Making Sadza with Deaf Zimbabwean Women: A Missiological Reorientation of Practical Theological Method toward Self-Theologizing Agency among Subaltern Communities

Missiological calls for self-theologizing among faith communities present the field of practical theology with a challenge to develop methodological approaches that address the complexities of cross-cultural, practical theological research. Although a variety of approaches can be considered critical correlative practical theology, existing methods are often built on assumptions that limit their use in subaltern contexts. This study seeks to address these concerns by analyzing existing theological methodologies with sustained attention to a community of Deaf Zimbabwean women struggling to develop their own agency in relation to child rearing practices. This dilemma serves as an entry point to an examination of the limitations of existing methodologies and a constructive, interdisciplinary theological exploration. The use of theological modeling methodology employs my experience of learning to cook sadza, a staple dish of Zimbabwe, as a guide for analyzing and reorienting practical theological methodology. The study explores a variety of theological approaches from practical theology, mission oriented theologians, theology among Deaf communities, and African women’s theology in relationship to the challenges presented by subaltern communities such as Deaf Zimbabwean women. Analysis reveals that although there is much to commend in these existing methodologies, questions about who does the critical correlation, whose interests are guiding the study, and consideration for the cross-cultural and power dynamics between researchers and faith communities remain problematic for developing self-theologizing agency. Rather than frame a comprehensive methodology, this study proposes three attitudes and guideposts to reorient practical theological researchers who wish to engender self-theologizing agency in subaltern communities. The creativity of enacted theology, the humility of using checks and balances in research methods, and the grace of finding strategies to build bridges of commonality and community offer ways to reorient practical theological methodologies toward the development of self-theologizing agency among subaltern people. This study concludes with discussion of how these guideposts can not only benefit particular work with a community of Deaf Zimbabwean women, but also provide research and theological reflection in other subaltern contexts.

The Construction of Arbitrary Stable Dynamics in Non-Linear Neural Networks

In this paper, two methods for constructing systems of ordinary differential equations realizing any fixed finite set of equilibria in any fixed finite dimension are introduced; no spurious equilibria are possible for either method. By using the first method, one can construct a system with the fewest number of equilibria, given a fixed set of attractors. Using a strict Lyapunov function for each of these differential equations, a large class of systems with the same set of equilibria is constructed. A method of fitting these nonlinear systems to trajectories is proposed. In addition, a general method which will produce an arbitrary number of periodic orbits of shapes of arbitrary complexity is also discussed. A more general second method is given to construct a differential equation which converges to a fixed given finite set of equilibria. This technique is much more general in that it allows this set of equilibria to have any of a large class of indices which are consistent with the Morse Inequalities. It is clear that this class is not universal, because there is a large class of additional vector fields with convergent dynamics which cannot be constructed by the above method. The easiest way to see this is to enumerate the set of Morse indices which can be obtained by the above method and compare this class with the class of Morse indices of arbitrary differential equations with convergent dynamics. The former set of indices are a proper subclass of the latter, therefore, the above construction cannot be universal. In general, it is a difficult open problem to construct a specific example of a differential equation with a given fixed set of equilibria, permissible Morse indices, and permissible connections between stable and unstable manifolds. A strict Lyapunov function is given for this second case as well. This strict Lyapunov function as above enables construction of a large class of examples consistent with these more complicated dynamics and indices. The determination of all the basins of attraction in the general case for these systems is also difficult and open.

The Synthesis of Arbitrary Stable Dynamics in Non-linear Neural Networks II: Feedback and Universality

We wish to construct a realization theory of stable neural networks and use this theory to model the variety of stable dynamics apparent in natural data. Such a theory should have numerous applications to constructing specific artificial neural networks with desired dynamical behavior. The networks used in this theory should have well understood dynamics yet be as diverse as possible to capture natural diversity. In this article, I describe a parameterized family of higher order, gradient-like neural networks which have known arbitrary equilibria with unstable manifolds of known specified dimension. Moreover, any system with hyperbolic dynamics is conjugate to one of these systems in a neighborhood of the equilibrium points. Prior work on how to synthesize attractors using dynamical systems theory, optimization, or direct parametric. fits to known stable systems, is either non-constructive, lacks generality, or has unspecified attracting equilibria. More specifically, We construct a parameterized family of gradient-like neural networks with a simple feedback rule which will generate equilibrium points with a set of unstable manifolds of specified dimension. Strict Lyapunov functions and nested periodic orbits are obtained for these systems and used as a method of synthesis to generate a large family of systems with the same local dynamics. This work is applied to show how one can interpolate finite sets of data, on nested periodic orbits.