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Historians of science usually set the year 1543 as the beginning of the scientific revolution, when Copernicus published the Theory of the Operation of the Ball of Heaven for the first time to abandon the geocentric view and set the earth in motion. Although this is a convenient and reasonable choice, it is not the only good choice. Before Copernicus, a scientific breakthrough driven by artistic rather than astronomical needs was also of far-reaching significance: Philippo Brunelleski (Filippo Brunelleschi) invented perspective after 1420.

Brunellesky demonstrated his ability to depict images accurately through the excellent experiment shown in figure 1. Fifteen years after he completed the experiment, Leon Batista Alberti (Leon Battista Alberti) came up with a classic explanation for the technique. It involves a very interesting new type of geometry: projective geometry.

Figure 1: Brunellesky's device, the viewer can compare the reflected image with the object itself by removing the mirror. Bruneleski and Alberti's work had a great impact on the artists of the time. Obviously, it enables artists to depict scenes more accurately. It also built up great confidence for the people at that time: people finally made a great discovery that obviously surpassed the ancient Greeks and Romans. For artists, what they seek is no longer to restore the lost heritage, but to develop a new kind of creativity.

We can see projective geometry in Perugino's masterpiece delivery of Keys (1481-1482) in figure 2. The floor tiles of the city square, the parallel lines marked by buildings, and the relative size of characters and scenery all show scientific and accurate painting skills.

Figure 2: the Beauty of Perspective: Perujino's delivery of the key (1481-1482) some people sometimes think that there is a fundamental difference between science and art in their methods and categories, because science strives for objectivity while art is subjective in nature. Perspective science proves the superficiality of this statement. As far as perspective is concerned, what we care about is what people see in a particular position and from a particular point of view. In fact, it can be defined as an objective study of subjectivity.

More noteworthy is the way in which we predict basic scientific concepts that determine our understanding of the laws of nature. Most people are not familiar with many important ideas in modern physics. In the original paper, they may appear abstract and obscure and difficult to accept, so popular science workers must often use metaphors and analogies. But it is a challenge to find metaphors that are both faithful to the original ideas and easy to understand; what is more challenging is to show the beauty of these ideas in an appropriate way. Over the years, I have struggled with this problem many times. Here, I am happy to come up with a solution that I am really satisfied with.

Projective geometry, a Renaissance artistic innovation, contains not only metaphors, but also real models of grand, delicate, and esoteric ideas:

The principle of relativity holds that the same object can be faithfully and completely expressed in many different ways. In this sense, relativity is the essence of projective geometry. We can paint the same scene from many different angles. The distribution of pigments on the canvas will be different, but they all depict the same information about the object, but are presented in different ways.

Symmetry is closely related to relativity, although now our attention is focused on the object of painting rather than on the audience. "unchanging change" is the essence of symmetry. Consider the most symmetrical shape: circle. Rotate the circle at any angle around the center of the circle, this transformation changes the position of each point on the circle, but the whole circle does not change. Similarly, if we move the traced object-- such as rotating it, or changing its position-- we will change its appearance. But its projection description-the sum of the views provided by all possible perspectives-remains the same because you can move the easel to counteract the change.

Invariance is the opposite of relativity. When we change our perspective, many aspects of objects have different representations, but all of these representations have some common characteristics. For example, a straight line in an object still appears as a straight line from any angle, although they have different directions and positions on the canvas; if three lines intersect in the actual object, then no matter from any angle, their projections still meet at the same point. All the features that represent common are called invariance. Invariants are important because they define the objective characteristics of the object, which are valid from any point of view. They defined the nature of its "objective reality".

At the forefront of modern physics, related experiments are very difficult. Simple experiments have been completed, and the principles they reveal have been thoroughly absorbed by the relevant theories. Previous physicists patiently accumulated data and then used them to infer laws, but this induction is no longer practical. On the contrary, the effective method now is to guess the laws, deduce their results, and how to verify these conjectures experimentally, so as to find out whether nature really operates according to these laws.

If it is not experimental data, what is the basis of the conjecture? One word, aesthetic. As mentioned above, symmetry is the most important source of inspiration for contemporary physicists and provides us with the most abundant results. The equations we propose can be expressed in many forms, but their essential contents are the same.

In fact, there are incredible similarities between the principle of symmetry embodied in the basic Law of Physics and the two new artistic perspectives.

In deformed works of art such as twisted cylinders made by Istv á n Orosz in figure 3 below, people can use devices such as mirrors and lenses to achieve more complex transformations than ordinary perspective. Similarly, in general relativity, people can rearrange the so-called metric flow to achieve the appearance of the same space-time under different transformations. This is the essence of Einstein's "generalized covariation". )

Figure 3: in transfiguration art, modern artists such as Istv á n Orosz have expanded the connotation of perspective. Morphing art not only allows images to change with changes in viewpoint, but also includes changes caused by plane mirrors and lenses. Einstein obtained his theory of gravity by looking for special symmetry equations, the essence of which will not be changed by the transformation of time and space.

Our theory of other basic interactions-electromagnetic force, weak force and strong force-is also based on transformations that are less common in art, but not unknown. Instead of moving points in the image, they change colors in different places in different ways. Henry Matisse (Henri Matisse) used this idea to draw several compelling paintings.

Figure 4: the woman in the Hat (1905) by Henri Matisse, the details of which introduce another kind of "perspective": the audience moves in the "color space" rather than in the real space. Image source wiki. Today, science and art interact positively in many ways. To cite a few examples: fractals have always been a source of inspiration for graphic art and provided the impetus for the creation of gorgeous artificial "landscapes"; astronomical images are often used in false colors, and posters with such artificial color images are often used for decoration; movies and sports broadcasts contain a wealth of creative digital image processing.

But the possibility of creative cooperation between science and art is far from exhausted. In fact, I think we just scratched the surface.

Physicists often praise the beauty of physical concepts and equations, and it is true. On the other hand, human beings are strong visual creatures. Therefore, it is worthwhile to transform these beautiful concepts and equations into intuitive and visible forms by modern means such as signal processing and computer graphics, so that physicists can directly understand the connotation of the concept. ordinary people can also appreciate and enjoy the beauty of modern physics. In particular, we need better ways to bring ourselves into sensory contact with high-dimensional space, such as the space we encounter in quantum theory and dealing with big data. Just as Brunelesky uses perspective and projection to show the scene in three dimensions, contemporary physicists who use art to compare science have a lot of work to do.

Author: Frank Wilczek

Translator: Tibetan idiot

Revision: miss circle pi

Original link: Why physics needs art to help picture the universe

This article comes from the official account of Wechat: Institute of Physics, Chinese Academy of Sciences (ID:cas-iop), author: Frank Wilczek

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