by Yohan J. John

Probability theory is a relative newcomer in the history of ideas. It was only in the 19th century, two centuries after Isaac Newton ushered in the scientific revolution, that thinkers began to systematize the laws of chance. In just a few generations, the language of probability has seeped into popular discourse — a feat that older branches of mathematics, such as calculus, have not quite managed. We encounter numbers that express probabilities all the time. Here are a few examples:

• “With a 6-sided die, the probability of rolling a 5 is 1 in 6, or around 16.7%. “
• “The chance of rain tomorrow is 60%.”
• “The chance of Bernie Sanders winning the 2016 US Presidential Election is 15%.”

What exactly do these numbers — 16.7%, 60%, 15% — mean? Does the fact that we use the words 'chance' or 'probability' for all three suggest that dice, rainfall, and elections have something in common? And how can we assess the accuracy and usefulness of such numbers?

Mathematicians, scientists and philosophers agree on the basic rules governing probability, but there is still no consensus on what probability is. As it turns out, there are several different interpretations of probability, each rooted in a different way of looking at the world.

Before we get to the interpretations of probability, let us review the basic mathematical rules that any interpretation must conform to. Let's imagine we have a set of possible events: S = {A, B, C,…Z}. The set S is called a possibility space or a reference class. The probability of event 'A' is symbolized by P(A), and its value must be between 0 and 1. A value of 0 means the event cannot occur, and a value of 1 means the event definitely occurs. For the set of possible events, P(S) = 1. This means that some event from the set S will occur, and nothing outside the set can occur. In other words, the probability that something will occur must be 100%. Finally, for any two events 'A' and 'B' that cannot happen simultaneously, the probability that either one or the other will occur is just the sum of the two individual probabilities, so P(A or B) = P(A) + P(B).

The Stanford Encyclopedia of Philosophy lists 6 major interpretations of probability, but for our purposes it makes sense to look at the three that are most common and easily understood. These are

• Classical probability — a way to quantify “balanced ignorance”
• Frequentist probability — a way to quantify observations of a random process
• Subjective probability — a way to quantify subjective degree of belief

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Ataturk

Turkish Embassy, Karachi

16 August, 1957

Mrs. Mariam Jan, “Katrina”

Pindi Point, Murree, West Pakistan

Dear Madam, I have received your letter.

Thank you very much for good wishes

expressed therein. I have pleasure

enclosing herewith a photograph

of Mustafa Kemal Ataturk,

as requested. Yours faithfully

for Ambassador of Turkey

Ercument Yavuzalp, First Secretary.

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by Mara Naselli

One evening in early March, my husband and I ventured into the French Quarter in New Orleans. We were merely tourists, exploring that old settlement at the elbow of the Mississippi River, its strange contradictions of high and low, youth and age, Old World and New World—shop windows of silver sets and sequined masks alongside alligator heads and beads. We had walked through Jackson Square in the hush of a thick fog in the early morning. We had seen a subdued bronze plaque noting a slave market, though there is nothing to remind passers by of the men and women dressed in blue suits and calico and made to dance. That evening after nightfall, we turned onto Bourbon Street. Bar after bar, live bands blared classic rock covers. Young men strolled with their oversized hurricane drinks. A wispy silhouette of a woman danced in a window. On one balcony, young women danced topless and slung themselves over the ironwork while a gaggle of men ogled. A certain currency of bodies persists. Bourbon Street assaults the senses, alcohol numbs the effects. After a block of this abuse we turned the corner. Diminutive creole cottages leaned into the street with wooden shutters and prim geraniums. Down the way we noticed a bookshop. The light was on.

The tiny shop smelled of old paper and dust. It was crammed with books stacked on the floor, on the counter, sideways on shelves. After some time, my husband emerged with a 1950 special edition of Thomas de Quincey’s Confessions of an English Opium-Eater. The boards were decorated with a green marble haze and the interior was printed in two-color ink. It had lithographs and an ex libris plate from a certain Bertha Ernestine Bloodworth (who, I later discovered, finished a dissertation on Florida place-names in 1959). I had read the Confessions before and dismissed them. Virginia Woolf’s mother admired De Quincey, but I could not muster any affection for him. He was too damn full of himself, I thought, and reading him felt like tolerating someone who takes too much pleasure in the sound of his own voice. But now this green volume and its mysterious provenance, fine printing, strange angular illustrations—it was too interesting to pass up. To find it after wandering through the kaleidoscopic delirium a couple blocks away seemed providential. The bookseller mistook my enthusiasm. He handed me How to Grow Your Own Opium and offered a deal for the two. I declined the how-to and handed him $12.50. We returned to our foul-smelling hotel, made tea to preoccupy our senses, and I gave Mr. De Quincey a second chance.

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by Mara Jebsen

“This world is white no longer, and it will never be white again.”

—James Baldwin, “Stranger in the Village”

Two years ago this summer, Miley Cyrus 'twerked' against a backdrop of several bent-over black women, Trayvon Martin’s death created a nightmare vision of hoodies and skittles, and Kanye West marketed Confederate flag t-shirts. A horror movie called “Purge” 'treated' American audiences to a dystopic image of a future in which the white residents of gated communities sadistically torment a homeless black man as part of a sanctioned new order. It was a strange time in the history of American violence and cool, one that we are currently living out, and trying to make sense of.

Ten years before what I call in my head “The Summer of Bad Moves,” Rick Moody published “Against Cool,” an essay which attempts the impossible: to trace the history of coolness in this country. The essay knows it can't do that, but wants to, nonetheless, because:

“. . .in an absence of clearly delineated American ethics, in a period of cultural relativism, in a political environment in which both American parties have amplified their rhetoric to such a degree that the other side is beneath contempt, in which religion seems no longer able to rationally or effectively deploy its messages except through moral intimidation or force, in which families are no longer the ethical bulwarks they felt themselves to be in the past, in such a millennial instant cool has become the system of ethics in America.”

He is talking about 2003. Cool has changed, clearly, but the cultural climate seems familiar.

Moody's strategy for tracking cool in this essay is odd, but impressive. He moves fluidly between moments in music and casual language, in literature and eventually commerce–roughly dating the beginning of coolness with Miles Davis' “Birth of the Cool”–until he has constructed a sort of narrative in which cool (sometimes the word, sometimes the spirit) gets passed around from jazz musicians to beat poets to punks and hippies to Kool-Aid and other products.

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by Carl Pierer

Fig. 1

Braids are fairly simple to picture. A few interleaved strands of string, say, gives a complex and mesmerising object. They are aesthetically appealing, as their widespread use as ornament testifies. While most will be familiar with the standard braid used for braiding hair, there is basically no limit to complexity and beauty. Yet, braids are more than merely nice, artistic adornments for clothes and jewellery. The more and deeper you delve into braids and their complex interconnections, the more fascinating they become. Trying to look at them with a mathematical eye opens up pathways and connections to many deep and beautiful fields of pure mathematics.

Studied as mathematical objects, braids need to be defined rigorously. However, for present purposes it is enough to specify what we intuitively have in mind when thinking about braids. (Fig. 1) may well serve as an example. A braid consists of a certain number of strands n, say, together with a specification of how and where these strands cross each other. Furthermore, these strands (if they are not crossing) run parallel and we may adopt the convention that they are running from top to bottom. To avoid ambiguity, we require further that there are no two crossings at the same horizontal level. It is clear that for the braid to have any crossings at all, it must have at least two strands. If a braid does not have any crossings, it is called the trivial braid.

Fig. 2

Braids also have a close connection to (mathematical) knots. Mathematical knots are simply everyday knots where the loose ends have been joined together. If you take an overhand (or trefoil) knot (Fig. 2) and join the loose ends, you have a mathematical knot. Imagine an extension cords where one end has been plugged into the other. One important feature is that there is no way of undoing this mathematical knot by pulling or stretching or any other deformation that does not break the connection. If you reconsider our

Fig. 3

initial braid (Fig. 1), imagine that the ends have been joined up as in (Fig. 3). As all loose ends are now joined up, we can consider (Fig. 3) as a mathematical knot. Indeed, every mathematical knot can be expressed as a braid. Unfortunately, this is not a one to one correspondence. So, two different braids may end up as the same

Fig. 4

knot. Or one and the same braid may give you two different knots. One problem is that there is no particular reason to join up ends of the braid as we did in (Fig. 3). If we have an even number of strands, we can equally well join up the endings that are next to each other (as in Fig. 4), which would give a very different beast altogether. Indeed, this is not a knot anymore but a so-called link, because it consists of 4 different components. A knot is a one component link. However, this connection between braids and knots is not the main concern here.

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by Shadab Zeest Hashmi

The sun burnishes the walls every day for just over three quarters of an hour out of the fourteen I spend at my shop; the mannequin assumes a buttery glow then, her organza scarf liquefies in the golden light. The CD skips at mi amour every time but this hiccup is also golden and otherworldly. The sun lifts my surroundings, the merchandise, the credit card machine, the shelves, during this portion of time in a grandiose gesture; it’s our secret— the book I’ve been writing for years has a life somewhere and this is a furtive daily reminder. I’d rather not have customers at a moment so personal in a public place; I’m at a shopping mall, selling jewelry and shawls.

I’ve named my business “Moriama”— a variant of “Moraima” (or Mariam), the last empress of Al Andalus; my manuscript is a series of poems set in Al Andalus. No one knows or cares about this but I’m advised by friends to do away with the “World Gem Bazaar” part of the sign— too “middle-eastern” in 2003. The spectrum of emotions in response to the pressure to hide my identity for fear of hostility will permeate the poems describing the atmosphere of the inquisition as my book on Al Andalus progresses. Across from me is a mattress store. As I polish and arrange African garnets and checkerboard-cut citrines, nomad jewelry from Afghanistan and London Blue Topaz pendants, someone rolls and rolls dough next door, breathing in cinnamon powder and sugar I imagine, or mops spill after spill of coffee. We’re connected to each other by repetition, as if we were phrases of the same poem.

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by Mathangi Krishnamurthy

The bell clangs loudly and I shuffle back into class trying to avoid the boys running in at dangerous speeds. I find my desk and sidle into place. I almost bump into Solomon. Solomon never studies, so the teachers always ask him to sit by me. All he does, though, is copy my notes. The afternoon sun sends bright rays into class and I inch away from him to find a cool spot on the tiny bench. The room smells of heat and dust, and I see particles floating. I feel temporarily dizzy.

I often daydream through classes. Things come easily to me, and I both know and doubt this. I am deeply suspicious that this will someday be found out, and exposed as fraud. So I am most always simultaneously attentive, and anxious at school. But daydreams come easily, because school is boring.

Solomon is gazing out of the window in his sleepy manner. Some day, I want to be Solomon, who is so cool, so uncaring, and hardly ever worried about the teachers. Mostly, it just seems to be that the world passes him by, and that he is on some other mission; something dangerous, and adult-like. I often see him hanging out by the school stile with the older boys. They all must know something about him that I don't, because there he looks happy, instead of sullen, and quiet. Solomon is really, really, dark and his white shirt often soiled. My blue pinafore, in contrast, is always immaculately pressed, its pleats like the lines of a ruler. Solomon's knees are scruffier than mine, and mine a little, only because I fell down the colony hillock last week. He never says anything in class, so I am not even sure what his voice sounds like. I imagine it to be deep. I often turn my eyes away when he looks at me. It's easy, because we sit side by side, parallel to each other, like the eyes of a cow. The only time he looks towards me is English class, where I cover my notes with my left arm, even as I can feel his eyes boring into my flesh.

Mrs. D walks in, brisk and monochromatic. She is wearing a beige sari today, and I stare up into her almost double chin. She is so tall and so pale. Her severe light brown hair is capped close to her head, but falls at her nape into a wispy ponytail. Her mouth is set in a straight line, but two front teeth escape and soften the severity. Her name is Roda, or at least, that is how I think it is spelled. I found it by accident, when Mrs.R called out to her in the teachers' room. She is pretty when she smiles. She might smile any moment, and she always smiles at me. The noise drowns as she commands us to settle down and hand in our homework.

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by Hari Balasubramanian

A selection of facts, research and personal impressions.

In February this year, I traveled to the small town of Angangueo in Central Mexico. A 4-hour bus trip from Mexico City, Angangueo is in a rural part of the state of Michoacan, in the mountainous trans-volcanic belt. Here, in a few select high elevation forests with oyamel (fir) and pine trees, millions of monarch butterflies from east of the Rocky Mountains congregate each year, after an astonishingly long journey – over 3500 km – from Canada and the northern reaches of the US.

The monarchs stay in Mexico from November to March. When the sun is shining, the butterflies – which otherwise huddle together in tightly packed and well camouflaged clusters on the branches and bark of oyamel trees – take to the air, like a beehive that has been stirred. If the sun stays up, as it did the day I visited, the monarchs quickly fill the sky and everything around you; you can even hear the faint flutter of their wings. I was in the very thick of things when this photograph was taken [1]. Every speck in the picture below, however faint, is a butterfly.

Monarchs have fascinated me for years now. In Massachusetts, a few months prior to my Mexico visit, I'd seen the odd monarch or two flying unhurriedly, seemingly without a purpose. So languid was their flight – the classic flap, flap and glide – that there was no way to tell that each butterfly, following some mysterious signals – its reproductive system having been put on pause, allowing the organism to focus on the rigors of the coming journey – was leaving for a distant forest in Mexico.

It's worth reiterating this: each butterfly that migrates south starts the journey alone and has never made the journey before. When birds make long journeys, there are often older individuals that guide the young. In the case of monarchs there is no guide. The recent discovery that the thin, seemingly inconsequential antennae of monarchs house circadian clocks that help in orientation only deepens the wonder [ref. and figure]. Traveling by day and over land, a monarch, “with a mass 20% that of a penny” [2], covers thousands of kilometers in a two month period.

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by Charlie Huenemann

How wonderful it would be to be a systematic thinker! One marvels at the Aristotles, the Aquinases, the Descarteses, the Kants, and the Hegels and the Marxes (well, the Karl Marxes anyway), the Freuds – those who know how to approach anything, how to incorporate any material into a systematic empire, those who can see the universe as fulfillments of their own plans. It may sound like I am satirizing them, but I really do admire them: I admire their imagination, their enthusiasm, and their persistence. Chiefly I admire their ability to take their own thought so seriously, since every time I have tried to construct a system, it turns into fits of giggles.

What causes such a mindset? Let us first see if we can discern its preconditions – those elements necessary for the possibility of system-building, as it were. One must first be convinced that reality, or human experience, is coherent – a big assumption, granted, but absolutely required for a system. And the coherence must be intelligible to a finite human mind, and specifically the specific mind of the specific system-builder. One must further believe that the coherent, intelligible world order has a kind of hierarchy that allows for some parts of it to be more basic, more foundational, or more universal than others. For the system builder is not so deluded as to believe that all of the facts can be fit within a single head: only the organizing principles need be grasped and kept forever in one’s mental field of vision.

That the world is a coherent, intelligible hierarchy – this much at least must be believed by any would-be builder of a system. But no one is going to leave it at that! To harbor that belief is to have the ambition to explain the hierarchy, and propound it to oneself and to the world. I’d say the belief and the ambition go hand in hand – but then again, if anyone has ever had the belief without the ambition, we probably would not have heard of them. Oh yes, a final thing: the system has to be new, if we are dealing with a genuine builder, and not a worker bee.

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by Thomas R. Wells

The proponents of gun control in America are losing the argument and will continue to do so. Their complacency, typical of the left, that they are on the right side of history has blinded them to the fact that they have chosen to fight on the wrong ground. They keep harping on about guns killing people. As if guns were like cigarettes, and as if the numbers were big enough to matter.

I. The Public Health Argument Doesn't Work

Guns are indeed an excellent killing technology. They are really very good at transforming an intention to kill into its achievement. However, that doesn't mean that they are a particularly significant cause of death and it is rather ridiculous to imply that removing guns from citizens would change death rates much. America is not 42^nd in the world for life-expectancy because of guns, but because of much more significant effects like the social gradient in health.

Let's go into this a little more.

We hear a lot about the large number of deaths caused by guns in America – now up to 33,000 per year. This seems like a big number. It is nearly as big as the rate of death from car accidents (another area in which America is an international outlier, by the way). But 2/3 of gun deaths are suicides. Most of those deaths would still occur if people didn't have access to guns. Many murders committed with guns would also go ahead without them, albeit with a smaller chance of success.

Mass killings by individual loonies get far more attention than they deserve. It feels like there are a lot of them, and perhaps they are even increasing – 133 between 2000 and 2014. But in a country with 320 million people and poor funding of mental health services there are always going to be murderous loonies making the national news somewhere. These atrocities make for wonderful news stories, full of pathos and inspiring great moral indignation. But they are statistically irrelevant to Americans' public health. They are not an argument for gun control.

The overarching assumption that murders are caused by weak gun control laws is weak. The decline of gun control began in the 1980s, but the murder rate in America has actually fallen by half since then (back to what it was in 1950). The reason is that rates of violence have a lot more to do with social conditions and inequality than with particular technologies. Most of America is nearly as safe as Western Europe, but some areas of concentrated hopelessness have the murder rates of Central America. The real causes of violence are something America is particularly bad at addressing, among rich countries, perhaps because the left in America spends most of its time campaigning for things that have little to do to with social justice.

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I recently found myself marooned with a large group of astronomers in a remote 11th century abbey in Tuscan countryside. Despite the picturesque beauty of the landscape not to mention the abbey's splendid library; still the days (I must admit) stretched on and on…

I guess it's true that google is making me stupid, but I discovered that it is a lot harder for me than it used to be to read for hours on end. And without any wireless nor any real means of getting myself back to civilization, I decided to hatch a means of escape. It wasn't all that hard actually, it was just a matter of reminding him (the astronomer with the driver's licence) that located not all that faraway from the abbey was what has been called “the best picture in the world.”

Has anyone else read that wonderful essay by Aldous Huxley called “The Best Picture?”

It is a brilliant essay –and the title says it all. But, wait, you ask, how can there be such a thing as “the best picture” in the world? Isn't it an absolutely ludicrous suggestion to make?

Of course it is, and this is not lost on Huxley–for as you can see in the essay, he addresses this absurdity immediately:

The greatest picture in the world…. You smile. The expression is ludicrous, of course. Nothing is more futile than the occupation of those connoisseurs who spend their time compiling first and second elevens of the world's best painters,eights and fours of musicians, fifteens of poets, all-star troupes of architects and so on. Nothing is so futile because there are a great many kinds of merit and an infinite variety of human beings. Is Fra Angelico a better artist than Rubens? Such questions, you insist, are meaningless. It is all a matter of personal taste.And up to a point this is true. But there does exist, none the less, an absolute standard of artistic merit. And it is a standard which is in the last resort a moral one. Whether a work of art is good or bad depends entirely on the quality of the character which expresses itself in the work. Not that all virtuous men are good artists, nor all artists conventionally virtuous. Longfellow was a bad poet, while Beethoven's dealings with his publishers were frankly dishonourable.But one can be dishonourable towards one's publishers and yet preserve the kind of virtue that is necessary to a good artist. That virtue is the virtue of integrity, of honesty towards oneself.

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The Horses of Chauvet

the horses of Chauvet
lope through a cave
eloquently old and new

true and lush
as the love and lust
our progenitors knew
and craved
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by Jim Culleny
6/28/15
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Chauvet Cave

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by Emrys Westacott

My Facebook profile describes my political views as “very liberal.” In the US this is a shorthand way of indicating that I support gay rights, government-run health care, stricter gun laws, abortion rights for women, abolition of the death penalty, reduced military spending, environmental protection, campaign finance reform, the United Nations, Charles Darwin, the Toyota Prius, and higher taxes on people richer than me.

When I get together with other very liberals—which is quite often, since I'm married to one—a favorite topic of lamentation is the blindness of our political opponents. Why don't they get it? Why don't they see that we'd all be better off if we spent more on education and less on weapons systems; that if they really want to see fewer abortions they should support rather than oppose sex education in school and universal healthcare; that violent crime in the US is more likely to be reduced by having stricter gun control laws than by increasing the number of executions.

Our discussions of such matters follow a predictable course. After a round of annoyed tongue clicking, irritation gradually mounts until we reach a crescendo of infuriation and incredulity, from which we subside, with much headshaking, onto the soft but comfortless pillow of our usual answer. Why don't they get it? Because, to quote Samuel Beckett, “people are bloody ignorant apes!”

I believe something like the same kind of incredulity characterizes the view that many Europeans have of American politics. Whether the issue is denial of climate change, teaching creationism, resisting even minimal gun control, or opposing a more efficient health care system, the first impulse is to shake the head and ask, “How stupid can you get?”

As an explanation of why millions of people don't agree with me, the “ignorant ape” hypothesis has the virtue of simplicity. But I can't help feeling that it lacks depth. After all, in other areas of life conservatives aren't any more stupid than me or my fellow VLs. They make perfectly good parents, neighbors, and colleagues. So why do our wonderfully cogent arguments have so little purchase on their thinking?

I believe one key reason is that when it comes to political topics and stances, rational cogency often counts for less than symbolic meaning. In any debate, on any topic, the ideal is for the outcome to be determined entirely by the force of the best evidence and arguments. Indeed, submission to the argument is largely what we mean by scientific or scholarly objectivity. But submission to the argument seems to be less common in politics than in most other spheres. Instead, it is the symbolic significance of a political position that often decides whether a person endorses it or rejects it. This is true in every society; think for, instance, of the headscarf controversy in France. But it is perhaps more true in the US than in most other developed countries because for some reason symbols seem to play a bigger part in American political culture.

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