by Jonathan Kujawa

To say math is about numbers is like saying writing is about words. You can use words well or badly, but in the end it is the things and ideas they represent which are important. Just so with numbers.

I have a clear memory of learning in middle school that the plots of Shakespeare's plays were nothing but retreads of older tales. With the certainty of youth I wrote off Shakespeare as nothing but an over-glorified plagiarist. It took a few years to come around to the realization you don't read Shakespeare after all these years for the plots, but for his deep study of human nature and unmatched skill with words. Will could put the right words in the right order and really zing: “How well he's read, to reason against reading!” or “Things won are done, joy's soul lies in the doing”.

But, as every logophile knows, words as words are fun, too. Every language has a rich vocabulary. It can be great fun to flip through a dictionary and find words which are unexpected, funny sounding, intriguing, insightful, etc. I am terrible at foreign languages. Not only am I tone deaf to pronunciation, but my memory always locks onto the words which are interesting, obscure, and utterly useless in everyday communication. Twenty years after studying Hungarian I remember hepehupás is the word for bumpy. Why? For the singularly silly reason that saying it makes you sound like you're bumping along a rutted country road.

In just the same way there are numberphiles who enjoy curious numbers. They have raging internet arguments over the great Pi vs. Tau controversy. They know why 1729 is called a “taxi cab” number. Or why Google is called Google.

Here be giants.

I myself have a fondness for what I call Brobdingnagian Numbers. Brobdingnag is the land of giants in Gulliver's Travels. When doing math you find yourself using such staggeringly large numbers that you become numb to how big they really are. But it's worth taking note of them and it can be quite fun to collect the ridiculously large numbers you come across in your travels.

My snarky middle school self wouldn't have cared about such things since you can always add one to get a bigger number. But we've already established that he was an idiot who didn't know how to appreciate the finer things in life and we choose to ignore him.

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Bidding Adieu
.

gimme a new piece of
the big Mysterium
—the words had barely left his lips
when he died again in cognate delirium
choking on the language of things

clues

science is a big Imperium
religion is too
but one (at least) gives credit to
what the other calls g-o-d
for having offered to all: experience
and the capacity to question
—to cogitate and guess at what is and what’s not,
what’s coming and what is, as we speak, bidding

adieu

Jim Culleny
8/15/15

by Kathleen Goodwin

Education is arguably the most interesting lens by which one is able to view the race issue at the core of American society. I would venture that there are many white Americans who pay lip service to the value of diversity but wouldn't dream of sending their children to a school that isn't predominantly white. It's a complex hypocrisy, however, considering that schools with a white minority are underfunded, overcrowded, and underperforming with very few exceptions.

The two most recent episodes of the Chicago Public Media produced “This American Life” perform a deep dive into racial desegregation of public schools in American cities. Over the course of two hours, the podcast's creators explore a tactic that few districts are willing to tackle in modern America—actively dismantling the structures that allow white kids to go to school with mostly other white kids in good schools and for black and Latino kids to go to segregated subpar schools. One of the contributors to the podcast, Nikole Hannah-Jones, herself a product of an integration program in a small Iowa town, summarizes the argument for desegregation:

“I think it's important to point out that it is not that something magical happens when black kids sit in a classroom next to white kids…What integration does is it gets black kids in the same facilities as white kids. And therefore, it gets them access to the same things that those kids get– quality teachers and quality instruction.”

The most successful method of ensuring that black and Latino children receive a quality education is by integrating school systems because “separate but equal”, in addition to being morally repugnant, has never been a legitimate reality in the U.S. However when school desegregation is implemented white parents oppose it—to the point of rioting as the 1970s in Boston revealed. By the late 1980s most school districts decided that integration wasn't worth the trouble it caused. The first episode makes this point apparent with clip after clip of angry white parents at a town meeting after it is announced that their affluent Missouri school district must absorb the students from a poor, predominantly black district that has lost accreditation, coincidentally the same district that Michael Brown attended.

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by Misha Lepetic

“Dear Cecil! I have no secrets from you.”
~ Oscar Wilde, The Canterville Ghost

Remember Cecil the Lion? It wasn't that long ago, but given the half-life of outrage on the Internet, I will forgive you a moment of head-scratching. Let me summarize that Cecil was lured from his protected home in Zimbabwe to an adjoining game reserve only to be shot, tracked for 40 hours, finished off, and finally decapitated by a dentist from Minnesota and his co-conspirators, all of whom, the Internet has resoundingly agreed, are cowards. Said dentist, a certain Walter Palmer, has since seen his business vandalized, and has gone into hiding after receiving death threats against himself and his family. He has generally been subjected to enough unpleasantries that would rival the most botched root canal. Such is the nature of Internet justice today.

You may cry, He deserves it! Killing such a magnificent beast, etc etc. I don't dispute the obviously reprehensible barbarism of this act. But the anachronistic nature of big game hunting has been followed up by the equally anachronistic resurgence of public shaming and mob justice. So let's take a closer look at how – or better yet, why – the citizenry of the Internet fearlessly takes up the mantle of vigilantism, and to what effect. I've decided to divide this post into two parts: this first part will discuss a few concrete examples of public shaming, and the second will look at some theoretical frameworks that may help us make sense of it all.

*

Before Cecil the Lion, there was Justine Sacco. For those of you with exceptionally long Internet memories – and to be clear, I'm not sure why having a long memory for things Internet-related is that useful, as it's just depressing to see the same things repeated in ever-quickening cycles – Sacco was the senior director of corporate communications for IAC, a billion-dollar media corporation. Jetting off to South Africa for family holidays in winter 2013, she tweeted a few poorly considered thoughts to her 170 followers but struck outrage gold with the one that said “Going to Africa. Hope I don't get AIDS. Just kidding. I'm white!”

We could try to parse what she actually meant by that. For example, a generous interpretation would be that she was sarcastically musing on the conditions of white privilege. It's more likely that she wasn't thinking very much at all. What is certain is that, by the time her plane landed, her career was effectively over.

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by Lee Basham and Matthew R. X. Dentith

Theories about conspiracy theories are rife, with historians, cultural studies scholars, psychologists and sociologists all contributing to the ongoing debate as to whether belief in conspiracy theories is, in fact, irrational, what kind of people believe conspiracy theories, and what, if anything, should we do about the prevalence of belief in them. So, what say the philosophers? In the last two decades philosophers like Charles Pigden, Brian L. Keeley, David Coady and, yes, ourselves, have taken a close look at conspiracy theories, and the news is in: belief in conspiracy theories is not irrational and the conspiracy theorist, despite the opprobrium expressed towards her, has emerged as good a thinker as you or us. Their theories are intriguing, and often constructed with a careful eye to the standards of both logic and evidence that we all share. “They” are just like us. In fact, “they” are us. Charles Pigden's simple observation, well-summarized by David Coady, ably demonstrates this.

1) Unless you believe that the reports of history books and the nightly news are largely false, you are a conspiracy theorist.

2) If you do believe that the reports of history books and the nightly news are largely false, you are a conspiracy theorist.

Conclusion: We're all conspiracy theorists.

This conclusion, however, flies in the face of a recent article published in Aeon, “Bad thinkers”, by the University of Warwick's Quassim Cassam. Cassam wants us to accept the common wisdom that belief in conspiracy theories is problematic. Like Richard Hofstadter and Karl Popper before him, Cassam takes it that the problem with conspiracy theories lies not so much to do with the theories themselves but, rather, in the intellectual character of those who would believe them. Which is to say that rather than judging conspiracy theories on the evidence, our suspicion of them comes out of worries about the kind of people who turn out to be conspiracy theorists. After all, most of us have been in a situation where, when presented with a long list of reasons to believe some conspiracy theory, our immediate response has been to focus our attention on the character of our conspiratorial companion. However, Cassam's argument for why this is the right move for us to make doesn't just mistake political piety for intellectual virtue, but treats a willingness to challenge political beliefs as mere gullibility.

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by Yohan J. John

This is the era of metrics: it seems that if we are to hack a path through the information jungle of the 21st century, we must be armed with an arsenal of scores, quantities, indices, factors, grades, and ratings. Our corporate and governmental overlords seem most comfortable parlaying in the seemingly objective language of numbers.

But can complex social and biological conditions be boiled down to scores? To GDP-per-capita, or a happiness index, or a body mass index? Social and biological metrics are attempt to quantify things that often seem unquantifiable: the overall health of a country or of a person, the ability of a school to educate its pupils, the quality of a consumer product, and even the aesthetic value of a movie, TV show, or musical album.

I've always been uncomfortable with this process of quantification: on the one hand reducing any phenomenon to a single number seems like a major oversimplification, and on the other, the procedures for generating such numbers are often opaque. How exactly is inflation calculated? Or the cost of living? How do Nielson ratings work? Or the Netflix recommendation system? My discomfort with metrics began to crystallize and expand when I was introduced to a somewhat obscure “law” that should perhaps be more widely known outside of the dismal science that originated it.

Goodhart's Law was originally formulated as follows: “Any observed statistical regularity will tend to collapse once pressure is placed upon it for control purposes.” The word 'statistical' probably doesn't excite most people. But if we cut to the essence of what is being said, we find a rule of thumb (it's not a real law of nature) that might have implications well beyond the world of economics:

“When a measure becomes a target, it ceases to be a good measure.”

Let's unpack this idea with a few examples. We can start with academic testing. Written examinations are a time-honored way to assess whether a student has learned something. But when tests scores become the metric by which to judge the performance of schools and teachers, then the connection between the test score and the quality of education often breaks down. This is because teachers “teach to the test“, or even cheat in order to raise scores. By making test scores the target, rather than one among many factors that go into the assessment process, the people involved are incentivized to find the path of least resistance that leads to the highly specific targeted outcome. This drive to find the easiest route to higher test scores is what breaks the correlation between test scores and the more general goal of quality education. You can do well on a test because you have a degree of mastery of the subject, or because you were trained in a mechanical fashion to do the specific test, with no care given to your ability to apply what is learned in other potentially important contexts. [1]

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The computer revolution has transformed education over the past quarter century. PowerPoint, greatly improved graphical and multi-media capabilities, e-books, Wikis, online student collaboration, flipped classrooms, clicker quizzes, open-access online courses (MOOCs), and the inexhaustible wealth of material available on the internet have opened up all sorts of interesting possibilities. (At the same time, discretely hidden smart phones, college-essay mills, and the inexhaustible wealth of material available on the internet have raised new challenges to teachers worried about academic dishonesty.)

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I translate, from the Urdu, Mother’s dream for Harry the shrink

Naked,
except for my nikab,

roped to a round pillar
on a sand dune

the sun’s anvil,
my feet dancing.

The turbaned Bedouin,
henna-dyed beard,

Champion Lovemaker
peace be upon Him

raked His fingers at me.
Quicksand rose to my thighs.

My heart sank.
I awoke.

Harry the shrink turns towards me,
and says, “Repressed sexual fantasy,

need for intimacy.
Nakedness: vulnerability;

nikab veiling her face
below the eyes: anonymity.

Bondage suggests either
a desire to be submissive, or

a yearning to be free.
Sinking into quicksand:

reversion into the subconscious.
Guilt about her desires

drives her to religion—
the Champion Lovemaker—

to rekindle her self esteem,
and make her feel better.”

“What is he saying to you?” Mother
asks. It’s my dream, after all.”

I resort to diplomacy. “Mother,
doctor sahib says I should help you

write down or tape record your dreams.
They are windows to your soul.”

By Rafiq Kathwari, whose debut collection, ‘In Another Country,’ is forthcoming in September from Doire Press.

by Usha Alexander

Why Harper Lee’s second novel, Go Set a Watchman, is more profound and important than her first

Even before its publication, Go Set a Watchman had become controversial, acquiring a whiff of conspiracy, inauthenticity, and foul play. It seemed unbelievable that Harper Lee would publish again after more than half a century of quiescence—and that too a novel written long ago and thematically near to her first and only novel, To Kill a Mockingbird. Published in 1960, Mockingbird has become an American classic and standard reading in every American high school. It is revered for its poignant telling of a thoughtful and courageous white man who does his best to hold up the candle of racial justice in the Jim Crow South. How could anything new live up to that? Why would Lee imperil her own legacy?

Since the release of Watchman, many readers have indeed announced their heartbreak over the revelations and struggles contained within. This new story takes place in the same small Alabama town we came to know in Mockingbird, where the endearingly wild little Scout grew up learning from her father, Atticus Finch, to recognize the humanity of those who seemed different from herself. But it’s now twenty years later and we meet the young woman Scout has grown into. On a visit from New York to her hometown in the mid-50s, the twenty-six year old Jean Louise Finch—who no longer goes by her childhood nickname—finds it transformed by time, the postwar economy, and the emergent Civil Rights movement. Much of the story centers around Jean Louise’s sense of unbelonging in the place where her roots remain yet deeply felt, and the cognitive dissonance she suffers as she discovers the people she most loved and trusted to be unapologetic racists:

Why doesn’t their flesh creep? How can they devoutly believe everything they hear in church and then say the things they do and listen to the things they hear without throwing up? … Everything I have ever taken for right and wrong these people have taught me—these same, these very people. So it’s me, it’s not them. Something has happened to me.

They are all trying to tell me in some weird, echoing way that it’s all on account of the Negroes… but it’s no more the Negroes than I can fly and God knows, I might fly out of the window any time, now.

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by Thomas R. Wells

Every week or so a literature professor publishes an eloquent essay about what literature is good for. Here's a nice example. The backdrop is the decades long decline of literature degree programmes in the Anglophone world. This is why you need us!, they argue, somewhat plaintively.

These essays tend to circle around the same handful of arguments. An especially prominent theme, most frequently associated with Martha Nussbaum's defence of the humanities, is that literature is good for us because it promotes empathy, and the practice of empathy is the heart of liberal ethics and the functioning of civilised society.

Unfortunately, defending literature in this way multiplies rather than reduces philistinism. By mistaking means and ends it excludes the very heart of the matter from consideration. The joy of literature is transmuted into duty. This is in line with how professional academics understand literature – as their daily work, albeit work that they love. But if this is how the people who claim to love literature talk about it, no wonder reading is in decline.

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Struck With Rust
.

from a chair close by the hydrangea in white,
and a wheelbarrow old and purely struck with rust,

the hydrangea’s lace planets in close galaxies of
three-petal poems,

the barrow’s hard, black tire and load of pulled weeds
which, until the other day, into life were thrust

now busted, heaped in a dry, foot-deep dome
in the barrow’s bed—

soon this pile of past-life will go, returning home
to nowhere in particular, but home nonetheless

to be (in quantum parts, by chance) reassigned
a place in the eternal ring

to bloom again, to be particles
in the Unknown’s newest thing
.

by Jim Culleny
8/2/15

by Charlie Huenemann

Philosophy students are typically taught the wrong lesson from the great Scottish skeptic David Hume. The standard story goes something like this. British empiricists like Locke and Berkeley wanted to connect everything we know to what we experience through the senses. The welcome consequence of this strategy is that all the stuff we see and interact with stays known – but the spooky invisible stuff, ranging from magical spirits to substantial forms and other metaphysical clutter, all goes by the wayside. But (the story continues) Hume pointed out that this strategy ends up far more corrosive than anyone expected: for, if we hold our beliefs to what we actually experience, we shall have no knowledge of causality. We see one event, and another; but never do we experience the metaphysical glue that connects the two, and forces the second event to follow the first.

The take-away lesson is that, according to Hume, we really have no knowledge of causality, and – if we are rational – we should be completely surprised every time we strike a match. This of course seems utterly loony, and it leads to spirited classroom arguments (which by itself, I’ll allow, is a good reason to teach Hume this way). How could it possibly be right that the fully rational person would not see causality at work in the world?

Well, it isn’t; and in truth, Hume never thought it was. As he defended himself to an incredulous correspondent,

… I never asserted so absurd a Proposition as that any thing might arise without a Cause: I only maintain’d, that our Certainty of the Falsehood of that Proposition proceeded neither from Intuition [sense experience] nor Demonstration; but from another Source.

Hume wasn’t a skeptic about causality. He only maintained that the causal knowledge we have does not arise from our sense experience or from our reasoning.

What’s the difference? It turns out to be an interesting one. In the first (wrong) story, the lesson is that there is no such thing as causality. That’s certainly a bold claim, but it’s not in the least compelling. No one can take it seriously except as some kind of trivial philosophical nut to crack. In the second (correct) story, the lesson is that human knowledge is not as straightforward as philosophers would like. What we know does not boil down to rational inferences from observations and arguments. It’s more natural, more organic, than that.

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by Carl Pierer

Fig. 1: a Ceilidh as Braid

This column last month, here, provided a first glimpse at the fascinating field of braids. Beneath their obvious beauty – to which their widespread aesthetic use bears testimony – lies a deep complexity. They allow for explorations of many beautiful areas of mathematics. They branch into topology, group theory, and geometry, to give some examples. The previous essay explored the theoretical side of braids, the most important results of which were:

• A mathematical concept of braids: Consisting 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.
• The word problem: Thus defined, a braid can be represented with a description of how the strands cross each other. Let σ­_I mean the i^th strand is crossing over the i+1^th strand and a negative power, σ­_i^-1 (read: sigma i inverse), mean the i^th strand crosses under the i+1^th strand. Then, a description of a braid using σ­_I's is called a braid word. The problem is: given two braids, how can we decide whether they are the same? More particularly, given a braid, how do we determine whether it is trivial?
• A solution to the word problem: The method of handle reduction. If a braid contains handles, it can be reduced. If the braid is the same as the trivial braid, this algorithm will return the trivial braid. If the braid is not trivial, this algorithm will return an equivalent braid that does not contain any handles.

It ended there with a very cursory glance at the connection between braids and dances. This idea deserves to be dealt with in greater depth, for it is not only in the abstract spheres of pure mathematics that braids demonstrate a fascinating depth. Rather surprisingly, their mathematical properties find unexpected applications to the more practical problems of motion planning for robots.

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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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