Category Archives: History of science

Hypatia – What do we really know?

The fourth century Alexandrian mathematician and philosopher Hypatia has become a feminist icon. She is probably the second most well known woman in #histSTM after Marie Curie. Unfortunately, down the centuries she has been presented more as a legend or a myth intended to fulfil the teller’s purposes rather than a real human being. As Alan Cameron puts it in his excellent essay, Hypatia: Life, Death, and Works:[1]

A pagan in the Christian city of Alexandria, she is one of those figures whose tragic death inspired a legend which could take almost any form because so few facts are known. As a pagan martyr, she has always been a stick to beat Christians with, a symbol in the continuing struggle between science and revealed religion. The memorable account in Gibbon begins wickedly “On a fatal day in the holy season of lent.” As a woman she can be seen as a feminist as well as a pagan martyr. Her name has been a feminist symbol down the centuries more recently a potent name in lesbian and gay circles. As an Egyptian, she has also been claimed as a black woman martyr. There is an asteroid named after her, a crater on the moon, and a journal of feminist studies. As early as 1886, the women of Wichita Kansas, familiar from the movies of our youth as a lawless western cattle town, formed a literary society called the Hypatia Club. Lake Hypatia in Alabama is a retreat for freethinkers and atheists. Rather less in tune with her scholarly activity, there is Hypatia Capital, a merchant bank whose strategy focuses on the top female executives in the Fortune 1000.

A few minutes’ googling will produce countless eulogies of Hypatia as a uniquely gifted philosopher, mathematician and scientist, the second female scientist after Marie Curie, the only woman in antiquity appointed to a university chair, a theorist who anticipated Copernicus with the heliocentric hypothesis. The 2009 movie Agoragoes even further in this direction. A millennium before Kepler, Hypatia discovered that earth and its sister planets not only go round the sun but do so in ellipses, not circles. She remained unmarried, and could therefore be seen as a model of pagan virginity. Alternatively, since the monks are said to have killed her because of her influence on the prefect of Egypt, she could be seen as a slut. It is fascinating to observe how down the centuries she served as a lay figure for the prejudices of successive generations.

So what do we know about the real Hypatia? The answer is almost nothing. We know that she was the daughter of Theon (c.335–c.405) an Alexandrian mathematician and philosopher, most well known for his edition of The Elements of Euclid. We don’t know her birth date with estimates ranging from 350 to 370 CE. Absolutely nothing is known about her mother to whom no references whatsoever exist. It is assumed that she was educated by her father but once again, whilst highly plausible, no real evidence exists for this assumption. If we take a brief looked at the available sources for her biography the reason for all of this uncertainty becomes very clear.

The only source we have from somebody who actually knew Hypatia is Synesius of Cyrene (c.373–probably 413), who was one of her Christian students around 393 CE. In 410 CE he was appointed Bishop of Ptolemais. There was an edition of his letters, which contains seven letters to Hypatia and some to others that mention her. Unfortunately his letters tell us nothing about he death as he predeceased her. His last letter to her was written from his deathbed in 413 CE. Two of his letters, however, request her assistance for acquaintances in civil matters, which indicates that she exercised influence with the civil authorities.

Our second major source is Socrates of Constantinople (c.380–died after 439) a Christian church historian, who was a contemporary but who did not know her personally. He mention her and her death in his Historia Ecclesiastica:

There was a woman at Alexandria named Hypatia, daughter of the philosopher Theon, who made such attainments in literature and science, as to far surpass all the philosophers of her own time. Having succeeded to the school of Plato and Plotinus, she explained the principles of philosophy to her auditors, many of whom came from a distance to receive her instructions. On account of the self-possession and ease of manner which she had acquired in consequence of the cultivation of her mind, she not infrequently appeared in public in the presence of the magistrates. Neither did she feel abashed in going to an assembly of men. For all men on account of her extraordinary dignity and virtue admired her the more.

The third principle source is Damascius (c.458–after 538) a pagan philosopher, who studied in Alexandria but then moved to Athens where he succeeded his teacher Isidore of Alexandria (c.450–c.520) as head of the School of Athens. He mentions Hypatia in his Life of Isidore, which has in fact been lost but which survives as a fragment that has been reconstructed.

We also have the somewhat bizarre account of the Egyptian Coptic Bishop John of Nikiû (fl. 680–690):

And in those days there appeared in Alexandria a female philosopher, a pagan named Hypatia, and she was devoted at all times to magic, astrolabes and instruments of music, and she beguiled many people through her Satanic wiles. And the governor of the city honoured her exceedingly; for she had beguiled him through her magic. And he ceased attending church as had been his custom… And he not only did this, but he drew many believers to her, and he himself received the unbelievers at his house.

It is often claimed that she was head of The Neo-Platonic School of philosophy in Alexandria. This is simply false. There was no The Neo-Platonic School in Alexandria. She inherited the leadership of her father’s school, one of the prominent schools of mathematics and philosophy in Alexandria. She however taught a form of Neo-Platonic philosophy based mainly on Plotonius, whereas the predominant Neo-Platonic philosophy in Alexandria at the time was that of Iamblichus.

If we turn to her work we immediately have problems. There are no known texts that can be directly attributed to her. The Suda, a tenth-century Byzantine encyclopaedia of the ancient Mediterranean world list three mathematical works for her, which it states have all been lost. The Suda credits her with commentaries on the Conic Sections of the third-century BCE Apollonius of Perga, the “Astronomical Table” and the Arithemica of the second- and third-century CE Diophantus of Alexandria.

Alan Cameron, however, argues convincingly that she in fact edited the surviving text of Ptolemaeus’ Handy Tables, (the second item on the Suda list) normally attributed to her father Theon as well as a large part of the text of the Almagest her father used for his commentary.  Only six of the thirteen books of Apollonius’ Conic Sections exist in Greek; historians argue that the additional four books that exist in Arabic are from Hypatia, a plausible assumption.

All of this means that she produced no original mathematics but like her father only edited texts and wrote commentaries. In the history of mathematics Theon is general dismissed as a minor figure, who is only important for preserving texts by major figures. If one is honest one has to pass the same judgement on his daughter.

Although the sources acknowledge Hypatia as an important and respected teacher of moral philosophy there are no known philosophical texts that can be attributed to her and no sources that mention any texts from her that might have been lost.

Of course the most well known episode concerning Hypatia is her brutal murder during Lent in 414 CE. There are various accounts of this event and the further from her death they are the more exaggerated and gruesome they become. A rational analysis of the reports allows the following plausible reconstruction of what took place.

An aggressive mob descended on Hypatia’s residence probably with the intention of intimidating rather than harming her. Unfortunately, they met her on the open street and things got out of hand. She was hauled from her carriage and dragged through to the streets to the Caesareum church on the Alexandrian waterfront. Here she was stripped and her body torn apart using roof tiles. Her remains were then taken to a place called Cinaron and burnt.

Viewed from a modern standpoint this bizarre sequence requires some historical comments. Apparently raging mobs and pitched battles between opposing mobs were a common feature on the streets of fourth-century Alexandria. Her murder also followed an established script for the symbolic purification of the city, which dates back to the third-century. There was even a case of a pagan statue of Separis being subjected to the same fate. There is actually academic literature on the use of street tiles in street warfare[2]. What is more puzzling is the motive for the attack.

The exact composition of the mob is not known beyond the fact that it was Christian. There is of course the possibility that she was attacked simply because she was a woman. However, she was not the only woman philosopher in Alexandria and she enjoyed a good reputation as a virtuous woman. It is also possible that she was attacked because she was a pagan. Once again there are some contradictory facts to this thesis. All of her known students were Christians and she had enjoyed good relations with Theophilus the Patriarch of Alexandria (384–412), who was responsible for establishing the Christian dominance in Alexandria. Theophilus was a mentor of Synesius. Also the Neoplatonic philosophy that she taught was not in conflict with the current Christian doctrine, as opposed to the Iamblichan Neoplatonism. The most probably motive was Hypatia’s perceived influence on Orestes (fl. 415) the Roman Prefect of Egypt who was involved in a major conflict with Cyril of Alexandria (c.376–444), Theophilis’ nephew and successor as Patriarch of Alexandria. This would make Hypatia collateral damage in modern American military jargon. In the end it was probably a combination of all three factors that led to Hypatia’s gruesome demise.

Hypatia’s murder has been exploited over the centuries by those wishing to bash the Catholic Church but also by those wishing to defend Cyril, who characterise her as an evil woman. Hypatia was an interesting fourth-century philosopher and mathematician, who deserves to acknowledged and remembered for herself and not for the images projected on her and her fate down the centuries.

[1]Alan Cameron, Hypatia: Life, Death, and Works, in Wandering Poets and Other Essays on Late Greek Literature and Philosophy, OUP, 2016 pp. 185–203 Quote pp. 185–186

[2]You can read all of this in much more detail in Edward J. Watts’ biography of Hypatia, Hypatia: The Life and Legend of an Ancient Philosopher, OUP, 2017, which I recommend with some reservations.



Filed under History of Mathematics, History of science, Ladies of Science, Myths of Science

Galileo’s the 12th most influential person in Western History – Really?

Somebody, who will remain nameless, drew my attention to a post on the Presidential Politics for America blog shortly before Christmas in order to provoke me. Anybody who knows me and my blogging will instantly recognise why I should feel provoked if they just read the opening paragraph.

Despite the paradigm-shifting idea of our #28 Nicolaus Copernicus, for nearly a century afterward his heliocentric theory twisted in the solar wind. It took another man to confirm Copernicus’s daring theory. That alone would make this other man an all-time great contributor to Western science, but he gifted us so much more than merely confirming someone else’s idea. He had a series of inventions, discoveries, and theories that helped modernize science. His accomplishments in mechanics were without precedent. His telescope observed what was once unobservable. Perhaps most importantly, he embodied, furthered, and inspired a growing sentiment that truth is a slave to science and facts, not authority and dogma.

This man was Galileo Galilei, and he’s the 12thmost influential person in Western History.

Before I start on my usually HistSci_Hulk demolition job to welcome the New Year I should point out that this crap was written by somebody claiming to be a history teacher; I feel for his student.

This post is part of a long-term series on The Top 30 Most Influential Western European Figures in History; I kid you not! Sorry, but I’m not a fan of rankings in general and to attempt to rank the historical influence of Western Europeans is in my opinion foolhardy at best and totally bonkers at worst.

We turn our attention to his #11 Galileo Galilei. We start with the very obvious false claim, the very first one in fact, Galileo did not ‘confirm Copernicus’s daring theory.’ Next up we have the statement: ‘He had a series of inventions, discoveries, and theories that helped modernize science.’

Only in his teens, he identified the tautochronic curve that explains why the pendulum behaves as it does. This discovery laid the groundwork for Christian [sic] Huygens to create the world’s first pendulum clock, which became the most accurate method of keeping time into the twentieth century. 

It is Christiaan not Christian Huygens. Galileo discovered the isochronal principle of the pendulum but the earliest record of his researches on the pendulum is in a letter to his patron Guidobaldo del Monte dated 2 November 1602, when he was 38 years old. The story that he discovered the principle, as a teenager was first propagated posthumously by his first biographer Viviani and to be taken with a pinch of salt. He didn’t discover that the free circular pendulum swing is not isochronal but only the tautochrone curve is; this discovery was actually made by Huygens. There is no evidence that Galileo’s design of a never realised pendulum clock had any connections with or influence on Huygens’ eventually successfully constructed pendulum clock. That pendulum clocks remained the most accurate method of keeping time into the twentieth century is simply wrong.

The precocious Galileo also invented thethermoscope…

 It is not certain that Galileo invented the thermoscope; it is thought that his friend Santorio Santorio actually invented it; he was certainly the first during the Renaissance to publish a description of it. The invention was attributed to Galileo, Santorio, Robert Fludd and Cornelius Drebble. However, the principle on which it was based was used in the Hellenic period and described even earlier by Empedocles in book On Nature in 460 BCE. This is part of a general pattern in the Galileo hagiography, inventions and discoveries that were made by several researchers during his lifetime are attributed solely to Galileo even when he was not even the first to have made them.

At just 22, he published a book onhydrostatic balance, giving him his first bit of fame.

 This ‘book’, La Bilancetta or The Little Balance was actually a booklet or pamphlet and only exists in a few manuscripts so during his lifetime never printed. He used it together with another pamphlet on determining centres of gravity to impress and win patrons within the mathematical community such as Guidobaldo del Monte and Christoph Clavius; in this he was successful.

He attended medical school but, for financial reasons, he had to drop out and work as a tutor. Nevertheless, he eventually became chair of the mathematics department at theUniversity of Pisa.

He studied medicine at the University of Pisa because that was the career that his father had determined for him. He dropped out, not for financial reasons but because he wanted to become a mathematician and not a physician. He studied mathematics privately in Florence and having established his abilities with the pamphlets mentioned above was, with the assistance of his patrons, appointed to teach mathematics in Pisa. However, due to his innate ability to piss people off his contract was terminated after only three years. His patrons now helped him to move to the University of Padua.

He taught at Padua for nearly 20 years, and it’s there where he turned from reasonably well-known Galileo Galilei to Galileo[emphasis in original]. Like the great Italian artists of his age, he became so talented and renowned that soon just his first name sufficed.

This is simply rubbish. He remained virtually unknown outside of Padua until he made his telescopic discoveries in 1610. He turned those discoveries into his exit ticket and left Padua as soon as possible. As for his name, he is, for example, known in English as Galileo but in German as Galilei.

We now turn to mechanics the one field in which Galileo can really claim more than a modicum of originality. However, even here our author drops a major clangour.

Through experimentation, he determined that a feather falls slower than a rock not because of the contrasting weight but because of the extra friction caused by the displacement of Earth’s atmosphere on the flatter object. 

Through experimentation! Where and when did Galileo build his vacuum chamber? Our author missed an opportunity here. This was, of course, Galileo’s most famous thought experiment in which he argues rationally that without air resistance all objects would fall at the same rate. In fact Galileo’s famous use of thought experiments doesn’t make an appearance in this account at all.

Galileo built on this foundation a mathematical formula that showed the rate of acceleration for falling objects on Earth. Tying math to physics, he essentially laid the groundwork for later studies of inertia. These mechanical discoveries provided a firm launching point for Isaac Newton’s further modernization of the field.

It is time for the obligatory statement that the mean speed formula the basis of the mathematics of free fall was known to the Oxford Calculatores and the Paris Physicists in the fourteenth century and also the laws of free fall were already known to Giambattista Benedetti in the sixteenth century. As to inertia, Galileo famously got it wrong and Newton took the law of inertia from Descartes, who in turn had it from Isaac Beeckman and not Galileo. In the late sixteenth and early seventeenth centuries several researchers tied mathematics to physics, many of them before Galileo. See comment above about attributing the work of many solely to Galileo. We now turn to astronomy!

In the early 1600s, despite Copernicus’s elegant heliocentric model of the solar system having debuted more than a half-century earlier, skeptics remained. Indeed, there was an ongoing divide among astronomers; some favored the Copernican model while others clung to the traditional Ptolemaic premise adopted by the Catholic Church, which put the earth at the universe’s center. Even Tycho Brahe, a leading post-Copernican astronomer, favored geocentrism, though his Tychonic system did make some allowances for Copernicus’s less controversial ideas. Brahe’s position helped him avoid the fate of heliocentrist Giordano Bruno who was burned at the stake by the Catholic Inquisition in 1600. This heated astronomical climate awaited Galileo Galilei.

There is nothing particularly elegant about Copernicus’ heliocentric model of the solar system. In fact it’s rather clunky due to his insistence, after removing the equant point, of retaining the so-called Platonic axiom of uniform circular motion. His model was in fact more cluttered and less elegant than the prevailing geocentric model from Peuerbach. Sceptics didn’t remain, as our author puts it, implying in this and the following sentences that there was no reason other than (religious) prejudice for retaining a geocentric model. Unfortunately, as I never tire of repeating, Copernicus’ model suffered from a small blemish, a lack of proof. In fact the vast majority of available empirical evidence supported a geocentric system. You know proof is a fundamental element of all science, including astronomy. If I were playing mythology of science bingo I would now shout full house with the introduction of Giordano Bruno into the mix. No, Giordano was not immolated because he was a supporter of heliocentricity.

Like Bruno, Galileo knew Copernicus was right, and he set out to prove it. Early in the seventeenth century, he received word about a new invention created by the German-Dutch spectacle-makerHans Lippershey In 1608, Lippershey used his knowledge of lenses to make a refracting telescope, which used lenses, an eye piece, and angular strategies to bend light, allowing in more of it. More light could clarify and magnify a desired object, and Lippershey’s rudimentary design could make something appear about three times bigger. Galileo, though he never saw a telescope in person nor even designs of one, heard a basic description of it, checked the information against his brain’s enormous database, realized it could work, and built one of his own. A better one.

Comparing Bruno with Galileo is really something one should avoid doing. Our author’s description of how a refracting telescope works is, I admit, beyond my comprehension, as the function of a refracting telescope is apparently beyond his. The claim that Galileo never saw a telescope, which he made himself, has been undermined by the researches of Mario Biagioli, who argues convincingly that he probably had seen one. I love the expression “checked the information against his brain’s enormous database.” I would describe it not so much as hyperbole as hyperbollocks!

With his improved telescope he could magnify objects thirty times, and he immediately pointed it to the once unknowable heavens and transformed astronomy in numerous ways:

I will start with the general observation that Galileo was by no means the only person pointing a telescope at the heavens in the period between 1609 and 1613, which covers the discoveries described below. He wasn’t even the first that honour goes to Thomas Harriot. Also, all of the discoveries were made independently either at roughly the same time or even earlier than Galileo. If Galileo had never heard of the telescope it would have made virtually no difference to the history of astronomy. He had two things in his favour; he was in general a more accurate observer that his competitors and he published first. Although it should be noted that his principle publication, the Sidereus Nuncius, is more a press release that a scientific report. The first telescope Galileo presented to the world was a 9X magnification and although Galileo did build a 30X magnification telescope most of his discoveries were made with a 20X magnification model. The competitors were using very similar telescopes. “…the once unknowable heavens” we actually already knew quite a lot about the heavens through naked-eye observations.

  • It was assumed that the moon, like all the heavenly spheres, was perfectly smooth. Galileo observed craters and mountains. He inferred, accurately, that all celestial objects had blemishes of their own.

This was actually one of Galileo’s greatest coups. Thomas Harriot, who drew telescopic images of the moon well before Galileo did not realise what he was seeing. After seeing Galileo’s drawings of the moon in the Sidereus Nuncius, he immediately realised that Galileo was right and changed his own drawing immediately. One should, however, be aware of the fact that throughout history there were those who hypothesised that the shadows on the moon were signs of an uneven surface.

  • Though Jupiter had been observed since the ancient world, what Galileo was the first to discover was satellites orbiting around it — the Jovian System. In other words, a planet other than the Earth had stuff orbiting it. It was another brick in Copernicus’s “we’re not that important” wall.

And as I never tire of emphasising, Simon Marius made the same discovery one day later. I have no idea what Copernicus’s “we’re not that important” wall is supposed to be but the discovery of the moons of Jupiter is an invalidation of the principle in Aristotelian cosmology that states that all celestial bodies have a common centre of rotation; a principle that was already violated by the Ptolemaic epicycle-deferent model. It says nothing about the truth or lack of it of either a geocentric or heliocentric model of the cosmos.

  • Pointing his telescope at the sun, Galileo observed sunspots. Though the Chinese first discovered them in 800 BC, as Westerners did five hundred years later, no one had seen or sketched them as clearly as Galileo had. It was another argument against the perfect spheres in our sky.

Telescopic observations of sunspots were first made by Thomas Harriot. The first publication on the discovery was made by Johannes Fabricius. Galileo became embroiled in a meaningless pissing contest with the Jesuit astronomer, Christoph Scheiner, as to who first discovered them. The best sketches of the sunspots were made by Scheiner in his Rosa Ursina sive Sol (Bracciano, 1626–1630).

  • Galileo also discovered that Venus, like the moon, has phases (crescent/quarter/half, waxing/waning, etc.). This was a monumental step in confirming Copernicus’s theory, as Venusian phases require certain angles of sunlight that a geocentric model does not allow.

The phases of Venus were discovered independently by at least four observers, Thomas Harriot, Simon Marius, Galileo and the Jesuit astronomer Paolo Lembo. The astronomers of the Collegio Romano claimed that Lembo had discovered them before Galileo but dating the discoveries is almost impossible. In a geocentric model Venus would also have phases but they would be different to the ones observed, which confirmed that Venus, and by analogy Mercury, whose phases were only observed much later, orbits the Sun. Although this discovery refutes a pure geocentric system it is still compatible with a Capellan system, in which Venus and Mercury orbit the Sun in a geocentric model, which was very popular in the Middle ages and also with any of the Tychonic and semi-Tychonic models in circulation at the time so it doesn’t really confirm a heliocentric model

  • The observable hub of the Milky Way galaxy was assumed to be, just as it looks to us, a big, milky cloud. Galileo discovered it was not a cloud, but a huge cluster of stars. (We now know it numbers in the billions.)

Once again a multiple discovery made by everybody who pointed a telescope at the heavens beginning with Lipperhey.

Galileo not only confirmed Copernicus’s heliocentric theory, but he allowed the likes of Johannes Kepler to more accurately plot out the planets’ orbits, Isaac Newton to explain how it was happening, and Albert Einstein to explain why. It was such a colossal step forward for the observable universe that some people didn’t even believe what they were seeing in the telescope, electing to instead remain skeptical of Galileo’s “sorcery.”

Galileo did not in any way confirm Copernicus’ heliocentric theory. In fact heliocentricity wasn’t confirmed until the eighteenth century. First with Bradley’s discovery of stellar aberration in 1725 proving the annual orbit around the sun and then the determination of the earth’s shape in the middle of the century indirectly confirming diurnal rotation. The telescopic observations made by Galileo et al had absolutely nothing to do with Kepler’s determination of the planetary orbits. Newton’s work was based principally on Kepler’s elliptical system regarded as a competitor to Copernicus’ system, which Galileo rejected/ignored, and neither Galileo nor Copernicus played a significant role in it. How Albert got in here I have absolutely no idea. Given the very poor quality of the lenses used at the beginning of the seventeenth century and the number of optical artifacts that the early telescopes produced, people were more than justified in remaining skeptical about the things apparently seen in telescopes.

Ever the watchdog on sorcery, it was time for the Catholic Church to guard its territory. Protective of geocentrism and its right to teach us about the heavens, the Church had some suggestions about exactly where the astronomer could stick his telescope. In 1616, under the leadership of Pope Paul V, heliocentrism was deemed officially heretical, and Galileo was instructed “henceforth not to hold, teach, or defend it in any way.”

The wording of this paragraph clearly states the author’s prejudices without consideration of historical accuracy. Galileo got into trouble in 1615/16 for telling the Catholic Church how to interpret the Bible, a definitive mistake in the middle of the Counter Reformation. Heliocentrism was never deemed officially heretical. The injunction against Galileo referred only to heliocentrism as a doctrine i.e. a true theory. He and everybody else were free to discuss it as a hypothesis, which many astronomers preceded proceeded to do.

A few years later, a confusing stretch of papal leadership got Galileo into some trouble. In 1623,Pope Urban VIII took a shine to Galileo and encouraged his studies by lifting Pope Paul’s ban. A grateful Galileo resumed his observations and collected them into his largest work, 1632’s “Dialogue Concerning the Two Chief World Systems” In it, he sums up much of his observations and shows the superiority of the newer heliocentric model. The following year, almost as if a trap were set, the Catholic Inquisition responded with a formal condemnation and trial, charging him with violating the initial 1616 decree. Dialogue was placed on the Church’s Index of Prohibited Books.

Maffeo Barberini, Pope Urban VIII, had been a good friend of Galileo’s since he first emerged into the limelight in 1611 and after he was elected Pope did indeed show great favour to Galileo. He didn’t, however, lift Paul V’s ban. It appears that he gave Galileo permission to write a book presenting the geocentric and heliocentric systems, as long as he gave them equal weight. This he very obviously did not do; Galileo the master of polemic skewed his work very, very heavily in favour of the heliocentric system. He had badly overstepped the mark and got hammered for it.  He, by the way, didn’t resume his observations; the Dialogo is based entirely on earlier work. One is, by the way, condemn after being found guilty in a trial not before the trial takes place when one is charged or accused.

Galileo’s popularity, combined with a sheepish Pope Urban, limited his punishment to a public retraction and house arrest for his remaining days. At nearly 70, he didn’t have the strength to resist. Old, tired, and losing his vision after years of repeatedly pointing a telescope at the brightest object in the solar system, he accepted his sentence. Blind and condemned, his final years were mostly spent dictating “Two New Sciences,” which summarized his 30 years of studying physics.

Galileo’s popularity would not have helped him, exactly the opposite. People who were highly popular and angered the Church tended to get stamped on extra hard, as an example to the masses. Also, Urban was anything but sheepish. The public retraction was standard procedure for anyone found guilty by the Inquisition and the transmission of his sentence from life imprisonment to house arrest was an act of mercy to an old man by an old friend. Whether Galileo’s telescopic observations contributed to his blindness is disputed and he hadn’t really made many observations since about 1613. The work summarised in the Discorsi was mostly carried out in the middle period of his life between 1589 and 1616.

The author now veers off into a discussion, as to who is the father or founder of this or that and why one or other title belongs to Copernicus, Newton, Aristotle, Bacon etc. rather than Galileo. Given his belief that one can rank The Top 30 Most Influential Western European Figures in History, it doesn’t surprise me that he is a fan of founder and father of titles. They are, as regular readers will already know, in my opinion a load of old cobblers. Disciplines or sub-disciplines are founded or fathered over several generations by groups of researchers not individuals.

His article closes with a piece of hagiographical pathos:

Moreover, Galileo’s successes were symbolic of a cornerstone in modern science. His struggle against the Church embodied the argument that truth comes from experience, experiments, and the facts — not dogma. He showed us authority and knowledge are not interchangeable. Though the Inquisitors silenced him in 1633, his discoveries, works, and ideas outlived them. For centuries, he has stood as an inspiration for free thinkers wrestling against ignorant authority.

This is typical exaggerated presentation of the shabby little episode that is Galileo’s conflict with the Catholic Church. It wasn’t really like that you know. Here we have the heroic struggle of scientific truth versus religious dogma, a wonderful vision but basically pure bullshit. What actually took place was that a researcher with an oversized ego, Galileo, thought he could take the piss out of the Pope and the Catholic Church. As it turned out he was mistaken.

Being a history teacher I’m sure our author would want me to grade his endeavours. He has obviously put a lot of work into his piece so I will give him an E for effort. However, it is so strewn with errors and falsities that I can only give him a F for the content.

























Filed under History of Astronomy, History of Optics, History of science, Myths of Science, Renaissance Science

Christmas Trilogy 2018 Part 1: The Harmonic Isaac

Isaac Newton is often referred to, as the ‘father’ of modern science but then again so is Galileo Galilei. In reality modern science has many fathers and some mothers as well. Those who use this accolade tend to want to sweep his theological studies and his alchemy under the carpet and pretend it doesn’t really count. Another weird aspect of Newton’s intellectual universe was his belief in prisca theology. This was the belief that in the period following the creation humankind had perfect knowledge of the natural world that got somehow lost over the centuries. This meant for Isaac that in his own scientific work he wasn’t making discoveries but rediscovering once lost knowledge. Amongst, what we would now regard as his occult beliefs, Isaac also subscribed to the Pythagorean belief in Harmonia (harmony), as a unifying concept in the cosmos.


Robert Fludd’s Pythagorean Monocord

Although he was anything but a fan of music, he was a dedicated student of Harmonia, the mathematical theory of proportions that was part of the quadrivium. According to the legend Pythagoras was the first to discover that musical interval can be expressed as simple ratios of whole numbers related to a taut string: 1:1 (unison), 2:1 (octave), 3:2 (perfect fifth), 4:3 (perfect fourth), 5:4 (major third), 6:5 (minor third). Unfortunately, anybody who has studied the theory of music knows these ratios don’t quite work. If you start on a given tone and move up in steps of a perfect fifth you don’t actually arrive back at the original tone seven octaves higher after twelve fifths but slightly off. This difference is known as the Pythagorean comma. This disharmony was well known and in the sixteenth and seventeenth centuries a major debate developed on how to ‘correctly’ divide up musical scale to avoid this problem. The original adversaries were Gioseffo Zarlino (1570–1590) and Vincenzo Galilei (1520–1591) (Galileo’s father) and Kepler made a contribution in his Harmonice Mundi; perhaps the most important contribution being made by Marin Mersenne (1588–1648) in his Harmonie universelle, contenant la théorie et la pratique de la musique.


Harmonie Universelle title page

Here he elucidated Mersenne’s Laws:

Frequency is:

  1. Inversely proportional to the length of the string (this was known to the ancients; it is usually credited toPythagoras)
  2. Proportional to the square root of the stretching force, and
  3. Inversely proportional to the square root of the mass per unit length.

Source: Gouk p. 115

As a student Newton took up the challenge in one of his notebooks and we don’t need to go into his contribution to that debate here, however it is the first indication of his interest in this mathematics, which he would go on to apply to his two major scientific works, his optics and his theory of gravity.

After he graduated at Cambridge Newton’s first serious original research was into various aspects of optics. This led to his first published paper:

A Letter of Mr. Isaac Newton, Professor of the Mathematicks in the University of Cambridge; Containing His New Theory about Light and Colors: Sent by the Author to the Publishee from Cambridge, Febr. 6. 1671/72; In Order to be Communicated to the R. Society

In which he described his experiments with a prism that showed that white light consists of blended coloured light and that the spectrum that one produces with a prism is the splitting up of the white light into its coloured components. Previous theories had claimed that the spectrum was produced by the dimming or dirtying of the white light by the prism. Newton wrote an extensive paper expanding on his optical research, An hypothesis explaining the properties of light, but due to the harsh criticism his first paper received he withheld it from publication. This expanded work only appeared in 1704 in his book, Opticks: A Treatise of the Reflections, Refractions, Inflections & Colours of Light. Here we can read:

In the Experiments of the fourth Proposition of the first Part of this first Book, when I had separated the heterogeneous Rays from one another, the Spectrum ptformed by the separated Rays, did in the Progress from its End p, on which the most refrangible Rays fell, unto its other End t, on which the most refrangible Rays fell, appear tinged with this Series of Colours, violet, indigo, blue, green, yellow, orange, red, together with all their intermediate Degrees in a continual Succession perpetually varying . So that there appeared as many Degrees of Colours, as there were sorts of Rays differing in Refrangibility.

This is of course the list of seven colours that we associate with the rainbow today. Before Newton researchers writing about the spectrum listed only three, four or at most five colours, so why did he raise the number to seven by dividing the blue end of the spectrum into violet, indigo and blue? He did so in order to align the number of colours of the spectrum with the notes on the musical scales. In the Queries that were added at the end of the Opticks over the years and the different editions we find the following:

Qu. 13. Do not several sorts of Rays make Vibrations of several bigness, which according to their bignesses excite Sensations of several Colours, much after the manner that the Vibrations of the Air, according to their several bignesses excite Sensations of several Sounds? And particularly do not Vibrations for making a Sensation of deep violet, the least refrangible the largest for making a Sensation of deep red, and several intermediate sorts of Rays, Vibrations of several intermediate bignesses to make Sensations of the several intermediate Colours?

Qu. 14. May not the harmony and discord of Colours arise from the proportions of the Vibrations propagated through the Fibres of the optick Nerves into the Brain, as the harmony and discord of Sounds arise from the proportions of the Vibrations of the Air? And some Colours, if they be view’d together, are agreeable to one another, as those of Gold and Indigo and other disagree.

In the An Hypothesis, Newton published a diagram illustrated the connection he believed to exist between the colours of the spectrum and the notes of the scale.


Source: Gouk p. 118

Interestingly Voltaire presented Newton’s theory in his Elemens de la philosophie de Newton (1738), again as a diagram.


Source: Gouk p. 119

Turning now to Newton’s magnum opus we find the even more extraordinary association between his theory of gravity and the Pythagorean theory of harmony. Newton’s Law of Gravity is probably the last place one would expect to meet with Pythagorean harmony but against all expectations one does. In unpublished scholia on Proposition VIII of Book III of the Principia(the law of gravity) Newton claimed that Pythagoras had known the inverse square law. He argued that Pythagoras had discovered the inverse-square relationship in the vibration of strings (see Mersenne above) and had applied the same principle to the heavens.

…consequently by comparing those weights with the weights of the planets , and the lengths of the strings with the distances of the planets, he understood by means of the harmony of the heavens that the weights of the planets towards the Sun were reciprocally as the squares of their distances from the Sun.[1]

Although Newton never published this theory David Gregory (1661–1708) did. David Gregory was a nephew of the physicist James Gregory who in 1684 became professor of mathematics at the University of Edinburgh, where he became “the first to openly teach the doctrines of the Principia, in a public seminary…in those days this was a daring innovation.”[2]


Davis Gregory bust Source: Wikimedia Commons

In 1691, with Newton’s assistance, he was appointed Savilian Professor of Astronomy at Oxford going on to become an important mathematician, physicist and astronomer. He worked together with Newton on the planned second edition of the Principia, although he did not edit it, dying in 1708; the second edition appearing first in 1713 edited by Richard Bentley. In his Astronomiae physicae et geometricae elementa, a semi-popular presentation of Newton’s theories first published in Latin in 1702


Gregory wrote the following:

The Elements of Astronomy, Physical and Geometrical By David Gregory M.D. SavilianProfessor of Astronomy at Oxfordand Fellow of the Royal Society (1615)

The Author’sPreface

As it is manifest that the Ancients were apprized of, and had discover’d the Gravity of all Bodies towards one another, so also they were not unacquainted with the Law and Proportion which the action of Gravity observ’d according to the different Masses and Distances. For that Gravity is proportional to the Quantity of Matter in the heavy Body, Lucretiusdoes sufficiently declare, as also that what we call light Bodies, don’t ascend of their own accord, but by action of a force underneath them, impelling them upwards, just as a piece of Wood is in Water; and further, that all Bodies, as well the heavy as the light, do descend in vacuo, with an equal celerity. It will be plain likewise, from what I shall presently observe, that the famous Theorem about the proportion whereby Gravity decreases in receding from the Sun, was not unknown at least to Pythagoras. This indeed seems to be that which he and his followers would signify to us by the Harmony of the Spheres: That is, they feign’d Apolloplaying on a Harp of seven Strings, by which Symbol, as it is abundantly evident from Pliny, Macrobiusand Censorinus, they meant the Sun in Conjunction with the seven planets, for they made him the leader of that Septenary Chorus, and Moderator of Nature; and thought that by his Attractive force he acted upon the Planets (and called it Jupiter’s Prison, because it is by this Force that he retains and keeps them in their Orbits, from flying off in Right Lines) in the Harmonical ration of their Distances. For the forces, whereby equal Tensions act upon Strings of different lengths (being equal in other respects) are reciprocally as the Squares of the lengths of the Strings.

I first came across this theory, as elucidated by Gregory, years ago in a book, which book I have in the meantime forgotten, where it was summarised as follows:

Gravity is the strings upon which the celestial harmony is played.









[1]Quoted from 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 The inspiration and principle source for this blog post.

[2]Quoted from Significant Scots: David Gregory



Filed under History of Astronomy, History of Mathematics, History of Optics, History of science, Newton

Internalism vs. Externalism?

This is one of those blog posts where I do some thinking out loud[1]. I not really sure where it’s going and it might not end up where I intended it to. I shall be skating on the thin ice of historiography. The dictionary defines historiography as follows:

  1. The wring of history
  2. The study of the development of historical method, historical research, and writing
  3. Any body of historical literature[2]

I’m using the term in the sense of definition (2) here. Formulated slightly differently historiography is the methodology of doing history, i.e. historical research and the reporting of that research in writing. Maybe unfortunately there isn’t just one historiography or methodology for doing history there are historiographies, plural that often conflict or even contradict each other, dividing historians into opposing camps indulging in trench warfare with each other through their monographs and journals.

On the whole I tend to view historiographies with a jaundiced eye. I have a maxim for historiographies: ‘Historiography becomes dogma and dogma blinds.’ I like to mix and match my methodologies according to what I happen to be engaged in at any given moment. A single methodology or historiography is just one perspective from which to view a given historical topic and it is often useful to view it from several different perspectives simultaneously, even seemingly contradictory ones.

Since I have been involved in the history of science, and I realise with somewhat horror that is a good half century now, one of the on going historiography debates, or even disputes, within the disciple has been Internalism vs. Externalism.


Definitions are very slippery things but if I was asked to explain what this means my first simple answer would be internalism is the historical study of the facts, hypotheses, theories etc. that science has produced and externalism is the historical study of the contexts in which those facts, hypotheses, theorems etc. were discovered, developed, formulated etc.

To give an abstract example from the history of mathematics an internalist would be interested in when mathematician X first proved theorem Y and the technical method that he used to do so. They might investigate on whose or which work X built his own work  and also possibly, who picked up on X’s proof and extended it mathematically; anything extraneous to that wouldn’t not be the concern of our imaginary internalist. An externalist would, however, be at least as interested in the context in which X carried out his mathematical endeavours. They would possibly look at X’s biography, how X came to be doing this work at all, what were X’s motivations for this particular piece of research, in which context (university, court mathematicus, insurance mathematician etc.) X was carrying out this work, who was financing it and why etc., etc. From this brief description it should be clear that the perspective of the internalist is a very narrow, very focused one, whereas that of the externalist is a very broad, very sweeping one, although any given externalist investigation might only concentrate on one or two of the various perspectives that I have listed.

Extreme internalism assumes that just presenting the ‘facts’ in the history of science is adequate because science is somehow independent of the world/society/culture in which it arose/developed/originated. Science is totally objective in some way and doesn’t need a context. Extreme internalism also tends to be highly presentist. That is it looks back through history and selects those events/developments in science that can be identified within science, as it exists today. It sees science as cumulative and progressive even teleological. It’s destination being some sort of complete truth.

Externalism sees science at any given point in time as a product of the world/society/culture in which it arose/developed/originated. The externalist historical picture includes all the bits the researchers of the period got wrong and were subsequently jettisoned somewhere down the line on the way to the present. Externalism sees any period of science, as not just embedded in its world/society/culture but as an integral part of the whole of that world/society/culture that cannot and should not be viewed independently.

To give just a couple of very simple examples out of my own main personal historical area of interest: An internalist is only interested in Kepler’s three laws of planetary motion as results that are still valid today. They are not interested in the complex twists and turns of Kepler’s battle to find the first two laws, which he outlines in great detail and great depth in his Astronomia nova. As for the third law, they take it gladly and ignore all of the remaining five hundred pages of the Harmonice Mundi, with its bizarre theories of consonance and dissonance, and cosmic harmony. As for Kepler’s distinctly unscientific motivations, the internalist shudders in horror. For the externalist everything that the internalist rejects is an interesting field of study. They are not just interested in Kepler’s laws as results but in how he arrived at them and what was driving him to search for them in the first place.

Turning to Newton, it is now a commonplace that he devoted far more time and energy to studying alchemy and theology that he did to either physics or mathematics. For the internalist these ‘non-scientific’ areas are an irrelevance to be ignored, all that matters are the scientific results, the law of gravity, the calculus etc. Externalists have shown that the various diffuse areas of Newton’s thoughts and endeavours are intertwined into a complex whole and if one really wants to understand the man and his science then one must regard and attempt to understand that whole.

Where do I stand on this issue? I think it should be obvious to anybody who regularly reads this blog that I am a convinced externalist. I am, however, happy to admit that when I first became interested in the history of mathematics as a teenager I was to all intents and purposes an internalist. Who discovered this or that theorem and when? Who developed this or that method of solving this or that type of problem? These were the questions that initially interested me. I also had strong presentist and even Whiggish tendencies. For those who have forgotten or maybe don’t know yet, the Whig theory of history is the belief that human existence or in this case science, is progressing towards some sort of final truth. Over the years, as I learnt more, my views changed and I became slowly but surely an externalist. This change was, at the latest, completed as I worked for many years, my apprenticeship, in a research project into the history of formal logic. This project was official called, Case Studies into a Social History of Formal Logic, where social is a synonym for external.

As I see it extreme internalism is not just too narrow, too focused but is actually distorting. The internalist history of mathematics, for example, when considering antiquity tends to concentrate on what could be called higher mathematics–the Euclids, Archimedes et al– who only represent a very small minority of those engaged in mathematical pursuits in their period and whose results were only interesting to an equally small minority. In doing so they ignore the vast majority of mathematical practitioners surveyors, bookkeepers extra, whose work actually contributed more in real terms to their societies than that of the ‘star’ mathematicians. A good example is the much-touted Babylonian mathematics, which was largely developed by clerks doing administration not by mathematicians. This fact is simply ignored by internalist historians of mathematics, who are only interested in the results.

Turning to the High Middle Ages and Renaissance, traditional internalist history of mathematics tend to simply ignore this period as having no mathematics worth mentioning. In reality it was the mathematical practitioners of this period–astrologers, astronomers, geographers, cartographers, surveyors, architects, engineers, instrument designers and makers, globe makerset al.–who created the mathematics that drove the so-called scientific revolution.

Having being very rude about internalist history of science I should point out that I by no means reject it totally, in fact exactly the opposite. Anybody who opens Newton’s Principia for the first time, even in the excellent modern English translation by Cohen and Whitman would probably understand very little of the mathematics and physics that they would find there. They have a choice either to spend several months chewing through Newton’s masterpiece or alternatively to turn to Cohen excellent internalist guide to the contents. The same is true of virtually any historical STEM text. Close internalist readings and interpretations help the historian to comprehension. Having gained that internalist comprehension they should, in my opinion, embed that comprehension into its wider externalist context.

Historians of science should be simply historian, in the first instance, investigating the breadth and depth of a discipline within its social context. However this also implies a solid understanding of the science involved, i.e. the internal aspects. You can’t investigate the role of a scientific discipline within a social context if you don’t understand the science. This means for me, that a good historian of science must be both an internalist and an externalist, weaving together both approaches into a coherent whole.

All of the above is of course my own subjective take on the dichotomy and they are certainly other viewpoints and other opinions on the issue. As always, readers are welcome to ventilate their views in the comments.

For any future historian, who might be interested in my motivation for writing this post, it was inspired by a request from a reader to write something on the ‘conflict’ between internalist and externalist histories of science and illustrate it with examples of the two different approaches with reference to my own blog posts. I’m not sure if that which I have written really fulfils their request and as should be obvious I, as a convinced externalist, can’t really supply the desired examples. However I am grateful to the reader for having motivated me to write something on the topic even if it not really what they wanted.

[1]If I was being pretentious I might have said, “Where I philosophise” but I don’t regard my stream of consciousness meanderings as rigorous enough to be dignified with the term philosophy.

[2]Collins English Dictionary online.



Filed under History of science, Uncategorized

The Jesuit Mirror Man

Although the theory that a curved mirror can focus an image was already known to Hero of Alexandria in antiquity and also discussed by Leonardo in his unpublished writings; as far as we know, the first person to attempt to construct a reflecting telescope was the Italian Jesuit Niccolò Zucchi.


Niccolò Zucchi Source: Wikimedia Commons

Niccolò Zucchi, born in Parma 6 December 1586, was the fourth of eight children of the aristocrat Pierre Zucchi and his wife Francoise Giande Marie. He studied rhetoric in Piacenza and philosophy and theology in Parma, probably in Jesuit colleges. He entered the Jesuit order as a novice 28 October 1602, aged 16. Zucchi taught mathematics, rhetoric and theology at the Collegio Romano and was then appointed rector of the new Jesuit College in Ravenna by Cardinal Alessandro Orsini, who was also a patron of Galileo.

In 1623 he accompanied Orsini, the Papal legate, on a visit to the court of the Holy Roman Emperor Ferdinand II in Vienna. Here he met and got to know Johannes Kepler the Imperial Mathematicus. Kepler encouraged Zucchi’s interest in astronomy and the two corresponded after Zucchi’s return to Italy. Later when Kepler complained about his financial situation, Zucchi sent him a refracting telescope at the suggestion of Paul Guldin (1577–1643) a Swiss Jesuit mathematician, who also corresponded regularly with Kepler. Kepler mentions this gift in his Somnium. These correspondences between Kepler and leading Jesuit mathematicians illustrate very clearly how the scientific scholars in the early seventeenth century cooperated with each other across the religious divide, even at the height of the Counter Reformation.

Zucchi’s scientific interests extended beyond astronomy; he wrote and published two books on the philosophy of machines in 1646 and 1649. His unpublished Optica statica has not survived. He also wrote about magnetism, barometers, where he a good Thomist rejected the existence of a vacuum, and was the first to demonstrate that phosphors generate rather than store light.

Today, however Zucchi is best remember for his astronomy. He is credited with being the first, together with the Jesuit Daniello Bartoli (1608–1685), to observe the belts of Jupiter on 17 May 1630.  He reported observing spots on Mars in 1640. These observations were made with a regular Galilean refractor but it is his attempt to construct a reflecting telescope that is most fascinating.

In his Optica philosophia experimentis et ratione a fundamentis constituta published in 1652 he describes his attempt to create a reflecting telescope.


Optica philosophia title page Source: Linder Hall Library

As I said at the beginning, and have described in greater detail here, the principle that one could create an image with a curved mirror had been known since antiquity. Zucchi tells us that he replaced the convex objective lens in a Galilean telescope with bronze curved mirror. He tried viewing the image with the eyepiece, a concave lens looking down the tube into the mirror. He had to tilt the tube so as not to obstruct the light with his head. He was very disappointed with the result as the image was just a blur, although as he said the mirror was, “ab experto et accuratissimo artifice eleboratum nactus.” Or in simple words, the mirror was very well made by an expert.


Optica philosophia frontispiece

Zucchi had stumbled on a problem that was to bedevil all the early attempts to construct a reflecting telescope. Mirror that don’t distort the image are much harder to grind and polish than lenses. (The bending of light in a lens diminishes the effect of imperfections, whereas a mirror amplifies them). The first to solve this problem was Isaac Newton, proving that he was as skilled a craftsman as he was a great thinker. However, it would be more that fifty years before John Hadley could consistently repeat Newton’s initial success.

All the later reflecting telescope models had, as well as their primary mirrors, a secondary mirror at the focal point that reflected the image either to the side (a Newtonian), or back through the primary mirror (a Gregorian or a Cassegrain) to the eyepiece; the Zucchi remained the only single mirror telescope in the seventeenth century.

In the eighteenth century William Herschel initially built and used Newtonians but later he constructed two massive reflecting telescopes, first a twenty-foot and then a second forty-foot instrument.


Herschel’s Grand Forty feet Reflecting Telescopes A hand-coloured illustration of William Herschel’s massive reflecting telescope with a focal length of forty feet, which was erected at his home in Slough. Completed in 1789, the telescope became a local tourist attraction and was even featured on Ordnance Survey maps. By 1840, however, it was no longer used and was dismantled, although part of it is now on display at the Royal Observatory, Greenwich. This image of the telescope was engraved for the Encyclopedia Londinensis in 1819 as part of its treatment of optics. Herschel’s Grand Forty feet Reflecting Telescopes Source: Wikimedia Commons

These like Zucchi’s instrument only had a primary mirror with Herschel viewing the image with a hand held eyepiece from the front of the tube. As we name telescopes after their initial inventors Herschel giant telescopes are Zucchis, although I very much doubt if he even knew of the existence of his Jesuit predecessor, who had died at the grand old age of eighty-three in 1670.



Filed under History of Astronomy, History of Optics, History of science, History of Technology, Newton, Renaissance Science

Cosmographer to a Grand Duke and a Pope

Egnatio Danti is not a name that is known outside the circle of Renaissance historians of science. If you mention his name people often think you are talking about Dante the Italian medieval poet. Even Wikipedia asks, “Did you mean Dante?” when you type in his family name. But Egnatio Danti (1536-1586) an Italian monk friar, who was an artist, mathematician, astronomer and cartographer, was involved in several important mathematical projects in the sixteenth century.


Egnatio Danti portrait by Bartolomeo Passerotti (1529 – 1592) Source: Wikimedia Commons

Danti was born in Perugia in April 1536 into a family that basically predetermined his life and his career. His grandfather was Pier Vincenzo Rinaldi a goldsmith from profession and a poet, architect and astronomer by inclination. Nicknamed Dante by his friends he styled himself Dante de Rinaldi, which became shortened to Danti. Pier Vincenzo produced an Italian translation of Sacrobosco’s Sphere in the early 1490s the contents of which he passed on to his children, Teodora and Guilo along with his artistic talents. Teodora studied painting under Pietro Perugino, who also taught Raphael. She went on to become a successful artist in her own right. Guilo became an architect and the father of Vincenzo (born 1530) and Egnatio.

Egnatio learnt drawing from his father and mathematics from his aunt. His elder brother became a student of Michelangelo and went on to become a successful sculptor. In 1555, aged 19, having attended Perugia University Egnatio joined the Dominican order, where he continued his studies of mathematics, philosophy and theology. As a Dominican he was consistently conservative in his views: an Aristotelian in physics, a Ptolemaic astronomer and a Thomistic astrologer.

In the 1560s Giorgi Vasari the artist and historian of Renaissance art had been commissioned by Cosimo I de’ Medici Grand Duke of Tuscany


Agnolo Bronzino – Cosimo I de’ Medici in armour Source: Wikimedia Commons

to refurbish Palazzo Vecchio the official ducal residence.


Palazzo Vecchio Source: Wikimedia Commons

One of the Vasari’s projects was the Guardaroba Nuova a room conceived to house Cosimo’s chamber of curiosity or wunderkammer.


Source: Fiorani The Marvel of Maps p. 57

The room was furnished with carved walnut cabinets constructed by the master carpenter, Dionigi di Matteo Nigetti. The doors of the cabinets were to be decorated with mural maps depicting the whole world. When Vasari came to look for an artist-cartographer to complete this commission, Vincenzo Danti, who was also working in the Palazzo recommended his younger brother and Egnatio was hired.

Fifty-seven maps were commissioned, one for each cabinet door; Egnatio produced the cartoon for all of the maps but only painted thirty-one of them between 1563 and 1575; Stefano Bonsignori painted twenty-seven between 1577 and 1586. Egnatio also designed and constructed a large terrestrial globe that stands in the centre of the room.


Terrestrial Globe with cabinets in background Source: Wikimedia Commons

A matching celestial globe that was planned to be lowered from the ceiling was never realised. The maps are ordered according to the principle of Ptolemaeus’ Geographia and the original concept was that each cabinet would house the treasures from that part of the world depicted by the map on its door.


Source: Fiorani The Marvel of Maps p. 81

As can be seen the maps are three dimensional pictorial maps but where possible the latitude and longitude for the picture location are accurate.


Source: Fiorani The Marvel of Maps p. 110 Note that the map is up side down!

Much pleased with his cartographical-artist monk friar Cosimo appointed Danti ‘Cosmographer to the Grand Duke of Tuscany’ and assigned him a chair in mathematics at the university with minimal teaching obligations in 1571. Danti moved into the Palazzo, a move that did not please his superiors in the Dominican Order and began life as court cosmographer. He was required to teach cosmography–cartography, astronomy, and mathematics–to the Duke’s children, both male and female, and other assorted courtiers. A duty that he took very seriously writing and publishing a series of textbooks, many of them translations, in Italian for his pupils. A second requirement of his position was the creation and construction of mathematical and astronomical instruments for Cosimo. He also became the go-to instrument maker for the upper classes of Tuscany using the status of his position to bestow his favours in this area on carefully chosen customers for rather large sums; the money going to his order and not to him personally.


Source: Fiorani The Marvel of Maps p. 48


Egnation Danti, Astrolabe, ca. 1568, brass and wood. Florence, Museo di Storia della Scienza Source: Fiorani The Marvel of Maps p. 49

Many of Cosimo’s activities were intended to project his image as a great Renaissance Prince and to this end he offered his support and sponsorship to the Catholic Church in the question of the necessary calendar reform; in this role he saw himself as Caesar and Danti as his Sosigenes. Sosigenes of Alexander was the Greek astronomer, who, according to Pliny the Elder, was consulted by Julius Caesar on the design of the Julian calendar. To this end Cosimo sponsored the instillation of an armillary sphere and a quadrant on the façade of the Santa Maria Novella church in Florence by Danti in 1574 to better determine the length of the year, a necessary prerequisite for a calendar reform.


Source: Heilbron p. 64


Source: Heilbron p. 66

Along with the two instruments mounted on the façade of the church Danti drew up plans for and began the construction of a meridiana within the building. This is a straight line scale laid out on the floor of the building along which a beam of sunlight. projected through a hole high up in the wall, travels throughout the year, which can be used to exactly mark the times of the equinoxes. In Florence this project remained incomplete.

This exercise gained Danti the patronage of Cosimo’s son Cardinal Ferdinando de’ Medici for whom he procured an excellent Mercator astrolabe.


Ferdinando I de’ Medici Source: Wikimedia Commons

To help the Cardinal understand to workings of his fine gift, Danti wrote a treatise on the astrolabe dedicated to the Cardinal. However, even Ferdinando’s patronage could not avert the disaster looming on the horizon in Danti’s live. Already too ill to attend the inauguration of the armillary sphere at the vernal equinox on 11 March 1574, Cosimo died on 21 April in the same year to be succeeded by his eldest son Francesco I de’ Medici.


Agnolo Bronzino–Francesco I de’ Medici

Francesco did not share his father’s interest in cosmography and appears to have had a personal antipathy towards the Dominican astronomer. Following pressure from Francesco, Danti was ordered by the Dominican General on 23 September 1575 to repair to a convent outside of Tuscany within 24 hours. This was just two weeks after the autumn equinox, suggesting that there had been an agreement to allow Danti to measure the equinoxes of 1575 before his banishment. Danti was sent to San Domenico in Bologna.

The civic authorities of Bologna were delighted to have a mathematicus of Danti’s rank in their city and immediately planned a second chair of mathematics for him at the local university. However, the Superior of the Dominican Order initially blocked the move, on the one hand disturbed by Danti’s increasing celebrity status and on the other wishing to retain his services as a teacher for their own monks. However the recently elected Pope, Gregory XIII, who was Bolognese, a great admirer of cartography and having himself been a professor at the university, supported the appointment. His illegitimate son Giacomo Boncompagni intervened on Danti’s behalf and he became professor for mathematics at the University of Bologna on 28 November 1576.


Scipione Pulzone – Giacomo Boncompagni

Here he taught courses in cosmography similar to those that he had taught in the de’ Medici palace in Florence. In Bologna Danti constructed a small meridiana in the Inquisition chamber of the San Domenico, which was too short to fulfil the desired function, so he constructed a full length one in the San Petronio Basilica. During his time in Bologna Danti continued to win influential patrons by the selective construction of high quality astronomical instruments as gifts.


Source: Heilbron p. 73

In 1577 he returned to his hometown of Perugia to attend to his brother Vincenzo, who was ailing. Whilst in the town he was commissioned by the town authorities to carry out a survey and cadaster (public register showing the details of ownership and value of land; made for the purpose of taxation) of Perugia, a task that he completed in a month making all of his measurements from horseback using a radio latino.


Source: Heilbron p. 76

Danti presented the results of his labours in the form of a fifteen feet square mural map on the governor’s palace.


Source: Fiorani p. 160

He also presented a copy of the map to the Pope’s illegitimate son Giacomo Boncompagni, who then commissioned him to carry out a similar survey of the Papal States supplying him with the necessary finances and manpower to complete the task. Once more he distinguished himself with the speed and quality with which he carried out the work.


Examples of Danti’s survey drawings Source: Fiorani p. 169

Danti was now brought to the Vatican to work directly for Pope Gregory.


Lavinia Fontana–Pope Gregory XIII

In 1579 he was commissioned to produce his second great gallery of maps along the walls of the recently constructed upper gallery on the east wing of the Belverdere. This time the theme was not the world, as in Florence, but the whole of Italy. At the top end of the gallery were two complete maps of Italy, Italia antiqua and Italia nova.


Italia antiqua Source: Wikimedia Commons


Italia nova Source: Wikimedia Commons

As one proceeded down the gallery the states on the east coast were presented on the left-hand west wall and those on the west coast on the right-hand east wall. This created the illusion of a walk along the Apennine ridge from Northern Italy to Sicily in the south. Danti planned and designed all of the maps but they were painted by a team of artists. The whole project took just two years to complete.


Campania Source: Wikimedia Commons


Pedemontium et Monsferratus Source: Wikimedia Commons

Each of the murals not only contains the map of its given district but also contains illustrations of significant historical happenings that took place there.


The Siege of Malta Source: Atlas Obscura

Fiorani (see below) says that this was the first ever atlas of Italy. Given that Italy as a country didn’t exist at this time but was an uneasy collection of independent states the project throws up some interesting questions as to Gregory’s intentions in commissioning it. Did he envisage a united Italy under his leadership?

In 1580 Danti was officially appointed Papal Cosmographer and at the same time appointed astronomical advisor to the Papal commission on calendar reform. His is one of the nine signatures on the final recommendations as presented to the Pope.

Whilst working in the Vatican Danti also created a new meridiana in the Tower of Winds.


Source: Heilbron between pp 180-181

On 14 November 1583 in recognition of his services Gregory appointed him Bishop of Altari. Gregory’s successor Pope Sixtus V summoned back to Rome in 1586 to assist in the re-erection of the Vatican Obelisk.


Re-erection of the Vatican Obelisk by the Renaissance architect Domenico Fontana in 1586 Source: Wikimedia Commons

Egnatio Danti died on 19 October 1586, today he is largely forgotten but, although often restored and modified over the centuries, Danti’s two great galleries of maps still exist as a monument to a great Italian Renaissance artist, cosmographer, mathematician, astronomer, instrument maker, textbook author and teacher.

This blog post is largely based on two excellent books: John Heilbron’s The Sun in the Church[1]a fascinating history of the construction of meridiana in the Early Modern Period and Francesca Fiorani’s The Marvel of Maps[2]a beautiful book on the Renaissance map galleries. Heilbron’s book is really a must read for anybody interested in the history of Early Modern astronomy and is available as a good value paperback. Fiorani’s book is one of the best books that I have read in recent years. It covers an extensive range of historical aspects of the central theme, all of them excellently researched and presented. The book is a real pleasure to read and the illustrations are first class. The only drawback is the price, weighing in at $150 on and more expensive elsewhere. I got lucky and picked up a ridiculously cheap second hand copy in perfect condition.







[1]J. L. Heilbron, The Sun in the Church: Cathedrals as Solar Observatories, Harvard University Press, Cambridge, Massachusetts & London England, 1999

[2]Francesca Fiorani, The Marvel of Maps: Art,Cartography and Politics in Renaissance Italy, Yale University Press, New Haven & London, 2005


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

Two Greek scholars butting heads in the Renaissance and the consequences for astronomy

The adversaries of the title were Georg of Trebizond (1395–1472) and Basilios Bessarion (1403–1472). There is an ironic twist to their names. George of Trebizond derived his name from his ancestors, who originated in the Empire of Trebizond but he was born in Crete. His later antagonist Basilios Bessarion, however, was born in Trebizond.

At sometime unknown point, whilst he was still relatively young, George of Trebizond moved to Italy, where he learnt Latin and acted as amanuensis to the politician Francesco Barbaro (1390–1454) in Venice. A brilliant Aristotelian scholar he entered the entourage of Pope Nicholas V (1397–1455) a convinced Aristotelian.


George of Trebizond Source: Wikimedia commons

Basilios Bessarion was educated in Constantinople then went in 1423 to study Plato under Georgius Gemistus (c.1355–c. 1452), known as Plethon, a highly influential revivalist and teacher of Neo-Platonism. He became an orthodox monk, advancing to abbot in 1436 and metropolitan of Nicaea in 1437. In 1439 he travelled with the Orthodox delegation to Italy to try to persuade the Catholic Church to join the Orthodox Church in a crusade against the Ottoman Turks. Bessarion’s political position led to him being heavily criticised in Byzantium and so he stayed in Italy where Pope Eugene IV (1383–1447) appointed him a cardinal of the Catholic Church. A convinced humanist he devoted his life to spreading support for humanism and to amassing a large private library, containing an extensive collection of Greek manuscripts. He presented his library to the Senate of Venice in 1468 and the 482 Greek manuscripts and 264 Latin manuscripts today still form the core of the St. Mark’s Biblioteca Marciana.


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

Initially Bessarion and George of Trebizond were friends and Bessarion did much to support his colleague. However in the early 1450s their friendship began to unravel. In that year George undertook a translation from Greek into Latin of Ptolemaeus’ Mathēmatikē Syntaxis or as it is better known the Almagest, as a replacement for Gerard of Cremona’s twelfth-century translation from Arabic.  Bessarion lent him his best Greek manuscript for the purpose and suggested that he used Theon of Alexandria’s Commentary, as a guide. He duly produced his translation and an extensive commentary in nine months finishing in December 1451. His work was hurried, sloppy and strewn with errors and the Pope’s evaluator Jacopo di San Cassiano (ca.1400–ca.1454) judged the work deficient and the Pope, Nicholas V, rejected the dedication. Bessarion took issue with George’s treatment of Theon. The incident ruined George’s reputation and he was forced to flee from Rome.

The situation between the two Greek immigrants escalated when in 1458 George published a vicious attack on Plato in his Comparatio Aristotelis et Platonis, which historian James Hankins has described as “one of the most remarkable mixtures of learning and lunacy ever penned.” In this work he accused Plato of being a traitor to Athens, a besmircher of rhetoric, an advocate of paedophilia, and a pagan who lent aid and comfort to Greek Christians. Bessarion, a Platonist, could not let this stand and issued a powerful response, In calumnatorem Platonis, which was printed in 1469. The situation became even more heated when George offered to dedicate his Commentary on the Almagest to Mehmet II, the Ottoman Turk Sultan, who had conquered Constantinople and ended the Byzantine Empire. George entreated Mehmet to convert to Christianity, to conquer Rome and thus to unite Islam and Christianity under his sovereignty. Bessarion got hold of George’s correspondence with Mehmet and appealled to the Pope, Pius II (for whom George might have been working as an agent!), accusing George of treachery and George was imprisoned for four months in 1466-67. Released from prison, George now offered to dedicate both translation and commentary to Matthias Corvinus (1443–1490), the king of Hungary.

We now need to back peddle to 1460. In that year, Bessarion, who was a Papal legate, visited Vienna to negotiate with Frederick III and made the acquaintance of Georg von Peuerbach (1423–1461), who was at the time the leading astronomical scholar in Europe. Bessarion, still deeply upset by George’s abortive Almagest efforts, asked Peuerbach to produce a new commentary on Ptolemaeus’ work. Peuerbach acquiesced and began immediately to produce an epitome or digest of the Almagest. This was an updated, modernised, shortened, mathematically improved version of the Almagest. Peuerbach died in 1461, having only completed the first six of thirteen book of his epitome. He did, however, extract the deathbed promise from his star pupil, Regiomontanus, to finish the work. In the same year Regiomontanus left Vienna for Italy as a member Bessarion’s entourage, where he spent the next four years learning Greek, finishing the epitome and acting as Bessarion’s manuscript collector and librarian. The Epitome of the Almagestis a masterpiece:

The Epitome is neither a translation (an oft repeated error) nor a commentary but a detailed sometimes updated, overview of the Almagest. Swerdlow once called it “the finest textbook of Ptolemaic astronomy ever written.”[1]

I’ve already written an earlier blog post on Regiomontanus so we don’t need to outline the rest of his life but Shank does have an interesting hypothesis. He suggests that Regiomontanus went to Hungary at Bessarion’s behest in order to counter any influence that George might win at the Court of Corvinus through his second attempt to rededicate his Almagest and Commentary.


Johannes Regiomontanus, Woodcut Source: Wikimedia Commons

When he set up his printing business in Nürnberg, Regiomontanus published Peuerbach’s lectures on astronomy, Theoricae Novae Planetarum, as his first book.


Georg von Peuerbach: Theoricarum novarum planetarum testus, Paris 1515 Source: Wikimedia Commons


Peuerbach Theoricae novae planetarum 1473 Source: Wikimedia Commons

Although he included the Epitome in his publisher’s prospect he didn’t succeed in publishing it before his untimely death in 1476. The Epitoma in Almagestum Ptolemae was first published in 1496 in Venice by Johannes Hamman. Together with Peuerbach’s lectures the Epitome became the standard textbooks for teaching astronomy at the European universities for much of the next century. The influence of the Epitome goes much deeper than this in the history of astronomy.


Title page Epitoma in Almagestum Ptolemae Source: Wikimedia Commons

It is well known that Copernicus modelled his De revolutionibus on Ptolemaeus’ Almagest. In fact text analysis has shown that he actually modelled his magnum opus on the Peuerbach-Regiomontanus Epitome, for example taking most of his knowledge of Arabic astronomy from Regiomontanus’ work. This is, however, rather minor compared to what several expert think is the most important influence that Regiomontanus had on Copernicus.


Nicolaus Copernicus portrait from Town Hall in Toruń – 1580 Source: Wikimedia Commons

According to ancient Greek cosmology the planets orbit the earth with uniform circular motion. Any extended observation of the planets show that this is not the case and it was the job of the astronomers to construct geometrical model, which corrected the visible deviation from the cosmological norm; these deviations are known as the anomalies. Ptolemaeus had basically two geometrical tools to describe planetary orbits. With the eccentric deferent the centre of the circle that describes the orbit, the deferent, is not in the same position as the earth, i.e. the earth is not at the centre of the planets orbit. The alternative is the epicycle-deferent model in which the planet is carried around an epicycle, which is itself carried around the deferent. The mathematician Apollonius (late 3rdcentury–early 2ndcentury BCE) had shown that the two models were in fact mathematically equivalent; meaning any motion that could be described with the one model could equally well be described with the other.

Ptolemaeus, however, argued in the Almagest that whereas the retrograde motion (the so-called second anomaly, when the planet appears to reverse its orbital direction for a period of time) of the outer planets could be described with either model that of the inner planets (Venus and Mercury) could only be described with the epicycle-deferent model. In Book XII of the Epitome, Regiomontanus proved that the second anomaly of the inner planets could also be described with the eccentric deferent model. Without going into detail this seems to have led Copernicus directly to his heliocentric system for the inner planets, which he then extended to the outer ones.

Thinking hypothetically, if George had not written his translation of and commentary on the Almagest, then Bessarion would not has asked Peuerbach to write the Epitomeand Regiomontanus might never have provided Copernicus with that vital clue.

Regiomontanus wrote a second book inspired by George’s work. His Defensio Theonis contra Georgium Trapezuntium is a vast rambling mathematical work centred on a defence of Theon of Alexandria against what he saw as George’s unfair treatment of him. He accused George as having both misrepresenting Theon and plagiarising him. This work has never been published but Regiomontanus’ antagonism against George was known at the time. The Defensio was announced in Regiomontanus’ prospect and also in works published by Erhard Ratdolt. This situation led to a rather strange claim made by Pierre Gassendi. In the 1650s Gassendi published a collective biography of the great astronomers Brahe, Copernicus, Regiomontanus etc. in which he claimed that Regiomontanus was murdered in Rome by two of George’s sons in 1476. George had many vocal critics, none of whom were murdered and sensible historians think that Regiomontanus died in one of the epidemics that regularly swept Rome.


[1]Michael H. Shank, Regiomontanus and Astronomical Controversy in the Background of Copernicus, pp. 79-109 in Rivka Feldhay and F. Jamil Ragep eds., Before Copernicus: The Cultures and Contexts of Scientific Learning in the Fifteenth Century, McGill-Queen’s University Press, Montreal& Kingston, London, Chicago, 2017, p. 90

This blog post owes much to the above paper and to Michael H. Shank, The Almagest, Politics, and Apocalypticism in the Conflict between George of Trebizond and Cardinal Bessarion, in Almagest International Journal for the History of Scientific Ideas, Volume 8, Issue 2, 2017, pp. 49-83


Filed under Early Scientific Publishing, History of Astronomy, History of science, Renaissance Science, Uncategorized