Ideological conversion has been the subject of extensive inquiry in recent decades. One of many areas of confusion regarding this topic involves the often reported radical, stepwise, nature of some conversions, subjectively experienced as ‘snapping’. Such conversions stand in contrast to others which are reported to be gradual transitions, sometimes occurring so slowly that no specific experience of conversion occurs at all. On reviewing extensive written reports of conversions from autobiographies, from therapists, and from sociologists, social psychologists, and others, the frequent occurrence of both types of conversions seems incontrovertible. This paper attempts to delineate the conditions under which one or the other type of conversion is to be expected.

The nature of the problem can be readily couched in terms of mathematical catastrophe theory. Catastrophe theory was developed as a means for better understanding nonlinear transitions in biology and in other sciences. The term catastrophe is potentially confusing, as it has nothing to do with the importance, magnitude, or devastating consequences of the event, such as is often implied in non-mathematical uses of the term. In mathematics, all that is meant by a catastrophe is a nonlinear transition from one state to another. Consider, for example, opening a stuck lid on a pickle jar. As increasing pressure is applied, nothing happens, the lid remains stuck. But at some point, a minuscule increase in pressure will cause the lid to become unstuck.