Finally, the difference in incentives between discovery and invention impedes the necessary interaction between discovery and invention. To illuminate these relationships, let us start with the interactions within the process of discovery itself. An important component of discovery is the direct pursuit of basic knowledge by scientists and mathematicians. Science has become a specialized activity which advances through the interactions of specialists such as empiricists, theorists, mathematicians and engineers. Empiricists discover new phenomena, which stimulate theorists to explain with new models and theories.
Theorists then use formal mathematical methods to deduce the implications of their models.
Empiricists either confirm or reject these implications on the basis of experiments and hypothesis testing. In addition, engineers using new discoveries create new instruments such as new observation devices and computers, which in turn promote further empirical and theoretical studies. Similarly, mathematicians in discovering the structure of formal relationships, create new tools that theorists can use in constructing formal models of behavior. Through the interactions of specialists, then, new formal models for explaining and predicting behavior are created 4 . The next step is to describe the interactions between discovery and invention.