Archive for the ‘Theories’ 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

Scientific theories are like maps – there are course-grain maps (and theories) and fine-grain maps (and theories)

September 3, 2007

Scientific theories are like maps.

“Maps are approximate pictures of an underlying reality; a map of Oskaloosa, Iowa is only an approximate representation of the real Oskaloosa.  The only perfect map of Oskaloosa is Oskaloosa itself, which is too big to fit into the glove compartment of your car and thus not very useful.  Just as map makers idealize and leave out certain features of the terrain, scientists simplify and idealize their theories.  What is included or left out will depend on the purpose of the map or theory.  If you are driving across the country, you might just need a course-grained map that shows the major highways.  If, on the other hand, you were going to visit your great-aunt on Ford Avenue in Oskaloosa, you would need a fine-grained map that shows the street grid of Oskaloosa, but not all the highways in the country.”

“The course- and fine-grained maps (and theories) must agree with each other and the observations of the underlying reality.  If a highway map places a river in a particular location, the river must be in the same location on the local map, and must agree with observations of where the river actually is.  One cannot just move roads and rivers around for the purpose of making the maps easier to draw.”

“Science requires different levels of abstraction for different phenomena.  Scientific theories can be big picture and course-grained like a highway map, or fine-grained like a local street map. Both are equally valid; they just need to agree with each other and conform to reality.”

The Origin of Wealth by Eric D. Beinhocker