In their exhaustive study of the cognitive operation of analogy, Hofstadter and Sander arrive at a paradox: the creative and inexhaustible production of analogies in our thought must derive from a “reminding” operation based upon the availability of the detailed totality of our experience. Yet the authors see no way that our experience can be stored in the brain in such detail nor do they see how such detail could be accessed or retrieved such that the innumerable analogical remindings we (...) experience can occur. Analogy creation, then, should not be possible. The intent here is to sharpen and deepen our understanding of the paradox, emphasizing its criticality. It will be shown that the retrieval problem has its origins in the failure of memory theory to recognize the actual dynamic structure of events. This structure is comprised of invariance laws as per J. J. Gibson, and this event “invariance structure” is exactly what supports Hofstadter and Sander’s missing mechanism for analogical reminding. Yet these structures of invariants, existing only over optical flows, auditory flows, haptic flows, etc., are equally difficult to imagine being stored in a static memory, and thus only exacerbate the problem of the storage of experience in the brain. A possible route to the solution of this dilemma, based in the radical model of Bergson, is also sketched. (shrink)