Some of the most profound philosophies change the way we see the world or rather count it. They can shed light on something as fundamental as elementary school concepts. They inspire us to contest these ‘given’ facts under a logical framework, question them and understand them better. This is the basis of any scientific approach.
A lot of my friends, even now, question the purpose of learning algebra and geometry in high school. They quickly come to the conclusion that learning advanced mathematics is irrelevant and find the topics purposeless. Many of them detest it; they grow fundamentally weak in those subjects and hence can’t see through the concept beyond their immediate application. But if you ask an architect, he/she will be able to tell you the applications of trigonometry in building plans, a computer programmer will appreciate the usefulness of Fourier transformations and believe it or not most of the compression algorithms (that let you video call and play online games) use very nuanced mathematical models.
As the title suggests, this article talks about our understanding of numbers and set theory in general. As trivial as it might sound, this theory forms the basis of our understanding of the everyday world and is hence worth introspecting. In their simplicity, lies the idea of inclusion which if expanded to a social construct can lead to a more open and free thinking process. This idea is something which each one of us should question, especially in the current Indian scenario where political parties try to promote jingoism by targeting a common enemy or ‘the other’. In that way, it liberates our mind off the prejudices and stereotypes we harbour and helps fosters dialogue among very sects of the society. A thought-provoking short film on these lines is Chris Marker’s French animated documentary THÉORIE DES ENSEMBLES (1991).
Contemporary French philosopher Alain Badiou treats mathematics as the language of truth; which encourages us to question the nature of prime numbers, of arithmetic operations and what does it mean to apply them or the meaning of the omnipresent statement - ‘let x be the number of …..’. I am talking about Badiou when he says that ‘One is not a number but a function.’ What does he mean by this? As baffling as this argument might sound, its logical explanation is quite thought-provoking. It goes like this —
When we explain to a child what does 1 mean, we usually give examples like ‘a finger’ or ‘an apple’. On the basis of this notion, the child begins to progress down the number line: two becomes ‘a finger with another one’ or ‘an apple with another apple in a basket’. Things start getting messy once amorphous objects come into play. Because there is no such thing as ‘one sand’ or ‘one milk’. The idea of one has the sense of boundary or limit embedded in it. Hence we use terms like ‘a handful of sand’ or ‘a litre of milk'. These ‘volumes’ become the benchmark to indicate larger or smaller quantities of these object. A 1000th part of one litre becomes one millilitre (milli means 1/1000th) and so on. Similarly, physicists use the word quantum to describe the smallest possible discrete unit of any physical property, such as energy or matter.
But my contention is interested in investigating this idea at a macro level. We often define or describe our world in categories. One world, a nation, our community, my group. We try to give these amorphous terms a demarcation that reduces the scope of their meaning and subsequently our thinking about them. When we decide to include some in a set and leave others, we define its identity. If these identities are concrete, they give birth to conformity and consequently rigid standards of living. Just like a handful of sand or ‘a’ bite of an apple are no strict forms, so should our idea of nation, community and world be. This not just includes the synergy between fellow human beings, but also between humans and other species of the planet. Only when we consider them a part of our world (here I jab at the human-centric approach to design), can we truly empathise with each other and make this world liveable for everyone. That is the true essence of democracy: it is a clash of two ideas, not two identities.
Finally, I want to leave you with John Lennon’s Imagine which echo the idea of true oneness and inclusion.
