The Mammoth Book of Best New Science Fiction: 23rd Annual Collection (37 page)

“Well, I know
I’m
not me, so it’s only fair to assume others might not be themselves either.”

“You know what’ll happen now? This world will be disinfected. Word will be passed to the Proprietors by my masters, and ships will come. Ships carrying bombs. Did you know this world has an indigenous biosphere with a billion-year history? It has a species of plant that photosynthesizes moonlight. All that diversity, all that biomass, will disappear.
You
will disappear. You are an infestation. They will be very thorough.”

“If even one of me survives, grandfather, I survive. I am both very and literally single-minded.”

“And where you survive, people will die. I know this. I am the only surviving citizen of Railhead, after all, which is why the military trained me to be your chaperone. I need hardly remind you that I had a sister once, whose resemblance to you is no amazing coincidence – ”

“That’s even less fair. You
asked
me to look like this,
and
to never grow old like you do. I’ve had to learn how to be your sister and daughter and granddaughter, and you
never
let me learn to be your wife – ”

Krishna grimaced and waved the conversation away with a gnarled hand. “That is a thing we are never going to do. It’s probably just an accident you didn’t kill me. Out of every million spiders an ant colony kills, one evolves ant-smell and walks right into the anthill. Maybe my brainwaves just taste nasty. The ship that set me down here has a pilot capable of landing a Proprietor shuttle manually. With his hand on the control globe and my voice in the ear of the nav system, we will, together, be able to fly any of the vessels in this terminal. They are, mostly, still intact, if alarmed at the fact that the biologicals are fighting among themselves. I have located a suitable ship, an orbital cargo transport, at grid reference 45° 250’ 63” south, 0° 0’ 158” west. Shortly, the ship that brought me will set down its pilot and he and I and you will fly that transport out of here. He and I and you
alone
, I must stress. I have grown accustomed to your company. I assure you, though, that when we return home to Railhead there’ll be more company than just me. Scientific teams will telefactor down to us every now and then to examine you, to figure out how you operate – ”

“Brother, father, grandfather – you know very well that all your military teams want to do is figure out how to make more of me. Besides, none of your scientific teams have visited us for a very long time. I don’t think anyone is going to be listening for your signal.” She screwed up her face as if tasting vinegar. “I can’t go home. It would be like deliberately driving a needle into my eye. You have no idea. Besides, I do not require your company any longer.”

His hands trembled on the stick. “What did you say?”

She looked indicatively at a point behind his left shoulder. He turned.

“Hello, grandfather,” said a voice. A male voice.

He growled softly in his throat. “I am no grandfather of yours.”

“Nor of hers.” The resemblance was picture perfect. Gangly limbs, skinned knees and elbows, festival clothes. It had been the anniversary of First Planetfall. Mother and father had baked a cake in the shape of a rocket he had been too young to remember.

He banged the stick on the ground like a sorcerer dispelling demons. “Out! Out of my shape!”

His own youthful face smirked back at him. “Shan’t.”

He poled himself forwards towards himself, breathing with difficulty. “You can’t kill me.”

“But I can get out of your way easier than air.” He skipped away from himself easily to just outside stick range. “Your heart is beating a mite too fast for your health, by the way. I can hear it, grandfather. If any vessel leaves this world, it leaves with all of us or none.”

Krishna drew himself up to his full height. His spine complained, unaccustomed to being made straight. “That is transparently not compatible with the offer I have made. I give you one hour to discuss it amongst yourselves – ”

“We have no need to discuss it; we are of one mind.”

“Nevertheless, I give you one hour, after which time my transport will leave. In the meantime, please indulge an old man by allowing him what may after all be his last walk with something that looks like his sister. I must make it clear that this world will be destroyed. This is not raving; this is a fact.”

She simulated genuine concern. “Grandfather, you shouldn’t do that. Your skin provides virtually no resistance against blast and gamma.”

He shrugged. “I can see no better solution. Shall we walk? Your other selves tire me.”

The cyclopean avenues of seamless concrete that constituted the Proprietors’ original city loomed overhead. Their crumbling summits had been crowned a livid birdshit grey by the local flora.

“In the right light this could be home,” he said. “The sky is blue enough, and there is not one blade of grass. I believe this is the most hospitable part of the planet, and yet it resembles a desert. The native vegetation is poikilohydric. It specializes in being soaked and dried alternately. We are now in the dry season.”

“I can’t accompany you, Grandfather. To try to make me go back is to attempt to put an explosion back in a hand grenade. To be cooped up in a box? My only company a being with one tenth my service life, and when that lifespan’s at an end, then what?”

The boundaries of the terminal were walls of hand-cut masonry, slave-built, recent. Beyond them a low bluff rose out of the die-flat dry seabed the settlement had been built of. Krishna was forced to speak haltingly as they climbed the bluff. His heart was throbbing in his chest like a wounded hand. “The box is planet-sized – and the majority of company you keep – you kill.”

“But not all! I only killed a thousand on Railhead. The larger the world, the greater the likelihood of immunity. A world with a billion inhabitants might yield a million companions.”

“And only – nine hundred and ninety nine million graves.” Krishna powered himself over the bluff with the stick; what he had been walking towards came into view, standing on the dry sea bed surrounded by armed crewmen. She had not been expecting to see it, and stopped dead.

“It’s a shuttle,” she said redundantly.

“Yes.” He began poling himself along with the stick; he had to move faster. “The shuttle that brought me here – to be precise . . . it circled around behind the bluff and landed here right after take-off. We will have to hurry – if we want to board – the crew will turn on the burners if they believe anyone but you and I is coming . . . Did you really believe – I’d give you the location of the ship we were leaving on?”

“I keep telling you; I am not going with you.”

Krishna nodded. He could not count the beats of his heart now; it was like that of a bird. “Then I have – no option.” He pulled out the small fragment of his god that he took with him on long journeys, held it to the light. “Behold my travel god. You have paid – little enough attention to it over the years. It was in fact given me by my masters. It contains a very small travel bomb which can nevertheless – split this planet in two; and that, sister daughter granddaughter,
will
kill all of you.”

Her face lost its look of certainty for the first time. “It’s a rock.”

“It’s a bomb,” said Old Krishna. “Though also still a god.”

She looked at the rock in real terror. “When will it detonate?”

“When I want it to.” He whipped back his hand and threw; the god bounced several times on the wall of the bluff before being lost in the heat haze. “Now it is a rock – among several million rocks. Find it – if you can. As your other selves are all of one mind with you, they now know my shuttle is here – they are therefore coming here – and they will be coming quickly . . . Believe me, I know this . . . But they’re coming from the wrong end of the terminal . . . And they’re trying – to worm their way aboard a Proprietor military transport that has orders – not to allow any unauthorized personnel inside it – ”

He had to stop. There were men with guns around him now, ushering him into the loading lock. The take-off sparklers were already lit. Turning to look up the bluff, he could see figures silhouetted against the sun. Figures that were humanoid, but certainly not human. They would have taken other shapes, faster shapes. She was still dawdling twenty metres behind him. Trying to delay him.

She still had time.

The loading lock door whined shut, slowly, interminably, narrowing to a metre-wide sliver. She had still not moved. Eventually, he could not bear it any longer, and turned his face away.

When he turned back, she was holding him up against acceleration, his head in her hands, while men clung on to safety grips on the walls around him. Someone was yelling into a communicator, “GET US AIRBORNE! GET US SOME HEIGHT NOW!” Something heavy clanged off the outside hull.

She turned his head to face her. “Was it all bullshit? It sounded like it.”

“Complete bullshit,” he gasped weakly. “A good thing I’m having a – heart attack, or you’d have been able to tell I was lying just by listening to my – heartbeat.”

She held him close, supporting him, as the acceleration mounted and the shuttle rolled towards orbit.

“Try to relax. Don’t exert yourself. We’ll get you through this.”

“Just promise me this is one ship you’ll – never get off. If you never make planetfall, your aggression algorithms may – never kick in. Stay in space – travel hopefully – never arrive – ”

She held him close and made a very reasonable facsimile of tears until the acceleration lessened and they came to take him off her.

“Give us room! Give us room! Let us get him some oxygen!”

She shook her head. “His heart has stopped.”

The certainty of the statement gave them pause. They separated from her, treating her with the respect prudent men give to things they cannot explain. She sank down against the wall, trying to let gravity drag her miserably to the floor. Gravity refused to do so. She had to suffer in mid-air.

INFINITIES

Vandana Singh

New writer Vandana Singh was born and raised in India, and currently resides in the United States with her family, where she teaches physics and writes. Her stories have appeared in several volumes
of Polyphony
, as well as in
Strange Horizons, InterNova, Foundation 100, Rabid Transit, Interfictions, Mythic, Trampoline
, and
So Long Been Dreaming.
She’s published a children’s book in India,
Younguncle Comes to Town
, and a chapbook novella,
Of Love and Other Monsters.
Her most recent books are another chapbook novella,
Distances
, and her first collection,
The Woman Who Thought She Was a Planet.

In the moving story that follows, Singh gives us a study of a mathematician whose innate compassion and sense of fair play are tested throughout a turbulent life – and perhaps beyond.

An equation means nothing to me unless it expresses a thought of God.

Srinivasa Ramanujan,
Indian mathematician (1887–1920)

A
BDUL KARIM
is his name. He is a small, thin man, precise to the point of affectation in his appearance and manner. He walks very straight; there is gray in his hair and in his short, pointed beard. When he goes out of the house to buy vegetables, people on the street greet him respectfully. “Salaam, Master Sahib,” they say, or “Namaste, Master Sahib,” according to the religion of the speaker. They know him as the mathematics master at the municipal school. He has been there so long that he sees the faces of his former students everywhere: the autorickshaw driver Ramdas who refuses to charge him, the man who sells paan from a shack at the street corner, with whom he has an account, who never reminds him when his payment is late – his name is Imran and he goes to the mosque far more regularly than Abdul Karim.

They all know him, the kindly mathematics master, but he has his secrets. They know he lives in the old yellow house, where the plaster is flaking off in chunks to reveal the underlying brick. The windows of the house are hung with faded curtains that flutter tremulously in the breeze, giving passersby an occasional glimpse of his genteel poverty – the threadbare covers on the sofa, the wooden furniture as gaunt and lean and resigned as the rest of the house, waiting to fall into dust. The house is built in the old-fashioned way about a courtyard, which is paved with brick except for a circular omission where a great litchi tree grows. There is a high wall around the courtyard, and one door in it that leads to the patch of wilderness that was once a vegetable garden. But the hands that tended it – his mother’s hands – are no longer able to do more than hold a mouthful of rice between the tips of the fingers, tremblingly conveyed to the mouth. The mother sits nodding in the sun in the courtyard while the son goes about the house, dusting and cleaning as fastidiously as a woman. The master has two sons – one is in distant America, married to a gori bibi, a white woman – how unimaginable! He never comes home and writes only a few times a year. The wife writes cheery letters in English that the master reads carefully with finger under each word. She talks about his grandsons, about baseball (a form of cricket, apparently), about their plans to visit, which never materialize. Her letters are as incomprehensible to him as the thought that there might be aliens on Mars, but he senses a kindness, a reaching out, among the foreign words. His mother has refused to have anything to do with that woman.

The other son has gone into business in Mumbai. He comes home rarely, but when he does he brings with him expensive things – a television set, an air-conditioner. The TV is draped reverently with an embroidered white cloth and dusted every day but the master can’t bring himself to turn it on. There is too much trouble in the world. The air-conditioner gives him asthma so he never turns it on, even in the searing heat of summer. His son is a mystery to him – his mother dotes on the boy but the master can’t help fearing that this young man has become a stranger, that he is involved in some shady business. The son always has a cell phone with him and is always calling nameless friends in Mumbai, bursting into cheery laughter, dropping his voice to a whisper, walking up and down the pathetically clean drawing-room as he speaks. Although he would never admit it to anybody other than Allah, Abdul Karim has the distinct impression that his son is waiting for him to die. He is always relieved when his son leaves.

Still, these are domestic worries. What father does not worry about his children? Nobody would be particularly surprised to know that the quiet, kindly master of mathematics shares them also. What they don’t know is that he has a secret, an obsession, a passion that makes him different from them all. It is because of this, perhaps, that he seems always to be looking at something just beyond their field of vision, that he seems a little lost in the cruel, mundane world in which they live.

He wants to see infinity.

It is not strange for a mathematics master to be obsessed with numbers. But for Abdul Karim, numbers are the stepping stones, rungs in the ladder that will take him (Inshallah!) from the prosaic ugliness of the world to infinity.

When he was a child he used to see things from the corners of his eyes. Shapes moving at the very edge of his field of vision. Haven’t we all felt that there was someone to our left or right, darting away when we turned our heads? In his childhood he had thought they were farishte, angelic beings keeping a watch over him. And he had felt secure, loved, nurtured by a great, benign, invisible presence.

One day he asked his mother:

“Why don’t the farishte stay and talk to me? Why do they run away when I turn my head?”

Inexplicably to the child he had been, this innocent question led to visits to the Hakim. Abdul Karim had always been frightened of the Hakim’s shop, the walls of which were lined from top to bottom with old clocks. The clocks ticked and hummed and whirred while tea came in chipped glasses and there were questions about spirits and possessions, and bitter herbs were dispensed in antique bottles that looked at though they contained djinns. An amulet was given to the boy to wear around his neck; there were verses from the Qur’an he was to recite every day. The boy he had been sat at the edge of the worn velvet seat and trembled; after two weeks of treatment, when his mother asked him about the farishte, he had said:

“They’re gone.”

That was a lie.

My theory stands as firm as a rock; every arrow directed against it will quickly return to the archer. How do I know this? Because I have studied it from all sides for many years; because I have examined all objections which have ever been made against the infinite numbers; and above all because I have followed its roots, so to speak, to the first infallible cause of all created things.

Georg Cantor, German mathematician (1845–1918)

In a finite world, Abdul Karim ponders infinity. He has met infinities of various kinds in mathematics. If mathematics is the language of Nature, then it follows that there are infinities in the physical world around us as well. They confound us because we are such limited things. Our lives, our science, our religions are all smaller than the cosmos. Is the cosmos infinite? Perhaps. As far as we are concerned, it might as well be.

In mathematics there is the sequence of natural numbers, walking like small, determined soldiers into infinity. But there are less obvious infinities as well, as Abdul Karim knows. Draw a straight line, mark zero on one end and the number one at the other. How many numbers between zero and one? If you start counting now, you’ll still be counting when the universe ends, and you’ll be nowhere near one. In your journey from one end to the other you’ll encounter the rational numbers and the irrational numbers, most notably the transcendentals. The transcendental numbers are the most intriguing – you can’t generate them from integers by division, or by solving simple equations. Yet in the simple number line there are nearly impenetrable thickets of them; they are the densest, most numerous of all numbers. It is only when you take certain ratios like the circumference of a circle to its diameter, or add an infinite number of terms in a series, or negotiate the countless steps of infinite continued fractions, do these transcendental numbers emerge. The most famous of these is, of course, pi, 3.14159 . . . , where there is an infinity of non-repeating numbers after the decimal point. The transcendentals! Theirs is a universe richer in infinities than we can imagine.

In finiteness – in that little stick of a number line – there is infinity. What a deep and beautiful concept, thinks Abdul Karim! Perhaps there are infinities in us too, universes of them.

The prime numbers are another category that capture his imagination. The atoms of integer arithmetic, the select few that generate all other integers, as the letters of an alphabet generate all words. There are an infinite number of primes, as befits what he thinks of as God’s alphabet . . .

How ineffably mysterious the primes are! They seem to occur at random in the sequence of numbers: 2, 3, 5, 7, 11 . . . There is no way to predict the next number in the sequence without actually testing it. No formula that generates all the primes. And yet, there is a mysterious regularity in these numbers that has eluded the greatest mathematicians of the world. Glimpsed by Riemann, but as yet unproven, there are hints of order so deep, so profound, that it is as yet beyond us.

To look for infinity in an apparently finite world – what nobler occupation for a human being, and one like Abdul Karim, in particular?

As a child he questioned the elders at the mosque: What does it mean to say that Allah is simultaneously one, and infinite? When he was older he read the philosophies of Al Kindi and Al Ghazali, Ibn Sina and Iqbal, but his restless mind found no answers. For much of his life he has been convinced that mathematics, not the quarrels of philosophers, is the key to the deepest mysteries.

He wonders whether the farishte that have kept him company all his life know the answer to what he seeks. Sometimes, when he sees one at the edge of his vision, he asks a question into the silence. Without turning around.

Is the Riemann Hypothesis true?

Silence.

Are prime numbers the key to understanding infinity?

Silence.

Is there a connection between transcendental numbers and the primes?

There has never been an answer.

But sometimes, a hint, a whisper of a voice that speaks in his mind. Abdul Karim does not know whether his mind is playing tricks upon him or not, because he cannot make out what the voice is saying. He sighs and buries himself in his studies.

He reads about prime numbers in Nature. He learns that the distribution of energy level spacings of excited uranium nuclei seem to match the distribution of spacings between prime numbers. Feverishly he turns the pages of the article, studies the graphs, tries to understand. How strange that Allah has left a hint in the depths of atomic nuclei! He is barely familiar with modern physics – he raids the library to learn about the structure of atoms.

His imagination ranges far. Meditating on his readings, he grows suspicious now that perhaps matter is infinitely divisible. He is beset by the notion that maybe there is no such thing as an elementary particle. Take a quark and it’s full of preons. Perhaps preons themselves are full of smaller and smaller things. There is no limit to this increasingly fine graininess of matter.

How much more palatable this is than the thought that the process stops somewhere, that at some point there is a pre-preon, for example, that is composed of nothing else but itself. How fractally sound, how beautiful if matter is a matter of infinitely nested boxes.

There is a symmetry in it that pleases him. After all, there is infinity in the very large too. Our universe, ever expanding, apparently without limit.

He turns to the work of Georg Cantor, who had the audacity to formalize the mathematical study of infinity. Abdul Karim painstakingly goes over the mathematics, drawing his finger under every line, every equation in the yellowing textbook, scribbling frantically with his pencil. Cantor is the one who discovered that certain infinite sets are more infinite than others – that there are tiers and strata of infinity. Look at the integers, 1, 2, 3, 4 . . . Infinite, but of a lower order of infinity than the real numbers like 1.67, 2.93, etc. Let us say the set of integers is of order Aleph-Null, the set of real numbers of order Aleph-One, like the hierarchical ranks of a king’s courtiers. The question that plagued Cantor and eventually cost him his life and sanity was the Continuum Hypothesis, which states that there is no infinite set of numbers with order between Aleph-Null and Aleph-One. In other words, Aleph-One succeeds Aleph-Null; there is no intermediate rank. But Cantor could not prove this.