Category Archives: History of science

STOMP, STOMP, STOMP … NEWTON DID WOT!

Oh dear! The HISTSCI_HULK has been woken from his post festive slumbers and is once again on the rampage. What has provoked this outbreak so early in the new year? He chanced to see a post, that one of my followers on Facebook had linked to, celebrating Newton’s new-style birthday on 4 January. As is well-known, we here at the Renaissance Mathematicus celebrate Newton’s old-style birthday, but that’s another story. 

The post is on a website called Wonders of Physics, is the work of an Indian physicist, Vedang Sati, and is titled:

10 Discoveries By Newton That Changed The World

I have reproduced the whole horror show below. Let us examine it.

Isaac Newton is one of the few names that will forever be enshrined in physics history and that too with a lot of glamour associated. Contributions of none other physicist match, his, well, Einstein’s, or not even his!? The following are Newton’s ten most well-known works that changed the world later on. 

A strong hagiographical vibe going down here, which doesn’t bode well.

Laws of motion

1. An object will remain at rest or move in a straight line unless acted upon by an external force.

2. F=ma.

3. For every action, there is an equal and opposite reaction. 

Newton’s three laws of motion, along with thermodynamics, stimulated the industrial revolution of the 18th and 19th centuries. Much of the society built today owes to these laws.

Remember these are supposedly the things that Newton discovered. His first law of motion, the law of inertia, was first formulated by Galileo, who, however, thought it only applied to circular motion. For linear motion it was first formulated by Isaac Beeckman and taken over from him by both René Descartes and Pierre Gassendi. Newton took it from Descartes. The second law, which was actually slightly different in the original form in which Newton used it, was taken from Christiaan Huygens. The third law was probably developed out of the studies of elastic and inelastic collision, which again originates by Descartes, who got much wrong which was corrected by both Huygens and Newton. Newton’s contribution was to combine them as axioms from which to deduce his mechanics, again probably inspired by Huygens. He tried out various combinations of a range of laws before settling on these three. Sati’s following statement is quite frankly bizarre, whilst not totally false. What about the Principia, where they occur, as the foundation of classical mechanics and perhaps more importantly celestial mechanics.

Binomial Theorem

Around 1665, Isaac Newton discovered the Binomial Theorem, a method to expand the powers of sum of two terms. He generalized the same in 1676. The binomial theorem is used in probability theory and in the computing sciences.

The binomial theorem has a very long history stretching back a couple of thousand years before Newton was born. The famous presentation of the binomial coefficients, known as Pascal’s Triangle, which we all learnt in school (didn’t we?), was known both to Indian and Chinese mathematicians in the Middle Ages. Newton contribution was to expand the binomial theorm to the so-called general form, valid for any rational exponent. 

Inverse square law

By using Kepler’s laws of planetary motion, Newton derived the inverse square law of gravity. This means that the force of gravity between two objects is inversely proportional to the square of the distance between their centers. This law is used to launch satellites into space.

I covered this so many times, it’s getting boring. Let’s just say the inverse square law of gravity was derived/hypothesized by quite a few people in the seventeenth century, of whom Newton was one. His achievement was to show that the inverse square law of gravity and Kepler’s third law of planetary motion are mathematically equivalent, which as the latter in derived empirically means that the former is true. Newton didn’t discover the inverse square law of gravity he proved it.

Newton’s cannon

Newton was a strong supporter of Copernican Heliocentrism. This was a thought experiment by Newton to illustrate orbit or revolution of moon around earth (and hence, earth around the Sun)

He imagined a very tall mountain at the top of the world on which a cannon is loaded. If too much gunpowder is used, then the cannon ball will fly into space. If too little is used, then the ball wouldn’t travel far. Just the right amount of powder will make the ball orbit the Earth. 

This thought experiment was in Newton’s De mundi systemate, a manuscript that was an originally more popular draft of what became the third book of the Principia. The rewritten and expanded published version was considerably more technical and mathematical. Of course, it has nothing to do with gunpowder, but with velocities and forces. Newton is asking when do the inertial force and the force of gravity balance out, leading to the projectile going into orbit. It has nothing to do directly with heliocentricity, as it would equally apply to a geocentric model, as indeed the Moon’s orbit around the Earth is. De mundi systemate was first published in Latin and in an English translation, entitled A Treatise of the System of the World posthumously in 1728, so fifty years after the Principia, making it at best an object of curiosity and not in any way world changing. 

Calculus

Newton invented the differential calculus when he was trying to figure out the problem of accelerating body. Whereas Leibniz is best-known for the creation of integral calculus. The calculus is at the foundation of higher level mathematics. Calculus is used in physics and engineering, such as to improve the architecture of buildings and bridges.

This really hurts. Newton and Leibniz both collated and codified systems of calculus that included both differential and integral calculus. Neither of them invented it. Both of them built on a two-thousand-year development of the discipline, which I have sketch in a blog post here. On the applications of calculus, I recommend Steven Strogatz’s “Infinite Powers”

Rainbow

Newton was the first to understand the formation of rainbow. He also figured out that white light was a combination of 7 colors. This he demonstrated by using a disc, which is painted in the colors, fixed on an axis. When rotated, the colors mix, leading to a whitish hue.

In the fourteenth century both the German Theodoric of Freiberg and the Persian Kamal al-Din al-Farsi gave correct theoretical explanations of the rainbow, independently of one another. They deliver an interesting example of multiple discovery, and that scientific discoveries can get lost and have to be made again. In the seventeenth century the correct explanation was rediscovered by Marco Antonio de Dominis, whose explanation of the secondary rainbow was not quite right. A fully correct explanation was then delivered by René Descartes. 

That white light is in fact a mixture of the colours of the spectrum was indeed a genuine Newton discovery, made with a long series of experiments using prisms and then demonstrated the same way. Newton’s paper on his experiments was his first significant publication and, although hotly contested, established his reputation. It was indeed Newton, who first named seven colours in the spectrum, there are in fact infinitely many, which had to do with his arcane theories on harmony. As far as can be ascertained the Newton Disc was first demonstrated by Pieter van Musschenbroek in 1762. 

Reflecting Telescope

In 1666, Newton imagined a telescope with mirrors which he finished making two years later in 1668. It has many advantages over refracting telescope such as clearer image, cheap cost, etc.

Once again, the reflecting telescope has a long and complicated history and Newton was by no means the first to try and construct one. However, he was the first to succeed in constructing one that worked. I have an article that explains that history here.

Law of cooling

His law states that the rate of heat loss in a body is proportional to the difference in the temperatures between the body and its surroundings. The more the difference, the sooner the cup of tea will cool down.

Whilst historically interesting, Newton’s law of cooling holds only for very small temperature differences. It didn’t change the world

Classification of cubics

Newton found 72 of the 78 “species” of cubic curves and categorized them into four types. In 1717, Scottish mathematician James Stirling proved that every cubic was one of these four types.

Of all the vast amount of mathematics that Newton produced, and mostly didn’t publish, to choose his classification of cubics as one of his 10 discoveries that changed the world is beyond bizarre. 

Alchemy

At that time, alchemy was the equivalent of chemistry. Newton was very interested in this field apart from his works in physics. He conducted many experiments in chemistry and made notes on creating a philosopher’s stone.

Newton could not succeed in this attempt but he did manage to invent many types of alloys including a purple copper alloy and a fusible alloy (Bi, Pb, Sn). The alloy has medical applications (radiotherapy).

Here we have a classic example of the Newton was really doing chemistry defence, although he does admit that Newton made notes on creating a philosopher’s stone. If one is going to call any of his alloys, world changing, then surely it should be speculum, an alloy of copper and tin with a dash of arsenic, which Newton created to make the mirror for his reflecting telescope, and which was used by others for this purpose for the next couple of centuries.

Of course, the whole concept of a greatest discovery hit list for any scientist is totally grotesque and can only lead to misconceptions about how science actually develops. However, if one is going to be stupid enough to produce one, then one should at least get one’s facts rights. Even worse is that things like the classification of the cubics or Newton’s Law of Cooling are anything but greatest discoveries and in no way “changed the world.” 

You might wonder why I take the trouble to criticise this website, but the author has nearly 190,000 followers on Facebook and he is by no means the only popular peddler of crap in place of real history of science on the Internet. I often get the feeling that I and my buddy the HISTSCI_HULK are a latter-day King Cnut trying to stem the tide of #histSTM bullshit. 

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Filed under History of science, Myths of Science, Newton

The Epicurean mathematician

Continuing our look at the group of mathematician astronomers associated with Nicolas-Claude Fabri de Peiresc (1580-1637) in Provence and Marin Mersenne (1588–1648) in Paris, we turn today to Pierre Gassendi (1592–1655), celebrated in the world of Early Modern philosophy, as the man who succeeded in making Epicurean atomism acceptable to the Catholic Church. 

Pierre Gassendi Source: Wikimedia Commons

Pierre Gassendi was born the son of the peasant farmer Antoine Gassend and his wife Fançoise Fabry in the Alpes-de-Haute-Provence village of Champtercier on 22 January 1592. Recognised early as something of a child prodigy in mathematics and languages, he was initially educated by his uncle Thomas Fabry, a parish priest. In 1599 he was sent to the school in Digne, a town about ten kilometres from Champtercier, where he remained until 1607, with the exception of a year spent at school in another nearby village, Riez. 

In 1607 he returned to live in Champtercier and in 1609 he entered the university of Aix-en-Provence, where his studies were concentrated on philosophy and theology, also learning Hebrew and Greek. His father Antoine died in 1611. From 1612 to 1614 his served as principle at the College in Digne. In 1615 he was awarded a doctorate in theology by the University of Avignon and was ordained a priest in 1615. From 1614 he held a minor sinecure at the Cathedral in Digne until 1635, when he was elevated to a higher sinecure. From April to November in 1615 he visited Paris for the first time on Church business. 

Cathédrale Saint-Jérome de Digne Source: Wikimedia Commons

In 1617 both the chair of philosophy and the chair of theology became vacant at the University of Aix; Gassendi applied for both chairs and was offered both, one should note that he was still only twenty-four years old. He chose the chair for philosophy leaving the chair of theology for his former teacher. He remained in Aix for the next six years. 

When Gassendi first moved to Aix he lived in the house of the Provencal astronomer Joseph Gaultier de la Valette (1564–1647), vicar general of Aix and Peiresc’s observing partner. Whilst living in Gaultier’s house he got to know Jean-Baptiste Morin (1583–1556), who was also living there as Gaultier’s astronomical assistant. Although, in later years, in Paris, Gassendi and Morin would have a major public dispute, in Aix the two still young aspiring astronomers became good friends. It was also through Gaultier that Gassendi came to the attention of Peiresc, who would go on to become his patron and mentor. 

Jean-Baptiste Morin Source: Wikimedia Commons

For the next six years Gassendi taught philosophy at the University of Aix and took part in the astronomical activities of Peiresc and Gaultier, then in 1623 the Jesuits took over the university and Gassendi and the other non-Jesuit professors were replaced by Jesuits. Gassendi entered more than twenty years of wanderings without regular employment, although he still had his sinecure at the Cathedral of Digne.

In 1623, Gassendi left Aix for Paris, where he was introduced to Marin Mersenne by Peiresc. The two would become very good friends, and as was his wont, Mersenne took on a steering function in Gassendi’s work, encouraging him to engage with and publish on various tropics. In Paris, Gassendi also became part of the circle around Pierre Dupuy (1582–1651) and his brother Jacques (1591–1656), who were keepers of the Bibliothèque du Roi, today the Bibliothèque nationale de France, and who were Ismael Boulliau’s employers for his first quarter century in Paris.

Pierre Dupuy Source: Wikimedia Commons

The Paris-Provence group Peiresc (1580–1637), Mersenne (1588–1648), Morin (1583–1656), Boulliau (1605–1694), and Gassendi (1592–1655) are all members of the transitional generation, who not only lived through the transformation of the scientific view of the cosmos from an Aristotelian-Ptolemaic geocentric one to a non-Aristotelian-Keplerian heliocentric one but were actively engaged in the discussions surrounding that transformation. When they were born in the late sixteenth century, or in Boulliau’s case the early seventeenth century, despite the fact that Copernicus’ De revolutionibus had been published several decades earlier and although a very small number had begun to accept a heliocentric model and another small number the Tychonic geo-heliocentric one, the geocentric model still ruled supreme. Kepler’s laws of planetary motion and the telescopic discoveries most associated with Galileo still lay in the future. By 1660, not long after their deaths, with once again the exception of Boulliau, who lived to witness it, the Keplerian heliocentric model had been largely accepted by the scientific community, despite there still being no empirical proof of the Earth’s movement. 

Given the Church’s official support of the Aristotelian-Ptolemaic geocentric model and after about 1620 the Tychonic geo-heliocentric model, combined with its reluctance to accept this transformation without solid empirical proof, the fact that all five of them were devout Catholics made their participation in the ongoing discussion something of a highwire act. Gassendi’s personal philosophical and scientific developments over his lifetime are a perfect illustration of this. 

During his six years as professor of philosophy at the University of Aix, Gassendi taught an Aristotelian philosophy conform with Church doctrine. However, he was already developing doubts and in 1624 he published the first of seven planned volumes criticising Aristotelian philosophy, his Exercitationes paradoxicae adversus aristoteleos, in quibus praecipua totius peripateticae doctrinae fundamenta excutiuntur, opiniones vero aut novae, aut ex vetustioribus obsoletae stabiliuntur, auctore Petro Gassendo. Grenoble: Pierre Verdier. In 1658, Laurent Anisson and Jean Baptiste Devenet published part of the second volume posthumously in Den Hague in 1658. Gassendi seems to have abandoned his plans for the other five volumes. 

To replace Aristotle, Gassendi began his promotion of the life and work of Greek atomist Epicurus (341–270 BCE). Atomism in general and Epicureanism in particular were frowned upon by the Christian Churches in general. The Epicurean belief that pleasure was the chief good in life led to its condemnation as encouraging debauchery in all its variations. Atomists, like Aristotle, believed in an eternal cosmos contradicting the Church’s teaching on the Creation. Atomist matter theory destroyed the Church’s philosophical explanation of transubstantiation, which was based on Aristotelian matter theory. Last but no means least Epicurus was viewed as being an atheist. 

In his biography of Epicurus De vita et moribus Epicuri libri octo published by Guillaume Barbier in Lyon in 1647

and revival and reinterpretation of Epicurus and Epicureanism in his Animadversiones in decimum librum Diogenis Laertii: qui est De vita, moribus, placitisque Epicuri. Continent autem Placita, quas ille treis statuit Philosophiae parteis 3 I. Canonicam, …; – II. Physicam, …; – III. Ethicam, … and his Syntagma philosophiae Epicuri cum refutationibus dogmatum quae contra fidem christianam ab eo asserta sunt published together by Guillaume Barbier in Lyon in 1649,

Gassendi presented a version of Epicurus and his work that was acceptable to Christians, leading to both a recognition of the importance of Epicurean philosophy and of atomism in the late seventeenth and early eighteenth centuries. 

Gassendi did not confine himself to work on ancient Greek philosophers. In 1629,  pushed by Mersenne, the scientific agent provocateur, he wrote an attack on the hermetic philosophy of Robert Fludd (1574–1637), who famously argued against mathematics-based science in his debate with Kepler. Also goaded by Mersenne, he read Descartes’ Meditationes de prima philosophia (Meditations on First Philosophy) (1641) and published a refutation of Descartes’ methodology. As a strong scientific empiricist, Gassendi had no time for Descartes’ rationalism. Interestingly, it was Gassendi in his Objections (1641), who first outlined the mind-body problem, reacting to Descartes’ mind-body dualism. Descartes was very dismissive of Gassendi’s criticisms in his Responses, to which Gassendi responded in his Instantiae (1642). 

Earlier, Gassendi had been a thorn in Descartes side in another philosophical debate. In 1628, Gassendi took part in his only journey outside of France, travelling through Flanders and Holland for several months, although he did travel widely throughout France during his lifetime. Whilst in Holland, he visited Isaac Beeckman (1588–1637) with whom he continued to correspond until the latter’s death. Earlier, Beeckman had had a massive influence on the young Descartes, introducing him to the mechanical philosophy. In 1630, Descartes wrote an abusive letter denying any influence on his work by Beeckman. Gassendi, also a supporter of the mechanical philosophy based on atomism, defended Beeckman.

Like the others in the Mersenne-Peiresc group, Gassendi was a student and supporter of the works of both Johannes Kepler (1571–1630) and Galileo Galilei (1564–1642) and it is here that he made most of his contributions to the evolution of the sciences in the seventeenth century. 

Having been introduced to astronomy very early in his development by Peiresc and Gaultier de la Valette, Gassendi remained an active observational astronomer all of his life. Like many others, he was a fan of Kepler’s Tabulae Rudolphinae (Rudolphine Tables) (1627) the most accurate planetary tables ever produced up till that time. Producing planetary tables and ephemerides for use in astrology, cartography, navigation, etc was regarded as the principal function of astronomy, and the superior quality of Kepler’s Tabulae Rudolphinae was a major driving force behind the acceptance of a heliocentric model of the cosmos. Consulting the Tabulae Rudolphinae Gassendi determined that there would be a transit of Mercury on 7 November 1631. Four European astronomers observed the transit, a clear proof that Mercury orbited the Sun and not the Earth, and Gassendi, who is credited with being the first to observe a transit of Mercury, published his observations Mercvrivs in sole visvs, et Venvs invisa Parisiis, anno 1631: pro voto, & admonitione Keppleri in Paris in 1632.

He also tried to observe the transit of Venus, predicted by Kepler for 6 December 1631, not realising that it was not visible from Europe, taking place there during the night. This was not yet a proof of heliocentricity, as it was explainable in both the Capellan model in which Mercury and Venus both orbit the Sun, which in turn orbits the Earth and the Tychonic model in which the five planets all orbit the Sun, which together with the Moon orbits the Earth. But it was a very positive step in the right direction. 

In his De motu impresso a motore translato. Epistolæ duæ. In quibus aliquot præcipuæ tum de motu vniuersè, tum speciatim de motu terræattributo difficulatates explicantur published in Paris in 1642, he dealt with objections to Galileo’s laws of fall.

Principally, he had someone drop stones from the mast of a moving ship to demonstrate that they conserve horizontal momentum, thus defusing the argument of those, who claimed that stones falling vertically to the Earth proved that it was not moving. In 1646 he published a second text on Galileo’s theory, De proportione qua gravia decidentia accelerantur, which corrected errors he had made in his earlier publication.

Like Mersenne before him, Gassendi tried, using a cannon, to determine the speed of sound in 1635, recording a speed of 1,473 Parian feet per second. The actual speed at 20° C is 1,055 Parian feet per second, making Gassendi’s determination almost forty percent too high. 

In 1648, Pascal, motivated by Mersenne, sent his brother-in-law up the Puy de Dôme with a primitive barometer to measure the decreasing atmospheric pressure. Gassendi provided a correct interpretation of this experiment, including the presence of a vacuum at the top of the tube. This was another indirect attack on Descartes, who maintained the assumption of the impossibility of a vacuum. 

Following his expulsion from the University of Aix, Nicolas-Claude Fabri de Peiresc’s house became Gassendi’s home base for his wanderings throughout France, with Peiresc helping to finance his scientific research and his publications. The two of them became close friends and when Peiresc died in 1637, Gassendi was distraught. He preceded to mourn his friend by writing his biography, Viri illvstris Nicolai Clavdii Fabricii de Peiresc, senatoris aqvisextiensis vita, which was published by Sebastian Cramoisy in Paris in 1641. It is considered to be the first ever complete biography of a scholar. It went through several edition and was translated into English.

In 1645, Gassendi was appointed professor of mathematics at the Collège Royal in Paris, where he lectured on astronomy and mathematics, ably assisted by the young Jean Picard (1620–1682), who later became famous for accurately determining the size of the Earth by measuring a meridian arc north of Paris.

Jean Picard

Gassendi only held the post for three years, forced to retire because of ill health in 1648. Around this time, he and Descartes became reconciled through the offices of the diplomat and cardinal César d’Estrées (1628–1714). 

Gassendi travelled to the south for his health and lived for two years in Toulon, returning to Paris in 1653 when his health improved. However, his health declined again, and he died of a lung complaint in 1655.

Although, like the others in the group, Gassendi was sympathetic to a heliocentric world view, during his time as professor he taught the now conventional geo-heliocentric astronomy approved by the Catholic Church, but also discussed the heliocentric systems. His lectures were written up and published as Institutio astronomica juxta hypotheseis tam veterum, quam Copernici et Tychonis in 1647. Although he toed the party line his treatment of the heliocentric was so sympathetic that he was reported to the Inquisition, who investigated him but raised no charges against him. Gassendi’s Institutio astronomica was very popular and proved to be a very good source for people to learn about the heliocentric system. 

As part of his campaign to promote the heliocentric world view, Gassendi also wrote biographies of Georg Peuerbach, Regiomontanus, Copernicus, and Tycho Brahe. It was the only biography of Tycho based on information from someone, who actually knew him. The text, Tychonis Brahei, eqvitis Dani, astronomorvm coryphaei vita, itemqve Nicolai Copernici, Georgii Peverbachii & Ioannis Regiomontani, celebrium Astronomorum was published in Paris in 1654, with a second edition appearing in Den Hague in the year of Gassendi’s death, 1655. In terms of historical accuracy, the biographies are to be treated with caution.

Gassendi also became engaged in a fierce dispute about astronomical models with his one-time friend from his student days, Jean-Baptiste Morin, who remained a strict geocentrist. I shall deal with this when I write a biographical sketch of Morin, who became the black sheep of the Paris-Provencal group.

Like the other members of the Paris-Provencal group, Gassendi communicated extensively with other astronomers and mathematician not only in France but throughout Europe, so his work was well known and influential both during his lifetime and also after his death. As with all the members of that group Gassendi’s life and work is a good example of the fact that science is a collective endeavour and often progresses through cooperation rather than rivalry. 

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Filed under History of Astronomy, History of Mathematics, History of Physics, History of science

Christmas Trilogy 2021 Part 2: He was the author of rambling volumes on every subject under the sun?

The acolytes of Ada Lovelace are big fans of Sydney Padua’s comic book, The Thrilling Adventures of Lovelace and Babbage (Penguin, 2015). One can not deny Padua’s talent as a graphic artist, but her largely warped (she claims mostly true) account of their relationship is based on heavy quote mining and even distortion of quotes to make Lovelace look good and Babbage less than good. Just to give one example, there are many, many more, of her distortion of known facts she writes: 

I believe Lovelace used music as an example not only because she was steeped in music theory, but because she enjoyed yanking Babbage’s chain, and he famously hated music (my emphasis)

There is no evidence whatsoever that Babbage hated music, in fact rather the opposite. What Padua is playing on is Babbage’s infamous war with the street musicians of London and was about noise pollution and not about music per se. In fact, anybody, who has listened to a half-cut busker launching into their out of tune rendition of Wonderwall for the third time in an hour, would have a lot of sympathy with Babbage’s attitude.

I’m not going to analyse all the errors and deliberate distortions in Padua’s work, but I will examine in some detail one of her bizarre statements:

It’s not clear why Babbage himself never published anything other than vague summaries about his own machine. He published volumes of ramblings on every subject under the sun (my emphasis) except that of his life’s work (my emphasis)

Calling the Analytical Engine “his life’s work” shows an ignorance of the man and his activities. This is a product of a sort of presentism that has reduced Charles Babbage in the popular imagination to “the inventor of the first computer” and blended out the rest of his rich and complicated life. A life full of scientific, mathematical, and socio-political activities. The Analytical Engine was a major project in Babbage’s life, but it was far from being his life’s work.

The Illustrated London News (4 November 1871) Source: Wikimedia Commons

Babbage actually only published a total of eight books over a period of forty years, none of which is in anyway rambling. If we look at the list a little more closely, then it actually reduces to three.

  1. (1825) Account of the repetition of M. Arago’s experiments on the magnetism manifested by various substances during the act of rotation, London, William Nicol
  2. Babbage, Charles (1826). A Comparative View of the Various Institutions for the Assurance of Lives. London: J. Mawman.
  3. Babbage, Charles (1830). Reflections on the Decline of Science in England, and on Some of Its Causes. London: B. Fellowes.
  4. Babbage, Charles (1832).On the Economy of Machinery and Manufactures London: Charles Knight.
  5. Babbage, Charles (1837).The Ninth Bridgewater Treatise, a Fragment. London: John Murray.
  6. Babbage, Charles (1841).Table of the Logarithms of the Natural Numbers from 1 to 108000. London: William Clowes and Sons.
  7. Babbage, Charles (1851).The Exposition of 1851. London: John Murray
  8. Babbage, Charles (1864).Passages from the Life of a Philosopher, London, Longman

No: 1 on our list is a thirty-page scientific paper co-authored with John Herschel and like No: 6, a book of log tables, need not bother us here. No: 2 is a sort of consumers guide to life insurance and is not really relevant here. Statistical tables of life expectancy and insurance schemes based on them had become a thing for mathematicians since the early eighteenth century, Edmund Halley had dabbled, for example. The leading English mathematician John Joseph Sylvester (1814–1897) worked for a number of years as an insurance mathematician. No:5 The Ninth Bridgewater Thesis gives Babbage’s views on Natural Theology, which he developed in a separate paper on his rational explanation for miracles based on programming of his Difference Engine, which I have dealt with here. No. 8 is of course his autobiography, a very interesting read. All of Babbage’s literary output has a strong campaigning element.

This leaves just three volumes that we have to consider in terms of the Padua quote, Reflections on the Decline of Science in England, and on Some of Its Causes, On the Economy of Machinery and Manufactures, and The Exposition of 1851

Reflections on the Decline of Science in England, and on Some of Its Causes is as it’s title would suggest a socio-political polemic largely directed as the Royal Society. Babbage thought correctly that there had been a decline in mathematics and physics in the UK over the eighteenth century, which was continued into the nineteenth. He began his attacks on the scientific establishment during his time as a student at Cambridge, when together with John Herschel and George Peacock he founded the Analytical Society, which campaigned to replace the teaching of Newton’s dated mathematics and physics with the much more advanced material from the continent. His Reflections on the Decline of Science upped the ante, as the now established Lucasian Professor for mathematics he launched a full broadside against the scientific established and in particular the Royal Society. 

Babbage was not alone in his wish for reform and he and his supporters were labelled the Declinarians. The Declarians failed in their attempt to introduce reform into the Royal Society, but the result of their campaign was the creation of the British Association for the Advancement of Science, which was founded in 1831 by William Harcourt, David Brewster, William Whewell, James Johnston, and Babbage. Babbage’s book was regarded as the spearhead of the campaign. The BAAS was a new public mouthpiece for the scientific establishment that was more open, outward going, and liberal than the moribund Royal Society.

Babbage’s On the Economy of Machinery and Manufactures from 1832, might be considered Babbage’s most important publication. Following the death of his first wife in 1827, Babbage went on a several-year tour of the continent visiting all the factories and institutions, which used and/or dependent on automation of some sort, studying and investigating. On his return from the continent, he did the same in the UK, once again examining all of the industrial applications of automation that he could find. This research took up more than ten years and Babbage became, probably, the greatest living authority on the entire subject of automation. This knowledge led him in two different directions. On the one hand it lay behind his decision the abandon his Difference Engine, a special-purpose computer, and instead invest his energy in his planned Analytical Engine, a general-purpose computer. On the other hand, it led to him writing his On the Economy of Machinery and Manufactures

When it appeared On the Economy of Machinery and Manufactures was a unique publication, nothing quite like it had ever been published before. The book deals with the economic, social, political, and practical aspects of automation, and has been called on influential early work on operational research. It grew out of an earlier essay in the Encyclopædia Metropolitana An essay on the general principles which regulate the application of machinery to manufactures and the mechanical arts (1827). The book was a major success with a fourth edition appearing in 1836. From the second edition onwards, it included an extra section on political economy, a subject not included in the first edition.

The book also contains a description of what is now known a Babbage’s Principle, which emphasises the commercial advantage of more careful division of labour. An idea already anticipated in the work of the Italian economist Melchiorre Gioja (1767–1829). The Babbage’s Principle means dividing up work processes amongst several workers according to the varying skills. Such a division of labour was behind the origin of his Difference Engine. In the eighteenth century the French government had broken-down the calculation of mathematical tables to simple steps with each computer, those doing the calculations, often women, just doing one of two steps before passing the calculation onto the next computer. The Difference Engine was designed to automate this process.

Babbage never the most diplomatic of intellectuals thoroughly annoyed the publishing industry by including a detailed analysis of book production in On the Economy of Machinery and Manufactures including revealing the publishing trade’s profitability.

Babbage’s book had a major influence on the development of economics in the nineteenth century and was quoted in the work of John Stuart Mill, Karl Marx, and John Ruskin. The book was translated into both French and German. It has been argued that the book influenced the layout of the Great Exhibition of 1851 and it to this we turn for Babbage’s last book, his The Exposition of 1851

View from the Knightsbridge Road of The Crystal Palace in Hyde Park for Grand International Exhibition of 1851. Dedicated to the Royal Commissioners., London: Read & Co. Engravers & Printers, 1851Source: Wikimedia Commons

The book is Babbage’s analysis of the Great Exhibition of 1851, brought into life by the Royal Society for the Encouragement of Arts, Manufactures and Commerce, and for which the original Crystal Palace was created. The Great Exhibition also led to the establishment of the V&A, the Natural History Museum, and the Science Museum to provide permanent homes for many of the exhibits. This was the first world fair and Babbage was personally involved. One of the working modules of his Difference Engine was on display and in the windows of his house, which lay on the route to the exhibition, he demonstrated his optical signally device for ships, inviting visitors to the Crystal Palace to post the signalled number in his letterbox. To a large extent The Exposition of 1851 is a coda to both Reflections on the Decline of Science and On the Economy of Machinery and Manufactures, which leads us an answer to the question of Babbage’s life’s work.

Padua thinks incorrectly that the Analytical Engine was his life’s work, a fallacy that is certainly shared by those, who only know Babbage as the inventor of the “first computer.” In reality, Babbage’s life’s work was the promotion and advancement of science and technology, his calculating engines representing only one aspect of a much wider vision. From his days as a student fighting for an improvement in the teaching of the mathematical sciences at Cambridge University, through his campaign to modernise the Royal Society, which led instead to the creation of the BAAS, he was also instrumental in founding the Astronomical Society. His research on automation leading to the highly influential On the Economy of Machinery and Manufactures and his direct and indirect involvement in the Great Exhibition. All of these served one end the promotion and advancement of science and its applications.  

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Renaissance Science – XXV

It is generally acknowledged that the mathematisation of science was a central factor in the so-called scientific revolution. When I first came to the history of science there was widespread agreement that this mathematisation took place because of a change in the underlaying philosophy of science from Aristotelian to Platonic philosophy. However, as we saw in the last episode of this series, the renaissance in Platonic philosophy was largely of the Neoplatonic mystical philosophy rather than the Pythagorean, mathematical Platonic philosophy, the Plato of “Let no one ignorant of geometry enter here” inscribed over the entrance to The Academy. This is not to say that Plato’s favouring of mathematics did not have an influence during the Renaissance, but that influence was rather minor and not crucial or pivotal, as earlier propagated.

It shouldn’t need emphasising, as I’ve said it many times in the past, but Galileo’s infamous, Philosophy is written in this grand book, which stands continually open before our eyes (I say the ‘Universe’), but can not be understood without first learning to comprehend the language and know the characters as it is written. It is written in mathematical language, and its characters are triangles, circles and other geometric figures, without which it is impossible to humanly understand a word; without these one is wandering in a dark labyrinth, is not the origin of the mathematisation, as is falsely claimed by far too many, who should know better. One can already find the same sentiment in the Middle Ages, for example in Islam, in the work of Ibn al-Haytham (c. 965–c. 1040) or in Europe in the writings of both Robert Grosseteste (c. 1168–1253) and Roger Bacon, (c. 1219–c. 1292) although in the Middle Ages, outside of optics and astronomy, it remained more hypothetical than actually practiced. We find the same mathematical gospel preached in the sixteenth century by several scholars, most notably Christoph Clavius (1538–1612).

As almost always in history, it is simply wrong to look for a simple mono-casual explanation for any development. There were multiple driving forces behind the mathematisation. As we have already seen in various earlier episodes, the growing use and dominance of mathematics was driving by various of the practical mathematical disciplines during the Renaissance. 

The developments in cartography, surveying, and navigation (which I haven’t dealt with yet) all drove an increased role for both geometry and trigonometry. The renaissance of astrology also served the same function. The commercial revolution, the introduction of banking, and the introduction of double entry bookkeeping all drove the introduction and development of the Hindu-Arabic number system and algebra, which in turn would lead to the development of analytical mathematics in the seventeenth century. The development of astro-medicine or iatromathematics led to a change in the status of mathematic on the universities and the demand for commercial arithmetic led to the establishment of the abbacus or reckoning schools. The Renaissance artist-engineers with their development of linear perspective and their cult of machine design, together with the new developments in architecture were all driving forces in the development of geometry. All of these developments both separately and together led to a major increase in the status of the mathematical sciences and their dissemination throughout Europe. 

This didn’t all happen overnight but was a gradual process spread over a couple of centuries. However, by the early seventeenth century and what is generally regarded as the start of the scientific revolution the status and spread of mathematics was considerably different, in a positive sense, to what it had been at the end of the fourteenth century. Mathematics was now very much an established part of the scholarly spectrum. 

There was, however, another force driving the development and spread of mathematics and that was surprisingly the, on literature focused, original Renaissance humanists in Northern Italy. In and of itself, the original Renaissance humanists did not measure mathematics an especially important role in their intellectual cosmos. So how did the humanists become a driving force for the development of mathematics? The answer lies in their obsession with all and any Greek or Latin manuscripts from antiquity and also with the attitude to mathematics of their ancient role models. 

Cicero admired Archimedes, so Petrarch admired Archimedes and other humanists followed his example. In his Institutio Oratoria Quintilian was quite enthusiastic about mathematics in the training of the orator. However, both Cicero and Quintilian had reservations about how too intense an involvement with mathematics distracts one from the active life. This meant that the Renaissance humanists were, on the whole, rather ambivalent towards mathematics. They considered it was part of the education of a scholar, so that they could converse reasonably intelligently about mathematics in general, but anything approaching a deep knowledge of the subject was by and large frowned upon. After all, socially, mathematici were viewed as craftsmen and not scholars.

This attitude stood in contradiction to their manuscript collecting habits. On their journeys to the cloister libraries and to Byzantium, the humanists swept up everything they could find in Latin and/or Greek that was from antiquity. This meant that the manuscript collections in the newly founded humanist libraries also contained manuscripts from the mathematical disciplines. A good example is the manuscript of Ptolemaeus’ Geographia found in Constantinople and translated into Latin by Jacobus Angelus for the first time in 1406. The manuscripts were now there, and scholars began to engage with them leading to a true mathematical renaissance of the leading Greek mathematicians. 

We have already seen, in earlier episodes, the impact that the works of Ptolemaeus, Hero of Alexander, and Vitruvius had in the Renaissance, now I’m going to concentrate on three mathematicians Euclid, Archimedes, and Apollonius of Perga, starting with Archimedes. 

The works of Archimedes had already been translated from Greek into Latin by the Flemish translator Willem van Moerbeke (1215–1286) in the thirteenth century.

Archimedes Greek manuscript

He also translated texts by Hero. Although, he was an excellent translator, he was not a mathematician, so his translations were somewhat difficult to comprehend. Archimedes was to a large extent ignored by the universities in the Middle Ages. In 1530, Jacobus Cremonensis (c. 1400–c. 1454) (birth name Jacopo da San Cassiano), a humanist and mathematician, translated, probably at request of the Pope, Nicholas V (1397–1455), a Greek manuscript of the works of Archimedes into Latin. He was also commissioned to correct George of Trebizond’s defective translation of Ptolemaeus’ Mathēmatikē Syntaxis. It is thought that the original Greek manuscript was lent or given to Basilios Bessarion (1403–1472) and has subsequently disappeared.

Bessarion had not only the largest humanist library but also the library with the highest number of mathematical manuscripts. Many of Bessarion’s manuscripts were collected by Regiomontanus (1436–1476) during the four to five years (1461–c. 1465) that he was part of Bessarion’s household.

Basilios Bessarion Justus van Gent and Pedro Berruguete Source: Wikimedia Commons

When Regiomontanus moved to Nürnberg in 1471 he brought a large collection of mathematical, astronomical, and astrological manuscripts with him, including the Cremonenius Latin Archimedes and several manuscripts of Euclid’s Elements, that he intended to print and publish in the printing office that he set up there. Unfortunately, he died before he really got going and had only published nine texts including his catalogue of future intended publications that also listed the Cremonenius Latin Archimedes. 

The invention of moving type book printing was, of course, a major game changer. In 1482, Erhard Ratdolt (1447–1522) published the first printed edition of The Elements of Euclid from one of Regiomontanus’ manuscripts of the Latin translation from Arabic by Campanus of Novara (c. 1220–1296).

A page with marginalia from the first printed edition of Euclid’s Elements, printed by Erhard Ratdolt in 1482
Folger Shakespeare Library Digital Image Collection
Source: Wikimedia Commons

In 1505, a Latin translation from the Greek by Bartolomeo Zamberti (c. 1473–after 1543) was published in Venice in 1505, because Zamberti regarded the Campanus translation as defective. The first Greek edition, edited by Simon Grynaeus (1493–1541) was published by Jacob Herwegens in Basel in 1533.

Simon Grynaeus Source: Wikimedia Commons
Editio princeps of the Greek text of Euclid. Source

Numerous editions followed in Greek and/or Latin. The first modern language edition, in Italian, translated by the mathematician Niccolò Fontana Tartaglia (1499/1500–1557) was published in 1543.

Tartaglia Euclid Source

Other editions in German, French and Dutch appeared over the years and the first English edition, translated by Henry Billingsley (died 1606) with a preface by John Dee (1527–c. 1608) was published in 1570.

Title page of Sir Henry Billingsley’s first English version of Euclid’s Elements Source Wikimedia Commons

In 1574, Christoph Clavius (1538–1612) published the first of many editions of his revised and modernised Elements, to be used in his newly inaugurated mathematics programme in Catholic schools, colleges, and universities. It became the standard version of Euclid throughout Europe in the seventeenth century. In 1607, Matteo Ricci (1552–1610) and Xu Guanqui (1562–1633) published their Chinese translation of the first six books of Clavius’ Elements.

Xu Guangqi with Matteo Ricci (left) From Athanasius Kircher’s China Illustrata, 1667 Source: Wikimedia Commons

From being a medieval university textbook of which only the first six of the thirteen books were studied if at all, The Elements was now a major mathematical text. 

Unlike his Euclid manuscript, Regiomontanus’ Latin Archimedes manuscript had to wait until the middle of the sixteenth century to find an editor and publisher. In 1544, Ioannes Heruagius (Johannes Herwagen) (1497–1558) published a bilingual, Latin and Greek, edition of the works of Archimedes, edited by the Nürnberger scholar Thomas Venatorius (Geschauf) (1488–1551).

Thomas Venatorius Source

The Latin was the Cremonenius manuscript that Regiomontanus had brought to Nürnberg, and the Greek was a manuscript that Willibald Pirckheimer (1470–1530) had acquired in Rome.

Venatori Archimedes Source

Around the same time Tartaglia published partial editions of the works of Archimedes both in Italian and Latin translation. We will follow the publication history of Archimedes shortly, but first we need to go back to see what happened to The Conics of Apollonius, which became a highly influential text in the seventeenth century.

Although, The Conics was known to the Arabs, no translation of it appears to have been made into Latin during the twelfth-century scientific Renaissance. Giovanni-Battista Memmo (c. 1466–1536) produced a Latin translation of the first four of the six books of The Conics, which was published posthumously in Venice in 1537. Although regarded as defective this remained the only edition until the latter part of the century.

Memmo Apollonius Conics Source: Wikimedia Commons

We now enter the high point of the Renaissance reception of both Archimedes and Apollonius in the work of the mathematician and astronomer Francesco Maurolico (1494–1575) and the physician Federico Commandino (1509-1575). Maurolico spent a large part of his life improving the editions of a wide range of Greek mathematical works.

L0006455 Portrait of F. Maurolico by Bovis after Caravaggio Credit: Wellcome Library, London, via Wikimedia Commons

Unfortunately, he had problems finding sponsors and/or publishers for his work. His heavily edited and corrected volume of the works of Archimedes first appeared posthumously in Palermo in 1585. His definitive Latin edition of The Conics, with reconstructions of the fifth and sixth books, completed in 1547, was first published in 1654.

Maurolico corresponded with Christoph Clavius, who had visited him in Sicily in 1574, when the observed an annular solar eclipse together, and with Federico Commandino, although the two never met.

Federico Commandino produced and published a whole series of Greek mathematical works, which became something like standard editions.

Source: Wikimedia Commons

His edition of the works of Archimedes appeared in 1565 and his Apollonius translation in 1566.

Two of Commandino’s disciples were Guidobaldo del Monte (1545–1607) and Bernardino Baldi (1553–1617). 

Baldi wrote a history of mathematics the Cronica dei Matematici, which was published in Urbino in 1707. This was a brief summary of his much bigger Vite de’ mathematici, a two-thousand-page manuscript that was never published.

Bernadino Baldi Source: Wikimedia Commons
Source: Wikimedia Commons

Guidobaldo del Monte, an aristocrat, mathematician, philosopher, and astronomer

Guidobaldo del Monte Source: Wikimedia Commons

became a strong promoter of Commandino’s work and in particular the works of Archimedes, which informed his own work in mechanics. 

In the midst of that darkness Federico Commandino shone like the sun, for his learning he not only restored the lost heritage of mathematics but actually increased and enhanced it … In him seem to have lived again Archytas, Diophantus, Theodosius, Ptolemy, Apollonius, Serenus, Pappus and even Archimedes himself.

Guidobaldo. Liber Mechanicorum, Pesaro 1577, Preface
Source: Wikimedia Commons

When the young Galileo wrote his first essay on the hydrostatic balance, his theory how Archimedes actually detected the substitution of silver for gold in the crown made for King Hiero of Syracuse, he sent it to Guidobaldo to try and win his support and patronage. Guidobaldo was very impressed and got his brother Cardinal Francesco Maria del Monte (1549–1627), the de’ Medici family cardinal, to recommend Galileo to Ferinando I de’ Medici, Grand Duke of Tuscany, (1549–1609) for the position of professor of mathematics at Pisa University. Galileo worked together with Guidobaldo on various projects and for Galileo, who rejected Aristotle, Archimedes became his philosophical role model, who he often praised in his works. 

Galileo was by no means the only seventeenth century scientist to take Archimedes as his role model in pursuing a mathematical physics, for example Kepler used a modified form of Archimedes’ method of exhaustion to determine the volume of barrels, a first step to the development of integral calculus. The all pervasiveness of Archimedes in the seventeenth century is wonderfully illustrated at the end of the century by Sir William Temple, Jonathan Swift’s employer, during the so-called battle of the Ancients and Moderns. In one of his essays, Temple an ardent supporter of the superiority of the ancients over the moderns, asked if John Wilkins was the seventeenth century Archimedes, a rhetorical question with a definitively negative answer. 

During the Middle Ages Euclid was the only major Greek mathematician taught at the European universities and that only at a very low level. By the seventeenth century Euclid had been fully restored as a serious mathematical text and the works of both Archimedes and Apollonius had entered the intellectual mainstream and all three texts along with other restored Greek texts such as the Mathematical Collection of Pappus, also published by Commandino and the Arithmetica of Diophantus, another manuscript brought to Nürnberg by Regiomontanus and worked on by numerous mathematicians, became influential in development of the new sciences.  

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Filed under History of Mathematics, History of Physics, History of science, Renaissance Science

We plumb the depths of boundless history of science stupidity 

Late on Friday evening, Renaissance mathematicus friend and star historian of medieval science, Seb Falk, posted a couple of paragraphs from an Oberserver newspaper interview with the physicist and self-appointed science communicator Michio Kaku, from April this year. The history of science content of those paragraphs was so utterly, mindbogglingly ludicrous that it had me tossing and turning all night and woke from his deep winter sleep the HISTSCI_HULK, who is now raging through my humble abode like a demented behemoth on speed. What was it that set the living history of science bullshit detector in such a state of apoplexy? I offer up the evidence:

How much, do you think, would Isaac Newton understand of your book?
I think he would appreciate it. In 1666 we had the great plague. Cambridge University was shut down and a 23-year-old boy was sent home, and he saw an apple fall on his estate. And then he realised that the laws that control an apple are the same laws that control the moon. So the epidemic gave Isaac Newton an opportunity to sit down and follow the mathematics of falling apples and falling moons. But of course there was no mathematics at that time. He couldn’t solve the problem so he created his own mathematics. That’s what we are doing now. We, too, are being hit by the plague. We, too, are confined to our desks. And we, too, are creating new mathematics.

This paragraph is, of course, the tired old myth of Newton’s Annus mirabilis, which got continually recycled in the early months of the current pandemic and, which I demolished in a blog post back in April 2020, so I won’t bore you with a rehash here. However, Kaku has managed to add a dimension of utter mind shattering ignorance

But of course there was no mathematics at that time. He couldn’t solve the problem so he created his own mathematics.

Just limiting myself to the Early Modern Period, Tartaglia, Cardano, Ferrari, Bombelli, Stiefel, Viète, Harriot, Napier, Kepler, Galileo, Cavalieri, Fermat, Descartes, Pascal, Gregory, Barrow, Wallis and many others are all not just turning in their graves, but spinning at high speed, whilst screaming WHAT THE FUCK! at 140 decibels.

The real irony is that not only did Newton not codify the calculus during his non-existent Annus mirabilis–he didn’t create it, it evolved over a period of approximately two thousand years–but when he wrote his Principia twenty years later, he used a modernised version of Euclidian geometry, which was created some two thousand years earlier, and not the calculus!  

There is more to come:

There are many brilliant scientists whose contributions you discuss in the book. Which one, for you, stands out above the rest?
Newton is at number one, because, almost out of nothing, out of an era of witchcraft and sorcery, he comes up with the mathematics of the universe, he comes up with a theory of almost everything. That’s incredible. Einstein piggybacked on Newton, using the calculus of Newton to work out the dynamics of curved spacetime and general relativity. They are like supernovas, blindingly brilliant and illuminating the entire landscape and changing human destiny. Newton’s laws of motion set into motion the foundation for the Industrial Revolution. A person like that comes along once every several centuries.

Where to start? To describe the late seventeenth and early nineteenth centuries as “an era of witchcraft and sorcery” is simply bizarre. This is the highpoint of the so-called Scientific Revolution, it is the Augustan age of literature that in Britain alone produced Swift, Pope, Defoe, and many others, it is the age of William Hogarth, it is the age in which modern capitalism was born and, and, and… Yes, some people still believed in witchcraft and sorcery, some still do today, but it was by no means a central factor of the social, political, or cultural life of the period. This was the dawn of the Enlightenment, for fuck’s sake, the period of Spinosa, Locke, Hume and, once again, many others. 

The “Newton is at number one, because, almost out of nothing” produces howls of protest echoing down the centuries from Kepler, Stevin, Galileo, Torricelli, Descartes, Pascal, Huygens et al

With respect to Steven Strogatz, I will grant him his hyperbolic “mathematics of the universe”, but Newton’s physics covers just a very small area of the entire world of knowledge and is in no way a “theory of almost everything.” 

I should leave the comments on Einstein, to those better qualified to condemn them than I. However, I find the claim that “Einstein piggybacked on Newton” simply grotesque. Also, the calculus that Newton and Leibniz codified, which became the mathematics of Newtonian physics, although Newton himself did not use it, is a very different beast to the tensor calculus used in the general relativity theory. In fact, the only thing they have in common is the word calculus, I would expect someone with a doctorate in physics to know that.

One is tempted to ask if the Guardian has fired all of its science editors and replaced them with failed door to door vacuum cleaner salesmen. It’s the only rational explanation as to why the science pages of the Observer were adorned with such unfathomably dumb history of science. It is supposed to be a quality newspaper!

The HISTSCI_HULK has in the meantime thrown himself off the balcony into the snowstorm and was last seen stomping off into the woods muttering, The horror! The horror!

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Filed under History of science, Myths of Science

Renaissance Science – XXIV

It might be considered rational to assume that during the period that is viewed as the precursor to the so-called scientific revolution, which is itself viewed as the birth of modern science, that the level of esotericism and the importance of the occult sciences would decline. However, the exact opposite is true, the Renaissance saw a historical highpoint in the popularity and practice of esotericism and the occult sciences. We have already seen how astro-medicine or iatromathematics came to dominate the practice of medicine in this period and horoscope astrology continued to be practiced by almost all astronomers till well into the seventeenth century. We also saw how, not just due to the efforts of Paracelsus, the practice and status of alchemy also reached a high point during this period. Now, I would like to take a look at the emergence of natural magic during this period and the processes that drove it.

There was nothing new about the supposed existence of magic in the Renaissance, but throughout the Christian era magic was associated with demonic forces. It was thought that people, who practiced magic, were calling on the power of the devil. Augustinus, who had been a practicing astrologer and believed that astrology worked, thought it could only do so through demonic forces thus his famous condemnation of the mathematici, by which he meant astrologers and not mathematicians. What was new in the Renaissance was the concept of a magic, natural magic, that was not dependent on demonic forces. This is the origin of the concept of the distinction between black magic and white magic, to use the more modern terms for it. Various groups of texts that found prominence in the Renaissance humanist search for authentic texts from antiquity were instrumental in this development. In roughly the order of there emergence they were the philosophy of Plato and in particular the work of the Neoplatonists from the third century CE, the Hermetic Corpus, and the Jewish Kabbalah. In the first two of these the humanist scholar Marsilio Ficino (1433–1499) played a pivotal role. 

Marsilio Ficino from a fresco painted by Domenico Ghirlandaio in the Tornabuoni Chapel, Santa Maria Novella, Florence Source: Wikimedia Commons

Ficino was the son of Diotifeci d’Angolo a physician whose patron was Cosimo de’ Medici (1389–1464) a major supporter of the humanist Renaissance. Ficino became a member of the Medici household and Cosimo remained his patron for his entire life, even appointing him tutor to his grandson Lorenzo de’ Medici (1449–1492).

Cosimo de’ Medici portrait by Jacopo Pontormo Source: Wikimedia Commons

At the Council of Florence (1438-1444), an attempt to heal the schism between the Orthodox and Catholic Churches, Cosimo de’ Medici became acquainted and enamoured with the Greek Neoplatonic philosopher Georgius Gemistus Pletho (C. 1355–c. 1450), who was also the teacher of Basileios Bessarion (1403–1472) another highly influential Renaissance scholar.

Portrait of Gemistus Pletho, detail of a fresco by Benozzo Gozzoli, Palazzo Medici Riccardi, Florence Source: Wikimedia Commons 

Returning home Cosimo decided to refound Plato’s Academy and appointed Ficino to head it, who then proceeded to learn Greek from Ioannis Argyropoulus (c. 1415–1487), another Greek, who came to Italy during the Council of Florence.

Ioannis Argyropoulos as depicted by Domenico Ghirlandaio Source: Wikimedia Commons

Today Plato is regarded as one of the greatest and most important of all Western philosophers, there is a saying that Plato is just footnotes to Socrates and Alfred North Whitehead (1861–1947) once quipped that Western philosophy is just footnotes to Plato, so it might seem strange to us that during the Renaissance Plato was virtually unknown in Europe. In the Early Middle Ages, the only one of Plato’s worked that was known in Latin was the Timaeus (c. 360 BCE) his speculations on the nature of the physical world, about which George Sarton infamously wrote in his A History of Science (Harvard University Press, 1959):

The influence of Timaeus upon later times was enormous and essentially evil. A large portion of Timaeus had been translated into Latin by Chalcidius, and that translation remained for over eight centuries the only Platonic text known in the Latin West. Yet the fame of Plato had reached them, and thus the Latin Timaeusbecame a kind of Platonic evangel which many scholars were ready to interpret literally. The scientific perversities of Timaeus were mistaken for scientific truths. I cannot mention any other work whose influence was more mischievous, except the Revelations of John the Devine. The apocalypse, however, was accepted as a religious book, the Timaeus as a scientific one; errors and superstition are never more dangerous than when offered to us under the cloak of science. 

George Sarton  A History of Science (Harvard University Press, 1959)

Strong stuff! Somehow Plato got ignored during the so-called Scientific Renaissance and unlike Aristotle his works were not translated into Latin at this time. In 1462 Cosimo de’ Medici supplied Ficino with Greek manuscripts of Plato’s work and commissioned him to translate them into into Latin, a task that he carried out by 1468-69, the works being published in 1484. Ficino also translated the work of many of the Neoplatonist in particular the work of Porphyry (c. 234–c. 305) and Plotinus (c. 204–270 CE). 

So, what does this revival in the philosophy of Plato have to do with magic, natural or otherwise? The answer lies in that which Sarton found so abhorrent in Plato’s philosophy of science. Plato’s philosophy of scienced is heavily laced with what can be simply described as a heavy dose of mysticism and it is this aspect of Plato’s philosophy that is strongly emphasised by the third century Neoplatonists. I’m not going to go into great detail as this blog post would rapidly turn into a monster, there have been numerous thick books written about the Timaeus alone but will only present a very brief sketch of the relevant concepts.

According to Plato the cosmos was created by the demiurge, the divine craftsman, as a single living entity, which he then endowed with a world soul. It was this concept of the Oneness of the cosmos that was at the core of the philosophy of the third century Neoplatonists and in Ficino’s own personal interpretation of Platonic thought. How this relates to natural magic, I will explain later after we have looked at Ficino’s translation of the Hermetic Corpus. 

In 1460, Leonardo de Candia Pistola, one of the agents Cosimo de’ Medici had sent out to search European monasteries for ancient manuscripts, returned to Tuscany with the so-called Corpus Hermeticum. This is a collection of seventeen Greek texts supposedly of great antiquity and written by Hermes Trismegistus a legendary Hellenistic creation combining elements of the Egyptian god Thoth and his Greek counterpart Hermes. Ficino interrupted his translation of Plato and immediately began translating the texts of the Corpus Hermeticum into Latin; he translated the first fourteen of the texts and Lodovico Lazzarelli (1447–1500) translated the other three.

Lodovico Lazzarelli (via his muse) presents the manuscript of Fasti christianae religionis to Ferdinand I of Aragon, king of Naples and Sicily. (Beinecke MS 391, f.6v) Source: Wikimedia Commons

There are other Hermetic texts most notably the Emerald Tablet an Arabic text first known in the eight or early nine century and the Asclepius already know in Latin during the Middle Ages. 

Once again, the subject is far to extensive for an analysis in a blog post, so I will only sketch a brief outline of the salient points. The hermetic texts are a complex mix of religious-philosophical magic texts, astrological texts, and alchemical texts. The religious-philosophical aspect has a strong similarity to the Platonic theory of the One, the cosmos as a single living entity. In hermeticism, God and the cosmos are one and the same thing. God is the All and at the same time the creator of the All. Hermeticists also believed in the principle of a prisca theologica, that there is a single true, original theology, which for Christian Hermeticists originates with Moses. They believed Hermes had his knowledge direct from Moses. A central tenet of Hermeticism was the macrocosm-microcosm theory, as above so below. Meaning the Earth is a copy of the heavens, astrology and alchemy are instances of the forces of the heavens working on the Earth. 

Macrocosm-Microcosm Lucas Jemnnis Museum Hermeticum (1625)

Combining Neoplatonic philosophy and Hermeticism, Renaissance humanists developed the concept of natural magic. Rather than a magic based on demonic influence, natural magic works by tapping directly into the forces of the cosmos that are the source of astrology and alchemy. 

The Kabbalah is a school of Jewish esoteric teaching that is supposed to explain the relationship between the unchanging, infinite, eternal God and the mortal, finite cosmos, God’s creation. Renaissance humanist believed in the ideal of the tres linguæ sacræ (the three holy languages)–Latin, Greek, and Hebrew–the languages needed for Biblical studies. The scholars of Hebrew stumbled across the Jewish Kabbalah and began to incorporate it into the Renaissance mysticism. Giovanni Pico della Mirandola (1463–1494) an Italian Renaissance nobleman and student of Ficino

Giovanni Pico della Mirandola portrait by Cristofano dell’Altissimo (c. 1525–1605) Source: Wikimedia Commons

founded or created a Christian Kabbalah, which he wove together with Platonism, Neoplatonism, Aristotelianism, and Hermeticism. A heady brew! Given his own personal philosophy, which included a form of natural magic that he called Theurgy, operation of the gods, I find it more than somewhat ironic that Pico is hailed as an early rejecter of astrology.

The Christian Kabbalah was developed by Pico’s most noted follower in this area, the German humanist, Johannes Reuchlin (1455–1522), who not only propagated the Christian Kabbalah but fiercely defended Jewish literature against the strong Anti-Semitic movement to ban and burn it in the early sixteenth century.

Johann Reuchlin, woodcut depiction from 1516 Source: Wikimedia Commons

He was a highly influential teacher of Hebrew and became professor for Hebrew at the University of Ingolstadt. Amongst his most notable students were his nephew Philip Melanchthon (1497–1560) (it was Reuchlin who suggested that Philip adopt the humanist name Melanchthon a Greek translation of his birth name, Schwartzerdt) and the Nürnberger reformer, Andreas Osiander (1498­–1522), who famously authored the Ad lectorum at the beginning of Copernicus’ De revolutionibus. Even Martin Luther consulted Reuchlin on Hebrew and read his texts on the Kabbalah, whilst disagreeing with him.

Hermeticism was adopted by many leading thinkers in the Early Modern Period including Giordano Bruno (1548–1600), Francesco Patrizi (1529–1597) (an influential and much discussed philosopher in the period, who is largely forgotten today except by specialists), and Robert Fludd (1574–1637), who notoriously disputed with Johannes Kepler, rejecting Kepler’s mathematics-based science for one based on what might be described as hermetic mandalas. Even Isaac Newton (1642–1727) processed a substantial collection of hermetic literature. 

The English Renaissance historian Frances Yates (1899–1981) argued in, her much praised, Giordano Bruno and the Hermetic Tradition (1964) that hermeticism played a central role in the emergence of heliocentric astronomy in the Early Modern Period. Even Copernicus appears to quote Hermes Trismegistus in his De revolutionibus in his hymn of praise of the Sun to justify its central position of the cosmos:

At rest, however, in the middle of everything is the sun. For in this most beautiful temple, who would place this lamp in another or better position than that from which it can light up the whole thing at the same time? For, the sun is not inappropriately called by some people the lantern of the universe, its mind by others, and its ruler by still others. [Hermes] Trismegistus labels it a visible god and Sophocles’ Electra, the all-seeing. 

Yates’ thesis is now largely rejected by historians of astronomy, but her book is still praised for making people aware of the extent of hermeticism in the Early Modern Period. It is difficult to assess if hermeticism had any direct or indirect influence on the development of science during the period, but it was certainly very present in the intellectual atmosphere of the period.

Before I turn to natural magic it is interesting to note that the highly influential, humanist scholar Isaac Casaubon (1559–1614), who through the much-propagated philological analysis of texts was able to show, at the beginning of the seventeenth century, that the Corpus Hermeticum was not as ancient as its supporters claimed but was created in the early centuries of the common era and was thus contemporaneous with the Neoplatonic texts. Casaubon’s analysis was largely ignored by the supporters of hermeticism in the seventeenth century.

Isaac Casaubon artist unknown Source: Wikimedia Commons

 As already stated above natural magic was the belief into the possibility to directly tap into the forces within the single, living, cosmic organism, of the Neoplatonists and Hermeticists, that were present in astrology and alchemy. One of the strongest propagators of natural magic was the German polymath Heinrich Cornelius Agrippa von Nettesheim (1486–1535).

Heinrich Cornelius Agrippa von Nettesheim Source: Wikimedia Commons

He presented his views on the topic in his widely read De Occulta Philosophia libri III (Three Books of Occult Philosophy) the first volume of which was published in Paris in 1531 and the full three volumes in Cologne in 1533.

Man inscribed in a pentagram, from Heinrich Cornelius Agrippa’s De Occulta Philosophia libri III . The signs on the perimeter represent the 5 visible planets in astrology. Source: Wikipedia Commons

In an earlier work, De incertitudine et vanitate scientiarum atque artium declamatio invectiva (Declamation Attacking the Uncertainty and Vanity of the Sciences and the Arts, Cologne 1527) he wrote the following explanation of natural magic:

Natural magic is that which having contemplated the virtues of all natural and celestial and carefully studied their order proceeds to make known the hidden and secret powers of nature in such a way that inferior and superior things are joined by an interchanging application of each to each: thus incredible miracles are often accomplished not so much by art as by nature, to whom this art is a servant when working at these things. For this reason magicians are careful explorers of nature, only directing what nature has formally prepared, uniting actives to passives and often succeeding in anticipating results; so that these things are popularly held to be miracles when they are really no more than anticipations of natural operations … therefore those who believe the operations of magic to be above or against nature are mistaken because they are only derived from nature and in harmony with it.

The other major figure of natural magic was the Italian polymath Giambattista della Porta (1535(?)–1615), a respected figure in the Renaissance scientific community, who authored the Magia Naturalis, first published as a single volume in 1558, which grew to twenty volumes by 1589.

Giambattista della Porta artist unknown Source: Wikimedia Commons

I have written an extensive blog post on della Porta and his book here, so I won’t add more here. He describes natural magic thus:

Magick is nothing else but the knowledge of the whole course of Nature. For, whilst we consider the Heavens, the Stars, the Elements, how they moved, and how they changed, by this means we find out the hidden secrecies of living creatures, of plants, of metals, and of their generation and corruption; so that this whole science seems merely to depend upon the view of Nature … This Art, I say, is full of much virtue, of many secret mysteries; it openeth unto us the properties and qualities of hidden thins, and the knowledge of the whole course of Nature; and it teacheth us by the agreement and the disagreement of things, either so to sunder them, or else to lay them so together by the mutual and fit applying of one thing to another, as thereby we do strange works, such as the vulgar sort call miracles, and such men can neither well conceive, nor sufficiently admire … Wherefore, as many of you as come to behold Magic, must be perswaded that the works of Magick are nothing else but the works of Nature, whose dutiful hand-maid magick is.

Both Agrippa and della Porta were widely read and important parts of the philosophical debates around science in the Renaissance but it is difficult to say whether their concept of natural magic any influence on the development of science in this period. It can and has been argued that because natural magic was inductive by nature that it influenced the adoption of induction in the scientific method in the seventeenth century. There exists a debate amongst historians to what extent Francis Bacon was or was not influenced by hermeticism and natural magic. Others such as Bruno and John Dee certainly were. Dee included magic as one of the mathematical disciplines in his Mathematicall Praeface to Henry Billingsley’s English translation of The Elements of Euclid.

It probably seems strange to include a long essay on what is basically occult philosophy in a series on Renaissance science, but one can’t ignore the fact that Neoplatonism, hermeticism and natural magic were all separately and in various combinations an integral part of the intellectual debate of the period between fourteen and seventeen hundred.

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Filed under History of Alchemy, History of Astrology, History of science, Renaissance Science

The astronomical librarian 

I’m continuing my look at the French mathematician astronomers of the seventeenth century with some of those, who were both members of Nicolas-Claude Fabri de Peiresc’s group of telescopic, astronomical observers, as well as Marin Mersenne’s informal Academia Parisiensis, starting with Ismael Boulliau (1605–1694), who like Peiresc and Mersenne was also a prominent member of the Republic of Letters with about 5000 surviving letters. 

Ismael Boulliau Source: Wikimedia Commons

Boulliau was born in Loudun, France the second son of Ismael Boulliau a notary and amateur astronomer and Susanne Motet on 28 September 1605. The first son had been born a year earlier and was also named Ismael, but he died and so the name was transferred to their second son. Both of his parents were Calvinists. His father introduced him to astronomy and in his Astronomia philolaica (1645) Ismael junior tells us that his father observed both Halley’s comet in 1607 and the great comet of 1618. The later was when Boulliau was thirteen years old, and one can assume that he observed together with his father. 

Probably following in his father’s footsteps, he studied law but at the age of twenty-one he converted to Catholicism and in 1631, aged twenty-six, he was ordained a priest. In 1632 he moved to Paris and began to work for Pierre Dupuy (1582–1651) and his brother Jacques (1591–1656), who were keepers of the Bibliothèque du Roi, today the Bibliothèque nationale de France. Boulliau held this position until the death of the Dupuy brothers and during that time travelled widely in Europe collecting books and manuscripts for the library. 

Pierre Dupuy Source: Wikimedia Commons

Boulliau also enjoyed the patronage of the powerful and influential de Trou family, who were closely connected with the library and who financed his book collecting travels. Following the death of the Dupuy brothers he became employed by the French ambassador to the United Provinces, a member of the de Trou family, a secretary and librarian. In 1666, following a dispute with his employer, he became librarian at the Collège de Laon in Paris. For the last five years of his live he returned to the priesthood in the Abbey St Victor near Paris where he died aged 89. Although Boulliau was an active member of Mersenne’s Academia Parisiensis he never became a member of the Académie des sciences, but he was elected one of the first foreign associates of the Royal Society on 4 April 1667. 

Abbey of St. Victor, 1655 Source: Wikimedia Commons

 Like Peiresc, Boulliau was a polymath with extensive knowledge of a wide range of humanities topics, which was useful in his work as a librarian, but, as with Peiresc, it is scientific activities that are of interest here. He continued to make astronomical observations throughout his life, which were of a high level of accuracy. In his Principia, Newton puts him on a level with Kepler for his determination of the planetary orbits. In Book 3 Phenomenon 4 of Principia Newton writes: 

But of all astronomers, Kepler and Boulliau have determined the magnitude of the orbits from observations with the most diligence. 

Boulliau’s first significant scientific publication was, however, not in astronomy but in optics, his De natura lucis (On the Nature of Light) (1638) based on the discussions he was having with Gassendi on the topic. This work is not particular important in the history of optics but it does contain his discussion of Kepler’s inverse square law for the propagation of light.

Source: Wikimedia Commons

His first astronomical work Philolaus (1639), which places him firmly in the Copernican heliocentric camp but not, yet a Keplerian was next. 

He now changed tack once again with a historical mathematical work. In 1644, he translated and published the first printed edition of Theon of Smyrna’s Expositio rerum mathematicarum ad legendum Platonem utilium a general handbook for students of mathematics of no real significance. Continuing with his mathematical publications. In 1657, he published De lineis spiralibus (On Spirals) related to the work of Archimedes and Pappus on the topic.

Source: Wikimedia Commons

Much later in 1682, he published Opus novum ad arithmeticam infinitorum, which he claimed clarified the Arithmetica infinitorum(1656) of John Wallis (1616–1703).

Source: Wikimedia Commons

All of Boulliau’s work was old fashioned and geometrical. He rejected the new developments in analytical mathematics and never acknowledged Descartes’ analytical geometry. As we shall see, his astronomy was also strictly geometrical. He even criticised Kepler for being a bad geometer. 

Boulliau’s most important publication was his second astronomical text Astronomia philolaica (1645).

Source: Wikimedia Commons

In this highly influential work, he fully accepted Kepler’s elliptical orbits but rejects almost all of the rest of Kepler’s theories. As stated above his planetary hypothesis is strictly geometrical and centres round his conical hypothesis:

“The Planets, according to that astronomer [Boulliau], always revolve in circles; for that being the most perfect figure, it is impossible they should revolve in any other. No one of them, however, continues to move in any one circle, but is perpetually passing from one to another, through an infinite number of circles, in the course of each revolution; for an ellipse, said he, is an oblique section of a cone, and in a cone, betwixt the vertices of the ellipse there is an infinite number of circles, out of the infinitely small portions of which the elliptical line is compounded. The Planet, therefore, which moves in this line, is, in every point of it, moving in an infinitely small portion of a certain circle. The motion of each Planet, too, according to him, was necessarily, for the same reason, perfectly equable. An equable motion being the most perfect of all motions. It was not, however, in the elliptical line, that it was equable, but in any one of the circles that were parallel to the base of that cone, by whose section this elliptical line had been formed: for, if a ray was extended from the Planet to any one of those circles, and carried along by its periodical motion, it would cut off equal portions of that circle in equal times; another most fantastical equalizing circle, supported by no other foundation besides the frivolous connection betwixt a cone and an ellipse, and recommended by nothing but the natural passion for circular orbits and equable motions,” (Adam Smith, History of Astronomy, IV.55-57).

Boulliau’s Conical Hypothesis [RA Hatch] Source: Wikimedia Commons

Boulliau’s theory replaces Kepler’s second law, and this led to the Boulliau-Ward debate on the topic with the English astronomer Seth Ward (1617–1689), the Savilian Professor of astronomy at Oxford University.

Bishop Seth Ward, portrait by John Greenhill Source: Wikimedia Commons

Ward criticised Boulliau’s theory in his In Ismaelis Bullialdi astro-nomiae philolaicae fundamenta inquisitio brevis (1653), also pointing out mathematical errors in Boulliau’s work. 

Boulliau responded to Ward’s criticisms in 1657, acknowledging the errors and correcting but in turn criticising Ward’s model in his De lineis spiralibus. A year earlier Ward had published his own version of Keplerian astronomy in his Astronomia geometrica (1656).

Source: Wikimedia Commons

This exchange failed to find a resolution but this very public debate between two of Europe’s leading astronomers very much raised awareness of Kepler’s work and was factor in its eventual acceptance of Kepler’s elliptical heliocentric astronomy. 

It was in his Astronomia philolaica that Boulliau was the first to form an inverse squared theory of attraction between the sun and the planets. 

As for the power by which the Sun seizes or holds the planets, and which, being corporeal, functions in the manner of hands, it is emitted in straight lines throughout the whole extent of the world, and like the species of the Sun, it turns with the body of the Sun; now, seeing that it is corporeal, it becomes weaker and attenuated at a greater distance or interval, and the ratio of its decrease in strength is the same as in the case of light, namely, the duplicate proportion, but inversely, of the distances that is, 1/d2 ​.

Here we see the influence of Kepler’s theory of light propagation, which as noted Boulliau discussed in his De natura lucis. However, having set up this hypothesis Boulliau goes on to reject it. 

… I say that the Sun is moved by its own form around its axis, by which form it was ignited and made light, indeed I say that no kind of motion presses upon the remaining planets … indeed [I say] that the individual planets are driven round by individual forms with which they were provided …

Despite Boulliau’s rejection of his own hypothesis, during Newton’s dispute with Hooke over who should get credit for the theory of gravity, he gives Boulliau the credit in a letter to Edmond Halley.

…so Bullialdus [i.e., Boulliau] wrote that all force respecting ye Sun as its center & depending on matter must be reciprocally in a duplicate ratio of ye distance from ye center, & used that very argument for it by wch you, Sr, in the last Transactions have proved this ratio in gravity. Now if Mr Hook from this general Proposition in Bullialdus might learn ye proportion in gravity, why must this proportion here go for his invention?

In 1667, Boulliau published a final astronomy book, Ad astronomos monita duo in which he was the first to establish the periodicity of the variable star, Mira Ceti.

Source:

His estimate of the period 333 days was only out by a one day. Mira had first been recognised as a variable star by David Fabricius beginning 3 August 1596.

Apart from his publications Boulliau kept Mersenne’s correspondence network alive for another thirty years after Mersenne’s death, communicating with Leopoldo de’ Medici (1617–1675) in Italy, Johannes Hevelius (1611–1687) in Danzig and Christiaan Huygens (1629–1695). Huygens first imparted his discovery of the rings of Saturn to Boulliau and Boulliau distributed Huygens’ System sarturnium (1658) in Paris. Boulliau also distributed Pascal’s Letters D’Amos Dettonville (1658–1659) to English and Dutch mathematicians, his challenge on the mathematics of the cycloid, an important publication in the development of calculus.

Ismael Boulliau is a prime example of a scholar, who didn’t make any major discoveries or develop any major theories himself but still had a very significant influence on the development of science.

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Filed under History of Astronomy, History of Mathematics, History of Optics, History of science, The Paris Provencal Connection

Renaissance Science – XXII

Perhaps surprisingly, land surveying as we know it today, a mathematical discipline utilising complex technological measuring instruments is very much a product of the practical mathematics of the Renaissance. Why surprisingly? Surveying is an ancient discipline that has its origins in humanity becoming settled many thousands of years ago. Ancient monuments such as the pyramids or Stonehenge definitely required some level of surveying in their construction and there are surviving documents from all literate ancient societies that refer to methods or the practice of surveying. 

All surveying uses some aspects of geometry and as Herodotus famously claimed geometry (Greek: geōmetría from geōmétrēs), which literally means measurement of earth or land, had its origins in Egyptian surveying for tax purposes. According to his account, King Sesostris divided all the lands in Egypt amongst its inhabitants in return for an annual rent. However, every year the Nile floods washing away the parts of the plots:

The country is converted into a sea, and nothing appears but the cities, which looked like islands in the Aegean. 

Those whose land had been lost objected to paying the rent, so Sesostris summoned those affected to appear before him.

Upon which, the king sent persons to examine, and determine by measurement the exact extent of the loss: and thenceforth only such a rent was demanded of him as was proportionate to the reduced size of his land. From this practice, I think, geometry first came to be known in Egypt, whence it passed into Greece.

According to legend, both Thales and Pythagoras, are reputed to have learnt their geometry in Egypt.

In all early cultures surveying was fairly primitive with measurements being made with ropes and measuring rods. In Egypt, surveyors were known as rope stretchers (harpedonaptai), the ropes used for measuring being stretched to avoid sagging.

A rope being used to measure fields. Taken from the Tomb of Menna, TT69. (c. 1500–1200 BCE) Source: Wikimedia Commons

Longer distances were either measured by estimation or by pacing. In ancient Egypt and Greece Bematistae (step measurer) where trained to walk with equal length paces and the historical records of Alexander the Great’s campaigns suggest that they were indeed highly accurate. This measuring of distances by pacing in reflected in our word mile, which is the Latin word for a thousand, mille, meaning a thousand paces.

The Latin for surveyor was agrimensores, meaning field measurers. They were also called gromatici after the groma a surveyor’s pole, an early instrument for determining lines at right angles to each other. 

The groma or gruma was a Roman surveying instrument. It comprised a vertical staff with horizontal cross-pieces mounted at right angles on a bracket. Each cross piece had a plumb line hanging vertically at each end. It was used to survey straight lines and right angles, thence squares or rectangles. They were stabilized on the high ground and pointed in the direction it was going to be used. The helper would step back 100 steps and place a pole. The surveyor would tell him where to move the pole and the helper would set it down.

(Lewis, M. J. T., Surveying instruments of Greece and Rome, McGraw Hill Professional, 2001, p. 120)
Staking out a right angle using a groma

Another instrument used for the same purpose was the dioptra. The dioptra was a sighting tube or, alternatively an alidade, that is a rod with a sight at each end, attached to a stand. If fitted with protractors, it could be used to measure angles. Hero from Alexandria wrote a whole book on this instrument and its use but there are doubts that the dioptra in the complex form described by Hero was actually used in field surveying.

Dioptra as described by Hero of Alexandria Source: Wikimedia Commons

The methods used by the Romans in field surveying were described in the works of technical authors such as Sextus Julius Frontinus (c. 40–103 CE) and Gaius Julius Hyginus (c. 64 BCE–17 CE).

All of the surveying described in antiquity was fairly small scale–measuring fields, determining boundaries, laying out military camps, etc–and geometrically centred on squares and rectangles. Cartography was done using astronomical determinations of latitude and longitude, whereby the latter was difficult, and distances estimated or paced. Nothing really changed in Europe during the medieval period. The surveying that was done was carried out using the same methods that the Romans had used. However, during the fifteenth century things began to change substantially and the first question is why?

The rediscovery of Ptolemaeus’ Geographia at the beginning of the fifteenth century, as described here, and the subsequent substantial increase in cartographical activity, as described here, played a major role, but as already stated above Ptolemaic cartography relied almost exclusively on astronomical methods and did not utilise field surveying. However, there was an increased demand for internal accuracy in maps that astronomical methods could not supply. Secondly, changes in land ownership led to an increased demand for accurate field surveying of estates that required more sophisticated methods than those of the agrimensores. Lastly, we have a good example of the knowledge crossover, typical for the Renaissance, as described in Episode V of this series. The surveyors of antiquity were artisans producing practical knowledge for everyday usage. In the Renaissance, university educated scholars began to interest themselves for this practical knowledge and make contributions to its development and it is these developments that we will now look at. 

The biggest change in surveying was the introduction of the simple geometrical figure the triangle into surveying, as Sebastian Münster, one of the most influential cosmographers (today we would say geographer) of the period, wrote in a German edition of his Cosmographia. Beschreibung aller Lender durch Sebastianum Münsterum in 1550:

Every thing you measure must be measured in triangles.

Actually, the theory of similar triangles, as explained in Euclid’s Elements, had been used in surveying in antiquity, in particular to determine the height of things or for example the width of a river. A method that I learnt as a teenager in the Boy Scouts.

What was new as we will see was the way that triangles were being used in surveying and that now it was the angles of the triangles that were measured and not the length of the sides, as in the similar triangles’ usage. We are heading towards the invention and usage of triangulation in surveying and cartography, a long-drawn-out process.

In his Ludi rerum mathematicarum (c. 1445), the architect Leon Battista Alberti describes a method of surveying by taking angular bearings of prominent points in the area he is surveying using a self-made circular protractor to create a network of triangles. He concludes by explaining that one only needs to the length of one side of one triangle to determine all the others. What we have here is an early description of a plane table surveying (see below) and step towards triangulation that, however, only existed in manuscript 

Alberti Ludi rerum mathematicarum 

Münster learnt his geometry from Johannes Stöffler (1452–1531), professor for mathematics in Tübingen, who published the earliest description of practical geometry for surveyors. In his De geometricis mensurationibus rerum (1513),

Johannes Stöffler Engraving from the workshop of Theodor de Brys, Source: Wikimedia Commons

Stöffler explained how inaccessible distances could be measured by measuring one side of a triangle using a measuring rod (pertica) and then observing the angles from either end of the measured stretch. However, most of the examples in his book are still based on the Euclidian concept of similar triangles rather than triangulation. In 1522, the printer publisher Joseph Köbel, who had published the Latin original, published a German version of Stöffler’s geometry book. 

Joseph Köbel Source: Wikimedia Commons

Both Peter Apian in his Cosmographia (1524) and Oronce Fine in his De geometria practica (1530) give examples of using triangles to measure distances in the same way as Stöffler.

Source

Fine indicating that he knew of Stöffler’s book. Apian explicitly uses trigonometry to resolve his triangles rather than Euclidian geometry. Trigonometry had already been known in Europe in the Middle Ages but hadn’t been used before the sixteenth century in surveying. Fine, however, still predominantly used Euclidian methods in his work, although he also, to some extent, used trigonometry.

A very major development was the publication in 1533 of Libellus de locorum describendum ratione (Booklet concerning a way of describing places) by Gemma Frisius as an appendix to the third edition of Apian’s Cosmographia, which he edited, as he would all edition except the first. Here we have a full technical description of triangulation published for the first time. It would be included in all further editions in Latin, Spanish, French, Flemish, in what was the most popular and biggest selling manual on mapmaking and instrument making in the sixteenth and seventeenth centuries.

Source: Wikimedia Commons

1533 also saw the publication in Nürnberg by Johannes Petreius (c. 1497–1550) of Regiomontanus’s De triangulis omnimodis (On triangles of every kind) edited by the mapmaker and globe maker, Johannes Schöner (1477–1547).

Source:

This volume was originally written in 1464 but Regiomontanus died before he could print and publish it himself, although he had every intention of doing so. This was the first comprehensive work on trigonometry in Europe in the Early Modern Period, although it doesn’t cover the tangent, which Regiomontanus handled in his Tabula directionum (written 1467, published 1490), an immensely popular and oft republished work on astrology. 

Regiomontanus built on previous medieval works on trigonometry and the publication of his book introduces what Ivor Grattan Guinness has termed The Age of Trigonometry. In the sixteenth century it was followed by Rheticus’ separate publication of the trigonometrical section of Copernicus’s De revolutionibus, as De lateribus et angulis triangulorium in 1542. Rheticus (1514–1574) followed this in 1551 with his own Canon doctrinae triangulorum. This was the first work to cover all six trigonometric functions and the first to relate the function directly to triangles rather than circular arcs.

Source: Wikimedia Commons

Rheticus spent the rest of his life working on his monumental Opus Palatinum de Triangulis, which was, however, first published posthumously by his student Lucius Valentin Otho in 1596. Rheticus and Otho were pipped at the post by Bartholomaeus Pitiscus (1561–1613), whose Trigonometriasive de solutione triangulorum tractatus brevis et perspicuous was published in 1595 and gave the discipline its name.

Source: Wikimedia Commons

Pitiscus’ work went through several edition and he also edited and published improved and corrected editions of Rheticus’ trigonometry volumes. 

Through Gemma Frisius’ detailed description of triangulation and sixteenth century works on trigonometry, Renaissance surveyors and mapmakers now had the mathematical tools for a new approach to surveying. What they now needed were the mathematical instruments to measure distances and angles in the field and they were not slow in coming.

The measure a straight line of a given distance as a base line in triangulation surveyors still relied on the tools already used in antiquity the rope and the measuring rod. Ropes were less accurate because of elasticity and sagging if used for longer stretches. In the late sixteenth century, they began to be replaced by the surveyor’s chain, made of metal links but this also suffered from the problem of sagging due to its weight, so for accuracy wooden rods were preferred. 

A Gunter chain photographed at Campus Martius Museum. Source: Wikimedia Commons

In English the surveyor’s chain is usually referred to as Gunter’s chain after the English practical mathematician Edmund Gunter (1581–1626) and he is also often referred to erroneously as the inventor of the surveyor’s chain but there are references to the use of the surveyor’s chain in 1579, when Gunter was still a child. 

He did, however, produce what became a standardised English chain of 100 links, 66 feet or four poles, perches, or rods long, as John Ogilby (1600–1676) wrote in his Britannia Atlas in 1675:

…a Word or two of Dimensurators or Measuring Instruments, whereof the mosts usual has been the Chain, and the common length for English Measures 4 Poles, as answering indifferently to the Englishs Mile and Acre, 10 such Chains in length making a Furlong, and 10 single square Chains an Acre, so that a square Mile contains 640 square Acres…’

An English mile of 5280 feet was thus 80 chains in length and there are 10 chains to a furlong. An acre was 10 square chains. I actually learnt this antiquated system of measurement whilst still at primary school. The name perch is a corruption of the Roman name for the surveyor’s rod the pertica. 

To measure angles mapmakers and surveyors initially adopted the instruments developed and used by astronomers, the Jacob staff, the quadrant, and the astrolabe. An instrument rarely still used in astronomy but popular in surveying was the triquetum of Dreistab. The surveyors triquetum consists of three arms pivoted at two points with circular protractors added at the joints to measure angles and with a magnetic compass on the side to determine bearings. 

Surveyors then began to develop variants of the dioptra. The most notable of these, that is still in use today albeit highly modernised, was the theodolite, an instrument with sights capable of measuring angles both vertically and horizontally. The name first occurs in the surveying manual A geometric practice named Pantometria by Leonard Digges (c. 1515–c. 1559) published posthumously by his son Thomas (c. 1546–1595) in 1571.

Leonard Digges  A geometric practice named Pantometria Source

However, Digges’ instrument of this name could only measure horizontal angles. He described another instrument that could measure both vertical and horizontal angles that he called a topographicall instrument. Josua Habermehl, about whom nothing is known, but who was probably a relative of famous instrument maker Erasmus Habermehl (c. 1538–1606), produced the earliest known instrument similar to the modern theodolite, including a compass and tripod, in 1576. In 1725, Jonathan Sisson (1690–1747) constructed the first theodolite with a sighting telescope.

Theodolite 1590 Source:

A simpler alternative to the theodolite for measuring horizontal angles was the circumferentor. This was a large compass mounted on a plate with sights, with which angles were measured by taking their compass bearings.

18th century circumferentor

Instruments like the triquetum and the circumferentor were most often used in conjunction of another new invention, the plane table. Gemma Frisius had already warned in his Libellus de locorum describendum rationeof the difficulties of determining the lengths of the sides of the triangles in triangulation using trigonometry and had described a system very similar to the plane table in which the necessity for these calculation is eliminated. 

Surveying with plane table and surveyor’s chain

The plane table is a drawing board mounted on a tripod, with an alidade. Using a plumb bob, the table is centred on one end of a baseline, levelled by eye or after its invention (before 1661) with a spirit level, and orientated with a compass. The alidade is placed on the corresponding end of the scaled down baseline on the paper on the table and bearings are taken of various prominent features in the area, the sight lines being drawn directly on the paper. This procedure is repeated at the other end of the baseline creating triangles locating the prominent figures on the paper without having to calculate.

Philippe Danfrie (c.1532–1606) Surveying with a plane table

As with the theodolite there is no certain knowledge who invented the plane table. Some sources attribute the invention of the plane table to Johannes Praetorius (1537–1616), professor for mathematics at the University of Altdorf, as claimed by his student Daniel Schwentner (1585–1636). However, there was already a description of the plane table in “Usage et description de l’holomètre”, by Abel Foullon (c. 1514–1563) published in Paris in 1551. It is obvious from his description that Foullon hadn’t invented the plane table himself. 

The plane table is used for small surveys rather than mapmaking on a large scale and is not triangulation as described by Gemma Frisius. Although the Renaissance provided the wherewithal for full triangulation, it didn’t actually get used much for mapping before the eighteenth century. At the end of the sixteenth century Tycho Brahe carried out a triangulation of his island of Hven, but the results were never published. The most notable early use was by Willebrord Snel (1580–1626) to measure one degree of latitude in order to determine the size of the earth in 1615. He published the result in his Eratosthenes batavus in Leiden in 1617. He then extended his triangulation to cover much of the Netherlands.

Snel’s Triangulation of the Dutch Republic from 1615 Source: Wikimedia Commons

In the late seventeenth century Jean Picard (1620–1682) made a much longer meridian measurement in France using triangulation. 

Picard’s triangulation and his instruments

In fourteen hundred European surveyors were still using the same methods of surveying as the Romans a thousand years earlier but by the end of the seventeenth century when Jean-Dominique Cassini (1625–1712) began the mapping of France that would occupy four generations of the Cassini family for most of the eighteenth century, they did so with the fully developed trigonometry-based triangulation that had been developed over the intervening three hundred years. 

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Filed under History of Astronomy, History of Cartography, History of Geodesy, History of Mathematics, History of science, Renaissance Science

The amateur, astronomical, antiquarian aristocrat from Aix

In a recent blog post about the Minim friar, Marin Mersenne (1588–1648), I mentioned that when Mersenne arrived in Paris in 1619 he was introduced to the intellectual elite of the city by Nicolas-Claude Fabri de Peiresc (1580-1637). In another recent post on the Republic of Letters I also mentioned that Peiresc was probably, the periods most prolific correspondent, with more than ten thousand surviving letters. So, who was this champion letter writer and what role did he play in the European scientific community in the first third of the seventeenth century?

Nicolas-Claude Fabri de Peiresc by Louis Finson Source: Wikimedia Commons

Nicolas-Claude Fabri was born, into a family of lawyers and politicians, in the town Belgentier near Toulon on 1 December in 1580, where his parents had fled to from their hometown of Aix-en-Provence to escape the plagues. He was educated at Aix-en-Provence, Avignon, and the Jesuit College at Tournon. Having completed his schooling, he set off to Padua in Italy, nominally to study law, but he devoted the three years, 1600–1602, to a wide-ranging, encyclopaedic study of the history of the world and everything in it. 

In this he was aided in that he became a protégé of Gian Vincenzo Pinelli (1535–1601) a humanist scholar and book collector, his library numbered about 8,500 printed works, with all-embracing intellectual interests, whose main areas were botany, optics, and mathematical instruments.

Gian Vincènzo Pinelli Source: Rijksmuseum via Wikimedia Commons

Pinelli introduced Fabri to many leading scholars including Marcus Welser (1558–1614), Paolo Sarpi (1552–1623) and indirectly Joseph Scaliger (1540–1609). Pinelli also introduced him to another of his protégés, Galileo Galilei (1564–1642). One should always remember that although he was thirty-eight years old in 1602, Galileo was a virtually unknown professor of mathematics in Padua. When Pinelli died, Fabri was living in his house and became involved in sorting his papers.

In 1602, Fabri returned to Aix-en-Provence and completed his law degree, graduating in 1604. In the same year he assumed the name Peiresc, it came from a domain in the Alpes-de-Haute-Provence, which he had inherited from his father. He never actually visited Peiresc, now spelt Peyresq.

Village of Peyresq Source: Wikimedia Commons

Following graduation Peiresc travelled to the Netherlands and England via Paris, where he made the acquaintance of other notable scholars, including actually meeting Scaliger and also meeting the English antiquarian and historian William Camden (1551–1623).

Returning to Provence, in 1607, he took over his uncle’s position as conseiller to the Parliament of Provence under his patron Guillaume du Vair (1556–1621), cleric, lawyer, humanist scholar and president of the parliament.

Guillaume-du-Vair Source: Wikimedia Commons

In 1615 he returned to Paris with du Vair as his secretary, as du Vair was appointed keeper of the seals during the regency of Marie de’ Medici (1575–1642). Peiresc continued to make new contacts with leading figures from the world of scholarship, and the arts, including Peter Paul Rubens (1577–1640).

Peter Paul Rubens self-portrait 1623

Peiresc acted as a go between in the negotiations between Reubens and the French court in the commissioning of his Marie de’ Medici Cycle. Just one of Peiresc’s many acts of patronage in the fine arts.

Marie de’ Medici Cycle in the Richelieu wing of the Louvre Source: Wikimedia Commons

In 1621 de Vair died and in 1623 Peiresc returned to Provence, where he continued to serve in the parliament until his death in 1637.

Peiresc was an active scholar and patron over a wide range of intellectual activities, corresponding with a vast spectrum of Europe’s intellectual elite, but we are interested here in his activities as an astronomer. Having developed an interest for astronomical instruments during his time as Pinelli’s protégé, Peiresc’s astronomical activities were sparked by news of Galileo’s telescopic discoveries, which reached him before he got a chance to read the Sidereus Nuncius. He rectified this lack of direct knowledge by ordering a copy from Venice and borrowing one from a friend until his own copy arrived.

Source: Wikimedia Commons

He immediately began trying to construct a telescope to confirm or refute Galileo’s claims, in particular the discovery of the first four moons of Jupiter. At this point in his life Peiresc was still a geocentrist, later he became a convinced heliocentrist. We know very little about where and how he acquired his lenses, but we do know that he had various failures before he finally succeeded in observing the moons of Jupiter for himself, in November 1610. In this he was beaten to the punch by his fellow Provencal astronomer Joseph Gaultier de la Valette (1564–1647), vicar general of Aix. At this point it is not clear whether the two were competing or cooperating, as they would then later do with Gaultier de la Valette becoming a member of Peiresc’s Provencal astronomical observation group. Shortly thereafter, Peiresc became the first astronomer to make telescopic observations of the Orion Nebular and Gaultier de la Valette the second. This is rather strange as the Orion Nebular is visible to the naked eye. However, apparently none of the telescopic astronomy pioneers had turned their telescopes to it before Peiresc.

In one of the most detailed astronomical images ever produced, NASA/ESA’s Hubble Space Telescope captured an unprecedented look at the Orion Nebula. … This extensive study took 105 Hubble orbits to complete. All imaging instruments aboard the telescope were used simultaneously to study Orion. Source: Wikimedia Commons

Peiresc, like Galileo, realised that the moons of Jupiter could be used as a clock to determine longitude and began an observation programme of the moons, viewing them every single day that the weather conditions permitted, well into 1612. Having compiled tables of his observations he sent one of his own protégés Jean Lombard, about whom little is known, equipped with suitable instruments on a tour of the Mediterranean. Lombard observed the satellites at Marseille in November 1611 and then proceeded to Malta, Cyprus and to Tripoli observing as he went, until May 1612. Meanwhile, Peiresc made parallel observation in Aix and Paris, he hoped by comparing the time differences in the two sets of observations to be able to accurately determine the longitude differences. Unfortunately, the observations proved to be not accurate enough for the purpose and the world would have to wait for Giovanni Domenico Cassini (1625–1712) to become the first to successfully utilise this method of determining longitude. Peiresc’s own observation were, however, the longest continuous series of observations of the Jupiter moons made in the seventeenth century and displayed a high level of accuracy even when compared with this of Galileo.

I mentioned, above, Peiresc’s Provencal astronomical observing group. Peiresc employed/sponsored young astronomers to help him with his observation programmes, supplying them with instruments and instructions on how to use them. This group included such notable, future astronomers, as Jean-Baptiste Morin (1583–1556),

Jean-Baptiste Morin Source: Wikimedia Commons

Ismaël Boulliau (1605–1694),

Ismaël Boulliau Source: Wikimedia Commons

and Pierre Gassendi (1592–1655). Peiresc’s patronage extended well beyond this. Gassendi had held the chair of philosophy at the University of Aix-en-Provence since 1617 but in 1623 the university was taken over by the Jesuits and Gassendi was replaced by a Jesuit and became unemployed.

Portrait of Pierre Gassendi by Louis-Édouard Rioult Source: Wikimedia Commons

From then until he again found regular employment in 1634, Peiresc provided him with a home base in his own house and financed his travels and research. Similarly, Peiresc, having introduced Mersenne to Parisian intellectual circles in 1619, continued to support him financially, Mersenne as a Minim friar had no income, supplying him with instruments and financing his publications. 

Marin Mersenne Source: Wikimedia Commons

Patronage played a central role in Peiresc’s next venture into astronomy and another attempt to solve the longitude problem. There has been much talk in recent decades about so-called citizen science, in which members of the public are invited to participate in widespread scientific activities. Annual counts of the birds in one’s garden is a simple example of this. Citizen science is mostly presented as a modern phenomenon, but there are examples from the nineteenth century. Peiresc had already launched a variation on citizen science in the seventeenth century.

In order to determine longitude Peiresc further developed a method that had been in use since antiquity. Two astronomers situated in different location would observe a lunar or solar eclipse and then by comparing their observations they could determine the local time difference between their observations and thus the longitude difference between the locations. By the seventeenth century predicting eclipses had become a fairly accurate science and Peiresc thought that if he could organise and coordinated a world spanning network of observers to accurately observe and record an eclipse, he could then calculate a world spanning network of longitude measurements. The idea was good in theory but failed in practice.

Most of Peiresc’s team of observers were amateurs–missionaries, diplomats, traders, travellers–whom he supplied with astronomical instruments and written instructions on how to use them, even paying travelling expenses, where necessary. Peiresc organised mass observations for lunar eclipses in 1628, 1634, and 1635 and a solar eclipse in 1633. Unfortunately, many of his observers proved to be incompetent and the results of their observations were too inaccurate to be usable. One positive result was that Peiresc was able to correct the value for the length of the Mediterranean. Before one is too hard on Peiresc’s amateur observers, one should remember that in the middle of the eighteenth century the world’s professional astronomical community basically failed in their attempt to use the transits of Venus to determine the astronomical unit, despite being equipped with much better instruments and telescopes.

Although, Peiresc’s various astronomical activities and their results were known throughout Europe by word of mouth through his various colleagues and his correspondence, he never published any of his work. Quite why, is not really known although there are speculations.

Peiresc was a high ranking and highly influential Catholic and he applied that influence in attempts to change the Church’s treatment of astronomers he saw as being persecuted. He interceded on behalf Tommaso Campanella (1568–1639), actively supporting him when he fled to France in 1634.

Tommaso Campanella portrait by Francesco Cozza Source: Wikimedia Commons

More famously he personally interceded with the Church on behalf of Galileo, without any great success.

Nicolas-Claude Fabri de Peiresc’s career is, like that of his friend Mersenne, a good illustration that the evolution of science is a product of widespread cooperation of a community of practitioners and not the result of the genial discoveries of a handful of big names, as it is unfortunately too often presented. Morin, Boulliau, Gassendi and Mersenne, who all made serious contributions to the evolution of science in the seventeenth century, did so with the encouragement, guidance, and very active support of Peiresc.

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Filed under History of Astronomy, History of Navigation, History of science, Renaissance Science, The Paris Provencal Connection

Musical, mathematical Minim, Marin Mersenne 

In the seventeenth century, Marin Mersenne (1588–1648) was a very central and highly influential figure in the European intellectual and scientific communities; a man, who almost literally knew everybody and was known by everybody in those communities. Today, in the big names, big events, popular versions of the history of science he remains only known to specialist historian of science and also mathematicians, who have heard of Mersenne Primes, although most of those mathematicians probably have no idea, who this Mersenne guy actually was. So, who was Marin Mersenne and why does he deserve to be better known than he is?

Marin Mersenne Source: Wikimedia Commons

Mersenne was born 8 September 1588, the son of Julien Mersenne and his wife Jeanne, simple peasants, in Moulière near Oizé, a small commune in the Pays de la Loire in North-Western France. He was first educated at the at the nearby College du Mans and then from 1604 to 1609 at the newly founded Jesuit Collège Henri-IV de La Flèche. The latter is important as in La Flèche he would have received the mathematical programme created by Christoph Clavius for the Jesuit schools and colleges, the best mathematical education available in Europe at the time. A fellow student at La Flèche was René Descartes (1596–1650) with whom he would become later in life close friends.

René Descartes at work Source: Wikimedia Commons

However, it is unlikely that they became friends then as Mersenne was eight years older. Leaving La Flèche he continued his education in Greek, Hebrew, and theology at the Collège Royal and the Sorbonne in Paris. In 1611 he became a Minim friar and a year later was ordained as a priest. The Minims are a mendicant order founded in Italy in the fifteenth century. From 1614 to 1618 he taught philosophy and theology at Nevers but was recalled to Paris in 1619 to the newly established house on the Place Royal (now Place des Vosges), where he remained, apart from travels through France, to Holland, and to Italy, until his death. 

View map of an area of Paris near Place Royale, now Place des Vosges, showing the Minim convent where Mersenne lived and the Rue des Minimes, not far from the Bastille, undated, but before 1789 (paris-grad.com) Source: Linda Hall Library

In Paris he was introduced to the intellectual elite by Nicolas-Claude Fabri de Pereisc (1580–1637)–wealthy astronomer, antiquarian, and patron of science–whom he had got to know in 1616. 

Nicolas-Claude Fabri de Peiresc by Louis Finson Source: Wikimedia Commons

Settled in Paris, Mersenne began a career as a prolific author, both editing and publishing new editions of classical works and producing original volumes. In the 1620s his emphasis was on promoting and defending the Thomist, Aristotelian philosophy and theology in which he’d been educated. In his first book, Questiones celeberrimae in Genesim (1623), 

he attacked those he saw as opponents of the true Catholic religion, Platonist, cabbalistic and hermetic authors such as Telesio, Pomponazzi, Bruno and Robert Fludd. His second book, L’impiété des déistes, athées, et libertins de ce temps (1624), continued his attacks on the propagators of magic and the occult. His third book, La Vérité des sciences (1625), attacks alchemists and sceptics and includes a compendium of texts over ancient and recent achievements in the mathematical sciences that he saw as in conformity with his Christian belief. The latter drew the attention of Pierre Gassendi (1592–1655), who became his closest friend. I shall return to their joint activities in Paris later but now turn to Mersenne’s own direct scientific contributions, which began to replace the earlier concentration on theology and philosophy.

Pierre Gassendi Source: Wikimedia Commons

Mersenne’s scientific interests lay in mathematics and in particular what Aristotle, who was not a fan of mathematics, claiming it did not apply to the real world, called the mixed sciences or mixed mathematics i.e., astronomy, optics, statics, etc. Here he compiled to collections of treatises on mixed mathematics, his Synopsis Mathematica (1626) and Universae geometriae synopsis (1644). In his Traité de l’Harmonie Universelle (1627), to which we will return, Mersenne gives a general introduction to his concept of the mathematical disciplines:

Geometry looks at continuous quantity, pure and deprived from matter and from everything which falls upon the senses; arithmetic contemplates discrete quantities, i.e. numbers; music concerns har- monic numbers, i.e. those numbers which are useful to the sound; cosmography contemplates the continuous quantity of the whole world; optics looks at it jointly with light rays; chronology talks about successive continuous quantity, i.e. past time; and mechanics concerns that quantity which is useful to machines, to the making of instruments and to anything that belongs to our works. Some also adds judiciary astrology. However, proofs of this discipline are borrowed either from astronomy (that I have comprised under cosmology) or from other sciences. 

In optics he addressed the problem of spherical aberration in lenses and mirrors and suggested a series of twin mirror reflecting telescopes, which remained purely hypothetical and were never realised.

Source: Fred Watson, “Stargazer: The Life and Times of the Telescope”, Da Capo Press, 2004, p. 115

This is because they were heavily and falsely criticised by Descartes, who didn’t really understand them. It was Mersenne, who pushed Descartes to his solution of the refraction problem and the discovery of the sine law. He wrote three books on optics, De Natura lucis (1623); Opticae (1644); L’Optique et la catoptrique (1651). Although his theoretical reflecting telescopes were published in his Harmonie universelle (1636), see below.

Mersenne also wrote and published collections of essays on other areas of mixed mathematics, mechanics, pneumatics, hydro- statics, navigation, and weights and measures, Cogitata physico-mathematica (1644); Novarum observationum physico- mathematicarum tomus III (1647). 

Mersenne dabbled a bit in mathematics itself but unlike many of his friends did not contribute much to pure mathematics except from the Mersenne prime numbers those which can be written in the form Mn = 2n − 1 for some integer n. This was his contribution to a long search by mathematicians for some form of law that consistently generates prime numbers. Mersenne’s law whilst generating some primes doesn’t consistently generate primes but it has been developed into its own small branch of mathematics. 

It was, however, in the field of music, as the title quoted above would suggest, which had been considered as a branch of mathematics in the quadrivium since antiquity, and acoustics that Mersenne made his biggest contribution. This has led to him being labelled the “father of acoustics”, a label that long term readers of this blog will know that I reject, but one that does to some extent encapsulate his foundational contributions to the discipline. He wrote and published five books on the subject over a period of twenty years–Traité de l’harmonie universelle (1627); Questions harmoniques (1634); Les preludes de l’harmonie universelle (1634); Harmonie universelle (1636); Harmonicorum libri XII (1648)–of which his monumental (800 page) Harmonie universelle was the most important and most influential.

Title page of Harmonie universelle Source: Wikimedia Commons

In this work Mersenne covers the full spectrum including the nature of sounds, movements, consonance, dissonance, genres, modes of composition, voice, singing, and all kinds of harmonic instruments. Of note is the fact that he looks at the articulation of sound by the human voice and not just the tones produced by instruments. He also twice tried to determine the speed of sound. The first time directly by measuring the elapse of time between observing the muzzle flash of a cannon and hearing the sound of the shot being fired. The value he determined 448 m/s was higher than the actual value of 342 m/s. In the second attempt, recorded in the Harmonie universelle (1636), he measured the time for the sound to echo back off a wall at a predetermined distance and recorded the value of 316 m/s. So, despite the primitive form of his experiment his values were certainly in the right range. 

Mersenne also determined the correct formular for determining the frequency of a vibrating string, something that Galileo’s father Vincenzo (1520–1591) had worked on. This is now known as Mersenne’s Law and states that the frequency is inversely proportional to the length of the string, proportional to the square root of the stretching force, and inversely proportional to the square root of the mass per unit length.

The formula for the lowest frequency is f=\frac{1}{2L}\sqrt{\frac{F}{\mu}},

where f is the frequency [Hz], L is the length [m], F is the force [N] and μ is the mass per unit length [kg/m].

Source: Wikipedia

Vincenzo Galileo was also involved in a major debate about the correct size of the intervals on the musical scale, which was rumbling on in the late sixteenth and early seventeenth centuries. It was once again Mersenne, who produced the solution that we still use today.

Although Mersenne is certainly credited and honoured by acoustic researchers and music theorists for his discoveries in these areas, perhaps his most important contribution to the development of the sciences in the seventeenth century was as a networker and science communicator in a time when scientific journals didn’t exist yet. 

Together with Gassendi he began to hold weekly meetings in his humble cell with other natural philosophers, mathematicians, and other intellectuals in Paris. Sometime after 1633 these meetings became weekly and took place in rotation in the houses of the participants and acquired the name Academia Parisiensis. The list of participants reads like an intellectual who’s who of seventeenth century Europe and included René Descartes, Étienne Pascal and his son Blaise, Gilles de Roberville, Nicolas-Claude Fabri de Pereisc, Pierre de Fermat, Claude Mydorge, the English contigent, Thomas Hobbes, Kenhelm Digby, and the Cavendishes, and for those not living in or near Paris such as Isaac Beeckman, Jan Baptist van Helmont, Constantijn Huygens and his son Christiaan, and not least Galileo Galilei by correspondence. When he died approximately six hundred letters were found in his cell from seventy-nine different correspondents. In total 193 scholars and literati have been identified as participants. Here it should be noted that although he tended to reject the new emerging sciences in his earlier defence of Thomist philosophy, he now embraced it as compatible with his teology and began to promote it.

This academy filled a similar function to the Gresham College group and Hartlib Circle in England, as well as other groups in other lands, as precursors to the more formal scientific academies such as the Académie des sciences in Paris and the Royal Society in London. There is evidence that Jean-Baptist Colbert (1619–1683), the French Minister of State, modelled his Académie des sciences on the Academia Parisiensis. Like its formal successors the Academia Parisiensis served as a forum for scholars to exchange views and theories and discuss each other’s work. Mersenne’s aim in establishing this forum was to stimulate cooperation between the participants believing science to be best followed as a collective enterprise.

Mersenne’s role was not restricted to that of convener, but he functioned as a sort of agent provocateur deliberately stimulating participants to take up research programmes that he inaugurated. For example, he brought Torricelli’s primitive barometer to Paris and introduced it to the Pascals. It is thought that he initiated the idea to send Blaise Pascal’s brother-in-law up the Puy de Dôme to measure the decreasing atmospheric pressure.

Blaise Pascal, unknown; a copy of the painting of François II Quesnel, which was made for Gérard Edelinck in 1691. Source: Wikimedia Commons

Although they never met and only corresponded, he introduced Christiaan Huygens to the concept of using a pendulum to measure time, leading to Huygens’ invention of the pendulum clock.

Portrait of Christiaan Huygens (1629-1695) C.Netscher / 1671 Source: Wikimedia Commons

It was Mersenne, who brought the still very young Blaise Pascal together with René Descartes, with the hope that the brilliant mathematicians would cooperate, in this case he failed. In fact, the two later became opponents divided by their conflicting religious views. Mersenne also expended a lot of effort promoting the work of Galileo to others in his group, even offering to translate and publish Galileo’s work in French, an offer that the Tuscan mathematician declined. He did, however, publish an unpublished text by Galileo on mechanics, Les Mechaniques de Galilée.

Although not the author of a big theory or big idea, or the instigators of a big event, Mersenne actually contributed with his activities at least as much, if not more, to the development of science in the seventeenth century as any of the more famous big names. If we really want to understand how science develops then we need to pay more attention to figures like Mersenne and turn down the volume on the big names. 

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Filed under History of Mathematics, History of Optics, History of science, The Paris Provencal Connection