Scientific Method

In 1913, Niels Bohr used the term model for his published description of the hydrogen atom. This term is now used to characterize theories developed long before Bohr's time. Essentially, a model implies some correspondence between the model itself and its object. A single correspondence is often enough to provide a very useful model, but it should never be forgotten that the intent of creating the model is to make predictions.

There are many types of models. A conceptual model refers to a mental picture of a model that is introspectively present when one thinks about it. A geometrical model refers to diagrams or drawings that are used to describe a model. A mathematical model refers to equations or other relationships that provide quantitative predictions.

It is an interesting fact that if a mathematical model predicts the future accurately, there may be no need for interpretation or visualization of the process described by the mathematical equations. Many mathematical models have more than one interpretation. But the interpretations and visualization of the mathematical model should facilitate the creation of new models.

New models are not constructed from observations of facts and previous models; they are postulated. That is to say that the statements that describe a model are assumed and predictions are made from them. The predictions are checked against the measurements or observations of actual events in nature. If the predictions prove accurate, the model is said to be validated. If the predictions fail, the model is discarded or adjusted until it can make accurate predictions.

The formulation of the scientific model is subject to no limitations in technique; the scientist is at liberty to use any method he can come up with, conscious or unconscious, to develop a model. Validation of the model, however, follows a single, recurrent pattern. Note that this pattern does not constitute a method for making new discoveries in science; rather it provides a way of validating new models after they have been postulated. This method is called the scientific method.

The scientific method: 1) postulates a model consistent with existing experimental observations; 2) checks the predictions of this model against further observations or measurements; 3) adjusts or discards the model to agree with new observations or measurements.

The third step leads back to the second, so, in principle, the process continues without end. (Such a process is said to be recursive.) No assumptions are made about the reality of the model. The model that ultimately prevails may be the simplest, most convenient, or most satisfying model; but it will certainly be the one that best explains those problems that scientists have come to regard as most acute.

Paradigms are models that are sufficiently unprecedented to attract an enduring group of adherents away from competing scientific models. A paradigm must be sufficiently open-ended to leave many problems for its adherents to solve. The paradigm is thus a theory from which springs a coherent tradition of scientific research. Examples of such traditions include Ptolemaic astronomy, Copernican astronomy, Aristotelian dynamics, Newtonian dynamics, etc.

To be accepted as a paradigm, a model must be better than its competitors, but it need not and cannot explain all the facts with which it is confronted. Paradigms acquire status because they are more successful than their competitors in solving a few problems that scientists have come to regard as acute. Normal science consists of extending the knowledge of those facts that are key to understanding the paradigm, and in further articulating the paradigm itself.

Scientific thought should in principle be cumulative; a new model should be capable of explaining everything the old model did. In some sense the old model may appear to be a special case of the new model. In fact, whether this is so seems to be open to debate.

The descriptive phase of normal science involves the acquisition of experimental data. Much of science involves classification of these facts. Classification systems constitute abstract models, and it is often the case that examples are found that do not precisely fit in classification schemes. Whether these anomalies warrant reconstruction of the classification system depends on the consensus of the scientists involved.

Predictions that do not include numbers are called qualitative predictions. Only qualitative predictions can be made from qualitative observations. Predictions that include numbers are called quantitative predictions. Quantitative predictions are often expressed in terms of probabilities, and may contain estimates of the accuracy of the prediction.