Chandrashekhar Limit: When does a white dwarf star collapse?

The Chandrasekhar Limit can be expressed as the maximum nonrotating mass which can be supported against gravitational collapse by electron degeneracy pressure. This is commonly understood to be about 1.4 solar masses (i.e. 1.4 times the mass of the sun or about 333,000 times greater than the mass of the earth).

The Chandrashekhar Limit is an upper limit for the mass of a white dwarf. It has been observed that so-called main-sequence stars with a mass greater than about 8 solar masses are unable to lose enough mass to form a stable white dwarf at the end of their lives, and so they form either a neutron star or a black hole.

A brilliant and gifted physicist, Subrahmanyan Chandrasekhar (Nobel, Physics, 1983) had a very public disagreement about what became known as the Chandrashekhar Limit with Arthur Stanley Eddington (while Chandrashekhar was a junior scientist at Cambridge). Eddington ridiculed Chandrashekhar by terming his work "stellar buffoonery". Chandrashekhar had the last laugh, and a Nobel, in 1983. The bitterness surrounding this event contributed to Chandrashekhar moving to the University of Chicago. He returned to this important work only after about three decades.

NASA has honoured him by naming the third of its four "Great Observatories'" after Chandrasekhar. The Chandra X-ray Observatory was launched and deployed by Space Shuttle Columbia on July 23, 1999.

One episode of the BBC Radio 4 series "Test tubes and tantrums" considers this controversy (Chandrashekhar vs Eddington) - podcast available at: http://www.bbc.co.uk/radio4/science/testtubesandtantrums.shtml

Dulce et decorum est pro patria mori

My friend, you would not tell with such high zest
To children ardent for some desperate glory,
The old Lie; Dulce et Decorum est
Pro patria mori.

Wilfred Owen (composed 1917)

So, sad. Tangmarg, Baramula, Kashmir and the two young officers killed today (Major KP Vinay and Major DR Raman). Major Vinay was due to be married later this month. So many other young lives blighted by war ... We have been here before.

Burma, India and Realpolitik

FT, 30th Sep 07 "India pressed to take lead on democracy":

In private, Indian officials reject criticism. “We’re not bothered about criticism of our relations with Myanmar, given the west’s record in supporting military governments in our neighbourhood,” said one. “We’re not the only democracy that works with generals.”

Brahma Chellaney, a security affairs expert, concurs: “The US is going along with the fraudulent elections in Pakistan while wanting India to do more on Burma. India applies the same principle to Burma as to Pakistan: while it would like democracy to flourish, it will not make it the central plank of its foreign policy in either country.”

Paul Simon on DiMaggio: A metaphor for our times?

What is the larger significance of DiMaggio's death? Is he a real hero? Let me quote the complete verse from ''Mrs. Robinson'':

Sitting on a sofa on a Sunday afternoon
Going to the candidates' debate
Laugh about it, shout about it
When you've got to choose
Every way you look at it you lose.

Where have you gone, Joe DiMaggio?
A nation turns its lonely eyes to you
What's that you say Mrs. Robinson
Joltin' Joe has left and gone away.

In these days of Presidential transgressions and apologies and prime-time interviews about private sexual matters, we grieve for Joe DiMaggio and mourn the loss of his grace and dignity, his fierce sense of privacy, his fidelity to the memory of his wife and the power of his silence.

'The Silent Superstar' By Paul Simon
New York Times, March 9, 1999

How mathematical should economics be?

Manmohan Singh on economics (LSE, 2006):

In more recent decades we see excessive specialization in social sciences, and economists fancy themselves to be social engineers and technocrats. But we must never forget that economics began, after all, as political economy. Economic policy making has always involved political choices since it has political consequences. IG belonged to a generation that recognized this ground reality. He knew that the choices our economists were recommending for adoption by our country had to be marketed in the political marketplace of a functioning democracy. It was not enough that these choices were rational, or that their costs and benefits could be measured. It was not enough that the arguments were intellectually consistent or were mathematically tested. In a democracy such choices had to be also politically defendable and acceptable.

Rule of law

In modern democracies, the notion of rule of law is paramount. Even when many governments may not fully adhere to its precepts, our rulers often simply pay lip service to its ideals and to the defence of republican values. Two influential comments on the notion of rule of law are the following:

1. Thomas Paine (Common Sense, 1776):

But where, say some, is the king of America? I'll tell you Friend, he reigns above, and doth not make havoc of mankind like the Royal of Britain. Yet that we may not appear to be defective even in earthly honors, let a day be solemnly set apart for proclaiming the charter; let it be brought forth, placed on the divine law, the word of God; let a crown be placed thereon, by which the world may know, that so far as we approve of monarchy, that in America the law is king. For as in absolute governments the king is law, so in free countries the law ought to be king; and there ought to be no other. But lest any ill use should afterwards arise, let the crown at the conclusion of the ceremony be demolished, and scattered among the people whose right it is.

2. John Adams (1735-1826: framer of the Massachusetts Constitution. Quote below from The First Part, Art. XXX (1780))

In the government of this commonwealth, the legislative department shall never exercise the executive and judicial powers or either of them: the executive shall never exercise the legislative and judicial powers, or either of them: the judicial shall never exercise the legislative and executive powers, or either of them: to the end it may be a government of laws and not of men.

Another gem from Paine (Common Sense, 1776):

A long habit of not thinking a thing wrong, gives it a superficial appearance of being right, and raises at first a formidable outcry in defense of custom.

Bulleh Shah, Carvaka and Sufi Poetry

I have been struck by the beauty, wit, cadence and deep rooted philosophical questions within some poetry composed by Sufi poets. It is a salutary lesson that the Sufi school - celebrating the syncretic and assimilative traditions of Islam, Sikhism and Hinduism - was attacked, vilified and ultimately replaced by the more strict Wahabi school, which has contributed to ideas such as the so-called ‘clash of civilisations’ and much more irrationality, bias and intolerance. Sufi music has, of course, been popularised by the likes of Nusrat Fateh Ali Khan, Junoon and Rabbi Shergill. I was struck by the profound philosophical undertones within Rabbi’s ‘Bulla ki Jana’which has become a very well known song.

It is a great tragedy that Pakistan has officially accorded national language status to Urdu, English and Arabic - none of which are native to Pakistan, while Punjabi in Pakistani Punjab is merely a spoken language now. In India, matters are no better. Punjabi is highly vernacularised and looked down upon by the elites who prefer highly Sanskritised Hindi (and English) and regard Punjabi mainly as a rough, unadorned language, thus ignoring its contributions to India’s literature and culture, and in maintaining India’s tradition of oral renditions of literary works. Interestingly, admirers of Sufi poetry in Pakistan are pinning their hopes for the defence and preservation of the Punjabi language on the efforts of the Sikh minority within Pakistan.
What is undeniable is the influence of Urdu and Persian syncretic influences on the Punjabi of this period (late 17th - early 18th century).

This period was also the age of Enlightenment and the renaissance in Europe, which brought to the fore the ideas of Kant, Rousseau and Voltaire. In my view, in terms of the intriguing, perplexing, existentialist questions posed by other philosophers, Bulleh Shah’s poetry holds its own. The Sufi poetry of Sultan Bahu, Waris Shah and Shah Hussain is well known - it is only recently that Bulleh Shah has been rediscovered. Bulleh Shah’s poetry brings out another interesting aspect - the influence of the Hindu Carvaka (pronounced Charvaka) or the Lokayata school of belief dating c. 600 BC (qhich mainly questioned the existence and onmipotence of god). Like the Carvaka school and its attack on Brahmanical excesses and superstition, Bulleh Shah’s poetry includes direct attacks on anyone claiming control over religion, including comparing religious clerics to barking dogs and crowing roosters. India's Nobel laureate in economics, Amartya Sen, was engaged in discussion with his grandfather. Amartya Sen declared that since he was Marxist (and consequently atheist) and did not follow any particular school of Hindu faith, he was not Hindu at all. His grandfather’s reply: ‘Yes, you are a Hindu - of the Carvaka school.’ This school was redicovered through a study of Madhavacharya’s Sarva-Darsana-Sangraha [c. 1400 AD]. The following gives a flavour of Lokayata beliefs. The Hindu sage Brihaspati, regarded by some as the founder of the Carvaka school,
argues as follows:



Roughly translated, this Sanskrit quotation goes as follows: As long as you live, live happily; take a loan and drink ghee. After a body is reduced to ashes, where will it come back from?

The Art of Rhetoric

The Romans, especially in the early and late Republic, greatly valued skills in debating and public speaking. Julius Ceasar was widely regarded as an accomplished and extremely skilled author and orator. For example, his political opponent Cicero (Marcus Tullius Cicero, consul of Rome in 63) spoke very highly of his Commentaries. In fact, Suetonius (c. 69-130 AD) writing in The Lives of the Twelve Caesars notes that Cicero remarked: "Does anyone have the ability to speak better than Caesar?" Fortunately such skills are not lost. For those who have followed the astonishing advances in particle physics in the first half of the last century, such abilities will be evident from an excerpt from the Nobel Prize acceptance speech made by Clinton Davisson (1881-1958, Nobel Prize in Physics in 1937 for the discovery of electron diffraction):

"Troubles, it is said, never come singly, and the trials of the physicist in the early years of this century give grounds for credence in the pessimistic saying. Not only had light, the perfect child of physics, been changed into a gnome with two heads - there was trouble also with electrons. In the open they behaved with admirable decorum, observing without protest all the rules of etiquette set down in Lorentz’ manual, but in the privacy of the atom they indulged in strange and unnatural practices; they oscillated in ways which no well-behaved mechanical system would deem proper. What was to be said of particles which were ignorant apparently of even the rudiments of dynamics? Who could apologize for such perversity - rationalize the data of spectroscopy? A genius was called for, and a genius appeared. In 1913 Niels Bohr gave us his strange conception of "stationary" orbits in which electrons rotated endlessly without radiating, of electrons disappearing from one orbit and reappearing, after brief but unexplained absences, in another."

Rgveda: The Nasadiya Sukta (after ná ásat "not the non-existent")

नासदासीन्नोसदासीत्तादानीं नासीद्रजो नो व्योमापरो यत |
किमावरीव: कुहकस्यशर्मन्नम्भ: किमासीद्गहनं गभीरं || १ ||

न मृत्युरासीदमृतं न तर्हि न रात्र्याऽआह्नऽआसीत्प्रकेतः |
आनीदवातं स्वधया तदेकं तस्माद्धान्यन्नपर: किन्चनास || २ || [...]

इयं विसृष्टिर्यतऽआबभूव यदि वा दधे यदि वा न |
योऽअस्याध्यक्ष: परमे व्योमंत्सोऽअंग वेद यदि वा न वेद || ७ ||

The quote above derives from the Creation Hymn which is the 129th hymn of the 10th Mandala of the Rgveda/ ऋग्वेद [c. 1200–900 BC (the early Vedic period)]. The Rig Veda is a collection of more than 1,000 hymns which represents the first extensive composition in any Indo-European language. O'Flaherty: "Fraught with paradox, the hymns are meant to puzzle, to surprise, to trouble the mind". Very roughly paraphrased as:
[1] There was neither non-existence nor existence then; there was neither the realm of space nor the sky which is beyond. What stirred? Where? In whose protection? Was there water, bottomlessly deep?
[2] There was neither death nor immortality then. There was no distinguishing sign of night or day. That one breathed, windless, by its own impulse. Other than that, there was nothing beyond. [...]
[7] Whence this creation has arisen – perhaps it formed itself, or perhaps it did not—the one who looks down on it, in the highest heaven, only he knows – or perhaps he does not know.
Translation by: Wendy Doniger O’Flaherty.

गणित की कक्षा! इंगलैंड और अमेरिका में समय का फ़र्क

क्या हिना!!!! आज हम शायद तीन या चार बजे उठ गए थे! शिकागो और इंगलैंड में ६ घंटे का फ़र्क है और न्यू यॉर्क और इंगलैंड में ५ घंटे का| इंगलैंड में समय आगे है! :-)

R, R graphics and Sweave

One of the best econometric software packages available to researchers is the package R (www.r-project.org), which is made available under the GNU-GPL license - which basically means it is free to use. It is based on the iconic Bell Labs S language and it has a very large and uptodate menu of implemented techniques used in econometrics, biometrics, maths, physics and engineering. It's object oriented character makes it very flexible indeed. Combined with LateX (using the package Sweave [www.ci.tuwien.ac.at/~leisch/Sweave/]), R commands can be embedded into a LaTeX document [www.ctan.org], which means that you have full documentation and output in one place, which can be easily compiled to execute all estimations and to create the final document in one step.

In the process, R creates publication quality graphics which are often of a very high quality and quite innovative as well. For instance, the graphic shown above is Fig. 2 from the paper Grosjean, PH, Ch. Spirlet & M. Jangoux, 2003. A functional growth model with intraspecific competition applied to a sea urchin, Paracentrotus lividus. Can. J. Fish. Aquat. Sci., 60:237-246. (Try doing this in Excel or EViews).

Caesar's Proconsulship in Gaul (58-51 BC)

Shortly after the end of his consulship (59 BC) Caesar left Rome to take up his new position as Governor of Transalpine Gaul or Narbonensis (Provence), Cisalpine Gaul (plains along the river Po) and Illyricum (the Dalmatian coast) for the years 58-54. It was clear that Caesar planned to engage in a campaign of conquest of entire Gallia, Belgae and the Helvetii. Within Gaul the Haedui had been recognised as allies of Rome by the Roman Senate. The Haedui were attacked by Germanic tribes led by Ariovistus (who had himself been recognised as a king and friend by the Roman Senate during Caesar's consulship in 59). The Haedui petitioned Rome for help against Ariovistus and Caesar, as Governor and Proconsul, was authorised to deal with Ariovistus's threat. The main strategic issue was this. Ariovistus claimed the rights of conquest over parts of Gaul, arguing that Roman interests and authority extended only until Transalpine Gaul. But Caesar noted that German reinforcements in Gaul were continuing and it would be a matter of time before such enemy forces would be in a position to invade Transalpine and Cisalpine Gaul, and ultimately Rome itself. The Helvetii had defeated the Romans in 107 and earlier, in 387, the Gauls had sacked Rome. In 58, Caesar defeated the Helvetii in the Battle of Bibracte. Shortly afterwards Caesar defeated Ariovistus who never regained his former power and died in 54. Of course, eventually Caesar defeated Vercingetorix in the Battle of Alesia in 52. In 51 after winning the Battle of Uxellodunum, Gaul was 'pacified', as it were.

The origins of war in Europe are long standing, historic and complex. It is in this backdrop that the achievements of the EU must be assessed, especially reconciliation between Germany and France who have been historic foes. The Poles have been won round - but at what cost, one wonders, given the EU's propensity for horse trading. 

हिना अब न्यू यॉर्क में है

अभी तक तो छोटी थी पर अब बड़ी हो गयी है...

EU solidarity

It is sort of interesting to follow the vexed consultation  at the EU summit in Brussels. The Poles and the British are putting up a spirited defence of their national interests. Many bloggers have been alluding to a well-known British sketch from an episode of the 1970s TV comedy "Fawlty Towers" titled: 'The Germans' or 'Don't Mention The War'. However, the issues are complex and keenly contested. Poland feels pressurised by both Russia and Germany (on different issues). Germany and many other EU member states feel that the EU must be strengthened and the peace dividend from EU integration should be maximised through dialogue and reconciliation. A breakthrough seems unlikely ... but Germany only needs to wait 13 years more before hosting  a similar EU summit again (if the number of member states remains the same).