Archive for the ‘Model’ Category

Heroic Oversimplification for Modeling our World

October 20, 2007

The invention of deliberately oversimplified theories is one of the major techniques of science, particularly of the “exact” sciences. The biophysicist employs simplified models of the cell, the cosmologist uses simplified models of the universe, and so on.

It may be useful to examine one successful scientific abstraction, to see what it is like and for the sake of the hints it may give us. We choose one which is surely an example of a heroic oversimplification.

Let us assume that we may, in order to study their motions, replace each of the major bodies of the Solar System by a point; that each point experiences a mutual attraction; that we may estimate the attractive force by multiplying the mass of one point by the mass of the other, after which we divide that product by the square of the distance between the points; and that we may neglect all else.

The fact is that this theory, the Theory of Gravitation, has been adequate for predicting the motions of the planets for two and one-half centuries – and this in the face of constant checking by positional astronomers, who, it can fairly be said, carry precision to extremes. The worst strain has come from the orbit of Mercury, which unaccountably drifted from the predicted place by one-fifth of a mil (a foot, at a distance of a mile) per century, thus showing that the theory is rough after all, just as it looks. The improved theory, by Einstein, accounts for this discordance.

The Compleat Strategyst by J.D. Williams

Questions of origins play prominent roles in most sciences. Where do economies come from?

September 7, 2007

Questions of origins play prominent roles in most sciences. It would be difficult to imagine modern cosmology without the Big Bang, or biology without evolution.

“Where do economies come from?”

Traditional economic courses begin with “assume an economy.”

The process of economy formation presents us with a first-class scientific puzzle.

Joshua Epstein and Robert Axtell, researchers at the Brookings Institute, decided to conduct an experiment to see if they could grow an economy from scratch. Like biologists trying to cultivate life in vitro in a petri dish, Epstein and Axtell wanted to see if they could spark economic life in silico, in the simulated world of a computer.

They wanted to go back to the very beginning, to a state of nature, and have a model that included nothing more than people with a few basic abilities, and an environment with some natural resources. They wanted to find out the minimum conditions required to set off a chain reaction of economic activity. What would it take to get the system to start climbing the ladder of increasing economic order?

[My Comment] To make a long story short, Epstein and Axtell created a model they called Sugarscape, and the model was successful in spawning economic activity. The thing of interest to me, however, is the notion described in the preceding paragraph – get back to fundamentals, rethinking how we got to where we are now (this applies not just to economies, but to everything), and considering whether we have arrived at a desirable place.

The Origin of Wealth by Eric D. Beinhocker