This paper presents an explanation of why the quantification of the mechanism of catalytic cracking has eluded researchers for more than 60 years. The problem seems to lie in a set of dichotomies-pairs of related effects-which cause unanticipated changes in the parameter space within which catalytic cracking takes place. The consequences of these separate and overlapping effects are discussed below using our interpretation of catalytic cracking as a chain reaction. Quantitative expressions are derived on the basis of this postulate to describe the activity, selectivity, paraffin-to-olefin ratio, and volume expansion in catalytic cracking and to show how these quantities are affected by the presence of the dichotomies.