Infinity(∞)

“Bigger than the biggest thing ever and even bigger than that.” This was Douglas Adams’ description of that mind-bending, awe-inspiring and even frightening concept that is known as infinity. At some point or other we have all fixated upon what the largest number is, the furthest distance we can travel or whether the universe goes on forever. The earliest Hindu thinkers decided in around 4th century BC that infinity was that which could not be measured arithmetically. This quality therefore was equated with the concept of a timeless, space less God. Throughout history, infinity has troubled philosophers no end - especially the Greeks. The Atomists of Greece believed that space could be separated into individual points, a view that was challenged by Zeno, who in a series of famous paradoxes illustrated that in fact, finite things are made of infinite quantities of smaller things. Since then, thinkers assorted- mathematicians, philosophers even psychologists have pondered on this ultimate ineffable.

In mathematics, which one mathematician views as the science of infinity, various attempts have been made to bridge the gap between the infinite and finitude-to complete the incomplete, to catch it and tame it. Cantor, the father of the modern concept of the infinite, through a series of logical paradoxes developed set theory according to which everything is based on finite sets and showed that infinite sets are not bigger finite sets, that the two types of sets were substantially different. He went on to show that there are different kinds of infinity- of different sizes, a non-intuitive concept of magnificent proportions.

Astronomers continue to ponder on the infinitude of space. A world without end is something we humans have tried to rationalize since we studied the movement of the spheres. Yet despite our best available evidence which suggests that the universe is infinite, this is based on a finite observable part of the universe. Therefore perhaps, the question of the infinitude of space shall always remain unknown.

The human mind has struggled to grapple with the concept of infinity. Simone de Beauvoir, the French writer said, “I am incapable of conceiving infinity and yet I do not accept infinity.” Our very language seems firmly rooted in the finiteness of things. We have starting points and ending points (determined by us). We count, and then we stop (our decision, imposed on an infinite universe). We put one thing inside another (and the container is contained by the atmosphere, which is contained by Earth which is contained by the Galaxy and so on, ad infinitum). In all these cases, we arbitrarily define both the parameters of the system and the rules of inclusion or exclusion. Yet, we fail to see that WE are the source of the finiteness around us. The evolutionary pressures to survive seem to have produced in us this blessed blindness. No decision can be based on an infinite amount of data. No commerce can take place where numbers are always infinite. We had to limit our view and our world drastically, only so that we will be able to expand it later, gradually and with limited, finite, risk.


Yet the ability “to see the world in a grain of sand, and to see heaven in a wild flower, hold infinity in the palm of your hands, and eternity in an hour” as William Blake did, is in a sense, liberating. An American organization, called the Society for Dissemination of the Concept of Infinity has traveled throughout America posting up billboards with the words “Have you thought about Infinity today?” They seem to believe that if human beings accept the concept of a boundless universe the daily concerns that bedevil us begin to seem trivial in comparison. Yet often the very opposite is achieved. Martin Buber, an Israeli philosopher described how trying to grapple with the concept of infinity often made him suicidal with fear. The Greeks coined the term aperiophobia, to describe the fear of infinity that gripped those who pondered on it.

Yet can infinity actually exist? Using my unique opportunity to play the layman’s card, I’d hazard the thought that along with romantic love, dark matter and the existence of hidden dimensions, the idea of infinity may be one of those concepts whose causal connections lie beyond the grasp of current science. The Harvard mathematician Robert Kaplan thinks it is a purely theoretical construct existent “only within the fertile imagination of the mathematician,” and that, as Aristotle believed, only potential infinities can exist. In other words, we don’t know whether infinity can or cannot exist.

What we do know for sure however, is that the idea of infinity will continue to frighten and liberate humankind in one way or another….forever and ever.