Plato’s Allegory of the ‘Cave’ and Hyperspaces: Sonic Representation of the ‘Cave’ as a Four-Dimensional Acoustic Space via an Interactive Art Application

Abstract

Mathematician and philosopher Charles Howard Hinton posited a plausible correlation between higher-dimensional spaces, also referred to as ‘hyperspaces’, and the allegorical concept articulated by the Ancient Greek philosopher Plato in his work, Republic, known as the ‘Cave.’ In Plato’s allegory, individuals find themselves situated in an underground ‘Cave’, constrained by chains on their legs and neck, perceiving shadows and sound reflections from the ‘real’ world cast on the ‘Cave’ wall as their immediate reality. Hinton extended the interpretation of these ‘shadows’ through the induction method, asserting that, akin to a 3D object casting a 2D shadow, the ‘shadow’ of a 4D hyper-object would exhibit one dimension less, manifesting as a 3D object. Building upon this conceptual framework, the authors posit a correlation between the perceived acoustic space of the bounded individuals within the ‘Cave’ and the characteristics of a 4D acoustic space, a proposition substantiated mathematically by scientific inquiry. Furthermore, the authors introduce an interactive art application developed as a methodical approach to exploring the hypothetical 4D acoustic space within Plato’s ‘Cave’, as perceived by the bounded individuals and someone liberated from his constraints navigating through the ‘Cave.’

Keywords

• Socrates
• Plato
• hyperspaces
• fourth spatial dimension
• Plato’s Cave
• Charles Howard Hinton