by Jonathan Kujawa

Last month at 3QD we discovered that Pascal's Triangle contains all sorts of surprises. Like most things in mathematics, there is no end to the things you can uncover if you keep digging and have a curious mind. If we revisit the Triangle with our eye open for curiosities we notice that the sequences of numbers which run parallel to the side of the triangle look a bit interesting [1]:

Okay, the first line is just a sequence of 1s and is pretty darn boring. The second sequence is the counting numbers and is only slightly better than the 1s since anyone over the age of five who knows the addition rule for the Triangle can see why they are there.

But the third row! They seem to follow some sort of pattern, but it's not quite so obvious what it might be. We already have the hint that they're called the Triangular Numbers. If you were a boring person devoid of curiosity, you could go on with your life never knowing what's going on. But you're not and you know the Triangle rewards the curious. The following image explains why they're called the Triangular Numbers:

From Wikipedia.

Once you notice that the pattern, it's not too hard to see that the nth number in this sequence is the number of balls needed to make a triangle which has n balls along one side (to go from one triangle to the next you just add another row to one side and counting those additional balls amounts to the addition rule of Pascal's Triangle). It's also not too hard to see [2] that the nth Triangular Number is given by the formula n(n+1)/2.

Let's agree that the 0th triangular number is 0. Not only is it reasonable to say the triangle with no balls on each side is made from 0 balls, we'll see it also turns out to be a convenient convention.

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by Jalees Rehman

There are at least two ways of how the topic of trust in God is broached in Friday sermons that I have attended in the United States. Some imams lament the decrease of trust in God in the age of modernity. Instead of trusting God that He is looking out for the believers, modern day Muslims believe that they can control their destiny on their own without any Divine assistance. These imams see this lack of trust in God as a sign of weakening faith and an overall demise in piety. But in recent years, I have also heard an increasing number of sermons mentioning an important story from the Muslim tradition. In this story, Prophet Muhammad asked a Bedouin why he was leaving his camel untied and thus taking the risk that this valuable animal might wander off and disappear. When the Bedouin responded that he placed his trust in God who would ensure that the animal stayed put, the Prophet told him that he still needed to first tie up his camel and then place his trust in God. Sermons referring to this story admonish their audience to avoid the trap of fatalism. Just because you trust God does not mean that it obviates the need for rational and responsible action by each individual.

It is much easier for me to identify with the camel-tying camp because I find it rather challenging to take risks exclusively based on the trust in an inscrutable and minimally communicative entity. Both, believers and non-believers, take risks in personal matters such as finance or health. However, in my experience, many believers who make a risky financial decision or take a health risk by rejecting a medical treatment backed by strong scientific evidence tend to invoke the name of God when explaining why they took the risk. There is a sense that God is there to back them up and provide some security if the risky decision leads to a detrimental outcome. It would therefore not be far-fetched to conclude that invoking the name of God may increase risk-taking behavior, especially in people with firm religious beliefs. Nevertheless, psychological research in the past decades has suggested the opposite: Religiosity and reminders of God seem to be associated with a reduction in risk-taking behavior.

Daniella Kupor and her colleagues at Stanford University have recently published the paper “Anticipating Divine Protection? Reminders of God Can Increase Nonmoral Risk Taking” which takes a new look at the link between invoking the name of God and risky behaviors. The researchers hypothesized that reminders of God may have opposite effects on varying types of risk-taking behavior. For example, risk-taking behavior that is deemed ‘immoral' such as taking sexual risks or cheating may be suppressed by invoking God, whereas taking non-moral risks, such as making risky investments or sky-diving, might be increased because reminders of God provide a sense of security. According to Kupor and colleagues, it is important to classify the type of risky behavior in relation to how society perceives God's approval or disapproval of the behavior. The researchers conducted a variety of experiments to test this hypothesis using online study participants.

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by Misha Lepetic

“New York isn't your fantasy.
You're the fantasy in New York's imagination.”
~ John DeVore, New York Doesn't Love You

There is a time-honored genre of literature that masochistically trucks with the fatalism and rejection of living in, loving and eventually leaving New York City. I know this is a real genre, because the fact that there is an anthology proves it. Writers especially, perhaps due to the ephemerality of their profession, seem to have an axe to grind when it comes to leaving New York. It's not that no other city generates this passion; rather, no other city has fetishized and memorialized this ambivalence to such an extent. To these writers, leaving New York is tantamount to an admission of failure, and they passionately rationalize the ways in which they have not failed. But New York evolves, like any other city, and it is worth asking if the reasons for leaving these days are substantially different from those of previous decades.

Joan Didion's 1967 classic essay “Goodbye To All That” sets the confessional tone that is implied in all of these narratives: “But most particularly I want to explain to you, and in the process perhaps to myself, why I no longer live in New York.” Didion's narrative concerns the years required for the imperceptible shading from wide-eyed ingénue to a vaguely numb and indifferent denizen. Her prose is compassionate, and wears the weariness of experience lightly: “It was a very long time indeed before I stopped believing in new faces…Everything that was said to me I seemed to have heard before, and I could no longer listen”. In the end, she does not fling New York away in disgust – she accompanies her husband to Los Angeles for a sabbatical away from the city. As a result she leaves New York almost accidentally, like remembering a few days after the fact that you forgot your umbrella in a restaurant, then deciding it wasn't worth the trouble of going back to get it.

Contrast this genteel regretfulness with John DeVore's recent aphoristic punch-up, “New York Doesn't Love You“:

New York will kick you in the hole, but it will never stab you in the back. It will, however, stab you multiple times right in your face.

No one “wins” New York. Ha, ha.

You will lose. Everyone loses. The point is losing in the most unexpected, poignant way possible for as long as you can.

Complaining is the only right you have as a New Yorker. Whining is what children do. To complain is to tell the truth. People who refuse to complain, and insist on having a positive outlook, are monsters. Their optimism is a poison. If given the chance they will sell you out.

DeVore lives in a different New York from Didion: he doesn't really elaborate on what success might actually look like, for himself or for anyone else. Your plan, whatever it may be, will go wrong. Fifty years of water flowing underneath the Brooklyn Bridge will do that.

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by Madhu Kaza

I was jetlagged during the week in early March 2014 when I heard the news that air traffic controllers had lost contact with Malaysia Airlines Flight 370. The news seemed at first like a seamless detail added to my mental fog. I had just returned to New York from India where I had spent much of January and February thinking about plane crashes. I had begun research on a project that I vaguely imagined would be a history of Indian aviation accidents, and I had spent many days examining news archives that documented incidents and their aftermaths. I had studied the names and capacities different aircraft, learned some of the aviation terminology such as “controlled flight into terrain” (which despite the reassuring word “controlled” is not a good thing), and begun to log a timeline of events. As I read the newspaper accounts I couldn't ignore the political dimensions of these disasters, either, whether they involved international coordination for search and rescue operations, the cover-up of lax security and safety measures, the response of the airlines to victims' families or the settlement of lawsuits. I also noticed that initial newspaper reports often contained inaccuracies that had to corrected later as more information emerged. As much as anything else, I became fascinated by how these articles were written, how the narratives of these disasters took shape over time and by what they told and what they left out. Out of whatever facts were reported and the scant details of these articles, I would try to imagine what it was like to experience these events as a witness, a survivor, a family member of a victim, a responder, or a reader of the morning paper. I became increasingly curious, in particular, about how disaster shapes one's experience of time.

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by Kathleen Goodwin

I recently read the surgeon and public health researcher Atul Gawande's latest book, “Being Mortal” in which he writes about end-of-life care in the American healthcare system, which has developed into a series of increasingly radical attempts to postpone death, often at the expense of the comfort of patients during their remaining life. Gawande argues that doctors should refocus their goals on quality rather quantity of life. He advocates for physicians to educate patients about their healthcare options and then assist them in making informed decisions. A few weeks after reading Gawande's book my younger sister was hospitalized for 5 days with an acute case of bacterial pneumonia. An otherwise healthy 22-year old, she was not the type of patient considered in “Being Mortal” but I was surprised to find that many of the topics Gawande described appear to be relevant regardless of the patient's prognosis.

Some healthcare providers have acknowledged that empowering patients and reducing their suffering is a secondary concern in modern medicine and usually far from a priority. A doctor's main goal is to heal but in many cases this seems to lead to a sacrifice of a patient's autonomy and comfort, in the name of an eventual return to full health. It's a practical cost-benefit analysis— distilling years of medical training into layman's terms in order to explain a diagnosis, options for care, and the possible effects of procedures and medications with every individual patient would prevent physicians from having the time to see other patients and would net out to fewer patients healed. In terms of quantifiable success, a patient's experience in a hospital is measured by morbidity and mortality not by the comfort of her stay. Concurrently, in the U.S. healthcare system doctors are generally paid for services rendered and are incentivized to see as many patients as possible.

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by Tamuira Reid

I remember being five years old and sitting in the pediatrician's office as my mother explained the problem. She talks in voices, doctor. Three or four of them at a time. I stand by her door and listen and it is frightening, I tell you. Just frightening.

After hours of testing, more to appease my worried mother than anything else, Doctor Wolfe looked gently at the two of us and said, Yes, your daughter does have a special condition. And it is called a wonderful imagination. Mrs. Reid, your daughter is creating stories that she is simply too young to write down.

A few years later, those voices would become my first poems, first one-act plays. They would become my lifeline.

For as easy as writing came to me, the rest of school did not. I'd stare out the window for hours on end, dreaming of what the world had in store for me, instead of learning the algebraic equations my teacher scribbled across the board in front of us. I would read chapbooks during recess and perform monologues out in the open field behind the block of modular classrooms. I was bright but uninspired. I remember tutors being involved. I remember hushed conversations between my parents behind closed doors.

It wasn't until I ran away to college that I began to really engage in my lessons. I remember the first class vividly. Professor Lesy walked into the room with a small grey boom box under one arm and a bundle of books and papers under the other. His hair was long and unkempt, shirt wrinkled. Coke-bottle glasses. When he finally sat down at the head of the table, pushing the play button to release classical music into the air, he looked at each one of us and said, If you can't write from your heart, you have no business writing at all.

Day after day, workshop after workshop, we picked up our essays now covered in ink. He demanded the truth from us; we gave him half of it. We gave him what we thought he wanted to know. As the semester progressed, we began to let go of what we thought we knew about writing and realized we knew nothing at all. That writing is a process, a craft, not necessarily an inherent gift.

I wrote everyday for the entire first year of my college career. I wrote first thing in the morning and last thing at night. I wrote with coffee, I wrote with beer. I wrote until my hands would cramp so badly that I'd be forced to take a break, smoking cigarettes out in the cold New England night.

It wasn't shocking that I connected to writing this way. I'd always loved writing. What was surprising, however, was how I would fall into teaching.

When Lesy would get up in front of the room, he had this incredible, commanding presence that seemed to grab you around the neck and say, Look at me! What I tell you is divine truth! You will never hear anything more interesting than what I'm about to say right now! He had us completely enraptured, under his psychotic but totally intoxicating spell. It was kind of magical.

He gave a solid performance, day in and day out. And that is exactly what it was: a performance.

I wanted to perform.

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by Mandy de Waal

“I never realised that I had a problem until quite recently. Before this I thought it was normal. I thought that everyone thinks (about money) the way I do,” says Charles Hugo (not his real name) on the phone from an upmarket seaside resort on South Africa's Cape coast.

“It doesn't matter how much money I earn, I always feel I need more.” As Hugo describes his relationship with money, his speech is carefully measured. The forty-something year old former banker-cum-currency trader pauses for a while during our conversation, and then adds: “It was only recently I realised I have a problem.”

For as long as Hugo can remember money has featured as a complex protagonist in his life. The dominant force in his decision making, this man measures everything in terms of what it will cost him and if the value he'll be getting from the transaction will be worthwhile. It doesn't matter if the transaction is an emergency trip in an ambulance or going into a restaurant for a sirloin.

“Every time a decision needs to be made, the first thing I think about is the financial impact. It doesn't matter what it is. I will always find a money angle to each and every decision,” he says. “If someone has a problem I won't think about the person or the emotion.” For Hugo cash is cognitive king.

“I used to think everyone was like this. That money came first in everyone's lives. It's only during the past couple of years that I've realised this is not the case.” Today Hugo – who doesn't want his identity to be revealed publicly – is in his early forties. Hugo talks about having a problem and about being obsessed with money. A couple of times the word ‘addiction' enters the conversation. “I have an addiction to money,” he says, adding that his ‘obsession' with money causes problems in his interpersonal relationships because he thinks very differently from those he cares about.

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OLD FORMS WILL NOT BE ENTERTAINED

(a sign at the India Consulate, New York)

For David Barsamian

Old chants to the Ganges shall not be entertained
Dead cows float in holy water unrestrained

Family roots shall be ascertained
Nationality of mother should reign

Old friends shall not be entertained
I pledge allegiance to the newly-famed

Object of Journey shall be explained
To find out etymology of Kashmir-curfewed

Old profession shall not be entertained
Shall I reincarnate as Poet-un-Chained?

An old form (in triplicate) shall be obtained
First copy drained, second birdbrained, third scatterbrained

Enemy passports will be stamped Foreordained
Will heart-rending appeals ever be sustained?

Alternative gods shall be deported
Against the ruins of a world what is regained?


By Rafiq Kathwari, whose first book of poems is forthcoming in September 2015 from
Doire Press, Ireland. More work here.

by Yohan J. John

Metaphor is a hallmark of human communication, and a vital tool of scientific thinking. Along with its more formal cousin, analogy, metaphor allows us to create linguistic and conceptual bridges from the known to the unknown. Some of the greatest breakthroughs in science began with an analogical leap between seemingly unrelated concepts. Isaac Newton brought the heavens down to earth when he realized that the movement of the moon around the earth was analogous to the motion of a ball thrown so hard that it just keeps falling perpetually. This line of reasoning led Newton to realize that the same deterministic laws held for both terrestrial and cosmic phenomena. The scientific revolution that took place in the wake of this discovery brought Enlightenment thinkers to the conclusion that the universe worked like clockwork: its components interlocking like cogs and gears that whirred with coordinated mechanical precision. The vibrations of a violin string and the propagation of sound and light were linked by analogy with wave motion. Analogies also helped usher in the atomic age: Ernest Rutherford likened the atom to the solar system, with electrons wheeling around a central nucleus like planets around the sun. The twin revolutions of communication and genetics gave rise to one of the world's most powerful and popular scientific metaphors: the idea that the DNA molecule — the bearer of heredity from one generation to the next — was a code, or a blueprint, or even “the book of life”. Phrases like 'genetic code' have become so common that we frequently forget that it is a metaphor at all. [1]

Over the course of a series of essays, I'd like to investigate the metaphor of code, and how it came to dominate biology. Our investigation of the code metaphor must revolve around two related questions. Firstly, how did the nuts-and-bolts talk of cells, membranes, proteins and chemical bonds become engulfed in a sea of words like 'encoding', 'decoding', 'transcription', 'translation' and 'editing' — the language of telecommunication and cryptography? Secondly, despite the successes of the code metaphor, might it obscure some of the most intriguing and difficult problems in biology? Before we even get to biology, it will be useful to lay some groundwork, and understand what modern scientists mean when they use words like “information” and “code”. So in the first part of this series, I'd like to review the seminal work that led to the modern conception of information. [2]

Beginning in the 19th century, successive waves of technological innovation transformed the way humans communicated with each other. Telegraphs and telephones made the near-instantaneous, global exchange of information possible. The technology, and the sheer pace of change, brought new questions to the forefront of scientific thinking. What exactly is happening when we send a telegram, or make a phone call? When we send a message, what is being transmitted along the wires, or through the ether? In other words, what is information?

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by Namit Arora

What to make of the verdict in Delhi’s Assembly elections this month? After a dismal show in the national election last year, when many had written it off, the Aam Aadmi (‘common man’) Party achieved a crushing win in Delhi with 67/70 seats. Delhi may be electorally small but being the capital of the nation and of empires past, the headquarters of the national media, and a trendsetter for other regions, its control has great emotional significance—all too evident in AAP’s main rival BJP’s desperate eleventh-hour tactics to win in Delhi.

The verdict has drawn many explanations: AAP’s strategy, grassroots campaign, and populist promises; people’s disaffection with the fueling of communal strife by RSS, VHP, and other BJP-affiliated Hindu right-wingers; the invisibility of BJP’s much-hyped ‘development’; BJP’s arrogance, disorganization in Delhi, and its dirty campaign; AAP’s success in framing this as a two-way contest which enabled anti-BJP votes to consolidate behind AAP; Modi’s $18K splurge on a suit—in retrospect, a major wardrobe malfunction, and so on. Whatever the mix of factors, last year’s ‘Modi wave’ now seems subdued, if not stalled.

Various polls show that AAP won due to greater support from the poor, the rural sections, slum dwellers, lower castes and Dalits, religious minorities, students, and women voters of Delhi—an enviable constituency for social liberal democrats like me. I’m not a member of AAP or any other party but I wanted AAP to win—not only because the alternatives were much worse but also because, despite some lamentable populism, there are many hopeful and progressive things in AAP’s politics and 70-point manifesto. These include two innovations it already practices: transparency in campaign finance and ensuring candidates have no heinous criminal charges. AAP’s win may bolster BJP’s opposition in upcoming state elections. It may even slow the rise of BJP’s communalism and its model of development in which corporate sector growth is prioritized far above social welfare and primary services—a GDP-growth led model akin to neoliberalism and almost always marked by rising disparity, shrinking safety nets, crony capitalism, and faster ecological damage. Indeed, why pursue GDP and corporate sector growth if not to primarily help increase human knowledge and reduce human suffering?

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by Aditya Dev Sood

This standalone piece is part of a special series on Startup Tunnel, a new incubator based in New Delhi. Links to earlier articles appear at the end of the article.

This past week I led a workshop on building pitchdecks, not only for our own startups but for a wider crew of entrepreneurs. I’d asked the assembled group to help me whiteboard out the essential information they thought should be included in a pitchdeck. One bullet point, nearly overlooked towards the end of the list, said: Competition and Competitive Advantage. At this point I asked the group whether they didn’t also want to talk about creating a new monopoly?

Folks seemed to shift uncomfortably in their seats… apparently not. Why not? I asked. Do you mean like a public sector company, someone said. Ah, ah, ah, no, I said, realizing that the term monopoly wasn’t an abstract concept in the Indian context, but a real and oppressive part of our not-so-distant past. Yes, perhaps I’m being a bit loose with the term monopoly — I don’t mean state-sanctioned and absolute monopoly — I mean the kind of market leadership, let’s say more than 50% market-share, that can resemble monopolistic dominance. Don’t you want that? Well, VCs want to know that the space is real, said one founder. We want to work in an area where there is a good chance of success, said another, and that means there will already be competitors.

But isn’t that a problem? I asked. If the area you’re working in can already be defined as a competitive landscape it isn’t really all that new. In which case, how innovative is your startup concept? Think of any major startup that you’re inspired by these days and you’ll see they’re all near monopolies: SpaceX, Tesla, Airbnb, Dropbox, Snapchat. Before they came along, no one was doing what they’re doing. Now that they exist, people will come along and try to emulate them, but they’ve actually created a new market, in which they’ll continue to enjoy dominance. In some sense, that’s the only way these kinds of valuations can even be justified, either economically or socially or even in terms of the public good. These startups have created fundamentally new value and new social-technological possibilities that never existed before.

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by Carl Pierer

Madam,

Thank you for opening my eyes concerning the question whether students should be beaten to study Maths up to the age of 18. Your well-argued and logically impeccable column in the Times establishes beyond reasonable doubt that no one needs to know any Maths further and above the mere basics. It is absolutely clear what those basics are, and they don't need further definition (obviously, knowing times tables is essential and needed, whereas being able to solve quadratic equations is far beyond basic).

Moreover, you successfully avoid the many times rehashed bad arguments in debates about education. Instead, you focus on the points that do indeed form the basis of any good and progressive line of argument. These are: (i) to think about reforms in terms of the education currently successful people have had, (ii) to do away with skepticism about inductive inferences, (iii) to consider a general education system in terms of highly talented and successful people, (iv) to not let yourself be confused by the subtleties of the subject matter as there really is just one thing at stake, (v) to insist that there is something wrong with the subject itself if the curriculum doesn't teach what is “useful”. Unfortunately, the brevity of your column prevented you from exploring the full force of your arguments. Allow me to do so on your behalf.

With one of your examples you solve two age-old problems in philosophy. You write: “The top western country [in the Pisa international league tables] is Liechtenstein. Know anyone who has changed the world who was educated in Liechtenstein? I don't either, but that is the European country we are hoping to emulate.” First off, this solves the problem of induction. The problem is that the inference from “All Swans I've observed so far are white” to “All swans are white” is not necessarily true, i.e. it's logically possible that “All swans I've observed so far are white” is true and “Not all swans are white” is true as well. But why do people wrack their brains over this? Your argument establishes that we merely need to assert the conclusion, isn't it just trivially true that since you don't know anyone who was educated in Liechtenstein and changed the world, there is nobody? At least 200 years of philosophy over and done with.

This conclusion is also a very important one, because obviously if Liechtenstein is doing well in the Pisa league tables and still there is no one who was educated there and changed the world, then the education in Liechtenstein cannot be that good. At least not as good as in Britain, where plenty of world-changing people were educated. Pisa league tables, your argument shows, are not a suitable means of measuring which educational system produces world-changing people. A general education is precisely about the upbringing of exceptional individuals and not the provision of basic numeracy and literacy. Since the Pisa examinations only manage to test the level of the latter, educational policy makers who are concerned with the questions that really matter should stop emulating countries that do well in the Pisa league tables.

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by Hari Balasubramanian

Observations and pictures from a visit in October 2014 to the Andean town of Cuenca and the surrounding area.

1. Surgeries in an Isuzu Truck

Since 1994, a small team of clinicians has been bringing elective surgeries to Ecuador's remotest towns or villages, places that have do not have hospitals in close proximity. From the city of Cuenca – Ecuador's third largest town, where they are based – the team drives a surgical truck to a distant village or town. Though a small country by area, the barrier of the Andes slices Ecuador into three distinct geographic regions: the Pacific coast in the west; the mountainous spine that runs through the middle; and the tremendously bio-diverse but also oil rich jungle expanse to the east, El Oriente, home to many indigenous tribes. Apart from a few major cities – Quito, Guayaquil, Cuenca – towns and villages tend to be small and remote.

Each year the team goes on 12 surgical missions, roughly one per month. A trip lasts around 4 days: a day's drive to get to the place; 2 days to conduct 20-30 surgeries (sometimes more sometimes less); and then a day to return. Patients pay a nominal/reduced fee if they can: the surgeries are done irrespective of the patient's ability to pay. The clinicians belong to a foundation called Cinterandes (Centro Interandino de Desarollo – Center for Inter-Andean Development).

Amazingly, the very same Isuzu truck (see above) has been in use for more than 850 missions and has seen 7458 surgeries from 1994-2014! The truck itself is not very large; in fact, it cannot be, because it has to reach places that do not have good roads. The mobile surgery program has the lowest rates of infection in the country (see [1] for more details). Not a single patient has been lost. The cases to be operated on have to be carefully chosen. Because of the lack of major facilities nearby, only surgeries with a low risk of complication can be done. Hernias and removal of superficial tumors are the most common. Hernias can be debilitating, yet patients may simply choose to live with them for many years rather than visit a far-off urban hospital. For many, leaving work for a few days and traveling to get a health problem fixed is not an option.

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Dis Hate Taste Kiss

Mind is what the brain does.
…………………… —Marvin Minsky
.

………. imagine this:

this morning was so cold I thought, frostbite
and a vision (gloves) occurred

if I hadn’t thought cold
my hands may just as well have felt
they were in Aruba, and gloves absurd

………. then the wind hissed
.
.
being mindful is
the best way to miss frostbite
know bliss dis hate taste kiss
.

by Jim Culleny
2/13/14