PAUL ERDÖS


We have all heard of unusual geniuses in art and music, even in science sometimes. But there are extraordinary individuals in every creative field. It is not easy for everyone to understand, let alone appreciate, the work and value of their contributions to human thought and culture.

In the field of mathematics, for example, there have been quite a few exceptionally gifted people, and some of them lived rather unusual lives, bordering on the eccentric. As in music, some of the marvelous capacities of the human spirit are expressed through such geniuses.

Paul Erdös (born: 26 March 1913) was one of them. He born in Hungary and of Jewish parents, but he never felt strong affiliation to any region or religion, seeing himself only as a human being. He had no interest in politics or pettiness of any sort. He had equal contempt for communism and capitalism and their major spokes-nations of the 20th century. He derisively referred to the U.S. as Samland (Uncle Sam’s country) and the Soviet Union as Joedom (the realm of Joseph Stalin).

His highly technical output is far too esoteric to be translated into everyday language. He received some of the highest awards and prizes conferred on the practitioners of the profession, like the Cole Prize and a letter of appreciation from the Fields Medal Committee. Because had  passed the age of forty he was not eligible for the medal which he richl;y deserved otherwise.

Though some of these came with a hefty check, Erdös cared little for money. He gave it away to poor students or as prize money. He himself lived a very sparse life. Like religious ascetics, he never married.

But there is at least one major accomplishment of Erdös that must be intelligible to many people. All we need to know is that a prime number N is one which cannot be written as the product of different numbers (other than as 1 x N). Now consider the number 4 and its double 8. Between these two there are two primes 5 and 7. Or consider 15 and its double 30. Between them we have the primes 17, 19, 13, and 29. In the 19th century it was known conjectured (the Bertrand Postulate) that between any number x and its double 2x, there are is always at least one prime, as illustrated above. In the 20th century some eminent mathematicians proved it, but the proof was complicated. At 19, Erdös gave an elegant proof for this result in number theory. He also proved (without invoking complex numbers) the so called prime number theorem which gives an estimate with an upper limit for the number of primes there are below a stipulated number.

Since he was interested in little else aside from mathematics, all of Erdös’s intellectual energies were devoted to mathematics. His primary interest was in number theory. But he was also a major architect of what is called discrete mathematics which is of enormous import in computer science. He collaborated (wrote joint papers) with at least 462 mathematicians: more than anyone else had done.  He authored more than 1500 papers during his lifetime. More were published posthumously.

Erdös had a pungent wit. As an atheist who had suffered under fascist regimes, he described God as a Supreme Fascist. He referred to children as epsilons (small entities in the mathematical jargon). He did not care for marriage, referring to women as bosses and to men as slaves in the context. He suggested the following for his epitaph: Végre nem butulok tovább (Finally I am becoming stupider no more).

Paul Hoffman’s The Man Who Loved Only Numbers is an enjoyable biography of this genius. Epic poets, composers of magnificent music, great painters and mathematicians: They all function in higher realms where they create or harvest rich fruits and share them with the rest of us, if we are sophisticated enough to be able to relish them.

March 26, 2011

Sivapuránam (Civapuránam)


Caiva-ciddántam is a metaphysical-philosophical-spiritual school which takes the Civa (Shiva) Principle as the fundamental substratum in the world. It is very ancient and has a North Indian version as well as a South Indian. In both systems Civa is transcendent as well as immanent, but it also has a personal form, helpful in the worship mode.  Divinity itself is beyond categories, those who worship it in the Civa mode must be beyond the constraints of caste and creed, and see Divinity in one and all.

Indeed, Caiva ciddántam attributes sacredness to all life. In its framework, the Divine gives its grace to all who seek it, sometimes even to those who do not. All life may be regarded as an expression of grace. The Divine participates in the course of every life, yet remains untouched by it all. All of creation is nothing but a reflection of divine ecstasy.

Three entities are real: pati which is the Divine, pasu which is the soul, and pásam which is the rope that binds the pacu to the worldly domain and constrains it from receiving the light from the pati and thus attain perfection. Through jñána (divine knowledge) and bhakti, (devotion) the bonds of pásam may be cut and one attains ultimate freedom.

Another key idea in the framework of Caiva ciddántam is that for interaction between the Divine and the human to occur, both should be on the same plane. Either the Divine comes down to our level (avatára), or we must raise ourselves to the level of the Divine. This transformation is said to occur in two stages: First there is the nullification of the physical dimension, or rather purification of the gross elements of which the body is formed (bhútashuddhi), and then through mantras the body becomes a one of spiritual energy (shaktadeha). By this process is civakarana (transformation into Civa) achieved.

In the Tamil tradition there are fourteen canonical texts expounding the principles of Caivaciddánta. Of these CivajñAnabodam of  MaikanDadévaris regarded as the most important.

Aside from their metaphysical and spiritual visions, the Caiva poets of the tradition have made some of the most outstanding contributions to the rich realm of Tamil poetry. Their songs are so moving, and their visions so penetrating that these poets are remembered and recited in Civa temples all over the Tamil world, and they are venerated such as few poets are in any culture of the world.

The Caiva hymns are more than bhakti-poetry. They hymns break new  grounds in various kinds philosophical thinking. Some of these were developed in the later MeykaNda Sastras. A note on the ci in Civan: The mantra syllable ci-káram, embodies the conception of creation as bringing into  light the essence of Caiva Ciddanta.

March 21, 2011

Now you can get my translation and commentaries of this classic in Tamil spiritual literature on Amazon.com.

Disaster in Japan


Life-destroying disasters arise from Nature’s periodic whims such as hurricanes and earthquakes. But there are also calamities that result from social injustice and iniquities, fanatical beliefs, racial and religious tensions, and the like.

Reflections on these matters are certainly stimulating and clarifying when we are in the comfort zone of home and hearth, but when, for no fault at all, one is thrown into the quagmire of violent political conflicts, or when one’s modest life course is rudely jarred by Nature’s blind fury, what is one to do?

Under such circumstances, our worldviews can be shattered. Some cling even more dearly to the God from whom they still expected love and mercy, because that faith gives them the strength of heart to bear the burden. Others are tempted to abandon their long-held trust in such a God.

But those who are not directly affected often feel a moral obligation to help their fellow creatures on the planet, in however small and symbolic a measure, with no consideration of race or religion, nationality or history.

What, one may wonder, is the source of this innate morality that touches so many people, if not all? I don’t know, and in a context like this, I  am reminded of the poem:

When Disaster Strikes

When lightning strikes a praying crowd
And the pious burn and die;
When earthquakes bury decent folk
And orphaned children cry;

When sick and old are abandoned too
And people lose their mind:
Try not for these and disasters such
Answers clear to find.

There are times to ask if God’s just a thought
Or indeed a fact.
There are times at which we need to go
And at once begin to act.

With loss and pain and intense grief
We don’t have much to gain,
From arguments on heaven and hell.
They’ll all be just in vain.

Let’s search and see what we can do
For those who are in need,
Let’s see how we can help and heal,
How we can clothe and feed.

It does not matter if we do not know

Why there’s pain around.

What we need are helping hands,

Not learned views and sound.

March 12, 2011

Scientific understanding of ethics and experiences


People have traditionally attributed love of children to non-natural causes, which is fine.

However, suppose that science/empiricism  is able to establish  that through our efforts to understand fully how all these wondrous dimensions of being fully human (as also the not-so wondrous aspects) happen to arise?

Wouldn’t that understanding make us a little richer, without undermining in any way the glory of love and reverence?

That is certainly one function of science: Not to devalue the human person by unraveling our physical and evolutionary essence, but to enhance our appreciation of it all  by serious and systematic exploration of what we and the Universe are all about.

The majesty and the beauty of the rainbow are a sheer joy to behold.

But is it wrong to uncover beneath it Snell’s law of refraction?

But as to the benefits of a scientific understanding of certain dimensions of being human, I am not convinced such  understanding at the theoretical level would have any impact on our ethical behavior any more than that an understanding of the Fourier components of an aria magnificently belted out by a diva should necessarily enhance our reason for delighting in it. Fostering love and caring through Sunday-school instruction or dominical sermon or a swami-talk can be no less valuable than telling us it is all through the Vivekananda-gene or the Theresa neurons in our brains that we become the good guys/gals.

Scientific understanding of anything invariably deepens our appreciation of it, but it need not – as is sometimes feared – rob us of its experiential aspect: In other words, whether it is in knowing the molecular structure of a chocolate bar that titillates our taste buds, or that of the aroma from a rose that gives a kick to our olfactory system, nor indeed knowing what causes the love we experience for God or mortal: None of these need be diminished by a scientific understanding of how it all comes about.

Our experiences are rich as their are. But (metaphorically speaking) the angel  is in the details. Often, the quest for the angels is mistaken for enticement by the devil.

March 10, 2011

How might the discovery of alien life affect religion?


In this context it is also important to distinguish between aliens as conceived by modern extra-terrestrial astronomy and the aliens of mythic lore. In modern astronomical thought, aliens refer to entities which have evolved biologically in distant planetary systems quite independently of terrestrial life, and are believed to have attained sufficient technological and other intellectual sophistication to be able to at least attempt contact with other similar creatures in the star-studded stillness of space, of whose existence they must have been scientifically convinced. On the other hand, in traditional religious/cultural views, those inhabitants (angels, jinns, cherubim, devas, and the like) of distant worlds were already connected to humans some way or another. Therefore, the question posed is really inappropriate because the same word (alien) has two quite different connotations in science and in religions. It is not unlike asking how the discovery of black holes might affect religion. Ancient religions have talked about hell, but that is not quite the same as the explosive singularity of a supernova.

From a global scientific/cultural perspective even a slight indication of the existence of extra-terrestrial life anywhere in the universe would be a fascinating, and indeed a shocking and most remarkable discovery. Concrete proof of an advanced ET civilization would be more than an eye-opener: It would be the most revolutionary discovery in all of human discovery. Yet, it is not likely to jolt the collective consciousness of humanity as much as it should, because few people have reflected on the moral, religious, and conceptual significance of something like that. We will cease to be special and singular in this vast universe that seems to stretch beyond our maximum spatial needs. Affirmations of God creating Man on the last day of His/Her creation-project may have to be drastically re-considered, because any confirmation of extra-terrestrials would demolish the centrality, primacy, and uniqueness of terrestrial consciousness in the universe which is a fundamental tenet of all religions. Confirmation of ETs will shake the very foundations of all human-centered religions.

However, if a religion subscribes to the view that human consciousness is a spark of a Cosmic Fire (as Hinduism does), and also realizes that there are countless  bio-friendly planetary niches in the vast universe (as current astronomy suggests), then from the perspective of that religion, it is extremely likely that similar sparks have found thriving spots elsewhere in the cold galactic expanse, embodied in carbon-based, silicon-based, or whatever frames. From such a perspective (which is not incompatible with Hindu visions) discovery of the existence of aliens ought to  be greeted with more applause than apprehension.

March 9, 2011

Lorne Ladner, Ph.D., The Lost Art of Compassion: Discovering the Practice of Happiness in the Meeting of Buddhism and Psychology, 2004.


We live in an extraordinary age of wonderful scientific breakthroughs and marvelous technological achievements. Possibilities for cure of pernicious diseases and for health and longevity keep increasing. But ours is also an age of spiritual anguish and moral confusions, of promiscuous sex and savage violence. Crudeness, combativeness, and religious intolerance seem to be on the rise. In this context, it is refreshing to read a book that brings us wholesome worldviews that could help restore some balance in human interactions, based on both scientific  and spiritual insights on compassion.

Though the title and principal theme of the book relate to compassion – the cardinal virtue in Gautama Buddha’s teachings – the author, who is a trained psychologist and practitioner of Buddhism,  gives his readers many worthy understandings of the human mind and human capacities for good. Here is a healthy blend of religion and science, of ethics and reasoned thought.

The book is spiced with interesting anecdotes which make it interesting  and thoughtful reflections which make it worth reading. The connections between Buddhist tenets and findings of current psychology add scientific support to the recommendations in the book. Perhaps one can find scientific support for the virtues prescribed in other religions also: such as love and caring, tolerance and humility. Reminders of eventual death and the ephemeral nature of existence may not be original thoughts: after all, they are the most ancient themes for poets and philosophers. But in the context of preaching ethics, they can inspire restraining attituides on people on the verge of rash or harsh behavior. There are also intelligent analyses of the  basic urge for happiness in the book. The author presents a clarification of the notion of happiness which should be useful to readers.

There is no question but that raw aggressiveness and self-centered acts of cruelty and exploitation seem to pervade modern societies, but we don’t have enough data on the  misbehavior of past generations to fault only people of the modern age. In any case, the book is meant to transform them to gentler and more civilized modes. This in itself is commendable.

However, it is important to remember that our appraisal of the world’s moral status is often derived from the daily news. This view of the world is, for many, very different from the world in which most people normally live during their waking hours. In everyday life and  day to day interactions most people in most societies are carting and kind and decent. When calamities arise, not just in our neighborhood but in distant lands too, the outpouring of  compassion and concrete assistance has generally been at more than a modest level. In the so-called richer countries, millions of people donate generously for the poor and the needy in distant lands. In other words, the art of compassion is not as lost as the title of the book suggests.

Then again, it is not clear that even among peoples where Buddhism is the principal faith, there is the kind of universal compassion that one would romantically imagine in that framework. When one reads about the Sermon on the Mount or the Ten Commandments in Tibet, the reader should not assume that all the people in Judeo-Christian societies put those nuggets of ethical wisdom into daily practice. We are all, after all, human beings capable of the best and also of the worst that the human animal is capable of.

This is not to say that the  wisdom and perspectives spelled out in this book are not relevant or significant. Irrespective of one’s religious affiliation or absence thereof, one can benefit enormously by following the recipes for Compassion Practices given in the last sections of the book, à la Dale Carnegie. These instructions are meaningful, enriching, and practical. If only all were to make honest attempts to live up to them the world would surely be a better place.

This is the kind of book that can have only positive impact on readers, especially on those who are in the early stages of value-formation.

March 7, 2011