by Rishidev Chaudhuri

Asymptotic reasoning is ubiquitous in mathematics and the natural sciences, representing both a general approach to problems as well as a collection of techniques. It is one way of answering the question, “Which features of the world are relevant for our understanding?” Often, the behavior of a system gets simpler as it gets larger: only some of the features that are relevant for understanding a small system are necessary for understanding a very large one. The averaging out of fluctuations in the long-term is perhaps the most obvious example of this. Asymptotic analysis attempts to describe the behavior of an object (function, physical system, algorithm) as some quantity gets very large or very small. It is thus fundamentally the study of particular sorts of approximations, albeit approximations that can be made as precise as one wants, and a guide to which features of an object can safely be ignored.

To start with a simple example, look at what happens to the square of a number and to its cube as the number gets bigger and bigger. Both the square and the cube race off to infinity, but one does so faster than the other. 1³ and 1² are the same; 2³ is twice as big as 2²; 3³ is thrice as big as 3² and so on. For any number N, N³ is N times as big as N², and as N gets really big the function N² is dwarfed by N³. So to see how the behavior of a function could become simpler as it approaches infinity, look at the behavior of

N³+N²

If we are thinking asymptotically, we would say that this function behaves like N³: for any degree of approximation we choose the contribution of N² will be irrelevant for large enough N. Here “large enough” depends on the degree of approximation we want. If we decide that irrelevant means “contributes less than 1% to the value of the function”, then N² is irrelevant once we reach N=100; if instead we decide that it means less than 0.01%, then we must wait till N=10,000, and so on. The crucial point here is that we can satisfy any desired degree of approximation, no matter how stringent.

Read more »

by Michael Blim

For America’s liberals, these are soul-trying times. The romance with Barack Obama is over. They have discovered, as one pundit in the Washington Post put it, there he is an Eisenhower Republican. In fairness to Obama, he never promised to be anything else, as perceptive commentators before the election noted. Yet, as the stuff of liberal wish-fulfillment, Obama could not be resisted: a self-identified African-American, a Harvard lawyer trained by some of the best minds liberalism still possessed, and a product of Hyde Park Chicago liberal patronage with some church-related street organizing thrown in, Obama embodied the dream of a new multicultural liberalism that would overcome social tensions by the force of his example. And liberalism would become the majority creed once more.

The economic crisis of the last three years has put paid to the wish, and the Obama administration shows every indication of putting an end to American liberalism, the one hundred-year plus political movement that sought a state dedicated to human improvement, equal opportunity, and the regulation of capitalism.

American liberalism arose at the turn of the 20^th Century when the middle class produced by our nation’s massive industrial great leap forward began to make money and to thirst for the power to remake American society in its own image. It strived to make an America that was educated, efficient, and fair. Convinced that social problems could be solved through scientific study and pragmatic policy-making that prescribed specific remedies, American liberalism sought to regulate business abuses, restore competition in markets, and to build, albeit incrementally, a welfare state. It sought the upper hand politically by eschewing social democracy, thus rejecting any real need for power sharing with labor and the working class. Ensnared by its own narcissistic self-regard, it imagined itself the guardian of the general interest; every other group or class was just a special interest.

Read more »

by Tom Jacobs

I stick a patch on my shoulder and I think of Einstein’s brain. It’s in a vat, the brain, that is. A brain in a vat. The body is long gone, but the brain remains. A controlled-release of nicotine enters my bloodstream and I also think of Dean Moriarty, the father I never found. I think of Einstein’s brain and of old Dean Moriarty, each barreling down toward the vanishing point of I-80, one beside the other, pursuing the ever-receding sunset.

Einstein’s brain travelled across country in a jar. His brain sat shotgun (well, in the trunk, actually, but it’s nicer to think of his brain sitting shotgun). Then there is Kerouac/Sal Paradise with Cassady/Moriarty, careening down I-80, the interstate that slices right through the US all the way out to San Francisco. And then back again, culminating at the? ass end of I-80, at the George Washington Bridge, the view of which was once afforded to me out the bedroom window of one of my first apartments in the city. I would look at the bridge and imagine the road beyond, and the bald head of the sun sinking into the earth, and think of “all that raw land that rolls in one unbelievable huge bulge over to the West Coast, and all that road going, all the people dreaming in the immensity of it.” My mind travels Westward into the night like Einstein’s be-vatted brain, but my body remains rooted in my apartment on 181st street. And really, my mind, too, is trapped in the envelope of my body, such as it is, that stares out the window imagining all the people dreaming.

Dickhead that I am, I don’t know if this is important or silly.

Read more »

by Sue Hubbard

Can art regenerate a community? Can building an architect designed gallery in a socially deprived area change its fortunes? Everyone wants a Bilbao Guggenheim. Almost overnight Bilbao was transformed from a culturally moribund commercial centre in an unfashionable corner of Spain’s Basque region to a must-see destination. After its opening in 1997 hundreds of thousands of tourists began to pour into the city just to visit Frank Ghery’s new building. Then came the knock- on effects: the new hotels, the expanding of the airport, the upgrading of facilities and extra employment and, hey-presto, Bilbao was changed forever.

It was a far sighted decision by the local burghers even though there was, at the time, much opposition. But the result is one of the most extraordinary and beautiful modern buildings you will see anywhere. Tate St. Ives, above Porthmeor beach, has also been a success. But here the project was built on an historic legacy, for St. Ives has, due to its especial clarity of light, had a thriving artistic community since the 19^th century. The tiny fishing village, a popular middle-class holiday destination, already attracted people who might be expected to visit a gallery.

But the opening of Turner Contemporary this week, in the rundown seaside resort of Margate, most famous in recent years as the childhood home of the artist Tracey Emin, has a bigger challenge on its hands.

Read more »

by Misha Lepetic

“The architect is primary… is the real cornerstone of any culture, of any society.”
Frank Lloyd Wright, 1958

What is the responsibility of the architect or designer within the contemporary context of urbanism? If we’re to begin with the preceding quote, taken from an interview with an astonishingly anti-urbanist Frank Lloyd Wright, it is an unconditional, Roarkian supremacy. If these sentiments had prevailed, of course, Le Corbusier would have ensured that today’s Paris would look very different.

Wright, his avatar Howard Roark, and Le Corbusier exemplify extreme, or perhaps extremely self-aware, instances of one of the great struggles in architecture: the uncomfortable fact that the world is full of people, and that architects are primarily educated in the total discourse of buildings. However, the increasing urbanization of the human race relegates the efficacy of architecting individual buildings as, at best, proofs-of-concept and as, at worst, vanity projects. And many such buildings placed in proximity to one another do not add up to a coherent urban solution.

This is not to say that architects and planners have not frequently thought on a comprehensive, urban scale. Christopher Wren’s plans for London following the Great Fire, mostly unrealized, and Georges-Eugène Haussmann’s revision of Paris, mostly enacted, show us otherwise. But these plans revolved did not concern themselves with the citizenry as such. In the case of Wren, the self-interest of the merchants and landowners in fact prevented the plan’s execution. And despite the net benefits, the social consequences of Haussmann’s plan for Parisian identity are still hotly contested: the destruction of over 20,000 houses and buildings was not just about making room for the wide boulevards, but also led to the displacement of untold thousands of the poor to the suburbs of Paris, while speculators grew wealthy from flipping the new apartments to the rapidly rising bourgeoisie (see Balzac’s The Rise and Fall of César Birotteau for a particularly wonderful account of pre-Haussmannian property speculation and bankruptcy).

Read more »

by Quinn O'Neill

As an atheist, I sometimes get asked if I’m afraid of what'll happen when I die. Naturally, I'm not afraid of going to Hell or any other supernatural place and I'm not afraid of being dead, but admittedly, there is something that scares me. I'm afraid that I could someday exist in (or as) another body.

My position is not so much that we can exist in more than one body but that we don’t know that we can’t, or even how probable it would be. To be clear, I'm not suggesting any kind of dualism or that we might be reincarnated with our current attributes and personality traits. Consistent with a naturalistic view of the world, I accept that consciousness and perception of self are generated by the brain, so when the brain dies there's nothing left – no thoughts, no personality, and no spirit. The chance of an identical physical copy of my brain arising again is very small, so perhaps I needn't worry.

But it’s here that the worry creeps in. Is an identical physical copy of my brain what it would take for me to experience being alive again? In order to establish that subjective consciousness is restricted to a single body, we'd have to understand how it works and we really don't.

From a naturalistic perspective, the brain is what makes us who we are. Presumably, if we could create perfect physical copies of ourselves right down to the wiring of our brains and the neural connections that store our memories, we could effectively recreate ourselves. But there’s a problem, because even if I could perfectly replicate myself and make a thousand copies, I would perceive only one of these as “self”. In other words, whatever makes me uniquely me is not something that I could even in theory share with an identical physical copy. The only thing that could distinguish me from such copies is position. Only the location of my perspective would be unique.

This is a bit of a conundrum. To an objective observer encountering me and one of my copies, there’d be two identical copies of me, each thinking itself the original. From my point of view, however, there’d be a big difference between the copies – I’d be one of them and the other would be someone else.

Read more »

Editor's Note: Akeel Bilgrami has kindly given us permission to publish here the text of a lecture that he delivered at The New School and which is also included in the Chomsky Notebook collection of writings.

by Akeel Bilgrami

Though there is much radical –and often unpleasant– disagreement on the fundamental questions around academic freedom, these disagreements tend to be between people who seldom find themselves speaking to each other on an occasion such as this or even, in general, speaking to the same audience. On this subject, as in so much else in the political arena these days, one finds oneself speaking only to those with whom one is measurably agreed, at least on the fundamental issues. As proponents of academic freedom, we all recognize who the opponents of academic freedom are but we seldom find ourselves conversing with them in academic conferences. We only tend to speak to them or at them in heated political debates when a controversy arises, as for instance at Columbia University over the promotion of faculty in Middle Eastern studies, or in those states where the very idea of a curricular commitment to modern evolutionary biology is viewed with hostility. I will not be considering such controversial cases of overt political influence on the academy. This is not because they are not important. The threats they pose are very real, when they occur, and the need for resistance to these threats is as urgent as anything in the academy. But they raise no interesting intellectual issues at a fundamental level over which anyone here is likely to be disagreed. If there is disagreement in a forum of the kind at which we are presently gathered, it is likely to be on relatively marginal questions, such as, for instance, whether academic freedom is a special case of the more basic constitutional right to free speech or whether instead it is a special form of freedom tied to the specific mission of universities.

What might a philosopher contribute to these more marginal questions? In this brief lecture, I would like to make a fuss about a standard argument for a conception of academic freedom which we all seem to subscribe to when it is coarsely described but which, when we describe it more finely, and look at the arguments more closely, is quite implausible and leads directly to thoroughly confused ideas about displaying ‘balance’ in our classrooms and our pedagogy quite generally. I will then use some of the points and distinctions I make in this critique to explore whether there is scope for locating more subtle and interesting (and actually more pervasive) kinds of threat to academic freedom than the obviously controversial ones that I mentioned above which all of us here, I assume, find an abomination, and which, as I said, raise no interesting issues for any of us, even if they ring urgent alarms. At the very end, I will venture to advocate imbalance of a very specific kind in the ‘extra-mural’ domain, when it is neither inquiry nor classroom curriculum that is at stake but the effort to engage the intellectual and political culture at large.

Read more »

by Justin E. H. Smith

Going through a difficult separation? Feeling lonely? Well I've got just the book for you. It's called After Kinship, and it's by Janet Carsten. She says that the focus on the affine pair as the basic unit of anthropological theory was really only a projection of mid-twentieth-century Euro-American ideology into an ethnographic field where bonds of kinship are by and large much more fluid than Lévy-Bruhl et al. were able to understand. I don't know why they keep this kind of stuff away from the 'self help' section of the bookstore. It cheers me right up.

I went to the Lawrenceville Petco and inquired about getting a cat to keep me company. “I'd really like a cat,” I said to the teen-aged employee, “but I'm worried about hygiene.”
“Cats are only as filthy as their owners,” she said, rehearsing some bit of wisdom she did not seem fully to comprehend.
“Well, suppose I'm filthy,” I replied.
“Oh. Maybe you should get, like, a hermit crab?”

I received a message from a former student. “Hey,” it started out, “I heard you're retired now. That's too bad! You were a great teacher!” For the record, I'm 38, and I'm on a temporary research sabbatical. And I am not a 'teacher'.

Facebook now has sidebar ads that are supposed to speak to the particular interests and desires of the social-networking site's individual users. Recently I've been getting an ad that beckons: “Hey Philosopher! Find your market!”

Now this is why I can't have a cat: Just today I discovered an uneaten basket of raspberries, purchased in January, at the bottom of my desk drawer. It was sitting on top of the copy of Being and Time that I've been carrying around with me for complicated reasons I need not go into here. Little remained of the raspberries, as they had been gradually replaced by thousands upon thousands of fruit flies. If I had a cat, I would have joked to her: Well look at that, countless generations of them have come and gone since January, and they still haven't outgrown their Heidegger phase.

Read more »

by Maeve E. Adams

“I think therefore I’m Liberal”; “I think therefore I’m Dangerous”; “I think therefore I’m Single”; “I think therefore I’m Vegetarian”; and my personal favorite “I think therefore I’m Ham.” These phrases—emblazoned on t-shirts, billboards and, in the case of the latter, the headers of blogs—offer up perverse reinventions of Renee Descartes’ oft-cited (and oft-misunderstood) theory of human consciousness and existence, articulated in his Meditations on First Philosophy (1641).

These modern slogans do not, however, make much sense if we try to see them as a logical extension of Cartesian philosophy. Descartes’ theory is not strictly partisan, for starters. His excursus is, in part, an attempt to make sense of what makes all (or at least most) humans human—what makes them more than “rocks and turnips” (44) or “blueberries and doorknobs” (78), as Jonathan Kramnick might say, with characteristically wry humor, if he were writing about Descartes.

Kramnick’s new book, Actions and Objects: from Hobbes to Richardson (Stanford, 2010), from which I have borrowed these phrases, is not strictly about Cartesian philosophy. Kramnick’s delightfully written and keenly insightful new book is, however, about a series of related philosophical conundrums concerning human consciousness that preoccupied a wide array of writers in the late-seventeenth and eighteenth centuries. These writers run the whole gamut, from philosophers like Thomas Hobbes, John Locke and David Hume to the poet known as Rochester and novelists Eliza Haywood and Samuel Richardson. In theorizing conceptions of consciousness, as Kramnick discusses, these writers debated attendant theories of existence, motivation, feeling and action that still preoccupy philosophers of mind today. In throwing a wide net, Kramnick’s book reminds us that these seemingly strictly philosophical questions were engaged by writers who came at them through a myriad of genres of writing.

Read more »

by Hartosh Singh Bal

Like so many others in India, I grew up on tales from the Mahabharata and the Ramayana and the books of Enid Blyton. Well produced children’s books with an Indian context were rare, and now looking back I’m not sure as children we needed such a context. Most children’s books are lived out in world of fantasy, where more things are possible than we ever allow ourselves to imagine as an adult. The Mahabharata and the Ramayana, related either as oral tales or in abridged and sanitized versions, fulfilled such a role admirably and even today I find the flying broomsticks, magic spells and talking animals of Harry Potter somewhat tame compared to all that I took for granted as a child.

In this world Enid Blyton fitted in admirably, I’d say Enid Blyton was a better children’s writer for those reading her in India than in England. For us the world she described was a land of fantasy as unreal and magical as Narnia or the Shires. Meals of tongue sandwich and lemonade at the bottom of the garden had a magical quality, now rather sadly and blandly dispelled after tasting tongue as an adult. In this magical world I now learn there were undertones of racism, but these were lost on us, a golliwog was just another inhabitant with no existence for us as a caricature. In the same way it was only as an adult that I registered that the Narnia books were an allegory, the Lion as a stand in for Christ was thankfully lost on us in India.

Read more »

By Syed Haider Shahbaz

“On the day they were going to kill him, Santiago Nasar got up at five-thirty in the morning to wait for the boat the bishop was coming on.” Gabriel Garcia Marques, Chronicle of a Death Foretold.

“Before we had religion and other nonsense. Now for everyone there should be someone to whom one can speak frankly, for all the valour that one could have one becomes very alone.” Hemingway, For Whom the Bell Tolls.

Our lives are but the chronicles of a death foretold. Day to day, from birth, there is only one certainty: we will die. And so, like Marquez’s narrative, begins our journey; from the first sentence we know the end – the certainty of our death. Yet, the narrative is gripping. Life is compelling – in its own many small and mysterious ways. And what, after all, is compelling? How does Marquez make us read when he has whispered the end into our ears, casually, like the news of our death?

There are some things in life that they do not talk about in the classroom. One of them is holes. Not just any holes – bodily holes: assholes, vaginas, noses, sweat pores, mouths, ears, penises. Because of my friends, I became obsessed with holes. They liked peering in their assholes. At least, Martin did. He tried to write a poem about his asshole. The poem, well enough, made him fall in love with his asshole. Its darkness, its depth, its wrinkles and curves, the small pieces of shit stuck all over it. How manly, he said, he thought. Whenever he came out to drink whiskey in his ill-fitted plaid shirts, ginger hair, armed with an accent and a childish smile, he talked of his asshole. We all knew his asshole intimately and adored it as intensely as him. It became his muse. And we all peered into our assholes. Deep down, and smiled, privately.

Read more »

by Mara Jebsen

Part one, with photos by Syreeta Mcfadden (thebellepoque.tumblr.com)

1. I like the sound of poetisa!

2. Louise Bourgeois drove a screwdriver

down through my skull at the Guggenheim.

3. I am so proud to be une poete, the sun

makes a raging silver shape

out of a car, flips it

onto my retinas, shouts it there

incandescent, a good knife.

Read more »

Translated from the Urdu by new 3QD writer Rafiq Kathwari:

WE WILL SEE

That promised day
Written into tablets of pre eternity

It’s inevitable
We, too, will see

Colossal mountains of tyranny
Floating like wisps of cotton

The earth shaking and rattling
Beneath our stomping feet

Swords of lightning clashing
Over the heads of despots

Idols flung out
From sacred monuments

Crowns tossed into the air
Thrones demolished

And we the pure and the rejected
Seated on cushions.

Only the name of God will remain
Who is both absent and present

The witness, the witnessed
A cry will rend the sky

“I am Truth”
Which is you as well as I

And the beloved of God will reign
You I We Us

Faiz Ahmed Faiz
San Francisco, 1979

Rafiq Kathwari is a rebel poet and social entrepreneur who divides his time between his adopted home New York and his native Kashmir, where he empowers artisans. Poke him on Facebook.

by Robert P. Baird

In a recent review of The Pale King, David Foster Wallace’s posthumously published “novel,” Garth Risk Hallberg writes:

In the end, Wallace’s body of work amounts to an extended philosophical experiment. Can “morally passionate, passionately moral” fiction help free us from the prisons we make? To judge solely by his suicide, the experiment would seem to have failed.

Of course Hallberg doesn’t end there; he goes on to say that “watching [Wallace] loosed one more time upon the fields of language, we’re apt to feel the way he felt at the end of his celebrated essay on Federer at Wimbledon: called to attention, called out of ourselves.” This is fine stuff, and credible: Hallberg is a serious and intelligent critic, and what he says about the fragments assembled into The Pale King fits the expectations established by Wallace’s earlier writing.

Still, it’s the earlier sentences that interest me more. In identifying a philosophical, even therapeutic aspiration in Wallace’s work, Hallberg is cashing out Wallace’s famous assertion that “fiction’s about what it is to be a fucking human being.” Hallberg draws a line from Wallace’s art through his life to his death, a line we can trace with almost syllogistic precision: if Wallace’s life was the test of his art, and if his suicide marked a failure of his life, then so, too, must his death stand as a capital judgment on his art.

I admire this formula, even as I find myself troubled by it. I admire it because it lays out in especially stark terms a dilemma whose presence has imposed itself, often in unresolved and unsettling ways, on most of the reviews and reminiscences written in the runup to and aftermath of the publication of The Pale King. Hallberg’s great service is to name the question that all of us face in the wake of Wallace’s suicide: namely, how should his death affect the way we read his books?

Read more »

by Fred Zackel

Once at twilight I was Zorro. My neighbors called my mom. She called me into the house and explained how a ten year old with a black mask and a Daisy air rifle prowling through backyards at twilight in our neighborhood might be seen as something different in an adult’s eyes.

The astonishing amount of mythological stuff just goes to show the ancients had a ton of time to ruminate on odd, perhaps deviant, human behavior. These peoples are curious and imaginative and undogmatic, even without the precise knowledge of what they were describing, and they dreamed up stories to tell adults when the kids were in the room and listening.

We always lie in front of the kids. To hear some children's animal shows, we tried giving the dodo bird mouth-to-mouth resuscitation … and it didn't work. No. We extincted them. Some for food. And most for fun. Because we like hearing the discharge from our guns as we slaughtered them. Because we felt powerful killing from a distance. But mostly for the fun.

I saw a lovely silly wise-ass joke earlier this week. “Vegetarian is an old Indian word for lousy hunter.”

Remember hearing Aesop’s tale about the Fox and the Grapes? The tale goes over our heads these days, but twenty-six centuries ago, folks who heard it understood the gnawing hunger, despair, and denial of imminent death by starvation. The ancients didn’t have the massive amounts of cheap food that we have now.

Think again of the desperation within Aesop’s Fables. Foxes do not eat grapes unless no other food is available. The hunger of the fox for the grapes is impervious to reason. How loudly is your stomach growling? Sour grapes? Naw, that’s not what it was. In fact, the fox was too weak to jump high enough to reach a cluster of grapes on a trellis. As the fox walks away, regardless of what it says, starvation rules its future.

The fox walks off to die.

Aesop is noir, baby. Noir.

Read more »

by George Wilkinson

In the broadest sense, sleep is defined as a period of inactivity and loss of awareness. Most humans sleep 7–8 h per night, and if we are deprived of sleep, our cognitive performance, metabolism and health suffer. Sleep clearly contributes to several important physiological functions. Hypotheses for sleep benefits include overall rest and healing; cellular metabolism or replenishment; and brain-specific functions such as synaptic adjustments important for memory. Specifically, scientists believe our brains require sleep to process what we experienced during the day. However, the specific relationship between sleep hygiene and memory function remains controversial.

In recent years, seminal insights into the control and genetics of sleep have come from studies in flies, fish, and worms. Genetic screens have identified mutations that affect sleep across species, pointing to an evolutionarily conserved regulation of sleep. Moreover, a number of laboratories have identified sleep-dependent changes in gene expression, including in genes involved in learning and memory consolidation. A recent article in the open-access journal PLoS One explores the possible connection between memory and sleep in the regulation of one such gene, brain-type Fatty acid binding protein 7 (Fabp7), in sleep and long-term memory formation in flies.

Read more »