Rice. 4. Light curve of SN 1572 according to visual observations by astronomers of the 16th century. All measurements after the brightness peak were made by Tycho Brahe. A detailed study of such stars and their light curves made it possible in the 20th century to discover the accelerated expansion of the Universe.

The appearance of a “new” star in the sky (at maximum brightness it was comparable to Venus and was visible even during the day) aroused great interest both among astronomers and among the population. Many researchers (including Kepler's teacher Mikhail Mestlin and John Dee) tried to determine its exact coordinates and parallax. Thomas Digges also made similar observations. In 1573, he published a book in which he summarized the results of his observations. Using very simple instruments like a “Jacob’s staff” (two crossed slats, one of which slides over the other - Fig. 5), he measured the angular distances of the nova from 6 stars of the constellation Cassiopeia. In 1977, English astronomers Stephenson and Clark compared the results of the determination of the coordinates of SN 1572 by Digges and Tycho Brahe with the position of the centroid of the supernova remnant. It turned out that the coordinates obtained by both researchers (they were, by the way, the same age) coincided with the position of the radio source and the optical nebula at the site of the supernova explosion. What was unexpected was that, despite the greater scatter of Digges’s individual measurements, the average position of the supernova according to his data turned out to be significantly more accurate than that of Tycho Brahe. The researchers concluded that there was likely a small systematic error in Tycho's measurements or data processing that was not present in Digges.

Rice. 5. Jacob's Staff (illustration from John Seller's Practical Navigation, 1672). For many centuries, the “staff” remained one of the main tools of astronomers.

In addition to the coordinates of SN 1572, Thomas Digges tried to estimate its daily parallax and found that it did not exceed two arc minutes. It followed from this that the star is located significantly further than the Moon, whose parallax is approximately 1°. Similar results were obtained by other astronomers (most notably Tycho Brahe) and they meant that, contrary to the teachings of Aristotle, great changes could also occur in the world of stars.

The results of supernova observations allow us to classify Thomas Digges as one of the most outstanding observers of his time. However, Digges's most significant contribution to astronomy was as a popularizer of the Copernican system.

In 1576 he republished his father's popular almanac Prognostication Everlastinge, leaving the main text unchanged but adding several appendices. The most important of the appendices is the work “A Perfit Description of the Caelestiall Orbes, according to the most ancient doctrine of the Pythagoreans, lately revived by Copernicus and Geometrical Demonstrations approved” (approximate translation of the title - “A Perfect Description of the Celestial Spheres in accordance with the ancient doctrine Pythagoreans, revived by Copernicus, supported by geometric demonstrations"). In this short work, Digges gives a summary of Copernicus's book and gives his own diagram of the heliocentric system (Fig. 6). The cardinal difference between this scheme and the one previously considered by Copernicus is the absence of a sphere of fixed stars. According to Digges, the stars, the nature of which he does not specify, are located at different distances from the Sun, filling infinite space. It is curious that Digges does not write that this is his own diagram, and therefore many readers must have assumed that the idea of ​​​​an infinite universe was also due to Copernicus.

Rice. 6. The structure of the Universe according to Thomas Digges (1576).

Approximate translation of the inscription on the diagram:

« This sphere of stars extends endlessly in all directions. The indestructible palace of happiness is decorated with countless, eternal and magnificent lights, surpassing our Sun in quantity and quality and (he is a container) carefree heavenly angels filled with beautiful endless joy, this is the home of the elite»

The work of Thomas Digges, written in English, contributed to the widespread dissemination of Copernican ideas in England. It is assumed that Giordano Bruno, who lived in England from 1583 to 1585, was most likely familiar with Digges’ book. It was he, Giordano Bruno, who took the next step towards the modern picture of the world - the recognition of stars as objects similar to our Sun.

Digges believed that the number of stars is infinite, but we observe only a limited number of them, since most stars are too far away and therefore too faint to observe: “the greatest part rest by reason of their wonderfull distance invisible unto us.” The famous British cosmologist Edward Harrison believes that Thomas Digges was the first researcher to realize that the darkness of the night sky needs an explanation. The solution proposed by Digges himself was, of course, incorrect, although it seemed obvious at his time.

In addition to astronomy, Thomas Digges was involved in military and applied issues, sat in parliament, built a harbor and castle in Dover, and took an active part in the war between England and the Netherlands. Digges's two sons also left their mark on history. One of them, Sir Dudley Digges (1583–1639), became a famous politician and statesman (in Canada there is Cape and Digges Islands, named in his honor by Henry Hudson, a friend of Dudley). Another son, Leonard Digges (1588–1635), was a poet and translator who may have known Shakespeare (two of Leonard's poems in memory of Shakespeare are known).

Concluding the story about the beginning of the history of the photometric paradox, I would like to mention that the name of Shakespeare is associated not only with the son of Thomas Digges, but also with himself. The first connection is quite obvious - after Thomas's death, his widow Anne married again, and her second husband in 1603 was Thomas Russell, a close friend of Shakespeare, who was appointed by him as executor of his will. The other connection is less formal, rather unexpected, and will require a certain sense of humor from the reader.

In 1996, American astrophysicist Peter Asher hypothesized that Thomas Digges is the prototype for Prince Hamlet in Shakespeare's play. According to Ussher, the play "Hamlet" describes in allegorical form the collision of four different cosmological models known at the turn of the 16th and 17th centuries - the geocentric system of Ptolemy, the heliocentric system of Copernicus, the heliocentric system modified by Digges (an infinite Universe without a sphere of fixed stars) and, finally, , a compromise model of Tycho Brahe (this model combined the features of geo- and heliocentric systems).

According to Ussher, the characters in “Hamlet” are deciphered as follows: Claudius, King of Denmark, of course, Claudius Ptolemy, and he embodies the reigning, but already outdated geocentric system; Tycho Brahe's system is embodied through Guildenstern and Rosencrantz (these are the names of Tycho's ancestors, depicted in his portrait sent for distribution to England), whose execution in England symbolizes the death of this hybrid system; Hamlet himself is, of course, Thomas Digges. The character personifying Copernicus is not in the play, but his indirect presence can be found in Hamlet’s desire to return to Wittenberg to study, and Claudius prevents this. Usher explains that the university in Wittenberg (Germany) was one of the first strongholds of Copernicanism (Rheticus, the only student of Nicolaus Copernicus, worked there and contributed significantly to the publication of his main work). The reason why Shakespeare encrypted the main theme of the play was the execution of Giordano Bruno in 1600 (Hamlet is supposed to have been written in 1600-1601).

Thomas Digges's father and teacher was the mathematician and surveyor Leonard Digges (c.1520-c.1559). After the death of his father, Thomas Digges was trained by the mathematician and philosopher John Dee.

Digges served as Member of Parliament for Wallingford in 1572 and 1584. During the war with the Spanish Netherlands (1586-1594) he served in the army. In 1582 he was engaged in fortification work at the Dover Harbor fortress.

Digges was married to Anna, the daughter of the British officer Sir Warham St. Ledger. His sons were Sir Dudley Digges (1583-1639), politician and diplomat, and Leonard Digges (1588-1635), poet.

Scientific activities

Digges described his astronomical views in his work "A perfect description of the celestial spheres according to the ancient doctrine of the Pythagoreans, revived by Copernicus, supported by geometric demonstrations"(1576), which is an appendix to the book of his father Leonard Digges. Unlike Nicolaus Copernicus, Thomas Digges (probably the first European scientist) suggested that the stars in the Universe are located not on one sphere, but at different distances from the Earth - moreover, to infinity:

The sphere of the fixed stars extends infinitely upward and is therefore devoid of movement.

Nevertheless, the idea of ​​​​the infinity of the Universe allowed Digges to formulate for the first time the prototype of the photometric paradox. He saw the solution to this riddle in the fact that distant stars are not visible due to their remoteness.

Another problem discussed in Perfect description, is the rationale for the unobservability of the Earth's daily rotation. At the same time, Digges gives the example of physical phenomena on a ship moving uniformly on a calm sea. Digges' analysis is very similar to that given by Galileo Galilei in his famous book Dialogues about the two most important systems of the world and anticipates the principle of relativity. Perhaps, in order to show the lack of influence of movement on the course of phenomena occurring on moving bodies, Digges conducted experiments on throwing objects from the mast of a moving ship.

Another achievement of Thomas Digges is an attempt, jointly with John Dee, to measure the daily parallax of the Nova that erupted in 1572 (Tycho Brahe's supernova). The absence of noticeable parallax allowed him to conclude that this star is far beyond the orbit of the Moon and thus does not belong, contrary to Aristotle, to the “sublunar world” (Tycho Brahe, Michael Möstlin and some other scientists came to the same conclusion approximately simultaneously). Digges believed that the New Star was a miracle that arose in the will of the Lord and proved His infinite power. Digges associated the change in its brightness with a change in the distance to the star, occurring due to the rotation of the Earth around the Sun.

Together with his father Leonard, Digges was involved in the construction of a reflecting telescope. There is reason to believe that these efforts were partially successful.

The image of Digges in literature

American astronomer Peter Asher ( Peter D. Usher) suggested that Thomas Digges is the prototype of Shakespeare's Hamlet. In this case, one of the semantic layers of Shakespeare’s famous play is the dispute between the main systems of the world that existed in the 17th century. According to this interpretation, the prototype of Claudius (Hamlet's uncle, who illegally usurped his father's throne) is Claudius Ptolemy, Rosencrantz and Guildenstern - Tycho Brahe, the author of an intermediate world system where all the planets revolve around the Sun, which itself revolves around the Earth.

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Notes

After the clash at Vyazma, where Kutuzov could not restrain his troops from the desire to overturn, cut off, etc., the further movement of the fleeing French and the Russians who fled after them, to Krasnoye, took place without battles. The flight was so fast that the Russian army running after the French could not keep up with them, that the horses in the cavalry and artillery became weak and that information about the movement of the French was always incorrect.
The people of the Russian army were so exhausted by this continuous movement of forty miles a day that they could not move faster.
To understand the degree of exhaustion of the Russian army, you only need to clearly understand the significance of the fact that, having lost no more than five thousand people wounded and killed during the entire movement from Tarutino, without losing hundreds of people as prisoners, the Russian army, which left Tarutino numbering one hundred thousand, came to Red in the number of fifty thousand.
The rapid movement of the Russians after the French had just as destructive an effect on the Russian army as the flight of the French. The only difference was that the Russian army moved arbitrarily, without the threat of death that hung over the French army, and that the backward sick of the French remained in the hands of the enemy, the backward Russians remained at home. The main reason for the decrease in Napoleon's army was the speed of movement, and the undoubted proof of this is the corresponding decrease in Russian troops.
All of Kutuzov’s activities, as was the case near Tarutin and near Vyazma, were aimed only at ensuring, as far as was in his power, not to stop this movement disastrous for the French (as the Russian generals wanted in St. Petersburg and in the army), but assist him and facilitate the movement of his troops.
But, in addition, since the fatigue and huge loss that occurred in the troops due to the speed of movement appeared in the troops, another reason seemed to Kutuzov to slow down the movement of the troops and to wait. The goal of the Russian troops was to follow the French. The path of the French was unknown, and therefore the closer our troops followed on the heels of the French, the greater the distance they covered. Only by following at a certain distance was it possible to cut the zigzags that the French were making along the shortest path. All the skillful maneuvers that the generals proposed were expressed in the movements of troops, in increasing the transitions, and the only reasonable goal was to reduce these transitions. And Kutuzov’s activity was directed towards this goal throughout the entire campaign, from Moscow to Vilna - not by accident, not temporarily, but so consistently that he never betrayed it.
Kutuzov knew not with his mind or science, but with his whole Russian being, he knew and felt what every Russian soldier felt, that the French were defeated, that the enemies were fleeing and it was necessary to see them out; but at the same time, he felt, along with the soldiers, the full weight of this campaign, unheard of in speed and time of year.
But to the generals, especially not the Russians, who wanted to distinguish themselves, to surprise someone, to take some duke or king prisoner for something - it seemed to the generals now, when every battle was disgusting and meaningless, it seemed to them that now was the time fight and defeat someone. Kutuzov only shrugged his shoulders when, one after another, he was presented with plans for maneuvers with those poorly shod, without sheepskin coats, half-starved soldiers, who in one month, without battles, had melted to half and with whom, under the best conditions of ongoing flight, it was necessary to go to the border the space is larger than that which was traversed.
In particular, this desire to distinguish themselves and maneuver, overturn and cut off was manifested when Russian troops encountered French troops.
So it happened near Krasnoye, where they thought to find one of the three columns of the French and came across Napoleon himself with sixteen thousand. Despite all the means used by Kutuzov in order to get rid of this disastrous clash and in order to save his troops, for three days Krasny continued to finish off the defeated gatherings of the French with the exhausted people of the Russian army.
Toll wrote the disposition: die erste Colonne marschiert [the first column will go there then], etc. And, as always, everything was not done according to the disposition. Prince Eugene of Wirtemberg shot at the fleeing crowds of Frenchmen from the mountain and demanded reinforcements, which did not come. The French, running around the Russians at night, scattered, hid in the forests and made their way further as best they could.
Miloradovich, who said that he did not want to know anything about the economic affairs of the detachment, which could never be found when he was needed, “chevalier sans peur et sans reproche” [“knight without fear and reproach”], as he called himself , and eager to talk with the French, sent envoys demanding surrender, and lost time and did not do what he was ordered.
“I give you guys this column,” he said, driving up to the troops and pointing to the cavalrymen at the French. And the cavalrymen on thin, tattered, barely moving horses, urging them on with spurs and sabers, at a trot, after great exertion, drove up to the donated column, that is, to a crowd of frostbitten, numb and hungry Frenchmen; and the donated column threw down its weapons and surrendered, which it had long wanted.
At Krasnoe they took twenty-six thousand prisoners, hundreds of cannons, some kind of stick, which was called a marshal's baton, and they argued about who had distinguished himself there, and were happy with that, but they very much regretted that they did not take Napoleon or at least some hero, Marshal, and reproached each other and especially Kutuzov for this.
These people, carried away by their passions, were blind executors of only the saddest law of necessity; but they considered themselves heroes and imagined that what they did was the most worthy and noble thing. They accused Kutuzov and said that from the very beginning of the campaign he had prevented them from defeating Napoleon, that he only thought about satisfying his passions and did not want to leave the Linen Factories because he was at peace there; that he stopped the movement near Krasny only because, having learned about Napoleon’s presence, he was completely lost; that it can be assumed that he is in a conspiracy with Napoleon, that he is bribed by him, [Wilson's Notes. (Note by L.N. Tolstoy.) ], etc., etc.
Not only did contemporaries, carried away by passions, say so, but posterity and history recognized Napoleon as grand, and Kutuzov: foreigners as a cunning, depraved, weak old court man; Russians - something indefinable - some kind of doll, useful only because of its Russian name...

Renaissance Science. Triumphant discoveries and achievements of natural science from the times of Paracelsus and Galileo. 1450–1630 Boas Hall Marie

Chapter 4 The Great Controversy

Great debate

Whenever I occasionally met a person who supported the Copernican view, I asked whether he always believed in it. Among a large number of people I interviewed, many said that they had held the opposite opinion for a long time, but changed it, convinced by the power of the arguments. Questioning them one by one to see how well they had mastered the other side's arguments, I found that they always had formulaic formulations at the ready, in other words, I never understood why they changed their position: out of ignorance, vanity, or to demonstrate your erudition. On the other hand, when I asked the Peripatetics and the followers of Ptolemy (out of curiosity I asked many) how well they had studied the book of Copernicus, it turned out that only a few had seen it and, it seemed to me, no one understood it.

It is very difficult to fairly judge the impact of a new scientific idea in the days leading up to book reviews and scientific conferences. It turns out that in this case you are entirely dependent on the assessment of comments, arguments for and against. How, for example, should one perceive an indifferent assessment of a scientist coupled with fierce attacks and no less fierce defense of people who have nothing to do with the scientific world? One can only try to evaluate the evidence creatively, remembering that mention at all, even in an unfavorable light, is an achievement.

In the case of Copernicus there is a further complication: his theory had been known in certain circles for many years before the publication of De Revolutionibus in 1453, thanks to the Little Commentary, rumors and Rheticus's First Tale. During his lifetime, he was highly valued in astronomical circles and was even called a potential bishop of astronomy. (Interestingly, not many of those who eagerly awaited his theory embraced it when it was finally published.) Historians are sometimes surprised and saddened that not all astronomers were immediately converted, and some were even actively converted. opposed. In fact, one should rather be surprised that so many have made efforts to understand a new complex theory, the correct assessment of which requires considerable mathematical knowledge.

In fact, De Revolutionibus was sufficiently popular to warrant a second edition (Basel, 1566), with the First Tale (now in its third edition) as an appendix. Of course, many must have learned more from Rheticus rather than from Copernicus, and, apparently, not everyone who talked eloquently about his new theory read his work. However, there were many astronomers who made active use of mathematical methods, and, however slow the progress of new ideas had been in the 16th century, within half a dozen years of its publication Copernicus' theory was in use. Extensive discussions followed. By the end of the century, even literary figures such as Montaigne knew enough about the Copernican system to mention its application in their writings. Its spread was most rapid in Germany, the center of astrology and the production of astronomical instruments, where there were such large universities as in Wittenberg, where Rheticus studied. But due to some unevenness of intellectual development, new astronomical ideas were noticed most quickly in England and Spain - countries considered culturally and scientifically backward. This probably happened because the old ideas were not too ingrained in them.

It seems strange that at first Copernicus was glorified as an observational astronomer. This is really strange, because, as far as is known, he made almost no observations and did not attach much importance to their accuracy. Even Tycho Brahe, the greatest of the observing astronomers from Hipparchus to Herschel, treated the observations of the “incomparable Copernicus” with great respect, although he was surprised to find them somewhat crude. Obviously, the emphasis on Copernicus's observational achievements was partly a result of the first practical use of his new system - in the calculation of planetary tables. In De Revolutionibus, Copernicus presented rough tables, and then Erasmus Reinhold (1511–1553), professor of astronomy at Wittenberg, compiled new and improved tables, complete enough to take the place of the hopelessly outdated alphonsines. Reinhold named the tables Prussian, in honor of his patron, the Prussian Duke (1551). Reinhold's attitude to Copernican theory is very peculiar. In 1542, while editing Purbach's New Theory of the Planets, he declared (presumably based on the First Tale) that Copernicus should become the "restorer of astronomy" and the new Ptolemy. When De Revolutionibus was released,

Reingold realized that the Copernican system could become the basis for calculating new tables. However, he was not an ardent admirer. It was quite enough for him that Copernicus created a new convenient apparatus that significantly simplifies calculations.

Rheingold's position was the same as that of many calculating astronomers. His Prussian tables were indeed widely used and helped to achieve the calendar reform that Copernicus had hoped for. They were often revised for other countries and expanded. The first such case occurred in 1556, when a work appeared entitled “Tables for the Year 1557, Compiled in accordance with the Principles of Copernicus and Reinhold for the Meridian of London” (Ephemeris for the Year 1557 according to the Principles of Copernicus and Reinhold for the Meridian of London). Its author, John Field, had nothing to tell the world about the merits of the Copernican system (or, indeed, about anything else, since he remained unknown). The foreword was written by the mathematician, astrologer, spiritualist, and proponent of experimental science, John Dee (1527–1608). In it, the scientist explained that he convinced his friend to compile the tables because he decided that the work of Copernicus, Reingold and Rheticus made the previous tables obsolete. But he did not consider the preface to be the appropriate place for a critical discussion of the merits of the Copernican system. And he did not do this either in this preface or in other works either. Apparently he had no desire to accept the physical reality of the computational and hypothetical system.

After the works of Reinhold, all calculating astronomers had to reckon with Copernicus. Thus, Pontus de Thiard, who was a supporter of the Copernican system, in his “Tables of the Eight Spheres” (Ephemeris of the Eight Spheres), published in 1562, praised Copernicus as the “restorer of astronomy” only on the basis of his contribution to astronomical calculations. All these tables were a development of the old ones, and not because they were more modern. Tycho Brahe learned from his own experience how much higher they are. Wanting to observe the conjunction of Saturn and Jupiter, he discovered an error in the Alfonsines for a whole month. There was also an error in the Prussian tables - for several days. This is, of course, a lot, but still better than in Alfonsines.

Although the Copernican system was often referred to in the writings of non-professionals in the 16th century, there were few easy ways to gain a clear understanding of its contents. Apart from the work of Rheticus, there were no presentations of it at a primitive level. Only one university program included it: the statutes of the University of Salamanca were revised in 1561, and it was stipulated that mathematics (read alternately with astrology) should include Euclid, Ptolemy and Copernicus at the student's choice. No records survive, and we do not know whether they chose Copernicus or not during the sixty years they had the opportunity. It is hardly surprising that the Copernican system was not taught in other universities: astronomy was considered an elementary science, and professors were expected to expound its basic elements as part of the general education of art students. For future doctors who needed knowledge of medical astrology, delving into the Copernican system could become extremely difficult, since the astrological tables and instructions were Ptolemaic. The same could be said about everyday and literary references to astronomy. By the way, even today students do not begin their acquaintance with science by studying the latest achievements in nuclear physics, and fifty years ago students did not study Einstein before they understood Newton.

Robert Record wrote about this in The Castle of Knowledge (1556), one of his series of treatises on mathematics, pure and applied. Record's name is associated with two universities: after completing his medical studies at Cambridge, he taught mathematics in London - an extremely sought-after profession, given his great interest in navigation. In The Castle of Knowledge there is a dialogue between teacher and student, showing not only the deep respect that the author has for Copernicus, but also teaches him to carefully weigh his arguments. The teacher argues that there is no need to discuss whether the Earth moves or not, because its immobility “is so ingrained in the minds of people that they will consider it madness to question it,” which, naturally, prompted the student to make a careless generalization: “Still, sometimes it happens that the opinion held by many is not true.” The master objected: “This is how some people judge this problem. After all, the great philosopher Heraclides Ponticus and two also great followers of the Pythagorean school, Philolaus and Ecphantus, had the opposite opinion, and Niketus (Nicetas) of Syracuse and Aristarchus of Samos had strong arguments in favor. But the foundations are too complex to go into at this first acquaintance, so I will leave them until next time... Nevertheless, Copernicus, a man of great experience, diligent in observations, revived the opinion of Aristarchus of Samos and confirmed that the Earth not only moves in a circle around its own center, but also from the exact center of the world. Understanding this requires deep knowledge..."

Robert Record undoubtedly realized that the young student was in no position to judge and speak out against the new system, nor for it. His student considered it all empty vanity, and the master was forced to reproach him, saying that he was still too young to have his own opinion. This is, of course, true, but very few people have the knowledge to have their own opinion.

Many people besides Record were favorable to the Copernican system, but did not consider it a sufficiently established part of generally accepted astronomy to be included in the initial presentation. A typical example is Michael Maestlin (1550–1631), professor of astronomy in Tübingen. He belonged to a younger generation than Reinhold, and found it possible to accept the Copernican system without even attempting to advocate it publicly to begin with. His textbook Epitome of Astronomy (1588), probably a collection of his lectures, contains only Ptolemaic views, but Copernican applications appeared in later editions. The fact that Kepler (1571–1630) was his student shows that Maestlin discussed the new doctrine with talented students - for Kepler became a strong supporter of Copernicus even before he was a competent astronomer, and later defended his ideas publicly. In 1596, Maestlin began publishing Kepler's first book and, on his own initiative, added Rheticus's First Tale, with a preface praising Copernicus. Whatever his views had been before this time, by 1590 he undoubtedly revised them. After the condemnation of the Copernican doctrine by the Catholic Church, the Protestant Maestlin proposed a new edition of De Revolutionibus, although he did not go beyond writing a preface. Another position was taken by Christopher Rothman, an astronomer under the Landgrave of Hesse, who carried on a long correspondence with Tycho Brahe, in which he fiercely defended Copernicus and proved the inconsistency of Tycho's counter-arguments. True, he did not publish anything about this. While there may be many reasons for astronomers' silence, it is not necessarily a lack of conviction. It seems likely that they simply saw no reason to defend their position. In short, one cannot judge the influence of Copernicus and his theory by the absence of references to him in textbooks. Even Galileo preferred to lecture only on Ptolemy's astronomy.

At the same time, the public recognition of Copernicus' theory had a certain appeal for the radical thinkers of the 16th century. Wanting to get away from what they called the interference of scholastic Aristotelianism, they fervently supported any theory that satisfied their craving for innovation. Many discussions about the Copernican system were framed within the framework of anti-Aristotelianism. It seems that Copernicus's defense is partly a response to the intellectual joy of novelty and the desire to have his own way. Be that as it may, the best way to criticize Aristotle is to overturn the cosmological basis of his natural philosophy. Perhaps it is anti-Aristotelianism that explains why so many favorable references to Copernicus were made by people who were not only astronomers, but even scientists, and why he is often associated with the free-thinking Epicureanism of Lucretius. An interesting and not very well known example took place at the Academy, organized by members of the French Pleiades. There were in fact several academies, some informal, others formally associated with the royal court, which existed more or less continuously from 1550 until the end of the century. (It is strange to imagine that Henry III, in the dark days of the religious wars, could listen to the poets of the Pleiades and discuss the merits of Greek music.) These groups, organized by poets and initially having purely literary purposes, quickly moved from poetry to music, and then in the Pythagorean spirit – to mathematics and natural philosophy. There were discussions about the state of astronomy and the possible significance of Copernicus' new theories. Their opponents considered such discussions to be an example of the unlimited speculative freedom of thought characteristic of the Pleiades.

In 1557, a work entitled “Dialogue of Guy de Braes against the New Academies” was published. Here de Bruet, using real members of the Pleiades as speakers, attacked the novelty of their opinions, including science. According to de Bruet, Ronsard believed that astronomy should represent a physical truth, which means he could not accept the idea of ​​​​the mobility of the Earth, for which there was no empirical evidence, and Baif viewed astronomy as a series of hypotheses and therefore argued: “In astronomy there is no guarantee of principles . For example, that the Earth is motionless: because, although Aristotle, Ptolemy and some others agreed on this, Copernicus and his imitators [obviously the reader of 1557 knew that there were those who accepted the doctrines of Copernicus] argue, that it moves because the heavens are huge and therefore motionless. Because (he says) if the sky is not infinite and if there is nothing beyond it, then it is limited by nothing, which is impossible. Everything that exists is somewhere. If the sky is infinite, it must be motionless, and the Earth must be mobile.”

One of the most interesting aspects of this attack is the attribution to Copernicus of the belief (which he did not actually have) that the Universe is infinite. There was clearly a mixture of radical ideas here. It was argued that the Academicians were Epicureans and at the same time followers of Copernicus. It is easy for a person without a university education to confuse the Copernican argument - that the sphere of the fixed stars must be very large - and the Epicurean assertion that the Universe must be infinite.

The Atlantic coast of the Iberian Peninsula and the Strait of Gibraltar according to Ptolemy. From "Cosmography", printed in 1486 in Ulm

Peas from De Historia Stirpium (Basel, 1542). Among the vegetables illustrated by Fuchs are asparagus and several types of cabbage

Primitive bull

Bishop fish. From Gesner's Historia Animalium (1551–1587)

Anatomical demonstration as it was presented in the 15th century, from Mondino's Anatomy (Venice, 1493). A professor comments on the abdominal organs being shown by his assistant.

Vesalius demonstrates the muscles of his arm. From De Humani Corporis Fabrica (Basel, 1535)

One of the figures showing the entire human skeleton. From De Humani Corporis Fabrica Vesalius

Pump invented by Jacques Besson. From his Theaters des Instrnmens (Lyon, 1579). A fanciful machine presented as needlessly complicated to perform a simple job, suggests an element of fiction in many Renaissance engineering books

Crane from Le Diverse et Artificiose Machine (Paris, 1588). The passion of Renaissance engineers for complex gears and pulleys is clearly visible.

Whether Ronsard and Baif really argued about the merits of Copernicus' teachings, as well as about the relative qualities of verses in Latin and the languages ​​of the world, or about new and old poetic styles, cannot be said with certainty. But astronomical problems were actually of interest to other “academicians.” Almost simultaneously with the “Dialogues” of de Bruet, the book “The Universe” (L’Univers) was published by Pontus de Thiard (1521–1605), a knowledgeable astronomer and clergyman, whom fate destined to become the Bishop of Chalons. “The Universe” consists of two dialogues, the first about the state of philosophical thought. Here Tiard discusses the Copernican system in detail. Having named the Greek sources of the theory, he gives a French translation of Copernicus's description of the spheres and gives his own arguments for the motion of the Earth. The main arguments of the first book of De Revolutionibus have been treated quite fully. Despite the full description, Tiar refused to commit himself. He allowed himself to say only the following: all this is quite curious and important only for astronomers.

In truth, his demonstrations are simple and his observations are accurate—worth supporting. Nevertheless, whether his theory is correct or not, our knowledge of the Earth, so far as we have it at the present time, has not changed at all. And now, as before, nothing prevents us from believing that it is a heavy, cold and dry element, which, based on the generally accepted religious opinion, is motionless.

This is a cautious but honest expression of opinion. Tiard loved free discourse, but this did not mean that he wanted to reject generally accepted religious opinion and that he himself considered such views to be valid.

A physicist determined to criticize Aristotle's theory of motion can hardly fail to appreciate the benefits of a passing attack on Aristotle's cosmology.

This was the case, for example, with G. Benedetti (1530–1590), whose Book of Diverse Speculations on Mathematics and Physics was a treatise directed against Aristotle. Benedetti is a mathematical physicist, not an astronomer. But he enthusiastically praised the theory of Aristarchus, explained in a divine manner by Copernicus, against which Aristotle's arguments have no force. Thus, another blow was dealt to Aristotle's authority. Likewise, Richard Bostock, an almost forgotten English writer, in “The Difference between the ancient Phisicke... and the latter Phisicke, 1585,” considered it natural to compare the physicist Paracelsus and the astronomer Copernicus. As is known, Paracelsus was not the first to express his ideas: he was only a “restorer” of ancient true doctrines. As Bostock stated, Paracelsus was no more the “author and inventor” of medicinal chemistry than Nicolaus Copernicus, who lived at the same time as Paracelsus and returned to us the true positions of the stars, was, according to experience and observation, the author and inventor of the movements of the stars.

Whether Bostock was a follower of Copernicus or not is irrelevant, and he had no idea exactly what Copernicus did. Another thing is important: in England and Italy in 1585, if someone wanted to criticize Aristotle and defend scientific novelty, they usually resorted to Copernicus as an example and weapon. By 1585, any scientific audience - mathematical, physical or medical - had some understanding of Copernicus' theory. And those who wanted to arrange a free discussion of it could do so without hindrance.

Just as scientific radicals praised Copernicus's theory as having shaken the authority of Aristotle, those who denied scientific novelty disagreed with Copernicus's theory. In the 16th century, as in the 20th century, people far from science considered scientific theories to be incomprehensible, and scientists to be restless creatures constantly striving to disrupt the established order of things. The most furious attacks on Copernicus were carried out by people far from science, and they were guided by a fear of novelty. Having been educated in one system, such people did not even think about understanding and accepting another idea or, moreover, weighing the advantages and disadvantages of each. This was especially true if the new system involved a disruption of what was considered common sense, the order and harmony of the universe. Once astronomers came to accept a heliostatic universe, scientists were unwilling to separate science from common sense, which is the basis of antagonism toward science to this day. Two worlds appeared: astronomers who believed that the moving Earth copied the movement of the planets around the Sun, and the world of other people who accepted the geostatic and geocentric system. The Copernican system could not help but provoke hostility because it raised the uncomfortable question of how much one could trust one’s senses. Therefore, Copernicus was criticized primarily by poets, and the wave of criticism subsided only when, at the end of the 17th century, science again regained order and stability.

In the last quarter of the 16th century, the Copernican system, although it did not gain many supporters, became widely known. After thirty years of fierce debate, even people far from science were aware of the fundamental problems. They did not like the fact that astronomers disturbed their philosophical peace, just as the physical peace in the heavens was disturbed by strange signs. Indeed, events in the heavens—the nova of Cassiopeia in 1572 and the long succession of comets between 1577 and the turn of the century—brought widespread attention to astronomy and the furious debate of astronomers who seemed to take a kind of perverse pleasure in foaming at the mouth in defending absurd things. This point of view was expressed by Guillaume du Bartas, whose work “The Week, or the Creation of the World” (La Sepmaine, ou Creation du Monde, 1578) was one of the most widely read didactic poems at the end of the 16th century. Excerpts from it have been translated into English several times. Du Bartas was familiar with ancient sources, and did not hesitate to borrow from Lucretius, especially in literary matters, but he fiercely opposed what seemed to him to contradict his rather narrow ideas about orthodox cosmology. Even Aristotle was criticized for his ideas about the infinity of the world. In his opinion, the age tends to play with innovations, and scientists will accept any absurdity, as long as it is new. After discussing God's creation of the world, the elements, and the geography of the Earth, he proceeds to describe the magnificent heavens, shining with lights that are spoiled only by the extravagant views of modern scientists.

...some madmen live today,

Full of stubbornness

Twisted minds that can't sail calmly

Along the calm channel of our common seas.

These are the ones (at least in my opinion)

Scribblers who think (think - what a joke!)

That neither the heavens nor the stars rotate,

They don't dance around the globe,

And the Earth itself, our heavy ball,

It turns in a circle every twenty-four hours.

And we are like earth-fed novices,

Who have just arrived on the ship to leave

When they leave the shore for the first time, they believe

That the ship is stationary, but the earth is moving.

So the flickering candles filling the vault of heaven

Equally distant, they remain motionless.

So never an arrow shot up

It will not fall in the same place - on the shooter.

Just like a stone

Thrown up on a ship,

It will fall not on the deck, but in the water

Astern if the wind is good.

So birds flying into the distance

From the Western Moors to the morning light,

And Zephyr, who decided in midsummer

Visit Evre in his land,

And the cannonballs escaping from the barrel of a cannon

(The roar of which was drowned out by heavenly thunder),

They will fall hopelessly behind, they will cease to be fast,

If our round Earth jumps every day

at full speed…

The author further argues that everything in nature is against the arguments of Copernicus, who endowed the Earth with movement and made the Sun the center of everything, and insists on the need to “continue the conversation about the movement of the heavens and their constant course.”

It is obvious that Du Bartas knew quite well the simplest arguments against the Copernican system and was clearly not alone in considering it the most destructive of all the stupid innovations of the new astronomy. He was also not the only one who believed that the best way to get rid of absurd ideas was to ridicule them. Similar attacks, although not as expressive, are contained in Jean Bodin’s work “The Comprehensive Theater of Nature” (Theater of Universal Nature, 1597). In this work, the French political theorist and scourge of witches takes an encyclopedic look at the entire natural world. Bodin mentions Copernicus as the man who “updated” the opinions of “Philolaus, Timaeus, Ecphantus, Seleucus, Aristarchus of Samos, Archimedes and Eudoxus”, doing this because the incredible speed of the celestial spheres is difficult for the human mind to comprehend and easier to reject. Baudin clearly knew less about the Copernican system than Barthas. He wrote twenty years later and could well have relied on rumors. He believed that Copernicus had abolished epicycles, having no idea that Copernicus was using the argument that immobility is nobler than movement (so that the nobler heavens should be at rest, and the baser Earth should be in motion). Baudin considered the whole theory absurd, and in any case, “if the Earth moved, neither an arrow shot vertically upward, nor a stone thrown from the top of a tower would fall perpendicularly, but only a little in front or behind.”

The rejection of the Copernican system clearly shows the discomfort that reigned in the minds of people, and the fact that at the end of the 16th century even an elementary discussion about astronomy could not proceed without reference to his ideas. Only a skeptic could dismiss the problem of choosing between Ptolemy and Copernicus and declare with Montaigne: “What will we reap if we understand which of them is right? And who knows, maybe in a hundred years a third opinion will arise that will successfully eclipse both predecessors?

Most literate people believed that the uncertain state of astronomy would remain so. Many preferred to look back when everything was orderly and unambiguous: the Earth under man’s feet remained motionless, and the heavens were as the eye saw them. Donne immortalized this position. Although his lines were written in 1611, when the skies were once again in disarray thanks to the telescope, they correspond to the complaints of the previous generation.

The new philosophy questions everything.

The element of fire has gone out;

The sun is lost, and the earth, and not a single sage

He won't tell you where to look for them.

People freely admit that this world has run out of steam,

When in the planets and firmament

They are looking for so many new things; then they see

How everything is falling apart

Everything is in ruins, all communication has disappeared.

All resources, all connections.

If the Copernican doctrine thus influenced all poets, it is not surprising that they rejected it. Especially in a century when everything was questioned, declined and disintegrated - at least in religion and politics. Why would they welcome chaos among the stars?

At the same time, many scientists involved in natural philosophy, and primarily mathematicians, found the Copernican system to liberate the spirit. They liked the freedom it offered from the shackles of a small world, although at the cost of losing their comfortable certainty. Brave and strong-willed people not only welcomed Copernicus - they tried to surpass him. And the system has reached a critical state - its breaking point. One of the first astronomers who wished to expand the Copernican universe was Thomas Digges (d. 1595), an Englishman born at the time De Revolutionibus was published. His father Leonard Digges was a gentleman surveyor who wrote extensively on applied mathematics, including astrology. He took part in Wyatt's Rebellion and encountered considerable difficulties in publishing his works. Therefore, many of them remained unpublished after his death in 1558. He commissioned his friend John Dee to educate his son, and young Digges subsequently called Dee his second father in mathematics. Thomas Digges followed in the footsteps of both fathers and actively participated in the movement, which aimed to teach practical mathematics to the common people. He also became an observational astronomer. Together with other leading astronomers (Dee was among them, but only Digges's work was published earlier and was considered the best), he made a series of observations of a strange new star (nova) that appeared in the familiar constellation Cassiopeia in 1572. His observations were published the following year under the witty title "Mathematical wings or scales" (Alae seu Scalae Mathematicae, 1573). "Libra" - trigonometric theorems needed to determine stellar parallax: Digges considered nova a new fixed star and thought that its appearance provided a unique opportunity to test Copernicus' theory. (Digges erroneously believed that the decrease in magnitude after its first unexpected appearance would be periodic, and hoped that it might be parallactic in nature, the result of apparent motion.)

Although he was unable to use the star in this way, Digges had no doubt about the truth of the Copernican system. He was so convinced of her that he even violated his filial duty. In 1576, while reviewing his father's twenty-year-old work entitled A Prognostication Everlasting, an almanac dealing mainly with meteorological predictions, he found it intolerable to think that another work based on the doctrine of Ptolemy would be presented to the public, and in our century, when one rare mind (seeing the constant errors that are discovered from time to time, as well as the absurdity in theories that do not recognize the mobility of the Earth) after long work created a new theory - a model of the world.

Copernicus came to his theory and new model of the world through long, serious and deep reflection. This does not mean that noble English minds were deprived of the same opportunity - adherence to philosophy. Digges recognized that Copernicus created not just a mathematical hypothesis, but a physical picture of the world. And he appended to the Eternal Prediction a short article with a long Elizabethan title, “A Perfit Description of the Celestial Orbes according to the most ancient doctrine of the Pythagoreans.” , lately revised by Copernicus and by Geometrical Demonstrations Approved).

This "perfect" account is essentially a translation of the first book of De Revolutionibus, but with the addition of an important new concept from the translator. To the Pythagorean doctrines of Copernicus, Digges added a new dimension for the celestial sphere. Due to the lack of stellar parallax, Copernicus postulated that the celestial sphere with giant stars was very large. For Digges, this was a sign of the greatness of God. But why didn’t God continue this sphere upward until it touched the firmament? From a physics point of view, this is an interesting question. If, as Digges believed, the sphere of fixed stars, decorated with countless lights, stretched upward without end, then they must be at different distances from the Sun and the Earth. They were all very large, but it is likely that different sizes only meant different distances to the Earth. And the number of stars must be infinite - there are many more of them than we see.

It seems that we see those that are in the lower part of the sphere [of fixed stars], and the higher they are, the smaller and smaller they seem until our sight can no longer distinguish them. Due to the enormous distances, most of the stars are hidden from us.

Digges's universe is not the closed world of Copernicus. Star space is not limited from above. Digges connected the astronomical heavens with the theological heavens. Having broken the boundaries of the finite Universe and destroyed the upper limits of the celestial sphere, Digges thought about eliminating the boundary between the starry sky and the firmament. If you can fly between the stars (which are like our Sun), then you will go straight to heaven. This is clear from Digges' chart. It shows a “sphere” of fixed stars, but the stars are scattered around the outside of the sphere, right up to the very edge of the illustration. The Digges diagram reported: “The sphere of the fixed stars extends infinitely in height spherically, and is therefore motionless: a palace of bliss, adorned with countless burning candles, surpassing our Sun in quantity and quality, the home of the heavenly angels, in which there is no sorrow, but only infinite happiness, abode for the elect."

This may seem mystical, but Digges undoubtedly pushed the boundaries of the real physical world: the stars broke their bonds and no longer hung in the firmament, but were scattered over vast spaces, and they themselves had sizes that are difficult to imagine.

Thus, one of the first steps was taken that disrupted the comfortable peace of the ancients. At that time, this may not have seemed new: many attributed all innovations to Epicureanism and confused enormity with infinity. Digges could well be considered to have revived the opinions of Democritus, Epicurus and Lucretius. Certainly English readers already had access to Copernicus's arguments in their own language, although it is doubtful that some of the readers who looked to the Eternal Prediction for the weather forecast for the following winter bothered to study the information about Copernicus in the appendix. Yet for one reason or another, at the end of the 16th century, the opinion was established that the Copernican Universe required a huge space - if not infinity. Many believed that it was infinity.

The next radical revision of the Copernican Universe was made by a man who had nothing in common with Digges. His ideas were based only on astronomical observations, and not on mystical reasoning. Not being a fan of Copernicus, Tycho Brahe did not accept his system and created his own - a competing one, but still some of his radical concepts were accepted by Copernicus’ supporters. Over time, Tycho Brahe's attitude towards the Copernican theory of the Universe improved much more than that of his staunch supporters.

Tycho Brahe (1546–1601) became interested in astronomy by observing the heavens. It was a call from the soul, because Tycho had no mentors, and he chose astronomy against the will of his relatives. His father, as Tycho claimed, did not even want his son to learn Latin (a Danish aristocrat does not need it). But he was raised by an uncle who understood the value of a classical education, and at the age of fifteen Tycho Brahe was sent to the University of Leipzig. In his autobiography (Tycho Brahe called it “What we, with God’s help, have managed to accomplish in astronomy and what, with His benevolent support, remains to be accomplished” 1) he noted that from the very beginning he studied astronomy independently and secretly. He gained his first knowledge by studying astrological tables. This interest remained with him forever, but he switched his main attention to astronomical observations. He made his first observations in 1563 at the age of sixteen, using improvised instruments. Thirty-five years later, Tycho Brahe recalled with bitterness that his mentor did not give him the money to buy real ones. Then Tycho Brahe observed the conjunction of Saturn and Jupiter. The difference between the results of observations of the alphonsine and the “Copernican” tables already convinced him that the main tool of astronomy was careful observation. He needed good, professionally made instruments, which he acquired when he moved from Leipzig to the astronomical center of Augsburg. Here he also became interested in alchemy, calling it “terrestrial astronomy,” and upon returning home, he became closely involved in alchemical experiments. But the sudden appearance of a new star in Cassiopeia in 1572 determined his career once and for all. This unprecedented phenomenon required careful observations, the report of which (“On the New Star,” 1573) attracted the attention of the King of Denmark, who, wanting to keep such a promising scientist (national prestige required not only military, but also intellectual success), granted Tycho Brahe the island of Ven. Unheard-of generosity convinced Tycho Brahe not to go to Basel, as he had previously planned. Instead, he spent twenty-one years on the island, which he made a center of astronomical research. Here he built the fantastic castle of Uraniborg with observatories and laboratories, designed new astronomical instruments of enormous size (before the invention of the telescope this was the only way to achieve accuracy), and here he trained a galaxy of young people who came to the island to get any job from the greatest astronomer with the time of Hipparchus.

Like Hipparchus, Tycho Brahe understood that the appearance of a new star required the compilation of a new star catalogue. He devoted most of his energy and twenty years of his life to this project. But he was extremely interested in nova itself. An amazing phenomenon: a new star in a well-known constellation, and when it was first noticed, it had the same brightness as Jupiter. Tycho Brahe, Digges, Mestlin, Dee and many other astronomers studied it with admiration and bewilderment. Tycho Brahe, Digges and Maestlin (still an amateur astronomer) tried to measure the parallax of the nova not to test Copernicus' theory, but because this star at first glance should have been in the sublunar (terrestrial) sphere. It could also be a meteorological phenomenon, such as a rainbow, meteor or comet, since the phenomenon was related to terrestrial space, and the heavens of Aristotle's cosmology were considered perfect, eternal and unchanging. Everything that is located under the Moon should show its relative proximity by a visible shift in position relative to the stellar background.

However, the most careful observations showed that the nova stubbornly refused to show parallax. Tycho Brahe, Digges and Mestlin, based on this, came to the conclusion that it belongs to the sphere of fixed stars. In this regard, there came the recognition that the heavens had changed, and therefore were not perfect. But not all astronomers agreed with the observations. Some argued that nova shows parallax, others, such as Dee, that it moves in a straight line from the Earth and this explains the fact that it is dimming. Many, including Digges, classified it as a comet. Tycho Brahe boldly accepted the inevitable conclusions, since he was completely confident in the accuracy of his observations. He could not explain the change in brightness and color of the new star (like all novae, its color changed from white to red-yellow to red), but he had no doubt that it was in the "ethereal sphere." He described in great detail what its astrological significance might be - after all, such a rare event could not but have a strange and, of course, miraculous significance. Its astronomical importance was also, of course, very great. Tycho Brahe realized that he could “lay the foundations of a renaissance in astronomy” by making long and careful observations.

At Uraniborg, Tycho Brahe observed the positions of the fixed stars and planets, the Sun and the Moon, year after year, improving the instruments and techniques of observation, and eventually achieved an accuracy far greater than that of any other astronomer. The error did not exceed four minutes of arc - the limit of accuracy for the naked eye. Tycho Brahe was aware of the superiority of his methods, and he always tried to maintain the highest standards. After leaving Uraniborg, he wrote:

“...not all observations are made with the same accuracy and are equally important. Those that I produced in Leipzig in the days of my youth, until I was 21 years old, I usually call children's and consider dubious. Those that I produced later, when I was not 28 years old [that is, before 1574], I call youthful and consider them quite suitable. As for the observations that make up the third group, which I made in Uraniborg for about 21 years with great care with the help of high-precision instruments at a more mature age, until I was 50 years old, then I call them observations of my maturity, quite reliable and accurate , – this is my opinion about them” 1.

Ironically, very precise astronomical observations did not help Tycho Brahe in his theoretical work. Although he announced that he was “based on the latest observations, trying to lay the foundations and develop a new astronomy,” he practically did not use them. He did create a new astronomy based on observations, but these were all observations from 1572 and 1577. Later study of comets only confirmed what Tycho Brahe already knew. And his planetary tables were not needed in the general description of his system he made. However, the accumulated information was not in vain. Kepler used it in calculations on which he based a new theory, far from the works of Tycho Brahe, but in many respects derived precisely from them.

Observations of the great comet of 1577 became the basis for the development of Tycho Brahe's system. The only description of it made by the author is inserted into the story about the orbits of comets. As in 1572, Tycho Brahe made the most careful observations. He tried again to measure the parallax, but was convinced that it was too small. Then comets, like the new star, should be located in ethereal regions, which, as it turns out, can change. This was confirmed with the appearance of other comets. Tycho wrote that all the comets that he observed moved in ethereal spaces and never appeared under the Moon, which Aristotle and his followers had been convinced of for many centuries without any reason. Observations of comets prompted Tycho Brahe to discover an even greater disorder in the heavens, according to Aristotle. If a geocentric universe is filled with crystalline spheres, where should comets be? Moreover, Tycho Brahe believed in a heliocentric Universe. Their special relationship with the Sun had already been noticed: for example, the applied mathematician Peter Apian (1495–1552), observing comets in the 1530s, was shocked by the fact that their tails always point away from the Sun. But for Ptolemy, the space above and below the Sun is completely filled with the spheres of the planets, and here even the introduction of a new sphere could not help.

Tycho Brahe, noticing that no matter how he arranged the spheres of the planets, the paths of comets would certainly intersect them, decided that since comets are always located above the Moon, perhaps there were no crystalline spheres supporting and moving the planets. He made such a revolutionary decision with complete equanimity. As he wrote in 1588 in a review on the study of comets (“On the latest phenomena in the ethereal world”), the title of the review itself is a challenge to traditionalism and a manifesto of the new astronomy:

“...there are actually no spheres in the heavens...the ones that the authors invented to “save face” exist only in their imagination, so that the movements of the planets and their orbits can be comprehended and, perhaps, recorded using numbers. So there is no point in going to the trouble of finding a real sphere to which the comet can be attached so that they rotate together. Modern philosophers agree with the ancients whether they are convinced that the heavens are divided into different spheres of solid and impenetrable matter. Some of them have stars attached to them so that they rotate together. But even if there were no other evidence, comets alone prove that such an opinion is not true. Comets have been repeatedly observed moving in the highest ether, and they cannot in any way be connected with the spheres.”

It's so easy to deny the reality of the crystalline spheres, to change the meaning of the word Orb– from the “sphere” to the “circular path” or to the “orbit” - a truly revolutionary idea, the same as moving the Earth from the center of the Universe. Since the 4th century BC. e. astronomers accepted without hesitation the reality of the solid spheres that support the planets. What else could keep the planets in the heavens? How else can one give physical reality to mathematical concepts? With the abandonment of crystalline spheres, there was an urgent need to find something else to keep the planets in orbit. But Tycho Brahe never mentioned this problem.

Now that it has been assumed that there are no solid spheres, it is only necessary to redistribute the Ptolemaic spheres to make room for comets moving around the Sun. Tycho Brahe wrote: “The heavenly world is huge. From what happened earlier it is clear that the comet moves within the space filled with ether. It seems that it is impossible to give a complete explanation of the whole problem until we know in what part of the widest ether and near what orbits of the planets [the comet] follows its path ... "

Ptolemy's system was inapplicable under these conditions: cumbersome, overloaded with equants and extra epicycles, and too full to leave room for comets. The "recent innovation of the great Copernicus" was elegant and beautiful from a mathematical point of view, but presented even greater difficulties. Tycho Brahe wrote:

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