Yosemite National Park (HD timelapse video)

Yosemite National Park, USA

Source:  Yosemite HD from Project Yosemite on Vimeo.

Background: here

Understanding the Sufis with William Dalrymple (video)

William Dalrymple (Wikipedia) (born 1965) is a remarkable scholar and traveller.

I first knew of him through his excellent travel book In Xanadu (1989), recounting a journey he undertook in 1986, during his second summer as an undergraduate (senior history scholar) reading history at Trinity College, Cambridge, that retraced the path taken by Marco Polo from the Church of the Holy Sepulchre in Jerusalem to the site of Shangdu, famed as Xanadu in English literature, in Inner Mongolia, China.

From the Wikipedia article on Dalrymple:

"Dalrymple has lived in India on and off since 1989 and spends most of the year at his farmhouse in the outskirts of Delhi, but summers in London and Edinburgh.

"Dalrymple's interests include India, Pakistan, Afghanistan, the Middle East, Mughal rule, the Muslim world, Hinduism, Buddhism, the Jains and early Eastern Christianity.

"All of his seven books have won major literary prizes, as have his radio and television documentaries. His first three books were travel books based on his journeys in the Middle East, India and Central Asia. His early influences included the travel writers such as Robert Byron, Eric Newby, and Bruce Chatwin. More recently, Dalrymple has published a book of essays about South Asia, and two award-winning histories of the interaction between the British and the Mughals between the eighteenth and mid nineteenth century. His books have been translated into more than 30 languages."

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I just came across Dalrymple's excellent 2005 TV documentary, Sufi Soul, that investigates Sufi music and spirituality (in Syria, Turkey, Morocco, Pakistan, and India), a subject that has received scant attention in the West. For me, it has opened a new door onto a fascinating vista.

Sufi Soul (High video quality. No subtitle)

Another copy of Sufi Soul (of lower quality, with English subtitle)

Ivan Sytin: A Russian better known in Chinese than in English

I just bought a book entitled "为书籍的一生" ("My Life for the Book", here (in Chinese); Жизнь для книги), a re-printed 1963 Chinese (mainland) translation of the memoirs of Ivan Dmitrievich Sytin (Иван Дмитриевич Сытин (Russian Wikipedia article, with good Google translation), 绥青), a prominent Russian publisher in the era immediately preceding the Russian Revolution of 1917.

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"Through sharp and unremittingly ironic observations, Sytin describes with insight and amusement or dismay Tsarist Russia's bureaucracy, the Orthodox Church, the Imperial court, and a number of the country's most renowned writers, including Anton Chekhov, Leo Tolstoy, Maxim Gorky, and journalist Vlas Doroshevich."

"Sytin's memoir, a tale of Great Russian society voiced by a parvenu, depicts a pre-Revolutionary Russia of small shops, churches, convents, deep religious faith, and flawed rulers. While the Revolution eventually deprived Sytin of all means to continuing publishing, his resilience and enterprise remain a lasting legacy."

It appears that Sytin's memoirs has not been translated into English (a English translation is due for publication in June 2012), and is little known in English.

A reliable indicator of Sytin's obscurity among the Anglophones is the absence of an English Wikipedia article on him.


Sytin is therefore a rare instance of a notable Western figure whom I would not have known about were I not literate in Chinese.

Ruud, Charles A. (1990). Russian Entrepreneur: Publisher Ivan Sytin of Moscow, 1851 - 1934. Montreal: McGill-Queen's University Press (amazon)

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(source)

Ivan Dmitrievich Sytin (24 January (5 February) 1851 - 23 November 1934), Russia's leading pre-Revolution publisher of books, magazines, and the top daily newspaper, Russian Word (Russkoye slovo).

Ivan Dmitrievich Sytin, had literate but poor peasant parents and only two years of schooling in his native village of Gnezdnikovo, Kostroma Province. Venturing first to the Nizhny Novgorod Fair at fourteen as helper to a fur-trading uncle, he apprenticed at fifteen to a Moscow printer-merchant who helped him start a business in 1876, the year of his marriage to a cook's daughter who would be vital to his success.

Like his mentor, Sytin issued calendars, posters, and tales that itinerant peddlers sold to peasants throughout the countryside. When in 1884 Leo Tolstoy needed a publisher for his simple books (the Mediator series) meant to edify the same readership, his choice of Sytin raised this unknown to respected status among intellectuals. Sytin then began to publish for well-educated readers and branched into schoolbooks, children's books, and encyclopedias by investing in the new mass-production German presses that cut per-unit costs. His rise as an entrepreneur who exploited the latest technology led contemporaries to tag him "American" in method.

Sytin claimed that he became a newspaper publisher in 1894 at Anton Chekhov's urging, and he hired able editors and journalists who made his Russian Word the most-read liberal daily in Russia. Lessening censorship and rapid industrialization in the last decades of the tsarist regime helped Sytin add to his publishing ventures and kept him a millionaire through the economic disruption of World War I. After the 1917 Revolution, Sytin received assurances from Vladimir Lenin that he could publish for the Bolshevik regime, only to be cast off as a capitalist after Lenin died in 1924. The final decade of his life was marked by gloom, austerity, and obscurity, offset only by his church attendance and his writing of memoirs (published in the USSR in 1960 in a shortened edition). His downtown Moscow apartment is today an exhibition center in his honor.

Bibliography

Lindstrom, Thaïs. (1957). "From Chapbooks to Classics: The Story of Intermediary." American Slavic and East European Review 16:190 - 201.

Ruud, Charles A. (1990). Russian Entrepreneur: Publisher Ivan Sytin of Moscow, 1851 - 1934. Montreal: McGill-Queen's University Press.

Watstein, J. (1971). "Ivan Sytin - An Old Russian Success Story." Russian Review 30:43 - 53. (first page)


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(source)

Ivan Sytin was called a person of rare gifts. He came from a peasant family, and his only legacy was his father's blessing. At the age of 14 he came to Moscow to make a success of his life. Sytin began with joining the book shop of merchant Sharapov. “I was tall and sturdy. I could do any kind of work,” said Sytin later. “My duties were to clean my boss's shoes, lay the table for shop-assistants, bring food for them; in the morning I had to bring water and firewood to the house, buy provisions at the market. I did everything honestly, neatly and on time”.

Soon the boss came to appreciate the efforts of the bright and zealous teenager, and appointed him his own valet. He fostered the love for reading in him. At first Sytin read religious books, then the boss began to give him rare editions. For Sharapov book trade was an accidental undertaking, and so he knew little about it, relying mostly on his assistants.

As a result of ten years of assiduous work Sytin acquired extensive experience and earned some money. With the help of his master he opened a small lithographic business, which paved the way for an enormous book and magazine publishing enterprise. When he worked at Sharapov's shop he listened to tradesmen's stories and came to the conclusion that ordinary people needed good books whose value was accessible to them. That is why he began his undertaking with printing books by the famous Russian novelists Anton Chekhov, Leo Tolstoy, Alexander Pushkin and others. Inexpensive and well published, his books were in great demand. In addition Sytin began to print the “Popular Calendar”, a kind of handy encyclopedia that found its way to virtually every Russian family. By printing inexpensive but necessary edition he defeated his competitors and soon became the boss of Russia's book publication. For Sytin commerce was a means, not a goal. However, as an entrepreneur he had to abide by the laws of the book market with its free prices and competition. To compensate for the publication of inexpensive books Sytin printed costly editions, such as encyclopedias in luxury book covers meant for well-to-do people.

The success of Sytin's enterprise was based not only on his business grasp and willingness to take the risks, but also on his use of advanced printing equipment and ability to organize an excellent system of marketing.

His dream was to build near Moscow a publishing town equipped with the latest machinery, with excellent houses for the workers, with schools, hospitals and theaters, all in the name of books.

However that dream was not to come true. After the 1917 Bolshevik Revolution his publishing house was nationalized and Sytin lost his business. His attempts to engage in publishing books under the Soviet government ended in failure. The last years of his life he in poverty and obscurity. Sytin died in 1934. However history has preserved the memory of the man who did so much to promote enlightenment in Russia.

The Joy of Quiet: Pico Iyer

The joy of quiet

As our lives become more hectic, the need to slow down becomes more urgent

by Pico Iyer (source)

About a year ago, I flew to Singapore to join the writer Malcolm Gladwell, the fashion designer Marc Ecko and the graphic designer Stefan Sagmeister in addressing a group of advertising people on "Marketing to the Child of Tomorrow".

Soon after I arrived, the chief executive of the agency that had invited us took me aside. What he was most interested in, he began - I braced myself for mention of some next-generation stealth campaign - was stillness.

A few months later, I read an interview with the perennially cutting-edge designer Philippe Starck. What allowed him to remain so consistently ahead of the curve? "I never read any magazines or watch TV," he said, perhaps a little hyperbolically. "Nor do I go to cocktail parties, dinners or anything like that." He lived outside conventional ideas, he implied, because "I live alone mostly, in the middle of nowhere".
Around the same time, I noticed that those who part with US$2,285 (S$2,965) a night to stay in a cliff-top room at the Post Ranch Inn in Big Sur pay partly for the privilege of not having a TV in their rooms; the future of travel, I'm reliably told, lies in "black-hole resorts", which charge high prices precisely because you can't get online in their rooms.

Has it really come to this?

In barely one generation we've moved from exulting in the time-saving devices that have so expanded our lives to trying to get away from them - often in order to make more time.

The more ways we have to connect, the more many of us seem desperate to unplug. Like teenagers, we appear to have gone from knowing nothing about the world to knowing too much all but overnight.

Internet rescue camps in South Korea and China try to save kids addicted to the screen. Writer friends of mine pay good money to get the Freedom software that enables them to disable (for up to eight hours) the very Internet connections that seemed so emancipating not long ago.

Even Intel (of all companies) experimented in 2007 with conferring four uninterrupted hours of quiet time every Tuesday morning on 300 engineers and managers. (The average office worker today, researchers have found, enjoys no more than three minutes at a time at his or her desk without interruption.) During this period the workers were not allowed to use the phone or send email, but simply had the chance to clear their heads and to hear themselves think. A majority of Intel's trial group recommended that the policy be extended to others.


URGENCY OF SLOWING DOWN

The average American spends at least eight-and-a-half hours a day in front of a screen, Nicholas Carr notes in his eye-opening book The Shallows, in part because the number of hours American adults spent online doubled between 2005 and 2009 (and the number of hours spent in front of a television screen, often simultaneously, is also steadily increasing).

The average American teenager sends or receives 75 text messages a day, though one girl in Sacramento managed to handle an average of 10,000 every 24 hours for a month. Since luxury, as any economist will tell you, is a function of scarcity, the children of tomorrow, I heard myself tell the marketers in Singapore, will crave nothing more than freedom, if only for a short while, from all the blinking machines, streaming videos and scrolling headlines that leave them feeling empty and too full all at once.

The urgency of slowing down - to find the time and space to think - is nothing new, of course, and wiser souls have always reminded us that the more attention we pay to the moment, the less time and energy we have to place it in some larger context.

"Distraction is the only thing that consoles us for our miseries," the French philosopher Blaise Pascal wrote in the 17th century, "and yet it is itself the greatest of our miseries." He also famously remarked that all of man's problems come from his inability to sit quietly in a room alone.

When telegraphs and trains brought in the idea that convenience was more important than content - and speedier means could make up for unimproved ends - Henry David Thoreau reminded us that "the man whose horse trots a mile in a minute does not carry the most important messages".

Even half a century ago, Marshall McLuhan, who came closer than most to seeing what was coming, warned, "When things come at you very fast, naturally you lose touch with yourself." Thomas Merton struck a chord with millions, by not just noting that "Man was made for the highest activity, which is, in fact, his rest", but by also acting on it, and stepping out of the rat race and into a Cistercian cloister.



LESS AND LESS TO SAY

Yet few of those voices can be heard these days, precisely because "breaking news" is coming through (perpetually) on CNN and Debbie is just posting images of her summer vacation and the phone is ringing. We barely have enough time to see how little time we have (most Web pages, researchers find, are visited for 10 seconds or less).

And the more that floods in on us (the Kardashians, Obamacare, Dancing with the Stars), the less of ourselves we have to give to every snippet. All we notice is that the distinctions that used to guide and steady us - between Sunday and Monday, public and private, here and there - are gone.

We have more and more ways to communicate, as Thoreau noted, but less and less to say. Partly because we're so busy communicating. And - as he might also have said - we're rushing to meet so many deadlines that we hardly register that what we need most are lifelines.

So what to do? The central paradox of the machines that have made our lives so much brighter, quicker, longer and healthier is that they cannot teach us how to make the best use of them; the information revolution came without an instruction manual.

All the data in the world cannot teach us how to sift through data; images don't show us how to process images. The only way to do justice to our onscreen lives is by summoning exactly the emotional and moral clarity that can't be found on any screen.
'INTERNET SABBATH'

Maybe that's why more and more people I know, even if they have no religious commitment, seem to be turning to yoga, or meditation, or tai chi; these aren't New Age fads so much as ways to connect with what could be called the wisdom of old age.

Two journalist friends of mine observe an "Internet sabbath" every week, turning off their online connections from Friday night to Monday morning, so as to try to revive those ancient customs known as family meals and conversation. Finding myself at breakfast with a group of lawyers in Oxford four months ago, I noticed that all their talk was of sailing - or riding or bridge: Anything that would allow them to get out of radio contact for a few hours.

Other friends try to go on long walks every Sunday, or to "forget" their mobile phones at home. A series of tests in recent years has shown, Mr Carr points out, that after spending time in quiet rural settings, subjects "exhibit greater attentiveness, stronger memory and generally improved cognition. Their brains become both calmer and sharper".

More than that, empathy, as well as deep thought, depends (as neuroscientists like Antonio Damasio have found) on neural processes that are "inherently slow". The very ones our high-speed lives have little time for.

BENEFIT OF DISTANCE

In my own case, I turn to eccentric and often extreme measures to try to keep my sanity and ensure that I have time to do nothing at all (which is the only time when I can see what I should be doing the rest of the time).

I've yet to use a mobile phone and I've never Tweeted or entered Facebook. I try not to go online till my day's writing is finished, and I moved from Manhattan to rural Japan in part so I could more easily survive for long stretches entirely on foot, and every trip to the movies would be an event.

None of this is a matter of principle or asceticism; it's just pure selfishness. Nothing makes me feel better - calmer, clearer and happier - than being in one place, absorbed in a book, a conversation, a piece of music. It's actually something deeper than mere happiness: It's joy, which the monk David Steindl-Rast describes as "that kind of happiness that doesn't depend on what happens".

It's vital, of course, to stay in touch with the world, and to know what's going on; I took pains this past year to make separate trips to Jerusalem and Hyderabad and Oman and St Petersburg, to rural Arkansas and Thailand and the stricken nuclear plant in Fukushima and Dubai. But it's only by having some distance from the world that you can see it whole, and understand what you should be doing with it. For more than 20 years, therefore, I've been going several times a year - often for no longer than three days - to a Benedictine hermitage, 40 minutes down the road, as it happens, from the Post Ranch Inn. I don't attend services when I'm there, and I've never meditated, there or anywhere; I just take walks and read and lose myself in the stillness, recalling that it's only by stepping briefly away from my wife and bosses and friends that I'll have anything useful to bring to them.

The last time I was in the hermitage, three months ago, I happened to pass, on the monastery road, a youngish-looking man with a three-year-old around his shoulders.

"You're Pico, aren't you?" the man said, and introduced himself as Larry; we'd met, I gathered, 19 years before, when he'd been living in the cloister as an assistant to one of the monks.

"What are you doing now?" I asked.

"I work for MTV. Down in LA."

We smiled. No words were necessary.

"I try to bring my kids here as often as I can," he went on, as he looked out at the great blue expanse of the Pacific on one side of us, the high, brown hills of the Central Coast on the other. "My oldest son" - he pointed at a seven-year-old running along the deserted, radiant mountain road in front of his mother - "this is his third time".

The child of tomorrow, I realised, may actually be ahead of us, in terms of sensing not what's new, but what's essential.

Pico Iyer is the author, most recently of The Man Within My Head.

The mathematical mind

The following is an excellent anonymous response (here) to the question: What is it like to have an understanding of very advanced mathematics?

I would characterize the mathematical mind as rigorous (precise, exact), flexible, and  subtle.

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• You can answer many seemingly difficult questions quickly. But you are not very impressed by what can look like magic, because you know the trick. The trick is that your brain can quickly decide if question is answerable by one of a few powerful general purpose "machines" (e.g., continuity arguments, the correspondences between geometric and algebraic objects, linear algebra, ways to reduce the infinite to the finite through various forms of compactness) combined with specific facts you have learned about your area. The number of fundamental ideas and techniques that people use to solve problems is, perhaps surprisingly, pretty small -- see http://www.tricki.org/tricki/map for a partial list, maintained by Timothy Gowers.
• You are often confident that something is true long before you have an airtight proof for it (this happens especially often in geometry). The main reason is that you have a large catalogue of connections between concepts, and you can quickly intuit that if X were to be false, that would create tensions with other things you know to be true, so you are inclined to believe X is probably true to maintain the harmony of the conceptual space. It's not so much that you can imagine the situation perfectly, but you can quickly imagine many other things that are logically connected to it.
• You are comfortable with feeling like you have no deep understanding of the problem you are studying. Indeed, when you do have a deep understanding, you have solved the problem and it is time to do something else. This makes the total time you spend in life reveling in your mastery of something quite brief. One of the main skills of research scientists of any type is knowing how to work comfortably and productively in a state of confusion. More on this in the next few bullets.
• Your intuitive thinking about a problem is productive and usefully structured, wasting little time on being aimlessly puzzled. For example, when answering a question about a high-dimensional space (e.g., whether a certain kind of rotation of a five-dimensional object has a "fixed point" which does not move during the rotation), you do not spend much time straining to visualize those things that do not have obvious analogues in two and three dimensions. (Violating this principle is a huge source of frustration for beginning maths students who don't know that they shouldn't be straining to visualize things for which they don't seem to have the visualizing machinery.) Instead...
• When trying to understand a new thing, you automatically focus on very simple examples that are easy to think about, and then you leverage intuition about the examples into more impressive insights. For example, you might imagine two- and three- dimensional rotations that are analogous to the one you really care about, and think about whether they clearly do or don't have the desired property. Then you think about what was important to the examples and try to distill those ideas into symbols. Often, you see that the key idea in the symbolic manipulations doesn't depend on anything about two or three dimensions, and you know how to answer your hard question.
  
  As you get more mathematically advanced, the examples you consider easy are actually complex insights built up from many easier examples; the "simple case" you think about now took you two years to become comfortable with. But at any given stage, you do not strain to obtain a magical illumination about something intractable; you work to reduce it to the things that feel friendly.
• To me, the biggest misconception that non-mathematicians have about how mathematicians think is that there is some mysterious mental faculty that is used to crack a problem all at once. In reality, one can ever think only a few moves ahead, trying out possible attacks from one's arsenal on simple examples relating to the problem, or using analogies with other ideas one understands. This is the same way that one solves problems in one's first real maths courses in university and in competitions. What happens as you get more advanced is simply that the arsenal grows larger, the thinking gets somewhat faster due to practice, and you have more examples to try, perhaps making better guesses about what is likely to yield progress.
  
  Indeed, most of the bullet points here summarize feelings familiar to many serious students of mathematics who are in the middle of their undergraduate careers; as you learn more mathematics, these experiences apply to "bigger" things but have the same fundamental flavor.
• You go up in abstraction, "higher and higher". The main object of study yesterday becomes just an example or a tiny part of what you are considering today. For example, in calculus classes you think about functions or curves. In functional analysis or algebraic geometry, you think of spaces whose points are functions or curves -- that is, you "zoom out" so that every function is just a point in a space, surrounded by many other "nearby" functions. Using this kind of zooming out technique, you can say very complex things in short sentences -- things that, if unpacked and said at the zoomed-in level, would take up pages. Abstracting and compressing in this way allows you to consider extremely complicated issues while using your limited memory and processing power.
• The particularly "abstract" or "technical" parts of many other subjects seem quite accessible because they boil down to maths you already know. You generally feel confident about your ability to learn most quantitative ideas and techniques. A theoretical physicist friend likes to say, only partly in jest, that there should be books titled "______ for Mathematicians", where _____ is something generally believed to be difficult (quantum chemistry, general relativity, securities pricing, formal epistemology). Those books would be short and pithy, because many key concepts in those subjects are ones that mathematicians are well equipped to understand. Often, those parts can be explained more briefly and elegantly than they usually are if the explanation can assume a knowledge of maths and a facility with abstraction.
  
  Learning the domain-specific elements of a different field can still be hard -- for instance, physical intuition and economic intuition seem to rely on tricks of the brain that are not learned through mathematical training alone. But the quantitative and logical techniques you sharpen as a mathematician allow you to take many shortcuts that make learning other fields easier, as long as you are willing to be humble and modify those mathematical habits that are not useful in the new field.
• You move easily between multiple seemingly very different ways of representing a problem. For example, most problems and concepts have more algebraic representations (closer in spirit to an algorithm) and more geometric ones (closer in spirit to a picture). You go back and forth between them naturally, using whichever one is more helpful at the moment.
  
  Indeed, some of the most powerful ideas in mathematics (e.g., duality, Galois theory [http://en.wikipedia.org/wiki/Gal..., algebraic geometry [http://en.wikipedia.org/wiki/Alg...) provide "dictionaries" for moving between "worlds" in ways that, ex ante, are very surprising. For example, Galois theory allows us to use our understanding of symmetries of shapes (e.g., rigid motions of an octagon) to understand why you can solve any fourth-degree polynomial equation in closed form, but not any fifth-degree polynomial equation. Once you know these threads between different parts of the universe, you can use them like wormholes to extricate yourself from a place where you would otherwise be stuck. The next two bullets expand on this.
• Spoiled by the power of your best tools, you tend to shy away from messy calculations or long, case-by-case arguments unless they are absolutely unavoidable. Mathematicians develop a powerful attachment to elegance and depth, which are in tension with, if not directly opposed to, mechanical calculation. Mathematicians will often spend days thinking of a clean argument that completely avoids numbers and strings of elementary deductions in favor of seeing why what they want to show follows easily from some very deep and general pattern that is already well-understood. Indeed, you tend to choose problems motivated by how likely it is that there will be some "clean" insight in them, as opposed to a detailed but ultimately unenlightening proof by exhaustively enumerating a bunch of possibilities. In A Mathematician's Apology [http://www.math.ualberta.ca/~mss..., the most poetic book I know on what it is "like" to be a mathematician], G.H. Hardy wrote:
  
  "In both [these example] theorems (and in the theorems, of course, I include the proofs) there is a very high degree of unexpectedness, combined with inevitability and economy. The arguments take so odd and surprising a form; the weapons used seem so childishly simple when compared with the far-reaching results; but there is no escape from the conclusions. There are no complications of detail—one line of attack is enough in each case; and this is true too of the proofs of many much more difficult theorems, the full appreciation of which demands quite a high degree of technical proficiency. We do not want many ‘variations’ in the proof of a mathematical theorem: ‘enumeration of cases’, indeed, is one of the duller forms of mathematical argument. A mathematical proof should resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way."
  
  [...]
  
  "[A solution to a difficult chess problem] is quite genuine mathematics, and has its merits; but it is just that ‘proof by enumeration of cases’ (and of cases which do not, at bottom, differ at all profoundly) which a real mathematician tends to despise."
• You develop a strong aesthetic preference for powerful and general ideas that connect hundreds of difficult questions, as opposed to resolutions of particular puzzles. Mathematicians don't really care about "the answer" to any particular question; even the most sought-after theorems, like Fermat's Last Theorem [http://en.wikipedia.org/wiki/Fer..., are only tantalizing because their difficulty tells us that we have to develop very good tools and understand very new things to have a shot at proving them. It is what we get in the process, and not the answer per se, that is the valuable thing. The accomplishment a mathematician seeks is finding a new dictionary or wormhole between different parts of the conceptual universe. As a result, many mathematicians do not focus on deriving the practical or computational implications of their studies (which can be a drawback of the hyper-abstract approach!); instead, they simply want to find the most powerful and general connections. Timothy Gowers has some interesting comments on this issue, and disagreements within the mathematical community about it [ http://www.dpmms.cam.ac.uk/~wtg1... ].
• Understanding something abstract or proving that something is true becomes a task a lot like building something. You think: "First I will lay this foundation, then I will build this framework using these familiar pieces, but leave the walls to fill in later, then I will test the beams..." All these steps have mathematical analogues, and structuring things in a modular way allows you to spend several days thinking about something you do not understand without feeling lost or frustrated.
  
  Andrew Wiles, who proved Fermat's Last Theorem, used an "exploring" metaphor:
  "Perhaps I can best describe my experience of doing mathematics in terms of a journey through a dark unexplored mansion. You enter the first room of the mansion and it's completely dark. You stumble around bumping into the furniture, but gradually you learn where each piece of furniture is. Finally, after six months or so, you find the light switch, you turn it on, and suddenly it's all illuminated. You can see exactly where you were. Then you move into the next room and spend another six months in the dark. So each of these breakthroughs, while sometimes they're momentary, sometimes over a period of a day or two, they are the culmination of—and couldn't exist without—the many months of stumbling around in the dark that precede them." [ http://www.pbs.org/wgbh/nova/phy... ]
• In listening to a seminar or while reading a paper, you don't get stuck as much as you used to in youth because you are good at modularizing a conceptual space and taking certain calculations or arguments you don't understand as "black boxes" and considering their implications anyway. You can sometimes make statements you know are true and have good intuition for, without understanding all the details. You can often detect where the delicate or interesting part of something is based on only a very high-level explanation. (I first saw these phenomena highlighted by Ravi Vakil, who offers insightful advice on being a mathematics student: http://math.stanford.edu/~vakil/...)
• You are good at generating your own questions and your own clues in thinking about some new kind of abstraction. One of the things I've reliably heard from people who know parts of mathematics well but never went on to be professional mathematicians (i.e., write articles about new mathematics for a living) is that they were good at proving difficult propositions that were stated in a textbook exercise, but would be lost if presented with a mathematical structure and asked to find and prove some "interesting" facts about it. This kind of challenge is like being given a world and asked to find events in it that come together to form a good detective story. Unlike a more standard detective, you have to figure out what the "crime" (interesting question) might be, and you have to generate your own "clues" by building up deductively from the basic axioms. To do these things, you use analogies with other detective stories (mathematical theories) that you know and a taste for what is "surprising" or "deep". This is the hardest thing in this answer to articulate precisely but also the thing that I would guess is the "strongest" thing that mathematicians have in common.
  
  Concretely, this amounts to being good at making definitions and formulating precise conjectures using the newly defined concepts that other mathematicians find interesting. One of the things one learns fairly late in a typical mathematics education (often only at the stage of starting to do research) is how to make good, useful definitions.
• You are easily annoyed by imprecision in talking about the quantitative or logical. This is mostly because you are trained to quickly think about counterexamples that make an imprecise claim seem obviously false.
• On the other hand, you are very comfortable with intentional imprecision or "hand waving" in areas you know, because you know how to fill in the details. Terence Tao is very eloquent about this here [ http://terrytao.wordpress.com/ca... ]:
  
  "[After learning to think rigorously, comes the] 'post-rigorous' stage, in which one has grown comfortable with all the rigorous foundations of one’s chosen field, and is now ready to revisit and refine one’s pre-rigorous intuition on the subject, but this time with the intuition solidly buttressed by rigorous theory. (For instance, in this stage one would be able to quickly and accurately perform computations in vector calculus by using analogies with scalar calculus, or informal and semi-rigorous use of infinitesimals, big-O notation, and so forth, and be able to convert all such calculations into a rigorous argument whenever required.) The emphasis is now on applications, intuition, and the 'big picture'. This stage usually occupies the late graduate years and beyond."
  
  In particular, an idea that took hours to understand correctly the first time ("for any arbitrarily small epsilon I can find a small delta so that this statement is true") becomes such a basic element of your later thinking that you don't give it conscious thought.
• Before wrapping up, it is worth mentioning that mathematicians are not immune to the limitations faced by most others. They are not typically intellectual superheroes. For instance, they often become resistant to new ideas and uncomfortable with ways of thinking (even about mathematics) that are not their own. They can be defensive about intellectual turf, dismissive of others, or petty in their disputes. Above, I have tried to summarize how the mathematical way of thinking feels and works at its best, without focusing on personality flaws of mathematicians or on the politics of various mathematical fields. These issues are worthy of their own long answers!
• You are humble about your knowledge because you are aware of how weak maths is, and you are comfortable with the fact that you can say nothing intelligent about most problems. There are only very few mathematical questions to which we have reasonably insightful answers. There are even fewer questions, obviously, to which any given mathematician can give a good answer. After two or three years of a standard university curriculum, a good maths undergraduate can effortlessly write down hundreds of mathematical questions to which the very best mathematicians could not venture even a tentative answer. (The theoretical computer scientist Richard Lipton lists some examples of potentially "deep" ignorance here: http://rjlipton.wordpress.com/20...) This makes it more comfortable to be stumped by most problems; a sense that you know roughly what questions are tractable and which are currently far beyond our abilities is humbling, but also frees you from being very intimidated, because you do know you are familiar with the most powerful apparatus we have for dealing with these kinds of problems.

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A two part question to determine if you "think like a mathematician," from Prof. Eugene Luks, Bucknell University, circa 1979.


Part I: You're in a room that is empty except for a functioning stove and a tea kettle with tepid water in it sitting on the floor. How do you make hot water for tea?

Answer to Part I: Put tea kettle on stove, turn on burner, heat until water boils.


Part II: Next, you're in another room that is empty except for a functioning stove and a tea kettle with tepid water in it sitting on a table. How do you make hot water for tea?

Non-mathematician's answer to Part II: Put tea kettle on stove, turn on burner, heat until water boils.
Mathematician's answer to Part II: Put the tea kettle on the floor.

Why? Because a solution to any new problem is elegantly complete when it can be reduced to a previously demonstrated case.

Algebra, algorithm and Uzbekistan

A page from al-Khwārizmī's Algebra (source)

The words "algebra" and "algorithm" were introduced to Latin Christendom through the 12th century Latin translation of the works of a Persian polymath, born in Khwarezm (in present day Uzbekistan), and working in the House of Wisdom in Baghdad during the Abbasid Caliphate.

He is al-Khwarizmi ("from Khwarezm", c.780-850) (Algoritmi in Latin, hence "algorithm"), a mathematician, geographer, and astronomer.

Algebra and Algorithm happen to be two subjects of which I have a modest degree of mastery. Their history illustrates the role of the Islamic civilization in bridging the Classical Greco-Roman world and the High Middle Ages and beyond.

As expected, there is an impressive Wikipedia article on al-Khwarizmi (here), where we learn the following:

In the twelfth century, Latin translations of al-Khwarizmi's work on the Indian numerals, introduced the decimal positional number system to the Western world.  His Compendious Book on Calculation by Completion and Balancing presented the first systematic solution of linear and quadratic equations in Arabic. In Renaissance Europe, he was considered the original inventor of algebra, although we now know that his work is based on older Indian or Greek sources.  He revised Ptolemy's Geography and wrote on astronomy and astrology.

Some words reflect the importance of al-Khwarizmi's contributions to mathematics. "Algebra" is derived from al-jabr, one of the two operations he used to solve quadratic equations. Algorism and algorithm stem from Algoritmi, the Latin form of his name. His name is also the origin of (Spanish) guarismo and of (Portuguese) algarismo, both meaning digit.

His name may indicate that he came from Khwarezm (Khiva), then in Greater Khorasan, which occupied the eastern part of the Greater Iran, now Xorazm Province in Uzbekistan. Abu Rayhan Biruni calls the people of Khwarizm "a branch of the Persian tree"

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Further interesting facts: Khwarezm, a region to the south of the Aral Sea, saw the rise of the Khwarazmian Empire (1077-1231, culturally Persianate, ethnically Turkic),  first as vassals of the Seljuqs, Kara-Khitan, and later as independent rulers,  until the Mongol invasions of the 13th century. Xorazm (or Khorezm, a variant spelling of Khwarezm) is the name of a present day province of Uzbekistan.

Interestingly, the Khwarezmians were briefly in control of Jerusalem, during 1244-1247. (See this for details)

Frederick II of the Holy Roman Empire gained control of Jerusalem by treaty with the Ayyubid (the dynasty founded by Saladin) sultan al-Kamil in 1229. Control of the city changed hands several times between the Ayyubids and the Christians  from 1239 to 1244. In 1244 Jerusalem was in Christian hands.

The Khawarezmi Turks, displaced by the advancing Mongols and allied with the Ayyubids, invaded Jerusalem (The siege of Jerusalem in 1244) on July 11, 1244, and the city's citadel, the Tower of David, surrendered on August 23. The Khwarezmians then ruthlessly decimated the city's population, leaving only 2,000 people, Christians and Muslims, still living in the city. This attack triggered the Europeans to respond with the Seventh Crusade, although the forces of King Louis IX of France never even achieved success in Egypt, let alone advancing as far as Palestine.

Egyptian Ayyubid Sultan al-Malik al-Salih then decided to use his new Mamluk army to eliminate the Khwarezmians, and Jerusalem soon returned to Egyptian Ayyubid rule in 1247.

(source)

The Khanate of Khiva existed in the historical region of Khwarezm from 1511 to 1920, except for a period of Persian occupation by Nadir Shah between 1740–1746.


Panoramic view of Khiva, Khorezm Province, Uzbekistan, a UNESCO World Heritage Site (for high resolution view: here)

First Anglo-Japanese trade agreement (1613): a Bodleian treasure

(source)

In 1613 Shogun Tokugawa Ieyasu made a personal agreement with representatives of the East India Company, granting them trade privileges in Japan.

The East India company had been drawn to Japan by what it imagined would be abundant selling opportunities.

The exhibit at the Bodleian Library, dated 12 October 1613, is thought to be one of two copies given to John Saris, commander of the Clove, which reached Hirado on 11 June 1613, almost two years and two months after leaving England.

Ieyasu's seal is visible at the top of the document, which grants Saris privileges for trade in Japan

Continue here for an image and a translation of the agreement, and a video.