Wednesday, 30 October 2013

S6.187 - Chide of Chaotica!


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.

Logan glanced at his watch. "We can't wait forever on QT," he decided. "Let's start comparing notes."

The logarithm function currently stood in front of the viewscreen on the bridge of his ship. He moved his gaze quickly over the others who were standing around him, to gauge their agreement: ParaB (the conic bunny), Cosecant (from trigonometry), Radik (cube root), Hevvi (heaviside), Signum (sign) and Flora (floor).



"I don't trust the fractals," Radik offered.

"Pfft. You don't trust anyone," Hevvi said pointedly.

Radik shot a glare back at her. "I'm serious! We asked for explanations, they keep telling us to wait. It's already been how many days since Logan and Csc went to that bar?!"

"They've said we're not ready," Cosecant cut in, before the tensions between Radik and the step functions could further escalate. "I'm inclined to agree. I couldn't make any sense of this 'Norm' person who represents Statistics! It was like looking at a... a Stereogram, yet the image refused to come to me."

"The whole fractal landscape here has that kind of effect on us," ParaB reminded. "Good news is me and QT have finally managed to adjust our quadcorder to compensate. I think the problem is rooted in Hausdorff dimensions."

Signum tilted her head sideways, one of her twintails nearly hitting herself in the shoulder. "In the who with the what now?"

"Essentially fractional dimensions," ParaB clarified. "Consider, while we live in a two dimensional world, and can conceive of a third, our visualizing beyond those - or between those! - is another thing entirely. Every individual will interpret such chaos slightly differently."

Logan nodded. "Makes sense. Something similar happens when you look outside my ship while it's flying, as it can move through the third, maybe even fourth dimension."

"Whoa, seriously? Four dimensions now?!" Radik said, throwing his arms up. "When will the chaos stop?"


Signum, Heaviside and Flora. No evil here?

"With invaders from the fifth dimension!" Signum declared. "Such that only Captain Proton can save us!" Her exclamation was met with silence, as everyone turned to stare. The partially pink haired girl finally shrugged sheepishly. "What? It was on a TV show once."

Sunday, 27 October 2013

S6.186 - Banding Together


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.

"How about this," Para suggested. "We'll split into two groups. One group attempts to map out the area, to see if Versine might be out here already. The other group tries to contact mathematics, to see if she, or anyone else who's there, is able to help."


Tangent shook her head. "No! You're missing my point. Current trig and Archaic Trig don't get along! If they realize what you're doing, and learn that Versine is related to your efforts, they'll flip out!"

"So distract trig," Elly said simply.

"How??" 

"A band." All eyes turned to see who had spoken, making Root jump a bit in his seat. "I just mean, music was our backup plan, right? We were going to hang out in music if we couldn't get back to math. Didn't Secant mention starting a group called 'Your X Girlfriends'?"

Expona lifted an eyebrow. "You're saying we recruit all of trig into a band?" she said, dubiously.

"Or an orchestra!" Para mused, tapping her index finger to the side of her mouth. "That could even be fun! And since I already know lots about musical composition, I can coordinate them from right here in Maud's bar! Okay, new idea. While I do that, Elly, you can quietly see about making a mystic link back to our subject. Meanwhile, I know Lyn's done some exploring already, so I'm sure we can get her to organize--"


I won't stand for it! ...I'll sit down!
"Excuse me?" Expona interrupted, rising to her feet. "What's with all the orders? I don't recall electing you as our leader here!" The parabola stopped talking and shrank back a bit.

"Perhaps Para isn't the leader, but along with ParaB, she's our telepathic point of contact with Fractal City," Elly reminded. She looked to the bunny girl. "I don't mind working on the link."

"Plus Para can talk to the readers!" Root added, leaning on one of his arms and grinning at the parabola. "She's awesome! I'm fine with whatever she decides!"

"It does sound like a reasonable plan of action," Tangent said, squirming a bit in her chair. "I can even see the music helping to calm Cosine."

Expona let out a long breath. "I'm not saying it isn't reasonable," she explained. "I'm saying the parabola's being bossy!"

"If you feel she's delegating, we can always put things up to a vote instead," Maud suggested to the redhead.

"That's not... like even that would be fair?!" Expona objected. "I know you're all inclined to side with blondie's opinions! You never... ah, screw it, who cares anyway." She sat back down in her chair, crossing her arms angrily across her chest. There was a moment of uncertainty, then everyone's attention turned back to either Para or Tangent.

Only Para's gaze lingered on the exponential function long enough to see the expression of sadness and longing flicker across the redhead's face.

Wednesday, 23 October 2013

S6.185 - Where and Pieces


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.

"Versine? That archaic trig function??" Expona said in surprise.

"Correct me if I'm wrong," Root said slowly, "but did Versine not try to blow up all of you trigonometric functions less than a year ago?"


As I recall you had a blast with her.
"Time is relative," Elly murmured quietly from her seat.

Tangent nodded. "Yeah, she did. Which is why I'm bringing this to you. The rest of my family, they'll think I'm the insane one. But Cosine... she's TRYING to act like she's fine now, but I know my sister better than that. She's falling to pieces! I don't know why she refuses to let me help her!!"

Para winced, thinking back on her own recent facade of joy. She wondered if maybe talking to Cosine about her own experiences would help. Or make things worse.

Maud rubbed his chin. "Okay, I admit, I didn't see that suggestion coming. It does raise an interesting question. Namely is Versine even out here with us? I've never seen her. I just assumed she was stuck back in our subject area, with all the child functions."

More glances were exchanged. "Is it possible she's out here, but not out HERE?" Para asked. "Like, she was blown into some other community or something?"

"I suppose," Maud acknowledged. "We talk a good game, but we haven't explored much beyond this immediate area."

"Well, wherever Versine is, she's unaware of us, as she hasn't swooped in to capitalize on recent events," Expona reasoned. "Could we maybe get Signum to help us locate her? Surely the sign function could point us in the right direction."

"Signum's in Fractal City," Root reminded.

"Duh. But Dr. Nisano is working on re-establishing regular communication," the redhead countered.


SCIENCE!
Tangent winced. "Oh, please don't encourage his mad science by using that name. His manic attitude has been worse since the loss of his inverse! Go back to calling him ArcSin, or Nis. Anyway, I don't want the other trigonometric functions to know about this suggestion! Are you sure you don't have any better ideas??"

"Perhaps Hyper can create some magical device to assist Cosine," Elly finally put in, leaning forwards and adjusting her orbital hairpiece. "That is, once the hyperbola has come to terms with the idea that she is a magical girl."

"Oh right! How's that realization working out for her?" Maud asked.

Elly turned to him. "Hyper is currently attempting to contact her magical guide. She believes it will manifest to her as a fuzzy animate cube, about ten centimetres on each side."

Everyone turned to stare at Elly. "Okay. Not well then," Maud concluded. The ellipse merely shrugged.

Sunday, 20 October 2013

S6.184 - Old Friends?


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.

Root stared at his girlfriend. "Um, Para, what are you doing?"

The blonde let out a breath, then reached up to adjust the hairband that held her parabolic rabbit ears. "Sorry. Been trying to automate this quick little psychic projection beyond the fourth wall for each episode. For the benefit of new readers."

"Wait, what now?!" Expona said. She leaned forwards at the table to look at Para, her leather outfit making faint noises. "That's incredibly disconcerting!"

Para looked back at the redhead. "We've been reporting on events in the human world for a while now. We've even commented on our own hit counts. This is simply a natural extension of that, don't you think?"

"No!" the exponential argued. "Talking to a reader is creepy and makes you seem like a stalker! What did you say anyway?"

"Nothing bad," Para assured. "It's just, it seems rude not to at least acknowledge them sometimes, now that I'm able to address them."

Maud cleared his throat. "Well, for those of us who aren't at that level of awareness, perhaps we can return to the matter at hand? Hm?" Everyone fell silent, and the modulus function shifted his gaze around the table, looking at each of the mathematical representations in turn.




Para, the second degree polynomial. Root, Para's inverse (for the positive domain at least) who was their resident computer tech. Expona, the redheaded exponential function, inverse to Logan. Elly, the ellipse, who had seemed a more sedate choice of conic for the group, compared to her circle cousin Circe. And Tangent, the younger sister of the trig twins - or at least, younger sister of Cosine. Now that Sine was dead.




"Cosine is going insane," Tangent murmured, breaking the silence. "And I can only think of one thing that might help." Tears welled up in her eyes, and she dropped her face into her hands, shoulders shaking.

Para rose, moving around the table to embrace the young brunette. "Root, go find Lyn," she suggested quietly. Tan had formed a close friendship with the line, given how they were both connected to slope.

"No," Tangent protested, quickly rubbing her eyes on her arm. "No, I've cried enough in Lyn's lap already. I'm here for a reason! I... I wanted Maud to gather all of you here in his bar to see if you had any better ideas, before... before I pitch in something that's from completely out in left field." She drew in a quick breath, her nose snorting. "So... so what are our options? How can we help an already emotionally torn Cosine deal with the huge increase in mathematical requests, now that Sine isn't around?"


There was a brief silence. "You mean aside from waiting until Logan and his group find probability, blast us back into our subject, and recover our child functions?" Expona clarified. Tangent nodded. There was another pause. "Well, I got nothing," the redhead concluded, looking none too pleased about the admission.

"What's your idea, Tangent?" Maud ventured. "Maybe that will spark something."

The young girl looked around the table at the other relations. She took in another breath. "It's..." She had to swallow once more before she could actually say it. "It's Versine. I think we have to find Versine."

Wednesday, 16 October 2013

S6.183 - Babble On Project


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.

QT ran for the hotel elevator, late for the meeting at Logan's gazebo downstairs. "PleaseDontStartWithoutMe, PleaseDontStartWithoutMe," the quartic panted to herself as she stabbed multiple times at the call button. She supposed she should be thinking of an excuse. She couldn't tell the others the real reason why she was late.

Well, okay, she could tell them that she'd overslept. She couldn't tell them she'd overslept because she and ParaB, the conic version of the parabola, had been getting intimate together the previous night. Again. QT's cheeks went pink at the memory.

Of course, they both knew they had to stop their tryst. They were just using each other. QT was using ParaB to satiate her biquadratic inclinations, and ParaB was using QT so that the conics would have an advocate within the polynomial family. It was all convenience, nothing more.

Oh, but then why did ParaB's lips have to feel so good? QT was starting to hate being all alone in the night.


The elevator dinged and the doors opened. QT took a step inside, and then let out a little shriek. There was already somebody there.

The person turned to look at her. Or so QT assumed - it was impossible to be certain, as the form in the elevator was entirely concealed by their clothing. They had a shapeless cloak on their body, a pointed collar around their neck, and their head was hidden within some strange construction of constant width... which seemed to have a snowflake stuck onto the front. Getting over her initial shock, QT deliberately turned to face away from him. Her. It.

"And so it begins..." the being murmured, it's voice echoing oddly.

QT hit the button for the lobby. As the doors slid closed, she wondered if it would be rude to ignore her companion for the whole trip. "There is a whole in your mind," the being continued unnervingly, as if it could read her thoughts.

"What do you want?" she murmured without turning. There was no response. She glanced over her shoulder, then turned back to face the front. "No one here is exactly what he appears," she sighed.


"Nothing's the same anymore," the being affirmed. QT had no idea what to say to that, so she remained silent. An uncomfortable silence settled, until: "Why are you here? Do you have anything worth living for?"

The quartic girl felt the hairs on the back of her neck go up. She spun on her heel. "What do you WANT?" she repeated, now completely unnerved.

An opening within the snowflake seemed to open and close. "Never ask that question!" came the angry response. The elevator dinged for the lobby. QT fled through the doors before they had even fully opened.

The echoes of their conversation remained long after she had gone.

Series 6: Stat Us

The updating archive for this series will be located here:

                         http://sites.google.com/site/taylorspolynomials/series-6

STAT  US

Previous series' archives can be found on that website; their recaps can be found at this link.

Sunday, 13 October 2013

Author Explains: Word Wide Web

Pic by Errol of Debs and Errol

IN BRIEF: "Taylor's Polynomials" is a web serial which includes math, urban fantasy, pop culture, and wordplay. If you like some of those things, hopefully you're already on board. But if you need more convincing, let me break it down for you... post by post.

I previously explained about the math references. Then about the setting, including how I incorporate mashups from popular culture. It's now time to veer away from the content, to deal with my writing style. Where my plea to writers is very similar to the one for the math geeks - keep me honest!


III) WORDPLAY



Here's a Tangent: A Day in My Life,
 as told in first person plural.
If you haven't done so yet, the first thing I'll do is encourage reading the prior two posts. Quick recap either way: The conics are "eccentric", because that has a mathematical context beyond the english definition. Logan's ship is larger in the subscript, as it's his "base" of operations. Are you catching my drift? I tend to incorporate a lot of these puns into the serial because that's the way my mind works.

Most straight out math puns were used early on. I've now started to create characters outside the basic high school functions. In particular, I'm now playing with the names.


Pictured: Howie Mandelbrot
Julia Set mashes up with Julia Child to make Julia Childset. The Vicsek fractal pairs with Vic Fontaine from 'Star Trek: DS9', generating Vicsek Fontaine - he owns the Overline bar. And you haven't seen her yet, but I'm rather pleased with how my diplomat, the Dr. Elizabeth Weierstrass function is turning out. (Her hair is continuous, but not differentiable!)

The episode titles themselves are also word riffs of one sort of another.
-"I Now Pronounce You" was the entry involving the ?(x) and [x] functions, (which are hard to pronounce), where we learned that they were married.
-"In Security" was the entry where Cosecant and Radik clashed over ship security, and their own insecurities. (You can't handle the truth tables!)
-"Cut Vertex" was the entry where the depressed Parabola pricked herself with a knife. (Do we not leak?) I grant she was not in vertex form at the time. It did inspire this post on my other blog, Why I Write Series 5.

I suppose in my mind, I'm a bit like Terry Prachett, just nowhere near as good. But give it a few years, I might reach J. K. Rowling levels. (Daigon Alley, ha ha! ... She wins.)


WRAP DOWN


Honestly, that's about all I have to say about the writing. It's not ALL about twisting words - for a short story sample of my writing see "Time for a Superheroine" (on my other blog). I'm now hoping YOU might have more to say, in the comments. You can also comment on my drawing ability, hopefully it's been improving too?


Alternatively, send fan art. That's
a MichelleScribbles commission.
Part of the reason I hope for commentary is to get a sense for what you (the audience) are anticipating. Or want to see. As far as plot goes, I write in a very linear fashion, meaning I don't have a clear sense of how an arc will wrap up when I begin, only vague ideas. That's the nature of a serial.

There we have it! Three posts later, I've explained what I've got to offer you. Still not sold? I demand that you tell me WHY! Comment, oh my god, someone, ANYONE, IS ANYBODY OUT THERE?!? HELLLOOOOO???

In all seriousness, let me take the opportunity of Canadian Thanksgiving to thank everyone who's already been reading. Extra thanks to those who've let me know:
-@MorganBallantin who also wrote me this guest post;
-@mrburkemath for giving me a shoutout on his blog for my "Makin' a Graph" parody;
-@ed_realist and @davidwees for their blog comments;
-@jensilvermath who's remarked at me through Twitter;
-Carl Joshua Quines, who comments occasionally on the Facebook page;
-And an extra shoutout to my math colleagues at school for their occasional remarks, not to mention putting up with the crazy teacher in their midst.

I'll conclude by saying that if it's the constant TEXT aspect you don't like, we may have to part ways. But not before I can point you at two mathy-cultural webcomics, in place of me! They're currently publishing, and I quite enjoy them:


Actually, check those out regardless!

As for me, Series 6, Stat Us, starts this Wednesday, with the "Babble On Project". (I really need to get on with my drawing.) Maybe I'll see you here again? It's less than 5 minutes out of your day, you know. It might be nice if, in a sense, we could spend that time together?



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Wednesday, 9 October 2013

Author Explains: Pop Culture

Pic by Errol of Debs and Errol

IN BRIEF: "Taylor's Polynomials" is a web serial which includes math, urban fantasy, pop culture, and wordplay. If you like some of those things, hopefully you're already on board. But if you need more convincing, let me break it down for you... post by post.


I previously explained about the math references I use in "Taylor's Polynomials". Yet perhaps you're not a maths geek, just a geek generally? Then this is the post for you.


II) THE REFERENCES



The Ellipse is watching you
To start, I'll clarify my setting. Picture someone struggling with a math problem. They're not understanding it, but they're persevering, trying their best, until suddenly - they have a flash of insight! My claim? The insight was (possibly) one of my characters seeing the struggle, and giving a gentle nudge in the right direction.

My serial exists on a meta-level. The characters are aware of our world, but exist on a separate "plane". (Their own deities are TPTB - which is not The Powers That Be, but rather Transcendental Pi-Type Beings.) Is that fantasy? A type of science fiction? I'm not entirely sure. I can tell you that the references I make within the story DO trend to those genres!

To date, I have referenced or parodied events from at minimum the following elements of pop culture:
Doctor Who, Stargate, Star Trek, Knight Rider, Wizard of Oz, The Spoony Experiment, Back to the Future, Katy Perry, Being Erica, Sailor Moon, Sliders, Quantum Leap, and most recently, Cheers.


Don't get the parabola angry. You won't like her when she's angry.

By the way, the first entry of Series 6 will be the "Babble On Project". Because the serial needs more Straczynski.

Maybe I'm like "Demo Reel" in text form -- if you get the "Channel Awesome" reference, great! If you don't, who cares? It's not central to the plot, plus I have other things you might understand!

What follows is a break down of the major ongoing serial elements, as related to their source material. My hope is that, whether you see the connections or not, the items can be enjoyed independently! As elements of an ongoing science fiction fantasy cultural mashup style story. Um, with math.


LOGAN'S SHIP



Logan's ship.  Abridged.
It began as a combination of 'Doctor Who', 'Star Trek' and 'D&D'. A blue "dread" gazebo (don't attack it) that flies around through the various math dimensions and is larger on the inside. Well, larger in the subscript beneath the gazebo trapdoor - after all, it is logarithm's base of operations. The bridge layout borrows from Star Trek, and they use hypersprays, so named because they were invented by the Hyperbola.

The ship has since become a well from which I can draw other references. QT and ParaB invented a "quadcorder" that's about as reliable as Al's handlink in 'Quantum Leap', and Radik III recently tried to install a Super Pursuit Mode, adding 'Knight Rider' to the pop culture list. Will there be more? Maybe.


THE ANGLE ZONE



If there is a Wizard, I suspect it's Versine
It's a mashup of 'Wizard of Oz' with 'Star Trek'. The AZ (Angle Zone) is where Trigonometry lives. SLIGHT SPOILER for Series 3: To the north is primary trig (the command and navigation functions), who wear red. In the west, reciprocals (security and engineering), who wear yellow and have a winking habit. In the east, inverses (science and medical), who wear blue and are munch kins - they like eating together. In the south, reciprocal inverses who wear purple and are of no specified department, though ArcCot has been known to shout "Objection!" (from Ace Attorney). In the middle of it all, Origin Central, and the green building that was part of Versine's evil plot back in Series 3.

Hey, while we're on the subject of Series 3, the climax involved a "mind meld", done in the style of the Replicators from 'Stargate SG-1'.


THE CONE OF SCIENCE


This is from the 'Stargate' series, though the name is a play on words from the "Cone of Silence" in 'Get Smart'. As envisioned by Hyper, it's a double napped cone that will transmit material from one cone location to another. (The lower cone to the upper one, and vice versa, though they're not physically connected.)


Cone of Science: Re-materialization sequence

It's kind of like what goes on in 'The Fly', except when it works, it behaves more like the Ring Transporters from 'Stargate'. Regrettably, it's never quite worked properly.


DR. NISANO



Inverse Sine, aka Dr. Nisano
'The Spoony Experiment' is a show (formerly on That Guy With the Glasses) which includes a mad scientist character named "Dr. Insano", as portrayed by Noah Antwiler. The character was so popular he spawned parody versions, including Linksano from "Atop the Fourth Wall" (also on TGWTG)... and the current persona of ArcSin here, 'Dr. Nisano'.

It's the swirly glasses that make the gag. It sort of surprises me how long it took before this association came together for me - after all, I was calling the scientist 'Nis' ('Sin' backwards), and had put him in the science department. Insano, Nisano, they're anagrams for goodness sakes.


OTHER MISCELLANEOUS


Those are the key ongoing plot points - but wait! There's more! For instance, I made a reference to Katy Perry tying Michael Jackson in number one hits from a single album in this entry. I also do song parodies ("filk")... many of them on the side rather than directly in the narrative, but sometimes they're included.


Hyperbola, inventing A Certain Scientific Railgun
The 'Z-Axis Points Module' from Series 2 was a play on the ZPM from 'Stargate'. ParaB throwing her tiara in a parabolic arc in Series 4 was riffing on 'Sailor Moon'. The images for Mink and Con drew blatantly from 'Doctor Who', their unpronounceability a nod to 'Victor Borge' phonetic punctuation.

I snuck a picture from 'Twitter Math Camp' into Series 5, and the 'Cheers' reference was in the last episode for that Series. And yet, there's more! Look, anyone remember the TV Show "Beat the Geeks"? First, it needed more female geeks. Second, I don't know why I remember all this stuff, but it often gets into my serial.


In conclusion, I'm saying that if you like Fantasy/SciFi stories, you may be amused when you read. If you are somewhat in tune with pop culture (current, or from my childhood), the amusement will even have context. But even if you're not into any of that, hey, flying gazebo ship! Don't you want to see more?

No? You're not sold yet? Math is not your thing, and you figure that if you don't understand EVERY reference I'm making, the story won't make sense to you. FINE. Do you at least like wordplay? Speaking as a writer, I think that's a good thing to have in your back pocket.

We're coming up to my final post in this set, geared towards the writers.  Then Series 6: STAT US launches this time next week!


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Sunday, 6 October 2013

Author Explains: The Math

Pic by Errol of Debs and Errol

IN BRIEF: "Taylor's Polynomials" is a web serial which includes math, urban fantasy, pop culture, and wordplay. If you like some of those things, hopefully you're already on board. But if you need more convincing, let me break it down for you... post by post.


This first post is for the math geeks. Part of the reason I want you to be reading is to keep me honest! While I do research before I post, sometimes I go out of my depth - is the math correct?? Tell me!

Perhaps some of you have even been to this blog before - then left, not understanding what I was doing. This time, read on. I'll make the connections very explicit.


I) THE MATH



Personified Parabola
I am a high school mathematics teacher, and this is, first and foremost, a mathematical web serial. All of the characters are mathematical functions. But mathematical knowledge is not a prerequisite! The Modulus function runs an Absolute Value Bar, the Parabola has a curved hairband and three forms, and the Conic family is eccentric... if you get the joke, great! If not, they're just characters. This brings me to my first point:
If you don't know much math, this may be a fun way to learn something.

Which immediately leads to my second point:
If you DO know math, this may be a fun way to learn something new.

Are you a middle school math teacher wondering about high school? Are you a high school math student wondering about fractals? Are you a non-math educator wondering how you might go cross curricular? Are you NOT involved in education, but enjoy READING? Look, learning something isn't required! Yet all that stuff has been in here.

Plus I can be subtle about it. Here's more "points":


HAIRSTYLE GRAPHS



The "modulus" function
Every character has some aspect of their graph pictured within their hair. This is the main reason why I began by drawing for the serial myself. Hairstyles even became a minor plot point in Series 3.

This means that, merely seeing the characters, you will be exposed to what each of their graphs look like. With any luck, if you chance to graph a function later in your life, it will trigger a recollection - or maybe it's triggering a memory from your high school days.


Minkowski's ?(x)
I try to be really careful about maintaining this when designing new characters. For the step functions, Heaviside is zero until she takes on the identity of a particular function, so her right twintail is set "at zero", and the other is higher, "at one". I found Minkowski's question mark function on a graph from 0 to 1, hence the earrings of "0" and "1" each side of the hair. There was some debate as to whether the Conway Box function was a similar function, or an inverse; unable to find a graph, I reflected Minkowski's hairdo in the line y=x and made the situation somewhat ambiguous.

I challenge you to find a mistake.

The obvious problem here is that it's a visual gag, and I'm not able to draw every character for every episode! It's a web serial, not a web comic; I don't have the time nor the skill to produce the latter. So if you only come once or twice, you may never see the character drawn, and you won't necessarily pick up on this.

Come more often!


FAMILIES AND INVERSES


Something else you might notice after a dozen views. Visually, certain mathematical families share certain traits. The polynomials are all blonde. They all have a bow in their outfit to represent the existence of a y-intercept. Odd degree functions have short hair and green eyes. Even degree functions have long hair and blue eyes. Moving away from the polynomials, trigonometry are all brunettes, and have more wavy hair.


Character Pairings?
Gender doesn't even need the visual, thanks to using personal pronouns. Most of the key high school functions (parabola, sine, exponential) are female. Their inverses are MALE. There's a running gag in my world that a function and her inverse are destined to marry... which may give me the opportunity to comment on gay marriage in the future. I am being completely serious.


Trigonometric Reciprocals.
In degree mode. Do you see why?
Among other things, I like to think this helps to distinguish between Sine and Sin^-1, aka ArcSin - whom I've also dubbed 'Nis' (Sin backwards). They have different outputs, which is seen on their T-Shirts. Further, we know Cosecant ISN'T an inverse (except to ArcCsc), because she's female... she also wears a Reciprocal Tie.

Of course, there are some functions which are their own inverses, notably Line (female, to match the other polynomials) and the Reciprocal (male since XY=1 and XY implies male). More subtleties, Lyn loses her y-intercept bow when she goes standard form, as vertical lines have no (or infinite) y-intercept. Reci is also always "under some 1" - that being Hyper, the main hyperbola, of which XY is simply a special case. Oh, and speaking of the language I use...


MATHEMATICAL LANGUAGE


First, nicknames. I use "Cosecant" and "Csc" interchangeably the way normal stories might use "Candice" and "Candi" as meaning the same person. I've heard no complaints. (Seriously, SAY SOMETHING!) Second, I have to be extra careful not to use an english word that has a different meaning mathematically. Because that's the sort of thing you probably only notice when it's WRONG.


Circe.
More geek than greek.
For a simple example, I said the conics are eccentric - except for Circe. (She's simply a little power mad.) That's because mathematically, a circle has no eccentricity. For a more complicated example, I realized I couldn't have a "transformation sequence" to switch the quadratic between vertex and standard forms. Because mathematically, transformation means rotate, reflect, slide, or resize! Not exactly the meaning I wanted, namely it being the SAME character, expressed differently. Hence I went with a "form change" sequence instead.

In conclusion, ALL of this is meant to be a bit of math tutorial without shoving it in your face that THIS IS A MATH TUTORIAL, because that's no fun. At the end of the day, my hope is it's fun to read. I doubt you'll pick up on everything even if you do come for every update! Yes, that's another challenge.

But then, the math is merely the vehicle, with functions as the getaway drivers. It's all happening within a larger universe. Thus if you're not buying into the math "angle", let me explain to you about my many and various science fiction/fantasy/pop culture aspects. Next post.


Logarithm's base might look familiar.