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.