Our Approach 🎨
We want to build a history of mathematical activities by looking at them as forms of practice. We bring together tools, texts, local knowledge (lores), and records from different kinds of occupations to tell stories that help us see how mathematical practices happen in real life and how they shape society. We also want to move beyond only using famous or canonical texts to understand the history of knowledge. Instead, alongside texts we also look at the social memory of practices and practitioners, as well as objects such as account ledgers, sculptures, and other things made by practitioners.
Surviving records of a practice, whether they be texts or tools, will typically be in the everyday language context of the practitioners. Texts and tools which were in circulation in "vernacular" are major sources for our learnings. Various Indian (broad) language traditions have extensive records and artefacts which speak to everyday practices of different professionals and their pedagogic contexts. However, these are rarely historically scrutinised or even catalogued.
Through various collaborative efforts, this archive tries to bring such materials together for the interested public, whether professional academics or others, to explore, ask questions, and reconstruct narratives of mathematical practices as well as the various relationalities between practices and the general public. We feel this is particularly important in the subcontinent, where occupational practices became one of the axes around which the graded hierarchy of caste was organised and vice versa; where there was a separation of mental and manual labour. Our archive is also an attempt to demonstrate how knowledge and practice are mutually constituted.
That said, archival records such as palm leaf manuscripts, texts, inscriptions, tools, and instruments, removed from their sites of practice, are only fragments of the past. By contextualising these records, through social histories, ethnographies, conversations with practitioners or their descendants, reflections on the public subjected to these practices, and by enlivening them through practical reproduction, we begin to understand the social and political worlds which constituted such practices and in turn how such practices shaped the social and political.
Our learnings suggest that interrogating the relations between texts, practitioners as social actors, and practices, can help understand computational practices in their everyday socio-political contexts [See Babu, 2022]. Texts (like Kanakkatikaram) embody such relationalities. Our inquiries strive to go beyond texts and reconstruct the history of mathematical practices as embedded in various occupational practices and social memories surrounding the figure of the practitioner. Texts, then, need to be understood in relation to both practice and practitioner. More importantly, this approach enables us to engage with practices that do not have texts, such as village blacksmithing.
There are several manual-like texts for certain crafts such as sculpture, both in regional languages (e.g. ciṟpa cennūl) and in Sanskrit (e.g. Māyamata). At any given time, very few individuals could likely situate and understand the content of these texts. Instead, the fact that forms of these crafts and arts have continued to thrive points to the centrality of learning and knowledge transmission at work. Traditional stone and wood sculptors in South India, the bronze sculptors of Swamimalai in Thanjavur, artisanal groups like carpenters and blacksmiths continue to operate and transmit specialized knowledge through work. [Page 25, Babu, 2022]
The figure of the practitioner as embedded in social memory tells us what the actions of the practitioner meant for the public and how these actions were understood, remembered, and transmitted across generations. It also reveals the ways in which practitioners were perceived within the social order, including the expectations, responsibilities, and consequences attached to their work.
“It is very common among the Tamil speaking public to identify the computational act, or the mathematical mind, as a manipulative one: a cunning mind that constantly schemes, plots and destroys. Central to this perception is also the dislike the Kaṇakkaṉ incited by his role in the aid of his master, the administration or the rich landlord, the Zamindar, a common theme carried in popular culture. Consider the rather harsh usage that Sivasubramanian records from the people: ‘Kaṇakkaṉ cettāl piṇam, Kaṇakkaṉ āttāl cettāl maṇam’ which means that if the Kaṇakkaṉ dies, it is just a matter of a corpse, but if his mother dies, then it is an occasion.” (Page 90, Babu, 2022)
The relation between the place of learning, place of work, and the consequences of the work/practice for people is another axis of our focus. As mentioned above, in some cases the place of work and place of learning are indistinguishable, whereas in others there are designated places of learning that provide practitioners with initial training before they move on to the workplace, where learning also continues.
The work serves specific social functions, especially in a caste-based society, thus having consequences for the public. Scrutinising texts, practices, and practitioners thus becomes a way to understand the relation between place of learning, place of work, and the consequences of the practice for the general public.
How the mathematics learned at the tinnai schools enters the lives of the village public through the functions of the village accountant is something well documented by Dr. Senthil Babu. The ways in which value, measurement, and calculation are related. That is, how a measure produced through the physical act of measuring is transformed into an abstract value through computation, is another prominent theme we are exploring in our historical studies.
The Tamiḻ and Malayalam word, kaṇakku, which simultaneously means calculation, accounting, mathematics, or, in a compound, calculator/accountant/mathematician, possibly best captures the conceptual shift we aspire to have.