Hypnotized by Models

By Callahan, Gene; Murphy, Robert P. | Freeman, March 2005 | Go to article overview

Hypnotized by Models


Callahan, Gene, Murphy, Robert P., Freeman


We live in an age where abstract models of the real world are held in high regard. Wall Street firms hire mathematicians and physicists to create sophisticated mathematical representations of various assets and markets. Meteorologists employ computer simulations in an attempt to anticipate the path of storms and predict next week's weather. Marketing firms try to model how consumers will respond to a proposed ad campaign. Military strategists conduct virtual battles and wars. Bridges are built, planes are flown, giant buildings are raised, and crops are planted with the aid of abstract systems of equations.

The current respect for abstract modeling is not unfounded. Ever since the scientific revolution that took place during the sixteenth and seventeenth centuries, mathematical models of the physical world have continually increased humans' ability to manipulate their environment. On the other hand, repeated attempts to port the mathematical techniques that have proved so successful in the physical sciences directly to the social sciences have produced few positive results to date. But those who view the current methods of the physical sciences as the only valid way to achieve objective knowledge have claimed that this record of failure is due entirely to the relative youth of the social vis-à-vis the physical sciences and the greater complexity of their subject matter. Given enough time, they contend, mathematical models will depict the behavior of individuals and the evolution of social phenomena just as well as they handle inanimate matter and energy today.

For the time being we will set aside the question of whether those who contend that true social science must be based on mathematical modeling have a rational or empirical case for their stance. Instead, we will first point out that, for anyone engaged in the fascinating project of creating and perfecting abstract models, it is easy to forget that however useful and sophisticated his models might be, they are still only skeletal images of some subset of a complete human experience. Watching a simulation of a hurricane on a computer screen is a far cry from actually being in the midst of one. The chaos that ensues once a real battle is underway is never captured in a model of the conflict. A mathematical description of the atmospheric refraction of light at sunset does not convey the power of the setting sun as a metaphor for old age and death, the wistful nature of a winter sunset on a lonely moor, or the romantic mood created by watching the sun sink into the sea as one stands with a lover on a desert isle's beach.

Correctly interpreting the relationship between a model and the raw experience from which it was abstracted is a matter of skilled judgment. A model cannot interpret itself; it asserts that if certain aspects of a particular situation closely conform to specifications contained in the model, then we can expect certain other circumstances to arise, either with full certainty or with some measure of probability. The question of how well a model captures the essence of some event in the real world cannot be answered mechanically.

All this implies an important pragmatic point about the application and misapplication of models: Skill at developing and manipulating the abstractions comprising a model does not necessarily correlate to skill at interpreting how that model relates to reality. Someone who is extraordinary at modeling various investment opportunities may be a disaster if he actually trades the securities he has modeled, which is why investment banks employ experienced traders to put their models into practice. A person who can develop top-notch simulations of the potential battle scenarios might be awful at responding to the constant surprises presented by a real battle, which is why armies have experienced officers in charge of their troops during an actual conflict.

Among economists, it is the Austrians who have been most keenly aware of the difference between being good at creating models and being good at interpreting their application to real events. …

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