Pizlo Zygmunt, de Barros J Acacio
Department of Cognitive Sciences, University of California, Irvine, Irvine, CA, United States.
School of Humanities and Liberal Studies, San Francisco State University, San Francisco, CA, United States.
Front Comput Neurosci. 2021 Aug 23;15:681162. doi: 10.3389/fncom.2021.681162. eCollection 2021.
Perceptual constancy refers to the fact that the perceived geometrical and physical characteristics of objects remain constant despite transformations of the objects such as rigid motion. Perceptual constancy is essential in everything we do, like recognition of familiar objects and scenes, planning and executing visual navigation, visuomotor coordination, and many more. Perceptual constancy would not exist without the geometrical and physical permanence of objects: their shape, size, and weight. Formally, perceptual constancy and permanence of objects are invariants, also known in mathematics and physics as symmetries. Symmetries of the Laws of Physics received a central status due to mathematical theorems of Emmy Noether formulated and proved over 100 years ago. These theorems connected symmetries of the physical laws to conservation laws through the least-action principle. We show how Noether's theorem is applied to mirror-symmetrical objects and establishes mental shape representation (perceptual conservation) through the application of a simplicity (least-action) principle. This way, the formalism of Noether's theorem provides a computational explanation of the relation between the physical world and its mental representation.
知觉恒常性是指尽管物体发生了诸如刚体运动等变换，但其被感知到的几何和物理特征仍保持不变这一事实。知觉恒常性在我们所做的一切事情中都至关重要，比如识别熟悉的物体和场景、规划和执行视觉导航、视觉运动协调等等。如果没有物体的几何和物理恒常性，即它们的形状、大小和重量，知觉恒常性就不会存在。从形式上讲，物体的知觉恒常性和恒常性是不变量，在数学和物理学中也被称为对称性。由于100多年前埃米·诺特提出并证明的数学定理，物理定律的对称性获得了核心地位。这些定理通过最小作用量原理将物理定律的对称性与守恒定律联系起来。我们展示了诺特定理如何应用于镜像对称物体，并通过应用简单性（最小作用量）原理建立心理形状表征（知觉守恒）。通过这种方式，诺特定理的形式主义为物理世界与其心理表征之间的关系提供了一种计算解释。
