Explanation and Prediction

Models are used to organize human thought in the form of explanations. When we understand how a phenomenon results from other basic principles, we gain a number of advantages. Not least is the feeling of confidence that we have actually understood it; people often claim to have a grasp on or have their head around an idea when they finally understand it. Explanation plays a major role in this sort of understanding. Explanation also assists in memory; it is easier to remember that putting a lid on a flaming pot can quench the flame if one knows the explanation that fire requires air to burn. Most important for the context of the Semantic Web, explanation makes it easier to reuse a model in whole or in part; an explanation relates a conclusion to more basic principles. Understand­ing how a pot lid quenches a fire can help one understand how a candle snuffer works. Interpretability and explanation are vital for establishing trust in a model and to effectively support decision­making. You are more likely to trust my model, if I can provide results you can interpret and explanations so that you can under­stand why the model is appropriate. Interpretability and explanation are the keys to understanding when a model is applicable and when it is not.

Closely related to this aspect of a model is the idea of prediction. When a model provides an adequate explanation of a phenomenon, it can also be used to make predictions. This aspect of models is what makes their use central to the scientific method, where falsification of predictions made by models forms the basis of the methodology of inquiry.

Explanation and prediction typically require models with a good deal more for­mality than is usually required for human communication. An explanation relates a phenomenon to first principles; these principles, and the rules by which they are related, do not depend on interpretation by the consumer but instead are in some objective form that stands outside the communication. Such an objective form, and the rules that govern how it works, is called a formalism.

Formal models are the bread and butter of mathematical modeling, in which very specific rules for calculation and symbol manipulation govern the structure of a mathematical model and the valid ways in which one item can refer to another. Explanations come in the form of proofs, in which steps from premises (stated in some formalism) to conclusions are made according to strict rules of transfor­mation for the formalism. Formal models are used in many human intellectual endeavors, wherever precision and objectivity are required.

Formalisms can also be used for predictions. Given a description of a situation in some formalism, the same rules that govern transformations in proofs can be used to make predictions. We can explain the trajectory of an object thrown out of a window with a formal model of force, gravity, speed, and mass, but given the initial conditions of the object thrown, we can also compute, and thus predict, its trajectory.

Formal prediction and explanation allow us to evaluate when a model is appli­cable. Furthermore, the formalism allows that evaluation to be independent of the listener. One can dispute the result that 2 + 2 = 4 by questioning just what the terms 2, 4, +, and = mean, but once people agree on what they mean, they cannot (reasonably) dispute that this formula is correct.

Formal modeling therefore has a very different social dynamic than informal modeling; because there is an objective reference to the model (the formalism), there is no need for the layers of interpretation that result in Talmudic modeling. Instead of layers and layers of interpretation, the buck stops at the formalism.