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An orrery, also called a planetarium, shows the choreography of planets as they dance with coordinated precision around the Sun.  Early models were geocentric (Earth-centered), including the ancient Antikythera device and large mechanical clocks.

This model was made in Paris by the Delamarche family of instrument makers.  Charles François Delamarche (1740-1817) was one of the leading orrery makers in Paris. His son Felix Delamarche (d. 1847) continued in the craft after his father’s death. 

Orreries are named after Charles Boyle (1676-1731), Earl of Orrery. Heliocentric (Sun-centered) orreries with 6 planets replicate the solar system as it was known before the discovery of Uranus in 1781 by William Herschel.  Neptune was discovered by J.G. Galle in Berlin in 1846, after its prediction by Urbain Le Verrier. 

How many planets are present in this orrery? 

Can you deduce from this information when was it made?

Athanasius Kircher, Musurgia universalis (Rome, 1650)

This 17th-century treatise on music shows a mechanical, water-driven harpsichord. Water enters on the right side of the diagram, turning a gear mechanism that animates a cylinder roll and keyboard. Musical notation cut into the cylinder roll determines the keys depressed for any given time. This is similar to the many organ rolls still preserved at the American Organ Institute at OU.

On the far left, blacksmiths strike hammers upon an anvil, recalling the story of Pythagoras discovering the mathematical ratios of the musical scale from the chance hearing of blacksmiths at work. The blacksmith ensemble, with its visual reference to Pythagoras, served as an emblem of the mathematical and musical basis of natural order. 

The dance of skeleton figures reminds us of our mortality, a pious commonplace lest an evening of music lead to unrestrained frivolity. 

Standard textbooks of mathematics in the 16th and 17th centuries would not be adopted for university courses today! Topics they included that are no longer staples of the curriculum include music, astronomy, cartography, cryptography, fortification, and engineering. In their chapters on music, textbooks touched upon elements of music theory and the working of musical instruments, commonly assuming that the universe itself is a musical instrument that expresses harmonic proportions. This work by Kircher, a Jesuit at the Rome College (Collegio Romano), represents in expanded form how early mathematics textbooks covered the world of music making.

Most of Kircher’s 40 or so books were lavishly illustrated. This volume is no exception, including memorable depictions of birds’ songs in musical notation, or, in a section on acoustics, statues with concealed “speaking tubes” by which they appear to speak, making remote voices audible to anyone who passes by. 

One of the more bizarre ideas Kircher mentioned is a hypothetical instrument called a Katzenklavier (”cat piano”), which might perhaps be constructed for the entertainment of a melancholy prince. In this adaptation of a harpsichord, cats arranged in sequence according to the pitches of their yowls would be prompted to sing by the striking of hammers on their tails.

Vincenzo Galilei, Dialogo della Musica Antica et della Moderna (Florence, 1581)

From childhood, Galileo’s world was shaped by music. His father, Vincenzo Galilei, was a prominent music theorist who contributed to the development of Italian opera. This book, Vincenzo’s major work, was acquired in Fall 2014 with generous assistance from the Athletics Department.

Both Vincenzo and Galileo played the lute. Vincenzo’s compositions for the lute were widely appreciated, and as a young man Galileo gave lectures on the acoustics of the lute. 

Vincenzo undertook a comprehensive program of experimental testing to determine the effects of string length, tension or thickness upon pitch. As a result, Vincenzo critiqued purely numeric tuning schemes in favor of acoustical and empirical methods.

Vincenzo, like his son Galileo, rejected authority in favor of an emphasis on experimental methods of discovery, and communicated research results in an engaging literary genre. In Galileo’s own Dialogo, the character named Sagredo repeats some of Vincenzo’s arguments, while the character named Salviati adds Galileo’s further reflections upon the weight of strings and frequency of vibrational motion. Together, father and son transformed music from a study of numerical relations in an ideal world to an empirical study in the physical world which incorporated acoustics and accommodated fretted instruments.

This copy once belonged to the French collector Jean Ballesdens (1595-1675), and contains manuscript corrections and musical annotations.

During Galileo’s World, Eugene Enrico, OU Ruth Verne Davis Reaugh Professor of Music, conducted a performance of Vincenzo’s music by the classical ensemble Accademia Filarmonica.

Johann Kepler, Mysterium cosmographicum (Tübingen, 1596)

By far the best known 16th-century defender of Copernicus was Johann Kepler. In this work he demonstrated that vast empty regions lying between the planetary spheres, which were required by Copernicus, were not wasted space. Rather, these gaps perfectly matched, within the limits of observational error, the geometry of the five regular Pythagorean solids.

In the Mysterium, Kepler addressed two major differences between the systems of Ptolemy and Copernicus and turned them both to Copernicus’ advantage.

First, the number of the planetary spheres: in the Earth-centered Ptolemaic system there are 7 planets, including the Sun and the Moon, not counting the outermost sphere of fixed stars. In the Copernican system, there are only 6 planets, not counting the outermost sphere of fixed stars: The Sun and the Earth switch places. The number of planets decreases by one, because the Moon is demoted; it becomes a satellite of the Earth, within the Earth’s sphere, rather than a planet. So Kepler asked, why should there be only 6 planets instead of 7?

Second, and more critically, the distances of the planets: In the Ptolemaic system all the planetary spheres nest together with no intervening spaces. By contrast, in the Copernican system, the spheres of the planets become thin, separated by large distances. Skeptics asked, why would the Divine Architect have wasted so much empty space? Indeed, Kepler calculated that the gaps are quite large, so that most of the universe is empty space.

Kepler’s blueprints of the universe used the five regular Pythagorean solids to address both the number of the planets and the amazing proportions of the planetary spheres. 

Kepler mailed copies to various scholars, including Galileo and Tycho Brahe. Galileo was not persuaded by what seemed to him to be the work of a Lutheran mystic. He read no farther than the first few pages, but he wrote back to Kepler that he had already been a Copernican for several years. Tycho likewise was not amused at Kepler’s flights of fancy, but was impressed by his mathematical ability. So Tycho, who was then the Imperial mathematician and astronomer, offered him a job in Prague as a calculating assistant.

For Kepler, the mystery of the universe was now revealed, because the Divine Architect knew Pythagorean geometry and used it to construct a Copernican universe! Instead of nesting one planetary sphere immediately after another, in the ideal blueprints of the cosmos, the Creator alternated planetary spheres with regular solids. The vast empty regions lying between the planetary spheres, as required by Copernicus, were not wasted space. Rather, these gaps perfectly matched the geometry of the solids within the limits of observational error.

“And how intense was my pleasure from this discovery can never be expressed in words…. Day and night I was consumed by computing, to see whether this idea would agree with the Copernican orbs, or if my joy would be carried away by the wind. Within a few days everything worked, and I watched as one body [regular solid] after another fit precisely into its place among the planets” (Kepler, Mysterium cosmographicum).

Nicolaus Copernicus, De revolutionibus orbium coelestium (Nuremberg, 1543)

Copernicus argued that the Sun rather than the Earth lies in the center of the universe. The Earth moves as a planet around the Sun. In 1543 little proof was available that the Earth moves; there were many reasons not to accept it. Ptolemaic astronomy, as represented in the Epitome of Regiomontanus, was neither overly complex nor inaccurate. The most important advantage offered by Copernicus was a vision of the universe as a coherent and integrated system, where all the planets move together in elegant harmony.

Why did Copernicus do this? Why did he believe it? How revolutionary was De revolutionibus?

The book begins with an unsigned preface “To the Reader, on the Hypotheses of this Work.” The preface suggests that one should read the book and instead of taking offense, interpret it hypothetically. Mathematical works were often regarded as hypothetical because one could “save the phenomena” with various mathematical devices, even with false ones. This same argument later repeatedly plagued Galileo. The preface was unsigned because this was the middle of the Reformation and the preface was written by a leading Lutheran theologian who served as the final editor of the manuscript. Copernicus was a Catholic who worked in a cathedral in northern Poland. 

In a prefaced letter, Nicolaus Schönberg, a Cardinal, asked Copernicus to publish his book and even offered to pay for its printing. Although often overlooked, Copernicus had support from the highest levels of the Church. Indeed, Copernicus dedicated the book to none other than the pope. In his preface, he asserted that astronomy is a work of mathematics, for mathematicians. Theologians should understand, before they criticize, that the current system was no credit to the deity.

In Book I Copernicus laid out his basic assumptions, including that the universe is spherical and that the Earth is spherical. Ptolemy began the Almagest in the same way. Copernicus departed from Ptolemy by switching the positions of the Sun and the Earth, which the work of Regiomontanus had made theoretically possible. 

In 1543 proof that the Earth moves could not come from observations. Nor was Ptolemaic astronomy overly complex: Copernicus used about the same total number of circles as Ptolemy. And in theory, a geocentric system may be updated to yield accurate predictions for any epoch, as occurs in any planetarium today with an observer-centered mechanical-optical star projector. When he conceived the heliocentric cosmos, Copernicus’ aim was not to account for new observations but to equal the Epitome in mathematical power. 

The most important advantage offered by Copernicus was a vision of the universe as a coherent and integrated system, where all the planets move together in elegant harmony. In contrast, Ptolemy considered each planet in isolation. In the geocentric cosmos, each planet was explained separately by its own individual model, and the models did not even share the same center. Copernicus compared this fragmented portrait of the cosmos with a sculpture assembled piece-meal, more like a monster than the well-proportioned form of a man.

When the Counter-Reformation began in earnest after the Council of Trent, the Catholic reception of Copernicus became immensely complicated by the desire to avoid unsanctioned novelties. A Catholic astronomer once hailed by cardinals and popes now became suspect, associated with northern heretics. In 1616, this work by Copernicus was put on the Index of prohibited books, suspended until it could be corrected.

The OU copy of Copernicus is a “censored” copy. Notice how the heading on the page facing the cosmic section is emended. Where the original heading reads, “Demonstration of the triple motion of the Earth,” the handwritten correction states, “Demonstration of the hypothesis of the triple motion of the Earth.” This is one of the corrections mandated by the Inquisition in 1620 when it became permissible to read Copernicus again, following its suspension in 1616.