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The best scientific theories are simple, straightforward, effectively predict the results of observations and contain internal elegance. The simplest equations of Newton F = ma and Einstein E = mc

The original model of the “elegant Universe”, Mysterium Cosmographicum [The Mystery of the Universe] Kepler was symmetrical, beautiful and based on mathematics, which was not used before. But our warning story about how it turned out to be a huge scientific failure.

Before Kepler, there were three main systems describing the Universe [the solar system in terms of that time]:

- The model of Ptolemy, in which the Earth was stationary, and everything revolved around it in a circle, used equants , defenders and epicycles .
- The Copernican model, in which the Sun was still and the Earth was one of six planets orbiting it, also used epicycles.
- The Tycho Brahe model, or the geo-heliocentric model, in which the Sun rotated around the Earth, and all other planets — around the Sun in circles, also using epicycles.

Kepler, creating scientific work decades before Galileo, considered heliocentric systems promising, but they needed more than just circles. To support them, an elegant mathematical structure was required. In a fit of genius, at just 24, Kepler published an idea that he considered the most beautiful of his ideas.

Since six planets revolved around the Sun (everything that is behind Saturn will be discovered only 200 years later), Kepler decided that there should be six unique orbits: one on each of the planets. But why six? Why not more, why not less? Why are there such distances between them? The connection between orbits and mathematics became his idea of an elegant universe:

I plan to demonstrate that God, creating the universe and placing the spheres, meant five regular geometric polyhedra, and limited them to the number, proportions and movement of the spheres.

You see, in three dimensions from regular polygons, you can create exactly five polyhedra , no more and no less. They were discovered by the ancient Greeks 2000 years ago, and sometimes they are called Plato polyhedra (although they were discovered long before Plato). Kepler imagined a system of nested spheres, described and inscribed around each of the polyhedra, resulting in six spherical orbits, in which the planets move.

The sphere of Mercury must be the innermost, and is inside the octahedron, a regular polyhedron consisting of eight equilateral triangles. The sphere of Venus is described around it - it is also inscribed in the icosahedron, a 20-sided figure consisting of equilateral triangles. Around it is described the sphere of the Earth, inscribed in the dodecahedron, whose 12 faces are pentagons. A sphere of Mars is inscribed around it, inscribed in a tetrahedron: a tetrahedral polyhedron with sides in the form of equilateral triangles. Around the tetrahedron is described the Jupiter sphere, inscribed in a cube, the final polygon. And the last sphere is described around it, with the orbit of Saturn.

Kepler’s idea was indeed ingenious; based on it, it was possible to accurately calculate the ratio of the radii of all orbits. The problem was revealed when comparing calculations with observations. The relations of the calculated radii of the orbits of Mercury and Venus, Venus and Earth, Earth and Mars corresponded to reality quite well, but the last two worlds could not meet the radii predicted by Kepler. In particular, the model was refuted by the orbit of Mars, which did not correspond to any circle. And although Kepler continued to work on it, and even published a second edition 20 years later, his most remarkable contribution was that most scientists are incapable of: discarding their favorite hypothesis.

But it was not the nested spheres that managed to predict the movement of the planets, but ellipses. The three Kepler laws , on the movement of planets in ellipses around the Sun, on equal areas described by radii for equal periods of time, and on equality of relations between the squares of the orbits of planets and the cubes of the major semiaxes of their orbits, have refuted and replaced Mysterium Cosmographicum. The success of elliptical orbits paved the way for Newton's law of the world, and gave rise to astrophysics. Despite Kepler’s unfading love of the most ingenious idea, the Universe was better described by a less elegant model. Having set aside his hopes and letting the experimental data behave further, he was able to achieve breakthroughs that the less gifted mind would not have noticed.

In physics, there is a temptation to succumb to reductionism: to describe as many phenomena as possible with the least possible means. The idea of the existence of the theory of everything, the only theory capable of predicting and describing everything that can be described or predicted in the Universe with the greatest possible accuracy, serves as a dream and the ultimate goal of many scientists. However, there are no guarantees that such a dream can even come true in principle. As the famous physicist Lincoln Wolfenstein wrote:

Kepler’s lesson is not that we should refrain from posing seemingly fundamental questions; the lesson is that we are not given to find out if there are simple answers to them, and where they can be found.

Elegance, beauty and reductionism can open up incredible opportunities for successful predictions of new physical phenomena, but there are no guarantees that these predictions will come true. Making a new breakthrough in fundamental science, our dreams and hopes of approaching the unifying theory of everything with the help of mathematical beauty and additional symmetry are shared by many, but no one guarantees them. May we all be just as open to the fact that we are being informed of the data that Kepler was, and will be able to follow them no matter where they lead us.

Source: https://habr.com/ru/post/412233/