In this paper I review and summarize the logical process through which Doering and Roth (Tetrahedron 1963, 19, 715) conceived of the possible existence of an isomer of molecular formula C10H10 that has a "fluxional" structure. That is, the molecule has a structure in which every carbon atom is equally bonded, or not bonded, to every other carbon. The evidence for its "fluxional" structure is that it gives a sharp singlet in its proton NMR spectrum. In order for the 10 protons, each bonded to a carbon atom, to be chemical-shift equivalent, Doering and Roth conclude that "all ten carbon atoms [must] inevitably wander over the surface of a sphere in ever changing relationship to each other."
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Addison Ault (2001) studied this question.