Digital sundials, paradoxical sets, and Vitushkin's conjecture (Q1086694)

A digital sundial is an ''object'' whose shadow at any given time shows the digits of that time. The existence of such a magic clock is a consequence of a more general result of the author on finding sets with prescribed projections [Proc. Lond. Math. Soc., III. Ser. 53, 48-64 (1986; Zbl 0602.28005)]. In this article the author discusses the underlying construction, earlier related results of Besicovitch, Davies and Marstrand, and a recent use of such constructions by the reviewer to disprove a conjecture in complex function theory.