 Welcome everyone. Welcome and good morning everyone. I am Shweta Naik from the First Institution HPCSE Mobile. I work in Mathematics Education and Mathematics Education Research. We are here today for the preliminary talk in Epistemi 9. So welcome everyone. Welcome Dr. Babu and your team at French Institute. So Dr. Babu is going to speak on mathematical experience and alienation towards social histories of practice. He needs no introduction. Actually, he's very popular in several circles. But nonetheless, it's my pleasure to introduce him. He's a dear colleague. Dr. Santil Babu is a historian of mathematics based at the French Institute of Pondicherry in South India. He's involved in studies concerning nature, knowledge and labour. He's coordinating a research program in the social history of vernacular mathematical practices in medieval South India in collaboration with chair, history and philosophy of mathematics at EPS Zurich. His book, Mathematics and Society, Numbers and Measures in Early Modern South India will be soon published by Oxford University in 2022. So look for it. He's a member of the editorial board of the series, Verum Faktum, Studies in Political Epistemology. And he's also a member of the Politically Mathematics Collective in India. So most collaborations that he is in, he has given the website address. So you can find those in the proceedings that he has given his abstract. He has also motivated many of us to question hegemonies in our work, question our work. So I am very thankful to the work that Dr. Santil Babu does. So I'll stop here without much delay and handing over to Dr. Babu. To the participants, you can type in your questions any time that they occur to you or you can wait till end and type them or write them in the chat box. So Dr. Babu, over to you. Thank you Shradha. Good morning everyone. Thank you. So at the outset I wanted to say that this is really a collective presentation with all my friends and colleagues. Some of us sitting in the room, some of us hopefully listening in. And it's been part of the initiatives taken by the Politically Mathematics Collective, which is a group of some of us individuals and collectors who have been trying to subject contemporary mathematical practices to public scrutiny and not let it out of the framework of analysis and to see how it actively or renders oppression and exploitation possible in the neoliberal expert framework. And that's what has brought us together. The collective involves a lot of people involved in mathematics education, very few historians of course, and a lot of working mathematicians. And so we've been meeting regularly. We have discussions and then identify public issues and then try and create pedagogic resources, especially addressing not so much the formal classroom in school and college, although not out of it, but also to kind of create new organized spaces of knowledge sharing with the working people directly. That's been our objective and hopefully we'll keep doing it. And thank you all for joining and listening. And this talk and presentation was actually put together over the last couple of years with a lot of people involved in doing the fieldwork, in organizing the thought process. And therefore, I just wanted to acknowledge everyone's contribution to this and I'm presenting on everyone's behalf. Hopefully I'll give justice to what everyone has contributed to the process. So since it is largely a community of mathematics and science education thing, and to the limited knowledge that I have about mathematics education as a practice, mostly history of mathematics is used as an adjunct to clarify aspects of mathematics teaching. But we have been some of us at least have been wondering can history of mathematics be much more actively deployed to reframe some of the controls of mathematics education teaching, not entirely confined to the formal classroom, but also outside institutional learning. So and why history of mathematics therefore becomes important to open up new questions in mathematics education. It also means that we need to subject the history of mathematics as a practice and to reframe its own priorities and objectives to include a different idea of mathematics as work and as practice. And particularly in the Indian context, what inspired us was that mathematics is often written as a series of activities of the mind and these become the hegemonic histories of mathematics. The typical lineage is starting from 3rd century B.C. Aryabhata and end up with Srinivasa Raman in the 21st century dotted with Bhastra and Brahma Gupta and the Kerala school and so on. So what we want to do is to rewrite the histories of mathematics as mathematical practices, as working occupations of what real people do as part of their routine hard work, as part of their routine jobs. And in a caste society, because occupations are caste-based and it involves physical segregation, the work of mathematics then served a political function. And in each of these occupations, there are different modes of abstraction that cuts through and as part of these occupations such as the school teacher who taught elementary mathematics in pre-colonial India or the revenue accountant or the sculptor, the artisan, the blacksmith and all of them there are different modes of abstraction that is integral to their routine everyday occupations. And the orders of abstraction in these practices we think are computational or mathematical and if you don't particularly use the modern idea of mathematics, we are back to the 15th and 16th century for example. So our program particularly the social history of mathematical practices program that some of us are trying to attempt is to therefore not to render privilege to the activities of the mind alone or not to render privilege to the activity of the hand either, but then to bring the hand and the mind together and to reconstruct a different kind of history of mathematics. And in the Indian context particularly, it need not be, as it is often construed to be, there is Sanskrit mathematics, there is Tamil mathematics, there is Marathi mathematics and there is Asami, not like that. But it's not about any one particular language because in the Indian context, then the language parochialism takes over and it becomes its own kind of trajectory. We don't want to subject the practitioners mathematics to that framework, but to undertake such a program to all Indian languages, but not any one single practice, not just of the Brahmin astronomer, but also include the mathematical computational practices that are part of the agrarian material and the bureaucratic place. And this then enables us to look for practitioners in particular time and in particular place who was left behind their own occupational practices as texts. And then if you take texts as records of practices and then start looking at the world of practices behind the texts, which they have recorded, then we get a huge purpose of material to in which the social history of mathematical practices can be rewritten. And that's roughly the kind of broad framework under which we are trying to do our work. And if mathematical practices is conceived as work, we also then are forced to confront with formal mathematics. And the canonized formal mathematics becomes historical in certain other processes, such as the format of the textbooks, the proof-generated definition that defines most of contemporary mathematics, then masked, we think, the structures of alienation. And this alienation is necessarily about how work and occupation then become trajectories of alienation by creating certain values that is moving away from the actual source of the value creation, which is often labor. So when social history of mathematical practices work is conceived, then we can understand how the possibility of alienation, which we call alienability is structured into mathematical practices. And these mathematical practices render alienation possible through modes of abstraction. And we all know the contested histories of abstraction, where someone thinks abstraction is quite liberating, politically and emotionally at times. And then abstraction also becomes prescribed to knowledge, especially at the hands of experts, who kind of assume the responsibility to prescribe knowledge to the world and to solve other people's problems. And abstraction also gains the dimension of a particular process of codification, where particularly these texts that we're talking about often tell us how these texts codify the practice of somebody else, not necessarily of the people who are practicing the occupations, but by someone else codifying the practices of somebody else. And in the process, it moves away from the occupational context, erasing caste in the Indian thing. And therefore then it becomes abstracted as fragments of history. And then you construct a hegemonic history of mathematics that has nothing to do with the actual context of practice in which the practitioner made mathematics possible. And we all know or familiar with the idea of civilization, which has a mode of convenience possibly. But when it becomes ritualized, you actually consolidate most of mathematical practices in historical, the way it is received into the classroom or into the textbook or into the way it is talked about and conceived in the popular culture. So for today, I will take four different historical cases, one contemporary, and then try and hopefully discuss how mathematics makes alienation possible, builds alienability to it by looking at the broad consumer work and value creation. And there are four different contexts that I wanted to talk about. One is 15th century Europe through the writings of Nicolaus Copernicus, and how for him money was a measure of value. Then we come back to the 12th century South India during the heydays of the so-called glorious empire of the Cholas in South India, and how the measuring rod, the physical measuring device then became the main conduit for the manipulation of value and the alienation of labor. Third, we take the 16th century South Indian case of a how pearl traders and pearl merchants created value for pearls by raising labor out of the process of valuation. And finally, we talk about working women in contemporary India, where the microfinance industry, the so-called non-banking finance sector then extracts wages and creates a wealth for corporate capital by constantly measuring their trust through an elaborate computational apparatus that becomes the financial infrastructure. These are the four different cases that I thought we'll choose to illustrate how mathematics make alienation possible. To come to the first case, we take the writings of Nicola Copernicus, and we all are familiar with the Copernican revolution and to most of the historians until recently, the Copernican revolution was all about something that happened in the mind. And the French humanist historian dictated the counters of the history of science of studying the emergence of modern science through the writings of Copernicus, and then to him it was primarily their mental and intellectual attitude. And for Marx and Engels, it was a breathtaking kind of change, all supposed to have taken place in the realm of your thought. And Thomas Poon, one of the most influential thinkers in the history of science, he actually talks about how Copernicus as a man in the middle of the night, in the mind of the Copernican revolution happened in the mind of a man deeply immersed in Christ once had a night. So given these kind of imageries of the Copernican revolution, which is always associated with the birth of modern science itself, we want to look at Copernicus instead as a church official. As a church official and as part of a job to do astronomy as a professional, and he was also a church official to a county where he was almost administering the revenue apparatus of the particular county, and he was also advisor to the king of Poland. And why they have chosen Copernicus as a church official, as a worker, as an everyday practitioner of astronomy, and as a mathematician when he decides to speak and provide advice to the king of Poland, because what connects all his professional qualities as an astronomer, as a revenue surveyor in a little county to the church, and as an advisor to the king that he was constantly measuring the heavens, measuring land, and measuring value. So we wanted to bring how this various notions of measurement in Copernicus works enables him to speak to the king as an advisor. And why we have particularly chosen measurement as a prism to look into the practices of the church official in 15th century Europe is that, like we all know in most of the measurement, it always offers justice and fairness, the idea of measurement, but in spaces that are constitutively unequal. So the promise to eliminate arbitraryness in the activity of measurement evades the abstraction process that comes after measurement, as we'll see in most of the cases. And what's important to the idea of measurement is also the idea of a common standard, and the complex histories of standardization in histories in different cultural context tells us that measurement, the window of measurement actually provides us a possibility to link social histories of mathematics with the possibility of alienation that it imbibes for itself. So in the particular case of Copernicus, you know, the goal for money and the uniform circular motion in the planetary sphere then become the two most common standards. And in order to introduce the particular intellectual context in which Copernicus practice as a church official and an advisor to the king can be situated, is that, you know, sometime around the 14th century here, I follow the works of Joel K, who has written this book about the birth of modern science. And he says, by around the 14th century after the post I was totally untaught, which makes individual consciousness relegated to the background of a serious political and theological process in the 13th century. And by the time in the 14th century, when the medieval university, European University was being structured and conceived, the scholars realized that market equality uses the geometric product of building inequalities, almost like cross diagonals, each exchanger seeking to benefit more than other from the other exchange. And that kind of defines how individuals are beastly subjecting themselves to a process of unequal exchange. And it creates a geometry of exchange relationships, which is kind of then connected to the way the ideas of nature were conceived around the same time. And this distinction between the natural order and the market order in the context of conceiving equality or the possibility of it then comes about and the models of nature that was beginning to shape themselves in about the 14th century Europe was that it was that nature was dynamic, it was self equalizing, that it was relativistic, and it was probabilistic and geometrical. And within this model somewhere, people say they could situate the birth of modern science itself in this process. And therefore, K talks about the six conceptual backgrounds that emerge, which helps us relate to how the orders of nature and the orders of the market kind of came together, somewhere actively mediated by the European University in the 14th century. And we see how the mathematics and the geometry of exchange became intricately tied at the public practice as professional practice in the 15th century in most of the cases, in most of the countries in Europe around that time. The idea of equality, the mean and the equalization in exchange, money as a medium and measure comes quite prominently around that time. Relativity of value in exchange, there is an idea of common valuation in exchange and all of this somehow contributing to create and elaborate social geometry of a rapidly monetizing society. And that's the context around in which Copernicus functions. And it is also useful to keep in mind that the beginning of the 14th century also, then it was not all peaceful in Europe. One enormous amount of merchant capital funding, the so-called exploration of the Americas, but in effect, creating a huge infrastructure of imperial conquest and plunder and murder of the people for mining silver and gold out of the American land, which was brought back to Europe. And we have this process going on. And we also have a widespread peasant revolts in 15th century Europe. And, you know, so everybody was trying to understand this nature of unrest. On the one hand, you are plundering someone else. On the one hand, you are facing revolts from within your own peasantry. And this was quite a troubled time. And Copernicus, as an advisor, as a mathematician who is speaking to the king, therefore writes this treatise kind of a letter to the king of Poland on currency reforms. And what is the idea of the money? And we take that as our source today, along with the rather astronomical works, to illustrate how the everyday practice of the church official astronomer mathematician comes together against the background of imperial conquest and physical plunder and murder of another people and then facing a peasant, active peasant revolt in the 15th century Europe. And then so we can kind of understand how Copernicus talks about coinage. And to him, he tells the king of Poland, you know, so the coin, you know, carries metal and it is the most convenient and the most pragmatic functional way to operate money. And the coin has a face value. And what is the face value is the symbol of authority, that it ordains an universal symbol, rendering a legal and jurisdictional authority to the value of metal, so that it is seemingly just and trustworthy. All right. But then what is the intrinsic value is the actual weight and the proportion of the metal that goes into the making of the coin, not to mention the expenditure that goes into melting the coin itself. And then the burden of minting the coin and the burden of rendering legal political authority to, you know, in the name of creating trust in the coin, then is actually inscribed by the Royal Insignia. And therefore the symbolic value then adds to the intrinsic value of the metal. But then the problem there is that, but the value of the metal keeps changing, you know, especially if you all know the history of the so-called explorations and voyages of the conquest of the Americas, we all know how so many bankers and mercantile capital then got lost in the anticipation of Julian, including, you know, America Vespucci, if you read his work called the Novus Mundus, which is written around the same time, then, you know, the idea of navigation itself, you know, becomes the geometric exploration of the world, but as provides a template for extraction of precious metals from other countries. So in the light of the fluctuating prices of the metal versus bullion, you know, the intrinsic value is supposed to constantly changing. And then Copernicus talks about the wear and tear of usage and, of course, inflation. And he says, you know, what are the possibilities of subverting the promise of justice that the symbolic value and therefore the royal authority on the coin itself becomes worse. You can, you know, so this often the possibilities of he anticipates corruption, he anticipates cheating. And then he says, what are the possible ways in which justice can be denied is through defective weight of the metal in the coin or defective proportions or both. And therefore, he says whenever there is the basement of coinage, whenever there is supposed to be a currency reform, most of us in India have gone through this very, the painful memory of demonetization ourselves. And it's something akin to what happened in the 15th century Europe and quite frequently. So is that, you know, we have when the new coin replaced the whole coin based on the proportion of silver, and it's based on the change, the constantly fluctuating price of metal itself. And then Copernicus says, when the new should replace the whole coin, it should be done completely. And then he says, the idea of the dearer money or the sound money and the cheaper money is that the more that money is cheaper, it actually breeds laziness among the working people. And then therefore, he says it should be absolutely ensured that everyone returns the whole money completely, not without a single coin should be left in the thing because that becomes cheaper and makes people lazy. And while the mass of money rent, if it does remain behind, the whole money remains behind, then he says there is an incest and widespread complaint of soaring prices, especially on gold, silver, food and wage. And the workman's labor, he says, cultivates slot and laziness and ambulance by making the money cheaper. And he has this particular authoritative prescriptive knowledge as a professional where he says that every 25 years, the currency reform has to be therefore necessarily done in order to eliminate the possibility of people becoming slothful and indulgent. And we see how the weight and proportion of the metal therefore then becomes a template for the making of value through the money. And therefore, money becomes the measure. And in the process of money becoming a common, becoming a measure to him, the hegemony Prussian Empire and its flooring becomes the most fundamental whole standard. And just as the royal insignia, then the king, the monarch, it is his responsibility to preserve the standard of money, which is to establish the gold standard. And therefore, by guaranteeing the establishment and maintenance of the standard, then the monarchy ensures the unity of the social through political authority, just like the sun does so in the planetary sphere. So in his, you know, in the so-called revolutionary work, then he talks about how, you know, the middle of everything is the sun, he compares it to the royal throne. And therefore, it is royalty and monarchy that actually ensures the harmonious linkage between the motion of spheres, just like in real life, that the king has to ensure the gold standard and therefore create social unity through political authority. And in this cosmopolitical order, that Copernicus quite elaborately constructs through his advice to the king of Poland, we, how do, I mean, we actually do realize how less just like the uniform circular motion, the uniformity of the circle that ensures the harmony of spheres for the planetary cosmos. The Prussian gold standard, the flooring, you know, the weight of silver and metal is, reminds the fundamental measure of all money and therefore all work in society, which has to be, you know, done by the king. And the value that is created out of this prescriptive knowledge rendered by the mathematician astronomer is the value of the stability of state power, which then enables the making of money out of commerce. And if you enable the making of money out of commerce, then you are also enabling making money out of money. And therefore society goes on smoothly, peacefully, but without even for a moment talking about how you are actually plundering and murdering people and mining, this thing completely erasing the value of labor, which provided the metal, which is the fundamental measure of all money is what in this cosmopolitical order that Copernicus creates. And we'll come to the second case, how to the 12th century South India, where we talk about, so this is 12th century South India, roughly it could be seen as, you know, the Chola Empire, sometime it's big in the process of the Empire building, begin sometime in the 9th century, achieves his peak in the 10th and the 11th century and the 12th century, you find a heavy monetization that this process is going through. And then the dark black thing, the Chola Mandalam is at the center of the thing, which is right at the heart of what is today, the Cauvery Delta of South India. And we find in this particular discussion, we'll talk about how a physical re-engineering of the land itself through the process of a Empire building, then creates an elaborate computational apparatus to abstract the value of the land away from the context of labor, and then provide a political authority to a particular caste group in this case, establishing a Brahmin hegemony, the 12th century. And we see how these three things come together through the activity of standardizing the measuring rod, which of course is also contested by peasants revolting against the state and the landowners over a period of about 50, 60 years, sometime in the 12th century. And that's roughly the story that we'll talk about now. And why do we say that the heart of the Chola Empire, the Chola Mandalam, we have a process which starts sometime around the 10th century, like historians have documented, is the establishment of what are called Brahmadeyas. And these Brahmadeyas are primarily exclusively Brahmin settlements, which are also called the Agraharas, and was created for the Brahmins. And it happened and did a process where the king was trying to part with the part of his revenue, which was growing bigger. And then he mobilizes and settles Brahmins all over the country, and then shares his own income with that of the Brahmins, and makes them, new settlements are created, and the rights of cultivation and overlouching is given to the Brahmins. And this particular relationship between the royalty and the Brahmins then creates a hegemonic apparatus, which has continued to kind of reshape South Indian history in many ways. And you see in this map all the little dots, these were the roughly in about the 12th century what are called the Brahmadeya settlements. So you see how in the entire Chola Mandala was inundated with his Brahmadeyas, creating a very strong alignment between the royalty and pastage money through the Brahmin settlements. And one of the interesting feature for our discussion today at least, is that there is a, as I said before, there is a process of mobilizing the Brahmin settlements for the purpose of augmenting revenue, and to the larger purpose of building an empire, and by collecting taxes. And therefore, the king and the Brahmin could share the income from the land. And one particular aspect of the Brahmadeya is that, so in order in the process of reshaping the land, so the parallel irrigation canals, a new system of alignment with the land and canals is done. And a particular school of political geographers have mapped how the alignment between land and caste actually happens. So we will see in the next few slides as to how this particular alignment, which is physical re-engineering of the earth happens, and how in this process it was ensured that one single caste, there is no discrimination within the caste in the Arizona thing. All of them are Brahmins, all of them are learned, all of them are Vedic Brahmins, and they cannot be known discrimination. So how do you deal with the problem of ensuring equal distribution of land proportionately, ensuring fertility and access to water to all the Brahmins who are all equal? You cannot have discrimination in the quality of land while you are distributing to the same caste, isn't it? And therefore, this is handled by this pattern of, called the Kannaru and Saduram, which is, you know, in many other parts in the rest of the world as well, in Japan, in China, and most other cultures. We find, especially in deltaic areas, we find this interesting pattern of what is called the checkerboard structure of land, which is the square grid. As you can see in the cadastral map of the village called Devara in Patna, where we went and did our work recently, followed by a certain geographers who have already observed this pattern. So we see that this elaborate checkerboard pattern of the land happens only in the Brahmin settlements, the Brahmadeyas, or what are also called the Chaturvedi Mangalas. So this, so, fertility and access to water is assured to each and every Brahmin who are brought in and settled in this kind of villages. And slowly we find in the process, the Brahmins and temples are becoming the new rich landowners of the empire, speaking for the royalty, addressing the royalty, but also converting the previously existing free cultivators into tenants, and to whom they will be collecting taxes from. So if we went through this elaborate process of physical reshaping and re-engineering of the earth through a geometric distribution of land, then, so you inscribe castage money onto the earth. It has material, has how castage money can get. And in this new arrangement, one thing which is completely noticeable is that the existing slave labor system remains intact. It is not disturbed at all. The free cultivators becoming tenants, the tenants becoming subject to the new landowners who all belong to you, the same caste, who are the Brahmins, but then the slave labor continues to persist at the same time without, which is actually the source of labor that makes all the revenue calculations possible. So in this quiet pattern, just to be able to understand, we have think so how, for instance, this axis, the x-axis is the Raja Raja Vaipa, which is particularly called the head canon of the thing. So that runs below. And then you have the drainage canal, the Vadi, which runs on the other side. And then you divide the land in terms of Karnar, which is the first one, the second, third port like that. And then each square within the Karnar then therefore gets access to water through field canals in between running crisscross right through the, so this geometric arrangement then ensured a notional equality or material equality, so to say, and ensuring irrigation infrastructure and we're not quite sure if entirely all of it happened from about the 10th century or what was the, if there was no square grid at all previously, but there is enough conjecture to say that the presence of the Karnar is Sathiram. The presence of the square grid is in all Brahmadeya settlements, in these Brahmin settlements, in the Agra Haras, and then a particular process of revenue extraction happens around the 11th century. So if you bring the reshaping of the earth and the reshaping of private administration together, then we have enough evidence to understand that how the empire building exercise by establishing Brahmin hegemony actually perpetuated and reinforced the extraction of labor through slavery in about the 12th century. And how does this extraction is ensured is where the manipulation and the possibilities of computational practices comes into the picture. So once you have geometrically, materially inscribed hegemony on to the earth, then how do you then extract revenue out of the land, but to be able to make labor subject to this process of elaborate extraction is by a particular process, which was computation, which was quite universal in most of the medieval world, in most other civilizations and cultures as well, this process of quantification of quality. And what do you mean by that is that how do you then fold one measure into the other? It's literally folding two measures together to make one measure or an index of the measure. And what is also can be understood as commensuration. So in the Chola times, we have the quantification of quality by happening through the system called the Madakr. Madaki in Tamil means folding literally. And we have in the system of Madakr, you know, for instance, there are 14 grades of land that we find from the inscriptions. And there are two possibilities of organizing the Madakr system. So assuming just to I'm putting it very simply. So if there is like 100 acres of land, then depending on the quality of the land, whether it's irrigator, depending on the type of the soil, how many crops can it be made out in a particular case, depending on various variables, then you organize and grade the land into the thing. And notionally, then bend the land, expand it or shrink it in terms of its quality. So if it is 100 acres of wetland or very good soil, then it actually become 160 acres by the time it enters the account and register. Yeah. And if it is very poorly irrigated of a very dry soil, less cropping is possible, it probably becomes 60 or 40 or whatever this folding the shrinking and it's called Madaki and Viriway in Tamil. So this system, which is completely notional, you know, abstracting the physical area of the land into an abstract notion of quality. But then the revenue assigned and the taxation demanded out of, you know, each parcel of land will be based on the potential that the land has to yield revenue, which is primarily in terms of grain. And there is also this elaborate system of labor as tax, which is called the labor or slave labor, and both grain and labor become interchangeable commodities. And while grain and labor become interchangeable commodities, which is central to the augmentation of revenue to establish cash stage money and therefore building of the empire, we find the geometric redistribution of the land integrates itself with the notional computational apparatus, which is commensuration by folding one measure into the other quality into quantity. And, and then this arbitration, you know, of course, there is a lot of conflict between geometry and the arithmetic manipulation comes through. And then in order to ensure that, you know, that labor remains alienated, we find a lot of possibilities of manipulation that happens in the 12th century through the measuring rod. And the measuring rod is often inscribed on the walls of temples like this that you see, you see the thin line in the inscription. So, so usually this the standard measuring rod is inscribed onto the temple walls. It's supposed to be transparent, open to public audit. And you say, you know, if you all have disputes about your land, then go and measure yourself against this standard rod, which is the temple. And but then the problem with the measuring rod is that once we have the geometric redistribution enshrined onto the earth, and we have an elaborate computational apparatus through the empire's accountant by grading and folding and, you know, all the commensuration is happening at the end of the accountant, then we have one physical device of measurement, which is the measuring rod, which is supposed to orbit the disputes, but then the measuring rod itself was not very uniform. So there's always multiple standards of measuring rods. And, you know, sometimes there is also the local rod are called, you know, the local measuring rod, and then the royal rod, which is usually about 24 feet, as we have found in some of that instances. So we find the complex histories of standardization, then becoming, you know, becoming part and parcel of empire building, contesting standardization, and creating conflicts between labor and this thing. So we find in the process, these are typically how inscriptions are written on the walls. And we see some about a corpus of inscription that we're still trying to study with most of us here. Should be Pearson and some of us in the room. We're trying to see with the guidance of Subrayalu, who has taught us how to put together a geographical presence of a particular phenomena from about that spread over the entire parliament that you see earlier on the map, that there are two phases to the building up of a conscious building up of a resistance. And in the first phase, it starts around 1170 AD, we find that people are the land owners are trying to contest the state, because along with the Brahmins and the cultivators, there are also state officials who are constantly trying to drain taxation from the cultivators who represent the royal authority, which is always far away and distant. And when the royal authority is far away and distant, the possibility of manipulations at the local becomes enormous. And it is actually done through the revenue accountant who was placed at the village level. And in this emerging contestation between the possibility of revenue extraction and the interchangeability of labor and brain as commodity, as compulsory labor, as slave labor in the name of the king, then the pressure because of reasons of military fiscal reasons or because of reasons of expansion around this time that the Cholayampi was undertaking. And there was a heavy tax extraction of tax around this time. And this is resisted over the about 40, 50 years that we are trying to reconstruct now and hopefully write about it very soon, is that the first phase, the landowners are contesting the royal authority saying, we are not being able to pay the tax fully. And then they have the specific complaint against the state officials who are the delegates of the royal authority in the locality. And they're saying this manipulation of the Madaka system, which is that we are deliberately doing the folding in terms of shrinking and expanding their real land and then arbitrarily fixing tax. So the notional computational apparatus renders itself to manipulation for reasons of extraction. And in the second phase, we find from about the turn of the 12th century, we find how the cultivators who are under the Karniyalas and under the Brahmin lands are actually threatening the landowners that they are not being able to subject themselves to this heavy process of extraction. And they're often threatened to flee. And their actual instances of how the entire cultivators have fled the land as a matter of protest and resistance and boycott and saving outside the village. And then passing resolutions, which does not include labor, of course, in that resolution. And we find the resolution like in these temple walls, where they say this, the state officials in order to extract direct revenue, what they are doing is actually manipulating the measuring rod and then increasing the total acreage of the land and demanding more tax instead of actually following the standard rod, which is inspired on the temple wall. So the possibility of manipulation then becomes real on both counts. Once you have ensured the geometric equality to establish the Brahmin hegemony, then the abstract computational apparatus takes over the process of extraction and renders itself possible to alienation of labor, which of course always remains invisible. Nobody talks about them. But the process of valuation begins at the notional creation of this computational apparatus through the commensuration process, which is folding one measure into the other, and also by despite the presence of a physical, we can possibly bend the physical device of the measuring rod, but they can notionally expand it or shrink it and then alter it in order to suit the purpose of extraction. And the third case that we talk about is largely the pearl state, the precious stones. On the side of extraction is the 16th century Gulf of Mana. So these are migrating oysters in nature. The actual labor process is of diving and hunting, which is the primary source of value to beat the pre-colonial times or after the colonial takeover. So we find the figure of the merchant trader reaping the gains of this labor, which is completely erased from the process of valuation, which can be identified and studied through the text that we are trying with my colleague Parthas here. And he has done this wonderful job of reconsidering the text so that you can see through the text that how geometry and arithmetic comes together in the process of making value by erasing the labor process, which is in the actual process of diving. So we find these are the little seeds, which are called the pearl colanders, of which the pearl merchant then grates and sorts the metal into the thing. And then the Muthukana cube, the text that we are working on actually provides a grammar to how many holes, the size of the holes in each seed. And the seed is divided into particular angular segments. And then there is an elaborate description of how the physical geometric device needs to be constructed. And once the physical geometric device grates and sorts the pearls, then the process of arithmetic takes over, which is the computation of value. And that arithmetic is done through the process of commensurating three different qualities by folding them into one, which is the Cebu. And we think it is an index. And the Cebu consists of the calculation of three different qualities, which are the size, the luster and the weight. And the geometrical distribution in the physical device, which is the colander, the seed, then makes possible the arithmetic tabulation of value. And we see yet again in history, the process of, in this case, through the practitioner of the merchant trader of pearls, we see the measurement of value begins after labor. And finally, I would like to talk about one of the most important works. I mean, most of us are preoccupied with and therefore important and also I think very important for all of us to wake up and listen to the voices of the working women all over the country through the microfinance industry and how it operates through the establishment of a very intense process of extraction, which remains masked and disguised by an algorithmic industry, often industrial scale, literally. And the gap between the wages of the working women and the creation of large capital for corporate today in neoliberal India, guided by its ripening administration, is that the household need for debt then becomes a actual demand for credit in the financial market. And this has happened at a time when public welfare schemes are financialized and increasing uncertainty in terms of income and expenses has become reality. And we are trying to study how interest rate modeling, scheduling or optimized to maximize repayment efficiency. And this creates a recursive loan burden at the household. And Ganesh has put together this diagram to show how between the household, which is actually the source of labor and the site of social reproduction of labor, which is the working women's wages is not being able to address the needs of its own social reproduction at the household. And particularly because when health and education become the sources of rent to the state, which then uses the rent of the wage as the rent in order to, through this elaborate infrastructure, by making it a source of demand for credit, and then hands it over to the complex of the fintech. Fintech is the pseudonym or an euphemism of how it completely inundated with the host of microfinance companies, which is also called the non-backing finance sector shamelessly by the Reserve Bank of India. And then this fintech complex then makes through the legal instruments of the state, and then creates this two thing, which is ranking and scoring of the credit worthiness on the one hand through the creation of algorithmic instruments. And we see the elaborate process create a credit and repayment schedule. So the scoring and ranking becomes quite central to the running of this elaborate business of extraction of the working women's wage. And there are quite a few models of scoring and ranking. And each of them arbitrarily choose their own variables. Most of it is about the possibility of repayment of course, but then they also follow and profile the household of each and every working woman through building variables on credit utilization, credit history type of credit, balance, recent behavior available. And we also find how increasingly working mathematicians, mathematics graduates, PhD scholars are being employed by the finance industry in order to be able to do active modeling, which is actually a cartographic enterprise, mathematician doing the mapping of the working woman's vulnerability. And then make maps of seasonality and vulnerability together. And then to see at what particular instance when the working woman is the most vulnerable that you can actually push more credit into the household. And that's the job of the mathematician today in the finance industry achieves. And so that is done by the so-called credit worthiness mapping. And we have companies such as Highmark who actually proudly announced in their website that they have one of the most qualified and organized databases that profiles and addresses each and every single working woman in the country. In fact, that is that ambitious goal in order to be able to profile the life of each and every single working woman in the country. And you see that how the apparatus of compound interest then creates this credit and repayment schedule to the fintech algorithms supported by the mathematical models and creating a repayment schedule for that. And in both of them is done by this algorithmic instruments, which are actually making ranking mechanisms and the resulting scores then may either force the women to take more credit or to be able to extract more revenue out of the household and then never to be able to able for the working woman to address the social reproduction concerns of the household. And how this is done is through creating a recursive debt trap. And then you see if I take loan from the first microfinance institution, a company, then usually because welfare is financialized, because the state has withdrawn, because I'm supposed to buy the ability to work the power of labour from the market, which actually because of reasons of under-employment, unemployment, and the increasing shortfall, the possibility to reproduce my own labour at the household, I am invariably not being able to pay the principal and the compound interest to the first creator. And therefore, I go to the second one, which can usually be another MFI or to the local loan shark or to the so-called informal credit market in the country, which controls about 60 to 70 percent of credit industry in the country even today, despite the very recent data of the microfinance institution is to be in a way to take women out of the circuit of indebtedness. But actually, we see how loan after loan then enters into the working woman's household through this elaborate creation of the financial infrastructure, which is computational by subjecting women to a complete cycle of indebtedness. So this is one of the most important consequences to us is that it polarizes the women into good debtors and bad debtors. So if the repayment schedule is done properly, then women became the well-behaved women, then especially during the COVID pandemic that we've seen, they are being able to fragment the local social fabric, the possibility of solidarity, and the possibility of coming to the possibility of mutual aid, which was integral to the social fabric of the working human through this financialization and actually became fragmented. And this infrastructure therefore becomes integral to the alienation of labor. So we see in all these instances how if we reframe and ground mathematics as work, like in the case of the church official, Copernicus, the state astronomer, and the revenue official of the Cholas, or the mercantile trader in the 16th century, and finally also in the case of the contemporary working mathematician who is working for the finance industry today, you see the possibilities of alienation is orchestrated and built. And alienability is built into mathematics by making erasing labor in the first instance, always after the instance of measurement and creating a value creating apparatus of the labor. And then, but at the same time, we have the promise of universality, we have the promise of professional virtuosity, we find, we have the promise of transparency and fairness, but all the time evading the practice of mathematics in particularly when grounded in occupations and work. And this process of alienation, then you can call it, there are abstraction is double edged, it cuts both ways. If its abstraction is liberating, abstraction is also oppressive, but then we need to choose which abstraction is better for us, all right. But then one of the objectives that we constantly keep searching for is that is there a non alienating mathematical practices that can actually make political partisan chief possible that makes us stand in solidarity with the working people and then to subvert and then to question the process of alienation that some of these working practices and knowledge practices when they come together. And that's one of the abiding purpose of the politically mathematics collective. And we hope it's an open invitation to all of you to come and join us and contribute your continuing work. Thank you. Thank you so much, Babu. What a powerful talk. Thank you so much. Yeah. I'm sure everyone here is feeling the same the way I am feeling. It was really a great talk and a lot of questions and discussion points that takes us from here. What we'll do, given that there is less time, we'll take three questions maybe and then we'll request organizers to do something more around these lines. So Babu, I'll read the questions from the chat one by one and then you and your colleagues can respond to that. Is that okay? Yeah, sure. Yeah. Sorry, I didn't realize I was... No, no. So there is a question from Ravi Subramanyam. How do the claims and contestations by merchant guiles of medieval South India figure into this narrative? How did they mediate surplus extraction and harnessing of computation for this? About merchants? Yeah. So... Yeah, merchant guiles like the 500 and so on. Sorry, Ravi. You were talking about merchant guiles. Okay. So we know, at least on the inscription, we know very less about and then there is a debate among historians as to can we actually look for the presence of a guild, like in the European case here. But then we do find from about the middle of the 12th century a process of monetization where trade, particularly artisanal produce in clothes and edible products such as oil, then seem to organize themselves into these guiles. But very few records of practices of these working people are available. But learning from what Professor Subraailu has spoken to us about the presence of these merchant guiles, there is this intimate connection between the royalty and especially we've seen about from about the 14th century there is a conscious effort to settle these merchants into areas where there is less possibility of production and then therefore to create more enterprise. Only to such an extent that we actually know the presence of these merchant guiles but not enough things. But there are some works especially done about medieval being by Vijay Ramaswamy and others which kind of throws open to the window of the presence of these merchants. But their computational practices in medieval India is not available to us unfortunately because what are available are highly fragmented pieces of information in the inscriptions on temple walls. So do you have any follow-up question Subramanian? No thanks. So there is another question from Karan Head of you mentioned several forms of alienation occurring during the period of South Indian history you are studying. Can you generalize as to whether alienation was increasing over this period? Also I am interested in hearing your ideas on the relations between alienation and the development of mathematics. Thanks Karan. It's definitely yes, surplus extraction was reaching phenomenal proportions in large empires like this Polish historian Witol Kula says the larger the possibility of extraction the finer the measurement gets. And therefore when the finer the measurement gets then you delegate more responsibility to the bureaucracy. And therefore the mediation of extraction then is increasingly removed from the directly coercive authority of the state and then elaborated bureaucratic structure. And then since historians like some of us we actually study the leftovers of the bureaucratic practices it takes a lot more effort to see how surplus extraction then drives most of this centralizing state apparatus and increases the coercive authority of the state on one hand and therefore direct expropriation of labor in most cases especially in the Chola thing for instance we have we do have a political fragmentation of the empire itself starting from out the 13th century onwards but then it does not mean that you know it eliminated slavery or this thing the slavery persisted right through the 14th and 15th century even through the formation of the Vijay Nagarabh period in South India where new avenues of extraction were continuously created but not stopped. And this thing of course if you read the inscriptions or the records of this thing we'll all find exchange in slavery or exchange of slave labor for instance in very nicely written and so on but in actually read behind the lines it is a lot more extraction happening. And this thing about alienation in development mathematics I wish some of us more actively talk about it and it's not something that we should be afraid of talking you know so what and the quest for the search of a mathematical practice which will make you know labor non-alienable is actually the commonly shared quest and then in history if we move away from the hegemony of the mind and bring the hand and the mind together and then study real practices I think there is a possibility to have much more understanding about the dialectics of alienation and the development of mathematics not the historical formal proof generated definition of mathematics that we all actually know about but then the real practitioners mathematics which is part of the everyday. Well Karen do you have any follow-up question on that? No that's fine I'm really looking forward to reading your published references I hope you let everyone know. Yeah so there are several requests like that Babu in the chat box hope you get time to read those others have also wished to read your publication. There is a comment from Lodaya. So I'll just read it it's not a question for traders it was very important for both boy and girl children to know writing and arithmetic. So can think of education as a distinguishing advice and measurement standards with templates rules as regulating device. If you want to comment anything on this Babu otherwise there are some more questions I think. Yes Kamal that's interesting that you say that but we have we have very little understanding of the nature of the pedagogic apparatus you know we have you know because we only have few very very fragmented evidence of what could have been the nature of curriculum and the pedagogic transactions in the schools and you want to reconstruct the actual you know questions of access the orientation of the curriculum you know if you want to ask a functionality and then align it with with the social enterprises and the goals of various professions around that time it's quite easy to do but then you know we have to be also careful to see how professional virtuosity cannot be you know transposed on to the orientation of the curriculum itself but then I see that you know that education actually in terms of access did become a device of distinction and the possibility of regulation therefore as I was trying to say is that the idea of regulation then only to a point after that it actually becomes a device to perpetuate exploitative structures isn't it and therefore the regulatory authorities you know always promise and in the process of promise actually remain evasive in the actual activity and that's what I was trying to say that came across. Thank you Nauru there is there are a lot more questions but I'll take few more. Superintendent your question I'll come back again I'll give some chance to some new participants and then I'll come back at this time. There is a question from Ayush that I'm curious if you see the financial technologies I think that is what it means and land measurement complex system as parallel to the apparatus of measurement in education with its structure of merit status and elitization of labour with folks like me elite and institutions as sort of the mediators of the state like the land measurement officials. Yes Ayush I think I think you see it very clearly all of us do see it and you know and the times of increasing techno managerial apparatus that is you know not just really most of educational institutions are becoming you know we have seen very recently how cases of you know victimization have become the routine order in this kind of institutions in the in the questions of inner productivity to this increased sense of managerial and production centered thing and project-based funding is pushing the limits of you know this alignment between knowledge and solidarity a bit more difficult I think as we all are definitely confronting it most of the time but yeah this this this official term the bureaucratic authority you know the interesting thing about it is that you know they often do not realize that rulemaking as an epistemic activity actually you know continues into the anticipation of the possibility of its own denial and therefore when they anticipate the possibility of the denial of your own rules from being followed then actually you become very quiescent in the process right so then it's like you know you you all the time keep enacting loss in anticipation of its own violation and in the process creating an elaborate requires evaporation right and that's what happens when bureaucratic managers take over education institutions right and therefore and that is the caution that we do have to keep in mind and therefore instead therefore our appeal I mean the appeal of the politically mathematical especially is to you know cultivate a natural sense of partisanship and to be able to abide by the concerns of the working people yeah as our everyday practice in order then hopefully it will subject the creeping in of the techno managerial thing into the curricular process itself Ayush do you have any follow-up question comment on this no that was really helpful and brought brought clarity thank you Babu I agree with somebody who's saying you know you should have given four talks it was it was really great to hear thank you yeah so I am Babu hope you're not very tired I'm going to take liberty like Deepa said no no no I'll ask you more questions that are here there is a question from Ishan Santra in the context of the conclusion diagram on the common patterns where do we mathematicians and math educational researchers figure what is type of our labor what does it contribute to to the already existing elimination by increasing the radius of mathematical area if I do not want to contribute to that as a math and researcher what should I do what are the immediate actionable points as math education for math educational researchers thanks Ishan you probably know better you are a practitioner yourself so but then if you want to take this as an opportunity to talk about the possibilities then as I just said it's to us one of the things that has become central is to go beyond conventional institutional spaces you know not just confine ourselves to the formal classroom but to be able to you know identify concerns of the working people as central concerns of our own work and then imagine mathematics education in the real spaces of the neighborhood you know the household the trade union spaces and so on so if so what happens if you actually move away and then you know talk about organized exchange of knowledge not because it is you know the so-called idiom of you know being science for the people you know carrying science you know carry science to the people not in that manner but the the challenge of democratization of knowledge today are the contours of which are very different as we know and when contractual science the doing of science has become increasingly contractualized you know the objectives and orientation of the practice of science itself is you know given over to the corporate then I think it's all the more important for us to firmly stand by the working people not not just a notional tokenish rhetorical idea of solidarity but in reality actually stand by and then you know align our interests with that and then and then I think we have a lot more to do in terms of what would that pedagogics space look like you know as a mathematics education researcher or a science education researcher. Thank you Babu. Ishan do you have any comment or further question in this regard? So there are there are two more questions Babu so this is from Shreya she says thank you so much Babu and given a notional computations you talked of in establishing Brahman hegemony over land revenue and then what you said of how more the extraction increase the finer measurement and more elaborate it got in terms of political demands of working women can one go beyond depth translation to in fact create elaborate computations of the historical depth their own computations of justice so to speak do working mathematicians inclined towards social justice concerns and Shreya's have ideas on what such computations and measures could entail. That's what you were supposed to work together on Shreya so anyway so I think so one of the things especially Tathagat is I mean exactly he's what is more primary concern is to look at issues so if we have to account for in fact when we're going and studying inscriptions you know it's this complete stark absence of there is a large presence of credit the complete absence of women on the one hand you know so this idea of what could have been the sources of social reproduction of all the Corby labor all the compulsory labor was very stark and then so that I was in fact saying is one where to compute you know all the time and leisure that you know that this computational apparatus and the building of it is actually took place then would it be able to would be would be able to reverse the computation in favor of finding the possibilities of justice so that's something that I think it's a very central task that is in front of us and all the historical debt you know so that it does not become yet another you know matrix calculations and so on which usually assumes the tone of technocracy that you know a problem more than me and you know so to work out what would be the computations and measures you know to make justice much more approximate than what it seems right now I think something that I you know that we all have to learn from I think especially some of the things that we are trying to attempt now which is to is one where to elaborate on the flow of wealth out of the working humans wages and how it becomes rent in the absence of public education and public health and then how the market uses the rent through the formal banking system and then delivers it as a source of capital to cooperate this thing the flow of wealth is mapped and you know then probably there the possibility of you know how how the reversal how the computations of justice can be worked out that's one possibility that we are considering and then most of the working women are also quite telling and they are saying look the more you come and speak to us as if you know we don't know how we are being oppressed or how we are being exploited to the micro-connect industry but they're asking us to consciously go and speak to the industry itself and say if you are a university trained then you understand their language and then you go spend more time with them instead of coming to us and then tell us about how they think and the thought process in which they work and you come back and tell us as to how they how that that process actually ends up being exploited right so if you have to bring these two tasks together then I think the possibility of a non-alienating computational practice which is which brings us much more closer to the uh to justice yeah yeah thanks for Shreya do you have any uh returning comment no thank you very much Babu just one thing that of course I assume that will be of concern for everyone that that would then have implications I assume for mathematics education programs in the sense of what education in like what kind of math that programs will be needed to have math graduates get out and do this kind of computational work rather than get into FinTech companies working out like the vulnerability of working within I suppose so how to move in that direction thank you very very much for this and really big salam to lovely work that Yola do thank you Shreya Babu there is a similar question on this line from Ravi Subramaniam but in a more general sense and also I think about creation of mathematics is what reflections you have on what what could be the kind of mathematics that can be supportive of liberation yeah one is uh to uh to consciously uh been away from uh contractual uh neoliberal practice of science that I think uh and then to subject ourselves to scrutiny our own practice as to what do we do with our own students what do we do with our own uh ways of thinking and when do we say that we align with power when we say that we uh we might be able to refuse to align with power you know with your particular thought but not just in terms of professional work where you know where I go meet working when write a paper about it but not that but then to be able to alter and change the our own process of work and cultivate the strong sense of partisanship I think and then I think this political partisanship has become very central because if it becomes uh you know my it's my 95 job but after five I am uh doing something else now I don't think uh you know that often creates a predicament for us and all of us are constantly facing it in our everyday work and you know that would be more than me and therefore it's uh the search for a non-alienating uh mathematical practice about the possibilities of liberation uh we'll have to see but I think to begin with you know the search for this non-alienating non-alienating practice of mathematics I think is like the working women demand from us you know you go speak and understand their thought process and how do they end up becoming such so exploitative is something that you know uh you come back and translate uh that thought process towards I think the the working the intricacies and the inner world of uh the techno managerial the contractual the neoliberal uh the practitioners of science and mathematics I think uh and also we all know that uh you know uh this elaborate a certification industry that higher education has become and you know so if if you want if you want to continue to remain part of that industry then how do you redefine our own relationship not just professionally but also politically to that industry I think or two beginning points that we constantly do talk about and think about but uh mathematics for liberation uh yes of course you know definitely we have to look and organize these spaces of knowledge exchange outside formal institutions and then bring those concepts back into the institutions and create this heavy traffic and very active basis between the two spaces I think uh would be a beginning yeah so our time is up uh thank you so much Babu there is one more question from Bremendam about article by Sarma but you can read it and maybe respond later or chat later we have to close the session uh the poster session is at 11 was supposed to be at 11 20 it will happen at 11 25 now with five minutes break but I want to say uh thank you so much uh and I share with everyone here when I say that we need some follow up uh task discussion workshop after this and it's a request to organizers uh to do something on this line I I'm sure I share everyone's feelings here so let's give a big round of hand for Babu and his team so thank you so much thank you everyone I hope uh all of us will consider working with us the politically mathematics collective and hopefully we'll be able to do some work together again