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They can all be accommodated! In the same way as we did with the rationals and irrationals we deduce that the set of transcendentals is uncountable. So they are much more numerous than the algebraic numbers. The amazing thing is that Cantor proved this in and by that time only a very few numbers had been proven to be transcendental and here was Cantor proving that most numbers were transcendental!

It was only in that p was shown to be transcendental. Cantor now has two types of infinity, two cardinalities, that of the set of natural numbers and that of the set of reals. Are there other cardinalities? He looked to see if the points of the plane are more abundant than the points of the real line and showed that they were not! He had to look elsewhere and the result is one of his most powerful. First I need to introduce a concept. The proof is again by contradiction. We assume a set, A, can be placed in one-to-one correspondence with its power set and obtain a contradiction.

Elements of A Elements of P[ A ]. Now we define the set B as the set of each and every element of the original set A that is not a member of the subset with which it is matched. Now B is just a subset of A so must appear somewhere in the right-hand column and so is matched with some element of A say z.

Then z satisfies the defining property of B which is that it consists of elements which do not belong to their matching subset so z does not belong to B! Then z satisfies the defining property of B which is that it consists of elements which do not belong to their matching subset so z does belong to B!

In each case we have a contradiction so the only conclusion is that are our original assumption that the set A could be put in one-to-one correspondence with its power set is wrong. The continuum hypothesis was a problem that occupied Cantor for years and he was never able to solve it, sometimes writing to colleagues that he had proved it true then shortly afterwards writing that he had proved it false! His difficulties were not surprising as we shall see.

Any infinite subset of the real numbers is either countable, i. In Cohen showed that beginning with the axioms of set theory we could not prove the continuum hypothesis either. Together these results showed that the continuum hypothesis was independent of the other axioms of set theory.

Is it a member of itself or not? Other mathematicians began to axiomatise set theory to try to exclude the possibility of contradictions. My theory stands as firm as a rock; every arrow directed against it will return quickly to its 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.

Device is incompatible to play the video. Share this lecture. Bookmark this lecture. Professor Raymond Flood. His first year of lectures as Gresham Professor of Geometry was titled Shaping Modern Mathematics : The 19 th Century saw the development of a mathematics profession with people earning their living from teaching, examining and researching and with the mathematical centre of gravity moving from France to Germany. Read More. Extra Lecture Materials. Word Transcript PowerPoint Presentation.

Download audio file. This is part of the series: Great Mathematicians, Great Mathematics. History of mathematics Mathematics. Let me give a little background to nineteenth century mathematics and how Cantor fitted in. For him, a set was: any collection into a whole of definite and separate objects of our intuition or of our thought.

I will give some examples and introduce some notation. I will show you some surprising examples of countable sets. Slide: sets Cantor defined a set as: any collection into a whole M of definite and separate objects m of our intuition or of our thought Broadly speaking a set is a collection of objects.

There are three ways to denote sets. We could just list all the members of the set, usually within curly brackets. Cantor put one-to-one correspondence like this: Two sets M and N are equivalent … if it is possible to put them, by some law, in such a relation to one another that to every element of each one of them corresponds one and only one element of the other.

But what about the case when M and N are infinite? Now Cantor was moving into unmapped and exciting new territory. As we will see these two premises gave strange results.

N : 1 2 3 4 5 … n … E : 2 4 6 8 10 … 2n … This is a one-to-one correspondence between the natural numbers and the even natural numbers we pair each natural number with its double so according to Cantor these two infinite sets are of the same size.

Slide: Definition of infinity Indeed we will in a sense turn this paradox on its head and define an infinite set as one that can be put into one-to-one correspondence with a proper subset of itself. A one-to-one correspondence showing this is given as: N : 1 2 3 4 5 6 7 8 9 … Z : 0 1 -1 2 -2 3 -3 4 -4 … This is a one-to-one correspondence but note that it does not preserve the natural order of the integers. Cantor now made the definition: Slide: countably infinite or denumerable.

So E and Z are countably infinite or countable, for short. And we note that adding a finite number of members to a countable set still leaves it countable. And we note that adding a countable set to a countable set still leaves it countable. A countably infinite number of buses each with countably infinite passengers!

And so and so on! Slide: Afraid not! Afraid not! Rationals Let us try to think of an infinite set that does not have gaps between its elements the way the integers have. So the set of all fractions is countable.

So, are all infinite sets countable? Slide: The reals Our approach uses proof by contradiction. Slide: construct the number b Now construct the number which I will call b as follows: Its first decimal place will be chosen different from the first decimal place of x 1.

So b will be different from a 1. So b will be different from a 2. So b will be different from a 3. So b will be different from a 4. So b will be different from a 5. And so on Its n th decimal place will be chosen different from the n th decimal place of x n. So b will be different from a n. Slide: b is not on the list This tells us that our original assumption that there is a one-to-one correspondence between the natural numbers and all the real numbers in the interval between 0 and 1 was wrong.

In other words the set of real numbers in the interval between 0 and 1 is not countable. Slide: cardinality of the reals is the same as that of the interval of the reals between 0 and 1 We can show that the cardinality of the reals is the same as that of the interval of the reals between 0 and 1.

The cardinality of the reals is often denoted by c for the continuum of real numbers. Slide: Decimal expansion of a rational terminates or repeats Rationals can also be thought of as the collection of decimals which terminate or repeat e. The converse is also true — a repeating decimal is a fraction e.

Slide: Table without algebraic numbers Let me summarise in table form some of the results we have obtained. So, in a sense, there are many more irrationals than rationals.

It is possible to show that the irrationals have indeed cardinality the same as the reals. People remember Shridhar Bapat fondly because they remember themselves fondly, remember those years fondly, when the first flowers of the videotape underground bloomed in the smoky air of Lower Manhattan, in burnt-out basements and moldering once-grand hotels, in unheated lofts and screening rooms. They were by turns infantile, mind-bending, self-obsessed and eerily prescient, a motley tribe of longhairs and losers, communitarians and Uptown-gallery poseurs, attended by a coterie of tech-heads armed with duct tape, Q-tips, and obscure expertise acquired the hard way.

The revolutionary weapon that made all of this possible was the Sony Portapak, a Japanese invention that arrived on American shores in Eleven hundred dollars would get you a bulky open-reel videotape recorder, a separate camera unit with a built-in mic, a battery pack, and a power adapter.

A twenty-minute reel of tape set you back fifteen bucks — and unlike film, required no further developing or processing. It could be played back right away, or you could just erase it and start over. With the Portapak, suddenly the first generation raised on broadcast television had acquired the means to create stations of their own.

For Shridhar and for scores of others, this medium that barely existed became a way of life. It was a milieu in which the old media seemed exhausted, wrung dry after two decades of successive -isms and movements. Just as the human nervous system is the analogue of the brain, television in symbiosis with the computer becomes the analogue of the total brain of world man. Early video exploited video feedback both as a tool for creating utopian communications systems and as a source for psychedelic pattern-making.

A night watching — or making — videotapes with Shridhar was a trip to the other side. Om Serendipity R. House of the Horizontal Synch Star Drive. I saw a small iridescent sphere of almost unbearable brilliance. At first I thought it was revolving; then I realized that this movement was an illusion created by the dizzying world it bounded. I saw the Aleph from every point and angle, and in the Aleph I saw the earth and in the earth the Aleph and in the Aleph the earth; I saw my own face and my own bowels; I saw your face; and I felt dizzy and wept, for my eyes had seen that secret and conjectured object whose name is common to all men but which no man has looked upon — the unimaginable universe.

He had these eyes, this dark brown color, and kind of a beautiful, interesting face. A very low voice that he never raised. At one point some French video artists came wanting to do a show at The Kitchen but they spoke only French.

Their milieu — the whole New York avant-garde at the time, really — was full of outsiders and expatriates. His father, Shriram C. Shridhar was two. Shridhar spent most of his childhood in suburban Westchester. His Westchester idyll came to an end in when his father was transferred to Ghana. Shridhar graduated from Ecolint in As I go out into the big bad world, leaving behind me this womb to beat all wombs, I wish you success in whatever you end up doing. Fate, mystical inner knowledge et al.

When the dust finally settled, many were expelled, Shridhar among them. From London he made it back to New York and somehow found his way downtown, quickly becoming the quintessential video scenester.

Seeing him there next to names that were famous or at least, recognizable , I wondered who he was and why I had never heard of him. But I asked around, and before long my inbox was inundated with emails, solicited and not, from artists and TV people, public-access activists and professors, all of whom wanted me to know something about Shridhar.

I spent the next year interviewing dozens of them. But even then, his story was full of holes — lies, too — and it ended in the biggest, blackest hole of them all. His history was itself a kind of cipher, an almost imperceptible gap in the now-accepted narrative of video history, one that opened up onto an alternate recension of that history.

Last year, when The Kitchen celebrated its fortieth anniversary with The View from a Volcano , an exhibition of artifacts and photographs documenting its development, Shridhar appeared just once, a small face in a group shot on a wall near the door, hardly visible amid all the famous lava bombs going off in the other parts of the room. He was part of the first generation there in , along with his friend Susan Milano, another young long-hair named Dimitri Devyatkin, and Rhys Chatham, the seventeen-year-old director of music programming.

He was a highly effective curator — though in those days they disdained the term, with its exclusivist connotations. It helped that Shridhar was more at home behind the scenes — more interested in rigging the equipment, setting up screenings, and soliciting others to contribute than in putting himself forward as an artist or figurehead. Liz Phillips served spaghetti on an amplified tabletop while Yoko and John circulated among the artists, asking questions. A camera above the bed captured and transmitted the face of anyone who lay down on it to all the TVs.

These were tumultuous, formative years. His parents had left for India, leaving him an apartment on West rd Street that he shared with an old high-school friend named Conrad Sheff. He transferred from the New School to Columbia and then flunked out, losing his student visa in the process. Shridhar never made the trip.

Then one late night in October he was mugged on his way back uptown and severely beaten. Sometime afterward Shridhar lost or left his place on rd and moved to an apartment in the Village, from which he was evicted — he told friends for health code violations — and eventually wound up sharing yet another apartment with Conrad Sheff, this time on the Bowery.

People took advantage of him. We were getting overpowered by artists and people who could get grants. There turned out to be a lot of egos in that anti-ego culture. I found it massively distasteful, self-regarding, self-involved… at some point the focus on fine art became its death-knell. Well respected, well liked. After the Vasulkas left for teaching gigs in Buffalo in , Carlotta Schoolman took over video programming.

Or was it erased? She remembered him with great fondness, tinged with a sense of failure. One of the few completely uncontroversial things you can say about Shridhar: the man loved to drink.

By the mids, it was becoming a big problem. That whole electro-cybernetic loop and its magic? The salvific promise of feedback? Long since gone. In an instantly famous essay for the inaugural issue of October , published in the spring of , Rosalind Krauss argued that video would save no one.

Before you build up too much expectation, be prepared for a sad story, with little to show. The devils that tormented Shridhar included his upper-class diplomat parents, their plans for Shridhar, his revolt against his family, his battle with alcohol, loneliness, homelessness, the art world, the gallery and foundation world.

There is not much to glorify. I would question what it is you really expect to find and what your motivation is in writing this article. I expect readers to wonder why you decide to write about him. I send you my warmest wishes and hopes for success. There were all sorts of scraps, notes, and postcards with his name on them in the archive. One caught my eye immediately: an unopened letter from the alcoholism clinic at St.

Will give you the no. Thank god this week is almost over! Sorry about all those weird messages. I hope I can continue to help with the Festival in any way you find appropriate in the coming year. Shridhar was a legendary drinker and prone to binges. Almost everyone I talked to had a story about him getting wasted or getting them wasted or both. I would never drink that much again in my life.

He knew the Village better than anyone I ever knew. He knew the bars, the cheap restaurants. He had already fallen into a state of emergency of his own, with his closest friends leaving New York or already long gone, taking jobs at television networks or universities.

The rag-tag, free-spirited atmosphere of the early video scene was professionalizing and institutionalizing. One such place was Anthology Film Archives on Wooster Street, which had finally established a video department and hired Shigeko Kubota to run it.

Anthology founder Jonas Mekas was famously dismissive of video. Shridhar worked there part-time and sometimes slept in the basement. Shridhar made common cause with Bob Harris, a buddy who remained close to him — as close as anyone could be — for the rest of his life, and with another once-ubiquitous video scenester and East Village rambler, the irascible dreadlocked poet, drunk, and video-shaman Al Robbins.

Al and Shridhar loved to talk video, and there was more than ever to talk about. The two of them were often seen together, hanging out, making video, arguing, drinking, and fighting — not necessarily in that order. Conrad Sheff moved to Massachusetts for med school in He was spotted here and there, a wino on the East Side, just north of the UN. He leaves the barest of traces: a handbill advertising a screening of Aleph Null at the Mudd Club in the early eighties; another thanking him for assisting on a series of Al Robbins video installations at Anthology and the Brooklyn Museum.

The giving up of activities that are based on material desire is what great learned men call the renounced order of life [sannyasa]. And giving up the results of all activities is what the wise call renunciation [tyaga]. A article in the New York Times profiled one man who had had been living there on-and-off for thirty years, whenever things got tight.

Times were tight then, what with rising rents and unemployment, and more and more people were sleeping on subways or in homeless shelters, or taking their chances living rough in jerry-rigged tunnel spaces. We know that the steam pipes that made Burma Road and non-places like it attractive to homeless people during New York winters were insulated with asbestos, and that fans installed to mitigate the heat for maintenance workers ensured that the air in the tunnels was shot through with asbestos particles.

Burma Road may have been a refuge, but it was no place to live. Leanne Mella had known Shridhar from film and video screenings in the s. They fell out of touch when she left the city, but she saw him once more, in the mids, when she was back and working at the Whitney.

Shigeko Kubota told her that Shridhar was in the hospital. She found him in the psych ward at Roosevelt Hospital on 9th Avenue. He looked awful, but there was something about him that made her believe him, despite his reputation for tall tales and outright lies. So he became homeless, and then he moved in with this woman who lived beneath Grand Central. And there he stayed, for years. Then one day he got sick or hurt or both and had to resurface.

She called Paik, and he and Shigeko called people like Leanne. It was not easy to see him, or for him to be seen. It was result of the booze in the same way that video art was the result of the Portapak. In the dharmasastra texts it is a duty of the twice-born — of Brahmins like Shridhar, who mentioned his caste background often — to end their lives with an act of renunciation and a period of wandering.

Sannyasins abandon their hearth-fires, perform their own death-ceremonies, and renounce the world. Shridhar was, at his best, most charitably, a failed Duchampian underground man, a video sannyasin without fixed address, income, or family ties. By , he was dead.

Nam June Paik arranged a memorial service for him at Anthology Film Archives, in the room named for Maya Deren — another Ecolint alum, and an artist Shridhar was obsessed with. Victor Han remembers there being about forty people there. Nam June asked everyone to come up and say a few words, and afterward, his ashes were scattered in a park in Westchester where he liked to play as a child.

But he may as well have been talking about the ease with which Shridhar was elided from that history. I think of him a lot. I miss him. Whenever I met Abu Hamza at the immigration detention center in Lukavica, on the outskirts of Sarajevo, he carried a brown diary with him, filled with notes neatly inked in Arabic and the language formerly known as Serbo-Croatian.

Perhaps he was rehearsing some new human-rights slogan to raise awareness about the plight of people like himself, Islamists from the Arab world who had fought alongside the Sarajevo government during the — Bosnian war. It turned out to be simpler than all that. It intrigued him. There must be other forms of life.

Over the years, he and I had talked regularly about miraculous happenings during the war: bodies of martyrs that smelled of musk, angels intervening on the side of the Muslim bodies of martyrs that smelled of musk, angels intervening on the side of the Muslims. During a mujahid assault on a Serb-held hilltop, the opposing forces inexplicably aimed their artillery upward and fired into the sky.

In captivity, the Serbs reportedly told the mujahideen that they had been shooting at horsemen in white attacking them from the air. At the end of the war, most of the Arab mujahideen — seen as mythical figures by some, reviled as monsters by others — left Bosnia. Many returned to ordinary lives, some pursued jihad in other besieged Muslim lands, while others turned against Arab regimes and their superpower sponsor.

Many of the Arab volunteers, especially those from the Gulf, had been disappointed by the discovery of openly pork-eating, alcohol-drinking Bosnian Muslims. They even experimented with communal agricultural work. Many families were started. There were tensions, of course — not only among the Serbs left in the village, but also among the Muslims. Relations between one Egyptian ex-fighter and his German convert wife broke down after he took an Albanian woman as a second spouse in hopes of conceiving a child.

The ensuing drama was the talk of the town. Both the man and his ex-wife are back in Germany now. He was interrogated by the CIA in Indonesia on suspicions of Al Qaeda ties but never charged; she published a tell-all memoir about being married to a mujahid.

There was also the battle of the satellite dish. Abu Hamza possessed the only private satellite dish in the community. Some of the brothers questioned why he got to have something expressly forbidden to the rest of them. But Abu Hamza insisted that his case was special. Unlike most of the others, Abu Hamza spoke the local language fluently; the satellite dish was important for knowing what was being said about them in the media and to expose his children to the wider world.

It turned out that what was being said about them was largely hostile. Debate, such as it was, centered on whether this odd Islamic commune was a terrorist training camp or merely a backward fundamentalist enclave. Bosnia may have a Muslim plurality, but after decades of socialism, Islam is as much an identity as a prescription for religious practice. One of the supposed bright spots in this dismal scene has been the hope of one day being welcomed into Europe, as neighboring Slovenia and Croatia have.

In the summer of , NATO peacekeepers evicted nearly all the mujahideen from the village, returning their homes to the original owners.

Some left the country while others, like Abu Hamza, found new homes and girded themselves for the struggles to come. As a prominent ex-mujahid, Abu Hamza would have been imprisoned and tortured if he returned to Syria. September 11 came not too long after, and the campaign against Arabs intensified. The immigration police took him away two days later. Abu Hamza was the very first inmate at Lukavica. He was already in custody when the prison had its official ribbon-cutting ceremony.

None of the long-term inmates had come to the Bosnian war directly from their home countries, so their itineraries were more telling than their origins. One Algerian I met had made the hajj to Saudi Arabia in the early nineties to flee the civil war in his country, then overstayed his visa and found work with Islamic charities. His job took him to Peshawar and then to the Balkans, where he was compelled to quit something about money and his Saudi bosses and ended up joining the Bosnian army.

Foreigners in the army could easily obtain citizenship — but as with Abu Hamza, a special multinational commission working from secret evidence revoked his citizenship.

Refugee turned pilgrim turned humanitarian turned mujahid turned prisoner — by now we should just call him an immigrant, right?

His story was hardly atypical. But human rights groups, citing the likelihood that the Arabs would experience imprisonment and torture or worse upon returning, have fought the efforts to deport these men and challenged their indefinite detention. Abu Hamza has spent more than three and a half years behind bars.

The response to the Bosnatanamo campaign — and to the plight of the Arab detainees generally — has been a collective shrug. Abu Hamza and his comrades are a reminder of a time when Europe turned a blind eye as Bosnians were slaughtered, when Muslims of conscience came to fight on their behalf.

It so happens that Abu Hamza is an inconvenient reminder of more than one ideological era. Born Imad al-Husin in Damascus in everyone calls him Abu Hamza, after Hamza, his first-born son , he arrived in to study medicine at the University of Belgrade, one of thousands of such students from young postcolonial states who flocked to what was still one of the great capitals of the Non-Aligned Movement.

Marshal Josip Broz Tito died in , but the nation he had championed remained a beacon for international students until , when Yugoslavia fell apart and the world of Non-Alignment was turned inside out. Yet it was bilingual students from socialist-leaning Arab states like Abu Hamza who played crucial roles as translators and intermediaries for Islamist aid workers and volunteer fighters arriving from the Middle East.

As NATO bombs fell on Libya, a right-wing Serbian nationalist party held a rally in Belgrade to show its support for its erstwhile ally. Banners like Non-Alignment and Islam can be taken down and rolled up as circumstances dictate, but people often get left behind. As Abu Hamza languishes in prison, the world seems to have moved on; just look at how much satellite television has changed. The Qatari media juggernaut is all about regional integration: its multi-ethnic staff is drawn from across most of the former Yugoslavia and broadcasts to more than sixteen million people who share the same language — or, as we are required to say so as not to offend nationalist sensibilities, three different languages that happen to be mutually intelligible.

Firoza is a staff nurse at the government hospital in Riyadh, Saudi Arabia. Firoza moved there from Malappuram in South India over ten years ago, and she loves her job; or at least, having a job in the Gulf, where she makes much more than she would at home.

At home she prays, she reads, and she watches movies. The movies come from a shop close by which stocks a good selection of titles in Malayalam, the language spoken in her native state, Kerala. The movie is about three wayward sons and their long-suffering mother, and the travails of elderly neglect. The movie startled her into thinking of her own mother, enough to make her phone home. Then she rang up her friends and recommended the movie enthusiastically.

Finally, she called the director — his cell phone number was listed on the back cover. She told him that she had enjoyed the movie very much and that its message had got her thinking. But she also had a few concerns.

Why were there no other women in the movie? Where were the neighbors, the relatives? Firoza was certain that they would have come to her rescue — or at least said something? Kodiyathur apologized. There should have been more about the social landscape in the story.

But the movies that Kodiyathur makes, that Firoza loves, are not your standard Hollywood hit or Bollywood blockbuster; they are unusual even for films produced in Kerala. Firoza is a fan of what is called Home Cinema — movies made on extremely low budgets, shot in record time, and released only on Video Compact Disk VCD. And they are sold in the tens of thousands, mostly to people like Firoza — migrants from Kerala, South India, now living in the Gulf.

Western visitors often wonder about the lives of South Asians on the Arabian Peninsula, who constitute nearly half of the population of the United Arab Emirates and more than half of the foreign population living in Saudi.

Where do they go? What do they do in their spare time? The answer, for many, is: they go home after a long day of work and consume media in their own languages. And somehow, amid the vast array of television channels, not to mention endless quantities of Internet media, there is still a place for artisanal cinema — the kind of down-to-earth, unvarnished, and unpretentious film that makes up in heart what it lacks in hype.

Kodiyathur, also an amateur thespian, had formed a drama troupe called Sarga Sangama Art Fusion a few years earlier with some friends. But at that wedding Kodiyathur happened to pay attention to the wedding videographer. Wedding videos in Kerala as elsewhere in South Asia are a kind of marital aid — what the bride and groom and their assembled families cannot choreograph in reality is produced for them in the studio, complete with jump cuts, psychedelic dissolves, theme music, and back-lit, soft-focus endings.

They are also an art form in their own right. Why not hire the wedding videographer to shoot one of his plays? I met him at a hotel in Kozhikode, the seaside city on the Malabar Coast that is the heart of the Kerala Home Cinema industry. Kozhikode is very old — when Vasco da Gama arrived in the City of Spices in , he found a trade network between Arabs and the locals that had been thriving for over five hundred years.

Like most people here, Kodiyathur is a Mappila Muslim, part of a community whose distant ancestors adopted Islam from Arab traders and which has developed a culture and a dialect that infuses Malayalam with a smattering of Arabic. We played the cassette on one, and recorded the good takes on the other — that was how I edited the film.

Then I wrote copies of it to VCD. That producer, Razak Vazhiyoram, who had business overseas, had an epiphany of his own. Why not make a movie about Keralites in the Gulf? Vazhiyoram was willing to pay for travel to Qatar to shoot, and he had the inklings of a story. He makes a triumphant return only to find his family ungrateful and unwelcoming, and he is forced to emigrate again to keep them in the style they have become accustomed to.

Back in Doha, broken, he dies alone. Parethan proved that there was a market for Malayalam home cinema in the Gulf; it proved there was a market for it, period, and spawned a clutch of imitators. Salam Kodiyathur may have been the first, but today there are about a dozen directors making Home Cinema in the Kozhikode district alone, and a successful film in the genre can sell close to a hundred thousand copies. But for many Muslims in North Kerala, going out to the movies is forbidden, anyway.

Home Cinema films focus on social issues of particular interest to the Mappila Muslim community — the travails of the common man, family, and traditions. His storylines resonate with his audience more than any mass-produced film ever could; you might call him the bard of the Mappila Muslim.

He does not bother to add subtitles to his movies, on the assumption that no one who does not understand the language would possibly be interested in them. Parethan Thirichu Varunnu , the movie that started it all, feels astonishingly polished for its low-budget roots. There are no big sets, and most of the Gulf scenes are shot indoors, but the story makes deft use of flashbacks and jumps; plot points are brought out economically; the dialogue is effective.

An early scene in which the protagonist talks to a visa agent about getting to the Gulf is shot as they walk through a paddy field. In fact, Parethan looks and feels like a Nollywood film; specifically, Osuofia in London, a blockbuster that is still to this day the highest grossing film ever made in Nigeria.

The films share themes and motifs: the idyllic village versus the big bad otherworld; home and away; the journey from impoverished but happy innocence to the difficult lives of the rich and the want-to-be rich. Both films moralize about the depredations of over-there, communicating the vicarious pleasures and dangers of travel to viewers back home — and the vicarious comfort of home to viewers abroad. Kodiyathur made his first movie for 2 lakh rupees.

In this, Malayalam Home Cinema films also resemble an artisanal film industry closer to home. Malegaon films are made largely for Malegaon, and bring home the lure of elsewhere, whereas Malayalam Home Cinema offers a distinctly different fantasy — the fantasy of home. The typical timeframe for creating a Home Cinema movie is radically compressed.

The script takes a month or so; then the cast is assembled, and the shooting is completed in under two weeks. Kodiyathur has a formula, and it works. My movies are all shot in one small village around here. I watched Olappurakkenthinu Irumbu , his latest film, the one Firoza called him up to complain about.

Kodiyathur himself plays the son who would like to be dutiful, but whose efforts to take care of his mother are undermined by his selfish wife, played by Dolly Phillip, a well-known actress from Kerala TV serials. The promotional materials for the film are dominated by a man in a saffron robe, with nerd glasses and sandalwood on his forehead. People want to come see him. The google-eyed guy with the wavy hair and the cruel mouth gets nearly as much airtime as the lead character, their two stories intersecting at the end.

Salam took me to visit a sound recording studio in Kozhikode where I met Saiju, a young sound engineer who has worked on several Home Cinemas. And Home Cinema dubbing goes very fast because everyone knows everyone else — all the actors have come here before, the music directors and musicians, too. Salam nods. And most of the actors in my movies are regulars — some of them were even members of my drama troupe from before!

That speeds up the whole process considerably. The economics of the business are interesting. The director and producer strike deals with a variety of distributors, who effectively license the right to produce the discs. The covers and stickers are printed in Kerala and shipped to the distributor, along with the film on miniDV, who then makes copies of the movies, packages them, and gets them into shops and libraries. Marketing is handled by Kodiyathur and his producer.

They print poster-sized versions of the DVD covers, which can be hung in the shops. They also take out ads in the Malayalam-language press. Kodiyathur shows me a copy of a Malayalam paper published in Saudi Arabia. They have everything there. Kodiyathur has one excellent trick up his sleeve, publicity-wise. The next morning, I spend some time with K. Mansoor, whose visiting card describes him as a timber merchant. Mansoor is dressed in a white shirt and spotless white lungi, and he almost shyly mentions that besides timber, he is interested in getting into politics.

He contacted him after the success of Parethan. The movies I found in Kozhikode were being sold for between 80 and rupees; prices are higher in the Gulf. If a film sold a hundred thousand copies, that would mean a gross income of 80 to lakhs. There is income, too, from advertising. There are tiny logos on the back covers: a visa consultant, a hotel, a brand of electronics. Similar advertisements for businesses on both sides of the Arabian Sea are interspersed in the movie itself.

Between direct sales, licensing, and advertising, everyone stands to make pretty good money. Somewhat unusually for a filmmaker whose films are massively pirated, Kodiyathur seems not especially worried about piracy. I ask him about his future plans.

Kodiyathur is a modest visionary, his canniness and humility both emblematized by his one-cell-phone customer service line. He is almost stoically matter-of-fact. But on one occasion he confided that the Arabs he met abroad always say that South Asians have no culture. It was an odd charge to hear from a parvenu country that spends millions of dollars to coax cultural products out its citizens, whose film festivals are full of European and American films.

But it was ironic, too. For there is a body of cinema about life in the Gulf, that is consumed by the majority of the population of the Gulf, that requires no special pleading or state subsidy to exist. Call it Gulfiwood: the popular culture of the Arab working class, most of whom happen to be Indian. The American participation has been variously wrongheadedly PC, expensive, beautiful, boring, or, in the case of one California-based artist named Lita Albuquerque, outright controversial.

She planned to build a hexagonal honeycomb structure at the pyramids; some detractors claimed it was the Star of David. In making each selection, the State Department would announce an open call for American curators to propose artists and projects.

For the iteration of the Biennale, the State Department took the unusual step of awarding the curatorial platform not to an individual curator but to an American museum.

The Museum brings to light the shared experiences of immigrants and ethnic groups, paying tribute to the diversity of our nation. Ayari, in the meantime, was in the audience, along with Ameri and a representative from the State Department. What was initially conceived of as a one-hour discussion ended up extending into two or more, as the very basis of the selection — the Arab American meme — inspired impassioned debate, if not outright vitriol, on the part of some of the local artists present in the room.

Nadia Ayari: The discussion at Townhouse has become mythic in our experience, a myth of an experience. Mahmoud Khaled: Frankly, we were surprised when we saw the selection. We had a pretty established idea about the American pavilion at the Cairo Biennale. They used to send over big names, people like Daniel Martinez or Paul Pfeiffer.

So this was a surprise. I mean, the Biennale is a professional international event that hopefully brings with it a new language. We expected a certain quality, especially coming from the American pavilion. Ranya Husami: When I got the invitation to curate the pavilion, I thought about whether I should walk away.

It was a difficult position to be in. I sought the advice of a lot of people. I do have an allergic reaction to the Arab American category. NA: I consider myself an Arab and an American. I grew up in Tunisia and moved to the US when I was eighteen. I know the experience of being an Arab in America is very different from being an Arab living in the Arab world.

And as identity politics—based as it is, there is validity to the category. But sure, the pigeonholing is a problem. Annabel Daou: What is an Arab American anyway? I lived in Lebanon for the first nineteen years of my life. I consider myself Lebanese, probably, before I consider myself American. A lot of people had suggested [the artist] Diana Al-Hadid, but I guess I was hoping for someone who was a little more under the radar.

AD: I put together a proposal for a project that was meant to explore the ambiguities of social and geographic, but also personal or emotional, location. The answers were sometimes complex, sometimes enigmatic, sometimes straightforward. It became a sound piece accompanying a visual work in which I charted my own locations. RH: The museum kept reminding me they wanted something that would resonate with their mission. The museum wanted several artists that would address Arab Americanness — like four!

It was ludicrous. I had something like four days to get three new artists. I approached others. Some artists said no, understandably. We went through different phases in this process. At one point the museum wanted to make a bigger show, so they asked Ranya to add artists, but they claimed it was the State Department that wanted that.

They made all sorts of demands. I withdrew at one point… I had a lot of hesitations. You felt you were always making a concession to some sort of position or agenda. RH: When I had originally called each of the artists about the project, I was honest about the situation and the difficulties involved. It was more like, Are you game?

And most were and found it an interesting paradigm. We said, collectively, what could we do with this situation? The problem became part of the work itself.

NA: Sure, we all had qualms about being grouped together in this Arab American woman thing. It had always been a one-person pavilion and suddenly you needed four women? RH: It was discussions like that one that left us with the title of the exhibition, this Orienteering concept. Rather than having a structured counter-narrative, it was about destructuring things. It allowed us to be very free and very loose. AD: I guess the conversation between us leading up to the Biennale was, like, why should we pussyfoot around this?

Or they expected we would be horrible Americans. They were ready to roll their eyes and I knew it. It started off with us explaining what Orienteering was, and then Sarah spoke. If I recall correctly, she had a major allergic reaction to the title and also had a big sensitivity to us working with the Arab American Museum in the first place. They really had it in for us.

They had it in for Ranya especially, even though, in the end, it was me and Nadia who pulled that title together. We thought that the Egyptian art scene — and this is where we got it wrong — would recognize that this was a strategic response to a set of circumstances, an attempt to create something productive out of the reality of the situation.

But then this would have required them to have looked at the work first or at least to have read the catalog essay.

The preceding question should have been, What is this museum of Arab American art? Is it an ethnographic museum? What does it mean when this museum commissions contemporary art? They found this Arab Americanism something to be celebrated rather than critically conceived. MK: The fact that it was organized by an Arab American museum raises important questions about the difference between art and culture.

There was a certain amount of realism about our work and what it represented rather than us trying to come up with some clever idea. The title came after a lot of thought about what could possibly hold us all together. Nadia and I had been joking about how the idea of mapping always seems to come up in relation to work by Arab artists. In the end you could say our work was pulled together in a map-like way. We were finding our way, finding spots that were sometimes disparate, sometimes cohesive.

It's easy. Ask the guest in room 1 to move to room 2, the guest in room 2 to move into room 3, the guest in room 3 to move into room 4, and so on. If there were only finitely many rooms, the guest in the last room would have nowhere to go, but since there are infinitely many, everybody will find a new abode.

You'll have to ask the guests to move simultaneously though, because if you ask them to move one after the other, the move might take an infinite amount of time, since infinitely many guests have to move.

Using this trick you can actually accommodate any finite number of new guests. If new guests arrive, simply ask each existing guest to move to the room whose number is plus the number of their existing room.

As an example, if there are new guests, then the guest currently in room needs to move into room. But things get better still. Suppose an infinite number of new guests arrive, forming an orderly queue outside the hotel. In this case, ask each existing guest to move into the room whose number is twice the number of their current room. So, a guest staying in room moves to room. After this manoeuvre only the even numbered rooms are occupied: rooms , , , and so on.

The odd numbered rooms are all free, so you can put your first new guest into room 1, the second new guest into room 3, the third new guest into room 5, and so on. Everybody is happy. Suppose an infinite number of coaches arrive, each carrying an infinite number of new guests. Assume, for simplicity, that the coaches are numbered 1, 2, 3, etc, and that the seats in each coach are also numbered 1, 2, 3, etc. You start by asking each existing guest to move into the room whose number is twice the number of their current room, as before.

This leaves the odd numbered rooms free again. Now tell the passenger of coach 1 with seat 1 to move into room 3, the passenger of coach 1 with seat 2 into room the passenger of coach 1 with seat 3 into room , and so on. In other words, the passenger of coach 1 with seat moves into room. Any power of is odd, so all these rooms are guaranteed to be free. What about people arriving in the second coach? In other words, the guest with seat in coach 2 moves into room.

How do you continue this for the third coach? Well, 3 and 5 are consecutive prime numbers. The next prime number along is 7, so we put the passenger of coach 3 with seat number into room. The next prime number after 7 is 11, so we put the passenger of coach 4 with seat number into the room.

Generally, you put the passenger of coach with seat number into the room , where is the prime number. Are all these rooms guaranteed to be free?



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