by Rishidev Chaudhuri

It is an oddly well-kept secret that mathematical learning is a very active process, and almost always involves a struggle with ideas. To a large extent, this is due to the nature of mathematical intuition: grasping a mathematical idea involves seeing it from multiple angles, understanding why it's true in a broader context and understanding its connections with neighboring ideas. And so, when you sit down to read through a proof or the description of an idea, you rarely do just that. Instead, digestion more often involves settling down with a pen and a piece of paper and interrogating the concept in front of you: “What is this statement saying? Can I translate it into something else? Can I find a simpler case that will help me gain insight into this general context? What about this makes it true? What would be the consequences if this statement were false? What contradictions would I encounter if I tried to disprove it? How does this concept reflect those that have gone before? How do the various assumptions used to prove this statement factor in? Are all of them necessary? Are there other ways to frame this fact that seem fundamentally different?” And so on. And this interrogation often involves taking your pencil and paper on long digressions, slow rambling explorations of ideas that help clarify the one you're trying to understand.

Similarly, proving a mathematical statement or solving a problem is an unfolding of false sallies and blind alleys, of ideas that seem to work but fail in very particular ways, of realizing that you don't understand a problem or a concept as well as you thought. And again, these are not wasted. In almost every case, if someone were to just give you a proof or a solution and you didn't either try to come up with it first or actively interrogate it once you had it (which is almost the same thing), you'd learn that the statement was true, but learn very little about why it was true or what it meant for that statement to be true. And much of the learning in a math class happens not in the lectures but afterwards, in the time spent on problem sets (and, if you had a choice between attending the lectures and doing the problem sets, you should always pick the latter).

Unfortunately, most people make it through a high school mathematical education without being taught this. This has unfortunate consequences and makes mathematical learning exceedingly vulnerable to expectation and self-belief, so that it is often seen as something you either can or can't do, and many people see the struggle as a sign of a lack of ability rather than as an intrinsic part of the learning. There are certainly children who, for whatever accident of genetics, upbringing or attentional prowess start out by being quicker at math. But this seems swamped by differences in temperament and confidence, or by the effect that initial quickness has on confidence. How you engage with the setbacks of learning seems more important than how quick you are¹.

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Which matters more, Philosophy or Ecology?

How many thoughts can dance on the head of a
radioactive pin, and for how long?
–Roshi Bob

Does Philosophy Matter

It’s high summer
wild green thrusts itself
against the bounds
of clipped lawns
Huns of sumac
amassed at a farm’s edge
surge toward logical
rows of beets and
well-reasoned
ranks of peppers
ignoring the protocol
of invitation under
the wingspread
of a hawk clueless
about the theological
knots of Aquinas
—a hawk who can’t imagine
the ontological argument,
who just wheels like
Gump’s feather rising
and falling on a whim
of wind scanning for lunch
without thinking I think,
therefore I am, being
without the anguish of Hamlet’s
big question; someone whose
knowledge is written in cells
—a bird whose understanding
is unscorched by the burning of books
unscathed by the thoughts of the dead,
the ideologies of idiots,
the desperation to say
what cannot be said
— someone snared nevertheless
in the terminal webs
of bi-pedal thinkers who
plumb and mine the shadows
in their heads

by Jim Culleny
8/5/11

by Quinn O'Neill

Eager hands caressed the small of her back, made their way over the crest of her buttocks, and temporarily cupped them like a pair of cantaloupes. Sadly, this isn’t an excerpt from a cheesy Harlequin romance, it’s airport security in 2011. The buttocks were mine and I didn’t enjoy the experience at all.

I’d read about this sort of thing happening to other people, but somehow it didn’t seem real until it happened to me. Ironically, it was the first time I’d ever felt the urge to become violent in an airport and it was inspired by airport security measures. Mostly my anger was directed at myself. I didn’t approve of what had taken place and yet I stood there and let it happen like a Victorian bride thinking of England on her wedding night.

My experience was undoubtedly mild compared to some of the more invasive gropings that have taken place at the hands of TSA employees. I was felt up at a Canadian airport prior to a domestic flight and so my “pat-down” was presumably of the standard variety, although more invasive than I’d ever experienced. Now, as I contemplate a move to the US from my current home in Montreal, my biggest fears relating to travel aren’t of terrorism or plane crashes, but of inevitable violations of my privacy at airport security gates.

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by Misha Lepetic

Anyone who can be replaced by a machine deserves to be.
~Dennis Gunton

A noteworthy popular intellectual trend in recent years might be called “How Everything Works, In Spite of Itself.” Roughly, the trajectory can be described by James Gleick’s Chaos, which appeared in 1988; M. Mitchell Waldrop’s Complexity in 1992; and Steven Johnson’s Emergence, debuting in 2001. On the even more popular side, one can glance at Gladwell’s Tipping Point and Surowiecki’s Wisdom of Crowds, although more serious readers ought to be referred to Stuart Kauffman’s The Origins of Order. What unites these works – or rather, the trend that these books represent – is a perennial desire to see our world defined in terms of simple rules that, once intuited, reveal themselves as pervasive and universal. What are the consequences of this point of view, as we attempt to better understand societies and urbanism?

In a very real sense, this desire for heuristic happiness can be drawn straight back to the Enlightenment, if not even earlier. One can imagine Kepler experiencing equal parts delight and relief when his (only three, and very simple) laws of planetary motion persisted in their universality; or Newton’s, when he was able to derive these laws from the inverse square law of gravity. Whew! Kind of a shame to have to leave those Platonic solids behind, but there is something to be said for simplicity.

The principles derived by scientists working in the fields of chaos and complexity offer similar mercies. The desired outcome is more or less as follows: create a game of as few rules as possible, that in turn creates outcomes that are intricate, beautiful and pleasingly lifelike. Computer-assisted simulations such as Tim Conway’s Game of Life and Mitchell Resnick’s StarLogo have catalyzed the demonstration of how lifelike patterns evolve from simple rules. These simulations not only provide legitimate insights into real world processes, but also speak to us in a titillating fashion, inviting us to observe and name the resulting shapes generated by generations of cellular automata interacting with one another.

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by Colin Marshall

None of us really think about it anymore, especially if we grew up in Crocodile Dundee’s pop-cultural heyday, but… how weird is Australia? This land mass, just large enough to qualify for continent status, hanging out by itself underneath Asia? Starkly arid and desolate, for the most part, between its eastern and western edges? Ten thousand miles from England, yet full (in a sense) of Brits? Without a doubt, Australia makes the short list of countries that can freak you out if you think hard enough about them. It doesn’t sit at the top — stiff competition from Turkmenistan, Paraguay, and North Korea — but which filmmakers bother to actively engage with it? The Mad Max pictures grew more grotesque as they went along, but in a speculatively flamboyant way that didn’t really engage the actual weirdness. Baz Luhrmann seems to hold a grasp on some of his homeland’s deep askewness, but his movies tend to convert it into mere eccentricity.

But if we’re keeping it to high international profiles, we’ve got to talk about Nicolas Roeg. Despite suffering the apparent disadvantage of growing up in London and not, say, Alice Springs, he nevertheless managed, in his solo directorial debut Walkabout, to deliver an Australia never seen before — or, for that matter, since. More specifically, he delivers an Australian outback, and a drama in it, never seen before or since, dropping a sixteen-year-old schoolgirl and her six-year-old brother right into the thick of it. Cinephiles, or even enthusiasts of modern myth, know the rest of the story: the uniformed, near-albinistically white siblings — credited only as “Girl” and “White Boy” — just about succumb to dehydration when they come across a young Aboriginal tribesman — “Black Boy” — who ultimately leads them back to their civilization, though only after a series of fatal failures to communicate.

That plot opens up a minefield of potential cinematic embarrassments, including but not limited to telling the story with a standard “survival” movie or, worse, telling it with a standard “noble savage” movie. The Girl and the White Boy owe their lives to the Black Boy, true, but Roeg doesn’t convey it with a broadside against Western civilization, colonial arrogance, excessive whiteness, or what have you, even though those seem like tacks the film has to take. I’d dragged my feet on seeing it for the first time because of my fear that Roeg, who had become one of my favorite filmmakers immediately after I saw The Man Who Fell to Earth, would succumb to obvious moralistic clichés. How foolish of me; watching any given Roeg film should assure you that, even when he uses time-worn components of plot or character — and he usually does — he fits them together with a box of tools all of his own cockeyed invention.

How do we know Walkabout won’t put us through a typical plodding spectacle of uptight urbanites reluctantly chomping down on sticks, leaves, and bugs at the urging of cautious but giving sun-browned natives brimming with simple wisdom from generations of close communion with Mother Earth? The signs come early and often, starting with the way the brother and sister wind up stranded so far into the outback in the first place. We see their buttoned-down father express squinting, frowny displeasure at his job, home, and family, and it feels like the brim of a very old hat indeed — until he drives the kids out into the country, tells them to set up a picnic, and then pulls out his revolver and opens fire on them. They run; he keeps missing, perhaps deliberately. By the time he’s set fire to the car and done himself in, the Girl and the White Boy have nowhere to go but away, as far and as fast as they can manage.

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by Michael Blim

Call them aftershocks: the sovereign debt crises and the return to zero growth and recession in developed countries, along with the current world stock market “correction.” Add in the wry spectacle of the flight to U.S. bonds as doubt that America will ever pay off its debts, and you have the rather sorry description of a world economy still reeling from the earthquake of 2008.

Different sets of players do their bits. Economists and the world financial elite keep trying to treat each crisis discreetly, finding a cause here, a remedy there, and hoping that the rest of the world economy will keep vamping as they fix each one. Financial market traders, selling on good news, and buying on bad, or the other way around if it suits them, put words to the numbers. “The markets are worried about Libya,” ‘the market is pricing in the impact of unemployment rates on overall demand,” and so on. The “market” in this turn of phrase is like an open-source mind transforming words into numbers, which of course makes one wonder how those chatty traders have mind enough to change the numbers back into words again. Finally, nightly news reports put the two tracks, words and numbers, back together, and each of us tries to understand what just happened, and with more preoccupation what might happen tomorrow.

Each of the estates in their way is trying to handle the aftershocks of the crisis that began in the fall of 2008. The economists and financial elite are trying to end them, or contain their damage. The market players are betting on scenarios that will make them money. And the news media are trying to write the story as others tell it to them.

Yet the estates have neither fixed “the problem,” nor assuaged the fear that the 2008 economic earthquake was the global North’s “big one,” and that the world as we know it has undergone a profound and fundamental change. The great tectonic plates upon which the world economy stands have shifted its center south and east to the “emerging economies.” And the collision between the emerging and developed economies, the cause of the quake, has left the latter so deeply damaged that the failure of successive rescue efforts threatens the short-term viability of the world economy itself.

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“THE PRESIDENT IS HUMAN. HE GETS SICK”

— White House Press Secretary Responding to Reporters' Questions in The New York Times, January 9, 1992

A thousand tiny dots of light:
I diminish the noise.

Duped smirk on aging face,
eyes eclipsed by spectacles,

The President,
previously recorded,

vomits,
moving his lips slowly.

Watching me watching him
he holds my stare

kindly, gently.
Reading my thoughts,

George Herbert Walker Bush
C
O
L
L
A
P
S
E
S.

By Rafiq Kathwari / rafiqkathwari.com / @brownpundit

The classically understood flow of information in present day organisms flows from DNA to RNA to protein. However, RNA can both store heritable information and carry out biochemical activities, and is thus capable of the functions principally served by DNA and protein. The RNA world hypothesis proposes that life based on RNA predated the current tripartite arrangement. However, the RNA world is not exclusively confined to the distant past. Recent studies of non-coding RNAs show that the roles of RNA have continued to evolve and expand alongside DNA and protein.

It’s become increasingly clear that genomes contain quite a bit of DNA which does not code for protein, but is nevertheless transcribed into RNA, yielding an abundance of RNA transcripts– and that this tendency gets more pronounced in more complex organisms. In humans, approximately 10- to 20-fold more genomic sequence is transcribed to non-coding RNA than to protein-coding RNA. One interesting non-coding RNA category is the micro-RNA (miRNAs), a class of short RNAs which can dock onto and affect other RNA transcripts. A very recent essay in Cell magazine proposes that these miRNAs form a sort of exchange currency in the cell, in that longer RNA species (including non-coding forms) regulate one another’s behavior by controlling levels of the miRNAs. Increased abundance in any “target” RNA will remove miRNAs from circulation, with consequences for other targeted RNAs.

One exciting feature of this hypothesis is the central role posited for mi-RNAs– very broadly affecting both coding and noncoding RNAs while remaining essentially intrinsic to the RNA economy. (the miRNA life cycle in present day life depends on proteins at several crucial steps, but target recognition itself is thought to be protein independent.) This is of particular interest since mi-RNAs may be relics of the RNA world. mi-RNAs have been indentified in all living realms and in viruses, and their recognition sequences are remarkably conserved, suggesting they derive from ancient common ancestors (or from co-evolving groups). Along with transfer RNAs and ribosomal RNAs, mi-RNAs may be a fundamental legacy of early terrestrial life.

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by Fred Zackel

Next week, on August 28, 2011, the National Mall in Washington D.C. will be unveiling the Martin Luther King Jr. Memorial. This day will also mark the 48th Anniversary of the famous “I Have a Dream” speech.

America has been unimaginably lucky. Some of our Presidents were great writers, and some were great speakers. Dr. Martin Luther King, Junior’s writings, plus his speeches, stand with the best from our Presidents.

Martin Luther King, Jr. Check out his Letter from the Birmingham Jail. He wrote it on whatever paper he could find in jail. Read it aloud. Feel the rhythms on your tongue and hear his voice. See how wide-ranging his intellect was. The depth of his arguments. See how persuasive he was. And the breadth of his empathy for humanity.

Put yourself in jail, in his place, and imagine the best you could do under those same situations. He began writing his famous letter on strips of paper slipped to him in jail. More amazingly, he even apologized for its length: “I can assure you that it would have been much shorter if I had been writing it from a comfortable desk, but what else can one do when he is alone in a narrow jail cell, other than write long letters, think long thoughts and pray long prayers?”

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Justin E. H. Smith

[This is a short excerpt from my current book project, Language and Animals, about which you will be hearing more soon. –JEHS]

Some decades after M. F. K. Fisher, following Jean-Anthelme Brillat-Savarin, implored us to 'consider the oyster', David Foster Wallace asked us do the very same thing with a lobster. It was not at his request that I first did so, and neither was he the first to make the request. In the Essay on Classification of 1851, the Swiss zoologist Louis Agassiz also asked us to consider the lobster, but what he really wanted was something rather more radical: he wanted us to consider the lobster alone, to consider the world as if the lobster had no relatives, no exoskeletal cousins next to which we might be able to make some sort of sense of this odd creature:

[S]uppose, for instance, that our Lobster (Homarus americanus) were the only representative of that extraordinarily diversified type [the 'Articulata'], –how should we introduce that species of animal into our systems? Simply as a genus with one species by the side of all the other classes with their orders, families, etc., or as a family containing only one genus with one species, or as a class with one order and one genus, or as a class with one family and one genus? And should we acknowledge, by the side of Vertebrata, Mollusca, and Radiata, another type, Articulata, on account of the existence of that one Lobster, or would it be natural to call it by a single name, simply as a species, in contradistinction to all other animals? (Agassiz, Essay on Classification, London, 1859, 5).

If you think the lobster is peculiar, just imagine how peculiar, how utterly non-pareil, it would be if it were the only articulate (i.e., exoskeletal) animal in existence? How could we even begin to say what it is if there were nothing else like it?

We might ask something more radical still: Ecce homo. Consider the human. Next, consider the human alone, without any animal relatives, endoskeletal or otherwise. What would such a creature be like? Standing in relation to nothing that is like it, and at the same time not it, how would we know what sort of being we were beholding?

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By Haider Shahbaz

In 1917, Marcel Duchamp contributed Fountain, a urinal, to the exhibit of the Society of Independent Artists. The Society was ‘independent’ – but not that much. They rejected the urinal, insisting it was not art. Duchamp defended the piece by Mr. Mutt (his alter ego) in the following words: “Mr Mutt made the fountain with his own hands or not has no importance. He CHOSE it. He took an article of life, placed it so that its useful significance disappeared under the new title and point of view – created a new thought for that object.”

Gertrude Stein is similarly a characteristically modern writer in that she is producing art from everyday life. She is choosing everyday objects and then creating thoughts for them. Her work, ‘Tender Buttons’, is divided into three parts: Objects, Food, Rooms. The aim is to describe everyday objects and spaces that Stein is familiar with and lives in. These are domestic objects: A cup and saucer, a long dress, sugar, milk and rooms come together to be assembled in Stein’s mind and to leave it as written art. These domestic objects are the essential components of her everyday experience. However Stein does not simply borrow from experiences and people and try to reproduce them on paper in their traditional way of description. Stein is aiming for the pure self, the completely subjective rendition of the commonplace object as it exists inside her. In order to do this, she is breaking down life into its components of experience, into sights and sounds and resemblances and repetitions. For example, she describes a petticoat in a single line, extremely personally, as such: “A light white, a disgrace, an ink spot, a rosy charm.” Like Walker says, commenting on the Cezanne and Picasso stills hanging on Stein’s walls in Paris, “…this text is far from a literal transcription of the immediate sense-data that enter the ‘stream of consciousness.’ Like the Cezanne and Picasso still lifes of apples that hung on the walls of Stein’s atelier, it is a deliberate artistic model, not a naïve reproduction of the ‘real’.”(134, Gertrude Stein, Jayne L. Walker. UMP, Amherst, 1984). Thus, the petticoat becomes subjective, it becomes Stein’s interior, Stein’s ‘self’. ‘Tender Buttons’ is about this particular rendition of the commonplace into an artistic subjective model. For Stein, art is the rendition of everyday life into highly individualized descriptions of that life.

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by Tolu Ogunlesi, in The Huffington Post (photo from Wikipedia):

A few weeks ago, at the height of the News of the World scandal, I appeared on the BBC's World Have Your Say to talk about how – or if – unfolding events in the UK were shaping the way Nigerians regarded their colonial overlords. Not long after that I contributed to a Guardian article on a similar theme.

Apart from a few newspaper editorials and columns, I didn't get the impression the average Nigerian had much of an opinion regarding the phone-hacking. (It's hard to say how much this may have had to do with the fact that Nigeria doesn't have a voicemail culture)

On the day David Cameron visited Lagos, while his citizens were demanding his urgent return home to deal with the crisis, Lagosians seemed more concerned about the traffic his presence in town was causing. “Why do they block the road [because] a dignitary is in town? Do they block roads in London when [Nigerian President Jonathan] visits?” one Facebook status queried.

The ongoing riots (like the parliamentary expenses scandal) are another matter though. Nigerians – like the rest of the world – have opinions about that. Some of it is self-deprecating (Blackberry messages joking that Nigerians-in-London are turning down an evacuation offer from their government; preferring a temporarily-burning London to their perpetually dysfunctional homeland); the rest drawing on something close to Schadenfreude (reports of the Gaddafi regime insisting that Mr. Cameron has “lost his legitimacy and must go”; and of Iranian President Mahmoud Ahmadinejad describing Britain's treatment of the rioters as “savage”).

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morning. please don't
slide again. nothing truly
happened yet. shocking.
its shocking, the rate
so much nothing happens at. now through
the window, two pigeons flash
the full wing-work; the span of what
god gave them; circling, they switch
positions mid-air, my new favourite
band hits its drum and flute
solo : a bubbling like cold
water pipes a shudder of happiness
through me. candle, don't you
burn. clock, don't you tick, i want
another. . .

i've got it
bad. sour & sweet
tooth, great greedy
gut, eyeballs too big
for my life; want that big life
like a well-directed movie; string
of scenes. each more tender
& shining than the last; lets have a brother
& sister race through yellow grass to the brown
river; lets have a hero–brave-
chested, brooding, his truck
veering off the lackluster
path. lets have paris, moscow, romantic
montana, a pardoned
criminal blinking dust
in bald new light, and vastly different
moons preserved
in our windows every night. (some
weighty in syrup like canned
peaches, some slim
little wafer of paper. . .)

… oh between dreams, passions–everything's
ivory. bland & soaped & thudding
& all the happening happened already. so
lets have the crescendo
round this way again; i'm ready as always
to be lifted. let's live the life
made for us by the giants. they'll swing us
over the shoulder–
we'll get carried away.