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Chaos

Explore a revolutionary field of mathematics and discover new ways to think about the world with this mind-expanding course.
Chaos is rated 4.5 out of 5 by 119.
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Rated 5 out of 5 by from Amazing topic, opened my eyes, life-changing Highly recommend this video. The content is excellent. The topic covers basic laws of nature and life. So need this too.
Date published: 2024-07-07
Rated 5 out of 5 by from Extra-ordinary Just finished this course (have owned it for years without having the opportunity to sit down and watch. It pairs nicely with the course on Complexity. The only fault I have with this course is that I think the first five lectures could be condensed into a single lecture. This is history of science that could easily be glossed over in favor of more details of math behind the theory. I have had four university courses in Diffy Qs, but others may not be able to follow a more technical treatment. Perhaps more simulations could be added as well since I enjoy them so much. The simulations provided were mind boggling and each lecture surpassed the previous one in surprises. The magnification of the Mandelbrot mapping is particularly spooky even though I have seen it many times before.
Date published: 2024-05-28
Rated 4 out of 5 by from Words are not enough. A course on a distinctly mathematical subject that is clearly designed for those with no previous knowledge of deterministic systems and differential calculus is an exercise in arm waving. Not only were the lectures devoid of equations save for a single nonlinear logistic difference equation (AKA the logistic map), but the course guidebook was no better. As a result, the essential concepts of state space, iterated maps, bifurcations and orbit maps are just so many words. The axis labeling of plots was less than helpful. That said, much of the anecdotal material is of considerable interest. Lecture 11 (Universal Features of the Route to Chaos) reminded me of a long-ago lecture: 18 Apr 1985, 19:30, at the Franklin Institute (Philadelphia, PA), my wife and I listened to mathematical physicist Mitchell Jay Feigenbaum (1944–2019) describe chaos theory and fractals, also without any reference to the underlying mathematics. On the positive side, Lectures 16 to 24 about the relevance of the subject to real world phenomena were excellent and fully justified Prof. Strogatz’s effort. The course guidebook has an excellent bibliography; the recommendation to read Chaos: Making a New Science (1987) by James Gleick was followed, and afterward I intend to read Strogatz’s own book, Nonlinear Dynamics and Chaos. So, the course is a clear success in stimulating further study. HWF & ISF, Mesa AZ.
Date published: 2024-01-20
Rated 1 out of 5 by from Bad explanation of chaos theory Wrong definition of choas theory needs to refo the video on chaos theory completely
Date published: 2023-07-20
Rated 5 out of 5 by from for the interdisciplinary thinker this course would have provided with a new approach for my phd research. 30 years too late. better late than never.
Date published: 2023-02-04
Rated 2 out of 5 by from Left Me Adrift I purchased “Chaos” in DVD format several years ago. The presenter, Dr. Strogatz, seems quite intelligent and successfully made the subject interesting for me. There’s plenty of food for thought. Nevertheless, the meal has not been completely served, at least to this layman. To summarize my take-away, even though well-settled math may lead to an accurate near term result, mathematical predictions over the long range are problematic, sometimes even erratic. The presentation is confusing in this regard. Are these longer term mathematic predictions thwarted by an incorrect mathematical formulation? Are measurements of initial conditions incorrect? Is iterative processing defeated by rounding errors? Do non-linear relationships exaggerate small input or computational errors? Do quantum effects on the smallest scales defeat newtonian mathematics over time on the larger scales? For me this question remains unanswered: Does Deterministic Chaos inherently exist in complex natural systems or is Chaos a cloak thrown over multiple less mysterious sources of error?
Date published: 2022-03-21
Rated 5 out of 5 by from Very interesting and informative The professor goes into all the ramifications of chaos theory and explains them so clearly and easily with words and graphs.
Date published: 2022-03-04
Rated 4 out of 5 by from A good course for the non-specialist This course provides a good overview on the field of non-linear dynamics and chaos theory. Professor Strogatz is very careful in explains the principles and does not assume any deep previous knowledge. As such the pace is a bit slow for the more numerate and almost feels that he is stretching things out to fill the allotted time. I found his book more helpful as it is not a fully rigorous exposition and thus a good gentle read.
Date published: 2021-08-04
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Overview

Chaos theory—the study of the behavior of sensitive systems over time—affects nearly every field of human knowledge, from the arts to zoology. Journey with Cornell University Professor Steven Strogatz to the heart of this revolutionary field and discover new ways to think about the world. From the surprising tale of how chaos theory was discovered, to the ways it can help us solve mysteries like the nature of consciousness, Chaos gives you a solid introduction to a fascinating discipline that has more to do with your life than you may realize.

About

Steven Strogatz

One of the things that I think is so powerful about ecology, and something I share with my students all the time, is that not everything in ecology and ecological change has to be really complicated.

INSTITUTION

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 Dynamics and Chaos-the most widely used textbook on chaos theory-and Sync: The Emerging Science of Spontaneous Order (chosen as a Best Book of 2003 by Discover magazine). Lauded for his exceptional teaching abilities, Professor Strogatz holds a Communications Award-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. He also received the Tau Beta Pi Excellence in Teaching Award from Cornell University's College of Engineering and the E. M. Baker Memorial Award for Excellence in Undergraduate Teaching from MIT.

By This Professor

The Chaos Revolution

01: 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?

32 min
The Clockwork Universe

02: 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?

29 min
From Clockwork to Chaos

03: 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.

31 min
Chaos Found and Lost Again

04: 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.

30 min
The Return of Chaos

05: 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."

30 min
Chaos as Disorder-The Butterfly Effect

06: 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.

32 min
Picturing Chaos as Order-Strange Attractors

07: 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."

29 min
Animating Chaos as Order-Iterated Maps

08: 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.

32 min
How Systems Turn Chaotic

09: 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.

32 min
Displaying How Systems Turn Chaotic

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.

31 min
Universal Features of the Route to Chaos

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.

30 min
Experimental Tests of the New Theory

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.

30 min
Fractals-The Geometry of Chaos

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.

32 min
The Properties of Fractals

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.

31 min
A New Concept of Dimension

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!

31 min
Fractals Around Us

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.

31 min
Fractals Inside Us

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.

32 min
Fractal Art

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.

31 min
Embracing Chaos-From Tao to Space Travel

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.

29 min
Cloaking Messages with Chaos

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.

31 min
Chaos in Health and Disease

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?

31 min
Quantum Chaos

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.

31 min
Synchronization

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.

32 min
The Future of Science

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.

31 min