Emanuel Derman: Metaphors, Models, & Theories
Synopsis (via Derman Edge.org)
Theories deal with the world on its own terms, absolutely. Models are metaphors, relative descriptions of the object of their attention that compare it to something similar already better understood via theories. Models are reductions in dimensionality that always simplify and sweep dirt under the rug. Theories tell you what something is. Models tell you merely what something is partially like.
My Favorite Excerpts (via Derman @ Edge.org)
WHY IS A MODEL A MODEL?
A model airplane, however complex, is simple when compared to the real thing.
There is a gap between the model and the object of its focus. The model is not the object, though we may wish it were.
A model is a metaphor of limited applicability, not the thing itself. Calling a computer an electronic brain once cast light on the function of computers. Nevertheless, a computer is not an electronic brain. Calling the brain a computer is a model too. In tackling the mysterious world via models we do our best to explain the thus-far incomprehensible by describing it in terms of the things we already partially comprehend. Models, like metaphors, take the properties of something rich and project them onto something strange.
A model focuses on parts rather than the whole. It is a caricature which overemphasizes some features at the expense of others.
WHY IS A THEORY A THEORY?
Models are analogies, and always describe something relative to something else. Theories, in contrast, are the real thing. They don’t compare; they describe the essence, without reference. Every fact, as Goethe wrote, is a theory.
In that sense, a theory is the ultimate non-metaphor.
It takes intuition to discover theories. Intuition may sound casual but it results from intimate knowledge acquired by careful observation and painstaking effort.
Right way To Use models
1. Avoid too much axiomatization
2. Good Models are Vulgar in a Sophisticated Way
3. Sweep Dirt Under The Rug, But Let Users Know About It
4. Think of Models as Gedanken Experiments
5. Beware of Idolatry