Marin Mersenne

Chapter 1 · From La Flèche to a Religious Order

A labourer's son who took vows and never left

1588 – 1620 · Maine · La Flèche · Paris

Marin Mersenne was born in 1588 in Maine, in north-western France, to a labouring family of modest means. He was sent to the new Jesuit college at La Flèche, where he overlapped with René Descartes — Descartes was eight years younger, and the friendship formed there lasted both their lives.

He went on to study theology and Hebrew in Paris, and in 1611 entered the Order of Minims, a strict Franciscan order committed to poverty, humility and a perpetual Lenten diet. He took vows and remained a friar for the rest of his life.

This is not incidental. His position gave him three things. It gave him time — the Minims of the Place Royale had no parish duties comparable to a secular priest's. It gave him respectability, which meant he could correspond with anybody and defend controversial work without immediate suspicion. And it gave him an institution with houses across Europe, and travelling brothers who could carry letters.

His early published work is theological polemic: enormous volumes attacking atheists, deists, and above all the Renaissance magical tradition — Robert Fludd, the alchemists, the astrologers, the practitioners of natural magic who claimed hidden sympathies between things.

It was in the course of attacking them that he arrived at his real position: that the answer to a claim about nature is a measurement.

Why this matters

Mersenne's campaign against occult natural philosophy pushed him toward measurement as the only reliable answer to a claim about the world.

You have the friar with time, standing and a network. What would you ask?

Ask Mersenne

• “What did entering the Minims make possible for you?”
• “Why attack the magicians and alchemists so hard?”
• “How did arguing with occultists lead you to measurement?”
• “What was Descartes like as a schoolboy at La Flèche?”
• “Did the Church ever object to what you were doing?”

Chapter 2 · The Cell at the Place Royale

Europe's science, copied out by hand and sent on

1620s – 1648 · Paris

There were no scientific journals. The Royal Society was founded in 1660, the Académie des Sciences in 1666 — both after Mersenne's death. If you made a discovery in the 1630s, you told people you knew.

Mersenne made himself the person everybody knew. His cell at the convent of the Minims on the Place Royale in Paris became the meeting place of French natural philosophy, and his correspondence — running to thousands of letters with more than seventy correspondents — did the work journals did later.

He wrote to Descartes in Holland, Galileo in Italy, Torricelli, Fermat, Roberval, Gassendi, Étienne and Blaise Pascal, Hobbes, the young Huygens. When something reached him, he copied it and forwarded it. He posed problems to several people at once and circulated the answers. He arranged meetings. He sent Descartes's *Meditations* around to hostile philosophers to collect objections, then printed the objections and Descartes's replies alongside the text — an early and deliberate act of peer review.

He held that a discovery kept private was not a discovery at all. He was also scrupulous about attribution: say plainly what you measured yourself and what you were merely told.

Much of his energy went into circulating other men's work rather than his own, and he thought that right. Whether it was a sacrifice or the achievement is a fair question.

Why this matters

Before journals existed, Mersenne's correspondence was the infrastructure of European science, and he invented something very close to peer review in the process.

You have the letters going out across Europe. What is your question for him?

Ask Mersenne

• “How did you decide who should see what?”
• “Why collect objections to Descartes and print them with the book?”
• “Was giving your time to other men's work a sacrifice?”
• “What did you do when two correspondents claimed the same result?”
• “How long did a letter take to reach Italy?”

Chapter 3 · Making Pitch a Number

Harmonie universelle, 1636

1636 · Paris

*Harmonie universelle*, published in 1636, is an enormous book about sound and music, and it contains his best work.

In it he set out what determines the pitch of a stretched string. The frequency falls as the string is made longer. It rises as the string is tightened — as the square root of the tension. And it falls as the string is made thicker or heavier — as the square root of the mass per unit length. These relations are still taught as Mersenne's laws.

But the genuinely clever move is how he attached a *number* to a pitch.

A very long, heavy, slack string vibrates slowly enough that you can watch it and count the swings against a pendulum. That gives you a frequency in vibrations per second for a string you cannot hear as a note. Then, since he knew how frequency scales with length, tension and thickness, he could scale up from the countable string to an audible one and calculate how many vibrations a second a musical note corresponds to.

Before this, a pitch was a place in a scale. After it, a pitch was a number.

He also heard, in a single plucked string, the fainter higher tones sounding along with the fundamental — the harmonics — and reported that a string sounds not one note but several at once, which is the beginning of the analysis of timbre.

“The sound of a string is to that of another as the roots of the weights that stretch them.”

— Marin Mersenne, Harmonie universelle (1636)

Why this matters

Mersenne turned pitch from a musical position into a measured number, which is the step that made acoustics a physical science.

You have the slow string counted by eye. What would you ask?

Ask Mersenne

• “How do you count the vibrations of a string too fast to see?”
• “What happens to the pitch when you tighten a string?”
• “What are the fainter tones you heard in one plucked string?”
• “Why does making a string thicker lower the note?”
• “Did musicians take any notice of your measurements?”

Chapter 4 · A Gun, a Distance and a Pendulum

The first good measurement of the speed of sound

1630s – 1640s · Paris

Mersenne measured how fast sound travels. The method is simple and it is exactly right.

Stand a known distance from a gun. Light travels effectively instantaneously over such a distance, so the flash arrives at once; the sound arrives later. Time the gap with a pendulum whose period you know. Divide the distance by the delay.

He also used echoes: stand a measured distance from a wall, shout, and time the return of the echo over twice that distance.

His figure came out at roughly 450 metres per second in the units he used. The true value at ordinary temperatures is about 343. He was too high by something like a third, which for a first careful measurement of a quantity nobody had ever measured is a genuine achievement — and he was clear that it was a measurement rather than a deduction.

He also established that the speed does not depend on the pitch of the sound or on how loud it is, which is not obvious and which matters: it means high and low notes from an orchestra arrive together.

What he did not do is put his two results together. He had a frequency, in vibrations per second, and he had a speed, in distance per second. Dividing one by the other gives a wavelength. He had no concept of wavelength, so the wave equation is not his.

Why this matters

Mersenne had both a frequency and a speed and never combined them, because he lacked the idea of wavelength — a clear case of a missing concept blocking an obvious step.

You have the flash, the report and the pendulum. What would you ask?

Ask Mersenne

• “Why can you treat the flash of the gun as arriving instantly?”
• “What made your figure too high by a third?”
• “How do you know a loud sound does not travel faster?”
• “You had a frequency and a speed — why not divide one by the other?”
• “What did you think sound actually was?”

Chapter 5 · The Primes, Galileo, and What Came After

A translation that carried risk, and a circle that became an institution

1634 – 1648 and after · Paris · Florence

In 1634, the year after Galileo's condemnation, Mersenne translated and published Galileo's mechanics in France, and later helped circulate the *Two New Sciences*. A Catholic friar publicly promoting a condemned author's work was not a risk-free act, and he did it deliberately, on the grounds that the mechanics was measurement and not doctrine.

He also worked on number theory. In 1644 he published a list of exponents for which he claimed numbers of the form two to that power minus one are prime. These are the Mersenne primes. His list contained errors — he included two exponents that do not give primes and omitted three that do — and it took nearly three centuries to check completely. But he had picked out a family of numbers with a deep structure, and the largest known prime has been a Mersenne prime for most of the last hundred years, because the form permits an unusually efficient test.

He died in Paris on 1 September 1648, aged sixty. At his own request his body was given for anatomical dissection.

The circle that had met in his cell continued meeting after his death, moving between the houses of Habert de Montmor and others, and it was one of the direct ancestors of the Académie des Sciences founded in 1666. When Huygens came to Paris to lead it, he was joining an institution that had grown out of a friar's room.

Why this matters

The Académie des Sciences grew directly out of the circle that met in Mersenne's cell, which makes his hospitality a piece of institutional history.

You have the primes, the risky translation and the circle that outlived him. What is your question?

Ask Mersenne

• “Why publish Galileo in France the year after his condemnation?”
• “How did you choose the exponents on your list of primes?”
• “Does it trouble you that your list had mistakes in it?”
• “Why give your body for dissection?”
• “Would you rather be remembered for the letters or for the acoustics?”

What Mersenne changed

Mersenne's laws of the vibrating string are still taught, and his measurement of the speed of sound was the first good one anybody made. His correspondence network held European science together for three decades before journals or academies existed, and the circle that met in his cell became one of the direct ancestors of the Académie des Sciences. The Mersenne primes still carry his name and still supply the largest known prime.

A debate that continues

How to weigh Mersenne's own discoveries against his role as an organiser is genuinely arguable, and his list of prime exponents contained errors that took nearly three centuries to resolve.

Keep exploring — ask Mersenne

• “Who in your circle was the most underrated?”
• “Should a discovery ever be kept private?”
• “What would you have measured next?”

Related lives

• René Descartes — Who Conserved The Quantity Of Motion
• Blaise Pascal — Who Carried A Barometer Up A Mountain
• Galileo Galilei — Father of Modern Science
• Christiaan Huygens — Who Watched From A Moving Boat

Related themes

Sound and waves · Frequency and pitch · How science is organised