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 can tie knots in three dimensions because one-dimensional ropes “catch on each other”. This is why a long rope wound around itself, if done right, won’t come apart. We trust knots with our lives ...