Solution interview part 3

"What is the number one?" she asked.
"That's easy," said Mark. "It's the successor to zero." He grinned.
"That's a good answer from math theory. The successor to one is two and so forth. Easy enough, but what is the predecessor for zero?"
"Negative one, I guess," said Mark.
"It's not turtles all the way down," Sam said and laughed. "Negative numbers come from subtraction, which is derived later by negating addition. We're not at addition yet. Okay, we're side tracked. One is defined as the successor to zero. That answer means you had a very good math theory class. What other properties does the number one have?"
"Identity, um, something else," said Mark.
"Identity is good, what is identity?"
"Some number multiplied by one is the same number."
"Very nice, and the something else, do you remember?"
"No."
"Identity is multiplication. What's before multiplication?"
"Addition. Um, uh, some whole number N plus one is defined as the successor of N."
"Very nicely done," said Sam. "Now on to multiplication which is the usual order people do things in school. What is the inverse of the identity function?"
"Any number divided by one is the same number," said Mark. "What's the deal with all these nonsense questions?"
"That's not a very nice attitude," Sam said. "I need to interview an intern for my lab. I have some experiments I'm verifying before I go to the Cern Hadron super collider."
"Cool," said Mark. "They shut down for a while."
"Again," clarified Sam. "They have some instrumentation issues. They have some equipment refactoring to do as well. They are always shutting down for a while after each batch of experiments they run. The whole thing is so big and complex that by the time they finish building something it's nearly obsolete. They are constantly playing catch up and I'm trying to put them ahead of the curve."
"Neat. My dad's company finances some of the equipment there."
"I know," Sam said. "So now, you've got good fundamentals in conceptual thought without the common affliction of rote memorisation of facts," said Samantha. "Now to see how you think in one of your weak subjects like biology. This is my favourite question because no one really knows the answer. You can't even Google it! Don't worry if you don't know it, I want to hear what kind of ideas you have."
"Huh?" asked Mark. "Is this like those questions where they ask you how much Mount Everest weighs or something like that?"
"No this one is a good question. Put on your thinking cap for a second. We know that cats love seafood. They love fish, shrimp, and crab. The most popular symbol of a cat treat is a dead fish. A blue fish with black lines for scales and 'X's for eyes. They love fish, right?"
"Sure. You're the cat lady."
"I don't have any cats. Another feature of cats is they tend to dislike water. They aren't hydrophobic, but they don't want to get wet. There's only one cat that I know of that spends meaningful time in the water: the Bengal tiger. A Bengal tiger will swim for miles in the open estuaries of the mangroves. So the question is, how did the cat learn to eat any kind of seafood? Why do cats like fish at all if they hate water?"
Mark was silent. He grinned slowly. "That's a really good question," he said. "Maybe they descended from the Bengal?"
"Not every cat descended from a Bengal tiger. Bengals are unique in that they have adapted to water. If you see a trait that is very specific to one species in one area then you could assume it must be a very specific selection in one area, or else that it is selected against in all other areas. Also, the Bengal is a large cat. I'm referring to the common small cat, _Felidaes_."
"Huh. I guess that they've been living around humans who hunted fish in some areas. Like the Egyptians who worshipped cats, say."
"Nice guess. The Egyptians were indeed probably the first humans who domesticated cats, maybe 10,000 years ago. But that's the weakness of your theory. The dog has been domesticated for hundreds of thousands of years. Dogs were useful as nomadic hunters looked for prey. Humans didn't settle down and farm wheat until maybe fifteen or twenty thousand years ago. The storage of wheat would attract mice, which made cats useful.  So they eat rats, that makes sense. Dogs being domesticated far earlier means that dogs should prefer fish, or at least some dogs. I don't know any dogs that like fish more than the average cat."
"Further, you'd have to point to some evidence of humans cohabitating with cats in the same place with a lot of fish. That place would have to precede most of the future generations of partly-domesticated cats today. For example, you'd have to find early enough archaeological dig site near the sea, with lots of human bones, cooking pots, cat bones inside huts, and fish bones. All in one place at one time, and then trace a lot of cat lines back to that area."
Mark stared at a point above Sam's head. He unconsciously reached for his phone.
"The Internet won't help you," Sam insisted.
"Oh," Mark said and put his phone down again. "Um, maybe fish has some kind of amino acid or protein that cats love. Like potassium in an avocado or something, that they need."
Sam smiled. "It's a good idea, but you have to show what that ingredient or vitamin is. And you'd have to show it was mostly abundant in fishes. Then you'd further have to show that this need for the ingredient was present (perhaps latent) in other cat families as well. Those cats would have to supplement this ingredient some other way because obviously they survive without seafood in their diet."
"What the fuck, with the cat questions and the metaphysical physics and shit?" asked Mark.
"Please don't use obscene language," said Samantha.
A high-pitched beeping suddenly blared from a speaker on the wall. A bright strobe flashed from the same wall-mounted box. Down the hallway, a combination of whoops, loud chirps, and even a bell could be heard at various distances.
"Fire." said Sam calmly. Then, quickly, "Oh crap. My experiments!" She suddenly stood and grabbed her hair.
Mark stood just as quickly. "What? Where?" he asked.
"The third floor," Sam yelled and walked out of the conference room. Mark grabbed his phone and headphones and followed her quickly. Sam was ahead of him but he caught up quickly.
"Maybe we should leave the building," he yelled above a fire alarm that whooped nearby.
In between whoops, a strangely calm male voice said, "Fire. Fire. Please evacuate the building. Fire. Fire."
Sam shook her head and hurried her pace to a hallway door marked with a green exit sign. She opened the door and started up the stairs. "I'm going to make sure everything is okay," she said.
Mark saw two students running down the stairs and followed them with his eyes. He looked up at Sam disappearing upward. He looked down again and put his headphones around his neck. He stuffed his phone into his hoodie pockets in front. Then he followed her upstairs.
On the third floor, Samantha walked quickly down the hallway toward her laboratory. White smoke billowed ominously in the middle of the hallway. Two firemen in full heat suits and respiration masks appeared in the middle of the smoke and turned toward her door. One tried the handle to the lab but it was locked. The other raised his axe.
"Stop!" cried Sam, raising her hand. She held up her ID badge in her other hand. "I have the lab key!" she yelled.
The second firefighter held his axe over his shoulder hesitantly, then put it down. Sam strode up to him and shoved him aside with her shoulder. She held her badge in front of the card reader next to the door lock, then opened the door. The first firefighter grabbed her arm to pull her back as huge volumes of smoke engulfed them from inside the lab.
Mark had stayed back and couldn't see Sam or the firefighters as they were hidden from view by the smoke. He could hear Sam yelling and screaming in pain. Instinctively he rushed forward toward her voice.
"Get off me! Let me go!" Samantha was yelling above the cacophony of sirens. Mark plowed into something bulky with combinations of hard and soft parts. He and the bulky item fell to the ground.
Sam finally shook loose of the first fireman's grip and stumbled forward toward her door. She found the doorjamb with her hands and walked inside. She strode a precise path through the empty whiteness. She reached her destination by feeling along a table edge inside the lab. She switched off the fog machine after fumbling along the surface of the machine.
Outside, the second fireman and Mark wrestled on the ground in the hallway. The smoke began to settle toward the ground and dissipate. The first fireman came over and grabbed both of the men by the shoulders and lifted them up so they could see. Mark struggled against the grip on his shoulder. He realised he could see now and it slowly dawned on him that he couldn't smell smoke and wasn't coughing.
"What the hell?" he asked.
The firemen realised what was going on and took off their respirator masks. "It's steam?" asked the first fireman. The whooping siren turned off but a high-pitched chirp and ringing bell could still be heard.
Mark walked toward the lab door and cried out in pain. A loud clunk and clanging metal noise was heard. Mark hopped on one leg in the knee-high fog. "I kicked the axe!" he screamed.
Samantha appeared from inside the lab. "Stop being a baby," she said. She reached down and fished around, finally finding the wooden handle. She stood up and handed the axe to one of the firemen. "Everything is okay here," she said. "I'll file a report later."
Mark fell down against the wall and asked, "What the fuck?"
"Please don't use profane language," Sam said. The only sound they could hear was the ringing of the external bell. "It was just a little fog. I think you can be my intern. You have the job," she said. She nodded to the firemen and walked back into the laboratory. She pulled out a doorstop and used it to wedge open the door.