The principle of the staircase that always goes down in Ghost Blowing Lantern

The never-ending infinite loop of stairs is called the Penrose Stairs. It is also called the Suspended Soul Staircase in our country, which is the staircase that always goes down in Ghost Blowing Lantern.

In the Penrose Ladder, people can never find its highest or lowest point, and there is no end. It was created by Roger Penrose, a famous British mathematical physicist and emeritus professor of mathematics at Oxford University, and His father proposed. The Penrose ladder can be said to be the world's most famous geometric paradox about two- and three-dimensional space.

The Penrose Staircase will never exist in real life. In fact, it is an optical illusion caused by our visual system momentarily consciously projecting a three-dimensional figure on a two-dimensional figure. Although the Penrose ladder cannot exist in three-dimensional space, as long as it is placed in a higher-order space, the Penrose ladder can be easily realized, like a M?bius strip or a Klein bottle.

In addition, if you want the Penrose ladder to be realized in reality, you must rely on human illusion (or sensory misjudgment) to achieve it.

Required conditions:

1. "Gentle slope phenomenon" and background light and shadow effects: offset people's visual angle judgment;

2. Steps" "Plane" small angle rise: rely on small angles to offset the ankle joint's judgment of the angle. For example, if the angle is less than 5 degrees, it is difficult for people to rely on the posture of the ankle joint (or "climbing feeling") to judge whether it is horizontal;< /p>

3. Each step must fulfill its own drop, rather than dozens of steps to realize the drop of one step;

Principle of the gentle slope phenomenon:

When people After going down a steep slope (for example, an angle of 30 degrees), then a medium steep slope (for example, only 15 degrees), and finally switching to a small steep slope (5 degrees). Due to the contrast effect, people may think that they are "going uphill", but in fact Going up is going downhill.

This phenomenon may be encountered when driving on some special mountain roads. At this time, people clearly feel that they are going uphill, but they may slide faster and faster in neutral. Even after parking, they feel that the car is going "uphill". Slide in the "slope" direction.

When walking, this phenomenon is usually caused by

A. Background environment,

B. The posture (or inclination) of the ankle joint,

C. Corrected by the "sense of climbing";

When constructing the Penrose Ladder (Suspended Soul Ladder), the above three correction methods can be avoided:

A. Light, shadow and background are used to offset the influence of the environment (for example, the pattern on the wall itself is also skewed);

B. Relying on a small inclination to offset the angle judgment of the ankle joint (the heel is 10cm higher than the toe). It can be felt, but if it is only 0.2cm, the feeling will be very subtle or even completely undetectable);

C. Relying on "step movement" to distort the climbing feeling, long-term uphill or downhill will cause It brings an obvious "effort" or "effort-saving" feeling, but if it is just a few steps up and down the slope, the feeling will be very small. If there is an up and down step in the middle, this effect will also be eliminated;

< p>The "flat" steps rise at a small angle

The human body has an insensitive area for angle perception. Large angles (such as 30 degrees) are just to maintain the center of gravity. We will have a clear feeling when we stand up. , but it is difficult to perceive at small angles.

Without any other basis for judgment, people subconsciously think that the plane of the steps is "horizontal", but it is precisely here that sensory deception is carried out.

At a small inclination angle of 5 degrees, the tan value is about 0.09, which means that if the step length is 220cm, it can rise 20cm with an inclination angle of 5 degrees.

Using an inclination angle of 1 degree to raise it 20cm only requires less than 12 meters.

Finally:

1. People need to "go down" (up) from a large angle slope to the hanging soul ladder area to achieve the gentle slope effect

2. Each step is 20cm high and more than 5 meters long. It rises at a small angle of less than 5 degrees and the end of each step is actually level with the end of the previous step

3. Utilize The "light and shadow effect" gives a mural with the same inclination as the plane of the step, and it is continuous

4. The "falling section" of the step must be perpendicular to the next step, that is, it should be "vertical to The "lower" part also has an off-angle to keep the two steps vertical.

Extended information:

The Klein bottle was first proposed by the German geometry master Felix Klein. In 1882, the famous mathematician Felix Klein Klein discovered the famous "bottle" that would later bear his name.

The Klein bottle is a non-orientable two-dimensional compact manifold, while the sphere or tire surface is an orientable two-dimensional compact manifold. If you observe the Klein bottle, one thing seems confusing - the neck and body of the Klein bottle intersect. In other words, some points on the bottle neck and some points on the bottle wall occupy a three-dimensional space. the same location in . But this is not the case.

In fact, the bottleneck of the Klein bottle passes through the fourth dimensional space and is connected to the bottom circle of the bottle, and does not pass through the bottle wall. To use the analogy of a kink, if you think of it as a curve on a plane, it seems to intersect with itself, and then it seems to be broken into three parts. But it is actually easy to understand that this figure is actually a curve in three-dimensional space. It does not intersect with itself, but is a continuous curve.

Reference material: Baidu Encyclopedia - Penrose Ladder