Category Archives: History of Astrology

Alphabet of the stars

The brightest star in the night sky visible to the naked eye is Sirius the Dog Star. Its proper astronomical name is 𝛂 Canis Majoris. Historically for navigators in the northern hemisphere the most important star was the pole star, currently Polaris (the star designated the pole star changes over time due to the precession of the equinox), whose proper astronomical name is 𝛂 Ursae Minoris. The astronomical name of Sirius means that it is a star in the constellation in Canis Major, the greater dog, whilst Polaris’ name means that it is a star in Ursus Minor, the little bar. But what does the alpha that precedes each of these names mean and where does it come from?

A constellation consists of quite a large number of stars and this means that we need some sort of system of labelling or naming them for star catalogues, star maps or celestial atlases. The system that is used is the letters of the Greek alphabet. These are however not simply attached at random to some star or other but applied according to a system. That system was determined by apparent brightness.

Anybody who looks up into the night sky, when it is cloud free and there is no light pollution, will quickly realise that the various stars vary quite substantially in brightness. The ancient Greek astronomers were very much aware of this and divide up the stars into six categories, or as they are known magnitudes, according to their perceived or apparent brightness. Our unaided perception of the stars does not take into account their differing distances, so a very bright star that is very far away will appear less bright than not so bright star that is much nearer to the Earth. The earliest record of this six-magnitude scheme (one is the brightest, six the dimmest) is in Ptolemaeus’ Mathēmatikē Syntaxis, but it was probably older. The attribution, by some, to Hipparchus is purely speculative. Ptolemaeus also indicates intermediate values by writing greater than or less than magnitude X.

Using this basic framework inherited from Ptolemaeus, the early modern German astronomer Johann Bayer (1572–1625) labelled each of the stars in his maps of the constellations in his Uranometria (first published Augsburg, 1603) with a letter of the Greek alphabet, starting with alpha, in descending order of brightness, creating what is now known as the Bayer designation for stars. In this system the Greek letter is followed by a three-letter abbreviation of the constellation name. So, Aldebaran in the constellation Taurus is designated 𝛂 Tauri, abbreviated 𝛂 Tau. Who was Johann Bayer and what is the Uranometria?

Johann Bayer was born in Rain, a small town in Bavaria about forty kilometres north of Augsburg. He attended the Latin school in Rain and then probably a higher school in Augsburg.


Rain by Matthäus Merian 1665 Source: Wikimedia Commons

He entered the University of Ingolstadt in 1592, where, having completed the foundation course, he went on to study law, graduating with a master’s degree around sixteen hundred. Leaving the university, he settled in Augsburg, where he worked as a lawyer until his death in 1625. The University of Ingolstadt had a strong tradition of the mathematical science over the preceding century, home to notable mathematicians and astronomers such as Johannes Werner, Johannes Stabius and Andreas Stiborius at the end of the fifteenth century and father and son Peter and Phillip Apian in the middle of the sixteenth. It was certainly here that Bayer acquired his love for mathematics and astronomy. He also acquired an interest in archaeology and would later in life take part in excavation in the Via Nomentana during a visit to Rome.


Main building of the University of Ingolstadt 1571 Source: Wikimedia Comms

In 1603 Bayer’s Uranometria was published in Augsburg by Christophorus Mangus, or to give it its full title the Uranometria: omnium asterismorum continens schemata, nova methodo delineata, aereis laminis expressa. (Uranometria, containing charts of all the constellations, drawn by a new method and engraved on copper plates), that is a star atlas. The name derives from Urania the muse of astronomy, which in turn derives from the Greek uranos (oυρανός) meaning sky or heavens, it translates as “measuring the heavens” in analogy to “geometria”, measuring the earth.


Title page of Uranometria Source: Wikimedia Commons

The Uranometria contains fifty-one star-maps engraved on copper plates by Alexander Mair (c. 1562–1617). The first forty-eight carts contain the northern-hemisphere constellations listed and described by Ptolemaeus. For the northern constellations Bayer used Tycho Brahe’s star catalogue, which hadn’t been published yet but was available through various sources. He, however, added one thousand more stars.


Canis Major with Sirius very prominent on his nose Source


Ursa Mino with Polaris on the end of his tail Source:

The forty ninth chart contains twelve southern-hemisphere constellations unknown to Ptolemaeus. Bayer took the star positions and constellation names for this southern-hemisphere chart from the 1597 celestial globe created by Petrus Plancius (1552–1622) of the observations collected for him by the Dutch pilot Pieter Dirkszoon Keyser (c. 1540–1596), which was printed by Jodocus Hondius (1563–1612).


Chart of the Southern-Hemisphere ConstellationsSource

The final two charts are planispheres labelled Synopsis coeli superioris borea (Synopsis of the northern hemisphere) and Synopsis coeli inferioris austrina (Synopsis of the southern hemisphere).


Synopsis coeli superioris borea Source


Synopsis coeli inferioris austrina Source

For each star chart there is a star catalogue. In the first column the stars are listed according to their Ptolemaic number and then in their second column Bayer gives them the Bayer designation. Because the Greek alphabet only has twenty-four letters and some constellations have more than twenty-four stars, Bayer continues his list with the Latin alphabet using lower case letter except for the twenty-fifth star, which is designated with a capital A to avoid confusing a small with an alpha. The listing is not done strictly by order of brightness, listing the stars rather by the Ptolemaic magnitude classes. This means that by several constellations the star designated with an alpha is not actually the constellations brightest star.

Bayer was not the first astronomer to produce printed star maps in Europe (there are earlier printed Chinese star maps) that honour goes to the planispheres produced by Stabius, Dürer and Heinfogel in 1515.


Dürer Northern Hemisphere Star Map Source: Wikimedia Commons

His was also not the first printed star atlas that being the Sfera del mondo e De le stelle fisse (The sphere of the world and the fixed stars) of Alessandro Piccolomini (1508–1579), both published in 1540 and often together. Piccolomini was an Italian humanist, philosopher and astronomer best known for his popularisations of Greek and Latin scientific treatises, which he translated into the vernacular.


Portrait of Alessandro Piccolomini (1508-1579) engraving by Nicolas II de Larmessin Source: Wikimedia Commons

De le stelle fisse has charts of forty-seven of the Ptolemaic constellations, Equuleus (the little horse or foal) is missing. The book has a star catalogue organised by constellation, a series of woodblock plates of the constellations, tables indicating the stellar locations throughout the year and a section dealing with risings and settings of stars with reference to the constellations of the zodiac.


However, unlike the Dürer planispheres and Bayer’s Uranometria, Piccolomini’s De le stelle fisse doesn’t have constellation figures.


The book was very popular and went though, at least, fourteen editions during the sixteenth century. Piccolomini designated the stars in his catalogue with the letters of the Latin alphabet and there is the strong possibility that Bayer was inspired by Piccolomini in adopting his system of designation.

Bayer’s atlas was not free of problems. In the first edition the star catalogues were printed on the reverse of the constellation charts. This meant that it was not possible to consult the catalogue whilst viewing the chart. Also, the lettering of the catalogue showed through the page and spoiled the chart. To solve these problems the catalogue was printed separately in a smaller format under the title Explicatio charecterum aeneis Uranometrias in 1624, the year before Bayer’s death.


It was republished in 1640, 1654, 1697 and 1723. Unfortunately, the Explicatio was marred by printing errors from the start, which got progressively worse with each new edition.

The Uranometria was republished often, and editions are known from in 1624, 1639, 1641, 1648, 1655, 1661, 1666 and 1689. It set standards for star atlases and planispheres and continued to influence the work of other star cataloguers down into the eighteenth century.The next time that a popular science programme on the telly or a science fiction story starts on about Alpha Centauri, the next closest star to our solar system, then you will know that this is the Bayer designation for a magnitude one, possibly the brightest, star in the constellation Centaurus, a centaur being the half man half horse creature from Greek mythology. It’s actually slightly more complex than Bayer believed because Alpha Centauri is now known to be a triple star system and is now designated α Centauri A (officially Rigil Kentaurus), α Centauri B (officially Toliman), and α Centauri C (officially Proxima Centauri).


Uranometria Centaurus with Alpha Centauri on the near side front hoof Source


Filed under History of Astrology, History of Astronomy, Renaissance Science

A flawed survey of science and the occult in the Early Modern Period

There is no shortage of good literature on the relationships between science and magic, or science and astrology, or science and alchemy during the Early Modern Period so what is new in Mark A. Waddell’s Magic, Science, and Religion in Early Modern Europe[1]? Nothing, because it is not Waddell’s aim to bring something new to this material but rather to present an introductory textbook on the theme aimed at university students. He sets out to demonstrate to the uninitiated how the seemingly contradictory regions of science, religion and magic existed in the Early Modern Period not just parallel to but interwoven and integrated with each other.  Waddell’s conception is a worthy one and would make for a positive addition to the literature, his book is however flawed in its execution.


Image with thanks from Brian Clegg

The book actually starts well, and our author sets out his planned journey in a lengthy but clear and informative introduction. The book itself is divided into clear sections each dealing with a different aspect of the central theme. The first section deals with the Renaissance discoveries of hermeticism and the cabala and the concept of natural magic, as a force to manipulate nature, as opposed to demonic magic. Although limited by its brevity, it provides a reasonable introduction to the topics dealt with. My only criticisms concerns, the usual presentation of John Dee as a magus, whilst downplaying his role as a mathematician, although this does get mentioned in passing. However, Waddell can’t resist suggesting that Dee was the role model for Marlowe’s Faustus, whereas Faustus is almost certainly modelled on Historia von D. Johann Faustus, a German book containing legends about the real Johann Georg Faust (c. 1480–c. 1541) a German itinerant alchemist, astrologer, and magician of the German Renaissance. A note for authors, not just for Waddell, Dee in by no means the only Renaissance magus and is not the role model for all the literary ones.

Waddell’s second section deals with demonic magic, that is magic thought to draw its power from communion with the Devil and other lesser demons. As far as I can tell this was the section that most interested our author whilst writing his book. He manages to present a clear and informative picture of the period of the European witch craze and the associated witch hunts. He deals really well with the interrelationship between the belief in demonic witchcraft and the Church and formal religion. How the Church created, propagated and increasingly expanded the belief in demonic magic and witches and how this became centred on the concept of heresy. Communion with the devil, which became the central theme of the witch hunts being in and of itself heretical.

Following this excellent ´section the book starts to go downhill. The third section of the book deals with magic, medicine and the microcosm. Compared with the good presentation of the previous section I can only call this one a mishmash. We get a standard brief introduction to medieval academic medicine, which Waddell labels premodern, with Hippocrates, Galen and a nod to Islamic medical writes, but with only Ibn Sīnā mentioned by name. This is followed by a brief description of the principles of humoral medicine. Waddell correctly points out the academic or learned doctors only represent one group offering medical assistance during this period and gives a couple of lines to the barber-surgeons. It is now that the quality of Waddell’s presentation takes a steep nosedive.

Having correctly pointed out that medieval academic medicine was largely theoretical he then, unfortunately, follows the myth of “and then came Andy”! That is, we jump straight into Andreas Vesalius and his De fabrica, as I quote, “the beginnings of what we would understand as a rigorous and empirical approach to the study of anatomy.” Strange, only two weeks ago I wrote a post pointing out that Vesalius didn’t emerge out of the blue with scalpel raised high but was one step, albeit a very major one, in a two-hundred-year evolution in the study of anatomy. Of course, Waddell dishes up the usual myth about how seldom dissection was before Vesalius and corpses to dissect were rare etc, etc. Whereas, in fact, dissection had become a regular feature of medical teaching at the European universities over that, previously mentioned two-hundred-year period. Waddell closes his Vesalius hagiography with the comment that Vesalius’ De fabrica “was a crucial step in the more widespread reform of medical theory and practice that took place over the next 150 years” and although his book goes up to the middle of the eighteenth century, we don’t get any more information on those reforms. One of his final comments on Vesalius perpetuates another hoary old myth. He writes, “Vesalius made it permissible to question the legacy of antiquity and, in some cases, to overturn ideas that had persisted for many hundred years.” Contrary to the image created here, people had been challenging the legacy of antiquity and overturning ideas since antiquity, as Edward Grant put it so wonderfully, medieval Aristotelian philosophy was not Aristotle’s philosophy. The same applies to all branches of knowledge inherited form antiquity.

Having dealt with Vesalius, Waddell moves on to the philosophy of microcosm-macrocosm and astro-medicine or as it was called iatromathematics, that is the application of astrology to medicine. His basic introduction to the microcosm-macrocosm theory is quite reasonable and he then moves onto astrology. He insists on explaining that, in his opinion, astrology is not a science but a system of non-scientific rules. This is all well and good but for the people he is dealing with in the Early Modern Period astrology was a science. We then get a guide to astrology for beginners which manages right from the start to make some elementary mistakes. He writes, “You might know what your “sign” is, based on when you were born […]. These refer to the twelve (or according to some, thirteen) signs of the Western zodiac, which is the band of constellations through which the Sun appears to move over the course of a year.” The bullshit with thirteen constellations was something dreamed up by some modern astronomers, who obviously know nothing about astrology, its history or the history of their own discipline for that matter, in order to discredit astrology and astrologers. The only people they discredited were themselves. The zodiac as originally conceived by the Babylonians a couple of millennia BCE, mapped the ecliptic, the apparent annual path of the Sun around the Earth, using seventeen constellations. These were gradually pared down over the centuries until the Western zodiac became defined around the fifth century BCE as twelve equal division of the ecliptic, that is each of thirty degrees, starting at the vernal or spring equinox and preceding clockwise around the ecliptic. The most important point is that these divisions, the “signs”, are not constellations. There are, perhaps unfortunately, named after the constellations that occupied those positions on the ecliptic a couple of millennia in the past but no longer do so because of the precession of the equinoxes.

Although, Waddell gives a reasonable account of the basics of astro-medicine and also how it was integrated with humoral medicine but then fails again when describing its actual application. A couple of examples:

There were cases of surgeons refusing to operate on a specific part of the body unless the heavens were aligned with the corresponding zodiac sign, and it was not uncommon for learned physicians to cast their patient’s horoscope as part of their diagnosis.


Though the use of astrology in premodern medicine was common, it is less clear how often physicians would have turned to astrological magic in order to treat patients. Some would have regarded it with suspicion and relied instead on genitures alone to dictate their treatment, using a patient’s horoscope as a kind of diagnostic tool that provided useful information about that person’s temperament and other influences on their health. Astrological magic was a different thing altogether, requiring the practitioner to harness the unseen forces and emanations of the planets to heal their patient rather than relying solely on a standard regimen of care.

This is a book about the interrelationships between magic, religion and science during the Early Modern period, but Waddell’s lukewarm statements here, “there were cases of surgeons refusing to operate…, not uncommon for learned physicians…” fail totally to capture the extent of astro-medicine and its almost total dominance of academic medicine during the Renaissance. Beginning in the early fifteenth century European universities established the first dedicated chairs for mathematics, with the specific assignment to teach astrology to medical students.

During the main period of astrological medicine, the most commonly produced printed products were wall and pocket calendars, in fact, Gutenberg printed a wall calendar long before his more famous Bible. These calendars were astronomical, astrological, medical calendars, which contained the astronomical-astrological data that enabled physicians and barber-surgeons to know when they should or should not apply a particular treatment. These calendars were universal, and towns, cities and districts appointed official calendar makers to produce new calendars, every year. Almost no physician or barber-surgeon would consider applying a treatment at an inappropriate time, not as Waddell says, “cases of surgeons refusing to operate.” Also, no learned physicians in this time would begin an examination without casting the patient’s horoscope, to determine the cause, course and cure for the existing affliction. The use of what Waddell calls astrological magic, by which he means astrological talismans, by learned physicians was almost non-existent. This is aa completely different area of both astrology and of medicine.

Within the context of the book, it is obvious that we now turn to Paracelsus. Here Waddell repeats the myth about the name Paracelsus, “The name by which he is best known, Paracelsus, is something of a mystery, but historians believe that it was inspired by the classical Roman medical writer Celsus (c. 25 BCE–c. 50 CE). The prefix “para-“ that he added to that ancient name has multiple meanings in Latin, including “beyond,” leading some to speculate that this was a not-so-modest attempt to claim a knowledge of medicine greater than that of Celsus.” This is once again almost certainly a myth. Nowhere in his voluminous writings does Paracelsus mention Celsus and there is no evidence that he even knew of his existence. Paracelsus is almost certainly a toponym for Hohenheim meaning ‘up high’, Hohenheim being German for high home. By the way, he only initially adopted Paracelsus for his alchemical writings. The rest of his account of Paracelsus is OK but fails to really come to grips with Paracelsus’ alchemy.

To close out his section on medicine, Waddell now brings a long digression on the history of the believe in weapon salve, a substance that supposedly cured wounds when smeared on the weapon that caused them, an interesting example of the intersection between magic and medicine. However, he misses the wonderful case of a crossover into science when Kenhelm Digby suggested that weapon salve could be used to determine longitude.


The next section A New Cosmos: Copernicus, Galileo, and the Motion of the Earth, takes us into, from my point of view, a true disaster area:

In this chapter, we explore how the European understanding of the cosmos changed in the sixteenth and seventeenth centuries. It was on the single greatest intellectual disruptions in European history, and in some ways we are still feeling its effects now, more than 450 years later. The claim that our universe was fundamentally different from what people had known for thousands of years led to a serious conflict between different sources of knowledge and forms of authority, and forced premodern Europe to grapple with a crucial question: Who has the right to define the nature of reality?

This particular conflict is often framed by historians and other commentators as a battle between science and religion in which the brave and progressive pioneers of the heliocentric cosmos were attacked unjustly by a tyrannical and old-fashioned Church. This is an exaggeration, but not by much. [my emphasis]

Waddell starts with a standard account of Aristotelian philosophy and cosmology, in which he like most other people exaggerates the continuity of Aristotle’s influence. This is followed by the usual astronomers only saved the phenomena story and an introduction to Ptolemy. Again, the continuity of his model is, as usual, exaggerated. Waddell briefly introduces the Aristotelian theory of the crystalline spheres and claims that it contradicted Ptolemy’s epicycle and deferent model, which is simply not true as Ptolemy combined them in his Planetary Hypothesis. The contradiction between the two models is between Aristotle’s astronomical mathematical homocentric spheres used to explain the moments of the planets (which Waddell doesn’t mention), which were imbedded in the crystalline spheres, and the epicycle-deferent model. Waddell then hypothesises a conflict between the Aristotelian and Ptolemaic system, which simply didn’t exist for the majority, people accepting a melange of Aristotle’s cosmology and Ptolemy’s astronomy. There were however over the centuries local revivals of Aristotle’s homocentric theory.

Now Copernicus enters stage right:

Copernicus had strong ties to the Catholic Church; he was a canon, which meant he was responsible for maintaining a cathedral (the seat of a bishop or archbishop), and some historians believe he was ordained as a priest as well.

If a student writes “some historians” in a paper they normally get their head torn off by their teachers. Which historians? Name them! In fact, I think Waddell would have a difficult time naming his “some historians”, as all the historians of astronomy that I know of, who have studied the question, say quite categorically that there is no evidence that Copernicus was ever ordained. Waddell delivers up next:

Most probably it [De revolutionibus] was completed by the mid-1530s, but Copernicus was reluctant to publish it right away because his work called into question some of the most fundamental assumptions about the universe held at the time.

It is now generally accepted that Copernicus didn’t published because he couldn’t provide any proofs for his heliocentric hypothesis. Waddell:

He did decide to circulate his ideas quietly among astronomers, however, and after seeing his calculations were not rejected outright Copernicus finally had his work printed in Nuremberg shortly before his death.

Here Waddell is obviously confusing Copernicus’ Commentariolus, circulated around 1510 and  Rheticus’ Narratio prima, published in two editions in Danzig and Basel, which I wouldn’t describe as circulated quietly. Also, neither book contained  calculations. Waddell now tries to push the gospel that nobody really read the cosmological part of De revolutionibus and were only interested in the mathematics. Whilst it is true that more astronomers were interested in the mathematical model, there was a complex and intensive discussion of the cosmology throughout the second half of the sixteenth century. Waddell also wants his reader to believe that Copernicus didn’t regard his model as a real model of the cosmos, sorry this is simply false. Copernicus very definitely believed his model was a real model.

 Moving on to Tycho Brahe and the geo-heliocentric system Waddell tells us that, “[Tycho] could not embrace a cosmology that so obviously conflicted with the Bible. It is not surprising, then, that the Tychonic system was adopted in the years following Brahe’s death in 1601”

At no point does Waddell acknowledge the historical fact that also the majority of astronomers in the early decades of the seventeenth century accepted a Tychonic system because it was the one that best fit the known empirical facts. This doesn’t fit his hagiographical account of Galileo vs the Church, which is still to come.

Next up Waddell presents Kepler and his Mysterium Cosmographicum and seems to think that Kepler’s importance lies in the fact that he was ac deeply religious and pious person embraced a heliocentric cosmos. We then get an absolute humdinger of a statement:

There is more that could be said about Kepler, including the fact that he improved upon the work of Copernicus by proposing three laws of planetary motion that are still taught in schools today. For the purpose of this chapter, however, Kepler is significant as someone who embraced heliocentricity and [emphasis in the original] faith.

With this statement Waddell disqualifies himself on the subject of the seventeenth century transition from a geocentric cosmos to a heliocentric one. Kepler didn’t propose his three laws he derived them empirically from Tycho’s observational data and they represent the single most important step in that transition.

We now have another Waddell and then came moment, this time with Galileo. We get a gabled version of Galileo’s vita with many minor inaccuracies, which I won’t deal with here because there is much worse to come. After a standard story of the introduction of the telescope and of Galileo’s improved model we get the following:

[Galileo] presented his device to the Doge (the highest official in Venice) and secured a truly impressive salary for life from the Venetian state. Mere weeks later he received word from the court of the Medici in Galileo’s home in Tuscany, that they wanted a telescope of their own. The Venetian leaders, however had ordered Galileo to keep his improved telescope a secret, to be manufactured only for Venetian use, and Galileo obliged, at least temporarily.

When they bought Galileo’s telescope they thought, erroneously, that they were getting exclusive use of a spectacular new instrument. However, it soon became very clear that telescopes were not particularly difficult to make and were freely available in almost all major European towns. They were more than slightly pissed off at the good Galileo but did not renege on their deal. The Medici court did not request a telescope of their own, but Galileo in his campaign to gain favour by the Medici, presented them with one and actually travelled to Florence to demonstrate it for them. We now move on to the telescopic discoveries in which Waddell exaggerates the discovery of the Jupiter moons. We skip over the Sidereus Nuncius and Galileo’s appointment as court philosophicus and mathematicus in Florence, which Waddell retells fairly accurately. Waddell now delivers up what he sees as the great coup:

The problem was that the moons of Jupiter, while important, did not prove the existence of a heliocentric cosmos. Galileo kept searching until he found something that did: the phases of Venus.

The discovery of the phases of Venus do indeed sound the death nell for a pure geocentric system à la Ptolemy but not for a Capellan geo-heliocentric system, popular throughout the Middle Ages, where Mercury and Venus orbit the Sun, which orbits the Earth, or a full Tychonic system with all five planets orbiting the Sun, which together with the Moon orbits the Earth. Neither here nor anywhere else does Waddell handle the Tychonic system, which on scientific, empirical grounds became the most favoured system in the early decades of the seventeenth century.

We then get Castelli getting into deep water with the Grand Duchess Christina and, according to Waddell, Galileo’s Letter to the Grand Duchess Christina. He never mentions the Letter to Castelli, of which the Letter to the Grand Duchess Christina was a later extended and improved version, although it was the Letter to Castelli, which got passed on to the Inquisition and caused Galileo’s problems in 1615. Waddell tells us:

In 1616 the Inquisition declared that heliocentrism was a formal heresy.

In fact, the eleven Qualifiers appointed by the Pope to investigate the status of the heliocentric theory delivered the following verdict:

( i ) The sun is the centre of the universe (“mundi”) and absolutely immobile in local motion.

( ii ) The earth is not the centre of the universe (“mundi”); it is not immobile but turns on itself with a diurnal movement.

All unanimously censure the first proposition as “foolish, absurd in philosophy [i.e. scientifically untenable] and formally heretical on the grounds of expressly contradicting the statements of Holy Scripture in many places according to the proper meaning of the words, the common exposition and the understanding of the Holy Fathers and learned theologians”; the second proposition they unanimously censured as likewise “absurd in philosophy” and theologically “at least erroneous in faith”.

However, the Qualifiers verdict was only advisory and the Pope alone can official name something a heresy and no Pope ever did.

Waddell gives a fairly standard account of Galileo’s meeting with Cardinal Roberto Bellarmino in 1616 and moves fairly rapidly to the Dialogo and Galileo’s trial by the Inquisition in 1633. However, on the judgement of that trial he delivers up this gem:

Ultimately, Galileo was found “vehemently suspect of heresy,” which marked his crime as far more serious than typical, run-of-the-mill heresy.

One really should take time to savour this inanity. The first time I read it, I went back and read it again, because I didn’t think anybody could write anything that stupid. and that I must have somehow misread it. But no, the sentence on page 131 of the book reads exactly as I have reproduced it here. Maybe I’m ignorant, but I never knew that to be suspected of a crime was actually “far more serious” than actually being found guilty of the same crime. One of my acquaintances, an excellent medieval historian and an expert for medieval astronomy asked, “WTF is run-of-the-mill heresy?” I’m afraid I can’t answer her excellent question, as I am as perplexed by the expression, as she obviously is.

Enough of the sarcasm, the complete sentence is, of course, total bollocks from beginning to end. Being found guilty of suspicion of heresy, vehement or not, is a much milder judgement than being found guilty of heresy. If Galileo had been found guilty of heresy, there is a very good chance he would have been sentenced to death. The expression “run-of-the-mill heresy” is quite simple total balderdash and should never, ever appear in any academic work.

Waddell now draws his conclusions for this section, and they are totally skewed because he has simple ignored, or better said deliberately supressed a large and significant part of the story. In the final part of this section, “Science versus Religion?”, he argues that the Church was defending its right to traditional truth against Galileo’s scientific truth. He writes:

This was not a fight between winners and losers, or between “right” and “wrong.” Instead, this is a story about power, tradition, and authority, about who gets to decide what is true and on what grounds.


Organised religion, exemplified here by the Catholic Church, had an interest in preserving the status quo [emphasis in original] for many reasons, some of which were undeniably self-serving.


The ideas of Aristotle and Ptolemy were still taught in virtually every European university well into the seventeenth century, making the Church’s allegiance to these ideas understandable. At the same time, the Church also recognised another source of authority, the Christian scriptures, which stated clearly that the Earth did not move. On both philosophical and theological grounds, then, the Church’s position on the immobility of the Earth was reasonable by the standards of the time.  

The above quotes have more relationship to a fairy tale than to the actual historical situation. Due to the astronomical discoveries made since about 1570, by1630 the Catholic Church had abandoned most of the Aristotelian cosmology and never adopted  Aristotelian astronomy. They fully accepted that the phases of Venus, almost certainly observed by the Jesuit astronomers of the Collegio Romano before Galileo did, refuted the Ptolemaic geocentric astronomy. Instead by 1620 the Church had officially adopted the Tychonic geo-heliocentric astronomy, not, as Waddell claims, on religious grounds but because it best fit the known empirical facts. Despite efforts since 1543, when Copernicus published De revolutionibus, nobody, not even Galileo, who had tried really hard, had succeeded in finding any empirical evidence to show that the Earth moves. Waddell’s attempt to portrait the Church as at best non-scientific or even anti.scientific completely ignores the fact that Jesuit and Jesuit educated mathematicians and astronomer were amongst the best throughout the seventeenth century. They made significant contributions to the development of modern astronomy before the invention of the telescope, during Galileo’s active period, in fact it was the Jesuits who provided the necessary scientific confirmation of Galileo’s telescopic discoveries, and all the way up to Newton’s Principia. Their record can hardly be described as anti-scientific.

The Church’s real position is best summed up by Roberto Bellarmino in his 1615 letter to Foscarini, which is also addressed to Galileo:

Third, I say that if there were a true demonstration that the sun is at the centre of the world and the earth in the third heaven, and that the sun does not circle the earth but the earth circles the sun, then one would have to proceed with great care in explaining the Scriptures that appear contrary; and say rather that we do not understand them than that what is demonstrated is false. But I will not believe that there is such a demonstration, until it is shown me. 

Put simple prove your theory and we the Church will then reinterpret the Bible as necessary, which they in fact did in the eighteenth century following Bradley’s first proof that the Earth does actually move.

Waddell then goes off on a long presentist defence of Galileo’s wish to separate natural philosophy and theology, which is all well and good but has very little relevance for the actual historical situation. But as already stated, Waddell is wrong to claim that the phases of Venus prove heliocentrism. Worse than this Galileo’s Dialogo is a con. In the 1630s the two chief world systems were not Ptolemy and Copernicus, the first refuted and the second with its epicycle-deferent models, which Galileo continues to propagate, abandoned, but the Tychonic system and Kepler’s ecliptical astronomy, which Waddell like Galileo simply chose to ignore.

One last comment before I move on. Somewhere Waddell claims that Galileo was the first to claim that the Copernicus’ heliocentric model represented reality rather than simply saving the phenomena. This is historically not correct, Copernicus, Tycho and Kepler all believed that their models represented reality and by 1615, when Galileo first came into confrontation with the Church it had become the norm under astronomers that they were trying to find a real model and not saving the phenomena.

Waddell’s account of the early period of the emergence of modern astronomy sails majestically past the current historical stand of our knowledge of this phase of astronomical history and could have been written some time in the first half of the twentieth century but should not be in a textbook for students in the year 2021.

With the next section we return to some semblance of serious state-of-the-art history. Waddell presents and contrasts the mechanical philosophies of Pierre Gassendi and René Descartes and their differing strategies to include their God within those philosophies. All pretty standard stuff reasonably well presented. The section closes with a brief, maybe too brief, discourse on Joseph Glanvill’s attempts to keep awareness of the supernatural alive against the rationalism of the emerging modern science.

The penultimate section deals with the transition from the Aristotelian concept of an experience-based explanation of the world to one based on experiments and the problems involved in conforming the truth of experimental results. In my opinion he, like most people, gives far too much attention/credit to Francis Bacon but that is mainstream opinion so I can’t really fault him for doing so. I can, however, fault him for presenting Bacon’s approach as something new and original, whereas Bacon was merely collating what had been widespread scientific practice for about two centuries before he wrote his main treatises. Specialist historians have been making this public for quite some time now and textbooks, like the one Waddell has written, should reflect these advances in our historical awareness.

Waddell moves on to alchemy as another source of experimentation that influenced the move to an experiment-based science in the seventeenth century. To be honest I found his brief account of alchemy as somewhat garbled and meandering, basically in need of a good editor. He makes one error, which I found illuminating, he writes:

Aristotle in particular had taught that all metals were composed of two principles: Mercury and Sulphur

Aristotle thought that metals were composed of two exhalations, one is dry and smoky, the other wet and steamy. These first became widely labeled as Mercury and Sulphur in the ninth century writings of the Arabic alchemist Jābir ibn-Hayyān, who took it from the mid-ninth century work, the Book of the Secrets of Creation by Balīnūs. I find this illuminating because I don’t know things like this off by heart, I just knew that Mercury-Sulphur was not from Aristotle, and so have to look them up. To do so I turned to Principe’s The Secrets of Alchemy. Now, according to Waddell’s bibliographical essays at the end of the book, Principe is his main source for the history of alchemy, which means he read the same paragraph as I did and decided to shorten it thus producing a fake historical statement. When writing history facts and details matter!

Having introduced alchemy we now, of course, get Isaac Newton. Waddell points out that Newton is hailed as the epitome of the modern scientist, whereas in fact he was a passionate exponent of alchemy and devoted vast amounts of time and effort to his heterodox religious studies. The only thing that I have to criticise here is that Waddell allocates Newton and his Principia to the mechanical philosophy, whereas his strongest critics pointed out that gravity is an occult force and is anything but conform with the mechanical philosophy. Waddell makes no mention of this here but strangely, as we will see does so indirectly later.

The final section of the book is a discussion of the enlightenment, which I found quite good.  Waddell points out that many assessments of the enlightenment and what supposedly took place are contradicted by the historical facts of what actually happened in the eighteenth century.

Waddell draws to a close with a five-page conclusion that rather strangely suddenly introduces new material that is not in the main text of the book, such as Leibniz’s criticism that Newton’s theory of gravity is not mechanical. It is in fact more a collection of after thoughts than a conclusion.

The book ends with a brief but quite extensive bibliographical essay for each section of the book, and it was here that I think I found the reason for the very poor quality of the A New Cosmos section, he writes at the very beginning:

Two important studies on premodern astronomy and the changes it experienced in early modern Europe are Arthur Koestler’s The Sleepwalkers: A History of Man’s Changing Vision of the Universe (Penguin Books, 1990) and Thomas Kuhn’s The Copernican Revolution: Planetary Astronomy in the Development of Western Thought (Harvard University Press, 1992)

The Sleepwalkers was originally published in 1959 and The Copernican Revolution in 1957, both are horribly outdated and historically wildly inaccurate and should never be recommended to students in this day and age.

All together Waddell’s tome  has the makings of a good and potentially useful textbook for students on an important set of themes but it is in my opinion it is spoilt by some sloppy errors and a truly bad section on the history of astronomy in the early modern period and the conflict between Galileo and the Catholic Church.

[1] Mark A. Waddell, Magic, Science, and Religion in Early Modern Europe, Cambridge University Press, Cambridge & London, 2021


Filed under Book Reviews, History of Alchemy, History of Astrology, History of Astronomy, History of medicine, History of science, Renaissance Science

Christmas Trilogy 2020 Part 3: The peregrinations of Johannes K

We know that human beings have been traversing vast distances on the surface of the globe since Homo sapiens first emerged from Africa. However, in medieval Europe it would not have been uncommon for somebody born into a poor family never in their life to have journeyed more than perhaps thirty kilometres from their place of birth. Maybe a journey into the next larger settlement on market day or perhaps once a year to an even larger town for a fair on a public holiday. This might well have been Johannes Kepler’s fate, born as he was into an impoverished family, had it not been for his extraordinary intellectual abilities. Although he never left the Southern German speaking area of Europe (today, Southern Germany, Austria and the Czech Republic), he managed to clock up a large number of journey kilometres over the fifty-eight years of his life. In those days there was, of course, no public transport and in general we don’t know how he travelled. We can assume that for some of his longer journeys that he joined trader caravans. Traders often travelled in large wagon trains with hired guards to protect them from thieves and marauding bands and travellers could, for a fee, join them for protection. We do know that as an adult Kepler travelled on horseback but was often forced to go by foot due to the pain caused by his piles.[1]

It is estimated that in the Middle ages someone travelling on foot with luggage would probably only manage 15 km per day going up to perhaps 22 km with minimal luggage. A horse rider without a spare mount maybe as much as 40 km per day, with a second horse up to 60 km per day. I leave it to the reader to work out how long each of Kepler’s journeys might have taken him.


Johannes Kepler Source: Wikimedia Commons

Johannes’ first journey from home took place, when he attended the convent-school in Adelberg at the age of thirteen, which lies about 70 km due west of his birthplace, Weil der Stadt, and about 90 km, also due west of Ellmendigen, where his family were living at the time.


Adelberg Convent Source: Wikimedia Commons

His next journey took place a couple of years later when he transferred to the Cistercian monastery in Maulbronn about 50 km north of Weil der Stadt and 30 west of Ellmendingen.


Maulbronn Monastery Source: Wikimedia Commons

Finished with the lower schools in 1589, he undertook the journey to the University of Tübingen, where he was enrolled in the Tübinger Stift, about 40 km south of Weil der Stadt.


The Evangelical Tübinger Stift on the banks of the Neckar Source: WIkimedia Commons

Johannes’ first really long journey took place in 1594, when on 11 April he set out for Graz the capital city of Styria in Austria to take up the posts of mathematics teacher in the Lutheran academy, as well as district mathematicus, a distance of about 650 km. The young scholar would have been on the road for quite a few days.


Graz, Mur und Schloßberg, Georg Matthäus Vischer (1670) Source: Wikimedia Commons

Although he only spent a few years in Graz, Kepler manged at first to stabilise his life even marrying, Barbara Müller, and starting a family. However, the religious conflicts of the period intervened and Kepler, a Lutheran Protestant living in a heavily Catholic area became a victim of those conflicts. First, the Protestants of the area were forced to convert or leave, which led to the closing of the school where Kepler was teaching and his losing his job. Because of his success as astrologer, part of his duties as district mathematicus, Kepler was granted an exception to the anti-Protestant order, but it was obvious that he would have to leave. He appealed to Tübingen to give him employment, but his request fell on deaf ears. The most promising alternative seemed to be to go and work for Tycho Brahe, the Imperial Mathematicus, currently ensconced in the imperial capital, Prague, a mere 450 km distant.


Prague in the Nuremberg Chronicle 1493 Source: Wikimedia Commons

At first Kepler didn’t know how he would manage the journey to Prague to negotiate about possible employment with Tycho. However, an aristocratic friend was undertaking the journey and took Johannes along as a favour. After, several weeks of fraught and at times downright nasty negotiations with the imperious Dane, Kepler was finally offered employment and with this promise in his pocket he returned to Graz to settle his affairs, pack up his household and move his family to Prague. He made the journey between Graz and Prague three times in less than a year.

Not long after his arrival in Prague, with his family, Tycho died and Kepler was appointed his successor, as Imperial Mathematicus, the start of a ten year relatively stable period in his life. That is, if you can call being an imperial servant at the court of Rudolf II, stable. Being on call 24/7 to answer the emperor’s astrological queries, battling permanently with the imperial treasury to get your promised salary paid, fighting with Tycho’s heirs over the rights to his data. Kepler’s life in Prague was not exactly stress free.

1608 saw Johannes back on the road. First to Heidelberg to see his first major and possibly most important contribution to modern astronomy, his Astronomia Nova (1609), through the press and then onto the book fair in Frankfurt to sell the finished work, that had cost him several years of his life. Finally, back home to Prague from Frankfurt. A total round-trip of 1100 km, plus he almost certainly took a detour to visit his mother somewhere along his route.

Back in Prague things began to look rather dodgy again for Kepler and his family, as Rudolf became more and more unstable and Johannes began to look for a new appointment and a new place to live. His appeals to Tübingen for a professorship, not an unreasonable request, as he was by now widely acknowledged as Europe’s leading theoretical astronomer, once again fell on deaf ears. His search for new employment eventually led him to Linz the capital city of Upper Austria and the post of district mathematicus. 1612, found Johannes and his children once again on the move, his wife, Barbara, had died shortly before, this time transferring their household over the comparatively short distance of 250 km.


Linz anno 1594 Source: Wikimedia Commons

Settled in Linz, Kepler married his second wife, Susanna Reuttinger, after having weighed up the odds on various potential marriage candidates and the beginning of a comparative settled fourteen-year period in his life. That is, if you can call becoming embroiled in the Thirty Years War and having your mother arrested and charged with witchcraft settled. His mother’s witchcraft trial saw Johannes undertaking the journey from Linz to Tübingen and home again, to organise and conduct her defence, from October to December in 1617 and again from September 1620 to November 1621, a round trip each time of about 1,000 km, not to forget the detours to Leonberg, his mother’s home, 50 km from Tübingen, from where he took his mother, a feeble woman of 70, back to Linz on the first journey.

In 1624, Johannes set out once again, this time to Vienna, now the imperial capital, to try and obtain the money necessary to print the Rudolphine Tables from Ferdinand II the ruling emperor, just 200 km in one direction. Ferdinand refused to give Kepler the money he required, although the production of the Rudolphine Tables had been an imperial assignment. Instead, he ordered the imperial treasury to issues Kepler promissory notes on debts owed to the emperor by the imperial cities of Kempten, Augsburg and Nürnberg, instructing him to go and collect on the debts himself. Kepler returned to Linz more than somewhat disgruntled and it is not an exaggeration that his life went downhill from here.

Kepler set out from Linz to Augsburg, approximately 300 km, but the Augsburg city council wasn’t playing ball and he left empty handed for Kempten, a relatively short 100 km. In Kempten the authorities agreed to purchase and pay for the paper that he needed to print the Rudolphine Tables. From Kempten he travelled on to Nürnberg, another 250 km, which he left again empty handed, returning the 300 km to Linz, completing a nearly 1,000 km frustrating round trip that took four months.

In 1626, the War forced him once again to pack up his home and to leave Linz forever with his family. He first travelled to Regensburg where he found accommodation for his family before travelling on to Ulm where he had had the paper from Kempten delivered so that he could begin printing, a combined journey of about 500 km. When the printing was completed in 1627, having paid the majority of the printing costs out of his own pocket, Kepler took the entire print run to the bookfair in Frankfurt and sold it in balk to a book dealer to recoup his money, another journey of 300 km. He first travelled back to Ulm and then home to his family in Regensburg, adding another 550 km to his life’s total. Regensburg was visited by the emperor and Wallenstein, commander in chief of the Catholic forces, and Kepler presented the Tables to the Emperor, who received them with much praise for the author.

In 1628, he entered the service of Wallenstein, as his astrologer, moving from Regensburg to Wallenstein’s estates in the Dutchy of Sagan, yet another 500 km. In 1630, the emperor called a Reichstag in Regensburg and on 8 October Kepler set out on the last journey of his life to attend. Why he chose to attend is not very clear, but he did. He journeyed from Zagan to Leipzig and from there to Nürnberg before going on to Regensburg a total of 700 km. He fell ill on his arrival in Regensburg and died 15 November 1630.


Regensburg Nuremberg Chronicle 1493 Source: Wikimedia Commons

The mathematical abilities of the young boy born to an impoverish family in Weil der Stadt fifty-eight-years earlier had taken him on a long intellectual journey but also as we have seen on a long physical one, down many a road.


[1] I almost certainly haven’t included all of the journeys that Kepler made in his lifetime, but I think I’ve got most of the important ones. The distances are rounded up or down and are based on the modern distances by road connecting the places travelled to and from. The roads might have run differently in Kepler’s day.

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Filed under History of Astrology, History of Astronomy, Renaissance Science

The solar year ends and starts with a great conjunction

Today is the winter solstice, which as I have explained on various occasions, in the past, is for me the natural New Year’s Eve/New Year’s Day rather than the arbitrary 31 December/1 January.


Obligatory Stonehenge winter solstice image

Today in also the occurrence of a so-called great conjunction in astronomy/astrology, which is when, viewed from the Earth, Jupiter and Saturn appear closest together in the night sky. Great conjunctions occur every twenty years but this one is one in which the two planets appear particularly close to each other.


Great conjunctions played a decisive role in the life of Johannes Kepler. As a youth Kepler received a state grant to study at the University of Tübingen. The course was a general-studies one to prepare the students to become Lutheran schoolteachers or village pastors in the newly converted Protestant state. Kepler, who was deeply religious, hoped to get an appointment as a pastor but when a vacancy came up for Protestant mathematics teacher in Graz, Michael Mästlin recommended Kepler and so his dream of becoming a pastor collapsed. He could have turned down the appointment but then he would have had to pay back his grant, which he was in no position to do so.

In 1594, Kepler thus began to teach the Protestant youths of Graz mathematics. He accepted his fate reluctantly, as he still yearned for the chance to serve his God as a pastor. Always interested in astronomy and converted to heliocentricity by Michael Mästlin, whilst still a student, he had long pondered the question as to why there were exactly six planets. Kepler’s God didn’t do anything by chance, so there had to be a rational reason for this. According to his own account, one day in class whilst explaining the cyclical nature of the great conjunctions in astronomy/astrology, which is when, viewed from the Earth, Jupiter and Saturn appear closest together in the night sky, he had a revelation.  Looking at the diagram that he had drawn on the board he asked himself, “What if his God’s cosmos was a geometrical construction and this was the determining factor in the number of planets?”


Kepler’s geometrical diagram of the cyclical nature of the great conjunctions in his Mysterium Cosmographicum Source: Linda Hall Library

Kepler determined from that point on in his life to serve his God as an astronomer by revealing the geometric structure of God’s cosmos. He first experimented with various regular polygons, inspired by the great conjunction diagram, but couldn’t find anything that fit, so he moved into three dimensions and polyhedra. Here he struck gold and decided that there were exactly six planets because their orbital spheres were separated by the five regular Platonic solids.


Source: Wikimedia Commons


He published this theory in his first academic book, Mysterium Cosmographicum (lit. The Cosmographic Mystery, alternately translated as Cosmic MysteryThe Secret of the World) 1597. The book also contains his account of the revelation inspired by the great conjunction diagram. This was the start of his whole life’s work as a theoretical astronomer, which basically consisted of trying to fine tune this model.

In the early seventeenth century, Kepler was still deeply religious, a brilliant mathematician and theoretical astronomer, and a practicing astrologer. As an astrologer Kepler rejected the standard Ptolemaic sun sign i.e., Aquarius, Virgo, Gemini, etc., astrology. Normal horoscope astrology. Sun signs, or as most people call them star signs, are 30° segments of the circular ecliptic, the apparent path of the Sun around the Earth and not the asterisms or stellar constellations with the same names. Kepler developed his own astrology based entirely on planetary aspects, that is the angles subtended by the planets with each other on the ecliptic. (see the Wikipedia article Astrological aspect). Of course, in Kepler’s own astrology conjunctions play a major role.

Turning to the so-called Star of Bethlehem, the men from the east (no number is mentioned), who according to Matthew 2:2, followed the star were, in the original Greek, Magoi (Latin/English Magi) and this means they were astrologers and not the sanitised wise men or kings of the modern story telling. Kepler would have been very well aware of this. This led Kepler to speculate that what the Magoi followed was an important astrological occurrence and not a star in the normal meaning of the word. One should note that in antiquity all visible celestial objects were stars. Stars simple Asteres, planets (asteres) planētai wandering (stars) and a comet (aster) komētēs, literally long-haired (star), so interpreting the Star of Bethlehem as an astrological occurrence was not a great sketch.

His revelation in 1603 was that this astrological occurrence was a great conjunction and in fact a very special one, a so-called fiery trigon, one that links the three fire signs, Aries, Leo, Sagittarius.


Calculating backwards, Kepler the astronomer, determined that one such had occurred in 7 BCE and this was the star that the Magoi followed.

Whether Kepler’s theory was historically correct or an accepted view in antiquity is completely impossible to determine, is the Bible story of Jesus’ birth even true? In Kepler’s own time, nobody accepted his deviant astrology, so I very much doubt that many people accepted his Star of Bethlehem story, which he published in his De Stella Nova in Pede Serpentarii (On the New Star in the Foot of the Serpent Handler) in 1606.

I’m sure that a great conjunction on the date of the winter solstice has a very deep astrological significance but whether astrologers will look back and say, “Ah, that triggered this or that historical occurrence” only the future will tell.

I thank all of those who have read, digested and even commented upon my outpourings over the last twelve months and fully intend to do my best to keep you entertained over the next twelve. No matter which days you choose to celebrate during the next couple of weeks, in which way whatsoever and for what reasons, I wish all of my readers all the best and brace yourselves for another Renaissance Mathematicus Christmas Trilogy starting on 25 December.



Filed under History of Astrology, History of Astronomy, Renaissance Science

Illuminating medieval science


There is a widespread popular vision of the Middle ages, as some sort of black hole of filth, disease, ignorance, brutality, witchcraft and blind devotion to religion. This fairly-tale version of history is actively propagated by authors of popular medieval novels, the film industry and television, it sells well. Within this fantasy the term medieval science is simply an oxymoron, a contradiction in itself, how could there possible be science in a culture of illiterate, dung smeared peasants, fanatical prelates waiting for the apocalypse and haggard, devil worshipping crones muttering curses to their black cats?

Whilst the picture I have just drawn is a deliberate caricature this negative view of the Middle Ages and medieval science is unfortunately not confined to the entertainment industry. We have the following quote from Israeli historian Yuval Harari from his bestselling Sapiens: A Brief History of Humankind (2014), which I demolished in an earlier post.

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.

On medieval science we have the even more ignorant point of view from American polymath and TV star Carl Sagan from his mega selling television series Cosmos, who to quote the Cambridge History of Medieval Science:

In his 1980 book by the same name, a timeline of astronomy from Greek antiquity to the present left between the fifth and the late fifteenth centuries a familiar thousand-year blank labelled as a “poignant lost opportunity for mankind.” 

Of course, the very existence of the Cambridge History of Medieval Science puts a lie to Sagan’s poignant lost opportunity, as do a whole library full of monographs and articles by such eminent historians of science as Edward Grant, John Murdoch, Michael Shank, David Lindberg, Alistair Crombie and many others.

However, these historians write mainly for academics and not for the general public, what is needed is books on medieval science written specifically for the educated layman; there are already a few such books on the market, and they have now been joined by Seb Falk’s truly excellent The Light Ages: The Surprising Story of Medieval Science.[1]  


How does one go about writing a semi-popular history of medieval science? Falk does so by telling the life story of John of Westwyk an obscure fourteenth century Benedictine monk from Hertfordshire, who was an astronomer and instrument maker. However, John of Westwyk really is obscure and we have very few details of his life, so how does Falk tell his life story. The clue, and this is Falk’s masterstroke, is context. We get an elaborate, detailed account of the context and circumstances of John’s life and thereby a very broad introduction to all aspects of fourteenth century European life and its science.

We follow John from the agricultural village of Westwyk to the Abbey of St Albans, where he spent the early part of his life as a monk. We accompany some of his fellow monks to study at the University of Oxford, whether John studied with them is not known.


Gloucester College was the Benedictine College at Oxford where the monks of St Albans studied

We trudge all the way up to Tynemouth on the wild North Sea coast of Northumbria, the site of daughter cell of the great St Alban’s Abbey, main seat of Benedictines in England. We follow John when he takes up the cross and goes on a crusade. Throughout all of his wanderings we meet up with the science of the period, John himself was an astronomer and instrument maker.

Falk is a great narrator and his descriptive passages, whilst historically accurate and correct,[2] read like a well written novel pulling the reader along through the world of the fourteenth century. However, Falk is also a teacher and when he introduces a new scientific instrument or set of astronomical tables, he doesn’t just simply describe them, he teachers the reader in detail how to construct, read, use them. His great skill is just at the point when you think your brain is going to bail out, through mathematical overload, he changes back to a wonderfully lyrical description of a landscape or a building. The balance between the two aspects of the book is as near perfect as possible. It entertains, informs and educates in equal measures on a very high level.

Along the way we learn about medieval astronomy, astrology, mathematics, medicine, cartography, time keeping, instrument making and more. The book is particularly rich on the time keeping and the instruments, as the Abbott of St Albans during John’s time was Richard of Wallingford one of England’s great medieval scientists, who was responsible for the design and construction of one of the greatest medieval church clocks and with his Albion (the all in one) one of the most sophisticated astronomical instruments of all time. Falk’ introduction to and description of both in first class.


The book is elegantly present with an attractive typeface and is well illustrated with grey in grey prints and a selection of colour ones. There are extensive, informative endnotes and a good index. If somebody reads this book as an introduction to medieval science there is a strong chance that their next question will be, what do I read next. Falk gives a detailed answer to this question. There is an extensive section at the end of the book entitled Further Reading, which gives a section by section detailed annotated reading list for each aspect of the book.

Seb Falk has written a brilliant introduction to the history of medieval science. This book is an instant classic and future generations of schoolkids, students and interested laypeople when talking about medieval science will simply refer to the Falk as a standard introduction to the topic. If you are interested in the history of medieval science or the history of science in general, acquire a copy of Seb Falk’s masterpiece, I guarantee you won’t regret it.

[1] American edition: Seb Falk, The Light Ages: The Surprising Story of Medieval Science, W. W. Norton & Co., New York % London, 2020

British Edition: Seb Falk, The Light Ages: A Medieval Journey of Discover, Allen Lane, London, 2020

[2] Disclosure: I had the pleasure and privilege of reading the whole first draft of the book in manuscript to check it for errors, that is historical errors not grammatical or orthographical ones, although I did point those out when I stumbled over them.


Filed under History of Astrology, History of Astronomy, History of Cartography, History of Mathematics, History of Navigation, History of science, Mediaeval Science, Myths of Science

Video-menu launched on the Marius-Portal

Regular readers of this blog will know that I am part of a group of historians of astronomy, who have, since 2014, been involved in restoring the reputation of the Franconian astronomer Simon Marius (1573-1624) .


Simon Marius Source: Wikimedia Commons

As part of our efforts we have created a Simon Marius web portal. This portal has recently acquired a new section.

There is now a short film, which in two minutes describes the career and the most important research results of the margravial court astronomer Simon Marius. The animated film visualises his discoveries with historical images and can be viewed on the Marius-Portal. This contribution was sponsored by the Nuremberger film production company 7streich.

The completion of the English language translation of the animated clip has been taken as an opportunity to install a new menu “Video – Films and Podcasts.” As well as the animated clip, there are 19 lectures, TV and Internet reports easily accessible. The majority of the films are in German but there are two English lectures, one from myself and one from Renaissance Mathematicus friend and occasional guest blogger, Professor Chris Graney. The Simon Marius Society maintains the Marius-Portal, which with 34 menu languages lists all documents by or about Simon Marius and–where possible–makes digitally available.

Marius discovered the four largest moons of Jupiter, independently of Galileo Galilei, also in January 1610. They prove that not all celestial bodies orbit the Earth. Marius propagated an interesting geo-heliocentric model, a historically important steppingstone on the route from a geo- to a heliocentric model of the cosmos.

Illustrations from the Marius short film and Marius-Portal


Montage of the first orbital presentation of the Jupiter system by Simon Marius from 1611 with a view of Ansbach from Matthäus Merian from 1648 (Town Archive Ansbach). Marius-Portal/7streich


Montage of historical illustrations of Galileo Galilei and Simon Marius Marius-Portal/7streich

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Filed under History of Astrology, History of Astronomy, Simon Marius

Astrology in the age of Newton

My Annus Mythologicus blog post was recently retweeted on Twitter in response to an inane tweet from Richard Dawkins and somebody questioned the reference in it that Newton was inspired to take up mathematics upon reading a book on astrology. This was not a nasty attack but a genuine statement on interest from somebody who had difficulty believing a man, who has been called the greatest mathematician ever, should have had anything to do with an astrology book. There is a sort of naïve belief that it is impossible for the people in the age of Newton, which is touted as the birth of the age of modern science and rationalism, could have had anything to do with the so-called occult sciences. This belief led many people, who should have known better, to try and sweep Newton’s very active engagement with alchemy under the carpet. During Newton’s lifetime astrology lost its status as a university discipline but was still all pervasive and permeated all aspects and levels of society. In what follows I will sketch some of the details of the role of astrology in the age of Newton.


Newton – 1677 Source: Wikimedia Commons

The Renaissance/Early Modern Period could with justification be called the golden age of astrology in Europe. This period was actually coming to an end during Newton’s lifetime, but astrology had by no means totally disappeared. That golden age began roughly with the beginning of the fifteenth century. During the first half of the century the humanist universities of Northern Italy and Poland created the first regular, dedicated chairs for mathematics and astronomy, which were in fact chairs for astrology, created to teach astrology to medical students. Teaching astrology to medical students was one of the principle obligations of the professors for mathematics at these universities and continued to be so well down into the seventeenth century. This trend continued with the creation of the first such chair in Germany, at the University of Ingolstadt, in the early 1470s. Astrological medicine, or iatromathematics to it is formal name was just one branch of astrology that flourished in this period.

Medical astrology was along with astrological meteorology considered to be a form of natural astrology and even those, who rejected natal astrology, for example, accepted the validity of natural astrology. Opposed to natural astrology was judicial astrology collective term for a group of other forms of astrology. Natal astrology, or genethliacal astrology, is the classic birth horoscope astrology that everybody thinks of, when they first hear the term astrology.  Other forms of judicial horoscope astrology are mundane astrology concerns the fate of nations etc., horary astrology answers question by casting a horoscope when the question is presented, and electional astrology, which is used to determine the most appropriate or auspicious time to carry out a planned action.

All these forms of astrology were widespread and considered valid by the vast majority during the fifteenth and sixteenth centuries. Astrology was firmly established in the fabric of European society and almost all of the active astronomers were also active astrologers right down to those astronomers, who were responsible for the so-called astronomical revolution. Georg Peuerbach, Regiomontanus, Tycho Brahe, Johannes Kepler and Galileo Galilei were all practicing astrologers and in fact owed much of the patronage that they received to their role as astrologer rather to that of astronomer, although the terms were interchangeable in this period. The terms Astrologus, Astronomus and Mathematicus were all synonym and all had astrologer in the modern sense as their principle meaning. Following the invention of moving type printing in about 1450, by far and away, the largest number of printed articles were astrological ephemera, almanacs, prognostica, and writing and single sheet wall calendars. A trend that continued all the way down to the eighteenth century.

During the fifteenth and sixteenth century efforts to give astrology a solid empirical footing were central to the activities of the astronomer-astrologers. Starting with Regiomontanus several astronomers believed that the inaccuracies in astrological forecasting were due to inaccuracies in the astronomy on which it was based. The reform of astronomy, for exactly this reason, was a principle motivation for the research programmes of Regiomontanus, Tycho Brahe and Wilhelm IV, Landgrave of Hessen-Kassel. Another approach was through astro-meteorology, with astronomer keeping weather diaries in which they noted the horoscope for the day and the actual weather on that day. They were looking for correlations, which they failed to find, but the practice led to the beginnings of modern weather forecasting. Notable weather diarists were Tycho Brahe and Johannes Werner. There were also attempts to find genuine correlations between birth charts and biographies of prominent people. Such biographical horoscope collections existed in manuscript before the invention of movable type printing. One of the largest, still extant, such manuscript collections is that of Erasmus Reinhold, a professor of mathematics at Wittenberg. The first such printed collection was that of Gerolamo Cardano, Libelli duo: De Supplemento Almanach; De Restitutione temporum et motuum coelestium; Item Geniturae LXVII insignes casibus et fortuna, cum expositione, printed and published by Johannes Petreius, specialist for astrological literature, in Nürnberg in 1543; the same year as he published Copernicus’ De revolutionibus.


During the first half of the seventeenth century the failures to find empirical evidence for astrology, a change in the philosophy underpinning science, astrology was justified with Aristotelian metaphysics, and changes in the ruling methodologies of mainstream medicine led to a decline in the academic status of astrology. Although a few universities continued teaching astrology for medical students into the eighteenth century, astrology as a university discipline largely ceased to exist by 1660. However, astrology was still very much woven into the fabric of European society.

Newton was born in 1642, which meant he grew up during the Civil War and the Interregnum. Astrology was used by both sides as propaganda during Civil War. Most famously William Lilly (1602–1681) publishing powerful pamphlets on behalf of the parliamentary side.


Portrait of Lilly, aged 45, now housed in the Ashmolean Museum at Oxford Source: Wikimedia Commons

This caused him major problem following the restitution. Lilly’s Christian Astrology (1647) was a highly influential book in the genre. Lilly was friends with many important figures of the age including Elias Ashmole (1617–1692) an antiquary who gave his name to the Ashmolean Museum of Art and Archaeology in Oxford, which was founded on his collection of books, manuscripts many objects. Ashmole was a passionate astrologer and a founding member of the London Society of Astrologers, which included many prominent intellectuals and existed from 1649 to 1658 and was briefly revived in 1682 by the astronomer, astrologer, printer and globemaker Joseph Moxon (1627–1691).


Joseph Moxon. Line engraving by F. H. van Hove, 1692. Source: Wikimedia Commons

Moxon successfully sold Ptolemaic globes in the last quarter of the seventeenth century, which were intended for astrologers not astronomers. Moxon’s Ptolemaic globes reflect an actual fashion in astrological praxis that could be described as back to the roots. In the middle of the seventeenth century many astrologers decide that astrology wasn’t working, as it should, because the methodology used had drifted to far from that described by Ptolemaeus in his Tetrabiblos. This movement was led by the Italian P. Placido de Titis (1603 – 1668) whose Physiomathematica sive coelestis philosophia published in 1650 with an improved 2nd edition, 1675.



Alongside Moxon another English supporter of this back to the roots movement was John Partridge (1644–c. 1714), who published the first ever English translation of Ptolemaeus’ Tetrabiblos in 1704. Partridge was one of the most well-known astrologers of the age until he got skewered by Jonathan Swift in his infamous Isaac Bickerstaff letters beginning in 1708.

V0004503ER John Partridge. Line engraving by R. White, 1682, after hims

John Partridge. Line engraving by R. White, 1682 Credit: Wellcome Library, London. Wellcome Images Source: Wikimedia Commons John Partridge. Line engraving by R. White, 1682, after himself. 1682 By: Robert WhitePublished: – Copyrighted work available under Creative Commons Attribution only licence CC BY 4.0

We always talk about the big names in the histories of astronomy and mathematics, but it is often more insignificant practitioners, who teach the next generation. In this Newton’s education in astronomy followed the norm and he learnt his astronomy from the books of Vincent Wing (1619–1668) Astronomia Britannica (1669)


Author portrait of Vincent Wing engraved by T. Cross (Frontispiece to the “Astronomia Britannica” of 1669) Source: Wikimedia Commons

and Thomas Streete (1621–1689) Astronomia Carolina, a new theorie of Coelestial Motions (1661).


They were the two leading astronomers in England during Newton’s youth and were both practicing astrologers. The two men were rivals and wrote polemics criticising the errors in the others work. Streete was friends with several other astronomers such as Flamsteed, who also used the Astronomia Carolina as his textbook, or Halley together with whom Streete made observation. Streete was Keplerian and it’s Kepler’s astronomy that he presents in his Astronomia Carolina , although he rejected Kepler’s second law and presented the theories of Boulliau and Ward instead. It is very probable that reading Streete was Newton’s introduction to Kepler’s theories.

Flamsteed, as already said, like Newton, a student of Steete, actually cast an electional horoscope for the laying of the foundation stone of the Royal Observatory in 1675 although he didn’t actually believe in astrology but was maintaining a well-established tradition.


Another example of this sort of half belief can be found in the attitude of Newton and Halley to comets. The two of them did far more than anybody else to establish comets as real celestial bodies affected by the same physical laws as all other celestial bodies and not some sort of message from the heavens. However, whilst neither of them believed in the truth of astrology both retained a belief that comets were indeed harbingers of doom.

As I said at the beginning Newton grew up and lived all of his life in a culture permeated with a belief in astrology. At the end of the seventeenth century astrological ephemera–almanacs, prognostica, etc.–were still a mass market phenomenon.


Zodiac man in EPB/61971/A: Goldsmith, 1679. An almanack for the year of our Lord God, 1679 (London: Printed by Mary Clark, for the Company of Stationers, 1679), leaf B2 recto. Image credit: Elma Brenner. Source:

A large annual fair such as Sturbridge in 1663, the largest annual fair in Europe, would have had a large selection of astrological literature on offer for the visitors; a public many of whose yearly almanac was the only printed book that they bought and read.


It is perfectly reasonable that a twenty-one year old Newton, just entering his second year at Cambridge university, stumbled across an astrological publication that awakened his mathematical curiosity as reported separately by both John Conduitt and Abraham DeMoirvre, in their memoirs based on conversations with Newton.


Filed under History of Astrology, History of Astronomy, Newton, Renaissance Science

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

The Moon is the Earth’s nearest celestial neighbour and the most prominent object in the night sky. People have been tracking, observing and recording the movements of the Moon for thousands of years, so one could assume that calculating its orbit around the Earth should be a reasonable simple matter, however in reality it is anything but.

The problem can be found in the law of gravity itself, which states that any two bodies mutually attract each other. However, that attraction is not restricted to just those two bodies but all bodies attract each other simultaneously. Given the relative masses of somebody standing next to you and the Earth, when calculating the pull of gravity on you, we can, in our calculation, neglect the pull exercised by the mass of your neighbour. With planets, however, it is more difficult to ignore multiple sources of gravitational force. We briefly touched on the gravitational effect of Jupiter and Saturn, both comparatively large masses, on the flight paths of comets, so called perturbation. In fact when calculating the Earth orbit around the Sun then the effects of those giant planets, whilst relatively small, are in fact detectable.

With the Moon the problem is greatly exacerbated. The gravitation attraction between the Earth and the Moon is the primary force that has to be considered but the not inconsiderable gravitational attraction between the Sun and the Moon also plays an anything but insignificant role. The result is that the Moon’s orbit around the Sun Earth is not the smooth ellipse of Kepler’s planetary laws that it would be if the two bodies existed in isolation but a weird, apparently highly irregular, dance through the heavens as the Moon is pulled hither and thither between the Earth and the Sun.

Kepler in fact did not try to apply his laws of planetary motion to the Moon simply leaving it out of his considerations. The first person to apply the Keplerian elliptical astronomy to the Moon was Jeremiah Horrocks (1618–1641), an early-convinced Keplerian, who was also the first person to observe a transit of Venus having recalculated Kepler’s Rudolphine Tables in order to predict to correct date of the occurrence. Horrocks produced a theory of the Moon based on Kepler’s work, which was far and away the best approximation to the Moon’s orbit that had been produced up till that time but was still highly deficient. This was the model that Newton began his work with as he tried to make the Moon’s orbit fit into his grand gravitational theory, as defined by his three laws of motion, Kepler’s three laws of planetary motion and the inverse square law of gravity; this would turn into something of a nightmare for Newton and cause a massive rift between Newton and John Flamsteed the Astronomer Royal.


Portrait of Newton at 46 by Godfrey Kneller, 1689 Source: Wikimedia Commons

What Newton was faced with was attempting to solve the three-body problem, that is a general solution for the mutual gravitational attraction of three bodies in space. What Newton did not and could not know was that the general analytical solution simple doesn’t exist, the proof of this lay in the distant future. The best one can hope for are partial local solutions based on approximations and this was the approach that Newton set out to use. The deviations of the Moon, perturbations, from the smooth elliptical orbit that it would have if only it and the Earth were involved are not as irregular as they at first appear but follow a complex pattern; Newton set out to pick them off one by one. In order to do so he need the most accurate data available, which meant new measurement made during new observations by John Flamsteed the Astronomer Royal.


Source: Wikimedia Commons

For Newton solving the lunar orbit was the most pressing problem in his life and he imperiously demanded that Flamsteed supply him with the data that he required to make his calculations. For Flamsteed the important task in his life, as an observational astronomer, was to complete a new star catalogue on a level of observational accuracy hitherto unknown. The principle interests of the two men were thus largely incompatible. Newton demanded that Flamsteed use his time to supply him with his lunar data and Flamsteed desired to use his time to work on his star catalogue, although to be fair he did supply Newton, if somewhat grudgingly with the desired data. As Newton became more and more frustrated by the problems he was trying to solve the tone of his missives to Flamsteed in Greenwich became more and more imperious and Flamsteed got more and more frustrated at being treated like a lackey by the Lucasian Professor. The relations between the two degenerated rapidly.

The situation was exacerbated by the presence of Edmond Halley in the mix, as Newton’s chief supporter. Halley had started his illustrious career as a protégée of Flamsteed’s when he, still an undergraduate, sailed to the island of Saint Helena to make a rapid survey of the southern night skies for English navigators. The men enjoyed good relations often observing together and with Halley even deputising for Flamsteed at Greenwich when he was indisposed. However something happened around 1686 and Flamsteed began to reject Halley. It reached a point where Flamsteed, who was deeply religious with a puritan streak, disparaged Halley as a drunkard and a heathen. He stopped referring him by name calling him instead Reymers, a reference to the astronomer Nicolaus Reimers Ursus (1551–1600). Flamsteed was a glowing fan of Tycho Brahe and he believed Tycho’s accusation that Ursus plagiarised Tycho’s system. So Reymers was in his opinion a highly insulting label.


Portrait of Edmond Halley painted around 1687 by Thomas Murray (Royal Society, London) Source: Wikimedia Commons

Newton only succeeded in resolving about half of the irregularities in the Moon’s orbit and blamed his failure on Flamsteed. This led to one of the most bizarre episodes in the history of astronomy. In 1704 Newton was elected President of the Royal Society and one of his first acts was to call Flamsteed to account. He demanded to know what Flamsteed had achieved in the twenty-nine years that he had been Astronomer Royal and when he intended to make the results of his researches public. Flamsteed was also aware of the fact that he had nothing to show for nearly thirty years of labours and was negotiating with Prince George of Denmark, Queen Anne’s consort, to get him to sponsor the publication of his star catalogue. Independently of Flamsteed, Newton was also negotiating with Prince George for the same reason and as he was now Europe’s most famous scientist he won this round. George agreed to finance the publication, and was, as a reward, elected a member of the Royal Society.


Prince George of Denmark and Norway, Duke of Cumberland Portrait by Michael Dahl c. 1705 Source: Wikimedia Commons

Newton set up a committee, at the Royal Society, to supervise the work with himself as chairman and the Savilian Professors of Mathematics and Astronomy, David Gregory and Edmond Halley, both of whom Flamsteed regarded as his enemies, Francis Robartes an MP and teller at the Exchequer and Dr John Arbuthnotmathematician, satirist and physician extraordinary to Queen Anne. Although Arbuthnot, a Tory, was of opposing political views to Newton, a Whig, he was a close friend and confidant. Flamsteed was not offered a place on this committee, which was decidedly stacked against him.


David Gregory Source: Wikimedia Commons

Flamsteed’s view on what he wanted published and how it was to be organised and Newton’s views on the topic were at odds from the very beginning. Flamsteed saw his star catalogue as the centrepiece of a multi-volume publication, whereas all that really interested Newton was his data on the planetary and Moon orbits, with which he hoped to rectify his deficient lunar theory. What ensued was a guerrilla war of attrition with Flamsteed sniping at the referees and Newton and the referees squashing nearly all of Flamsteed wishes and proposals. At one point Newton even had Flamsteed ejected from the Royal Society for non-payment of his membership fees, although he was by no means the only member in arrears. Progress was painfully slow and at times virtually non-existent till it finally ground completely to a halt with the death of Prince George in 1708.

George’s death led to a two-year ceasefire in which Newton and Flamsteed did not communicate but Flamsteed took the time to work on the version of his star catalogue that he wanted to see published. Then in 1710 John Arbuthnot appeared at the council of the Royal society with a royal warrant from Queen Anne appointing the president of the society and anybody the council chose to deputise ‘constant Visitors’ to the Royal Observatory at Greenwich. ‘Visitor’ here means supervisor in the legal sense. Flamsteed’s goose was well and truly cooked. He was now officially answerable to Newton. Instead of waiting for Flamsteed to finish his star catalogue the Royal Society produced and published one in the form that Newton wanted and edited by Edmond Halley, the man Flamsteed regarded as his greatest enemy. It appeared in 1712. In 1713 Newton published the second edition of his Principia with its still defective lunar theory but with Flamsteed name eliminated as far as possible.


John Arbuthnot Portrait by Godfrey Kneller Source: Wikimedia Commons

The farce did not end here. In 1714 Queen Anne died and the Visitor warrant thus lost its validity. The Tory government fell and the Whigs regained power. Newton’s political sponsor, Charles Montagu, 1st Earl of Halifax, died in 1715 leaving him without a voice in the new government. Flamsteed, however, was friends with the Lord Chamberlain, Lord Boulton. On 30 November 1715 Boulton signed a warrant ordering Newton and co to hand over the remaining 300 copies of their ‘pirate’ catalogue to Flamsteed.  After some procrastination and some more insults aimed at Flamsteed they finally complied on 28 March 1716. Flamsteed “made a Sacrifice of them to Heavenly truth”, that is he burnt them. Flamsteed had in the mean time published his star catalogue at his own expense and devoted the rest of his life to preparing the rest of his life’s work for publication. He died in 1719 but his widow, Margaret, and two of his former assistants, Joseph Crosthwait and Abraham Sharp, edited and published his Historia coelestis britannia in three volumes in 1725; it is rightly regarded as a classic in the history of celestial observation. Margaret also took her revenge on Halley, who succeeded Flamsteed as Astronomer Royal. Flamsteed had paid for the instruments in the observatory at Greenwich out of his own pocket, so she stripped the building bare leaving Halley with an empty observatory without instruments. For once in his life Newton lost a confrontation with a scientific colleague, of which there were quite a few, game, set and match

The bitter and in the end unseemly dispute between Newton and Flamsteed did nothing to help Newton with his lunar theory problem and to bring his description of the Moon’s orbit into line with the law of gravity. In the end this discrepancy in the Principia remained beyond Newton’s death. Mathematicians and astronomers in the eighteen century were well aware of this unsightly defect in Newton’s work and in the 1740s Leonhard Euler (1707­–1783), Alexis Clairaut (1713–1765) and Jean d’Alembert (1717–1783) all took up the problem and tried to solve it, in competition with each other.  For a time all three of them thought that they would have to replace the inverse square law of gravity, thinking that the problem lay there. Clairaut even went so far as to announce to the Paris Academy on 15 November 1747 that the law of gravity was false, to the joy of the Cartesian astronomers. Having then found a way of calculating the lunar irregularities using approximations and confirming the inverse square law, Clairaut had to retract his own announcement. Although they had not found a solution to the three-body problem the three mathematicians had succeeded in bringing the orbit of the Moon into line with the law of gravity. The first complete, consistent presentation of a Newtonian theory of the cosmos was presented by Pierre-Simon Laplace in his Traité de mécanique céleste, 5 Vol., Paris 1798–1825.

Mathematicians and astronomers were still not happy with the lack of a general solution to the three-body problem, so in 1887 Oscar II, the King of Sweden, advised by Gösta Mittag-Leffler offered a prize for the solution of the more general n-body problem.

Given a system of arbitrarily many mass points that attract each according to Newton’s law, under the assumption that no two points ever collide, try to find a representation of the coordinates of each point as a series in a variable that is some known function of time and for all of whose values the series converge uniformly.

Nobody succeeded in solving the challenge but Henri Poincaré’s attempt to find a solution although not successful, contained enough promising leads that he was awarded the prize. As stated a solution to the problem was found for three bodies by Karl F Sundman in 1912 and generalised for more than three bodies by Quidong Wang in the 1990s.

The whole episode of Newton’s failed attempt to find a lunar theory consonant with his theory of gravitation demonstrates that even the greatest of mathematicians can’t solve everything. It also demonstrates that the greatest of mathematicians can behave like small children having a temper tantrum if they don’t get their own way.




Filed under History of Astrology, History of Mathematics, History of Physics, Newton

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

In the seventeenth century large parts of Europe were still Catholic; in 1616 the Catholic Church had placed De revolutionibus and all other texts promoting a heliocentric world-view on the Index of Forbidden Books and in 1632 they added Galileo’s Dialogo sopra i due massimi sistemi del mondo (Dialogue Concerning the Two Chief World Systems), so the question arises, how was knowledge of the heliocentric model disseminated? The answer is, somewhat surprisingly, that the dissemination of the heliocentric hypothesis was, even in Catholic countries, widespread and through diverse channels.

First off, although De revolutionibus was placed on the Index in 1616, it was only placed there until corrected. In fact, somewhat against the norm, it was actually corrected surprisingly quickly and, with a few rather minor changes, became freely available again for Catholic scholars by 1621. The astronomers within the Church had been able to convince the theologians of the importance of Copernicus’ work as an astronomy book even if one rejected the truth of the heliocentric hypothesis. The only changes were that any statements of the factual truth of the hypothesis were removed, so anybody with a censured copy could quite happily think those statements back into place for himself.

The Lutheran Protestant Church also rejected the heliocentric hypothesis but never formally banned it in anyway. In fact, from very early on, the astronomers and mathematicians at the Lutheran universities had begun teaching Copernicus’ work as a purely mathematical, instrumentalist thesis, whilst rejecting it as a true account of the cosmos. It was used, for example, by Erasmus Reinhold (1511–1553) using Copernicus’ data and mathematical models to calculate the Prutenicae Tabulae (1551), without however committing to heliocentricity. They maintained this instrumentalist approach throughout the seventeenth century utilising the most up to date books as they became available, without crediting the hypothesis with any truth. From about 1630 onwards, Kepler’s Epitome Astronomiae Copernicanae (3 Vols. 1617–1621) and his Tabulae Rudolphinae (1627) became the leading textbooks for teaching the heliocentric hypothesis. The latter was used both sides of the religious divide because it was quite simply vastly superior in its accuracy to any other volume of planetary tables on the market.

However, the mainstream pro heliocentricity texts were not the only published sources spreading the information of the heliocentric hypothesis and making the information available across Europe. One, perhaps surprising, source was the yearly astrological almanacs.


These annual pamphlets or booklets contained the astronomical and astrological data for the coming year, phases of the moon, hours of sunlight, any eclipse or planetary conjunctions etc. They also included basic horoscopes for the year covering political developments, weather forecasts, health issues and whatever. These were immensely popular and printed on cheap paper and not bound were reasonably cheap, so they sold in comparatively vast numbers, having much larger editions than any printed books. The market was fiercely contested so to make sure that their product was preferred by the potential customers, who came from all levels of society, the authors and/or publishers included editorials covering a wide range of topic. These editorials often contained medical issues but in the seventeenth century they also often contained popular expositions of the heliocentric hypothesis. Given the widespread consume of these publications it meant that basic knowledge of heliocentricity reached a large audience.

Another important source for the dissemination of the heliocentric hypothesis was in the writings of some of those who, nominally at least, opposed it. I will now take a brief look at two of those authors the Italian, Jesuit astronomer, mathematician and physicist Giovanni Battista Riccioli (1598–1671) and the French, priest, philosopher, astronomer and mathematician Pierre Gassendi (1592–1655) both of whom were highly influential and widely read scholars in the middle of the seventeenth century.

Pierre Gassendi is one of those figures in the history of science, who deserve to be better known than they are. Well known to historians of science and philosophy he remains largely unknown to those outside those disciplines. He was a central figure in the intellectual life of Europe in the middle of the seventeenth century part of the philosophical circle in Paris that included René Descartes, Marin Mersenne, Thomas Hobbes and Jean-Baptiste Morin amongst others. He also travelled to Holland and made the acquaintance of Isaac Beeckman. Probably his most important contribution to the evolution of science was his attempt to reconcile Epicurean atomism with Christian theology.


Pierre Gassendi after Louis-Édouard Rioult. Source: Wikimedia Commons

Throughout his life he actively promoted the work of both Kepler and Galileo. He wrote and published a biography of Nicolas-Claude Fabri de Peiresc (1580–1637), his patron, an astronomer and another supporter of the works of Galileo.  Shortly before the end of his life he published a collective biography of Tycho Brahe, Nicolaus Copernicus, Georg von Peuerbach and Johannes Regiomontanus: Tychonis Brahei, equitis Dani, astronomorum Coryphaei, vita; accessit Nicolai Copernici; Georgii Peurbachii, et Joannis Regiomontani, astronomorum celebrium vita (1654).


In 1645 Gassendi was appointed professor of mathematics at the Collège Royal in Paris and during his time there he wrote and published an astronomy textbook presenting both the Tychonic and heliocentric astronomical systems, Institvtio astronomica, iuxta hypothesis tam vetervm, qvam Copernici, et Tychonis. Dictata à Petro Gassendo … Eivsdem oratio inauguralis iteratò edita (1647).


Although, as a Catholic priest, he presented the Tychonic system as the correct one his treatment of heliocentricity was detailed, thorough and very sympathetic. Perhaps somewhat too sympathetic, as it led to him being investigated by the Inquisition, who however gave him a clean bill of health. Because of his excellent reputation his book was read widely and acted as a major source for the dissemination of the heliocentric hypothesis.

Like Gassendi, Riccioli was an important and influential figure in seventeenth century science. From 1636 he was professor in Bologna where did much important work in astronomy and physics as well as being the teacher of Giovanni Domenico Cassini (1625–1712), who we will meet later in this series.


Riccioli as portrayed in the 1742 Atlas Coelestis (plate 3) of Johann Gabriel Doppelmayer. Source: Wikimedia Commons

He is perhaps best known for his pioneering selenology together with his former student, Francesco Maria Grimaldi (1618–1663), which provided the nomenclature system for the moons geological features still in use today.  As stated earlier it was Riccioli, who provided the necessary empirical proof of Galileo’s laws of fall. He also hypothesised the existence of, what later became known as the Coriolis effect, if the Earth did in fact rotate.

If a ball is fired along a Meridian toward the pole (rather than toward the East or West), diurnal motion will cause the ball to be carried off [that is, the trajectory of the ball will be deflected], all things being equal: for on parallels of latitude nearer the poles, the ground moves more slowly, whereas on parallels nearer the equator, the ground moves more rapidly.

Having failed to detect it, it does exist but is too small to be measured using the methods available to Riccioli, he concluded that the Earth does not in fact rotate.

This was just one of many arguments pro and contra the heliocentric hypothesis that Riccioli presented in his Almagestum novum astronomiam veterem novamque complectens observationibus aliorum et propriis novisque theorematibus, problematibus ac tabulis promotam (Vol. I–III, 1651), a vast astronomical encyclopaedia that became a standard astronomical textbook throughout Europe. Although Riccioli rejected the heliocentric hypothesis his very detailed and thorough analysis of it with all its strengths and weaknesses meant that his book became a major source for those wishing to learn about it.


Frontispiece of Riccioli’s 1651 New Almagest. Source: Wikimedia Commons

This famous frontispiece shows a semi-Tychonic system being weighed against a heliocentric system and being found more substantial. Ptolemaeus lies on the ground under the scales obviously defeated but he is saying “I will rise again”.

As we have seen, although not provable at that stage and nominally banned by the Catholic Church, information on and details of the heliocentric hypothesis were widespread and easily accessible throughout the seventeenth century from multiple sources and thus knowledge of it and interest in it continued to spread throughout the century.










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

Christmas Trilogy Part 3: The emergence of modern astronomy – a complex mosaic: Part XXVI


In popular presentations of the so-called scientific or astronomical revolutions Galileo Galilei is almost always presented as the great champion of heliocentricity in the first third of the seventeenth century. In fact, as we shall see, his contribution was considerably smaller than is usually claimed and mostly had a negative rather than a positive influence. The real champion of heliocentricity in this period was Johannes Kepler, who in the decade between 1617 and 1627 published four major works that laid the foundations for the eventual triumph of heliocentricity over its rivals. I have already dealt with one of these in the previous post in this series, the De cometis libelli tres I. astronomicus, theoremata continens de motu cometarum … II. physicus, continens physiologiam cometarum novam … III. astrologicus, de significationibus cometarum annorum 1607 et 1618 / autore Iohanne Keplero …, which was published in 1619 and as I’ve already said became the most important reference text on comets in the 1680’s during a period of high comet activity that we will deal with in a later post.


Source: ETH Library Zurich

Chronologically the first of Kepler’s influential books from this decade was Volume I (books I–III) of his Epitome Astronomiae Copernicanae published in 1617, Volume II (book IV) followed in 1620 and Volume III (books V–VII) in 1621. This was a text book on heliocentric astronomy written in question and answer dialogue form between a teacher and a student spelling out the whole of heliocentric astronomy and cosmology in comparatively straight forward and simple terms, the first such textbook. There was a second edition containing all three volumes in 1635.


Second edition 1635 Source

This book was highly influential in the decades following its publication and although it claims to be a digest of Copernican astronomy, it in fact presents Kepler’s own elliptical astronomy. For the first time his, now legendary, three laws of planetary motion are presented as such together. As we saw earlier the first two laws–I. The orbit of a planet is an ellipse and the Sun is at one of the focal points of that ellipse II: A line connecting the Sun and the planet sweeps out equal areas in equal times–were published in his Astronomia Nova in 1609. The third law was new first appearing in, what he considered to be his opus magnum, Ioannis Keppleri Harmonices mundi libri V (The Five Books of Johannes Kepler’s The Harmony of the World) published in 1619 and to which we now turn our attention.


Source: Wikimedia Commons

Kepler’s first book was his Mysterium Cosmographicum published in 1597 with its, to our way of thinking, somewhat bizarre hypothesis that there are only six planets because the spaces between their orbits are defined by the five regular Platonic solids.


Kepler’s Platonic solid model of the Solar System from Mysterium Cosmographicum Source: Wikimedia Commons

Although his calculation in 1597 showed a fairly good geometrical fit for his theory, it was to Kepler’s mind not good enough and this was his motivation for acquiring Tycho Brahe’s newly won more accurate data for the planetary orbits. He believed he could quite literally fine tune his model using the Pythagorean theory of the harmony of the spheres, that is that the ratio of the planetary orbits build a musical scale that is only discernable to the enlightened Pythagorean astronomer. The Harmonices Mundi was that fine tuning.

The first two books of the Harmonices Mundi layout Kepler’s geometrical theory of music, which geometrical constructions produced harmonious musical intervals and which disharmonious ones, based on which are constructible with straight edge and compass, harmonious, and which are not, disharmonious. The third book is Kepler’s contribution to the contemporary debate on the correct division of the intervals of the musical scale, in which Vincenzo Galilei (1520–1591), Galileo’s father, had played a leading role. The fourth book is the application of the whole to astrology and the fifth its application to astronomy and it is here that we find the third law.

In the fifth Kepler compare all possible ratios of planetary speeds and distances constructing musical scales for planets and musical intervals for the relationship between planets. It is here that he, one could say, stumbles upon his third law, which is known as the harmony law. Kepler was very much aware of the importance of his discovery as he tells us in his own words:

“After I had discovered true intervals of the orbits by ceaseless labour over a very long time and with the help of Brahe’s observations, finally the true proportion of the orbits showed itself to me. On the 8th of March of this year 1618, if exact information about the time is desired, it appeared in my head. But I was unlucky when I inserted it into the calculation, and rejected it as false. Finally, on May 15, it came again and with a new onset conquered the darkness of my mind, whereat there followed such an excellent agreement between my seventeen years of work at the Tychonic observations and my present deliberation that I at first believed that I had dreamed and assumed the sought for in the supporting proofs. But it is entirely certain and exact that the proportion between the periodic times of any two planets is precisely one and a half times the proportion of the mean distances.”

Translated into modern notation the third law is P12/P22=R13/R23, where P is the period of a planet and R is the mean radius of its orbit. It can be argues that this was Kepler’s greatest contribution to the history of the emergence of heliocentricity but rather strangely nobody really noticed its true significance until Newton came along at the end of the seventeenth century.

However they should have done because the third law gives us is a direct mathematical relationship between the size of the orbits of the planets and their duration, which only works in a heliocentric system. There is nothing comparable for either a full geocentric system or for a geo-heliocentric Tychonic or semi-Tychonic system. It should have hit the early seventeenth-century astronomical community like a bomb but it didn’t, which raises the question why it didn’t. The answer is because it is buried in an enormous pile of irrelevance in the Harmonices Mundi and when Kepler repeated it in the Epitome he gave it no real emphasis, so it remained relatively ignored.

On a side note, it is often thought that Kepler had abandoned his comparatively baroque Platonic solids concepts from the Mysterium Cosmographicum but now that he had, in his opinion, ratified it in the Harmonices Mundi he published a second edition of the book in 1621.


Second Edition 1621 Source

Ironically the book of Kepler’s that really carried the day for heliocentricity against the geocentric and geo-heliocentric systems was his book of planetary tables based on Tycho Brahe’s data the Tabulae Rudolphinae (Rudolphine Tables) published in 1627, twenty-eight years after he first began working on them. Kepler had in fact been appointed directly by Rudolph II in Prague to produce these tables at the suggestion of Tycho in 1601. Turning Tycho’s vast collection of data into accurately calculated tables was a horrendous and tedious task and over the years Kepler complained often and bitterly about this burden.


Tabulae Rudolphinae The frontispiece presents in graphic form a potted history of Western astronomy Source

However, he persevered and towards the end of the 1620s he was so far. Because he was the Imperial Mathematicus and had prepared the tables under the orders of the Emperor he tried to get the funds to cover the printing costs from the imperial treasury. This proved to be very difficult and after major struggles he managed to acquire 2000 florins of the more than 6000 that the Emperor owed him, enough to pay for the paper. He began printing in Linz but in the turmoil of the Thirty Years War the printing workshop got burnt down and he lost the already printed pages. Kepler decamped to Ulm, where with more difficulties he succeeded in finishing the first edition of 1000 copies. Although these were theoretically the property of the Emperor, Kepler took them to the Frankfurt book fair where he sold the entire edition to recoup his costs.

The Tabulae Rudolphinae were pretty much an instant hit. The principle function of astronomy since its beginnings in Babylon had always been to produce accurate tables and ephemerides for use initially by astrologers and then with time also cartographers, navigators etc. Astronomical systems and the astronomers, who created them, were judged on the quality and accuracy of their tables. Kepler’s Tabulae Rudolphinae based on Tycho’s data were of a level of accuracy previous unknown and thus immediately won many supporters. Those who used the tables assumed that their accuracies was due to Kepler’s elliptical planetary models leading to a gradually increasing acceptance of heliocentricity but this was Kepler’s system and not Copernicus’. Supported by the Epitome with the three laws of planetary motion Kepler’s version of heliocentricity became the dominant astronomical/cosmological system over the next decades but it would be another thirty to forty years, long after Kepler’s death, before it became the fully accepted system amongst astronomers.









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