感知空间本质上是非欧几里得的吗？
Is perceptual space inherently non-Euclidean?
作者信息
Fernandez Julian Martin, Farell Bart
机构信息
Institute for Sensory Research, Syracuse University, Syracuse, NY, 13244, USA.
出版信息
J Math Psychol. 2009 Apr 1;53(2):86-91. doi: 10.1016/j.jmp.2008.12.006.
Abstract
It is often assumed that the space we perceive is Euclidean, although this idea has been challenged by many authors. Here we show that, if spatial cues are combined as described by Maximum Likelihood Estimation, Bayesian, or equivalent models, as appears to be the case, then Euclidean geometry cannot describe our perceptual experience. Rather, our perceptual spatial structure would be better described as belonging to an arbitrarily curved Riemannian space.
摘要
人们常常认为我们所感知的空间是欧几里得空间，尽管这一观点已受到许多作者的质疑。在这里我们表明，如果空间线索按照最大似然估计、贝叶斯或等效模型所描述的那样进行组合（情况似乎确实如此），那么欧几里得几何就无法描述我们的感知体验。相反，我们的感知空间结构更适合被描述为属于一个任意弯曲的黎曼空间。
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