Chaos Theory: Destroying Mathematical Economics from Within?

by Murray N. Rothbard

The hottest new topic in mathematics, physics, and allied sciences is "chaos theory." It is radical in its implications, but no one can accuse its practitioners of being anti- mathematical, since its highly complex math, including advanced computer graphics, is on the cutting edge of mathematical theory.

In a deep sense, chaos theory is a reaction against the effort, hype, and funding that have, for many decades, been poured into such fashionable topics as going ever deeper inside the nucleus of the atom, or ever further out in astronomical speculation. Chaos theory returns scientific focus, at long last, to the real "microscopic" world with which we are all familiar.

It is fitting that chaos theory got its start in the humble but frustrating field of meteorology. Why does it seem impossible for all our hot-shot meteorologists, armed as they are with ever more efficient computers and ever greater masses of data, to predict the weather?

Two decades ago, Edward Lorenz, a meteorologist at MIT stumbled onto chaos theory by making the discovery that ever so tiny changes in climate could bring about enormous and volatile changes in weather. Calling it the Butterfly Effect, he pointed out that if a butterfly flapped its wings in Brazil, it could well produce a tornado in Texas.

Since then, the discovery that small, unpredictable causes could have dramatic and turbulent effects has been expanded into other, seemingly unconnected, realms of science.

The conclusion, for the weather and for many other aspects of the world, is that the weather, in principle, cannot be predicted successfully, no matter how much data is accumulated for our computers. This is not really "chaos" since the Butterfly Effect does have its own causal patterns, albeit very complex. (Many of these causal patterns follow what is known as "Feigenbaum's Number.")

But even if these patterns become known, who in the world can predict the arrival of a flapping butterfly?

The upshot of chaos theory is not that the real world is chaotic or in principle unpredictable or undetermined, but that in practice much of it is unpredictable. And in particular that mathematical tools such as the calculus, which assumes smooth surfaces and infinitesimally small steps, is deeply flawed in dealing with much of the real world. (Thus, Benoit Mandelbroit's "fractals" indicate that smooth curves are inappropriate and misleading for modeling coastlines or geographic surfaces.)

Chaos theory is even more challenging when applied to human events such as the workings of the stock market. Here the chaos theorists have directly challenged orthodox neoclassical theory of the stock market, which assumes that the expectations of the market are "rational," that is, are omniscient about the future. If all stock or commodity market prices perfectly discount and incorporate perfect knowledge of the future, then the patterns of stock market prices must be purely accidental, meaningless, and random ("random walk"), since all the underlying basic knowledge is already known and incorporated into the price.

The absurdity of believing that the market is omniscient about the future, or that it has perfect knowledge of all "probability distributions" of the future, is matched by the equal folly of assuming that all happenings on the real stock market are "random," that is, that no one stock price is related to any other price, past or future. And yet a crucial fact of human history is that all historical events are interconnected, that cause and effect patterns permeate human events, that very little is homogeneous, and that nothing is random.

With their enormous prestige, the chaos theorists have done important work in denouncing these assumptions, and in rebuking any attempt to abstract statistically from the actual concrete events of the real world. Thus, the chaos theorists are opposed to the common statistical technique of "smoothing out" the data by taking twelve-month moving averages of monthly data-whether of prices, production, or employment. In attempting to eliminate jagged "random elements" and separate them out from alleged underlying patterns, orthodox statisticians have been unwittingly getting rid of the very real-world data that need to be examined.

These are but a few of the subversive implications that chaos science offers for orthodox mathematical economics. For if rational expectations theory violates the real world, then so too does general equilibrium, the use of the calculus in assuming infinitesi mally small steps, perfect knowledge, and all the rest of the elaborate neoclassical apparatus.

The neoclassicals have for a long while employed their knowledge of math and their use of advanced mathematical techniques as a bludgeon to discredit Austrians; now comes the most advanced mathematical theorists to replicate, unwittingly, some of the searching Austrian critiques of the unreality and distortions of orthodox neoclassical economics.

In the current mathematical pecking order, fractals, non-linear thermodynamics, the Feigenbaum number, and all the rest rank far higher than the old-fashioned techniques of the neo-classicals.

This does not mean that all the philosophical claims for chaos theory must be swallowed whole--in particular, the assertions of some of the theorists that nature is undetermined, or even that atoms or molecules possess "free will." But Austrians can hail the chaos theorists in their invigorating assault on orthodox mathematical economics from within.

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The hottest new topic in mathematics, physics, and allied sciences is "chaos theory." QUOTE]

Es viejo ya el artículo caramba ...

Sí, bueno, nuevo no es (1988). No obstante lo que comenta es interesante, en mi opinión, ya que aún se sigue investigando en la aplicación de las matemáticas en sistemas dinámicos huyendo así del paradigma clásico (esto en eco p.e).

Tiene que ver con: Newtonian time in economics - Wikipedia, the free encyclopedia

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Esta claro que los modelos matemáticos clásicos son solo burdas aproximaciones, y que no son capaces de preveer efectos inesperados. Para eso de momento solo está la mente humana, como llevan denunciadndo los austríacos durante años.

En mi lista de lectura está el libro "Black Swam" de Nassim Nicholas Taleb, que es un economista que predijo la crisis actual y que trabaja con el nombrado Benoit Mandelbrot, usando la teoría del caos y los fractales para intentar predecir el mercado. Sus conclusiones: Nadie tiene ni puta idea de lo que va a pasar y los bancos están tomando demasiado riesgos porque el sistema se vuelve más grande y por tanto más resistente pero que cuando caiga, caerá también a lo grande.

Aquí una entrevista a los dos (atención al principio al puteo de Taleb en la televisión norteamericana denunciando que los bancos tienen que parar de especular y ser más prudente):



Aquí un trozo de una conferencia de Taleb diciendo que los economistas tienen el mismo valor cientifico que los obispos:

Tengo que admitir que yo me descojonaba con el desparpajo con que algunos ejpertos en análisis técnico se apropiaron del termino "Teoría del Caos" para justificarse en las tertulias radiofónicas de intereconomía. La verdad, es como si vas al rastro y en medio del regateo con un merchero, te suelta "Según el Teorema de Lorentz estamos llegando a un punto de equilibrio inestable".

¿¿¿Sabrá esta gente las tonterías que está diciendo???

Edit:

No había Visto lo de Mandelbrot. Otra palabreja para despistar a lerdos, eh, pillines.

Muchos sistemas dinámicos no tienen solución. Los que la tienen parten de condiciones iniciales bien determinadas.Si además las condiciones iniciales son variables económicas y varían al instante por condicionantes políticos... pues eso , mejor apagar e irse.

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La teoría del caos está en plena vigencia, y no para de dar mazazos a los modelos matemáticos complejos en todos los campos, desde los modelos climáticos a los económicos.

Por cierto hugolp, de Taleb me leí "Fooled by randomness", un libro brillante y "Dynamic Hedging-Managing Vanilla and Exotic Options" (buen libro para entender a fondo las opciones, pero un poco tostón). Me apunto "The Black Swan" a ver si lo encuentro

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Yo me lo estoy leyendo ahora. Voy por la mitad y lo encuentro decepcionante.

El libro (por ahora) es de filosofía "todo a 100", y en 200 páginas se recogen reflexiones que podrían haberse escrito en 20. El escritor es muy, muy arrogante. Le encanta hablar de sí mismo. De lo guay que es. De lo muy aleccionadora que fue su etapa de corredor de bolsa. De lo muy tontos que eran todos menos él. De todos lo idiomas que habla. De lo mucho que viaja. De lo mucho que sabe de filosofía...

En fin. Volveré sobre este hilo cuando lo termine, por si he cambiado de opinión.

En este blog se tradujeron el libro hace ya tiempo:

Babalum

Muy recomendable el blog entero.

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La verdad no envejece.