Sunday 29 December 2013

S6.203 - Piece Offering

The Story So Far: The inhabitants of Fractal City have been teaching personified math about the nature of their existence. Very soon, a decision will be made as to whether the high school functions are reunited - or recycled.

The meeting with the Characteristic Function had finally been set. That afternoon, Logan gathered everyone together back on the bridge of his gazebo. That is, with the exception of Flora, who was going over Council reports. "All right," Logan declared. "Anything new to report?"

"Of course not," Radik snapped. "For weeks, the fractals have been avoiding us. Aside from Julia, Mandelbrot, and now Weierstrass bringing us updates."

"Is it deliberate avoidance though?" Cosecant mused. "Or are they simply busy with their own lives? I have been able to spot a few more of them around, compared to when we first arrived."

Signum tilted her head. "Perceiving them may simply be due to our increasing awareness of Hasselhoff dimensions."

"Hausdorff dimensions," ParaB corrected out of the corner of her mouth.

"Can you give us any insight into the Council, now that Flora's apparently a member?" QT asked of Signum.

"Flora's not talking," Hevvi said before Signum could answer. "We can tell you that there are ships called 'Hyper Jumpers', which are used to move through the hyperspace between Jump Gates. In fact, we are planning to use one to get home. So when you head off to statistics - that's it. We're parting ways."

The high school functions exchanged glances, then Logan nodded. "Understood." He looked to ParaB. "Any news from the rest in Purgatory?"

ParaB shook her head. "They activated the Jump Gate that Para found. Nothing happened. ArcSin - who is managing without his Nisano glasses, by the way - thinks it's still in the process of powering up. He also plays a pretty good double bass."

"This is getting us nowhere," Radik pointed out. "We should be talking about how we're going to confront this CF person."

"Uh? What confront?" QT said, looking startled. "We're simply going to ask Characteristic Function for the password to the Statistics Jump Gate."

"And you think he or she is going to just hand it over?" Radik challenged.

"He's got a point," Cosecant remarked. "The outcome with CF is far from certain, according to the Fractals. I've been considering bringing CF a peace offering. We could have the replimator on board create something."

"Hah. What can you offer up to a more powerful being?" Hevvi asked, crossing her arms.

"Ar, perhaps we could make pieces of infinity!" Logan proposed, rubbing his hands together. He returned everyone's looks of confusion with a shrug. "What? They're like pieces of eight, but rotated ninety degrees."

<— TO XMAS 2013 INDEX 6 TO 2014 ASIDE —>

Wednesday 25 December 2013

S6.202b - "O Factor Tree" Singalong

Happy December 25th! Time for this year's holiday singalong special. If you haven't seen the connection between Greatest Common Factors and Venn Diagrams before, click the link below!

Thy primes are so amazing

Julia Childset and Howie Mandelbrot get into the spirit

Thanks for checking out "Taylor's Polynomials" this year!
 (First visit? Links to the archive are on the right there.)


Sunday 22 December 2013

S6.202 - Psy Kicks

The Story So Far: The inhabitants of Fractal City have been teaching personified math about the nature of their existence. Very soon, a decision will be made as to whether the high school functions are reunited - or recycled.

'That was it?' Para mused, lying in bed with two fingers pressed to her temples.

'Pretty much,' ParaB responded. Two fingers tapped at her own head as she looked out over the Fractal landscape, from the balcony of her room at the Hilbert Hotel. 'Weier showed us back to our hotel, after which I spent some time with QT going over her Quadcorder scans.'

'You're giving off a vibe which tells me there's more,' Para accused her conic counterpart. 'If it's bleeding through our psychic link despite me trying not to pry, it's probably important.'

ParaB felt her cheeks burning. Of course, she and QT had done more than look at scans. But she didn't think that's what Para was picking up. 'It's... uh. Okay. When that guy Koch said 'If you go to Statistics, you won't die', I think he was talking to me. And only to me.'

A pause. 'Seriously?'

'Yeah. But he's right, I don't understand why.'

'Are you feeling depressed? That is, ah, are you doing something that might cause personal harm if you stayed?'

'No! Moreover, why would being in Statistics save me??' The orange haired bunny girl shook her head and let out a sigh of frustration. 'I should have followed up on it, but I was caught off guard. Never mind. I'll see if I can track down Koch again. In the meantime, what's new on your end?'

Para rolled over onto her front. 'Well, the orchestra idea seems to be working out, even if the Versine search isn't. Elly's picked up echoes of us being in mathematics, which is weirding her out. Oh, and Reci found an invisible path leading off the cliffs. I checked it out. It leads to an isle in the middle of nowhere, where there's a huge ring, housing four sets of metal chevrons or something. Bizarre.'

ParaB caught herself on the railing of the balcony. 'Seriously?'

'Yeah, wh-- ooh, I got that thought. You think it's one of those Jump Gates?'

'It's as Signum described. What else could it be??'

'Point - would explain the dialing device we found.' Para mused on that for a moment. 'Seemed totally inert though. I'll get ArcSin and ArcCos to have a look at it.'

'Oh. Hyper's still busy on her magic kick?'

'Yuh huh. No word from her "spiritual guide".'

'Joy.' ParaB pinched the bridge of her nose. 'I suppose if its a ring, it's more up the alley of the ArcTrig anyway. See what they can do. After all, if we can get ourselves onto this Gate Network, it may give us a voice on Council. Right now, all their votes are too damn close.'

Para nodded. 'Though in fairness, we are sort of a rogue faction.'

'So what?' ParaB challenged. 'The pro-rogue idea is all the rage with governments of late!' Her outburst was met with silence. After close to a minute, one of her bunny ears twitched. 'Too obscure on that riff?'

'I think so,' Para agreed.


Wednesday 18 December 2013

S6.201 - Step Up

The Story So Far: The inhabitants of Fractal City have been teaching personified math about the nature of their existence. Very soon, a decision will be made as to whether the high school functions are reunited - or recycled.

"Don't take Koch too seriously," Julia soothed. "He often speaks in riddles."

"More to the point, he abstained from our vote!" Hill remarked, folding his arms as he stared at Logan. "I was against you being here at all. As were Henon and Pinski."

"Mmm. Compared to us, their formulas are all so... so restrictive," Henon said dryly from the main table. Pinski didn't say anything, merely adjusted his monocle.

"Well, they haven't run screaming from the room yet," Candice said, smiling as she draped herself over her podium. "So things are going just fine!"

Cosecant cast her own glance over the assembled. They really were a mixed bag, now that she looked closer. She also noted that only Weier, Julia and Can-Tor bothered to meet her gaze. "Three against," Csc said. "At least one abstention. Can I ask how many of you were in favour of this gathering?"

"Four," Weierstrass admitted immediately. "It was a close call. That said, what we now have to decide is whether a member of the step functions is prepared to join us at a podium."

"Wait, what?" Hevvi said in surprise.

"You have the ability to come here through a Jump Gate," Thomae 'Popcorn' West said, without looking up from her book. "Same as me. And as Can-Tor said, you haven't run screaming. So one of you is now entitled to represent your steppe, the same way I'm representing unique functions."

The three step ladies exchanged glances, as eyes in the room turned to them expectantly. Then, without a word, Flora stepped forth, moving behind one of the empty podiums that was present. Weierstrass nodded. "All right then. We are now twelve. Logan! Is it still the wish of your group that we facilitate your path to statistics?"

The redhead looked sidelong at Koch, then at his companions, then nodded. "It is."

Weier looked back out at the room. "In light of this new information, all those in favour of bringing CF to town?" She raised her own hand, as did Julia, Can-Tor, Flora, and after a moment, Vicsek. "Those against?" Bert, Henon, Pinski, and Popcorn all raised their hands.

"Nothing against you," Popcorn remarked, looking towards Logan. "Just don't like CF being around. Freaky person."

"Mmm. That's why I'm abstaining," Howie said, crossing his arms.

"Ha! You'd be against it, except you don't want to be seen agreeing with Bert!" Henon shouted across the table. Howie simply grunted.

"Regardless, motion carries, 5-4," Weier concluded. She picked up a gavel and knocked it against the table, then looked to Logan. "At this point, I would ask you who are guests to step outside for a moment. I'll escort you out of the X-Mansion as soon as we deal with one more item of business."


Sunday 15 December 2013

S6.200 - Hi Council

The Story So Far: The inhabitants of Fractal City have been teaching personified math about the nature of their existence. Very soon, a decision will be made as to whether the high school functions are reunited - or recycled.

QT gasped as they walked into the Council room. Granted, the space itself wasn't terribly interesting. Slightly elliptical, it featured a small presiding table at one focus. That table resembled a half circle, having five chairs around the circumference. Facing it were a couple of horseshoes, situated one behind the other, which contained small podiums. Thus not unusual.

No, the reason for the gasp was who QT saw at the chairs and podiums.

Dr. Weierstrass and Howie Mandelbrot both moved to sit on chairs at the main table, Weier taking the centre position. "Now then," the diplomat began, looking towards the new group of arrivals. "You know Julia and Howie already. But there is another formula iteration fractal like them. At the far left of the table, meet Henon Mappe. Also up here with us, Koch, of base-motif fame." She gestured to either side of the table as she made the introductions.

The year is 2013. The place, Fractal City.

QT tried to read the expressions of the advisory council. It was difficult, as her mind was still trying to process their appearances - an impossible effort in the case of Koch, who was cloaked in a suit. He was, indeed, the one she had encountered in the elevator.

"Moving around the room," Weier continued, "Is Sir Pinski, noted architect... Visek Fontaine, entertainer... and Candice Torrent, our inventor, whom you've also met." The dark skinned girl flashed them a smile.

"Continuing is Hill Bert, securities - note Bert is actually his given name... Mel Blancmange, psychologist... and Thomae West, who is not a fractal but is currently representing lesser used relations. Such as the Minkowski Question Mark."

"You can call me 'Popcorn'," Mae said, glancing up from a book she was holding.

"Pleased to meet you all," Logan said, before stepping to the side, gesturing at his companions. "On our side, we have 'Evvi, Signum and Flora, who are step functions, Cosecant, representing Trig, ParaB, representing conics, QT, representing polynomials, and me, Logan. I'm the inverse exponential."

There was a pause, then to the surprise of everyone present, Koch spoke. "If you go to Stat'st'cs, you won't die," he stated matter-of-factly.

"Pardon me?" Logan objected, stepping back in front of ParaB to better glare at Koch, eye-to-eye. "Are you implying we WILL die if we do NOT go??"

The being in the encounter suit seemed to shake his head. "You do not understand. But you will."


Wednesday 11 December 2013

S6.199 - Cliff Notes

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.

"There you are!" Root approached the darker haired function, shaking his head. "Honestly magic boy, what's with calling me out to such a remote meeting place?" He gestured out at the blackness that stretched beyond the cliff edge.

Reci adjusted his tie. "I figured you wouldn't believe me unless you saw... wait, what did you call me?"

Root grinned. "Magic boy. After all, if Hyperbola's now a magical girl, and you're a form of hyperbola..."

The reciprocal made a face. "Okay, no. I mean, I get it. You don't like conics because of their grudge against your girlfriend, but come on. I'm different. I have no squared terms."

"True. You're just always under some 1, doing whatever it is Hyper tells you..."

"Hey! I participated in your raid against the conics when they kidnapped Para. You think Hyper authorized me to attack her house?!"

Root's smile faded. "Okay. Point taken, Reci."

"Good. And I've been thinking of changing my name to Rhys, actually," the reciprocal admitted, now grinning himself. "What do you think?" Root simply stared. "Okay. Anyway, the reason I called you out here was because of the invisible bridge."

The silver haired function did a double take. "The invisible what?"

"Bridge. As you know, Lyn and Tan sometimes run off and play, including out here by the cliffs. Being worried for my reciprocal, I figured I should scout along the perimeter, make sure there were no dangerous overhangs, that sort of thing."

"Mmm hmmm. You're sure you weren't scouting for a picnic location for you and Sexi?"

"Shut up. My point is this." Reci moved to the cliff edge, briefly getting down on his hands and knees and feeling about. He then stood, and took three paces out into the blackness. Root let out a cry of horror and ran forward to grab for the other function - only to see Reci seemingly standing on thin air.

"What... what the heck?" Root knelt down to feel about himself, realizing that Reci had placed a few stones in the grass to act as markers. As he reached out, past the cliff edge, there seemed to be something solid. It was difficult to tell if it was artificial or natural, but it was certainly invisible. "A bridge," he yielded. "Where does it go?"

"Beats me," Reci said, stepping past Root to get back to solid ground. "It's not really wide, so it might not be very long. But I thought in light of the Versine talk - which I FINALLY heard about, by the way - it might be important. Moreover, I thought it'd make sense to tell you at a time when Para was keeping all the trig distracted."

"That's good thinking," Root acknowledged. "Have you told anyone else?"

Reci shook his head. "Nope. Which doesn't mean someone else hasn't found it too. Much as I hate to admit it, you are talking to the guy who is least likely to be on top of things."

"Meh. You're getting better." Root stood back up. "I'll let Para know then. Since she can fly, she's likely the best choice to investigate."

"She can FLY?!"

"Thanks for the tip," Root concluded, brushing his hands off on his pants. "If you come up with anything else, let me know - hey, what with your new name, I can refer to your intel as Rhys' Pieces!" He grinned anew.

Reci glared. "Go away now."


Sunday 8 December 2013

S6.198 - Fractal Designs

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.

Weier turned to Mandelbrot. "Right then. At this point, they're as ready as they're going to get. Time to meet the council."

Howie nodded back. "You and Can-Tor lead the way, I'll follow behind."

QT held up the Quadcorder. "Can I continue to take readings?"

"As you like," Weierstrass said. She gestured to all of them, then followed Candice Torrent out of the room. The group trailed after, Logan taking point as they went down a hall, piling into an elevator. After going down an unknown number of floors, they all emerged and headed towards a set of double doors, situated at the T-section of a hall. Julia Childset stood outside, smiling as she spotted them.

Can you see the changes?
Except not Julia. She was subtly different. Which Howie had implied earlier, by saying that one of her other, infinite incarnations was currently in the position. Even as they approached, she slipped through the doors into the room beyond.

"So," Hevvi asked as they approached the doorway. "How many of you fractals are in there, exactly?"

Weierstrass turned. "There are five of us on the Advisory Council. Six others are currently present from their respective divisions."

ParaB lifted an eyebrow. "So many? Is there some reason we're meeting all of you, and not merely that characteristic function of a set? After all, they're the one who has that statistics password, right?"

"We have yet to decide whether you're ready," Howie broke in. "That said, Council foresees three outcomes from this encounter." Everyone turned to look at him then, though he didn't continue until after receiving a nod from Weier.

"First, you may not even be able to resolve half of the images of those present. In such an event, we will send you on your way - you can return when and if you have achieved enlightenment." He held out a hand to prevent immediate commentary. "Second, you may be able to perceive everyone, but decide yourselves that you are not ready, or require more training, and thus depart in your gazebo of your own volition. And third..."

"Third, we ARE ready, and thus talk to the characteristic function," Cosecant concluded, when Howie paused.

"Close," he countered. "It's more that we would book you an appointment. CF isn't in town at the moment."

"Oh good, so more waiting," Radik groused. ParaB winced.

"Now, now. Don't make us regret helping you out," Weier cautioned. "Our Council was not unanimous in the decision to bring you on board. Some were against. Many abstained. Not all the fractals will be pleased to see you." She looked to the double doors and then back. "That said, are you ready to proceed?"

The high school relations exchanged glances both among themselves, and with the step functions. "Let's get to it then," Logan concluded, speaking for everyone.

With that, Weierstrass opened the doors and marched inside.


Wednesday 4 December 2013

S6.197 - Mind Over Matters

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.

"It's okay. We understand your reluctance," Dr Weierstrass said soothingly. "Your beliefs are being completely turned around. No one is expecting you to suddenly be okay with that."

"I can't see it..."
"Except here's something I don't understand," Logan said, speaking up again. "I just tried to see Can-Tor as white. I couldn't. Is that because she really IS brown, or has my mind simply closed off again?"

What are your
"Bit of both," Can-Tor answered. "How I look to you now comes from the vibe I'm giving off - the vibe of how I want to be perceived. You're presently open enough to accept the difference, but are perhaps still closed to anything outside normal expectations."

"So you coming in here off Weier's remark was a test," Radik realized. "To see if we were open enough!" He made a face. "Well, open to it or not, I don't like the implications!"

"Then you'll hate this," Howie said. "The way you look now, it's simply a mathematical projection... literally. You've had your own points and lines transformed from one plane into a human image. Yet your PREFERRED state may NOT be how you currently appear."

"Whoa, what? It's not like we can change what we look like now!" Cosecant protested. "We're invariant!"

"Why?" Weier asked.

"Oh for... fine," Heaviside said. "We are math. We can apparently go super deformed, if you're any indication, so I'll buy we can change appearance. But this means, what? Deep down we're all from the asian plane?"

Several of the others winced.  "Ooh, 'Evvi," QT said.  "No... just no, math stereotypes bad."

Not so invariant?
ParaB hummed. "I think I get it though," she said slowly. "We have the ability to re-map ourselves. To be perceived in a different way by outsiders. Perhaps even to be perceived as a different gender."

"That's chaos though," Cosecant pointed out. "If anyone can look like anyone else... well, I could steal your identity!"

"Don't misunderstand us. There's limitations," Weierstrass said. "And if you try to change yourself without being careful, you could Glitch. So we don't recommend it." She smiled. "For now, we merely wanted you to be aware of the issue, before you met the other fractals."

"Especially Koch," Howie put in.

"Oh yes," Weier said. "The Koch snowflake. For the record, even we're not actually sure what his - or her? - appearance is... Koch wears an encounter suit at all times."

"I think I met him!" QT gasped.

Weier nodded. "Koch is one of the earliest fractal curves to have been described. He manages to be very mysterious, despite the fact that much of known mathematics, including you, is older than him."

ParaB's mouth twitched. "Let's not talk age. After all, even if I'm over two thousand in human terms, I was only generated a couple of years back."

"It's fine. You don't look a day over 21," QT soothed.


Sunday 1 December 2013

S6.196 - Why Axis

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.

"Now wait a minute!" Cosecant said, stepping forwards to look more closely at the latest arrival into the room. "I saw you in the Overline bar! You... you were caucasian then! Uh, weren't you?"

"I've been upgraded," Candice Torrent retorted with a smile.

"Can-Tor," Dr. Weierstrass said warningly. "Don't mess with them."

"Perception filters," Howie Mandelbrot broke in. "You high school functions have them in spades. They're clouding your reality." He jerked his thumb at Can-Tor. "If you thought she was white before, that perception became your reality." He inclined his head towards Hevvi. "Step functions, filters are less of a problem, but I gather you all have trouble seeing the fractal landscape here."

"Aha. Not only the landscape, but also some inhabitants," Logan reasoned, stroking his chin. "That's why we couldn't make ANY sense of this 'Norm' fellow for statistics, that time in the bar. His image wouldn't resolve because we weren't yet equipped to see him."

"Bah! It's a trick," Radik declared. He glared at Elizabeth Weierstrass. "Or are you about to tell me you're a different skin colour too?"

"We are as you perceive us," Weier said. "That is the nature of mathematics."

"That's not an answer," Radik argued. "For instance, if I take a picture of you, and post it on a website, you can't appear caucasian to one person and asian to another!"

How does Can-Tor
appear to YOU?
Can-Tor held up an iPad. She tapped at it, then turned the image towards Radik. "Do you see a cup, or two faces?" She slid the picture to the side, another appearing in it's place. "How about here, an old woman or a young woman?" Tap, new image. "Which of these two objects is the larger one?"

"I see what you're getting at," ParaB broke in. "But those are crafted illusions. It's different with things like race and gender."

"Why?" Weierstrass said simply.

"Because... well, we all know what a white person looks like."

"Why?" Weierstrass repeated.

"Because... we just do. It's genetics," ParaB continued.

There's a link for
writers in that WHY.

ParaB frowned, suddenly less sure of herself. "QT, can you back me up here? Say something medical."

The catgirl shook her head. "I can't speak to the so-called human perspective. But in math, let's say we look at a graph - we can all agree on what me, X^4, looks like! There's no way to perceive the maths there any differently."

"No way?" Can-Tor said, pulling up an image on her iPad again.

"Agh! Stop talking at us in questions!" Hevvi said, stamping her foot. "It's really irritating!"

"What? What was that, 'Evvi?" Signum asked, lifting her hand to her ear.