Self-reference (1)

Self-reference is at the root of well-known paradoxes, but also of a profound crisis in the foundations of logic and mathematics. At the heart of the famous incompleteness theorem of Gödel, one can find a variant of the sentence "This proposition is false". Beyond thorny philosophical problems, self-reference allows us to play with infinity, both in art and in mathematics. Thus, certain sequences of numbers possess symmetries that one would never have been able to imagine without having reflected on the rich notion of self-similarity, which reveals, for our greatest pleasure, "self-descriptive" and even "fractal" sequences. Readers will discover the continuation of this ambitious two-part feature in the next issue (Tangente 192).