Archive for the ‘Chaos’ Category

Availability Cascades [Activists Take Note, Big Data Project?]

Saturday, February 25th, 2017

Availability Cascades and Risk Regulation by Timur Kuran and Cass R. Sunstein, Stanford Law Review, Vol. 51, No. 4, 1999, U of Chicago, Public Law Working Paper No. 181, U of Chicago Law & Economics, Olin Working Paper No. 384.

Abstract:

An availability cascade is a self-reinforcing process of collective belief formation by which an expressed perception triggers a chain reaction that gives the perception of increasing plausibility through its rising availability in public discourse. The driving mechanism involves a combination of informational and reputational motives: Individuals endorse the perception partly by learning from the apparent beliefs of others and partly by distorting their public responses in the interest of maintaining social acceptance. Availability entrepreneurs – activists who manipulate the content of public discourse – strive to trigger availability cascades likely to advance their agendas. Their availability campaigns may yield social benefits, but sometimes they bring harm, which suggests a need for safeguards. Focusing on the role of mass pressures in the regulation of risks associated with production, consumption, and the environment, Professor Timur Kuran and Cass R. Sunstein analyze availability cascades and suggest reforms to alleviate their potential hazards. Their proposals include new governmental structures designed to give civil servants better insulation against mass demands for regulatory change and an easily accessible scientific database to reduce people’s dependence on popular (mis)perceptions.

Not recent, 1999, but a useful starting point for the study of availability cascades.

The authors want to insulate civil servants where I want to exploit availability cascades to drive their responses but that’a question of perspective and not practice.

Google Scholar reports 928 citations of Availability Cascades and Risk Regulation, so it has had an impact on the literature.

However, availability cascades are not a recipe science but Networks, Crowds, and Markets: Reasoning About a Highly Connected World by David Easley and Jon Kleinberg, especially chapters 16 and 17, provide a background for developing such insights.

I started to suggest this would make a great big data project but big data projects are limited to where you have, well, big data. Certainly have that with Facebook, Twitter, etc., but that leaves a lot of the world’s population and social activity on the table.

That is to avoid junk results, you would need survey instruments to track any chain reactions outside of the bots that dominate social media.

Very high end advertising, which still misses with alarming regularity, would be a good place to look for tips on availability cascades. They have a profit motive to keep them interested.

Is It Foolish To Model Nature’s Complexity With Equations?

Thursday, October 29th, 2015

Is It Foolish To Model Nature’s Complexity With Equations? by Gabriel Popkin.

From the post:

Sometimes ecological data just don’t make sense. The sockeye salmon that spawn in British Columbia’s Fraser River offer a prime example. Scientists have tracked the fishery there since 1948, through numerous upswings and downswings. At first, population numbers seemed inversely correlated with ocean temperatures: The northern Pacific Ocean surface warms and then cools again every few decades, and in the early years of tracking, fish numbers seemed to rise when sea surface temperature fell. To biologists this seemed reasonable, since salmon thrive in cold waters. Represented as an equation, the population-temperature relationship also gave fishery managers a basis for setting catch limits so the salmon population did not crash.

But in the mid-1970s something strange happened: Ocean temperatures and fish numbers went out of sync. The tight correlation that scientists thought they had found between the two variables now seemed illusory, and the salmon population appeared to fluctuate randomly.

Trying to manage a major fishery with such a primitive understanding of its biology seems like folly to George Sugihara, an ecologist at the Scripps Institution of Oceanography in San Diego. But he and his colleagues now think they have solved the mystery of the Fraser River salmon. Their crucial insight? Throw out the equations.

Sugihara’s team has developed an approach based on chaos theory that they call “empirical dynamic modeling,” which makes no assumptions about salmon biology and uses only raw data as input. In designing it, the scientists found that sea surface temperature can in fact help predict population fluctuations, even though the two are not correlated in a simple way. Empirical dynamic modeling, Sugihara said, can reveal hidden causal relationships that lurk in the complex systems that abound in nature.

Sugihara and others are now starting to apply his methods not just in ecology but in finance, neuroscience and even genetics. These fields all involve complex, constantly changing phenomena that are difficult or impossible to predict using the equation-based models that have dominated science for the past 300 years. For such systems, DeAngelis said, empirical dynamic modeling “may very well be the future.”

If you like success stories with threads of chaos, strange attractors, and fractals running through them, you will enjoy Gabriel’s account of empirical dynamic modeling.

I have been a fan of chaos and fractals since reading Computer Recreations: A computer microscope zooms in for a look at the most complex object in mathematics in 1985 (Scientific American). That article was reposted as part of: DIY Fractals: Exploring the Mandelbrot Set on a Personal Computer by A. K. Dewdney.

Despite that long association with and appreciation of chaos theory, I would answer the title question with a firm maybe.

The answer depends upon whether equations or empirical dynamic modeling provide the amount of precision needed for some articulated purpose.

Both methods ignore any number of dimensions of data, each of which are as chaotic as any of the others. Which ones are taken into account and which ones are ignored is a design question.

Recitation of the uncertainty of data and analysis would be boring as a preface to every publication, but those factors should be upper most in the minds of every editor or reviewer.

Our choice of data or equations or some combination of both to simplify the world for reporting to others shapes the view we report.

What is foolish is to confuse those views with the world. They are not the same.

Nonlinear Dynamics and Chaos:

Thursday, April 9th, 2015

Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Steven H. Strogatz by Daniel Lathrop.

For someone with Steven Strogatz‘s track record on lucid explanations, it comes as no surprise that Latrop says:


In presenting the subject, the author draws from the past 30 years of developments that have advanced our understanding of dynamics beyond the linear examples—for instance, harmonic oscillators—that permeate current physics curricula. The advances came from theoretical and computational scholars, and the book does a great job of acknowledging them. The methods and techniques that form the bulk of the book’s content apply useful concepts—bifurcations, phase-space analysis, and fractals, to name a few—that have been widely adopted in physics, biology, chemistry, and engineering. One of the book’s biggest strengths is that it explains core concepts through practical examples drawn from various fields and from real-world systems; the examples include pendula, Josephson junctions, chemical oscillators, and convecting atmospheres. The illustrations, in particular, have been enhanced in the new edition.

The techniques needed to understand the behavior of nonlinear systems are inherently mathematical. Fortunately, the author’s excellent use of geometric and graphical techniques greatly clarifies what can be amazingly complex behavior. For example, in carefully working through the development and behavior of the Lorenz equations, Strogatz introduces a simple waterwheel machine as a model to help define terms and tie together such key concepts as fixed points, bifurcations, chaos, and fractals. The reader gets a feel for the science behind the differential equations. Moreover, for each concept, the mathematics is accompanied by clear figures and nicely posed student exercises.

Rate this one as must buy!

Ahem, I guess you noticed that political science, sociology, psychology, sentiment, etc. aren’t included in the title?

Blake LeBaron of Brandeis University penned an answer to “Has chaos theory found any useful application in the social sciences?,” which reads in part:


One of several key ideas in chaos is that simple models can generate very rich (and random-looking) dynamics. Implicit in some early work in the social sciences was a hope that simple chaotic models of social phenomena could be matched up with many of the near-random and difficult-to-explain empirical patterns that are observed. This early goal has proved elusive.

One problem is that determining if a time series was generated by deterministic chaos is not easy. (A time series is a data set showing the state of a system over a period of time–a sequence of voting results, for instance, or the fluctuating price of gold.) There is no single statistic capable of being estimated that indicates what is going on in a social system. Also, many common time-series problems (such as seasonality and trends) can confuse most of the diagnostic tools that people use. These complications have led to many conflicting results. Building an easy-to-use test that can handle the intricacies of a real-world time series is a tough problem, one which will probably not be solved anytime soon.

A second difficulty is that most of the theoretical structure in chaos is based on purely deterministic models that have no noise, or at most just a very small amount of noise, affecting the dynamics of the system. This approach works well in many physical situations, but it does not offer a very good picture of most social situations. It is hard to look at social systems isolated from the environment in the way that one can analyze fluid in a laboratory beaker. Once noise plays a major role in the dynamics, the problems involved in analyzing nonlinear systems become much more difficult.

A great illustration of why “low noise” techniques have difficulty providing meaningful results when applied to social systems. Social systems are noisy, very noisy. That isn’t to say you can’t ignore the noise and make decisions on the results, but you could save the consulting fees and consult a Ouija Board instead. Social engineering programs, both liberal and conservative in the United States suffer from a failure to appreciate the complexity of human interaction.

PS: I did see in the index that Steven cites Romeo and Juliet but I will have to await the arrival of a copy to discover what was said.

Nonlinear Dynamics and Chaos

Tuesday, May 27th, 2014

Nonlinear Dynamics and Chaos – Steven Strogatz, Cornell University.

From the description:

This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. It closely follows Prof. Strogatz’s book, “Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering.” The mathematical treatment is friendly and informal, but still careful. Analytical methods, concrete examples, and geometric intuition are stressed. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors. A unique feature of the course is its emphasis on applications. These include airplane wing vibrations, biological rhythms, insect outbreaks, chemical oscillators, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with the mathematical theory. The theoretical work is enlivened by frequent use of computer graphics, simulations, and videotaped demonstrations of nonlinear phenomena. The essential prerequisite is single-variable calculus, including curve sketching, Taylor series, and separable differential equations. In a few places, multivariable calculus (partial derivatives, Jacobian matrix, divergence theorem) and linear algebra (eigenvalues and eigenvectors) are used. Fourier analysis is not assumed, and is developed where needed. Introductory physics is used throughout. Other scientific prerequisites would depend on the applications considered, but in all cases, a first course should be adequate preparation.

Storgatz’s book “Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering,” is due out in a second edition in July of 2014. First edition was 2001.

Mastering the class and Stogatz’s book will enable you to call BS on projects with authority. Social groups are one example of chaotic systems. As a consequence, the near religious certainly of policy wonks on outcomes of particular policies is mis-guided.

Be cautious with those who response to social dynamics being chaotic by saying: “…yes, but …(here follows their method of controlling the chaotic system).” Chaotic systems by definition cannot be controlled nor can we account for all the influences and variables in such systems.

The best you can do is what seems to work, most of the time.