by Jonathan Kujawa

Mathematicians have a soft spot in their hearts for mathematical trifles. These beguiling little puzzles are more amusing than important, and also often devilishly hard. These are the sorts of math problems professional mathematicians are embarrassed to admit they spend time thinking about (but would be the first to tell you if they solved it!). Call them mathematical guilty pleasures.

Fermat's Last Theorem is such a trifle. Those old enough to remember might recall seeing it in the news twenty or so years ago. It's the theorem which says that for any natural number n greater than three, you can't find integers a, b, and c which satisfy the equation:

But, to be honest, at the end of the day people don't seriously care that it is impossible to find a, b, and c which solve, for example:

But what fun would life be if you're always serious? Let's be unserious for a moment. Fermat's Last Theorem is tantalizing. It is easy to find a, b, and c which are solutions when the n is equal to two. For example, 3, 4, and 5 work. These solutions are called Pythagorean Triples because they exactly give the three sides to a right triangle and the equation becomes the famous Pythagorean Theorem [1]. There are infinitely many Pythagorean Triples, so shouldn't there also be infinitely many solutions when n is three, four, or five? What makes two so special?

The first person to ask the question was Fermat in 1637. He wrote a note in his copy of Diophantus's Arithmetica that:

It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers. I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

You would have to have a heart of stone to not be tempted to try a few examples after reading that.

Fermat never wrote down his proof and in all likelihood he was mistaken. Indeed, it took 300+ years for math to develop enough high powered tools to tackle his simple little challenge. It wasn't until the mid 1990s that Andrew Wiles was able to affirmatively prove Fermat's “Theorem”. And while there was a great deal of excitement about Wiles's work, the real benefit Fermat's trifle was all the high powered tools mathematicians developed while wrestling with it. They are now invaluable in number theory, cryptography, and elsewhere [2].

Let me now tell you about another enticing mathematical morsel which is still unsolved: the Square Peg Problem (SPP). The history is a bit murky, but it is generally credited to Otto Toeplitz in 1911. The SPP is the conjecture that if you draw a curve on a sheet of paper without picking up your pencil and which begins and ends at the same place, then you can find four points on the curve which form the corners of a square. Such a square is called an inscribed square.

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by Ahmed Humayun

Islam has a new caliph, at least if the Iraq-based militant organization that calls itself the Islamic State is to be believed.* In what was touted to be his first public appearance, self-proclaimed caliph Abu Bakr al-Baghdadi spoke about the necessity for implementing Sharia and using war to defeat the enemies of God, the obligation incumbent upon all Muslims to choose a leader, and issued a call for Muslims to join the jihad under his tutelage. While Bin Laden was fond of holding forth wearing commando jackets in rugged terrain, Baghdadi wears resplendent black robes and delivers his incitement to war in the form of a Friday sermon from a grand and stately pulpit in a mosque in the northern Iraqi city of Mosul.

The media-savvy proclamation of Abu Bakr al-Bagdadi is not a response to popular grassroots clamor in the Muslim world. Nor should we overstate the success of the Islamic State – twenty thousand fighters, at the most, will not suffice to restore a transnational global caliphate. Polls conducted in different Muslim majority societies certainly indicate strong support for Islam in public life—and in particular, for the role of Islamic law in delivering justice and organizing society. Yet there is no indication that Muslims yearn for the return of the caliphate, an institution that was already moribund at the dawn of the 20^th century before its abolition by Turkey in 1924.

As with any fledgling movement, militants assert their ideological claims to be natural and inevitable, rooted in history and justified by theology. The truth, however, is that there is little consensus among Muslims on the specific role that Islam should play in contemporary state and society. While this ambivalence has limited the moral and political resonance of militant proclamations, it has also created an opportunity to exploit the general ideological appeal of Islam. This is why militant ideology matters.

Yet we will have to look beyond religious debates in order to understand the growing strength of militant groups such as the Islamic State across large swathes of Muslim majority societies. A key factor has been the growing weakness of the political status quo and the perception of its illegitimacy for various reasons that might include failing authoritarianism, the corruption of ruling elites and the dysfunctional governance they impose, and the force of kinship bonds that disdain the boundaries of modern nationalisms.

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In the beginning was the word —John 1:1

Entreaty

send me a poem that hunkers on haunches
watching for the day to begin, that waits
for the right word to come with the sun
during the last hours of the night-watch
when all are asleep except the watcher
and there is still rustling in the underbrush,
the wordless sounds of something moving in the dark,
in the raw underpinning of the day,
in the interval between now and now,
at the birth of light, at the end of night
send me a poem that does not lie
that does not yield, but does not smite
.

by Jim Culleny
7/7/14

by Yohan J. John

Attitudes toward science in the public sphere occupy an interesting spectrum. At one extreme there are the cheerleaders — those who seem to think that science is the disembodied spirit of progress itself, and will usher us into a brave new world of technological transcendence, in which we will merge with machines and upload our minds to the cloud. At the other extreme there is decidedly less exuberance. Science in its destructive avatar is often called scientism, and is seen as a hegemonic threat to religions and to the humanities, an imperial colonizer of the mind itself.

The successes of science give the impression that it has no limitations, either in outer space or inner space. But this attitude attributes to science somewhat magical powers. The discourse surrounding science might benefit from an awareness that its successes are closely tied to its limitations. The relationship between scientists and the rest of society needs mutual understanding and constructive criticism, rather than a volatile mix of reverence, fear, and mistrust. The veil of the temple of knowledge must be torn in two — or at least lifted up from time-to-time.

To this end, it might be illuminating to see scientific ideas as tools forged in workshops, rather than spells divined by wizards in ivory towers. The tool metaphor also reminds us that science is not merely an outgrowth of western philosophy — it is also the result of the painstaking work of “miners, midwives and low mechanicks” whose names rarely feature in the annals of Great Men. [1]

So what sort of toolbox is science? I'd like to argue that it's a set of lenses. These lenses allow us to magnify and clarify our perceptions of natural phenomena, setting the stage for deeper understanding. The lenses of science reveal the symmetries of nature, so we might call them the Symmetry Spectacles. The Symmetry Spectacles are normally worn by mathematicians and theoretical physicists, but I think that even laypeople interested in science might find that the world looks quite interesting when viewed through them.

So what is symmetry? Most people have an intuitive sense of what symmetry is. Symmetry connotes evenness, or balanced sameness. An asymmetrical object is skewed, off-balance, and uneven. It is easy to grasp that a scalene triangle is asymmetrical, whereas an isosceles triangle is symmetrical. To many people an equilateral triangle seems even more symmetrical than an isosceles triangle. The goal of a formal approach is to make explicit our intuitions about symmetry. Mathematicians and theoretical physicists define symmetry as follows:

Symmetry is immunity to a possible change.

How can we apply this notion of symmetry to the scalene, isosceles and equilateral triangles?

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by Debra Morris

Imagine flipping through a copy of the academic journal Sociology and Social Research. One article in particular—”Our Schizoid Culture”—catches your eye. The author is well-known: a professor of sociology, soon-to-be editor-in-chief of the American Sociological Review, and, in something of a blow to “two cultures” thinking, future poetry editor for the Humanist magazine. Certainly you could quibble with a number of statements, and some of them seem so wide-ranging as to be inarguable, but in general you share the author's dismay at the “great deal of irrational, contradictory behavior” within contemporary American culture. You agree: “When an individual exhibits similar symptoms, the psychiatrist calls him neurotic, or if he lacks ‘insight' into his difficulties, psychotic.” This is what accounts for, and in your mind fully justifies, the article's tone: honest, emphatic, no-nonsense, but also deeply attuned to ordinary pain and suffering—quite unlike the academic caviling to which you're accustomed. Yes, someone needs to say it: in many domains of life our culture is so confused, so riven, as to be quite, well, unwell. Really, all politics aside, it would be hard to argue with any of this:

We praise competition, but practice merger and monopoly…. We praise business organization but condemn and prevent labor organization…. We give heavier and more certain sentences to bank robbers than to bank wreckers. We boast of business ethics but we give power and prestige to business [disruptors]…. Everybody is equal before the law, except … women, immigrants, poor people.… We ridicule politicians in general but honor all officeholders in particular and most of us would like to be elected to something ourselves. We think of voting as the basis of democracy, but … seldom find more than fifty per cent of eligible voters actually registering their ‘will.'… Democracy is one of our most cherished ideals, but we speak of upper and lower classes, ‘look down on' many useful occupations, trace our genealogies…. We believe in the brotherhood of man, but we are full of racial, religious, economic, and numerous other prejudices and invidious distinctions. We value equality, but tolerate greater inequality of wealth and income than has ever existed in any other society…. We drape nude statues and suppress noble books…. We try to foster participative recreation, but most of it is passive, much of it vicious, and almost all of it flagrantly commercialized…. This is the age of science, but there is more belief in miracles, spirits, occultism, and providences than one would think possible…. Our scientific system produces a specialism that gives great prestige and great technical skill, but not always great wisdom…. The very triumphs of science produce an irrational, magic-minded faith in science….

Realize, now, that the article was written in 1935. The author was Read Bain, professor of sociology at Miami University in Ohio. As a founding editor of the American Sociological Review, he would become embroiled in early disputes between the “scientists” and “humanists” in his own discipline. He was thus involved in theorizing—and, in that spontaneous way of so many early- to mid-20^th-century American academics—practicing in the mode of a “public intellectual,” that figure who today, apparently, is nowhere to be found.[i] In terms of Bain's analysis as synopsized above, and even more to the point, in terms of the social critique it so earnestly propounds, what struck me when first reading it was how contemporary it sounded and how apt its reproaches were.

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by Lisa Lieberman

As a break from the seriously depressing topics I’ve been writing about lately, and in honor of Bastille Day, I offer this tribute to French gangster films.

First off, you need the fedora. The gangster accessory de rigueur, it was already iconic by the time Paul Muni popularized the look in Scarface (1932). Al Capone, Clyde Barrow, John Dillinger, Machine Gun Kelly were all photographed wearing one. Baby Face Nelson was astute enough to recognize the souvenir value of his trademark fedora, bartering it for food and a place to hide after a botched bank job.

By the time Bogey donned one to play ‘Bugs' Fenner alongside Edward G. Robinson in Bullets or Ballots (1936), it was a bit passé. Robinson, you will note, sports a derby, signaling his authority over his fedora-wearing lackeys. (That's Bogey on the right, with the gun.)

Leave it to the French to reinvent the gangster look and give it panache. In Pépé le Moko (1937), Jean Gabin wears the hat, but he adds a gallic touch: a silk scarf. Gabin's character has style—something his American counterparts lacked—but more importantly, he's got heart. Love will be his undoing, and we're not talking about a fling with some cheap, two-timing dame. We're talking epic love, the kind of love that inspires poetry and songs. Ah, l'amour.

Director Julien Duvivier gives us a tragic hero in the classical tradition who is the victim of fate. Pépé is wanted in France for various crimes. He's been hiding out in the Casbah of Algiers for two years, sheltered by the local inhabitants who will take any opportunity to defy the colonial authorities. He may be king of the Algerian underworld, but exile has turned bitter for Pépé, whose longing for Paris recalls Ovid's lament in the Tristia: “Say that I died when I lost my native land.” Here we see him looking mournfully out over the rooftops of the Casbah to the sea, toward France and freedom, both of which elude him.

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HISTORY’S MOST PERSECUTED MINORITY IS INSENSITIVE TO THE ASPIRATIONS OF WORLD’S MOST DISPOSSESSED TRIBE

by Rafiq Kathwari

My sister-in-law and I sat in the back seat of the Volkswagen as my older brother drove

in desperate rain through red lights to Maimonides. “Kicking,” she said, putting my

hand over her round belly. Shy, I lowered my gaze to her flip-flops on the car floor. She

gave birth to a son in Brooklyn eight years to the day JFK was shot in Dallas. A new

alien in New York, I babysat my cute nephew in a stark rental on Park Avenue in

Yorkville, with a view of Gimbels, now a long extinct department store. His dad rode the

IRT to work on Pine Street; his mom was a salesperson in Herald Square at Korvettes

another extinct store. The boy and I both discovered Big Bird on a Zenith console, my

first TV exposure at age 22. Our Park Avenue closets were stocked with handmade

Numdah rugs Grandfather had shipped from our ancestral home, Kashmir, hoping we’d

become rich fast carpeting America from sea to shining sea. I watched him dunk hoops

in Perturbia, his long hair swishing to Metallica, “Soldier boy, made of clay.” He hunted

jackrabbits at the family farm upstate, where he signed up at the local NRA, his dad’s

rifle on the boy’s shoulder. He scaled a peak one summer in Kashmir, the knotty dispute

forever a passionate subject at the dining table, sweetened often by ice cream after the

dishes were washed, and reruns of All In The Family wrapped up Prime Time. He

praised Allah at the Islamic Center Sunday School on California Road to which I once

gave a brand name vacuum cleaner that failed to suck up the holier-than-thou Talibs.

Allah alone knows what seeds they sowed in his receptive mind for he made his little

sister weep, shaming her for wearing leotards to her ballet class. She loved ballet classes,

and she always looked up to her big brother. He persuaded his dad to stop serving liquor

to guests, and he made his parents proud calling out the Call to Prayer at an annual apple

picking at the farm, an odd religious intrusion that on a crisp Fall day made me feel sad,

because I like my cider with a splash of vodka.

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by Charlie Huenemann

Denying the existence of the material world never goes down well. No matter how clever and compelling the arguments, most of us want to insist that matter exists – and as our insistence becomes more vehement, we start pounding tables, as if that will impress our interlocutors.

Time and again over the years, I have tried selling idealism to students through George Berkeley's arguments. “You know, all you ever experience are perspectives of the world, right? So what idea can you possibly have of a world existing in itself, independently of any perspective? None, of course. So why not dispense with it, and just believe in perspectives that are coordinated with one another?” No dice. They are unmoved.

And I have also tried the more Greco-Germanic route. “You know, the more we strive to understand the physical world around us, the more we end up expressing the world in mathematical structures and relations. So why not think of the world as a set of mathematical structures, and forget about the alleged 'matter' that is supposed to instantiate those structures?” Again, blank stares (thought perhaps it is because I used the word “instantiate”).

In any case, most of us feel a deep need to assert the reality of the material world. Indeed, some of us sneer at the idea of trying to go without it. “Good luck crossing the street,” some may advise a would-be idealist. “The cars might not share your philosophy.” But I wonder – what is behind this deep need? What does the idea of “matter” do for us to earn such dedication on our part?

The more I have thought about it, the more I am drawn to an “obstaclean” theory of matter. To put the theory as simply as possible: matter is ultimately stuff that gets in our way. Material objects are obstacles, pure and simple. We might want this or that, and so we embark upon some plan, but then – wham! Something gets in our way. We didn't plan for that, and we certainly didn't want it. It's there independently, on its own. That's what matter does. That's what matter is. It is the sh*t that gets in our way.

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by D.E. Wittkower, Evan Selinger and Lucinda Rush

Some time has passed since Nicholas Kristof published his controversial Op-Ed “Professors, We Need You!“, and the time is ripe for us to approach the issue afresh. After briefly revisiting the controversy, we’ll offer some thoughts about how to promote public engagement by changing academic cultures and incentives.

When Kristof’s Op-Ed came out back in February, it provoked widespread discussion about whether academics—particularly in the social sciences and humanities—are socially relevant. Much of the heat stemmed from Kristof’s biting central claim: “Some of the smartest thinkers on problems at home and around the world are university professors, but most of them just don’t matter in today’s great debates.”

Rebuttals to Kristof came swiftly and appeared in different venues.

The New York Times itself published critical responses that highlighted the existence of socially relevant academic contributions in lots of places, including “use inspired research” and “blogs, TED talks, congressional and expert-witness testimony, support of social movements, advice to foundations, consultation with museums, summer programs for schoolteachers and work with prisoners.”

This crucial point that a wider net needs to be cast for defining ‘engagement’ was expressed elsewhere, too. Undeniably, counter-examples abound, including in high profile fora. “Kristof need only open the pages of the Nation, the New York Review of Books, the London Review of Books, the Boston Review, The American Conservative, Dissent, The American Prospect.” Indeed, a recent article in The Chronicle of Higher Education suggests that there’s actually robust public academic engagement occurring. “Spend a few hours reading news and opinion pieces, surfing interesting blogs, or dipping into conference-based hashtags on Twitter, and you will find academic voices speaking out—everywhere.”

Shortly after Kristof’s piece ran, the hashtag #EngagedAcademics gained traction on Twitter. Its creator Chuck Pearson lamented that when Kristof wrote about academics he was referring to “research one schools,” and perpetuating an argument predicated upon undue, elitist assumptions: “It still assumes that academics are those pipe-smoking, office-dwelling, masses-disdaining figures from another place. In other words—as the New York Times is so prone to do, when talking about higher education—it assumes that regional universities and state colleges don’t exist. It assumes that teaching-centered liberal arts colleges don’t exist. It assumes that most church-affiliated schools don’t exist. Good heavens, don’t even speak of the community colleges. And it assumes that everyone who could possibly serve as a public intellectual is a FULLPROF or is on the path to FULLPROF status. Non-tenure-track instructors? Visiting professors? God forbid, adjuncts?”

Finally, beyond the questions over whether Kristof was missing all the action happening right in front of him, some worried that asking academics to be more relevant might very well be a tacit invitation to requesting they avoid rocking the boat with controversial assertions: “. . . if ‘relevance’ means becoming mouthpieces of our new ruling class, then Kristof can keep it.”

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by Charlie Huenemann

In 1671, in some letters exchanged with the French mathematician Pierre de Carcavy, Leibniz mentioned his plans to create a calculating machine. Apparently, he had been inspired by a pedometer, probably thinking that if machines could count, they could then calculate. Within a couple of years, he hired a craftsman build a wooden prototype of his machine, and he packed it along in a trip to London in 1673.

He presented the machine to the Royal Society, but his presentation failed. The machine was supposed to not only add and subtract, but multiply, divide, and even extract square and cube roots. But it just didn't work, though everyone was faintly impressed by the attempt. Well, almost everyone. Robert Hooke made close examination of the machine and asked detailed questions of its inventor. Afterward he set about both disparaging Leibniz's attempt to his friends and making a copy of the machine himself and showing it off.

Leibniz went back home, improved his design, and hired a better craftsman. Then, after two decades of tinkering, adjustments, and debugging, he finally had something to show: the Stepped Reckoner.

A little over a year ago, Stephen Wolfram visited the Leibniz Archive in Hanover and saw the Stepped Reckoner for himself, as well as Leibniz's cramped and ingenious pages of calculations and designs. Wolfram notes that the most interesting “idea before its time” element in the device is Leibniz's appreciation for binary arithmetic. Really, the central idea of modern computing is right there, enshrined in beautifully sculpted gears, with a crank on the side.

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Again

My father, at the kitchen table,
in a rare expression of mystery,
said, I think life is a cycle
But he was not a mystical man to me,
nose to the grindstone he ground
day after day, pressed
by incessant work, bound
to contingencies
like Sisyphus to his stone
linearly, but uphill
in his black boots and socks
his blue shirt and pants
cinched with a black belt,
sometimes a fedora,
often a smile through
cigarette-clinched lips,
he trucked on (unbeknownst to me,
and despite his flat trajectory)
mulling over vicissitudes,
contemplating repetitions,
weighing the properties of circles,
as does any common philosopher
hoping to unravel the hiddeness
under blood and bone,
coming to the conclusion
that to begin again
was the only thing that made sense
to him
.

by Jim Culleny
7/1/14

by Mathangi Krishnamurthy

Last week I ran into a faintly familiar face and looked at him quizzically as he said, “You asked a good question yesterday. At the talk.” I thanked him, we muttered names; I don't think I heard his name, and I don't think he caught mine. We exchanged a sentence in a bakery of some repute and then went our opposite ways. I felt suitably flattered; the feeling lasted for an hour.

One could argue that the politics of this encounter lie in prolonging its affect without ever completing its narrative. After all, they tell me that the beauty of the fleeting encounter lies in its imminent disappearance. All narratives as we well know, are already rigged, and the novel, as we are told again and again, has been long dead. (Don't believe any of it). This man that I will never see again, this woman who I will not call. Futures, possibilities, rumours, closures, openings, continuations, none need ever bother except to open oneself to these delicious punctuations. But still, aren't some chance encounters also the beginning of long fantasies? And hence I think about the politics of the chance encounter. A glance here, a smile there, a blink-and-you-miss-it moment participating in no pre-determined destiny and yet one that has the possibility of solidifying into fate (never ill-fatedness).

In her beautiful book Cruel Optimism, Lauren Berlant calls this a “situation”, “a state of things in which something that will perhaps matter is unfolding amidst the usual activity of life.” In Berlant's words, this is “a state of animated and animating suspension that forces itself on consciousness, a sense of the emergence of something in the present that may become an event.” I therefore understand vaguely that one shared stop in a present continuous time-frame adds to the je ne sais quoi of daily life, staving the disenchantments of modernity, holding at bay my certain knowledge that nothing will happen today. After all, how would we live life if we were to actually believe that nothing will happen today? So the chance encounter punctuates such hope, delivering small bits of evidence that guarantee the possibility of that event, the one event that will deliver us all.

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by Thomas Rodham Wells

The contemporary animal rights movement owes a great intellectual debt to Peter Singer's pathbreaking book ‘Animal Liberation' (1975). In that book Singer made a break with the dominant moral argument for treating animals well, the Kantian line that mistreating animals is a bad – inhumane – thing for humans to do. In its place, Singer advanced a utilitarian case against harming animals, such as by using them for food or experiments, in terms of respecting their right to have their suffering counted equally with that of humans.

Singer's book has had an enormous influence, directly and indirectly, on how many people see the moral status of animals. I include myself among them. But nevertheless I am not sure it is a good book. Despite its rhetorical effectiveness and despite going through multiple revised editions, Singer's official argument is far from compelling. And this is a problem for the animal rights movement. For if Singer's utilitarian account is only a kind of sentimentalism in academic drag then the intellectual respectability it has granted the animal rights movement is a sham. Singer's utilitarianism can't do the job it is supposed to do – it can neither justify the normative conclusions of the book nor meet the minimalist standard of internal coherence. Furthermore, the domination of Singer's flawed argument in the intellectual self-understanding of the animal rights movement may be crowding out other more relevant ethical accounts, most obviously those that directly engage with sentimentalism rather than being embarrassed by it.

In this essay I will focus on the utilitarian case for vegetarianism. Singer argues for the moral recognition of the suffering of animals in the livestock industry and exhorts his readers to end it by not eating meat. But both the form and content of his argument are open to strong challenges.

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by Carl Pierer

It is a good situation for European students in Scotland. We get to study at excellent universities with outstanding research. We do not pay any tuition fees. The institutions are well funded. As part of the EU, access and living is easy. What more could we wish for?

The campaign against Independence for Scotland usually raises worries that this, our, privileged situation might be put at risk by a yes vote. Leaving the United Kingdom might mean that universities in Scotland will lose access to UK-wide research funds. English, Welsh and Northern Irish students would have the status of European students, probably making it illegal for the universities in Scotland to charge them the fees they charge now. Supporters of Independence retort that they have plans for how to cope with these problems. With both sides presenting disagreeing “evidence” for their cause, it is difficult to estimate which hypothetical promise is more likely to be kept. The argument offering the most economic route wins the battle for plausibility.

However, facts about higher education in an independent Scotland would require Scotland to be independent. The issues at hand, the impossibility of a transnational research fund to name just one, cannot be decided upfront. Therefore, this article is not in the business of arguing for either case. Rather, it sketches a framework for a less economised higher education in an independent Scotland.

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