by Hari Balasubramanian

Decisions under demand uncertainty – the so called newsvendor problem.

In October 2007, my father and I took a day train from Bangalore to Chennai. About halfway into the 7-hour journey is a station called Jolarpet, where the train stops for ten minutes. As at other stations, there were dozens of vendors – each with a simple wheeled stall or a wooden basket or a steel container – engaged in a frenzy of small scale entrepreneurship. All sorts of items were being sold: snacks, tea, coffee, water, bananas, flowers, cheap Chinese goods – toys, combs, and, in what became a curiosity and a topic of detailed conversation among our fellow travelers, pens that doubled as flashlights.

But my father was most interested in those who sold vadas, a South Indian specialty, a round, deep-fried snack with a hole in middle – like a donut but not sweet at all – made from a batter of lentils (I've described just one variety). My father felt the vadas sold by vendors at the Jolarpet station were better than those made in the train's pantry. They were hot, had just the right texture, and the timing – late afternoon – was just right to have them with coffee. Three fairly busy trains – including the Bangalore-Chennai Brindavan Express on which we were traveling that day – arrive at Jolarpet station at roughly the same time. “How many vadas get sold?” my father wondered. “Maybe a thousand of them, maybe even more.”

That comment got me thinking. If you are a vendor, the critical question is how many vadas should I make? The vadas have to be fried right before the train arrives so that they are hot and ready to sell during the ten minutes that the train stops. If I fry too many and not enough passengers buy them then what I am left with is wasted, since a vada that is not freshly made is unappetizing. On the other hand, if I fry too few, then I lose the opportunity to sell to passengers who need them. So what is the right number to make given this uncertainty in demand?

The technical name for this dilemma is the newsvendor problem. Replace vadas with newspapers and you have an identical situation. If a newsvendor on the street doesn't sell enough newspapers, what's left is wasted since today's newspaper won't sell tomorrow. If the vendor has too few newspapers and runs out of them, then potential customers are lost.

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by Leanne Ogasawara

In Japan, I knew a gentleman who ran a 200 year old miso shop. K san was also a bon vivant par excellance! Studying Samurai-style (Enshu school) tea ceremony, he wore stylish kimono by day and organized French film festivals for our town on the weekends. He also spent a fortune on tea bowls and art, which he often would show to his friends.

Everyone in town knew him and his miso shop was a gathering place of local luminaries.

Of all the interesting things he was involved in, my favorite was his gramophone club. Once a month like-minded collectors would show up with a favorite record (or not) and sit around listening to old records while drinking sake. Need I say more? The man had endless curiosity and tremendous style. He was my kinda guy!

Speaking of which, I recently finished the most unusual book by Normon Cantor, called Inventing the Middle Ages. The book is about twenty prominent 20th century Medievalists and their impact on the study of the history of the Middle Ages. When I first heard that this book was not just a best seller but was so popular it was even available on Audible, I could hardly believe it! Really? I love anything related to the Middle Ages and so would have read the book no matter what, but I must admit that I was utterly fascinated by the popularity– as well as the controversy surrounding this book, which after all was on such an obscure topic.

So, I picked up the book immediately.

I wasn't disappointed either.

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by Bill Benzon

There can be little doubt that President Obama’s eulogy for Clementa Pinckney was an extraordinary performance and a powerful statement about the state of race relations in the United States of America. But it is also a bit puzzling, for that statement took the form of a sermon. As such, it was religious discourse and not secular political discourse.

That’s what I want to talk about, not to reach any specific conclusions, but to raise questions, to call for a conversation about and an examination of the role of religious discourse in civic life.

Rather than develop those questions directly, I want to place Obama’s eulogy on the table to a moment and consider a recent conversation between Glenn Loury, an economist at Brown University, and John McWhorter, a linguist at Columbia. That will establish the context in which I offer a few remarks about Obama’s performance. Then I want to place in evidence a statement that Robert Mann made about Laudato Si’, the recent and quite remarkable encyclical by Pope Francis.

The ‘Cult’ of Ta-Nehisi Coates

Loury and McWhorter had this conversation at Bloggingheads.tv on July 21, 2015. After opening pleasantries and some remarks about Obama, they move on to discuss the ascendancy of Ta-Nehisi Coates as a commentator on race relations in America. Starting at somewhat after nine minutes in McWhorter argues that Coates has become somewhat like the priest of a religion:

There is now what a Martian anthropologist would call a religion. Which is that one is to understand the role of racism in America’s past and present.

And Coates has reached a point, and this is not anything that I ever predicted, where he is the priest of it. Because, and this is the crucial point, James Baldwin […] his point was often that race IS America, that the race problem is the essence of America and where it needs to go. And people read that and they quoted it but it wasn’t something that ordinary white readers really felt at the time.

Whereas today, really, that is something that whites feel such that Coates is revered. He is not considered somebody where you actually assess whether what he’s saying is true, you’re only supposed to criticize him in the gentlest of terms. He’s a priest of a religion.

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by Eric Byrd

As a teenager who just wanted battles, I tried to read The Face of Battle and was baffled by the historiographic argument of Keegan's introduction, a long essay that, I now see, echoes Virginia Woolf's manifesto “Modern Fiction” and applies its prescriptions to historical prose. Keegan called to writers of military history as Woolf called to the novelists of her time – “Let us record the atoms as they fall upon the mind in the order in which they fall, let us trace the pattern, however disconnected or incoherent in appearance, which each sight or incident scores upon the consciousness.” Keegan urged historians to turn away from tidy narratives of battle and acknowledge the horizonless confusion experienced by even the best-positioned participants of those battles; urged them to understand that most soldiers don't even know when they are engaged in battle, or at least “battle” as it was understood by the Victorians: a national apotheosis or histrionic downfall; the Hinge of Destiny; and he recommended the historian read and take to heart the chaotic combat scenes in Tolstoy's War and Peace, just as Woolf prescribed Tolstoy, Dostoevsky and Chekhov to the fiction writer tempted by pat characterization, superficial psychology, all-too-conclusive action, and purely material relations.

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by Brooks Riley

‘I can sleep when I’m dead.’

That’s how Rainer Werner Fassbinder justified his hell-bent, frenetic, productive/destructive dervish whirl through a short existence, trailing an oeuvre of 45 films, 21 plays and countless screenplays. He was 37 when he died.

He’s been sleeping now for 33 years—a well-earned rest he wasn’t quite ready for but did nothing to prevent. He died of an overdose, of life and of every substance that helped fuel his march through it. This year he would have turned 70.

Walking past the Rainer Werner Fassbinder Technical College last week, I found myself doing what I often do with the dead: I imagined his ghost, the Tatar warrior of grunge, clad in filthy Levis and an old leather vest, striding out the door, coming over to me and giving me that bear hug of his.

Was machst Du den hier? he asks, stunned to find me living in his home town of Munich.

What am I doing here? It’s a good question for which I have no easy answer, other than the chain of unrelated circumstances that has brought me here, over and over again, at various times in my life. Now I’ve been here longer than I’ve been anywhere else.

Fassbinder’s Munich is not my Munich. We never had that much in common, except a love of film and a breezy friendship. Now he lies in a pricey part of town, far from the bars he frequented or the studio where he made many of his films. He’s been honored with his very own Platz, the Rainer-Werner-Fassbinder Platz, in a new residential area near the train station. And a technical college, of all things.

We weren’t always friends. The first time I met him, when a colleague and I were the first to interview him on his first trip to New York, he was restless and impatient, fulfilling an obligation with intelligence but without enthusiasm. Fassbinder could be rude and intimidating, with a bad-boy reputation that served him well against intruders, a category that included nearly everyone outside his inner circle of cast and crew, his only friends. He had many admirers out there in the world, myself included, but none could break through that barrier he put up to all those who would befriend him or wish him well. He had no time.

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by Misha Lepetic

“We are at home with situations of legal ambiguity.
And we create flexibility, in situations where it is required.”
~Neuromancer

Consider a few hastily conceived scenarios from the near future. An android charged with performing elder care must deal with an uncooperative patient. A driverless car carrying passengers must decide between suddenly stopping, and causing a pile-up behind it. A robot responding to a collapsed building must choose between two people to save. The question that unifies these scenarios is not just about how to make the correct decision, but more fundamentally, how to treat the entities involved. Is it possible for a machine to be treated as an ethical subject – and, by extension, that an artifical entity may possess “robot rights”?

Of course, “robot rights” is a crude phrase that shoots us straight into a brambly thicket of anthropomorphisms; let's not quite go there yet. Perhaps it's more accurate to ask if a machine – something that people have designed, manufactured and deployed into the world – can have some sort of moral or ethical standing, whether as an agent or as a recipient of some action. What's really at stake here is the contention that a machine can act sufficiently independently in the world that it can be held responsible for its actions and, conversely, if a machine has any sort of standing such that, if it were harmed in any way, this standing would serve to protect its ongoing place and function in society.

You could, of course, dismiss all this as a bunch of nonsense: that machines are made by us exclusively for our use, and anything a robot or computer or AI does or does not do is the responsibility of its human owners. You don't sue the scalpel, rather you sue the surgeon. You don't take a database to court, but the corporation that built it – and in any case you are probably not concerned with the database itself, but with the consequence of how it was used, or maintained, or what have you. As far as the technology goes, if it's behaving badly you shut it off, wipe the drive, or throw it in the garbage, and that's the end of the story.

This is not an unreasonable point of departure, and is rooted in what's known as the instrumentalist view of technology. For an instrumentalist, technology is still only an extension of ourselves and does not possess any autonomy. But how do you control for the sort of complexity for which we are now designing our machines? Our instrumentalist proclivities whisper to us that there must be an elegant way of doing so. So let's begin with a first attempt to do so: Isaac Asimov's Three Laws of Robotics.

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If you talk about it, it’s not Tao
If you name it, it’s something else

What can’t be named is eternal
Naming splits the eternal to smithereens

Not tangled in desire you embrace the unknown
Tangled in desire you see only what you want

But the unknown and what you want
have one source. Call it no place

No place or darkness
……….. —from the Tao Te Ching of Lao Tzu,
………….. 6th Century BC

Lao Tzu's Lament

at first I think, I’ve got it!
then I think, Ah no, that’s not it
I think, it’s more like a flaming arrow
shot into the marrow
of the bony part of everything

………. but some summer nights
………. it’s hanging overhead so bright

then right there I lose it
I let geometry and time confuse it
then it’s silent and won’t sing a thing

………. but some summer nights
………. it’s croaking from a pond so right

then again I lose it
let theology and time confuse it
then it’s silent and won’t sing a thing

……………….. I’m thinking I’ve been here before
……………….. feet two inches off the floor
……………….. thinking, is this something true?

sometimes I think, I’ve lost it!
though I never could exhaust it
because it’s lower than low is
and wider than wide is
deeper than deep is
higher than high is

………. but some fresh spring days
………. it’s cuttin’ through the fog and the haze

……………….. I’m thinking I’ve been here before
……………….. feet two inches off the floor
……………….. thinking, is this something true?
.
.

song by Jim Culleny, 7/15/15
Copyright: Jim Culleny, 6/23/15
all rights reserved

Recording:
Jim Culleny Vocal and rhythm guitar
Joe Podlesny: Bass, lead guitar
Engineering: Joe Podlesny
Production: Joe Podlesny and Jim Culleny

by Jonathan Kujawa

Last week humanity had a moment of triumph. We (well, really the folks at NASA) successfully flew the New Horizons spacecraft over three billion miles at speeds exceeding 51,000 miles per hour (30 times the speed of the proverbial speeding bullet) to Pluto — a target only two-thirds the size of our moon. While zooming past at over 30,000 miles per hour the spacecraft gathered a wealth of images and data which we'll be studying for years to come. Until New Horizons our best image of Pluto was this one from the Hubble Space Telescope [1].

Before New Horizons.

But now we have pictures like this [2]:

After New Horizons.

If you have an iota of curiosity you you can't help but think that's pretty darn cool. Last year the European Space Agency did something I found even more impressive: they flew the Rosetta spacecraft over 4 billion miles and landed it on a comet 2.5 miles in diameter which travels at over 34,000 miles per hour. In both cases the spacecraft provides us with fantastic new data about our solar system, but just getting it there already counts for a lot in my book.

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by Tamuira Reid

Go because you're still holding onto the baby weight even though your baby is four.

Because you have nowhere else to go today. Because you're not over him.

Go because the depression is eating you alive, from the inside out. Go because you forget what happy feels like. (Go because you know how clichéd that sounds. Go because you don't want to be a fucking cliché.)

Go because you want to get laid. Go because you want to be naked again without reaching for the sheet. Go because the last time you really lifted something it was your dress, over your head, on the night you made your son. Go because you want to glisten with sweat like the models in the Lululemon ads. Go because you are a nerd who uses the word “glisten” still. Go because you're tired of your thighs chaffing as they rub together. Go because you're mom is worried you might be a lesbian, because all of your friends are gay men and you haven't had sex since 2010. Go because you want to get out of your head because your head scares you. Go because it's either the gym or the bar and we all know where the bar gets you.

Get a trainer. Pick a protein powder. Buy a duffle bag.

Learn the difference between a dumbbell and a barbell. That it's deadlift not deadweight. Learn to press. To plank. To lunge. Learn to hide the pain radiating through your knees and hips. Hide your age. Especially when the twenty-four year-old next to you looks bored going at speeds that would rip the cartilage right from your bones. Secretly decide to hate her. Secretly decide to be her.

Feel like an imposter, like someone will come to the treadmill at any second and pull you off by the neck. You are an outsider here but not for long.

Stop keeping a hair diary, the one the dermatologist told you to start when your hair began to fall in huge clumps, the one where you count every strand to report back how lazy your follicles are being. Stress levels lower when your glutes are firing. So forget about meditation tapes and visualization and rainforest gong music. You don't need to listen to rain or crickets or steel drums to fall asleep anymore. You will be out before your train leaves the station, your head resting on the guy's shoulder next to you. He'll feel sorry for you, even as your drool saturates the fabric of his Brooks Brothers shirt, the one his wife spent an hour ironing before she had coffee this morning. Because that's what newlyweds do.

You've never been a newlywed. Your relationships last about as long as your gym memberships. Make this time the exception. Be ready for the change.

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by Jalees Rehman

Billions of cells die each day in the human body in a process called “apoptosis” or “programmed cell death”. When cells encounter stress such as inflammation, toxins or pollutants, they initiate an internal repair program which gets rid of the damaged proteins and DNA molecules. But if the damage exceeds their capacity for repair then cells are forced to activate the apoptosis program. Apoptotic cells do not suddenly die and vanish, instead they execute a well-coordinated series of molecular and cellular signals which result in a gradual disintegration of the cell over a period of several hours.

The remains of an apoptotic cell are being engulfed and ingested by a phagocytic white blood cell. Image via National Library of Medicine.

What happens to the cellular debris that is generated when a cell dies via apoptosis? It consists of fragmented cellular compartments, proteins, fat molecules that are released from the cellular corpse. This “trash” could cause even more damage to neighboring cells because it exposes them to molecules that normally reside inside a cell and could trigger harmful reactions on the outside. Other cells therefore have to clean up the mess as soon as possible. Macrophages are cells which act as professional garbage collectors and patrol our tissues, on the look-out for dead cells and cellular debris. The remains of the apoptotic cell act as an “Eat me!” signal to which macrophages respond by engulfing and gobbling up the debris (“phagocytosis“) before it can cause any further harm. Macrophages aren’t always around to clean up the debris which is why other cells such as fibroblasts or epithelial cells can act as non-professional phagocytes and also ingest the dead cell’s remains. Nobody likes to be surrounded by trash.

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by Shadab Zeest Hashmi

Once, in Italy, I had gelato in a place with a hidden door that opened into a garden with a gazebo. When I discovered it, it was like entering a movie set. Minutes ago I had herded my young children, negotiated foot traffic carrying ice cream and now I was in the middle of a surprise garden— surrounded by clear glass and a fruity scent. I had barely taken in the scene when I realized the baby needed to be changed; we finished our gelato quickly and left.

The delight was so abrupt that I’m not sure if this visit really happened, that there exists such a garden and gazebo in Turin where you can eat gelato. Did I imagine it? It’s a mercurial but lucid memory; it returns again and again.

There are other recurring flashes similar to this, most of them having to do with books: sitting by the window, reading “Of Mice and Men” as the sky raged with all its monsoon might, the drama of rain in real life entering the world of the novel. I still see the pages in the luscious light of Peshawar rain.

And numerous others: reading “Far from the Madding Crowd” on long summer afternoons, to the click-clicking of the ceiling fan, the faint aroma of lunch still in the air, lounging by the gas heater reading P.G. Wodehouse and eating hot sohan halva during winter-break. My mother reading aloud from an old copy of “mirat ul uroos,” an Urdu classic, the light and shadows on its yellowed pages, her clear, soft voice, my eyes lingering on the corners of the white walls, watching my grandmother’s glow-in-the-dark “time piece” from Mecca as I listened to the story.

A good book creates an uncanny silence, a bubble around the reader so that not only is the world of its offering vivid and deeply felt but the sensory reality of the reader as well: the smooth lamination on library books, the vanilla scent of the paper, the peculiar tone of light falling on the pages, the thumb, the forefinger, the folded paperback. Text blends in, binds with the texture of the sensory moment; the book becomes one with the reader.

The first book of poems I read on kindle was Fady Joudah’s “Textu”— I wasn’t sure how much the “reading device” would take away from me. As I fell into the rhythm of the short poems, their jagged, tender, stark, subtle world, there was a hush, then the sound of the wind chimes came from the patio with incredible clarity, the lamplight took on the glow of Japanese paintings, a familiar filter from childhood.

The brief, dreamlike, lasting spells, the residue of the reading life fills the writing life with the basic element: wonder. Once lodged in memory, it carries on— refilling, refueling the writer. These are the small, deep pockets of memory I reach into when I sit down to write.

by Kathleen Goodwin

There have been 170 homicides in Baltimore thus far in 2015, putting the city on track for a record-setting year. 43 of these occurred in May in the aftermath of Freddie Gray's death, more than double the average number of homicides recorded in May between 2009-2014 and the most since 1971, when the city had approximately 300,000 more residents. The Baltimore Sun has created a homicide database that lists the age and race of the victims—as well as the date and address where each murder occurred, plotted on an accompanying map. In addition to the sheer volume, it's immediately striking that the 2015 homicides are particularly clustered west of Eutaw Place, including the neighborhood of Sandtown-Winchester where Freddie Gray grew up. Homicide locations are sprinkled across the eastern and western sections of the city, while there are glaring blank spaces in a swath extending south from the Johns Hopkins undergraduate campus, through the Inner Harbor tourist area, and extending east to the Hopkins medical campus. As has been often repeated, there are two Baltimores—or rather an educated white Baltimore sandwiched between the predominantly black and poor areas that were being shown in the national media coverage of the rioting this spring. Considering persuasive data that suggests that the neighborhood where you spend your formative years is correlated to your relative success and stability as an adult, Baltimore is a case study in the way segregation of neighborhoods has created a concentrated areas of poverty and violence, manifesting in antagonism with the police and dramatically reduced life expectancy.

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by Madhu Kaza

I sit on a bench and a few doors down he's on his bench. We're on Sullivan Street. It's Thursday, it's July, it's late afternoon, it's early evening, and the heat begins to lift. He's an elderly Italian man. His white hair, white shirt, white shorts, white knee socks, and white sneakers are all slightly dingy. I watch the sky, the buildings of this little street, the people passing on the sidewalk. He watches the people. I'm leaning back against the window of a bakery, my body impassive. I imagine I'm taking pictures of the moments unfolding before me, now, now, and now –Thursday and July. I could just as easily be sitting inside at a window gazing out. Except, the man.

Unlike me he sits alert, eager. He leans forward with one hand resting on a cane, the grey plastic and aluminum kind. He faces left, in my direction, looking out for an oncoming pedestrian, his mouth open in anticipation. He engages each person who approaches with his whole body, turning on his bench until eventually he is facing right. Then he watches the figures from behind as they drift towards Houston Street and disappear. He has the look of someone watching a race horse making the rounds. He leans into the activity of the street.

We look at each other, aware but without any demonstration. I'm watching the street, and I'm watching him, and he's looking at me and though he speaks to the children strolling by and to the UPS man and to the young woman sipping an iced coffee, he doesn't call out to me. I'm uneasy and relieved. If he spoke to me it would bring us into a recognizable relation — the I and the you of conversation, of pleasantries, when in fact we are already in a closer relation, tenuously connected but on the same side of these passing moments. For this portion of my day is now fixed to him, we are in tandem, two foci in an ellipse. It is his presence and his distance that keeps me seated, maintaining my vigil for the day.

When the sky darkens I finally stand up to leave. I consider turning South and walking away from him in order to disappear quietly from the scene. But my curiosity leads me in his direction. I am unsure of what will happen. I don't know if he will speak to me as I pass. But even more mysterious to me, is whether I will say anything to him. And if I do, what will come of it? A brisk exchange or something more?

I walk and he turns toward me and follows my movement as he has done with the others. I glance at him and see a deeply wrinkled round face, dull blue eyes. His mouth is slack, he looks at me. I don't smile. I don't say a word and neither does he. As I pass by I sense that something has been lost and something greater has been preserved as I move on into the unspoken reprieve of the night.

By Namit Arora

The highs and lows of identity politics, and why despising it is no smarter than despising politics itself.

Our identity is a story we tell ourselves everyday. It is a selective story about who we are, what we share with others, why we are different. Each of us, as social beings in a time and place, evolves a personal and social identity that shapes our sense of self, loyalties, and obligations. Our identity includes aspects that are freely chosen, accidental, or thrust upon us by others.

Take an example. A woman may simultaneously identify as Indian, middle-class, feminist, doctor, Dalit, Telugu, lesbian, liberal, badminton player, music lover, traveler, humanist, and Muslim. Her self-identifications may also include being short-tempered, celibate, dark-skinned, ethical vegetarian, and diabetic. No doubt some of these will be more significant to her but all of them (and more) make her who she is. Like all of our identities, hers too is fluid, relational, and contextual. So while she never saw herself as a ‘Brown’ or ‘person of color’ in India, she had to reckon with that identity in America.

Identity politics, on the other hand, is politics that an individual—an identitarian—wages on behalf of a group that usually shares an aspect of one’s identity, say, gender, sexual orientation, race, caste, class, disability, ethnicity, religion, type of work, or national origin. Any group—majority or minority, strong or weak, light or dark-skinned—can pursue identity politics. It can be a dominant group led by cultural insecurities and chauvinism, or a marginalized group led by a shared experience of bigotry and injustice (the focus of this essay). Both German Nazism and the American Civil Rights movement exemplify identity politics based on the racial identity of their constituent groups, as do the white nationalism of Donald Trump’s presidential campaign and the activism of the Black Lives Matter movement in the U.S. Both Hindutvadis and Dalits are identitarians of religion and caste, respectively. As Eric Hobsbawm noted in his essay Identity Politics and the Left, labor unions, too, have long pursued identity politics based on social class and the identity of being an industrial worker.

Life, and identity politics, can amplify certain aspects of our identity while suppressing others. During the Sri Lankan Civil War, the Tamil Tigers elevated Tamil national identity over that of caste. Gender identity turns secondary in some contexts: Indian women often close ranks with Indian men when White Westerners lecture them on sexual violence in India. Likewise, Dalit women often close ranks with Dalit men when upper-caste women expound on gender violence among them. Especially after September 11, 2001, many European citizens and residents with complex ethno-linguistic roots faced a world hell-bent on seeing them as, above all, ‘Muslims’.

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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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