[3L5-GS-1] Fundamental AI, theory, algorithm:

[3L5-GS-1-01] Toward demonstration of four dimensional perception

Basic mathematics for planar perspective projection and orthogonal transformation in four dimensional space

〇SHOHEI HIDAKA¹, Takuma Torii², Kohske Takahashi³ (1. Japan Advanced Institute of Science and Technology, 2. Tokyo Denki University, 3. Ritsumeikan University)

Keywords:Four dimensional perception, Orthogonal matrix, Projective space

Can we intuitively perceive and manipulate some object in higher than three dimensional space? The present study aims to build a theoretical framework to explore and validate human’s capability to perceive an object in four dimensional space. In machine learning, multivariate analysis, and other applications, orthogonal matrices are used to transform objects in vector space by keeping their metric relationship invariant. Four or higher dimensional space, any orthogonal matrix has some component visible and invisible through any two dimensional projection. This study proposes a systematic method to naturally visualize four dimensional objects by decomposing any orthogonal matrix into the visible invisible components.