Popular Lectures

by J. C. Sprott


The New Science of Chaos

The ability to make accurate quantitative predictions and to replicate experiments with the same result are hallmarks of the scientific revolution. In the last few decades it has come to be widely recognized that deterministic systems governed by simple equations can behave unpredictably. This phenomenon is called "chaos," and it has excited the imagination of the public as well as the interest of scientists in diverse fields. Examples of chaos will be shown using simple apparatus and computer simulations.

This talk is available on video.
This talk uses computer animations from the Chaos Demonstrations program.


A Fractal View of the World

Since the time of the ancient Greek philosophers, we have been taught that the geometry of lines and surfaces and solids is the proper description of the world. Recently, a new type of geometry has emerged in which the fundamental objects are "fractals." Fractals have non-integer dimension and self-similar structure on all scales. Natural objects such as rivers, mountains, clouds, snowflakes, trees, plants, and landscapes are best described by fractal geometry. Examples of fractals will be shown, and methods will be described whereby you can generate fractal patterns on your computer and analyze their properties.

This talk is available as a PowerPoint Presentation.
This talk uses computer animations from the Chaos Demonstrations program.


Fractals for Kids

This is a tale of how a physics professor at a major research university came to write a coloring book for children. What better way to learn about fractals than to actually try to draw one by hand? I will explain what fractals are, survey some of the many ways of making fractal images, and show lots of pretty (colored) pictures. Suitable for all ages.

This talk is available as a PowerPoint presentation.


Strange Attractors - From Art to Science

From the dawn of science until just a few years ago the phenomenon of chaos was largely unknown. Now chaos is seen everywhere. Is chaos the exception or the rule? Computer experiments that assess the prevalence of chaos will be described. Millions of equations are solved and the solutions catalogued. A portion of these solutions are chaotic and produce strange attractors--fractal objects of great beauty and mathematical interest. A collection of these objects will be exhibited, and some of their unusual and interesting properties will be described.

This talk is available as a PowerPoint Presentation and in HTML format.
A version tailored to a physics audience is available in PowerPoint and HTML format.
A version given at the Santa Fe Institute is available in PowerPoint and HTML format.


Can a Monkey with a Computer Create Art?

While studying chaotic dynamical systems, I inadvertently generated a few million fractal images, called strange attractors.  These images were selected by the computer from among a few billion cases that were analyzed.  I showed a few thousand of these to about a dozen artists and scientists who evaluated them aesthetically.  From that I discovered a strong correlation between their aesthetic quality and mathematical properties such as fractal dimension and Lyapunov exponent.  Then I was able to train the computer to be even more selective and to produce thousands of images, all different, and most which are aesthetically appealing.  I will describe the process and show examples of the images produced in this way and will even produce some new ones during the talk.

This talk is available as a PowerPoint Presentation and in HTML format.


Mathematical Models of Love and Happiness

Steve Strogatz has proposed a two-dimensional linear continuous-time dynamical model of the love/hate relationship between two individuals.  I will describe the rich dynamics of this simple model and suggest some nonlinear extensions and models of love triangles with chaotic solutions.  I will also describe a related linear model for the time evolution of one's happiness in response to external stimuli (hedonics).  I will show how the models are related and will discuss some implications for psychotherapy and for a personal philosophy of life. An important implication of the happiness model is that one cannot expect to be either exclusively happy or exclusively unhappy over long periods.  A similar response can occur with love/hate.  Also, one's subjective feelings are more volatile and often opposite to those perceived by others.

This talk is available as a PowerPoint Presentation and in HTML format.
A condensed version in PowerPoint is also available.


Is it Noise, or is it Chaos?

Many quantities in nature fluctuate in time. Examples are the stock market, the weather, seismic waves, sunspots, heartbeats, and plant and animal populations. New tests are being developed to determine whether such fluctuations are random or whether they are examples of deterministic chaos, in which case there may be a simple underlying cause. If evidence of chaos is found, it may be possible to improve the short-term predictability. Methods for distinguishing chaos from noise will be described, and examples will be shown.

A version of this talk is available as a PowerPoint Presentation.
This talk is based on examples from the Chaos Data Analyzer program.


Simple Chaotic Systems and Circuits

Many new chaotic systems with algebraically simple representations will be described.  These systems involve a single third-order autonomous ordinary differential equation (jerk equation) with various nonlinearities.  When the nonlinearities are piecewise linear, they can be easily implemented electronically in circuits with diodes and operational amplifiers.  Several new simple and robust chaotic electrical circuits will be described and demonstrated.

This talk is available as a PowerPoint Presentation and in HTML format.
A version given for the New England Complex Systems Institute is available in PowerPoint and HTML format. See also a video clip from that presentation.
A version given for the 2004 Gordon Conference on Physics Research and Education: Classical Mechanics and Non-linear Dynamics is available in PowerPoint format.


Elegant Chaos: Algebraically Simple Chaotic Flows

The quest for algebraically simple chaotic systems began fifty years ago when Ed Lorenz discovered chaos in a simple model of atmospheric convection. By now, dozens of chaotic systems, some even simpler than the celebrated Lorenz attractor, have been identifed and studied. This talk will describe a 20-year effort to find even simpler chaotic systems as summarized in a recently published book by the same title in which 280 examples, most of which have never been previously published, are cataloged. Some new chaotic electrical circuits will also be described and demonstrated.

Ref: http://www.worldscibooks.com/chaos/7183.html
This talk is available as a PowerPoint Presentation.


The Science of Complexity

Many interesting phenomena arise from the interaction of a large number of individual components. Examples include turbulent fluids, the stock market, the ecosystem, and the brain. Recent advances in computing permit such systems to be studied using simple models with a large number of variables. These models exhibit many of the general properties of natural complex systems such as chaos, self-organization, evolution, adaptation, and artificial intelligence. Some of these models will be described, and their dynamical behavior will be illustrated with computer animations.

This talk is available as a PowerPoint Presentation and in HTML format.


Self-Organization - Nature's Intelligent Design

Complex patterns are common throughout nature, from the distribution of the galaxies in the Universe to the organization of neurons in the human brain. It is generally assumed that such complex structure must have a complex cause, but it may be that the patterns spontaneously arise through the repeated application of simple rules. This talk will provide examples of self-organization in nature and will describe six simple computer models that can replicate the features of these patterns. The models typically produce fractal spatial structure and chaotic temporal dynamics characterized by power laws and unpredictability, even when the models are simple and purely deterministic. The work has application to fields as diverse as physics, ecology, political science, economics, sociology, and art.

This talk is available on video (2008 talk).
This talk is available on video (2013 talk).
This talk is available as a PowerPoint Presentation and in HTML format
and in an expanded PowerPoint version used at a SCTPLS workshop in July 2009.


Chaotic Dynamics on Large Networks

  Many systems in nature are governed by a large number of agents that interact nonlinearly through complex feedback loops. When the networks are sufficiently large and interconnected, they typically exhibit self-organization and chaos. This talk describes the results of computer simulations of such large networks and shows the conditions under which chaos can be expected for an unweighted network of ordinary differential equations with sigmoidal nonlinearities and unit coupling. The largest Lyapunov exponent is used as the signature and measure of chaos, and the study includes the effects of damping, asymmetries in the distribution of coupling strengths, network symmetry, and sparseness of connections. Minimum conditions and optimal network architectures are determined for the existence of chaos. The results have implications to the design of social and other networks in the real world in which weak chaos is desired or as a way of understanding why certain networks might exist on “the edge of chaos.”

This talk is available as a PowerPoint Presentation.


Chaos in Easter Island Ecology

Easter Island in the South Pacific, with an area the same as the city of Madison, WI is one of the most remote inhabited spots in the world, located over 2000 km from its nearest inhabited neighbor. As such, it offers an opportunity to study a relatively simple ecology with possible global implications. Its human population is thought to have grown to a peak of about 10,000 during the millenia leading up to the year 1700, and then to decline to a mere 110 by the year 1877. The usual explanation is that the inhabitants overconsumed the abundant palm trees that were used for cooking, housing, fishing boats, and for transporting the large stone statues for which the island is famous, leading to starvation, war, disease, and possibly cannibalism. In this talk, I will describe some recent simple mathematical models for the rise and fall of their civilization and will show that one of these models has chaotic solutions, not previously known.

This talk is available as a PowerPoint Presentation.


A Physicist's Brain

The human brain is perhaps the most complex object in the entire Universe, capable of remarkable feats. Although much progress has been made in understanding its composition and operation, much about it remains a mystery. This talk will describe a very simple model of the brain that, like a digital computer, is capable of universal computation, in principle solving any problem with the right program. The model brain behaves chaotically, following definite rules, but exhibiting a degree of unpredictability and novelty. A program (p-brain) will be demonstrated and trained in real time to produce aesthetically appealing visual art, many examples of which will be shown.

This talk is available as a PowerPoint Presentation.


Is Global Warming for Real?

Probably, but if you're a skeptic, this talk will not likely convince you. What I will do is use ice core data from Greeland and ice cover data from Lake Mendota in a case study of various time-series analysis techniques, both linear and nonlinear. I will show the limitations and weaknesses of the various techniques and the wide variety of predictions that they make. I will show the chaotic output of an artificial neural network trained on the data and demonstrate a new computer program that others can use to make time-series forecasts in fields as diverse as meteorology, ecology, and finance. Finally, I will make a prediction of when the ice will thaw on Lake Mendota.

This talk is available as a PowerPoint Presentation.


Lessons Learned from 19 Years of Chaos and Complexity

As we conclude the nineteenth year of the Chaos and Complex Systems Seminar, I would like to discuss some of the lessons I have learned from listening to over 500 talks, from my own research, and from the many books and articles I have read on the subject. This will be a rather personal and subjective talk and thus probably controversial. In particular, I will argue that the feedback, nonlinearities, and self-organization that characterize all real dynamical systems are more likely to ameliorate the dire consequences that others have predicted than to exacerbate them as so many fear. This is not a prediction that our problems will vanish or an argument for ignoring them. On the contrary, our choices and actions are the means by which society will reorganize to become even better in the decades to follow, albeit surely not a Utopia.

This talk is available as a PowerPoint Presentation and in condensed written form.


Magnetic Fusion - Energy of the Future

It has been known for half a century that almost unlimited energy is locked inside the nucleus of hydrogen and other light elements that are abundant throughout the world. It has been proposed to extract that energy using a new type of reactor that employs intense magnetic fields and special gases called "plasmas" that are heated to hundreds of millions of degrees. We now stand on the brink of building such fusion reactors, which would in essence be miniature stars. The problems and the prognosis will be discussed.

A variant of this talk is available as a PowerPoint Presentation and in HTML format.


The Wonders of Physics

Much has been written about the problem of scientific literacy among students and adults in the United States. In 1984 the University of Wisconsin began a program called "The Wonders of Physics" in which entertaining presentations involving exciting physics demonstrations are taken to schools and to other public settings in an attempt to generate interest in science. This program has reached over 70,000 people and is available on video. The goals and nature of the program will be described.

This talk is available as a PowerPoint Presentation and in HTML format.
Actual presentations of The Wonders of Physics can also be arranged.


Seasons, Tides, and Phases of the Moon

Many recent studies have documented the problem of scientific illiteracy.  A short video (A Private Universe) will illustrate the extent of misunderstanding of basic astronomical facts by even well-educated adults.  In an animated slide presentation, a number of simple questions about the motion and properties of the Earth, Sun, and Moon will be asked and answered.  Even professional astronomers may be surprised by some of the answers.

This talk is available as a PowerPoint Presentation and in HTML format.
See also a handout for teachers in MS-Word format.


Radio Communications

Most of us spend much time listening to the radio and watching television, and we tend to take them for granted.  This talk will discuss the basic physics behind the production, transmission, and reception of radio waves, including properties of the waves, choice of frequencies, types of modulation, antennas, and the role of the ionosphere in long range propagation.  The operation of television and radar will be briefly described.

This talk is available as a PowerPoint Presentation and in HTML format.


Anti-Newtonian Dynamics

This talk describes a world in which Newton’s first and second laws hold, but Newton’s third law takes the form that the forces between any two objects are equal in magnitude and direction. An example of a system to which such a model might apply is a fox chasing a rabbit. The dynamics for such a system exhibit curious and unfamiliar features including chaos for two bodies in two spatial dimensions.

This talk is available as a PowerPoint Presentation.


Other Talks

These are more advanced or specialized talks, some of which are variants of the popular lectures above for particular audiences, or talks prepared and/or given by my collaborators.

Biographical Synopsis - J. C. Sprott

Julien Clinton Sprott, born September 16, 1942 in Memphis, Tennessee, received his B.S. in physics from the Massachusetts Institute of Technology in 1964 and his Ph.D. in physics from the University of Wisconsin in 1969. He worked at the Oak Ridge National Laboratory for several years before returning to the University of Wisconsin to join the physics faculty in 1973. In 2008, he became an Emeritus Professor of Physics.

His research has been primarily in the area of experimental plasma physics and controlled nuclear fusion. In 1989 his interests turned to nonlinear dynamics, chaos, fractals, and complexity. He has authored or coauthored over 400 scientific papers in these and related fields.

Professor Sprott has written a number of books, including "Introduction to Modern Electronics", "Numerical Recipes and Examples in BASIC," "Strange Attractors: Creating Patterns in Chaos," "Chaos and Time-series Analysis," "Images of a Complex World: The Art and Poetry of Chaos," "Physics Demonstrations: A Sourcebook for Teachers of Physics," and "Elegant Chaos: Algebraically Simple Chaotic Flows."  He has produced dozens of educational videos and has given his popular presentation of "The Wonders of Physics" over 250 times to a total audience of about 100,000. He has produced several commercial educational software programs, one of which won the first annual "Computers in Physics" award for innovative software in physics education.

He received the John Glover Award from Dickinson College, the Van Hise Outreach Award for Excellence in Teaching from the University of Wisconsin-Madison, a Lifetime Achievement Award from the Wisconsin Association of Physics Teachers, and a Distinguished Service Award from the UW Physics Department for his work in public science education. He is a fellow of the American Physical Society and a member of Sigma Xi, the American Association of Physics Teachers, and the Society for Chaos Theory in Psychology and the Life Sciences.


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J. C. Sprott