Metacognition in Sebastian`s Door: mathematics, education and art

The aim is to show metacognition in how mathematics and culture are related in the sculptural work of Master Sebastián; with a deep playful character from which it emerges. Constituting a kind of artistic syncretism of apparently divergent beliefs between the plastic world, pure mathematics, abstract geometry and computational cybernetics. Methodology, study with a qualitative approach, the variables to consider were: Bach's baroque music with the canon and fugue, Gödel's theorem with the incompleteness of the axiomatic system; Eschery lithographs the reiteration of forms; Borje's literary-mathematical paradoxes; recursive programming routines in artificial intelligence systems (expert systems, mathematics) and Sebastián's sculpture. In conclusion, the convergence between Bach's baroque music can be identified, through the generation of the canon and the fugue; Gödel's theorem on the incompleteness of the axiomatic system, the reiteration of forms that invent themselves in Escher's lithographs, the literary-mathematical paradoxes in the stories of Jorge Luis Borges, and the use of recursive routines in the programming of expert systems or artificial intelligence. This game of plastic metamorphosis with which Sebastián surprised us a few years ago, turns out to predate the concept of the transformers, long before Hollywood made them a commercial success. As in the most diverse efforts of syncretism, Sebastián has traveled close to profanation as the staunch conservatives of the elite of scientists and artists can describe it.