The Infinite is "in a sense both is and is not."

I flung open the window and observed the conflict between the two boys from the adjacent apartments, which was nothing new. Their history, which I learned from my mother, reveals that their dads were rivals for a long time, and that their fathers were also rivals as well. Undoubtedly, their children may be rivals one day, I suppose so, and this will continue forever…

I was wondering over the word, “forever… and rephrased it “infinite”. And I remember, I once attempted to explain infinity to some first-year pupils. I told them the following story: "I was about to eat a slice of cake when a friend stepped in, so I offered her half out of courtesy. Before I could eat my half, another friend came by, so I split it again. This happened again and again—gradually, my snack kept getting smaller. How much cake would I have at the end of this?" "None!" many of the students yelled. I wrote a sum on the board: ½ + ¼ + . . . We agreed that, eventually, if you kept writing numbers forever, they had to add up to one. I was pretty sure that their murmurs no longer dreamed of cake. I invite them to shift their focus on “infinite.”

One of them ask the interesting question— “in this way we can never cross the road” by going half the distance, then half the distance, with half remaining, the next step is half of one-half, or a quarter. Although each step brings one closer, one never actually reaches the other side of the road, even after taking an infinite number of steps. If matter were to be infinitely divisible, then each object would in principle contain a potentially infinite collection of particles necessarily. 

Another student got up and narrate the most famous Zeno's paradox of the tortoise and Achilles where Achilles never overtakes the tortoise, since however many steps he completes, the tortoise remains ahead of him, involving infinity. I was amused to listen and was pondering over the issue. Yes, quantum mechanics rules out, or at least poses a formidable barrier to, notions of endless divisibility. I was bewildered.  

As a greenhorn, I had the kind of epiphany to explore the wonder of infinity that took me to "A Trip to Infinity" –-a movie full of puzzles and paradoxes, that helps one to attune to the vastness of the universe and grasp what it would mean for something to go on forever, and ever, and ever…

Who hasn't gazed up at the stars in the dead of night and wondered if space is an infinite void? Mathematics has long mystified infinity. The word apeiron, which had meanings of being limitless, vague, undefined, and formless, was used by the ancient Greeks to denote infinity. Aristotle's "potential infinity," an outlier from the overall trend of the time, was a reflection on infinity, which was far from inspiring a "horror of the infinite" in the Greeks.

In this animated film, the world's most cutting-edge scientists and mathematicians go in search of the mind-bending implications of the infinite. In images and interviews, the film contemplates whether there are physical manifestations of infinity. It has moments of math-magic, which include a concept of "The Infinite Hotel," based on a thought experiment by a German mathematician David Hilbert, which has infinitely many rooms. Indeed, despite the fact that the hotel is already full of guests, a new guest who turns up at reception is readily accommodated. Some have thought that his argument goes against the possibility of physically realized infinities. Perhaps there can be infinitely many stars even though there cannot be a hotel with infinitely many rooms. Even if there could be a hotel with infinitely many rooms, it is clearly absurd to suppose that there could be an infinite hotel in which guests come and go infinitely. Perhaps the event described in the story was told at a very high level of abstraction. 

It is because of the tension between our finite lives and the seemingly unbounded range of our imagination that we are so intrigued by the infinite. Young people can think that life will last forever, it is full of infinite possibilities; older people, realizing that it will not, look for a veneer of immortality in their legacies. The paradox is that even a finite universe's inhabitants can believe it to be endless.

 

In the past, it was widely believed that a literary work, like a novel had only one true meaning. But the idea was abandoned with the rise of hermeneutics in the humanities. Today, practically every literary critique agrees that a novel has as many interpretations as there are readers. Given the history of literature and its relation to the social contexts in which it is produced and received, the concept must not be ruled out.  Do we not often say that any language allows for an infinite number of possible sentences with limited stocks of alphabets? Did not every viewer understand "Monalisa" in a different way, and interpretations are still being sought after today? The painting appears in books, chocolate, advertising posters, and countless other products.

Thus, the engagement with infinity traverses the history of cosmology, astronomy, physics, theology, and the social sciences in almost every age and time. Mathematical infinities occur as an endless sequence of counting numbers: 1, 2, 3... Spatial and temporal concepts of infinity occur in physics when one asks if there are infinitely many stars or if the universe will last forever. Kant gives ‘proofs’ of antinomies regarding the extent and divisibility of space and time.

His ‘thesis’ says that:

“The world has a beginning in time”; and “The world has a finite extension”.

His ‘antithesis’ says:

“The world has no beginning in time”; and “The world has infinite extension”.

In a metaphysical discussion of God or the Absolute, there are questions about whether an ultimate entity must be infinite! 

In a social context, one can imagine how our court cases are lengthened to the vanishing point of a painter’s view. Millions of cases are pending in the courtroom; arguments are going on from both sides. Dates are given months after months, and a verdict is pronounced when arguments are exhausted in Archimedes’ way of solving the ‘justification by exhaustion’. One, who has a bit of an idea of Indian logic, knows the word "anvastha," which does not explain the causal relationship but instead carries on to an endless series, which is a fallacious way of arguing. Aristotle’s rejection of "actual" infinity may be for this reason only, as distinguished from "potential" infinity.

Under the "infinite future" view, space may continue much as it is now, with the galaxies drifting farther and farther apart. Alternatively, in the "finite future" view, a cosmic catastrophe at some definite time in the future may destroy the universe: a parallel sheet of space will collide with our universe, annihilating everything. In any of the catastrophic, finite future scenarios, speculation exists that the end of the universe may be followed by the birth of a new universe, in which case the future may in some sense be infinite after all. 

Italian astronomer Bruno proposed an unbounded universe in his book On the Infinite Universe and Worlds: "Innumerable suns exist; innumerable earths revolve around these suns in a manner similar to the way the seven planets revolve around our sun. Living beings inhabit these worlds," which defends multiverse hypothesis of the cosmos. One can relish the metaphor given by Leibnitz that there are infinitely many possible worlds and God has actualized our "this very universe" which after all is the "best possible world."

Perspective artwork uses the concept of vanishing points, roughly corresponding to mathematical points at infinity, located at an infinite distance from the observer. This allows artists to create paintings that realistically render space, distances, and forms.  Variations of chess played on an unbounded board are called infinite chess.

The two-envelope-paradox is such a problem. A person is given two indistinguishable envelopes, each of which contains a sum of money. One envelope contains twice as much as the other. The person may pick one envelope at random, but before he opens it he is given the chance to take the other envelope instead. The famous mystification is evoked by confusing the situation. The person is presented with the paradox of changing his decision infinitely.

Thus, friends! Our politicians find some solace in the idea that there isn't enough room in a finite area to adequately tackle an infinite number of difficulties. The tempting dance and taunting arguments will continue to lure one into a number zero. One can have numbers like 0.0000000001, for instance, which is endlessly perplexing. Incidentally, it takes us to the point that the foundation of mathematics itself is unstable when one removes the plaster to uncover the structure underneath and discovers that important load-bearing beams are lacking in the lower levels. The surprising thing, though, is that even a finite cosmos can appear endless to its inhabitants. 

Look, my friends!  In two opposing mirrors, in constant light reflection, one finds infinite images reflecting inside. However, is it not true that when tea becomes a daily ritual, it occupies a central stage in our life style?

 

So my friend! Go and have a good sleep and if an insomniac, a simple act of counting imaginary sheep would be a portal into the world of wonder. It will never run out of natural numbers to do the job: 

"Numbers are like the bright stars in the sky at night, while real numbers are darkness"