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.

中文翻译：

---

Quantum GestART：识别和应用数学、艺术和感知组织之间的相关性

数学可以帮助分析艺术并激发新的艺术作品。考虑到例外和选择，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变为另一种艺术媒介。我们提出了一种基于图解思维和量子形式主义的方法。我们利用将复杂形式分解为一组简单的形状、复杂图像的离散化和狄拉克符号，想象一个“原型”世界，可以将其连接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（起始、持续时间、响度、音调范围）相关联。