Steady-state Theorem Research Articles

The Mathematics of Acting: A Workbook by Dréa Lewis

Reviewed by: The Mathematics of Acting: A Workbook by Dréa Lewis Mary Trotter The Mathematics of Acting: A Workbook. By Dréa Lewis (she/her). Coppell, TX: Dream of Dréa, 2019; pp. 122. The Mathematics of Acting: A Workbook is born out of a thesis project, but has the potential to fill a great need in an acting classroom comprised of students who may, or may not, come with a background in math or science. Dréa Lewis begins by explaining how she came to write the book. Frustrated at how the principles of her college acting training had become jumbled or forgotten, she sought another way into the work. The book addresses how to make a connection to character through four different areas: Mind, Body, Voice, and Face. In this approach, however, science is the foundation for exploration. Lewis utilizes math-based principles and activities to more efficiently explore character, taking the reader through her personal experiences of working as an engineer and actor. Each section offers helpful visuals, learning activities, and brain games. There are also exercises applicable to each area that would make great additions to a classroom for beginning actors or non-theatre majors. The final chapters consist of worksheet pages on which students can write scenes and express creativity based on the four areas explained in the text. Lewis also offers a “sample journal” she kept during the creation of a character for the first role she was cast in outside of graduate school. These pages offer a look at how her techniques and exercises can be applied by an actor outside of the classroom. “Math & Mind” is the first area of analysis. Lewis’s initial aim is to help actors to understand the personality of the character. Utilizing the Myers-Briggs Type Indicator and the Steady State Theorem, she defines what the constants are for a character and forecasts how a character might respond to circumstances in the play. Lewis then uses questions developed by Paul Tieger and Barbara Barron-Tieger in the The Art of Speed Reading People to help the character become more tangible. These questions define how the character energizes, gathers information, makes decisions, and organizes the world. The actor uses answers to these questions to inform how the character connects with other characters and responds to events. Here, Lewis uses the concept of parabolic trajectory and the second law of thermodynamics to explore how energy and emotion transfer from one character to the next and thus affect the trajectory of a scene. To tackle the second area, “Math & Body,” Lewis begins by referencing some techniques more commonly known to the theatre professional: Alexander Technique and Feldenkrais Method. Expanding on this work, she uses calculus and geometry to encourage actors “to be aware [End Page 46] of angles [they] can position [their] body in, and achieve physical expressions of a character” (31). Lewis implements the Cartesian Coordinate System to analyze the distance between specific points of the body and explore position and movement. These exercises could be particularly helpful for young actors having trouble being present in the body. The discoveries of the second area lead Lewis to the third, “Math & Voice,” and allow her to use her experience as a computer engineering student studying aerodynamics. She applies Bernoulli’s Principle and the understanding of speech rate and latency to the expression of emotion, and argues that “great storytellers possess super reflexes which is manifested by projecting different resonances (throat, neck, nasal, and head), and by creating space to attach notes to words while speaking” (43). Relating the emotional state of a character to the number of speech sounds per minute, Lewis offers a new, more mathematical way of thinking about how an actor might express the content of a scene. In the fourth area, “Math & Face,” Lewis draws on Charles Darwin’s contributions to genetic science in The Expression of the Emotions in Man and Animals, using a face map to analyze which areas of the face are affected for which expression. She makes the point that the recognition of a change in emotion is expressed first in the face, and that actors can reverse this process by...

A Generalized Growth Model and the Direction of Technological Progress

Based on a general growth model, this paper finds that the steady-state direction of technological progress is determined by the scale return of the production function and the relative factor supply elasticities. A specific version of that model extends Acemoglu (2002) to provide the underlying determinants of the supply elasticities and demonstrates that the relative price (Hicks, 1932) and relative market size (Acemoglu, 2002) have only a short-term impact on the direction of technological progress. A consequence of the analysis is that the steady-state technological progress is purely labor-augmenting (i.e. delivers Uzawa’s steady-state theorem) if and only if the scale return of the production function is constant and the supply elasticity of capital is infinite. Analogously, an infinite labor supply elasticity is required if labor-augmenting technological progress is to be excluded prior to the Industrial Revolution. Accordingly, changing factor supply elasticities may have induced the Industrial Revolution.