Author's Notes: So, this chapter is infinitely more fun than the last; I think it's my favorite so far. I had a lot of fun with the rhythm of speaking; I'm not sure it came across all that well, but that's okay, I guess. Oh yeah, and there's some pretty important plot stuff going on... whatever...
Daniel was writing furiously in his journal. He stopped, and thought... "Sam?" he called out. "Come take a look at this."
Sam herself had been keeping Daniel company, examining some of the stones that Elena had been studying: they were grey and smooth, and looked like they had been carved. Sam set them aside and stood next to Daniel. "What am I looking at?" she asked, staring at the wall he was so intent upon.
"Well, as you know, at first I thought this might be like those spheres that...Thor and his friends used." Daniel explained. "But nothing happens if you touch it." Journal in one hand and his pen in his mouth, Daniel walked forward and placed his hand in the middle of the circle, demonstrating. "It also looks a little different; it looks like there might be some kind of fluid inside..." He slurred around the pen before taking it out of his mouth and stepping back. He waved his hand in front of the red half-sphere in a circular motion, miming the swirling that Sam could faintly see. "Anyway, I got to thinking about the riddles that we'd encountered before... look here." Sam stepped forward to get a better look at what the archaeologist was pointing at. "There are hash marks." He told her. "I think it might be a sort of... combination lock."
"Okay." Sam replied, half-smiling. "What's the combination?"
Daniel looked at her blankly. "I don't know." He frowned and focused his attention elsewhere, pointing with his pen. "This is Babylonian cuneiform. At first I thought this was some variation of the text, but I think it's... a decimal point. Or at least a place marker of some sort." He paused, taking a look at his notes. "If I'm right, it's 2.728. Now, my Calculus is a little sketchy, but –"
"Logarithms." Sam concluded.
"Right."
"It's base e." She expounded. "Natural logarithms." Sam found her curiosity growing. "What else is there?"
Daniel continued pointing to various portions of text. "Well, this is a number, and then this would indicate weight, or mass... and this indicates the passage of time."
Sam shrugged and shook her head. "I don't know."
Daniel stared for a moment. "Alright." He moved on. "This... uh, well, this is simple subtraction, I think. This indicates the smallest measurement of time: If you have 5 and remove 3..."
"2 seconds? Were they advanced enough to get to seconds?" Sam asked, referring to ancient Babylon.
Daniel raised his eyebrows. "Well, if it's Thor's technology..."
Sam nodded. "Okay. What else?"
"This is... just a..." Daniel searched for a better word; any word other than the one he currently had: "...squiggle." he finished lamely, inwardly frowning at resorting to a Jackism.
"A squiggle?" Sam was surprised as well.
"I don't recognize it." Daniel explained. "It's not any kind of word or... or letter." He looked back down at his journal. "I don't know."
Sam studied the squiggle for a moment; suddenly, it became clearer. "Wait." She touched Daniel's arm, getting his attention. "What's that?" she pointed to some shapes that were above the line.
Daniel looked at it. "Uh, it's just a number."
"And this one too?" Sam pointed to some text below the line.
Daniel nodded. "Yeah."
"You think there's some sort of fluid inside this thing?" Sam was growing more excited: pieces of the puzzle were clicking for her.
"It's just a guess." Daniel replied, waiting for her to expound so the puzzle could come together for him as well.
"It's looking for amplitude." Sam answered, somewhat triumphantly.
Daniel's brow furrowed; it wasn't yet clear to him. "Amplitude of what?"
"I don't know." Sam told him, "But I think this squiggle is a sine wave." She followed the curve with her finger. "If I'm right, then these all make up the formula for damped oscillations." She gestured in the general direction of everything Daniel had just pointed out to her.
Instead of growing less confused, Daniel was becoming more so. "For what?"
Sam looked over at him, taking in his body language; she attempted to simplify. "Okay: you throw a tennis ball into a tank of water. What happens with each bounce?"
"It loses energy." Daniel answered.
"Right, because of the resistance of the water. It loses amplitude. You find the final amplitude by finding the product of the initial times base e to the quantity of time divided by 2 times the decay time. It's physics." After her explanation of the equation for damped oscillations, Sam wasn't surprised to find Daniel still looking a little bewildered. "Can you write down all these numbers for me?" she asked.
A few minutes later, after Daniel had given her all the data, and with the help of a good calculator, Sam was well on her way to solving the equation.
"Okay." She said, entering the last number. She stared at it for a moment. "Wow."
"What?" Daniel peered over her shoulder to look at the display.
"It's a round number." Sam replied. "I mean, significant digits alone –"
"It's incredibly advanced." Daniel filled in.
"Yeah." She affirmed. "How many hash marks are there?"
Daniel walked back over to the sphere. "Uh... seven."
Sam thought, then nodded. "Okay. Turn it to five... then two... then six."
Daniel did as told. He took a step closer, putting his ear to the stone circle. "Hear that?"
"Yeah." Sam came up next to him.
"Whatever's inside..." Daniel continued listening, "it's draining."
Daniel took a step back again, startled by something. Sam followed his line of sight: more writing had appeared, this time glowing on the sphere itself.
Sam looked at Daniel. "Now what?"
"I don't know." He replied, leafing through his journal as Jack walked in.
"Hey kids." Jack greeted. "Whatcha doin?" Almost immediately, he noticed the glowing shapes. "Well, that's new."
"It's the number one over...time..." Daniel spoke up.
"Frequency." Said Sam.
"Physics?" came Daniel.
"What?" Jack questioned.
"Yeah." Sam nodded excitedly. "I'm guessing we have to emit some frequency and direct it toward this... lock."
"Lock?" Jack tried to catch up with what was happening.
"You can find the frequency?" Daniel plowed right over him.
"Yeah." As did Sam. "We have time and amplitude."
"Hey!" Jack shouted, waving his arms crazily. "What the heck are you two talking about?"
Sam turned to her commanding officer. "Sorry, Sir" she apologized. "Daniel figured out that this sphere is a sort of lock."
Daniel nodded. "And after I translated the symbols, Sam figured out that this was an equation for damped oscillations."
"Which made sense since Daniel thought there might be fluid inside the sphere." Continued Sam.
"So Sam made a calculation based on the equation and the values given, gave me the combination, and made the water drain." Daniel added.
"At which point this appeared, which Daniel said is one over time, which is –"
"Frequency?" Jack joined the conversation again.
"Exactly." Daniel answered.
"What?" Jack asked.
"What?" Daniel repeated.
The two men stared at one another for a moment...
"Sir," Carter caught the attention of both again, "if we emit the correct frequency, we can open whatever this opens. If I use our coms and maybe the CB from one of the –"
"Hold on a minute!" Jack cut her off. "First of all, this thing is probably locked for a good reason! Second of all, that's a pretty lame-ass lock, if all you have to do is whistle at it –"
"I think it's more advanced than that, Sir." Sam told him. "Based on the numbers I've calculated, the frequency is going to be very high; much higher than anything the human ear can detect. I don't think any random noise is going to do it. Besides which, there was the fluid in the sphere. Without draining it, the frequency never would have been correct."
"Not to mention figuring out the frequency to begin with." Daniel pointed out. "And it wasn't exactly easy getting down here."
Jack raised and finger, head bobbing up and down. "Which brings us back to the first point: what are we gonna let out?"
"Jack –"
"Ah!" the colonel silenced Daniel with a hand. "Sit tight." He ordered. "We'll open the thing, but I wanna get Teal'c in here first." He turned to leave. "Don't touch anything while I'm gone!" he called behind him.
Daniel's forehead creased; he picked up his journal and flipped a page. He paused, then stuck out a hand toward the circle again.
"Daniel!" the younger man turned, seeing Jack's head hanging down from the floor above. "What'd I just say?"
Author's Notes: The physics stuff I think should be pretty accurate – unfortunately, I had to take the class... Calculus-based Physics is not my Phriend.