and worries, this was, for now, a happy rat.

* With the exception of her candies. Which she usually tried to forget about, so that they would still be there.

 

[Kaii Nashirou]

While Cryle recovered, Kaii was already at work to fulfil the request for a teacher. If Swift wanted to be shown how to do the math. Kaii would happily oblige. He knew for sure Swift was capable of doing the basic arithmetic. That was a start and frankly speaking everything that would be needed. Taking the piece of paper, he put down an assortment of numbers he just thought of that would be sufficient to make a gear. Then he took the drawing compass, one with a piece of charcoal instead of a spike as well as a simple pen.

"Those values here are defining what we do wish to build and are paramount in doing the rest of calculations. You start with number of teeth and size of what we call the pitch circle. From that you can calculate the module, something that is very important in dealing with gears and it only takes a simple division..." Kaii explained as he also written down the necessary numbers and shown the division process step by step. He of course could do those in his head with no issue, but if Swift wanted to see it all to the detail, Kaii would oblige.

Continuing on, Kaii further explained to Swift how to obtain the other circles needed to the teeth from starting values as well as briefly, yet thoroughly explained how angles work in maths and mentioned what is sine and cosine function. "I do not expect you to remember those and while you can calculate them, most use specialist compasses or do have sheets with the end-value based on an angle. For now, you may ask me, calculating those is repetitive and wastes time and I do happen to remember all of those with sufficient precision."

Amidst explaining how to calculate the last needed values like the height and width of the tooth. Cryle came in with a list of what Kaii assumed were gears she would work on, leaving the rest to Swifttail. He didn't mind her choosing what to work on, though he did decide to interject one thing. "I respect eagerness, but mind the fact I too am here and wish to work on my own project." He knew anyways that this wouldn't be the last and final form of what he intended to build. Many prototypes would come before that point is reached. Kaii knew thus there would be a lot of work for him to do still, but he wished to work, hence why he made his request. She did also did show a method to do divisions. The marble fox didn't mind the help either.

Finally, Kaii got to once more showing how to draw the involute and thus specify the shape of the gear. After about an hour, Swift had now been subjected to seeing twice, in great detail, how to make a gear, on paper, starting from just the most basic parameters. Despite the fact that most of the math was done before and checked by Kaii for the schematic, including all the values, Swift now knew how it was made. Or at least Kaii had hoped so.

The marble fox finally could leave him to work, though before he started he put his paw on his friend's shoulder. "I believe you, even if you make a mistake or get stuck, you simply will end up learning what to do next time instead." And with that he turned to Cryle that was happily ratting out the way their mind worked with numbers that Kaii saw through, even if it was messy. After all, anyone who saw how Kaii did maths for himself (or tried to read it) typically called him insane.

"Cryle, would you mind telling me more about what you did?" Kaii now asked curiously, wishing to see what progress she had made. He himself finally starting to work himself on the very task he taught the platinum fox. It was known that this Marble fox was a paragon of efficiency, but the way he had done the math indeed was bordering on insanity. There was nothing clean to it like what he had shown to Swift, nor it was sensible like Cryle's was. It was however very fast, even if only truly readable by his own mind.

 

[SwifttailTheFox]

Swifttail leaned forward, eyes narrowing as Kaii’s compass swept another neat curve across the page. He tried to keep up, but when the marble fox started saying words like sine, cosine, and tangent, his thoughts hit a wall.

“Sine, cosine, tangent... what in blazes do those even mean?”

He’d never been taught these concepts in Iskatyut. Back home, shaping metal was more like sculpting clay than reading numbers off a page. You watched the color, felt the give, judged the shape and style by eye. Heat, rhythm, instinct.

Now, all these circles and fractions made his head spin. Still, he followed Kaii’s paw as best he could, tracing invisible arcs on the workbench absentmindedly, hoping touch might teach what numbers couldn’t.

When Cryle slid a paper toward him, he took it with a grateful grin, not quite realizing what it was until his eyes tracked the tidy rows. "Cheers, Cryle. Looks proper tidy." The neat columns and careful measurements suddenly clicked in his mind. She’d made a guide for him. A lifeline.

His gaze lifted to her, pangs of jealousy flickering through his features. She made it all look easy... too easy. Her pencil darted like a dancer, spinning out calculations while he was still trying to remember which circle was which. A little envy stirred in him, but it wasn’t sour; it was the kind that burned into motivation. He wanted to prove he could stand alongside them. Pull his own weight in this new world of numbers and precision.

He swallowed hard, tail flicking before he found his voice.
"Well mate... I... I’ll try m’best. I suppose learnin’ ain’t ever been without work. Just not used to it bein’ so brain focused."

The words came with a nervous laugh, but there was a steadiness in his paws now as he reached for the pencil.

The page blurred a little at first. Equations, numbers... it all looked like a foreign language to him. He hunched closer, tongue peeking between his teeth, and started scratching out figures the best he could. Some patterns made sense, the equations clicking, though others simply refused to stick. A few mistakes crept in. He caught some, missed others.

But he didn’t give up. Before long, the scratch of graphite on parchment subsided. Somewhat shakily, he submitted the work to Kaii for review.

"Righty then... How'd I do, Kaii?"