Turning a sphere inside out

In a world with four spatial dimensions, it would be possible to turn a sphere inside out. To understand this, let's start with a 2D analogy. Imagine a rubber band lying flat on a piece of paper. To a 2D creature living on that paper, the rubber band appears as a solid, unbroken loop. A circle that seems impossible to turn inside out without cutting it. But for us, with access to the third dimension, flipping the rubber band is easy. It involves lifting and twisting it through the space above the paper. A direction the 2D creature can't perceive. Now imagine we are like that 2D creature, but in three dimensions. To a 4D creature, we appear flat. To them, a rubber ball is like the rubber band in our analogy. It isn't closed in the fourth dimension. A 4D creature could effortlessly flip the ball inside out without puncturing it. They can simply twist it through a region of space we can't perceive.