by Jonathan Kujawa

This spring I had the pleasure of spending several months as a visitor at the Mittag-Leffler Institute in Sweden. Hanging on the wall above my desk was a copy of this print:

The Mittag-Leffler Institute has two patron saints: Gösta Mittag-Leffler and Sofia Kovalevskaya. The Institute is located in Mittag-Leffler's home just outside Stockholm. He donated his home and its extensive library in 1916 with the goal of establishing a place for mathematicians to visit and collaborate. Both were built using Mittag-Leffler's personal wealth (which he obtained the old fashioned way: he married into it). Nowadays there are a number of such institutes, but at the time it was the first of its kind.

Over my desk, however, was the watchful eye of Kovalevskaya. She was a truly remarkable woman who obtained significant results on differential equations during the second half the nineteenth century. Those being the times, she struggled to find opportunities to study mathematics. When she finally earned her PhD in 1874 she was the first woman in Europe to do so. And even then it was only thanks to rule-bending by the famous Weierstrauss. In 1883 Mittag-Leffler used his considerable influence to procure Kovalevskaya a position at the University of Stockholm. In addition to mathematics, Kovalevskaya wrote several books. Sadly, she died in 1891 at the young age of 41. For a taste of her life, I recommend Alice Munro's short story “Too Much Happiness”.

Whenever I had a bad math day [1], Kovalevskaya's portrait gently and kindly reproached me. At my age she had done all of the remarkable things mentioned above. Almost to the day, when I arrived at the Institute I was the age she was when she passed away. Every day when I arrived it was yet another day more than she had, and as a white, middle-class, American male I couldn't hardly claim any disadvantages to Kovalevskaya! As I'd leave for the day, she would tsk, tsk over all my dead ends and miscalculations.

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by Omar Ali

On December 2, 2015 Syed Farooq Malik, a young American of Pakistani origin (born in Illinois) was attending his workplace holiday party in San Bernadino. He left the party early (it is not clear if there was an argument of some sort before he left) and then returned with his wife, Pakistani-American Tashfeen Malik, and the couple opened fire on his coworkers and left after 4 minutes. Fourteen people were killed, 21 injured. It has since emerged that the couple had 2 assault rifles, thousands of rounds of ammo and several pipe bombs. They had also rented a Ford Expedition SUV a few days before the attack and used it for the attack as well as in the subsequent chase and confrontation with the police. Though they managed to escape the scene of the crime, they were eventually shot dead after an exchange of fire with the police. They had left their 6 month old baby girl with her grandmother on the morning of the attack. Sometime after the shooting, Tashfeen Malik also reportedly posted a “pledge of allegiance to ISIS” on her facebook page.

It has since emerged that Farooq Malik had a normally religious upbringing but had become “more religious” in the last two years. According to his (estranged) dad, he was obsessed with Israel and “shared the ideology of ISIS leader Abu Bakr al-Baghdadi”. And it seems that his wife was brought up in far more Islamist fashion than he was. Her father is a Pakistani who works in Saudi Arabia and supposedly became “more religious” there. She lived in both Pakistan and Saudi Arabia and was a full-time niqabi when she attended Bahauddin Zakariya University’s pharmacy department. She also attended classes at Al-Huda, an Islamist organization that runs schools to teach “pure Islam” in many countries. After marriage, she did not show her face even to her father-in-law and her brother-in-law and stayed in seclusion in her California apartment. She did not attend the baby shower thrown by her husband’s coworkers (the same people the couple later went to shoot) and it is very likely that she was more “radical” than her husband. It seems likely that the two of them decided to kill people because they wanted to strike a blow for their version of Islam, but the actual choice of target (i.e. where a group of people would be murdered) may still have involved some “workplace grievance” (though no convincing grievance has yet been revealed).

Post-Script: it is now clear that perpetrators were jihadists, had been turned down by some jihadist organizations, may have thought of bigger targets, and that one friend may have had some prior knowledge of their intentions.

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How could something so beautiful not be right

—Margaret Wertheim, on Einstein’s equations
……………….. for his General Theory of Relativity

The elegance of the simplest things
makes them right. The shape of a smooth stone
cannot be argued against —one touch
is testimony of its rightness. Its small heft
says, I'm here. Its mass, snapped by a spinning tire
shattering a windshield is evidence
of the absoluteness of its being.
Its adherence to universal laws says, I belong.
Its pleasing roundness
rolling in the cup of your palm
proves its truth. The way it rests in light,
glowing amber in harmony
with the color of the rising sun
is as much a claim to rightness
as the perfection of equations
or the presence of love.
Its contours, quanta, its silence,
strange and familiar as they are,
are as correct and beautiful
as this fleeting breath.
How in truth could anything
so beautiful not be right?
.

by Jim Culleny
11/28/15

by Paul Braterman

If Isaac Newton is the father of modern physics, then Antoine Lavoisier is the father of modern chemistry. Newton was knighted, and died in his bed at age 84. Lavoisier died at age 50, on the guillotine.

A civil servant scientist

Lavoisier originally trained as a lawyer, but studied science at the same time, and set about earning admission to the Academy of Sciences. This he achieved at the remarkably young age of 25, with a combination of pure science (composition of gypsum), and applications (problems of street lighting and water supply). He invested his inherited fortune in membership of a curious body called the Company of Tax Farmers. This was involved in the collection of indirect taxes throughout the whole of France, while its members individually lent money to the Crown, thus simultaneously taking on the roles of bankers, administrative civil servants, and investors in government securities.

Lavoisier's administrative responsibilities included supervising the Gunpowder Administration. Gunpowder is a mixture of sulphur, charcoal, and saltpetre (potassium nitrate). At the time, this last was obtained from fermenting organic matter with human and animal manure. French production had become haphazard, and lack of gunpowder was one reason for France's defeat in the Seven Years War/French and Indian War of 1754 – 1763. The Dutch had developed a system using beds of manure mixed with rotting vegetation, which Lavoisier copied, to such good effect that within a few years France was able to supply the material to its allies. French exports of saltpetre played an essential role in the American Revolution, and Lavoisier was able to write “One can truly say that North America owes its independence to French gunpowder”.

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Withered Rose

A version after Iqbal

By what words can I deem you
desire of the nightingale's heart?
The morning breeze was your cradle,
the garden a tray of perfumes.

My tears rain like dew,
and in my barren heart your ruin
an emblem of mine,
my life a dream of roses.

By Rafiq Kathwari, whose debut collection, In Another Country, is available here.

aby Maniza Naqvi

This is about the biography of an American woman who was the author of key militant interpretations and texts which are followed by extremists today. She left New York in the 1960s and went to Egypt and then from there came to live in Lahore with the founder of the Jamaat e Islami Maulana Maududi. She lived in Lahore till she died in 2012 at the age of seventy- eight. This is also about an Austro-Hungarian man who became the spiritual advisor of the House of Saud. It is about Maryam Jameela, an American woman whose given name by her parents was Margaret Marcus and an Austro Hungarian man— Muhammad Asad whose given name was Leopold Weiss. It is about them then, and it is about us now.

The first time I saw razor wire was along the checkpoint at Eretz in Gaza, a dozen years and change ago. And then more recently I'd seen it coiled atop the compound walls of the offices and homes of donor agencies in Addis Ababa, a city changing fast with shanty towns being mowed down to create overpasses and underpasses, Malls and residential paradises for the purchasing powerful foreigners and visiting and returning diaspora. And I'd seen it at the peripheries of a holiday lakeside resort in Malawi built on land grabbed from fishermen, razor wire, presumably to keep the animals out. Now I stared at the knife's edge of gobs of razor wire at ground level in Lahore. And the last time I'd seen such an array of foreign corporate journalists passing through the barricades to speak to the local citizens as the notable and primary experts on that country, on just about every aspect of it, was well—in Bosnia. Now here they were, ‘conflict' experts, some the same, doing the same thing in Lahore.

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The City

After Faiz Ahmad Faiz's “Yahan Se Sheher ko Dekho”

Look
My city bedecks itself in fetters

The carefree walk
The careless talk

No more

The head held high
The feet unbound

No more

No more
I trust

Light from dark
Wine from blood
Joy from mourning

Flowers in my city
Wilt into the dust

by Anjum Altaf, who curates the The South Asian Idea Weblog, a learning resource for college students in South Asia.

Aging Face

With mirrors the aging face became personal.
It hung before only on the heads of others,
but with realization that the still surface
of a pond returned the image of the seer,
when polished metals revealed a clear and troubling truth,
when a silver-backed square of glass
served up serial images of hard fact so precisely
denial was impossible,
the aging face became a self portrait
in intimate time, like a film frame
on a reel of a fresh spring field
which, between glimpses,
had been raked by a ruthless gardener
determined to turn new life into that
which can only be remembered

Jim Culleny
11/16/15

by Carl Pierer

Among the many tools available to mathematicians attempting to prove a statement is something called “proof by contradiction” or reduction ad absurdum. The general method of the proof is a very smug one: Let the statement to be proved be Φ. The strategy, then, is to suppose that Φ is false and to consequently derive a contradiction. Now there are quite a few, infinitely many one might say, ways of going about this. This shan't be our concern. What is of interest here is the question as to what kind of contradiction forms the end of such a proof. Let us distinguish 2 cases:

• Internal contradiction. The proof takes the form of:

Suppose ¬Φ. Then γ.

Δ.

∴, ¬γ.

Contradiction! ∴ Φ.

Here, we deduce an immediate consequence (γ) from the assumption that ¬Φ and then proceed by a sequence of logical steps (Δ) to show that this leads to ¬γ – a blatant contradiction. For example, let us say our statement to prove is:

Φ: is not a rational number

Then, ¬Φ is ” is a rational number” and an immediate consequence of this would be:

γ: Then we can write √2 = m/n , where m,n are natural numbers, such that m,n are coprime. That is, m/n is an irreducible fraction.

One standard proof then goes as follows:

1. Then, 2 = m²/n²

2. So, 2n² = m²

3. This means, m is even.

4. So m can be written as m = 2k for some natural number k.

5. Thus: 2n² = (2k)²

6. Ergo, 2n² = 4k²

7. And hence: n² = 2k²

8. So n is even.

9. Then 2 divides both n and m.

10. Therefore, ¬γ.

Now, we have the desired contradiction, and therefore we conclude Φ.

• External contradiction. Here, the proofs take the following form:

Suppose ¬Φ. Then:

Δ.

∴ μ.

But ¬μ! Contradiction. Therefore, Φ.

Here, ¬μ is some generally accepted mathematical truth, such as 1 ≠ 2. In contrast to the internal contradiction, it need not be a statement that is a consequence of ¬Φ. ¬μ is some statement in the general corpus of mathematical truths (i.e. proven statements) and is not necessarily linked in its content to Φ.

Now, the astute reader might question the meaningfulness of the distinction between internal and external contradiction. In particular, since μ appeared in the proof of Φ, there must be a sequence of logical derivations that relate the two. So, one might ask, how much sense does it make to distinguish between a “direct” consequence of ¬Φ and one that is related by a longer sequence of logical steps? Certainly, formally speaking, such an objection is valid. But there seems to be an intuitive sense in which some consequences are more immediate than others, and this is all that is needed at this stage.

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by Charlie Huenemann

Plato, as we know, told tales of an abstract realm beyond the senses, a realm beyond the dim and dark cave we call “the world.” It was a realm of forms, first glimpsed through the discipline of mathematics, and more thoroughly known through philosophical cross-examination, or dialectic. It’s not clear just how much religion there was in Plato’s own philosophy, but that philosophy certainly was enlarged into mystical proportions by the time of Plotinus (204-270 c.e.).

We can get a richer sense of this notion – that the pure intellect can grasp divinity – by exploring the life of Hypatia, a mathematician, astronomer, and philosopher who lived in the great city of Alexandria about a century after Plotinus. Hypatia was brilliant and utterly dedicated to the life of the intellect. She was famous as a philosopher and mathematician, and a school formed around her. She was also beautiful (it is said), and attracted many suitors; but she resisted them all in deference to the requirements of her philosophy. She became caught up in a power struggle between the city's governor and its Christian bishop, and met a grisly death at the hands of the bishop's supporters.

Hypatia's life and death has been refashioned many times over the centuries, usually in the attempt either to attack or to defend organized religion. Just reading a pair of book titles is enough to give the general idea. In 1720, the infamous atheist John Toland published Hypatia, or the History of a Most Beautiful, Most Virtuous, Most Learned and in Every Way Accomplished Lady; Who Was Torn to Pieces by the Clergy of Alexandria, to Gratify the Pride, Emulation, and Cruelty of the Archbishop, Commonly but Undeservedly Titled St. Cyril. (Earlier times featured the most informative book titles!) Toland's book was answered promptly in a pamphlet by Thomas Lewis, entitled The History of Hypatia, a Most Impudent School-Mistress of Alexandria: In Defense of St. Cyril and the Alexandrian Clergy from the Aspersions of Mr. Toland. I know of these titles from a more recent work with the decidedly more neutral title, Hypatia of Alexandria, by Maria Dzielska (1995). Dzielska offers an overview of all the various uses in both fiction and scholarly literature to which Hypatia has been put to use, and then delivers a very plausible and thorough account of what we can plausibly put forward as the facts of the case.

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by Mara Naselli

One evening in February 2012, I was in a Chicago noodle shop looking for a table for one. The television was on—a news report from Syria. The Syrian Army had begun its attack on Homs. The frame of the screen, jostling in the confusion, captured the faces of a woman and a boy. The woman was distraught. The boy, bewildered. I watched agape, for an instant transposing myself in the place of the woman and my own sons in the place of the boy. Children cannot take in their shattering world. The slight young man waiting tables that evening must have seen something in my expression. He changed the channel to a soccer match.

The poet and artist David Jones was just nineteen years old when he enlisted in the Royal Welsh Fusiliers as an infantryman in the British army in January 1915. Later that year, just after his twentieth birthday, he was serving on the western front until he was wounded in July 1916.

For the next two decades Jones wrote In Parenthesis, his account of his experiences in the First World War. It is not an easy read. There are many different kinds of language at work in Jones’s modern epic—not just the Welsh, English, and Cockney of the infantrymen and officers, but also the military jargon and slang, rhymes, and popular songs. There are also the well-known allusions to Arthurian legend, Shakespeare, Lewis Carroll, Hopkins, Coleridge, and others. Jones’s language—its syntax, sound, and diction—was so foreign to me, I found myself enchanted and lost. I copied out long passages, including the footnotes, to track this myriad mind at work.

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by Tasneem Zehra Husain

The development of [my] thought-world is in a certain sense a continuous flight from wonder.

—Albert Einstein

We are marked in large part by our celebrations: what we celebrate, and how we choose to do so, says a lot about who we are. As a global society, we seem to be increasingly fascinated with genius, and almost sixty years after his death, Einstein continues to be emblematic of this phenomenon. Over time, he has become larger than life – more myth than man.

In the annals of physics, Einstein's footprints are everywhere; his contributions as various and scattered as if they too, were subject to the brownian motion he elucidated. Along most paths he trod, he left staggering achievements in his wake. Einstein made crucial contributions to a nascent quantum theory, his incisive explanation of the photoelectric effect was so brilliant, it won him the Nobel Prize, and yet, most physicists, if asked to name Einstein's definitive work, would unblinkingly pick general relativity. The theory celebrates its hundredth birthday in a couple of weeks, and festivities are underway across the globe.

Over four successive Thursdays in November 1915, Einstein presented his (still developing) theory to the Prussian Academy of Sciences in Berlin. He laid down The Formal Foundations on 4 November 1915, and worked feverishly every day, polishing and honing the theory, coaxing out some of the gems that lay hidden within, until finally, on 25 November he unveiled the spectacular Field Equations of Gravitation.

“Hardly anyone who truly understands it will be able to escape the charm of this theory,” wrote Einstein in this final paper, and his remark has stood the test of time, just as well as his equations have. The General Theory of Relativity is a work of unparalleled beauty; in fact, it exemplifies what it means for a physical theory to be beautiful, and is often quoted as the canonical example of such.

There is an air of inevitability about general relativity, which Nobel Laureate Steven Weinberg equates with beauty. “In listening to a piece of music or hearing a sonnet one sometimes feels an intense aesthetic pleasure at the sense that nothing in the work could be changed, that there is not one note or one word that you would want to have different,” he writes. It is so with general relativity. No idea or symbol seems extraneous or out of place.

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by Paul Braterman

For disrespectful blogging and criticism of the religious authorities, one thousand lashes, to be administered 50 at a time. A fine of one million Riyals (roughly £170,000). 10 years in jail. If, like me, you have been wondering what horrible crimes could merit so severe a punishment, now you can find out.

I across a selection of Raif Badawi's writings in my local Waterstone's, and see that it has been published in the US, UK, and Canada, and that it is also available in French, German, and Italian. I do not know if there is an Arabic version; if there is, it will certainly not be available in the author's native Saudi Arabia. However, the attempts to silence Badawi have ensured him a far wider audience than he could ever have thought possible.

Having read the offending blog posts, I am shocked. Not because they are strident, or violent, or opposed to religion, or subversive of government, but because they are none of these things, and yet have attracted so extreme a reaction.

A brief foreword to the book (see below) is followed by a short preface, by the bilingual TV journalist Constantin Schreiber. This places Badawi's writings in context, and describes how the hopes he expressed in the days of the Arab Spring have been dashed by events. Unlike Schreiber, I am neither an Arabic speaker nor an expert on events in the Middle East, so I am doing my best here using the English language translation and my own limited background knowledge. If I have been guilty of any mistakes or misinterpretations, I hope that better-informed readers will point these out.

The first piece is a plea for freedom of thought and expression, using a quotation from the Quran itself in support. The second, a complaint against censorship and the outrage synthesised to justify it, begins with the unconsciously prophetic words

Many of the Islamist activists of Saudi Arabia dream of the return of an era along gone: they fantasize about the times of the caliphs. Those caliphs were known to banish and murder their opponents.… The modern Islamists hope history will repeat itself.

Indeed, we now once again have a self-styled caliph, at the head of the entity known as Daesh, [1] that now of all times needs no further discussion by me.

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