Sridakshinamurtistotram Stotram (Part XI) at Advaitin -- Conclusion

Shri V. Subrahmanian concludes his beautiful exposition of Sri Dakshinamurthy Stotram in his Part XI. Here, he explains the 10th shloka, the phala sruti, of the stotra:


sarvAtmatvamiti sphuTIkRRitamidam yasmAdamuShmin-stave
tEnAsya shravaNAt tadartha-mananAt dhyAnAccha sankIrtanAt |
sarvAtmatva-mahA-vibhUti-sahitam syAdIshvaratvam svataH
siddhyEt tat punaraShTadhA pariNatam chaishvaryam-avyAhatam ||


Here is the link to previous ones. Read the rest of this entry >>

Ramana's Dakshinamurthy

"The carving of Dakshinamurti over the Patalaling Siva shrine, where Ramana Maharshi spent much time doing sadhana."

The above photograph is part of a collection of Atmajyothi's tour to Ramana Ashram at Arunachaleshwara. Read the rest of this entry >>

Sridakshinamurtistotram Stotram (Part X) at Advaitin

Shri V. Subrahmanian continues the exposition of Sri Dakshinamurty Stotram. In part X he translates the verse 9 of the stotra:


bhUrambhAmsyanalo-`nilo-`mbaramahar-naatho himAmshuH pumAn-
ityAbhAti charAcharAtmakamidam yasyaiva mUrtyaShTakam |
nAnyat-kinchana vidyate vimRRishatAm yasmAt-parasmAd-vibhO-
stasmai shrIguru-mUrtaye nama idam shrIdakShiNaa-mUrtaye ||

Link to previous ones. Read the rest of this entry >>

Swami Prabhavananda and Swami Nikhilananda

This post is about two of my beloved monks of the famed Ramakrishna Order. Online links to their biographies: Swami Nikhilananda (1 and 2) and Swami Prabhavananda (1 and 2).

Lives: The similarities in their lives simply cannot be missed. Swami Prabhavananda was born in 1893, while Swami Nikhilananda was born in 1895. Swami Prabhavananda was an initiated disciple of Swami Brahmananda, the spiritual son of Ramakrishna while Swami Nikhilananda was a initiated disciple of Sarada Devi, the spiritual wife of Ramakrishna. (It is interesting that both have the same Ramakrishna-number -- similar to Erdos number in Mathematics -- 2.) Both of the Swami's were sent at a very young age to USA to continue the work started by Swami Vivekananda.

Both of the Swamis established their Vedanta centres (as Ramakrishna Maths outside India are called) in the west at Los Angeles by Swami Prabhavananda and in the east at New York by Swami Nikhilananda. They both became famous in the modern world for their books and lectures mainly centering around Vedanta. Swami Nikhilananda was well known for his translations of Shankara's works while Swami Prabhavananda was well known for his collaborations and interactions with people like Aldous Huxley, Frederick Manchester and Christopher Isherwood (the latter two are his collaborators). They both continued to be the presidents of the centres they started till the day they left this world. Swami Nikhilananda left this world at 1973, while Swami Prabhavananda left this world in 1976.

Works: I think that Prabhavananda gives a simple from the heart commentary, while Nikhilananda gives a more scholarly translation (I wanted to, but did not use the phrase more-accurate for Swami Nikhilananda).

• Upanishads: Upanishads: Breath of the eternal by Swami Prabhavananda was simple, refreshing and introductory. Swami Nikhilananda wrote two translations of the Upanishads. One of them a 4-volume edition (amazon-link) is considered a master piece in itself and also has the commentary on the Upanishads by Adi Shankara. It also has a near 100 page introduction. So that lesser souls like us can read the Upanishads, The Swami has also written one volume abridged edition. Even the latter has a detailed introduction (mostly taken from the introduction to the former). Both of these introductions are a great introduction of the Vedanta to any serious student. A major portion of the introduction -- in both the 4 volume and 1 volume editions -- is aptly titled "Discussion of Brahman in the Upanishads".
  
  
• Bhagavad-Gita: The Song of the Lord Bhagavad Gita by Swami Prabhavananda was very simple and beautiful. The translation by Swami Nikhilananda included a translation of the commentary by the Great Adi Shankara. It also includes a great introduction.
  
  
• Biographies of their Parama Acharya: Swami Nikhilananda is well known for his translation for the excellent translation of Gospel of Sri Ramakrishna (which I have not read) and its abridged version (which I have read). Swami Prabhavananda's disciple Christopher Isherwood has written Ramakrishna and his Disciples which is enchanting. I put it in the category of Swami Prabhavananda because of he is a disciple of Swami Prabhavananda. In the introduction of the book, he begins with the striking words: "this book is about Ramakrishna, the phenomenon".
  
  
• Other Works by Swami Nikhilananda: Swami Nikhilananda has translated Mandukya Upanishad including Gaudapada Karika (book not available online in USA. Only in RK mission book shops in India.), Drg-Drsya-Viveka and Adi Shankara's Self-Knowledge (Atma-Bodha). The latter book is commendable for its introduction that has a good introduction to Vedanta Philosophy, and its appendix that has a beautiful translation of many devotional hymns written by Adi Shankara.
  
  
• Other works by Swami Prabhavananda: The Swami has translated Adi Shankara's Viveka Chudamani Crest Jewel of Discrimination as well as Patanjali's Yoga Sutras: How to Know God. Swami Prabhavananda's Sermon on the Mount according to Vedanta is a book I would recommend to any Christian for the simplicity with which the core of Christianity (the Lord's prayer) echoes Vedanta.
  

May you read the works of the great men and progress towards realizing Brahman within Your Self.

[This post is another in admiration of Ramakrishna Math in spreading Vedanta in the west. Previous one is here.

About spreading of Vedanta in India, there is a third monumental figure, Swami Ranganathanananda. Describing him would be attempted in another post. Until then, read these wiki-entry, quotations from Ranganathananda, his obituary (he passed away in 2005) review of his biography.] Read the rest of this entry >>

Articles by Arun Shourie

A pointer to some articles written by Arun Shourie. His clarity of thought, preciseness and knowledgeability and the honest to call a spade as such, make each of his writings a piece in itself.

In Weak to the Strong, Strong to the Weak, he argues how partisan has been the practise of extreme-liberalism in India, atleast in the depiction of pictures of Dieties:

...
"But nude representations are a part of our tradition. Look at Konark, look at Khajuraho," the advocates have been shouting.
...
What basis is there for declaring the women portrayed there are Saraswati or Sita or Lakshmi ?
...
Many Hindus also notice the other thing -- the one I mentioned as the reason as against the rationalization for no artist ever being galvanized by the creative urge when it comes to painting the features of the Prophet. They notice that the artists do not do so, not because these masters cannot do so, nor because their muse never goads them in this direction, but because they know that, were they to do so, they would be set upon.
...

On Anne Besant and the current president of the congress. (This article was written in 1999, when the congress sychophants raised a hungama for the window of Rajiv Gandhi to become their president.)

Every act, every thought had been in the public domain for forty years in Mrs Besant's case. Every act, every thought has been shrouded behind the speech-writer's script, the PR advisor's sheen today.
...
The Congress-presidency came after twenty years' unremitting labour in the service of India in Mrs. Besant's case. It has come as a measure of desperation by persons who have no other way of acquiring office today.

==

Many more at http://arunshourie.voiceofdharma.com/articles.htm. The pointer was found in a comment to an excellent post (read it) on Atanu's blog. [Thanks to him, and the blogger.] Read the rest of this entry >>

Drg-Drsya-Viveka available online

Thanks to a post on advaitin mailing-list, I discovered a complete online edition of Drig-Drsya-Viveka by Swami Nikhilananda.

This short work of 46 verses, whose title means "Wisdom of the Seer and the Seen" talks about the Self as Consciousness (pragyanam-brahma) and perceiver/witness of everything. That the translation has been done by Swami Nikhilananda, who is well known for his translation of many wonderful books (my favorites: Self-knowledge and Bhagavad Gita) adds credit to this book. Even Shri. Subrahmanya Iyer says in the introduction:

The Swami's great literary merits are already so well and so widely known that this work of his needs little introduction from laymen like me. It is a time-honoured belief, a belief as old as the oldest Upanishads, that Vedantic Truth is best taught by those that live it, not by those that merely talk about it. Bhagavan Sri Ramakrsna Paramahamsa, the 'Real Mahatman' of the late Prof. Max Muller, was one such rare and great teacher. And the Vedantic works that are published by the reverend Order of Sannyasins founded by such a Guru have so great a spiritual charm that they make these works most welcome to all earnst seekers after Truth.

Here are a couple of verses:

Verse 1: The form is perceived and the eye is the perceiver. It (eye) is perceived and the mind is the perceiver. The mind with its modifications is perceived and the Witness (the Self) is verily the perceiver. But It (the Witness) is not perceived (by any other).

Verse 2: The forms (objects of perception) appear as various on account of such distintions as blue, yellow, gross, subtle, short, long, etc. The eye, on the other hand, sees them, itself remaining one and the same.

Verse 3: Such characteristics of the eye as blindness, sharpness or dullness, the mind is able to cognize because it is a unity. This also applies to (whatever is perceived through) the ear, skin, etc.

Verse 4: Consciousness illuminates (such other mental states as) desire, determination and doubt, belief and non-belief and non-belief, constancy and its opposite, modesty, understanding, fear and others, because it (Consciousness) is a unity.

Verse 5. This Consciousness [eternal Witness of all changes] does not rise [meaning birth] nor set [death]. It does not increase; neither does it suffer decay. Being self-luminous, it illuminates everything else without any other aid.

In veses 13-15, the book talks about the two powers of Maya: avarna (one that viels/conceals Brahman) and vikshepa (one that projects something else as Brahman). The next verses describe the differences between Nirguna and Saguna Brahman and the modes of attaining each of these.

Note on Saguna Vs. Nirguna Brahman: It is perceived by many that the Upanishads are ambivalent about Saguna vs. Nirguna Brahman. They have case because MahaNarayana Upanishad seems to declare Brahman as Naarayana, Svesavatara Upanishad declares Rudra as Brahman and Ganesha Atharva Sirsha Upanishad declares Brahman as Ganapathi. On the other hand, Mandukya Upanishad and verses from BrihadAranyaka and Chandogya seem to declare Brahman as Nirguna. The learned Swami points out in his introduction to Upanishads that many Upanishads are very clear about which Brahman they are talking about by the use of pronoun "He" for Saguna Brahman and "It" for Nirguna Brahman.

A recommendation: I found that reading Ramana Maharshi's commentary on Drg-Drsya-Viveka helped in understanding it. His commentary is in the book "The Collected works of Ramana Maharshi" and also available online from the Ramana-Maharshi.org website under downloads.

[The original post at advaitin mailing-list also links a classic Advaita text: Yoga Vasistha. I am yet to read it.]

Read the ancient text (including the commentary by Swami Nikhilananda and Ramana Maharshi) and contemplate on the nature of the Self!

Postscript: The following link is also relevant. Read the rest of this entry >>

Happy New Year!

Asatoma Sadgamaya
Tamasoma Jyothirgamaya
Mrutyorma Amruthangamaya
Om Shanthi Shanthi Shanthi.

May the New year bring intellectual-discrimination and the destruction of the Ego consciousness in the minds and hearts of all human beings. Read the rest of this entry >>

Shri Dakshinamurthy Stotram (Part IX) at Advaitin

In his exposition of Shri Dakshinamurthy Stotram at Advaitin, Shri. V. Subrahmanian comments on the verse 8:


Vishvam pashyati kArya-kAraNatayA sva-svAmi-sambandhataH
ShiShyAchAryatayA tathaiva pitRR^I-putrAdyAtmanA bhedataH |
Svapne jAgrati vA ya eSha puruSho mAyAparibhrAmitaH
Tasmai ShrIgurumUrtaye nama idam shrIdakshiNaamUrtaye ||

Part IX-a, Part IX-b, Part IX-c, Part IX-d, Part IX-e, IX-f, IX-g, IX-h and IX-i

link to previous ones.

==

A translation of Pratha Smarana Stotram by Shankara. Another translation is at celextel.org (free login needed). Here is the original:

Pratha smarami hrudhi samsphuradathma thathwam,
Sathchithsugam paramahamsagathim thureeyam,
Yath swapna jagara sushupthamavaithi nithyam,
Thad brahma nishkalamaham na cha bhootha Sangha. 1

Prathar bhajami cha mano vachasa magamyam,
Vacho vibhaanthi nikhila yadanugrahena,
Yam nethi nethi vachanai nigama avochan,
Tham deva devamachyuthamaahooragryam. 2

Prathar namami thamasa paramarka varnam,
Poornam santhanapadam purushothamakhyam,
Yasminnidham jagadamasesha bhootham,
Rajwam bujangama iva prathibhasitham vai. 3

==

A translation of Kaupeena Panchakam by Shankara. Here is the original:

Vedantha Vakhyeshu Sada ramantho,
Bhikshannamathrena trishtimantha,
Vishokamantha karane charantha,
Kaupeenavantha Khalu bhaghyavantha 1

Moolam tharo kevalam ashrayantha,
Panidhvayam bhokthuma manthrayantha,
Kandhamiva sreemapi kuthsayantha,
Kaupeenavantha Khalu bhaghyavantha 2

Swananda bhava pari thushti mantha,
Sushantha sarvendriya vruthi mantha,
Aharnisam brahma sukhe ramantha,
Kaupeenavantha Khalu bhaghyavantha 3

Dehadhi bhavam parivarthayantha,
Swathmana athmanyavalokayantha,
Naantha na Madhyam na bahi smarantha,
Kaupeenavantha Khalu bhaghyavantha 4

Brahmaksharam pavanamucharantho,
Brahmahamasmeethi vibhavayantha,
Bhikshashino dikshu paribramayantha,
Kaupeenavantha Khalu bhaghyavantha 5


==

Postscript: Please see this link for more details on Dakshinamurthy Stotram. Read the rest of this entry >>

Jiddu Krishnamurti on Google and YouTube

The videos of Jiddu Krishnamurti are available on Google Videos (http://video.google.com/videosearch?q=J.Krishnamurti) and YouTube (http://www.youtube.com/profile?user=KFoundation).

Great way to spend one's time watching/listening to a great man who speaks from the depths of his heart.

Postscript: You may be interested in this website for many discources by JK. [Thanks to the author of a comment for providing this excellent resource!] Read the rest of this entry >>

Will you remember 9/11?

There was a recent spate of posts in the blog world describing where the authors were on that fateful day. Today on the event of Japanese attack on Pearl Harbour on another fateful day, the New York Times ran a opinion special section, and asked the readers to post their comments on the futuristic question:

Do you remember Pearl Harbor? How confident are you that we will never forget the attacks of 9/11?

Most readers responded, according to their age. The older ones, who had been through both the events were sadful. The younger ones responded in another way. One comment by one hsing lee however, stands out of the rest and thus worthwhile to be quoted in full here:

Will the world remember 9/11?

Oh, the world will remember 9/11/01, to be certain.

A billion East Indians have not forgotten that Mahatma Gandhi’s Satyagraha movement, a movement of non-violent resistance, was born on 9/11/1906.

A billion Muslims have not forgotten that the European colonization of the Middle East - the British Mandate of Palestine, the first move toward the state of Israel eventually being forced on the Palestinian people, began on 9/11/1922… it’s why the Islamists chose this date, 79 years later, to attack the Twin Towers.

The people of Chile will never forget the CIA sponsored coup of 9/11/1973, perpetrated by Augusto Pinochet to overthrew the government of Salvador Allende, who was democratically elected by the Chilean people but disliked by the Republican Party.

The question should not be, “will we remember 9/11?”

The question SHOULD be, “can we learn the lesson of how 9/11/1922 applies to 9/11/2001, and then apply those lessons to George W Bush’s actions in Iraq and Afghanistan before it’s too late?”

An occupying army will always give rise to resistance. That resistance led to Jewish Terrorism against the British, then Terrorism by both Muslims and Jews against each other, and finally to Muslim Terrorism against America on that fateful day in 2001.

Like begets like. Hate begets hate. Chickens ALWAYS come home to roost.

And right now, George W Bush is making thousands more Osama Bin Ladens, and thousands more potential 9/11’s through his actions in Afghranistan and Iraq.

Like WILL beget like, unless we choose NOT to remember 9/11 as a day of violence, conquest, terrorism and displacement, and instead choose to remember it as the day a great man, a young lawyer from India, chose to take on the British Empire, and win, armed only with the heart of a Nation, and the truth.

Many of you will choose to use this day in history as justification for more violence, more hate, and more vengeance. An eye for an eye, you’ll call it. Perhaps you SHOULD heed the wisdom of the Mahatma… an eye for an eye will make the whole world blind.

Or are you already too blind to see?

Peace

By pointing Americans and the world to what happened on another 9/11, Hsing Lee shows what is the problem with the current world. Thank you Hsing Lee, for speaking the words in my heart.

I am sure that a couple of centuries from now, people would be celebrating 9/11/1906, on which the seemingly ideal-but-impractical theory of Civil Disobedience proposed by Thoreau was implemented by an extraordinarily brave lawyer from India. I salute you Mahatma Gandhi! Read the rest of this entry >>

Shankara's Introduction to his Commentary on Gita

On Gita Jayanthi, by some strange coincidence, I happened to start the English translation of the Srimad Bhagavad Gita by Swami Nikhilananda. The learned Swami -- from an institution which I immensely respect -- has done an excellent English translation of the commentary of Shankara. Shankara, when he wanted to start, some can say reinstate, the philosophy of Advaita in the pavithra bhoomi (sacred land) of India, wrote a commentary on the Bhagavad Gita. This was a part of his commentary on each of the text of prasthana-traya, the other two being The Upanishads and The Brahmasutras. The Bhagavad Gita is a part of Mahabharata and technically should be considered a smriti (remembered) text. It is however considered a sruti (revelatory) text due to its source (Lord Krishna, an avatar) and the influence upon Indians of generations.

The Bhagavad Gita, being such a great source of daily-inspiration for millons of Indians spanning across centuries, has been called by some scholars as a book that is (1) not amenable to Advaitic interpretation and (2) has many inconsistent thoughts. The scholars -- including the great Sarvepalli Radhakrishnan himself -- had to go through great pains in writing translations of Gita. They had to use classifications like (1) the first six chapters (called karma-shatkam) talk about the concept of renunciation of the deeds of karma as a method of liberation, (2) the next six chapters (called bhakti-shatkam) talk about the love of the personal God as a method of liberation and (3) the last six chapters (called gyana-shatkam) talk about the way of knowledge as a method of liberation.

Another great scholar, Eliot Deutsch, the learned scholar who has written the books exposing the philosophical content on Advaita and source books on Advaita, himself had to use the terms "progressive teaching of Gita" for explaining the "inconsistency" of the Gita.

All this may confuse a spiritual-student -- including the author of this post -- to mistakenly conclude about the message of the Gita. This is particularly true when: (1) if the student is mature enough to search for message in the Gita, but not mature enough -- as the author of the post was -- to understand the message that was clear (hind sight is always 20/20). (2) Also, in students who have a reasonable amount of maturity and thirst for knowledge, the words "The gita is not considered an Advaitic Text" can lead one away from Gita, when it is known that Advaita is the crux of indian philosophical systems. If such a student searches for a message in Upanishads, he is bound to be more confused, as the Upanishads are too experiences of seers. The Upanishads themselves being experiences of different seers in different times and situations would surely confuse any such student.

The way out of that confusion is, as it always should have been, the well known axiom: "go to the source". Shankara, being a brilliant philosopher himself does not have an inch of confusion and dispels all confusions from any such students hearts. The commentary of Shankara on Gita, nay Shankara's introduction itself to the Gita itself, is enough to dispel any such doubts on any spiritual practitioner. Before beginning such a reading, let us begin an old prayer that explains the significance of each Gita in the context of Upanishads:

The Upanishads are as a herd of cows; Krishna the Son of a cowherd, is their Milker. Arjuna is the calf, the supreme ambrosia of the Gita the milk, and the wise man the drinker.

Here is the introduction:

Of the two kinds of dharma dealt with in the Vedas: the one characterized by activity and the other by renunciation. This twofold Dharma, the cause of the stability of the world order and also the direct means by which men attain prosperity and the Highest Good [Liberation], was followed by members of the different castes -- the brahmin, kshatriya, and the rest -- and of the different dharmas, desirous to secure their welfare.

People parctised the Vedic dharma for a long time. Then lust arose among them; discrimination and wisdom declined. Unrigheousnedd began to outweigh righteousness. Thus, when unrighteousness prevailed ine world, Vishnu [the all pervading one], the First Creator, also known as Narayana, wishing to ensure the continuance of the universe, incarnated Himself, in part, as Krishna. He was born to Devaki and Vasudeva for the protection of the brahmins on earth and their spiritual ideal. By the protection of the brahmin ideal, the dharma of the Vedas is preserved, since all different castes and ashramas are under its control.

The Lord, the eternal Possessor of Knowledge, Soveignty, Power, Strength, Energy, and Vigour, brings under His control maya -- belonging to Him as Vishnu -- the primordial Nature, characterized by the three gunas. And then, through the maya, He is seen as though born, as though endowded with a body, and as though showing compassion for men; for He is, in reality, unborn, unchanging, the Lord of all created beings, and by nature eternal, pure, illuminated, and free.

Though the Lord had nor purpose of His own to serve, yet, with the sole desire of bestowing favour on men, He taught this twofold Vedic dharma to Arjuna, who was deeply sunk in the ocean of grief and delusion; for a dharma spreads and grows when accepted by high-minded persons.

It is this dharma taught by the Lord that the omniscient and venerable Vyasa, the compiler of Vedas, embodied in seven hundred verses under the name of the Gita.

This scripture, the Gita, is a compendium of the essential teachings of the whole of the Vedas; its meaning is extremely difficult to grasp. Many commentators desiring to present a clear idea of that meaning, have explained the words, and the meaning of the words of the sentenses, and also the arguments. But, I find that, to the people of ordinary understanding, these explanations convey diverse and contradictory meanings. Therefore, I intend to write a brief commentary on the Gita, with a view to determining precisely what it signifies.

The ultimate aim of the Gita is, in a word, the attainment of the Highest Good, characterized by the complete cessation of relative existence and its cause. This is realized by means of that dharma whose essence is devotion to Self-knowledge attained through the renunciation of all action. With reference to this dharma laid down in the Gita, the Lord says in the Anugita:

"That dharma is quite sufficient for the attainment of Brahman." (Mahabharatha Chapter on Ahsvamedha, xvi 12)
In the same treatise it is said:
"He who is righetousness and without unrighteousness -- he who is absorbed in one Goal, silent and without thinking."
"Knowledge is characterized by renunciation."

In the concluding chapter of the Bhagavad Gita, Sri Krishna says to Arjuna: "Abandon all dharmas and come to Me alone for shelter." (XVIII 66)

The dharma characterized by activity and prescribed for the different castes and ashramas is, no doubt, a means of securing worldly welfare and also of attaining the regions of the gods; but when it is practised in a spirit of self-surrender to the Lord, and without desire for fruit, it leads to the purification of the mind. A man of pure mind becomes fit to acquire devotion to the path of knowledge and attains Knowledge. Thus by means of the dharma of activity, one ultmately realizes the Highest Good. With this view in mind the Lord says in the Gita: "He who works without attachment, resigning his actions to Brahman." (V. 10) "The yogis act, without attachment, for the purification of the heart." (V. 11)

The purpose of the two fold dharma described in the Gita is the attainment of the Highest Good. The subject-matter is the Supreme-Reality known as Vasudeva, the Ultimate Brahman. It expounds both in a specific manner. Thus the Gita treats of a specific subject, with a specific end in view, and there is a specific relation between the subject-matter and the object.

Knowledge of the Gita enables one to attain the goal of all human aspiration. Hence my attempt to explain its teachings.

May we all mature enough to understand the real message in Gita.
Om Tat Sat! Read the rest of this entry >>

Link to FAQ in Polyhedral Computation by Fukuda

Here is a link to the extremely useful and well written FAQ in polyhedral computation by Fukuda. Here is a PDF version.


See the sections on face-lattice, polarity aka. duality and Minkowski-Weyl. The number of facets of a d-dimensional, n-vertex polytope grows linearly with n. However, its slope is so high that it grows intractable within no time (fascinating!).

Note: See the sub-sections where many problems, simple and hard, are discussed.

11/25: Probably the polylib-page on Polyhedra , with material taken from Schrijver's book is useful for definitions. Read the rest of this entry >>

LibraryThing: fun stuff with books

I recently became a member of LibraryThing, which allows people to keep an online catalogue of books. It has a simple interface to add books (with a search engine backed up my Amazon power!) and allows one to see some fun stats. Here are some: My author gallery, my author cloud and my tag cloud. Read the rest of this entry >>

Matrix Cook Book and parody of P = / != NP.

The Matrix Cook Book looks very useful and has ben added to the quick links. It was a quick link in Suresh's Geomblog. The Geomblog also has a parody of a typical P=/!=P conversaton in comp.theory. Thanks for both Suresh! Read the rest of this entry >>

Ramakrishna Mission and TTD

Being an admirer of expositions of Vedanta by great men, many of whom happen to be from Ramakrishna Mission, it fills up by heart with immense joy when I see the following on the backcover of a translation of Upanishads book:



The words say "Tirumala Tirupathi Devasthanam is supporting Ramakrishna Mission in bringing these books at low prices." Tirupathi Venkateshwara supporting Ramakrishna Mission is the manifestation of the statement from Bhagavad Gita: "Dharma Samsthapanarthaya Sambhavaami Yuge Yuge", where Naarayana supports Dharma and the Vedic truths in many forms.

---

Some of the books on Vedanta I have read by people of the great order:

1. Upanishads and Bhagavad Gita by Swami Prabhavananda
   
2. Self-Knowledge etc. Swami Nikhilananda
   
3. Upanishads by Swami Sarvananda (both English and Telugu)
   
4. Lectures on Mandukya by Swami Ranganathananda
   
5. The Upanishads by Swami Gambhirananda
   

I have an intuitive feeling that, in the last century, Ramakrishna Mission has atleast matched the peethams set up by Shri Adi Shankara in propagating Vedanta. Read the rest of this entry >>

Convex Polytopes and notes from Develin's works

Mike Develin is a Mathematician who has written a compendium (PDF link) to accompany Ziegler's wonderful book. Also, the first two chapters of his thesis (PDF link) are a great read for anyone interested in convex polyhedra. Some notes:

On homogenization and equivalence:

Given a polytope P\subset \mathbb{R}^d, we can form a cone associated to it by considering the cone of all points {(1,v)} where v \in V. Two crucial points: (1) The shape of the polytope can be recovered by intersecting this cone with the hyperplane x = 1. (2) You might notice that the shape of the polytope we obtain is dependent on the orientation of the polyhedral cone in R^d. This leads to the very important concept of projective equivalence. Two polytopes are defined to be projectively equivalent if they can be obtained as cross-sections of the same polyhedral cone one dimension higher; this notion of equivalance is stronger than the notion of combinatorial equivalence, where two polytopes are equivalent if their faces have same combinatorial structure, and weaker than the notion of affine equivalence, which relates polytopes which are affinely isomorphic to each other.

On polarity:

the face-lattice L(P) is just a partially ordered set, or poset with elements being the faces of the polytope and F < G if F \subseteq G.
...
One key property of polytopes is that the intersection of any two faces is itself a face, which corresponds to the fact that any two elements of the poset have a unique maximal lower bound. The aforementioned notion of combinatorial equivalence corresponds to two polytopes having the same face lattice.

With face lattice, it is easy to give a combinatorial description of the polar polytope P^\Delta. The polar polytope realizes the full power of the duality between the two formulations of polytopes, in terms of vertices and in terms of inequalities. Assuming that P is full-dimensional (embedded in R^d, where d is the dimension of P), P^\Delta is the object in the dual space V^* consisting of those linear functionals f for which f(x) \le 1 holds everywhere on P. To do this, we need to pick the position of the origin inside P, but once we have done this, the entire combinatorial and indeed projective type of P^\Delta is determined. Furthermore, the face-lattice of P^\Delta is precisely the opposite poset of L(P).
...

... the Farkas lemma implies that the polar polytope is the convex hull of the facet-defining functionals, which provides a natural correspondence between the vertices of P^\Delta and the facets of P. In fact, the lattices are isomorphic under this correspondence; the face lattice is completely determined by which subsets of {1,2,...,n} are facets, so this, along with the fact that the vertices of P correspond to the facets of P (as constraint f(x) <= 1 on P is equivalent to the intersection of half-spaces f(v) <= 1 for v \in V) exhibits explicit correspondence.

Thanks Mike!

Postscript (11/05): The chapter "Basic Properties of Convex Polytopes" is available via the following link: ftp://ftp.math.tu-berlin.de/pub/combi/ziegler/WWW/archiv/049polychap2.ps.gz(with thanks to Prof. Ziegler). The chapter is from the book: Handbook of Discrete and Computational Geometry with the following table of contents. Read the rest of this entry >>

Happy Deepavali!

The souls were drenched in the darkness of unreality,
tied up by the demon of duality,
to the chains of karma and samskaras.

The blue one in his infinite compassion was coming to rescue,
"I too would come", said his shakti.
"That is a battleground and the souls are in a pity state,
you would be sorry to see them" said the lord.
"more the reason", said his shakti,
"further, victory is not possible without me".
"Ok", said the Lord.

Battle ensured. It was bloody.
The hordes of the souls,
that had no time to wait for emancipation,
had already become trophies in the other side.
The darkness of unreality, was so immense,
that even the lord thought to himself,
"I am the manifestation of brahman,
why is this darkness taking so long?"
He sat meditating.

His shakti thought,
"This is no ordinary battleground,
the oppressed souls are refusing,
to see the true light within them."
"The demon does not have the power
to stand before even one of them."
"The chains are rusty and the
demon is unreal, to tie these souls."
"What is needed is self-realization."
"Let me help them by revealing myself".

She said to them,
"I am satya, the truth and reality. See me!"
"You oppressed souls! know that
this darkness of unreality does not exist,
this demon of duality does not
have power over you."
"Know thyself!
Know that your inner self,
is as infinite, and as potent,
as that which drives the lord here."
"tat tvam asi. tat tvam asi".

The souls realized the illusory nature of the demon,
it was Brahman everywhere.
The lord wokeup and smiled,
it was Brahman everywhere.
Filled everywhere was,
the radiance of a thousand suns,
it was Brahman everywhere.
Not that there was a time when it was not,
it was Brahman everywhere.
Truth, peace and joy prevailed.
Om Shanthi Shanthi Shanthi. Read the rest of this entry >>

Audio renditions of Sri Dakshinamurthy Stotram

Here are two audio renditions of Sri Dakshinamurthy Stotam:

1. From Kamakoti.org, thanks to this post on advaitin.


2. By unknown artists in fusion style, thanks to this post on advaitin.

Postscript: Please see this link for more details. Read the rest of this entry >>

tera teeyaga raada ...

It is said that when Thyagaraja, went to Tirupathi, a curtain was drawn -- as it usually done, so that seva, or alankar can be done -- between him and his lord. He waited long, and when he -- the life long devotee of Rama, the absolute in the form of prince of Ayodhya -- could not wait any longer to see his lord, he sang:

tera teeyaga raada naaloni
tera teeyaga raada
tirupathi venkata ramana matsaramagu tera teeyaga raada

which roughly means

Oh lord, please remove the curtain of ignorance which separates us.

He of course was referring to his saguna-brahman as Sita-pati. What difference does it make when the devotee is longing for uniting with his lord, whether it be nirguna or saguna? What difference does it make, when all he wants is, to be removed of his ignorance or EGO. The ego, which is the final obstruction between a devotee and his God, the jiva and his Ishvara, the Vishistadvaitic-atman and its qualified-with-attributes-brahman, the soul attaining its Nirvana, the Advaitic-eternal-atman with the eternal-brahman?

Not surprisingly, the curtain fell off and Thyagaraja is said to have finally merged with Rama-brahma?

==

What use is of feelings if they do not come into practise in daily life? What use is the ability to remove the ego when with oneself, when in any kind of communication, nay even presence of others does it manifest itself? Is this the way of the world? Probably not. The key may be to pray to the Goddess Maya herself, to Ma Kali, Ma Lalitha Tripurasundari to reveal herself.


... Dakshinamurthy ruupini
Sanakadi Samaradhya Siva Gyana Pradayini ...

(from Lalitha Sahasranamam)
O southward-facing one (O kind one), who gave the eternal knowledge to Sanaka and others, please do the same to me. Read the rest of this entry >>

Sridakshinamurtistotram at advaitin

Disambiguation (1, 2 and 3) at advaitin between shridakshinamurthy stotram, that begins with "vishwam darpana drishya maana nagari tulyam" and others. It seems that there are three stotras by Shankara on Dakshinamurthy and the convention seems to be to call the most popular one (one that begins with "vishwam") as ShriDakshinamurthy Stotram. It is erroneously called astakam, as it obviously does not have eight shlokas.

==

Shri Subramanian continues his exposition of the ShriDakshinamurthy Stotram. In part VIII, he comments on verse 7 of the stotra.

bAlyaadhiShvapi jAgradaadiShu tathA sarvAsvavasthAsvapi
vyAvR^ittaasvanuvartamaanamahamityantaH-sphurantam sadaa |
svAtmaanam prakaTIkaroti bhajatAm yo mudrayaa bhadrayaa
tasmai shrIgurumurtaye nama idam shrIdakShiNAmUrtaye || 7 ||

Here are Part VIII-a, Part VIII-b, Part VIII-c, Part VIII-d, Part VIII-e and Part VIII-f.

There is a mistake in numbering VIII-e as VIII-f. Here is a supplementary comment on the word 'dhira' VIII-d dhira.

Link to previous ones.

==

Prof. VK's page on Shri Dakshinamurthy stotram. Read the rest of this entry >>