Ad oculos. Images, imagination and abstract thinking

The unusual edition of Elements of Euclid released for publishing in 1847 by Oliver Byrne offers the occasion to suggest a few elements for discussion on the uniqueness of the ‘representation’ of geometric-mathematical thinking – and more in general of the abstract thinking – enshrined in its ‘nature of a pure imaginative vision able to connect the intelligible with the tangible’. The purpose is, thus, a reasoning on images and communicative artefacts, that, when articulated, provide different variations of the idea of ‘transcription’ of complex theoretical structures from one language (that of abstract logic) to another (that of sensory experience), with a view to facilitate, ease and make more accurate the noetic process. Images able over time to facilitate the understanding of complex and abstract theoretical principles – since able to show them in an extremely concrete way, ad oculos, - and which at some points could reveal the horizons of art interpretation to inscrutable and figurative meaningless formulas.