# Marin Mersenne

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Marin Mersenne, Marin Mersennus or le Père Mersenne (September 8, 1588 – September 1, 1648) was a French theologian, philosopher, mathematician and music theorist. He is the author of the tract The impiety of deists.

Most frequently cited is Mersenne's estimate (from Quaestiones celeberrimae in Genesim, 1623) that Paris counted 50,000 atheists or libertines. At a time when the total population of Paris was about 300,000, this is an astonishing one out of six Parisians.

## Life

Marin Mersenne (pronounced Mehr-SENN) was born of peasant parents near Oizé, Maine (present day Sarthe). He was educated at Le Mans and at the Jesuit College of La Flèche. On July 17, 1611, he joined the Minim Friars, and, after studying theology and Hebrew in Paris received his full holy orders in 1613.

Between 1614 and 1618, he taught theology and philosophy at Nevers, but he returned to Paris and settled at the convent of L'Annonciade in 1620. There, with other kindred spirits such as René Descartes, Étienne Pascal, Gilles de Roberval and Nicolas-Claude Fabri de Peiresc, he studied mathematics and music. He corresponded with Giovanni Doni, Constantijn Huygens and other scholars in Italy, England and Holland. He was a staunch defender of Galileo, assisting him in translations of some of his mechanical works. For four years, Mersenne devoted himself entirely to philosophic and theological writing, and published Quaestiones celeberrimae in Genesim (1623); L'Impieté des déistes (1624); La Vérité des sciences (Truth of the Sciences against the Sceptics, 1624). It is sometimes incorrectly stated that he was a Jesuit. He was educated by Jesuits, but he never joined the Society of Jesus. He taught theology and philosophy at Nevers and Paris. In 1635 Mersenne met with Tommaso Campanella, but concluded that he could "teach nothing in the sciences (...) but still he has a good memory and a fertile imagination." Mersenne asked if René Descartes wanted Campanella to come to Holland to meet him, but Descartes declined. He visited Italy fifteen times, in 1640, 1641 and 1645.

He died through complications arising from a lung abscess.

## Works

### Quaestiones celeberrimae in Genesim (1623)

Quaestiones celeberrimae in Genesim

It was written as a commentary on the Book of Genesis and comprises uneven sections headed by verses from the first three chapters of that book. At first sight the book may appear to be a collection of treatises on various miscellaneous topics. However Robert Lenoble has shown that the principle of unity in the work is a diatribe against magical and divinatory arts, cabalism, animistic and pantheistic philosophies. He mentions Martin Del Rio's Investigations into Magic and criticises Marsilio Ficino for claiming power for images and characters. He condemns astral magic and astrology and the anima mundi a concept popular amongst Renaissance neo-platonists. Whilst allowing for a mystical interpretation of the Cabala, he wholeheartedly condemned its magical application - particularly to angelology. He also criticises Pico della Mirandola, Cornelius Agrippa and Francesco Gorgio with Robert Fludd as his main target. Fludd responded with Sophia cum moria certamen (1626), wherein Fludd admits his involvement with the Rosicrucians. The anonymous Summum bonum (1629), another critique of Mersenne, is an openly Rosicrucian text. The cabalist Jacques Gaffarel joined Fludd's side, while Pierre Gassendi defended Mersenne.

### Other

Mersenne is remembered today thanks to his association with the Mersenne primes. However, he was not primarily a mathematician; he wrote about music theory and other subjects. He edited works of Euclid, Apollonius, Archimedes, and other Greek mathematicians. But perhaps his most important contribution to the advance of learning was his extensive correspondence (in Latin) with mathematicians and other scientists in many countries. At a time when the scientific journal had not yet come into being, Mersenne was the center of a network for exchange of information.

His philosophical works are characterized by wide scholarship and the narrowest theological orthodoxy. His greatest service to philosophy was his enthusiastic defence of Descartes, whose agent he was in Paris and whom he visited in exile in the Netherlands. He submitted to various eminent Parisian thinkers a manuscript copy of the Meditations on First Philosophy, and defended its orthodoxy against numerous clerical critics.

In later life, he gave up speculative thought and turned to scientific research, especially in mathematics, physics and astronomy. In this connection, his best known work is Traité de l'harmonie universelle (also referred to as Harmonie universelle) of 1636, dealing with the theory of music and musical instruments. It is regarded as a source of information on 17th-century music, especially French music and musicians, to rival even the works of Pietro Cerone.

One of his many contributions to musical tuning theory was the suggestion of

$\sqrt\sqrt{2\over3-\sqrt2}$

as the ratio for an equally-tempered semitone ($\sqrt[12]{2}$). It was more accurate (0.44 cents sharp) than Vincenzo Galilei's 18/17 (1.05 cents flat), and could be constructed using straightedge and compass. Mersenne's description in the 1636 Harmonie universelle of the first absolute determination of the frequency of an audible tone (at 84 Hz) implies that he had already demonstrated that the absolute-frequency ratio of two vibrating strings, radiating a musical tone and its octave, is 1 : 2. The perceived harmony (consonance) of two such notes would be explained if the ratio of the air oscillation frequencies is also 1 : 2, which in turn is consistent with the source-air-motion-frequency-equivalence hypothesis.

He also performed extensive experiments to determine the acceleration of falling objects by comparing them with the swing of pendulums, reported in his Cogitata Physico-Mathematica in 1644. He was the first to measure the length of the seconds pendulum, that is a pendulum whose swing takes one second, and the first to observe that a pendulum's swings are not isochronous as Galileo thought, but that large swings take longer than small swings.

## Bibliography

### Works by Mersenne

• Euclidis elementorum libri, etc. (Paris, 1626)
• Les Mécaniques de Galilée (Paris, 1634)
• Questions inouies ou récréation des savants (1634)
• Questions théologiques, physiques, etc. (1634)
• Harmonie universelle (Paris, 1636-7)
• Nouvelles découvertes de Galilée (1639)
• Cogitata physico-mathematica (1644)
• Universae geometriae synopsis (1644)

### Other resources

• Marin Mersenne - The Birth of Modern Geometry (UK Open University TV documentary made in 1986 and transmitted on BBC2)