sume that nature is uniform, that the unsampled remainder is similar in behavior to our samples, that today’s natural laws will still be valid tomorrow. Without this assumption, all is chaos.
Types of Explanation
Induction is explanation, and explanation is identification of some type of order in the universe. Explanation is an integral part of the goal of science: perceiving a connection among events, deciphering the explanation for that connection, and using these inductions for prediction of other events. Some scientists claim that science cannot explain; it can only describe. That claim only pertains, however, to Aristotelian explanation: answering the question “Why?” by identifying the purpose of a phenomenon. More often, the scientific question is “How?” Here we use the inclusive concept of explanation as any identification of order.
Individual events are complex, but explanation discerns their underlying simplicity of relationships. In this section we will consider briefly two types of scientific explanation: comparison (analogy and symmetry) and classification. In subsequent sections we will examine, in much more detail, two more powerful types of explanation: correlation and causality.
Explanation can deal with attributes or with variables. An attribute is binary: either present or absent. Explanation of attributes often involves consideration of associations of the attribute with certain phenomena or circumstances. A variable, in contrast, is not merely present or absent; it is a characteristic whose changes can be quantitatively measured. Explanations of a variable often involve description of a correlation between changes in that variable and changes in another variable. If a subjective attribute, such as tall or short, can be transformed into a variable, such as height, explanatory value increases.
The different kinds of explanation contrast in explanatory power and experimental ease. Easiest to test is the null hypothesis that two variables are completely unrelated. Statistical rejection of the null hypothesis can demonstrate the likelihood that a classification or correlation has predictive value. Causality goes deeper, establishing the origin of that predictive ability, but demonstration of causality can be very challenging. Beyond causality, the underlying quantitative theoretical mechanism sometimes can be discerned.
Comparison is the most common means of identifying order, whether by scientists or by lay people. Often, comparison goes no farther than a consideration of the same characteristic in two individuals. Scientific comparison, however, is usually meant as a generalization of the behavior of variables or attributes. Two common types of comparison are symmetry and analogy.
Symmetry is a regularity of shape or arrangement of parts within a whole -- for example, a correspondence of part and counterpart. In many branches of science, recognition of symmetry is a useful form of pattern recognition. To the physicist, symmetry is both a predictive tool and a standard by which theories are judged.
In his book on symmetry, physicist Hermann Weyl [1952] said: “Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty, and perfection.”
I’ve always been confident that the universe’s expansion would be followed by a contraction. Symmetry demands it: big bang, expanding universe, gravitational decel-
