Category Archives: History of science

The House of Wisdom is a Myth

When I first got really interested in the history of science, the history of science of the Islamic empires was not something dealt with in any detail in general works on the topic. If you wanted to get to know anything much about what happened in the various areas of the world dominated by Islamic culture in the period between the seventh and sixteenth centuries then you had to find and read specialist literature produced by experts such as Edward Kennedy. Although our knowledge of that history still needs to be improved, the basic history has now reached the popular market and people can inform themselves about major figures writing in Arabic on various areas of science between the demise of classical antiquity and the European Renaissance such as the mathematician Muḥammad ibn Mūsā al-Khwārizmī, the alchemist Abū Mūsā Jābir ibn Hayyān, the optician, Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham or the physician Abū Bakr Muhammad ibn Zakariyyā al-Rāzī. These and a handful of other ‘greats’ are not as well known as their later European counterparts but knowledge of them, usually under their popular names, so al-Khwarizmi, Jabir, al-Haytham and al-Razi, is these days quite widespread amongst well educated and well read people. There is even a flourishing popular book market for titles about Islamic science.

Amongst those non-professionals, who interest themselves for the topic, particularly well known is the so-called House of Wisdom, a reputed major centre for scientific translation and research in Baghdad under the Abbasid Caliphs. This reputed academic institution even provided the title for two of the biggest selling popular books on Islamic science Jim al-Khalili’s The House of Wisdom: How Arabic Science Saved Ancient Knowledge and Gave Us the Renaissance and Jonathan Lyons’ The House of Wisdom: How the Arabs Transformed Western Civilisation. Neither Jim al-Khalili nor Jonathan Lyons is a historian of science, let alone Islamic science; al-Khalili is a physicist and broadcaster and Lyons is a journalist and herein lies the rub. Real historians of Islamic science say that the House of Wisdom never existed, at least not in any form remotely resembling the institution presented by al-Khalili, Lyons and other popular sources including, unfortunately Wikipedia, where the article is largely based on Lyons’ pop book.

The picture painted by al-Khalili and Lyons, and to be fair they didn’t create it but copied it from other fantasts, is of a special academic research institution set up by the early Abbasid Caliphs, staffed with leading scientific scholars, who carried out a sponsored programme of translating Greek scientific texts, which they them analysed, commented and developed further. Here academic exchanges, discussions, conferences took place amongst the leading scientific scholars in the Abbasid Empire.

The reality looks very different.[1]To quote Gutas (page 54):

It is in this light that the very scanty reliable reports about the bayt al-hikmashould be evaluated. Much ink has been used unnecessarily on description of the bayt al-hikma, mostly in fanciful and sometimes wishful projections of modern institutions and research projects back into the eighth century. The fact is that we have exceedingly little historical [emphasis in original] information about the bayt al-hikma. This in tself would indicate that it was not something grandiose or significant, and hence a minimalist interpretation would fit the historical record better.

The bayt al-hikma, to give it its correct name, which doesn’t really translate as house of wisdom, was the palace archive and library or repository, a practice taken over by the Abbasid Caliphs from the earlier Sassanian rulers along with much other royal court procedure to make their reign more acceptable to their Persian subjects. The wisdom referred to in the translation refers to poetic accounts of Iranian history, warfare, and romance. The Abbasid Caliphs appear to have maintained this practice now translating Persian historical texts from Persian into Arabic. There is absolutely no evidence of Greek texts, scientific or otherwise, being translated in the bayt al-hikma.

Much is made of supposed leading Islamic scientific scholars working in the bayt al-hikmaby the al-Khalili’s, Lyons et al. In fact the first librarian under the Abbasids was a well-known Persian astrologer, again a Sassanian practice taken over by the Abbasids. Later al-Khwarizmi and Yahya ibn Abi Mansur both noted astronomers but equally noted astrologers served in the bayt al-hikmaunder the Abbasid Caliph al-Ma’mun.

We will give Gutas the final word on the subject (page 59):

The bayt al-hikmawas certainly also not an “academy” for teaching the “ancient” sciences as they were being translated; such a preposterous idea did not even occur to the authors of the spurious reports about the transmission of the teaching of these sciences that we do have. Finally it is not a “conference centre for the meeting of scholars even under al-Ma’mun’s sponsorship. Al-Ma’mun, of course (and all the early Abbasid caliphs), did host scholarly conferences or rather gatherings, but not in the library; such gauche social behaviour on the part of the caliph would have been inconceivable. Sessions (magalis) were held in the residences of the caliphs, when the caliphs were present, or in private residences otherwise, as the numerous descriptions of them that we have indicate.

As a final comment we have the quite extraordinary statement made by Jim al-Khalili on the BBC Radio 4 In Our Time discussion on Maths in the Early Islamic World:

In answer to Melvyn Braggs question, “What did they mean by the House of Wisdom and what sort of house was it? It is supposed to have lasted for 400 years, it is contested”

Jim al-Khalili: “It is contested and I’ll probably get into hot water with historians but let’s say what I think of it. There was certainly potentially something called the house of wisdom a bit like the Library of Alexandria many centuries earlier, which was a place where books were stored it may have also been a translation house. It was in Baghdad this was in the time of al-Ma’mun, it may have existed in some form or other in his father’s palace…”

Bragg: “Was it a research centre, was it a place where people went to be paid by the caliphs to get on with the work that you do in mathematics?”

Al-Khalili: “I believe it very well could have been…” He goes on spinning a fable, drawing parallels with the Library of Alexandria

History is not about what you choose to believe but is a fact-based discipline. Immediately after al-Khalili’s fairy story Peter Pormann, Professor of Classics & Graeco-Arabic Studies at the University of Manchester chimes in and pricks the bubble.

Pormann: “There’s the myth of the House of Wisdom as this research school, academy and so on and so forth, basically there is very little evidence…”

Listen for yourselves!

I find Bragg’s choice of words, repeated by al-Khalili, “it is contested” highly provocative and extremely contentious. It is not contested; there is absolutely no evidence to support the House of Wisdom myth as presented by Lyons, al-Khalili et al. What we have here is another glaring example of unqualified pop historians propagating a myth and blatantly ignoring the historical facts, which they find boring.

[1]The facts in the following are taken from Dimitri Gutas, Greek Thought, Arabic Culture: The Graeco-Arabic Translation Movement in Baghdad and Early Abbasid Society (2nd–4th/8th–10th centuries), Routledge, Oxford, ppb. 1998 pp. 53-60 and Lutz Richter-Bernburg, Potemkin in Baghdad: The Abbasid “House of Wisdom” as Constructed by 1001 inventions In Sonja Brentjes–Taner Edis­–Lutz Richter-Bernburg eds., 1001 Distortions: How (Not) to Narrate History of Science, Medicine, and Technology in Non-Western Science, Biblioteca Academica Orientalistik, Band 25, Ergon Verlag, Würzburg, 2016 pp. 121-129


Filed under History of Islamic Science, History of science, Myths of Science

Nit-picking – Authors who should know better

In my most recent reading I have come across three separate examples of professional historians making a mess of things when they turn the hand to the history of science.

First up we have Jerry Brotton’s The Renaissance: A Very Short Introduction[1]. I’m a fan of Oxford University Press’ Very Short Introduction series and also of Brotton’s A History of the World in Twelve Maps[2], so I was expecting to enjoy his Very Short Introduction to the Renaissance and in general I wasn’t disappointed.

Nit Picking001

He chooses to lay the emphasis in his book on the fact that the Renaissance wasn’t a purely European phenomenon but a global one and writing from this perspective he opens up a novel vista on this period of history. However when he turns to the history of Renaissance science he, in my opinion, drops a major clangour.

He introduces his chapter on the topic with Christopher Marlowe’s Doctor Faustus, telling us that:

Once Faustus has sold his soul, he asks Mephistopheles for a book ‘where I might see all characters and planets of the heavens’. The most controversial book that Faustus could have consulted was On the Revolutions of the Celestial Spheres by the Polish canon and astronomer Nicolaus Copernicus.[3]

We’ll ignore the Polish on this occasion and turn instead to what Brotton says about the book:

Copernicus’s revolutionary book overturned the medieval belief that the earth lay at the centre[my emphasis] of the universe. Copernicus’s vision of the heavens showed, along with all the other known planets, rotated around the sun. Copernicus subtly revised the work of classical Greek and Arabic astronomy scholars. He argued that ‘they did not achieve their aim, which we hope to reach by accepting the fact that the earth moves’.

Copernicus tried to limit the revolutionary significance of his ideas by accommodating them within a classical scientific tradition. But the Catholic Church was horrified and condemned the book. Copernicus’s argument overturned the biblical belief that the earth – and humanity with it – stood at the centre of the universe[4][my emphasis].


It was neither the biblical nor the medieval belief that the earth stood at the centre of the universe and removing the earth from this centre was not Copernicus’ offence. It was setting the earth in motion and stopping the motion of the sun that the Church found intolerable, as it contradicted several biblical passages. The myth about Copernicus displacing humanity from the centre of the universe is as far as I know and eighteenth or even nineteenth century invention and actually contradicts the medieval view of the position of the earth. The earth was not at the centre but at the bottom of the universe in the dregs. I once wrote a short blog post quoting Otto von Guericke on this subject, for those to lazy to click through:


Since, however, almost everyone has been of the conviction that the earth is immobile since it is a heavy body, the dregs, as it were, of the universe and for this reason situated in the middle or the lowest region of the heaven

Otto von Guericke; The New (So-Called) Magdeburg Experiments of Otto von Guericke, trans. with pref. by Margaret Glover Foley Ames. Kluwer Academic Publishers, Dordrecht/Boston/London, 1994, pp. 15 – 16. (my emphasis)

Need I really point out that the Church didn’t condemn De revolutionibus but in 1616 merely placed it on the Index until corrected, a procedure that was carried out with surprising rapidity. A small number of statements claiming that heliocentricity was a fact rather than a hypothesis were removed and the book approved for use by 1620.

Our next offender is another respected Renaissance historian, Andrew Pettegree, in his The Book in the Renaissance[5].

Nit Picking002

Once again this is a book that in general I find excellent and highly stimulating but like Brotton he disappoints when dealing with the history of science. Like Brotton he starts with Copernicus and De revolutionibus, he tells us:

In 1539 a young mathematician, Georg Joachim Rheticus, embarked on a journey of momentous consequence for the history of science. Rheticus is not a name well known even to scholars. At this point in his life he had little to distinguish him from other graduates at Wittenberg University apart from a family scandal: his father, a medical doctor, had been convicted of embezzlement and beheaded. In 1538 Rheticus left Wittenberg and settled in Nuremberg. Here he fell in with Johann Schoener, the city’s most distinguished astronomer: the following year he set off alone for Frauenberg, a small cathedral city on the Baltic coast beyond Danzig.

The purpose of this journey was to visit the renowned astronomer, Nicolas Copernicus. Although Copernicus had travelled in Europe earlier in his life, from 1510 he was permanently settled in his Polish-Prussian homeland, relatively remote from the major centres of European Scholarship. To ingratiate himself with the older man Rheticus had been provided with three valuable scientific volumes for Copernicus’s library. This was a gift with a purpose. The texts were the work of a Nuremberg printer, Johannes Petreius, who wanted Rheticus to persuade Copernicus to let him publish the master-work it was widely believed he would soon have ready for the press. The gift of the three texts was to demonstrate that only Germany’s greatest centre of scientific publishing could do justice to Copernicus’s work: and to help Rheticus prise the precious manuscript from the old man’s hands.

Copernicus kept Rheticus guessing. He seems to have enjoyed the younger man’s company, and it was 1541 before Rheticus could set off back to Wittenberg, clutching the manuscript of what would be Copernicus’s major text. De revolutionibus (Of the Revolution of the Heavenly Spheres). The following year he journeyed on to Nuremberg, where Petreius was waiting to set it on his press: it took until 1543 before the text, complete with its famous woodcut diagrams of Copernicus’s heliocentric system was ready for sale[6].

The story that Pettegree tells here is a very well-known one in the history of science that has been repeated, in one form or another, in numerous publications, but he still manages to get a whole series of fundamental facts wrong. Firstly, I would claim that whilst maybe not known to the general public, the name Rheticus is well-known to scholars. I think being appointed professor for the lower mathematics (i.e. arithmetic and geometry) at the University of Wittenberg in 1536 did distinguish him from other graduates of that university. He didn’t leave Wittenberg in 1538 and settle in Nuremberg but went on an official sabbatical armed with a letter of introduction written by the Rector of the university Philipp Melanchthon. One of the scholars he went to visit on that sabbatical, mentioned in that letter of introduction, was Johannes Schöner, the professor of mathematics at the Egidien Oberschule in Nürnberg a position to which he had been appointed on Melanchthon’s recommendation. Rheticus visited Schöner almost certainly to study astrology, a subject dear to Melanchthon’s heart.

Copernicus lived in Warmia (Ermland in German) an autonomous self governing Prince Bishopric. Rheticus took not three but six books as a gift to Copernicus of which four had been printed and published by Petreius in Nürnberg. When Rheticus visited Copernicus he was largely unknown and to describe him as renowned is more than a bit of a stretch. His renown came posthumously following the publication of De revolutionibus. There were rumours of a hypothesis and possibly a book, rumours created by the circulating manuscript of the Commentariolus but to state that Petreius or anybody else for that matter outside of Warmia knew of a master-work that would soon be ready for the press is once again an exaggeration. Rheticus’ mission could better be described as look see if Copernicus has anything substantial that could be of interest to a printer publisher specialised in astrological/astronomical and mathematical texts.

Copernicus did not keep Rheticus guessing. Firstly Rheticus suffered a period of illness and then travelled to Königsberg, where he wrote a chorography of Prussia for Duke Albrecht in 1541. Copernicus was reluctant to present his hypothesis to the world because he knew that he could not fulfil the promise that he had given in the Commentariolus that he would prove his hypothesis. To calm his fears Rheticus wrote and published his Narratio Prima in 1540 in Danzig, with a second edition appearing in Basel in 1541. This presented a brief first account of the heliocentric system and its positive reception convinced Copernicus to entrust Rheticus with his manuscript.

All in all a more than somewhat different story to that present to us by Pettegree

Next up we have my current bedtime reading Michael Bravo’s North Pole: Nature and Culture[7], which I’m enjoying immensely.

Nit Picking003

Although the emphasis of the book is on the polar voyages and expeditions beginning in the modern period the book starts much earlier. The first chapter contrasts the views of the North Pole of the ancient Greek astronomers, who saw it as the downwards extension of the North celestial pole and the Inuit who live/lived in the Arctic. The second chapter deals with the representations of the North Pole made by the cartographers and globe makers of the Early Modern Period, a topic of great interest to me, as regular readers will know. It is here that Bravo displays a surprising lack of accurate research. He tells us:

Apian was fortunate to have studied in nearby Vienna, introducing him to the work of a circle of highly talented mathematicians in Nuremberg, Ingolstadt and Vienna who were working under the patronage of Maximilian I, Holy Roman Emperor (1459–1519)…[8]

This is indeed correct and is something that I have written about in several posts and about which Darin Hayton has written a whole book, his The Crown and the Cosmos: Astrology and the Politics of Maximilian I, which I reviewed here. Bravo then goes on to discuss the Werner-Stabius cordiform map projection, which is of course a polar projection centred on the North Pole. All well and good up till now. After an extensive discussion of the cordiform projection, its use and its impact Bravo goes on to say:

Introducing the perspective of viewing the Earth from above brought cosmography into line with the new developments in drawing, projection and perspective pioneered in Renaissance Europe. Albrecht Dürer (1471-1528), one of the most remarkable German artists, was the son of a prominent goldsmith in Nuremberg. Dürer’s precocious talent for drawing broadened into printmaking, writing and an extraordinary rich span of philosophical interests. His studies of perspective spanned much of his life and he brought back to northern Europe the principles of linear perspective he encountered while studying in Bologna. He later moved to Vienna to work with Stabius and Werner under the patronage of Maximilian I[my emphasis] Dürer and Stabius published the first polar star chart in 1515[9].


As a Dürer fan, it’s nice to see him getting a nod for more than his Rhinoceros and yes Maximilian was one of his patrons, but the sentence I have placed in italics manages to include two major errors in just sixteen words. Firstly if Dürer had moved to Vienna, he would have only met Stabius and not Werner. The two knew each other from their mutual time at the University of Ingolstadt in the early 1480s but whereas Werner moved first to Rome and then to Nürnberg on the completion of his studies, Stabius stayed in Ingolstadt eventually becoming professor of mathematics before moving to Vienna as court historian and mathematician on Conrad Celtis’ Collegium poetarum et mathematicorum. The two of them continued to work together not by being in the same city but through correspondence. Needless to say Dürer never left Nürnberg and never moved to Vienna, his various shared projects with Stabius were either conducted by letter or by Stabius journeying to Nürnberg. I should point out the Dürer-Stabius-Heinfogel star maps were not the first polar star charts but the first European printed polar star charts, there are earlier manuscript ones and also earlier printed Chinese ones.

All of the things that I have criticised above are facts that are comparatively easy to find and verify with a relatively small amount of research work, so there really is no excuse for getting them wrong. It would be bad enough if the authors were beginners, amateurs or wanna be historians. But in each case we have to do with a justifiably renowned historian and author, so there is really no excuse for this level of sloppiness.

[1] Jerry Brotton, The Renaissance: A Very Short Introduction, OUP, Oxford, 2006

[2]Jerry Brotten, A History of the World in Twelve Maps, Allen Lane, London, 2012

[3] Brotton p. 99

[4] Brotton p. 99

[5] Andrew Pettegree, The Book in the Renaissance, Yale University Press, New Haven & London, 2011

[6] Pettegree pp. 273–274

[7]Michael Bravo, North Pole: Nature and Culture, Reaktion Books, London, 2019

[8] Bravo p. 56

[9] Bravo p. 60


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

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

Part I Part II Part III Part IV

As I already mentioned in Part II, Copernicus wrote his first work on his heliocentric theory in about 1510, the Commentariolus, which remained in manuscript but seems to have enjoyed a fairly wide distribution, as we will see later. However, Copernicus was not the only show in town in the astronomical world of the sixteenth century. Before I continue with his story I will look at what else of significance was taking place.

In Part I we learnt how Toscanelli took a new approach in his treatment of comets, viewing them as objects to be astronomically observed and not just as meteorological phenomena as the Aristotelian had; his lead was followed in Vienna by Peuerbach and Regiomontanus. In the 1530s there was a series of spectacular comets, which attracted the attention of the new class of European astronomers and their observations led to more new developments.


Girolamo Fracastoro (c. 1477–1553) was the first European to draw attention to the fact that a comets tail always points away from the sun in his Homocentrica (1538); a seemingly trivial discovery but one that correctly interpreted played an important role in re-determining the role of comets.


Portrait of Girolamo Fracastoro by Titian, c.1528 Source: Wikimedia Commons

Peter Apian also independently the same discovery in his Astronomicum Caesareum (1540). Strangely the discovery is usually only attributed to Apian.


Apian’s depiction of comet’s tail facing away from the sun Source: Wikimedia Commons

The Fracastoro/Apian discovery had been made much earlier by the Chinese but this was not known in Europe. Johannes Schöner was stimulated by the situation to publish Regiomontanus’ work on determining the parallax of a moving comet, a problem that was taken up again in a correspondence between John Dee and Tycho Brahe later in the century. Comets were no longer just astrological harbingers of doom but had become objects of astronomical interest.

In a European wide debate that included Copernicus, amongst others, both Gerolamo Cardano in Milan and Jean Pena, Royal Professor of Mathematics in Paris, came up with a new comet concept. Comets were supralunar and transparent; they functioned like a lens that focused the sunlight, the focused light being then the tail of the comet. A serious breach had been made in the accepted Aristotelian cosmology. Not only were comets supralunar but they were also supralunar object that demonstratively changed, an affront for the Aristotelian concept of a perfect, unchanging heaven.

Of course, these new radical ideas were not instantly accepted by the European astronomical community and it was a community, which discussed and debated their observations and theories with each other. However, it stimulated that community to plan observation programmes to be carried out the next time comets would appear in the heavens over Europe. Unfortunately, when the next spectacular comet appeared over Europe in 1556, one generation of capable astronomers was already dead and the next one was still in its childhood (Tycho was ten and Mästlin was six years old) or in the case of Kepler not yet born.

PII: 0160-9327(79)90035-8

An astronomical broadsheet by Paul Fabricius, showing the map of the 1556 comet’s course Source: Wikimedia Commons

Urania was, however generous, delivering a supernova in 1572 and a great comet in 1577 for the delectation of the eager European community of astronomers.


Red circle upper left hand corner remnant of 1572 supernova Source: Wikimedia Commons

The discovery, observation and analysis of these celestial phenomena are, in the popular history of astronomy books, almost exclusively attributed to Tycho Brahe. This attribution creates a distorted picture of what actually happened. Astronomers, amateur and professional, all over Europe observed both the supernova and the comet, attempted to determine parallax and thus the distance of them and wrote up and published their results and opinions is a veritable flood of publication, largely pamphlets.

The results covered a wide spectrum, from definitely supralunar over non-measurable parallax to definitely sublunar. Tycho, Michael Mästlin and Thaddaeus Hagecius ab Hayek (1525–1600), all influential astronomers, all determined that the observed phenomena were clearly supralunar. For those who have not come across him Thaddaeus Hayek was professor of mathematics at the University of Prague and personal physician to the Holy Roman Emperor Rudolf II and played a central role in bringing both Tycho and Johannes Kepler to Rudolf’s Court in Prague.


Thaddaeus Hagecius ab Hayek Source: Wikimedia Commons

In the acceptance of the fact that the celestial phenomena of the 1570s were supralunar and thus demolished a large chunk of Aristotelian cosmology i.e. that he heaven are perfect and unchanging, at the time, Mästlin’s word counted more than Tycho’s but the placet of widespread acceptance was lent to this opinion through its confirmation by the leading Catholic astronomer, Christoph Clavius (1538–1612). We will return to the role of comets in the emergence of modern astronomy in a later post but before I depart here I want to comment on the categorical rejection of the supralunar nature of the supernova of 1572 and the comet of 1577 by the Nürnberger artist and astrologer/astronomer Georg Busch (ca. 1530–1579).

Born in Nürnberg, Busch moved to Erfurt where he worked as an artist and from about 1550 as an astrologer/astronomer. Busch published two books on the 1572 supernova, which he consistently referred to as a comet: Von den Comet, welcher in diesem 1572. Jar in den Monet Novembris erschienen, Erfurt, 1572 (On the Comet, which appeared in this Year of 1572 in the Month of November) and Entschuldingung and Schutzrede Georgij Busch… Erfurt, 1573 (Apology and Defence of Georg Busch…(the title goes on and on). The second pamphlet is a defence against criticism. Both publications went through several editions showing that the ‘modern’ astronomers didn’t by any means have the field to themselves. Busch’s publications even made it into Tycho’s annotated catalogue of the comet publications. What I personally love is Busch’s description of the nature of comets:

“…the comet was composed of a sort of obnoxious gas generated by human sin, which floated heavenward until ignited by the wrath of God. As it burned the comet became a prolific celestial polluter, showering its effluence widely over Earth and thereby causing pestilence, Frenchmen, sudden death, bad weather…”

Observant readers might have noticed that Fracastoro’s account of the direction of comet’s tails was in a book entitled Homocentrica.

The central argument of this publication was a rejection of the epicycle-deferent model of Ptolemaeus and a return to the homocentric spheres model of the cosmos propagated by Eudoxus and above all Aristotle. This is, of course, highly reactionary in the sixteenth century when most important astronomers were moving away from Aristotelian orthodoxy but Fracastoro was a well-known and highly respected author so his opinion was by no means rejected out of hand. Later in the century Christoph Clavius (1538–1612), the defender in chief of Ptolemaic astronomy, regarded Fracastoro’s homocentricity as a greater threat than Copernicus’ heliocentricity.

It should be clear that far from representing a boring, orthodox conformity that was shaken out of its torpid stupor by Copernicus publishing his heliocentric hypothesis, the sixteenth century debate on astronomy and cosmology was a lively exchange of ideas and concepts some old and some new.









Filed under History of Astronomy, History of science, Renaissance 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 Agora goes 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 her 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