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The role of celestial influence in the complex structure of medieval knowledge.

My entire life has followed a rather strange and at time confusing path that bears no relationship to the normal career path of a typical, well educated, middle class Englishman. It has taken many twists and turns over the years but without doubt one of the most bizarre was how I got to know historian of astrology Darrel Rutkin. We met on a bus, when he a total stranger commented that he knew the author of the book that I was reading, Monica Azzolini’s excellent, The Duke and the Stars: Astrology and Politics in Renaissance Milan. You can read the story in full here. At the time Darrel was a fellow at the International Consortium for Research in the Humanities: Fate, Freedom and Prognostication. Strategies for Coping with the Future in East Asia and Europe in Erlangen, where he was working on his book on the history of European astrology. Darrel and I became friends, talking about Early Modern science and related topics over cups of coffee and he twice took part in my History of Astronomy tour of Nürnberg. Before he left Erlangen he asked me if I would be interested in reading and reviewing his book when he finished writing it. I, of course, said yes. Some weeks ago I received my review copy of H. Darrel Rutkin, Sapientia Astrologica: Astrology, Magic and Natural Knowledge, ca. 1250–1800: I.Medieval Structures (1250–1500): Conceptual, Institutional, Socio-Political, Theologico-Religious and Cultural and this is my review.


As should be obvious from the impressive title this is not in anyway a popular or even semi-popular presentation but a very solid piece of hard-core academic research. What I have, and will discuss here, is just volume one of three, which weighs in at over six hundred pages. In his work Rutkin present two theses the first of which he explicates in Volume I of his epos and the second of which forms the backbone of the two future volumes. The central thesis of Volume I is summed up in the slightly intimidating twelve-word term “astrologizing Aristotelian natural philosophy with its geometrical-optical model of celestial influences.” A large part of the book is devoted to constructing this object and I will now attempt to produce a simplified description of what it means and how it operated in medieval Europe.

It is common in the history of astrology to treat it as a separate object, as if it had little or nothing to do with the rest of the contemporary knowledge complex. It is also very common to lump astrology together with magic and the other so-called occult sciences. For the High Middle Ages, the period that his book covers, Rutkin rejects both of these approaches and instead proposes that astrology was an integral and important part of the accepted scientific knowledge of the period. His book is divided into five sections each of which I will now outline.

The first section is an eighty-nine-page introduction, which contains a detailed road map of the author’s intentions including a brief summary of what he sees as the current situation in various aspects of the study of the subject under investigation. This also includes an excursion: Astrological Basics: Horoscopes and Practical Astrology. This section is not based on the author’s own work but on that of Roger Bacon, one of the central figures of the book, so if you want to know how a leading medieval astrologer set up and worked with a horoscope then this is the right place to come.

The first section of the book proper deals with the relationship between astrology and natural philosophy in the thirteenth century and it is this section that defines and explains our intimidating twelve-word term from above. Rutkin’s analysis is based on four primary sources; these are an anonymous astrological text the Speculum Astronomiae, written around 1260 and often attributed to Albertus Magnus, an attribution that Rutkin disputes, the writings of Albertus Magnus (before 1200–1280), those of Thomas Aquinas (1225–1274) and those of Roger Bacon (ca. 1220­–1292), as well as numerous other sources from antiquity, and both the Islamic and Christian Middle Ages. In this first section he first presents those writings of Aristotle that contain his thoughts on celestial influence, which form the philosophical foundations for the acceptance of astrology as a science. He then demonstrates how the Speculum Astronomiae, Bacon and Albertus expanded Aristotle’s thoughts to include the whole of horoscope astrology and imbedded it into medieval Aristotelian natural philosophy, this is our “astrologizing Aristotelian natural philosophy.” He also shows how Thomas, whilst not so strongly astrological, as the others, also accepts this model. The technical astrology that is considered here is a highly mathematical, read geometrical, one based on the radiation theories of the Arabic scholar al-Kindi in his De radiis stellarum, as originally introduced into European thought by Robert Grosseteste (1175–1253) in his optical theories and adopted by Bacon. This explains how every geographical point on the earth at every point in time has a unique horoscope/astrological celestial influence: the “geometrical-optical” part of our intimidating twelve-word term. This also ties in with Aristotle’s geographical theories of the influence of place on growth and change. What comes out of this analysis is an astrological-geographical-mathematical-natural philosophical model of knowledge based on Aristotle’s natural philosophy, Ptolemaeus’ astronomy and astrology, and al-Kindi’s radiation theory at the centre of thirteenth century thought.

Rutkin does not simple state an interpretation of Albertus’, Bacon’s or Aquinas’ views but analyses their actual writings in fine detail. First he outlines one step in a given thought process then he quotes a paragraph from their writings in English translation, with the original in the footnotes, including original terms in brackets in the translation if they could possible be considered ambiguous. This is followed by a detailed analysis of the paragraph showing how it fits into the overall argument being discussed. He proceeds in this manner paragraph for paragraph cementing his argument through out the book. This makes hard work for the reader but guarantees that Rutkin’s arguments are as watertight as possible.

The second section of the book proper deals with the subject of theology, a very important aspect of the medieval knowledge complex. Rutkin shows that both Albertus and Thomas accepted astrology within their theology but were careful to show that celestial influence did not control human fate, providence or free will these being the dominion of their Christian God. This is of course absolutely central for the acceptance of astrology by Christian theologians. Bacon’s attitude to astrology and theology is completely different; he builds a complete history of the world’s principle religions based on the occurrence of planetary conjunctions, explaining why, as a result, Christianity is the best religion and addressed to the Pope, for whom he is writing, how one needs to combat the religion of the Anti-Christ.

The third section of the book proper now turns to the vexed question of the relationship between astrology and magic. Rutkin shows that both the Speculum Astronomiae and Albertus in his writing accept that astrology can be used to create magical images or talisman for simple tasks such as killing snakes. However, this is the limit of the connection between the two areas, other aspects of magic being worked by evil spirits or demons. Thomas, not surprisingly rejects even this very circumscribed form of astrological magic regarding all of magic to have its roots in evil. Bacon is much more open to a wider range of connections between the areas of astrology and magic.

Having set up the place of astrology in the medieval knowledge complex of the thirteenth century, the fourth and final section of the book proper takes brief looks at the evidence for its use in various fields within Europe in the period up to 1500. Fields sketched rather than covered in great detail included mathematics, medicine, teaching in the various faculties at the universities, annual prognostications at the universities and to close astrology in society, politics and culture.

Does Rutkin succeed in proving his central thesis for this his first volume? History is not like mathematics and does not deliver conclusive proofs but Rutkin’s thesis is argued in great detail with an impressive array of very convincing evidence. His work is rock solid and anybody wishing to refute his thesis is going to have their work cut out for them. That is not to say that with time, new research and new evidence his thesis will not undergo modification, refinement and improvement but I think its foundations will stand the test of time.

His second main thesis, which will be presented in the two future volumes of his work, is to explain how and why the medieval, mathematics based (read mathematical astrology), Aristotelian natural philosophy that had been created in the High Middle Ages came to replaced by a very different mathematics based, system of natural philosophy in the seventeenth and eighteenth centuries. Having ploughed my way through Volume I, I very much look forward to reading both future volumes.

It goes without saying that the book has an impressively long bibliography of both primary and secondary sources that the author has consulted. I consider myself reasonably well read on the history of European astrology but if I were to sit down and read all of the new, interesting titles I discovered here, I would be very busy for a number of years to come. There is also a first class index and I’m very happy to report that the book also has excellent footnotes, many of which I consulted whilst reading, rather than the unfortunately ubiquitous endnotes that plague modern publishing.

Before I move to a conclusion I wish to point out a second way to read this book. As it stands this is not a book that I would necessarily dump on an undergraduate or a historian, whose interest in the fine detail of Rutkin’s argument was peripheral but that is not necessary or at least not in its totality. I have already mentioned that the introduction contains a detailed road map to the whole volume and as well as this, each of the four sections has an introduction outlining what the section sets out to show and a conclusion neatly summarising what has been demonstrated in the section. By reading main introduction and the introductions and conclusions to the sections a reader could absorb the essence of Rutkin’s thesis without having to work through all of the documentary proof that he produces.

In general I think that Rutkin has set standards in the historiography of medieval astrology and that his book will become a standard work on the topic, remaining one for a long time. I also think that anybody who wishes to seriously study medieval European astrology and/or medieval concepts of knowledge will have to read and digest this fundamental and important work.

I’m posting this today, having pulled it up from the back of a list of planned blog posts because today Darrel’s book is being formally presented at the University of Venice, where he is currently working in a research project, this afternoon with Monica Azzolini as one of those discussing the book and so a circle closes. I shall be there with them in spirit.





Filed under Book Reviews, History of Astrology, Uncategorized

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

Although highly anticipated the expectation placed upon De revolutionibus and the reactions to it were highly diverse and covered a very wide spectrum from complete acceptance to total rejection with many variation in between. It would be impossible in a blog post series such as this one to deal with the multitude of single reactions that would require a fairly substantial book; in fact I have two such books sitting next to my computer at the moment–Pietro Daniel Omodeo, Copernicus in the Cultural Debates of the Renaissance: Reception, Legacy, Transformation (Brill, 2014) & Jerzy Dobrzycki ed., The Reception of Copernicus’ Heliocentric Theory (D Reidel, 1972)–which I recommend to anybody who wants an in depth, blow by blow account. What I intend to do here is sketch the basic trends of that reception.

Famously Robert Westman once claimed that only ten people in the whole world accepted Copernicus’ heliocentric hypothesis, including his cosmology, completely between its publication in 1553 and the year 1600. His list actually misses a couple of total accepters such as Gemma Frisius, who acknowledged his acceptance in his foreword to Johannes Stadius’ ephemerides, and the Englishman John Feild who made the same acknowledgement in his ephemerides. However, it does include three others who either dropped or appeared to drop their acceptance. Christoph Rothmann (born between 1550 & 1560 died probably after 1600) one of Wilhelm IV’s astronomers (of which more later), who had an extensive dispute with Tycho Brahe, who of course didn’t accept Copernicus’ cosmology, on the subject and in the end, and according to Tycho was converted to his point of view.  Diego de Zúñiga (1536–1597), a Spanish Augustinian hermit and academic, who wrote a defence of the heliocentric hypothesis in his In Job commentaria (1584) but later in life rejected Copernicus’ hypothesis as incompatible with Aristotelian philosophy, probably under religious pressure from his superiors. The most peculiar renegade was Copernicus’ first and initially strongest supporter, Rheticus. Having gone quiet on Copernicus and his hypothesis for some time after he moved to Kraków, in a correspondence with Pierre de la Ramée (1515-1572) he announced that he had erected a large gnomon in Kraków and was now practicing the true astronomy of the Egyptians, whatever that might be. Summa summarum, one can say without much contradiction that there were never more than about fifteen, and probably less, true Copernican in the world before 1600 or even before 1609/10 when the publications of Kepler and the invention of the telescope became game changers.

There were a few astronomers, who simply rejected Copernicus’ hypothesis without comment and some, who simply ignored it but they won’t interest us here because the evidence shows that the vast majority did react to it in some way or another. As already mentioned earlier Owen Gingerich carried out a survey of all known surviving copies of the 1st(Nürnberg 1543) and 2nd(Basel 1566) editions of De revolutionibus[1]and his analysis of the annotation and marginalia of the readers clearly shows that the majority took very little notice of the first cosmological part of the book but concentrated their reading instead on the technical parts of the book, the mathematical models and the data.

This rejection of the heliocentric aspect of Copernicus’ work was a simple and direct consequence of the fact that he could not provide any empirical evidence to support his claims that the Earth revolved on its own axis and that it orbited a stationary Sun. Both claims very clearly contradicted the evidence of one’s own senses, we still say the Sun rises and sets, and suggested consequences that Copernicus was unable to answer. If the Earth is rotating at approximately 1600 kilometres an hour at the equator, why doesn’t everything on the surface get blown off by the headwind? And if the Earth is orbiting the Sun, why can’t we detect stellar parallax? These are just two of the possible objections to which Copernicus could not provide scientific answers.

The answers, based on assumptions, which he did propose would prove with time and new developments in science to be fundamentally correct but at the time there were merely unsubstantiated assumptions. In answer to the first he suggested that everything on the Earth’s surface would be carried along with it in some sort of envelope. This turned out to be correct but Copernicus lacked the physics necessary to explain how this would function. In fact the history of physics of the seventeenth century, as we shall see, consisted to a large extent of developing the knowledge to provide this explanation. As far as stellar parallax was concerned, or rather the lack of it, Copernicus simply and correctly assumed that the stars were simply too far away for the parallax to be detected with the naked-eye. However, Copernicus and almost all of his contemporaries still believed in the sphere of the fixed stars and if this sphere was so far away that stellar parallax was undetectable then the distance between the orbit of Saturn and the sphere of the fixed stars would have to be inconceivably vast and thus not very acceptable. Simply put, why all of that empty space out there?

The ambivalence towards Copernicus magnum opus is nicely illustrated by the Welsh mathematicus Robert Recorde (c. 1512–1558) in his The Castle of Knowledge (1556) the first English text to refer to the Copernican hypothesis. On the subject of the possible motion of the Earth he wrote:

             But as for the quietness of the earth, I need not to spend any time in proving of it, since that opinion is so firmly fixed in most men’s heads, that they accompt it mere madness to bring the question in doubt. And therefore it is as much folly to travail to prove that which no man denieth, as it were with great study to dissuade that thing which no man doth covet, neither any man allow: or to blame that which no man praiseth, neither any man liketh.

Scholar: Yet sometimes it chanceth, that the opinion most generally received, is not most true

Master: And so do some man judge of this matter, for not only Eraclides [Heraclides] Ponticus, a great Philosopher, and two great clerks of Pythagoas school, Philolaus and Ecphantus, were of the contrary opinion, but also Nicias [Hicetas] Syracusius, and Aristarchus Samius, seem with strong arguments to approve it: but the reasons are too difficult for this first Introduction, and therefore I will omit them till another time. And so I will do the reasons that Ptolemy, Theon and others do allege, to prove the earth to be without motion: and the rather, because those reasons do not proceed so demonstrably, but they may be answered fully, of him that holds the contrary. I mean, concerning circular motion: marry, direct motion out of the centre of the world seemeth more easy to be confuted, and that by the same reasons, which were before alleged for proving the earth to be in the middle and centre of the world.

Scholar: I perceive it well: for as if the earth were always out of the centre of the world, those former absurdities would at all times appear: so if at any time the earth should move out of his place, those inconveniences would then appear.

Master: That is truly to be gathered: how be it, Copernicus, a man of great learning, of much experience, and of wonderful diligence in observation, hath renewed the opinion of Aristarchus Samius, and affirmeth that the earth not only moveth circularly about its centre, but also may be, yea and is, continually out of the precise centre of the world 38 hundred thousand miles: but because the understanding of that controversy dependeth of profounder knowledge than in this Introduction may be uttered conveniently, I will let it pass till some other time.

Scholar: Nay sir in good faith, I desire not to hear such vain fantasies, so far against common reason, and repugnant to the consent of all the multitude of Writers, and therefore let it pass for ever, and a day longer.

Master: You are too young to be a good judge in so great a matter: it passeth for your learning, and theirs also that are much better learned than you to improve [i.e. disprove] his supposition by good arguments, and therefore you were best to condemn nothing that you do not well understand but another time, as I said, I will so declare his supposition, that you shall not only wonder to hear it, but also peradventure be as earnest then to credit it, as you are now to condemn it.


In this exchange Recorde appears to both reject and praise Copernicus’ hypothesis. Unfortunately we will never know his true opinion as he died before he could write the advanced text that he promises his readers here. What, however, is very clear is that Recorde is very well informed about the history of both diurnal rotation and the heliocentric hypothesis.

Some of the readers, who only considered the mathematical parts of the book, simply took Copernicus’ models for the various planets and applied them to a geocentric system, hoping thereby to produce a better predictive model for the position of the planets. Other took this remodelling a step further and using Copernicus’ mathematical models revived the Capellan model, well-known and much loved in the Middle Ages; a geocentric system in which Mercury and Venus orbit the Sun, which in turn orbits the Earth.


Naboth’s representation of Martianus Capella’s geo-heliocentric astronomical model (1573) Source: Wikimedia Commons

Others took this thought one step further and developed, what is now known the Tychonic system, named after Tycho Brahe (1546–1601), although he was by no means the first or the only astronomer to publish this system in the second half of the sixteenth century, all claiming to have developed it independently. In this helio-geocentric system all of the planets except the Moon, orbit the Sun, which together with the Moon orbits the stationary Earth. Heliocentric, geocentric and helio-centric model based on Copernicus’ parameters and mathematical model can and have been shown to be mathematically equivalent with nothing to recommend one over the other, without further information.


The Tychonic System Source: Wikimedia Commons

One interesting but slightly confusing development was that some geocentric and helio-geocentric astronomers accepted the arguments for the Earth spinning on its own axis, diurnal rotation, whilst still rejecting the Earth orbiting the Sun. As I wrote here in an earlier blog post, this idea goes back at least to Heraclides Ponticus (c.390 BCE–c.310 BCE) and was adopted or discussed and rejected many times over the centuries down to Copernicus’ times. The argument in its favour is a purely physical one. It is much simpler for the comparatively small Earth to rotate than for the vastly larger and heavier sphere of the fixed stars. This acceptance of diurnal rotation would prove to be an important steeping stone to the complete acceptance of the heliocentric model in the seventeenth century.

On major group, who showed great interest in Copernicus’ mathematics and above all in the planetary tables and ephemerides that they delivered were the astrologers. This basically means all professional and half professional astronomers, as they were almost all practicing astrologers. As stated above Robert Westman once claimed that there were only ten Copernicans in the whole world between 1543 and 1600, a historian of astrology correctly pointed out that all ten were practicing astrologers. Like Regiomontanus in the previous century (see Part II of this series) they all thought that more accurate astronomical data would improve the quality of their astronomical prognoses. Not only did they avidly consult the ephemerides of Stadius and Feild but several of them such as the Italian mathematicus Giovanni Antonio Magini (1555–1617) unsatisfied with Stadius’ and Feild’s accuracy also calculated their own new ephemerides. In the end, however, the astrologers recognised that although the errors in Copernican tables were different to those in Ptolemaic ones they were not much more accurate as we will see in the next instalment.

[1]Owen Gingerich, An Annotated Census of Copernicus’ De Revolutionibus(Nuremberg, 1543 and Basel, 1566), Brill, Leiden, Boston, Köln, 2002


Filed under History of Astronomy, Renaissance Science, Uncategorized

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

Copernicus first put his concept for a heliocentric cosmos in writing in a manuscript that today bears the title Nicolai Copernici de hypothesibus motuum coelestium a se constitutis commentariolus (roughly translated: Nicolas Copernicus’ short commentary on his hypothesis about the movement of the celestial bodies) of which three manuscripts are known to exist today. None of them, however, in Copernicus’ own handwriting. There is almost no direct evidence for the existence of this document in the sixteenth century and almost everything that we can say about its origin, its distribution and its impact is based on reasonable, speculative interpretation of indirect evidence.

It is disputed whether the title Commentariolus, for short, was written by Copernicus or was added at a later date; it has been speculated that it was added by Tycho Brahe, who possessed a copy, which is one of the three surviving copies and is now housed in the Viennese Court Library. In his Astronomiae Instauratae Progymnasmata (1602) Tycho wrote that his copy was given to him by Thaddaeus Hagecius (1525–1600). He also said that he had made several copies and distributed them to friends.


Title page of the Viennese Commentariolus manuscript Source: Wikimedia Commons

The Viennese manuscript was first found in 1877 but it is incomplete, missing a substantial part of Copernicus’ lunar theory. In 1881 a complete manuscript was found in the library of the Stockholm Observatory bound into a second edition of De Revolutionibus, which had been the property of Hevelius. The third manuscript was also found bound into a second edition of De revolutionibus that had belonged to Duncan Liddel (1561–1613) in the library of Saint Andrews University in Scotland. Liddel studied at various North German universities and was later a professor for mathematics at Helmstedt University before going on to qualify as a physician and becoming a professor for medicine. A fairly normal career path in the sixteenth century. He knew Tycho Brahe and visited him at least twice on the island of Hven. It should be noted that all three surviving copies of the Commentariolus were owned by people who lived after the publication of De revolutionibus and the death of its author.

The first probably mention of the Commentariolus occurred in 1514. The Cracovian physician, geographer and historian, Matthias of Miechow (1457–1523) noted in a library catalogue in the Jagiellonian Library dated 1 May 1514 the following:

Item sexternus theorice asserentis terram moveri, Solem vero quiescere

A quire of six leaves (sexternus) of a theory asserting that the Earth moves whereas the Sun is at rest.

It is assumed that this is a reference to the Commentariolus, probably a copy originally given by Copernicus to his Cracovian friend Canon Bernard Wapowski (1450–1535) a cartographer and historian.


Excerpt from the library catalogue of Matthias von Miechow (1457–1523) 1. Mai 1514 with the Commentariolus hint: „Item sexternus theorice asserentis terram moveri, Solem vero quiescere“. Source: Wikimedia Commons

There are no direct references to the Commentariolus before the publication of De Revolutionibus in 1543. However, there are various episodes in Copernicus’ life that can probably be attributed to knowledge of the Commentariolus.

Paul of Middelburg (1446–1534) sent out a general call to astronomers and rulers asking for suggestions and contributions towards a proposed calendar reform at the Lateran Council (1512–1517). Paul noted in 1516 that one of those who answered that call was Copernicus in a letter that no longer exists. Perhaps Copernicus was on Paul’s list because of the Commentariolus, he had at this point published no other astronomical works that might have motivate Paul to consult him.

In 1533 Johann Albrecht Widmannstetter (1506–1557), who was a papal secretary held a series of lectures to an audience of Pope Clement VII and some cardinals outlining Copernicus’ heliocentric theories for which he was richly rewarded by the Pope with a rare manuscript. It can be assumed that his source of knowledge of those theories was the Commentariolus.  Following the death of Pope Clement in 1534 Widmannstetter became secretary to Cardinal Nikolaus von Schönberg (1472–1537), who wrote a letter to Copernicus in 1536 concerning his theories and offering to have the manuscript of his theories (De revolutionibus) copied at his expense. This letter would be included in the published version of De revolutionibus.

In 1539 Martin Luther (1483–1546), in his cups, reputedly launched an attack on Copernicus’ heliocentric hypothesis, as recorded by Anton Lauterbach in the Tischreden (Table Talk) first published in 1566. (More details here)

There was mention of a certain astrologer who wanted to prove that the earth moves and not the sky, the sun, and the moon. This would be as if somebody were riding on a cart or in a ship and imagined that he was standing still while the earth and the trees were moving. [Luther remarked] “So it goes now. Whoever wants to be clever must agree with nothing that others esteem. He must do something of his own. This is what that fellow does who wishes to turn the whole of astronomy upside down. Even in these things that are thrown into disorder I believe the Holy Scriptures, for Joshua commanded the sun to stand still and not the earth [Jos. 10:12].”

Copernicus was not mentioned by name in Luther’s tirade and also no great details of the hypothesis. It can be assumed that indirect knowledge of the Commentariolus had come to Luther’s ears.

Our last possible indirect knowledge of the Commentariolus can be attributed to Georg Joachim Rheticus (1514–1574), who famously persuaded Copernicus to publish De revolutionibus. Rheticus set off for Frombork in 1539 already aware of the fact that Copernicus was propagating a heliocentric hypothesis. Did this knowledge come directly or indirectly from the Commentariolus?

So what does the Commentariolus consist of? In a very brief introduction Copernicus writes:

           Our Ancestors assumed, I observe, a large number of celestial spheres for this reason especially, to explain the apparent motion of the planets by the principle of regularity. For they thought it altogether absurd that a heavenly body, which is a perfect sphere, should not always move uniformly. They saw that by connecting and combining regular motions in various ways they could make any body appear to move to any position.

Callippus and Eudoxus, who endeavoured to solve the problem by use of concentric spheres, were unable to account for all planetary movements; they had to explain not merely the apparent revolutions of the planets but also the fact that these bodies appear to us sometimes to mount higher in the heavens, sometimes to descend; and this fact is incompatible with the principle of concentricity. Therefore it seemed better to employ eccentrics and epicycles, a system which most scholars finally accepted.

Yet the planetary theories of Ptolemy and most other astronomers, although consistent with the numerical data, seemed likewise to present no small difficulty. For these theories were not adequate unless certain equants were also conceived; it then appeared that a planet moved with uniform velocity neither on its deferent nor about the center of its epicycle. Hence a system of this sort seemed neither sufficiently absolute nor sufficiently pleasing to the mind.

Having become aware of these defects, I often considered whether there could perhaps be found a more reasonable arrangement of circles, from which every apparent inequality would be derived and in which everything would move uniformly about its proper center, as the rule of absolute motion require. After I had addressed myself to this very difficult and almost insoluble problem, the suggestion at length came to me how it could be solved with fewer and much simpler constructions than were formally used, if some assumptions (which are axioms) were granted me. They follow in this order[1].

In this brief introduction, which I have given here in full, Copernicus makes very clear why he thinks that astronomy needs reforming. He is in principle quite happy with an epicycle-deferent model but not with the use of equants, which he sees as violating the fundamental principle of uniform circular motion, a philosophically founded astronomical axiom that he wholeheartedly accepts. The equant point is an abstract off-centre point inside the orbit of a planet, which when used as the viewing point gives the planet on its epicycle-deferent uniform motion.


equant: A sphere that is centered at the center of the universe, but whose motion varies irregularly as if it were centered at another spot, called the equant point. This geometrical tool allowed Ptolemaic astronomers to construct orbits with the observed variations of speed without resorting to the ugliness of a sphere that was actually off center (an eccentric). The Planet is actually on the outer circle below, centered at E, the center of the universe. The sphere, however, moves as if it were centered at the point marked equant below, so that it takes equal times for the planet to move from 1 to 2, from 2 to 3, from 3 to 4 and from 4 back to 1, even though the distances vary. This produces a variation in the observed speed of the planet. Source

What is interesting is that he gives no indication of the bombshell that he is about to lob into the astronomy-cosmology debate with the assumptions that he wishes to be granted by his readers. They follow immediately on the introduction. He merely wishes to substitute a heliocentric system for the universally accepted geocentric system. Even more interesting, and totally frustrating for historians of astronomy, he gives absolutely no indication whatsoever how or why he came to adopt this radical step in order to rescue the uniform circular motion axiom. Copernicus’ assumptions (axioms) read as follows[2]:

1: There is no one center of all the celestial circles or spheres.

That there is, is one of the fundamental axioms of Aristotelian cosmology

2: The center of the earth is not the center of the universe, but only of gravity and the lunar sphere

That the earth is the centre of the universe is another of the Aristotelian axioms

3: All the spheres revolve about the sun as their mid-point, and therefore the sun is the center of the universe.

Bombshell lobed without comment!

4: The ratio of the earth’s distance from the sun to the height of the firmament is so much smaller than the ratio of the earth’s radius to its distance from the sun that the distance from the earth to the sun is imperceptible in comparison with the height of the firmament.

Copernicus needs this assumption to explain the lack of observable stellar parallax. Much is made of Copernicus’ vast increase in the size of the cosmos in comparison to Ptolemaeus. However in the Almagest Ptolemaeus states, “Moreover, the earth has, to the senses, the ratio of a point to the distance of the sphere of the so-called fixed stars[3].” Even Ptolemaeus’ cosmos is in principle unimaginably large.

5: Whatever motion appears in the firmament arises not from any motion of the firmament, but from the earth’s motion. The earth together with its circumjacent elements performs a complete rotation on its fixed poles in a daily motion, while the firmament and highest heaven abide unchanged.

The concept of diurnal rotation, the earth’s daily rotation about its own axis, had been hypothesised on many occasions throughout the history of astronomy as I explained in an earlier blog post. Copernicus would call upon some of those earlier examples as support for his own views in De revolutionibus. More interesting is the phrase “together with its circumjacent elements”, where Copernicus is basically saying that the earth carries its atmosphere with it when it rotates. This counters some of the arguments already listed by Ptolemaeus against diurnal rotation. The problem for Early Modern supporters of heliocentricity or simply diurnal rotation is they lacked the physics to explain how the earth could carry its atmosphere with in on its daily spin. We will return to this topic in a later episode.

6: What appear to us as motions of the sun arise not from its motion but from the motion of the earth and our sphere, with which we revolve around the sun like any other planet. The earth has, then, more than one motion.

The first sentence merely confirms the consequences of a heliocentric model. The second states another break with the Aristotelian axioms. According to Aristotle celestial bodies have just one type of natural motion, uniform circular motion and the earth also has just one type of natural motion upward or downward perpendicular to the earth’s surface.

7: The apparent retrograde and direct motion of the planets arises not from their motion but from the earth’s. The motion of the earth alone, therefore, suffices to explain so many apparent inequalities in the heavens.

This last assumption is, of course, the biggest selling point for the adoption of a heliocentric system but in the debates following the publication of De revolutionibus, the other arguments against heliocentricity weighed so heavily that this explanation for retrograde planetary motion got largely ignored.


Second page of the Stockholm manuscript with the assumptions Source: Wikimedia Commons

Copernicus now begins to fill in the details:

            Having set forth these assumptions, I shall endeavor briefly to show how uniformity of the motions can be saved in a systematic way. However I have thought it well, for the sake of brevity, to omit from this sketch mathematical demonstrations…[4]

Once again we have a confirmation that Copernicus’ main interest, as he sees it, is to restore the uniform circular motion axiom. I shall not into detail about the rest but the section headings are:

The Order of the Spheres

The Apparent Motion of the Sun

Equal Motion Should Be Measured Not by the Equinoxes but by the Fixed Stars

The Moon

The Three Superior Planets Saturn–Jupiter–Mars



Of interest here is that some of the epicycle-deferent models he outlines here differ from those that he would later develop for De revolutionibus indicating that this is an initial concept that would undergo development in the following thirty plus years, although he announces his intention to produce a larger more detailed work in the sentence I broke off above:

However I have thought it well, for the sake of brevity, to omit from this sketch mathematical demonstration, reserving these for my larger work[6].

We have no idea how many copies of the Commentariolus Copernicus made and distributed or how many further copies were made by others. As I have indicated above there is circumstantial evidence that it was read but the lack of any direct mentions before the publication of De revolutionibus, plus the fact that there seems to have been no heliocentricity debate triggered by it, as opposed to the debate triggered by Fracastoro’s Homocentrica (1538),and a couple of other contemporary published texts on the homocentric spheres model, indicate that the Commentariolus had very little impact on the sixteenth-century astronomical community.

















[1]3 Copernican Treatises: The Commentariolus of Copernicus, The Letter Against Werner, The Narratio Prima of Rheticus, Translated with Introduction, Notes and Bibliography by Edward Rosen, Dover Publications, Inc., New York, 1959 pp. 57-58

[2]Copernicus/Rosen pp. 58-59

[3]Ptolemy’s AlmagestTranslated and Annotated by G. J. Toomer, Princeton University Press, Princeton New Jersey, ppb. 1998 p. 43

[4]Copernicus/Rosen p. 59

[5]Copernicus/Rosen pp. 59-90

[6]Copernicus/Rosen p. 59


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

An open letter to an author

Dear Yuval,

if I may? Sometime around the publication in English of your trendy mega bestseller, Sapiens, I read something from you, I can’t remember if it was an essay or an extract from the book, on the Scientific Revolution, as part of the extensive sales campaign for your publication. To say the least, I was, to put it mildly, totally underwhelmed and decided that I really didn’t need to read your book. Since then whenever the subject of your book came up in conversations or on the Internet I made disparaging comments about your abilities as a historian of Early Modern science. Recently it occurred to me that I might be being somewhat unfair, my comments being based on a half remembered short piece of writing and that maybe I ought to give you a second chance. Eventually I ordered your book through interlibrary loan, my university library apparently doesn’t have a copy. When it arrived I sat down to read the Fourth Section of the book entitled The Scientific Revolution. You must excuse me but I have so much that I want to read that I don’t really have time to read your whole book.

The first page of waffle about time travelling peasants and battleships didn’t really impress me but then on the second page I stumbled across the following:

In 1500, few cities had more than 100,000 inhabitants. Most buildings were constructed of mud, wood and straw; a three-story building was a skyscraper. The streets were rutted dirt tracks, dusty in summer and muddy in winter, plied by pedestrians, horses, goats, chickens and a few carts. The most common urban noises were human and animal voices, along with the occasional hammer and saw. At sunset, the cityscape went black, with only an occasional candle or torch flickering in the gloom.

The evocative picture that you paint with your words in this paragraph reminds me of the Hollywood B-movie visions of medieval hovels and unwashed peasants that informed my childhood and in my opinion has about as much truth content as those movies of yore.

I am a historian of Renaissance science, hence the name of this blog, and I live just up the road from the German, Renaissance city of Nürnberg, where, belonging as I do the an active group of local historians, I conduct on a fairly regular basis guided tours of the history of astronomy of that city most, but not all, of which revolves around the year 1500, plus or minus 50 years. For your edification and education I would now like to take you on part of that tour to show what a Middle European city really looked like in 1500.

Before I start I will grant that few European cities had more than 100,000 inhabitants; Nürnberg, then the second biggest German city, only had a population of 40,000. Of course there were much bigger cities in other parts of the world, Middle East, India, China but as the entire world population has been estimated to lay between 400 and 500 million in 1500, it is not surprising that the major cities were much smaller than those of today. Scaling up proportionally a city of 40,000 in 1500 with a world population of 500 million is equivalent to a city of more than 500,000 in today’s world of 7,000 million inhabitants, slightly less than Nürnberg’s current population.

I always start my tour with this sundial, which was created in 1502.


Lorenzkirche Sundial Source: Astronomie in Nürnberg

As you can see it is a quite sophisticated sundial and if you know how, you can read the time on it in three different ways, from sunrise, from midday and according to the Great Nürnberger clock: a system between the medieval local time system and our equinoctial hours: A bit beyond the primitive culture that you sketch. I hear you muttering but what about clocks. We’ll get to one of those a bit later.

The sundial is on the side of the Lorenzkirche, one of Nürnberg’s two parish churches started in 1250 and finished in 1477.

Nürnberg St. Lorenz Türme von Westen

Source: Wikimedia Commons

As you can see it’s a rather impressive sandstone building with a slate roof, as were most of the city buildings in 1500. By the way, the streets were also paved. No dirt tracks here.

Our next station is the Heilige-Geist-Spital built in 1399 as an old peoples residence, a function it still fulfils today.


Heilige-Geist-Spital Source: Wikimedia Commons

Moving on, we come to the Market Place and the Frauenkirche built between 1352-1362.


Frauenkirche Source: Wikimedia Commons

The mechanical clock on the facade was built in 1509.


Source: Wikimedia Commons

The ball above the clock shows the phases of the moon, still accurate today. At twelve-noon everyday there is a complex mechanical display with fanfares by the trumpeters, drum rolls and bell ringing. This is followed by the seven Electors circling the Emperor in the middle, three times. Tourists from all over the world come to Nürnberg to witness this spectacle.

I like this 19th-century picture showing the Schöner Brunnen (Beautiful Fountain), also on the Market Place, which was built between 1385-1396.


Here it is in all its glory, today.


Schöner Brunnen. In the backgrounfd you can see the towers of the other parish church St. Sebald (14th century) Source: Wikimedia Commons

You might like this house, it was the home of a local artisan, Albrecht Dürer (1471–1525), you might have heard of him?


Source: Wikimedia Commons

In 1500, Nürnberg was a major industrial city, producing a very wide range of metal products, as well as being a leading European trading centre. In fact it was one of the biggest centres in Europe for the production of everything that could be made out of metal. For example, the Nürnberg craftsmen received an order from the Emperor, Charles V (1500–1558), for five thousand suits of armour, so we can assume that there was quite a lot of noise on the streets on the city. Nürnberg traded on a large scale with much of Europe. It was not unusual for the traders to attend the Frankfurter Fair with a waggon train of five hundred waggons

You can get a good overall impression of the city from this illustration out of the Schedelsche Weltchronik (known in English as the Nuremberg Chronicle), the world’s first printed encyclopaedia, printed and published in Nürnberg in 1493.


Nürnberg as depicted in the Nuremberg Chronicles 1493

By now I hope you will realise that the real historical Nürnberg in 1500 was radically different from your fairy tale description of a city in 1500. Having recovered from having read the paragraph reproduced above, I tried to persevere with your book but having come across several more equally dubious paragraphs in the next few pages, I must honestly say that I can’t be bothered. I have better things to do with my time. I can’t claim that this is a review of your book but I certainly won’t be recommending it to anybody, anytime soon.

No hard feelings











Filed under Autobiographical, Book Reviews, Uncategorized

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

Part I  Part II Part III

There is general agreement amongst historians of science that a major factor in the emergence of modern science in general and modern astronomy in particular was the (re)invention of moveable type printing and the arrival of the printed book in the middle of the fifteenth century. I say reinvention because moveable type printing emerged twice before in China in the eleventh century CE and in Korea in the fourteenth century, as I explained in an earlier post. For a long time it was a commonplace in the historical narrative that the printed book, like gunpowder and the compass, was a Chinese invention but extensive long-term research has failed to produce any evidence of a technology transfer and it is now thought that Johannes Gutenberg’s was an independent invention. Even within Europe Gutenberg was not the first to experiment with moveable type and his real invention was the printing press, inclusive printing ink.


Book Printers from Jost Amman  Professionals and Craftsmen

Less than twenty years after Gutenberg published his Bible, Regiomontanus printed and published the first printed astronomy book Peuerbach’s Theoricae Novae Planetarum (Nürnberg, 1473) followed by a handful of other astronomy/astrology books. Unfortunately he died before he could publish their Epytoma in almagesti Ptolemei, which was first published by Ratdolt in Venice in 1496. Both titles became standard astronomy textbooks throughout Europe for more than one hundred years. Famously also being the texts from which Copernicus learnt his astronomy and cosmology.


Theoricae Novae Planetarum Source: Wikimedia Commons

This marked the start of a wave of printed astronomy/astrology books throughout the sixteenth and seventeenth centuries including the works of Apian, Copernicus, Tycho, Kepler, Galileo and many other less well-known figures. Printing made reliable, consistent text available to a wide circle of readers. Whereas a copy of a manuscript in Copenhagen might well have serious deviations compared with a manuscript of the same work in Venice, printed copies of a book were in theory the same wherever their owners lived and worked.


The Astronomer from Jost Amman’s Professionals and Craftsmen Source: Wikimedia Commons

As I pointed out in a reply to an earlier comment in this series the printed great works of astronomy, such as Copernicus’ De revolutionibusor Apian’s Astronomicum Caesareum, would have been way beyond the pocket of the average university student of the period but the professional astronomers, their patron and the institutions could and did acquire copies thus making them, at least potentially, accessible to those students. Interestingly Kepler bought a second hand copy of Copernicus’ De revolutionibus when he was still a student.

However, printing advanced the general dissemination and progress of astronomy and its related fields through purpose written textbooks. The most obvious example of this is Peter Apian’s Cosmographia, originally published by the author in Landshut in 1524. This was a basic introduction to astronomy, astrology, surveying, cartography etc. In total, over the sixteenth century, the book went through thirty-two expanded and improved editions all of which were, somewhat strangely, edited and published by Gemma Frisius and not Apian. Similar textbooks were produced by Oronce Fine, Michael Mästlin and many other sixteenth century mathematical authors.


Title page of Apian’s Cosmpgraphia

It was not just major monographs that profited from the invention of movable type printing. Such astronomical/astrological tools as ephemerides benefited from a certain level of consistency given by print as opposed to hand written manuscripts with their copying errors. In fact a large part of Regiomontanus’ posthumous reputation was based on his printed ephemeris, one of the few books he was able to publish before his untimely demise.

Regiomontanus also led the way in producing printed astronomical/astrological calendars, volumes much in demand from all those working in the wider field of astronomy. In fact astronomical/astrological ephemera of all types–calendars, prognostica, single-sheet wall calendars, almanacs–became a mainstay of the early printing industry providing a much need flow of ready cash.


Regiomontanus Calendar Source: University of Glasgow

To give an idea of the scope of this activity, one of the calendars of Simon Marius (1573–1625), which had to be withdrawn because of political complaints by the local authorities, was said by the printer publisher to have had an edition of 12,000. Marius was only a small local astrologer; the editions of the calendars and prognostica of an Apian or a Kepler would have been much larger. An astronomical monograph, such as De revolutionibus, would have had high production costs and an edition of maybe 500. It would take several years before it turned a profit for the printer publisher if at all. The author got nothing for his troubles. A calendar (wall or pocket), prognostica or almanac had comparatively low production costs, a large edition and if the author was established sold very rapidly. The profits were usually shared fifty-fifty between the printer and the author, a reliable stream of income for both parties. Gutenberg raised some of the finance for his Bible by printing and issuing an astro-medical single-sheet wall calendar.

In an important work, Astrology and the Popular Press: English Almanacs 1500–1800historian Bernard Capp showed that astrological ephemera made up by far and away the largest sector of publishing in the early centuries of printing and more importantly that the editorial sections of the cheap almanacs were one of the major sources for disseminating the latest developments in astronomy, in particular, in the seventeenth century, heliocentricity.


Almanack by John Tulley, 1692. Book exhibited in the Cambridge Public Library, Cambridge, Massachusetts Source: Wikimedia Commons

Along with the development of moving type printing came an increased use of illustrations leading to a rapid development in the techniques used to produce them–woodblock printing, copperplate engraving and etching.


Woodblock cutter Jost Amman’s Professionals and Craftsmen Source: Wikimedia Commons

These techniques were then extended to other field related to astronomy, cartography and globe making. Printed copies of Ptolemaeus’ Geographia with maps were already being printed in the last quarter of the fifteenth century. There also quickly developed a market for large scale printed wall maps, the most famous early example being Waldseemüller’s world map that gave the very recently discovered fourth part of the world the name America after Amerigo Vespucci (1454–1512). Waldseemüller also seems to have printed the first terrestrial globe, a small globe containing the same map of the world. Unfortunately we only have a small number of printed globe gores and no surviving finished globes.


Waldseemüller World Map 1507 (Wikipedia Commons)

Johannes Schöner (1477–1547) was the first to start producing serial printed globes, his first terrestrial globe in 1515 and the matching celestial globe in 1517, establishing a tradition for matching pairs of printed globes that continued until the end of the nineteenth century. Judging by comments from his correspondence his globe printing enterprise was both very successful and very lucrative. Gemma Frisius (1508–1555) took up the baton producing printed globes to be sold with reprints of Schöner’s cosmographia, the descriptive book sold with each globe to explain how to use it. Gemma’s assistant was Gerhard Mercator, who would go on to become the most successful printed globe maker of the second half of the sixteenth century. Mercator’s globes inspired both the great Dutch cartographical houses of Hondius and Blaeu, who would dominate the European globe making and cartography industry in the seventeenth century. England’s first commercial globe printer, Joseph Moxon (1627–1691) learnt his handwork from Willem Janszoon Blaeu (c. 1570–1630). Printed globe making was big business in the sixteenth and seventeenth centuries and the globes were used to teach both astronomy and astrology.


Pair of globes by Gerard Mercator (Globe Museum, Austrian National Library).

Of course all of the above applies equally well to printed maps. Along with the demand for large wall maps, a market developed for collections of printed maps, what we now call atlases. Bound collection of manuscript maps existed before the invention of printing but being the product of hundreds of hours of manual labour these tended to be art treasures for rich patrons rather than practical books for everyday usage. The man, who did most to change this was Abraham Ortelius (1527–1598), whose Theatrum Orbis Terrarum, a bound, standardised, collection of maps, produced especially for traders first published in 1570 was a runaway success. Initial less successful was the more academic Atlas of his good friend and rival Gerhard Mercator. However, both publications laid the foundations for the commercial success of the cartographical publications of Blaeu and Hondius.


Theatrum Orbis Terrarum Title Page Source: Wikimedia Commons

A somewhat different approach was taken by Sebastian Münster (1488–1552), with his Cosmographia, first published in 1544, which was not just a collection of maps but also a full geographical and historical description of the world. In its numerous editions it was almost certainly the biggest selling book in the sixteenth century.


Title page of the first edition of Münster’s Cosmographia Source: Wikimedia Commons

Like nearly-all-the-other globe makers and cartographers described here Münster was an astrologer and astronomer. Other astrologer/astronomers in the sixteenth century, who were also commercially successful as cartographers were Peter and Philipp Apian, Oronce Fine and Michael Mästlin.

It should be clear from the above that the advent of movable type printing had a very large impact on the dissemination of astronomy and its related fields at the same time raising its status in the Early Modern Period in Europe and bringing it to a much wider audience.


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

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

You can read Part I here

Before we progress we need to take stock and deal with a couple of points that came up in a comment to Part I. This series is about the factors that led to the emergence of heliocentricity in Europe in the Early Modern Period. It doesn’t deal with any of the factors from earlier periods and other cultures that also explicitly and implicitly flowed into European astronomy. If one were to include all of those, it would be a total history of western astronomy that doesn’t even start in the West but in Babylon in about 2000 BCE. That is not what I intend to write and I won’t be doing so.

The other appears to contradict what I said above. At my starting point circa 1400 CE people became aware of a need to increase their usage of mathematical astronomy for a number of reasons that I sketched in Part I. Ptolemaic mathematical astronomy had been available in Europe in two Latin translations, the first from Greek the second from Arabic, since the twelfth century. However, medieval Europeans in general lacked the mathematical knowledge and to some extent the motivation to engage with this highly technical work. The much simpler available astronomical tables, mostly from Islamic sources, fulfilled their needs at that time. It was only really at the beginning of the fifteenth century that a need was seen to engage more fully with real mathematical astronomy. Having said that, at the beginning the users were not truly aware of the fact that the models and tables that they had inherited from the Greeks and from Islamic culture were inaccurate and in some cases defective. Initially they continued to use this material in their own endeavours, only gradually becoming aware of its deficiencies and the need to reform. As in all phases of the history of science these changes do not take place overnight but usually take decades and sometimes even centuries. Science is essential conservative and has a strong tendency to resist change, preferring to stick to tradition. In our case it would take about 150 years from the translation of Ptolemaeus’ Geographiainto Latin, my starting point, and the start of a full-scale reform programme for astronomy. Although, as we will see, such a programme was launched much earlier but collapsed following the early death of its initiator.

Going into some detail on points from the first post. I listed Peuerbach’s Theoricarum novarum planetarum(New Planetary Theory), published by Regiomontanus in Nürnberg in 1472, as an important development in astronomy in the fifteenth century, which it was. For centuries it was thought that this was a totally original work from Peuerbach, however, the Arabic manuscript of a cosmology from Ptolemaeus was discovered in the 1960s and it became clear that Peuerbach had merely modernised Ptolemaeus’ work for which he must have had a manuscript that then went missing. Many of the improvements in Peuerbach’s and Regiomontanus’ epitome of Ptolemaeus’ Almagest also came from the work of Islamic astronomers, which they mostly credit. Another work from the 1st Viennese School was Regiomontanus’ De Triangulis omnimodis Libri Quinque (On Triangles), written in 1464 but first edited by Johannes Schöner and published by Johannes Petreius in Nürnberg in1533.


Title page of a later edition of Regiomontanus’ On Triangle

This was the first comprehensive textbook on trigonometry, the mathematics of astronomy, published in Europe. However, the Persian scholar Abū al-Wafā Būzhjānī (940–988) had already published a similar work in Arabic in the tenth century, which of course raises the question to what extent Regiomontanus borrowed from or plagiarised Abū al-Wafā.

These are just three examples but they should clearly illustrate that in the fifteenth and even in the early sixteenth centuries European astronomers still lagged well behind their Greek and Islamic predecessors and needed to play catch up and they needed to catch up with those predecessors before they could supersede them.

After ten years of travelling through Italy and Hungary, Regiomontanus moved from Budapest to Nürnberg in order to undertake a major reform of astronomy.


City of Nürnberg Nuremberg Chronicles Workshop of Michael Wohlgemut Printed by Aton Koberger and published in Nürnberg in 1493

He argued that astrological prognostications were inaccurate because the astronomical data on which they were based was also inaccurate, which it indeed was. He had an ambitious two part programme; firstly to print and publish critical editions of the astronomical and astrological literature, the manuscripts of which he had collected on his travels, and secondly to undertake a new substantial programme of accurate astronomical observations. He tells us that he had chosen Nürnberg because it made the best scientific instruments and because as a major trading centre it had an extensive communications network. The latter was necessary because he was aware that he could not complete this ambitious programme alone but would need to cooperate with other astronomers.

Arriving in Nürnberg, he began to cooperate with a resident trading agent, Bernhard Walther, the two of them setting up the world’s first printing press for scientific literature. The first publication was Peuerbach’s Theoricae novae planetarum (New Planetary Theory)


followed by an ambitious catalogue of planned future publications from the astrological and astronomical literature. Unfortunately they only managed another seven publications before Regiomontanus was summoned to Rome by the Pope to work on a calendar reform in 1475, a journey from which he never returned dying under unknown circumstances, sometime in 1476. The planned observation programme never really got of the ground although Walther continued making observations, a few of which were eventually used by Copernicus in his De revolutionibus.

Regiomontanus did succeed in printing and publishing his Ephemerides in 1474, a set of planetary tables, which clearly exceeded in accuracy all previous planetary tables that had been available and went on to become a scientific bestseller.


However he didn’t succeed in printing and publishing the Epytoma in almagesti Ptolemei; this task was left to another important early publisher of scientific texts, Erhard Ratdolt (1447–1528, who completed the task in Venice twenty years after Regiomontanus’ death. Ratdolt also published Regiomontanus’ astrological calendars an important source for medical astrology.


Calendarius by Regiomontanus, printed by Erhard Ratdolt, Venice 1478, title page with printers’ names Source: Wikimedia Commons

The first printed edition of Ptolemaeus’ Geographia with maps was published in Bologna in 1477; it was followed by several other editions in the fifteenth century including the first one north of the Alps in Ulm in 1482.

The re-invention of moveable type printing by Guttenberg in about 1450 was already having a marked effect on the revival and reform of mathematical astronomy in Early Modern Europe.






Filed under Early Scientific Publishing, History of Astronomy, History of Cartography, History of Mathematics, Uncategorized

Christmas at the Renaissance Mathematicus – A guide for new readers


Being new to the Renaissance Mathematicus one might be excused if one assumed that the blogging activities were wound down over the Christmas period. However, exactly the opposite is true with the Renaissance Mathematicus going into hyper-drive posting its annual Christmas Trilogy, three blog posts in three days. Three of my favourite scientific figures have their birthday over Christmas–Isaac Newton 25thDecember, Charles Babbage 26thDecember and Johannes Kepler 27thDecember–and I write a blog post for each of them on their respective birthdays. Before somebody quibbles I am aware that the birthdays of Newton and Kepler are both old style, i.e. on the Julian Calendar, and Babbage new style, i.e. on the Gregorian Calendar but to be honest, in this case I don’t give a shit. So if you are looking for some #histSTM entertainment or possibly enlightenment over the holiday period the Renaissance Mathematicus is your number one address. In case the new trilogy is not enough for you:

The Trilogies of Christmas Past

Christmas Trilogy 2009 Post 1

Christmas Trilogy 2009 Post 2

Christmas Trilogy 2009 Post 3

Christmas Trilogy 2010 Post 1

Christmas Trilogy 2010 Post 2

Christmas Trilogy 2010 Post 3

Christmas Trilogy 2011 Post 1

Christmas Trilogy 2011 Post 2

Christmas Trilogy 2011 Post 3

Christmas Trilogy 2012 Post 1

Christmas Trilogy 2012 Post 2

Christmas Trilogy 2012 Post 3

Christmas Trilogy 2013 Post 1

Christmas Trilogy 2013 Post 2

Christmas Trilogy 2013 Post 3

Christmas Trilogy 2014 Post 1

Christmas Trilogy 2014 Post 2

Christmas Trilogy 2014 Post 3

Christmas Trilogy 2015 Post 1

Christmas Trilogy 2015 Post 2

Christmas Trilogy 2015 Post 3

Christmas Trilogy 2016 Post 1

Christmas Trilogy 2016 Post 2

Christmas Trilogy 2016 Post 3

Christmas Trilogy 2017 Post 1

Christmas Trilogy 2017 Post 2

Christmas Trilogy 2017 Post 3



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Filed under Odds and Ends, Uncategorized

It’s Solstice Time Again!

We are deep in what is commonly called the holiday season. For personal reasons I don’t celebrate Christmas and as I explained in this post starting the New Year on 1 January on the Gregorian Calendar is/was a purely arbitrary decision. I wrote there that I consider the winter solstice to be the best choice to celebrate the end and beginning of a solar cycle in the northern hemisphere.


Stonehenge Winter Solstice

Today at 22:23 UTC the sun will turn at the Tropic of Capricorn and begin its journey northwards to the Tropic of Cancer and the summer solstice.  Tropic comes from the Latin tropicus “pertaining to a turn,” from Greek tropikos “of or pertaining to a turn or change.”

I wish all of my readers a happy solstice and may the next 365 days, 5 hours, 48 minutes and 45 seconds bring you much light, joy, peace and wisdom. We can only hope that they will be better than the last 365 days, 5 hours, 48 minutes and 45 seconds (length of the mean tropical or solar year).

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Filed under Autobiographical, Odds and Ends, Uncategorized

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

Printing the Hindu-Arabic numbers

Arte dell’Abbaco, a book that many consider the first-ever printed mathematics book, was dated four hundred and forty years ago on 10 December 1478. I say many consider because the book, also known as the Treviso Arithmetic, is a commercial arithmetic textbook and some historians regard commercial arithmetic as a separate discipline and not really mathematics.

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Calculation from the Arte dell’Abbaco

The unknown author explains his book thus:

I have often been asked by certain youths in whom I have much interest, and who look forward to mercantile pursuits, to put into writing the fundamental principles of arithmetic, commonly called abbacus.

The Treviso Arithmetic is actually an abbacus book, those books on calculating with the Hindu-Arabic numerals that derive their existence from Leonardo Pisano’s Liber Abbaci. Like most abbacus books it is written in the vernacular, which in this case is the local Venetian dialect. If you don’t read 15thcentury Venetian there is an English translation by Frank J. Swetz, Capitalism and Arithmetic: The New Math of the 15thCentury Including the Full Text of the Treviso Arithmetic of 1478, Open Court, 1987.


Filed under Early Scientific Publishing, History of Mathematics, Renaissance Science, Uncategorized