Category Archives: Renaissance Science

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.


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

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Filed under History of Physics, Renaissance Science

Renaissance science – XLIII

The world has been full of sound since the Earth first acquired an atmosphere at least 3.8 billion years ago. Sound is the principle means with which humans communicate with each other. Hearing is one of the five senses with which humans perceive and explore the world in which they live. Sound in the form of music is one of the oldest and most widespread art forms that humans have created. All of this being so, it might come as a surprise to realise that the science of sound, acoustics, only really developed in any real sense in the eighteenth and nineteenth centuries. Acoustic derives from the Greek akoutikos = pertaining to hearing, from akoustos = heard, audible. Acoustics as the science of sound first appeared in the 1680s and meaning the acoustic properties of a building in 1885. However, the first tentative steps towards the science of acoustics took place in the Renaissance. Before we begin to examine those steps, we first need to look at what took place in antiquity, as this is the basis on which the Renaissance scholars built their theories. 

As usually this only refers to the developments within Europe, where there was historically no clear distinction between the terms we now use – sound, acoustics, music. Our first reference point in Pythagoras and his music theory. According to the well-known myth/legend/story, Pythagoras was walking past a smithy when he noticed the pitch of the sound made by the hammers varied with their weight and he decided to investigate the phenomenon. Pythagoras supposedly established that the weight of hammers or the length of strings on a monochord, a single stringed musical instrument, that produced a pleasing sound when sounded together, which we would now term harmonious, stood in whole number ratios to each other. So, a string twice as long as a given string will sound a note one octave lower than that of the given string:

In modern parlance, if a string sounds the note C when plucked, a string twice as long will sound a C an octave lower, so a ratio of 2:1. A perfect fourth has a ratio of 4:3 and a perfect fifth one of 3:2. The four numbers 1, 2, 3, 4 sum to ten making the Pythagorean tetractys.

The tetractys (Greek: τετρακτύς), is a triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row, which is the geometrical representation of the fourth triangular number. As a mystical symbol, it was very important to the secret worship of Pythagoreanism. There were four seasons, and the number was also associated with planetary motions and music

Wikipedia
Tetractys Source: Wikimedia Commons

The Pythagoreans also propagated the theory of the harmony of the spheres, which claimed that the planets in their orbits created a harmonious musical scale, which depending on who’s telling the story is either inaudible to human ears or only audible to the enlightened sage. 

As to be expected Aristotle had a theory on the nature of sound. He correctly attributes it to air pressure variations

Sound takes place when bodies strike the air, . . . by its being moved in a corresponding manner; the air being contracted and expanded and overtaken, and again struck by the impulses of the breath and the strings, for when air falls upon and strikes the air which is next to it, the air is carried forward with an impetus, and that which is contiguous to the first is carried onward; so that the same voice spreads every way as far as the motion of the air takes place. 

—Aristotle (384–322 BCE), Treatise on Sound and Hearing[1]

In On Things Heard, attributed to Strato of Lampsacus (c. 335–c. 269 BCE), in the only extant version made up of long extracts included in the Commentary on Ptolemy’s Harmonics of Porphyry (c. 234–c. 305 CE) it is stated that the pitch is related to the frequency of vibrations of the air and to the speed of sound.

Ancient Greek philosopher Strato of Lampsacus, depicted in the Nuremberg Chronicle Source Wikimedia Commons

Ptolemaeus’ Harmonikon or Harmonics is not so well known as his astronomical or geographical works but did, as we will see, have an influence during the Renaissance and especially on Johannes Kepler. Like the Pythagoreans he argued for music intervals based on mathematical ratios. However, whereas the Pythagoreans saw the perfect fifth 3:2, as the basis of the musical scale, Ptolemaeus preferred perfect fourths 4:3 and octaves. His book closes with general thoughts on the relationships between harmony, the soul, and the planets (harmony of the spheres).

A diagram showing Pythagorean tuning. Source: Wikimedia Commons

Turning from the philosophical and theoretical to the practical the De architectura of Vitruvius addresses the subject of acoustics in theatres. In Book V of his masterwork, Chapter 4 is titled Harmonic Principles. He apologises for using many Greek terms, explaining that there are not any Latin terms. There follows a lengthy discussion on the tones produced by the human voice and the intervals in singing. Chapter 5 is titled The EcheaSounding Vessels in Theatres and discusses the production of bronze vessels designed to produce harmonics and their placement within the theatre to improve the acoustics. 

Manuscript of Vitruvius; parchment dating from about 1390 Source: Wikimedia Commons

Moving on to the education system, because of the Pythagorean association of music with arithmetic, it became part of the quadrivium the mathematical part of the seven liberal arts–arithmetic, geometry, music, astronomy–whereby music was regarded as arithmetic in motion and astronomy was geometry in motion.

Quadrivium

The standard text for teaching music as a part of the quadrivium at the medieval university was the De institutione musica by Boethius (c. 480–524 CE), one of the four texts that he wrote on the quadrivium subjects. 

Lady Philosophy and Boethius from the Consolation, (Ghent, 1485) Source: Wikimedia Commons

In “De Musica”, Boethius introduced the threefold classification of music: 

  • Musica mundana – music of the spheres/world; this “music” was not actually audible and was to be understood rather than heard
  • Musica humana – harmony of human body and spiritual harmony
  • Musica instrumentalis – instrumental music
Boethius’ De institutione musica. This is a 15th-century copy of a Latin treatise on the Pythagorean-based theory of ancient Greek music, in which the text reflects an older (10th-century) tradition and the numerous diagrams related to ratio and pitch demonstrate later developments in the tradition 

Boethius’ Musica, Arithmetica, and Geometria were all printed for the first time in 1492 making the Pythagorean arithmetical theory of music widely available in the Renaissance.

As I explained in the episode of this series dealing with Vitruvius and De archtectura, it was also printed and published towards the end of the fifteenth century, not only in Latin but also fairly quickly in various vernacular languages. However, as I also pointed De archtectura was well-known in the Middle Ages but had little impact on medieval architecture. Having said that medieval churches often had acoustic jars, thought to have been inspired by Vitruvius’ enchae, inserted in strategic positions in the walls and flours to improve the acoustics. Unlike Vitruvius’ enchae, which were of bronze, the medieval acoustic jars were made of pottery. 

This brick structure comprises the walls of a 15th-century acoustic passage beneath a set of choir-stalls in a friary church. By placing empty pottery jars at strategic points within this passage the builders hoped to be able to improve the acoustics of the Choir by creating a sort of sound-stage for the singers above. Dr Dave Evans, City of Hull archaeologist (doing the pointing in the photo above)

We know from illustrations of instruments, people playing, singing, or dancing that there was a wide variety of music in the Middle Ages, and this is confirmed from written sources. However, the only form of medieval music from before eight-hundred CE, which we know in detail as music, is plain song or Gregorian chant. After eight hundred there are successive developments within a limited musical framework dominated by so-called modal music. There is a difference between modes and scales, which I’m not going to go into now. There was a definite development in the style of musical composition starting around the beginning of the fifteenth century and is regarded as the musical element of the Renaissance. To look more closely at this would however take us of course.  

For our purposes the important development was initiated by Gioseffo Zarlino (1517–1590) a composer and musical theorist.

1599 painting of Zarlino by an unknown artist Source: Wikimedia Commons

He was the first to prioritise the primacy of triad (a three note sequence) over the interval (two notes) that predominated in Pythagorean theory as central to Boethius. He also argued for various technical changes in intonation against the tradition Pythagorean system. Zarlino’s system as presented in his Istitutioni hamoniche (1558) was basically equivalent to that of Ptolemaeus in his Harmonikon.

Le Istitutioni Harmoniche by Gioseffo Zarlino, 1558 Source Brandeis University

Amongst his pupils was the lutenist, composer, and music theorist Vincenzo Galilei (1520­–1591). Galilei disagreed with his teacher on many issues preferring the Pythagorean system, which he presented in his Dialogo della musica antica et della moderna (1581).

Title page Dialogo della musica antica et della moderna (1581) Source

In defence of his system, he turned from pure theory to practical experiments with vibrating strings making him a pioneer in the systematic study of acoustic. He was assisted in his experiments by his, later more famous, son Galileo, and it is generally argued that Galileo acquired his interest in experimental physics working with his father in his youth. 

The Galileis, father and son produced experimental proof that the ratio of an interval is proportional to string length, varies with the square root of the tension applied. Galileo extended his father’s experimental investigations of vibrating strings, looking at the effect of area of the cross-section, and the density of the material used. He almost certainly did this whilst he was still young, but the results of his father’s and his research were first published in his Discorsi e dimostrazioni matematiche intorno a due nuove scienze (Discourses and Mathematical Demonstrations Relating to Two New Sciences) in 1638. 

Source: Wikimedia Commons

At the end of the First Day in the Discorsi, Galileo begins a discussion on vibrations (pages 127 to 150 in the original). He starts by discussing his pendulum experiments including his slightly incorrect version of the law of the pendulum, Galileo’s observation of isochronism was accurate only for small swings. On page 138 he moves onto the whole theory of vibrating strings, pitch, consonance, and dissonance. He explains consonance as occurring when the pulses of the two notes frequently coincide on the tympanum of the ear. He also explains that one can demonstrate this visually by setting a set of pendula with strings in the same ratio as vibrating strings, 3:2 for the perfect fifth for example. It is obvious that Galileo has given the subject a lot of thought and carried out lots of experiment. He also describes a way to demonstrate the wave nature of sound:

The same phenomenon is observed to better advantage by fixing the base of the goblet upon the bottom of a rather large vessel of water filled nearly to the edge of the goblet; for if, as before, we sound the glass by friction of the finger, we shall see ripples spreading with the utmost regularity and with high speed to large distances about the glass. I have often remarked, in thus sounding a rather large glass nearly full with water, that at first the waves are spaced with great uniformity, and when, as sometimes happens, the tone of the glass jumps an octave higher I have noticed that at this moment each of the aforementioned waves divides into two; a phenomenon that shows clearly that the ratio involved in the octave [forma dell’ ottava] is two.

(Discorsi pp. 142-143)[2]

The work of Vincenzo and Galileo Galilei on acoustics is a classic example of what defines Renaissance science. They proceed from artisan knowledge, that of a working musician, Galileo was like his father a lutenist, on stringing and tuning an instrument and through careful experimental investigation turn it into scientific knowledge. 

Although, Galileo discusses the factors that affect the pitch of a vibrating string–length, tension, cross-section, density–he doesn’t actually give a formula that combines the various factors; this was left up to the French mathematical scholar, Marin Mersenne ((1588–1648). Mersenne, who I have dealt with more fully here, personally knew Galileo and was a big fan of the Tuscan scholar’s work. He invested much effort into trying to persuade others to read Galileo’s books, which rather contradicts the popular image that Galileo was widely read in the seventeenth century. As I stated in my earlier post on him, Mersenne’s biggest contribution to science was in the field of acoustics, and I’m just going to quote what I wrote there:

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

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

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

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

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

We now need to go back a little and look at the harmony of the spheres as propagated by both the Pythagoreans and Ptolemaeus, as this too experienced a new lease of life in the Renaissance. Tycho Brahe designed and built his research centre Uraniborg on the Island of Hven in the second half of the 1570s. All the dimensions of the plan and façade of the building as well as the layout of the gardens surrounding it were in the Pythagorean harmonic ratios, as befits a temple to celestial research.

Tycho Brahe’s Uraniborg main building from Blaeu’s Atlas Maior (1663) Source: Wikimedia Commons

The man who took the whole concept of the harmony of the spheres furthest was Johannes Kepler in his monumental Harmonices mundi libri V (1619). As the scholar, who contributed the most to the foundations of modern heliocentric astronomy, much more than Tycho Brahe or Copernicus, on whose work he built, Kepler is usually regarded as one of the early modern scientists, but he was in fact a quintessential Renaissance figure. Blending practical knowledge, mathematics, mysticism, and rock-solid empirical science he constructed a wonderfully bizarre and totally unique synthesis. Ninety nine percent of his work usually simply gets ignored and he gets presented as the man, who discovered the three laws of planetary motion, as if he simply pulled them out of his hat, but Harmonices mundi libri V is the wonderful Renaissance creation, 508 large format pages in the modern English translation, that delivered up the third of the laws Kepler’s Harmonic Law

Kepler had already indicated in his Mysterium cosmographicum (1596) that he intended to fine tune his model of the cosmos, based on the five regular Platonic solids, with music or the harmony of the spheres.

He began working on his theories already in the 1590s, expressing his interest in music theory in his correspondence with Michael Mästlin (1550–1631), Edmund Bruce (fl. 1597-1605) and Herwart von Hohenburg (1533–1622). He wrote to Bruce on 14th December 1599 of his intention to write a work with the title De harmonice mundi listing the contents, which are those that the book would eventually have, although it took him almost twenty years to write it. He saw his book as a direct competitor to or update of Ptolemaeus’ Harmonikon, even going so far as to borrow a Greek manuscript of Ptolemaeus’ book and translating parts of it himself. By following a basic Pythagorean line in his theories, Kepler was rejecting to more modern music theories that had come to dominate in the seventeenth century. 

Books I & II Kepler deals with the construction of geometrical figures. In Book III he outlines Pythagorean music and number theory, as an introduction before presenting his own geometrical theory of consonance and dissonance based on numerical ratios of figures constructable with a straight edge and compass. In Book IV he applies his harmonic theories to his own more than somewhat deviant theories of astrology. It is in Book V that he now applies his theories to his model of the cosmos, beginning with the five Platonic solids then moving on to the motions of the planets, analysing all aspects of the planetary orbits for harmonious ratios.

Illustration from the Harmonice mundi taken from the English translation The Harmony of the World by Johannes Kepler, Translated into English with an Introduction and Notes by E.J. Aston, A.M. Duncan and J.V. Field, American Philosophical Society, 1997

All of this wonderfully bizarre theorising, in the end, delivered up Kepler’s third law of planetary motion his harmony law, perhaps the most important contribution to the mathematical theory of astronomy before Newton.

Newton, often regarded as the founder of much of modern science, was, himself, not immune to the allure of the Pythagorean theory of the harmony of the spheres, using it, as I outlined in an earlier post, to justify differentiating seven colours in the rainbow, seven colours, seven notes of the scale, a colour scheme that we still follow today. 

Penelope Gouk, The harmonic roots of Newtonian science, in John Fauvel, Raymond Flood, Michael Shortland & Robin Wilson eds., Let Newton Be: A new perspective on his life and works, OUP, Oxford, New York, Tokyo, ppb. 1989 p. 118

The Renaissance occupation with music theory yielded some strange fruit.  


[1]  “How Sound Propagates” (PDF). Princeton University Press.

[2] Dialogues Concerning Two New Sciences Galileo Galilei, translated by Henry Crew and Alfonso de Salvio, Dover, NY, 1954 p. 99

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Renaissance science – XLII

As with much in European thought, it was Aristotle, who first made a strong distinction between, what was considered, the two different realms of thought, theoretical thought epistêmê, most often translated as knowledge, and technê, translated as either art or craft. As already explained in an earlier post in this series, during the Middle Ages the two areas were kept well separated, with only the realm of epistêmê considered worthy of study by scholars. Technê being held to be inferior. As also explained in that earlier post the distinguishing feature of Renaissance science was the gradual dissolution of the boundary between the two areas and the melding of them into a new form of knowledge that would go on to become the empirically based science of the so-called scientific revolution. 

A second defining characteristic of the developing Renaissance science was the creation of new spaces for the conception, acquisition, and dissemination of the newly emerging forms of knowledge. We have followed the emergence of libraries outside of the monasteries, the establishment of botanical gardens as centres of learning, and cabinets of curiosity and the museums that evolved out of them, as centres for accumulating knowledge in its material forms. 

Another, space that emerged in the late Renaissance for the generation and acquisition of knowledge was the laboratory. The very etymology of the term indicates very clearly that this form of knowledge belonged to the technê side of the divide. The modern word laboratory is derived from the Latin laboratorium, which in turn comes from laboratus the past participle of laboare meaning to work. This origin is, of course, clearly reflected in the modern English verb to labour meaning to work hard using one’s hands, and all of the associated words, the nouns labour and labourer etc. It was only around 1600 that the word laboratorium came to signify a room for conducting scientific experiments, whereby the word scientific is used very loosely here. 

Of course, laboratories, to use the modern term, existed before the late sixteenth century and are mostly associated with the discipline of alchemy. Much of the Arabic Jabirian corpus, the vast convolute of ninth century alchemical manuscripts associated with the name Abū Mūsā Jābir ibn Ḥayyān is concerned with what we would term laboratory work. It would appear that medieval Islamic culture did not share the Aristotelian disdain for manual labour. However, in Europe, the practical alchemist in his workshop or laboratory actually working with chemicals was regarded as a menial hand worker. Although, it should be remembered that medieval alchemy incorporated much that we would now term applied or industrial chemistry, the manufacture of pigments or gunpowder, just to give two examples. Many alchemists considered themselves philosophical alchemists, often styling themselves philosopher or natural philosopher to avoid the stigma of being considered a menial labourer. 

The status of artisan had already been rising steadily since the expansion in European trade in the High Middle Ages and the formation of the guilds, which gave the skilled workers a raised profile. After all, they manufacture many of the goods traded. It should also be remembered that the universities were founded as guilds of learning, the word universitas meaning a society or corporation. 

So, what changed in the sixteenth century to raise the status of the laboratorium, making it, so to speak, acceptable in polite society? The biggest single change was the posthumous interest in the medical theories of Theophrastus of Hohenheim (c. 1493–1541), or as he is better known Paracelsus (c. 1493–1541), based on his medical alchemy, known as chymiatria or iatrochemistry, a process that began around 1560. 

Aureoli Theophrasti ab Hohenheim. Reproduction, 1927, of etching by A. Hirschvogel, 1538. Source: Wikimedia Commons

The new Paracelsian iatrochemistry trend did not initially enter the Renaissance university but found much favour on the courts of the European royalty and aristocracy and it was here that the new laboratoria were established by many of the same potentates, who had founded new libraries, botanical garden, and cabinets of curiosity. The Medici, Spanish and Austrian Hapsburgs, and Hohenzollerns all established laboratoria staffing them with their own Paracelsian alchemical physicians. Many of these regal loboratoria resembled the workshops of apothecaries, artisans, and instrument makers. Techné had become an integral part of the European aristocratic court. 

It was in the Holy Roman Empire that the Renaissance laboratory celebrated its greatest success. The most well documented Renaissance laboratory was that of Wolfgang II, Graf von Hohenlohe und Herr zu Langenburg (1546–1610). In 1587, having constructed a new Renaissance residence, he constructed a two-story alchemical laboratory equipped with a forge, numerous furnaces, a so-called Faule Heinz or Lazy Henry which made multiple simultaneous distillations possible, and a vast array of chemical glass ware.

Graf Wolfgang II. zu Hohenlohe-Weikersheim, Portrait by Peter Franz Tassaert in the great hall of the castle in Weikersheim Source: Wikimedia Commons

His library contained more than five hundred books, of which fifteen were about practical chemistry, for example from Georg Agricola (1494–1555), author of De re metallica, Lazarus Ecker (c. 1529–1594), a metallurgist, and books on distillation from Heironymous Brunschwig (c. 1450–c. 1512), thirty-three about alchemy including books from Pseudo-Geber (late 13th early 14th centuries), Ramon Llull (c.1232–1316), Berhard von Trevesian (14th century), and Heinrich Khunrath (c. 1560–1605), sixty-nine books by Paracelsus, and twelve about chemiatria including works by Leonhard Thurneysser (1531–1596), Alexander von Suchten (c.1520–1575) , both of them Paracelsian physicians, and Johann Isaac Hollandus (16th & 17th centuries!), a Paracelsian alchemist and author of very detailed practical chemistry books. The laboratory had a large staff of general and specialised workers but was run by a single laborant for sixteen years.

Wolfgang’s fellow alchemist and correspondent, Friedrich I, Duke of Württemberg (1557–1608) employed ten Laboranten in the year 1608 and a total of thirty-three between 1593 and 1608.

Friedrich I, Duke of Württemberg artist unknown Source: Wikimedia Commons

Friedrich had a fully equipped laboratory constructed in the old Lusthaus of a menagerie and pleasure garden. A Lusthaus was a large building erected in aristocratic parks during the Renaissance and Baroque used for fests, receptions, and social occasions.

New Lusthaus in Stuttgart (1584–1593) Engraving by Matthäus Merian 1616 Source: Wikimedia Commons

He also had laboratories in Stuttgarter Neue Spital and in the Freihof in Kirchheim unter Teckabout 25 kilometres south of Stuttgart, where he moved his court during an outbreak of the plague in 1594. Friedrich was interested in both chymiatria and the production of gold and gave a fortune out in pursuit of his alchemical aim. However, he also used his laboratories for metallurgical research.

Heinrich Khunrath (c. 1560–1605) was a Paracelsian physician, hermetic philosopher, and alchemist. In 159, he published his Amphitheatrum Sapientiae Aeternae (Amphitheatre of Eternal Wisdom) in Hamburg, which contains the engraving by Paullus van der Doort of the drawing credited to Hans Vredeman de Vries (1527–1604) entitled The First Stage of the Great Work better known as the Alchemist’s Laboratory.

Heinrich Khunrath Source. Wikimedia Commons
Amphitheatrum Sapientiae Aeternae title page Source: Wikimedia Commons
The First Stage of the Great Work better known as the Alchemist’s Laboratory. Source: Wikimedia Commons

Khunrath was one of the alchemists, who spent time on the court of the Holy Roman Emperor, Rudolf II, also serving as his personal physician.

Rudolf II portrait by  Joseph Heintz the Elder, 1594. Source: Wikimedia Commons

Rudolf ran several laboratories and attracted alchemists from over all in Europe.

Underground alchemical laboratory Prague Source

John Dee and Edward Kelly visited Rudolf in Prague during their European wanderings. Oswald Croll (c. 1563–1609) another Paracelsian physician, who visited Prague from 1597 to 1599 and then again from 1602 until his death, dedicated his Basilica Chymica (1608) to Rudolf.

Title page Basilica Chymica, Frankfurt 1629 Source: Wikimedia Commons

The Polish alchemist and physician Michael Sendivogius (1566–1623), who in his alchemical studies made important contributions to chemistry, is another who gravitated to Rudolf in Prague in 1593.

19th century representation of the alchemist Michael Sendivogius painted by Jan Matejko Art Museum  Łódź via Wikimedia Commons

His De Lapide Philosophorum Tractatus duodecim e naturae fonte et manuali experientia depromti also known as Novum Lumen Chymicum (New Chemical Light) was published simultaneously in Prague and Frankfurt in 1604 and was dedicated to Rudolf.

Michael Sendivogius Novum Lumen Chymicum 

The German alchemist and physician Michael Maier (1568–1622), author of numerous hermetic texts, served as Rudolf’s court physician beginning in 1609. 

Engraving by Matthäus Merian of Michael Maier on the 12th page of Symbola avreae mensae dvodecim nationvm Source: Wikimedia Commons

Along with Rudolf’s Prague the other major German centre for Paracelsian alchemical research was the landgrave’s court in Kassel. Under Landgrave Wilhelm IV (1532–1592), the court in Kassel was a major centre for astronomical research. His son Moritz (1572–1632) turned his attention to the Paracelsian chymiatria, establishing a laboratory at his court.

Landgrave Moritz engraving by Matthäus Merian from Theatrum Europaeum Source: Wikimedia Commons

Like Rudolf, Moritz employed a number of alchemical practitioners. Hermann Wolf (c. 1565­ 1620), who obtained his MD at the University of Marburg in 1585 and was appointed as professor for medicine there in 1587, served as Moritz’s personal physician from 1597. Another of Moritz’s personal physicians was Jacob Mosanus (1564–1616, who obtained his doctorate in medicine in Köln in 1591. A Paracelsian, he initially practiced in London but came into conflict with the English authorities. He moved to the court in Kassel in 1599. He functioned as Moritz’s alchemical diplomat, building connection to other alchemists throughout Europe. Another of the Kasseler alchemists was Johannes Daniel Mylius (1585–after 1628). When he studied medicine is not known but from 1612 in Gießen he, as a chymiatriae studiosus, carried out chemical experiments with the support and permission of the landgrave. In 1613/14 and 1616 he had a stipend for medicine on the University of Marburg. He was definitely at Moritz’s court in Kassel in 1622/23 and carried out a series of alchemical experiment there for him. How long he remained in Kassel is not known. He published a three volume Opus medico-chymicum in 1618 that was largely copied from Libavius’ Alchemia (see below)

Astrological symbol from Opus medico-chymicum Source: Wikimedia Commons

The most important of Moritz’s alchemist was Johannes Hartmann (1568–1631), Mylius’ brother-in-law.

Johannes Hartmann engraving by Wilhelm Scheffer Source: Wikimedia Commons

Hartmann originally studied mathematics at various Germany universities and was initially employed as court mathematicus in Kassel in 1591. In the following year he was appoint professor for mathematics at the University of Marburg by Moritz’s father, Wilhelm. In the 1590s, together with Wolf and Mosanus he began to study alchemy and medicine in the landgraves’ laboratory. In 1609, Moritz appointed Hartmann head of the newly founded Collegium Chymicum on the University of Marburg and professor of chymetria. Hartmann established a laboratory at the university and held lecture courses on laboratory practice. 

Collected works of Johannes Hartmann Source

The four German chymetria laboratory centres that I have sketched were by no means isolated. They were interconnected with each other both by correspondence and personal visits, as well as with other Paracelsian alchemists all over Europe. Both Croll and Maier although primarily associated with Rudolf in Prague spent time with Moritz in Kassel.

I now turn to Denmark, which in some senses was an extension of Germany. Denmark was Lutheran Protestant, German was spoken at the Danish court and many young Danes studied at German universities. Peder Sørensen (1542–1602), better known as Petrus Severinus, was one of the leading proponents of Paracelsian iatromedicine in Europe. It is not known where Severinus acquired his medical qualifications. In 1571, he became personal physician to King Frederick II until his death in 1588 and retained his position under Christian IV. In 1571, he published his Idea medicinæ philosophicæ, which was basically a simplified and clear presentation of the iatromedical theories of Paracelsus and was highly influential. 

Source

Severinus moved in the same social circles as Tycho Brahe (1546–1601) and the two were friends and colleagues. Severinus’ medical theories had a strong influence on the astronomer and Tycho also became an advocate and practitioner of Paracelsian alchemical medicine.

Portrait of Tycho Brahe at age 50, c. 1596, artist unknown Source: Wikimedia Commons

When Tycho began to construct his Uraniborg on the island of Hven in 1576, he envisaged it as temple dedicated to the muses of arts and sciences. The finished complex was not just a simple observatory but a research institute with two of the most advanced observatories in Europe, a papermill, a printing works and in the basement an alchemical laboratory with sixteen furnaces for conduction distillations and other chemical experiments.

An illustration of Uraniborg. The Tycho Brahe Museum Alchemical laboratory on the left at the bottom

Tycho took his medical research very seriously developing medicines with which he treated colleagues and his family.

In the south of Germany Andreas Libavius (c. 1550–1616) took the opposite path to Severinus, he totally rejected the philosophies of Paracelsus, which he regarded as mystical rubbish, whilst at the same time embracing chymetria. Having received his MA in 1581, somewhat late in life in 1588, he began to study medicine at the University of Basel. In 1591, he was appointed city physician in Rothenburg ob der Taube, later being appointed superintendent of schools. 

Andreas Libavius artist unknown Source: Wikimedia Commons

In 1597, Libavius published his Alchemia, an alchemical textbook, a rarity in a discipline that lived from secrecy. It was written in four sections: what to have in a laboratory, chemical procedures, chemical analysis, and transmutation. Although, Libavius believed in transmutation he firmly rejected the concept of an elixir of life. In the laboratory section of his Alchemia, he contrasted Tycho’s laboratory on Hven, which, being Paracelsian, he viewed as defective with his own vision of an ideal alchemical laboratory.

Source:Wikimedia Commons

Roughly contemporaneous with Libavius, the German physician and alchemist Daniel Sennert (1572­–1637), who played a significant role in the propagation of atomic theory in chemistry, introduced practical laboratory research into his work in the medical faculty of the University of Wittenberg. Sennert represents the beginning of the transition of the laboratory away from the courts of the rulers and aristocrats into the medical faculties of the universities. 

Portrait of Daniel Sennert engraved by Matthäus Merian Source: Wikimedia Commons

During the seventeenth century the medical, alchemical laboratory gradually evolved into a chemical laboratory, whilst remaining a part of the university medical faculty, a transmutation[1] that was largely complete by the early eighteenth century. Herman Boerhaave (1668 – 1738), regarded as one of the founders of modern chemistry in the eighteenth century, his Elementa Chemiae (1732) was one of the earliest chemistry textbooks, was professor of medicine at Leiden University. A generation earlier, Robert Boyle (1627–1691), who ran his own private laboratory, and whose The Sceptical Chymist (1661) was a transitional text between alchemy and chemistry, was still a practicing alchemist, although he rejected the theories of Paracelsus.  


[1] Pun intended

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History of science is global history

The simple statement that the history of science is global history is for me and, I assume, for every reasonably well-informed historian of science a rather trivial truism. So, I feel that James Poskett and the publishers Viking are presenting something of a strawman with the sensational claims for Poskett’s new book, HorizonsA Global History of Science[1]; claims that are made prominently by a series of pop science celebrities on the cover of the book. 

“Hugely Important,” Jim al-Khalili, really? 

“Revolutionary and revelatory,” Alice Roberts what’s so revolutionary about it?  

“This treasure trove of a book puts the case persuasively and compellingly that modern science did not develop solely in Europe,” Jim al-Khalili, I don’t know any sane historian of science, who would claim it did.

“Horizons is a remarkable book that challenges almost everything we know about science in the West. [Poskett brings to light an extraordinary array of material to change our thinking on virtually every great scientific breakthrough in the last 500 years… An explosive book that truly broadens our global scientific horizons, past and present.”] Jerry Brotton (The bit in square brackets is on the publisher’s website not on the book cover) I find this particularly fascinating as Brotton’s own The RenaissanceA Very Short Introduction (OUP, 2006) very much emphasises what is purportedly the main thesis of Horizons that science, in Brotton’s case the Renaissance, is not a purely Western or European phenomenon.

On June 22, Canadian historian Ted McCormick tweeted the following:

It’s not unusual for popular history to present as radical what has been scholarly consensus for a generation. If this bridges the gap between scholarship and public perception, then it is understandable. But what happens when the authors who do this are scholars who know better?

This is exactly what we have with Poskett’s book, he attempts to present in a popular format the actually stand amongst historian of science on the development of science over the last approximately five hundred years. I know Viking are only trying to drum up sales for the book, but I personally find it wrong that they use misleading hyperbole to do so. 

Having complained about the publisher’s pitch, let’s take a look at what Poskett is actually trying to sell to his readers and how he goes about doing so. Central to his message is that claims that science is a European invention/discovery[2] are false and that it is actually a global phenomenon. To back up his stand that such claims exist he reproduces a series of rather dated quotes making that claim. I would contend that very, very few historians of science actually believe that claim nowadays. He also proposes, what he sees as a new approach to the history of science of the last five hundred years, in that he divides the period into four epochs or eras, in which he sees science external factors during each era as the defining or driving force behind the scientific development in that era. Each is split into two central themes: Part One: Scientific Revolution, c. 1450–1700 1. New Worlds 2. Heaven and Earth, Part Two: Empire and Enlightenment, c. 1650–1800 3. Newton’s Slaves 4. Economy of Nature, Part Three:  Capitalism and Conflict, c. 1790–­1914 5. Struggle for Existence 6. Industrial Experiments, Part Four: Ideology and Aftermath, c. 1914–200 7. Faster Than Light 8. Genetic States.

I must sadly report that Part One, the area in which I claim a modicum of knowledge, is as appears recently oft to be the case strewn with factual errors and misleading statements and would have benefited from some basic fact checking.

New Worlds starts with a description of the palace of Emperor Moctezuma II and presents right away the first misleading claim. Poskett write:

Each morning he would take a walk around the royal botanical garden. Roses and vanilla flowers lined the paths, whilst hundreds of Aztec gardeners tended to rows of medicinal plants. Built in 1467, this Aztec botanical garden predated European examples by almost a century.[3]

Here Poskett is taking the university botanical gardens as his measure, the first of which was establish in Pisa in 1544, that is 77 years after Moctezuma’s Garden. However, there were herbal gardens, on which the university botanical gardens were modelled, in the European monasteries dating back to at least the ninth century. Matthaeus Silvaticus (c.1280–c. 1342) created a botanical garden at Salerno in 1334. Pope Nicholas V established a botanical garden in the Vatican in 1544. 

This is not as trivial as it might a first appear, as Poskett uses the discovery of South America to make a much bigger claim. First, he sets up a cardboard cut out image of the medieval university in the fifteenth century, he writes:

Surprisingly as it may sound today, the idea of making observations or preforming experiments was largely unknown to medieval thinkers. Instead, students at medieval universities in Europe spent their time reading, reciting, and discussing the works of Greek and Roman authors. This was a tradition known as scholasticism. Commonly read texts included Aristotle’s Physics, written in the fourth century BCE, and Pliny the Elder’s Natural History, written in the first century CE. The same approach was common to medicine. Studying medicine at medieval university in Europe involved almost no contact with actual human bodies. There was certainly no dissections or experiments on the working of particular organs. Instead, medieval medical students read and recited the works of the ancient Greek physician Galen. Why, then, sometime between 1500 and 1700, did European scholars turn away from investigating the natural world for themselves?[4]

His answer:

The answer has a lot to do with colonization of the New World alongside the accompanying appropriation of Aztec and Aztec and Inca knowledge, something that traditional histories of science fail to account for.[5]

Addressing European, medieval, medical education first, the practical turn to dissection began in the fourteenth century and by 1400 public dissections were part of the curriculum of nearly all European universities. The introduction of a practical materia medica education on a practical basis began towards the end of the fifteenth century. Both of these practical changes to an empirical approach to teaching medicine at the medieval university well before any possible influence from the New World. In general, the turn to empiricism in the European Renaissance took place before any such influence, which is not to say that that process was not accelerated by the discovery of a whole New World not covered by the authors of antiquity. However, it was not triggered by it, as Poskett would have us believe. 

Poskett’s next example to bolster his thesis is quite frankly bizarre. He tells the story of José de Acosta (c. 1539–1600), the Jesuit missionary who travelled and worked in South America and published his account of what he experienced, Natural and Moral History of the Indies in 1590. Poskett tells us: 

The young priest was anxious about the journey, not least because of what ancient authorities said about the equator. According to Aristotle, the world was divided into three climatic zones. The north and south poles were characterized by extreme cold and known as the ‘frigid zone’. Around the equator was the ‘torrid zone’, a region of burning dry heat. Finally, between the two extremes, at around the same latitudes as Europe, was the ‘temperate zone’. Crucially, Aristotle argued that life, particularly human life, could only be sustained in the ‘temperate zone’. Everywhere else was either too hot nor too cold.

Poskett pp. 17-18

Poskett goes on to quote Acosta:

I must confess I laughed and jeered at Aristotle’s meteorological theories and his philosophy, seeing that in the very place where, according to his rules, everything must be burning and on fire, I and all my companions were cold.

Poskett p. 18

Instead of commenting on Acosta’s ignorance or naivety, Aristotle’s myth of the ‘torrid zone’ had been busted decades earlier, at the very latest when Bartolomeu Dias (c. 1450–1500) had rounded the southern tip of Africa fifty-two years before Acosta was born and eight-two year before he travelled to Peru, Poskett sees this as some sort of great anti-Aristotelian revelation. He writes:

This was certainly a blow to classical authority. If Aristotle had been mistaken about the climate zones, what else might he have been wrong about?

Poskett p.18

This is all part of Poskett’s fake narrative that the breakdown of the scholastic system was first provoked by the contact with the new world. We have Poskett making this claim directly:

It was this commercial attitude towards the New World that really transformed the study of natural history. Merchants and doctors tended to place much greater emphasis on collecting and experimentation over classical authority.[6]

This transformation had begun in Europe well before any scholar set foot in the New World and was well established before any reports on the natural history of the New World had become known in Europe. The discovery of the New World accelerated the process but it in no way initiated it as Poskett would have his readers believe. Poskett once again paints a totally misleading picture a few pages on:

This new approach to natural history was also reflected in the increasing use of images. Whereas ancient texts on natural history tended not to be illustrated, the new natural histories of the sixteenth and seventeenth centuries were full of drawings and engravings, many of which were hand-coloured. This was partly a reaction to the novelty of what had been discovered. How else would those in Europe know what a vanilla plant or a hummingbird looked like?

Poskett pp.29-30

Firstly, both ancient and medieval natural history texts were illustrated, I refer Mr Proskett, for example, to the lavishly illustrated Vienna Dioscorides from 512 CE. Secondly, the introduction of heavily illustrated, printed herbals began in the sixteenth century before any illustrated natural history books or manuscripts from the New World had arrived in Europe. For example, Otto Brunfels’ Herbarium vivae eicones three volumes 1530-1536 or the second edition of Hieronymus Bock’s Neu Kreütterbuch in 1546 and finally the truly lavishly illustrated De Historia Stirpium Commentarii by Leonhard Fuchs published in 1542. The later inclusion of illustrations plants and animals from the New World in such books was the continuation of an already established tradition. 

Poskett moves on from natural history to cartography and produced what I can only call a train wreck. He tells us:

The basic problem, which was now more pressing [following the discovery of the New World], stemmed from the fact that the world is round, but a map is flat. What then was the best way to represent a three-dimensional space on a two-dimensional plane? Ptolemy had used what is known as a ‘conic’ projection, in which the world is divided into arcs radiating out from the north pole, rather like a fan. This worked well for depicting one hemisphere, but not both. It also made it difficult for navigators to follow compass bearings, as the lines spread outwards the further one got from the north pole. In the sixteenth century, European cartographers started experimenting with new projections. In 1569, the Flemish cartographer Gerardus Mercator produced an influential map he titled ‘New and More Complete Representation of the Terrestrial Globe Properly Adapted for Use in Navigation’. Mercator effectively stretched the earth at the poles and shrunk it in the middle. This allowed him to produce a map of the world in which the lines of latitude are always at right angles to one another. This was particularly useful for sailors, as it allowed them to follow compass bearings as straight lines.

Poskett p. 39

Where to begin? First off, the discovery of the New World is almost contemporaneous with the development of the printed terrestrial globe, Waldseemüller 1507 and more significantly Johannes Schöner 1515. So, it became fairly common in the sixteenth century to represent the three-dimensional world three-dimensionally as a globe. In fact, Mercator, the only Early Modern cartographer mentioned here, was in his time the premium globe maker in Europe. Secondly, in the fifteenth and sixteenth centuries mariners did not even attempt to use a Ptolemaic projection on the marine charts, instead they used portulan charts–which first emerged in the Mediterranean in the fourteenth century–to navigate in the Atlantic, and which used an equiangular or plane chart projection that ignores the curvature of the earth. Thirdly between the re-emergence of Ptolemy’s Geographia in 1406 and Mercator’s world map of 1569, Johannes Werner published Johannes Stabius’ cordiform projection in 1514, which can be used to depict two hemispheres and in fact Mercator used a pair of cordiform maps to do just that in his world map from 1538. In 1508, Francesco Rosselli published his oval projection, which can be used to display two hemispheres and was used by Abraham Ortelius for his world map from 1564. Fourthly, stereographic projection, known at least since the second century CE and used in astrolabes, can be used in pairs to depict two hemispheres, as was demonstrated by Mercator’s son Rumold in his version of his father’s world map in 1587. Fifthly, the Mercator projection if based on the equator, as it normally is, does not shrink the earth in the middle. Lastly, far from being influential, Mercator’s ‘New and More Complete Representation of the Terrestrial Globe Properly Adapted for Use in Navigation’, even in the improved version of Edward Wright from 1599 had very little influence on practical navigation in the first century after it first was published. 

After this abuse of the history of cartography Poskett introduces something, which is actually very interesting. He describes how the Spanish crown went about creating a map of their newly won territories in the New World. The authorities sent out questionnaires to each province asking the local governors or mayors to describe their province. Poskett notes quite correctly that a lot of the information gathered by this method came from the indigenous population. However, he once again displays his ignorance of the history of European cartography. He writes:

A questionnaire might seem like an obvious way to collect geographical information, but in the sixteenth century this idea was entirely novel. It represented a new way of doing geography, one that – like science more generally in this period – relied less and less on ancient Greek and Roman authority.

Poskett p. 41

It would appear that Poskett has never heard of Sebastian Münster and his Cosmographia, published in 1544, probably the biggest selling book of the sixteenth century. An atlas of the entire world it was compiled by Münster from the contributions from over one hundred scholars from all over Europe, who provided maps and texts on various topics for inclusion in what was effectively an encyclopaedia. Münster, who was not a political authority did not send out a questionnaire but appealed for contributions both in publications and with personal letters. Whilst not exactly the same, the methodology is very similar to that used later in 1577 by the Spanish authorities. 

In his conclusion to the section on the New World Poskett repeats his misleading summation of the development of science in the sixteenth century:

Prior to the sixteenth century, European scholars relied almost exclusively on ancient Greek and Roman authorities. For natural history they read Pliny for geography they read Ptolemy. However, following the colonization of the Americas, a new generation of thinkers started to place a greater emphasis on experience as the main source of scientific knowledge. They conducted experiments, collected specimens, and organised geographical surveys. This might seem an obvious way to do science to us today, but at the time it was a revelation. This new emphasis on experience was in part a response to the fact that the Americas were completely unknown to the ancients.

Poskett p. 44

Poskett’s claim simply ignores the fact that the turn to empirical science had already begun in the latter part of the fifteenth century and by the time Europeans began to investigate the Americas was well established, those investigators carrying the new methods with them rather than developing them in situ. 

Following on from the New World, Poskett takes us into the age of Renaissance astronomy serving up a well worn and well know story of non-European contributions to the Early Modern history of the discipline which has been well represented in basic texts for decades. Nothing ‘revolutionary and revelatory’ here, to quote Alice Roberts. However, despite the fact that everything he in presenting in this section is well documented he still manages to include some errors. To start with he attributes all of the mechanics of Ptolemy’s geocentric astronomy–deferent, eccentric, epicycle, equant–to Ptolemy, whereas in fact they were largely developed by other astronomers–Hipparchus, Apollonius–and merely taken over by Ptolemy.  

Next up we get the so-called twelfth century “scientific Renaissance” dealt with in one paragraph. Poskett tells us the Gerard of Cremona translated Ptolemy from Arabic into Latin in 1175, completely ignoring the fact that it was translated from Greek into Latin in Sicily at around the same time. This is a lead into the Humanist Renaissance, which Poskett presents with the totally outdated thesis that it was the result of the fall of Constantinople, which he rather confusingly calls Istanbul, in 1453, evoking images of Christians fleeing across the Adriatic with armfuls of books; the Humanist Renaissance had been in full swing for about a century by that point. 

Following the introduction of Georg of Trebizond and his translation of the Almagest from Greek, not the first as already noted above as Poskett seems to imply, up next is a very mangled account of the connections between Bessarion, Regiomontanus, and Peuerbach and Bessarion’s request that Peuerbach produce a new translation of the Almagest from the Greek because of the deficiencies in Trebizond’s translation. Poskett completely misses the fact that Peuerbach couldn’t read Greek and the Epitome, the Peuerbach-Regiomontanus Almagest, started as a compendium of his extensive knowledge of the existing Latin translations. Poskett then sends Regiomontanus off the Italy for ten years collecting manuscripts to improve his translation. In fact, Regiomontanus only spent four years in Italy in the service of Bessarion collecting manuscripts for Bessarion’s library, whilst also making copies for himself, and learning Greek to finish the Epitome.

Poskett correctly points out that the Epitome was an improved, modernised version of the Almagest drawing on Greek, Latin and Arabic sources. Poskett now claims that Regiomontanus introduced an innovation borrowed from the Islamic astronomer, Ali Qushji, that deferent and epicycles could be replaced by the eccentric. Poskett supports this argument by the fact that Regiomontanus uses Ali Qushji diagram to illustrate this possibility. The argument is not original to Poskett but is taken from the work of historian of astronomy, F. Jamil Ragip. Like Ragip, Poskett now argues thus:

In short, Ali Qushji argued that the motion of all the planets could be modelled simply by imagining that the centre of their orbits was at a point other than the Earth. Neither he nor Regiomontanus went as far as to suggest this point might in fact be the Sun. By dispensing with Ptolemy’s notion of the epicycle, Ali Qushji opened the door for a much more radical version of the structure of the cosmos.[7]

This is Ragip theory of what motivated Copernicus to adopt a heliocentric model of the cosmos. The question of Copernicus’s motivation remains open and there are numerous theories. This theory, as presented, however, has several problems. That the planetary models can be presented either with the deferent-epicycle model or the eccentric model goes back to Apollonius and is actually included in the Almagest by Ptolemy as Apollonius’ theorem (Almagest, Book XII, first two paragraphs), so this is neither an innovation from Ali Qushji nor from Regiomontanus. In Copernicus’ work the Sun is not actually at the centre of the planetary orbits but slightly offset, as has been pointed out his system is not actually heliocentric but more accurately heliostatic. Lastly, Copernicus in his heliostatic system continues to use the deferent-epicycle model to describe planetary orbits.

Poskett is presenting Ragip’s disputed theory to bolster his presentation of Copernicus’ dependency on Arabic sources, somewhat unnecessary as no historian of astronomy would dispute that dependency. Poskett continues along this line, when introducing Copernicus and De revolutionibus. After a highly inaccurate half paragraph biography of Copernicus–for example he has the good Nicolaus appointed canon of Frombork Cathedral after he had finished his studies in Italy, whereas he was actually appointed before he began his studies, he introduces us to De revolutionibus. He emphasis the wide range of international sources on which the book is based, and then presents Ragip’s high speculative hypothesis, for which there is very little supporting evidence, as fact:

Copernicus suggested that all these problems could be solved if we imagined the Sun was at the centre of the universe. In making this move he was directly inspired by the Epitome of the Almagest. Regiomontanus, drawing on Ali Qushji, had shown it was possible to imagine that the centre of all the orbits of the planets was somewhere other than the Earth. Copernicus took the final step, arguing that that this point was in fact the Sun.[8]

We simply do not know what inspired Copernicus to adopt a heliocentric model and to present a speculative hypothesis, one of a number, as the factual answer to this problem in a popular book is in my opinion irresponsible and not something a historian should be doing. 

Poskett now follows on with the next misleading statement. Having, a couple of pages earlier, introduced the Persian astronomer Nasir al-Din al-Tusi and the so-called Tusi couple, a mathematical device that allows linear motion to be reproduced geometrically with circles, Poskett now turns to Copernicus’ use of the Tusi couple. He writes:

The diagram in On the Revolution of the Heavenly Spheres shows the Tusi couple in action. Copernicus used this idea to solve exactly the same problem as al-Tusi. He wanted a way to generate an oscillating circular movement without sacrificing a commitment to uniform circular motion. He used the Tusi couple to model planetary motion around the Sun rather than the Earth. This mathematical tool, invented in thirteenth-century Persia, found its way into the most important work in the history of European astronomy. Without it, Copernicus would not have been able to place the Sun at the centre of the universe.[9] [my emphasis]

As my alter-ego the HISTSCI_HULK would say the emphasised sentence is pure and utter bullshit!

The bizarre claims continue, Poskett writes:

The publication of On the Revolution of the Heavenly Spheres in 1543 has long been considered the starting point for the scientific revolution. However, what is less often recognised is that Nicolaus Copernicus was in fact building on a much longer Islamic tradition.[10]

When I first read the second sentence here, I had a truly WTF! moment. There was a time in the past when it was claimed that the Islamic astronomers merely conserved ancient Greek astronomy, adding nothing new to it before passing it on to the Europeans in the High Middle Ages. However, this myth was exploded long ago. All the general histories of astronomy, the histories of Early Modern and Renaissance astronomy, and the histories of Copernicus, his De revolutionibus and its reception that I have on my bookshelf emphasise quite clearly and in detail the influence that Islamic astronomy had on the development of astronomy in Europe in the Middle Ages, the Renaissance, and the Early Modern period. Either Poskett is ignorant of the true facts, which I don’t believe, or he is presenting a false picture to support his own incorrect thesis.

Having botched European Renaissance astronomy, Poskett turns his attention to the Ottoman Empire and the Istanbul observatory of Taqi al-Din with a couple of pages that are OK, but he does indulge in a bit of hype when talking about al-Din’s use of a clock in an observatory, whilst quietly ignoring Jost Bürgi’s far more advanced clocks used in the observatories of Wilhelm IV of Hessen-Kassel and Tycho Brahe contemporaneously. 

This is followed by a brief section on astronomy in North Africa in the same period, which is basically an extension of Islamic astronomy with a bit of local colouration. Travelling around the globe we land in China and, of course, the Jesuits. Nothing really to complain about here but Poskett does allow himself another clangour on the subject of calendar reform. Having correctly discussed the Chinese obsession with calendar reform and the Jesuit missionaries’ involvement in it in the seventeenth century Poskett add an aside about the Gregorian Calendar reform in Europe. He writes:

The problem was not unique to China. In 1582, Pope Gregory XIII had asked the Jesuits to help reform the Christian Calendar back in Europe. As both leading astronomers and Catholic servants, the Jesuits proved an ideal group to undertake such a task. Christoph Clavius, Ricci’s tutor at the Roman College [Ricci had featured prominently in the section on the Jesuits in China], led the reforms. He integrated the latest mathematical methods alongside data taken from Copernicus’s astronomical tables. The result was the Gregorian calendar, still in use today throughout many parts of the world.[11]

I have no idea what source Poskett used for this brief account, but he has managed to get almost everything wrong that one can get wrong. The process of calendar reform didn’t start in 1582, that’s the year in which the finished calendar reform was announced in the papal bull Inter gravissimas. The whole process had begun many years before when the Vatican issued two appeals for suggestion on how to reform the Julian calendar which was now ten days out of sync with the solar year. Eventually, the suggestion of the physician Luigi Lilio was adopted for consideration and a committee was set up to do just that. We don’t actually know how long the committee deliberated but it was at least ten years. We also don’t know, who sat in that committee over those years; we only know the nine members who signed the final report. Clavius was not the leader of the reform, in fact he was the least important member of the committee, the leader being naturally a cardinal. You can read all of the details in this earlier blog post. At the time there were not a lot of Jesuit astronomers, that development came later and data from Copernicus’ astronomical tables were not used for the reform. Just for those who don’t want to read my blog post, Clavius only became associated with the reform after the fact, when he was commissioned by the pope to defend it against its numerous detractors.  I do feel that a bit of fact checking might prevent Poskett and Viking from filling the world with false information about what is after all a major historical event. 

The section Heaven and Earth closes with an account of Jai Singh’s observatories in India in the eighteenth century, the spectacular instruments of the Jantar Mantar observatory in Jaipur still stand today. 

Readers of this review need not worry that I’m going to go on at such length about the other three quarters of Poskett’s book. I’m not for two reasons. Firstly, he appears to be on territory where he knows his way around better than in the Early Modern period, which was dealt with in the first quarter Secondly, my knowledge of the periods and sciences he now deals with are severely limited so I might not necessarily have seen any errors. 

There are however a couple more train wrecks before we reach the end and the biggest one of all comes at the beginning of the second quarter in the section titled Newton’s Slaves. I’ll start with a series of partial quote, then analyse them:

(a) Where did Newton get this idea [theory of gravity] from? Contrary to popular belief, Newton did not make his great discovery after an apple fell on his head. Instead in a key passage in the Principia, Newton cited the experiments of a French astronomer named Jean Richer. In 1672, Richer had travelled to the French colony of Cayenne in South America. The voyage was sponsored by King Louis XIV through the Royal Academy of Science in Paris.

[…]

(b) Once in Cayenne, Richer made a series of astronomical observations, focusing on the movements of the planets and cataloguing stars close to the equator.

[…]

(c) Whilst in Cayenne, Richer also undertook a number of experiments with a pendulum clock.

[…]

(d) In particular, a pendulum with a length of just one metre makes a complete swing, left to right, every second. This became known as a ‘seconds pendulum’…

[…]

(e) In Cayenne, Richer noticed that his carefully calibrated pendulum was running slow, taking longer than a second to complete each swing.

[…]

(f) [On a second voyage] Richer found that, on both Gorée and Guadeloupe, he needed to shorten the pendulum by about four millimetres to keep it running on time.

[…]

(g) What could explain this variation?

[…]

(h) Newton, however, quickly realised the implications the implications of what Richer had observed. Writing in the Principia, Newton argued that the force of gravity varied across the surface of the planet. 

[…]

(i) This was a radical suggestion, one which seemed to go against common sense. But Newton did the calculations and showed how his equations for the gravitational force matched exactly Richer’s results from Cayenne and Gorée. Gravity really was weaker nearer the equator.

[…]

(j) All this implied a second, even more controversial, conclusion. If gravity was variable, then the Earth could not be a perfect sphere. Instead, Newton argued, the Earth must be a ‘spheroid’, flattened at the poles rather like a pumpkin. 

[…]

(k) Today, it is easy to see the Principia as a scientific masterpiece, the validity of which nobody could deny. But at the time, Newton’s ideas were incredibly controversial.

[…]

(l) Many preferred the mechanical philosophy of the French mathematician René Descartes. Writing in his Principles of Philosophy (1644), Descartes denied the possibility of any kind of invisible force like gravity, instead arguing that force was only transferred through direct contact. Descartes also suggested that, according to his own theory of matter, the Earth should be stretched the other way, elongated like an egg rather than squashed like a pumpkin.

[…]

(m) These differences were not simply a case of national rivalry or scientific ignorance. When Newton published the Principia in 1687, his theories were in fact incomplete. Two major problems remained to be solved. First, there were the aforementioned conflicting reports of the shape of the Earth. And if Newton was wrong about the shape of the Earth, then he was wrong about gravity.[12]

To begin at the beginning: (a) The suggestion or implication that Newton got the idea of the theory of gravity from Richer’s second pendulum experiments is quite simply grotesque. The concept of a force holding the solar system together and propelling the planets in their orbits evolved throughout the seventeenth century beginning with Kepler. The inverse square law of gravity was first hypothesised by Ismaël Boulliau, although he didn’t believe it existed. Newton made his first attempt to show that the force causing an object to fall to the Earth, an apple for example, and the force that held the Moon in its orbit and prevented it shooting off at a tangent as the law of inertia required, before Richer even went to Cayenne.

(c)–(g) It is probable that Richer didn’t make the discovery of the difference in length between a second pendulum in Northern Europe and the equatorial region, this had already ben observed earlier. What he did was to carry out systematic experiments to determine the size of the difference.

(l) Descartes did not suggest, according to his own theory of matter, that the Earth was an elongated spheroid. In fact, using Descartes theories Huygens arrived at the same shape for the Earth as Newton. This suggestion was first made by Jean-Dominique Cassini and his son Jacques long after Descartes death. Their reasoning was based on the difference in the length of one degree of latitude as measured by Willebrord Snel in The Netherlands in 1615 and by Jean Picard in France in 1670. 

This is all a prelude for the main train wreck, which I will now elucidate. In the middle of the eighteenth century, to solve the dispute on the shape of the Earth, Huygens & Newton vs the Cassinis, the French Academy of Science organised two expeditions, one to Lapland and one to Peru in order to determine as accurately as possible the length of one degree of latitude at each location. Re-enter Poskett, who almost completely ignoring the Lapland expedition, now gives his account of the French expedition to Peru. He tells us:

The basic technique for conducting a survey [triangulation] of this kind had been pioneered in France in the seventeenth century. To begin the team needed to construct what was known as a ‘baseline’. This was a perfectly straight trench, only a few inches deep, but at least a couple of miles long.[13]

Triangulation was not first pioneered in France in the seventeenth century. First described in print in the sixteenth century by Gemma Frisius, it was pioneered in the sixteenth century by Mercator when he surveyed the Duchy of Lorraine, and also used by Tycho Brahe to map his island of Hven. To determine the length of one degree of latitude it was pioneered, as already stated, by Willebrord Snell. However, although wrong this is not what most disturbed me about this quote. One of my major interests is the history of triangulation and its use in surveying the Earth and determining its shape and I have never come across any reference to digging a trench to lay out a baseline. Clearing the undergrowth and levelling the surface, yes, but a trench? Uncertain, I consulted the book that Poskett references for this section of his book, Larrie D Ferreiro’s Measure of the EarthThe Enlightenment Expedition that Reshaped the World (Basic Books, 2011), which I have on my bookshelf. Mr Ferreiro make no mention of a baseline trench. Still uncertain and not wishing to do Poskett wrong I consulter Professor Matthew Edney, a leading expert on the history of surveying by triangulation, his answer:

This is the first I’ve heard of digging a trench for a baseline. It makes little sense. The key is to have a flat surface (flat within the tolerance dictated by the quality of the instruments being used, which wasn’t great before 1770). Natural forces (erosion) and human forces (road building) can construct a sufficiently level surface; digging a trench would only increase irregularities.[14]

The problems don’t end here, Poskett writes:

La Condamine did not build the baseline himself. The backbreaking work of digging a seven-mile trench was left to the local Peruvian Indians.[15]

This is contradicted by Ferreiro who write:

Just as the three men completed the alignment for the baseline, the rest of the expedition arrived on the scene, in time for the most difficult phase of the operation. In order to create a baseline, an absolutely straight path, seven miles long and just eighteen inches wide, had to be dug into, ripped up from, and scraped out of the landscape. For the scientists, who had been accustomed to a largely sedentary life back in Europe, this would involve eight days of back breaking labour and struggling for breath in the rarefied air. “We worked at felling trees,” Bouguer explained in his letter to Bignon, “breaking through walls and filling in ravines to align [a baseline] of more than two leagues.” They employed several Indians to help transport equipment, though Bouguer felt it necessary that someone “keep an eye on them.”[16]

Poskett includes this whole story of the Peruvian Indians not digging a non-existent baseline trench because he wants to draw a parallel between the baseline and the Nazca Lines, a group of geoglyphs made in the soil of the Nazca desert in southern Peru that were created between 500 BCE and 500 CE. He writes:

The Peruvian Indians who built the baseline must have believed that La Condamine wanted to construct his own ritual line much like the earlier Inca rulers.[17]

Also:

Intriguingly some are simply long straight lines. They carry on for miles, dead straight, crossing hills and valleys. Whilst their exact function is still unclear, many historians now believe they were used to align astronomical observations, exactly as La Condamine intended with his baseline.[18]

The Nazca lines are of course pre-Inca. The ‘many historians’ is a bit of a giveaway, which historians? Who? Even if the straight Nazca lines are astronomically aligned, they by no means serve the same function as La Condamine’s triangulation baseline, which is terrestrial not celestial.  

To be fair to Poskett, without turning the baseline into a trench and without having the Indians dig it, Ferreiro draws the same parallel but without the astronomical component: 

For their part, the Indians were also observing the scientists, but to them “all was confusion” regarding the scientists’ motives for this arduous work. The long straight baseline the had scratched out of the ground certainly resembled the sacred linear pathways that Peruvian cultures since long before the Incas, had been constructing.[19]

Poskett’s conclusion to this section, in my opinion, contains a piece of pure bullshit.

By January 1742, the results were in. La Condamine calculated that the distance between Quito and Cuenca was exactly 344,856 metres. From observations made of the stars at both ends of the survey, La Condamine also found that the difference in latitude between Quit and Cuenca was a little over three degrees. Dividing the two, La Condamine concluded that the length of a degree of latitude at the equator was 110,613 metres. This was over 1,000 metres less than the result found by the Lapland expedition, which had recently returned to Paris. The French, unwittingly relying on Indigenous Andean science [my emphasis] had discovered the true shape of the Earth. It was an ‘oblate spheroid’, squashed at the poles and bulging at the equator. Newton was right.[20]

Sorry, but just because Poskett thinks that a triangulation survey baseline looks like an ancient, straight line, Peruvian geoglyph doesn’t in anyway make the French triangulation survey in anyway dependent on Indigenous Andean science. As I said, pure bullshit. 

The next section deals with the reliance of European navigators of interaction with indigenous navigators throughout the eighteenth century and is OK. This is followed by the history of eighteenth-century natural history outside of Europe and is also OK. 

At the beginning of the third quarter, we again run into a significant problem. The chapter Struggle for Existence open with the story of Étienne Geoffroy Saint-Hilaire, a natural historian, who having taken part in Napoleon’s Egypt expedition, compared mummified ancient Egyptian ibises with contemporary ones in order to detect traces of evolutions but because the time span was too short, he found nothing. His work was published in France 1818, but Poskett argues that his earliest work was published in Egyptian at the start of the century and so, “In order to understand the history of evolution, we therefore need to begin with Geoffroy and the French army in North Africa.” I’m not a historian of evolution but really? Ignoring all the claims for evolutionary thought in earlier history, Poskett completely blends out the evolutionary theories of Pierre Louis Maupertuis (1751), James Burnett, Lord Monboddo, (between 1767 and 1792) and above all Darwin’s grandfather Erasmus, who published his theory of evolution in his Zoonomia (1794–1796). So why do we need to begin with Étienne Geoffroy Saint-Hilaire?

Having dealt briefly with Charles Darwin, Poskett takes us on a tour of the contributions to evolutionary theory made in Russia, Japan, and China in the nineteenth century, whilst ignoring the European contributions. 

Up next in Industrial Experiments Poskett takes us on a tour of the contributions to the physical sciences outside of Europe in the nineteenth century. Here we have one brief WTF statement. Poskett writes:

Since the early nineteenth century, scientists had known that the magnetic field of the Earth varies across the planet. This means that the direction of the north pole (‘true north’) and the direction that the compass needle points (‘magnetic north’) are not necessarily identical, depending on where you are.[21]

Magnetic declination, to give the technical name, had been known and documented since before the seventeenth century, having been first measured accurately for Rome by Georg Hartmann in 1510, it was even known that it varies over time for a given location. Edmund Halley even mapped the magnetic declination of the Atlantic Ocean at the end of the seventeenth century in the hope that it would provide a solution to the longitude problem. 

In the final quarter we move into the twentieth century. The first half deals with modern physics up till WWII, and the second with genetic research following WWII, in each case documenting the contribution from outside of Europe. Faster than Light, the modern physics section, move through Revolutionary Russia, China, Japan, and India; here Poskett connects the individual contributions to the various revolutionary political movements in these countries. Genetic States moves from the US, setting the background, through Mexico, India, China, and Israel.  I have two minor quibbles about what is presented in these two sections.

Firstly, in both sections, instead of a chronological narrative of the science under discussion we have a series of biographical essays of the figures in the different countries who made the contribution, which, of course, also outlines their individual contributions. I have no objections to this, but something became obvious to me reading through this collection of biographies. They all have the same muster. X was born in Y, became interested in topic Z, began their studies at some comparatively local institute of higher education, and then went off to Heidelberg/Berlin/Paris/London/Cambridge/Edinburg… to study with some famous European authority, and acquire a PhD. Then off to a different European or US university to research, or teach or both, before to returning home to a professorship in their mother country. This does seem to suggest that opposed to Poskett’s central thesis of the global development of science, a central and dominant role for Europe.  

My second quibble concerns only the genetics section. One of Poskett’s central theses is that science in a given epoch is driven by an external to the science cultural, social, or political factor. For this section he claims that the external driving force was the Cold War. Reading through this section my impression was that every time he evoked the Cold War he could just have easily written ‘post Second World War’ or even ‘second half of the twentieth century’ and it would have made absolutely no difference to his narrative. In my opinion he fails to actually connect the Cold War to the scientific developments he is describing.

The book closes with a look into the future and what Poskett thinks will be the force driving science there. Not surprisingly he chooses AI and being a sceptic what all such attempts at crystal ball gazing are concerned I won’t comment here.

The book has very extensive end notes, which are largely references to a vast array of primary and mostly secondary literature, which confirms what I said at the beginning that Poskett in merely presenting in semi-popular form the current stand in the history of science of the last half millennium. There is no separate bibliography, which is a pain if you didn’t look to see something the first time it was end noted, as in subsequent notes it just becomes Smith, 2003, sending you off on an oft hopeless search for that all important first mention in the notes. There are occasional grey scale illustrations and two blocks, one of thirteen and one of sixteen, colour plates. There is also an extensive index.

So, after all the negative comments, what do I really think about James Poskett, highly praised volume. I find the concept excellent, and the intention is to be applauded. A general popular overview of the development of the sciences since the Renaissance is an important contribution to the history of science book market. Poskett’s book has much to recommend it, and I personally learnt a lot reading it. However, as a notorious history of science pedant, I cannot ignore or excuse the errors than I have outlined in my review, some of which are in my opinion far from minor. The various sections of the book should have been fact checked by other historians, expert in the topic of the section, and this has very obviously not been done. It is to be hoped that this will take place before a second edition is published. 

Would I recommend it? Perhaps surprisingly, yes. James Poskett is a good writer and there is much to be gained from reading this book but, of course, with the caveat that it also contains things that are simply wrong. 


[1] James Poskett, Horizons: A Global History of Science, Viking, 2022 

[2] Take your pick according to your personal philosophy of science.

[3] Poskett p. 11

[4] Poskett p. 16

[5] Poskett 16

[6] Poskett p. 23

[7] Poskett p. 59

[8] Poskett p. 61

[9] Poskett p. 62

[10] Poskett p. 62

[11] Poskett p. 84

[12] Poskett pp. 101-104

[13] Poskett p. 107

[14] Edney private correspondence 27.07.2022

[15] Poskett p. 108

[16] Ferreiro p. 107

[17] Poskett p. 111

[18] Poskett p. 110

[19] Ferreiro p. 107

[20] Poskett pp. 111-112

[21] Poskett p. 251

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Filed under Book Reviews, Early Scientific Publishing, History of Astronomy, History of botany, History of Cartography, History of Geodesy, History of Islamic Science, History of Navigation, Natural history, Renaissance Science

The Wizard Earl’s mathematici 

In my recent post on the Oxford mathematician and astrologer Thomas Allen, I mentioned his association with Henry Percy, 9th Earl of Northumberland, who because of his strong interest in the sciences was known as the Wizard Earl.

HENRY PERCY, 9TH EARL OF NORTHUMBERLAND (1564-1632) by Sir Anthony Van Dyck (1599-1641). The ‘Wizard Earl’ was painted posthumously as a philosopher, hung in Square Room at Petworth. This is NT owned. via Wikimedia Commons

As already explained there Percy actively supported four mathematici, or to use the English term mathematical practitioners, Thomas Harriot (c. 1560–1621), Robert Hues (1553–1632), Walter Warner (1563–1643), and Nathaniel Torporley (1564–1632). Today, I’m going to take a closer look at them.

Thomas Harriot is, of course, the most well-known of the four; I have already written a post about him in the past, so I will only brief account of the salient point here.

Portrait often claimed to be Thomas Harriot (1602), which hangs in Oriel College, Oxford. Source: Wikimedia Commons

He graduatied from Oxford in 1580 and entered the service of Sir Walter Raleigh (1552–1618) in 1583. At Raleigh’s instigation he set up a school to teach Raleigh’s marine captains the newest methods of navigation and cartography, writing a manual on mathematical navigation, which contained the correct mathematical method for the construction of the Mercator projection. This manual was never published but we can assume he used it in his teaching. He was also directly involved in Raleigh’s voyages to establish the colony of Roanoke Island.

Sir Walter Ralegh in 1588 artist unknown. Source: Wikimedia Commons

In 1590, he left Raleigh’s service and became a pensioner of Henry Percy, with a very generous pension, the title to some land in the North of England, and a house on Percy’s estate, Syon House, in Middlesex.[1] Here, Harriot lived out his years as a research scientist with no obligations.

Syon House Attributed to Robert Griffier

After Harriot, the most significant of the Wizard Earl’s mathematici was Robert Hues. Like Harriot, Hues attended St Mary’s Hall in Oxford, graduating a couple of years ahead of him in 1578. Being interested in geography and mathematics, he was one of those who studied navigation under Harriot in the school set up by Raleigh, having been introduced to Raleigh by Richard Hakluyt (1553–1616), another student of Thomas Allen and a big promoter of English colonisation of North America.  

Hakluyt depicted in stained glass in the west window of the south transept of Bristol Cathedral – Charles Eamer Kempe, c. 1905. Source: Wikimedia Commons

Hues went on to become an experienced mariner. During a trip to Newfoundland, he came to doubt the published values for magnetic declination, the difference between magnetic north and true north, which varies from place to place.

In 1586, he joined with Thomas Cavendish (1560–1592), a privateer and another graduate of the Harriot school of navigation, who set out to raid Spanish shipping and undertake a circumnavigation of the globe, leaving Plymouth with three ships on 21 July. After the usual collection of adventures, they returned to Plymouth with just one ship on 9 September 1588, as the third ever ship to complete the circumnavigation after Magellan and Drake. Like Drake, Cavendish was knighted by Queen Elizabeth for his endeavours.

Thomas Cavendish An engraving from Henry Holland’s Herōologia Anglica (1620). Animum fortuna sequatur is Latin for “May fortune follow courage.” Source: Wikimedia Commons

Hues undertook astronomical observations throughout the journey and determined the latitudes of the places they visited. In 1589, he served with the mathematicus Edward Wright (1561–1615), who like Harriot worked out the correct mathematical method for the construction of the Mercator projection, but unlike Harriot published it in his Certaine Errors in Navigation in 1599.

Source: Wikimedia Commons

In August 1591, he set out once again with Cavendish on another attempted circumnavigation, also accompanied by the navigator John Davis (c. 1550–1605), another associate of Raleigh’s, known for his attempts to discover the North-West passage and his discovery of the Falkland Islands.

Miniature engraved portrait of navigator John Davis (c. 1550-1605), detail from the title page of Samuel Purchas’s Hakluytus Posthumus or Purchas his Pilgrimes (1624). Source: Wikimedia Commons

Cavendish died on route in 1592 and Hues returned to England with Davis in 1683. On this voyage Hues continued his astronomical observations in the South Atlantic and made determinations of compass declinations at various latitudes and the equator. 

Back in England, Hues published the results of his astronomical and navigational research in his Tractatus de globis et eorum usu (Treatise on Globes and Their Use, 1594), which was dedicated to Raleigh.

The book was a guide to the use of the terrestrial and celestial globes that Emery Molyneux (died 1598) had published in 1592 or 1593.

Molyneux CEltial Globe Middle Temple Library
A terrestrial globe by Emery Molyneux (d.1598-1599) is dated 1592 and is the earliest such English globe in existence. It is weighted with sand and made from layers of paper with a surface coat of plaster engraved with elaborate cartouches, fanciful sea-monsters and other nautical decoration by the Fleming Jodocus Hondius (1563-1611). There is a wooden horizon circle and brass meridian rings.

Molyneux belong to the same circle of mariners and mathematici, counting Hues, Wright, Cavendish, Davis, Raleigh, and Francis Drake (c. 1540–1596) amongst his acquaintances. In fact, he took part in Drake’s circumnavigation 1577–1580. These were the first globes made in England apparently at the suggestion of John Davis to his patron the wealthy London merchant William Sanderson (?1548–1638), who financed the construction of Molyneux’s globes to the tune of £1,000. Sanderson had sponsored Davis’ voyages and for a time was Raleigh’s financial manager. He named his first three sons Raleigh, Cavendish, and Drake.

Molyneux’s terrestrial globe was his own work incorporating information from his mariner friends and with the assistance of Edward Wright in plotting the coast lines. The circumnavigations of Drake and Cavendish were marked on the globe in red and blue line respectively. His celestial globe was a copy of the 1571 globe of Gerard Mercator (1512–1594), which itself was based on the 1537 globe of Gemma Frisius (1508–1555), on which Mercator had served his apprenticeship as globe maker. Molyneux’s globes were engraved by Jodocus Hondius (1563–1612), who lived in London between 1584 and 1593, and who would upon his return to the Netherlands would found one of the two biggest cartographical publishing houses of the seventeenth century.

Hues’ Tractatus de globis et eorum usu was one of four publications on the use of the globes. Molyneux wrote one himself, The Globes Celestial and Terrestrial Set Forth in Plano, published by Sanderson in 1592, of which none have survived. The London public lecturer on mathematics Thomas Hood published his The Vse of Both the Globes, Celestiall and Terrestriall in 1592, and finally Thomas Blundeville (c. 1522–c. 1606) in his Exercises containing six treatises including Cosmography, Astronomy, Geography and Navigation in 1594.

Hues’ Tractatus de globis has five sections the first of which deals with a basic description of and use of Molyneux’s globes. The second is concerned with matters celestial, plants, stars, and constellations. The third describes the lands, and seas displayed on the terrestrial globe, the circumference of the earth and degrees of a great circle. Part four contains the meat of the book and explains how mariners can use the globes to determine the sun’s position, latitude, course and distance, amplitudes and azimuths, and time and declination. The final section is a treatise, inspired by Harriot’s work on rhumb lines, on the use of the nautical triangle for dead reckoning. Difference of latitude and departure (or longitude) are two legs of a right triangle, the distance travelled is the hypotenuse, and the angle between difference of latitude and distance is the course. If any two elements are known, the other two can be determined by plotting or calculation using trigonometry.

The book was a success going through numerous editions in various languages. The original in Latin in 1593, Dutch in 1597, an enlarged and corrected Latin edition in 1611, Dutch again in 1613, enlarged once again in Latin in 1617, French in 1618, another Dutch edition in 1622, Latin again in 1627, English in 1638, Latin in 1659, another English edition also in 1659, and finally the third enlarged Latin edition reprinted in 1663. There were others.

The title page of Robert Hues (1634) Tractatvs de Globis Coelesti et Terrestri eorvmqve vsv in the collection of the Biblioteca Nacional de Portugal via Wikimedia Commons

Hues continued his acquaintance with Raleigh in the 1590s and was one of the executors of Raleigh’s will. He became a servant of Thomas Grey, 15th Baron Gray de Wilton (died 1614) and when Grey was imprisoned in the Tower of London for his involvement in a Catholic plot against James I & VI in 1604, Hues was granted permission to visit and even to stay with him in the Tower. From 1605 to 1621, Northumberland was also incarcerated in the Tower because of his family’s involvement in the Gunpowder Plot. Following Grey’s death Hues transferred his Tower visits to Northumberland, who paid him a yearly pension of £40 until his death in 1632.

He withdrew to Oxford University and tutored Henry Percy’s oldest son Algernon, the future 10th Earl of Northumberland, in mathematics when he matriculated at Christ’s Church in 1617.

Algernon Percy, 10th Earl of Northumberland, as Lord High Admiral of England, by Anthony van Dyck. Source: Wikimedia Commons

In 1622-23 he would also tutor the younger son Henry.

Oil painting on canvas, Henry Percy, Baron Percy of Alnwick (1605-1659) by Anthony Van Dyck Source: Wikimedia Commons

During this period, he probably visited both Petworth and Syon, Northumberland’s southern estates. He in known to have had discussion with Walter Warner on reflection. He remained in Oxford discussing mathematics with like minded fellows until his death.

Compared to the nautical adventures of Harriot and Hues, both Warner and Torporley led quiet lives. Walter Warner was born in Leicestershire and educated at Merton College Oxford graduating BA in 1579, the year between Hues and Harriot. According to John Aubrey in his Brief Lives, Warner was born with only one hand. It is almost certain that Hues, Warner, and Harriot met each other attending the mathematics lectures of Thomas Allen at Oxford. Originally a protégé of Robert Dudley, 1st Earl of Leicester, (1532–1588), he entered Northumberland’s household as a gentleman servitor in 1590 and became a pensioner in 1617. Although a servant, Warner dined with the family and was treated as a companion by the Earl. In Syon house, he was responsible for purchasing the Earl’s books, Northumberland had one of the largest libraries in England, and scientific instruments. He accompanied the Earl on his military mission to the Netherlands in 1600-01, acting as his confidential courier.       

Like Harriot, Warner was a true polymath, researching and writing on a very wide range of topics–logic, psychology, animal locomotion, atomism, time and space, the nature of heat and light, bullion and exchange, hydrostatics, chemistry, and the circulation of the blood, which he claimed to have discovered before William Harvey. However, like Harriot he published almost nothing, although, like Harriot, he was well-known in scholarly circles. Some of his work on optics was published posthumously by Marin Mersenne (1588–1648) in his Universæ geometriæ (1646).

Source: Google Books

It seems that following Harriot’s death Warner left Syon house, living in Charing Cross and at Cranbourne Lodge in Windsor the home of Sir Thomas Aylesbury, 1st Baronet (!576–1657), who had also been a student of Thomas Allen, and who had served both as Surveyor of the Navy and Master of the Mint. Aylesbury became Warner’s patron.

This painting by William Dobson probably represents Sir Thomas Aylesbury, 1st Baronet. 
Source: Wikimedia Commons

Aylesbury had inherited Harriot’s papers and encouraged Warner in the work of editing them for publication (of which more later), together with the young mathematician John Pell (1611–1685), asking Northumberland for financial assistance in the endeavour.

Northumberland died in 1632 and Algernon Percy the 10th Earl discontinued Warner’s pension. In 1635, Warner tried to win the patronage of Sir Charles Cavendish and his brother William Cavendish, enthusiastic supporters of the new scientific developments, in particular Keplerian astronomy. Charles Cavendish’s wife was the notorious female philosopher, Margaret Cavendish. Warner sent Cavendish a tract on the construction of telescopes and lenses for which he was rewarded with £20. However, Thomas Hobbes, another member of the Cavendish circle, managed to get Warner expelled from Cavendish’s patronage. Despite Aylesbury’s support Warner died in poverty. 

Nathaniel Torporley was born in Shropshire of unknow parentage and educated at Shrewsbury Grammar Scholl before matriculating at Christ Church Oxford in 1581. He graduated BA in 1584 and then travelled to France where he served as amanuensis to the French mathematician François Viète (1540–1603).

François Viète Source: Wikimedia Commons

He is thought to have supplied Harriot with a copy of Viète’s Isagoge, making Harriot the first English mathematician to have read it.

Source

Torporley returned to Oxford in 1587 or 1588 and graduated MA from Brasenose College in 1591. 

He entered holy orders and was appointed rector of Salwarpe in Worcestershire, a living he retained until 1622. From 1611 he was also rector of Liddington in Wiltshire. His interest in mathematics, astronomy and astrology attracted the attention of Northumberland and he probably received a pension from him but there is only evidence of one payment in 1627. He was investigated in 1605, shortly before the Gunpowder Plot for having cast a nativity of the king. At some point he published a pamphlet, under the name Poulterey, attacking Viète. In 1632, he died at Sion College, on London Wall and in a will written in the year of his death he left all of his books, papers, and scientific instrument to the Sion College library.

Although his papers in the Sion College library contain several unpublished mathematical texts, still extant today, he only published one book his Diclides Coelometricae; seu Valuae Astronomicae universales, omnia artis totius munera Psephophoretica in sat modicis Finibus Duarum Tabularum methodo Nova, generali et facillima continentes, (containing a preface, Directionis accuratae consummata Doctrina, Astrologis hactenus plurimum desiderata and the Tabula praemissilis ad Declinationes et coeli meditations) in London in 1602.

Source

This is a book on how to calculate astrological directions, a method for determining the time of major incidents in the life of a subject including their point of death, which was a very popular astrological method in the Renaissance. This requires spherical trigonometry, and the book is interesting for containing new simplified methods of solving right spherical triangles of any sort, methods that are normally attributed to John Napier (1550–1617) in a later publication. The book is, however, extremely cryptic and obscure, and almost unreadable. Despite this the surviving copies would suggest that it was widely distributed in Europe.

Our three mathematici came together as executors of Harriot’s will. Hues was charged with pricing Harriot’s books and other items for sale to the Bodleian Library. Hues and Torporley were charged with assisting Warner with the publication of Harriot’s mathematical manuscripts, a task that the three of them managed to bungle. In the end they only managed to publish one single book, Harriot’s algebra Artis Analyticae Praxis in 1631 and this text they castrated.

Source

Harriot’s manuscript was the most advanced text on the topic written at the time and included full solutions of algebraic equations including negative and complex solutions. Either Warner et al did not understand Harriot’s work or they got cold feet in the face of his revolutionary new methods, whichever, they removed all of the innovative parts of the book making it basically irrelevant and depriving Harriot of the glory that was due to him.

For myself the main lesson to be learned from taking a closer look at the lives of this group of mathematici is that it shows that those interested in mathematics, astronomy, cartography, and navigation in England the late sixteenth and early seventeenth centuries were intricately linked in a complex network of relationships, which contains hubs one of which was initially Harriot and Raleigh and then later Harriot and Northumberland. 


[1] For those who don’t know, Middlesex was a small English county bordering London, in the South-West corner of Essex, squeezed between Hertfordshire to the north and Surry in the South, which now no longer exists having been largely absorbed into Greater London. 

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Filed under Early Scientific Publishing, History of Astrology, History of Astronomy, History of Cartography, History of Mathematics, History of Navigation, History of Optics, History of science, Renaissance Science

Renaissance science – XXXX

As we have seen in previous episodes, Ulisse Aldrovandi (1522–1605) was one of the leading natural historians of the sixteenth century. The first ever professor for natural history at the University of Bologna.

Ulisse Aldrovandi (1522 – 1605). attributed to Ludovico Carracci. Source: Wikimedia Commons

He created the university’s botanical garden, one of the oldest still in existence. Collected about 4760 specimens in his herbarium on 4117 sheets in sixteen volumes, which are still preserved in the university and wrote extensively on almost all aspects of natural history, although much of his writing remained unpublished at his death. However, despite all these other achievements in the discipline of natural history, visitors to Bologna during his lifetime came to see his teatro di natura (theatre of nature), also known as his natural historical collection or museum.  This was housed in the palatial country villa that he built with the money he received from the dowry of Francesca Fontana, his wife, when he married her. His theatre contained some 18,000 specimens of the diversità di cose naturali (diverse objects of nature). These included flora and fauna, as well as mineral and geological specimens. He wrote a description or catalogue of his collection in 1595. 

In 1603, after negotiation with the Senate, Aldrovandi arranged for his teatro di natura to be donated to the city of Bologna after his death in exchange for the promise that they would continue to edit and publish his vast convolute of unpublished papers. This duly took place, and his collection became a public museum in the Palazzo Poggi, the headquarters of the university, opening in 1617, as the first public science museum.

Palazzo Poggi Bologna c.1750 Source: Wikimedia Commons

As with all of his natural history undertakings, Aldrovandi’s natural history museum was not the first, there being already ones in the botanical gardens of the universities of Pisa, Padua, and Florence but none of them approached the scope of Aldrovand’s magnificent collection. Also, later, the University of Montpelier had its own natural history collection. However, it wasn’t just institutions that created these early natural history museums. Individual apothecaries and physicians also set about collecting flora and fauna. 

The apothecary Francesco Calzolari (1522–1609) had an impressive Theatrum Naturae in Verona with 450 species on display. 

Source: Wikimedia Commons
Francesco Calzolari’s Cabinet of curiosities. From “Musaeum Calceolarium” (Verona, 1622) Source: Wikimedia Commons

Likewise, the papal physician, Michele Mercati (1541–1593), who was superintendent of the Vatican Botanical Garden, had a notable collection concentrating on minerology, geology, and palaeontology in Rome 

Source: Wikimedia Commons
Engraving made by Antonio Eisenhot between 1572 and 1581, but published in 1717, representing the Vatican mineral collection as organized by Michele Mercati Source: Wikimedia Commons

The Neapolitan apothecary Ferrante Imperato (1523–1620?)  published Dell’Historia Naturale in Naples in 1599, which was based on his own extensive natural history collection and containing the first printed illustration of such a collection. 

Portrait of Ferrante Imperato by Tanzio da Varallo  Source: Wikimedia Commons
Title page of Dell’ historia naturale, Napoli, 1599, by Ferrante Imperato (1550-1625). Source: Houghton Library, Harvard University via Wikimedia Commons
Engraving from Dell’ historia naturale, Napoli, 1599, by Ferrante Imperato (1550-1625). Source: Houghton Library, Harvard University via Wikimedia Commons

In the sixteenth century it became very fashionable for rulers to create cabinets of curiosities also know by the German terms as Kunstkammer or Wunderkammer. These were not new and had existed in the two previous centuries but in the Renaissance took on a whole new dimension. These contained not only natural history objects but also sculptures and paintings, as well curious items from home and abroad, with those from abroad taking on a special emphasis as Europe began to make contact with the rest of the world. 

The curiosity cabinet is a vast topic, and I don’t intend to attempt to cover it in this blog post, also it is only tangentially relevant to the central topic of this blog post series. I will, however, sketch some aspect that are relevant. Although they covered much material that wasn’t scientific, they were fairly obviously inspired by various aspects of the increasingly empirical view of the world that scholars had been developing throughout the Renaissance. We don’t just go out and actually observe the world for ourselves, we also bring the world into our dwellings so that all can observe it there. They represent a world view created by the merging of history, art, nature, and science. Although principally the province of the rich and powerful, for whom they became a status symbol, some notable Wunderkammer were created by scholars and scholars from the various scientific disciplines were often employed to search out, collect, and then curate the object preserved in the cabinets. 

Some of these cabinets created by the Renaissance rulers also had sections for scientific instruments and their owner commissioned instruments from the leading instrument makers of the era. These are not the average instruments created for everyday use but top of the range instruments designed to demonstrate the instrument makers skill and not just instruments but also works of art. As such they were never really intended to be used and many survive in pristine condition down to the present day. One such collection is that which was initially created by Elector August of Saxony (1526–1586), can be viewed in the Mathematish-Physikalischer Salon in the Zwinger in Dresden. 

Portrait of the Elector August of Saxony by Lucas Cranach Source: Wikimedia Commons
Planetenlaufuhr, 1563-1568 Eberhard Baldewein et al., Mathematisch-Physikalischer Salon

Equally impressive is the collection initially created by Wilhelm IV, Landgrave of Hessen-Kassel, (1532-1592), who ran a major observational astronomy programme, which can be viewed today in the Astronomisch-Physikalische Kabinett

Portrait of Wilhelm IV. von Hessen-Kassel by Kaspar van der Borcht († 1610) Source: Wikimedia Commons
Equation clock, made for Landgrave William IV of Hesse-Kassel by Jost Burgi and Hans Jacob Emck, Germany, Kassel, 1591, gilt brass, silver, iron Source: Metropolitan Museum of Art, New York City via Wikimedia Commons

Not surprisingly Cosimo I de’ Medici Grand Duke of Tuscany (1519–1574)

Agnolo Bronzino, Porträt von Cosimo I de’ Medici in Rüstung, 1545, Source: Uffizien via Wikimedia Commons

had his cabinet of curiosities, the Guardoroba Nuova, in the Palazzo Vecchio in Florence, designed by the artist and historian of Renaissance art Giorgi Vasari (1511–1574), who, as I have documented in an earlier post, in turn commissioned the artist, mathematician, astronomer and cartographer, Egnatio Danti (1536–1586), to decorate the doors of the carved walnut cabinets, containing the collected treasures, with mural maps depicting the whole world. Danti also designed the rooms centre piece, a large terrestrial globe. 

Source: Fiorani The Marvel of Maps p. 57

The alternative name Wunderkammer became common parlance because various German emperors and other rulers somewhat dominated the field of curiosity cabinet construction. Probably the largest and most spectacular Wunderkammer was that of the Holy Roman Emperor, Rudolf II (1552–1612).

Rudolf II portrait by  Joseph Heintz the Elder 1594 Source: Wikimedia Commons

He was an avid art collector and patron, but he also collected mechanical automata, ceremonial swords, musical instruments, clocks, water works, compasses, telescopes, and other scientific instruments. His Kunstkammer incorporated the three kingdoms of nature and the works of man. Unusually, Rudolf’s cabinet was systematically arranged in encyclopaedic fashion, and he employed his court physician Anselmus de Boodt (1550–1632), a Flemish humanist, minerologist, physician, and naturalist to catalogue it. De Boodt had succeeded Carolus Clusius (1526–1609) as superintendent of Rudolf’s botanical garden.

Rudolf II Kunstkammer

Although it was a private institution, Rudolph allowed selected professional scholars to study his Wunderkammer. In fact, as well as inanimate objects Rudolf also studiously collected some of Europe’s leading scholars. The astronomers Nicolaua Reimers Baer (1551–1600), Tycho Brahe (1546–1601), and Johannes Kepler (1571–1630) all served as imperial mathematicus. The instrument maker, Jost Bürgi came from Kassel to Prague. As already mentioned, Carolus Clusius (1526–1609) and Anselmus de Boodt (1550–1632) both served as superintendent of the imperial botanical gardens. The later also served as personal physician to Rudolf, as did the Czech naturalist, astronomer, and physician Thaddaeus Hagecius ab Hayek (1525–1600). The notorious occultist Edward Kelly (1555-1597) worked for a time in Rudolf’s alchemy laboratory.

When Rudolf died his Wunderkammer was mostly transferred to Vienna by his brother and successor as Holy Roman Emperor, Matthias, where it was gradually dissipated over the years. Although, his was by far the most spectacular Rudolf’s was only one of many cabinets of curiosity created during the Renaissance by the rich and powerful as a status symbol. However, there were also private people who also created them; the most well-known being the Danish, naturalist, antiquary, and physician Ole Worm (1588­–1654).

Ole Worm and Dorothea Worm, née Fincke artist unknown Source: Wikimedia Commons

Son of Willum Worm a mayor of Aarhus, he inherited substantial wealth from his father. After attending grammar school, he studied theology Marburg and graduated Doctor of Medicine at the University of Basel in 1611. He also graduated MA at the University of Copenhagen in 1618. He spent the rest of his life in Copenhagen, where he taught Latin Greek, physics, and medicine, whilst serving as personal physician to the Danish King, Christian IV (1577–1648). He died of the bubonic plague after staying in the city to treat the sick during an epidemic.

As a physician he contributed to the study of embryology. Other than medicine he took a great interest in Scandinavian ethnography and archaeology. As a naturalist he determined that the unicorn was a mythical beast and that the unicorn horns in circulation were actually narwhal tusks. He produced the first detail drawing of a bird-of-paradise, proving that they, contrary to popular belief, did in fact have feet. He also drew from life the only known illustration of the now extinct great auk.

OLe Worm’s Great Auk Source: Wikimedia Commons

Worm is best known today for his extensive cabinet of curiosity the Museum Wormianum a great collection of curiosities ranging from native artifacts from the New World, to stuffed animals and fossils in which he specialised.

1655 – Frontispiece of Museum Wormiani Historia Source: Wikimedia Commons

As with other cabinets, Worm’s collection consisted of minerals, plants, animals, and man-made objects. Worm complied a catalogue of his collection with engravings and detailed descriptions, which was published posthumously in four books, as Museum Wormianum. The first three books deal respectively with minerals, plants, and animals. The fourth is archaeological and ethnographical items. 

Title page 
Museum Wormianum. Seu historia rerum rariorum, tam naturalium, quam artificialium, tam domesticarum, quam exoticarum, quæ Hafniæ Danorum in œdibus authoris servantur. Adornata ab Olao Worm … Variis & accuratis iconibus illustrata. Source

A private cabinet of curiosity that then became an institutional one was that of the Jesuit polymath, Athanasius Kircher (1602-1680). Kircher referred to variously as the Master of a Hundred Arts and The Last man Who Knew Everything belonged very much to the Renaissance rather than the scientific revolution during which he lived and was active.

Athanasius Kircher engraving by Cornelis Bloemaert Source: Wikimedia Commons

He was author of about forty major works that covered a bewildering range of topics, which ranged from the genuinely scientific to the truly bizarre. Immensely popular and widely read in his own time, he quickly faded into obscurity following his death. Born in Fulda in Germany, one of nine children, he attended a Jesuit college from 1614 till 1618 when he entered the Jesuit Order. Following a very mixed education and career he eventually landed in the Collegio Romano in 1634, where he became professor for mathematics. Here he fulfilled an important function in that he collected astronomical data from Jesuit missionaries throughout the world, which he collated and redistributed to astronomers throughout Europe on both sides of the religious divide. 

Given he encyclopaedic interests it was perfectly natural for Kircher to begin to assemble his own private cabinet of curiosities. In 1651, the Roman Senator Alfonso Donnini (d.1651) donated his own substantial cabinet of curiosities to the Collegio, and the authorities decided that it was best placed in the care of Father Kircher. Combining it with his own collection, Kircher established, what became known as the Musæum Kircherianum, which he continued to expand throughout his lifetime.

Musæum Kircherianum, 1679 Source: Wikimedia Commons

The museum became very popular and attracted many visitors. Giorgio de Sepibus published a first catalogue in 1678, the only surviving evidence of the original layout. Following Kircher’s death the museum fell into neglect but was revived, following the appointment of Filippo Bonanni (1638–1725), Kercher’s successor as professor of mathematics, as curator in 1698. Bonnani published a new catalogue of the museum in 1709. The museum prospered till 1773 till the suppression of the Jesuit Order led to its gradual dissipation, reestablishment in 1824, and final dispersion in 1913.

Filippo Bonanni, Musaeum Kircherianum, 1709 Source: Wikimedia Commons

As we have seen cabinets of curiosities often evolved into public museums and I will close with brief sketches of two that became famous museums in England in the seventeenth and eighteenth centuries. 

John Tradescant the Elder (c. 1570–1638) was an English, naturalist, gardener, and collector. He was gardener for a succession of leading English aristocrats culminating in service to George Villiers, 1st Duke of Buckingham. In his duties he travelled widely, particularly with and for Buckingham, visiting the Netherlands, Artic Russia, the Levant, Algiers, and France. Following Buckingham’s assassination in 1628, he was appointed Keeper of the King’s Gardens, Vines and Silkworms at Oatlands Palace in Surrey.

John Tradescant the Elder (portrait attributed to Cornelis de Neve) Source: Wikimedia Commons

On his journeys he collected seeds, plants, bulbs, as well as natural historical and ethnological curiosities. He housed this collection, his cabinet of curiosities, in a large house in Lambeth, The Ark.

Tradescant’s house in Lambeth: The Ark Source: Wikimedia Commons

This was opened to the public as a museum. The collection also included specimens from North America acquired from colonists, including his personal friend John Smith (1580–1631), soldier, explorer, colonial governor, and Admiral of New England.

His son, John Tradescant the Younger (1608–1662) followed his father in becoming a naturalist and a gardener.

John Tradescant the Younger, attributed to Thomas de Critz Source: Wikmedia Commons

Like his father he travelled widely including two trips to Virginia between 1628 and 1637. He added both botanical and other objects extensively to the family collection in The Ark. When his father died, he inherited his position as head gardener to Charles I and Henrietta Maria of France working in the gardens of Queens House in Greenwich. Following the flight of Henrietta Maria in the Civil War, he compiled a catalogue of the family cabinet of curiosities, as Museum Tradescantianum, dedicated to the Royal College of Physicians with whom he was negotiating to transfer the family botanical garden. A second edition of the catalogue was dedicated to Charles II after the restoration.

Source: Wikimedia Commons

Around 1650, John Tradescant the Younger became acquainted with the antiquarian, politician, astrologer and alchemist, Elias Ashmole (1617–1692), who might be described as a social climber.

Elias Ashmole by John Riley, c. 1683

Born into a prominent but impoverished family, he managed to qualify as a solicitor with the help of a prominent maternal relative. He married but his wife died in pregnancy, just three years later in 1641. In 1646-47, he began searching for a rich widow to marry. In 1649, he married Mary, Lady Mainwaring, a wealthy thrice widowed woman twenty years older than him. The marriage was not a success and Lady Manwaring filed suit for separation and alimony, but the suit was dismissed by the courts in 1657 and having inherited her first husband’s estate, Ashmole was set up for life to pursue his interests in alchemy and astrology, without having to work. 

Ashmole helped Tradescant to catalogue the family collection and financed the publication of the catalogue in 1652 and again in 1656. Ashmole persuaded John Tradescant to deed the collection to him, going over into his possessing upon Tradescant’s death in 1662. Tradescant’s widow, Hester, challenged the deed but the court ruled in Ashmole’s favour. Hester held the collection in trust for Ashmole until her death.

In 1677, Ashmole made a gift of the Tradescant collection together with his own collection to the University of Oxford on the condition that they build a building to house them and make them available to the general public. So, the Ashmolean Museum, the world’s second university museum and Britain’s first public museum, came into existence on 24 May 1683.

The original Ashmolean Museum building on Board Street Oxford now the Museum of the History of Science, Oxford Source: Wikimedia Commons

My second British example is the cabinet of curiosities of Hans Sloane (1660–1753), physician, naturalist, and collector.

Slaughter, Stephen; Sir Hans Sloane, Bt; Source: National Portrait Gallery, London via Wikipedia Commons

Sloane was born into an Anglo-Irish family in Killyleagh a village in County Down, Ulster. Already as a child Sloane began collecting natural history items and curiosities, which led him to the study of medicine. In London, he studied botany, materia medica, surgery, and pharmacy. In 1687, he travelled to Jamaica as personal physician to the new Governor Christopher Monck, 2nd Duke of Albemarle. Albemarle died in the following year, so Sloane was only in Jamaica for eighteen months, however, in this time he collected more than a thousand plant specimens and recorded eight hundred new species of plants, starting a lifetime of collecting.

Sloane married the widow Elizabeth Langley Rose a wealthy owner of Jamaican sugar plantation worked by slaves, making Sloane independently wealthy. There followed a successful career as physician, Secretary of the Royal Society, editor of the Philosophical Transactions, President of the Royal College of Physicians, and finally President of the Royal Society. Throughout his life, Sloane continued to collect. He used his wealth to acquire the natural history collections of Barbadian merchant William Courten (1572–1636), papal nuncio Cardinal Filippo Antonio Gualterio (1660–1728), apothecary James Petiver (c.1665–1718), plant anatomist Nehemiah Grew, botanist Leonard Plukenet (1641–1706), gardener and botanist the Duchess of Beaufort (1630–1715), botanist Adam Buddle (1662–1715), physician and botanist Paul Hermann (1646–1695), botanist and apothecary Franz Kiggelaer  (1648–1722), and botanist, chemist, and physician Herman Boerhaave (1668–1738).

 When he died Sloane’s collection of over seventy-one thousand items– books manuscripts, drawings, coins and medals, plant specimens and more–was sold to the nation for £20,000, well below its true value. It formed to founding stock of the British Museum and British Library, which opened in 1759.

Montagu House, c. 1715 the original home of the British museum

The natural history collection was split off to found the Natural History Museum, which opened in South Kensington in 1881.

The Natural History Museum. This is a panorama of approximately 5 segments. Taken with a Canon 5D and 17-40mm f/4L. Source: Wikimedia Commons

The Renaissance practice of creating cabinets of curiosities played a significant role in the creation of modern museums in Europe. It also provided scientists with collections of materials on which to conduct their research, an important element in the development of empirical science in the Early Modern Period. 

 

 

 

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Filed under History of botany, History of medicine, History of science, History of Technology, History of Zoology, Natural history, Renaissance Science

The sixteenth century dispute about higher order algebraic equations and their solution

The Early Modern period is full of disputes between scholars about questions of priority and accusations of the theft of intellectual property. One reason for this is that the modern concepts of copyright and patent rights simply didn’t exist then, however, that is not the topic of this post. One of the most notorious disputes in the sixteenth century concerned Niccolò Fontana Tartaglia’s discovery of the solution to one form of cubic equation and Gerolamo Cardano’s publication of that solution, despite a promise to Tartaglia not to do so, in his book Artis Magnae, Sive de Regulis Algebraicis Liber Unus, commonly known as the Ars Magna in 1545. A version of this story can be found is every general history of mathematics book and there are numerous versions to be found on the Internet. I blogged about it twelve years ago and maths teacher and historian, Dave Richeson wrote about it just last month in Quanta Magazine

Despite all of this, I am going to review a book about the story that I recently acquired and read, Fabio Toscano, The Secret FormulaHow a Mathematical Duel Inflamed Renaissance Italy and Uncovered the Cubic Equation.[1] 

Unlike most of my book reviews this is not a new book, it was originally published in Italian as, La formula segreta, in 2009 and the English translation appeared in 2020. I caught a glimpse of it on the Princeton University Press website at half price in their summer sale and on a whim decided to buy it.[2] I’m glad that I did, as it is an excellent retelling of the story using all of the original documents, which adds a whole new depth to it, not found in the popular versions. 

Toscano’s book, which is comparatively short, has six chapters each of which deals with a distinctive aspect of the sequence of historical events that he is narrating. The opening chapters introduces one of the principal characters in this story Niccolò Fontana, describing his lowly birth, his facial disfigurement delivered by a soldier during the 1512 storm of Brescia, which gave him the stutter by which he was known, Tartaglia. How the autodidactic mathematician became an abaco master, a private teacher of arithmetic, algebra, bookkeeping and elementary geometry.

The second chapter is a brief sketch of history of algebra up to the Renaissance. The elementary nature of ancient Egyptian algebra, the much more advanced nature of Babylonian algebra including the partial general solution of the quadratic equation. Partial, because the Babylonians didn’t acknowledge negative solutions. Here we have one of the few, in my opinion, failures in the book. There is no mention whatsoever of the Indian contributions to the evolution of algebra. This is important as it was Brahmagupta who, in the sixth century CE, introduced the full arithmetic of both positive and negative numbers and the full general solution of the quadratic equation. More importantly the Islamic algebraists took their knowledge of algebra from the Indians and in particular Brahmagupta. Another failure in this section is that Toscano repeats the standard myth of the House of Wisdom. Very positive is the fact that he explains the terminology of rhetorical algebra, the problems are all written out in words not symbols. He also explains that whereas we now just handle quadratic or cubic equations through the general form, in the Renaissance every variation was regarded as a separate equation. So, for example, if the x2 is missing from a cubic equation, this is a new equation that is handled separately. There are in fact, according to Omar Khayyam, fourteen different types of cubic equation. Apart from the omission of Indian algebra this whole chapter is excellent.

Toscano, The Secret Formula page 39

The third chapter takes us to the heart of the story and the event that made Tartaglia famous and would eventually lead to his bitter dispute with Cardano, the public contest with Antonio Maria Fior. In the most influential mathematics book of the era, his Summa de arithmetica, geometria, proportioni et proportionalita (Summary of arithmetic, geometry, proportions and proportionality) published in Venice in 1494, Luca Pacioli (c. 1447–1517) had stated that there was no possible general solution to the cubic equation, Fior had, however, acquired a general solution to the cubic equations of the form x3 + bx = c  and thought he could turn this into capital for his career. He challenged Tartaglia to a public contest thinking he held all the trumps. Unfortunately, for him Tartaglia had also found this solution, so the contest turned into a debacle for Fior and a great triumph for Tartaglia. If you want to know the details read the book. Toscano’s account of what happened, based on the available original sources is much more detailed and informative that the usual ones. We also get introduced to Messer Zuanne Tonini de Coi, another mathematician, who doesn’t usually get mentioned in the general accounts of the story but who plays a leading role in several aspects of it. Amongst other things, he was the first who tries to get Tartaglia to divulge the partial solution of the cubic that he has discovered, and it was he, who he first told Cardano about Tartaglia’s discovery.

In chapter four we meet the villain of the story the glorious, larger than life, Renaissance polymath, Gerolamo Cardano. We get a sympathetic description of Cardano’s less than auspicious origins and his climb to success as a physician against all the odds. Toscano does not over emphasise Cardano’s oddities and he had lots of those. We now get a very detailed account, once more based on original documents, of Cardano’s attempts to woo Tartaglia and seduce the secret of the partial cubic solution out of him. Cardano’s seduction was eventually successful, and he obtained the solution but only after swearing a solemn oath to reveal the solution to nobody until Tartaglia had published in his planned book. 

Chapter five takes us to Cardano’s breaking of that oath, his, I think justifiable reasons for doing so, and Tartaglia’s understandable outrage. The chapter opens with more exchanges about Tartaglia’s solution, which Cardano hasn’t truly understood, because of an error in Tartaglia’s encrypted poetical revelation of it. Having cleared this up Tartaglia begins to panic because Cardano is planning to publish a maths book his, Practica arithmetice et mensurandi singularis (The Practice of Arithmetic and Simple Mensuration), and he fears it will include his solution, it didn’t, panic over for now. We now get introduced to Cardano’s brilliant pupil and foster son, Lodovico Ferrari. Between the two of them, starting from Tartaglia’s solution, they find the general solutions of the cubic and the quartic or biquadratic equations putting algebra on a whole new footing but are unable to publish because of Cardano’s oath to Tartaglia. However, in 1542, Cardano and Ferrari travelled to Bologna and discovered in a notebook of Scipione Dal Ferro Tartaglia’s partial solution of the cubic made twenty years earlier than Tartaglia and obviously the source of Fior’s knowledge of the solution. Cardano no longer felt constrained by his oath and in 1545, his Ars Magna was published by Johannes Petreius in Nürnberg, containing all the algebra that he and Ferrari had developed but giving full credit to Scipione Dal Ferro and Tartaglia for their contributions. Tartaglia went ballistic!

The closing chapter deals with the final act, Tartaglia’s indignation over what he saw as Cardano’s treachery and the reaction to his accusations. Tartaglia raged and Cardano remained silent. Although, he had been very vocal in obtaining the cubic solution from Tartaglia, Cardano now withdrew completely from the dispute, leaving Ferrari to act as his champion. Tartaglia and Ferrari exchanged a total of twelve pamphlets, six each, full of polemic, invective, accusations, and challenges. Tartaglia trying, the whole time, to provoke Cardano into a direct response, accusing him of ghost-writing Ferrari’s pamphlets. Ferrari, in turn, constantly challenged Tartaglia to a face-to-face public confrontation, which he steadfastly rejected. Toscano reproduces a large amount of the contents of those pamphlets, upon which he judiciously comments. It is this engagement by the author that makes the book such a good read. Tartaglia finally caved in, probably as a condition of a new job offer, and met Ferrari in the public arena in Milan, fleeing the city on the evening of the first day of the confrontation, his reputation in tatters. What exactly took place, we don’t know, as Cardano and Ferrari never commented on the meeting, and we have only Tartaglia’s account that relates that he realised that the crowd was stacked against him with Ferrari’s supporters, and he could never win and so he departed.

Given the nature of the book, it has no illustrations. However, given the authors extensive use of both primary sources as well as authoritative secondary sources, it has an impressive number of endnotes, unfortunately not footnotes. Most of these are simple references to the source quoted and here the book uses a convention that I personally dislike. These references are mostly just something like [21.e]. The authors in the bibliography are sequentially numbered and if the author of more than one text these are identified by the small case letters. So, you are interested in the origin of a quote, you go to the endnotes, find there such a number, and then leaf through the bibliography to find out who, what, why, where! I do not like! Many of the items in the bibliography are texts from Italian historians, so the English edition has a short, but high quality, extra list of English titles on the topic. There is an excellent index.

It may seem that I have revealed too much of the contents of the book to make it worth reading but I have only sketched the outline of the story as it appears in the book, a story, which as I said at the beginning is very well know, the devil is as they say in the detail. By his very extensive use of the original sources, Toscano has given the popular story a whole new dimension, making his book a totally fascinating read for anybody interested in the history of mathematics. His book is also a masterclass in how to write high quality popular history of mathematics. 


[1] Fabio Toscano, The Secret FormulaHow a Mathematical Duel Inflamed Renaissance Italy and Uncovered the Cubic Equation, Translated by Arturo Sangalli, Princeton University Press, Princeton and Oxford, 2020

[2] More accurately the dastardly Karl Galle drew my attention to it, and I couldn’t resist the temptation, as it was not only cheap but came with free p&p. When I ordered it, I had forgotten that PUP distribute their book in Europe out of the UK. I try to avoid ordering books from the UK because, since Brexit, I now have to pay customs duty on book from the UK, on top of which the German postal service adds a €6 surcharge for paying the customs duty in advance, this would, in this case almost double the cost of the book. Normally, when I receive books from the UK, I get a note in my post box and have to go to the post office to pay the money due and pick up the book. For some reason, in this case, the postman simply delivered the book despite the label saying how much I was supposed to pay and so I didn’t have to pay it. You win some, you lose some!

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Filed under Book Reviews, History of Mathematics, Renaissance Science

Renaissance science – XXXIX

Over a series of episodes, we have followed how the Renaissance Humanists introduced materia medica into the university curriculum developing it from a theoretical subject to a practical empirical field of research and then over time, how the modern scientific study of botany developed out of it. We have also seen how some of the same energy was invested in laying down the beginnings of the modern scientific study of zoology. The beginnings of this evolution at the end of the fifteenth century coincided with the beginnings of the so-called Age of Discovery or Age of Exploration, which as I stated in the first episode on navigation I prefer to refer to as the Contact Period, when Europeans first came into contact with lands and peoples unknown to them, such as the Americas or sub-Saharan Africa, and at the same time vastly increased their knowledge of countries such as India; they also became acquainted with a vast number of new medicinal herbs and other plants as well as animals, which played an increasing role in their studies in these areas. 

Exotica out of the plant and animal kingdoms were not unknown to the European scholars, after all Alexander the Great had conquered Persia and Northern India and the Romans Northern Africa. They brought knowledge of these lands and their flora and fauna back into Europe and even imported many of those plants and animals. Famously, Hannibal crossed the Alps with his elephants and the Romans fed Christians to the lions in the Circus Maximus. Some of these exotica were also recorded in the works of Aristotle, Theophrastus, Dioscorides, and Pliny. Later in the Middle Ages the Islamic forces created an Empire that stretched from China to Spain and the Islamic scholars also recorded much of the flora and fauna of this vast Empire. A lot of that material came into Europe during the twelfth century Scientific Renaissance when large quantities of Arabic material was translated into Latin. 

However, this knowledge of natural historical exotica was purely second hand and the European recipients in the Middle Ages and Renaissance had no way of knowing how accurate it was or even if it was true. They had no first-hand empirical verification. Were the accounts of real plants and animals or mythical ones. Just looking at the proto-zoological works of both Conrad Gesner and Ulisse Aldrovandi illustrates this problem. Both of them include many animals that we now know never existed, myths and legends from other times and other cultures. They had no way of differentiating between the real and the mythical, although they both put hesitant question marks behind some of the mythical beasts that they served up for their readers.

The vastly increased voyages of trade and exploration, although one could simply write trade as almost all exploratory voyages where motivated by the hope of trade, during the contact period gave the Renaissance scholars the chance to go and search out and describe the exotica with their own eyes. When talking about Renaissance zoology we saw that the French naturalist Pierre Belon (1517–1564) travelled as a diplomate in Greece, Crete, Asia Minor, Egypt, Arabia, and Palestine between 1546 and 1549 and observed and wrote about natural history there. Under the botanists Carolus Clusius (1526–1609) translated Garcia de Orta’s important materia medica text Colóquios dos simples e drogas he cousas medicinais da Índia, into Latin from the original Portuguese and published it in Europe in 1567. He also acquired information about the flora of the Americas by questioning seafarers returning to the Iberian Peninsula from there. Clusius’ interest in the materia medica and natural history of the newly discovered Americas didn’t end with just collecting information from returnees, he also translated and published in Latin. the work of Nicolás Monardes (1493–1588)

Source: Wikimedia Commons

Monardes was born in Seville the son of Nicolosi di Monardis, an Italian bookseller, and Ana de Alfaro, the daughter of a physician. He graduated BA in 1530 and obtaining a first degree in medicine in 1533, began to practice medicine in Seville. He obtained a doctorate in medicine from the University of Alcalá de Henares in 1547. He wrote extensively on the materia medica of the Americas. In 1565, he published his Historia medicinal de las cosas que se traen de nuestras Indias Occidentales in Seville, which was based on the reports of a wide range of people returning from the Americas. In 1569, he published an extended version, his Dos libros, el uno que trata de todas las cosas que se traen de nuestras Indias Occidentales, que sirven al uso de la medicina, y el otro que trata de la piedra bezaar, y de la yerva escuerçonera. A second volume expanding on the material in the first two books, Segunda parte del libro des las cosas que se traen de nuestras Indias Occidentales, que sirven al uso de la medicina; do se trata del tabaco, y de la sassafras, y del carlo sancto, y de otras muchas yervas y plantas, simientes, y licores que agora nuevamente han venido de aqulellas partes, de grandes virtudes y maravillosos effectos appeared in Saville in 1571. A single edition of all three books, Primera y segunda y tercera partes de la historia medicinal de las cosas que se traen de neustra Indias Occidentales, que sirven en medicina; Tratado de la piedra bezaar, y dela yerva escuerçonera; Dialogo de las grandezas del hierro, y de sus virtudes medicinales; Tratado de la nieve, y del beuer frio was published in Saville in 1574, with a second edition appearing in 1580.

Source: Wikimedia Commons
Source: Wikimedia Commons

 In 1574, Platin in Antwerp published Clusius first translation De simplicibus medicamentis ex occidentali India delatis quorum in medicina usus est. Plantin published a revised edition, Simplicium medicamentorum ex novo orbe delatorum, quorum in medicina usus est, historia, in 1579. In 1582, Clusius produced a compendium of revised translations of the work of Garcia de Orta, Nicolás Monardes, and Cristóbal Acosta, to who we will return shortly. A further revised edition appeared in 1593 and a last revision in 1605. In 1577, John Frampton, a sixteenth century English merchant, published an English translation of the 1565 Spanish text, Ioyfull newes out of the newe founde worlde, wherein is declared the rare and singular vertues of diuerse and sundrie hearbes, trees, oyles, plantes, and stones, with their applications, as well for phisicke as chirurgerie in London. A new expanded edition based in the 1574 Spanish text appeared in 1580.

Source: Wikimedia Commons
Source: Wikimedia Commons

Before we turn to Acosta, we need to deal with Gonzalo Fernández de Oviedo y Valdés (1478–1557), who preceded him.

Gonzalo Fernández de Oviedo y Valdés Source: Wikimedia Commons

Oviedo was a Spanish, soldier, historian, writer, botanist, and colonist, who participated in the colonisation of the West Indies already in the 1490s. Born in Madrid, he was educated at the court of Ferdinand and Isabella, where he served as a page to the Infanta, Juan de Aragón, until his death in 1497. He then spent three years in Italy before returning to a position as a bureaucrat in the Castilian imperial project. In 1514, he was appointed supervisor of gold smelting in Santo Domingo and in 1523 historian of the West Indies. He travelled five more times to the Americas before his death. 

In 1526, he published a short work, La Natural hystoria de las Indias, with few illustrations, in Toledo. It was translated into Italian appearing in Venice in 1534, with French editions beginning in 1545, and English ones beginning in 1555. In 1535, part one of a longer and more fully illustrated Historia general de las Indias was printed in Seville, which contained the announcement of two further parts. He continued to work on a revised version of part one and on parts two and three until his death in 1557, but they were first published in an incomplete edition in 1851 entitled, Natural y General Hystoria de las Indias. English and French editions of the 1535 Seville publication appeared in 1555 and 1556 respectively. The Saville publication is a ragbag of topics but contains quite a lot of both botanical and zoological information. 

Source: Wikimedia Commons
Source: Wikimedia Commons

The Portuguese physician and natural historian, Cristóbal Acosta (c. 1525–c. 1594), whose work was partially included in Clusius’ 1582 compendium, is thought to have been born somewhere in Africa, because he claimed to be African in his publications.

Cristóbal Acosta Source: Wikimedia Commons

He first travelled to the East Indies, as a soldier, in 1550. He returned to Goa with his former captain, Luís de Ataíde, who had been appointed Viceroy of Portuguese India, in 1568, the year Garcia de Orta died. He worked as a physician in India and gained a reputation for collecting botanical specimens. He returned to Europe in 1572 and worked as a physician in Spain. In 1578, he published his Tractado de las drogas y medicinas de las Indias orientales (Treatise of the drugs and medicines of the East Indies). This work included much that was culled from Garcia de Orta’s Colóquios dos simples e drogas he cousas medicinais da Índia but became better known that Orta’s work. The last entry was a treatise on the Indian Elephant, the first published in Europe. The work was translated into Italian in 1585 by Francesco Ziletti.

Source: Wikimedia Commons

Cristóbal Acosta is not to be confused with José de Acosta (c. 1539–1600), the Jesuit missionary and naturalist.

José de Acosta Source: Wikimedia Commons

Born in Medina del Campo, Spain José de Costa joined the Jesuit Order at the age of thirteen. In 1569, he was sent by the Order to Lima, Peru. Ordered to cross the Andes to journey to the Viceroy of Peru, he and his companions suffered altitude sickness; Acosta, as one of the earliest to do so, gave a detailed description of the ailment, attributing it correctly to “air… so thin and so delicate that it is not proportioned to human breathing.” Acosta aided the Viceroy in a five-year tour through the Viceroyalty of Peru, seeing and recording much of what he experienced. He spent the year of 1586 in Mexico studying the culture of the Aztecs. In 1587, he returned to Spain. He published many, mostly theological, works in his lifetime but is best known as the author of De Natura Novi OrbisDe promulgatione Evangelii apud Barbaros, sive De Procuranda Indorum salute (both published in Salamanca in 1588) and above all, the Historia natural y moral de las Indias(published in Savile in 1590). 

Source: Wikimedia Commons

In his Historia natural y moral de las Indias he presented his observations on the physical geography and natural history of Mexico and Peru as well as the indigenous religions and political structures from a Jesuit standpoint. His book was one of the first detailed and realistic descriptions of the New World. Acosta presented the theory that the indigenous populations must have crossed over from Asia into the Americas. The work was translated into various European languages, appearing in English in 1604 and in French in 1617.

Historia natural y moral de las Indias Source: Wikimedia Commons

It should be noted that just as the early Renaissance natural historians in Europe relied, to a great extent, for their information on plants, herbs and animals on farmers, hunters, foresters, and others who lived and worked on the land, so the Europeans studying the materia medica and natural histories of Asia and the Americas depended very heavily on the information that they received from the indigenous populations. This was particularly the case in the next natural historians that I will briefly present.

Bernardino de Sahagún (c.1499–1590) was born Bernadino de Rivera in Sahagùn in Spain and attended the humanist University of Salamanca and there joined the Franciscan Order, changing his name to that of his birthplace, as was the Franciscan custom, and was probably ordained in 1527. He was recruited in 1529 to join the Franciscan mission to New Spain.

Source: Wikimedia Commons

He helped found the first European school of higher education in the Americas, the Colegio Imperial de Santa Cruz de Tlatelolco in 1536. He learnt the Aztec language Nahuatl in order to be able to confer with the indigenous population about materia medica and natural history. In 1558, he was commissioned by the new provincial of New Spain, Fra Francisco de Toral, to formalise his studies of native languages and culture. He spent twenty-five years researching the topic with the last fifteen spent editing, translating, and copying. He was assisted in his research by five graduates of the Collegio, all of whom spoke Nahuatl, Latin, and Spanish, and as well as helping him to interview the elders about the religious rituals and calendar, family, economic and political customs, and natural history, also participated in research and documentation, translation and interpretation, as well as painting the illustrations. In the text he credited them for their work by name. 

Out of this research Sahagún created a twelve volume General History of the Things of New Spain, the manuscript was sent to Philip II of Spain. It was never printed, and the manuscript was bought by Ferdinando de’ Medici, Grand Duke of Tuscany, in 1580. He put it on display in the Uffizi Gallery in Florence and it is generally known as the Florentine Codex. The volume that deals with natural history is titled Earthly Things and is the most heavily illustrated, containing paintings of thirty-nine mammals, one hundred and twenty birds and more than six hundred flowers. The hundreds of New World plants listed in the Florentine Codex are presented according to an Aztec system of taxonomy. The Aztec divided plants up into four main groups: edible, decorative, economic, and medicinal. 

The Florentine Codex Source: Wikimedia Commons
The Florentine Codex Source: Wikimedia Commons

Sahagún’s Historia general was not the only book on indigenous materia medica to emerge from the Colegio Imperial de Santa Cruz de Tlatelolco. In 1552, a native graduate, Martín de la Cruz wrote a Libellus de Medicinalibus Indorum Herbis (Little Book of the Medicinal Herbs of the Indians) in Nahuatl, which was translated into Latin by Juan Badianus de la Cruz (1484–later than 1552) an Aztec teacher at the Collegio. The original Nahuatl manuscript no longer exists. The manuscript is a compendium of two hundred and fifty medicinal herbs used by the Aztecs. The Latin manuscript sent to Spain changed hands many times over the years before landing in the Vatican Library. In 1990, it was returned to Mexico, where it now resides in library of the National Institute of Anthropology and History in Mexico City.

Libellus de Medicinalibus Indorum Herbis Source: Wikimedia Commons
Libellus de Medicinalibus Indorum Herbis Source: Wikimedia Commons

In the seventeenth century copies of the manuscript were made by Cassiano dal Pozzo (1588–1657) and Francesco Stelluti (1577–1652), both members of the Accademia dei Lincei. The Dal Pozzo copy in now in the Royal Library at Windsor but the Stelluti copy has disappeared. 

For many years, Ulisse Aldrovandi hoped to get a commission from the Spanish Crown to study the natural history of New Spain but in the end, King Philip II sent his personal physician, Francisco Hernández de Toledo (1514–1587) there to study the medicinal plants and animals.

Source: Wikimedia Commons

Of Jewish extraction, he studied medicine at the University of Alcalá from 1530 to 1536 and was connected with the leading scholars of the period. In the area of botanical studies, he won a good reputation for his study of the medical effectivity of plants and his translation into Spanish of Pliny’s Naturalis historia. In 1570, Francisco Hernández shipped out to the Americas accompanied by his son Juan, and the cosmographer Francisco Domínguez, who had been commissioned by the king to map New Spain.

Like Sahagún he learnt Nahuatl and acquired most of his knowledge by interviewing the indigenous population. He was accompanied in his work by three Aztec painters– baptized Antón, Baltazar Elías, and Pedro Vázquez–who provided the illustrations for his work. His work describes over three thousand plants unknown to Europeans, an incredible number when one considers that Dioscorides’ Materia Medica only contains about five hundred. Hernández sent at least sixteen bound volumes of manuscripts back the Philip before he returned in 1577. Theses were three volumes of twenty-four books on plants, one volume of six treatises on animals, eleven volumes of coloured illustrations, and at least one volume of dried plant specimens, there may have been more. 

As with Sahagún, there were problems when it came to the publication of his work. He intended to publish three editions, one in Spanish, one in Latin, and the third in Nahuatl for the indigenous population of New Spain. However, his voluminous material was in a mess, and he was unable to complete the mammoth task that he had undertaken, so the book remained unpublished in his lifetime. Philip II placed the manuscript in the library of the Monasterio y Sitio de El Escorial en Madrid (Royal Site of San Lorenzo de El Escorial), where it was destroyed in a fire in 1671. 

In 1580, Nardo Antonio Recchi (1540–1594) was appointed Hernández’s successor as Philip’s personal physician and took on the task of trying to bring order into Hernández’s chaos. Recchi produced a four-volume edition of Hernández’s work and Juan de Herrera (1530–1597), the architect of El Escorial began the process of preparing it for publication in 1582. However, by the time of his death in 1587 little progress had been made and the project died with him. However, Recchi had taken a copy of his manuscript back to Naples with him and it became the grail for all of the European natural historians, including, Giovanni della Porta, Ulisse Aldrovandi and Carolus Clusius, were eager to study the treasures that Hernández had brought back from the New World.

Part of Hernández’s work, the Index medicamentorum, an index that lists Mexican plants according to their traditional therapeutic uses, was published in Mexico City; the index was arranged according to body part, and it was ordered from head to toe. A Spanish translation appeared as an appendix to the medical treatises of Juan de Barrios (1562–1645) in 1607.  

A Spanish translation of Recchi’s four-volume edition was prepared by Fra Francisco Ximénez with the title, Quatro libros de la naturaleza y virtudes de las plantas y animales and published in Mexico City in 1615.

Source: Wikimedia Commons
Source: Wikimedia Commons

The Accademia dei Lincei under the leadership of Prince Federico Cesi (1585–1630) took up the task of publishing a Latin edition of Recchi’s work. A partial, heavily redacted edition under the title Francisci Hernandez rerum medicarum Novae Hispaniae Thesaurus appeared in print in 1628, however the project was laid on ice when Cesi died in 1630. Finally, a complete Latin edition of Recchi’s four volumes, edited by Johannes Schreck (1576–1630) and Fabio Colonna (1567–1640), was published in Rome, including material from Hernández’s original manuscripts not used by Recchi, with the title, Nova plantarum, animalium et mineralium mexicanorum historia a Francisco Hernández in indis primum compilata, de inde a Nardo Antonio Reccho in volumen digesta (1648–51)

Source:Wikimedia Commons

Of course, what I have sketched above was only the beginning of the European awareness of the natural history of the world outside of Europe and down to the present-day thousands of research expeditions by scientists from all other the world have continued to add to our knowledge of the extraordinary diversity of flora and fauna on our planet. 

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Filed under History of botany, History of medicine, History of Zoology, Natural history, Renaissance Science

Mathematician, astrologer, conjurer! 

It is almost impossible to imagine a modern university without a large mathematics department and a whole host of professors for an ever-increasing array of mathematical subdisciplines. Mathematics and its offshoots lie at the centre of modern society. Because popular history of science has a strong emphasis on the prominent mathematicians, starting with Euclid and Archimedes, it is common for people to think that mathematics has always enjoyed a central position in the intellectual life of Europe, but they are very much mistaken if they do so. As I have repeated on several occasions, mathematics had a very low status at the medieval European university and led a starved existences in the shadows. Some people like to point out that the basic undergraduate degree at the medieval university formally consisted of the seven liberal arts, the trivium and quadrivium, with the latter consisting of the four mathematical disciplines–arithmetic, geometry, music, and astronomy. If fact, what was largely taught was the trivium–grammar, logic, rhetoric–and large doses of, mostly Aristotelian, philosophy. A scant lip service was paid to the quadrivium at most universities, with only a very low-level introductory courses being offered in them. There were no professors for any of the mathematical disciplines.

Things only began to change during the Renaissance, when the first universities, in Northern Italy, began to establish chairs for mathematics, which were actually chairs for astrology, because of the demand for astrology for medical students. The concept of general chairs for mathematics for all educational institutions began with Philip Melanchthon (1497–1560), when he set up the school and university system for Lutheran Protestantism, to replace the previously existing Catholic education system, in the second quarter of the sixteenth century.

Melanchthon in 1526: engraving by Albrecht Dürer Translation of Latin caption: «Dürer was able to draw Philip’s face, but the learned hand could not paint his spirit».
Source: Wikimedia Commons

Melanchthon did so because he was a passionate advocate of astrology and to do astrology you need astronomy and to do astronomy you need arithmetic, geometry, and trigonometry, so he installed the full package in all Lutheran schools and universities. He also ensured that the universities provided enough young academic mathematicians to fill the created positions.  

Catholic educational institutions had to wait till the end of the sixteenth century before Christopher Clavius (1538–1612) succeeded in getting mathematics integrated into the Jesuit educational programme and installed a maths curriculum into Catholic schools, colleges, and universities throughout Europe over several decades. He also set up a teacher training programme and wrote the necessary textbooks, incorporating the latest mathematical developments.

Christoph Clavius. Engraving Francesco Villamena, 1606 Source: Wikimedia Commons

England lagged behind in the introduction of mathematics formally into its education system. Even as late as the early eighteenth century, John Arbuthnot (1667–1735) could write that there was not a single grammar school in England that taught mathematics.

John Arbuthnot, by Godfrey Kneller Source: Wikimedia Commons

This is not strictly true because The Royal Mathematical School was set up in Christ’s Hospital, a charitable institution for poor children, in 1673, to teach selected boys’ mathematics, so that they could become navigators. At the tertiary level the situation changed somewhat earlier. 

Gresham College was founded in London under the will of Sir Thomas Gresham (c. 1519–1579) in 1595 to host public lectures.

Gresham College 1740 Source: Wikimedia Commons

Sir Thomas Gresham by Anthonis Mor Rijksmuseum

Amongst other topics, professors were appointed to hold lectures in both geometry and astronomy. As with the Royal Mathematical School a century later these lectures were largely conceived to help train mariners. The instructions for the geometry and astronomy professors were as follows:

The geometrician is to read as followeth, every Trinity term arithmetique, in Michaelmas and Hilary terms theoretical geometry, in Easter term practical geometry. The astronomy reader is to read in his solemn lectures, first the principles of the sphere, and the theory of the planets, and the use of the astrolabe and the staff, and other common instruments for the capacity of mariners.

The first university professorships for mathematics were set up at Oxford University in 1619 financed by a bequest from Sir Henry Savile (1549–1622), the Savilian chairs for astronomy and geometry.

Henry Savile Source: Wikimedia Commons

Over the years it was not unusual for a Gresham professor to be appointed Savilian professor, as for example Henry Biggs (1561–1630), who was both the first Gresham professor and the first Savilian professor of geometry.

Henry Briggs

Henry Savile was motivated in taking this step by the wretched state of mathematical studies in England. Potential mathematicians at Cambridge University had to wait until a bequest from Henry Lucas (c. 1610–1663), in 1663, established the Lucasian Chair of Mathematics, whose first incumbent was Isaac Barrow (1630–1677), succeeded famously by Isaac Newton (1642–1726 os).  This was followed in 1704 with a bequest by Thomas Plume to “erect an Observatory and to maintain a studious and learned Professor of Astronomy and Experimental Philosophy, and to buy him and his successors utensils and instruments quadrants telescopes etc.” The Plumian Chair of Astronomy and Experimental Philosophy, whose first incumbent was Roger Cotes (1682–1716).

unknown artist; Thomas Plume, DD (1630-1704); Maldon Town Council; http://www.artuk.org/artworks/thomas-plume-dd-16301704-3186

Before the, compared to continental Europe, late founding of these university chairs for the mathematical sciences, English scholars wishing to acquire instruction in advanced mathematics either travelled to the continent as Henry Savile had done in his youth or find a private mathematics tutor either inside or outside the universities. In the seventeenth century William Oughtred (1574–1660), the inventor of the slide rule, fulfilled this function, outside of the universities, for some notable future English mathematicians. 

William Oughtred by Wenceslas Hollar 1646

One man, who fulfilled this function as a fellow of Oxford University was Thomas Allen (1542–1632), who we met recently as Kenhelm Digby’s mathematics tutor.

Thomas Allen by James Bretherton, etching, late 18th century Source: wikimedia Commons

Although largely forgotten today Allen featured prominently in the short biographies of the Alumni Oxonienses of Anthony Wood (1632–1695) and the Brief Lives of John Aubrey (1626–1697), both of them like Allen antiquaries. Aubrey’s description reads as follows: 

Mr. Allen was a very cheerful, facecious man and everybody loved his company; and every House on their Gaudy Days, were wont to invite him. The Great Dudley, Early of Leicester, made use of him for casting of Nativities, for he was the best Astrologer of his time. Queen Elizabeth sent for him to have his advice about the new star that appeared in the Swan or Cassiopeia … to which he gave his judgement very learnedly. In those dark times, Astrologer, Mathematician and Conjuror were accounted the same thing; and the vulgar did verily believe him to be a conjurer. He had many a great many mathematical instruments and glasses in his chamber, which did also confirm the ignorant in their opinion; and his servitor (to impose on Freshmen and simple people) would tell them that sometimes he should meet the spirits coming up his stairs like bees … He was generally acquainted; and every long vacation he rode into the country to visit his old acquaintances and patrons, to whom his great learning, mixed with much sweetness of humour, made him very welcome … He was a handsome, sanguine man and of excellent habit of body.

The “new star that appeared in the Swan or Cassiopeia” is the supernova of 1572, which was carefully observed by astronomers and interpreted by astrologers, often one and the same person, throughout Europe.

Star map of the constellation Cassiopeia showing the position of the supernova of 1572 (the topmost star, labelled I); from Tycho Brahe’s De nova stella. Source: Wikimedia Commons

Conjuror in the Early Modern Period meant an enchanter or magician rather than the modern meaning of sleight of hand artist and was closely associated with black magic. Allen was not the only mathematician/astrologer to be suspected of being a conjuror, the same accusation was aimed at the mathematician astronomer, and astrologer, John Dee (1527–c. 1609). At one public burning of books on black magic at Oxford university in the seventeenth century, some mathematics books were reputedly also thrown into the flames. Aubrey also relates the story that when Allen visited the courtier Sir John Scudamore (1542–1623), a servant threw his ticking watch into the moat thinking it was the devil. The anonymous author of Leicester’s Commonwealth (1584), a book attacking Elizabet I’s favourite Robert Dudley, Earl of Leicester (1532–1588) accused Allen of employing the art of “figuring” to further the earl of Leicester’s unlawful designs, and of endeavouring by the “black art” to bring about a match between his patron and the Queen. The same text accuses both Allen and Dee of being atheists. 

Anthony Wood described Allen as:

… clarrissimus vir [and] very highly respected by other famous men of his time … Bodley, Savile, Camden, Cotton, Spelman, Selden, etc. … a great collector of scattered manuscripts …  an excellent man, the father of all learning and virtuous industry, an unfeigned lover and furtherer of all good arts and sciences.

The religious controversialist Thomas Herne (d. 17722) called Allen:

… a very great mathematician and antiquary [and] a universal scholar. 

In his History of the Worthies of Britain (1662), the historian Thomas Fuller (1608–1661) wrote of Allen:

…he succeeded to the skill and scandal of Friar Bacon [and] his admirable writings of mathematics are latent with some private possessors, which envy the public profit thereof.

The jurist John Selden (1584–1654), even in comparison with the historian William Camden (1551–1623), the diplomat and librarian Thomas Bodley (1545–1613) and the Bible translator and mathematician Henry Savile, called Allen:

…the brightest ornament of the famous university of Oxford.

So, who was this paragon of scholarship and learning, whose praises were sung so loudly by his notable contemporaries?

Thomas Allen was the son of a William Allen of Uttoxeter in Staffordshire. Almost nothing is known of his background, his family, or his schooling before he went up to Oxford. It is not known how, where, when, or from whom he acquired his knowledge of mathematics. He began acquiring mathematical manuscripts very early and there is some indication that he was largely an autodidact. He went up to Trinity College Oxford comparatively late, at the age of twenty in 1561. He graduated BA in 1563 and was appointed a fellow of Trinity 1565. He graduated MA in 1567. He might have acquired his mathematical education at Merton College. There is no indication the Allen was a Roman Catholic, but he joined an exodus of Catholic scholars from Trinity, resigning his fellowship, and moving to Gloucester Hall in 1570.

In 1598 he was appointed a member of a small steering committee to supervise and assist Thomas Bodley (1535–1613) in furnishing a new university library. Allen and Bodley had both entered Oxford at around the same time, graduating BA in the same year, and remained live long friends. Allen’s patrons all played a leading role in donating to the new library. About 230 of Allen’s manuscripts are housed in the Bodleian, 12 of them donated by Allen himself when the library was founded and the rest by Kenhelm Digby, who inherited them in Allen’s will. 

Through his patron, Robert Dudley, 1st Earl of Leicester, Allen came into contact with John Dee and the two mathematician/astrologers became friends.

Robert Dudley, 1st Earl of Leicester artist disputed Source: Wikimedia Commons

The Polish noble and alchemist Olbracht Łaski (d. 1604), who took Dee with him back to Poland in 1583, also tried to persuade Allen to travel with him to the continent, but Allen declined the invitation. 

Olbracht Łaski Source: Wikimedia Commons

In this time of publish or perish for academics, where one’s status as a scholar is measured by the number of articles that you have managed to get published, it comes as a surprise to discover that Allen, who, as we have seen from the quotes, was regarded as one of the leading English mathematicians of the age, published almost nothing in his long lifetime. His reputation seems to be based entirely on his activities as a tutor and probably his skills as a raconteur. 

As a tutor, unlike a Christoph Clavius for example, there is not a long list of famous mathematicians, who learnt their trade at his feet. In fact, apart from Kenelm Digby (1603–1665) the only really well-known student of Allen’s was not a mathematician at all but the courtier and poet Sir Philip Sidney (1554–1586) for whom he probably wrote a sixty-two-page horoscope now housed in the Bodleian Library.

Sir Philip Sidney, by unknown artist, National Portrait Gallery via Wikimedia Commons

He may have taught Richard Hakluyt (1553–1616) the promotor of voyages of explorations.

Hakluyt depicted in stained glass in the west window of the south transept of Bristol Cathedral – Charles Eamer Kempe, c. 1905. Source: Wikimedia Commons

He did teach Robert Fludd (1574–1637) physician and occult philosopher

Source: Wikimedia Commons

as well as Sir Thomas Aylesbury (1576–1657), who became Surveyor of the Navy responsible for the design of the warships.

This painting by William Dobson probably represents Sir Thomas Aylesbury, 1st Baronet.
Source: Wikimedia Commons

At the end of his life, he taught and influenced the German scientific translator and communicator, Theodore Haak (1605–1690), who only studied in Oxford between 1628 and 1631.

Portrait of Theodore Haak by Sylvester Harding.Source: Wikimedia Commons

As a member of Gloucester Hall, he tutored the sons of many of the leading, English Catholic families. In this role, he tutored several of the sons of Henry Percy, 8th Earl of Northumberland the highest-ranking Catholic aristocrat in the realm. He probably recommended the Gloucester Hall scholar, Robert Widmerpoole, as tutor to the children of Henry Percy, 9th Earl of Northumberland. Percy went on to become Allen’s patron sometime in the 1580s.

HENRY PERCY, 9TH EARL OF NORTHUMBERLAND (1564-1632) by Sir Anthony Van Dyck (1599-1641). The ‘Wizard Earl’ was painted posthumously as a philosopher, hung in Square Room at Petworth. This is NT owned. Source: Wikimedia Commons

Allen became a visitor to Percy’s Syon House in Middlesex, where he became friends with the mathematician and astronomer Thomas Harriot (c. 1560–1621), who studied in Oxford from 1577 to 1580.

Portrait often claimed to be Thomas Harriot (1602), which hangs in Oriel College, Oxford. Source: Wikimedia Commons

When he died Harriot left instructions in his will to return several manuscripts that he had borrowed from Allen. Percy was an avid fan of the sciences known for his enthusiasm as The Wizard Earl. He carried out scientific and alchemical experiments and assembled one of the largest libraries in England. Allen with his experience as a manuscript collector and founder of the Bodleian probably advised Percy on his library. Harriot was not the only mathematician in Percy’s circle, he also patronised Robert Hues (1553–1632), who graduated from Oxford in 1578, Walter Warner (1563–1643), who also graduated from Oxford in 1578, and Nathaniel Torporley (1564–1632), who graduated from Oxford in 1581. Torporley was amanuensis to François Viète (1540–1603) for a couple of years. Torpoley was executor of Harriot’s papers, some of which he published together with Warner. All three of them were probably recommended to Percy by Allen. 

When Allen died, he had little to leave to anybody having spent all his money on his manuscript collection, which he left to Kenelm Digby, who in turn donated them to the Bodleian Library. But as we have seen he was warmly regarded by all who remembered him and, in some way, he helped to keep the flame of mathematics alive in England, at a time when it was burning fairly low. 

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Renaissance science – XXXVIII

There is a strong tendency to regard the so-called scientific revolution in the seventeenth century as a revolution of the mathematical science i.e., astronomy and physics, but as I have pointed out over the years many areas of knowledge went through a major development in the period beginning, in my opinion around 1400 and reaching, not a conclusion or a high point, but shall we say a stability by about 1750. During the seventeenth century one area of knowledge that experienced major developments was that of the life sciences, mostly in combination with medicine. One area that had intrigued humanity for millennia, which found an initial resolution during the second half of the seventeenth and first half of the eighteenth centuries was the puzzle of conception and procreation; in simple words, how are babies made? The starting point of this development is usually taken to be the work of the English physician, William Harvey (1578–1657),

William Harvey portrait attributed to Daniël Mijtens, c. 1627 Source: Wikimedia Commons

better known for his discovery of the blood circulation, who wrote a Exercitationes de Generatione Animalium, which was first published 1651, the main message of which was summed up on the frontispiece by the inscription Ex ovo omnia – All things come from an egg.[1]

The frontispiece Exercitationes de Generatione Animalium showing Zeus freeing all creation from an egg with the inscription Ex ovo omnia – All things come from an egg. Source Welcome Collection

It is not a coincidence that Harvey acquired his doctorate in medicine in Padua a Northern Italian, Renaissance Humanist university. Towards the end of the sixteenth century some of the Renaissance Humanist natural historians and physicians had taken up the study of embryology, not as many as had taken to botany or even as many as had taken to zoology, but the most significant work was produced by Hieronymus Fabricius ab Aquapendende (1533-1619), who was Harvey’s teacher.

As we have seen in this series as a whole, and specifically in the episodes on natural history, the Renaissance Humanists, who regarded themselves as the inheritors of classical antiquity, turned to sources from classical antiquity as their inspiration, motivation, and role models, when undertaking scientific endeavours. For the transition from materia medica to botany the major role model was Dioscorides, for zoology Pliny and Aristotle. For embryology, although both the Hippocratic Corpus and the Galenic Corpus both contain writings on the topic, it was principally to Aristotle that the Renaissance humanists turned as role model.

It has become fashionable in recent times to heavily criticise Aristotle both as a scientist and as a philosopher of science, and even to suggest that he hindered the advancement of science through his posthumous dominance. His critics, however, tend to ignore that he was for his time quite a good empirical biologist. Yes, he got things wrong and also made some, by modern standards, ridiculous statements, but a lot of his biological work was based on solid empirical observation, so with his embryology.

In the Early Modern Period, there was a heated debate between the supporters of two different theories of embryology preformation and epigenesis. The theory of preformation claimed that the male sperm contained a complete preformed, miniature infant, or homunculus, that was injected into the female womb where it grew larger over the pregnancy before emerging at birth. 

A tiny person (a homunculus) inside a sperm as drawn by Nicolaas Hartsoeker in 1695 Source: Wikimedia Commons

Opposed to this the theory of epigenesis in which the form of the infant emerges gradually, over time from a relatively formless egg. The theory of epigenesis was first proposed by Aristotle in his De Generatione Animalium (On the Generation of Animals). This work consists of five books of which the first two deal with embryology. I’m not going to give an account of all that Aristotle delivers here but just note two things. For Aristotle human procreation is the male sperm, activating the female menstrual blood. 

A brief overview of the general theory expounded in De Generatione requires an explanation of Aristotle’s philosophy. The Aristotelian approach to philosophy is teleological, and involves analyzing the purpose of things, or the cause for their existence. These causes are split into four different types: final cause, formal cause, material cause, and efficient cause. The final cause is what a thing exists for, or its ultimate purpose. The formal cause is the definition of a thing’s essence or existence, andAristotle states that in generation, the formal cause and the final cause are similar to each other, and can be thought of as the goal of creating a new individual of the species. The material cause is the stuff a thing is made of, which in Aristotle’s theory is the female menstrual blood. The efficient cause is the “mover” or what causes the thing’s existence, and for reproduction Aristotle designates the male semen as the efficient cause. Thus, while the mother’s body contains all the material necessary for creating her offspring, she requires the father’s semen to start and guide the process.

Source: The Embryo Project Encyclpopedia

 Secondly, he developed his theory of epigenesis by the empirical examination of the foetuses in incubating birds’ eggs.

Guillaume Rondelet (1507–1566) in his Libri de piscibus marinis in quibus verae piscium effigies expressae sunt (1554) and Pierre Belon (1517–1564) in his Libri de piscibus marinis in quibus verae piscium effigies expressae sunt and his Libri de piscibus marinis in quibus verae piscium effigies expressae sunt were both heavily influenced by Aristotle, and both included discussion on reproduction in their works. Famously, Leonardo da Vinci (1452–1519) carried out studies of the human embryo and foetus amongst his more general anatomical investigations but these first became known in the nineteenth century so played no role in the historical development of the discipline. 

A page showing Leonardo’s study of a foetus in the womb (c. 1510), Royal Library, Windsor Castle via Wikimedia Commons

The Italian physician Julius Caesar Aranzi (1529–1589),

Portrait of Julius Caesar Arantius (Giulio Cesare Aranzi, 1530–1589). From the Collection Biblioteca Comunale dell’Archiginnasio, Bologna, Italy. Source.

who was lecturer for anatomy and surgery at the University of Bologna, published his De humano foetu opusculum, which contains the first correct account of the anatomical peculiarities of the foetus in Rome in 1564. Further editions appeared in Venice in 1572 and in Basel in 1579. 

As with much else in sixteenth century zoology, a lead was taken by Ulisse Aldrovandi (1522–1605), who followed Aristotle in making daily examinations of fertilised chickens’ eggs, to follow the development of the embryo. He wrote in his Ornithologiae tomus alter de avibus terrestribus, mensae inservientibus et canoris (1600):

Source: Wikimedia Commons

“ex ovis duobus, et vinginti, quae Galina incubabat, quotidie unum cum maxima diligentia, ac curiositate” (each day, with the greatest care and curiosity, I dissected one of twenty-two eggy which a hen was incubating).

Although he describes in detail his embryological observation the lavishly illustrated volume only contains one picture of embryological interest, that of a chick in the act of hatching. 

Volcher Coiter (1534–1576), a Dutch student of Aldrovandi’s, who, before his studies with Aldrovandi, also studied with Gabriele Falloppio (1523–1562) and Bartolomeo Eustachi (c. 1505–1574), and then Guillaume Rondelet(1507–1566) after his time in Bolgna, and who became town physician in Nürnberg in 1569, also took up the systematic study of the development of chicken embryos at Aldrovandi’s urging.

Source: Wikimedia Commons

He published the results of his studies in his Externarum et Internarum Principalium Humani Corporis Partium Tabulae in Nürnberg in 1572, that is twenty-eight years before Aldrovandi published his.

Source: Welcome Library via Wikimedia Commons

Skeleton of a child from Externarum et Internarum Principalium Humani Corporis Partium Tabulae

It has been speculated that Aldrovandi was in fact publishing the results of Coiter’s research without acknowledgement. In 1575, Coiter published his book on ornithology De Avium Sceletis et Praecipius Musculis, which contains detailed anatomical studies of birds. 

As already stated above the major Renaissance work on embryology was by Hieronymus Fabricius ab Aquapendende (1533-1619), or more simply Girolamo Fabrici.

Source: Welcome Library via Wikimedia Commons

Hieronymus Fabricius got his doctorate in medicine under Gabriele Falloppio (1523–1562) in Padua in 1562. He succeeded Falloppio as professor for surgery and anatomy. Fabricius was responsible for the construction of the university’s first permanent anatomical theatre. Here he gave lectures and anatomical demonstrations dissecting the uterus and placenta of pregnant women in 1586. He began lecturing on the foetus in 1589 and embryology in 1592. 

Fabricius’ work displays attempts to balance traditional views and the knowledge he has won from his work. His first book on embryology, De formato foetu was published in about 1600 with many editions appearing between 1600 and 1620. His studies in embryology were much more extensive than any previous researcher and in this, his first publication on the topic, he divides embryology into three areas, firstly semen and the organs that generate it, secondly how semen interacts and generates the foetus, and finally the form of the foetus. His planned book on semen never appeared and is considered lost and his book on the generation of the foetus, De formation ovi et pulli, was published posthumously in 1621.

L0008411 Plate from “De formato foetu…” Fabricius, 1604 Credit: Wellcome Library, London. Wellcome Images images@wellcome.ac.uk http://wellcomeimages.org Plate from “De formato foetu…” Fabricius, 1604 Engraving 1604 De formato foetu. [De brutorum loquela. De venarum ostiolis. De locutione et eius instrumentis liber / Fabricius Published: 1604] Copyrighted work available under Creative Commons Attribution only licence CC BY 4.0 http://creativecommons.org/licenses/by/4.0/

In part one of De formato foetu, Fabricius discusses the form of the foetus and uterus based on his dissections. He discusses and criticises Aranzi’s De humano foetu opusculu.

L0008414 Plate from “De formato foetu…” Fabricius, 1604 Credit: Wellcome Library, London. Wellcome Images images@wellcome.ac.uk http://wellcomeimages.org – Engraving De formato foetu. [De brutorum loquela. De venarum ostiolis. De locutione et eius instrumentis liber Fabricus, Hieronymus Published: 1604 Copyrighted work available under Creative Commons Attribution only licence CC BY 4.0 http://creativecommons.org/licenses/by/4.0/

In part two he discusses the umbilical vessels, placenta etc. He follows the views of Galen and Aristotle although he gives some original but mistaken views on the placenta, which he had examined in greater detail than any previous investigators. 

L0008418 Plate from “De formato foetu…” Fabricius, 1604 Credit: Wellcome Library, London. Wellcome Images images@wellcome.ac.uk http://wellcomeimages.org – Engraving De formato foetu. [De brutorum loquela. De venarum ostiolis. De locutione et eius instrumentis liber Fabricus, Hieronymus Published: 1604 Copyrighted work available under Creative Commons Attribution only licence CC BY 4.0 http://creativecommons.org/licenses/by/4.0/

De formation ovi et pulli (On the Formation of the Egg and of the Chick) was earlier work than De formato foetu but only appeared in print two years after his death.

Source

This book is also in two parts the first of which deals with the formation of the egg, whilst the second covers the generation of the chick within the egg.

L0012570 Plate from “De formatione ovi et pulli”, Fabricius 1621 Credit: Wellcome Library, London. Wellcome Images images@wellcome.ac.uk http://wellcomeimages.org Chicken and egg. Engraving De formatione ovi et pulli Fabricius, Hieronymous Published: 1621 Copyrighted work available under Creative Commons Attribution only licence CC BY 4.0 http://creativecommons.org/licenses/by/4.0/

As before, the book is a balance act between the traditional views of Galen and Aristotle, and the knowledge that Fabricius had gained through his own research. Once again, he discusses and criticises Anzani’s views.

Both books are richly illustrated with engraved plates. 

Hieronymus Fabricius books represent the high point of Renaissance embryology and whilst far from perfect they laid the foundations for the work of his most famous student William Harvey. 


[1] The information on Harvey and his book is taken from Matthew Cobb’s excellent, The Egg & Sperm RaceThe Seventeenth-Century Scientists Who Unravelled the Secrets of Sex, Life and Growth, The Free Press, 2006, which tells the whole story outlined in it’s almost 19th century title.

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Filed under History of medicine, History of Zoology, Renaissance Science