In 1958, the British mathematician Roger Penrose and his geneticist father Leonid Penrose jointly proposed the Penrose Ladder: a ladder that always goes up or down. There is no end to the ladder. There is no highest or lowest point on this ladder. This is a variation of the triangle, a geometric paradox.

The Penrose ladder cannot exist in three-dimensional space, but it becomes very easy in high-dimensional space-time. In the three-dimensional world, it is as complex as a M?bius strip or a Klein bottle.

Why is the Penrose Staircase said to be the "ghost building a wall" in the scientific world?

Someone once made an animation in which the person in the animation was always going up the stairs, but he was still spinning in circles while walking up and down the stairs. He didn't believe it was true and kept walking up. Once a fish fell on a ladder, and he accidentally stepped on it. He stopped for a moment, ignored the fish, and continued to climb up.

As a result, he saw the fish he stepped on again on the way up the stairs, and the result repeated - no matter how hard he walked, he would always spin in the same position...< /p>

This is exactly the same as the "ghost beating the wall" in reality. "Ghost against the wall" means that when people walk in the suburbs at night, they are sometimes confused by the scenery in front of them. Their eyes and brain lose the ability to correct and distinguish, and they think they are walking in the right direction, but in fact they keep spinning in circles.

It is an infinite loop of stairs caused by an optical illusion. It has no highest point and no lowest point, but it has the visual feeling of going up and down the stairs. Strange geometric shapes constructed from optical illusions. An infinite loop of going downstairs or upstairs. If the previous picture wasn't obvious enough, take a closer look at this picture and it will become clear.

In 1958, the famous British mathematician Roger Penrose and his father, the geneticist Leonid Penrose, jointly proposed this interesting optical illusion geometry. pattern. Since then, the research and creation of optical illusion geometric patterns has begun.

As a geometric paradox, it goes against our geometric common sense and physical principles. In our three-dimensional world, an infinite loop of stairs is impossible to exist, because you will definitely reach the highest point. point or the lowest point, otherwise we would get a perpetual motion machine. Because when an object moves from high to low, it will release energy, and the infinite downward ladder naturally means that it can release infinite energy.

However, the Penrose ladder looks so natural visually, which reveals some inherent flaws or internal operating mechanisms of the human visual system. By cleverly setting the aspect ratio of the steps, human vision can be induced to make the impression of going uphill or downhill. This is the key trick in drawing the Penrose Stairs.