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The Tetrahedron Part=2 - By- Vandana Singh Vandana Singh is a former physicist, now a writer of science fact, science fiction and fantasy. She is also an editor of scientific and other works, and a member of Saheli, Austin. She is based in the greater Boston area. click here to read past articles by Vandana Singh. Click here to read part one of The Tetrahedron.

But by its very existence it had changed her. It had upset the nice, ordered world-view that her parents had induced her to adopt as her own. When she looked back on the days before the appearance of the Tetrahedron, she saw a stranger --- the average girl who went regularly to college, did well enough in her studies, helped out at home, and expected no more than an average sort of life. Some aspects of marrying Kartik had depressed her, but she had known that in time couples "adjusted", that --- on the average --- people got by. But now she could hardly stand the sight of Kartik, was missing most of her classes, had abandoned all her old friends, and divided her time between the Tetrahedron and the tea shack at the university, shamelessly fraternizing with a young man she barely knew. What had she become?

All she knew was that when she looked at the Tetrahedron she could forget everything but the wonder of it all. Where had it come from? Why had it chosen a busy street in the middle of New Delhi, of all places? What was its purpose?

A newspaper columnist had joked that the purpose of this device must have been to bring world peace, because after the initial fright, the global arms race was at a standstill. It was as though the world powers were watching and waiting, like the tourists gawking at the Tetrahedron in Delhi. The street was now blocked to traffic, of course, and a paved square had been set up in the parking lot of an adjacent building where a series of shops had sprung up as if overnight. Soft drinks, tea, hot samosas, cameras, film, knick-knacks such as plastic replicas of the tetrahedron were being sold at exorbitant prices. Foreign languages from all over the world mingled with radio music from the shops and live commentary from a TV station crewman. Rich businessmen rubbed shoulders with hippies and street urchins; Americans and Middle-Easterners, Japanese, Koreans, Kenyans all stood gawking and chattering together. People-watching became Maya's hobby. Her favorite pastime was to eavesdrop on the conversations that sprang up in her vicinity --- fragments of arguments, discussions, both academic and untutored --- it was a feast for the ears.

"...the heat, the dust! Why ever did the Tetrahedron choose such a place!"
"the weapons theory has been defused by now, no pun intended except for the politicians, paranoid as usual!"
"Beats me why it's here. Place wasn't even what I expected. No elephants, or dancing girls, or any of that shit. Got my camcorder along and for what? All that thing does there is to sit in one place while we sweat our butts off."
"Reason, there's a reason it's special, if you read the paper by MacArthur."
"...and they don't even eat monkey heads, man, so much for Indiana Jones... bunch of vegetarians."
"Don't grumble, dear, it was your idea."
"...what do you expect Hollywood to do, make documentaries?"
"Well, the Johnsons, they went all over this country couldn't stand their boasting."
"...did you ever hear of synchronicity? Meaningful coincidence."
"...got some shots of the cows on the roads, weird enough for me."
"...yes, like when you're thinking of a song and the DJ starts playing it --- what's that got to do with..."
"...only in a place like this, look at the traffic. By Western standards, with conditions like this, most people ought to be dead. What keeps them going, eh? How anything functions here is a small miracle. A modification of the Jungian concept of synchronicity..."
"...did you hear what happened to the Gustafsons? The hotel didn't have any record of their reservations, poor things. They ended up you'll never guess where."
"Never in Japan, no. Far more orderly people. There's something in the air over here, as though the chaos is intrinsic to the place."
"...in the home of the student they'd hosted ten years ago, back when they were in Tucson..."
"...dimensional anomalies...fellow called Bhaskar, native --- I mean Indian mathematician, cosmologist, yes, in the Times...no, no, the London Times, theorizes that dimensional anomalies must exist in this region, hence the Tetrahedron!"
"...intrinsic anarchy, I like that, no wonder we couldn't hold on to the Empire."

Maya listened, fascinated. Sometimes a man or woman in international tourist garb would come up to her and ask if she'd agree to be photographed in front of the Tetrahedron. She was always discomfited by these requests and would back away with a muttered "sorry". Mostly she kept a low profile, watching, listening, sipping a drink or two, letting her thoughts drift, thinking about her life, Kartik, her parents, wondering at the silence, the serenity of the Tetrahedron in the midst of all the noise and bustle.

At home, nobody guessed what was going on in Maya's head as she pounded spices in the little kitchen, or hung wet laundry on the nylon clothesline in the balcony. Washing dishes after dinner, she gazed moodily out of the window --- a view of rooftops and TV antennas, dusty, crowded streets, music and conversations blaring from tiers of lit, grimy open windows --- over all this, in a hazy, dark sky, glimmered a faint star or two. Maya wondered what she was going to do with her life.

Tea with Kartik. Endless teas and breakfasts and dinners with Kartik. When he came the next evening he looked tired and a little vulnerable, and she felt a small pang. Poor fellow, what kind of woman was he going to marry? But seeing her parents bustling about him, deferring to his every wish, she felt her old irritation arise again. To make matters worse Kartik started talking about the Tetrahedron. This time he was convinced China and North Korea had something to do with it too. After all, why stop at Pakistan? Maya set the teapot on the table down so loudly that everyone stopped talking and stared at her in amazement.

"What do you know about it?" she snapped at Kartik. Her heart was hammering in her chest. She was conscious for a moment that she was opening a door she would not be able to shut again. But her anger and confusion, held back as long as it had been, surged over what was left of common sense.

"China! Pakistan! Has it occurred to you that nobody --- not anybody --- can understand what that thing is? None of the foreign scientists, none of ours. Can't you see anything outside your own damned backyard?"

She turned on her heel and went into the kitchen, shaking violently, leaving a dead silence behind her.

Then a clink as her mother set down her cup, and her apologetic voice saying desperately to Kartik,
"Please understand, she is just, you know, sometimes women.. that time of the month.. she doesn't mean it."

And her father now beside her, looking at her in shock and hurt, saying "What have you done, child?"

What had she done? Insulted the man who was going to be her husband, damaged the fragile alliance between Kartik's parents and her own, lowered the family honor by behaving like a squabbling fish-wife instead of a girl from a respectable family. She looked at her father's upset face, at his shoulders stooping from disappointment, and burst into tears. She went blindly into the room she shared with her visiting sister and the child. Her sister patted her head.

"Listen, you donkey, that is no way to behave before marriage. You can quarrel all you want afterwards, look at Ashish and me, I shout at him all the time."

"I don't want to marry Kartik," she said between sobs. It was a relief to have said it at last. But she could hear her parents in the drawing room, anxiously trying to placate Kartik. She heard his chair scrape on the floor as he rose, heard him say,

"I hope I have not been mistaken in her. If she comes to her senses..."

Then the front door shut.

After that, for some days, she really tried. She hadn't understood before how vulnerable her parents were, how frightened at the thought that their youngest daughter might never get married. Three daughters had slowly depleted them of their meager savings, and Kartik's family had not even asked for gifts (the euphemism for the now illegal dowry). They'd never find anyone like him. So the very next day she went to the phone booth at the corner of her street, called Kartik and apologized rather stiffly. He did not say anything except to tell her that he was going out of town on business for two weeks, and he would think about this when he got back.

Three days of attending classes and bearing with the questions of her friends put her in such a black depression that she began to go to Patel Chowk again to join the never-ending crowd staring at the tetrahedron. One day when the square seemed particularly crowded she fought her way to the edge near the parking area, clutching her soft drink in her hand, to stand beneath the generous shade of an ancient tree. It was then that she noticed a white van marked with the words "Ravindra Refrigeration Systems" parked near her. It looked familiar --- she must have seen it there before without really noticing it. The side door of the van was open and a motley group of people were gathered around it, talking.

They were all so different from each other that it took her a moment to realize they were a group ---- three rather elderly men, two young women who looked Japanese, a lean young man who could have been from the Middle-East, and most incongruous of them all, an old lady in a beige salwaar-kameez perched in the open doorway of the van, knitting away. There was something indefinably different about them compared to the rest of the crowd --- they seemed relaxed, they hardly glanced at the tetrahedron, they spoke to each other in low, easy tones.

Maya wondered why she had never really noticed them before. But the tetrahedron attracted so many kinds of people that perhaps it was no wonder. Now someone with a loudspeaker was shouting, policemen were pushing the crowds aside with batons. Another politician? No, it was a movie star, said a plump woman in a purple sari excitedly to Maya. Look, Malini Mehra herself in a glittering pink sari with a daring backless blouse, at the souvenir booth, waving flirtatiously at the gawking, camera-clicking onlookers. The old Maya would have been thrilled at the sight, but the new Maya just glanced away. There, behind the trees, was the tetrahedron, the cause of all the excitement. As she glanced at its pinnacle rising into the sky above the treetops, she thought she saw one of the ubiquitous crows flying directly towards it. What was the bird doing? She squinted up at it but the sun, hazy in the polluted sky, was in her eyes. She thought she saw the bird reach one edge of the tetrahedron, then swerve as if to avoid it, but instead it disappeared.

She rubbed her eyes and blinked. The plump woman was still beside her, chattering away about Malini Mehra. "Did you see that?" Maya said. "Of course," said the woman, "Malini Mehra likes reds, they suit her skin, don't you think?" Maya looked away again, but the tetrahedron was just as before. Turning back she met the eyes of the old woman knitting in the doorway of the white van. The old lady smiled at her. Maya wondered if the woman had seen the crow vanish into the tetrahedron and whether it would be worth her while to go over to the van and ask. After all, the square was full of maniacs.

Later she met Samir at the tea-shop. He did not ask her where she had been the past two days. It was a relief to sit with him and watch old Ramu boil the tea in a battered saucepan over a kerosene stove. He added a thick pinch of powdered tea and cardamom to the simmering mixture of water and milk. The aroma filled her nostrils. Ramu's radio, tuned to a station that played only classic Hindi film songs, sat perched on the stained wooden counter.

She told Samir about what she had seen.

"I know, I wasn't quite close enough to see clearly if the crow did disappear. But so many strange things have happened."

Samir was looking at her thoughtfully. As he started to answer, a car stopped in the road across from them. A bright, confident, charming face leaned out of the window, radiating ethnic chic --- from the casually scooped up hair to the embroidered collar of what was probably a very expensive designer salwaar-kameez.

"Bhaiya, don't forget to be on time tonight!"

Bhaiya --- Elder brother. Samir waved and looked faintly embarrassed. "My sister," he said apologetically as the car drove off in a puff of dust. "It's her birthday today."

It occurred to Maya suddenly that Samir was from a quite different stratum of society than herself. She had known this all along but it had never mattered, never seemed important, until now. His English was polished, hers just fluent enough to get by. She remembered meeting a friend of Samir's on their way to the tea shack some days ago, and the way the friend had looked at her and then again at Samir with astonished surprise. Samir hadn't introduced her. The friend had smiled at Samir and dug him in the ribs and muttered something to him before sauntering off. Something about fraternizing with. words she could not catch. After that Samir had kept talking to her as though nothing had happened, but just for a fleeting moment he had looked discomfited. Abruptly Maya was aware of herself as hopelessly lower-middle-class, with all its implications. She didn't know anything about Samir's life, nor he about hers --- what was she doing here with him?

But he was talking on, oblivious.

"...and maybe it was nothing, but maybe, just maybe, you've hit on something here. Look," he drew out his notebook and tore off two pages. He tore one into a rough circle and put it against the edge of the other sheet, at right angles.

"Suppose you were a two-dimensional creature living on the surface of this flat sheet of paper. Would you know that this circle existed? No, because it is in the third dimension, right, which is not accessible to you. You would only see the straight line that is the intersection between the circle and the sheet where you exist."

She concentrated, pushing back her other thoughts.

"Oh, so if I put the edge of my hand against my face," she said, suiting the action to the word, "my face feels only the edge. It has no idea of the extent or shape of my hand."

"Yes, something like that. You see, it may be that the Tetrahedron is only a projection of a more complicated object in our three-dimensional world. This object extends in a dimension that is inaccessible to us --- all we perceive is the Tetrahedron. To us it appears closed. But in another dimension, there may be doors."

He stopped, lost in thought. Maya was fascinated.

"You mean that somehow the crow I saw got through into another dimension, got into the Tetrahedron? But I thought they'd done tests on the entire surface."

"Yes we did --- perhaps the door, if there is a door in another dimension, was closed at the time we bombarded it with radiation and whatnot. That would make sense, wouldn't it? "

"Yes, but--- " She frowned. "I don't completely understand."

He took a sip of his tea and set the glass down on the edge of the bench.

"Do you know what topology is?"

She shook her head.

"Simply put, it's a branch of mathematics that concerns itself with very general, basic properties of objects or spaces. Topologists look at what happens if you continuously deform the space or the object without breaking or tearing it. This is not making any sense, is it? Okay, let me give you an example. "

He held the page he had torn from his book in one hand, and the paper circle in the other.

"This rectangular page and the circle are topologically identical, because you can shrink or stretch one to become the other. And your chai glass is identical to them both because I can theoretically deform the sides until it's flat. But --- "

Now he tore a small hole in the middle of the page.

"Now this is no longer topologically equivalent to the circle, because by the rules of topology, however much you deform this page, you can't get rid of the hole. So the page without the hole is a simply connected two-dimensional surface, and the page with the hole is what we call multiply-connected."

"Oh! Like a tea-cup, I mean one with a handle, not Ramu's chai glasses."

"Yes, yes," he smiled delightedly at her, immensely pleased. "Topologically you and I are identical to a teacup, or a vada , if you like South Indian food--- the human alimentary canal is the analog of the hole in the vada !"

She was staring at him, wide-eyed.

"What has all this to do with ---"

"The Tetrahedron? Plenty. Topology is relevant in two ways. One, if the topological structure of the Universe is non-trivial, multiply connected in several dimensions, then it might provide shortcuts for faster-than-light travel. Like the wormholes in space that the newspapers keep talking about. Two, the true shape or structure of the tetrahedron itself. If we could see it completely in all the dimensions that it inhabits, we might see something topologically very complicated. It would be incomprehensible to us --- our notions of in and out, edge and surface would be lost, or at least very confused. Ever seen a Mobius strip?"

She shook her head, feeling awed and small at the same time. How much did he know! Now what was he doing? His hands, brown and slender, she'd never noticed before how nice his hands were --- tore a strip of paper from the long edge of the page. His eyes were alight with enthusiasm.

"Look at this strip of paper --- see how I can put the ends together to form a ring?" He suited the action to the word. "Now suppose, before I do that, I twist the paper once, like this. Now I put the ends together. A ring with a twist! This is a Mobius strip."

She put a tentative finger out to touch it. He smiled.

"Go on, move your finger along the outer surface, along the length of it, yes, just so!" He grinned at her surprise. "You start at the outer surface and before you know it, you are inside! Except that inside and outside have lost their meaning in this case, because a Mobius strip has only one surface, not two like the ring." He was talking fast in his excitement. "People think that spacetime may be a generalization of a Mobius strip or some similar non-trivial topological object, in several dimensions. So also an object like the Tetrahedron could be very complex, very interesting, if we could see it in its entirety"

Words failed her. She could see in her mind a complicated structure, with smoothly contoured edges and sculptured pathways curving dizzily, leading to hidden doors. But she didn't have the training to put it all into words that made sense. She stared at him in wonder and envy.

"I understand, I think."

He nodded approvingly.

"If the Tetrahedron is a projection in our space of a more complicated, multi-dimensional object, it might also explain the disappearance of the people who were on the road at the time the Tetrahedron appeared. Who knows?"

"You mean they might be inside the Tetrahedron?" she said incredulously. The thought had never occurred to her. Instead she had imagined that perhaps some kind of exchange had taken place, the tetrahedron for the people. That the bus riders, the car passengers and the bicyclists were at this very moment on some other world, walking about under alien skies with their mouths open. Another world! Her mind had conjured up bizarre vistas. Yet the thought of what the inside of the tetrahedron might be like was equally mind-boggling.

"They must have made a mistake," she said. "The aliens, I mean --- they could not have meant to come here to Earth. But how could people with so much technology make a mistake like that?"

Then she stopped and laughed at herself. Yes, the recent satellite fiasco, not to mention the Challenger tragedy of the last century. Technology was no guarantee against mistakes and stupidity.

Maya sat talking to Samir for another hour, her earlier doubts forgotten. He told her about current theories of the birth of the universe, the mysteries that arose with each new discovery. She liked the way he gesticulated in his excitement, the way his eyes seemed to see the wonders his words described. Now he was expounding on the eventual death of the universe.

"The solar system, of course, will die long before that," he said. "The sun will swell and swallow the earth, the moon, all the nearer planets, before collapsing into a white dwarf star."

She was silent, filled with wonder. He stopped to take a sip of his tea, and suddenly the radio blared. "Na yeh chand hoga, na taare rahenge" [There will be no more this moon, nor will the stars remain]

They both laughed at the same time.

"I always wondered how in Hindi films they contrive to have a song with the right words come on at the appropriate moment," he said, smiling. "Just the other day a similar coincidence happened. There I was, wondering about what kind of star the aliens are from, if they are aliens, that is, and Ramu's radio started playing "chand ke paas ik sitaara hai!" [There is a star by the moon]

It was very pleasant to be able to laugh companionably with somebody. (Maya wondered with a pang whether she and Kartik would ever have anything to laugh about.) Then she remembered fragments of a conversation she had overheard.

"It's syn... synchronicity," she said carefully. He looked impressed.

"That's a big word. Not a scientifically valid concept, of course, but wasn't it in one of the papers? Where did you come across it?"

"I heard it somewhere, I think." She felt a slight indignation. What did he think --- that she was hopelessly ignorant? Then she thought, depressingly, that it was true.

But Samir was getting up, setting his glass down on Ramu's counter with a rather awkward air.

"Got to go," he muttered. He looked shyly at her, as though seeing her for the first time. "See you tomorrow!"

She didn't understand until the radio sang the refrain again. "na yeh chand hoga, na taare rahenge, magar ham hamesha tumhaare rahenge" [There will be no more this moon, nor will the stars remain, yet I will always be yours]

She stood staring after him, her face hot with embarrassment. She hoped he didn't think --- surely he didn't? Then she remembered that she had forgotten to tell him about the white van and its peculiar occupants.

(To be Continued...).

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