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Namagiri and Ramanujan

Sunday, May 1st, 2016

[ by Charles Cameron — in which we glimpse the (female) divinity hidden behind infinity ]
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Ramanujan and Namagiri

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It is one of the curiosities of mathematics that the great Indian mathematician Srinivasa Ramanujan claimed to have received many, if not all, of his equations from the goddess Namagiri in dreams — and that this idea is all too often quietly omitted from discussions of his uncanny brilliance.

Now that The Man Who Knew Infinity is out in theaters, it might be wise to explore the connection between Namagiri and Ramanujan a little more closely.

Dream and waking, darshan and mathematics, inspiration and intuition, intuition and proof, quality and quantity — these polarities are all involved..

To its credit, the film contains the line:

You want to know how I get my ideas? God speaks to me.

However, the idea that “God” might be a goddess seems a reach too far for the screenwriters and director.

Viewing:

  • Matt Brown, The Man Who Knew Infinity
  • Here’s one version of the trailer:

    **

    Stephen Wolfram posted a fine article on his blog last week, Who Was Ramanujan?. He was willing to mention that Ramanujan’s friend and collaborator, GH Hardy, “could be very nerdy — whether about cricket scores, proving the non-existence of God, or writing down rules for his collaboration with Littlewood” — but fails in 31 pages to mention Ramanujan’s own belief that he received his equations from a goddess.

    All of which caused me to pose a question to Wolfram’s own algorithmic genie, Wolfram Alpha:

    Did Namagiri reveal equations to Ramanujan?

    WolframAlpha skipped the words “Did Namagiri reveal” and “to” and concentrated on responding to “equations” and “Ramanujan” — not quite up to par with AlphaGo, I’m afraid, let alone Ramanujan himself, or better, Namagiri.

    Below’s the DoubleQuote I made to by way of comment — note that I’ve only had space for the first line of WolframApha’s extended response:

    Tablet DQ ramanujan namagiri wolfram 1

    **

    Readings:

  • Stephen Wolfram, Who Was Ramanujan?
  • Hinduism Today, Computing the Mathematical Face of God
  • Huffington Post, Ramanujan’s Mock Modular Forms
  • The Hindu, American mathematicians solve Ramanujan’s “deathbed” puzzle
  • Sadhguru, Doorway to the Beyond
  • Paul Chika Emekwulu, Mathematical Encounters: For the inquisitive mind
  • The Hindu, The Man Who Knew Infinity: A misunderstood mind
  • Better angels, honest selves

    Tuesday, April 19th, 2016

    [ by Charles Cameron — two phrases, two anthropologies, two ways of virtue — Lincoln & Trump ]
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    SPEC DQ Lincoln Sharlet Trump

    **

    Jeff Sharlet is one of our finer writers about religion, and his piece on Donald Trump in Saturday’s NYT Magazine is worth your attention.

    Here, I simply want to contrast Lincoln‘s “better angels of our nature” with Sharlet‘s “lust, the envy, the anger of our more honest selves” — idealism and realism? sanctity and authenticity? — as phrases representing two approaches to human nature, each clearly enunciating a virtue in its own context.

    Sources:

  • Abraham Lincoln, First Inaugural Address
  • Jeff Sharlet, Donald Trump, American Preacher
  • War, Games and morale

    Sunday, December 20th, 2015

    [ by Charles Cameron — on gaming “living and moral forces” — with a whiff or two of Montaigne ]
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    the-mind-is-a-dangerous-weapon-even-to-the-possessor

    **

    Let’s start with Clausewitz, On War.

    He says — and we’d be wise to pay attention — “most of the matters dealt with in this book are composed of equal parts of physical and of moral causes and effects.” Earlier in the paragraph, he’d said, “The effects of physical and psychological factors form an organic whole which, unlike a metal alloy, is inseparable..” — which puts the physical and the moral on equal footing. He then tilts the board decisively in favor of the “moral” factors —

    One might say that the physical factors seem little more than the wooden hilt, while the moral factors are the precious metal, the real weapon, the finely-honed blade.

    Furthermore, these “moral factors” are “intangible” — or as Michael Handel puts it:

    In contrast to the physical forces, which are relatively easy to estimate, the equally important moral forces are more difficult to gauge.

    **

    Deputy Secretary of Defense Bob Work and Gen. Paul Selva, Revitalizing Wargaming is necessary to be prepared for future wars:

    For example, faculty and students at the Naval War College integrated wargaming into their entire course of study, analyzing the then-novel concept of carrier task force operations, the role of submarines in scouting and raiding, and how to provide logistics support to fleet operations spread over the vast Pacific Ocean. Wargames in classrooms at Quantico helped the Marine Corps develop new concepts for amphibious warfare and conceive of new techniques for capturing advanced naval bases. Wargamers at the Army War College explored how to employ tanks and artillery on infantry-dominated battlefields and examined the logistical challenges of fighting a war far from American shores.

    and:

    Most importantly, players should be able to observe and live with the consequences of their actions (where possible, based on previous rigorous analysis) in the face of a thinking and reacting competitor, and so come to understand dynamic military competition from the perspective of opposing sides. Actions taken by the players on both sides must have tangible consequences that are determined — where possible — by the actual performance of weapons and sensors in the real world, backed by a rigorous adjudication process using the best available analysis and professional judgment.

    **

    In the first of those paragraphs, we have “carrier task force operations”, “the role of submarines”, “logistics support”, “fleet operations”, “amphibious warfare”, “advanced naval bases”, “tanks and artillery”, infantry-dominated battlefields”, and more “logistical challenges”.

    Now admittedly, that’s pre-WWII wargaming — but no mention there of the impact of upcoming psychological forces such as the Nuremberg rallies, Hitler’s obsession with Wagner and Bayreuth, Leni Riefenstahl, Himmler’s occult interests, and so forth — not because they were known or in existence at the time, they weren’t, but because they constituted in the event precisely the sort of intangible morale boost / force multiplier that can tip a battlefield and slide a war, as per Clausewitz.

    Nary a mention of psychology, moral, morale, espirt, spirituality, religion, let alone Dempsey’s “apocalyptic, end-of-days strategic vision” which we now face in IS.

    And that second paragraph, dealing with the present and near future — the move to consider dynamic interaction is to be lauded, but once again we’rew in the realm of “weapons and sensors in the real world”. I’m led to the suspicion that current wargaming doesn’t know quite how to deal with “tangible consequences” that are not determined “by the actual performance of weapons and sensors” but by, ahem, passion.

    **

    Raisciac

    **

    If moral causes and effects are as potent as weapons, or even, as Clausewitz said, are themselves “the real weapon, the finely-honed blade”, games focused not on performances of weapons but on moral causes and effects — games that game passions — must surely have a significant role to play in revitalizing wargaming.

    America’s Anti-Agoge

    Wednesday, November 18th, 2015

    [by Mark Safranski, a.k.a. “zen“]

    “….Instead of softening their feet with shoe or sandal, his rule was to make them hardy through going barefoot. This habit, if practiced, would, as he believed, enable them to scale heights more easily and clamber down precipices with less danger.”

    – Xenophon, The Polity of the Lacedaemonians

    Be quiet! In your position, it is your job to create a place of comfort and home for the students who live in Silliman! Then why the fuck did you accept the position? Who the fuck hired you? You should step down! If that is what you think of being headmaster, you should step down! It is not about creating an intellectual space! It is not!”
    Jerelyn Luther, the Shrieker of Yale

    “I personally am tired of hearing that first amendment rights protect students when they are creating a hostile and unsafe learning environment for myself and for other students here.”

    – Brenda Smith-Lezama, Vice President of the Missouri Students Association 

    Much has been written this week of the protests at Mizzou and Yale universities now sparking more absurd copycats elsewhere.  Pundits have covered the dangerous illiberalism of campus political correctness and speculated that the students are the result of a generation of helicopter parenting. There were earlier essays recently on the “coddled” nature of elite university students generally and skewered Ivy League students in particular as the products of a deeply flawed, intellectually shallow,”meritocratic” rat race that serves as the gateway to the nation’s elite. There have also been conservative suggestions that the students lack the maturity to vote and a furious counterattack by social-justice faction lefties defending the students and their authoritarian anti-free speechsafe space” ideology.

    While all interesting and moderately important, I don’t think any of this gets to the heart of the matter.

    Up until today, every society in history has had a process, formal or informal, to prepare the next generation of leadership and inculcate virtues in them that would assure their society’s cultural continuity and physical survival. The ancient Chinese mandarinate was based on mastery of Confucian classics; the British Empire had its public schools and storied regiments where the sons of the gentry and peerage bonded; the samurai and daimyo of Tokugawa Japan continued to uphold bushido and cherish antique tactics in warfare centuries after Japan’s unification made such things more ritual than reality.

    The definitive example of an educational rite of passage from student to member of the ruling class however, remains the Agoge of ancient Sparta. Established, according to Spartan legend, by the semi-mythical law-giver Lycurgus, the agoge (“the upbringing”) existed to mold Spartan boys through a ferocious training regime into the hoplite soldier-citizens who comprised the social apex of Sparta’s militaristic oligarchy. The agoge ceaselessly battered the students with physical exertion, corporal punishment, exposure to the elements and hunger in a bid to harden them  in mind and body. There’s much about life under the agoge that moderns, even admirers of classical Greece, would find distasteful or even appalling, but it was very effective at inculcating that ascetic toughness, communal discipline, martial prowess and laconic wit that Spartans prized.  For at least three centuries, the agoge helped sustain Sparta’s qualitative military edge and its hegemony over the Greek world and subsequently, its political independence for two centuries more. Not a record that was frequently matched in history.

    America too has a system of education to prepare – or rather, certify – our future business, academic, judicial and political leaders based on matriculation at a small number of highly selective, elite universities and liberal arts colleges. Broadly speaking, this includes roughly the top 100 higher education institutions ranked by US News & World Report and narrowly, for filling the very top tiers of finance, law and government service, the Ivy League plus a handful of comparable schools. This would place Mizzou at the bottom of the barrel of our elite education system while Yale is at the very pinnacle. The kids going to exclusive, elite, universities are very bright for the most part, but even more so they are wealthy.

    This upper class status includes the campus protestors screaming loudest about their wretched oppression. The hunger striker of Mizzou’s father is a multi-multi-millionaire while the Shrieker of Yale reportedly comes from the relative poverty of her parents $750,000 home. The aggressive authoritarianism on display at Yale, Mizzou, Amherst, Dartmouth or Claremont is less the “Rage of a Privileged Class” than the petulant tantrum of the 1%.  In other words, despite their heroic efforts at a public pathos orgy of political correctness to portray themselves as victims in grave danger as they bullied and assaulted professors other students, these are spoiled rich kids used to getting their way, pitching an unholy fit to get undeserved power over others who disagree.

    However obnoxious and unlikable these petty tyrants are or how totalitarian their demands to end free speech and academic freedom, fire and expel all their critics or put social-justice commissars in charge of every university department, they didn’t educate themselves. The students embody, perhaps in a more militant form, what they were taught. The problem isn’t that this year has a random surplus of student radicals, or that sinister racist conspiracies exist in the administrations of our most left-wing universities as protestors claim or that these helicoptered students are all psychologically fragile waifs raised in a culture of self-love and psychodrama. No, the problem is that the system to educate our future leaders tends to inculcate deep hostility and loathing toward their fellow Americans, extolls anti-empirical, witch-hunting dogmatism as a virtue while rewarding narcissism and anti-social aggression in interpersonal relations. This needs to change.

    We have built an American anti-Agoge that cultivates values, ethics and habits in future leaders that are politically repulsive in their authoritarian rejection of Constitutional rights and are antithetical to ruling wisely or well. At times they would seem to conflict with a life as a functionally competent human being. Half of all Yale students in this pressure-cooker require at least some mental health counseling. This is an astounding statistic. Imagine if Polybius or Livy had written that half of the sons of the Patrician class were at least slightly mad. A toxic ruling class that is certain that they have been victimized by the citizens they govern and who lack the normal resilience to withstand minor stresses of life without concocting conspiracy theories or taking to their bed is a recipe for disaster. In a liberal democratic state such as ours, dependent as it is on the values of an open society to function politically, this state of affairs is a sign of political decay and creeping oligarchy.

    What is to be done?

    We did not arrive at this juncture overnight and fixing a fundamentally broken academic culture will take time, but here are a few simple suggestions to start.

    1. Legislation to Secure Academic Freedom, Due Process and Free Speech on Campus:  This will defang the PC bullies, social justice warriors and their allies in university administration by hamstringing their ability to coerce and punish dissent. Obviously, this will be easier in public universities but these provisions could be attached to receiving Federal funds, including guaranteed student loans.
    2. Draconian Reduction of University Administrative Positions relative to Tenured Faculty: This will save a great deal of money better spent elsewhere in by axing bureaucracy while de-funding and disempowering the diversity commissariat on campus that is the source of much illiberal mischief. Again, this is a matter more for state level action initially.
    3. Restore a Core Undergraduate Canon rooted in Real Courses in Real Academic Fields: This will reduce the Melissa Click problem of academic sinecures for full-time radical political activists posing as professors with Fifty Shades of Gray “scholarship”. The money saved by getting rid of an army of administrators in #2 leaves a lot of room to hire mathematicians, biologists, historians, economists, physicists, philosophers and linguists who earned a doctorate in something real.
    4. Require Elite universities Receiving Federal Funds to allocate 20% of their Student Body to Students from Middle-Class, Lower Middle Class and Working Class backgrounds, Geographically Balanced: I have mixed feelings about this in principle, but it would definitely break up the overwhelming UC-UMC Superzip monoculture at our gateway institutions and bring new talent and perspectives into our ruling class that the university administrators at present work extremely hard to systematically exclude. It will also increase social mobility and provide competition for the progeny of our game-rigging “meritocratic” elite.

    .

    None of these will usher in a utopia. Much of radical academia will muddle through doing what they have been doing until retirement, but the system itself will be on a trajectory for better health rather than for getting steadily worse.

    Jottings 14: Sincerity of the snake-handlers

    Wednesday, February 19th, 2014

    [ by Charles Cameron — a death at the Full Gospel Tabernacle in Jesus Name church in Middlesboro, and a glance at the Covenant, Sword and Arm of the Lord ]
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    There’s something very simple and profound about the sheer faith the snake handlers of the Holiness tradition bring to their worship. It’s not yo my aesthetic taste, and the doctrines espoused are, to my mind, literal-minded and unwise — but the faith, the trust moves me.

    Pastor Jamie Coots has now died of snake-bite in the course of woship:

    Like the police chief, Jeffrey Sharpe, interviewed above, in my own way and to my own degree I feel saddened by dis death.

    **

    I find myself feeling a similar fellow-feeling for the worshippers in this church, with it’s quite similar rusticity and simple ways. And what interests me here is that the group worshipping here is one whose theology I have very little sympathy for — the Covenant, Sword and Arm of the Lord or CSA, a Christian Identity paramilitary church whose 200-acre compound was besieged and shut down by the FBI in 1985.

    The opening of this video, from the trailer for Silhouette City directed by Michael Wilson, show us the worship of the CSA — and much as I dislike their racism and proneness to murderous violence, I find there’s something affecting in what this clip shows of the simple hearts of the believers. Reading Tabernacle of Hate, the autobiography of Kerry Noble whose quest for Christ brought him in contact with the group before it became infected with racism and hate, who went on to become its second in command and eventually left in disgust at all the hatred, I have the same feeling — of a simple piety led horribly astray.

    Here then is the clip — it’s the first 35 seconds I’m inviting you to watch — the movie then turns to present day, more mainstream uses of militant Christian imagery:

    **

    I don’t want to leave you on the sour note of CSA Christianity — so let me turn back to the Holiness snake-handlers.

    For a deeper glimpse into their ways, you could do worse than to watch this documentary:

    **

    May pastor Jamie Coots rest in peace.

    This, on Jamie’s son Cody Coots, from The Christian Post yesterday:

    The deadly rattlesnake that delivered the fatal bite to “Snake Salvation” pastor Jamie Coots in Middlesboro, Ky., last Saturday will be back in church to help praise the Lord in another heart-pounding service this Saturday, according to his son, Cody Coots.

    Cody, 21, who will be burying his serpent-handling father on Tuesday night, told TMZ that the snake will not be killed. His father’s death, he says, was “God’s way” of taking him home, and his family will embrace the deadly rattlesnake that delivered his death sentence at the Full Gospel Tabernacle in Jesus Name church in Middlesboro again this Saturday.


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