Category Archives: History of Astronomy

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

Christmas Trilogy 2017 Part 1: Isaac the Imperator

Isaac Newton came from a fairly humble although not poor background. His father was a yeoman farmer in Lincolnshire, who unfortunately died before he was born. A yeoman farmer owned his own land and in fact the Newton’s were the occupants of the manor house of Woolsthorpe-by-Colsterworth.

Woolsthorpe Manor, Woolsthorpe-by-Colsterworth, Lincolnshire, England. This house was the birthplace and the family home of Isaac Newton.
Source: Wikimedia Commons

Destined to become a farmer until he displayed little aptitude for life on the land, his mother was persuaded by the local grammar school master to let him complete his education and he was duly dispatched off to Cambridge University in 1661. Although anything but poor, when Newton inherited the family estates they generated an income of £600 per annum, at a time when the Astronomer Royal received an income of £100 per annum, his mother enrolled him at Cambridge as a subsizar, that is a student who earned his tuition by working as a servant. I personally think this reflects the family’s puritan background rather than any meanness on the mother’s part.

In 1664 Newton received a scholarship at Trinity and in 1667 he became a fellow of the college. In 1669 he was appointed Lucasian professor of mathematics. Cambridge was in those days a small market town and a bit of a backwater. The university did not enjoy a good reputation and the Lucasian professorship even less of one. Newton lived in chambers in Trinity College and it was certainly anything but a life of luxury.

Trinity College Great Court
Source: Wikimedia Commons

There is an amusing anecdote about David Hilbert writing to the authorities of Trinity at the beginning of the twentieth century to complain about the fact that Godfrey Hardy, whom he regarded as one of the greatest living mathematicians, was living in what he regarded as a squalid room without running water or adequate heating. What Hilbert didn’t realise was that Hardy would never give up this room because it was the one that Newton had inhabited.

Newton remained an obscure and withdrawn Cambridge don until he presented the Royal Society with his reflecting telescope and published his first paper on optics in 1672. Although it established his reputation, Newton was anything but happy about the negative reactions to his work and withdrew even further into his shell. He only re-emerged in 1687 and then with a real bombshell his Philosophiæ Naturalis Principia Mathematica, which effectively established him overnight as Europe’s leading natural philosopher, even if several of his major competitors rejected his gravitational hypothesis of action at a distance.

Having gained fame as a natural philosopher Newton, seemingly having tired of the provinces, began to crave more worldly recognition and started to petition his friends to help him find some sort of appropriate position in London. His lobbying efforts were rewarded in 1696 when his friend and ex-student, Charles Montagu, 1st Earl of Halifax, had him appointed to the political sinecure, Warden of the Mint.

Newton was no longer a mere university professor but occupant of one of the most important political sinecures in London. He was also a close friend of Charles Montagu one of the most influential political figures in England. By the time Montagu fell from grace Newton was so well established that it had little effect on his own standing. Although Montagu’s political opponents tried to bribe him to give up his, now, Mastership of the Mint he remained steadfast and his fame was such that there was nothing they could do to remove him from office. They wanted to give the post to one of their own. Newton ruled the Mint with an iron hand like a despot and it was not only here that the humble Lincolnshire farm lad had given way to man of a completely different nature.

As a scholar, Newton held court in the fashionable London coffee houses, surrounded by his acolytes, for whom the term Newtonians was originally minted, handing out unpublished manuscripts to the favoured few for their perusal and edification. Here he was king of the roost and all of London’s intellectual society knew it.

He became President of the Royal Society in 1703 and here with time his new personality came to the fore. When he became president the society had for many years been served by absentee presidents, office holders in name only, and the power in the society lay not with the president but with the secretary. When Newton was elected president, Hans Sloane was secretary and had already been so for ten years and he was not about to give up his power to Newton. There then followed a power struggle, mostly behind closed doors, until Newton succeeded in gaining power in about 1610 1710, Sloane, defeated resigned from office in 1613 1713 but got his revenge by being elected president on Newton’s death. Now Newton let himself be almost literally enthroned as ruler of the Royal Society.

Isaac Newton’s portrait as Royal Society President Charles Jervas 1717
Source: Royal Society

The president of the society sat at table on a raised platform and on 20 January 1711 the following Order of the Council was made and read to the members at the next meeting.

That no Body Sit at the Table but the President at the head and the two Secretaries towards the lower end one on the one Side and the other Except Some very Honoured Stranger, at the discretion of the President.

When the society was first given its royal charter in 1660, although Charles II gave them no money he did give them an old royal mace as a symbol of their royal status. Newton established the custom that the mace was only displayed on the table when the president was in the chair. When Sloane became president his first act was to decree that the mace was to be displayed at all meetings, whether the president was present or not. Newton ruled over the meetings with the same iron hand with which he ruled over the Mint. Meeting were conducted solemnly with no chit chat or other disturbances as William Stukeley put it:

Indeed his presence created a natural awe in the assembly; they appear’d truly as a venerable consessus Naturae Consliariorum without any levity or indecorum.

Perhaps Newton’s view of himself in his London years in best reflected in his private habitat. Having lived the life of a bachelor scholar in college chambers for twenty odd years he now obtained a town house in London. He installed his niece Catherine Barton, who became a famous society beauty, as his housekeeper and lived the life of a London gentleman, albeit a fairly quiet one. However his personal furnishings seem to me to speak volumes about how he now viewed himself. When he died an inventory of his personal possessions was made for the purpose of valuation, as part of his testament. On the whole his household goods were ordinary enough with one notable exception. He possessed crimson draperies, a crimson mohair bed with crimson curtains, crimson hangings, a crimson settee. Crimson was the only colour mentioned in the inventory. He lived in an atmosphere of crimson. Crimson is of course the colour of emperors, of kings, of potentates and of cardinals. Did the good Isaac see himself as an imperator in his later life?


All the quotes in this post are taken from Richard S, Westfall’s excellent Newton biography Never at Rest.




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

Not a student god dammit!

14th December was the anniversary of Tycho Brahe’s birthday and as is now usual on such occasions various people, including me, posted their Tycho scribblings on Twitter, Facebook et. al.

Source: Wikimedia Commons

As is also, unfortunately, usual several of them referred to Johannes Kepler either as Tycho’s pupil or student.

Kepler Memorial at his birthplace Weil der Stadt
Source: Wikimedia Commons

Now, both on Hven and later in Prague, Tycho ran what has been called a large scale research centre employing, over the almost thirty years he collected astronomical data in a systematic programme, a fairly large number of observational assistants. Some of these came to work with the noble Dane as experienced astronomical observers; others came to learn from him. Some of those who came to learn only stayed for a short period and having learnt returned home, some having learnt stayed and worked for a time as assistants. These can justifiably called pupils or students. For example,  Simon Marius, whom I have blogged about on several occasions came to Prague as a student for a few months in 1601, shortly before Tycho’s death, and returned home relatively quickly.

Simon Marius
Source: Wikimedia Commons

The great Dutch cartographer Willem Janszoon Blaeu visited Tycho on Hven for six months in 1595-6 both learning and contributing. He took Tycho’s star catalogue, in the form from a simple celestial globe with him when he left to start his own celestial globe production.

Willem Janszoon Blaeu
Source: Wikimedia Commons

Kepler’s presence in Prague was of a completely different nature. A graduate of the University of Tübingen, he had already worked as a maths teacher and district mathematicus in Graz for six years before he moved to Prague to work with Tycho. He had in 1596 already published his first volume of astronomical speculations, Mysterium Cosmographicum, and it was this that attracted Tycho’s attention in the job seeking German scholar. Kepler’s bizarre cosmological speculations were of less interest to Tycho than Kepler’s very obvious mathematical abilities.

Tycho didn’t take on Kepler as a pupil or student to learn the trade of astronomical observer, for which he would have been fairly useless having suffered from a visual defect since a childhood illness, but as a mathematician to reduce Tycho’s observational data to ephemerides, the practical tables of planetary positions used by cartographers, navigators and astrologers. The production of ephemerides was the principle function of astronomy from antiquity down to the seventeenth century. Tycho didn’t even employ Kepler himself but secured him a position at the court of Rudolph II, employed specifically to produce those ephemerides. Kepler was not Tycho’s pupil or student but his astronomical colleague at court, which is the principle reason why he succeeded him as Imperial Mathematicus. By the way, it took him tweet-six to produce those ephemerides, The Rudolphine Tables, complaining often over the years how tedious the task was. They were, because of their level of accuracies, however the principle reason why people began to accept the heliocentric system over the geocentric and helio-geocentric ones, so it was a well spent twenty-six years.

Monument of Tycho Brahe and Johannes Kepler in Prague
Source: Wikimedia Commons






Filed under History of Astronomy, Myths of Science

Observing for the long haul

The website Atlas Obscura has a rather interesting blog post about a virtually unknown Japanese amateur astronomer, Hisako Koyama (1916–??), who specialised in observing sunspots: How an Amateur Astronomer Became One of History’s Greatest Solar Observers

Koyama used the same Nikon 20-cm telescope, gifted to her by her father in her 20s, throughout the course of her life to create more than 10,000 sunspot sketches. //Kawade Shobo Shinsha Publishers


The largest sunspot of the 20th century, drawn by Koyama on April 5, 1947. HISAKO KOYAMA/NATIONAL MUSEUM OF NATURE AND SCIENCE

I enjoyed reading this post until I stumbled across the following sentence:

Her daily observations of the Sun’s dark spots, drawn by hand, are one of the most rigorous and valuable records of solar activity ever made, and put her alongside Galileo as a careful, dedicated observer of celestial spheres.

Why the comparison with Galileo? He was indeed a careful and very perceptive observer but his dedication to observational astronomy can be seriously questioned. The contents of his Sidereus Nuncius were the result of observations undertaken from late 1609 until spring 1610. Having published his observations and having used that publication to obtain a cushy position as court mathematicus and philosophicus in Florence, Galileo’s interest in serious observational astronomy declined substantially. He was always prepared to demonstrate his telescopes to persons of influence but his further contributions to astronomical research were more than somewhat limited. He went into battle on several fronts, claiming priority for himself on the discovery of sunspots and the phases of Venus but these were not unique discoveries and his priority claims were at best dubious. He did spend some time trying to improve his observations of the orbits of the moons of Jupiter, in order to use them as a clock to determine longitude. However, he never completed this task, leaving it, so to speak, to Cassini to complete much later in the seventeenth century. By late 1613 he had effectively given up observational astronomy altogether. Here his dedication to the discipline is being used as a yardstick for a woman who devoted forty years of her life to observing the sun, couldn’t the author of the piece find a better famous astronomer for the comparison?

Staying in the Early Modern Period, but going back before the invention of the telescope, our first candidate could and should be William IV Landgrave of Hessen-Kassel (1532–1592).


William IV of Hessen Kassel
Source: Wikimedia Commons

In 1560 William establish the first modern observatory in Europe. With a varying team of astronomers, most notably Christoph Rothmann (between 1550 and 1560–probably 1600) and Jost Bürgi (1552–1632), he carried out an intensive programme of celestial observations until his death in 1592. This programme produced a highly accurate catalogue of almost four hundred star positions, as well as accurate determinations of the planetary orbits. One person who was much influenced by William pioneering work was our next candidate, Tycho Brahe. William who was related to the Danish king, Friedrich II, was instrumental in convincing his relative to finance Tycho’s observatory on the island of Hven. Tycho armed with financial resources others could only dream of and supported by a comparatively large force of assistants, who he trained himself, devoted almost thirty years to observational astronomy. He created a catalogued of over seven hundred star positions measured with an accuracy unknown before, as well as years worth of highly accurate observations of the planetary orbits; data from which Johannes Kepler would go on to determine that the planets orbit the sun on ellipses and not circles.

1586 portrait of Tycho Brahe framed by the family shields of his noble ancestors, by Jacques de Gheyn.
Source: Wikimedia Commons

Moving on past Galileo we come to Giovanni Domenico Cassini (1625–1712) the real founder of telescopic astronomy, who devoted sixty-four years of his life to setting new standards of observational accuracy in astronomy, making many important discoveries along the way.

Giovanni Domenico Cassini
Source: Wikimedia Commons

Cassini’s near contemporary Johannes Hevelius (1611–1687), a true amateur astronomer, devoted thirty-eight years of his life and a large part of the fortune he made as a beer brewer to an extensive programme of astronomical observations, producing amongst other things the most detailed and accurate map of the moon in the 17th century.

Johannes Hevelius by Daniel Schultz
Source: Wikimedia Commons

England’s first Astronomer Royal, John Flamsteed (1646–1719), carried out a forty-three year programme of observations at a level of accuracy several factors higher than his predecessors to produce a new star catalogue of 3000 star positions. Amongst his many other achievements, he was the first to suggest that a second comet observed in winter 1680 was in fact the first comet going back to whence it came having orbited the sun. This realisation led Newton to include the orbits of comets in his considerations of universal gravity and Halley to do the historical research that led to his determining the orbital period of the comet that bears his name.

John Flamsteed by Godfrey Kneller, 1702
Source: Wikimedia Commons

Flamsteed House in 1824
Royal Observatory Greenwich
Source: Wikimedia Commons

Moving on into the eighteenth century we arrive at another great amateur, William Herschel (1738–1822) who, together with his sister Caroline (1750–1848) devoted nearly thirty years to the study of the heavens. As well as their famous discovery of the planet Uranus, they were pioneers in deep space astronomy, a discipline that would eventually lead to the discoveries of other galaxies beyond our own. Caroline would go on to make important astronomical discoveries of her own, as well as writing and editing the catalogues of deep space objects they had recorded.

Lithograph of Caroline Herschel, 1847
Source: Wikimedia Commons

William Herschel by Lemuel Francis,Abbott,1785
Source: Wikimedia Commons

All of the astronomers I have listed would make for better comparisons to the dedication of Hisako Koyama than Galileo and the first impression is that the author is just being lazy, “who’s an astronomer from history that everybody has heard of?” “Oh! I know Galileo, I’ll use him.” However it could be that she used him because Hisako Koyamma specialised in observing sunspots and Galileo was one of the first astronomers to observe sunspots with a telescope. He even got into a notorious dispute with the Jesuit astronomer Christoph Scheiner (1573–1650) over who first observed them and what they were. Galileo, rather shabbily, keep changing the date of his supposed first observation in order to claim priority.

All in vain as the first observations were made by Thomas Harriot (c. 1560–1621) and the first publication of sunspot observations was from Johannes Fabricius (1587–1616).


Portrait often claimed to be Thomas Harriot (1602), which hangs in Oriel College, Oxford. Source: Wikimedia Commons

Galileo won the dispute with Scheiner over the nature of sunspots demonstrating them to be on the sun’s surface and not orbiting it as Scheiner first proposed. Scheiner graciously acknowledged that Galileo was right and he was wrong but this did not stop Galileo falsely accusing Scheiner of plagiarism in his Il Saggiatore (1623) and then publishing some of Scheiner’s observations as his own in his Dialogo (1632).

Christoph Schiene
Source: Wikimedia Commons

Whereas Galileo only observed the sunspots for a brief period around 1613, Scheiner devoted many patient years to observing the sun publishing his observations in his Rosa Ursina sive Sol (1626–1630). Scheiner’s book remained the definitive work on solar astronomy until the nineteenth century so probably he would have been the best historical comparison for Hisako Koyama’s achievements.

Depiction of sunspot
from Scheiner’s Rosa Ursina
Source: Wikimedia Commons

1 Comment

Filed under History of Astronomy, History of science

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

Did Isaac leap or was he pushed?

In 2016 2017 it would not be too much to expect a professor of philosophy at an American university to have a working knowledge of the evolution of science in the seventeenth century, particularly given that said evolution had a massive impact on the historical evolution of philosophy. One might excuse a freshly baked adjunct professor at a small liberal arts college, in his first year, if they were not au fait with the minutiae of the history of seventeenth-century astronomy but one would expect better from an established and acknowledged expert. Andrew Janiak is just that, an established and acknowledged expert. Creed C. Black Professor of Philosophy and Chair of Department at Duke University; according to Wikipedia, “Duke is consistently included among the best universities in the world by numerous university rankings”. Janiak is also an acknowledge expert on Isaac Newton and author of Isaac Newton in the Blackwell Great Minds series, so one is all the more dumbfounded to read the following in his article entitled Newton’s Leap on the Institute of Arts and Ideas: Philosophy for our times website:


Isaac Newton 1677 after Peter Lely Source: Wikimedia Commons Comment from CJ Schilt (a Newton expert) on Facebook: On another note, that picture is probably not Newton, despite what Finegold thinks.


But wait a minute: what could be more amazing than a young man discovering a fundamental force of nature while sitting under a tree? For starters, we have to recognize how foreign Newton’s ultimate idea about gravity was to philosophers, astronomers and mathematicians in the era of the Scientific Revolution. Newton provided an answer to a question that hadn’t even been asked yet. The problem with understanding the distant past is that we take our twenty-first century ideas and attitudes for granted. We think, for example, that the following is obvious: if the planets, like the Earth and Jupiter, regularly orbit the Sun, there must be something that causes them to follow their orbits. After all, if nothing caused them to orbit the Sun, they would fly off into deep space. [my emphasis]That seems so obvious to us, it’s hard to imagine that for centuries, the world’s leading thinkers, from Aristotle to Ptolemy and onwards, did not have that idea at all. Instead, for many generations, leading philosophers and mathematicians thought this: the circle is a perfect mathematical form, and the planetary orbits are circular, so they are ever-lasting aspects of the natural world. To them, the orbits were so perfect that nothing caused them to occur. They simply were. [my emphasis] The question of what caused the planetary orbits was not even on the table for astronomers in those days. [my emphasis] Down on earth, apples fell from trees throughout history just as they do now. But philosophers and mathematicians didn’t have any reason to think that whatever causes apples to fall to the ground might somehow be connected to anything going on in the heavens. After all, the heavens were thought to be the home of everlasting motions, of perfect circles, and were therefore nothing like the constantly changing, messy world down below, where worms eat through apples as they rot on the ground.

So what is wrong with this piece of #histSTM prose? Let us start with the second of my bold emphasised segments:

Instead, for many generations, leading philosophers and mathematicians thought this: the circle is a perfect mathematical form, and the planetary orbits are circular, so they are ever-lasting aspects of the natural world. To them, the orbits were so perfect that nothing caused them to occur. They simply were.

Whilst it is true that, following Empedocles, Western culture adopted the so-called Platonic axioms, which stated that celestial motion was uniform and circular, it is not true that they claimed this motion to be without cause. Aristotle, whose system became dominant for a time in the Middle Ages, hypothesised a system of nested crystalline spheres, which working from the outside to the centre drove each other through direct contact; a system that probably would not have worked due to friction. His outer-most sphere was moved by the unmoved mover, who remained unnamed, making the theory very attractive for Christian theologians in the High Middle Ages, who simple called the unmoved mover God. Interestingly the expression love makes the world go round originates in the Aristotelian belief that that driving force was love. In the Middle Ages we also find the beliefs that each of the heavenly bodies has a soul, which propels it through space or alternatively an angel pushing it around its orbit.

All of this is all well and good but of course doesn’t have any real relevance for Newton because by the time he came on the scene the Platonic axioms were well and truly dead, killed off by one Johannes Kepler. You might have heard of him? Kepler published the first two of his planetary laws, number one: that the planetary orbits are ellipses and that the sun is at one focus of the ellipse and number two: that a line connecting the sun to the planet sweeps out equal areas in equal time periods in 1609, that’s thirty-three years before Newton was born. Somewhat later Cassini proved with the support of his teachers, Riccioli and Grimaldi, using a heliometer they had constructed in the San Petronio Basilica in Bologna, that the earth’s orbit around the sun or the sun’s around the earth, (the method couldn’t decide which) was definitely elliptical.

Part of the San Petronio Basilica heliometer.
The meridian line sundial inscribed on the floor at the San Petronio Basilica in Bologna, Emilia Romagna, northern Italy. An image of the Sun produced by a pinhole gnomon in the churches vaults 66.8 meters (219 ft) away fills this 168×64 cm oval at noon on the winter solstice.
Source Wikimedia Commons

By the time Newton became interested in astronomy it was accepted by all that the planetary orbits were Keplerian ellipses and not circles. Kepler’s first and third laws were accepted almost immediately being based on observation and solid mathematics but law two remained contentious until about 1670, when it was newly derived by Nicholas Mercator. The dispute over alternatives to Kepler’s second law between Ismaël Boulliau and Seth Ward was almost certainly Newton’s introduction to Kepler’s theories.

Turning to the other two bold emphasised claims we have:

 Newton provided an answer to a question that hadn’t even been asked yet. The problem with understanding the distant past is that we take our twenty-first century ideas and attitudes for granted. We think, for example, that the following is obvious: if the planets, like the Earth and Jupiter, regularly orbit the Sun, there must be something that causes them to follow their orbits. After all, if nothing caused them to orbit the Sun, they would fly off into deep space.


The question of what caused the planetary orbits was not even on the table for astronomers in those days.

I’m afraid that Herr Kepler would disagree rather strongly with these claims. Not only had he asked this question he had also supplied a fairly ingenious and complex answer to it. Also quite famously his teacher Michael Maestlin rebuked him quite strongly for having done so. Kepler is usually credited with being the first to reject vitalist explanations of planetary motion by souls, spirits or angels (anima) and suggest instead a non-vitalist force (vir). His theory, based on the magnetic theories of Gilbert, was some sort of magnetic attraction emanating from the sun that weakened the further out it got. Kepler’s work started a debate that wound its way through the seventeenth century.

Ismaël Boulliau, a Keplerian, in his Astronomia philolaica from 1645 discussed Kepler’s theory of planetary force, which he rejected but added that if it did exist it would be an inverse-square law in analogy to Kepler’s law of the propagation of light. Newton was well aware of Boulliau’s suggestion of an inverse-square law. In 1666 Giovanni Alfonso Borelli, a disciple of Galileo, published his Theoricae Mediceorum planetarum ex causis physicis deductae in which he suggested that planetary motion was the result of three forces.

Famously in 1684 in a London coffee house Christopher Wren posed the question to Robert Hooke and Edmond Halley, if the force driving the planets was an inverse-square force would the orbits be Keplerian ellipses, offering a book token as prize to the first one to solve the problem. This, as is well known, led to Halley asking Newton who answered in the positive and wrote his Principia to prove it; in the Principia Newton shows that he is fully aware of both Kepler’s and Borelli’s work on the subject. What Newton deliberately left out of the Principia is that in an earlier exchange it had in fact been Hooke who first posited a universal force of gravity.

As this all too brief survey of the history shows, far from Newton providing an answer to a question that hadn’t been asked yet, he was, so to speak, a Johnny-come-lately to a debate that when he added his contribution was already eighty years old.

The Institute of Arts and Ideas advertises itself as follows:

So the IAI seeks to challenge the notion that our present accepted wisdom is the truth. It aims to uncover the flaws and limitations in our current thinking in search of alternative and better ways to hold the world.

Personally I don’t see how having a leading philosopher of science propagating the lone genius myth by spouting crap about the history of science fulfils that aim.







Filed under History of Astronomy, History of science, Myths of Science, Newton

Galileo, The Church and that ban

Quite Interesting @qikipedia is the Twitter account of the highly successful British television comedy panel game QI (Quite Interesting). For those who are not aficionados of this piece of modern television culture it is described on Wikipedia thus:

The format of the show focuses on Davies and three other guest panelists answering questions that are extremely obscure, making it unlikely that the correct answer will be given. To compensate, the panelists are awarded points not only for the right answer, but also for interesting ones, regardless of whether they are right or even relate to the original question, while points are deducted for “answers which are not only wrong, but pathetically obvious”– typically answers that are generally believed to be true but in fact are misconceptions. These answers, referred to as “forfeits”, are usually indicated by a loud klaxon and alarm bell, flashing lights, and the incorrect answer being flashed on the video screens behind the panelists. [my emphasis]

Given the section that I have highlighted above the Twitter account should have points deducted to the sounds of a loud klaxon and an alarm bell accompanied by flashing lights for having tweeted the following on 12 September

It wasn’t until 1992 that the Catholic Church finally admitted that Galileo’s views on the solar system were correct – @qikipedia

Portrait of Galileo that accompanied the @qikipedia tweet


This is of course complete rubbish. In what follows I will give a brief summary of the Catholic Church’s ban on heliocentrism, as propagated by Galileo amongst others.

The initial ban on propagating heliocentrism as a proven theory, one could still present it as a hypothetical one, was issued by the Inquisition in 1616. Interestingly whilst the books of Kepler and Maestlin, for example, were placed on the Index of Forbidden Books, Copernicus’ De revolutionibus was not but merely banned temporarily until corrected, which took place surprisingly rapidly; correction meaning the removal of the very few passages where heliocentricity is presented as a fact. By 1621 De revolutionibus was back in circulation for Catholic astronomers. Galileo’s Dialogo was placed on the Index following his trial in 1632.

A title page of the Index of Forbidden Books 1758
Source: Linda Hall Library

Books openly espousing heliocentricity as a true fact, which was more that the science of the time could deliver, were placed on the Index by the Catholic Church, so all good Catholics immediately dropped the subject? Well no actually. The ban had surprising little effect outside of Italy. Within Italy, astronomers kept their heads below the parapet for a couple of decades but outside of Italy things were very different. Protestant countries, naturally, totally ignored the ban and even astronomers in Catholic countries on the whole took very little notice of it. The one notable exception was René Descartes who dropped plans to publish his book Le Monde, ou Traite de la lumiere in 1633, which contained his views supporting heliocentricity, the full text only appearing posthumously in 1677. Quite why he did so was not very clear but it is thought that he did it out of respect to his Jesuit teachers. However, Descartes remained the exception. Galileo’s offending Dialogo quickly appeared in a ‘pirate’ edition, translated into Latin in the Netherlands, where later his Discorsi, would also be published. I say pirate but Galileo was well aware of the publication, which had his blessing, but officially knew nothing about it.

Title page of the 1635 ‘pirate’ Latin edition of Dialogo
Source: The History of Science Collections of the University of Oklahoma Libraries

Within Italy once the dust had settled Catholic astronomers began to publish books on heliocentricity that opened with some sort of nod in the direction of the Church along the lines of, “The Holy Mother Church has in its wisdom condemned heliocentricity as contrary to Holy Scripture…” but then continued something like this “…however it is an interesting hypothetical mathematical model, which we will now discuss.” This face saving trick was accepted by the Church and everybody was happy. By the early eighteenth century almost all astronomers in Italy, with the exception of some Jesuits, were following this course.

In 1758 the ball game changed again as the then Pope basically dropped the ban on heliocentricity, although this was done informally and the formal prohibition stayed in place. The publication of a complete works of Galileo was even permitted with a suitable preface to the Dialogo pointing out its faults. From this time on Catholic astronomers were quite free to propagate a factual heliocentricity in their publications.

This was the situation up till 1820 when an over zealous Master of the Sacred Palace (the Church’s chief censor), Fillipo Anfossi, refused to licence a book containing a factual account of heliocentricity by Giuseppe Settele. Settele appealed directly to the Pope and after deliberations the ban on heliocentricity was formally lifted by the Church in 1821. The next edition of the Index, which didn’t appear until 1835, no longer contained books on heliocentricity. Anfossi and Settele only feature in the history of science because of this incidence.

So to summarise, the Church only banned factual claims for the heliocentric system but not hypothetical statements about it, so this is how Catholic astronomer got around the ban. In 1758 the Pope informally lifted the ban clearing the way for Catholic astronomers to write freely about it. In 1821 the ban was formally lifted and in 1835 books on heliocentricity were removed from the Index, so where did QI get their date of 1992 from?

In 1981 the Church constituted the Pontifical Interdisciplinary Study Commission to re-examine the Galileo trial, which came to rather wishy-washy conclusions. In 1992 the Pope held a speech formally closing the commission and saying that the whole affair had been rather unfortunate and that the Church had been probably wrong to prosecute Galileo.






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