Also in the HES/AEA session I organized in Atlanta was a paper by David Colander and Casey Rothschild entitled, "Sins of the Sons of Samuelson: Vision, Economic Pedagogy, and the Zigzag Wadnerings of Complex Dynamics," available at this link. They argue that Samuelson was aware of complex dynamics and how math models could simplify insights in Marshall and others that had been expressed only in the "zigzag wanderings" of literary expression. They blame the "sons of Samuelson" for turning the push to math models, certainly led by Samuelson, into a mindless dogma that oversimplified economics and misled many in many different ways. They proposed how to change intro textbooks to open students' minds to complexity (and Rothschild will be joining Colander as a coauthor in future editions of his popular intro textbook).

Rajiv Sethi has just posted on Samuelson's own interest in nonlinear dynamics, citing my mentioning a paper by Samuelson on Mark Thoma's blog, with Thoma linking to the Sethi piece. Sethi discusses the nonlinear version of Samuelson's multiplier-accelerator model, which appeared in the same year (1939) as his much more famous linear version. Sethi notes that I had brought this up on Thoma's blog only two weeks prior to Samuelson's death.

As a matter of fact I cite that paper by Samuelson in the paper I presented in the session at Atlanta, "Chaos Theory Before Lorenz," available on my website and also having appeared recently in print in a special issue of Nonlinear Dynamics, Psychology, and Life Sciences, honoring the late Edward Lorenz, the MIT climatologist who was reputed to have "discovered chaos on a coffee break" back in 1961. He was the person who coined the term "buttefly effect."

## 4 comments:

The link for "Sins of the Sons..." should be

http://www.aeaweb.org/aea/conference/program/retrieve.php?pdfid=115, not pdfid=15.

"Edward Lorenz, the MIT climatologist who was reputed to have "discovered chaos on a coffee break" back in 1961."

Reputed -- by people unaware of Poincare? ;)

(Nothing against Lorenz, of course. :))

Ken,

Thanks. Got it fixed.

Min,

Well, you should read my paper, which is about all those before Lorenz who had something to do with the ideas of chaos theory. It is a long list, much longer than Poincare, although he is on it prominently.

I would note that Poincare did have all the elements in theory of what we now call chaos theory. However, he never put them together in a single place. They are scattered about hither and thither in odd corners of his voluminous writings, although now much attention focuses on them. However, he was not the first on many counts.

While he was the first for certain pieces, he was not for most of them, with numerous mathematicians getting one or another (such as fractal attractors or fractal basin boundaries) prior to him, with a rather large number of people in the late 19th century beating him. If one is willing to be a bit more open interpretation, one can go with the case for the ancient Greek philosopher, Anaxagoras. I quote the prominent Otto Rossler on making the case for him, although that requires some interpretation.

Regarding "discovering chaos," it can be argued that just thinking of the possibility is one thing, and actually observing it either in physical reality or on a computer simulation is quite another. Poincare did neither of those. The first to observe it in physical reality were van der Pol and van der Mark in radio frequency tuning in 1927, reported in a paper in Nature of that year, "Frequency demultiplication," discussed in my paper. However, they did not realize what they had found. Likewise, Strotz, McAnulty, and Naines found it in a computer simulation of the Goodwin model in economics, published in 1953 in Econometrica, but also did not know what they had found.

I conclude the paper noting that while many, most prominently Poincare, had either discovered or understood elements of chaos theory before Lorenz, he was probably the first to observe it somehow and realize what he had found in terms of its mathematical implications. In that regard, it is not completely ridiculous to label him as he has been (and his paper pushed many others to study the topic).

i trace some of the confidence in stability of GET to a) the fact that while a unique general equilibrium exists, little emophasis was placed on dynamics (in a review in Am Ma Mon on it the idea was 'almost never' would a real economy find it, and most equilibria are 'hardly ever' stable, and then add SMD which (to me) takes out the idea samuelson's book emphasized that utility maximization is like a ball rolling down a hill----its more usually chaotic and b) samuelson's efficient market/random walk model (or Fama's), which basically argued one could 'Gaussianize' (which is in many ways equivalent to linearizing) away nonlinear (unstable) behavior.

the idera here is similar to the ergodic theorem in stat mech----one can assume often you can assume a complex system is a set of non-interacting idetical particles, and apply a law of large numbers to get some sort of gaussian-canonical ensemble, but in real cases (first explored in detail i think in the Fermi-Pasta-Ulam simulations) that is not what you find, because interactions eixst, and chaos is more likely (which can utimately be transforermed into some ensemble average over an attractor, which is not the typical one, though at times written in the same form).

i was actually looking at a 1993paper on a DSGE model of the NAFTA proposal by someone at UCLA (who wrote recently on immigration reform) His model actually got it right---massive rural to urban migration because of cheap US imports to mexico, and also massive ('illegal') immigration to the US. He said things could be done to cahnge that, but they werent done, is my impression. So DSGE if done right may have an ok static approximation, but alot of it is actually common sense.

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