Wednesday, 27 November 2013

S6.195 - Around the World



The Story So Far: The personified math-tans have been cast out of mathematics. Seeking probability in order to return, Logan and his crew made it to Fractal City - but not without cost. As his group try to understand the fractal inhabitants, the other mathematical relations struggle to come to terms with the repercussions of losing a primary function.


For another look at Tan and
Cot, see this (x, why?) entry
Cosine smiled as she looked down at her violin. Tangent felt her heart soar - she couldn't remember the last time her older sister had smiled. She exchanged a quick glance with her reciprocal, and Cotangent nodded back knowingly. The orchestra idea had apparently been a good one.

"Alright then, time to get back home," Secant stated, putting away her viola.

Tangent's eyes went wide - Lyn, Maud and Elly might not be clear yet! She had to stall for more time! She stepped forwards. "Wait! You can't go. Yet." Everyone's eyes went to her. "Because. Because it's time for... for... a new calendar special! Right, Para?"

Everyone's gazes then drifted to the quadratic. Off of Slope's knowing stare, the parabola pursed her lips. "Exactly! That's... uh... give me JUST a second to round up the family. Though those of you at home can click right here. Okay? Don't forget to come back to comment!"


http://sites.google.com/site/taylorspolynomials/specials/033-thecalendararoundtheworld


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Sunday, 24 November 2013

S6.194 - Contact Lenses



The Story So Far: The personified math-tans have been cast out of mathematics. Seeking probability in order to return, Logan and his crew made it to Fractal City - but not without cost. As his group try to understand the fractal inhabitants, the other mathematical relations struggle to come to terms with the repercussions of losing a primary function.

"I think maybe I will take up the trombone before this is all over," Elly remarked from where she was seated. "We'll give Circe a French Horn, it'll be grand."

Lyn put another crystal down onto the ground before looking over towards the ellipse. "So which conic gets the trumpet then?" she asked. Elly merely smiled quietly.

Maud dropped his last crystal and dusted off his hands. "Let's talk about that another time," he suggested. "After all, we're pretty much in the middle of the Trig camp here. It'll be best if we get completely out of the area before they finish their latest rehearsal with Para."


It will be crystal clear?
"Point. Slope will warn me if there's real trouble though," Lyn reminded, tapping at her communicator watch. She then stepped back to look at the two rings of crystals, which she and Maud had placed around Elly. The ellipse was now seated at the intersection of those rings, in a Lotus pose. "Is that set up properly then?"

"Mmmm," Elly said. "Now I have to shift my focus. Well, foci."

Lyn and Maud exchanged a glance. A few seconds passed. Then a minute. Maud cleared his throat, and was about to speak, when Elly raised one hand with her palm out. She shook her head gently, so the dark haired function demurred.

They had triangulated the relative position of math's Origin Central, located in the heart of the Angle Zone... or they had tried to do it. The process had been quick, albeit difficult, as the only trigonometry they could talk to was Tangent. Fortunately, Circe had helped as well. In the end, if Versine was still in mathematics, it seemed like being in this area would have the best chance of reaching her. Moreover, Elly would be the best person to do it.

Even so, the minutes ticking by started to make Maud uncomfortable. Lyn began to pace back and forth. Elly simply sat serenely, though a frown tugged at the corner of her mouth more than once.


It happened fast. All of the crystals flashed a bright green as Elly gasped, her gaze snapping up into the sky. Lyn didn't catch what happened immediately after. Maud did. The ellipse looked scared. Usually calm and composed, occasionally sarcastic or annoyed... Maud had never seen her scared. Until now.

Then the moment was gone, and Elly stood up, expression neutral, adjusting her orbital hairpiece. "Right. That's not going to work," she said definitively.

Lyn looked from the crystals to Elly. "Something happened though. Was it related to Versine?" Elly stared impassively towards the horizon, as if she hadn't heard. Lyn turned an inquisitive look at Maud.

"Why won't this contact work?" the modulus function asked. "What did you see?"

Elly opened her mouth to respond, but it took a few more seconds before she was able to speak. "I'm not sure. I can tell you this." Another pause. "I think Versine is there, in mathematics... but that I'm there too." She suddenly strode forwards and grabbed Maud's hand, as if reassuring herself as to his presence. Her gaze went from his hand up to him, and they exchanged an uncertain glance.


"You mean it felt like you were in two places at once?" Lyn said in confusion.

The ellipse shook her head slowly. "It felt like I, or at least the being here before you, was an echo. Like..." She dropped Maud's hand, struggling for the words. "Like I'm old copy of a file, which has been tossed in the recycle bin. A file which has since been replaced with something new and better... and I only exist now because the recycle bin hasn't been emptied. Yet."

A little chill went up Maud's spine. "When you say you... do you mean all of us? Are we all echos?"

"I think I need an ovaltine," was Elly's last word on the subject.


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Wednesday, 20 November 2013

S6.193 - Can Torrent Information



The Story So Far: The personified math-tans have been cast out of mathematics. Seeking probability in order to return, Logan and his crew made it to Fractal City - but not without cost. As his group try to understand the fractal inhabitants, the other mathematical relations struggle to come to terms with the repercussions of losing a primary function.

"Diplomacy, Howie," Weierstrass sighed. She looked at the others in the room. "It's not your fault. You're products of the system. But this is part of the reason why we're now devoting our efforts into bringing you on board."

"Can you actually construct and install new Jump Gates then?" Radik asked, eyebrows shooting up.

"It is possible," Dr. Weier affirmed. "It is also worth noting that there are other ways to access us through hyperspace. Such as your Cone of Science, from what I understand. Or timer devices that create wormhole bridges across the dimensions."

"Oh! The Conway box function had one of those," Cosecant recalled.

Logan rubbed his chin. "I wonder if I also have something similar to this in the Heart of my Gazebo."

"Strong thoughts can breach the barriers too," the Weierstrass function added. "Like ParaB's psychic link. In fact, stray thoughts is where a lot of our external communications originate. To the point where we constructed the X-Mansion overtop of the Jump Gate, to better serve the requests of students who want to pursue fractal education." She shook her head. "Too often, people like that are dismissed without cause, treated like weird math mutants or something."


"After all, no one likes math, right?" Howie remarked sarcastically. He shook his head. "Sometimes I think Bert Hill is right. We are the future, not them! They no longer matter."

"Howie..."

"Is one of those beacon Gates in our current Purgatory?" QT interrupted. All eyes went to her, and she intertwined her fingers. "Just, that's where everyone else is now. We'd be able to bring them here to join us."

Weierstrass and Howie exchanged a look of surprise. "It could be one of the two unknown Gates," Weier admitted. "But like probability, there's locks on them. Ones we haven't cracked."

"You're brilliant, QT!" ParaB said, clasping the blonde's hands. The eyes of both girls linked, and both sets of their cheeks began to darken. With effort, ParaB kept her gaze impassive as she turned her attention to Weier. "If there is one, and our counterparts find it, could they remove the password? Or otherwise activate it from their end?"

"I don't see why not," Weier remarked, a hint of amusement in her voice. "One thing at a time though - you may wish to simply depart in your gazebo before this day is over." She turned to Howie. "Tell Candice Torrent she can come in now."


Howie Mandelbrot nodded, raising his communicator to speak into it. Weierstrass shifted her gaze back to the other functions. "Candice Torrent, or Can-Tor as we call her, will probably look a bit different from anyone else you've seen."

Just then, the door opened, and a girl with dark, curiously segmented hair walked into the room. She was wearing a skirt that sported a similar pattern, along with a tank top. But the most surprising aspect of her appearance was that her skin seemed to have a naturally dark tone. She waved, then put her hands on her hips, before jutting one out to the side. "I know what you're thinking, but this is not a tan," she said, smiling quietly.

Radik's eye twitched. "Mind blown," he declared.


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Sunday, 17 November 2013

S6.192 - Jumping to Conclusions



The Story So Far: The personified math-tans have been cast out of mathematics. Seeking probability in order to return, Logan and his crew made it to Fractal City - but not without cost. As his group try to understand the fractal inhabitants, the other mathematical relations struggle to come to terms with the repercussions of losing a primary function.

All eyes were now on Elizabeth Weierstrass. "Dr. Weier, exactly what do you mean when you say 'experience another galaxy'?" Logan finally inquired.


"Metaphor. For statistics and probability," Weier answered. "The world you seek is accessible through our Jump Gate. But it's password protected. To get in, you'll first need to talk with the characteristic function of a set."

"Fine. So let's meet him or her and get on with it," Radik said, gesturing vaguely.

Weier shook her head. "Not so fast," the diplomatic woman countered. "You're products of an outdated education system. The fact you made it here at all is a minor miracle. Before you move on, I ask you... can you leave everything that you are behind? Your feelings, your politics, your agendas? Are you willing to accept even your own irrelevance?"

Hevvi let out a breath. "If you're just going to insult people, can I go? We step functions aren't with this high school group anyway."

Weier turned her gaze onto the Heaviside function. "If you like. In fact, we can send you all the way home. There is a Jump Gate on your steppe."

Flora drew in a sharp breath, and Signum's eyebrows went up. "Ohmigod. That thing?" the sign function said. "The big ring with the four long rails? We could never figure out what it was! It's a Pump Gate?"


There's a connection between rings and fields?

"Hm. So you did spot it. A Jump Gate, yes - with the right dialing equipment, it is capable of opening a vortex into hyperspace. We have one here in the basement of the X-Mansion."

The three step functions exchanged glances. Then Hevvi turned back to Weierstrass. "How many of these things are there?"

"Unknown," Weier answered. "At least seven. We manage the one here in Fractal City, directing the few communications that come through it. They're mostly from humans who have stumbled upon our existence by accident, or as part of their jobs, and who have then become curious."

"Along with the one in Fractal City, the one on the steppe, and the one to probability," Howie Mandelbrot chimed in, simultaneously counting off on his fingers. "There's one leading to lesser used functions like Mink and Con, one leading to the Argand Plane, and lastly two more that act only as beacons. We haven't figured out exactly where they go."

"Some Jump Gates only work intermittently," Weier noted. "Ours included."

"Hold on a minute!" ParaB said. "Our mission is to get back to our subject of mathematics," she reminded, scanning the others in the room. "If we can use a Jump Gate to go directly there, we don't need to worry about probability."

"Math has no Jump Gate," Howie said bluntly. "Because the system you work in cares for very little beyond standardized tests."


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Wednesday, 13 November 2013

S6.191 - That's Weierd



The Story So Far: The personified math-tans have been cast out of mathematics. Seeking probability in order to return, Logan and his crew made it to Fractal City - but not without cost. As his group try to understand the fractal inhabitants, the other mathematical relations struggle to come to terms with the repercussions of losing a primary function.

Howie Mandelbrot cleared his throat. "First, let me apologize to you for the delay in explanations. I know it's been a few weeks since your arrival, but allow me to clarify some of our reasoning."


He's actually a Professor here
"Hmph. Now that you've had time to dream up said reasons?" Radik said skeptically, just loud enough to be heard. He was elbowed in the side by Cosecant. Logan's entire group, QT and step functions included, were currently standing in a meeting room at the 'X-Mansion', a residence Mandelbrot had escorted them to that morning.

"I grant that part of the wait was to learn more about you, to see if you even had it within you to understand, given your origins," Mandelbrot continued. "But another part is that Julia was due for a switchover. This was accomplished yesterday, so we can now devote more time to you."

ParaB raised her hand. "Clarify switchover, please," she said when the fractal inclined his head in her direction.

"There are an infinite number of Julia Childsets," Howie responded. "Each of them is allowed to have a turn at being the coordinator. As such, the Julia you see today will be slightly different from the Julia you previously knew."

The mathematical relations exchanged glances. "It sort of makes sense," Cosecant said after a moment. "After all, one of Sine's child functions should have taken over for her, after she... you know."

"Mmmm. We suspected your tendency for succession only by death," Howie said, crossing his arms. "Kind of surprised assassination never became a thing in your community."

QT let out a gasp. "We're not savages!" she said, a look of shock and horror on her face. "We're well educated functions!"

"Education's part of your problem," the fractal shot back. He grimaced. "But we'll get to that."

"So will New Julia be joining us?" Cosecant asked.

"We'll see her soon. She's with some other people. Which brings me to the last reason for our delay, namely that we wanted to gather as many key community members as possible into one location. They are here now - and it's time you met our resident diplomat." He pulled a communicator from his pocket and flipped it open. "Send her in."


Moments later, the door to the room opened, and a female strode into the meeting room. Her short grey hair had curious peaks and jagged edges in it - obviously a continuous hairdo, but it was hard to differentiate any one strand of hair. She was wearing some sort of variation on fatigues, and had a fairly commanding presence. "Dr. Elizabeth Weierstrass," she declared, looking around at the others. "Call me Weier. Hausdorff dimension of one-point-five." She grinned, and put her hands to her hips. "Are you ready to experience a whole other galaxy?"


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Sunday, 10 November 2013

S6.190 - Map Quest



The Story So Far: The personified math-tans have been cast out of mathematics. Seeking probability in order to return, Logan and his crew made it to Fractal City - but not without cost. As his group try to understand the fractal inhabitants, the other mathematical relations struggle to come to terms with the repercussions of losing a primary function.

"Tha should get yer device workin' proper agin," Cotangent said, her accent coming across thickly in the heat of the moment. The engineer tossed her wrench onto Maud's bar. "How di' you break th' replimator anyway?"

"By creating a double bass," Maud admitted. "We'd never tried making anything that big before." He moved to test the electronic device.

"Those are th' instruments for us then?" Cotangent said, turning to look at Para, the only other function present. Cot gestured towards them, in a corner of the room.


String Theory
The bunny girl nodded enthusiastically, going over to grab one. "You were able to find ArcCot and the other reciprocal inverses?"

"Aye. They'd set up residence to th' southwest," Cot responded, accent now gradually becoming less pronounced. "They prefer ta keep ta themselves, but they'll come ta rehearsal this afternoon." Her attention turned back to the instruments. "All strings?"

"Mmm hmm!" Para held the double bass by the neck. "I'm thinking the different mathematical families should be different orchestral sections. Trig and strings, it makes sense when you think about the way they vibrate. You may have a natural aptitude!"

Cotangent rubbed her chin. "Could be something to that. Should be able to handle a bow, at any rate."

"Para! Para!" Lyn burst into the room, causing the parabola to set the instrument aside. "Para, I just realized..." Her eyes fell on Cotangent. "...absolutely nothing!"

The tall trig girl looked back and forth between the two polynomials. "Um? Somethin' goin' on?"

"No!" Lyn said definitively, only to immediately amend it with, "Kinda." Her eyes flicked to Para then back to Cot. "Writing out a map of our Purgatory is all. You know to the north is that fog, where my beta group spent time looking into other subject areas, yeah?"


"Aye," Cotangent agreed. "And to the south is the cliffs, and to the west and east, not much of anything beyond the structures that seemed to exist when we first got here."

"Along with the electronics within them, which you and Root managed to reactivate," Para reminded Cot as she approached them. "What's your point, Lyn?"

The line paused, choosing her words carefully. "Just that we're all living in a relatively similar configuration to how we were back in math. Consciously or not, it's like when we were 'injected' onto this range, the one-to-one mapping preserved our relative locations. With some variation, I grant, but don't you see what I'm getting at?"

Para exchanged a brief look with Cotangent, who shrugged. The bunny girl shook her head slowly. "No."


The line sighed. "If we were LOOKING for something - or someone - there's a natural hot spot where we might FIND it, relative to the bar here."

"Oh. OH!" Para realized. "Go tell Elly." Lyn nodded and dashed off, leaving Para to smile wanly at the trigonometric function. "The ellipse, um, lost a lot of her mystical crystals when we ended up here," the parabola explained, trying to think of an explanation that didn't involve Versine. "And she doesn't like replicating new ones. The vibe is different, or something. So we've been trying to think of a way to connect back with our subject area."

"Ah! Well, maybe music can help distract Elly, like with Cosine?" Cotangent offered. "For instance, ye could have her take up the trombone." Para simply nodded. She decided that, to avoid stringing Cot along, it was best to let the trombone comment slide.


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Wednesday, 6 November 2013

S6.189 - Add a Love Trace



The Story So Far: The personified math-tans have been cast out of mathematics. Seeking probability in order to return, Logan and his crew made it to Fractal City - but not without cost. As his group try to understand the fractal inhabitants, the other mathematical relations struggle to come to terms with the repercussions of losing a primary function.

"You said THAT?" QT gasped, trying to figure out if she was delighted or concerned.

"Radik was acting like an asymptote," ParaB grunted. "Toeing the line of decency." They were both in her hotel room later that afternoon, the bunny girl leaning back against the headboard of the bed. QT was lying next to her on the mattress, the catgirl's head nestled in ParaB's lap. The conic idly stroked her fingers through some of the polynomial's blonde hair as she spoke. "Trouble is, everyone knew his conjecture was valid."


At what point does the intersection of
parabola and quartic become obvious?
QT heaved a little sigh. "Yeah. We should stop this."

"No."

The quartic function blinked, and uncurled herself to look up at her lover. "That's a first. I thought we'd accepted that we were just using each other?"

"True," ParaB said, ceasing her hair stroking. "But it's not logical for us to continue saying we should stop, when it's become apparent that we're not going to. Not so long as you keep wearing that wonderful perfume, at any rate."

QT blinked. "I don't wear perfume."

ParaB sighed. "I know."

At first, the polynomial stared in confusion, then she felt her cheeks get warm. "Oh."

"That said," ParaB continued, "it creates a new problem. I don't THINK the others will judge our choices - well, aside from Radik - but we're now past the point of being able to bring it up in any manner that's not awkward."

QT scooted up on the bed to sit next to ParaB. "I suppose marching into a meeting and saying 'Hi guys, we're lesbians now!' is not the best approach, huh?"

"Are we lesbians?" ParaB challenged. "You still like guys, right? Because, you know, so do I. Like guys." She rubbed her forehead. "I'm not explaining myself very well."

QT bit down lightly on her lip. "I'm sorry. Was trying to be funny. If... if it helps, hearing you say we shouldn't stop has made me want to hold you in my arms."

"Well, then by all means, do that," ParaB said. Far too hastily, at least in her own opinion, so as QT wrapped her arms around the bunny's shoulders, she changed the subject. "By the way, that elevator encounter of yours, I'll mention it to the others before our next meeting with Julia, if that's okay."

"Oh yeah, that's fine," QT assured, nuzzling her head in near ParaB's neck as she hugged tight. "In fact, I was going to tell everyone myself, as a sort of apology for completely missing the meeting."

"Great. I'll try to make sure you wake up on time in the future too." Pause. "So anything in my recap of our talking points give you ideas?"


"No..." the catgirl murmured. "Something else is giving me ideas though." She nosed in against the bunny's head, and one hand disengaged to trace over the conic's curves.

Silence stretched on for a while then, with ParaB unsure of what to say. With a shiver, she finally settled for, "Not... not there."

"Mrr, we have before. Why not now?"

ParaB found her fingers gliding through QT's hair again. "I... I have no good answer for that. Carry on." The two of them ended up late for dinner.


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Sunday, 3 November 2013

S6.188 - Set Theory



The Story So Far: The personified math-tans have been cast out of mathematics. Seeking probability in order to return, Logan and his crew made it to Fractal City - but not without cost. As his group try to understand the fractal inhabitants, the other mathematical relations struggle to come to terms with the repercussions of losing a primary function.

"We've veered from the point," Logan decided. "The fractals. Anything else you've noticed during our time here? Even something unimportant. We want to be as prepared as possible before our next meeting with Julia Childset or Howie Mandelbrot."

"There's more Julia sets than Mandelbrots," Cosecant offered. "Watching from my hotel room, I've seen a lot more iterations of her out there."

"Could just be the part of the city we're in," ParaB noted. "For instance, anyone in the Angle Zone would see Trigonometric Functions as outnumbering Polynomials."

"That's true," Csc yielded. She shook her head. "But it feels like more than that."


He may have been writing with a Fontaine pen
"I've seen other fractal individuals," Radik offered. "They're mostly staying clear of us, but my imaginary roots help me to spot them. Thus far I've seen an iteration of that Vicsek guy you described from the bar," he said, nodding towards Logan. "Also segmented hair girl, a guy whose hair looks like a blancmange, and some... peculiar entity in what I'd describe as an encounter suit."

Logan rubbed his chin. "Were they all... how do I put this delicately... sort of super deformed?"

Radik nodded. "Yeah. I've wondered about that appearance issue myself."

"Hm. Anything else then?" the logarithm inquired.

The step functions all exchanged glances. "I'm not sure my seduction power works on fractals," Hevvi admitted after a moment. "And since I know I can 'turn on' any function, either they're immune because they fail the vertical line test, like ParaB, or they're something else entirely."

"How are you not sure yet?" ParaB asked.

"I haven't tried to push it, it's only been subtle suggestions."

"You can be subtle?" Radik muttered.


Heaviside glowered at him, so Logan quickly spoke up again. "Thank you, 'Evvi, the information - and trust - is appreciated," he responded. He glanced down at his watch. "With that, we should probably head out to breakfast. Don't want to give the fractals the impression that we're plotting something. ParaB, will you fill in QT?"

"Um. Yup," the conic said, deliberately avoiding Radik's suspicious glare.

"We all know you two are sleeping together," the cube root abruptly challenged. "First excuse was ship repairs, then consoling each other, lately your quadcorder modifications... please! Why not simply admit to your illicit intersections?! That would be a good step towards getting some much needed help!"

"I'm sorry, did I miss the bit where you had proof of those outrageous statements??" ParaB fired in his direction, feeling her cheeks growing warm. Radik simply glowered, as everyone else began uncomfortably looking elsewhere. "As I thought. You don't even have a lemma, let alone a theorem. Talk to me when you learn how to construct a VALID mathematical proof!"

With that, ParaB stalked off towards the ladder at the back of the bridge. The meeting effectively having ended, the others followed shortly thereafter.


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