> Four conditions must be satisfied to have a valid scientific theory: (1) There is a mathematical model expressing the theory. (2) Precise relationships, known

> Four conditions must be satisfied to have a valid scientific theory: (1) There is a mathematical model expressing the theory. (2) Precise relationships, known as “operational definitions,” are specified between terms in the theory and measurements of corresponding physical events. (3) There are validating data: there is a set of future quantitative predictions derived from the theory and measurements of corresponding physical events. (4) There is a statistical analysis that supports acceptance of the theory, that is, supports the concordance of the predictions with the physical measurements—including the mathematical theory justifying the application of the statistical methods. This definition appears rigorous at a glance, but it is deficient. We cannot properly test a theory if it only predicts things which we already expect to happen. Popper said that scientific theories must instead make "risky predictions": "Confirmations should count only if they are the result of risky predictions; that is to say, if, unenlightened by the theory in question, we should have expected an event which was incompatible with the theory–an event which would have refuted the theory."