"What are you on in Maths right now? Binomial expansion?"
"No one's getting it. The teacher's coming down
harder on me 'cause I'm older, but, I mean, geez..."
Kite laughed. "Binomial expansion's easy! It's tedious,
but there's no real talent to doing it. You're the real patient type so
I'd've thought you'd not have any problem with it."
"How, precisely, is this stuff easy?" Sora asked,
scowling.
"Well, give me an example, I'll show you."
"(x - y)^12."
Kite stopped midstep, and fell silent for a moment.
Sora watched him curiously, even moreso when Kite reanimated a few seconds
later, announcing, "x^12 - 12x^11y + 66x^10y^2 - 220x^9y^3 + 495x^8y^4
- 792x^7y^5 + 924x^6y^6 - 792x^5y^7 + 495x^4y^8 - 220x^3y^9 + 66x^2y^10
- 12xy^11 + y^12."
"You cheated," Sora said flatly.
"Nope. It's simple, I told you. The first step is
to get your exponents down, and those go in a set pattern that anyone can
guess. Once you've got that, you can either go Pascal's Triangle, but that
gets nutso after the first seven terms or so, or use factorial theorem,
which is what I did."
"Factorial theorem?"
"Yeah. (n!)/([n- k]!k!), where n = your total exponential
term and k = the greater of the two exponents for the term you're calculating.
It's especially good for finding specific terms in a sequence."
"I remember that now. The teacher was going on about
it in class," Sora sighed. "I didn't understand how it worked at all. Or
that triangle thing."
"You're meant to take it for granted that it functions,"
Kite said, shrugging. They continued their walk. "The simple how of it
is just to know that factorial theorem and Pascal's Triangle both expand
out to give you your coefficient. An even simpler way to think about it
would be 'factorial of one less than your higher exponent, over factorial
of the lower exponent.' You'll be crossing stuff out by the bucketsful,
too."
"Okay, but why does this all work, then?"
"Don't worry about that."
"No, really."
"Look, you don't have to understand why it
works. Unless you're planning to pursue maths as a career, the main objective
it just to know how it works. In the case of binomial expansion,
there's no real reason to Pascal's Triangle except that it works for what
you need to do."
"If you think you'll overcomplicate things otherwise..."
Sora began.
"Teachers overcomplicate things, that's the
problem. Do you think you're seriously going to need all this theory stuff
once you get to study the subjects you like? What subjects do you
like?"
"Japanese, I guess." This generated a short laugh
from Kite, to Sora's puzzlement. "What's so funny?" he asked sharply.
"Nothing-- I'm just remembering how when I first
met you, all you did was talk in l33t."
"\/\/4n+ 3j3 5|-|00ld 5+4r+ 4941n?" Sora challenged.
"No, no, that's okay..."
They spent the rest of the time en route to the
Carmina Gadelica marketplace trying out some sample problems. By the end
of a rather lengthy binomial raised to the 34th power, Sora seemed to be
getting a decent grasp of the concept, to say the least. He was also nursing
a headache.
Tutoring had been working out relatively well these
past few weeks, mostly for how open-ended the sessions tended to become.
Though they met regularly, it was always up to Sora how long sessions would
last, and the material that would be covered. There was no sense beating
a subject to death that he already understood, and similarly little point
in keeping silent about areas he was having problems in. He learned very
quickly there was less shame in admitting difficulty than in Kite badgering
it out of him at some later point. Because he would. He was insidiously
good at that sort of thing.
It was a Saturday afternoon and the servers were
beginning to fill up with younger players, those just getting out of their
half-day of school. Already the marketplace on Lambda server was beginning
to get crowded, limiting the two Twin Blades' movement, and causing them
to wonder why their charge couldn't have picked an emptier place to meet.
An Assist hired out his services to less experienced
players, usually when playing the game for its own merits had started to
grow old and the player needed something new to keep up interest. It used
to be an unofficial practice, but the advent of the Assist Guild had greatly
regulated the system, though people could still give out support services
without the guild, even if less efficiently. The greatest benefit to the
guild was that it advertized and was able to bring in much more business,
and the PCs running it tended to do a great job of matching the client
with an appropriate Assist.
Last week Kite and Sora had both gotten guild notices
for the same job. It was apparently a large-scale operation requiring at
least two allied parties, and both could really do with a high-powered,
preferably Level 99 or 100 Assist. So, they had both been requested. By
name, the guild reps had stressed.
That part didn't really impress them. Apart from
Balmung they were arguably the two most legendary players in The World,
and they received unsolicited requests like other people breathed. Most
could be safely ignored, a few could be safely accepted, and once in a
while were the scary ones. This, fortunately, didn't seem to be one of
those. By the sound of it, it was just a level-95 dungeon on Omega server
about ten levels long, for a rare item someone needed for a trade quest,
and that was all to be said. After other things they'd had to deal with,
this should be a cakewalk.
"So was there anything else?" Kite asked, turning
down onto a side-street nearing the meeting place.
"Well, I guess about quantum physics in relation
to a cat--"
"Oh, give that up already."
"Fine, fine." Sora glanced at his surroundings.
"We're nearly there. 'Spose we should get ready..."
"Ah, come on," Kite complained. "Do you have
to switch back into 'orae'?"
"That's what fits this character. I have an image
to uphold, you know."
"Why not just use 'boku' like the real you does?"
Sora scowled at him. "Tell you what. You don't tell
me to use 'boku,' I don't tell you to use 'watashi.'"
"That stung."
"Good."
And then:
"WAAAAIIIII!"
It was a shriek, a thousand nails clawing at a blackboard.
The whine of a hundred adoring pets and affectionate toddlers and the squeal
of every high-pitched anime girl ever inflicted upon human ears.
Sora and Kite froze in time to see, around the corner,
a cluster of maybe twenty or thirty PCs, though it looked like more than
a hundred, and all of them, saving a few, were female. Most of them were
short, brightly colored and the expressed age of 15, and quite a few were
Twin Blades. The ones in front --a number always changing as others struggled
to push forward for a better view-- mostly held up hand-crafted signs involving
crudely-painted hearts and terrifyingly affectionate proclamations. When
they saw they had gained Sora and Kite's attention, their screams of adoration
tripled in loudness, reaching new levels of ear-bleeding decibels.
It was their fan club.
"Oh good god," Kite whimpered, going into a defensive
stance.
"What do we do?"
"...RUN!"
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