Abstract
How the cilium appeared is still such a poorly defined question that current hypotheses range from a symbiotic spirochaete to a cellular eye. In this paper, the whole question is subdivided into a list of problems which are morphological, physiological and temporal. These problems are examined one by one, in order to analyse the most popular exogenous hypothesis of Margulis as well as other recent exogenous and endogenous hypotheses. To overcome fundamental topological and temporal difficulties, a new endogenous hypothesis is expounded, according to which the cilium derives from a cellular peduncle reinforced with microtubules. This hypothesis implies a geometrical rationale for the ninefold symmetry. In the last paragraph the consequences of the various hypotheses are compared.