4次元空間の可視化と認識
Visualization and recognition of four-dimensional space

私たちの知る世界は，「幅」「高さ」「奥行き」の3つの次元からなる空間です．一方で，数学においては，4次元以上の図形や空間も自然に扱われます．そして，それらは投影や切断といった手段によって，2次元や3次元の空間に映し出すことができます．

本研究の目的は，そのような映像を用いたインタラクティブな体験を通して，4次元の空間認識能力を獲得できるようにすることです．ここでいう空間認識能力(spatial cognition, spatial perception, spatial representation)とは主に，自分自身と周囲の物体との位置関係，向き，形状などを理解し，それらの変化を想像する能力のことです．4次元における空間認識能力と言われても存在すら疑わしく思われるかもしれませんが，実際のところ，その獲得は不可能なことではありません．既に複数の従来研究で，人が4次元の空間認識能力を発揮した例が報告されています．

しかしそれらの研究は，ごく単純な能力しか測っていなかったり，十分な事前知識を必要とするなど，まだ改善の余地を残しています．そのため現在は，より高度な空間認識能力をより多くの人が獲得できるようにするために，新たなシステムを開発しています．具体的には，直感的な操作システム，投影と切断を組み合わせた新たな表示システム，触覚提示，物理演算などの導入を行っています．

The world as we know it is a space consisting of three dimensions: width, height, and depth. On the other hand, in mathematics, shapes and spaces with four or more dimensions are naturally treated. They can be projected into two- or three-dimensional space by means of projection or cutting.

The purpose of our research is to enable users to acquire the ability to recognize four-dimensional space through interactive experiences using such images. Such abilities are called spatial cognition, spatial perception, or spatial representation, and mainly refer to the ability to understand the position, orientation, and shape of oneself and surrounding objects, and to imagine their changes. The ability to recognize space in four dimensions may seem doubtful, but in fact, it is not impossible to acquire this ability. Several conventional studies have already reported cases in which people have demonstrated the ability to recognize space in four dimensions.

However, there is still room for improvement, as these studies only measured very simple abilities and required sufficient prior knowledge. Therefore, we are currently developing a new system to enable more people to acquire more advanced spatial recognition abilities. Specifically, we are introducing an intuitive operation system, a new display system that combines projection and cutting, tactile presentation, and physical computing.

 

4次元多胞体の観察 (Observation of 4-dimensional polytopes)

4次元迷路の探索 (Exploring a four-dimensional maze)

投影と切断を組み合わせた表示システム (Display system that combines projection and cutting)

4次元の触覚提示システム (Four-dimensional tactile presentation system)