XENO'S PARADOX
By
Ashleigh Anpilova
Arriving back from lunch together, Ducky and Abby find an out of breath DiNozzo in the office and the other team members teasing him. When he discovers what the problem is, Ducky takes it upon himself to explain the theory of Xeno's Paradox.
An established relationship story.
Written: March 2007. Word count: 2,679.
Talking animatedly, Ducky and Abby came into the squad room. As she finally slipped her arm from his, Abby said again, "That was a lovely lunch, Ducky. I really enjoyed myself. Thank you."
"It was my pleasure, my dear. We must - Oh, is something the matter, Anthony?" Dropping his hat on McGee's desk, Ducky hurried across to where Tony DiNozzo half lay, half sat in his chair. His tie had been loosened, his collar was undone, his shirt was partly untucked, and his jacket was thrown over his desk. His face was red, he was visibly sweating and his breathing was labored. In fact, as he looked at Jethro's senior field agent, Ducky thought the young man looked quite ill. His fingers moved of their own accord to Tony's pulse; it was racing. Frowning, Ducky put his hand on Tony's forehead. As he did laughter, giggles if he was completely honest, came from behind him.
Still holding Tony's wrist, he turned around to see, to his surprise, McGee and Ziva clearly unable to contain their laughter. Abby was looking from Tony to the other two member of Jethro's field team; she looked puzzled.
Ignoring the children who were suddenly behaving more like children than they usually did, Ducky turned back to his 'patient'. "Anthony, what on earth -"
"Ah, don't waste your sympathy on him, Duck. He doesn't deserve it." Ducky glanced up again as his lover swept by him.
"Jethro?" Ducky was surprised at the blunt comment. He knew that Tony tried his beloved's patience on a daily, if not hourly basis, but that was part of the Anthony DiNozzo 'charm'. And despite the constant irritation he caused Jethro, Ducky also knew that his lover would be extremely sorry the day Tony decided to move on. The 'bear' his lover could sometimes be, was actually fond of all members of his team. Some, like his dear Abby, he was more fond of than others, but he cared for all of them. And if they were hurt or in trouble, then the bear tended to be in ascendance. Thus for Jethro to be so . . . so dismissive, it must mean that either Tony had done something extremely serious, far more than merely knocking over a cup of coffee, to upset Jethro, or he had been even more foolish than normal.
A new giggle now crept across the office, and Ducky saw that Abby had joined the McGee-Ziva huddle, which meant that he and he alone did not know what was wrong. And Ducky never liked not knowing about - well about anything.
"Are you going to tell me what has happened to you, Tony?" he asked, pleased to finally note that the racing pulse rate had slowed a little, and that Tony didn't look quite so flushed. His question merely elicited more laughter from the three remaining children, an unintelligible mutter from his lover, and caused Tony to glance away from him and to partially straighten up in his chair.
"No, it's fine, Ducky. I'm fine. It's nothing. Forget it." Tony straightened even more.
"If you're fine, DiNozzo, you can dress yourself again."
"Yes, boss. Sorry, boss." DiNozzo started to tidy himself up.
Ducky, however, refused to be dismissed as easily as that; everyone else knew; he intended to know too. Leaving Tony to his self-ministrations, he crossed the office, glancing at McGee, Abby and Ziva as he went by them, and came to a halt in front of his lover's desk. He simply waited.
After a moment or two, Jethro glanced up and met Ducky's gaze. A 'heaven spare me' look flashed across his face as he snapped, "McGee, tell Ducky."
"Really, boss," DiNozzo said swiftly. "There's nothing to tell. It's just . . . " He trailed off under the Gibbs-glare, sighed and said, his tone resigned, "Tell Ducky, Probie."
Ducky turned to face McGee and beamed at him.
Swallowing another giggle, McGee began to speak. "We were all just grabbing a sandwich, when -"
"Yeah, we don't all have time for long lunches out," Jethro muttered from behind Ducky.
McGee and Ziva looked startled, Abby just continued to smile her pussycat smile, and DiNozzo blinked a couple of times. Ducky simply turned back to face his lover and gazed serenely at him; the look in the dark blue gaze didn't match the words Jethro had spoken. Ducky hadn't needed the reassurance in the look to know that Jethro had been teasing, but he never objected when Jethro looked at him in their personal, private, intimate way.
Smiling softly, he turned back to McGee. "Please, do continue, Timothy," he said placidly.
After a half glance of his own at Jethro, McGee did that. "When a man, in his late thirties."
"He was forty," Ziva said firmly.
McGee glanced at her. "Okay, forty," he shook his head. "When this man grabbed Tony's money."
"Be precise, McGee. You write flawless reports for Gibbs, why can you not be as exact in your verbal reports."
McGee looked at Ziva. "Er, I'm not giving Ducky a report, Ziva. I'm simply telling him what happened. There's a difference."
"There is?"
"Yes."
Ziva sighed and looked perplexed. "I sometimes think I shall never understand your language. A report is a story, yes? It's an account, a statement, a description, it tells of what happened, yes?"
"Um, yes, I guess. But -"
"It tells of what happened. You are telling Ducky what happened. Therefore you are giving Ducky a report, yes?"
"Er . . ." McGee trailed off.
"Ziva dear, why do you not join me for tea later today and allow me to try to explain the difference to you?"
"Lunch with Abby, tea with Ziva. Hey, boss, you'd - Why don't you finish telling Ducky what happened, Probie." Tony added hurriedly. Ducky didn't need to be looking at Jethro to know that he would have again given Tony one of his famous ‘Gibbs-glares'.
"No, let me. Ducky, Tony had a five dollar bill in his hand, in his left hand, but maybe you do not need to know that, and this man grabbed it from him and ran off."
"And Tony took it upon himself to chase after the man."
"It was my money." Tony said indignantly.
"It was five dollars, Tony. Five. You spend twenty times that on a tie. Although how anyone can justify spending one hundred dollars on a tie is a mystery to me."
"That pretty much sums DiNozzo up," McGee muttered.
"It was my money," Tony said again.
"Ah, yes, but . . . But, let us not forget that in doing so, in deciding to chase after this man, the amount of damage you caused."
"Damage?" Ducky asked.
"How was I to know that woman would be so close behind me?"
"A woman who had just been shopping to buy a new dinner service. A new china dinner service."
"Oh, dear," Ducky said, trying not to smile.
"It gets better. Was it five or six people over whom you knocked drinks?"
"It was four. And one of those was only a splash."
"But that still isn't the best of it, Ducky."
"It isn't?"
"Oh, no. You see," McGee broke off to laugh again. "You see," he tried again. "You see," he attempted for the third time.
"Tony couldn't catch him," Ziva, now holding onto McGee's arm, finally managed.
Once more Abby, McGee and Ziva descended into laughter.
Ducky glanced around to see a faint flash of the same humor on his beloved's face. It wasn't anything the children would have noticed, but he did.
Tony sighed loudly and said, his voice flat, "It's true, Ducky. I couldn't. It didn't matter how fast I ran, he managed to stay ahead of me all the time. I kept getting closer and closer, but I couldn't catch him. Had to give up."
"Poor, baby," Abby said, her tone, like Jethro's moments earlier, belying her words.
"Oh, I know why that is, Anthony," Ducky said.
"You do?" Tony said, his tone a little hesitant."
"Oh, yes. That is what is known as Xeno's Paradox. Of course, it has been proven not to be true. However, the theory is an interesting one, and given your experiences today, together with other examples that I have witnessed, I have occasionally found myself speculating as to whether it has been dismissed too simply."
"Xeno's Paradox?" Tony asked. "What's that, some computer game? Hey, Elf Lord, that's up your street."
Ducky sighed softly. "No, Anthony. It is not a computer game. Xeno's Paradoxes are a famous set of thought provoking stories or puzzles, which were originally formulated in the mid-fifth century, B.C., by Xeno of Elea. If you wish, I could explain it to you, although I'm certain that you will already know a version of the most famous paradox."
"Thanks, Ducky, but another time, maybe. Got a lot of work to do."
"Not from me you haven't. The Director been sending you on secret errands again, DiNozzo?"
"No. No, boss, of course she hasn't. I just . . ."
"Come on, Duck, you can sit down here and tell them. They've wasted enough time already, what's a few more minutes going to matter."
"Oh, thank you, Jethro. Are you certain?" Ducky asked, already moving to sit in the seat his lover had vacated.
"Yeah. Need to go to the head anyway. Want me to bring you a cup of tea back?"
"That would be very kind of you, my dear. Thank you." Ducky smiled. And then noticing the look on Ziva's face, asked, "Is something the matter, Ziva?"
"'The head' is Marine talk for the bathroom, yes?"
"Yes."
"Then how come . . . "
"Why Ziva David, do you mean to say that your powers of observation have failed you. And you've been with us, how long is it now? Over a year. I'm surprised at you. Tsk, tsk for not noticing."
"What? What are you talking about, DiNozzo?"
"He means that whenever Gibbs comes back from the men's room, he always has a cup of coffee."
"But . . ." Ziva just shook her head. "You go on, Ducky, please. Tell us about Xeno's Paradox. I am certain it will be less complicated to understand."
"Very well." Ducky smiled, and settled himself more comfortably into Jethro's chair, the children were all looking at him with varying degrees of interest on their faces. "Xeno's Paradoxes have to do with motion, which is usually thought of as the distance someone or something travels over a period of time. Ever since Xeno formulated his paradoxes, more than two and a half millennia ago, philosophers, physicists and mathematicians have argued over how to answer the questions raised. Each paradox differs from all other paradoxes, as far as specifics go, however, all of them deal with the -" As Tony's and, to a lesser extent, McGee's eyes began to glaze over, Ducky hurriedly rethought where he had been going with his story. "Ah, yes. In the words of Aristotle, 'You can never catch up. In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead'."
"Huh?"
"Did your parents ever read the story of the Tortoise and the Hare to you when you were a child?"
"Mine did."
"Very good, Timothy. Well, the fable is in fact based on the most famous of Xeno's Paradoxes - 'The Tortoise and Achilles'. Simply put, according to the story, if in a race between Achilles and the tortoise, if the tortoise were given a head start, then Achilles would never be able to catch him."
"Never?"
"Indeed."
"But that's nonsense, of course Achilles will eventually catch the tortoise."
"Just as you would have eventually have caught the man today," Ziva said in her pseudo-sweet tone.
DiNozzo glared at her, but otherwise ignored her. "Go on, Ducky. It's nonsense, right?"
"Well, yes, Anthony, it is really. Of course, given time, Achilles will not only catch, but also overtake the slower tortoise. However, the paradox is based upon a mathematical consideration of the scenario. Basically what Xeno was saying is that if Achilles gives the tortoise a head start, that in order to overtake the tortoise, he must, in the first instance, run to the place from where the tortoise started. However, by then the tortoise will have moved on to another place, thus in order to overtake him, Achilles must run to the place to which the tortoise had moved. However, by that time -"
"The tortoise will have moved on. And Achilles will have to run on as well. So, even if Achilles runs forever, he'll never overtake the tortoise."
"Very good, Abigail." Abby half beamed and half frowned.
Ducky hid his own smile. It was a little naughty of him to call Abby 'Abigail', as he knew that the young woman disliked her full name; Ducky himself was rather fond of it. Of course he did have a habit of lengthening all shortened names back to their original form, and it rather irked him that Jimmy Palmer was indeed 'Jimmy'; it was the name his parents had given him at birth. Personally Ducky thought it a more than a little foolish choice; 'Jimmy' was quite an acceptable name now, whilst he was still a young man, but happened when he - Suddenly Ducky realized that he was rambling in his thoughts. He came to an abrupt halt and swiftly reviewed where he had got to with his story.
"So as Anthony pointed out, common sense tells us that Achilles will eventually catch the tortoise, but from the explanation I gave you above, you can see that it is impossible for him to do so. Hence the paradox: both pictures of reality cannot be true at the same time. Basically what Xeno is asking, is how one can deal with an infinite progression whilst doing each element individually. And as I explained, the debate over this paradox and Xeno's others has been going on for millennium, and I suspect will be going on long after we have all left the earth."
"That's depressing, Duck. Here's your tea."
"Thank you, Jethro. I'm afraid I may well have confused the children more than I helped them. I wonder if maybe I should -"
"I think I've got it, Ducky."
"Really, Anthony?"
"Yeah. According to his Xeno bloke, there was no way I could catch the man I was chasing because he had a head start on me, right? And because of the infinite whatsit and the whole moving forward thing, I never could have caught him. That's it, isn't it?"
"Well, yes, Tony, in essence that is what is being said. However, -"
"That's great then. I never could have caught him." And that note Tony smiled, nodded and turned his full attention on his computer screen.
"But, Anthony, as I -"
Jethro touched his shoulder; Ducky turned his head and looked up at his lover. "Leave it, Duck. He's happy."
"Well, yes, he does appear to be. It's just that . . . Oh, well, never mind."
"Tell you what, Duck. You explain it to me later when we get home. Or," Jethro added, as Ducky saw a sudden spark of inspiration hit his lover. "Better still why don't you go and explain it to Palmer, now?"
Ducky smiled brightly, patted Jethro's hand and stood up. "What an excellent idea, my dear Jethro. Yes, I shall do that thing. Mr. Palmer is always interested in my stories. " He gazed happily at Jethro.
Jethro smiled, and for a moment allowed his eyes to soften. "Catch you, later, Duck," he said, as he brushed his hand over Ducky's shoulder.
Pausing only to collect his hat from McGee's desk, Ducky made his way across the squad room to the elevators. Yes, Mr. Palmer would be an ideal student with whom Ducky could discuss Xeno's Paradoxes - all of them.
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