by Carl Pierer

It is necessary that two men have the same number of hair, gold, and others.[i]

This meme is taken from a scene in the Cohen brother's 1998 comedy “The Big Lebowski”. During a game of bowling, Walter, in the picture, gets annoyed at the other characters constantly overstepping the line. Drawing a gun, he asks: “Am I the only around here who gives a shit about rules?”[ii]

Considering that there are roughly 7 billion people on earth, a positive answer seems highly unlikely. But it is possible to do better. We can know with certainty, i.e. prove, that the creator of the meme is not the only one. This is a simple and straightforward application of a fascinating, intuitive and yet powerful mathematical principle. It is usually called “pigeonhole principle” (for reasons to be explained below) or “Dirichlet's principle”.

***

The German mathematician Gustav Lejeune Dirichlet was born in 1805 in Düren, a small town near Aachen. Although Dirichlet was no child prodigy, his love for mathematics and studies in general became apparent early in his life. His parents had him destined for the career of a merchant, but upon his insisting to attend the Gymnasium (secondary school), they sent him to Bonn, at the age of 12. After only two years, he transferred to a Gymnasium in Cologne, where he studied mathematics with Georg Simon Ohm (1789-1854), who is famous for his discovery of Ohm's Law. Dirichlet left this school after only one year, with a leaving certificate in his pocket but without an Abitur, which would cause him some troubles later in his life. At that time, students were required to be able to carry a conversation in Latin to pass the Abitur examination. With only three years of secondary education, Dirichlet could not comply with this crucial requirement. However, Dirichlet was fortunate that no Abitur was required to study mathematics.

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by Thomas Rodham Wells

You may have heard of the gender income gap. It is one of the most obvious signs that despite being equal in theory, women still lack real equality. Some of it is still due to active discrimination by people who still haven't got the equal treatment message. But much more of it is the result of a history of unjust gender norms and factual errors inscribed into our institutions, most notably the bundle of moral expectations we hold about what can be demanded of women rather than men in terms of unpaid care of children, the disabled and the elderly.

The problem is that fairness – the principle of the equal treatment of equals – is a poor guide to action here. Our history has bequeathed us a gender injustice complex of interlocking and mutually reinforcing institutional arrangements and moral values that altogether make women less economically valued than men. The outcome is pretty clear – women tend to earn much less than men – but it is hard to pin down specific violations of fair treatment by specific agents who can be held responsible. Sexist pigs are relatively easy to pick out and chastise, and in some cases may even be successfully prosecuted for discrimination or other misbehaviour. But it's rather harder to condemn a university educated couple for agreeing between themselves to follow the traditional model of male breadwinner and female homemaker. Even if that decision is replicated in household after household leading to dramatic aggregate differences in labour market participation rates for women, especially in full-time professional work.

It is true that a great many policies have been proposed, and sometimes even implemented, to address different pieces of the gender injustice complex, from quotas in boardrooms and the top management of public institutions to compulsory paternity leave. But such reforms struggle politically, not least because they seem to impose more unfairness – the unequal treatment of men and women because of their gender. A good many people, including many women, reasonably object to the incoherence of trying to solve a fairness problem by creating more unfairness. More positive measures, such as providing free child-care from tax revenues, are considered too expensive to fully implement. And for all the political capital these policies require to be put into action, each can only have incremental effects anyway because they only address one piece of the puzzle at a time. They rarely inspire much popular support.

We've been thinking about this the wrong way, distracted by the idea that unfairness must be produced by bad motives that are best addressed by cumulative moral exhortation, or something else equally cheap like training young women to 'lean in'. If we all want gender equality then eventually, surely, it will come about by itself.

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by Mathangi Krishnamurthy

Long years ago, when I waddled around in pigtails, I said aloud the magic words that for many years characterized how I felt about the world, my world. “I will settle in America”, I said. Neither did I know how heavy “settling” can be nor was I clued into the power of words. Carelessly, toddler-ly, I threw around that which would one day make my world.We didn't say politically correct things then. As far as we all knew, all of the Americas was North America, and all of North America was the US. My father had just returned from travels to the US, and he had brought back suitcases spilling over with things guaranteed to charm curmudgeonly three year olds.

America was then not only an idea but an escape. I was charmed into thinking that going to America indicated not only the newness of a world, but a not-ness of the one I inhabited. No school, no dreary days, no strange scapes of a scary adult world with its inexplicable sorrows and forbidding rules. America was fabulous, with its flowery denims, and video games, and automatic erasers. I was mesmerized by View-Masters, with their otherworldly scuffed gaze onto so-near foreign shores.

These were the eighties. India was a sovereign, socialist, secular, democratic republic with one, and later two, television channels. We all read the national pledge aloud in school, that went something to the effect of “India is my country and all Indians are my brothers and sisters”. We all suffered one heckler in every class who would mutter sotto voce “Well who do I marry then?” We received our news from singular sources and imagined our leaders sovereign, if ineffectual. We trusted secularism, even if in its often troubled avatar, tolerance. We muddled through power cuts, and ration cards, and held onto a quiet, steely middle-classness. Benedict Anderson would have pronounced us a truly well-imagined nation; or at least, some of us.

In this world, America's otherness beckoned ever so strongly with its free love (read sex), and rampant spending; with its alter-egoness of individualism and seeming control over the world. But India allied with the USSR. The mythical Russia communicated to us only held Mathematics books, fairy tales, and War and Peace in stock. I hated math, much preferred the Brothers Grimm, and to date, am at odds with the melancholies of Tolstoy.

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by Gerald Dworkin

Tom Paulin

In the light of the recent fire-storm over the hirefire of Steven Salaita, I thought it might be interesting to revisit a case which raised similar issues about whether there are limits to what a University may do with respect to controversial speech. This was a case which did not raise issues about hiring and firing and procedural justice so it may perhaps be a better one to focus on.

In 2002, the Harvard English Department invited the Irish poet Tom Paulin to give a poetry reading as the Morris Gray lecturer. Shortly thereafter it was brought to the attention of the inviters that Paulin had made the following statements in an interview to an Egyptian newspaper.

“Brooklyn-born settlers in the occupied territories should be shot dead. I think they are Nazis, racists, I feel nothing but hatred for them.” Brooklyn? Has the man no shame?

The newspaper also quoted him as saying: “I never believed that Israel had the right to exist at all.” In a poem published earlier in the Observer he referred to the “Zionist SS” .

Another comment was “There's something profoundly sexual to the Zionist pleasure w/#Israel's aggression. Sublimation through bloodletting, a common perversion.” Oh, sorry that was Steven Salaita.

As a result of this, and without as far as we know any influence by Harvard donors, the English Department retracted their invitation.

A hail of protests ensued. Strange bedfellows issued letters. This one came from Alan Dershowitz, Laurence Tribe and Charles Fried.

“By all accounts this Paulin fellow the English Department invited to lecture here is a despicable example of the anti-Semitic and/or anti-Israel posturing unfortunately quite widespread among European intellectuals (News, “Poet Flap Drew Summers' Input,” Nov. 14). We think he probably should not have been invited. But Harvard has had its share of cranks, monsters, scoundrels and charlatans lecture here and has survived.

What is truly dangerous is the precedent of withdrawing an invitation because a speaker would cause, in the words of English department chair Lawrence Buell, “consternation and divisiveness.” We are justly proud that our legal system insisted that the American Nazi Party be allowed to march through the heavily Jewish town of Skokie, Illinois. If Paulin had spoken, we are sure we would have found ways to tell him and each other what we think of him. Now he will be able to lurk smugly in his Oxford lair and sneer at America's vaunted traditions of free speech. There are some mistakes which are only made worse by trying to undo them.”

James Shapiro, of Columbia where Paulin was visiting, condemned Harvard's actions as “disastrous”.

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by Rishidev Chaudhuri

At first (and at second, and third) glance, the use of spices in the cuisines of the subcontinent is a subtle and mysterious art, full of musty cupboards staffed by aging apothecaries (and grandmothers) and intertwined with theories of humor-balancing and our particular relationship to the gods. Recipes and spice blends are passed on in scribbled old notebooks and on furtive scraps of paper, copied and recopied like the epics, with long lists of spices and proportions, some crossed out and replaced with others for inexplicable reasons. The spices are essential, we are told, the order in which they are added is crucial, the mind of the cook must be perfectly clear, and the incantations must be uttered perfectly resonantly.

But how to make sense of this confusion if one did not grow up hovering over a mortar and pestle? Or even if one did and was momentarily distracted (perhaps by adolescence)? One route is a close reading of existing recipes and practices, noting patterns, highlighting parsimonious explanations and gradually drawing grander and grander conclusions. Equally useful is naïve phenomenological experimentation: an analytic strategy, where we isolate and examine spices to see what they bring to our senses. In this we should be motivated by Blake's dictum that to know what is enough we must cross it: the most clarifying way to figure out what a spice is doing is to increase its proportions in a recipe ad absurdum, until the structure starts to crack and you glimpse what column of the edifice was being held up by that particular spice. Unfortunately, while this is the right way to conduct disciplined phenomenological inquiry, it is not the right way to make something to eat, and so we will scale our ambitions back and instead simply exaggerate the spice that is being studied and strip away some of the surrounding complexity. This is an ongoing project of mine, as I try to understand subcontinental food, and I'm particularly interested in collecting and devising one-note recipes that highlight a particular spice (see this article on pepper, for example).

Coriander fruits, also commonly called coriander seeds, are good for this kind of analysis. Their flavors are crucial to many subcontinental foods, and are part of what makes the cuisine distinctive. Yet, unlike a number of other spices, coriander tends to be gentle and forgiving. It's a friendly spice, with flavors of citrus and flowers mixed in with a warm spiciness. If you have coriander seeds in your pantry, chew on a few seeds as you read this and you'll smell and taste the flavors I mean (you can do this with the powder too, but it's less pleasant and it'll dry out your mouth). There's also a slight soapiness, which I'm told some people pick up on more than others. If you're curious about the chemistry of coriander, Harold McGee's book On Food and Cooking is wonderful (as usual).

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by Hari Balasubramanian

You might wonder who is conversing with whom. The best description I have is that these are two voices or perspectives in my head debating each other.

“This thing called the sense of self, the ego or the ‘I'. There are many claims floating around these days that confidently say that the sense of self is an illusion. Not sure what to make of this. If I accept such a claim then who or what is this ‘I' that just accepted the illusory nature of the self? It's like walking around in circles, like a dog chasing its tail and going nowhere.”

“You could say the ‘I' is some kind of energy in our conscious experience that comes together in such a way as to create the illusion.”

“Maybe so. But how does that help me? I still feel the sense of self exists; that's what is speaking right now! I can't just wish it away because somebody says it is an illusion. I can't wish it away even if my own intellect logically reasons out that it is an illusion. For example, I know very well that the body – the best proxy I have for the ‘I' – had a certain shape in the womb, a different shape as a baby, something entirely different as an adult, and will disintegrate after death. So I can reason pretty clearly that what we call the body is ever changing, from one moment to the next, that there is nothing constant there. Yet each one of us, without fail, invariably points to his or her body to claim that this is me…”

“I agree that there is something that always seems to be hovering around. And it is quite practical in claiming an ever-changing and perishable body, among a host of other perishable things, for itself. But when examined closely, the ‘I' cannot be pointed out as anything concrete – where is it?”

“It is right here, always the main point of reference, always claiming that this is me or this is not me. Or I like this or I do not like this, or I am neutral to this. We cannot even frame a sentence while conversing that does not have ‘I' or ‘you' or ‘this' or ‘that' in it. If consciousness of anything is there, the ‘I' is very much there mixed up with it. This is why – unless I experience it myself firsthand: I don't know what that would be like – the idea that the self is an illusion does not affect me. It's as if one moment the ‘I' feels strongly it exists, and then the very next moment the very same ‘I' cleverly changes hats and declares: ‘Well, I shouldn't take myself seriously, since there is strong evidence that I am an illusion!'”

“Still, don't you think there is some practical benefit to the idea of no-self, of not taking the ego seriously? When I observe my thoughts closely, I find there is very little control; I don't know where thoughts are coming from and what their source is. They just come and go; sometimes my mind is very busy, chaotic, and at other times very slow and relaxed. Everything – decisions, events, what captures my attention, how things unfold in time – seems so complex and intertwined. An emotion or idea or feeling or inspiration will surge up within me whether I want it or not. When this understanding sinks deep enough, I may learn to understand that others too are being driven by thoughts that are not under their control. So maybe the ‘I' can observe and train itself. It may or may not work – there are never any guarantees – but you remind yourself, all the time, to not take the ego seriously.”

“You have to do it all the time because this thing called the ‘I' is present all the time!”

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Hedge

we unload the freight of day
as night wraps up what day has told
there’s not much more to say—
myself in shade, eagle in her hold

both are restless in day’s throes.
who among us really understands
what night becomes, where daylight goes,
who know the ground, the place we stand?

still the worm in unturned earth makes way,
a cardinal, blood red, in a maple’s crown
is more tuned than I am to the stuff the earth displays:
what lifts it up, what presses down

what’s hidden keeps us on the edge
with those we love our only hedge
.

by Jim Culleny
4/25/13

by Grace Boey

Lately, I’ve been thinking a lot about Internet trolls. I’d always been vaguely aware of their presence, and had read some articles here and there about the threats they pose to constructive debate—but I never truly realized the full nature of their pestilence until I had to deal with them myself. Since I started publicly writing and commenting online, I’ve encountered abusive, non-constructive comments and emails on an increasingly frequent basis. I also co-manage an atheist social media page; I’m not the direct target of the trolls that lurk here, thankfully, but I do have to trawl through their vile comments, where they often abusively attack (or embarrass) causes I care about deeply.

Naturally, none of this has been good for my blood pressure. Last month, I became irritated enough to start work on a long exposition of online trolling—in the process, targeting specific trolls I’d personally encountered. Yes, hell hath no fury like a woman trolled, and I spent more time than I’d care to admit compiling comprehensive records of at least three of these individuals’ online activities. I even uncovered the physical, non-virtual identity of one of them.

You’d think I’d be happy for striking troll-hunter’s gold. Yet, the more I wrote and uncovered, the less I wanted to publish a piece bashing trolldom in general, let alone one that put specific individuals on the spot. Though I was pleased with the quality of the article, I refrained from running it. And very fortunately so—a couple of weeks after the piece would have been published, the Brenda Leyland troll-exposing controversy erupted.

Here’s what I've come to think: there’s very strong reason to believe that many compulsive Internet trolls need our active help. The impersonality of the internet makes it easy for them to dehumanize others, but for this same reason, it’s also easy for us to completely dehumanize them. But we must resist this temptation. Who are the people behind these monikers and computer screens, really? Why do they thrive on trolling, and why on earth don't they have anything better to do? How did they become this way? When we really stop to think about these questions, a disturbing social and psychological picture emerges. Virtual trolls may be a problem as much to their human selves as they are to their human victims.

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Lauren Davis extemporizes about how astronauts became known as gods:

The stories told of ancient beings so powerful that they could fling themselves into space and explore the points of light in the heavens. When Lady Adelaide moved into one of their unused crafts, many called it blasphemy. She called it research.

**

by Leanne Ogasawara

That's what I wanted to tell him about. But the evening when I finally had my chance to chat with a former astronaut and now NASA leader, I had lost my voice.

He was standing there holding court about the state of science education in the country. He was also discussing the lack of political vision, and I thought how the level of this decline came with an astounding –and perhaps corresponding– level of malaise. Looking back, other than World War II and perhaps the country's early days of Revolutionary politics, has anything truly excited and united people here more than scientific innovation and the space program? Apropos of this, not so long ago a friend, who had just turned 50, listed in a Facebook post several of what he considered to be the highlights of his half century on earth– and of eight great achievements, three were space related (and of the other five, only one, the eradication smallpox, was even serious).

Yes, space is exciting. It also generates wonder in people–especially children.

So, how could we let it decline?

Manned missions to Mars is the next big dream it seems. Not surprisingly, when the Dutch non-profit outfit Mars One held open applications for new astronauts, the largest group by far to apply were Americans–and this was for a one-way mission!

(Muslim applicants beware of UAE Fattwa Committee/ 'Haram' decree).

One could argue that discovery is something that is inherently part of the human condition and that space is just in our blood. So, also not surprisingly, the former astronaut mentioned above spoke excitedly about Mars. “A human astronaut can do what it took the robotic rover to do in a long day in under twenty minutes,” he said. “And, let's face it, Mars is the only place humans could possibly live,” he continued.

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by Josh Yarden

Here We Go A-Gain

I just finished reading the end of the Five Books of Moses, again, and even though I did not read the entire five books this year, or any other year for that matter, I have already started over from the beginning. This past week was the festival of Simchat Torah, dedicated to celebrating our connection to the text we have come to know as the first five books of the Bible. It marks the end of the cycle of weekly readings, and the beginning of the renewed cycle. We went strait from the account of Moses' passing (at the end of the Book of Deuteronomy) to the meditation on the creation of the world (at the beginning of the Book of Genesis), as though that is the natural order of the verses in a Torah scroll.

Each year is a new beginning in the cycle of Torah reading, but even if you were to read the 79,847 words of a complete Torah scroll, even if that is all you did all year, you would still have skipped over much of what there is to find there. There is always more there than previously met the eye, because the nearly eighty thousand words are presented in prose poems. Scratch the surface, and even the seemingly mundane legalistic sections are bursting with metaphor, wordplay, and oblique references to other parts of the text.

Revisiting the text is never quite returning to the same text. The words remain the same, but since a year has passed, or perhaps many, the reader is never quite the same as during a previous read. The old text now exists within a new context. As we approach familiar stories with additional sensibilities, we can gain something new each time we read it again. Many passages of Torah can be understood more deeply over time. Here is one illustration of how a story that will be coming around again soon is given to multiple interpretation.

Isaac Unbound

A young person reading the story of the binding of Isaac might imagine being tied down on an altar and prepared for sacrifice by a parent. Reading the same words as the parent of a young child makes it quite a different story. What could possess a person to even consider the possibility of sacrificing a child? Abraham was somehow stopped from committing the act of ritual slaughter, but that moment is nonetheless the last time that Abraham and Isaac speak or meet face to face in the biblical narrative. Indeed, later rabbinic writings retell the story as though Abraham had actually sacrificed his son.

Studying the biblical text anew provides some insight as to how the story could be understood that way. There are things we sacrifice, metaphorically speaking. People are at times among the ‘sacrifices' we make. Even though we do not physically cut them down, we do at times give up on people for various reasons, perhaps regrettably so. The parent of a young adult might come to wonder if in some sense, he had not in effect 'sacrificed' a relationship with a son or daughter on the 'altar' of something previously held with a blindly driven commitment… a career, or something even more frivolous. After sufficient damage is done, it may be too late to repair the relationship.

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by Matt McKenna

There was a time when American football was played without helmets, and there was a time when Dracula's best trick involved opening doors with his mind. Since those early days, however, both American football and the Dracula films have taken a turn for the extreme, and their body counts have increased as a result. That's not to say the days of yore were without death: football killed nineteen college athletes in 1905 and the Dracula character murdered a literal boatload of people in 1922's Nosferatu. But both the NFL and the Dracula films have clearly dialed up their intensity in the past decade to the detriment of both players' health and horror audiences' entertainment. It is therefore no surprise that these two institutions have become reflections of each other, entangled particles reacting in tandem to the pressure of consumerism that demands more/bigger/louder of everything upon that which it fixates. Indeed, the latest Dracula film, Dracula Untold, is a clear metaphor for the modern day NFL, an undead sports league that stalks the entertainment landscape leaving not two puncture wounds on the necks of its victims but rather chronic traumatic encephalopathy in the rattled brains of its players. Though the league currently has over a hundred million viewers in the United States, one has to wonder if football's dire health risks and the NFL's byzantine rules designed to protect players will eventually lead to the sport's eventual irrelevance in the same way that Dracula Untold's absurd death toll and convoluted mythology makes the film unwatchable.

The first on-screen appearance of Dracula in the 1922 silent German film Nosferatu technically wasn't an appearance by Dracula at all–the vampire was renamed Count Orlok in an attempt to avoid copyright infringement after the producers were unable to secure the rights to Bram Stoker's novel. But whatever. Dracula's/Count Orlok's powers are few and mainly limited to telekinetically opening and shutting things like doors and coffin lids–a cool trick for sure, but nothing compared to titular Transylvanian's abilities in Dracula Untold. Not satisfied with merely controlling doorways or converting the innocent living into the vile undead, the latest iteration of Dracula can summon the entirety of the planet's bats and hurl them at invading armies like an ICBM from an aircraft carrier. He also possesses a set of powers similar to Superman's including incredible strength, speed, endurance, flight, and so forth. That said, there are a few downsides to being a vampire in the Dracula Untold universe, mainly having to do with the fiending for human blood and the inability to go outside on a sunny day. Tradeoffs.

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by Eric Byrd

A few years ago Slate's culture editor David Haglund posted a piece called “Marilynne Robinson, the Terrence Malick of the Literary World.” Malick and Robinson, he said, are kindred artists. They share a pattern of striking debuts, mid-career hiatus, and late fertility; also, an unfashionable theological seriousness, and a deep attention to the connectedness of all life, a view of nature as a “shining garment in which God is concealed and revealed.” After happening upon Robinson's 1989 polemic Mother Country: Britain, the Welfare State, and Nuclear Pollution at a time when I was obsessed with Malick's latest film (and his first set in the present of filming) To the Wonder, I would add that their similar preoccupation with wholeness means a similar horror at environmental pollution, and a desire to remind their audiences that, all being connected, those who exploit the environment exploit their fellow man; and that the immediate toxic aftermath, and the red-handed schemes of disposal, first harm the poor and powerless.

In Mother Country Robinson situates the blithe disposal of nuclear waste in the Irish sea and the contamination of Cumbria within Britain's tradition of “expropriation and immiseration” of its poor, from the Poor Laws, to the displacements of industrialization, to the contemptuous coercions of the welfare state. To the Wonder was filmed in Bartlesville, Oklahoma, a town in which Malick lived part of his childhood, a town on the edge of a contaminated zone that embraces northeastern Oklahoma, and parts of Kansas and Missouri. A century of unrestricted lead and zinc mining (privileged war industries, supplying lead shot for the Civil War and shell casings for the World Wars) resulted in generations of intellectually delayed or disabled schoolchildren, cancer-ridden adults, and a landscape undermined by excavations and dotted with “chat piles,” hillocks of granular lead-laced waste on which miner's families used to picnic. Ben Affleck's character, Neil, an environmental scientist, is shown climbing one. Within the zone, Picher, Oklahoma, was in 2009 entirely abandoned – its 1,600 residents paid to leave – and now stands as a ghost town. Robinson was born and raised in Sandpoint, Idaho, near the Coeur d'Alene Basin, another condemned zone of lead-zinc mines.

To the Wonder is so exciting a development because it is a masterful integration of the autobiographical past and the social present. On first viewing I thought it was about hydraulic fracturing, “fracking” – which it is. Past pollutions inform ours. In the United States, for the sake of “energy independence” state governments, with the tacit approval of the Federal, are knowingly poisoning hundreds of rural communities. One of the most striking sequences of To the Wonder is Neil's survey of an endangered neighborhood. His presence, and the invasive intimacy of his work – locks are snipped from young hair, and bagged as specimens; excavators claw the properties – draws a crowd, fearful, agitated, almost hostile. They are sick and want to know why. A priest played by Javier Bardem despairs before the diseased and immiserated flock.

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by Sabeen Mahmud

Twenty-four years ago, I fell in love for the first time—with a Macintosh Plus computer which profoundly altered the course of my life and was significant in shaping my anti-establishment, anti-war, pro-freedom worldview. It became an invaluable portal into myriad subcultures, from beat poetry to the Yippies, fuelled by the dark meanderings of Pink Floyd.

After college, I spent the next several years developing multimedia products, exploring the intersection between technology, art, literature, and music. But, by the mid-2000s, I was getting increasingly restless. Karachi was a cesspool of chaos. People were leaving in droves, our politicians continued to make promises they had no intention of fulfilling, and the country lurched from one military dictatorship to another. It was a depressing time and my first moment of existential crisis. Disillusioned, I agreed to an offer to move to Delhi.

Beginning to dream

Whilst waiting for my visa to come through, I started fantasizing. What would it take to create a space that espoused liberal, secular values through its programming and projects?

The next day, the conversation moved out of my head and onto a whiteboard. I sketched out a fantasy space: a large open courtyard for theatre, dance, spoken word and improv performances, readings, talks, and film screenings. All around the courtyard would be smaller rooms for workshops and events, a bookshop, a coffeehouse, studios for artists and designers, shops for artisans to showcase their work, and a bed-and-breakfast that would pull in some income to subsidize operations. With Rs. 12,000 (about US $113) in my bank account, I ran a check on the cost of land through my estate agent who gave a ridiculous, astronomical figure which paralyzed me into inaction for months.

Toward the end of 2006, I was walking up the stairs to my office and the penny dropped. I realized that the grownups were right: I should start small, test, and iterate. So, trained by those key people in my life – my mother Mahenaz and my mentor Zak, I took a leap of faith and relinquished my Dehli plan to cater to my lofty ambitions settling on an 1800 square feet office, with an open(ish) on the second floor of a building.

Finding some money

I had decided that this little social enterprise in the making was to be a not-for-profit venture and with that model, raising capital from investors or getting a bank loan approved was not an option. We had Rs. 1,000,000 (about US $9,400) stashed for my grandmother's health fund. With her consent, I used the money to get things going.

In January 2007, we christened The Second Floor (T2F). After some quick consultations and brainstorming, PeaceNiche was born and T2F became its first project.

The target launch date for T2F was set for May 2007.

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by Jonathan Kujawa

This spring I attended the annual meeting of the Mathematical Sciences Research Institute. While there I heard a fantastic talk by Dr. Holly Krieger about which I'd like to tell you. If you'd like to hear Dr. Krieger tell you herself, I highly recommend the Numberphile video she hosted. You can see it here.

Dr. Krieger works in the area of dynamic systems. Faithful 3QD readers will remember that we ran into this topic a few months ago when we talked about the Collatz conjecture and the mathematics of billiards (see here). Dynamical systems is the field which studies systems (the weather, the stock market, the hands on a clock, a ball ricocheting around a billiard table) which changes over time according to some rule.

A seemingly simple example of this is the Fibonacci sequence. You probably saw it as kid:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269,….

This is the sequence of numbers which starts with a 0 and 1, and then each subsequent number is the sum of the previous two: 0+1=1, 1+1=2, 1+2=3, 2+3=5, etc. To a mathematician this is a dynamical system. We can think of the nth number in the sequence as the state of the system after n seconds and the addition rule tells us how the system changes from one second to the next.

Last time we talked about dynamical systems we were interested in the question of whether such a system ever returns to its starting state. A properly working clock always ends up back where it was twenty-four hours ago. At the other extreme, the stock market will never end up back in the exact same state. Somewhere in the middle we have the billiard ball. It may or may not return, depending on the shape of the table and where you start the ball.

From this point of view the Fibonacci sequence is boring as all get out. It just gets bigger and bigger forever. But Dr. Krieger is the sort who isn't satisfied with such an answer. She asks questions like: You get a new number every time, but is it really “new” or “mostly old” [1]?

What do I mean? Well, we first need to recall the prime numbers. These are numbers like 2, 3, 5, and 7 which can't be evenly divided by another number (except 1 and itself, of course). On the other hand, 4, 6, 8, and 9 are not prime as they can be divided by 2's and 3's. That is, a non-prime can be written as a product of other numbers (like 24=4×6). If you keep subdividing you can eventually write any number as product of primes (like 24=2x2x2x3).

You should think of the prime numbers as the atoms of numbers: every number can be broken down into primes and you can't go any further. To stretch the analogy a little further, most folks are more excited when you discover a new atomic element than if you “just” discover a new combination of old elements. In the same spirit, you might think to ask if the Fibonacci sequence is made up of a few primes used over and over (like using 2 and 3 to make 6, 9, 12, 18, and 864), or if new primes are used as you go along.

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