Cardinality
Summary: A serial killer is stalking the citizens of Las Vegas. Started out as a case file but the G/S aspect demanded equal representation. This is the edited version for this site. The original version can be found at my web site.
Rating: R for subject matter
A/N: No real spoilers. Many thanks to Burked for teaching me how to be a serial killer, among many other things.
Disclaimer: Obviously, I don't own anything related to CSI. If I did, certain characters would be getting more screen time – together!

"I cannot help it; in spite of myself, infinity torments me." – Alfred de Musset

Chapter 7

Dawn was approaching when Sara and Catherine arrived with the first batch of evidence from the theater. After logging it in, they headed towards the A/V lab, where Archie was excitedly talking with Brandenburg. When he saw their approach, me limped out to the hallway to join them.

"Make a new friend?" Catherine teased.

"I was showing him how to nest."

"I'm not sure I want to know the story behind that," Sara said with a grin.

"It's an old computer technique for speeding up computations. With today's faster processors, it's rarely used anymore. I explained it to Archie as I was getting some printouts ready for the briefing."

"Could you make out what that writing meant?"

"Actually, the math was pretty straightforward this time, Catherine. What it means to the killer is another question."

"Are you okay?" Sara asked softly. His limp was more pronounced than it had been earlier.

"I'm fine. I've just been standing too long. I'll be okay once I get home. I'll soak in the hot tub for a while. That'll get the swelling down."

"I guess that's one way of getting it back down," the blonde said, flashing Sara a knowing grin. Her colleague gave her an evil glare as they entered the Layout Room. "I think we can all use a vacation when this case is over."

"I don't imagine salmon fishing in Alaska wouldn't appeal to you," Max said, turning to smile at Sara.

"No, not really."

"How about snorkeling off the Grand Caymans? Visiting the volcanoes on Hawaii? A road trip to see the world's biggest ball of twine? Dollywood?"

"Why?" she asked with a laugh.

"So I know what to tempt you with," he said, grinning wickedly at her wide-eyed stare.

"You certainly don't waste any time," a surprised Catherine sputtered.

"No, I don't. Life's too short. I identify what I want, I formulate a plan and I go for it. That's how I ended up where I am today," he replied honestly.

Sara turned to stare at him, wondering if she should be flattered or not. While it was nice to have a man openly express an interest, his explanation had sounded almost impersonal. Max could easily have his choice of women. Hadn't he called her a "challenge" before? Was that all she was?

Sensing her confusion, Max turned to walk to her, but his knee buckled. Both CSIs moved to help him, Catherine grabbing his elbow while Sara slipped her arms around his waist. He rested his hand on her shoulder for support and gave her a smile, but it barely masked the pain.

"Thanks," he said softly, as he gingerly tried putting some weight on his injured leg.

"Sure," Sara replied, her voice equally calm as she watched him closely.

Nothing Max had done suggested he thought of her as a conquest. He'd been polite, respectful and friendly. His gifts had been excessive, but he had never tried to use them for leverage. He hadn't applied any pressure for a physical relationship.

She kept one arm around his waist, and rested the other hand on his chest as she helped him walk over to the table in the center of the room. Leaning against it, Max gave her an embarrassed smile and thanked her again.

Was he overcompensating? He'd mentioned he came from a very poor family. Although he had a scholarship, Max had worked through college to help his parents. At an Ivy League school, that would have made him the brunt of jokes. She remembered the way the full-scholarship students she'd known at Harvard had been treated.

Whatever it was, it was something they needed to talk about. Now was neither the time nor place, though.

"I think I have some ibuprofen in my locker. Would that help?" she asked softly, giving his arm a gentle squeeze after he nodded. Turning around, she paused when she saw Grissom staring at them intently, his expression clearly hurt.

Max glanced up when she stopped, easily finding the source of her discomfort. Using the table as a brace, he straightened up, giving Grissom a measured look. Despite Sara's assurances, it was obvious her boss was giving her troubles.

If his suspicions were correct, the man viewed Sara as his private property, and that rankled the mathematician. The entomologist had had plenty of opportunity to let her know he was interested in her. She deserved better than a man who not only denied her his company, but wanted to keep others from making her happy.

"Excuse me," Sara said as she twisted around to slide between Grissom and the doorframe.

For his part, Grissom watched her go in confusion. He'd been there to overhear the end of their conversation, and Brandenburg's comments had left him equally baffled. Sara was probably one of the least materialistic people he'd ever known. She couldn't be impressed by the money the mathematician was spending on her. Why didn't she tell him to stop with the expensive presents?

Walking into the room he noticed both Catherine and Brandenburg watching him. His friend seemed like she couldn't decide whether to be amused or embarrassed. The mathematician clearly wasn't happy.

Catherine decided to defuse the situation before the tension in the room got any worse. Walking over to the table, she looked at the stacks of printouts Brandenburg had arranged earlier, and then fixed Grissom with a pointed look.

"Say Max, we really appreciate all the time you've put into this. You've been a big help to the lab."

"For you, I have all the time in the world," he replied lightly, turning to give her a teasing look.

"One advantage of being unemployed."

When the other two turned to stare at him, Grissom realized he had actually said that out loud. From Catherine's evil glare, it must have sounded as rude as he thought it did. Belatedly, he smiled, trying to turn it into a joke.

"Or of being successful," the mathematician said, smiling at Grissom openly.

"Yeah," Catherine said quickly. "So, you thinking of going back to work? You're spending a lot of time here."

"I don't think I'd like being a CSI."

"Really?" Grissom said coolly.

"No. I don't think I could become detached enough. I don't know which would be worse: waking up each morning wondering if I was going to see something that would shock me, or worrying if there was nothing left that could faze me."

Catherine swore silently as her pager went off. It was Vega; they had been working a drive-by shooting. She couldn't ignore him. Hopefully, she wouldn't have to investigate another killing when she came back. The way those two were staring at each other, she expected them to literally start butting heads.

"Behave," she whispered softly to Grissom as she walked out.

Shaking her head, she spotted Sara in the DNA lab, in-between an animated Jacqui and Greg. She smiled ruefully when she saw Sara holding the bloody brush carefully, looking at it through the desk-mounted magnifying glass. She wouldn't want to be the mediator in that mess.

Greg would need to swab the brush for DNA before Jacqui could print it, since the chemicals she used would contaminate the blood evidence. But Greg could easily destroy the prints while collecting the swabs. Finding areas he could test that wouldn't ruin the prints was a tricky business, especially on a round brush. It would be harder to rule out areas least likely to have a print.

Walking by the doorway, she knocked lightly and pointed her thumb back at the Layout Room, hinting for Sara to get back as soon as possible. The brunette dropped her head, before turning her attention back to the brush, trying to find a compromise for the two lab techs.

Back in the Layout Room, Grissom walked around to the opposite side of the table as the mathematician sorted through his notes. His casual smile indicated he had heard Catherine's parting comment. That the younger man found it amusing didn't help his mood any.

Catherine had been correct. Brandenburg was helping the lab. Everyone else seemed to like him, for some unknown reason. Grissom found it hard to believe he would like the man even if he weren't involved with Sara, but had to admit he wasn't exactly impartial.

What did Sara see in Brandenburg? It could be physical, he supposed, but that wasn't a judgment Grissom felt qualified to make. He frowned lightly as he realized that probably wasn't one of the reasons Sara was attracted to him – he'd let himself go a bit over the last year.

He had ruled out the presents. She wasn't impressed by wealth. Could it be the attention? Maybe a simple acknowledgement of her was enough. All it had taken to keep her from leaving before was a plant. That may have worked once, but he needed to find a better way.

"Dangerous line of work you're in."

Grissom looked up to find the mathematician still going through his notes.

"It can be, but we take precautions," he replied, wondering where the younger man was going with this line of conversation.

"If you know what to look out for."

"Such as?"

Brandenburg regarded him carefully, weighing what he knew and had observed about Grissom. It hadn't left a good impression. He had told Sara his friends at the F.B.I. considered Grissom colorful. That had been a polite rephrasing of their comments.

No one questioned the entomologist's technical skill or knowledge, but his personality was another matter. He had a reputation of being difficult. He guarded his cases and information with a noticeable jealous streak. On occasion, Grissom had been known to treat people as experiments, rather than as people.

Brandenburg had worked on enough government contracts to know there was an element of inter-agency rivalry going on, but that didn't explain it all. The comments had been too consistent from too many people. Add in his own observations, and he'd reached the conclusion that Grissom was possessive. He wasn't willing to make the effort to make Sara happy, but he wouldn't let her go, either.

Not a nice guy, as his grandmother would say. Was Grissom even aware of the consequences of his actions?

"Long-term impact. 'He who fights with monsters might take care lest he thereby become a monster. And if you gaze for long into an abyss, the abyss gazes also into you.'"

"Nietzsche," Grissom supplied.

"Humans are social creatures, even if one is a loner," Brandenburg said, looking across the table at Grissom. "We judge our behavior by those around us. It sets the boundaries on what we consider to be acceptable."

"And?" Grissom asked shortly.

"Consider who you're around all the time. It has to color your perceptions. So what if you're rude, at least you didn't assault someone. Once you're comfortable with that, what does it matter if you're cruel, at least you didn't abuse someone. And once you become use to being emotionally abusive, Dr. Grissom, what follows after that?"

"I wouldn't know," he said quietly, turning to read one of the files he had brought in with him.

Despite his implications, Brandenburg was correct in a way. Some of the meanest people Grissom knew had worked in law enforcement. Being constantly surrounded by the worst of mankind did leave a mark on some people's souls.

But he wasn't like that. He didn't deliberately hurt people. Sara had to know that. Hopefully. What had Catherine said – how did his behavior look from Sara's perspective? No. Even if she thought he'd been deliberately mean, she wouldn't have told Brandenburg.

And it wasn't like the mathematician was in any position to judge. His innuendo from the theater still made Grissom angry. He was crass and lowbrow. Sara deserved someone who would treat her better than that.

Could he do it? He wanted to, but he couldn't express his feelings for her as openly. Part of it was professional; if they ever managed to get together, they would need to keep it outside of the lab. He could never send her expensive presents to work. The rest was personality. He just wasn't that demonstrative.

It was all confusing.

His contemplation was broken by Sara's approach. She stood outside the lab with a cup of water and a bottle of pills. Brandenburg made his way slowly across the room for the painkillers. Taking the empty cup, she tossed it away and brought in a stool for him. The rest of the team began wandering in as he thanked her.

While the others took up positions around the table, Brass leaned against the doorframe. "Max, remember some of us aren't scientists. Keep it simple, okay?"

"Certainly, but this isn't that difficult. The killer followed a fairly simple pattern this time," he said, moving the stool in front of the clear board. He then began drawing a 3-by-3 grid on the board. Starting with the center cell on the top row, Brandenburg wrote in the number one, and continued filling in the others cells.

8 1 6

3 5 7

4 9 2

"This is what is known as a magic square. If you add up the numbers in any row, column or along the diagonals, you'll get the same value. For a square this size, the sum is 15. The pattern to generate a magic square is pretty trivial for an odd-numbered grid," he said, limping towards the table.

"What the killer did at this scene was to paint four separate grids on the movie screen. Each one holds a different proof. He broke down each proof into sections, and followed that pattern," he said, pointing to the magic square on the board, "to fill in the cells."

He nodded to Sara, who passed him a photo showing one of the bloody grids. "The proof starts here," he said, pointing towards the top, center cell, "and is continued here," he said, moving his marker to the bottom, right cell. "And it continues for the rest of the proof."

"And all four of the grids follow the same pattern," Grissom confirmed.

"Yes, but the guy made a mistake. The cells holding the last two values are mixed up."

"The killer made mistakes at the other scenes, right?"

Brandenburg nodded at Warrick. "That's correct. I went back and reviewed the files from the first two murders. Some of them are simple transcription errors. He copied it down wrong on one line, but it was correct on the next. Some of the mistakes were true errors, though. They are fairly basic algebraic mistakes at the second scene, trig mistakes at the first."

"You don't think this was done by a mathematician, then?" Brass called out from the doorway.

"Not likely. The mistakes being made are relatively simple. I can't see how he'd have passed high school algebra, let alone a college-level class with that poor of an understanding of basic math skills."

"Or it's a mathematician with a hidden agenda."

Everyone stared at Grissom after his statement. They all swung to look across the room when Brandenburg responded.

"Or not so hidden."

"Or not as clever as he thinks."

"What made you ask if we were missing something from the first murder?" the police captain asked quickly. As much as he enjoyed the display, they had a case. Heads turned to Brass then back to Brandenburg. Besides Grissom, no one else on the team had heard his suggestive statement about Sara at the crime scene, and he wasn't about to make that public.

"Each of the grids contain an inductive proof," Brandenburg said, looking over at Brass. Seeing his confused look, he walked back to the board, and began writing out some addition problems.

"Induction, along with deduction and contradiction, are the three acceptable forms of mathematical proofs. Induction is typically used to show that a formula is true. The classic example is the formula for finding the sum of the integers between 1 and n. In that case, you multiply n by n 1 and divide by two," he said, jotting the equation on the board.

Sum n(n 1)÷2

"Let's take n 4 for an example:

1 2 3 4 10

4 x 5 20

20 ÷ 2 10

Okay?"

"Fine," Brass said.

"All right," Brandenburg said, writing another series of equations. "In all inductive proofs, the initial step is to always show that the formula is true for the first value. In our example, it would be for n 1."

1 1

1 x 2 2

2 ÷ 2 1

He paused to look around the room, making sure everyone had followed him, ending with Brass who nodded his understanding. "In all four of these proofs, the killer left out that very first step."

"He's taunting us," Grissom said. Seeing the confused look on the mathematician's face, he explained. "We never found the first victim."

"How do you know there was a first victim, then?"

"The killer is taking the blood from the previous victim and using it at the current scene," Grissom said.

"A generator," mumbled Brandenburg, as he shoved a pencil between his cast and arm, scratching furiously as he turned to look the photos.

"What?" Grissom said quickly.

"A generator. In a lot of cases, it's very easy to come up with a mathematical representation of a problem. The trouble is these problems can rarely be solved directly in real-life. Sometimes, a simplified approach is used. I'm sure you've had that problem."

"Wind resistance," Sara added. "You work with an approximation, since the actual formulas are too complicated."

"Exactly. Sometimes there's no way to find a simplification. In that case, you perform a type of numerical analysis. A common way is to pick a value that should be close to the expected answer. You stick that number into the formula and see what value you get. You then you can plug that new value back into the equations, to get a new value. You keep doing this until you get the answer."

"Does this relate to the other equations?" Catherine asked.

"Not that I can see. But this latest scene made me wonder if the killer is using the math as a vehicle for the message rather than as the message itself," Brandenburg said.

Grissom turned to regard him carefully. It was a possibility.

"It would also explain the mistakes. The killer doesn't really understand the math, but for some reason, it appeals to him," Brandenburg continued.

"Then what are the messages from the first two scenes?" Grissom asked, moving closer the mathematician.

The taller man shrugged as he rubbed his cast over his chin thoughtfully.

"The first set of equations dealt with polar coordinates, but he transformed the equations into much more difficult forms. A transformation, perhaps? Or the shapes are all curves. Something to do with twists or turns?

"The second series dealt with complex equations. Complex numbers have real and imaginary parts. He was trying to deform the contours. Changes, complexity, imaginary, not real …" he trailed off, yawning and moving to stand next to Sara. He gave her a friendly smile as he leaned against the table, taking some of the weight off his knee. "Or we're reading too much into them."

Grissom looked at the mathematician pointedly, trying to avoid Sara. He didn't want to see if she was returning his smile.

"You have experience as a psychological profiler, too?" Grissom asked, a trace of sarcasm evident in his voice.

The younger man looked at Grissom sharply. "Who knows why a crazy man does anything?" Brandenburg asked, stretching out his arm and resting it on the table behind Sara.

"What makes you think this is the work of a 'crazy man'?" Grissom countered, his irritation creeping into his voice. The symbolism of Brandenburg's action wasn't lost on him.

Sara looked up to dart her eyes between the two men in confusion. Their behavior made no sense whatsoever.

"Killing someone, draining their blood and leaving messages in someone else's blood doesn't exactly strike me as the work of someone in full control of their mental facilities," he said calmly, a hint of a smile on his face.

"Less than five percent of all serial killers are insane," Grissom stated.

Sara turned to look at Catherine, who rolled her eyes. She noticed Warrick and Nick staring at her, and Brass looked like he was trying not to laugh. What was going on? Why were people watching her?

She blinked slowly, turning back to stare at the two professors in confusion. Was this some sort of competition? Why? They were in completely unrelated fields. There was nothing for them to be arguing about.

Oh, no.

They weren't fighting over her. No. They wouldn't dare. No. Neither of them could possibly be that stupid.

They couldn't be.

"By the legal definition. All that states is that the killer had to be aware that what they were doing was wrong. Whether they had any control over it or not, or if they had any other issues, aren't taken into account, are they Dr. Grissom?"

"I merely process the evidence, Dr. Brandenburg. I don't presume to be an expert outside of my field."

"Right? Bugs, isn't it?" he said with a dismissive shrug.

The two men didn't break eye contact as Catherine shoved Nick and Warrick out of the room. Sara darted her eyes to Brass who looked as thunderstruck as she felt.

"And nearly thirty years experience."

"That's true. You've been at this a very long time," Brandenburg said slyly. "Since I was in middle school."

Sara felt her temper rising. They were that stupid – both of them.

Brass, recognizing the danger signs, let out an exaggerated yawn, drawing the attention towards himself and away from the blossoming confrontation in the Layout Room.

"Sorry, tired. This is getting to all of us. Let's take a break. Gil, I just remembered something. Come here," Brass said, heading out the door. Once they had walked down the hallways a bit, he turned to face his friend, shaking his head in disbelief.

"Didn't your mother ever tell you that it's rude to mark your territory in front of company?"

"What?"

"You're lucky Sara didn't hand both of you your cojones after that routine. He doesn't know her well enough to know how stupid that was, but you should."

"Jim…"

"Save it," Brass said shortly. "Look, I don't care what you do in your private life, but keep it out of the lab."

"I don't know what…"

"Give it a rest! What are you trying to do? Out-alpha the guy? Look at him! Don't start fights you can't win," he said quietly before walking back into the Layout Room.

Reluctantly returning to the room, he endured Sara's brief, angry glare before she walked back to the table. Brandenburg was sitting on the stool by the board. Surprisingly, he seemed sheepish. He had expected the younger man to be gloating; he had fared far better in the exchange.

"Okay," Brass said with forced joviality. "Anything else you can tell us, Max?"

"Have you linked the victims yet?"

"No," Sara stated coldly.

The mathematician gave her a brief look. Her irritation was obvious. Oddly, Grissom found that refreshing. At least he wasn't the only one in trouble.

"If you can get me any numerical information about them, birthdays, addresses, phone numbers, I'll try a pattern-recognition. It's one of the areas my company specialized in."

"Good, good," Brass said. "Sara and I can get that for you right now. Why don't you wait in the break room, Max? You can rest your leg. It seems to be bothering you."

"Thanks."

Leaving the room after the mathematician, Brass directed Sara to the A/V Lab. She glared at all the workers they passed, silently daring anyone to talk to her. How could they have done that? Some women may have found the idea of two men fighting over them romantic, but it merely pissed Sara off.

She wasn't some sort of trophy for them to rut over. She picked who she wanted to be with, and excess testosterone wasn't in her criteria. Right now, neither man seemed all that desirable.

Max at least had the common sense to say he was sorry immediately after Brass and Grissom had left. He had sounded sincere, too, apologizing for any embarrassment he may have caused her. He didn't try to rationalize his behavior, but she suspected his pain may have contributed to his short temper.

Grissom's attitude hadn't completely surprised her; his jealousy wasn't one of his endearing traits. It still hurt, though. He had been making an effort to improve his behavior, but it hadn't taken much for him to revert to his old ways.

Dammit! She had such hopes for him.

Sara paused briefly. It was true; she still had hopes they would get together. As nice as Max was, she wasn't in love with him. In time, she might fall for him, but she couldn't deny Grissom still held her heart, whether he appreciated it or not.

Brass looked at her with a bemused expression when she halted suddenly at the doorway.

"Don't say a word," she breathed heavily as she entered the room.

"Sorry, doll, but there's something you need to know. Max made a … joke … at the crime scene that Gil didn't appreciate. That display back there didn't come out of nowhere."

"What kind of joke?"

"The kind that Gil doesn't appreciate. He probably thought Max was being rude," Brass explained kindly, not adding that Sara had been the subject of the comment.

"Thanks," she said as they gathered the materials. At least that helped to explain Grissom's behavior, even if it didn't do much to dissipate her anger.

After giving the computer disk to Max, Sara escorted him from the building. Not only was she worried about his leg giving out again, she needed to drive him back to the parking garage to get his car. Walking past Grissom's office, she gave him a quick look.

His dejected expression was enough to make her start. Leading Max outside, she could understand how this was hard on Grissom. That was the first conversation she'd ever seen that he couldn't dominate. If the whole exchange hadn't been so pathetic, it would have been, well, pathetic.

Max was younger, bigger and at least in same intelligence range. Damn male ego. He obviously had felt threatened by Max.

What did she have to do? His alpha-male stunts didn't impress her. All she wanted was his respect and trust. If Grissom could manage that, the rest would follow naturally. Getting him to understand that was the hard part. Eventually she'd have to talk to him, but right now she was too angry.

Letting out a long sigh, Grissom ran his fingers through his hair after they left. He'd screwed this up badly. There had to be a way he could make it up to Sara. If he didn't, she'd never forgive him and any chances of their developing a relationship would be over.

Worse, Brandenburg would be there to pick up the pieces. Sara couldn't be too angry with him if she was leaving with him. She could have easily called him a cab. Dammit. As long as Brandenburg was around, she had a better alternative.

Watching the mathematician leave, Grissom couldn't help but wonder if there were any sling-wielding shepherds in Las Vegas.

TBC