Disclaimer: I don't own any Azumanga Daioh characters.
Note: It's late and I'm tired and blah, blah, blah.
At the end of another school day, a rare moment found the Wildcat Tomo in a peaceful state in the school's library.
Tomo sat at the end of a table with a book resting open in her hands. Her posture was slouched as her eyes roamed over the words printed in neat type across open pages. For once she did not simply understand the words as ink on paper, but rather she comprehended an insinuation pieced together by a process of paragraph accumulation.
After an hour she lowered the book with a fresh sense of understanding. There was a suggestion of didactic form, a possible window of application for the book's ideas. At last she had found the edge that she had been looking for.
The next day at P.E., Tomo gathered together the girls of her social circle.
"Sakaki," she said, pointing to the tallest girl, "I'd like to challenge you to a race."
"Not again," groaned the spectacled Yomi.
Kagura too shook her head in discouragement. "We've already settled this, Tomo. Sakaki wipes the track with your ass every time."
Tomo smirked. "Not this time. I'll make a promise here and now that if Sakaki beats me in this race, I'll be a personal servant to each of you girls for the rest of the month."
The girls exchanged a variety of perplexed expressions.
"Are you sure that you want to risk that?" Chiyo-chan asked, touching her hand to the Wildcat's forearm to see if her skin felt flushed in any way.
"I'm absolutely positive," Tomo nodded. "The race will be run fair and square, but with one conditional difference."
"Should've figured…" Yomi muttered and turned to walk away.
Tomo grabbed the girl by the collar of her shirt. "Now, now. The condition is that I will be given a three second lead, nothing more."
Kagura frowned and looked at Sakaki. "What do you think?"
Sakaki shrugged, indifferent to the concept of competition as always. She didn't believe that Tomo could beat her, but then again she didn't care.
"I guess," she said.
With the matter decided, the girls headed to the track where Tomo and Sakaki lined up at the beginning mark for the 100 meter dash. Yomi acted as the end point, standing at the other end of the track with her arms held out to the sides. Chiyo-chan took her place just behind the competitors and set her watch to timer mode.
"Get ready," she said. "When I say go, Tomo will start. Then I'll wait three seconds and say go again, and that one's for you, Sakaki."
Both of the runners crouched down and touched their finger tips to the tracks.
"Ready, set, go!" Chiyo shouted, starting the clock on her watch.
Tomo shot off at full speed down the track, her motions followed by a few skeptical gazes from the sidelines. At the end of her three second lead she had gained a good number of yards on her competition.
"Go!" Chiyo shouted again.
Sakaki took off at once. The length of her strides brought her even with Tomo in a matter of moments, and in an equal number of moments she surpassed the girl and was the first to dash by Yomi's outstretched arm.
Tomo slowed down before she even reached the finish line. She came to a stop and rested her hands to her knees to catch her breath.
Kagura jogged up to the Wildcat, followed by closely by Chiyo.
"That settles it, Tomo," Kagura said. "Sakaki won and you owe the rest of us a month's worth of servitude. What were you thinking anyway?"
Tomo straightened and looked at the girl with a grin. She shook her head and wagged her finger like a schoolmarm reprimanding a dumb student.
"Oh, poor Kagura. Can't you see? It was impossible for Sakaki to have won that race," she said.
Yomi came up to the three, adjusting her glasses with her index finger as she usually did when she got pensive. "I think you've been out in the sun too long. Sakaki beat you by a long shot. Everyone saw it."
"She may have been the first to cross the finish line, but that doesn't mean anything. If you could think logically like me then you would see the error in your conclusion."
Sakaki too came to the group and listened quietly to the exchange.
Yomi folded her arms with a sigh. "Oh, this should be interesting. Please, O great Tomo, enlighten the rest of us to the wonderful world of your ineffable reasoning."
Tomo picked up a rock from the side of the track and crouched down on the track itself.
"It's simple, really. Do you see this stretch of track that we just ran on?" she motioned to the area of the track in front of her as the other girls circled around.
"Yeah," said Kagura.
Using the rock, Tomo drew a small diagram on the track's surface, marking points as circles. "We'll call the starting line point A, and the finish line point C."
"All right," Yomi said and leaned over to get a better look at the picture, placing one hand to her knee and her other index finger to the bridge of her glasses.
"To make my lead legitimate," Tomo continued, "since we did agree that I would be given it, we'll say that the race started when Chiyo said 'go' for the second time."
"Uh huh," Chiyo agreed, copying Yomi's position.
"When Chiyo said 'go', Sakaki was here at point A, and I was here at what we'll call point B, some yards ahead of her."
"Uh huh," Yomi said a bit more slowly.
"A few seconds later, Sakaki was even with me, and then it looked as though she surpassed me, when in reality she was still behind me."
Yomi straightened back up and frowned. "You lost me."
"Me too," Kagura said, scratching the side of her head.
Tomo dropped the rock and stood up, dusting her hands together. "Before Sakaki reached the point where I was at, I had already gone a little ways past that point. So while she was at point B, I was at point B-and-then-some. Again when she passed the point where I was at then, I had already gone a little ways past that point. This continues on to infinity. So even though in physical terms it looked as though she raced right on past me, in logical terms because of that space I had gained at that three second lead, she will never be able to catch up with me."
The other girls looked at Tomo as though she had just crossed over into a whole other world of nonsensical convictions, even though the exact opposite was true.
"Tomo…" Yomi growled, her hands lifting towards the Wildcat's throat.
Suddenly from behind the group another girl stepped up to add her two bits of intellectual ammunition.
"You're wrong Tomo," Ayumu called. If a synthesis of thought processes and sixth-sense application were militaristic hardware, where Tomo would have resounded like the rattling patter of a semi-automatic, Ayumu ruptured like the concussion of a cerebral H-bomb, devastating the fabric of cognition and consciousness within a ten mile radius.
Tomo whirled about to face the non-believer. "What was that, Osakan girl? You wanna argue with the logistics of pure space and time?"
"No, actually I wanna use those same logistics to let you know that this race never even began," Ayumu replied.
The other girls started and jumped back, raising their arms in a preliminary defense against the awesome ridiculousness of the Osakan's claim. Somewhere in the distance, a bolt of lighting impacted the earth.
"What?" Tomo shouted.
Ayumu approached the group and crouched down by the drawing that Tomo had made of the three points.
"All right, come around here," she said. "The starting line is point A, and the finish line is point B. So this stretch of track has a bisecting point, what we'll call point A-and-a-half."
Kagura brought her hands to the sides of her head. "Can't you just say point B and have the finish line be point C?"
Ayumu shrugged, picking up the drawing rock. "All right, whatever. So now we're dealing with the starting point A and the mid point B, but then that has to have a bisecting point, right? So in order to even reach the half way point, you have to go across another half way point."
"Yeah, I suppose," Yomi said, rubbing the back of her neck.
"But even that has to have a bisecting point. This goes on and on, and then we have an infinite number of halfway points. So how do you expect to reach the end without even reaching one halfway point? In other words, how can you pass an infinite number of points in a finite time?"
Ayumu stood back up and the other girls grew quiet. For several long minutes they stood staring at each other until suddenly Tomo snapped out of her trance.
"Oh yeah?" she shouted, "Well maybe this race never even took place!"
Kagura pressed her hands back to her head and shut her eyes tight. "What're you saying now?"
"I'm saying that all motion is impossible!"
Tomo ran across the field to the bag of volley balls and basketballs sitting in the shade of some bleachers. Choosing a volley ball from the lot, she then ran back.
"Here," she said, throwing the ball straight up into the air.
The girls watched the ball rise high into the air, reach its pinnacle, and then drop back down. As the ball bounced, Chiyo-chan lifted her hand and examined her fingers carefully, wiggling them back and forth.
Once the ball came to a halt, Tomo turned to the others and placed her hands to her hips like a drill sergeant.
"At any given moment," she said, "no matter how infinitely small the moment, the ball was at a certain point in the air. That's time and space intersecting to form the ball's position. At these moments the ball is occupying a space equal to its size, and it is therefore at rest during these moments, like an infinite number of pictures being taken of it. The sum of an infinite number of these pictures of rest is not motion. Motion is impossible."
Again the girls fell into silence. Birds flew overhead and cicadas buzzed in their hiding places. On another part of the field, a soccer game reached its end with a score of 3-0 as a boy kicked the ball past an opposing goalie. A girl on the volleyball court dove too late to make a hit and her face connected with a small sand dune. Coach Kurosawa stood by the basketball courts, whistle held in her right hand and clipboard held in the other. Footsteps in the girl's locker room followed the dropping of a pair of red panties. A teacher of class 2-3 began to cough until he had to grip the edge of his desk. In the hallway, a boy stopped to slip an orange cat out from his book bag. A flake of paint in an upper corner of the girl's bathroom on the same level drifted to the ground. Yukari slouched over on her desk in the teacher's lounge, head tucked into the bend of her elbow as visions of yakitori resulted in a small strand of drool at the corner of her mouth.
Suddenly Ayumu blinked to the sound of Nyamo's whistle.
"Wh-what?" she asked, looking around at the others.
She received no response, and as the other girls turned to head back to the locker room and get changed, the area was returned to a state of gentle repose.
Note: Obviously this story was inspired by Zeno's paradoxes. Fun stuff for brains to gnaw on.
Edit 12/21/05: Azumi makes a good point that this story is rather OOC. That Tomo was sitting in the library reading a book is proof enough of that. However, proper characterization wasn't crucial for the story so I didn't bother tweaking it that much.