Visions (In).Finite

The Amar Chitra Katha comics are unmatched for their altogether superb rendition of India’s history, mythology and folklore. Their wealth of stories holds much in store for all manner of topics under the sun. As we resume our musings on infinity, it is to this treasured collection that we return, for one more tale of the emperor Akbar and his minister Birbal.

The Sycophant’s Praise

One fine day, a wandering minstrel, hard of circumstances, came calling to Akbar’s court, requesting to sing for the emperor. Permission granted, the bard was soon in his element, entertaining all present with his paeans of fulsome praise for the emperor, extolling him at one point as even greater than God. Ridiculous as it was, the melodious flattery certainly succeeded in buttering up the emperor, who presently dismissed the sycophant with a generous reward for his efforts.

Having sent the man away, Akbar noticed that the sharp witted Birbal, always known to call a spade a spade, had remained silent throughout the performance, not raising as much as an eyebrow at the overly exaggerated praise. On the contrary, Birbal had even nodded mildly at the ridiculous line of the emperor being greater than God! ‘Tell me how in God’s world can that be true’, Akbar now prodded his minister.

The best of emperors can be whimsical, and however high they may hold you in regard, Birbal knew he was only one mistake away from being expelled from court or worse, if he so much as made a single careless slip of the tongue. But Birbal was also a master of thinking on his feet, and sure enough, had a quite precocious answer up his sleeve.

With the look of a teacher indulging his favorite pupil, the witty minister told Akbar that the sycophant was indeed correct in one specific, if rather narrow way. If Akbar wished to banish a man from his kingdom, all he had to do was to issue a royal decree to deport the man for good. But if the Lord of the whole wide Universe wanted to do the same thing, where was it that He could banish anyone to?

Akbar was both impressed and grateful for how tactfully Birbal had opened his eyes, delivering a nuanced lesson in humility, but with no humiliation whatsoever. With this clever response, Birbal had also juxtaposed physical and metaphysical infinities quite artfully, blending them into the same conversation. But this little story can also reveal a lot more to us about finitude and infinity.

Glimpses from Finite

In the nineteenth century novel, Sartor Resartus, Scottish philosopher Thomas Carlyle speculates on our perception of the universe.

‘We sit as in a boundless Phantasmagoria and Dream-grotto; boundless, for the faintest star, the remotest century, lies not even nearer the verge thereof; sounds and many-colored visions flit around our sense; but Him the Unslumbering, whose work both Dream and Dreamer are, we see not; except in rare half-waking moments, suspect not…’

The vastness of infinity can overwhelm the human mind, so much so that we are all pretty sure there’s nobody who has actually ‘seen’ infinity. Hold that thought for a moment though, convincing as it may be. It turns out that anytime we see a physical object (or envision something in the mind’s eye, like the extent of Akbar’s kingdom) we see it as outlined by its boundaries. No form can be seen without cognizing its boundary, and thereby its background context. That background, which is the space surrounding the object, is by its very nature limitless, even while it may include other encompassing objects or boundaries.

Such would be the case for example with concentric circles, where the space beyond the outermost circle is boundless. The background, which we cannot help seeing whenever we apprehend a particular form, is essentially unbounded, and infinite. We might not notice or pay attention to it, but it is always there.

Even in our finite vision, infinity thus turns out not to be some inaccessible and fanciful abstraction, but sitting right under our noses, so to speak. The background of space is not so much hard to see, as it is impossible to avoid. While our finite vision cannot survey all of it in one glance, one is still always catching a glimpse of infinity.

This reasoning can apply not just to ‘substantial’ objects, but also to something as insubstantial as a rainbow, whose boundaries are most easily seen as merging into the endless expanse of the sky.

You can also apply it to intangible things like emotions. Consider an outburst anger or an upsurge of joy. When we are aware of these, we are ‘seeing’ them spring up, out of the blue as it were, from the skylike backdrop of awareness. We might also notice they have a temporal beginning and end, set against the infinite expanse of time.

With a little leap of thought, such reasoning can extend to theology. The question of boundaries here might be framed as ‘where do I end, and where does God begin’.

With regard to metaphysical boundaries, we are really talking of spheres of influence. As human beings, the outer personality of our physical form is enfolded by layers of our subtle bodies and mind, to constitute our personal aura. For most people, the human aura extends for a few feet beyond the physical body. In the case of evolved beings though, their auras can be seen by clairvoyants as extending out for miles in the shape of a radiant sphere, charged with the power to influence others with healing and blessings.

Similar is the case we find in astrology, where the auras of the planetary angels extend and overlap as spheres which intersect, and to some extent interpenetrate each other, bringing varying kinds of energetic influences over time to chart human destiny.  Ruling above all of this is the Aura Supreme, of the Lord of the Universe, the akhanda mandala or unbroken sphere, penetrated by none, but penetrating All…the benevolent sphere of universal love which influences all others, but is influenced by none. This is the sphere of metaphysical infinity, the sphere from which no one can be banished ever.

Perhaps Ramakrishna, that much loved spiritual genius of Bengal, said it best to the skeptical young Narendranath Dutta who went on to become the world famous Swami Vivekananda. To Naren’s insistent question of if he had seen God, Ramakrishna responded with a dazzling conviction ‘Yes, I see Him, only a little more clearly than I see you!’ The boundaries that Ramakrishna’s vision transcended, of course, extended far beyond Vivekananda’s physical form. It was a timeless Presence that Ramakrishna saw naturally emmbodied in the young man, who was hugely taken with the saint’s startling reply.

Inter Being

Even if we ignored the background, we cannot miss the object itself. The great Vietnamese Zen master Thich Nhat Hahn reveals with astonishing clarity how just contemplating the finite can reveal the universal, in as much as a single sheet of paper.

If you are a poet, you will see clearly that there is a cloud floating in this sheet of paper; Without a cloud, there will be no rain; without rain, trees cannot grow, and without trees, we cannot make paper. If we look even more deeply, we can see the sunshine, the logger who cut the tree, the wheat that became his bread, and the logger’s father and mother. Without all of these things, this sheet of paper cannot exist. In fact, we cannot point to one thing that is not here – time, space, the earth, the rain, the minerals in the soil, the sunshine, the cloud, the river, the heat, the mind. Everything co-exists with this sheet of paper. So we can say that the cloud and the paper ‘inter-are’. We cannot just be by ourselves alone; we have to inter-be with every other thing.

/Thich Nhat Hahn, ‘The Heart of the Prajnaparamita Sutra

Whether we look at an object, or whether we look at its background, we are thereby always glimpsing the infinite. This inter-being that Thich Nhat Hahn talks of is vast and cosmic in its scope, extending all the way up to the Unbroken Spere of the akhanda mandala. It is perhaps what Blake alludes to, when he penned those lovely lines…

To see a World in a Grain of Sand
And a Heaven in a Wild Flower 
Hold Infinity in the palm of your hand 
And Eternity in an hour

Measure(less) Mind

Mind is wont to measure and size up everything. Children obsess about their heights, adults about their weights and girths, including if the zero of the weighing scale has been fairly calibrated. Today’s trending measures include BMI, cholesterol, and the number of steps as reported by Fitbit or a less fancy pedometer. We also have measures, albeit subjective, for beauty and proportion, homely vs comely, and in short, for all things (and creatures) great and small.

But if there is one thing the mind cannot get the measure of, it is of itself, it’s own extent, and we cannot even be sure if there is a limit to it.

At the back of all preoccupation with the limited is the fascination for the limitless, which in psychological terms is the yearning for some sort of unrestricted freedom. Nobody has ever seen infinity, but every one of us had the taste of being bound and restricted, and therefore by reflex, the yearning for something free and unbound. We have also the sense that this yearning would not be there unless it was in some manner capable of being fulfilled, though we may not know exactly how. Mind suspects intuitively that the infinite is concealed by the finite, the extraordinary lurks under the veil of the ordinary, and the limitless is shrouded by the limited.

Infinite Vision

The finite can catch a glimpse of the infinite, but what would it be to gaze at infinity directly, without the intervening presence or support of the finite? This is the subjective experience of pure infinity, pristine and unconditioned, one beyond the reach of any mental gymnastics. This is the gazing into Absolute, all of it at once. As the Zen saying goes, it is ‘to swallow the Pacific Ocean in a single gulp’. How can a finite mind manage it? The approach has to be one  not of brute force, but strategy. This is the approach of subtle mirroring.

Perhaps gazing deep into the sky of outer space, with not even the stars to intervene, might bring us close to this experience. The mind, after all, is well known to take on the contours of the objects it is focused on.

Now just like if you kept travelling East you might at some point find yourself in the West, if you kept gazing into boundless space, your attention might at some point be thrown back into itself, doing an about turn as it were to go deep within. Gazing into all-encompassing outer space, the mind’s inner spaciousness then comes to the fore. A gap opens up into the mind’s inner sky, the window of Zen’s ‘satori’, bridging outer expanse of space with inner expanse of mind into the Celestial Everywhere.

In like manner, if one looked into the present moment deeply enough, mind’s sense of present time can open up into the Timeless Now, in whose archives everything even of the future happened long ago, so that this Moment is forever new.

Diving deep, beyond reach of words and thought, mind ultimately merges in the liberating expanse of its very own nature, of unconditioned awareness. In such awareness might be revealed how all the outer infinities, of our endless inter-being, of infinite space, of eternal time, and the all-encompassing love of the Unbroken Sphere, are but reflections of mind-nature, that of pristine freedom.

Such is the state of samadhi, the unbounded infinity of the wise. Shankara, most celebrated of India’s mystics, describes it eloquently. ‘Thou from whom all words recoil’.

While from his vantage point of the Dream-grotto, Thomas Carlyle echoes a similar understanding…

Think well, thou too wilt find that Space is but a mode of our human Sense, so likewise Time; We are – we know not what; Light-sparkles floating in the aether of Deity!’

The Deity of the Celestial Everywhere and Timeless Now.

Looking From Infinity

Glorious as infinte vision might be, what then is the value of the finite?

Just like with a shift of perception, we saw that the finite cannot avoid the infinite, could the flipside be true, that from the infinite eye, it would be impossible to avoid the finite?

From the North Pole, all directions point South. Wherefore from infinity, we might ask. How would the finite appear to the vision and gaze of the infinite?

The answer, truly speaking, can only be found in a consciousness that has tasted of satori or samadhi at least once. But that does not stop us from some creative speculation.

The vision of the finite that we may be privileged to see, from the wakefulness of infinite vision, may not necessarily be one of physical boundaries, but one of boundaries of consciousness.

The finite may appear as finite, but not necessarily in set and rigid contours as before. The boundaries may be like that of the spectrum of the colors of light, with each microtone of color merging seamlessly into the next micro-wavelength of radiation.

So it might be with levels of consciousness, from crystals and minerals, to plants and animals, human beings and stars, all the way to the brilliance of divine consciousness. All in all, the world of finitude appears much like a dreamlike vision, a smorgasbord of colors of every possible hue in consciousness. Speculations on the identity of the dreamer, if there is indeed one, or if dream and dreamer are one, and so on, are a wholly different philosophical cup of tea. All we know for sure is those who have chanced upon such a vision never stop speaking of its endless beauty.

From finite gazing (if unknowingly) into infinite, to infinity’s immaculate gazing at itself, and then back to looking ‘out of infinity’ in fresh colors, we have mirrored the path of the wise, who straddle finite and infinite, the dance of Relative and the play of Absolute Reality, with consummate ease.

These are the seers of Truth, the Rishis of every land and epoch. It is said of these noble ones, that immersed in the thrall of the Absolute, their all-pervading compassion never loses touch with the Relative. And immersed in the dance of the Relative, their all-pervading wisdom never loses sight of the Absolute. Theirs is the infinite kingdom.

So what of infinity as it relates to our own roamings, in the pursuits and concerns of life? There is this sense we’ve all had, at some point or other, that life is a journey, be that journey a wandering or a homecoming. The ideas of roaming, space and direction can be viewed from the perspective of metaphysics, but can also be complemented by some interesting insights from the world of arithmetic and geometry.

Our next blog post will embark on these journeys (in)finite.

Musings (In).Finite

Infinity is that strangest of things, in as much as it can be called a ‘thing’. It conjures up images of an expanse without limits, be it of vast landscapes, boundless oceans or limitless skies.  The borderless expanse of infinity is also a field of fertile imagination, one which reveals surprising twists and paradoxes that can entertain as much as they confound.

The idea of infinity has inspired many works of art and genius. One of the most innovative of enterprises of our times, Apple, has for its worldwide headquarters the very interesting address of ‘1, Infinity Loop’. Recently, infinity bubbled up in popular discourse courtesy the movie, ‘The Man Who Knew Infinity’. The movie portrays the life of Srinivasa Ramanujan, the divinely inspired Indian mathematician whose work of a century ago continues to create goosebumps for the most seasoned mathematicians of today.  

We have of course several flavors of infinity, drawing people of every ilk to come explore its territory. There’s the physical infinity of space, the temporal infinity of time, the mathematical infinity of numbers and sets, and the cosmic infinity of metaphysics. Scientists and artists, mathematicians and mystics alike have all been drawn to infinity’s domain in the most creative ways.

Pitching tent at base camp with their experiences and theories of the finite world, they have mounted inspired attempts up the slopes of infinity, a mountain whose peak has remained forever shrouded from view. The climb is daunting, but even the smallest of footholds gained reveals vistas of uncommon beauty, even as however far up one manages to go, the summit remains as elusive as ever. Which is as it should be, for infinity would not be what it is if there was even faint chance we could gain measure of it with our conventional ways.

Tricks In Finite

In daily life, the notion of infinity is often associated with anything that is outsized large, and therefore not amenable to easy comprehension. Clever folks can use ‘enormous’ or ‘infinitely big’ to gain a lot of accommodation. Large numbers can be intriguingly elastic, as seen in the following tale.

It is one of many tales of the Mughal emperor Akbar and his wise minister Birbal, illustrated in that hallowed collection of India’s comic book treasures, the legendary Amar Chitra Katha. The story illustrates some of the flexibility and fun afforded even by everyday large numbers, not to speak of infinity, the big daddy of them all.

The Crows of Agra

Birbal was far and away the cleverest and most astute minister in Akbar’s Mughal court in the capital city of Agra. It made him the emperor’s counsellor of first and last resort, and thus not surprisingly, the object of grinding envy and jealousy of several other courtiers. One could empathize with them, for the emperor had this most frustrating and consistent habit of ignoring their (usually unsolicited) advice in favor of Birbal’s. The courtiers could do little but try to reason out with the emperor, and when that fell on deaf ears, they took to complaining and spreading all sorts of rumors and calumny.

The whining of the courtiers grew into a persistent and loud chorus like a bunch of raucous crows with each passing day. The emperor humored them for a while, till one fine day he decided it was getting out of hand, and decided to show them their place once and for all. After the morning session of court, Akbar called the disgruntled courtiers to join him for a post-lunch stroll in the palace gardens, upon which they were told they would soon be joined by Birbal, and would all be given the same question to answer. The coterie of whiners were allowed the advantage of collectively working on the problem, while Birbal would have to figure it out alone.

Soon enough, Birbal was summoned to join their august company, and upon his arriving, the emperor looked up into the Agra skies to announce the question. The problem was to come up with the exact count of crows in the city of Agra. They had five minutes in all to figure this out, with the warning that random or incorrect answers would invoke harsh consequences.

The bumbling courtiers were flummoxed at this impossible and quite ridiculous test. Five minutes ticked by, while they gazed vacant and clueless into space as if beseeching heavenly assistance. Nothing of that sort transpired, and the emperor gave them first go at their (non)answer, which was a collective shaking of downturned heads at being teased and made fools of.

Akbar then turned to Birbal, who smiling at his rivals, astounded everybody, including the emperor himself, with a supremely confident answer. Pulling a number out of thin air, Birbal’s answer for the number of crows in Agra was the very large, yet very precise count of 116, 523!

The jealous courtiers were even more flabbergasted now. Surely Birbal had not set upon counting the crows to arrive at the number. The emperor, equally taken in by Birbal’s brazen confidence, decided in the interests of transparency and fairness to challenge Birbal to prove himself.

What if, Akbar demanded, the number of crows turned out to be greater than Birbal’s figure? Pat came Birbal’s clever reply, those would be relatives of Agra’s crows from elsewhere in the country come to visit their brethren. And what if the correct count of crows was lower. For which Birbal’s response was it would be on account of some of Agra’s crows having gone out of town visiting their relatives in the countryside!

This elasticity in the unknown number of crows provided the perfect cover for Birbal, whose brilliant mind knew that with any large and unverifiable number, there was always this clever margin for deliberate confusion and error. Adding or subtracting a few hundred, or even thousands of crows would matter for nothing, since there was no way for anybody to trap and count all the crows, of which there were clearly a humongous number to buffer for any and all eventualities. Birbal had beaten the whining coterie fair and square, and the emperor, naturally, was beaming and grinning.

If this feat be true of a hundred thousand, imagine the play with infinitely large numbers. Infinity can be infinitely accomodating, and fun to boot.

All Numbers Great and Small

The mind’s innate tendency and activity is to measure and grapple with everything, and if possible, all of them at once. Cognitive specialists however say we are rather severely limited in this regard. We cannot hold more than a few distinct objects in focus at once. Some say that magic number is 7, which is for most people more than they can handle, however good they are with multi-tasking or multi-focusing. Good luck then with an infinite number of objects!

C. Northcote Parkinson, the grand doyen of British management humor, illustrates this even better in his satirical portrayal of how budget discussions happen in corporate boardrooms. When an important sounding resolution with an atrocious price tag of a million or more pounds is debated, few of the board members dare to raise objections. For by doing so, the suited and booted worthies of the board, none of whom have mentally had occasion to handle anything more than a few thousand pounds in daily life, run the unpalatable risk of sounding stupid and incoherent. We thus have the frequent (and comical, if not for the monies involved) spectacle of million-dollar proposals passed for approval in the blink of an eye, considerations of genuineness or worthiness being given the hindmost.

On the flip end of the budgetary spectrum, similar is the case for proposals of value hundred pounds or less, such figures being beneath the dignity of the eminent members of the board to waste their valuable time and attention on. Nobody wants to be stuck with either the weight of a million pounds, or the nuisance of worthless pennies.

It is the mid-tier proposals of a few thousand pounds that excite the most fervent imagination, provoking all manner of passionate discussion and furious arguments and rebuttals in the boardroom. Every person on the board feels like they have bounden duty to make prevail their senile counsel as regards such sums of money. Each of them has known and can relate to what handling a few thousand pounds feels like on their annual bonus, and the prospects of retail therapy that it can afford for domestic happiness. Pound wise, mega pound foolish, it would seem, is the mantra at work.

Yet, the subjective experience of the same finite number can differ amongst people, and also in different contexts for the same person. A 100 is a big number/quantity to a child just beginning to learn counting, and a 108 can spark several connotations, including religious ones.

For most people, there is no tangible difference between 783 million vs. 784 million, whereas the difference of 1 million between these numbers in and as of itself is something enormous. For most people, the difference between 783 and 784 million is no different from between 783 and 784. All such humongous numbers are equally remote to the mind’s comprehension.

Transcending the Finite

Getting to ‘truly big’ numbers, we enter the domain of mathematical infinity. Things can get a little subjective here. We are bound to straddle into philosophy, for at some point, mathematics inevitably lends itself to philosophy.

If you have a fancy for large numbers, you’ve probably heard of the ‘googol’, which is 1 followed by a hundred 0’s. You then have the Googolplex, which is 1 followed by a googol zeroes.

The Googolplex is a staggeringly huge number. It is however staggeringly small when you consider Graham’s number, or similar such numbers that are defined on the basis of exponential powers. Things get better (as in bigger) if we take Googleplex raised to its own power, and exponentially bigger if we repeat the exercise recursively.

With such mental gymnastics, where does it leave us vis-à-vis infinity? All of this expert maneuvering with mega numbers, and it turns out we are still as distant from infinity as the simplest and most natural of all numbers, the one (and only) 1. Indeed, standing on the shores of infinity, 1 and Googleplex are like next door neighbors.

Thereby arises this beautiful implication to the Sanskrit word ‘Ananta’, meaning ‘that which has no end’, as an attribute of the divine. In the face of the unfathomable vastness of the divine, we might all be immeasurably closer than we think.

At the speed of thought, the numerical chasm between 1 and Googleplex is traversed in the blink of an eye. In thought-free awareness, which sees all of the infinite expanse of number at once, there is no distance to speak of anymore.

Like so, the angels are said to traverse the enormous distances between worlds at light speed, in the blink of an eye. At God speed, all worlds merge in omnipresence.

Invoking the Infinite

The name ‘Ananta’ is the second of three invocations in the daily Vedic ritual of ‘aachamanam’, which involves the sipping of water while reciting each of these invocations to the divine.

‘Venerations to Achyuta’

‘Venerations to Ananta’

‘Venerations to Govinda’

Achyuta, the first of the invoked names, connotes ‘unchangeable’, an appellation that holds most naturally for infinity. For it remains undiminished, whether out of the ocean of infinity you took just a sip, or as the Zen saying goes, drank the Pacific ocean in a single gulp. Sip and gulp both are of equally blissful completeness.

With the third name, one of the meanings of ‘Govinda’ is He who gives pleasure to the senses, the kind of happiness that is inexhaustible, that can only spring from the infinite.

We thus find the notions of infinity mirrored as much in spirituality as in math and science. This is no coincidence, for the worlds of mathematical infinity and Reality both overlap in beautiful no-mind.

The world of infinity has of course plenty more to offer. We’ll explore some of those insights in a sequel blog.

Till then, happy meanderings in whichever bubble of mind you find yourself in. To all bubbles, infinity sends immeasurably fond regards.