Chapter Four: Of Empirical Laws and Automatic Weapons

Somewhere in the bleak darkness that filled the subway car, Charlie heard someone cough. Somehow he had ended up flat on his stomach with his hands laced over the back of his head. At least I remembered what they taught us in Kindergarten. In a moment of elation at still being alive, Charlie almost laughed, but the urge quickly passed. He was still in the tunnel, now it was dark and they had just had their first aftershock.

"Did it collapse?" Two of the others were whispering as if the sound of their voices might make the tunnel come crashing down on their heads.

"I don't think so."

"Frankie? " Marcus's frantic voice filled the gloom.

Charlie reached under the bench behind him and felt around for his backpack. He dug around inside for his keys. A small silver penlight had been hanging from his keychain since Don had left for Quantico. A last minute present for an almost forgotten birthday. The small light suddenly illuminated the cabin and the other passengers looked up at him in shock.

"Sorry, I..um…I guess I should have warned you first."

"No shit."

"You want him to turn it back off?"

The question went unanswered.

"Shine that over here would ya?"

Charlie turned the light toward Marcus. In the dim illumination they found Frankie huddled nearby and just for a minute the light reflected something that could have been fear in Marcus's eyes. Then it was gone again and the gang leader extraordinaire persona was back.

"Well, Math Man, since you're such a smart guy, what do we do now?"

"We've got to get out of here."

Marcus gave him a reproachful look.

"Your not gonna freak out again are you?"

"I…..I really wasn't planning on it."

"Good. I'm not gonna take it very well if you get all freaked out again."

Frankie interceded on his behalf.

"Marcus, what about his head? If we get out of here, will he be able to walk that far?"

"Well?"

Charlie answered his one word inquiry trying to sound less freaked out than he really was.

"I think I can manage that better than just sitting in here. It's just that without the emergency power, there's no airflow in the cars and it might just get a little stuffy. I don't think I can take stuffy, dark and enclosed right now."

The other boys seemed hesitant to leave the car.

"But what if there's another earthquake?"

Charlie shook his head.

"There won't be."

"How the hell could you know that? What just happened then?"

"That was a seismic event that qualified as an aftershock."

Marcus learned forward and locked him in a fixed stare.

"Ok. Well, what if there's another aftershock then?"

"No….I mean…..it's not totally impossible, but it is highly improbable."

When no one responded, Charlie continued speaking.

"CalSci, that's where I teach…….they have a Seismological Laboratory, they've studied this for years, and a typical shallow earthquake of a seven point five magnitude has five aftershocks of at least five point five on the Richter Scale. Those aftershocks are evenly distributed from at least an hour to two days after the mainshock. This quake was no where near that powerful…we just jumped the tracks. And since we've already had one aftershock in the first 30 minutes, it's highly unlikely that another would occur before we were able to get clear of the tunnel."

Marcus shook his head to indicate he thought he understood.

"Right then, so we won't have another aftershock?"

"No…I mean…..yes. But they will follow the pattern, so we have a little time before the possibility of another one occurs."

"A pattern?"

With an enthusiastic nod, Charlie tried to explain.

"Yes, a pattern. There are patterns in everything. Aftershocks follow a very specific pattern that can be defined mathematically by using an empirical relation, something called Omori's law. It determines the temporal decay of aftershock rates. The rate of aftershocks is proportional to the inverse of time since the mainshock."

Even while holding tight to his guise and remaining sarcastic, Marcus was trying hard to comprehend what Charlie was saying and seemed to be doing a pretty decent job of it.

"So the longer after the earthquake happens, the less severe the aftershock's gonna be?"

"The frequency and intensity decreases by roughly the reciprocal of time after the mainshock, yes."

"So using your law thing, you can tell us exactly when the next aftershock will happen?"

Charlie leaned his head back and covered his face with his hands.

"No…It's not like that."

He tried not to sound to frustrated as he continued.

"The patterns I'm referring to describe only the mass behavior of aftershocks; the actual times, numbers and locations of the aftershocks are 'random', while tending to follow these patterns."

Frankie tilted his head at him.

"So you're full of crap."

"No."

Leaning forward again, Charlie tried to explain what he meant in terms a middle school kid would understand. "See Frankie, there is random as in irregular and then there is random as in anticipated. Aftershocks are both kinds of random…sort of."

The kid shook his head and offereda confused smile. Giving up on making sense to his audience, Charlie continued his explanation almost to himself now.

"They still follow an expected pattern, but it's unpredictable. Since this is an empirical law, values of the parameters are obtained by fitting to data after the mainshock occurs. So they have no physical basis in reference to the actual quake itself. It's only a pattern that will, to a certain degree, be followed."

Marcus was the only one who didn't look completely confused now.

"So you don't know because the results depend on what actually happens, like an experiment. So by doing the experiment, only then can you see the pattern and….."

Frankie cut off his brother's explanation.

"So you can't predict nothing?"

"I wouldn't say that."

Charlie couldn't hide his shock at Marcus's ability to at least act like he understood what an empirical law was. "But I do know that if there is another aftershock in the next two hours it will be an anomaly that would substantially decrease our likelihood of ever getting out of this tunnel."

Marcus narrowed his eyes at him and pulled himself to his feet.

"Well, Math Man, I only understood about half of whatcha said, and I still think you're full of crap, but you got my vote. Let's get the hell out of here."

"Well, since the windows and doors won't open in this car, we'll have to find a way to break….."
Before Charlie could finish his sentence, four consecutive explosions filled the small cabin followed by the sound of breaking glass.

He whipped his light around to find Marcus standing in the center of the car.

In his extended right hand a .45 caliber semi-automatic pistol was still smoking.

"WHAT THE HELL?"

Marcus turned to face Charlie and brought the gun down to his side.

"What? Bullets break glass."

Feeling like his heart was going to pound out of his chest; Charlie sat down hard on the nearest bench and put his head between his knees yet again.

The kid with the red shoes rolled his eyes at Marcus.

"Jeez man, you could have at least warned him first."

"Shut up Jose, we can get out now can't we?"

Charlie lifted his head and glared at young man holding the gun.

"Just put that thing away."

"Whatsamatter, Math Man? You don't like guns?"

Charlie scoffed at the question.

"It's really the bullets I have a problem with."

He looked apprehensively at the growing annoyance on the gang leader's face.

"So just…please, put it away."

Jose stepped up to the older boy.

"Marcus, man…Don't freak out the math dude. Put the piece away."

Marcus gave him a contemptuous grin.

"What? You gonna defend this guy cause he knows stuff? He's so smart; we can't remind him who's in charge down here?"

He turned back to the anxious math professor.

"The firepower makes you nervous huh?"

"No. You do."

Charlie's off-hand response stopped the others in their tracks. They turned to their ring leader, expecting him to instigate some sort of retaliation.

"I don't think I like the way you're talking to me. I want you to show me some respect."

Despite his apprehension, and the gun that was still in the kid's hand, Charlie could not contain the frustration he was feeling and he responded honestly to the statement.

"Respect? Why, because you have a gun? I have no reason to respect you, Marcus."

Any indication of humor had vanished from the boy's face as Charlie continued.

"But I can respect the gun…"

Marcus took several steps forward.

"Hey, I am respected on these streets. Me and my gun. Hated, but respected."

He waved the gun in Charlie's face to emphasize his point.

Charlie backed himself against the wall of the car as he instinctually reacted to having a gun pointed at him. His heart jumped into his throat and Charlie recalled the last time someone had pointed a gun in his direction. But he'd had Don there then. Don and a room full of federal agents, each with their own gun. Don had protected him. Don's not here, Charlie. Are you just going to stand here and get shot?

His effort to put as much distance between himself and that gun as he possibly could seemed to satisfy Marcus's ego and he gave Charlie a cold smile.

Charlie shook his head.

"This isn't respect Marcus. It's just fear."

Somehow, the idea of allowing this young man to interpret his reaction as reverence made Charlie feel sick to his stomach and he felt his frustration at the absurdity of his situation building.

"And I'm not even that afraid of you. I'm afraid of that gun. Because I know what it can do. The person who holds it doesn't mean anything. That gun would be just as dangerous in the hands of a five year old. And I'd be just as afraid of it as I am right now."

Marcus advanced across the car, keeping the gun leveled sideways at Charlie.

"Are you trying to piss me off?"

Surprised by his own reaction to having a gun shoved in his face, Charlie found his fear was being drowned by an unexpected anger. He took two steps away from the wall and actually moved closer to the gun.

"Yes, Marcus. OK. I'm trying to piss you off. Today when I got out of bed, I thought what the hell, let's get trapped underground with some bad ass and see if you can manage to piss him off………"

Charlie took a deep breath and tried to contain his outburst. He put his hands on the sides of his head, giving the other passengers an exasperated glare. "I have had a very, very bad day as I am sure you may have noticed since you have become an intricate part of it. So if you are planning on further complicating my moderately problematical existence by shooting me, just do it so I can get on with dying already."

Marcus continued to stare at him without speaking, and without lowering his gun.

With an anxious glance at his older brother, and the panicky mathematics professor, Frankie spoke up.

"Are you gonna freak out again?"

Charlie's knees were shaking, but he remained standing and refused to take his eyes off the gun or the young man who held it.

"No Frankie. I am not freaking out. I am perfectly calm. But your brother is pointing a gun at me. I've been shot at a couple of times in the past and it is really not on my list of things to do again. It's late, it really has been a very long day, I've developed a headache and I have a lecture in the morning. The door can be opened now and I would like to go home so I can go to bed."

Directing his unsteady voice back at Marcus, Charlie continued.

"So, if it's ok with everybody, I'd like to use the exit you so graciously gave us and get out of here."

After a few moments of silence Marcus lifted his gun and made a dramatic show of sticking it back into the waist band of his pants.

"Well, if the Math Man says it time to go, by all means, let's get moving."

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Authors Notes: Thanks again for all of your comments. To directly answer a question, (and in case anyone else is wondering) Don doesn't play a big part in this section of the story. It's all about Charlie's little misadventure. Don is inthe last two chapters, and he is also a very central character inpart two, so never fear. Brother Angst is just around the corner.

Chapter Five: Just a casual stroll down a long dark tunnel.