M. K. Gandhi opposed the census enumeration of “untouchables,” or Dalits, as a separate group in the Census of 1931. As a “Hindu reformer” who fought against untouchability, Gandhi wanted to include “untouchables” within the larger political category of “Hindu.” Yet this view ran against the lived experiences of Dalits, who pointed to the hypocrisy of the political construction of “untouchables as Hindus” when they were systematically excluded, humiliated, and treated as less than human, and blocked from entry into temples—reinforcing the “line of untouchability” that separated “untouchables” from “caste Hindus.” Political scientist Vivek Kumar Singh describes the irreconcilability of this position, arguing that “untouchables could, therefore, neither enter the temple nor leave it.”

Ambedkar vehemently opposed Gandhi's position. Gandhi saw himself as representing “the vast mass of untouchables” and believed that “untouchables” should remain within the Hindu fold, while Ambedkar demanded self-representation for “untouchables” through separate electorates and reservations. Gandhi resisted both separate electorates and reservations and also argued that the census enumeration of “untouchables” as a separate community would further enhance caste divisions, instead of empowering “untouchables.” Gandhi's perspective in the 1930s strongly influenced Congress political leaders, who believed they were the legitimate political representatives of “untouchables” as one of many communities within the “Hindu majority” during negotiations with the British to “quit India.”

Gandhi's advice to a government committee on how “untouchables” should be enumerated in the census—as Hindus—highlights the embeddedness of census politics within the politics of representation and the distribution of political power in “decolonizing” India.

This book is born out of privilege. As a US-born member of the South Asian diaspora, my identity as a Syrian Christian has allowed me to benefit from inherited caste- and class-privilege. Syrian Christians are a “privileged minority” that falls within the roughly 8 percent of the population of India, which the 1980 Mandal Commission report identifies as “‘forward’ non-Hindu castes and communities.” My family origins in Kerala and upbringing in the United States have provided me with innumerable resources and sources of advantage.

In the lengthy period that I have taken to write this book, I have spent considerable time trying to make sense of my observational and interview data. I am indebted to the vast body of scholarship and related activism of towering figures such as Jotirao and Savitribai Phule, Iyothee Thass, and B. R. Ambedkar and continuing in more recent writings of historians, social scientists, and activists of the late twentieth and early twenty-first centuries (detailed in my bibliography) that document the nature of caste hierarchy and its durability despite ongoing change and challenge. This scholarship has allowed me to contextualize my findings, despite my many blind spots, and pushed me to ask and answer questions about the institutional structures and ideologies that help to concentrate power and perpetuate gross inequalities and indignities across generations.

I am immensely grateful to the numerous people who shared their time and knowledge with me while I was conducting fieldwork in Bengaluru and other locations throughout India between 2011 and 2016. This project is only possible because of their generosity and patience. I am also extremely beholden to research assistance from Shalini Jamuna Kotresh, Arasi Arivu, and Devanshu Singh, who created a database of newspaper coverage, while Shalini also interviewed enumerated households. I am very appreciative for a research affiliation at the Institute for Social and Economic Change (ISEC) in Bangalore that provided me with an academic home while conducting fieldwork between 2012 and 2013.

“We were in disbelief that we won,” explained a caste census activist. After months of organizing, the campaign to include a caste-wise enumeration in Census 2011 had culminated in the Lok Sabha, or the lower house of Indian parliament, in early May 2010. The debate spanned three afternoon sessions in which nearly every speaker across the political spectrum supported the collection of caste-wise data in the upcoming decennial census. The leadership of the Indian National Congress Party (hereafter Congress), in power at the time through the coalition United Progressive Alliance (UPA) government, found itself backed into a corner and reversed its long-standing opposition to a caste-wise enumeration in the census. A remark by prime minister Manmohan Singh at the end of the debate, followed by finance minister Pranab Mukherjee's comment to reporters the next day that “caste will be included in the present census,” publicly confirmed that the UPA government would collect caste-wise data in the census for the first time since independence. The finance minister reiterated the government's position during a trip to Chhindwara the following day when he told reporters, “[T]he caste-based census was last conducted in the year 1931 and the practice should have continued in post-independence period also but it did not happen. Now the UPA government has taken an initiative in this regard.” Decennial censuses in independent India have limited data collection to Scheduled Castes (SCs) and Scheduled Tribes (STs)—two administrative categories consisting of Dalits, or “ex-untouchables,” and indigenous communities that have faced extreme indignities, violence, and structural exclusion—to determine the size of each group's affirmative action, or reservation, quota. Activists who had worked tirelessly for months to expand the caste-wise enumeration in the census were elated. Their coordinated campaign had involved public forums, conferences, speeches, rallies, and collaboration with political leaders to build a base of support at a time when both Congress and the Bharatiya Janata Party (BJP) opposed a caste count in Census 2011. Their success was tremendous given that since the 1950s, a range of commissions and organizations seeking to dismantle caste hierarchy had unsuccessfully advocated for the decennial census to collect and publish caste-wise data. Decades of effort finally met with success.

3.1 Introduction

In Chapter 1 on first- and second-order equations, we have seen that the solutions of linear first-order equations can be obtained in explicit form by converting the problem essentially to an integral calculus problem. We have also seen that there is no procedure in general to obtain the solutions of linear second-order equations with variable coefficients in explicit form. Nevertheless, we could obtain valuable information about the solutions by exploiting the linearity, superposition principle and so on. In this chapter, we consider a class of linear second-order equations whose solutions may be written down in explicit form. Since these solutions will be in the form of an infinite (power) series, eliciting the qualitative behaviour of solutions near some specified point or at infinity will be an important aspect. The results of this chapter are collectively called Frobenius theory. Some important equations, such as Bessel's equation, Hermite equation, Chebyshev equation, Laguerre equation, Airy equation and so on, are included in the class of equations considered here. Owing to the importance of these equations, which appear in applications frequently, the major properties of their solutions have been tabulated in mathematical handbooks. The interested reader may refer to Ref. [1]. We restrict the discussion to the real domain, though it is more advantageous to work in a complex domain. For example, the function (1 + x2)−1 as a function of the real variable x is smooth and has no singularity. However, when x is considered in the complex domain, this function has singularities at the points x = ±i. The discussion in the complex domain also requires tools from complex analysis. For these interesting and important results for the equations in the complex domain, the interested reader is referred to Refs. [7], [15], [29], [54], among others.

3.2 Real Analytic Functions

The class of equations we consider will have analytic coefficients. Roughly speaking, analyticity means convergent power series. We are familiar with power series in the context of Taylor's series and Maclaurin's series in calculus.

Discusses ethical questions raised by the life cycle of clothing, including those related to labor (e.g. sweatshops) and those related to the environmental impact of clothing production and disposal.

10.1 Homogeneous Equation: D’Alembert's Formula

The Cauchy problem or the initial value problem (IVP) for the one-dimensional wave equation is

Here, c > 0 is a constant, called the speed of propagation.

This equation models many real-world problems: small transversal vibrations of a string, longitudinal vibrations of a rod, electrical oscillations in a wire, torsional oscillations of shafts, oscillations in gases and so on. The wave equation is a prototype of hyperbolic equations. It has two real and distinct characteristics, given by x ± ct = constant. Using the characteristic variables ξ = x + ct and τ = x − ct, we have and hence,. Its general solution is therefore given by

Using the initial conditions in equation (10.1.1) to determine F and G results in the D’Alembert's formula for the solution u:

More generally, data can be prescribed on a non-characteristic curve: t = φ(x), with some conditions on φ, but an explicit formula for the solution may not be found. We state the foregoing in the following theorem:

Theorem 10.1. Suppose the initial conditions satisfy that u0 ∈ C2(ℝ) and u1 ∈ C1(ℝ). Then, the function u given by the D’Alembert's formula (10.1.2) is a C2 function in ℝ × [0, ∞) and satisfies equation (10.1.1) and hence unique.

10.2 Domain of Dependence and Other Concepts

The following observations based on the D’Alembert's formula (10.1.2) may be made. The value of the solution u at (x, t), t > 0 depends on the values of the initial data only in the interval [x − ct, x + ct] on the initial line t = 0, that is, the x-axis. This is referred to as the domain of dependence (of the solution) at (x, t). Similarly, a point y on the initial line can influence the value of u for some t > 0, only in a line segment. This is referred to as the range of influence of the point (y, 0). These are illustrated in Figure 10.1.

Considers how clothing is related to memory and personal identity. Examines how we communicate with clothing by considering both Roland Barthes’ semiotic account and a Gricean account of meaning. Considers how we might think of uniforms in light of these observations.

Considers legal restrictions on clothing, particularly in light of pluralism and multiculturalism. Examines several approaches to such restrictions. Analyzes and examines the notion of cultural appropriation when it comes to clothing, and discusses where the wrongs of appropriation lie.