**Why did Galileo refuse to reply to Kepler's letters? On the strange contrast between the mystic Kepler and the Galilean rationalist**

From "Mada" a scientific newspaper for each volume 1 number, January 1981, XNUMX Shebat XNUMX Published by the Weizmann Institute for Publications in Natural Sciences and Technology

November last year marked 350 years since the death of the great astronomer and geometer Johannes Kepler, who was born in 1571 in a town near Stuttgart in southern Germany and died on November 15, 1630. A clear picture of his work and personality began to take shape, based on his writings and letters since they first appeared in the middle of the last century; Starting in the middle of this century, they are in an advanced process of a second, more detailed edition. This picture leaves no doubt about the fact, which is unique in the history of science, that Kepler's scientific personality embodies the sharpest contrast between the irrational motives of a scientific researcher and his rational research method.

**Mystical belief in harmony**

Back in his years of study at the University of Tübingen, Kepler delved into the writings of Archimedes, Apollonius and Euclid until he thoroughly mastered the geometric methods of the ancient Greek sages. However, he was deeply influenced by the mystical worldview of the Pythagorean and Neoplatonic philosophers, in particular after a thorough study of the philosophy of Proclus (485-412) and his commentary on the first book of Euclid. This influence is evident in all of Kepler's writings, starting with his first book "Mysterium Cosmographicum" which was published in 1596, until the last of his major books "Harmonice Mundi", which appeared in 1619. The strength of this mystical influence did not fade throughout Throughout his life, and in all his publications and letters, he gave a clear expression to his strong belief in the existence of an overall harmony rooted in the structure of the cosmos and the mathematical laws that govern it.

A number of quotations from his first compositions and especially from his book "Razi Olam" will demonstrate this belief of his: "God created the heavenly bodies according to certain numbers"; "The Creator designed the human soul in such a way that it both expects and perceives harmonies. . . And proof of this is the actions of man in which his mind imprints harmonious proportions, such as singing, dancing, poetry, grammar and architecture"; "and therefore the nature under the moon, which was granted to man by the delegation of the Creator, is a much better geometry than what their thinking power has ever brought up The rational of human beings from their systematic study". Here Kepler emphasizes the part of unconscious mental forces in the knowledge of nature.

Kepler was convinced of the mathematical meaning of all natural events and believed with complete faith that this meaning is expressed in the harmonic properties. In this context, it is worth emphasizing his central idea in his book "Razi Olam", which preceded the discovery of his three famous laws regarding the movements of the planets. Kepler was an enthusiastic follower of the heliocentric theory of Copernicus, whose book "On the Rotations" appeared in; 1543 This theory opposed the geocentric theory of Ptolemy (Ptolemaeus), written around 150. Copernicus' method placed the sun at the center of the planetary system and assumed that the earth revolved around it as one of these six stars.

Based on his hypothesis, Copernicus was able to calculate the relative distances of the planets from the sun, while adhering to the concept of the ancient Greeks, that these stars move at equal speeds in circular orbits.

Kepler's goal was to discover a law that geometrically links these relative distances of the planets from the center of the system, because it was clear to him that we are not dealing here with microscopic data but with measurements whose relationships reveal the harmony of the system's structure. In his book he develops a very instructive idea about the mathematical aspect of the concept of harmony, which was the idea that guided Kepler in all his research: harmony means geometric symmetry and simple mispherical proportions. Since the sun is surrounded by six planets, there are five spaces between their orbits; And Kepler connected these five spaces with the five Platonic solids, that is, with the five perfect solids whose faces are either triangular, or square, or equilateral pentagons. These bodies are the tetrahedron (limited by 4 triangles), the cube (limited by 6 squares), the octahedron (limited by 8 triangles), the dodecahedron (limited by 12 pentagons) and the icosahedron (limited by 20 triangles).

Kepler hypothesized that the distances of the planets' orbits are such that the co-centric spheres they define precisely block the five Platonic bodies. It is not worth entering here into the details of Kepler's considerations and the reasons according to which he determined the order of these bodies, which are blocked by one another, since this theory remains a historical curiosity. However, great historical importance is attached to the fact that this guiding idea of the harmony of the world continued to fascinate Kepler throughout his search for simple symmetries and proportions in the planetary system and to constantly push him to discover additional data that reveal this harmony more precisely and prominently than the series of Platonic bodies. In the end it will become clear to Kepler that the blocking of the Platonic bodies in the spaces of the planets' orbits is nothing more than an unsatisfactory approximation, which does not correspond to the data of Copernicus' theory, that is, the average distances of the planets from the Sun.

**Give me a point of reference**

In the dozen years after the publication of his first book, Kepler's efforts were centered around the correction of these data, with the aim of achieving a more precise match between theory and experience. Even in ancient times it was known that the movement of the planets in their orbits is not equal in speed, assuming that the sun is the common center of these circles. However, this problem could be justified with the help of the assumption that the circles are eccentric with respect to the sun, ZA, that the centers of the circles do not converge with the sun.

This assumption allowed the Greek astronomers to hold the axiom that the motion of a planet is equivelocity with respect to the center somewhat distant from the Sun. Kepler's ambition was, first of all, to find more accurate values for this eccentricity of the orbits, and the first subject of his measurements was to improve the observational data of the eccentricity of the Earth's orbit, that is, a more accurate knowledge of the distances of the Earth from the Sun at different points of its orbit.

Kepler's ingenious idea in this task, testifies to the enormous power of his imagination. He wanted to hold on to a fixed reference point in space, which was easy to locate from time to time and by which the relative distances of the earth from the sun could be calculated. For this, choose the contrast point of Mars and the Sun as a grip point that defines the straight line Sun-Earth-Mars. After 687 days, the time of its complete orbit around the Sun, Mars returns to this point. At this time, a little less than two years, the earth is at a different point in its orbit, and the lines connecting it with Mars and the Sun together with the line of opposition of Mars to the Sun form a triangle, two of whose angles can be measured.

It is therefore possible to find the ratio of the sides of this triangle. With the help of repeated repetitions of this process, Kepler was able to determine the relative distances of the earth from the sun at different points of its orbit with much greater accuracy than had been achieved before him. It is worth noting by the way, that the portrait limit of the astronomical observations in the last years before the invention of the telescope reached 2 (minutes) of arc, that is, the limit of the natural separation capacity of the human eye. Considerable progress in these observations was made during the short period that Kepler served as an assistant to the great Danish scholar Tycho Brahe (1546-1601) during his stay in Prague, from 1600 until his death.

Determining these data revealed that the path of the country is somewhat different from the shape of the circle. After this stage of his measurements, Kepler applied the same method to different points of Mars' orbit. He used different points of opposition of Mars in relation to the Sun and the relative distances of the Earth from the Sun, which were already known to him. In this second phase of his measurements it was the relative distances of Mars from the vanishing sun that had to be measured. And here it became clear that it was in no way possible to continue with the assumption that the orbit of Mars is a circle, since the degree of eccentricity of this orbit is particularly large. Kepler tried in vain to postulate different elliptical orbit shapes and correlate them with the eccentricity data. Finally he reached the only conclusion that agrees with his measurements. The generalization of this conclusion regarding all the planets is Kepler's first law: "The planets move in ellipses around the sun, and the sun's place is at one of the centers of the ellipse". This law put an end to a 2000-year-old spell this year that would have covered the status of the circle and its uniqueness as the shape of the orbits of the celestial bodies.

**From harmony to harmony**

Following the discovery of the first law, Kepler tried to explain the mechanism of the solar system by raising a dynamic hypothesis, as many scientists tried after him. Also in his book "Razi-Olam" he proposed the existence of an attractive force, of a "repelling soul" in the sun, and continued to develop this idea. According to his hypothesis, the attractive force decreases and goes inversely proportional to the distance, and the rotation of the sun on an axis creates a vortex that drags the planets and drives them around. After reading Gilbert's book (William Gilbert 1544-1603) on the magnetism of the Earth (1600), he assumed that every planet has magnetism and its two magnetic poles, one of which is "friendly" to the sun and the other "hostile" to it, remain fixed in space. Due to this constancy of the poles, the planet will come somewhat closer to the sun, with its friendly pole facing it in part of its orbit, and will move away from it in the past over the other part of the orbit, where the hostile pole faces it. In this way, Kepler tried to explain the elliptical shape of the orbit.

This hypothesis has historical interest, but it is difficult to see it as a prediction of Newton's theory; After all, Kepler, although he emphasized the analogy between gravity and magnetism, did not identify the magnetic force as holding the planets in their orbits.

In his second major book, "Astronomia Nova de Motibus Stellae Martis" (Astronomia Nova de Motibus Stellae Martis), which appeared in 1609, there is also the formulation of Kepler's second law: since the sun is at the focus of the ellipse and its power decreases with distance, the speed of the planets It will be greater in the parts of the orbits closest to the sun and will decrease in the far parts of the orbits. It was therefore necessary to give up the axiom regarding their equal motion - the speed of the stars. But the second law restores the crown of harmony to its old age in a different way, expressing a new kind of equality. "The ray of travel connecting the planet with the sun passes in equal times over equal areas".

Almost ten more years of hard work passed before Kepler discovered his third law. Since the orbits of the planets are not circular, the hypothesis of elaborate bodies blocking them was invalidated, so he continued to search for other harmonic relationships within the solar system. According to the second law, the speed of a planet is maximum at perihelion, the point of greatest proximity to the sun, and is minimum at aphelion, the point of greatest distance from the sun. Kepler returned to the ancient Pythagorean idea of the "musical harmony of the wheels" and asked himself whether it is not possible that the ratio of the speeds at these two points equals the ratio of the vibrations of two sounds that together constitute a musical chord? He tested a series of such possible chords, and took into account the speed ratios at the ephelion and perihelion of a certain star, or at the ephelion of one star and the perihelion of a neighboring star, or at these two points of one star in relation to the corresponding points of another star. It is therefore a whole symphony of such possible chords. To determine the size of the following musical gains in the calculation, it was necessary to find a relationship between the average speed of a planet and its average distance from the sun, in other words - a law that relates the time of the star's revolution to half the major axis of the ellipse, which is the average distance from the sun.

After numerous and tiresome attempts, Kepler finally succeeded in discovering this law on May 15, 1618, as he announced with great excitement and a triumphant tone in his book "The Harmony of the World". And this is the wording of the third law: "The ratio of the revolution times of two planets in a square is proportional to the ratio of their average distances from the sun to the third power." For Kepler, this simple mispherical proportion reflects the harmony of the world that he persistently searched for during his 23 years of research. The guiding idea of the harmony inherent in the structure of the world is what kept him going until he discovered his three laws which were the kinematic infrastructure for Newton's law of dynamic gravity.

**Between Kepler and Newton**

It was found that Kepler discovered his laws in the same way of "blood, sweat and tears" that the other great scientists also had to follow until they reached the final stage of their research. This fact contradicts the view of the philosophers and poets of the German romantic period at the end of the 1775th century and the beginning of the 1854th century. The philosopher Friedrich Schelling (1772-1801), for example, pointed to Kepler as a clear example of the scientific genius who sees with an intuitive and unbiased vision all sides of the problem that concerns him. According to Schelling's definition, a work of genius is evident in that it is the fruit of seeing the whole before seeing its parts, and this definition suits Kepler's scientific way in contrast to Newton's. Newton is the systematic scientist who came to his discovery through the gradual construction of his theory, while assembling its parts one after the other and abstract mathematical analysis, within the framework of a mechanistic explanation of the phenomena of nature. This misconception of the people of German Romanticism arose from their longing for the unity of life and the supposedly superior simplicity of medieval culture, which was seen in their eyes in the glow of a closer affinity to human values and a more perfect communion of man with nature. For them, Kepler was the symbol of that era, as implied by the words of the romantic poet Novalis (XNUMX-XNUMX): "I will return to you, noble Kepler, who in the loftiness of your heart created for you a moral world full of spirit, whereas in our time it is considered wise to kill everything, to humiliate the The high instead of raising the low, and subduing even the human spirit and enslaving it to mechanistic laws." And as for Schelling's definition, it must be emphasized that Kepler's total perception was not based on his immediate vision of the elliptical shape of the planets' orbits, but rather it was embodied in the mystical motives for his research, in his belief in the totality of the harmonious laws of the structure of the world and in the idea of the guide, that this mathematical harmony is The true foundation upon which the astronomical facts are founded.

**Galilean's coolness**

Compared to the pretended contrast between Kepler and Newton, in the misconception of the romantic period, one must insist on a very real and instructive contrast - the contrast between the scientific personalities of Kepler and Galileo. Both were members of the same generation; Kepler was seven years younger than Galilei and died twelve years before him. Despite the historical significance of Kepler's laws, which became the basis of Newton's dynamic concept and the equations of motion of analytical mechanics, Kepler himself clearly represented the patterned approach to natural phenomena, as embodied in its purity in the cosmology of ancient Greece. Whereas Newton's dynamic approach was the natural continuation of Galileo's dynamic perception. Galileo is the founder of modern mechanics and he started a systematic study of speed and acceleration in practice, through experiments with a pendulum and the movement of balls along inclined planes (1).

Here is revealed the extreme contrast between the Protestant mystic Kepler, who aspired to discover the secret of the world-embracing harmonic pattern folded into a cosmic formula, and between the Galilean Catholic rationalist, the father of scientific professionalism, whose entire scientific morality was based on the idea that the study of nature begins with details, from grasping which it is possible to expand the canvas , to understand new facts and to perceive the legality of their combinations.

The contrast between Kepler and Galileo, which is undoubtedly rooted in the contrast in character, is reflected in Kepler's enthusiastic response, who enthusiastically promoted the astronomical discoveries of his Italian colleague, and Galileo's cool attitude towards Kepler, who only commented on the other's scientific achievements, and whose negative attitude is evident in the exchange of letters between them. In 1597 Kepler sent his book "Razi Olam" to Galilee and received a kind letter of thanks without commenting on the contents of the book. Kepler replies to this almost formal letter, but receives no reply. 13 years later, in April 1610, Galileo sent Kepler a copy of his book "Sidereus Nuncius" containing the astronomical discoveries he made with the help of the telescope he had built. A few days after receiving the book, Kepler responds to it in a detailed letter, which later also appeared in print as a pamphlet called "Dion on the Gospel of the Stars". Despite Kepler's numerous comments regarding both these discoveries and important optical problems that have a connection to the operation of the telescope - no answer came from Galilean. Kepler sends another letter, and Galilai answers briefly, without going into the actual problems. And Kepler's four other letters remain unanswered.

It seems that Galileo found no interest in Kepler's great achievements, since he rejected his entire scientific approach from the ground up. Evidence of this is a passage from Galileo's letter, which he wrote to one of his friends in 1634, four years after Kepler's death. And these are his words: "I have always admired and respected Kepler for his sharp mind and his free opinions (which were sometimes too free), but my philosophy is different and the purpose of change is different from his. Since we both wrote about the same subject, and in particular about the movements of the stars, it is possible that in the chapters we chanced upon the same conceptual field and attributed the same real cause to the same real phenomenon. However, such a thing did not happen even in one percent of my ideas."

The Galileo-Kepler affair is so fascinating, because it can be said that around these two poles - of the seekers of the cosmic formula and the seekers of the small factual detail, which may serve as a starting point for fruitful scientific continuation - around these two poles the axis of science has always revolved. Both were archetypes of opposite scientific figures, of different approaches to the study of nature, of which the history of science knows quite a few examples. In our generation, we were equals to Einstein, Kepler's passionate admirer, whose unified field theory was revealed to be the searcher for the cosmic formula, which includes the phenomena of gravity, electricity and quantum all together, and which he continued to search for until the day he died. On the other hand, Niels Bohr, in whom Galileo's type was embodied, as is evident in his scientific way, began with his model of the hydrogen atom and ended with the model of the droplet of the atomic nucleus - works in which he tried to decipher, one after the other, the meaning of special phenomena. It must be assumed that the progress of science is always conditional on the existence of these two opposing types of scientists, one-against-one, and even one-within-one another.

The character of Kepler serves as a very respectable example of a man of genius who, like Columbus, was dominated by one guiding idea all his life, thanks to which he reached the goal, which was in front of his eyes in its general lines, and which finally opened up a new and unexpected world for humanity. Schiller's distinction aimed at the discoverer of America is therefore also appropriate for Kepler: "A covenant was made forever between genius and nature; The promises of that one - it exists and will be fulfilled."

(1) See the article: "The Galilean Heritage", "Science" 5-1965 (226) pp. 230-XNUMX