In the illustration: A tesseract (a four-dimensional cube) and the "shadow" it casts on a plane—the quasicrystal discovered by Shechtman. According to Prof. Bartal, "The fact that a quasicrystal is a ...

We all know we live in three-dimensional space. But what does it mean when people talk about four dimensions? Is it just a bigger kind of space? Is it "space-time," the popular idea which emerged from ...