Category Archives: History of Astrology

Really! – Did the artist have a Tardis?

Those who read the occasional bursts of autobiographical information that appear here on the blog might be aware that I went to university at the tender age of eighteen as an archaeology student. I actually dropped out after one year but continued to work as a professional field archaeologist (that’s a digger to you mate) for several years. Given that I was already interested in the history of astronomy in those days and would eventually abandon archaeology for it, it would seem logical that I would be interested in archaeoastronomy, in particular because I studied under Richard Atkinson who together with Stuart Piggott carried out the first extensive, modern excavation of Stonehenge, the world’s most famous archaeoastronomical monument, in the 1950s. In fact my father also worked on that excavation. This assumption would be correct with reservations. There has been some excellent work in archaeoastronomy but unfortunately there has also been a large amount of highly dubious speculation on the topic.

In my opinion an example of the latter appeared in articles in The Guardian and on the Hyperallergic website a couple of days ago. The Guardian article was entitled, Two suns? No, it’s a supernova drawn 6,000 years ago, say scientists. This article tells us:

For decades, stone carvings unearthed in the Himalayan territory of Kashmir were thought to depict a hunting scene. But the presence of two celestial objects in the drawings has piqued the interest of a group of Indian astronomers.


Source: The Guardian

They have proposed another theory. According to a study published in the Indian Journal of History of Science, the Kashmir rock drawings may be the oldest depiction of a supernova, the final explosion of a dying star, ever discovered.

 “Our first argument was, there cannot be two suns,” Vahia said. “We thought it must have been an object that appeared and attracted the attention of the artists.”

 They settled on Supernova HB9, a star that exploded around 4,600BC.

Rewinding the map of the sky back that far revealed more clues.

Viewed from Kashmir, the supernova would have occurred somewhere near the Orion constellation. “Which is known as the scene of a hunter,” said Vahia.

“The supernova also went off just above the constellation of Taurus, the bull, which is also seen in the drawing,” Vahia added.


Source: The Guardian

So to summarise a group of astrophysicists decide that the rock drawing depicts a supernova from around 4,600 BCE that was visible in the sky in the area of the constellations Orion the hunter and Taurus the bull, which according to the researchers are also depicted in the drawing. It is by the latter claim that my bullshit detectors went off at full volume. I will explain.

The chosen supernova occurred in 4600 BCE, now I’m not an expert on prehistoric Indian asterisms, I don’t even know anybody who is, but I do know something about the Babylonian and ancient Greek ones. Taurus is indeed one of the oldest known asterisms but the earliest known mention of a bull asterism is in the Sumerian record, the Heaven’s Bull, in the third millennium BCE, that’s a couple of thousand years after the chosen supernova. Even worse it is not known whether the Sumerian asterism is the same one as the later Babylonian/Greek asterism Taurus. With Orion we have even more problems. The Sumerian asterism involving the stars of Orion was a sheep. For the ancient Egyptians the stars depicted their god Osiris. It was first the Greeks who created the asterism Orion although some mythologists see Orion as a representation of the Sumerian King Gilgamesh, who also fought a bull. This is of course highly speculative.

So we have astrophysicists identifying a rock drawing in India that is dated to the fifth millennium BCE with the constellations of Orion fighting Taurus, asterisms which don’t appear to have been identified till several thousand years later. Excuse me if I am somewhat sceptical about this identification. Just as a minor point I don’t think that the animal in the drawing actually looks like a bull, more like a stag in my opinion.







Filed under History of Astrology, History of Astronomy, History of science, Myths of Science, Uncategorized

Christmas Trilogy 2017 Part 3: Kepler’s big book

Johannes Kepler was incredibly prolific, he published over eighty books and booklets over a very wide range of scientific and mathematical topics during his life. As far as he was concerned his magnum opus was his Ioannis Keppleri Harmonices mundi libri V (The Five Books of Johannes Kepler’s The Harmony of the World) published in 1619 some twenty years after he first conceived it. Today in popular #histsci it is almost always only mentioned for the fact that it contains the third of his laws of planetary motion, the harmonic law. However it contains much, much more of interest and in what follows I will attempt to give a brief sketch of what is in fact an extraordinary book.


A brief glace at the description of the ‘five books’ thoughtfully provided by the author on the title page (1) would seem to present a mixed bag of topics apparently in some way connected by the word or concept harmonic. In order to understand what we are being presented with we have to go back to 1596 and Kepler’s first book Mysterium Cosmographicum (The Cosmographic Mystery). In this slim volume Kepler presents his answer to the question, why are there only six planets? His, to our eyes, surprising answer is that the spaces between the planets are defined by the regular so-called Platonic solids and as the are, and can only be, five of these there can only be six planets.

Using the data from the greatest and least distances between the planets in the Copernican system, Kepler’s theory produces an unexpectedly accurate fit. However the fit is not actually accurate enough and in 1598 Kepler began working on a subsidiary hypothesis to explain the inaccuracies. Unfortunately, the book that he had planned to bring out in 1599 got somewhat delayed by his other activities and obligations and didn’t appear until 1619 in the form of the Harmonice mundi.

The hypothesis that Kepler presents us with is a complex mix of ideas taken from Pythagoras, Plato, Euclid, Proclus and Ptolemaeus centred round the Pythagorean concept of the harmony of the spheres. Put very simply the theory developed by the Pythagoreans was that the seven planets (we are talking geocentric cosmology here) in their orbits form a musical scale than can, in some versions of the theory, only be heard by the enlightened members of the Pythagorean cult. This theory was developed out of the discovery that consonances (harmonious sounds) in music can be expressed in the ratio of simple whole numbers to each other (the octave for example is 1:2) and the Pythagorean belief that the integers are the building block of the cosmos.

This Pythagorean concept winds its way through European intellectual history, Ptolemaeus wrote a book on the subject, his Harmonice and it is the reason why music was one of the four disciplines of the mathematical quadrivium along with arithmetic, geometry and astronomy. Tycho Brahe designed his Uraniburg so that all the architectonic dimensions from the main walls to the window frames were in Pythagorean harmonic proportion to one another.


Tycho Brahe’s Uraniborg Blaeus Atlas Maior 1663 Source: Wikimedia Commons

It is also the reason why Isaac Newton decided that there should be seven colours in the rainbow, to match the seven notes of the musical scale. David Gregory tells us that Newton thought that gravity was the strings upon which the harmony of the spheres was played.

In his Harmony Kepler develops a whole new theory of harmony in order to rescue his geometrical vision of the cosmos. Unlike the Pythagoreans and Ptolemaeus who saw consonance as expressed by arithmetical ratios Kepler opted for a geometrical theory of consonance. He argued that consonances could only be constructed by ratios between the number of sides of regular polygons that can be constructed with a ruler and compass. The explication of this takes up the whole of the first book. I’m not going to go into details but interestingly, as part of his rejection of the number seven in his harmonic scheme Kepler goes to great lengths to show that the heptagon construction given by Dürer in his Underweysung der Messung mit dem Zirckel und Richtscheyt is only an approximation and not an exact construction. This shows that Dürer’s book was still being read nearly a hundred years after it was originally published.


In book two Kepler takes up Proclus’ theory that Euclid’s Elements builds systematically towards the construction of the five regular or Platonic solids, which are, in Plato’s philosophy, the elemental building blocks of the cosmos. Along the way in his investigation of the regular and semi-regular polyhedra Kepler delivers the first systematic study of the thirteen semi-regular Archimedean solids as well as discovering the first two star polyhedra. These important mathematical advances don’t seem to have interested Kepler, who is too involved in his revolutionary harmonic theory to notice. In the first two books Kepler displays an encyclopaedic knowledge of the mathematical literature.


The third book is devoted to music theory proper and is Kepler’s contribution to a debate that was raging under music theorist, including Galileo’s father Vincenzo Galilei, about the intervals on the musical scale at the beginning of the seventeenth century. Galilei supported the so-called traditional Pythagorean intonation, whereas Kepler sided with Gioseffo Zarlino who favoured the ‘modern’ just intonation. Although of course Kepler justification for his stance where based on his geometrical arguments. Another later participant in this debate was Marin Mersenne.


In the fourth book Kepler extends his new theory of harmony to, amongst other things, his astrology and his theory of the astrological aspects. Astrological aspects are when two or more planets are positioned on the zodiac or ecliptic at a significant angle to each other, for example 60° or 90°. In his Harmonice, Ptolemaeus, who in the Renaissance was regarded as the prime astrological authority, had already drawn a connection between musical theory and the astrological aspects; here Kepler replaces Ptolemaeus’ theory with his own, which sees the aspects are being derived directly from geometrical constructions. Interestingly Kepler, who had written and published quite extensively on astrology, rejected nearly the whole of traditional Greek astrology as humbug keeping only his theory of the astrological aspects as the only valid form of astrology. Kepler’s theory extended the number of influential aspects from the traditional five to twelve.

The fifth book brings all of the preceding material together in Kepler’s astronomical/cosmological harmonic theory. Kepler examines all of the mathematical aspects of the planetary orbits looking for ratios that fit with his definitions of the musical intervals. He finally has success with the angular velocities of the planets in their orbits at perihelion and aphelion. He then examines the relationships between the tones thus generated by the different planets, constructing musical scales in the process. What he in missing in all of this is a grand unifying concept and this lacuna if filled by his harmonic law, his third law of planetary motion, P12/P22=R13/R23.


There is an appendix, which contains Kepler’s criticisms of part of Ptolemaeus’ Harmonice and Robert Fludd’s harmony theories. I blogged about the latter and the dispute that it triggered in an earlier post

With his book Kepler, who was a devoted Christian, was convinced that he had revealed the construction plan of his geometrical God’s cosmos. His grandiose theory became obsolete within less than fifty years of its publication, ironically pushed into obscurity by intellectual forces largely set into motion by Kepler in his Astronomia nova, his Epitome astronomiae Copernicanae and the Rudolphine Tables. All that has survived of his great project are his mathematical innovations in the first two books and the famous harmonic law. However if readers are prepared to put aside their modern perceptions and prejudices they can follow one of the great Renaissance minds on a fascinating intellectual journey into his vision of the cosmos.

(1) All of the illustration from the Harmonice mundi in this post are taken from the English translation The Harmy of the World by Johannes Kepler, Translated into English with an Introduction and Notes by E.J. Aston, A.M. Duncan and J.V. Field, American Philosophical Society, 1997


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

The Albrecht Dürer or should that be the Bernhard Walther House?

On Saturday I did my history of astronomy tour of Nürnberg for some readers of this blog who were visiting the city[1]. As usually it ended at Nürnberg’s biggest tourist attraction the Albrecht Dürer House. There are of course good reasons for including Nürnberg’s most famous artist in such a tour, as readers of this blog should know. He wrote and published the very first printed maths book in German and was the artist involved in creating the first every printed European star maps. However this is another reason for including this building in a history of astronomy tour. Before it became the Albrecht Dürer House it had been the Bernhard Walther House and this was one of the reasons that motivated Dürer to purchase it. But who, I hear you say, was Bernhard Walther?

Bernhard Walther (Albrecht Dürer) House on Tiergärtentor Nürnberg
Photo: Monica Weidemann
Source: Wikipedia Commons

Bernhard Walther was born in Memmingen in Bavaria in 1430. The first really reliable fact we have about his life is when he became a citizen of Nürnberg in 1467; remember Nürnberg was an independent city-state in the fifteenth century. He was the general manager of the Nürnberg trading post of the Memmingen merchant traders the Vöhlin-Welser-Company. When Regiomontanus came to Nürnberg in 1471, he and Walther became friends and Walther became his astronomical assistant and companion. The accounts that claim that Walther was Regiomontanus’ patron are false, as are also the claims that the two of them built an observatory financed by Walther. They carried out their astronomical observations with portable instruments out in the streets. As well as astronomy Walther apparently learnt Greek from Regiomontanus, who had learnt the language whilst a member of Cardinal Bessarion’s household in Italy. We know of Walther’s abilities in the ancient language because they are mentioned in an ode that Conrad Celtis, the so-called arch humanist, wrote in his honour.

Regiomontanus had come to Nürnberg, according to his own account, to reform astronomy in two ways; firstly by starting a new programme of astronomical observations to replace those of Ptolemaeus corrupted by centuries of copying and recopying in manuscripts and secondly by printing and publishing new editions of the astronomical literature cleared of their errors through careful philological editing. Regiomontanus had chosen Nürnberg for his programme because the city made the best scientific instruments and because of its extensive communications network being aware of the fact that his programme was only achievable with the active assistance of other European astronomers. In an age without postal services, Nürnberg, as a major European trading city, had a private communications system second only to that of Venice.

Walther assisted Regiomontanus in both of his reform endeavours but they had only succeeded in publishing nine items, including the publishing house’s ambitious publication programme, when Regiomontanus again left Nürnberg in the direction of Rome to answer the Pope’s call to work on a calendar reform in 1475. Regiomontanus never returned from that journey, dying in Rome in 1476, presumable during some sort of epidemic. Walther did not continue the publishing endeavour, although he bought up Regiomontanus extensive collection of manuscripts, but he did carry on making a series of basic simple astronomical observations for the next almost thirty years. This was the first such series of astronomical observations carried out in Early Modern Europe, making Walther to an important if minor figure in the history of astronomy.

As the general manager of the trading company Walther occupied a house on the West side of the market place in Nürnberg, today Market Place No. 11. The original hose was destroyed in the Second World War.

Walther’s trading depot was on the west side of the Nürnberg market place, next door to the right of where the Körn & Berg bookshop now stands.

When he finally retired, seventy years old, he sold the house on the market place and bought the house on Tiergärtentor (The Zoo Gate) in 1501, which is now known as the Albrecht Dürer House. Walther substantially rebuilt the house adding the whole of what is now the top floor. He also had a small window let into the south gable with a stone window ledge; he used this window to make his astronomical observations resting his observing instruments on that stone ledge, this was his observatory. We know that Walther had this window constructed because in the document with which the city council gave permission for its construction, Walther had to give a guarantee that he wouldn’t empty his chamber pot out on to the roof of the neighbouring building.

Walther House with Observatory Window in the south gable
Photo: Nora Reim
Source: Astronomie in Nürnberg

Walther’s observation programme was comparatively simple and consisted largely of regularly determining the altitude of the Sun, observing eclipses and determining the positions of the planets during conjunctions etc. The latter set of observations leads to the assumption that the observations were principally for use by astrologers. This is not surprising as Regiomontanus was a practicing astrologer, with a very good reputation, whose stated intention in reforming astronomy was in order to improve astrological predictions. He claimed that such predictions were often wrong because the astronomical data on which they were based was inaccurate. Three of Walther’s observations found their way into Copernicus’ De revolutionibus, although we don’t know how they got there. Copernicus falsely attributes part of the used data to Johannes Schöner. In 1544 Schöner did publish Regiomontanus’ and Walther’s observations in his Scripta clarissimi Mathematici M. Joannis Regiomontani. Walther’s observation were, for their time, highly accurate only to be first superceded by those of Tycho Brahe at the end of the century.

Another little known Nürnberg astronomer, Conrad Heinfogel, referred to himself as a pupil of Bernard Walther and it was Heinfogel who provided the astronomical knowledge for Dürer’s star maps.

Largely forgotten today Walther was well known and highly regarded by his contemporaries and the astronomical community down to Tycho and Kepler, Tycho using Walther’s observations to check against his own. Walther died in 1504 and in 1509 Albrecht Dürer bought the house on the Tiergärtentor, partially because being himself a big fan of the mathematical sciences he desired to own Walther’s house. At the same time he also acquired ten manuscripts out of the Regiomontanus/Walther collection including an Elements of Euclid.

If you are ever in Nürnberg go round to the back of the Dürer house and you can see Walther’s observatory for yourself. However please be quite when doing so as the people who live next door get really pissed off with the tourists and the noise that they make.

[1] Any readers of the blog who visit Nürnberg are welcome to the same tour, you just need to arrange it in advance; all you have to do is buy me lunch at the end of it. A low price of a highly entertaining and educational tour that lasts between three and four hours!


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

The poetic astronomer


Regular readers of this blog will know that I can on occasion be a stroppy, belligerent, pedant, who gets rather riled up over people who spread myths of science and who has a tendency to give such people a public kicking on this blog. This tendency earned me the nickname, the HistSci_Hulk in earlier years. The subtitle to a podcast that I stumbled across yesterday on the BBC website provoked my inner Hist_Sci Hulk and has generated this post.

The podcast is a BBC Radio 4 “Radio 4 in Four” four minute documentary on the work of the Indian mathematician and astronomer, Aryabhata: Maths expressed as poetry. The subtitle was: In 5th century India, clever man Aryabhata wrote his definitive mathematical work entirely in verse and long before Galileo, argued the world was round [my emphasis]. It was that final clause that provoked my HistSci_Hulk moment.

I’ve lost count of how many times over the years I have explained patiently and oft not so patiently that educated society in European culture have known and accepted that the world is a sphere since at least the sixth century BCE. This is the most recent account here on the blog. Bizarrely in the podcast no mention is made of Aryabhata’s cosmological or astronomical views, so it is real puzzle as to why it’s mentioned in the subtitle. What is interesting is the fact that as a cosmologist Aryabhata held a fairly rare position, although he was a geocentrist he believed that the earth revolved around its own axis, i.e. geocentrism with diurnal rotation. You can read about the history of this theory here in an earlier blog post.

Statue of Aryabhata on the grounds of IUCAA, Pune. As there is no known information regarding his appearance, any image of Aryabhata originates from an artist’s conception.
Source: Wikimedia Commons

More interesting is the correct fact that Aryabhata wrote his astronomical/mathematical thesis in verse form. As the podcast points out this is because the culture in which he was writing was an oral one and complex facts are easier to remember in verse rather than in prose. What the podcast doesn’t say is that Aryabhata was not the only astronomer/mathematician to express his results in verse and was in this sense by no means unique. In fact he is part of a solid tradition of mathematical Sanskrit poetry.

India was not the only culture to use poetry to express scientific content. Probably the most famous example is the Latin poem De rerum natura by the first century BCE Roman poet Lucretius, which is the most extensive description of the physics of the ancient Greek atomists. The poem played a central role in the revival of atomism in the early modern period; a revival that several historians of science, such as David Lindberg, consider to be a key element in the so-called scientific revolution of the seventeenth century.

In astronomy/ astrology there is a poem from antiquity that played a significant role in the Renaissance. This is the Astronomica probably written by the poet Marcus Manilius in the first century CE; the first printed edition of this was published by Regiomontanus in Nürnberg in 1473.

Many people are not aware of some highly significant scientific poems from the eighteenth century written and published by Charles Darwin’s grandfather, Erasmus.

Joseph Wright of Derby, Erasmus Darwin (1770; Birmingham Museum and Art Gallery).
Source: Wikimedia Commons

Darwin’s The Loves of the Plants was the first work in English to popularise the botanical works of Linnaeus in English. The poem caused something of a scandal because it emphasised the explicit sexual nature of Linnaeus’ system of botanical nomenclature and was thus considered unsuitable for polite society. The Loves of the Plants was published together with another poem, The Economy of Vegetation, a more general poem on scientific progress and technological innovation, of which Darwin as a prominent member of the Lunar Society of Birmingham was very much aware. The Economy of Vegetation expresses an evolutionary view of progress. A footnote to The Loves of the Plants contains the first outlines of Darwin’s theory of biological evolution, which he would then expand upon in his prose work Zoonomia. Erasmus Darwin’s is an adaptive theory of evolution and is thus oft referred to as Lamarckian, although as Erasmus preceded Lamarck, maybe his theory should be referred to as Darwinian! A posthumous poem of Darwin’s, The Temple of Nature, contains a full description of his theory of evolution in verse.

Writing this led me to the thought that maybe editors of modern scientific journals should require their authors to submit their papers in iambic pentameters or in Shakespearean blank verse, with the abstracts written as sonnets. It would certainly make reading scientific papers more interesting.




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

An orb by any other name would circle as smoothly

Alan Stern, the principal investigator of the New Horizons Mission to Pluto is calling for a new definition for planets in order to return Pluto to, what he and other see as its former glory, the status of a planet. The so called demotion of Pluto caused the release of strong emotions amongst the distant planet’s fans and the stunning success of the New Horizons mission added fuel to the flames in the on going debate. Many of those participating seem to be somewhat unaware of the fact that the definition of what is a planet has changed down the centuries and I thought I would write a brief guide to the changing fortunes of the term planet since its inception in antiquity.

It should be made clear that I shall only be talking about European astronomy and not any other traditions such as Chinese, Indian, Mayan astronomies etc. European astronomy/astrology has its roots in ancient Babylon. The Babylonian tradition was most concerned with the Moon and the Sun but the Babylonians were aware of the planets Mercury, Venus, Mars, Jupiter and Saturn, which they like other ancient cultures regarded as divinities. They tracked their orbits over very long periods of time and developed algorithms to determine their appearances and disappearances for omen astrological purposes. They don’t appear to have been interested in the mechanism of the planetary orbits. I’m anything but an expert on Babylonian astronomy/astrology and I don’t know if they had a collective name for them.

The direct inheritors of the Babylonian celestial interests were the ancient Greeks and they were very much interested in orbital mechanics and they also coined the term planet. For the Greeks all illuminated objects in the heavens were stars (aster, astron), as I explained in an earlier post. The stars as we know them were the fixed stars because they appeared to remain in place relative to each other whilst the sphere of the fixed stars rotated about the celestial axis once every twenty-four hours. It was of course the Earth that rotated about its axis and not the stars but the Greeks were not aware of that. The illusion that the stars, visible to the naked-eye, are all equidistant to the Earth is easy to experience. Just go out into the countryside were there is no light pollution and look up at the night sky on a clear night. You will see the ‘sphere of the fixed stars’, as experienced by the ancient Greeks. Comets, much rarer and apparently random, were hairy stars, the word comet derives from the Greek aster kometes, literally long-haired star. The five planets known to the Babylonians and the Moon and the Sun were all present on a regular basis but unlike the fixed stars they appeared to wander around the heavens and so they became asteres planetai that is wandering stars, from planasthai to wander. The Greeks had seven wanderers Moon, Mercury, Venus, Sun, Mars, Jupiter and Saturn. The Earth was of course stationary at the middle of the whole system and so was not a planet.

16th-century representation of Ptolemy’s geocentric model in Peter Apian’s Cosmographia, 1524
Source: Wikimedia Commons

Subsequent European cultures and the Islamic Empire inherited the Greek model of the heavens with its seven wanderers and nothing of significance changed down the centuries until the Renaissance and the advent of Copernican heliocentrism in 1543. Copernicus’s new model was of course a major upheaval. The Sun became stationary and the Earth became a planet wandering through the heavens. The Moon acquired a strange new status, no longer orbiting the centre, now the Sun, but orbiting the Earth. Heliocentricity took more than one hundred years to become establish and Copernicus’ upheaval brought no immediate change of terminology.

The heliocentric order of the heavens from Copernicus’ De revolutionibus 1543

The first change came in 1610 with the telescopic discovery of the four largest moons of Jupiter by Galileo and Simon Marius. Here we have four new celestial bodies orbiting a planet, as with the Moon, and not the centre of the cosmos. At first Galileo referred to them as stars or planets, leading Kepler, who was at first not clear what the four new objects were, to panic and fear that Giordano Bruno was right and that all stars had planets. This conflicted with Kepler’s own finite universe cosmology. He was greatly relieved to discover that the new planets were in reality moons and coined the term satellite from the Latin satillitem meaning attendant, companion, courtier, accomplice or assistant. Kepler was very fond of creating new scientific terminology. The term was not adopted immediately but by the end of the seventeenth century astronomers differentiated between planets and satellites, around the same time as heliocentricity became firmly established and the Sun finally ceased to be a planet and the Earth finally became one. Around the same time astronomers became convinced that the Sun was actually one of the ‘fixed’ stars.

We entered the eighteenth century with six planets, Mercury, Venus, Earth, Mars, Jupiter and Saturn and so it remained until the musician and amateur astronomer William Herschel shocked the world with the discovery of a seventh one, Uranus on 13 March 1781. The first new planet discovered in about four thousand years of planetary astronomy.

William Herschel. Portrait by Lemuel Francis Abbott 1785, National Portrait Gallery, London
Source: Wikimedia Commons

In the middle of the eighteenth century Johann Elert Bode published what is now know as the Titus-Bode law in which the distance of the planets from the sun seemed to fit an arithmetical series with a gap in the series between Mars and Jupiter. Herschel’s discovery of Uranus beyond Saturn fit the Titus-Bode series, which led the German astronomer Baron Franz Xaver von Zach to organise a systematic search for that ‘missing planet’ between Mars and Jupiter. In fact the discovery was made by the Italian astronomer Giuseppe Piazzi, who was not part of Zach’s search team but discovered Ceres on 1 January 1801, exactly, where it should be according to the Titus-Bode law and then there were eight. Interestingly Piazzi lost Ceres and Carl Friedrich Gauss developed a new method of determining planetary orbits, which allowed astronomers to find it again. Very soon other astronomers discovered Pallas, Juno and Vesta and there were now eleven planets. It was not long before it became clear that the four new celestial bodies were somehow different to the other planets and Herschel coined the term ἀστεροειδής, or asteroeidēs, meaning ‘star-like, star-shaped’, in English asteroid. These smaller wanderers were also known as minor planets or planetoids although it was first in the later nineteenth century, by which time several more asteroids had been discovered that these terms became established and the number of planets was once again reduced, not to seven but to eight!

Piazzi’s book “Della scoperta del nuovo pianeta Cerere Ferdinandea” outlining the discovery of Ceres, dedicated the new “planet” to Ferdinand I of the Two Sicilies.
Source: Wikimedia Commons

It was eight because in the mean time both the English astronomer John Crouch Adams and the French astronomer Urbain Le Verrier had predicted the existence of an eighth planet based on gravitational anomalies in the orbit of Uranus and on 23 September 1846 the German observational astronomer discovered Neptune, the eighth planet, based on the predictions of Le Verrier.

Urbain Le Verrier
Source: Wikimedia Commons

In the late nineteenth century similar anomalies in the orbit of Neptune led Percival Lowell to predict the existence of a ninth planet and he set up his own observatory to search for it. In 1916 Lowell died without having found his predicted planet. However in 1929/30 the young Clyde Tombaugh discovered Pluto, the ninth planet.

From: O’Hara, Elva R. (2006). Clyde W. Tombaugh: Farm Boy Reached for the Stars. Borderlands 25.
Source: Wikimedia Commons

As with Ceres and the asteroids Pluto’s planetary status was challenged by the discovery of other orbiting objects in the Kuiper belt outside of the orbit of Neptune from the 1990s onward. The discovery of Eris in 2005 led to a serious reconsideration of Pluto’s planetary status and famously in 2006 the International Astronomical Union introduced a new formal definition of the term planet, which removed Pluto’s planetary status and according to Pluto’s fans demoted it to the status of a dwarf planet. At the moment there are five recognised dwarf planets Pluto, Ceres (the largest asteroid), Haumea, Makemake and Eris.

Eris (center) and Dysnomia (left of center), taken by the Hubble Space Telescope
Image NASA
Source: Wikimedia Commons

As I said at the beginning the Pluto fan club has not given up the fight and are now proposing a new definition of the term planet, which would not only return Pluto to its planetary status but also apparently the Moon. I hope I have shown that the term planet has gone through quite a lot of changes over the last two and a half thousand years or so since the ancient Greeks first coined it and we can, I think, assume that it will go through quite a few more in the future in particular with respect to the thousands of exoplanets that astronomers are busy discovering.


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

Why Mathematicus?

“The Renaissance Mathematiwot?”

“Mathematicus, it’s the Latin root of the word mathematician.”

“Then why can’t you just write The Renaissance Mathematician instead of showing off and confusing people?”

“Because a mathematicus is not the same as a mathematician.”

“But you just said…”

“Words evolve over time and change their meanings, what we now understand as the occupational profile of a mathematician has some things in common with the occupational profile of a Renaissance mathematicus but an awful lot more that isn’t. I will attempt to explain.”

The word mathematician actually has its origins in the Greek word mathema, which literally meant ‘that which is learnt’, and came to mean knowledge in general or more specifically scientific knowledge or mathematical knowledge. In the Hellenistic period, when Latin became the lingua franca, so to speak, the knowledge most associated with the word mathematica was astrological knowledge. In fact the terms for the professors[1] of such knowledge, mathematicus and astrologus, were synonymous. This led to the famous historical error that St. Augustine rejected mathematics, whereas his notorious attack on the mathematici[2] was launched not against mathematicians, as we understand the term, but against astrologers.

The earliest known portrait of Saint Augustine in a 6th-century fresco, Lateran, Rome Source: Wikimedia Commons

The earliest known portrait of Saint Augustine in a 6th-century fresco, Lateran, Rome
Source: Wikimedia Commons

However St. Augustine lived in North Africa in the fourth century CE and we are concerned with the European Renaissance, which, for the purposes of this post we will define as being from roughly 1400 to 1650 CE.

The Renaissance was a period of strong revival for Greek astrology and the two hundred and fifty years that I have bracketed have been called the golden age of astrology and the principle occupation of our mathematicus is still very much the casting and interpretation of horoscopes. Mathematics had played a very minor role at the medieval universities but the Renaissance humanist universities of Northern Italy and Krakow in Poland introduced dedicated chairs for mathematics in the early fifteenth century, which were in fact chairs for astrology, whose occupants were expected to teach astrology to the medical students for their astro-medicine or as it was known iatro-mathematics. All Renaissance professors of mathematics down to and including Galileo were expected to and did teach astrology.

A Renaissance Horoscope Kepler's Horoskop für Wallenstein Source: Wikimedia Commons

A Renaissance Horoscope
Kepler’s Horoskop für Wallenstein
Source: Wikimedia Commons

Of course, to teach astrology they also had to practice and teach astronomy, which in turn required the basics of mathematics – arithmetic, geometry and trigonometry – which is what our mathematicus has in common with the modern mathematician. Throughout this period the terms Astrologus, astronomus and mathematicus – astrologer, astronomer and mathematician ­– were synonymous.

A Renaissance mathematicus was not just required to be an astronomer but to quantify and describe the entire cosmos making him a cosmographer i.e. a geographer and cartographer as well as astronomer. A Renaissance geographer/cartographer also covered much that we would now consider to be history, rather than geography.

The Renaissance mathematicus was also in general expected to produce the tools of his trade meaning conceiving, designing and manufacturing or having manufactured the mathematical instruments needed for astronomer, surveying and cartography. Many were not just cartographers but also globe makers.

Many Renaissance mathematici earned their living outside of the universities. Most of these worked at courts both secular and clerical. Here once again their primary function was usually court astrologer but they were expected to fulfil any functions considered to fall within the scope of the mathematical science much of which we would see as assignments for architects and/or engineers rather than mathematicians. Like their university colleagues they were also instrument makers a principle function being horologist, i.e. clock maker, which mostly meant the design and construction of sundials.

If we pull all of this together our Renaissance mathematicus is an astrologer, astronomer, mathematician, geographer, cartographer, surveyor, architect, engineer, instrument designer and maker, and globe maker. This long list of functions with its strong emphasis on practical applications of knowledge means that it is common historical practice to refer to Renaissance mathematici as mathematical practitioners rather than mathematicians.

This very wide range of functions fulfilled by a Renaissance mathematicus leads to a common historiographical problem in the history of Renaissance mathematics, which I will explain with reference to one of my favourite Renaissance mathematici, Johannes Schöner.

Joan Schonerus Mathematicus Source: Wikimedia Commons

Joan Schonerus Mathematicus
Source: Wikimedia Commons

Schöner who was a school professor of mathematics for twenty years was an astrologer, astronomer, geographer, cartographer, instrument maker, globe maker, textbook author, and mathematical editor and like many other mathematici such as Peter Apian, Gemma Frisius, Oronce Fine and Gerard Mercator, he regarded all of his activities as different aspects or facets of one single discipline, mathematica. From the modern standpoint almost all of activities represent a separate discipline each of which has its own discipline historians, this means that our historical picture of Schöner is a very fragmented one.

Because he produced no original mathematics historians of mathematics tend to ignore him and although they should really be looking at how the discipline evolved in this period, many just spring over it. Historians of astronomy treat him as a minor figure, whilst ignoring his astrology although it was this that played the major role in his relationship to Rheticus and thus to the publication of Copernicus’ De revolutionibus. For historians of astrology, Schöner is a major figure in Renaissance astrology although a major study of his role and influence in the discipline still has to be written. Historians of geography tend to leave him to the historians of cartography, these whilst using the maps on his globes for their studies ignore his role in the history of globe making whilst doing so. For the historians of globe making, and yes it really is a separate discipline, Schöner is a central and highly significant figure as the founder of the long tradition of printed globe pairs but they don’t tend to look outside of their own discipline to see how his globe making fits together with his other activities. I’m still looking for a serious study of his activities as an instrument maker. There is also, as far as I know no real comprehensive study of his role as textbook author and editor, areas that tend to be the neglected stepchildren of the histories of science and technology. What is glaringly missing is a historiographical approach that treats the work of Schöner or of the Renaissance mathematici as an integrated coherent whole.

Western hemisphere of the Schöner globe from 1520. Source: Wikimedia Commons

Western hemisphere of the Schöner globe from 1520.
Source: Wikimedia Commons

The world of this blog is at its core the world of the Renaissance mathematici and thus we are the Renaissance Mathematicus and not the Renaissance Mathematician.

[1] That is professor in its original meaning donated somebody who claims to possessing a particular area of knowledge.

[2] Augustinus De Genesi ad Litteram,

Quapropter bono christiano, sive mathematici, sive quilibet impie divinantium, maxime dicentes vera, cavendi sunt, ne consortio daemoniorum animam deceptam, pacto quodam societatis irretiant. II, xvii, 37


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

Another public service announcement

Marius Book Launch

In September 2014 a conference was held in Nürnberg, as the climax of a year dedicated to celebrating the life and work of the Franconian astronomer, astrologer and mathematician Simon Marius, whose magnum opus Mundus Iovialis was published four hundred years earlier in 1614.

The papers held at that conference together with some other contributions from people who could not attend in person have now been collected together in the book Simon Marius und Seine Forschung, eds. Hans Gaab and Pierre Leich (= Acta Historica Astronomiae, Band 57) which will be official launched in the Thalia bookshop in Nürnberg on this coming Thursday, 13 October at 18:30 MET.

This volume contains papers by a wide range of scholars and could/should be of interest to anybody studying the histories of astronomy, astrology and/or mathematics in the Early Modern Period. It can be purchased online, after Thursday, directly from the publishers, Leipziger Universitätsverlag


For those who would like to know more about the book including a table of contents (Inhaltsverzeichnis) they can inform themselves on the Marius Portal here.

For those who cannot read German, an English edition of the book is in planning for next year, for which further contributions on the life and work of Simon Marius would also be welcome. If anybody has any questions regarding this volume I would be happy to answer them.


P.S. For those waiting for blogging to resume here at the Renaissance Mathematicus I can report that there is light at the end of the tunnel!





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