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.
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.
- Ecology
- Self-Organized Criticality of Landscape Patterning
- Self-Organization in Forest Evolution
- A Case Study for Self-organized Criticality and
Complexity in Forest Landscape Ecology
- Predator-Prey models of Rabbits, Trees, and Romance
- Chaos and Self-Organization in Spatiotemporal Models of
Ecology
- Competition with Evolution in Ecology and Finance
- Chaos in Low-Dimensional Lotka-Volterra Models of
Competition
- Mathematics
- Complex Behavior of Simple Systems
- Dynamics of High-Dimensional
Systems
- Simple Models of Complex Chaotic
Systems
- Multistability and Hidden Attractors
- Plasma
- The UW Plasma Physics Group
- History of UW Plasma Physics
- Memorial to Thomas W. Lovell
(1946-2005)
- University of Wisconsin -
Madison
- Psychology
- Memory across Eye-Movements: 1/f Dynamic in Visual
Search
- Ups and Downs: A Dynamical Systems Model of Human
Affective Fluctuations
- Cyclic Dynamics in Relentless Aging (70^{th }year
birthday party)
- The Wonders of Physics
- Twentieth Season
Celebration (2003)
- World Year of Physics
(2005)
- Celebration of New Lecture
Hall (2006)
- Physics of Water (2007)
- Physics of the Cosmos (2009)
- Physics of Sports (2010)
- Physics of the Arts (2011)
- Physics of The Wisconsin Idea
(2012)
- Thirtieth Season Celebration
(2013)
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.
Publicity Photo (or color version)
Detailed Vita
Calendar
J. C. Sprott