Chaos

Course No. 1333
Professor Steven Strogatz, Ph.D.
Cornell University
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Course No. 1333
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Course Overview

It has been called the third great revolution of 20th-century physics, after relativity and quantum theory. But how can something called chaos theory help you understand an orderly world? What practical things might it be good for? What, in fact, is chaos theory? "Chaos theory," according to Dr. Steven Strogatz, Director of the Center for Applied Mathematics at Cornell University, "is the science of how things change." It describes the behavior of any system whose state evolves over time and whose behavior is sensitive to small changes in its initial conditions.

The 24 lectures of Chaos take you to the heart of chaos theory as it is understood today. Taught by Professor Strogatz, an award-winning Ivy League professor and a scientist described by Nature magazine as "one of the most creative biomathematicians of the past few decades," Chaos introduces you to a fascinating discipline that has more to do with your everyday life than you may realize.

A Revolutionary Way of Thinking

Surprisingly, you have already encountered chaos theory before, although you might not have recognized it at the time. From the flapping of a butterfly's wings to the dripping of a leaky faucet, chaos theory draws a wealth of unordinary insight from the most ordinary of occurrences.

Chaos theory affects nearly every field of human knowledge and endeavor, from astronomy and zoology to the arts, the humanities, and business. It can:

  • help analysts understand price fluctuations in the stock market,
  • ensure a smooth flow of data traffic on the Internet, and
  • show insurance companies how to manage the risks of natural catastrophes.

This course shows you the importance of this revolutionary field and how it has helped us come closer than ever to solving some of life's mysteries. Today, the underlying mathematics of science's major unsolved problems—including the nature of consciousness, the origin of life, and cancer—are essentially nonlinear; express any of these problems as a mathematical system and you learn that the whole may be either more or less than the sum of its parts.

In its ability to tackle bewilderingly complex problems, chaos theory has revolutionized the way we perceive the world around us. It allows scientists to reach beyond a dependency on the analytical limitations of the deterministic, "clockwork" universe that was the legacy of thinkers like Galileo, Kepler, and especially Newton.

Throughout the lectures, Professor Strogatz makes the case for why chaos theory marks such a radical departure from traditional science:

  • It asks unusual questions at the everyday scale of human life.
  • It shifts the focus off the laws of nature and onto their consequences.
  • It uses the computer not as a calculating tool but as a means of amplifying intuition.
  • It does not reduce complex problems into their separate parts but puts the parts back together to help understand the whole.
  • It is radically interdisciplinary in an era of increasingly specialized disciplines.
  • It paints a topsy-turvy picture of the world in which simple systems can show complex behavior.
  • It is a scientific field in which change came about suddenly.

Follow the Exciting Story of Chaos

As you delve into this ever-evolving field, you learn the surprising tale of how chaos theory was discovered—a story that Professor Strogatz likens to a detective novel filled with twists and turns.

First glimpsed by the French mathematician Henri Poincaré, the notion of chaos theory was lost for nearly a century before being rediscovered—almost accidentally. It was revived by a mathematically oriented meteorologist named Edward Lorenz, whose development of the butterfly effect (the extreme sensitivity of a chaotic system to tiny changes in its initial conditions) had little impact until the 1970s and 1980s, when the wave of chaos theory finally crashed onto the shores of the scientific community.

As you follow the story of chaos theory's development, you approach the core ideas of chaos in the same way the world's greatest thinkers, grounded in their historical contexts, once did. This story not only helps you understand the fundamentals of this field, but it also helps you appreciate the extraordinary intellectual feat that chaos theory represents.

Learn Chaos Theory Visually

This course offers you a unique opportunity to get an expert's instruction on the field of chaos theory and is one of the only places outside the halls of academia where you can follow along with detailed computer graphics—specifically developed for this course—as visual aids.

"For understanding these core concepts [of chaos theory], pictures turn out to be much more powerful than formulas," notes Professor Strogatz. Forgoing a heavy reliance on advanced math, he uses clear and powerful computer graphics to clarify chaos theory's core concepts.

A large portion of the course explores the intimate relationship between chaos theory and fractals: shapes or processes whose structures repeat ad infinitum such that the tiniest parts resemble the original whole. You see how fractals are unique from more commonly known shapes like circles and cubes and how they can be used to describe a variety of processes and phenomena like the jagged coastline of Norway or the drip paintings of Jackson Pollock.

Find the Unordinary in the Ordinary

Professor Strogatz's expert guidance lays bare the complexities of chaos theory in a way that any interested layperson can understand. With the insights he provides in Chaos, news stories about key scientific discoveries and new directions in research take on a fresh importance.

Professor Strogatz is a teacher repeatedly honored by institutions and students alike. During his tenure at the Massachusetts Institute of Technology, he received the E. M. Baker Memorial Award for Excellence in Undergraduate Teaching, the university's only institute-wide teaching prize selected and awarded solely by students. In 2007, he received a lifetime achievement award for the communication of mathematics to the general public from the Joint Policy Board for Mathematics, which represents the four major American mathematical societies.

Whether charting the exciting history of the field, focusing on fractals as "the footprints of chaos," or journeying to the frontiers of chaos research, this course shows you new ways to think about and view the world around you.

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24 lectures
 |  Average 30 minutes each
  • 1
    The Chaos Revolution
    Chaos was once ignored by traditional science but is now both a pop sensation and a tremendously important field. But what is the science of chaos and why is it revolutionary and important? x
  • 2
    The Clockwork Universe
    The scientific revolution launched by Galileo, Kepler, and Newton left a great legacy: the idea of an orderly universe ruled by mathematical laws. But is there something disquieting in the idea of a vast, impersonal, clockwork universe of determinism with no room for chance? x
  • 3
    From Clockwork to Chaos
    By the late 19th century, three cracks appeared in determinism's foundations: relativity, quantum mechanics—and chaos. The "three-body problem" was considered the mathematical challenge of the era, and its solution, involving a still-unimagined chaos, eluded some of mathematics' greatest minds. x
  • 4
    Chaos Found and Lost Again
    Henri Poincaré's groundbreaking work on the three-body problem implied that a system governed by deterministic laws could still be unpredictable; chaos had crept into the clockwork. Although Poincaré invented a new, visual way of thinking about the mathematics involved, his brilliant discovery was quickly forgotten. x
  • 5
    The Return of Chaos
    For 70 years, chaos remained a scientific backwater. The calm ended with a thunderclap from a man fascinated by storms and weather. You see how Edward Lorenz discovered chaos in a model of weather patterns that allowed him to happen upon the "butterfly effect." x
  • 6
    Chaos as Disorder—The Butterfly Effect
    The butterfly effect—the extreme sensitivity of a chaotic system to tiny changes in its initial conditions—has become part of popular culture but is frequently misunderstood. You begin to understand not only its importance and power but also its limitations. x
  • 7
    Picturing Chaos as Order—Strange Attractors
    Your introduction to chaos has highlighted its unpredictable, random side, as exemplified by the butterfly effect. But there is also an amazing order inherent in chaos, and you learn how this can be visualized through the infinitely complex image known as a "strange attractor." x
  • 8
    Animating Chaos as Order—Iterated Maps
    If a strange attractor is analogous to an image created through time-lapse photography, Lorenz's "iterated map" might be the product of a series of strobe-light photographs. But despite its profound implications, Lorenz's discovery failed to attract the scientific community's notice. x
  • 9
    How Systems Turn Chaotic
    By the 1970s, there was an unprecedented convergence of disciplines. Researchers in mathematics, ecology, and fluid mechanics found themselves asking the same question: How does an orderly system suddenly turn chaotic? You see how a famous iterated map known as the logistic map reveals the most basic route. x
  • 10
    Displaying How Systems Turn Chaotic
    You deepen your understanding of the logistic map with the icon of chaos known as the orbit diagram. Its breathtaking imagery amounts to a Rosetta Stone for making sense of certain forms of chaos in the natural world. x
  • 11
    Universal Features of the Route to Chaos
    In 1978, physicist Mitchell Feigenbaum made a stunning breakthrough, showing that the logistic map displayed universal features so generic that they must also occur in nature, even though no laws of nature are built into it. You begin to understand how such universality arises. x
  • 12
    Experimental Tests of the New Theory
    In the early 1980s, painstaking experiments on such disparate systems as swirling fluids, electronic circuits, and oscillating chemical reactions confirmed the predictions of chaos theory. Overreaching by some advocates, however, has provoked a backlash of skepticism to this day. x
  • 13
    Fractals—The Geometry of Chaos
    The pioneers of chaos were bewildered by the fantastic shapes they encountered while trying to visualize chaos. In the first of several lectures devoted to these intricate shapes—now called fractals—you learn why they are so inextricably connected to chaos. x
  • 14
    The Properties of Fractals
    You are introduced to the two most distinctive properties of fractals—inexhaustible structural richness and "self-similarity," or the resemblance of the parts to the whole—before learning how the science of fractals came into being and its situation in the broader scientific landscape. x
  • 15
    A New Concept of Dimension
    Using some idealized geometric examples, you learn how to define the dimension of a fractal—discovering that the usual categories of one-, two-, or three-dimensional usually do not apply, and that fractals are so convoluted they fall somewhere in between, such as 1.26-dimensional! x
  • 16
    Fractals Around Us
    Fractals are not merely static geometric shapes but also can represent erratic processes in time, such as fluctuating stock prices, Internet data bursts, or earthquakes. You learn that their gyrations are wilder and more frequent than conventional statistical methods would predict and make their management more complex. x
  • 17
    Fractals Inside Us
    From lungs to nervous systems to the nutrient supply systems of plants, all living things are built from fractal networks. You examine this geometry of life, including a recent theory that invokes fractal architecture to explain one of the most comprehensive laws in biological science. x
  • 18
    Fractal Art
    This lecture shows you some of the manifestations of fractals in art, including the controversial drip paintings of Jackson Pollock. Some have suggested that they contain fractal characteristics that changed over the course of his career in a very systematic way. x
  • 19
    Embracing Chaos—From Tao to Space Travel
    Does chaos have practical applications? Because tiny nudges to a chaotic system can have potent effects, these systems are exceptionally responsive. You see the advantages of harnessing chaos in the dramatic story of how a NASA mathematician "surfed" the gravitational field to salvage a Japanese lunar mission gone wrong. x
  • 20
    Cloaking Messages with Chaos
    Although the feasibility of encrypting electronic messages by cloaking them in chaotic "noise" has been verified in real-world tests, questions remain. Could an eavesdropper crack the chaos? This lecture shows you what such an application could mean in a world of growing concerns about cyberterrorism, national security, and cell phone and Internet privacy. x
  • 21
    Chaos in Health and Disease
    Building on decades of biological research, chaos theorists have been asking questions about the dynamics of bodily rhythms. Can the mathematics of chaos help predict an epileptic seizure? Quell or prevent cardiac arrhythmias? Perhaps most controversially, can chaos in the body ever be a sign of health rather than of sickness? x
  • 22
    Quantum Chaos
    Can chaos theory coexist with quantum theory? Can it survive the descent to the strange world of the atom, where Newtonian trajectories dissolve into a haze of quantum probability waves? You see how scientists reconcile two radically different views of reality. x
  • 23
    Synchronization
    Large, complex systems having many interacting parts often display a remarkable capacity for organizing themselves, with their individual parts becoming synchronized. This lecture shows you systems as diverse as pendulum clocks, fireflies, heart cells, and menstrual cycles and takes you inside the opening-day swaying of London's Millennium Bridge. x
  • 24
    The Future of Science
    You review what you've learned and examine the future role of chaos theory. In a world where most of the major unsolved issues facing science—including cancer, consciousness, the origin of life, and AIDS—involve fundamentally nonlinear systems, chaos theory can be a crucial first step toward their solution x

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Your professor

Steven Strogatz

About Your Professor

Steven Strogatz, Ph.D.
Cornell University
Professor Steven Strogatz is the Jacob Gould Schurman Professor of Applied Mathematics and Professor of Theoretical and Applied Mechanics at Cornell University. He graduated summa cum laude from Princeton University with a B.A. in Mathematics and received his Ph.D. from Harvard University. Before joining Cornell University in 1994, Professor Strogatz was a faculty member at MIT. Professor Strogatz's books include Nonlinear...
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Reviews

Chaos is rated 4.6 out of 5 by 108.
Rated 4 out of 5 by from Fascinating stuff ! If chaos theory had come up in conversation prior to my viewing this course, I would have been rather lost! Now, while I am very far from being an expert, I could take part in a discussion on the subject in a modest way. Chaos theory has applications in many disciplines, even finance, philosophy and politics. Dr Strogatz is easy to listen to, makes his points clearly, has no weird tics. Step by step, he goes through a logical explanation of chaos theory, maintaining a brisk pace. You'll learn quickly that "chaos" does not mean "randomness". The great scientist Dr Edward Lorenz defined chaos as: When the present determines the future, but the approximate present does not approximately determine the future. Newton figures prominently in this course, but you don't have to be an expert in physics or mathematics to understand and follow the lectures; high-school algebra is enough. F=MA and "the butterfly effect" will become familiar to you if you don't already know about them. I enjoyed learning about those mystifying fractals in the final lectures! Several reviewers advise running this course twice or more, and I endorse that strongly. Happily, of course, you can choose specific lectures to re-run if only certain areas need reinforcement. Thoroughly recommended.
Date published: 2013-04-08
Rated 5 out of 5 by from Why you need this course "Chaos" may seem a threatening subject. But understanding the principles will have a revolutionary benefit for the student economically, intellectually, and it will reinforce you spiritually. You will wonder why you have not been taught to think about the world like this before. The graphic demonstrations are absolutely essential to the course and the guide is excellent. Appreciation of the rationale behind differential equations is helpful but not necessary. However, a math phobic will probably have difficulty. There are so many good things about this course. Strogatz nails Newtonian/Enlightenment limitations in his discussion of the 2-body problem. Lecture 8 uses photography to cleverly illustrate the mechanics of differential equations, strange attractors, and iterated maps. Strogatz is mindful of the limitations of current chaos solutions [lecture 12's "thermometer of complexity" is extraordinarily helpful]. By Lecture 14, you will clearly understand the difference between irregularities in time [chaos] and irregularities in space [fractals]. Lectures 16 & 17 discuss real world examples. I loved the outrageous improbabilities stock market crashes impose on a Bell curve model! The remaining lectures are clear sailing with less vital discussions of recent applications. Along the way, you will understand on why understanding that the internet doesn't act like voice traffic is important. You will better analyze earthquake predictions, the weather, and why insurance company payouts are critical data. Also exciting is Belbruno's salvage of a Japanese moon mission by combining 3 body chaotic solutions to gravity wells. This sounds intimidating but Strogatz easily shows how it was done, opening the way to low cost space travel. After showing why quantum mechanics and chaos should not co-exist, Strogatz unites them. The Rieman hypothesis of quantum chaos was an intellectual high but could be skipped if over-whelming. Cons, none of which diminish the importance of the course: 1. Positive feedback loops were nearly avoided. For example, known biochemical positive feedback gateways are an important basis for the non-linearity of heartbeats and neural firing discussed in the lectures. 2. The F-16 fly-by-wire example needed to show how its computers respond to predictable non-linearity rather than simple randomness, ie: what is its periodic behavior? 3. In lecture 19 (pp 85-6) an unneeded jab at 70% of his audience occurs. Here Strogatz oddly comments on creation stories: "...the void of the Hebrews, the malevolent disorder of the Christians...". He is factually wrong: both the Hebrews and the Christians have exactly the same books in their creation story. His quote from Lao Tzu might indicate an interest in Taoism because it finds order behind chaos. Tzu's quote ends: "I do not know its proper name but will call it Tao". The Pauline "unknown god" argument that might resolve Tzu's question wherein the ordering entity is all knowing, not unknown. If you are going there, please clarify "malevolence". No student should be allowed to graduate from university without understanding some version of this course. Lighthill's apology for misleading the public about the determinism of systems satisfying Newtonian dynamics needs to be etched in stone at the entrance to every university.
Date published: 2013-02-11
Rated 5 out of 5 by from Bravo! One of the best, or, possibly, the best out of all TC courses I listened to. Difficult concepts presented in engaging manner. Science teaching at its best! Bravo!
Date published: 2013-01-25
Rated 5 out of 5 by from Experience the "butterfly effect" for yourself! Chaos is the 18th course that I have purchased from “The Great Courses” and the 17th one that I have thoroughly enjoyed. Watching the content as presented by Professor Strogatz was captivating, so much so that I watched many of his presentations 2 or 3 times. That is how enjoyable I found him to be and the way he was able to explain the content in a reachable manner held my interest from one lesson to the next. He didn’t lecture me; he took me on a journey. If you don’t have a rigorous mathematical background, then you are in good hands. The graphs, diagrams, computer simulations and hands-on demonstrations make clear the material being taught. His child-like enthusiasm (and I mean that in the most complementary way) was infectious and kept ME excited to want to learn more. He is certainly an important participant and pioneer in this third great revolution of 20th-century mathematics and physics, the science of Chaos Theory. Yet you can still see awe and wonder in him during his presentations. It took the first few lectures for me to get used to his style of presentation but once I did, it was full speed ahead. Each lesson was lucid. You may not even realize that he is a mathematician given how easy it is to “get” what he is saying. His comments were insightful throughout as he explained the dynamics of chaotic systems. Many times I found myself turning my head and letting out an interested “really!” In a nutshell, chaos theory is defined at the science of how things change, describing the behaviour of any system whose state evolves over time and whose behaviour is sensitive to small changes in its initial conditions, the so-called “butterfly effect”. The practical applications of chaos theory amazed me, as did the fact that so many real world happenings in so many different disciplines can be described and analyzed using chaos. The practical things that chaos applies to is so diversified yet there are interdisciplinary commonalities between these disciplines. Chaos theory affects nearly every field of human knowledge and endeavour, from astronomy to population ecology to the arts and business. It is a member of the spectrum between order and randomness. You are told that chaos and randomness are not the same and shown in a (visual) manner that makes the concepts clear. At times we feel like we are listening to a mystery story as Strogatz narrates how the notion of chaos theory was first glimpsed by the French mathematician Henri Poincare, then lost for nearly a century before being rediscovered, or rather revived, by a meteorologist named Edward Lorenz. It was through Lorenz that the term “butterfly effect” came in to being, despite the fact that it almost became the “seagull” effect. I hope that Professor Strogatz makes a volume 2 of this course, digging deeper into the mathematics and physics of chaos. He has a few books available and I have 3 of them on my wish list. By the end of lesson 24 you will understand why he is repeatedly honoured by institutions and students alike. I highly recommend this course. It has made me a more interested and interesting person!
Date published: 2012-09-26
Rated 4 out of 5 by from Chaos This course would greatly benefit by the inclusion of some more math, either in the course itself or as an appendix in the book. The professor's attempt to make the subject understandable to those with a limited math background is admirable, but for others the qualitative and graphic explanations could be frustrating. Perhaps a separate, accompanying booklet at a more advanced level would also be useful. Having said this, the course is to be recommended, even as an introduction for those who wish to continue at a more advanced level.
Date published: 2012-06-16
Rated 5 out of 5 by from Your View of the World will be Altered I have just completed the 24 lecture series titled Chaos by Professor Steven Strogatz. The course is a remarkably lucid introduction to a very complex subject. Professor Strogatz is able to clearly present the mind-blowing subject matter without calculus and only a bit of algebra. I was so impressed that I purchased two of his books for further study. I highly recommend this course! Maybe God is mathematics.
Date published: 2012-05-31
Rated 4 out of 5 by from The Clockwork Universe takes another serious blow. As happened before with Relativity and Quantum Mechanics, Newton's clockwork universe takes another serious blow with Chaos, the subject of this fascinating course. Whether this field of study should be called Chaos, Chaos Theory, or Chaos Science is something you will have to decide after watching the course. Seemingly random results, but yet predictable. Is this an artifact of tiny computational round-off errors in digital computers, magnified by enormous numbers of iterations of formulas? If so, why does Chaos theory describe so many natural phenomenon - from weather to the layout of blood vessels, etc.? You can decide for yourself. Dr. Strogatz does a wonderful job describing current thinking about what Chaos Theory is today. He has quite a lot of contagious enthusiasm about its applications, and has wonderful and striking graphics to amaze us. Be prepared to have the envelope of your Common Sense expanded. This course should probably be viewed soon after watching the "Understanding Complexity" Teaching Company course, to which it is somewhat related.
Date published: 2012-04-25
Rated 5 out of 5 by from Chaos I watch Teaching Company videos while exercising. Sometimes I would find myself stopping my exercise routine and simply watching and listening with rapt attention to Dr. Strogatz's enthusiastic explanations of mind bending phenomena. Chaos is deterministic? I didn't know that. I give this course my highest recommendation for anyone wishing to challenge their thinking and expand their universe of thought.
Date published: 2012-03-18
Rated 5 out of 5 by from Organized Chaos WOW! This course was so fun that I hated for it to end. Dr. Strogatz presents this material clearly, personally and understandably. His enthusiasm is contagious---it's fun to see him get really excited, almost giddy, about an idea he's presenting. I learned so much from this course that I would encourage you to give it go. It took me 6 months to finish but only because I researched the people mentioned in the course, read all of the books by James Gleick and read Sync and the Calculus of Friendship by Dr. Strogatz himself. I started reading "Fly Me to the Moon" this week. As a result of this class, I not only learned some very mentally stimulating ideas, but I read books I had not heard of, conducted some very fun experiments on chaos, bought a fleet of metronomes to play with chaos and have employed much of what I learned to my work in business. The return on investment has been huge for me. Chaos is probably not what you think it is and it is probably far more applicable to your life than you imagine it could be. Thank you for a great course and a very fun ride! I will continue to play with my metronomes and my conduct experiments with chaos in fluids! Chris Reich, BizPhyZ
Date published: 2012-03-17
Rated 4 out of 5 by from Excellent Overview This course gives an overview of Chaos Theory for people without a mathematical background. In doing so many of the analogies used; akthough good; suffer from a lack of clarity that the math would have provided. A math-intensive version of this course would be an invaluable resource.
Date published: 2012-01-14
Rated 4 out of 5 by from Order Out of Chaos I recommend this course to all students, whether their principal interests are in the sciences or not. The idea that chaos is increasingly a concept along the spectrum between order and randomness is one all intellectually inclined people ought to explore. And this course is a wonderful way to explore how that idea developed in science over the past 50 years. Some students will believe that these newly discovered patterns of order that emerged from a chaos that previously seemed utterly "chaotic" are further signs of God's handiwork. Others will disagree. But I believe that all will marvel at how and in what ways these patterns of order were discovered in chaos and how they appear and play out. Further, I believe that all will agree with the professor that it is quite exciting to be optimistic to think that we may yet find new answers, new dimensions of order, as science begins to tackle matters even closer on the spectrum to what we now deem randomness. The professor is at his best in showing the many, often quite beautiful, ways in which chaos plays out in science, art, and our everyday lives. Professor Strogatz seems truly and appealingly amazed at these incredible manifestations, though he's made a long career of studying them. Trust me - you will be stunned and delighted, too. I'm glad the professor spends a good bit of the latter half of the course discussing the possibilities that chaos theory might play a role in helping solve major challenges in science that confront us in modern life. I suspect he's right, or at least reasonable to hypothesize. I certainly understand his excitement that the science he helped pioneer might even grow in relevance over future years. It is, however, in these final lectures where the professor weakens. Perhaps concerned about how far his lay audience can go with him or perhaps due to time limitations, he glosses over the details involving the connection between chaos theory per se and the associated science in these many areas. This leads to the feeling that the professor is either just skimming the surface or engaging largely in wishful thinking about the connection and solutions. In either case, Strogatz should have been less ambitious to try to cover the waterfront and instead gone into far deeper detail in one or two discrete areas, showing explicitly how solutions are being built out of the science on chaos that he had taught in previous lectures. This would have helped create greater order in the course (so to speak!), solidified the student's learning of the science itself, and better connected chaos theory to new uses in science. Having expressed that concern, however, I remain a big fan of this course and recommend it strongly.
Date published: 2011-12-27
Rated 5 out of 5 by from Chaos Is Totally Cool I have purchased many science courses from the Teaching Company, and the Chaos course is definitely in my top three. It is both the content and the presentation style of Professor Strogatz that impresses me. I am on my third viewing and I get more out of it each time. I'll divide this review into two parts. First, I recommend this course because of the content. Make no mistake, this is a challenging subject. The professor starts out with a clear foundation of what chaos is, and gives a brief and fascinating history of its origins. He also describes very clearly how chaos fits in with the larger discipline of physics. I am personally glad he does not demand a rigorous math background to be understood. He emphasizes visuals, including graphs, diagrams and hands-on demonstrations like the double-pendulum phenomenon. And the video footage of the near collapse of London's Millennium Bridge is totally cool. Secondly, I recommend this course because of the professor's presentation style. He is very enthusiastic and excited about so many of the strange and wonderful phenomena. His discussion on the "music of the primes" is a real standout. It's refreshing to witness awe and wonder from a top-notch academic. The mystical and mysterious aspects of chaos, self-organization, and fractals are front and center. Overall, I think a wide range of people will find this course interesting and approachable, and come away shaking their heads at the pervasive "order within disorder" embedded in the world of chaos.
Date published: 2011-08-24
Rated 5 out of 5 by from Better the 2nd time around I don't know what changed, exactly, but the SECOND time I watched this course, I totally loved it. Maybe I knew more math or had more physics under my belt--something like that. The DVDs just sat on a shelf, so I know they didn't change... The first time I watched this, I thought the course was pretty blotto and I found the instructor to be a bit odd. Then I watched it again after, perhaps, 9 months to a year had passed. I was knocked out! This course is simply jammed with dynamite information. And the instructor isn't odd--he is just meticulous in his presentation, & he is, at root, a mathematician. You have to cut mathematicians some slack. He is a very good instructor once you get used to his style, and he really knows his stuff. Chaos theory is hard to get your head around the first time you hear about it--well, it was for me. So give this course a few times to sink in. It is well worth the effort. (Prof. Strogatz wrote a wonderful book, really sweet, called something like "The Calculus of Friendship," about his long friendship with his high school calculus instructor. Neither man realized how important their correspondence had become to each of them. (They traded math problems, but more and more they traded personal info, too). When Strogatz divorced his first wife, the old teacher supported him through it--& now Strogatz is happily remarried. When the old teacher finally retired, Strogatz visited him & kept him apprised of life at Cornell & new thinking in math, etc. It was a brief but touching account of a friendship that started between a teenager & his math teacher but became something much more. It made me like Strogatz a lot . But I read the book AFTER I decided the course was great.)
Date published: 2011-07-13
Rated 3 out of 5 by from I'm not able yet to review this course fully, as I stopped watching after several lectures. Not that the material wasn't engaging--but, in contrast to the other reviewers, I found the professor's delivery irritating. Unlike virtually all other professors I've watched in TCo lectures, this one seems awkward in his presentation style--often pausing overly long, or at odd moments, as if to swallow nervously and regather his courage to carry on in front of the (film) audience. Perhaps I've been spoiled by other lecturers with smoother styles ; ) I may give the course another go, though, simply because so many other reviewers loved it.
Date published: 2011-06-03
Rated 5 out of 5 by from An Engaging Introduction to Chaos Strogatz is an excellent lecturer and presents the material clearly with minimal diversions into difficult mathematics. There is just enough math to show that there really is something to this! This course clearly defined the subject and presented some of its most startling discoveries in a concise way. My only complaint, if you could call it that, is that one of the most astounding discoveries of Chaos, iterated maps, was not explained in a way that helped me realize its truly profound nature. Only after thinking about it for days afterwards did I finally "get it". Also, Strogatz repeatedly alludes to some intrigue in this field in the late 80's and early 90's that Chaos theorists appear to still be smarting from. The more he hinted at it, the more I wanted to hear the whole story. Oh well, the material would probably be more appropriate in a lecture on the history of 20th century mathematics.
Date published: 2011-05-02
Rated 5 out of 5 by from Fascinating A very stimulating course that combines theory with practice and is tought by a lively & entertaining professor.
Date published: 2011-01-02
Rated 5 out of 5 by from A Mind Changing Course This course changed my view of the world. This was my first exposure to the concepts of chaos. I had of course seen the beautiful Mandelbrot pictures but never explored the concepts and mathematics that produced them. This course explores not only the fractals but also the concepts of determinism vs non determinism, order, chaos and randomness. All in such a clear concise way. I recommend it highly especially to those with little exposure to the new sciences.
Date published: 2010-12-06
Rated 5 out of 5 by from Chaos but not Complexity I love the lecturer. Dr. Strogatz is clear, witty (in sort of a geek way) and thoroughly charming. I enjoyed the course a great deal. My only disappointment was my ignorance of the difference between Chaos and Complexity. I really wanted to learn more about Complexity, but that turns out to be a different field, and needed a different course. I would purchase another course taught by Dr. Strogatz without hesitation.
Date published: 2010-11-06
Rated 5 out of 5 by from Superb! This course is superb! The professor's enthusiasm and verve for the topic rifles through to the audience throughout the entire course. Akin to the delivery of Professor Page in the "Understanding Complexity" course (the companion course if you buy the set), the instructor draws parallels from and explains the relevance of the course material to multiple disciplinary fields. He also demonstrates the impact of the course thematic content on "real life". One cannot help but get a panoramic and historical view of this material as well as a wonderful and up-to-date foundation in the subject matter. I commend this course to all who have an interest in this topic.
Date published: 2010-09-14
Rated 4 out of 5 by from Deterministic Randomness I have a much better understanding of chaos theory than before. In particular, the fact that chaotic and random are very different things. Chaotic systems are deterministic although they may appear random. In particular, the fine-grained structure packs the deterministic threads so closely together that very tiny changes in initial conditions soon cause widely divergent behavior (the "butterfly effect"). After emphasizing this, it was somewhat annoying to have him show some graph and say it is obviously chaotic when it looks pretty random to me. It was fascinating to me to see how much order there is in chaotic systems. The lecture on Feigenbaum's universality (which comes up again and again) was particularly interesting. Very different chaotic systems share very precise numerical values for certain ratios. The lectures on fractals were fun (and beautifully illustrated), but the connection to chaos was not as strong as I would have liked. It did help to get a good understanding of fractals and, in particular, fractional dimensionality so that is familiar when those terms are used to analyze chaotic systems. That being said, the divergence into fractals left less time for the subject matter of the course. Some of that time could have been better spent on explaining iterative maps better. It was interesting to compare chaos and quantum mechanics and why they are such different aspects of "predictable randomness" (if there is such a thing).
Date published: 2010-09-04
Rated 5 out of 5 by from wonderful teacher professor strogatz presents this very difficult topic in a fun and very down to earth way. can´t stop watching it.
Date published: 2010-07-07
Rated 5 out of 5 by from Excellent Intro + Applications I thoroughly enjoyed this set! For one who was never exposed to chaos theory, Prof. Strogatz has done a fantastic job of explaining the basics and delving into many applications. The course was conceptually accessible. My only criticism is regarding fractals. I wish Prof. Strogatz would have spent more time on the equations that generate the beautiful fractals that were so prominently featured at the beginning of the course. All in all, a fascinating and riveting tour of chaos. Highly recommended for anyone seeking a deeper appreciation of the subject.
Date published: 2010-04-21
Rated 5 out of 5 by from Exciting and Thought-Provoking Professor Strogatz demonstrated his talent for presenting very complex mathematical ideas in an extremely understandable way. I was riveted to my computer screen and looked forward to every lecture. I have never been so excited about mathematical concepts, although math was a major part of my academic and professional life. These lectures prompted me to do lots of thinking about the subject matter and to delve into research on the internet on chaos theory. I have just finished reading Dr. Strogatz's articles on various mathematical concepts which appeared in the New York Times and are available on the web. He has a wonderful talent for taking this material and making it understandable. Don't underestimate the effort needed to noodle over the concepts, refer to the guidebook, and read more about the material covered in the course. The time spent is worth every minute invested and will stimulate your thinking!
Date published: 2010-04-18
Rated 4 out of 5 by from Difficult Concepts I bought this course from the Teaching Company after watching a previous course on Meteorology in which the lecturer, Dr. Robert Fovell, made the connection between long range weather forecasting and chaos theory. This was an extremely difficult topic to dissect because so much of it is non-intuitive and, to use one of Professor Strogatz's favorite phrases, "non-linear." In fact, this is one of the main take-aways I have from this course.....chaos theory deals with non-normal, non-linear data. I found myself replaying several lecture topics to enhance my understanding. However, it was Steven Strogatz's engaging personality, eye contact with the camera, enthusiasm for the topic, and excellent presentation skills that made this course worthwhile. That said, I cannot recommend it to anyone who does not possess a background in science and mathematics.
Date published: 2010-04-12
Rated 5 out of 5 by from Outstanding! What a great course. Hard topics aren't that difficult when explained in such a thoughtful way. I will be watching the DVD's again. I bought the recommended readings. I guess the simpliest thing, and probably the most powerful thing, I can say is that the instructor inspired me. Buy this course if you want to see a world class scientist at the top of his game.
Date published: 2010-03-21
Rated 5 out of 5 by from Best course so far An excellent distillation of many complex and related topics with coverage of basic concepts and both theoretical and current applications of those concepts. Dr. Strogatz maintains a genuine enthusiasm and clarity thru the course [tho I suspect he has taught it often ]. His choice of how deep to go into theory and math behind each idea was perfect for me and his enthusiasm sustained both of us thru the course. Highly recommended.
Date published: 2010-03-20
Rated 4 out of 5 by from Mixed review Pros: If you've heard the terms 'chaos' and 'fractals' and 'the butterfly effect' thrown about in popular news and don't really know what they're talking about (but want to), you'll enjoy this course. It will introduce you too these concepts and throw in interesting anecdotal stories that you can share with friends at cocktail parties. Prof Strogatz has an enthusiasm for the topic that makes it fun. Cons: The course was at times frustratingly too shallow and at times too in-depth. There were certain points that he would go into excruciating depth about and others that he glossed over quite quickly. For example, there was a great amount of detail on iterated maps, but I wasn't even sure what the definition of 'chaos' was until about Lecture 6. And I understand what fractals are, but the link between fractals and chaos was tenuous and kind of assumed to be obvious. A pet peeve of mine was that he would often show a picture and say something like "Here's a system that's obviously chaotic." And while the picture looked random, it was not clear how it met the criteria for being chaotic. So overall I enjoyed the course and got a good intro to Chaos, there were certain aspects that left me puzzled.
Date published: 2010-03-16
Rated 4 out of 5 by from Challenging…Not For Everyone It is difficult to do justice to this course in a short review. Professor Strogatz is, without a doubt, an enthusiastic and entertaining lecturer who is one of the world’s experts on this topic. The course is well-organized and thorough. The problems are the length of the course and the challenges for the non-mathematician. If one’s goal is to be entertained by the beauty of fractals or to be able to discuss chaos glibly with colleagues, it would be better to consult Wikipedia, which has excellent discussions and illustrations. If, on the other hand, one is willing to spend twelve challenging hours in order to have a deeper knowledge of the theory of chaos and its implications and applications in our world, there is no better method than this course. You must be prepared to use the rewind button a great deal, especially if you are not familiar with concepts such as state space, iterated maps, and non-linearity. The course guide is excellent and is a handy resource for reviewing each lecture and making sure that you understand the terms. Overall, I am glad that I put in the effort and hope that some of the large amount of information survives in the chaotic tangle of my cerebral cortex.
Date published: 2010-03-16
Rated 4 out of 5 by from MIssed the Math It is obvious that Dr. Strogatz is very enthusiastic about the field of chaos and he understands it very well. In this course, he tries to teach a highly mathematical course without the mathematics. I suspect that those without the mathematics background were baffled by it and those with the mathematical background were frustrated by it. I wouldn't be surprised if Dr. Strogatz himself felt frustrated by the constraint of not using any mathematics. I would really enjoy taking one of his graduate courses in chaos theory, one in which he could use mathematics and in which he could assign homework. In a TTC format, though, the course falls short of its potential.
Date published: 2010-02-20
Rated 5 out of 5 by from Fascinating course This was one of my favorite courses from the Teaching Co. The instructor was very passionate about the subject and this translated into a continuously lively presentation of the subject. I had previously read a book and atrticles about Chaos but never really felt like I got an acceptable grasp of the topic. The instructor presented a scaffold of ideas which built upon one another to paint a very vivid picture of Chaos. His demonstrations and simulations were crucial in further clarifying many key points. If this topic interests you, don't miss it.
Date published: 2010-01-14
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