Solution Whitehouse part 3

Sam stared in disbelief and finally got up to move unsteadily to the window. She pulled back the curtains with her good arm and tried to look out the windows to see the moon. Or moons. Her room faced another wing of the hotel so she couldn't see much of the sky. What blue sky she did see contained no moon, real or otherwise. She craned her to the side so much to see south that her bad arm banged into the window and she screamed. Blackness engulfed her vision and she nearly fell onto the floor.
She was able to grope blindly, nearly doubled over, with her good arm to the edge of the bed. She took a long time to settle back into the hotel bed and prop herself up with a pillow.
Over the course of the next hour, news reports flooded in about the double moons. Pundits who knew nothing of astrophysics held forth on the cause of the optical illusion (for it must be an optical illusion; there was no way it could be a real phenomenon). Sam scoffed at them but didn't know what to believe. She jotted down some calculations on the hotel stationery pad.
The earth and moon exert approximately 2x10^20 Newtons of force on each other. Since the force equation for two objects is the product of their masses times a constant and divided by the square of the distance between them, doubling the number (and hence mass) of the moons would double the force between them. So Sam reasoned that two moons and one earth would put 4x10^20 Newtons of force. Of course, the angle of the interaction between the two moons and earth could make a big impact on the calculations.
The two moons in the camera images appeared to be about six diameters of moons apart. That is, using the diameter of the moon as a reference, like a coin, Sam guessed you could fit six moon-coins between the two. The moon rises approximately 1 hour later per day on average (a little less perhaps, her father had told her), which was approximately 12 degrees. The moon covered a part of the sky that was approximately half a degree. So Sam's guess at six moon diameters between them appeared to confirm the moons were lagging each other in orbit by one earth day.
This angle of 12 degrees meant that the moons were pulling on each other at an angle while the earth pulled both at a different angle. Assuming an isosceles triangle at the distance from the earth to the moon of 384,000 kilometres (or, a little more than 2.5 seconds round trip from the earth to the moon at the speed of light), with an acute angle of 12 degrees, Sam calculated 84 degrees offset for the force from earth to each moon. With two objects, the angle would be 90 degrees dead on, so 84 degrees would reduce the force of 4x10^20 Newtons by about 93%.
Given the two sides of the isosceles triangle of 384,000 kilometres, you can construct two right triangles by bisecting the original and find out half the calculated side using the Pythagorean Theorem:
A^2 + B^2 = C^2
Which yields a distance between the moon of 271,500 kilometres. Using Newton's gravitational formula:
F = (G * m1 * m2) / r^2
Would yield a force between the two moons of 4.5x10^17 Newtons. This was 10,000 times less than the force between the earth and the two moons. So it might be possible that the orbits would remain stable, Sam thought. She was not an orbital mechanics expert, however.
The news reports continued all day and into the night to discuss the problems that multiple moons would pose, including doubling the tides and increasing earthquakes. The earth's crust could warm up from the friction, one expert claimed. It was possible this could increase the effects of climate change. Sea ice could break up more quickly and melt faster, said another expert.
The stock market had swung into the largest sell-off of the last two centuries, only to come roaring back by bulls buying into the decline. The NASDAQ decided to close the markets early while the New York Stock Exchange struggled to keep up with orders. The NYSE was technically able to stay open, although most major stocks had collars and freezes in place that prevented most transactions from occurring.
On television, an expert from the Catholic Church said that this was predicted by a dead woman in Guadalajara some 2,500 years ago. The old guy who always predicted the end of the earth got quite a bit of airtime to discuss how this was surely the final sign of the end of the earth. This old guy believed that God's wrath would visit us due to sins such as allowing recreational use of marijuana, gay marriage, and the abolishing of daylight savings. He seemed to have convinced the CNN hosts that this was the case.
Most channels that had local news showed static shots of the sky with both moons clearly visible on a field of blue sky. Samantha flicked through these channels because the hosts usually said inane things along the lines of "Stay calm. There is no immediate danger." If there were danger, they wouldn't admit to it obviously. One oblivious local channel on the hotel network showed a daytime show of two children dressed as Mario and Luigi sporting ridiculously racist fat mustaches. The spun round cloth towels that were supposed to represent pizza doughs. The audience cheered as the kids threw the dough into the air and caught them on their hands.
"Oh please," said Sam to no one. "Do people really watch this?"
Samantha eventually fell asleep fitfully among her notes. The light from the television flickered over the wall and her bedspread, filling her dreams with hate and pain from her injuries.
----
The next morning, Samantha hobbled into the lobby. Over her right pants leg she wore a metallic knee brace. While struggling to walk and with her left arm in a cumbersome cast, she heard a familiar voice behind her that said, "Ms. Griffen! Ms. Griffen!"
Sam froze in horror and tried to shift to the left, then the right to try to hide. She nearly toppled over. Mark rushed up and helped steady her by her good arm.
"Ms. Griffen," he repeated. "I'm so glad to see you. What a coincidence! I was supposed to be staying at the Harrison, but my father's secretary made a mistake and I'm here." He paused, then continued, "Wow, you look terrible. No  offense."
"Of course I'm offended," Samantha said. "I'm in a lot of pain, only one week out from an airplane crash, and I've met one of the most despicable people on the planet. That was my mom. But you are a close second."
"Well, shit on me," Mark said bemused. "Listen, I'm serious. Let's talk. This coincidence can't be an accident. Also, the whole moon thing. I've been up all night looking at it on T.V. Here, sit down," he said and motioned to a lobby couch.
"I can't sit down," Sam said. "I need to get to a cab. The Secret Service said I shouldn't be late. I need to talk to the president immediately."
"Let me get you a cab," Mark offered. "I'll help you. I can back you up when you talk to the president. I read your email and I want to help you solve the mystery of the problems we're seeing."

Solution Whitehouse part 2

Samantha sent the email and hobbled to her bed. She sat painfully and slowly on the edge of the bed and tried to lift her legs to swing them in front of her. The whole process took ten minutes, after which she reclined slowly and settled onto the headboard and pillows. She looked for the remote to watch the television and spotted it out of reach on the hotel end table. She reached with her right hand like Luke Skywalker and concentrated.

"May the Force be with you," she said. She curled and stretched her fingers at the remote. "The Force is weak with this one," she said and laughed. A sharp pain in her side stopped her immediately and she tried not to laugh which caused her to giggle more. "Stupid broken bones everywhere," she said and laughed again, alternating between laughing and sharp pains. She looked at the remote again about a foot away from her outstretch hand and grunted with effort. "The Force..." she said and stopped.

The remote smoothly vacuumed into her hand. She felt dizzy and light-headed. A hot flash crossed her chest and down her arms and legs. She stared at the remote in her hands. "Nothing," she muttered to no one.

She pointed the remote at the television and saw the in-hotel menu guide extolling the adult offerings available. She switched through ten channels until she found CNN. The president was on the screen, calm and smiling. She listened to him assure the world that the missing cruise ship and the crashed airplane were not related. There weren't any terrorists at work, he assured everyone. In fact, he assured the world that the terrorists were not attacking as a result of their hatred for Americans getting rid of Daylight Saving.

The sound cut out as the president's mouth moved. The crawling text along the bottom read "PRESIDENT LETS OUT LONG STRING OF OBSCENITIES RELATED TO AIRPLANE CRASH..." It had been several seconds of presidential mouth and arms moving erratically before the sound came back on. Several people standing behind the president looked up in the sky and started pointing. The president paused and looked upward, shading his eyes against the glare. There was a general confusion and noise of confusion.

The television shifted to another point of view as a camera was aimed upward unsteadily. The screen shook and zoomed quickly in on a shocking view that was difficult to comprehend. Samantha sat up quickly and the sudden pain in her arm, legs, and side made her scream out in pain. She fell back and hurt her arm, legs, and side again as she fell back. She screamed again. She forced herself to breathe and squinted at the television again through watery eyes.

The announcer was speaking incoherently about not understanding what was on the screen. Samantha's vision finally cleared enough that she could see what the whole world was slowly realising. The screen showed two partially lit moons in the sky, one slightly behind the other and slightly fuller than the one in front. The smaller one in front seemed to dance and waver, then solidify. The one in back did a similar dance then solidified again.

The president calmly spoke into the microphone and tried to yell to get everyone's attention.

Potus said, "Pay no attention to this David Copperfield bullshit. Even the terrorists can't do a magic trick like this."

Solution Whitehouse

Samantha checked her email a few days later in her room at the Topaz hotel in Washington, D.C. One email dated the night before read:

_From: Thorne, Mark <thornem@staff.micron.edu
To: Griffen, Samantha, Ph.D. <griffens@staff.micron.edu>

Ms. Griffen, I'm sorry for the problems with the luggage. I'm currently in Washington D.C., to prepare for the Thorne Industries hearings at Capitol Hill. A lot of strange shit has been going on and I'm not really sure what to believe anymore. I promise to return your luggage at the college when I return.You can return my luggage to me any time when I return to the college. I don't need anything in it very badly._

Samantha was grumpy as only women can be. The turn of fates that drew them to D.C. was remarkable, but not outside the realm of mathematical probability. Perhaps the two people were entangled in a strange superposition and needed to be drawn together for some strange reason. It made no actual sense that there was any intent in the universe to do so. It was only a matter of discrete probabilities that extended out across a large summation of individual probabilities and ended with a coincidence, nothing more.

Sam replied:

_From: Griffen, Samantha, Ph.D. <griffens@staff.micron.edu>
To: Thorne, Mark <thornem@staff.micron.edu>

Dear Mark,

I do not have your luggage owing to an incident over the ocean near Long Island. You may have heard about a small problem with my flight. I do, however, know that you tried to steal my lab results and I don't think you should continue to work with me. I also think that you should not use such vulgar language in a written communication on staff computer systems. I will be glad to file an insurance claim for your personal belongings if you will give me an approximate value for the contents. Since you said you don't need anything in it very badly, I'll assume not.

I am also in Washington, D.C. and I'll be meeting with the president tomorrow morning to help sink your family's corporation. I can provide a lot of useful information that will help stop whatever plans your forebears have. The problems with the solid state division have cost lives, and nearly cost me my life. I sincerely hope you do not try to stop me. I hope that you will reconsider your loyalty to the corporation and help change the course of their intentions if you can. I don't believe that you will be able to stop anything from happening however. Your father and Mathiason are up to no good. They will be unable to change course unless they are confronted by a larger force than themselves.

Sincerely,

Samantha K. Griffen_

Solution Hospital

Sam woke up in the hospital a few days later after the ordeal of the airplane crash. She had spent a harrowing four minutes flying through outer space and then survived the initial impact with the water. Nearly an hour later, she was pulled onto a rescue boat and airlifted to the hospital where she stayed for a few days. Her mother had been notified and had flown in to see her daughter.
The nurse pulled back the curtains on Sam's "private" room which was shared by four patients who survived the wreck.
"Your mother's coming to visit you during visiting hours," she announced cheerfully.
Samantha groaned. "Step mother," she muttered.
The nurse heard the groaning. "It's okay, dear, you'll get your pain meds soon. That leg will heal just fine."
Sam nodded. She clicked the button next to the bed rail, hoping for the morphine release. The machine stubbornly refused to go over the allotment she was requesting. Sam ate some slimy jello and a plastic cup filled with orange juice for breakfast. It was hard to eat with one hand, even though it was her dominant right. The left arm was in a cast all the way to the neck and it was suspended from a pulley system next to her bed.
Before she had fully acclimatised to the idea of her mother arriving, her mother arrived.
"Hello, dear Sam," her mother clucked, standing next to the bed on Sam's left opposite the raised arm cast.
"Oh, mother," said Sam irritably, "did you come to gloat?"
"Oh, no. Not gloat," said her mother. "Although I do enjoy a bit of _schadenfreude_ every so often."
"I can't believe you won't give a bit of sympathy to another human being, much less your daughter," Sam said.
"Not my real daughter," corrected her mother.
"Why even bother to show up then?" Sam asked.
"Oh, I don't know. I thought maybe the news reports were a lie. You know, maybe nobody had survived the crash and I could be free of all my familial obligations once and for all."
"You're horrible. You probably killed dad, you evil witch."
"I didn't kill him." Sam's mom said with an evil smile. "I wouldn't have been able to collect the insurance and pension if I did."
"He was a good man. I don't know why he stayed with you," said Sam.
"He was a good man, all right," her mother agreed. "Until he had that dalliance with that wretched Thorne hussy."
"Maybe he had an affair because you were a despicable, loveless human being and drove him away," said Sam.
"That's not a valid excuse," her mother said.
"Mother!" cried Sam.
"I know, I know," her mother said. "I'm horrible, blah blah blah. You always say that. I don't know when the disillusionment set in on either side. Or which side it set in on first."
"I never hated you," said Sam.
"I couldn't tell," said her mother.
"You're too aloof. You don't even know there are other people around you, and that they have feelings and emotions. You don't even know what a person is, except a bunch of distractions from your mathematical proofs," said Sam.
"Oh, feelings. Please," said her mother. "If feelings actually existed then we could get rid of them. That would suit me fine."
"I'm still alive and making you feel embarrassed," Sam said. "I wasn't even wearing clean underwear when the plane crashed."
Her mother hissed. "I told you about that. What did I say about always having clean underwear? You should always have clean underwear. What if you died and they had to undress your corpse and found your dirty skivvies... Oh, too repulsive to imagine."
"I knew you'd be disappointed," Samantha said.
"We were always disappointed," said her mother. "You seemed bright... But of course, when the college rejections started pouring in, we knew..."
"Don't say 'we'. Dad was supportive."
"Maybe," her mother allowed. "It's funny because your father always wanted a daughter. I couldn't give him any children because my uterus was scraped thinner than a coconut shell during the sixties. He wanted a daughter, as I say, and so he wanted to adopt a girl. We never knew what sex you were going to be when we met your birth mother. She wouldn't tell us. You were Schrödinger's Baby. So we called you 'Sam'. 'Samantha' if your father got his way and 'Samuel' if I got mine."
"You've always told me that story."
"I didn't tell you that I wanted a boy because at least he would be worth a damn at math and science."
"It's a wonder how I don't kill myself every single day," said Samantha.
"At least you weren't an orphan after we adopted you. We must have done something of value in your life."
"That's not really enough, mom," said Samantha. "You're supposed to actually care for your children, not raise them like livestock. At least orphans don't hold out hope that their mother will love and care for them. Orphans just try to pass each day in survival. I thought I could be normal."
"Normal doesn't cut it," said her mom. "Or, rather, at least normal would have been acceptable. We never thought any man would be attracted to you, much less be apathetic enough to give you a loveless marriage of convenience."
"No man was ever attracted to me," Sam said bitterly. "It's hard to be excited about a relationship when the Mean Value Theorem is more interesting than going out on a date."
"We always thought there must be someone out there for you, at least mathematically speaking," said her mother.
"That's the difference between science and engineering," Sam said. "One is theoretical and the other is applied in the real world."
"But enough about you and the past," her mom said abruptly. "Tell me about the airplane crash?"
"I was a little freaked out," said Samantha.
"Ha," giggled her mother.
"You try going through a plane crash and see how composed you are," Sam retorted. "The plane kind of jolted a few times before it broke open. I thought I saw some strange things. Hallucinations, maybe altitude sickness as the plane was depressurising."
"You were sitting two rows behind the split, apparently."
"That's what they told me. I saw several people floating around as we fell. That must have been some people waiting in line for the bathroom."
"Wow," said her mother.
"I also... As I say, I was hallucinating," Samantha began.
"Go on," said her mother.
"I saw another plane. Two planes, strangely. One of them was the same plane as us, just phased out a bit. I saw myself sleeping in one of the chairs as we separated. We bumped up and I could see the other image of the airplane shaking and passengers moving as well."
"Out of body experience," said her mother. "Near death, fight or flight responses."
"I think so. But it's like the many universes theory. As if time were an actual storage dimension. Imagine if every copy of every possibility of the universe were being expressed in multiple dimensions. If they were to collide you could see a slightly different universe from ours that would be close but subtly different somehow."
"Nonsense," said her mother. "There are no multiple universes. You'd have to store every particle and each piece of information about that particle's position, spin, momentum, charge, and mass for every single combination... It's impossible."
"I know," said Sam. "You and dad raised me as a Copenhaganist. But you haven't seen the problems at in my lab or at CERN. I looked at all the data and we're seeing some very strange states. Strange things are happening at the macro level and they're bubbling up from the quanta."
"You sound like a science fiction novel," her mother scoffed.
"Well, you tell me, mother," Samantha retorted. "What would happen if the speed of light were changing?"
"Oh, I don't know," said her mother. "Your father was the astrophysicist."
"What if the Planck length was growing? What if the NSA somehow manipulated the Hubble to record a diffraction array from a ground laser and could gather the which-way information from a double-slit experiment? What if we looked at Schrödinger's cat and saw the cat as both dead and alive?"
"Impossible," repeated her mother.
"What if the plane I was on split in an interference pattern and instead of being awake, I was asleep? And what if I was asleep and had died like those other 115 passengers? What if the plane interfered with itself in an alternate dimension and crashed in the sky?"
"They are saying the GPS was faulty," said her mother. "I think you're delusional from whatever they're pumping into that saline bag, dear."
"You never cared anyway if I were alive or dead. Now you're just here to torture me more and mock me. Just leave already," Samantha cried.
"I bet I'd be a good mother in the alternate universe," her mom joked. "Maybe I'd be a good wife, too. That's probably too much to ask. Ten thousand universes couldn't contain that contradiction."
"I'm just trying to get well enough so I can go to the Thorne Industry hearings," Samantha said. "I can't do that with you upsetting my healing process."
"Yes, I suppose," said her mother. "I know someone who works at the Whitehouse. My niece. She could get you an interview with the president. I think it would help."
"I don't understand," said Sam.
"My niece. She is the president's personal assistant. She could get you into the Whitehouse. I could get you an audience with the president. Maybe he can help you fix this," her mother said.
"I don't understand why you're helping me, I mean," said Sam.
"Maybe I want to get back at that horrid Thorne family," said her mom as she smiled evilly.

Solution Airplane

Samantha sat in Row 33, Seat F. Transatlantic flights are a modern marvel, but they are also one of the most tedious experiences known to woman. Samantha could deal with rude flight attendants and even more rude passengers. But waiting in line for a lavatory is unacceptable. She had never flown in first class or business class, but she had heard that they get their own toilets. Standing in a queue in a three-foot aisle at 30,000 feet and needing desperately to pee is a ridiculous fact of life given the modern technology humans enjoy.
Sam calculates that each passenger in the queue takes approximately four  minutes each in the lavatory. There are two lavatories at the middle of the plane where she is. Each has a queue of four and six people, respectively. The queue for the lavatories has remained stable for the last several hours that Samantha looked back to check. Thus, she applies Little's Law which says that the number of customers in a stable system (L) equals the rate of arrival (λ) times the average service time (W). Since she knows the number of customers and the average service time, she computes:
L= λW
λ = L/W
λ = (10+2) customers / 4 minutes
λ = 3 customers per minute = 1 customer every 20 seconds.
Sure enough, another person has queued up for the lavatories as Sam stands there thinking and calculating. And just as surely, a person exits the lavatory and holds the door open for the next customer to enter to keep the number of customers stable.
The man says "Excuse me, excuse me. _Bitter, bitter_. Excuse me. _Danke_. Coming through," as he squeezes past the queue in the narrow aisle. Samantha wants let out a scream.
Approximately 4*2 minutes = 8 minutes later, she is able to enter the toilet and do her business. She is still wearing the same clothing from the day before, but they have been laundered overnight by the hotel staff. She is still wearing the boy's briefs however, and that could be the cause of the extra trips to the restroom. She presses the button on the toilet to flush down the contents. She realises too late she has left the cover up and witnesses a violent rush of dark blue liquid and feels the sharp tug of vacuum pressure on her ear drums. This, combined with the roar of the air filtration systems and the violent noise of her flushing, make waves of nausea reappear somewhere in the back of her head and throat.
She lowers the lid and steps into the aisle. There are ten eager faces staring back at her as she exits. She gropes through the aisle and steps on several toes asking people to please excuse her. Back at her seat which is mercifully on the aisle she tries to sleep. This has been impossible for her, though she usually is able to sleep on airplanes. She hates the inane pop culture that is fed to captive sheep via the back headrests of the chairs in front of them. She tries to do some work on her tablet but is unable to focus and feels a queasy floating that has been following her since takeoff. She determines she is probably going to be sick and will need to take a few days off when she gets home. She needs time to prepare some evidence for her bosses to present at the congressional hearings.
A mild shaking of the cabin reminds her to check her seat belt. It is on safely. She notices the passenger next to her is asleep and so is the man on the other side. Samantha estimates half the flight is asleep, including the airline stewardesses. She had seen them toward the back in a special section of the plane. They had retreated back to their seats around the four hour mark of the flight. The seats back there had small curtains that pulled around to give some privacy to the seats. They were just normal economy seats, however, and Sam could see these professional fliers crunched up like contortionists eyes closed and snoring like peaceful children. She was briefly ashamed for peering through the curtains and hurried past the aisle where they slept whenever she took a lap walking around the plane.
Sam checked her tablet and saw they were approaching the nine hour mark. The plane should be near the eastern coast of America by her calculation. She turned on the tiny screen in the back of the seat in front of her. She switched the remote over to the live flight path. An icon of the airplane showed where the airplane thought it was based on the GPS coordinates. It showed a location about 1/2 inch (on the screen) off the coast of New Jersey, just south of Long Island.
A violent jolt of turbulence causes Sam to drop her tablet on the floor. She turns off the display in front of her and reaches down to find her tablet. The plane shakes more, but more mildly this time. A ding-dong C note plays and the "Fasten Seat Belts" sign lights up. A few people from the queue at the lavatory wander back to their seats.
As Samantha continues to reach for her tablet blindly, she decides to look at her feet and sees two sets of feet like hers. One is a ghostly image laid on top of hers. She glances at her hand reaching for the tablet and sees two tablets, one a ghost and shimmering on top of the other. She looks to her left and sees two copies of the airplane row with a ghostly image wavering up and down on top of the real one. She can see a ghostly head of herself asleep, leaning on the wavering version of a headrest to the left of her ear.
Another violent shaking occurs as the two images overlap in her mind. Pain racks her arm and neck as she is snapped down, then up. She gapes in confusion as the ghostly image of the other plane, herself, and other passengers firm up and pull apart as the planes rips in half.
Then it is all noise and screaming and cold whipping wind as she falls through the air.