Mathematics can help analyze the arts and inspire new artwork. Mathematics can also help make transformations from one artistic medium to another, considering exceptions and choices, as well as artists' individual and unique contributions. We propose a method based on diagrammatic thinking and quantum formalism. We exploit decompositions of complex forms into a set of simple shapes, discretization of complex images, and Dirac notation, imagining a world of “prototypes” that can be connected to obtain a fine or coarse-graining approximation of a given visual image. Visual prototypes are exchanged with auditory ones, and the information (position, size) characterizing visual prototypes is connected with the information (onset, duration, loudness, pitch range) characterizing auditory prototypes. The topic is contextualized within a philosophical debate (discreteness and comparison of apparently unrelated objects), it develops through mathematical formalism, and it leads to programming, to spark interdisciplinary thinking and ignite creativity within STEAM.

数学可以帮助分析艺术并激发新的艺术作品。考虑到例外情况和选择以及艺术家的个人和独特贡献，数学还可以帮助从一种艺术媒介转换为另一种艺术媒介。我们提出了一种基于图解思维和量子形式主义的方法。我们将复杂形式的分解分解为一组简单的形状，复杂图像的离散化和Dirac表示法，想象一个“原型”世界，可以将其联系起来以获得给定视觉图像的细粒度或粗粒度近似值。视觉原型与听觉原型交换，表征视觉原型的信息（位置，大小）与表征听觉原型的信息（开始，持续时间，响度，音调范围）相关。