//------------------------------//
// Chapter One: Hyperbolic Functions 
// Story: Nightmare to Earth 
// by bobdat 
//------------------------------//

Day seven hundred and something dawned grey and misty. Mayumi woke me up as soon as the sun rose, since I would be going out searching again first thing. Better to be out early before anything else woke up.
I laced my shoes up and picked up the heavy sword, making my way past Darius at the door with a nod. Mayumi stopped me once I was a few yards beyond the entrance.
“I need you to go and check downtown. There's a shop, I marked it with a red sign. Bring back everything you can.” She whispered urgently. I smiled at her to show I understood, but inside I was cursing.

Downtown was dangerous and I held my sword a little closer as I approached. The sky was still dingy and uninspired, so I had plenty of dull light to hide in. The red sign, which used to be for a bus station, was resting against the crippled frontage of a row of shops, just off the main street. Small chunks of rubble, little more than gravel, crunched under my feet as I stepped uncertainly towards it.

I could easily see which shop Mayumi meant. The rest of them were either inaccessible or showed obvious fire damage. A few of them were gutted entirely. Only one, the furthest along, was still in reasonable condition and looked like I could enter.
The automatic sliding doors will worked, eerily. I paused before continuing, wondering whether this was a good or bad omen. The shop seemed to sell electronics, little spare parts and batteries. Maybe Mayumi was building a radio, but it would probably have been easier to convert another one we'd found intact a while ago.

Then I saw why she'd sent me. It was a mug, standing on the counter. Steam was rising lazily from the top. When I approached it, it seemed to contain black coffee. 
For the first time since I'd met Mayumi and Darius, I was about to meet another person.
“Hi, come with me.”

The hissing voice was clearly trying not to attract attention. It was coming from a hatch in the floor, which I promptly climbed into and shut behind me.
The darkness underground was broken by an orange lantern, which was in the rather shaky hand of a balding man with spectacles.
“Mayumi sent you?”
I nodded.
“Come with me.”

As we walked down the passageway, it occurred to me why there was coffee sitting outside. The things, if they entered the shop, would have thought nothing of it. But humans would instantly realise someone else must be around. Clearly whoever was living here was clever.
The passageway was roughly dug and dripped water occasionally. I did my best not to trip over the rough ruts that made up the floor, as the man continued onwards.

We ended up in a chamber, perhaps as big as the shelter I'd been living in. Once there, the man turned to me.
“Watch this.” He said, a smile playing on his lips. Maybe a smirk.
He flicked a switch and the entire room suddenly lit up. I looked up to see an electric lamp hanging from the ceiling.
“Wow.” I'd come across remnants of electricity whilst exploring the city – crossings that still had dull lights in them and flickering strip lights at night – but I'd never known it to be used. Clearly the automatic doors must be running from the same power source.

“I'm Professor Samuel Franklin, but everyone calls me the Prof. I know, it's a stupid name.”
“Who's everyone?”
“The people who look after me. I'm not really up to fighting those enemies.”
In the room were four bunks, all of which looked slept in. Apparently nobody else was around.
“Why?” I wanted to ask him why I was here, but the words just didn't make it out of my mouth.

“Why what? Why are we here? Why did Mayumi send you?” The Prof said, tinkering with some wires. “That's because she wanted you to meet us, or more specifically, me.” He smiled. “You see, I'll let you into a secret. Do you know why they call me Professor?”
“You worked at a university?” A reasonable guess.
“Correct, I was a lecturer. Do you know what I lectured in?”
“I didn't go to college.”
“No matter. I lectured in History.” He sensed my surprise. “You were expecting me to be a physicist or a chemist, someone like Einstein. Well, I'm sorry but I'm not. My head is full of information about the English Civil War and the French Revolution, not how to build machines.”

“They why did you get that light to work?”
“That wasn't me, it was the previous resident's.”
“So, why?”
“Why would anyone want to meet me? Good question.” He smiled that enigmatic smile again. My slow understanding clearly brought him pleasure. “It's because of a woman I met at university about forty years ago.”

I started to interrupt, but he held up a hand to stop me.
“Allow me to explain. This woman was a civil engineer, or at least a civil engineering student. She got me interested in the subject as an aside to History, and since then I've kept an enthusiasm for it. That's why I knew there was electricity here. And that's also why I know where the working telephone lines are. Did you know that from an ordinary telephone cable, you can contact practically anywhere in the world? Something must have happened in the English Channel, though, because I can't seem to get through to the U.K.”

He wandered around the room as he spoke, probably a relic of his lecturing days. 
“Because I can use the telephone, I've spoken to hundreds of others around the world. They're mainly in the same position as us; trapped, stuck in hideouts because of the ghosts. But when we're isolated, we're weak. We have to unite to become strong and rebuild the cities. I know that much from a lifetime's study of history. So that's why you're here. I'm heading to the coast, where there might be a boat to carry me to this central location, where we'll rebuild. But all the survivors, like you and I, have to go there. Mayumi knows this, and she wants Darius to come too.”

“So I'll be going with you?”
“Hopefully. Once we rebuild a city, with strong defences, we could even drive the ghosts away. Live peacefully again.” He seemed to be getting a little misty-eyed. “But the journey is exceptionally dangerous, and I need you and your companions to accompany me. Escort me.”
“Sounds like it's possible.” I was actually unsure, but in the end, anything was better than years in a shelter.
“Good. Anyway, I needed to see you specifically. You're from north of here, yes?”
“Yes, before I fled south.”
“We're going to have to travel back that way, so I need to ask you one important question. Is it safe?”
I paused to consider the question. When I'd fled, the scenes had been disturbing. Carnage was widespread. Fields burnt blacker than night. “No, it's not safe.”
“Are you sure?”
“This city is nothing in comparison to what happened when I left.”

Professor Franklin let me have a cup of coffee before I made my way back to my shelter. Despite the bad reputation that downtown had, I didn't see anything on my way back. Everything was just still.

Darius was out when I got back, and Mayumi was tidying the shelter.
“Did you meet him?”
“Yes. We're going to help him get to the coast?”
“And go with him.” Mayumi seemed determined. “We're leaving in two days. Darius had agreed to go. But I need to find what I'm looking for. Do you understand?”

Normally I just agreed with whatever she said, especially when she had her business face on. But in this case, I didn't understand.
“No, Mayumi. What are we looking for?”
“Before all this happened, I was part of a travelling group. The leader, who I know to be dead, had something extremely valuable. Not like diamonds or gold, but valuable to us. He was killed in a hotel room in this city, and the object I want is there. If we don't find it in the next two days, I'll have to come back.”
“What is it? Like, a computer?”
“No, it's a paper file.”
“What if it's been burnt?”
“It hasn't. I saw it on the day I last saw him, but foolishly I left it. Now, I'm going out tonight, because I think I might finally have worked out where it is. You and Darius have to stay here and wait two days; if I'm not back then, go and get the Professor.”
“Okay Mayumi.”

She smiled for the first time in weeks.
“I'm going once Darius gets back. You should get sleep, or read or something. It's the only break you'll be getting for a while.”

Once Darius' huge frame filled the shelter, Mayumi left. She had made her bunk and taken all of her personal items, not that there were many. She wasn't planning to come back, clearly. Darius seemed subdued so I just read some books we'd got hold of. Darius liked to read old magazines about basketball, and Mayumi didn't read, so I got pick of all the books I liked. Before, where I used to live, I'd mainly read biographies and stuff. Now though, I was working my way through all of the classics.

Whilst Darius cleaned his boots, I opened Crime and Punishment to the page I'd marked and continued reading. Dostoevsky was one of my favourite authors. 
I was really getting into some of the psychology when Darius interrupted me.
“If I tell you something, will you remember it?”
I put the book down, open. “I'll try.”
“You have to repeat it back to me when I ask you.”
“Okay, go ahead. I'll memorise it.”

He looked a little embarrassed behind the beard.
“What is it?” I reached for the book again, in case he lost his nerve and decided not to say anything.
“Just tell me that tanch squared minus one is shech squared.”
“What?”
“Tanch squared, minus one, equals shech squared.”
“Can you write it down?”

He wrote it on a piece of paper. 'tanh2(θ) – 1 ≡ sech2(θ)'. I put the paper in my pocket after studying it for a few minutes.
“If you don't mind me asking, why do you want to know that?”
“It's a mathematical identity.” He definitely looked embarrassed to admit it.
I smiled a little. “I didn't know you did maths.”
“I'm teaching myself.”
“So why... tan-huh-”
“No, it's tanch and shech.”
“Why tanch thingy?”
“Because it's fundamental. If we meet people from other countries, it'll mean exactly the same to them. Or even from other planets.”
I shrugged. “Okay. I'll learn it.” I had no idea what it meant, or why it was fundamental. I barely understood it, so personally I thought that the chances of others in different countries understanding it very slight. I went back to my book, which made much more sense.