Reconstructing the quantitative architecture of Dante's Comedy
Ambrogio Camozzi Pistoja · Zenodo (CERN European Organization for Nuclear Research) · 2016
When production records are lost, quantitative properties of an artifact may preserve evidence of how it was made. Dante’s Comedy provides a finite test case: its 100 cantos occupy thirteen line counts within a sixteen-state metrical range. We first examine poem-wide regularities in numerical-class frequency, canticle allocation and cumulative position. Drawing on medieval practical mathematics and geomantic computation, we then map the sixteen admissible states to sixteen four-row figures and examine five signatures involving parity balance, cumulative position, transitions, point-count occupancy and component incidence. An exhaustive comparison identifies 1,946,735 alternative bijections satisfying the five defined criteria, approximately one in 10.75 million alternatives. Purgatorio serves as a local test case, revealing concentric correspondences that preserve different quantities at different scales. Counterfactual constructions show that the recovered constraints do not uniquely determine the repertoire or its lower endpoint; these parameters are subsequently considered within a Timaean–Boethian framework of numerical harmonization. The reconstruction identifies a historically informed formal organization without establishing Dante’s use of the proposed encoding. Further evaluation requires extending the local analysis to Paradiso and Inferno, and the integration of the quantitative configurations with the verbal content of the poem.