A Pocketful of Stars (Applied Topology Book 1)

by Margaret Ball

  What did he think we were, computer nerds? “Wrong! To do that, we’d have to have a detailed image of how a computer works.”

  “You’re math majors, don’t you already know all that stuff?”

  “We’re pure mathematicians,” I tried to explain. Naturally, that meant nothing to him.

  “So that means what? I need to find some slightly sullied math majors? Some who’ve already lost their virginity? Or do I need to sully you… personally?” He gave me a slow once-over, obviously trying to embarrass me. I did not blush. Well, not very much.

  “Clean up your act!” Ingrid snapped. “She just meant, you’d have to talk to applied mathematicians for this.”

  “Actually, I don’t think that’s going low enough.” Ben joined the argument. “He might need a computer science major.”

  “These days, they’ve gone all theoretical. He really needs an… engineer.” Ingrid looked as if she wanted to wash her mouth out with bleach after using the E-word.

  “And there’s no way anybody in engineering could visualize abstractions well enough to do applied topology,” I finished. “So you see, it’s not possible to make this work.”

  “Sure it is. I’ll get somebody who understands computer architecture and they can explain it to you, then you guys can do the voodoo part. Or are you just giving me the runaround because you actually can’t do anything at all with your so-called magic?”

  “We do not,” Ingrid said icily, “call it magic. Boris.”

  “And you were just arguing that we could do more than we were admitting! Can’t you even stay on the same side of your own arguments?” I’d begun a slow burn when he tried to embarrass me, and this contradiction turned up the flame. “You ignorant, intellectually challenged imbecile, can’t you even follow a simple logical argument without holding onto the rope with both hands? It’s not our job to educate a dysfunctional kindergartener.”

  I had more to say along those lines, but “Boris” had tilted his chair back and was laughing. “Go on,” he urged. “How many more polysyllabic insults can you come up with?”

  “For you,” I said, “I’d better stick with insults of one syllable. Try this: If you want a big bang, you don’t need us, you need a gun!”

  He pushed his coat lapels back. “That, I’ve got.”

  Chapter 3

  After the spook took himself off on some unspecified errand, Ingrid actually lowered herself to refill the coffee maker. “It’s just because I want coffee,” she said, giving me her standard unfriendly stare. “I do not consider it my job. We need a receptionist.”

  Actually, I liked the idea. “Somebody to keep spooks out of our offices.”

  “To take telephone messages,” said Ben, who refuses to learn how to use a cell phone.

  “To buy a better class of pastries,” Ingrid said.

  We all sighed. The Center probably did have sufficient funding to hire a general-purpose dogsbody. Finding a normal person who wouldn’t be fazed by representing us was another problem entirely.

  “Anyway,” I told Ben, “you really want someone to lose telephone messages. Why do you keep giving girls the Center phone number, if you don’t want them to find you?”

  “I don’t have another phone number.”

  “Lia,” Ingrid said, “I have an idea. Let’s buy Ben a cell phone and whenever one of his girl friends calls here, we can give them that number.”

  “Waste of your money,” Ben said. “I’ll lose it. I don’t actually want any of my old girl friends to find me – not now.”

  Ingrid rolled her eyes. “He’s in love again!”

  “Just don’t tell us about this one,” I suggested, “and we’ll… keep losing your messages.”

  “The real problem,” Ingrid said, “is how to lose Boris.”

  She had a definite talent for bringing us back to earth. Grudgingly, I gave up fantasies of fresh pastries and good coffee, and shoved my mug over for Ingrid to refill. “This may take a lot more caffeine. Does anybody have an idea for how to satisfy him?”

  “I suggest we wrap up Lia in a pretty pink bow and deliver her to him,” Ben said, then pretended to flinch away from me. “What? Didn’t you notice the way he was looking at you?”

  “Sex maniac,” Ingrid said.

  “Well, he is.”

  “I meant you,” she told Ben. She looked at me. “Notice how Ben gets like this every time he falls in love?”

  “Only until he gets the girl.”

  “Then, of course, he falls out of love.”

  “And starts losing her phone messages.”

  “It’s not fair for you two to team up on me,” Ben protested. “I call sexism, workplace harassment, um…. anti-diversity working environment… Anyway, I have an idea. What about the Königsberg Bridges problem?”

  Ingrid and I both looked at him. “What about it?” It had, after all, been solved nearly three hundred years ago.

  Ben waved his hands and talked about arcs and vertices. Or if you prefer, lines and points.

  We all stared at our coffee cups for a while. Frankly, I would have preferred to be staring at a doughnut, but that was one topological identity that did not transfer to the real world.

  “If we haven’t seen the target computer, how do we visualize the arc?” Ingrid asked after a while.

  “And isn’t it likely that if it did work, it would move one or both of the computers instead of giving us access?” I added.

  “I didn’t say it was a fully worked out solution… Do you think he’s with the CIA?”

  “Well, he did imply that he wasn’t NSA,” I allowed.

  “Can the CIA run operations inside the country? I thought not.”

  “I think there’s some sort of loophole for counter-terrorism if it involves another country.”

  “I expect all those agencies do a lot of stuff they ‘can’t’ do,” said Ingrid. “Anyway, it’s bound to be CIA. Weren’t they the ones behind Men Who Stare At Goats?”

  “What happened to the goats?”

  “Nothing much, I don’t think.”

  “But they probably lost their funding.”

  Ben had backed off the graph theory approach to computer hacking after I mentioned physical transportation, but neither Ingrid nor I had any better ideas. She escaped to a class (funny, I thought all her classes were in the afternoon) and Ben and I batted ideas around without much progress. Convergent nets? Ultrafilters? By mid-day, we had covered two whiteboards with diagrams but still had not managed to persuade my laptop to bypass his password protection and read data directly off his iPad. “We can visualize the concepts just fine,” he said glumly. “We just don’t know enough about the insides of computers to visualize how they could be affected.”

  “That’s what I hate about applied math. You wind up having to think about all this messy and basically irrelevant stuff.”

  “Let’s get out of here for a while. Lunch?”

  The sandwich shop in the Student Union was loud, crowded, and stocked with cellophane-wrapped sandwiches that had probably been assembled in my freshman year. However, it was also cheap, air conditioned, and close to Allandale House, making it the Center’s favorite lunch place. I shoved a bill into Ben’s hand and plopped down inelegantly on two built-in plastic chairs at once. More or less. I had my butt in one, a hand and a knee on the next one, and An Overview of Hyperbolic Geometry marking our space on the white plastic table.

  “Get me anything but tuna salad,” I yelled over the babble. Ben nodded and threw himself into the maelstrom around the sandwich cooler. I sat back and enjoyed the air conditioning. After a morning of pretending that Allandale House was perfectly comfortable, I was in the mood to let the Student Union’s much more powerful system chill me until tiny ice crystals formed in my blood.

  Or at least until Ben got back with the sandwiches. It didn’t take him long today; I wasn’t even shivering when he dropped two cellophane-wrapped packages of white bread, brownish lettuce, and anonymous filling on e
ither side of Hyperbolic Geometry. I peered at mine.

  “It looks like tuna salad.”

  “No, it’s egg salad. See the yellow bits?”

  “If it’s tuna salad, those yellow bits are cause for grave concern.”

  “Oh, unwrap it. If it’s tuna salad, you can have mine instead.”

  “What did you get?”

  “Tuna salad. Like always. Look, Lia, I need to talk to you,” he yelled in my ear. “I need advice.”

  “Well, I think we should look at knot theory…”

  “Not about that! It’s about this girl.”

  When wasn’t it? “You really want to shout your love stories out to the entire Student Union?”

  “We could go to the Turtle Pond.”

  “Too hot!”

  Ben looked to his left. “No, it isn’t. Get up!” He grabbed my arm and hauled me out of the chair I’d worked so hard to defend.

  Vern Trexler was between us and the exit, with a tray full of hot, non-portable food. Well, I assumed it was food. Something brown flanked with wedges of something yellow, anyway. He mouthed something inaudible at us.

  “Sorry, Vern, we were just leaving!” I shouted.

  Sometimes I felt like we were not just the Cool Kids, we were the Mean Kids. But Ben was willing to be ruthless in search of privacy today, and he was my best friend. He definitely outranked Trexler in my private hierarchy.

  Of course, so did box turtles, water weeds and rounded rocks, all of which were in evidence at our second-favorite lunch spot.

  “Doesn’t that guy have any classes?” Ben griped. “How does he have the time to hang out on campus pestering us?”

  “Maybe he’s flunked out.” Not likely, this late in the school year. Still, it wasn’t a comfortable thought; Desperate Vern would be even worse than Whiny Vern.

  I hadn’t managed to get my blood so chilled that it was actually comfortable to sit by the Turtle Pond. But in early May it was bearable; Austin hadn’t yet settled down to the daily bombardment by sun that made it questionable whether human life could be sustained without air conditioning. By mid-July, the only way I’d be willing to hang out here would be if the turtles would make room in between the water weeds.

  “You’re Greek,” Ben said when I mentioned the heat. “You’re genetically adapted to this kind of climate. It’s pallid Nordic types like Ingrid and me who should be complaining.”

  “I may be of Greek heritage, but I’m not insane. You’re mistaking me for the rest of my family. Anyway, I was born in New Jersey. I’m just as American as you two Nordic types.” I ripped the cellophane off my sandwich.

  “It’s… Annelise,” Ben said.

  “It’s tuna salad,” I corrected him.

  “Never mind that. I need some advice.”

  “I told you. Knot theory…”

  “About Annelise!”

  I took a bite of my disgusting tuna salad sandwich. Ben was still looking hopefully at me when I had swallowed it.

  “Why? I don’t even know your latest true love.”

  “Well, she’s a girl. And you’re a girl.” He looked at me as though this biological fact was enough to give me special insight into his lady-love’s mind.

  “Technically.”

  “Huh? Don’t tell me you’ve suddenly decided to identify as male?”

  “Oh hell, no, I just mean I don’t have a lot of experience with dating.” I thought it over. “Or with other girls, actually. I’m not very social.”

  “No kidding, I’d never have guessed.”

  I pretended to swat him with the sandwich. “So, you want advice or don’t you?”

  “She – oh, never mind. You’ll laugh at me.”

  “Promise not to. I owe you.”

  “You do?”

  “For last year, when all this started.” We’d both been graduating seniors, both in Dr. Verrick’s general topology class for second-year graduate students (no, we weren’t lost; the four years of Verrick’s Honors Topology course covered six years of topology by ruthlessly ignoring all other types of mathematics), when it happened. My attempt to illustrate the Axiom of Choice for a kid I was tutoring, using the toys my little brother had left in the living room, went sideways and… the earth moved. Or, to be precise, Darth Vader moved out of a collection of action figures; a poker chip moved out of the chips scattered on the carpet; and one of Andros’ Cracker Jack prizes had separated itself from the rest of the pile.

  And I was freaked out of my ever-lovin’ mind.

  First I told my boyfriend. That… did not work out well.

  Ben had been the only other math student I dared tell at first. He hadn’t laughed at me when I tried to recreate the experiment and it didn’t work. And then he hadn’t run away when I tried again and it did work. He’d been the lone member of the “Lia Kostis isn’t crazy” club until first he, and then Ingrid Thorn, had discovered similar capabilities.

  It didn’t, as far as we could tell, have anything to do – directly, anyway – with mathematical talent. It seemed to be connected with how we proved theorems, rather than with how many theorems we proved. Each of us was known for having a killer intuition in general topology, for knowing when a statement was true even if we stumbled over translating that knowledge into a formal proof. Each of us had the same, eerily similar way of getting to that knowledge: we moved into a space inside our heads that was mostly black and empty, populated by glowing points and lines and planes of light. We manipulated the images in that space and saw, without words, why certain theorems had to be true. And now, when we consciously linked those images to real-world objects… little things happened in the world that shouldn’t have happened.

  Dr. Verrick not only refrained from turning us over to mental health professionals; he wrote letters, pulled strings, and created an independent Center for Applied Topology out of thin air. Got us office space at the top of Allendale House, paid us miserly stipends, and completely changed our lives. This was not exactly what I had envisioned doing after I got my degree.

  Not that I had any complaints. My last semester as an undergraduate had been devastating to my ambitions of getting a Ph.D. and becoming a serious topologist, and four years of studying with Dr. Verrick hadn’t prepared me for anything else. I had a place to live that wasn’t controlled by my family, almost enough to live on comfortably, and all the time I could ask for to explore what else a visualization of topological spaces could do by way of warping reality.

  Of course, Dr. Verrick hadn’t bothered to explain that we were not actually funded by the Moore Foundation, but by a secretive three-letter-agency using the Foundation as a pass-through.

  “You know what?” I said when my thoughts got back to that little bombshell. “If we’re actually being funded by the CIA, maybe Dr. Verrick won’t make us keep going to the Moore Foundation parties.”

  “He already knew about the CIA or whoever it is,” Ben pointed out, “when he started making us go. I think he’s got a secret agenda. Forcing mathematicians to be social.”

  “I don’t think so. He usually complains that we’re all too social at those parties. Anyway, it’s not like we’re all total introverts. I mean, look at you, you’ve got a girlfriend.” With great restraint, I left the word “another” out of that sentence.

  “She doesn’t take me seriously…” Ben complained that Annelise went out with him, sure, but she was also seeing other men.

  “Well,” I said, still exercising restraint, “you’ve seen a number of other girls.”

  “That was before I met Her. It’s different now.” Ben went on for a while about how his entire life was now dedicated to cherishing and caring for Annelise, until a turtle climbing up out of the water distracted him.

  “Look!”

  “Yeah? It’s a turtle. In case you haven’t noticed, there are a number of them around here.”

  “Yes, but I could swear that’s Caspica caspica – a Caspian Box Turtle.”

  “So?”

  “They�
�re only found in Mesopotamia. I just need a look at its plastron.” Ben grabbed for the turtle and it slid into the water with a startled plop.

  “Oh… I forgot you had a second major in Reptiles and Amphibians.”

  “Marine and Freshwater Biology. Oh well, I’m probably wrong. What would Caspica caspica be doing in central Texas?”

  “Maybe a veteran brought him back as a souvenir?”

  Ben scowled. “That’s terrible! This is way too far north for him to survive in the wild.”

  The humid May air lay heavily on my equally humid skin. “Wow, that has to be the first time anybody described Austin as ‘too far north’ of anywhere.”

  “Don’t be so provincial. For all you know, millions of Mexicans may think of Austin as the frozen north.”

  “Frozen? That’s pushing it.”

  “Hey. We did have some snow a few years ago, remember?”

  “Vividly.” And that time the snow didn’t even stick to the ground, but the city practically shut down anyway.

  “You and I were the only people who made it to class.”

  “And Dr. Verrick. Most of the other professors took off to dance in the falling snow.” We enjoyed the memory in silence for a few minutes before Ben got back to the topic of Annelise, who was apparently the most wonderful girl in the world except that she didn’t take him seriously.

  It was an easy mistake for anyone to make. Ben wasn’t exactly the most impressive person in the world – not physically, anyway. Oh, he was tall enough, and not only by my own unexacting standards; he was actually a couple of inches taller than Ingrid, who could have been cast as a Norse shield-maiden. But he didn’t get his light brown hair cut nearly often enough, and when he wasn’t wearing glasses his brown eyes had the vague look common to the extremely near-sighted. Because he was too impatient to try on clothes until he found some that actually fit his lanky frame, he tended to buy shirts that were way too big for his shoulders so as to get sleeves long enough for his arms. If you weren’t equipped to recognize the world-class intelligence behind those unfocused eyes you might easily underrate him.