The Mathematics and Culture workshop held at Ninasam over the last weekend of March was essentially an exercise at breaking down binaries. Recurrent themes that cropped up during the workshop were the tensions between mathematics and language, mathematics and storytelling, abstraction and empiricism, institutions and individuals, sciences and the arts, singular reality and multiple descriptions. Over the course of two days, each of these binaries was taken down, examined and dismantled. Mathematics and storytelling were found to have eerily common footing: they both dealt in fictionalisations. The debate between abstraction and empiricism collapsed into questions about whether the solution to an elitist abstraction is a return to empiricism, or a better abstraction. Mathematics was no longer a universal acultural entity, it was embroiled in debates on caste, access and institutions. And the question we returned back to again and again: What does mathematics mean to non-mathematicians?
Prof. Sundar Sarukkai
The Mathematics and Culture workshop took place at Ninasam, Heggodu, over the last weekend of March. The workshop began with Professor Sundar Sarrukkai outlining the key themes of the workshop and drawing out the complex relationship between mathematics and culture. Asim Siddiqui reviewed statistics both from India and abroad trying to unravel the mystery of ‘the missing girls’: why is it that there are fewer women mathematicians across the world than male mathematicians? Gopal Guru explored how caste is manifested in the practise and learning of mathematics. The session also dealt with the relationship between abstraction, empiricism and power. This was followed by a talk by Anupama who runs Brainstars, an organisation that is working towards making mathematics education more fun and interactive for children, for higher retention of knowledge, and decreased learning times. In afternoon session Vidvan Anooru Ananthakrishna Sharma, the renowned mirudhangam player, demonstrate the role of mathematics in rhythm in music. This was followed by ‘Mathematics and Storytelling’ by Dr Gayathri Prabhu, who narrated seven short stories that revolved around the themes of numbers, mathematics, and learning mathematics. The discussion lead to questions of the role of storytelling within science, and how fiction in the arts differs from fiction in science. This relationship between the arts and the sciences was continued in the next session, which was the screening of Chandralekha’s Lilavathi, with the dancer’s performative responses to mathematical problems. The day’s events concluded with a dramatised version of Harischandra Kavya adapted to the stage by the students of Ninasam.
Vidvan Anooru Ananthakrishna Sharma
Day 2 of the Mathematics and Culture workshop began with the presentations of two mathematicians from IISC. While B.J. Venkatachala’s presentation dealt with the role mathematics played in architecture, C.R. Pranesachar explored topics of mathematics through anagrams, puzzles and riddles. Dr Meera Baindur explored the twin topics of mathematics in the Vedic Age, and the role of mathematics in Sanskrit poetry. An interesting dichotomy cropped up, when it was found that most of Sanskrit mathematics was done through poetry. The penultimate session of the day was by Dr Nikhil Govind who enlarged the discussion to the educational and institutional challenges facing mathematics and other non-utilitarian disciplines today in India Professor Sundar Sarrukkai concluded the workshop by summing up its key points.
Mathematics as a language of truth:
One of the key themes that cropped up time and again at the Mathematics and Culture workshop at Ninasam was the question of whether mathematics is a human-made language used to describe reality, or whether it is a ‘higher’ order already present in nature. What is it about facts, measurements and abstractions that make us think that they are in some ways more valid descriptions of reality than, for instance, a poetic or story-based conception of reality? We assume the construction of mathematics to be universal, rational, and atemporal. These beliefs largely come from the fact that mathematical systems are largely seen as self-sustaining systems. That is, the ‘truth’ that 1+1=2: it will be true hundred years from now, as it was a thousand years ago.
Another stance to take, arguably dangerous, is that of mathematics as the representation of an ordering within nature. According to this view, mathematics has always existed in the world, and mathematicians are only ‘revealing’ this order. This construction of mathematics states that it is not only the best construction of reality, but that it is reality itself. This sets up mathematics as a ‘tyrant’ discipline, claiming singular and exclusive access to reality. By extension, if any other discipline has to adequately express reality, then it has to do so through mathematics.
However, one cannot entirely dismiss mathematics’ claim to truth. If I claim to be 5 feet 4 inches tall, this mathematical truth is going to remain constant no matter who measures my height or where. However, if I claim to be an honest person, or chose to add any other description to myself, its ‘truth’ is one that can be contested. Therefore, the ‘truth’ of mathematics appears to be ‘obvious’ whereas the truth of other language systems are not. But before jumping into the slug fight on either side, it is important to remember that mathematics and language are not as opposed as they would seem. The language of symbols found in mathematics needs the support of verbal language (‘verbal’ here being used loosely) and cannot stand alone. Similarly, one cannot draw a complete distinction between mathematics and other languages: where does one put words such as ‘meter’ or ‘feet’? Are they words in English or mathematics? Are they really two separate entities?
Through conversations over coffee (and chai, kashaya, lime and fruit juices), and debates during the sessions, philosophers, linguists, literary students, performers, theatre practitioners and mathematicians tried to beat out the complicated relationship of mathematics and language. Though no definite answer was found, several interesting questions were raised.
Mathematics as natural or cultural:
Is mathematics a representation of a natural order present within reality, or is it a cultural entity, created by humans, with a historicity of its own? Several mathematicians over the centuries have claimed that mathematics is present in nature, and that they have only ‘revealed’ what has always existed. Such a claim should be presented with certain precautions. The workshop, as is clear by its name, aimed to locate mathematics within culture and study its relationship with society.
One of the first points that turned up during discussions on Saturday was that there is no one mathematics that is practised across the world. There are several approaches to mathematics, with different methodologies, different notations, different assumptions, and different accompanying philosophies. One only has to compare our contemporary mathematical system with that of the ancient Chinese, Sanskrit or the Kerala mathematicians to understand that mathematics is very much rooted in culture and is not an independent entity. The mathematics we are familiar with now is one approach to quantifying reality, among several.
Theatrical representation of the Ninasam students
This idea of mathematics as an independent entity also comes from the belief that it is entirely abstract and rational. One of the themes addressed during the workshop was the existence of an ‘embodied mathematics.’ Our primary units of measurement still come from the body. Children learn to count on their fingers; we still measure heights and distances in feet. If our bodies were constructed differently, our systems of mathematics would probably be different as well.
The mathematics we practise is closely tied to what we perceive as being an external reality, and our perception is bound to our bodies and our culture. Just as it is impossible to rule out the role of the subject in the observation of reality, it is impossible to rule out culture in the historic construction of mathematics.
Mathematics as an institution:
As it became clear, mathematics exists in human culture. But how does it interact with, and within, a particular culture?
Prof. Gopal Guru
Mathematics, according to Professor Gopal Guru, is an academic playground for the elite. As a subject of abstraction, the study of mathematics requires economic backing, leisure hours and institutional access, luxuries that dalits does not have access to. Additionally, abstract mathematics exerts hegemonical control over local knowledge systems which are silenced in its presence. Instead, it is important to reclaim these local knowledge systems and alternate approaches to mathematics. There is also a possibility for empirical mathematics, more independent of abstractions, which is essentially the realm of the elite. However, one could argue that the solution to combating an existing elitist system is not to deny it, but rather to create a new and better system to replace it.
Another mystery which entered the workshop was the question of the ‘missing girls in mathematics’. It has been found that boys and girls do equally well in mathematics up till a certain age, after which women steadily drop out of mathematical studies. Various reasons for this have been suggested, including the presence of a ‘mathematical gene’ found only in boys or causes arising from the environment or that particular culture. Research has proved that countries which have better standards of gender equality are also likely to produce more women maths scholars. Mathematical ‘genius’ is not as innate as some people would like to believe, rather it arises from a complex set of cultural causes. It is important to acknowledge, however, that statistics of mathematical literacy can often be misleading. As seen in the debate about mathematics and caste, it is possible for people to have different approaches and understanding of mathematics that may not be captured in mainstream statistical surveys.
Dr. Nikhil Govind
The question about women mathematicians in institutions brings us to the question of where mathematics stands within institutions in India. Dr Nikhil Govind’s talk focused on mathematics as a field of research in India. Why is it that India, which has such a rich heritage in mathematics, has not produced any eminent mathematicians in the last five decades? Perhaps the problem lies in the complicated relationship between the country’s state and state-funded institutions. Decentralizing power and giving institutions an increased autonomy may be the answer. Additionally, the lack of differentiation between teaching institutions and research institutions already leads to further strains on academic research.
Mathematics as a cultural institution in India is one that is riddled with problems. Beyond the basic problems of access to dalits and women, the institution is also found to be suffering because of a lack of a vibrant research culture. Like the missing women, here is another mystery of mathematics in India: Where have the PhDs in mathematics gone?
Mathematics and storytelling:
Mathematicians would vehemently deny that mathematics is about storytelling. But this is the point that Professor Sundar Sarrukkai returns to, repeatedly: fiction and mathematics have far more in common than we think. At the most basic level, we build stories to help children understand complex abstract concepts through everyday analogies. We personify different forces, sometimes even give them personalities, and make them interact with each other. Think, for instance, of physical or biological processes represented as characters. As the child grows older and is better able to understand abstract concepts, she would be able to bypass the ‘medium’ of story and access the concept directly. But would this mean that after a certain point we outgrow these stories, and can deal only in concepts?
Dr. Gayathri Prabhu
Science regularly creates ideal systems which exist outside of reality, and are nothing more than fictionalisations. Theses fictionalisations enable the scientists to eliminate external factors and deal with a specific aspect of study. However, at the root, the ideal system remains a story that scientists have to tell themselves before they can reach a higher truth. Similarly, several scientific experiments, at the sub-atomic level, are explained as a series of actions involving objects, though scientists know that particles and objects behave very differently. However, the cloak of a narrative is needed for the scientist to make her point clearer. How then can one differentiate the truth in science and in literature, and claim that one is more important than the other, considering they both access it through a similar methodology? Though a scientific truth may be more empirically verifiable than the truth expressed through literature or the arts, one cannot dismiss the latter on the same basis. It may be different truth, and it may be a more complex one, but its nature remains that of truth.
Prof. Gopal Guru, Asim Siddiqui and Prof. Sundar Sarukkai
Needless to say, the workshop was much more than the sum of its sessions. Discussions spilled over into chai and coffee conversations, over meals, into morning walks and late night starlit circles. Most of the conversations revolved around the questions outlined above, as participants tiptoed around these topics, carefully chiselling away from different corners. The environment itself was a charged one, as philosophers, literary studies students and professors, theatre practitioners and performers shared ideas. The conversation never quite stopped in many ways, and continued… and continue in the form of questions that still persist in our minds.
Prepared by Chitralekha Manohar