<html> My conclusion from this exchange was that Barkley's article is indeed to a large extent tautologous, *and* that it is valuable, because expressing a common pattern in mathematics is one of the routes to scientific advance. I see Barkley as a committed leftist, with significant social skills, as Doug has, only different ones. This is an important quality in leftists, and by no means universal. While on the one hand Barkely is frequently skittishly disarming and humorous, the article adopts the tone of an authoritative academic article and demands respect. This is necessary to establish a bridgehead in bourgeois dominated economics. (Compare the tone of intellectual arrogance Marx and Engels often used in the ruthlessly competitive intellectual climate of the 19th century.) Keynes's reservations about the use of formulas is interesting and correct, but formulas are used in mainstream economics and Barkley is making a stand by proposing a formula for the volatility of markets. Barkley is also progressing in his project of linking specifically non-linear modelling of economic activity with the sort of critique that can make headway against right wing reductionism. The core of the article appears to be a remarkable attempt to note that the narrowness of the peak in the distribution curve of "asset price behaviour" relative to the tails ("leptokurtosis"), does not follow a normal distribution of random fluctuations in a continuous variable. The peaks are somehow steeper than in a normal Gaussian curve. Further to that, the pattern is remarkably similar to solar flares on the sun! I would certainly have preferred a much more discursive article but Barkley's article was not written for me or the rest of us on this list as such: it was written to command respect from mainstream economists, and from serious scientists looking at the pattern of non-linear phenomena. The question has to be discussed, why should the peaks of price valuation be higher than expected on random chance? Presumably the answer must be that there is some non-linear positive feedback as there is in the cycle of solar flares. Are these Keynes's animal spirits? As for questioning such a proposition by Barkley that is fine. One of Doug's skills as a moderator is that he is neither excessively intolerant nor bland. He will prod. That does not mean Barkely has no right to his opinions, or is obliged to reply. On the contrary, if he posts an article here he should expect the support that comes from basically other well intentioned people to probe it a little, be devil's advocate, or provide alternative explanations. It should become quite normal and helpful to the reorganisation of the left, that people can use e-mail lists such as this one, in this way. Chris Burford London PS I attach the abstract and the proper title, as taken from Barkley's web-site                                         VOLATILITY VIA SOCIAL FLARING                                                   J. Barkley Rosser, Jr.                                                   Professor of Economics                                                   MSC 0204                                                   James Madison University                                                   Harrisonburg, VA 22807 USA                                                   Tel: 540-568-3212                                                    Fax: 540-568-3010                                                    E-mail: rosserjb@jmu.edu                                                    December, 1999   ABSTRACT:      A new explanation of kurtosis in asset price behavior is proposed involving flare attractors.  Such attractors depend on chaotic fundamentals driving subsystems which trigger nonlinearly response functions each with a switching mechanism representing the changing of agents from stabilizing to destabilizing behavior.  Heterogeneous agent types are shown by a set of these response functions that are interlinked.  With a larger number of agent types system behavior resembles that of many financial markets.  Such a model is consistent with newer approaches relying upon evolutionary learning mechanisms with heterogeneous agents as well as models depending on fractal characteristics. </html>