Special Circumstances

Sine

From Passage to China by Amartya Sen published in the New York Review of Books, Volume 51, Number 19, December 2, 2004. Note that the link to the full article will probably disappear into a paid archive eventually.

Footnote [4]

An interesting example of the transmission of mathematical ideas and terms can be seen in the origin of the trigonometric term "sine." In his Sanskrit mathematical treatise completed in 499 AD, Aryabhata used jya-ardha (Sanskrit for "chord half"), shortened later into jya, for what we now call "sine." Arab mathematicians in the eighth century transliterated the Sanskrit word jya into the proximate sound of jiba and then later changed it to jaib (with the same consonants as jiba), which is a good Arabic word, meaning a bay or a cove, and it was this word that was later translated by Gherardo of Cremona (circa 1150) into its equivalent Latin word for a bay or a cove, viz., sinus, from which the modern term "sine" is derived. See Howard Eves, An Introduction to the History of Mathematics, (Saunders, sixth edition, 1990), p. 237. Aryabhata's jya was translated into Chinese as ming and was used in such tables as yue jianliang ming, literally "sine of lunar intervals." See Jean-Claude Martzloff, A History of Chinese Mathematics (Springer, 1997), p. 100.

The Day Lasts More than a Hundred Years by Chingiz Aitmatov

An aerial view of the Syr Darya River near Tyuratam.
Copyright © 2000 by Anatoly Zak

Trains in these parts went from West to East, and from East to West.

And on either side of the railway lines in these parts lay the great wide spaces of the desert -- Sary-Ozeki, the Middle lands of the yellow steppes.

The main plot of this novel which is set in Kazakhstan is the heroic story of Burannyi Yedigei's journey to bury his friend Kazangap in the Ana-Beiit cemetery following the traditions of his clan. Traditions which seem to have become increasingly irrelevant in a rapidly modernized world that Yedigei has to struggle against.

This `day' during which Yedigei has to complete this burial is contrasted with several much longer spans of time (hence the title) that stretch from his past, to the exploration of outer-space, to the timeless legends of his people.

Yedigei works at a railway siding at Burannyi near a large rocket launch facility, probably meant to suggest the Baikonur cosmodrome at Tyuratam. Yedigei's unwillingness to lose his customs or to permit any kind of change in Kazakhstan due to the modernization brought to his country by Russian influence is contrasted with the human discovery of a utopian civilization by a joint U.S.-Russian space station crew. The utopia is considered dangerous by the two superpowers (Aitmatov is writing when the Soviet Union was still going strong) and further contact with this utopia is forbidden. Don't read this book for its science-fiction sub-plot. Even though Aitmatov is prescient about a joint American-Russian space station, he is simply using the alien civilization as a plot device and the novel as a whole explores some general ideas, but not using the sf genre.

While the novel is about Kazakhs and the past legends of Kazakhs, it should be noted that Aitmatov himself is Kirghiz. The most compelling parts of the book are the legends of Yedigei's clan, such as the legend of the creation of the Ana-Beiit cemetery (Naiman-ana's tragic search for her son lost in war) or the love of the famous bard Raimaly-aga for the much younger Begimai (Aitmatov compares Raimaly-aga with Goethe). These legends are adapted and invented by Aitmatov with inspiration from the great Kirghiz epic poem, `The Manas'.

There are many instances where Stalinist purges are condemned by the characters in the book. However, Aitmatov never directly addresses the Russian influence in Kazakhstan. There are no negative Russian characters, only local Kazakhs who are in positions of power because of the Russians. While Aitmatov himself was the roving correspondent for Pravda in Central Asia and a member of the Supreme Soviet, in this novel he seems to be subtly painting a tragic picture of Soviet Central Asia.

The last part of the book is quite strong, but it might take some effort to make it there if you are not fascinated by the Central-Asian backdrop.

%T The Day Lasts More than a Hundred Years
%A Chingiz Aitmatov
%A :translated into English by F. J. French
%I Indiana University Press
%D 1980
%D :First Midland Book edition 1988
%G ISBN: 0253204828 (pb)
%G ISBN: 0253115957 (hc)
%P 352
%K literature, central-asia, science-fiction

Date written: 2000/05/13

Francis Crick on Philosophy of Science

From V.S. Ramachandran's eulogy, The Astonishing Francis Crick, by way of Kitabkhana.

He had very little patience with orthodox philosophers. He felt they became too prematurely trapped in matters of terminology. I am reminded of a seminar on consciousness he gave at the Salk in the eighties. A philosopher—whose name politeness forbids me from mentioning—raised his hand and said "But Dr Crick … you are attempting to solve the so-called problem of consciousness yet you haven't even bothered to define it...can you clearly define what you are talking about?" Crick's reply: "My dear chap, there was never a time in the pre-DNA era when a lot of us biologists sat around the table and said 'Let us first clearly define life before we explore it'. We just went out there, forged ahead and found out what it was. It's no doubt good to have a rough idea of what one is talking about but matters of terminology are best left to philosophers who spend most of their time on such things. Indeed clear definitions often emerge from empirical research. We now no longer quibble over questions like is a virus really alive". Semantic hygiene, Crick felt, was largely a waste of time. ...

The Sciences of the Artificial by Herbert A. Simon

Our speculations have carried us over a rather alarming array of topics, but that is the price we must pay if we wish to seek properties common to many sorts of complex systems.

This quote from the last chapter of this book appropriately sums up the goal and the message of this book. Herbert Simon takes us on a great journey through a possible science of complex systems, particularly artificial systems that are often called `self-organizing'. He conducts this discussion at the very heights of generality taking in diverse fields like architecture, computer science, artificial intelligence, machine learning, economics and social planning.

This book is a must-read for computer scientists. It gives concrete reasons why the word science is part of the name of this field and why it is reasonable to expect that the field itself is split up into hardware technicians, compiler writers, functional programmers, systems analysts, software engineers, algorithm analysts, complexity theorists among many other subfields.

The scope of this book is so expansive that almost any one in this technological and increasingly computational age that we inhabit might get something out of reading this book.

In many conversations with fellow computer scientists I have heard the line `Well, computer science is really not a science. It is more like engineering or a craft like carpentry.' This is a view shared, but usually unspoken, by scientists in other fields, like physics or biology. This book lays out the reasoning why analogies like this are misguided and are a short-sighted view to take especially if you are a computer scientist. It also explains why scientists in other fields are more similar to computer scientists than they imagine.

Herbert Simon is famous in two fields: artificial intelligence and economics. In AI, he is most famous for his work with Allan Newell on the General Problem Solver (GPS). His work on GPS and also his work in economics understandably forms a major part of the discussion here. However, even though whenever he descends into details, I disagreed with him on almost every point in which I had any expertise, the overall picture he paints is such an important one that it is foolish to ignore the goals that he pursues here.

The answers he gives to the questions he raises are very preliminary but the questions are so compelling that I'm sure answers will be found, eventually.

Computer Science is no more about computers than astronomy is about telescopes.

E.W. Dijkstra

%T The Sciences of the Artificial
%A Herbert A. Simon
%I Cambridge, MA: MIT Press
%D 1969
%G ISBN: 026269073X (pb)
%G ISBN: 0262191938 (hc)
%P 247
%K science, computer-science

Date written: 2000/05/01

Trespassers on the roof of the world by Peter Hopkirk

... Lurgan's impassive face changed. He considered the years to come when Kim would have been entered and made to the Great Game that never ceases day and night, throughout India. He foresaw honour and credit in the mouths of a chosen few, coming to him from his pupil. Lurgan Sahib had made E23 what E23 was, out of a bewildered, impertinent, lying, little North-West Province man.

"Kim", Rudyard Kipling

Tibet is geographically isolated, especially from the West. Part of the appeal of this kingdom has been this isolation. In fact, some people have conferred utopian ideals onto this land simply because of this isolation: the famous misnomer of `Shangri-La' invented by James Hilton.

This book chronicles each attempt by spies and explorers to pry open the mysteries of Tibet. The most compelling of these were the Indian spies who mapped large parts of Tibet working under Captain Montgomerie. People like Kishen Singh (code name 'A.K.'), Nain Singh and Sarat Chandra Das collected unparalled amounts of geographical material about Tibet. Sarat Chandra Das was incorporated by Rudyard Kipling into his novel "Kim" as the intrepid Hurree Chunder Mookherjee (sic).

While their exploits were published in the Royal Geographical Society, they were never officially acknowledged either by the British or subsequently by the Indian goverment. Their stories are amazing and even though only part of this book is devoted to them, this was reason enough for me to read this book. The question remains: why did these people perform these heroic deeds so far above the call of duty for the benefit of their British rulers? I suspect the answer is not a simple one: neither monetary incentives or loyalty to the British or an utopian ideal seem to be an answer. Their motivations were, I suspect, not very different from the other explorers from the West. The contributions of these Indian spies and explorers, in terms of maps and local information, were quantitatively greater than most of the other explorers in Tibet but their stories remain largely unknown to this day.

A more exhaustive history of these Pundit explorers in the pay of the British Empire is in the book "Pundits : British Exploration of Tibet and Central Asia" by Derek Waller (University Press of Kentucky, 1990).

This book is as exhaustive as possible about the various explorers who tried to storm Lhasa in their own ways and for their particular motivations. There is an amazing variety of them:

• Annie Royle Taylor who wanted to convert the Dalai Lama to Presbyterianism,
• Henry Savage Landor who was captured by the Tibetans and tortured for several days along with his two Indian servants Chanden Singh and Man Singh (who was a leper). They were released at the Tibetan border probably as a warning against further intrusions into Tibet.
• Ekai Kawaguchi, who not only reached Lhasa, but lived there for more than a year in disguise. He was presumed to be in touch with his teacher and one-time British spy - Sarat Chandra Das
• the Canadian Susie Rijnhart who returned from her ill-fated expedition to Tibet without her Dutch husband Petrus Rijnhart and her infant son Charles.
• the Russian Colonel Nikolai Prejevalsky who was turned away from the gates of Lhasa by Tibetan warrior monks.
• the US Air Force cargo plane that crash landed near Lhasa and whose crew were nearly lynched.

There are many such stories in this book. Many of them document stories of torture designed to deter further intrusions into Tibet but also about torture on the citizens of Tibet by the ruling theocracy. These stories, which are almost certainly true due to the multiple sources that report it, were then used by the British and the Chinese as a convenient excuse to invade Tibet. The reasoning provided then is exactly the same as in other colonial "interventions" in history: a double-barreled combination of (a) revenge for real or perceived slights by the ruling power and (b) the liberation of the oppressed populace.

The story of Heinrich Harrer which got a lot of attention from Hollywood (including the movie "Seven Years in Tibet") does not get much attention by Peter Hopkirk and Harrer is dismissed as a footnote in this history and appropriately so.

Most people know of the Chinese invasion of Tibet on November 7, 1950. However, not many historical sources point out the previous history of relations between Tibet and China and especially the role of the British and the Russians. This book is one of the few places which details this history. Since this is so rarely mentioned anywhere, I've included the full account below:

After the British invasion of Tibet in 1904 under the command of Col. Younghusband, the British enforced certain trade treaties with Lhasa and installed Captain O'Connor as the British trade commissioner in Gyantse. The British presence irked the Chinese who were used to having a permanent consul (called the amban) in Lhasa and whose influence was now displaced by that of the British. However, the British were not very comfortable with their position in Tibet and wished to pull out. The British Campbell-Bannerman government signed a treaty with China in April 1906 restoring Britain's recognition of Chinese suzerainty over Tibet. The British never consulted with the Tibetans on this matter. The following year, the Chinese signed a treaty with the other power in the region, the Russians granting the Chinese `suzerain rights' over Tibet. Again, the Tibetans were never consulted. Soon thereafter, the Chinese advanced into Tibet leaving a trail of slaughtered monks. In February 1910, two thousand Chinese troops seized Lhasa. The Dalai-Lama escaped to Sikkim in British India. After the October 1911 revolution in China, the Chinese garrison in Lhasa mutinied and the Tibetans took advantage of this and started a guerilla war against the Chinese. On January 6, 1913, the last of the Chinese marched out of Lhasa and the Dalai Lama returned to his capital. The Chinese invasion of 1950 cannot be divorced from this history thirty-seven years before and the politics of the powers in the region: Chinese, Russian and British.

It is important to note that most of the explorers mentioned in this book have written books of their own in which they detail their adventures. In fact, it was common for these `explorers' to finance their expeditions in this way. There is a veritable glut of these portraits of Tibet which are in direct contrast with the contemporary portrayal of Tibet in the media. For example, a useful book to read after this one is "Lhasa and its Mysteries" by Col. Austine Waddell (1905) which despite its title demystifies Tibet entirely. Waddell's book is particularly unsympathetic towards the Lhasa theocracy, which is not surprising since he chronicles the 1904 invasion of Tibet by the British. However, his cold prose is an effective counterbalance to the unabashed mysticism usually associated with any current writing about Tibet.

The British and Russian tug-of-war over India that was fought out over Central Asia is documented in "The Great Game" also written by Peter Hopkirk and in "Tournament of Shadows" by K. E. Meyer and S. B. Brysac.

More books on Tibet:

• "The Dragon in the Land of Snows: A History of Modern Tibet Since 1947" by Tsering Shakya (Columbia University Press, 1999). Recommended by Ian Buruma in his NY Review of Books article "Found Horizon" which reviews the books by Schell and Hilton (see below).
• "Virtual Tibet: Searching for Shangri-La from the Himalayas to Hollywood" by Orville Schell (Metropolitan Books, 2000)
• "The Search for the Panchen Lama" by Isabel Hilton (Norton, 2000)

%T Trespassers on the roof of the world
%T :the race for Lhasa
%A Peter Hopkirk
%I J. Murray
%D 1982
%G ISBN: 0719539382
%P 274
%K history

Date written: 2000/06/14

O Post Captain, My Captain

The notion of tenure is a natural topic of obsession for junior faculty in universities. Most normal people (non-academics) are nonplussed by this notion of a tenure-track position. And since most people will not find satire particularly enlightening, I offer an excerpt taken from Master and Commander by Patrick O'Brian. An excerpt, which I think, inadvertently sheds some light on the state of mind of those in a tenure-track position.

For those not familiar with the characters: Captain Jack Aubrey, an 18th century Royal Navy officer, has been given his first ship to command at the start of the novel, and in conversation with him is Stephen Maturin, the ship's doctor. This conversation occurs on page 271 (of 403) in the HarperCollins paperback.

'I wonder you should be so concerned about a mere title -- a tolerably Byzantine title,' observed Stephen, `After all, you are called Captain Aubrey now, and you would still only be called Captain Aubrey after that eventual elevation; for no man, as I understand it, ever says "Post-captain So-and-so". Surely it cannot be a peevish desire for symmetry -- a longing to wear two epaulettes?'

`That does occupy a great share of my heart, of course, along with eagerness for an extra eighteenpence a day. But you will allow me to point out, sir, that you are mistaken in everything you advance. At present I am called captain only by courtesy -- I am dependent on upon the courtesy of a parcel of damned scrubs, much as surgeons are by courtesy called Doctor. How should you like it if any cross-grained brute should call you Mr M the moment he chose to be uncivil? Whereas, was I to be made post some day, I should be captain by right; but even so I should only shift my swab from one shoulder to the other. I should not have the right to wear both until I had three years' seniority. No. The reason why every sea-officer in his right wits longs so ardently is this -- once you are over that fence, why there you are! My dear sir, you are there! What I mean is, that from then onwards all you have to do is to remain alive to be an admiral in time.'

`And that is the summit of human felicity?'

`Of course it is,' cried Jack, staring. `Does it not seem plain to you?'

`Oh certainly.'