Nonlinear Dynamics and Chaos – Steven Strogatz, Cornell University

This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. It closely follows Prof. Strogatz’s book, “Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering.”

The mathematical treatment is friendly and informal, but still careful. Analytical methods, concrete examples, and geometric intuition are stressed. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

A unique feature of the course is its emphasis on applications. These include airplane wing vibrations, biological rhythms, insect outbreaks, chemical oscillators, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with the mathematical theory. The theoretical work is enlivened by frequent use of computer graphics, simulations, and videotaped demonstrations of nonlinear phenomena.

The essential prerequisite is single-variable calculus, including curve sketching, Taylor series, and separable differential equations. In a few places, multivariable calculus (partial derivatives, Jacobian matrix, divergence theorem) and linear algebra (eigenvalues and eigenvectors) are used. Fourier analysis is not assumed, and is developed where needed. Introductory physics is used throughout. Other scientific prerequisites would depend on the applications considered, but in all cases, a first course should be adequate preparation.

Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics

Selections from Science and Sanity represents Alfred Korzybski’s authorized abridgement of his magnum opus, Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics. This second edition, published in response to the recent Korzybski revival, adds new introductory material and a revised index, providing an accessible introduction to Korzybski’s arguments concerning the need for a non-Aristotelian approach to knowledge, thought, perception, and language, to coincide with our non-Newtonian physics and non-Euclidean geometries, to Korzybski’s practical philosophy, applied psychology, pragmatics of human communication, and educational program. Selections from Science and Sanity serves as an excellent introduction to general semantics as a system intended to aid the individual’s adjustment to reality, enhance intellectual and creative activities, and alleviate the many social ills that have plagued humanity throughout our history.

Cradle to Cradle: Remaking the Way We Make Things

In Cradle to Cradle: Remaking the Way We Make Things, architect William McDonough and chemist Michael Braungart present an integration of design and science that provides enduring benefits for society from safe materials, water and energy in circular economies and eliminates the concept of waste.

The book puts forward a design framework characterized by three principles derived from nature:

Everything is a resource for something else. In nature, the “waste” of one system becomes food for another. Everything can be designed to be disassembled and safely returned to the soil as biological nutrients, or re-utilized as high quality materials for new products as technical nutrients without contamination.

Use clean and renewable energy. Living things thrive on the energy of current solar income. Similarly, human constructs can utilize clean and renewable energy in many forms—such as solar, wind, geothermal, gravitational energy and other energy systems being developed today—thereby capitalizing on these abundant resources while supporting human and environmental health.

Celebrate diversity. Around the world, geology, hydrology, photosynthesis and nutrient cycling, adapted to locale, yield an astonishing diversity of natural and cultural life. Designs that respond to the challenges and opportunities offered by each place fit elegantly and effectively into their own niches.

Rather than seeking to minimize the harm we inflict, Cradle to Cradle reframes design as a positive, regenerative force—one that creates footprints to delight in, not lament. This paradigm shift reveals opportunities to improve quality, increase value and spur innovation. It inspires us to constantly seek improvement in our designs, and to share our discoveries with others.

The Structure of Scientific Revolutions

A good book may have the power to change the way we see the world, but a great book actually becomes part of our daily consciousness, pervading our thinking to the point that we take it for granted, and we forget how provocative and challenging its ideas once were—and still are. The Structure of Scientific Revolutions is that kind of book. When it was first published in 1962, it was a landmark event in the history and philosophy of science. Fifty years later, it still has many lessons to teach.

With The Structure of Scientific Revolutions, Kuhn challenged long-standing linear notions of scientific progress, arguing that transformative ideas don’t arise from the day-to-day, gradual process of experimentation and data accumulation but that the revolutions in science, those breakthrough moments that disrupt accepted thinking and offer unanticipated ideas, occur outside of “normal science,” as he called it. Though Kuhn was writing when physics ruled the sciences, his ideas on how scientific revolutions bring order to the anomalies that amass over time in research experiments are still instructive in our biotech age.

This new edition of Kuhn’s essential work in the history of science includes an insightful introduction by Ian Hacking, which clarifies terms popularized by Kuhn, including paradigm and incommensurability, and applies Kuhn’s ideas to the science of today. Usefully keyed to the separate sections of the book, Hacking’s introduction provides important background information as well as a contemporary context.  Newly designed, with an expanded index, this edition will be eagerly welcomed by the next generation of readers seeking to understand the history of our perspectives on science.