Leonardo and gravity

Mory Gharib an engineer from Caltech has published an article about his interpretation of some diagrams he discovered in one of the Leonardo manuscripts, which he claims are Leonardo’s attempts to determine the acceleration due to gravity. I’m not going to comment on Gharib’s work, which looks interesting, but rather on the article published in ARS TECHNICA by science writer Jennifer Ouellette describing Gharib’s work, which contains some, in my opinion, bizarre statements. 

It starts with Ouellette’s title: Leonardo noted link between gravity and acceleration centuries before Einstein! Equating an experiment of Leonardo’s, assuming Gharib is correct in his suppositions, with Einstein’s general theory of relativity is so far fetched it’s absurd. Just in case you think it’s just a hyperbolic title we get it repeated more emphatically at the end of the first paragraph:

Clip from article

Further investigation revealed that Leonardo was attempting to study the nature of gravity, and the little triangles were his attempt to draw an equivalence between gravity and acceleration—well before Isaac Newton came up with his laws of motion, and centuries before Albert Einstein would demonstrate the equivalence principle with his general theory of relativity.

Now we have Leonardo not just raised on a pedestal with Einstein, but with Newton too. I could point out that Newton didn’t come up with his laws of motion he collated them from the work of others. The comparison with Newton comes again in the next paragraph:

What makes this finding even more astonishing is that Leonardo did all this without a means of accurate timekeeping and without the benefit of calculus, which Newton invented in order to develop his laws of motion and universal gravitation in the 1660s.

Two things are wrong with this. Firstly, as I will explain shortly, lots of people investigated the acceleration due to gravity before and after Leonardo but before Newton without using calculus. Secondly, Newton did not invent calculus, he collated, and systemised the work of many other, as did Leibniz. He also didn’t do this to develop his laws of motion and universal gravitation, in fact, as I have explained once before, contrary to popular opinion, Newton did not use calculus to write the Principia, but good old fashioned Euclidian geometry. Just for the record Newton’s work in this area was done in the 1680s not 1660s. 

We get served up an old dubious claim:

Leonardo foresaw the possibility of constructing a telescope in his Codex Atlanticus (1490) when he wrote of “making glasses to see the moon enlarged”—a century before the instrument’s invention.  

Most expert on the history of the telescope follow Van Helden and don’t think Leonardo was here referring to any form of telescope but rather a single magnifying lens held at arm’s length. 

Moving on:

The concept of inertia wasn’t even known at the time; Leonardo’s earlier writings show that he accepted the Aristotelian notion that one needs a continuous force for any object to move. 

It is true that the theory of inertia wasn’t known at the time but around 1500 Leonardo almost certainly used the post-Aristotelian impulse theory.

As a historian of Renaissance mathematics, the following truly boggled my mind:

Leonardo went even further, Gharib et al. assert, and essentially tried to model the data from his experiment to find the gravitational constant using geometry—the best mathematical tool available at the time. “There was no concept of equations or math, but Leonardo had such an intuitive understanding of math in its non-equation form,” Roh told Ars. “I think that’s where he started using geometry to write out equations, in a way. 

“There was no concept of equations or math…”!!!!!!!! Just savour this statement for a moment, I can’t even begin… Leonardo’s maths teacher, Luca Pacioli, might have a few words to say about that.

To close, I wish to suggest a list of people in Europe, who in various ways investigated the acceleration of gravity, post Aristotle before Leonardo, contemporaneously with him or after him but before Newton and before the invention of calculus, with whom Ms Ouellette might have compared Leonardo’s interesting endeavours rather than Newton and Einstein. 

We start in the sixth century CE with John Philoponus. Moving on to the fourteenth century we have the Oxford Calculatores, who derived the mean speed theorem. Staying in the same century we have Nicole Oresme, who produced a geometrical representation of the mean speed theorem. Post Leonardo in the sixteenth century we have Tartaglia, and Benedetti. At the end of the sixteenth and beginning of the seventeenth centuries we have Simon Stevin and some guy called Galileo Galilei, you might have heard of him.  

Renaissance Science – XLVII

In a previous post we have seen how hydrostatic, an area of physics first developed by Archimedes in the third century CE, underwent a modernisation and development during the Renaissance. Today we are going to look at another area of physics examined by Archimedes, which was also revived, and developed during the Renaissance, statics. To give a modern definition:

Statics is the branch of classical mechanics that is concerned with the analysis of force and torque (also called moment) acting on physical systems that do not experience an acceleration (a=0), but rather, are in static equilibrium with their environment. Wikipedia

In antiquity and the Middle Ages, the concept of force did not exist, so we here find the discipline developed around the concept of weight. Statics is one half of the discipline of mechanics from the ancient Greek μηχανική mēkhanikḗ, lit. “of machines” and in antiquity it is literally the discipline of the so-called simple machines: lever, wheel and axel, pulley, balance, inclined plane, wedge, and screw. 

Archimedes (c. 287–c. 212 BCE), whose work on the topic was his On the Equilibrium of Planes (Ancient Greek: Περὶ ἐπιπέδων ἱσορροπιῶν, Romanised: perí epipédōn isorropiôn) was not the first to tackle the subject. His work was preceded by a text known in Latin as the Questiones Mechanicae (Mechanical Problems), which in the Middle Ages was attributed to Aristotle (384­–322 BCE) but is now considered to actually be by one of his followers or by some to be based on the earlier work of the Pythagorean Archytas (c.420–350 BCE). There was also a On the Balance attributed, almost certainly falsely to Euclid (fl. 300 BCE), which won’t play a further role here. Later than Archimedes there was the Mechanica of Hero of Alexandria (c. 10–c. 70 CE), unknown in the phase of the Renaissance we shall be reviewing but discussed along with the work of Archimedes in Book VII of the Synagoge or Collection of Pappus (c. 290–c. 350 CE).

The two major texts are the pseudo-Aristotelian Questiones Mechanicae and Archimedes’ On the Equilibrium of Planes, which approach the topic very differently. The Questiones Mechanicae is a philosophical work, which derives everything from a first principle that all machines are reducible to circular motion. It gives an informal proof of the law of the lever without reference to the centre of gravity. The pseudo-Euclidian on the Balance contains a mathematical proof of the law of the lever, again without reference to the centre of gravity.

In Archimedes’ On the Equilibrium of Planes the centre of gravity plays a very prominent role. In the first volume Archimedes presents seven postulates and fifteen propositions to mathematically using the centre of gravity to mathematical demonstrate the law of the lever. The volume closes with demonstrations of the centres of gravity of the parallelogram, the triangle, and the trapezoid. Centres of gravity are a part of statics because they are the point from which, when a figure is suspended it remains in equilibrium, that is unmoving. In volume two of his text Archimedes presents ten propositions relating to the centres of gravity of parabolic sections. This is achieved by substituting rectangles of equal area, a process made possible by his work Quadrature of the Parabola (Greek: Τετραγωνισμὸς παραβολῆς).

Although already translated from Greek into Latin in the thirteenth century by William of Moerbeke (c. 1220 – c. 1286), On the Equilibrium of Planes remained largely unknown in medieval Europe. Thābit ibn Qurra (c.830 –901) had translated it into Arabic and he wrote two related works, his Kitab fi ‘l-qarastun (Book of the Steelyard)­–a steelyard is a single armed balance– and his Kitab fi sifat alwazn (Book on the Description of Weight) on the equal armed balance. 

Thābit ibn Qurra 

The pseudo-Aristotelian Questiones Mechanicae was well known in the Middle Ages and Jordanus de Nemore (fl. 13^th century) developed a scholastic theory of statics in his science of weights (scientia de ponderibus) presented in three texts, the first Elementa super demonstrationem ponderum, which presents the conclusions of Thābit ibn Qurra’s text on the steelyard deriving them from seven axioms and nine propositions. This is the earliest of the three and the only one definitely ascribable to Jordanus. The two later texts are usually attributed to the school of. The second text Liber de ponderibus is a reworking of the Elementa super demonstrationem ponderum. The third De ratione ponderis is a corrected and expanded version of the Elementa. In his work he proves the law of the lever by the principle of work using virtual displacements. Using the same method, the De ratione ponderis also proves the conditions of equilibrium of unequal weights on planes inclined at different angles.

FIRST EDITION of Jordanus’s De ratione ponderis, published by Curtio Troiano from a manuscript copy owned by Tartaglia, who had died in 1557. 

The Questiones Mechanicae went through more than a dozen editions between the end of the fifteenth century and the beginning of the seventeenth. The first Greek edition was in the Aldine edition of the works of Aristotle published in Venice in 1497, which was often reprinted. There were various Latin translations published in Paris, Venice, Rome. The engineers Antonio Guarino and Vannoccio Biringuccio (c. 1480 – c. 1539) both produced Italian translations, published respectively in Moderna 1573, and Rome 1582. The Questiones Mechanicae were also known to the authors of the Renaissance Theatre of Machines books, such as Agostino Ramelli (1531–c. 1610) and there was a strong correlation between the theoretical works on machines such as the Questiones Mechanicae and the works of Jordanus de Nemore and the strong interest in projected new machine designs.  

When we turn to the Renaissance mathematici were meet many of the same names as by the Renaissance revival of hydrostatics. In 1546, Niccolò Tartaglia (c.1500 – 1557) published his Quesiti ed invention diverse (Various Questions and Inventions) in Venice, which referenced some of the contents of the Questiones Mechanicae and the works of Jordanus. As did his student Giambattista Benedetti (1530 – 1590) in his Diversarum speculationum mathematicarum et physicarum liber published in Turin in 1585. 

Tartaglia also published Moerbeke’s Latin translations of both books of Archimedes’ On the Equilibrium of Planes together with his Quadrature of the Parabola and Book I of On Floating Bodies in 1543. 

However, it was the so-called Urbino School, who truly reintroduced and began to modernise Archimedes’ work on statics. Federico Commandino (1509 – 1575) found the Moerbeke translations of Archimedes defective and produced new Latin translations of them as well as a new Latin translation of Pappus’ Synagoge containing parts of Hero’s Mechanica. Convinced that some of Archimedes’ proofs in On Floating Bodies were not well grounded he wrote and published his own Liber de centro gravitatis solidorum (Book on the Centres of Gravity of Solid Bodies) in 1565.

Commandino laid the foundations of the revival in Archimedean mathematical statics in the sixteenth century, but it was his student Guidobaldo dal Monte (1545 – 1607), who using Commandino’s new translations, both published and unpublished, who erected the structure.

Guidobaldo dal Monte Source: Wikimedia Commons

Dal Monte reconstructed the statics of Questiones Mechanicae using an Archimedean mathematical approach with postulates and propositions in his Mechanicorum Liber published in Pesaro in 1577. Under dal Monte’s supervision, the mathematician and explorer, Filippo Pigafetta (1533 – 1604) published an Italian translation Le mechniche in Venice in 1581, indicating the interest in dal Monte’s work. New editions of both were published in 1615 and a German translation appeared in 1629. Dal Monte rejected the earlier concept that all machines could be reduced to circular motion, concentrating in the first instance on the lever and then describing other machines in terms of the lever. He presents detailed analyses of the both the balance and pully systems. 

Source: Wikimedia Commons

It should be noted that for dal Monte the theoretical discipline of mechanics cannot be separated from the study and construction of real machines, in his Mechanicorum Liber, he wrote:

Mechanics can no longer be called mechanics when it is abstracted and separated from machines.

Although he thought that the theoretical study of mechanics should be kept separate from the actual construction of machines. The primary source for dal Monte’s approach is Pappus’ Synagoge, of which he had access to both a Greek manuscript and the manuscript of Commandino’s Latin translation, which Commandino had been unable to publish before his death. In 1588, dal Monte edited and published that Latin translation, bringing Pappus’s synopses of Hero’s Mechanica and Archimedes’ On the Equilibrium of Planes to public attention for the first time in print. In the same year he published his own In duos Archimedis Aequeponderantium Libros Paraphrasis scholiss illustrata, a paraphrase of On the Equilibrium of Planes, both books were published in Pesaro by Hieronymus Concordia, who had also published the Mechanicorum Liber.

 In duos Archimedis Aequeponderantium Libros Paraphrasis scholiss illustrata

A third member of the Urbino School, dal Monte’s student, the mathematician and historian of mathematics, Bernardino Baldi (1553–1617), referenced and amplified the works of Commandino and dal Monte on statics in his own writings, in particular his In mechanica Aristotelis problemata exercitationes published posthumously in 1621.

The man, who broke the connection in statics with the Middle Ages was the Netherland’s engineer and mathematician, Simon Stevin (1548–1620). Stevin had read the Questiones Mechanicae and was aware of the medieval work on statics, but we don’t know how, he had read the relevant works of Archimedes, and Commandino’s Liber de centro gravitas solidorum, but does not seem to have read Papus’ Synagoge, and so was not aware of  Hero’s Mechanica.

Source: Wikimedia Commons

In 1586 he published three books in one volume: De Beghinselen der Weegconst (The Principles of the Art of Weighing), De Weegdaet (The Practice of Weighing), and De Beghinselen des Waterwichts (The Principles of the Weight of Water).

Source: Wikimedia Commons

De Beghinselen der Weegconst consists of two books. Book I has two parts of which the first deals with vertical weights with the law of the balance as central result. The second part deals with oblique weights with the law of the inclined plane as central result.  Book II is devoted to centres of gravity taking Commandino’s work as its starting point. Stevin rejected both circular motion and virtual displacement, the key arguments of the medieval discussion of weights. Regarding the latter he argued that when discussing equilibrium, it was nonsense to start with a discussion of motion, which is what virtual displacement entailed.

Stevin’s proof of the law of the inclined plane involves his famous Clootcrans, wreath of weights:

He derived the condition for the balance of forces on inclined planes using a diagram with a “wreath” containing evenly spaced round masses resting on the planes of a triangular prism (see the illustration on the side). He concluded that the weights required were proportional to the lengths of the sides on which they rested assuming the third side was horizontal and that the effect of a weight was reduced in a similar manner. It’s implicit that the reduction factor is the height of the triangle divided by the side (the sine of the angle of the side with respect to the horizontal). The proof diagram of this concept is known as the “Epitaph of Stevinus”. Wikipedia

From this Stevin derives the parallelogram of forces well before its existence is acknowledge by the mathematician.

Simon Stevin’s illustration [47] of the vector character of a force that is due to the weight G of a mass on a hillside with inclination. As indicated, a force can be decomposed into components. One can add vectors such as D, E, and B as their sum componentwise along Cartesian horizontal and vertical axes or, alternatively, use the parallelogram rule for the D and E (arrows) to obtain B. Because Stevin’s plot is in a twodimensional plane, B can be decomposed into, for instance, the two vectors D and E Source

Although Stevin insisted on writing and publishing in Dutch, his work was translated into Latin by Willebrord Snell (1580–1626) and was well known to the French natural philosophers of the middle of the seventeenth century, who went on to develop the science of mechanics

The work on statics of the Urbino School was well known, widely read and highly influential. In particular dal Monte was Galileo’s first patron and his work influenced the young natural philosopher. In c. 1600 Galileo wrote a manuscript Le manchaniche, which was heavily influenced by dal Monte’s work, but which was first published posthumously. Guidobaldo dal Monte only dealt with statics, keeping it separate from dynamics. Galileo brought statics and dynamics together as mechanics in his Discorsi e dimostrazioni matematiche intorno a due nuove scienze (Discourses and Mathematical Demonstrations Relating to Two New Sciences), published in 1638, combining the previous works of others with his own experiments and discoveries, opening acknowledging dal Monte’s influence.

Source: Wikimedia Commons

Galileo’s Discorsi was, together with other works such as those of Stevin and Beeckman, one of the foundation stones of modern mechanics.

Renaissance science – XLV

70.8% of the earth’s surface is covered by the world ocean; we normally divide it up–Atlantic Ocean, Pacific Ocean, Indian Ocean, etc.– but they are all interconnected in one giant water mass.

The world ocean Source: Wikimedia Commons

Only 29.2% of the surface is land but, on that land, there are many enclosed seas, lakes, ponds, rivers, and streams so there is even more water. The human body is about 60% water, and humans are sometimes referred to as a water-based life form. The statistics are variable, but a healthy human can exist between one and two months without food but only two to four days without water. Brought to a simple formular, water is life.

When humans first began to settle, they did so on or near sources of water–lake shores, streams, rivers, natural springs. Where there was no obvious water supply people began to dig wells, there are wells dating back to 6500 BCE. As settlements grew the problem of water supply and sewage disposal became important and the profession of water manager or hydraulic engineer came into existence. Channelling of fresh water and sewage disposal, recycling of wastewater etc. Initial all of this was powered by gravity but over time other systems of moving water, such as the bucket water wheel or noria were developed for lifting water from one channel into another, appearing in Egypt around the fourth century BCE.

Close-up of the Noria do Mouchão Portugal Source: Wikimedia Commons

Probably the most spectacular surviving evidence of the water management in antiquity are the massive aqueducts built by Roman engineers to bring an adequate supply of drinking water to the Roman settlements. Alone the city of Rome had eleven aqueducts built between 312 BCE and 226 CE, the shortest of which the Aqua Appia from 312 BCE was 16.5 km long with a capacity of 73,000 m³ per day and the longest the Aqua Anio Novus from 52 CE was 87 km long with a capacity of 189,000 m³ per day. The Aqua Alexandrina from 226 CE was only 22 km long but had a capacity of 120,00 to 320,000 m³ per day.

Panorama view of the Roman Aqueduct of Segovia in 2014 Built first century CE originally 17 kilometres long Source Wikimedia Commons

The simplest water clock or clepsydra, a container with a hole in the bottom where the water was driven out by the force of gravity dates back to at least the sixteenth century BCE.

A reconstruction of the water clock used in ancient Greece (Museum of Ancient Agora/Athens) Figure 5: Water Clock/Clepsydra Source

It evolved over the centuries with complex feedback mechanism to keep the water level and thus the flow constant. Water clocks reach an extraordinary level of sophistication as illustrated by the Astronomical Clock Tower of Su Song (1020–1101 CE) in China

The original diagram of Su’s book showing the inner workings of his clocktower Source: Wikimedia Commons

and the Elephant Clock invented by the Islamic engineer al-Jazari (1136-1206). Al-Jazari invented many water powered devices.  

Al-Jazari’s elephant water clock (1206) Source: Wikimedia Commons

Much earlier the Greek engineer Hero of Alexandria (c. 10–c. 70 CE), as well as numerous devices driven by wind and steam, invented a stand-alone fountain that operates under self-contained hydro-static energy, known as Heron’s Fountain. 

Diagram of a functioning Heron’s fountain Source: Wikimedia Commons

All of the above is out of the realm of engineers. Another engineer Archimedes (c. 287–c. 212 BCE), is the subject of possibly the most well-known story in the history of science, one needs only utter the Greek word εὕρηκα (Eureka) to invoke visions of crowns of gold, bathtubs, and naked bearded man running through the streets shouting the word. In fact, you won’t find this story anywhere in Archimedes not insubstantial writings. The source of the story is in De architectura by Vitruvius (C. 80-70–after c. 15 BCE), so two hundred years after Archimedes lived. You can read the original in translation below:

Vitruvius “Ten Books on Architecture”, Ed. Ingrid D. Rowland & Thomas Noble Howard, (CUP, 1999) p. 108

However, Archimedes did write a book On Floating Bodies, which now only exists partially in Greek but in full in a medieval Latin translation. This book is the earliest known work of the branch of physics known as hydrostatics. It contains clear statement of two fundamental principles of hydrostatics, Firstly Archimedes’ principle:

Any body wholly or partially immersed in a fluid experiences an upward force (buoyancy) equal to the weight of the fluid displaced

Secondly the principle of floatation:

Any floating object displaces its own weight of fluid.

As well these two fundamental principles, he also discovered that a submerged object displaces a volume of water equal to its own volume. This is the discovery that led to the legendary of mythical Eureka incident. A crown of pure gold would have a different displacement volume to one of a gold and silver amalgam. The bath story was, as we will see later, highly implausible because it would be very, very difficult to measure the difference in the displaced volumes of water of the two crowns.

Whilst water management continued to develop through out the Middle Ages, with the invention of every better water mills etc., In the Renaissance the profession hydraulic engineer saw developments in two areas. Firstly, the increase in wealth and the development of residences saw the emergence of the Renaissance Garden. Large ornamental gardens the usually featured extensive and often spectacular water features.

Garden of Villa d’Este Tivoli (1550–1572) Source: Wikimedia Commons

The Renaissance mathematici employed by potentates and aristocrats were often expected to serve as hydraulic engineers alongside their other functions as instrument makers, astrologers etc. Secondly the major increase in mining for precious and semi-precious metals meant ever deeper mines, which brought with it the problem of pumping water out of the mines.

Archimedes’ On Floating Bodies was translated into Latin by William of Moerbeke (c. 1215–1286) in the thirteenth century and no complete Greek manuscript is known to exist. This translation was edited by Nicolò Tartaglia Fontana (c. 1506–1557) and published in print along with other works by Archimedes by Venturino Ruffinelli in Venice in 1543, as Opera Archimedis Syracvsani philosophi et mathematici ingeniosissimi

Opera Archimedis Syracvsani philosophi et mathematici ingeniosissimi, 1543 Source

The Nürnberger theologian and humanist Thomas Venatorius (1488–1551) edited the first printed edition of the Greek manuscripts of Archimedes, in a bilingual Greek/Latin edition, which was published in Basel by Johann Herwagen in 1544. The Greek manuscript had been brought to Nürnberg by the humanist scholar, Willibald Pirckheimer (1470–1530) from Rome and the Latin translation by Jacopo da Cremona (fl. 1450) was from the manuscript collection of Regiomontanus (1436-1476).

Source

Venatorius claimed, in the foreword to the Archimedes edition to have studied mathematics under Johannes Schöner (1577–1547) but if then as a mature student in Nürnberg and not as a schoolboy. 

A reconstruction of On Floating Bodies was published by Federico Commandino (1509–1575) in Bologna in 1565. 

Source

Tartaglia, who also produced an Italian edition of On floating Bodies, was the first Renaissance scholar to address Archimedes work on hydrostatics. It did not play a major role in his own work, but he was the first to draw attention to the relationship between the laws of fall and Archimedes’ thoughts on flotation. Tartaglia’s work was read by his one-time student, Giambattista Benedetti ((1530–1590), Galileo (1564–1642), and Simon Stevin (1548–1620), amongst other, and was almost certainly the introduction to Archimedes’ text for all three of them. 

Benedetti replaced Aristotle’s concepts of fall in a fluid directly with Archimedes’ ideas in his work on the laws of fall, equating resistance in the fluid with Archimedes’ upward force or buoyancy. This led him to his anticipations of Galileo’s work on the laws of fall. 

Moving onto Simon Stevin, who wrote a major work on hydrostatics, his De Beghinselen des Waterwichts (Principles on the weight of water) in 1586 and a never completed practical Preamble to the Practice of Hydrostatics.

Source

One of Benedetti’s major works, Demonstratio propotionummotuum localiumcontra Aristotilem et omnes philosphos (1554) had been plagiarised by the French mathematician Jean Taisnier (1598–1562) Opusculum perpetua memoria dignissimum, de natura magnetis et ejus effectibus, Item de motu continuo (1562) and it was this that Stevin read rather than Benedetti’s original. Taisnier’s plagiarism was also translated into English by Richard Eden (c. 1520–1576) an alchemist and promotor of overseas exploration. Stevin a practical engineer ignored or rejected the equivalence between the laws of fall and the principle of buoyancy, concentrating instead on the relationship between flotation and the design of ship’s hulls. His major contribution was the so-called hydrostatic paradox often falsely attributed to Pascal. This states that the downward pressure exerted by a fluid in a vessel is only dependent on its depth and not on the width or length of the vessel. 

Of the three, Galileo is most well-known for his adherence to Archimedes. He clearly stated that in his natural philosophy he had replaced Aristotle with Archimedes as his ancient Greek authority, and this can be seen in his work. His very first work was an essay La Bilancetta (The Little Balance) written in 1586, but first published posthumously in 1644, which he presented to both Guidobaldo del Monte (1545–1607) and Christoph Clavius (1538–1612), both leading mathematical authorities, in the hope of winning their patronage. He was successful in both cases.

Galileo Galilei, La bilancetta, in Opere di Galileo Galilei (facsimile) Source:

Realising, that the famous bathtub story couldn’t actually have worked, Galileo tried to recreate how Archimedes might actually have done it. He devised a very accurate hydrostatic balance that would have made the discovery feasible. 

Later in life, when firmly established as court philosopher in Florence, Galileo was called upon by Cosimo II Medici to debate the principles of flotation with the Aristotelian physicist Lodovico delle Columbe (c. 1565–after 1623), as after dinner entertainment. As I have written before one of Galileo’s principal functions at the court in Florence was to provide such entertainment as a sort of intellectual court jester. Galileo was judged to have carried the day and his contribution to the debate was published in Italian, as Discorso intorno alle cose che stanno in su l’acqua, o che in quella si muovono, (Discourse on Bodies that Stay Atop Water, or Move in It) in 1612.

Source

As was his wont, Galileo mocked his Aristotelian opponent is his brief essay, which brought him the enmity of the Northern Italian Aristotelians. Although Galileo’s approach to the topic was Archimedean, he couldn’t explain everything and not all that he said was correct. However, this little work enjoyed a widespread reception and was influential.

Our last Renaissance contribution to hydrostatics was made by Evangelista Torricelli (1608–1647), a student of Benedetto Castelli (1578–1643) himself a student of Galileo, and like Stevin’s work it came from the practical world rather than the world of science.

Evangelista Torricelli by Lorenzo Lippi Source: Wikimedia Commons

Torricelli was looking for a solution as to why a suction pump could only raise water to a hight of ten metres, as recounted in Galileo’s Discorsi e Dimostrazioni Matematiche, intorno a due nuove scienze (Discourses and Mathematical Demonstrations Relating to Two New Sciences) (1638), a major problem for the expanding deep mining industry, which needed to pump water out of its mines. Torricelli in his investigations invented the Torricellian tube, later called the barometer, with which he demonstrated that there was a limit to the height of a column of liquid that the weight of the atmosphere, or air pressure, could support.

Torricelli’s experiment Source: Wikimedia Commons

He also incidentally demonstrated the existence of a vacuum, something Aristotle said could not exist. 

Torricelli’s work marks the transition from Renaissance science to what is called modern science. Building on the work of Benedetti, Stevin, Galileo, and Torricelli, Blaise Pascal (1623–1662) laid some of the modern foundation of hydrodynamics and hydrostatics, having a unit for pressure named after him and being sometimes falsely credited with discoveries that were actually made in the earlier phase by his predecessors. 

Painting of Pascal made by François II Quesnel for Gérard Edelinck in 1691. Source:Wikimedia Commons

Renaissance science – XLIV

This blog post is a modified version of two blog posts from my The emergence of modern astronomy–a complex mosaic series and yes it involves self plagiarism. I wrote it, rather than simply linking, because the content also belongs in this blog post series, which I wish to be complete and autonomous

Short popular presentations of the history of the origins of modern physics usually consist of three sections. In ancient Greece, Aristotle got almost everything wrong. In the Middle Ages, people clung religiously to Aristotle’s wrong theories. Then came Galileo and everything was light! A somewhat, sarcastic exaggeration but pretty close to the truth of what people like to believe and believe is the right verb because it bears little relation to what actually happened. You will note in my little parody that there is no mention of the Renaissance. This is because it just gets subsumed into the amorphous Middle Ages in this version of history. Galileo is always presented as a sort of messiah single handily casting a shining light into the dark reaches of medieval Aristotelianism and bringing forth, in a sort of virgin, birth modern physics. 

In reality, whilst the considerations of what became modern physics are based on the concepts of Aristotle, there were major developments between the fourth century BCE and the early seventeenth century, especially during the Renaissance, changes of which Galileo was well aware and on which he built his, not always correct, contributions. In what follows I’m going to briefly outline the evolution of the theories of motion from Aristotle down to the seventeenth century; the theories of motion that then emerged being the bedrock on which Isaac Newton constructed his physics.

When talking of the history of physics it is important to note that what Aristotle meant with the term, one that he coined, is very different to the modern meaning, one that only began to emerge in the eighteenth century. For Aristotle his ta physika literally means “the natural things” and his physics means the study of all of nature, a study that is also non-mathematical. For Aristotle the objects of mathematics do not describe anything real, so mathematics can not be used to describe the real world. He does allow the use of mathematics in the so-called mixed sciences–astronomy, optics, harmonics (music or more accurately acoustics)–all of which we would include, at least in part, in a general definition of physics but for Aristotle were not part of his ta physika.

Central to Aristotle’s theory of nature was the establishment of the general principle of change that governs all natural bodies. For Aristotle motion is quite simply change of place. Aristotle complicates this simple picture in that he differentiates between celestial and terrestrial motion and between natural and violent or unnatural motion. 

Simplest is his description of natural celestial motion, which is uniform circular motion, a concept that he inherited from Empedocles (c. 494 – c. 434 BCE, fl. 444–443 BCE) via his teacher Plato (c.425 BCE – 348/347 BCE). There is no violent or unnatural celestial motion. Aristotle’s theory of celestial motion is cosmology not astronomy and therefore not mathematical. The attempts to describe that motion mathematically are astronomical and thus not part of Aristotle’s physics.

Unlike celestial motion, both natural and violent terrestrial motion exist. For Aristotle, natural terrestrial motion is always perpendicular to the Earth’s surface and is the result of the four elements-earth, water, air, fire (another concept inherited from Empedocles)–striving to return to the natural places. So, the light elements–air and fire–travel upwards away from the Earth’s surface and the heavy elements–water and earth–fall downwards towards the Earth’s surface. In Latin this indication of heaviness is termed gravitas, object consisting principally of earth and/or water have gravitas and so they fall downwards.

Violent terrestrial motion is any motion that is not natural motion and must be brought about by the application of force. Simplified for something to move, other than falling, it has to be pulled or pushed. For Aristotle, the only contactless motion is the fall of water and earth due to gravitas and the rise of air and fire to their natural place in the world, all other motion requires contact between the object being moved and whoever or whatever is doing the moving. As with much of Aristotle’s philosophy these concepts are based on empirical observation of the real world and are not so wrong, as they are often painted. Aristotle does not have a quantitative law of fall, but he asserts that objects fall at speed proportion to their weight and inversely proportional to the density of the fluid they are falling through. This is often contrasted with Galileo’s “correct” law of fall that all objects fall at the same speed, but Galileo’s law is only valid for a vacuum. 

Source: Wikimedia Commons

Aristotle has major problems with projectile motion. If you throw a ball or shoot and arrow, then according to Aristotle, as soon as the ball leaves your hand or the arrow the bowstring then it should immediately stop moving and fall to the ground, which it very obviously doesn’t. He got round the problem by claiming that the projectile parts the air as it flies, which then rushed round to the back of the object to prevent a vacuum forming and pushes the projectile forwards. An explanation that people found difficult to swallow and I suspect that even Aristotle found it less than satisfactory.

It is exactly here in his theory of projectile motion that Aristotle’s theories of terrestrial motion were first challenged and that already in the sixth century CE by the Alexandrian philosopher John Philoponus (c. 490–c. 570). Philoponus broke with the Aristotelian-Neoplatonic tradition of his own times and subjected Aristotle to severe criticism, writing commentaries on many of Aristotle’s major works and most importantly on Aristotle’s Physics. Whilst in general accepting Aristotle’s concept that for violent movement to take place a force must be applied but supplemented it by writing that in the case of projectiles, they acquired a motive power from the source providing the initial projection, which dissipated over time. 

Philoponus didn’t restrict his concept to projectile motion, he also thought that the planets in their orbits had acquired the same motive when set in motion at the creation. Philoponus also rejects Aristotle’s theory of fall. It is obvious that one stone twice as heavy as another falls twice as fast. He apparently backed this up by doing empirical experiments. Showing that stones of differing weights fall at almost the same speed.

but this [view of Aristotle] is completely erroneous, and our view may be completely corroborated by actual observation more effectively than by any sort of verbal argument. For if you let fall from the same height two weights, one many times heavier than the other you will see that the ratio of the times required for the motion does not depend [solely] on the weights, but that the difference in time is very small. …

Because he fell into disgrace with the Church because of his religious writings, Philoponus’ Aristotle commentaries were little read in the West in the Early Middle Ages. However, they were read by Islamic scholars, such as Ibn Sina (c. 980–1037) (Avicenne), al-Baghdādī (c. 1080–1164), and al-Bitruji (died c. 1204), all adopted and modified Philoponus’ theory of projectile motion.

Avicenne Portrait (1271) Source: Wikimedia Commons

Whether directly from medieval manuscripts or through transmission by the translation movement, Philoponus’ work was known in Europe in the High Middle Ages. Amongst others, Thomas Aquinas (1225–1274) referenced but rejected it. It was the French scholastic philosopher, Jean Buridan (c. 1301–c. 1360), who adopted it and gave it both its final form and its name, impetus. Unlike Philoponus and his Islamic supporters, who thought that the implied motive force simply dissipated spontaneously over time, Buridan argued that the projectile was slowed and eventually brought to a halt by air resistance and gravity opposing its impetus. In Buridan’s more sophisticated version of Philoponus’ theory one can already see the seeds of the theory of inertia. 

Jean Buridan Source

When a mover sets a body in motion he implants into it a certain impetus, that is, a certain force enabling a body to move in the direction in which the mover starts it, be it upwards, downwards, sidewards, or in a circle. The implanted impetus increases in the same ratio as the velocity. It is because of this impetus that a stone moves on after the thrower has ceased moving it. But because of the resistance of the air (and also because of the gravity of the stone) which strives to move it in the opposite direction to the motion caused by the impetus, the latter will weaken all the time. Therefore the motion of the stone will be gradually slower, and finally the impetus is so diminished or destroyed that the gravity of the stone prevails and moves the stone towards its natural place. In my opinion one can accept this explanation because the other explanations prove to be false whereas all phenomena agree with this one.

Buridan, like Philoponus and al-Bitruji, thought that impetus most the motive force of the planets, there being in the celestial sphere no air resistance of gravity to weaken it. 

Impetus was established as the accepted theory of projectile motion at the beginning of the sixteenth century and it was the theory that Niccolò Fontana (c. 1500–1557), better known by his nickname, Tartaglia, used in his mathematical analysis of ballistics, his Nova scientia (1537), the first such book on the topic.

Tartaglia Source: Wikimedia Commons

Here we have a classic example of Renaissance science, the application of the scientific approach to an artisanal practice, gunnery. Because he was using the theory of impetus and not the theory of inertia, Tartaglia’s theories of the flight path of cannon balls is wrong, but his book was widely read and highly influential, Galileo owned a heavily annotated copy. 

Various projectile trajectories from Tartaglia’s Nova Scientia Source: Wikimedia Commons

Philoponus had also criticised Aristotle’s theory of fall and he was by no means the last medieval scholar to do so. The so-called Oxford Calculatores at Merton College, Thomas Bradwardine (c. 1300–1349), William of Heytesbury (c. 1313–c. 1372), Richard Swineshead (fl. c. 1340–1354) and John Dumbleton (c. 1310–c. 1349)–studied mechanics distinguishing between kinematics and dynamics, emphasising the former and investigating instantaneous velocity.

Merton College in 1865 Source: Wikimedia Commons

They were the first to formulate the mean speed theorem, an achievement usually accredited to Galileo. The mean speed theorem states that a uniformly accelerated body, starting from rest, travels the same distance as a body with uniform speed, whose speed in half the final velocity of the accelerated body. The theory lies at the heart of the laws of fall.

Nicole Oresme (c. 1320–1382), a Parisian colleague of Jean Buridan, in his own work on the concept of motion produced a graphical representation of the mean speed theorem,

Portrait of Nicole Oresme: Miniature from Oresme’s Traité de l’espère, Bibliothèque Nationale, Paris, France, fonds français 565, fol. 1r. Source: Wikimedia Commons

as did Giovanni di Casali (c. 1320–after 1374), a Franciscan friar, who encountered the mathematical physics of the Oxford Calculatores, whilst working as a lecturer at Cambridge University around 1340. He wrote a treatise on his ideas on motion in 1346, which was published as De velocitate motus alterationis (On the Velocity of the Motion of Alteration) in Venice in 1351. His work on mathematical physics influenced scholars at the University of Padua and possibly later Galileo.

Portrait of Nicole Oresme: Miniature from Oresme’s Traité de l’espère, Bibliothèque Nationale, Paris, France, fonds français 565, fol. 1r. Source: Wikimedia Commons

The most important work on the theories of motion by a Renaissance scholar is that of Giambattista Benedetti (1530–1590), a one-time pupil of Tartaglia. Addressing the law of fall, Benedetti in his Demonstratio proportionum motuum localium (1554) he argued that speed is dependent not on weight but specific gravity and that two objects of the same material, but different weights would fall at the same speed.

Source

Benedetti brought an early version of the thought experiment, usually attributed to Galileo, of viewing two bodies falling separately or conjoined, in his case by a cord.  Galileo considered a roof tile falling complete and then broken into two. Benedetti’s work was all done within the theory of impetus. Galileo’s first work on the topic, the unpublished De motu, written whilst he was still at the University of Pisa, also assumes the impetus theory and bears a strong resemblance to Benedetti’s work, which raises the question to what extent Galileo was acquainted with it. The opinions of the historians are divided on the topic.

Whereas Galileo almost certainly never threw balls off the Tower of Pisa, Simon Stevin (1548–1620), the mathematical engineer living and working in the newly established United Provinces, actually dropped lead balls of different weights from the thirty-foot-high church tower in Delft and determined empirically that they fell at the same speed, arriving at the ground at the same time. Stevin’s work was translated into both French and Latin and was widely read and highly influential in the France of Descartes, Mersenne, Gassendi et al. 

Anonymous Dutch painter / engraver, 17th century. Collection Leiden University, Icones Leidenses 40. Source: Wikimedia Commons

There is a significant list of Renaissance scholars who reached and published the same conclusion, the Dominican priest Domingo de Soto (1494–1560) in Spain, Gerolamo Cardano (1501–1576), Benedetto Varchi (c. 1502–1565), Giuseppe Moletti (1531–1588) and Jacopo Mazzoni (1548–1598) in Italy. Girolamo Borro (1512–1592) one of Galileo’s teachers in Pisa, actually carried out empirical experiments to test Aristotle’s laws of fall, throwing objects of different material and the same weights out of a high window. 

As can be seen from the above, when Galileo started working on the problems of motion towards the end of the sixteenth century, when he was still very much a Renaissance scientist, he was building on a strong tradition of criticisms and corrections to the Aristotelian theories stretching back to the early Middle Ages but also particularly vibrant in the sixteenth century. As already noted, Galileo earliest unpublished work, De Motu, was firmly entrenched in that tradition. 

Of course, Galileo would go on to make significant advances in both projectile motion and the laws of fall but in the first he was definitely strongly influenced by another Renaissance mathematician, the Urbino aristocrat, Guidobaldo del Monte (1545–1607). Del Monte was one of the influential figures the young Galileo turned too for assistance at the beginning of his career. Impressed by the young Tuscan, Del Monte helped him to his appointment as professor for mathematics at the University of Pisa and again when he moved to the University of Padua. 

Guidobaldo del Monte. Source:Wikimedia Commons

Galileo’s major contribution to the theory of projectile motion was the law of the parabola i.e., that the path of a projectile traces out a parabola. Galileo presents this in his Discorsi in 1638. However, it can be found in a notebook of del Monte’s from 1601, with a description of the proofs for this that are identical to those published by Galileo thirty-seven years later. The charitable explanation is that the two of them made this discovery together during one of Galileo’s visits to del Monte’s estate. The less charitable one is that Galileo borrowed del Monte’s results without acknowledgement, not the only time he would do such a thing.

The English polymath, Thomas Harriot (c.1560–1621) discovered the parabola law independently of del Monte/Galileo, but as with everything else didn’t publish his discovery. Bonaventura Cavalieri (1598–1647) did publish the parabola law, and in fact did so before Galileo, which brought an accusation of plagiarism from Galileo. Whether he borrowed the law from Galileo or discovered it independently is not known.

Bonaventura Cavalieri Source:Wikimedia Commons

On the laws of fall, Galileo carried out his famous series of experiments using an inclined plane to verify what many others had confirmed during the preceding century. Here the problem is that his inclined plane would not give the level of accuracy of the results that he published. This led the historian of science and Galileo expert, Alexander Koryé (1892–1964), to hypothesise that the inclined plane was a purely hypothetical experiment that Galileo never actually carried out. The modern consensus is that Galileo did in fact carry out his experiments but massaged his results to make them fit the required theoretical values. As we have seen the mean speed theorem was already well established, as was the principle that objects of different weights fall at the same speed.

Galileo’s supposed other great contribution was the law of inertia. Moving from impetus to inertia was the major breakthrough in concepts of motion in the history of physics as it turns the whole problem on its head. Whereas Aristotle asked what moves things, the principle of inertia asks what stops them moving. Aristotle takes still stand as the natural state of objects that has to be changed, inertia takes motion of as the natural state of objects that has to be changed. 

It is interesting to note that the supposedly modern scientist Galileo was in this concept trapped in the Greek paradigm of uniform circular motion being natural motion. Because of this, Galileo only defined inertia for circular motion:

“…all external impediments removed, a heavy body on a spherical surface concentric with the earth will maintain itself in that state in which it has been; if placed in a movement towards the west (for example), it will maintain itself in that movement.”^[1]

Galileo’s addiction to the concept of uniform circular motion is also clear in his Dialogo, where he completely ignored Kepler’s laws of planetary motion, with their elliptical orbits maintaining the Copernican deferent-epicycle model

The Netherlander, Isaac Beeckman (1588–1637) had independently developed the concept of inertia already in 1614 and unlike Galileo he applied it to both circular and linear motion. Although, like Harriot, Beeckman never published, his work was well known to the physicist in Paris especially Descartes (1596–1650), Mersenne (1588–1648) and Gassendi (1592–1655). Newton (1642–1727) took the principle of inertia from Descarte, and not from Galileo as is often falsely claimed as his first law, and Descarte had it from Beeckman. Beeckman was an archetypal Renaissance scientist, an artisan who turned his attention to empirical experiments and science.

When one looks below the surface of the superficial accounts of the history of physics, it become clear the Renaissance scholar contributed substantially to the development of the theories of motion in the period leading up to the so-called scientific revolution.

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^[1] Stillman Drake, Discoveries and Opinions of Galileo, Doubleday, New York, 1957, p.113

A Clock is a Thing that Ticks

As I have mentioned a few times in the past, I came late to the computer and the Internet. No Sinclairs, Ataris, or Commadores in my life, my first computer was a Bondi Blue iMac G3. All of which is kind of ironic, because by the time I acquired that G3, I was something of an expert on the history of computing and computing devices. Having acquired my G3, I then took baby steps into the deep waters of the Internet. My initial interest was in music websites starting with the Grateful Dead. Did I mention that I’m a Dead Head? One day I stumbled across Mark Chu-Carroll’s Good Math, Bad Math blog, which in turn introduced me to the Science Blogs collective of which it was a part. Here I discovered, amongst other, the Evolving Thoughts blog of John Wilkins. Who, more than any other, was responsible for me starting my own blog. Another blog that I started reading regularly was Uncertain Principles by the American physicist Chad Orzel, who wrote amusing dialogues explain modern physics to his dog Emmy. A publisher obviously thought they were good, they were, and they soon appeared as a book, How to Teach Physics to Your Dog (Scribner, 2010), launching his career as a writer of popular science books. This was followed by How to Teach Relativity to Your Dog (Basic Books, 2012) with the original book now retitled as How to Teach [Quantum] Physics to Your Dog. Leaving the canine world, he then published Eureka: Discovering Your Inner Scientist (Basic Books, 2014) followed by Breakfast With Einstein: The Exotic Physics of Everyday Objects (BenBella Books, 2018). 

All of the above is a longwinded introduction to the fact that this is a review of Chad Orzel’s latest A Brief History of Timekeeping: The Science of Marking Time, from Stonehenge to Atomic Clocks^[1].

Astute, regular readers might have noticed that I reviewed Davis Rooney’s excellent volume on the history of timekeeping About Time: A History of Civilisation in Twelve Clocks (Viking, 2021) back in September last year and they might ask themselves if and how the two books differ and whether having read the one it is worth reading the other? I follow both authors, and they follow each other, on Twitter and there were several exchanges during last year as to whether they were covering the same territory with their books. However, I can honestly report that if one is interested in the history of time keeping then one can read both books profitably, as they complement rather than copy each other. Whereas Rooney concentrates on the social, cultural, and political aspects of measuring time, Orzel concentrates on the physics of how time was measured.

The title of this blog post is the title of the introductory chapter of Orzel’s book. This definition I viewed with maximum scepsis until I read his explication of it:

At the most basic level a clock is a thing that ticks.

The “tick” here can be the audible physical tick we associate with a mechanical clock like the one in Union’s Memorial Chapel, caused by collision between gear teeth as a heavy pendulum swings back and forth. It can also be a more subtle physical effect, like the alternating voltage that provides the time signal for the electronic wall clock in our classrooms. It can be exceedingly fast, like the nine-billion-times-a-second oscillations of the microwaves used in the atomic clock that provides the time signals transmitted to smartphones via the internet, or ponderously slow like the changing position of the rising sun on the horizon.

In every one of these clocks, though, there is a tick: a regular repeated action that can be counted to mark the passage of time. 

I said above that what distinguishes Orzel’s book is a strong emphasis on the physics of timekeeping. To this end, the book had not one, but two interrelated but separate narratives. There is the main historical narrative in language accessible to every non-expert reader describing forms of timekeeping, their origins, and developments. The second separate narrative, presented on pages with a grey stripe on the edge, takes the willing reader through the physics and technical aspects behind the timekeeping devices described in the historical narrative. Orzel is a good teacher with an easy pedagogical style, so those prepared to invest a little effort can learn much from his explanations. This means that the reader has multiple possibilities to approach the book. They can read it straight through taking in historical narrative and physics explication as they come, which is what I did. They can also skip the physics and just read the historical narrative and still win much from Orzel’s book. It would be possible to do the reverse and just read the physics, skipping the historical narrative, but I, at least, find it difficult to imagine someone doing this. Other possibilities suggest themselves, such as reading first the historical narrative, then going back and dipping into selected explanations of some of the physics. I find the division of the contents in this way a very positive aspect of the book. 

Orzel starts his journey through time and its measurement with the tick of the sun’s annual journey. He takes us back to the Neolithic and such monuments as the Newgrange chamber tomb and Stonehenge which display obvious solar orientations. The technical section of this first chapter is a very handy guide to all things to do with the solar orbit. The second chapter stays with astronomy and the creation of early lunar, lunar-solar and solar calendars. Here and in the following chapter which deals with the Gregorian calendar reform there are no technical sections. 

In Chapter 4, The Apocalypse That Wasn’t, Orzel reminds us of all the rubbish that was generated in the months leading up to the apocalypse supposedly predicted by the Mayan calendar in 2012. In fact, all it was the end of one of the various Mayan cycles of counting days. Orzel gives a very good description of the Mayan number system and their various day counting cycles. An excellent short introduction to the topic for any teacher. 

Leaving Middle America behind, in the next chapter we return to the Middle East and the invention of the water clock or clepsydra. He takes us from ancient Egypt and the simplest form of water clock to the giant tower clock of medieval China. The technical section deals with the physics of the various systems that were developed to produce a constant flow in a water clock. In the simplest form of water clock, a hole in the bottom of a cylinder of water, the rate of flow slows down as the mass of water in the cylinder decreases. 

Chapter 6 takes us to the real tick tock of the mechanical clock from its beginnings up to the pendulum clock. Interestingly there is a lot of, well explained, physics in the narrative section, but the technical section is historical. Orzel gives us a careful analysis of what exactly Galileo did or did not do, did or did not achieve with his pendulum experiments. The chapter closes with the story how the pendulum was used to help determine the shape of the earth.

The next three chapters take as deep into the world of astronomy. For obvious reasons astronomy and timekeeping have always been interwoven strands. We start with what is basically a comparison of Mayan astronomy, with the Dresden Codex observations of Venus, and European astronomy. In the European section, after a brief, but good, section on Ptolemy and his epicycle- deferent model, we get introduced to the work of Tycho Brahe.

The rules of the history of astronomy says that Kepler must follow Tycho and that is also the case here. After Kepler’s laws of planetary motion, we arrive at the invention of the telescope, the discovery of the moons of Jupiter and the determination of the speed of light. If you want a good, accurate, short guide to the history of European astronomy then this book is for you. 

Chapter nine starts with a very brief introduction to the world of Newtonian astronomy before taking the reader into the problem of determining longitude, a time difference problem, and the solution offered by the lunar distance method as perfected by Tobias Mayer. Here, the technical section explains why the determination of longitude is a time difference problem, how the lunar distance method works, and why it was so difficult to make it work.

Of course, in a book on the history of timekeeping, having introduced the longitude problem we now have John Harrison and the invention of the marine chronometer. I almost cheered when Orzel pointed out that although Harrison provided a solution, it wasn’t “the” solution because his chronometer was too complex and too expensive to be practical. The technical section is a brief survey of the evolution of portable clocks. The chapter closes with a couple of paragraphs in which Orzel muses over the difference between “geniuses” and master craftsmen, a category into which he places both Mayer and Harrison. I found these few lines very perceptive and definitely worth expanding upon. 

Up till now we were still in the era of local time determined by the daily journey of the sun. Orzel’s next chapter takes us into the age of railways, and telegraphs and the need for standardised time for train timetables and the introduction of our international time zone system. The technical section is a fascinating essay on the problems of synchronising clocks using the telegraph and having to account for the delays caused by the time the signal needs to travel from A to B. It’s a hell of a lot more complex than you might think.

We are now firmly in the modern age and the advent of the special theory of relativity. Refreshingly, Orzel does most of the introductory work here by following the thoughts of Henri Poincaré, the largely forgotten man of relativity. Of course, we get Albert too.  The technical section is about clocks on moving trains and will give the readers brains a good workout. 

Having moved into the world of modern physics Orzel introduces his readers to the quantum clock and timekeeping on a mindboggling level of accuracy. We get a user-friendly introduction to the workings of the atomic clock. This was the first part of the book that was completely new to me, and I found it totally fascinating. The technical section explains how the advent of the atomic clock has been used to provide a universal time for the world. The chapter closes with a brief introduction to GPS, which is dependent on atomic clocks.

Einstein returns with his general theory of relativity and a technical section on why and how exactly gravity bends light. A phenomenon that famously provided the first confirmation of the general theory.

Approaching the end, our narrative takes a sharp turn away from the world of twentieth century physics to the advent and evolution of cheap wrist and pocket watches. In an age where it is taken for granted that almost everyone can afford to carry an accurate timekeeper around with them, it is easy to forget just how recent this phenomenon is. The main part of this chapter deals with the quartz watch. A development that made a highly accurate timepiece available cheaply to everyone who desired it. Naturally, the technical section deals with the physics of the quartz clock. 

The book closes with a look at The Future of Time. One might be forgiven for thinking that modern atomic clocks were the non plus ultra in timekeeping, but physicists don’t share this opinion. In this chapter Orzel describes various project to produce even more accurate timepieces.

Throughout the book are scattered footnote, which are comments on or addition to the text. The book is illustrated with grey scale drawing and diagrams that help to explicate points being explained. There is a short list of just seven recommended books for further reading. I personally own six of the seven and have read the seventh and can confirm that they are all excellent. There is also a comprehensive index.

Chad Orzel is a master storyteller and despite the, at times, highly complex nature of the narrative he is spinning, he makes it light and accessible for readers at all levels. He is also an excellent teacher and this book, which was originally a course that he teaches, would make a first-class course book for anybody wishing to teach a course on the history of timekeeping from any level from say around middle teens upwards. Perhaps combined with Davis Rooney’s About Time: A History of Civilisation in Twelve Clocks, as I find that the two books complement each other perfectly. Orzel’s A Brief History of Timekeeping: The Science of Marking Time, from Stonehenge to Atomic Clocks is a first-rate addition to the literature on the topic and highly recommendable. 

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^[1] Chad Orzel, A Brief History of Timekeeping: The Science of Marking Time, from Stonehenge to Atomic Clocks, BenBella Books, Dallas, TX, 2022

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. 

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.  

The man who printed the world of plants

Abraham Ortelius (1527–1598) is justifiably famous for having produced the world’s first modern atlas, that is a bound, printed, uniform collection of maps, his Theatrum Orbis Terrarum. Ortelius was a wealthy businessman and paid for the publication of his Theatrum out of his own pocket, but he was not a printer and had to employ others to print it for him.

Abraham Ortelius by Peter Paul Rubens , Museum Plantin-Moretus via Wikimedia Commons

A man who printed, not the first 1570 editions, but the important expanded 1579 Latin edition, with its bibliography (Catalogus Auctorum), index (Index Tabularum), the maps with text on the back, followed by a register of place names in ancient times (Nomenclator), and who also played a major role in marketing the book, was Ortelius’ friend and colleague the Antwerp publisher, printer and bookseller Christophe Plantin (c. 1520–1589).

Plantin also published Ortelius’ Synonymia geographica (1578), his critical treatment of ancient geography, later republished in expanded form as Thesaurus geographicus (1587) and expanded once again in 1596, in which Ortelius first present his theory of continental drift.

Plantin’s was the leading publishing house in Europe in the second half of the sixteenth century, which over a period of 34 years issued 2,450 titles. Although much of Plantin’s work was of religious nature, as indeed most European publishers of the period, he also published many important academic works.

Before we look in more detail at Plantin’s life and work, we need to look at an aspect of his relationship with Ortelius, something which played an important role in both his private and business life. Both Christophe Plantin and Abraham Ortelius were members of a relatively small religious cult or sect the Famillia Caritatis (English: Family of Love), Dutch Huis der Leifde (English: House of Love), whose members were also known as Familists.

This secret sect was similar in many aspects to the Anabaptists and was founded and led by the prosperous merchant from Münster, Hendrik Niclaes (c. 1501–c. 1580). Niclaes was charged with heresy and imprisoned at the age of twenty-seven. About 1530 he moved to Amsterdam where his was once again imprisoned, this time on a charge of complicity in the Münster Rebellion of 1534–35. Around 1539 he felt himself called to found his Famillia Caritatis and in 1540 he moved to Emden, where he lived for the next twenty years and prospered as a businessman. He travelled much throughout the Netherlands, England and other countries combining his commercial and missionary activities. He is thought to have died around 1580 in Cologne where he was living at the time.

Niclaes wrote vast numbers of pamphlets and books outlining his religious views and I will only give a very brief outline of the main points here. Familists were basically quietists like the Quakers, who reject force and the carrying of weapons. Their ideal was a quite life of study, spiritualist piety, contemplation, withdrawn from the turmoil of the world around them. The sect was apocalyptic and believed in a rapidly approaching end of the world. Hendrik Niclaes saw his mission in instructing mankind in the principal dogma of love and charity. He believed he had been sent by God and signed all his published writings H. N. a Hillige Nature (Holy Creature). The apocalyptic element of their belief meant that adherents could live the life of honest, law abiding citizens even as members of religious communities because all religions and authorities would be irrelevant come the end of times. Niclaes managed to convert a surprisingly large group of successful and wealthy merchants and seems to have appealed to an intellectual cliental as well. Apart from Ortelius and Plantin, the great Dutch philologist, humanist and philosopher Justus Lipsius (1574–1606) was a member, as was Charles de l’Escluse (1526–1609), better known as Carolus Clusius, physician and the leading botanist in Europe in the second half of the sixteenth century. The humanist Andreas Masius (1514–1573) an early syriacist (one who studies Syriac, an Aramaic language) was a member, as was Benito Arias Monato (1527–1598) a Spanish orientalist. Emanuel van Meteren (1535–1612) a Flemish historian and nephew of Ortelius was probably also Familist. The noted Flemish miniature painter and illustrator, Joris Hoefnagel (1542–1601), was a member as was his father a successful diamond dealer. Last but by no means least Pieter Bruegel the Elder (c. 1525– 1569) was also a Familist. As we shall see the Family of Love and its members played a significant role in Plantin’s life and work.

Christophe Plantin by Peter Paul Rubens Museum Platin-Moretus  via Wikimedia Commons Antwerp in the time of Plantin was a major centre for artists and engravers and Peter Paul Rubins was the Plantin house portrait painter.

Christophe Plantin was born in Saint-Avertin near Tours in France around 1520. He was apprenticed to Robert II Macé in Caen, Normandy from whom he learnt bookbinding and printing. In Caen he met and married Jeanne Rivière (c. 1521–1596) in around 1545.

Jeanne Rivière School of Rubens Museum Plantin-Moretus via Wikimedia Commons

They had five daughters, who survived Plantin and a son who died in infancy. Initially, they set up business in Paris but shortly before 1550 they moved to the city of Antwerp in the Spanish Netherlands, then one of Europe’s most important commercial centres. Plantin became a burgher of the city and a member of the Guild of St Luke, the guild of painter, sculptors, engravers and printers. He initially set up as a bookbinder and leather worker but in 1555 he set up his printing office, which was most probably initially financed by the Family of Love. There is some disagreement amongst the historians of the Family as to how much of Niclaes output of illegal religious writings Plantin printed. But there is agreement that he probably printed Niclaes’ major work, De Spiegel der Gerechtigheid (Mirror of Justice, around 1556). If not the house printer for the Family of Love, Plantin was certainly one of their printers.

The earliest book known to have been printed by Plantin was La Institutione di una fanciulla nata nobilmente, by Giovanni Michele Bruto, with a French translation in 1555, By 1570 the publishing house had grown to become the largest in Europe, printing and publishing a wide range of books, noted for their quality and in particular the high quality of their engravings. Ironically, in 1562 his presses and goods were impounded because his workmen had printed a heretical, not Familist, pamphlet. At the time Plantin was away on a business trip in Paris and he remained there for eighteen months until his name was cleared. When he returned to Antwerp local rich, Calvinist merchants helped him to re-establish his printing office. In 1567, he moved his business into a house in Hoogstraat, which he named De Gulden Passer (The Golden Compasses). He adopted a printer’s mark, which appeared on the title page of all his future publications, a pair of compasses encircled by his moto, Labore et Constantia (By Labour and Constancy).

Christophe Plantin’s printers mark, Source: Wikimedia Commons

Engraving of Plantin with his printing mark after Goltzius Source: Wikimedia Commons

Encouraged by King Philip II of Spain, Plantin produced his most famous publication the Biblia Polyglotta (The Polyglot Bible), for which Benito Arias Monato (1527–1598) came to Antwerp from Spain, as one of the editors. With parallel texts in Latin, Greek, Syriac, Aramaic and Hebrew the production took four years (1568–1572). The French type designer Claude Garamond (c. 1510–1561) cut the punches for the different type faces required for each of the languages. The project was incredibly expensive and Plantin had to mortgage his business to cover the production costs. The Bible was not a financial success, but it brought it desired reward when Philip appointed Plantin Architypographus Regii, with the exclusive privilege to print all Roman Catholic liturgical books for Philip’s empire.

THE BIBLIA SACRA POLYGLOTTA, CHRISOPHER PLANTIN’S MASTERPIECE. IMAGE Chetham’s Library

In 1576, the Spanish troops burned and plundered Antwerp and Plantin was forced to pay a large bribe to protect his business. In the same year he established a branch of his printing office in Paris, which was managed by his daughter Magdalena (1557–1599) and her husband Gilles Beys (1540–1595). In 1578, Plantin was appointed official printer to the States General of the Netherlands. 1583, Antwerp now in decline, Plantin went to Leiden to establish a new branch of his business, leaving the house of The Golden Compasses under the management of his son-in-law, Jan Moretus (1543–1610), who had married his daughter Martine (1550–16126). Plantin was house publisher to Justus Lipsius, the most important Dutch humanist after Erasmus nearly all of whose books he printed and published. Lipsius even had his own office in the printing works, where he could work and also correct the proofs of his books. In Leiden when the university was looking for a printer Lipsius recommended Plantin, who was duly appointed official university printer. In 1585, he returned to Antwerp, leaving his business in Leiden in the hands of another son-in-law, Franciscus Raphelengius (1539–1597), who had married Margaretha Plantin (1547–1594). Plantin continued to work in Antwerp until his death in 1589.

Source: Museum Plantin-Moretus

After this very long introduction to the life and work of Christophe Plantin, we want to take a look at his activities as a printer/publisher of science. As we saw in the introduction he was closely associated with Abraham Ortelius, in fact their relationship began before Ortelius wrote his Theatrum. One of Ortelius’ business activities was that he worked as a map colourer, printed maps were still coloured by hand, and Plantin was one of the printers that he worked for. In cartography Plantin also published Lodovico Guicciardini’s (1521–1589) Descrittione di Lodovico Guicciardini patritio fiorentino di tutti i Paesi Bassi altrimenti detti Germania inferiore (Description of the Low Countries) (1567),

Source: Wikimedia Commons

which included maps of the various Netherlands’ cities.

Engraved and colored map of the city of Antwerp Source: Wikimedia Commons

Plantin contributed, however, to the printing and publication of books in other branches of the sciences.

Plantin’s biggest contribution to the history of science was in botany.  A combination of the invention of printing with movable type, the development of both printing with woodcut and engraving, as well as the invention of linear perspective and the development of naturalism in art led to production spectacular plant books and herbals in the Early Modern Period. By the second half of the sixteenth century the Netherlands had become a major centre for such publications. The big three botanical authors in the Netherlands were Carolus Clusius (1526–1609), Rembert Dodoens (1517–1585) and Matthaeus Loblius (1538–1616), who were all at one time clients of Plantin.

Matthaeus Loblius was a physician and botanist, who worked extensively in both England and the Netherlands.

Matthias de Lobel (Lobelius),by Francis Delaramprint, 1615 Source: Wikimedia Commons

His Stirpium aduersaria noua… (A new notebook of plants) was originally published in London in 1571, but a much-extended edition, Plantarum seu stirpium historia…, with 1, 486 engravings in two volumes was printed and published by Plantin in 1576. In 1581 Plantin also published his Dutch herbal, Kruydtboek oft beschrÿuinghe van allerleye ghewassen….

Source: Wikimedia Commons

There is also an anonymous Stirpium seu Plantarum Icones (images of plants) published by Plantin in 1581, with a second edition in 1591, that has been attributed to Loblius but is now thought to have been together by Plantin himself from his extensive stock of plant engravings.

Carolus Clusius also a physician and botanist was the leading scientific horticulturist of the period, who stood in contact with other botanist literally all over the worlds, exchanging information, seeds, dried plants and even living ones.

Portrait of Carolus Clusius painted in 1585 Attributed to Jacob de Monte – Hoogleraren Universiteit Leiden via Wikimedia Commons

His first publication, not however by Plantin, was a translation into French of Dodoens’ herbal of which more in a minute. This was followed by a Latin translation from the Portuguese of Garcia de Orta’s Colóquios dos simples e Drogas da India, Aromatum et simplicium aliquot medicamentorum apud Indios nascentium historia (1567) and a Latin translation from Spanish of Nicolás Monardes’  Historia medicinal delas cosas que se traen de nuestras Indias Occidentales que sirven al uso de la medicina, , De simplicibus medicamentis ex occidentali India delatis quorum in medicina usus est (1574), with a second edition (1579), both published by Plantin.His own  Rariorum alioquot stirpium per Hispanias observatarum historia: libris duobus expressas (1576) and Rariorum aliquot stirpium, per Pannoniam, Austriam, & vicinas quasdam provincias observatarum historia, quatuor libris expressa … (1583) followed from Plantin’s presses. His Rariorum plantarum historia: quae accesserint, proxima pagina docebit (1601) was published by Plantin’s son-in-law Jan Moretus, who inherited the Antwerp printing house.

Our third physician-botanist, Rembert Dodoens, his first publication with Plantin was his Historia frumentorum, leguminum, palustrium et aquatilium herbarum acceorum, quae eo pertinent (1566) followed by the second Latin edition of his  Purgantium aliarumque eo facientium, tam et radicum, convolvulorum ac deletariarum herbarum historiae libri IIII…. Accessit appendix variarum et quidem rarissimarum nonnullarum stirpium, ac florum quorumdam peregrinorum elegantissimorumque icones omnino novas nec antea editas, singulorumque breves descriptiones continens… (1576) as well as other medical books.

Rembert Dodoens Theodor de Bry – University of Mannheim via Wikimedia Commons

His most well known and important work was his herbal originally published in Dutch, his Cruydeboeck, translated into French by Clusius as already stated above.

Title page of Cruydt-Boeck,1618 edition Source: Wikimedia Commons

Plantin published an extensively revised Latin edition Stirpium historiae pemptades sex sive libri XXXs in 1593.

This was largely plagiarised together with work from Loblius and Clusius by John Gerrard (c. 1545–1612)

John Gerard Source: Wikimedia Commons

in his English herbal, Great Herball Or Generall Historie of Plantes (1597), which despite being full of errors became a standard reference work in English.

Platin also published a successful edition of Juan Valverde de Amusco’s Historia de la composicion del cuerpo humano (1568), which had been first published in Rome in 1556. This was to a large extent a plagiarism of Vesalius’ De humani corporis fabrica (1543).

Another area where Platin made a publishing impact was with the works of the highly influential Dutch engineer, mathematician and physicist Simon Stevin (1548-1620). The Plantin printing office published almost 90% of Stevin’s work, eleven books altogether, including his introduction into Europe of decimal fractions De Thiende (1585),

Source: Wikimedia Commons

his important physics book De Beghinselen der Weeghconst (The Principles of Statics, lit. The Principles of the Art of Weighing) (1586),

Source: Wikimedia Commons

his Beghinselen des Waterwichts (Principles of hydrodynamics) (1586) and his book on navigation De Havenvinding (1599).

Following his death, the families of his sons-in-law continued the work of his various printing offices, Christophe Beys (1575–1647), the son of Magdalena and Gilles, continued the Paris branch of the business until he lost his status as a sworn printer in 1601. The family of Franciscus Raphelengius continued printing in Leiden for another two generations, until 1619. When Lipsius retired from the University of Leiden in 1590, Joseph Justus Scaliger (1540-1609) was invited to follow him at the university. He initially declined the offer but, in the end, when offered a position without obligations he accepted and moved to Leiden in 1593. It appears that the quality of the publications of the Plantin publishing office in Leiden helped him to make his decision.  In 1685, a great-granddaughter of the last printer in the Raphelengius family married Jordaen Luchtmans (1652 –1708), who had founded the Brill publishing company in 1683.

The original publishing house in Antwerp survived the longest. Beginning with Jan it passed through the hands of twelve generations of the Moretus family down to Eduardus Josephus Hyacinthus Moretus (1804–1880), who printed the last book in 1866 before he sold the printing office to the City of Antwerp in 1876. Today the building with all of the companies records and equipment is the Museum Plantin-Moretus, the world’s most spectacular museum of printing.

There is one last fascinating fact thrown up by this monument to printing history. Lodewijk Elzevir (c. 1540–1617), who founded the House of Elzevir in Leiden in 1583, which published both Galileo’s Discorsi e dimostrazioni matematiche intorno a due nuove scienze in 1638 and Descartes’ Discours de la Méthode Pour bien conduire sa raison, et chercher la vérité dans les sciences in 1637, worked for Plantin as a bookbinder in the 1560s.

Nikolaes Heinsius the Elder, Poemata (Elzevier 1653), Druckermarke Source: Wikimedia Commons

The House of Elzevir ceased publishing in 1712 and is not connected to Elsevier the modern publishing company, which was founded in 1880 and merely borrowed the name of their famous predecessor.

The Platntin-Moretus publishing house played a significant role in the intellectual history of Europe over many decades.

 

 

The emergence of modern astronomy – a complex mosaic: Part LI

 

By the middle of the nineteenth century there was no doubt that the Earth rotated on its own axis, but there was still no direct empirical evidence that it did so. There was the indirect evidence provided by the Newton-Huygens theory of the shape of the Earth that had been measured in the middle of the eighteenth century. There was also the astronomical evidence that the axial rotation of the other known solar system planets had been observed and their periods of rotation measured; why should the Earth be an exception? There was also the fact that it was now known that the stars were by no means equidistant from the Earth on some sort of fixed sphere but distributed throughout deep space at varying distances. This completely destroyed the concept that it was the stars that rotated around the Earth once every twenty-four rather than the Earth rotating on its axis. All of this left no doubt in the minds of astronomers that the Earth the Earth had diurnal rotation i.e., rotated on its axis but directly measurable empirical evidence of this had still not been demonstrated.

From the beginning of his own endeavours, Galileo had been desperate to find such empirical evidence and produced his ill-fated theory of the tides in a surprisingly blind attempt to deliver such proof. This being the case it’s more than somewhat ironic that when that empirical evidence was finally demonstrated it was something that would have been well within Galileo’s grasp, as it was the humble pendulum that delivered the goods and Galileo had been one of the first to investigate the pendulum.

From the very beginning, as the heliocentric system became a serious candidate as a model for the solar system, astronomers began to discuss the problems surrounding projectiles in flight or objects falling to the Earth. If the Earth had diurnal rotation would the projectile fly in a straight line or veer slightly to the side relative to the rotating Earth. Would a falling object hit the Earth exactly perpendicular to its starting point or slightly to one side, the rotating Earth having moved on? The answer to both questions is in fact slightly to the side and not straight, a phenomenon now known as the Coriolis effect produced by the Coriolis force, named after the French mathematician and engineer Gaspard-Gustave de Coriolis (1792–1843), who as is often the case, didn’t hypothesise or discover it first. A good example of Stigler’s law of eponymy, which states that no scientific discovery is named after its original discoverer.

Gaspard-Gustave de Coriolis. Source: Wikimedia Commons

As we saw in an earlier episode of this series, Giovanni Battista Riccioli (1594–1671) actually hypothesised, in his Almagustum Novum, that if the Earth had diurnal rotation then the Coriolis effect must exist and be detectable. Having failed to detect it he then concluded logically, but falsely that the Earth does not have diurnal rotation.

Illustration from Riccioli’s 1651 New Almagest showing the effect a rotating Earth should have on projectiles.[36] When the cannon is fired at eastern target B, cannon and target both travel east at the same speed while the ball is in flight. The ball strikes the target just as it would if the Earth were immobile. When the cannon is fired at northern target E, the target moves more slowly to the east than the cannon and the airborne ball, because the ground moves more slowly at more northern latitudes (the ground hardly moves at all near the pole). Thus the ball follows a curved path over the ground, not a diagonal, and strikes to the east, or right, of the target at G. Source: Wikimedia Commons

Likewise, the French, Jesuit mathematician, Claude François Millet Deschales (1621–1678) drew the same conclusion in his 1674 Cursus seu Mondus Matematicus. The problem is that the Coriolis effect for balls dropped from towers or fired from cannons is extremely small and very difficult to detect.

The question remained, however, a hotly discussed subject under astronomers and natural philosophers. In 1679, in the correspondence between Newton and Hooke that would eventually lead to Hooke’s priority claim for the law of gravity, Newton proffered a new solution to the problem as to where a ball dropped from a tower would land under the influence of diurnal rotation. In his accompanying diagram Newton made an error, which Hooke surprisingly politely corrected in his reply. This exchange did nothing to improve relations between the two men.

Leonard Euler (1707–1783) worked out the mathematics of the Coriolis effect in 1747 and Pierre-Simon Laplace (1749–1827) introduced the Coriolis effect into his tidal equations in 1778. Finally, Coriolis, himself, published his analysis of the effect that’s named after him in a work on machines with rotating parts, such as waterwheels in 1835, G-G Coriolis (1835), “Sur les équations du mouvement relatif des systèmes de corps”. 

What Riccioli and Deschales didn’t consider was the pendulum. The simple pendulum is a controlled falling object and thus also affected by the Coriolis force. If you release a pendulum and let it swing it doesn’t actually trace out the straight line that you visualise but veers off slightly to the side. Because of the controlled nature of the pendulum this deflection from the straight path is detectable.

For the last three years of Galileo’s life, that is from 1639 to 1642, the then young Vincenzo Viviani (1622–1703) was his companion, carer and student, so it is somewhat ironic that Viviani was the first to observe the diurnal rotation deflection of a pendulum. Viviani carried out experiments with pendulums in part, because his endeavours together with Galileo’s son, Vincenzo (1606-1649), to realise Galileo’s ambition to build a pendulum clock. The project was never realised but in an unpublished manuscript Viviani recorded observing the deflection of the pendulum due to diurnal rotation but didn’t realise what it was and thought it was due to experimental error.

Vincenzo Viviani (1622- 1703) portrait by Domenico Tempesti Source: Wikimedia Commons

It would be another two hundred years, despite work on the Coriolis effect by Giovanni Borelli (1608–1679), Pierre-Simon Laplace (1749–1827) and Siméon Denis Poisson (1781–1840), who all concentrated on the falling ball thought experiment, before the French physicist Jean Bernard Léon Foucault (1819–1868) finally produced direct empirical evidence of diurnal rotation with his, in the meantime legendary, pendulum.

If a pendulum were to be suspended directly over the Geographical North Pole, then in one sidereal day (sidereal time is measured against the stars and a sidereal day is 3 minutes and 56 seconds shorter than the 24-hour solar day) the pendulum describes a complete clockwise rotation. At the Geographical South Pole the rotation is anti-clockwise. A pendulum suspended directly over the equator and directed along the equator experiences no apparent deflection. Anywhere between these extremes the effect is more complex but clearly visible if the pendulum is large enough and stable enough.

Foucault’s first demonstration took place in the Paris Observatory in February 1851. A few weeks later he made the demonstration that made him famous in the Paris Panthéon with a 28-kilogram brass coated lead bob suspended on a 67-metre-long wire from the Panthéon dome.

Paris Panthéon Source: Wikimedia Commons

His pendulum had a period of 16.5 seconds and the pendulum completed a full clockwise rotation in 31 hours 50 minutes. Setting up and starting a Foucault pendulum is a delicate business as it is easy to induce imprecision that can distort the observed effects but at long last the problem of a direct demonstration of diurnal rotation had been produced and with it the final demonstration of the truth of the heliocentric hypothesis three hundred years after the publication of Copernicus’ De revolutionibus.

Léon Foucault, Pendulum Experiment, 1851 Source

The emergence of modern astronomy – a complex mosaic: Part XLIV

Whilst the European community mathematicians and physicist, i.e. those who could comprehend and understand it, were more than prepared to acknowledge Newton’s Principia as a mathematical masterpiece, many of them could not accept some of the very basic premises on which it was built. Following its publication the Baconians, the Cartesians and Leibniz were not slow in expressing their fundamental rejection of various philosophical aspects of Newton’s magnum opus.  

Francis Bacon had proposed a new scientific methodology earlier in the seventeenth century to replace the Aristotelian methodology.

Sir Francis Bacon, c. 1618

You will come across claims that Newton’s work was applied Baconianism but nothing could be further from the truth. Bacon rejected the concept of generating theories to explain a group of phenomena. In his opinion the natural philosopher should collect facts or empirical data and when they had acquired a large enough collections then the explanatory theories would crystallise out of the data. Bacon was also not a fan of the use of mathematics in natural philosophy. Because of this he actually rejected both the theories of Copernicus and Gilbert.

Newton, of course did the opposite he set up a hypothesis to explain a given set of seemingly related phenomena, deduced logical consequences of the hypothesis, tested the deduced conclusions against empirical facts and if the conclusions survive the testing the hypothesis becomes a theory. This difference in methodologies was bound to lead to a clash and it did. The initial clash took place between Newton and Flamsteed, who was a convinced Baconian. Flamsteed regarded Newton’s demands for his lunar data to test his lunar theory as a misuse of his data collecting. 

Source: Wikimedia Commons

The conflict took place on a wider level within the Royal Society, which was set up as a Baconian institution and rejected Newton’s type of mathematical theorising. When Newton became President of the Royal Society in 1704 there was a conflict between himself and his supporters on the one side and the Baconians on the other, under the leadership of Hans Sloane the Society’s secretary. At that time the real power in Royal Society lay with the secretary and not the president. It was first in 1712 when Sloane resigned as secretary that the Royal Society became truly Newtonian. This situation did not last long, when Newton died, Sloane became president and the Royal Society became fundamentally Baconian till well into the nineteenth century. 

Hans Sloane by Stephen Slaughter Source: Wikimedia Commons

This situation certainly contributed to the circumstances that whereas on the continent the mathematicians and physicists developed the theories of Newton, Leibnitz and Huygens in the eighteenth century creating out of them the physics that we now know as Newtonian, in England these developments were neglected and very little advance was made on the work that Newton had created. By the nineteenth century the UK lagged well behind the continent in both mathematics and physics.

The problem between Newton and the Cartesians was of a completely different nature. Most people don’t notice that Newton never actually defines what force is. If you ask somebody, what is force, they will probably answer mass time acceleration but this just tells you how to determine the strength of a given force not what it is. Newton tells the readers how force works and how to determine the strength of a force but not what a force actually is; this is OK because nobody else does either. The problems start with the force of gravity. 

Frans Hals – Portrait of René Descartes Source: Wikimedia Commons

The Cartesians like Aristotle assume that for a force to act or work there must be actual physical contact. They of course solve Aristotle’s problem of projectile motion, if I remove the throwing hand or bowstring, why does the rock or arrow keep moving the physical contact having ceased? The solution is the principle of inertia, Newton’s first law of motion. This basically says that it is the motion that is natural and it requires a force to stop it air resistance, friction or crashing into a stationary object. In order to explain planetary motion Descartes rejected the existence of a vacuum and hypothesised a dense, fine particle medium, which fills space and his planets are carried around their orbits on vortices in this medium, so physical contact. Newton demolished this theory in Book II of his Principia and replaces it with his force of gravity, which unfortunately operates on the principle of action at a distance; this was anathema for both the Cartesians and for Leibniz. 

What is this thing called gravity that can exercise force on objects without physical contact? Newton, in fact, disliked the concept of action at a distance just as much as his opponents, so he dodged the question. His tactic is already enshrined in the title of his masterpiece, the Mathematical Principles of Natural Philosophy. In the draft preface to the Principia Newton stated that natural philosophy must “begin from phenomena and admit no principles of things, no causes, no explanations, except those which are established through phenomena.” The aim of the Principia is “to deal only with those things which relate to natural philosophy”, which should not “be founded…on metaphysical opinions.” What Newton is telling his readers here is that he will present a mathematical description of the phenomena but he won’t make any metaphysical speculations as to their causes. His work is an operative or instrumentalist account of the phenomena and not a philosophical one like Descartes’.  

The Cartesians simply couldn’t accept Newton’s action at a distance gravity. Christiaan Huygens, the most significant living Cartesian natural philosopher, who was an enthusiastic fan of the Principia said quite openly that he simply could not accept a force that operated without physical contact and he was by no means alone in his rejection of this aspect of Newton’s theory. The general accusation was that he had introduced occult forces into natural philosophy, where occult means hidden.

Christiaan Huygens. Cut from the engraving following the painting of Caspar Netscher by G. Edelinck between 1684 and 1687. Source: Wikimedia Commons

Answering his critics in the General Scholium added to the second edition of the Principia in 1713 and modified in the third edition of 1726, Newton wrote:

Thus far I have explained the phenomena of the heavens and of our sea by the force of gravity, but I have not assigned a cause to gravity.

[…]

I have not been able to deduce from phenomena the reasons for these properties of gravity, and I do not feign hypotheses; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this experimental philosophy, propositions are deduced from the phenomena and are made general by induction. The impenetrability, mobility, and impetus of bodies, and the laws of motion and the law of gravity have been found by this method. And it is enough that gravity really exists and acts according to the laws that we have set forth and is sufficient to explain all the motions of the heavenly bodies and of our sea.

Newton never did explain the cause of gravity but having introduced the concept of a pervasive aethereal medium in the Queries in Book III of his Opticks he asks if the attraction of the aether particles could be the cause of gravity. The Queries are presented as speculation for future research.

Both the Baconian objections to Newton’s methodology and the Cartesian objections to action at a distance were never disposed of by Newton but with time and the successes of Newton’s theory, for example the return of Comet Halley, the objections faded into the background and the Principia became the accepted dominant theory of the cosmos.

Leibniz shared the Cartesian objection to action at a distance but also had objections of his own.

Engraving of Gottfried Wilhelm Leibniz Source: Wikimedia Commons

In 1715 Leibniz wrote a letter to Caroline of Ansbach the wife of George Prince of Wales, the future George III, in which he criticised Newtonian physics as detrimental to natural theology. The letter was answered on Newton’s behalf by Samuel Clarke (1675–1729) a leading Anglican cleric and a Newtonian, who had translated the Opticks into Latin. There developed a correspondence between the two men about Newton’s work, which ended with Leibniz’s death in 1716. The content of the correspondence was predominantly theological but Leibniz raised and challenged one very serious point in the Principia, Newton’s concept of absolute time and space.

In the Scholium to the definitions at the beginning of Book I of Principia Newton wrote: 

1. Absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything external, flows uniformly and by another name is called duration. 

Relative, apparent, and common time […] is commonly used instead of true time.

2. Absolute space, of its own nature without reference to anything external, always remains homogeneous and immovable. Relative space is any moveable or dimension of the absolute space…

Newton is saying that space and time have a separate existence and all objects exists within them.

In his correspondence with Clarke, Leibniz rejected Newton’s use of absolute time and space, proposing instead a relational time and space; that is space and time are a system of relations that exists between objects. 

 In his third letter to Clarke he wrote:

As for my own opinion, I have said more than once, that I hold space to be something merely relative, as time is, that I hold it to be an order of coexistences, as time is an order of successions.

Leibniz died before any real conclusion was reached in this debate and it was generally thought at the time that Newton had the better arguments in his side but as we now know it was actually Leibniz who was closer to how we view time and space than Newton. 

Newton effectively saw off his philosophical critics and the Principia became the accepted, at least mathematical, model of the then known cosmos. However, there was still the not insubstantial empirical problem that no proof of any form of terrestrial motion had been found up to the beginning of the seventeenth century.