Can Developing Women Create Primitive Art? and Other Questions of Value, Meaning and Identity in the Circulation of Janakpur Art

In this article, I examine the values and meanings that adhere to objects made by Maithil women at a development project in Janakpur, Nepal – objects collectors have called ‘Janakpur Art’. I seek to explain how and why changes in pictorial content in Janakpur Art – shifts that took place over a period of five or six years in the 1990s – occurred, and what such a change might indicate about the link between Maithil women’s lives, development, and tourism. As I will demonstrate, part of the appeal for consumers of Janakpur Art has been that it is produced at a ‘women’s development project’ seeking to empower its participants. And yet, the project’s very successes threaten to displace the producers (and what they produce) from their perceived qualities/identities as ‘traditional’ and ‘primitive,’ thereby bringing into question the authenticity of the ‘art’ they produce. The conundrum begs this question: can developing women produce primitive art?

Decomposing Blaschke Products And Polynomials

The goal of this paper is to contribute to the understanding of complex polynomials and Blaschke products, two very important function classes in mathematics. For a polynomial, $f,$ of degree $n,$ we study when it is possible to write $f$ as a composition $f=g\circ h$, where $g$ and $h$ are polynomials, each of degree less than $n.$ A polynomial is defined to be \emph{decomposable }if such an $h$ and $g$ exist, and a polynomial is said to be \emph{indecomposable} if no such $h$ and $g$ exist. We apply the results of Rickards in \cite{key-2}. We show that $$C_{n}=\{(z_{1},z_{2},...,z_{n})\in\mathbb{C}^{n}\,|\,(z-z_{1})(z-z_{2})...(z-z_{n})\,\mbox{is decomposable}\},$$ has measure $0$ when considered a subset of $\mathbb{R}^{2n}.$ Using this we prove the stronger result that $$D_{n}=\{(z_{1},z_{2},...,z_{n})\in\mathbb{C}^{n}\,|\,\mbox{There exists\,}a\in\mathbb{C}\,\,\mbox{with}\,\,(z-z_{1})(z-z_{2})...(z-z_{n})(z-a)\,\mbox{decomposable}\},$$ also has measure zero when considered a subset of $\mathbb{R}^{2n}.$ We show that for any polynomial $p$, there exists an $a\in\mathbb{C}$ such that $p(z)(z-a)$ is indecomposable, and we also examine the case of $D_{5}$ in detail. The main work of this paper studies finite Blaschke products, analytic functions on $\overline{\mathbb{D}}$ that map $\partial\mathbb{D}$ to $\partial\mathbb{D}.$ In analogy with polynomials, we discuss when a degree $n$ Blaschke product, $B,$ can be written as a composition $C\circ D$, where $C$ and $D$ are finite Blaschke products, each of degree less than $n.$ Decomposable and indecomposable are defined analogously. Our main results are divided into two sections. First, we equate a condition on the zeros of the Blaschke product with the existence of a decomposition where the right-hand factor, $D,$ has degree $2.$ We also equate decomposability of a Blaschke product, $B,$ with the existence of a Poncelet curve, whose foci are a subset of the zeros of $B,$ such that the Poncelet curve satisfies certain tangency conditions. This result is hard to apply in general, but has a very nice geometric interpretation when we desire a composition where the right-hand factor is degree 2 or 3. Our second section of finite Blaschke product results builds off of the work of Cowen in \cite{key-3}. For a finite Blaschke product $B,$ Cowen defines the so-called monodromy group, $G_{B},$ of the finite Blaschke product. He then equates the decomposability of a finite Blaschke product, $B,$ with the existence of a nontrivial partition, $\mathcal{P},$ of the branches of $B^{-1}(z),$ such that $G_{B}$ respects $\mathcal{P}$. We present an in-depth analysis of how to calculate $G_{B}$, extending Cowen's description. These methods allow us to equate the existence of a decomposition where the left-hand factor has degree 2, with a simple condition on the critical points of the Blaschke product. In addition we are able to put a condition of the structure of $G_{B}$ for any decomposable Blaschke product satisfying certain normalization conditions. The final section of this paper discusses how one can put the results of the paper into practice to determine, if a particular Blaschke product is decomposable. We compare three major algorithms. The first is a brute force technique where one searches through the zero set of $B$ for subsets which could be the zero set of $D$, exhaustively searching for a successful decomposition $B(z)=C(D(z)).$ The second algorithm involves simply examining the cardinality of the image, under $B,$ of the set of critical points of $B.$ For a degree $n$ Blaschke product, $B,$ if this cardinality is greater than $\frac{n}{2}$, the Blaschke product is indecomposable. The final algorithm attempts to apply the geometric interpretation of decomposability given by our theorem concerning the existence of a particular Poncelet curve. The final two algorithms can be implemented easily with the use of an HTML

Saving morality: Why we cannot, and why we must

Philosophers and laymen alike have often used morality to invite misconceptions of human life into ethics, and also of ethics into human life. The Kant/Williams discourse provides a rich backdrop on which to consider these misconceptions. But the misconceptionsof morality involved are just as numerous and just as serious. One thing that the Kant/Williams discourse shows is this: that ethics can be neither contained by nor cultivated without morality. Though much of Williams’ critique of Kantian morality is quite astute, thephilosophical and ethical wisdoms of morality abound in spite of these. Morality understands the fundamental condition of moral loss, and the sometimes irreducible quandaries that this condition places human beings in. It understands the nature of the moral law, and theintricacies that the levels of letter and spirit invite into human life. Perhaps more importantly, it understands the uncompromising relationship between moral loss and moral law, and how the human navigation of this relationship leads into the ethical realm via giving rise to ethical conviction. Finally, for all of its pressures, morality abounds in valuable wisdoms for the one discovering that the human soul occupies a place of ethical significance in the world. It is responsible for pointing out, grounding and providing a framework for some of the most fundamental truths about the world and human beings; and these are essential to any viable ethical theory and sensible conception of human life.