While I did not always appreciate mathematics as I do now, my appreciation today transcends the preciseness or richness of its language, elegance of solutions, and the breadth of its logic.

In many ways, it teaches me how I should learn about my self and about the world.

As children, we started with numbers. It seems to have been the way to learn math – three year olds enunciating one, two, three... It is just an abstraction – sounds made in sequence – meaning nothing. But it is an important way to recognize this system.

The concept of zero is also interesting. Humans have known nothingness since the beginning of time. No food. No firewood. No money. But it took generations after we understood numbers that we had a mathematical equivalent of nothing. Zero.

And then came the negative numbers. What would -17 mean to a 6 year old? Well, 20-17 made sense. You had 20 of something and you took 17 away. But what did -17 mean by itself?

Each new set of numbers, each new method forces the child to stretch her or his own understanding of the system – of the reality of mathematics. Consider, for example, the square root of -3. Imaginary numbers. It does not make sense at all. How can a negative number have a square root?

It is antithetical to everything we have learnt so far. Such a number does not exist. Let us just ignore it, have it thrown out of our lives. Which moron thought of such an idea? Let us hang her (or him?). Let us pass a dictat that such things will not be spoken and get on with our lives.

But alas, within our world of grades, of curriculum, of exams, this possibility does not exist. So we are forced to recognize it, deal with it, know its properties, even if we do not completely understand it.

So we know that -1 = ixi. And 2ix2i = -4. And -3i+5i=2i. And we go through the grade learning its properties, its rules and solving such problems. But most of us are hard pressed to explain what the hell it is.

It is only later, beginning to work on waves, and the phase of a wave, that all of this begins to fall in place. The question of how would we have understood or described such a large variety of processes without such a tool does not often confront us – we are now quite comfortable with imaginary numbers. Perhaps we would have constructed another tool – as abstract, and as complex. For the solutions have to be as complex as the problem it self.

I remember algebra and my utter confusion. Math with alphabets!!! And I remember an older cousin telling me to think of the variables as mere place holders for numbers till you figure out what the number might be. And that set me going. From place holder to a representative of a kind or a set of numbers, my understanding evolved.

And I could solve the equations. 4y+3=7. Hence y=1. And so on.

But then we came across this weird beast. Quadratic equations. Y^2-4=0. Then Y=2 and also, Y=-2. Wait. Hold on. How could Y be both 2 and -2. That did not make sense. It could either be 2 or -2. One of them had to be annihilated. Destroyed. Only then would this make sense. It is possible, right? Y=2 satisfies the equation. So let us just go with that. Or with -2. But just choose one.

But that was not possible. Annihilation of a number. And it forced us to change our ideas of solutions. There could be multiple solutions to a problem. Different positive numbers. Or numbers with different signs. Or they could be real AND imaginary numbers. Or they need not have been numbers at all – they could be an entire vector or a matrix. And in recognizing each of these solutions, and understanding what they meant, we evolved. Our thought process evolved. And the complexity of problems we could understand and address evolved.

But none of this could have happened if we had ignored a solution – a possibility – that seemed quite weird. And I have to thank my teachers for that – many whose names I have even forgotten. For ensuring that we acknowledged these weird possibilities, recognized, and understood them and then evolved with them.

I see a parallel of this process in our own lives. We constantly have to deal with the other – whether it be vis-à-vis gender, age, religion, economic class, caste, sexuality, or any other definition we care to create. Recently, a friend told me about his daughter coming home and saying “Baba, you are not my friend. My friends are girls. You are a boy.”

As a child, we had to deal with children of the other sex – how were they similar, how were they different. And in the process of acknowledging and recognizing this, we evolve intellectually. How we understand the other affects how our understanding evolves and how we interact with them.

Just as with math, our initial understanding of the other is through a reflection of ourselves. Thus, an imaginary number is a number with ‘i’ following it. And besides having a couple of different properties it behaves quite like regular numbers. At least that is how we begin to understand it. It is only when we understand and accept it in its similarity and differences with regular numbers that the complexity of our understanding evolves.

So also in our lives. How men treat women, or how women treat men depends on our understanding of the other. If we men see women as an inferior human, we treat them thus. However, our own evolution is stymied. It is only in understanding women – with their similarities and differences – that we men can have a richer understanding of our own lives, evolve, and address the complexity of the problems that face us. The same is true for women. Else, we throw away -2 from the solutions of the quadratic equation and hope it is OK.

Our world is a complex world with a variety of realities. The reality of a Hindu minority in a Mulsim country is different from that of a Muslim majority or that of a Muslim minority in a Hindu country or a Christian minority in a Hindu country. The reality changes from country to country. It changes based on gender and class within the community.

Our world view begins with ourselves and our surroundings. It defines who we are, what the world means to us and how we interact with the world. That is our reality. As we are confronted with realities of others, they force us to re-evaluate our worldview. They force us to rethink who we are and what the world means to us. This is uncomfortable. Much more uncomfortable than confronting imaginary numbers.

We can choose to ignore these realities. By saying they are not true realities. That they are perceptions of a lazy people. Or a stupid people. Or a dirty people. Or an evil people, angry people, inhuman people, barbarian people.

Or we can choose to annihilate them and every possibility of them that we can foresee. We do these through lobbying and enacting policies that marginalize other people, massacring them or finding ways to throw them out of our lives. And then we can carry on with our comfortable lives.

The Upanishads say that the fault of the contradiction is not in the components but in the observer. Shankara wrote: seeing things as separate is the sole cause of otherness. Solutions that include both 2 and -2 are not a contradiction. They seem like one to someone who does not understand. In fact, their presence forces us to evolve, our understanding to become more nuanced. Thus, Mahavir says that contradictions are possible – his philosophy of Anekantavada is based on this.

So also, with us. We can also choose to welcome other realities, growing and evolving by recognizing their validity, understanding them. The reality of tribal communities, is very different from our own. We can start by recognizing them, and accepting that their reality which is quite different from our development-oriented one is a valid reality. And in recognizing that and understanding it, we ourselves evolve.

We understand our selves better, we understand the world around us better and we understands our actions better. Our ethics is better defined, our values are better nuanced, and hence we evolve.

The reality of other religious groups, of other sects, of other classes, races, ages, genders are different from our own. Our world, our civilization, our people grow and evolve with a process that includes and understands other realities, other solutions, the other. As people, we have a choice – a choice of annihilation and of regression. Or a choice of learning, of maturity and of growth. As mathematics suggest. As do numerous thinkers and leaders.

For the growth our world is dependent on such intellectual, social and spiritual growth. It is only with such growth that we can do better things, live better, be better.

What will we choose?

- Sanat Mohanty

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