Category Archives: History of Astronomy

Who cares about facts? – Make up your own, it’s much more fun!

Math Horizons is a magazine published by Taylor & Francis for the Mathematical Association of America aimed at undergraduates interested in mathematics: It publishes expository articles about “beautiful mathematics” as well as articles about the culture of mathematics covering mathematical people, institutions, humor, games, cartoons, and book reviews. (Description taken from Wikipedia, which attributes it to the Math Horizons instructions for authors January 3 2009). Apparently, however, authors are not expected to adhere to historical facts, they can, it seems, make up any old crap.

The latest edition of Math Horizons (Volume 25, Issue 3, February 2018) contains an article by a Stephen Luecking entitled Albrecht Dürer’s Celestial Geometry. As I am currently, for other reasons, refreshing my knowledge of Albrecht the mathematician I thought, oh that looks interesting I must read that. I wish I hadn’t.

Luecking’s sub-title seems innocent enough: Renaissance artist Albrecht Dürer designed a specialty compass for astronomical drawings, but when you read the article you discover that Luecking says an awful lot more and most of it is hogwash. What does he have to say?


Albrecht Dürer Self-Portrait 1500 Source: Wikimedia Commons

Albrecht Dürer (1471–1528), noted Renaissance printer and painter, twice left his native Germany for sojourns to Italy, once from 1494 to 1495 and again from 1505 to 1507. During those years his wide-ranging intellect absorbed the culture and thinking of noted artists and mathematicians. Perhaps the most important
 outcome of these journeys was his
introduction to scientific methods. 
His embrace of these methods
 went on to condition his thinking 
for the rest of his life. 

So far so good. However what Dürer absorbed on those journeys to Italy was not scientific methods but linear perspective, the mathematical method, developed in Northern Italy in the fifteenth century, to enable artists to represent three dimensional reality realistically in a two dimensional picture. Dürer played a significant role in distributing these mathematical techniques in Europe north of the Alps. His obsession with mathematics in art led to him developing the theory that the secret of beauty lay in mathematical proportion to which de devoted a large part of the rest of his life. He published the results of his endeavours in his four-volume book on human proportions, Vier Bücher von Menschlicher Proportion, in the year of his death, 1528.


Title page of Vier Bücher von menschlicher Proportion showing the monogram signature of artist Source: Wikimedia Commons

If Dürer wanted to learn scientific methods, by which, as we will see Luecking means astronomy, he could and probably did learn them at home in Nürnberg. Dürer was part of the humanist circle of Willibald Pirckheimer, he close friend and patron.


Engraving of Willibald Pirckheimer at 53 by Albrecht Dürer, 1524. We live by the spirit. The rest belongs to death. Source: Wikimedia Commons

Franconian houses are built around a courtyard; Dürer was born in the rear building of the Pirckheimer house on the market square in Nürnberg. Although his parents bought their own house a few years later Albrecht and Willibald remained close friends and possibly even lovers all of their lives. Pirckheimer was a big supporter of the mathematical sciences—astronomy, mathematics, cartography and astrology—and his circle included, amongst others, Johannes Stabius, Johannes Werner, Erhard Etzlaub, Georg Hartmann, Konrad Heinfogel and Johannes Schöner all of whom were either astronomers, mathematicians, cartographers, instrument makers or globe makers some of them all five and all of them friends of Dürer.

Next up Luecking tells us:

One notable
consequence was Dürer’s abandonment of astrological subject
matter—a big seller for a printer
and publisher such as himself—in favor of astronomy.


Albrecht Dürer Syphilis 1496 Syphilis was believed to have an astrological cause Source: Wikimedia Commons

Luecking offers no evidence or references for this claim, so I could offer none in saying that it is total rubbish, which it is. However I will give one example that shows that Albrecht Dürer was still interested in astrology in 1517. Lorenz Beheim (1457–1521) was a humanist, astrologer, physician and alchemist, who was a canon of the foundation of the St Stephan Church in Bamberg, he was a close friend of both Pirckheimer and Dürer and corresponded regularly with Pirckheimer. In a letter from 8 December 1517 he informed Pirckheimer that Johannes Schöner was coming to Nürnberg with printed celestial globes that could be used for astrology, which if his wished could be acquired by him and Albrecht Dürer. He would not have passed on the information if he thought that they wouldn’t be interested. Beheim also cast horoscopes for both Pirckheimer and Dürer.


Gores for Johannes Schöner’s Celestial Globe 1517  Source: Hans Gaab, Die Sterne Über Nürnberg: Albrecht Dürer und seine Himmelskarten von 1515, Nürnberger Astronomische Gesellschaft, Michael Imhof Verlag, 2015 p. 115


Next up Luecking starts, as he means to go on, with pure poppycock. All of the above Nürnberger mathematician, who all played significant roles in Dürer’s life, were of course practicing astrologers.

Astronomy was not to be a casual interest. Just before his second trip to Italy, Dürer published De scientia motus orbis, a cosmological treatise by the Persian Jewish astronomer Masha’Allah ibn Atharī (ca. 740–815 CE). Since Masha’Allah wrote the treatise for laymen and included ample illustrations, it was a good choice for introducing Europeans to Arabic astronomy.

The claim that Dürer published Masha’Allah’s De scientia motus orbis is so mind bogglingly wrong anybody with any knowledge of the subject would immediately stop reading the article, as it is obviously a complete waste of time and effort. The book was actually edited and published by Johannes Stabius and printed by Weissenburger in Nürnberg in 1504.

The woodcut illustrations came from the workshop of Albrecht Dürer, but probably not from Dürer himself. There were traditionally attributed to Hans Süß von Kulmbach (1480–1522), one of Dürer’s assistants, who went on to become a successful painter in his own right, but modern research has shown that Süß didn’t move to Nürnberg until 1505, a year after the book was published.


Hans Süß portrait  Source: Wikimedia Commons

Although Luecking wants Masha’Allah to be an astronomer he was in fact a very famous astrologer, who amongst other things cast the horoscope for the founding of Bagdad. De scientia motus orbis is indeed a book on Aristotelian cosmology and physics but it includes his theory that there are ten heavenly spheres not eight as claimed by Aristotle. His extra heavenly spheres play a significant role in his astrological theories. It is very common practice for astrologers, starting with Ptolemaeus, to publish their astronomy and astrology in separate books but they are seen as complimentary volumes. From their beginnings in ancient Babylon down to the middle of the seventeenth century astronomy and astrology were always seen as two sides of the same coin.


Title page De scientia motus orbis Although this woodcut is usually titled The Astronomer I personally think the figure looks more like an astrologer Source: Wikimedia Commons

In 1509 Dürer purchased the entire library of Regiomontanus (1436–1476 CE) from the estate of Nuremberg businessman Bernhard Walther. Regiomontanus was Europe’s leading astronomer,
a noted mathematician, and a designer of astronomical instruments. Walther had sponsored Regiomontanus’s residency in Nuremberg between 1471 and 1475. Part of Walther’s largesse was to provide a print shop from which Regiomontanus published the world’s first scientific texts ever printed.

Regiomontanus was of course first and foremost an astrologer and most of those first scientific texts that he published in Nürnberg were astrological texts. Walther did not sponsor Regiomontanus’ residency in Nürnberg but was his colleague and student in his endeavours in the city. An analysis of Walther’s astronomical observation activities in Nürnberg after Regiomontanus’ death show that he too was an astrologer rather than an astronomer. When Regiomontanus came to Nürnberg he brought a very large number of manuscripts with him, intending to edit and publish them. When he died these passed into Walther’s possession, who added new books and manuscripts to the collection. The story of what happened to this scientific treasure when Walther died in 1504 is long and very complicated. In fact Dürer bought not “the entire library” but a mere ten manuscripts not when he bought Walther’s house, the famous Albrecht Dürer House, in 1509 but first in 1522.

In 1515, Dürer and Austrian cartographer and mathematician Johannes Stabius produced the first map of the world portraying the earth as a sphere.


Johannes Statius portrait by Albrecht Dürer Source: Wikimedia Commons

The Stabius-Dürer world map was not “the first map of the world portraying the earth as a sphere”. The earliest know printed world map portraying the earth as a sphere is a woodcut in a Buchlein über die Kunst Corsmographia, (Booklet about the Art of Cosmographia) published in Nürnberg in about 1490. There are others that predate the Stabius-Dürer map most notably on the title page of Waldseemüller’s Die Welt Kugel (The Earth Sphere) published in Straßburg in 1509.

There are no surviving copies of the Stabius-Dürer world map from the sixteenth century so we don’t actually know what it was produced for. The woodblocks survived and were rediscovered in the 18th century.

It is however dedicated to both the Emperor Maximilian, Stabius’s employer who granted the printing licence, and Cardinal Matthäus Lang, so it might well have been commissioned by the latter. Lang commissioned the account of Magellan’s circumnavigation on which Schöner based his world map of that circumnavigation.

Afterward, Stabius proposed continuing their collaboration by publishing a star map—the first such map published in Europe. Their work relied heavily on data assembled by Regiomontanus, plus refinements from Walther.

It will probably not surprise you to discover that this was not “the first such map published in Europe. It’s the first printed one but there are earlier manuscript ones, two of which from 1435 in Vienna and 1503 in Nürnberg probably served as models for the Stabius–Dürer–Heinfogel one. Their work did not rely “heavily on data assembled by Regiomontanus, plus refinements from Walther” but was based on Ptolemaeus’ star catalogue from the Almagest. There is a historical problem in that there was not printed copy of that star catalogue available at the time so they probably work from one or more manuscripts and we don’t know which one(s). The star map contains the same dedications to Maximilian and Lang as the world map so one again might have been a commission from Lang, Stabius acting as the commissioning agent. Stabius and Lang studied together at the University of Ingolstadt.


Stabs-Dürer-Heinfogel Star Map Northern Hemisphere Source: Ian Ridpath’s Star Tales

For more details on the star maps go here

The star map required imprinting the three- dimensional dome of the heavens onto a two- dimensional surface without extreme distortions, a task that fell to Stabius. He used a stereographic projection. In this method, rays originate at the pole in the opposite hemisphere, pass through a given point in the hemisphere, and yield a point on a circular surface.

You will note that I have included the name of Konrad Heinfogel to the producers of the map and it was actually he, and not Stabius, who was responsible for the projection of the map and the location of the individual stars. In fact in this project Johannes Stabius as commissioning agent was project leader, Konrad Heinfogel was the astronomical expert and Albrecht Dürer was the graphic artist hired to draw the illustration. Does one really have to point out that in the sixteenth century star maps were as much, if not more, for astrologers than for astronomers.

Luecking now goes off on an excurse about the history of stereographic projection, which ends with the following paragraph.

As the son of a goldsmith, Dürer’s exposure to stereographic projection would have been by way of the many astrolabes being fabricated in Nuremburg, then Europe’s major center for instrument makers. As the 16th century moved on, the market grew for such scientific objects as astrology slipped into astronomy. Handcrafted brass instruments, however, were affordable only to the wealthy, whereas printed items like the Dürer-Stabius maps reached a wider market.

Nürnberg was indeed the major European centre for the manufacture of scientific instruments during Dürer’s lifetime but scientific instrument makers and goldsmiths are two distinct professional groups, so Luecking’s argument falls rather flat, although of course Dürer would have well acquainted with the astrolabes made by his mathematical friends. Astrolabes are of course both astrological and astronomical instruments and astrology did not slip into astronomy during the 16th century. In fact the 16th century is regarded by historians as the golden age of astrology.

There now follows another excurse on the epicycle-deferent model of planetary orbits as a lead up to the articles thrilling conclusion.

In his 1525 book Die Messerung (On Measurement), Dürer presents an instrument of his own design used to draw these and other more general curves. This compass for drawing circles upon circles consisted of four telescoping arms and calibrated dials. An arm attached to the first dial could rotate in a full circle, a second arm fixed to another dial mounted on the end of this first arm could rotate around the end of the first arm, and so on.


Dürer’s four arm compass


Underweysung der Messung mit dem Zirkel und Richtscheyt Title Page

The title of Dürer’ 1525 book is actually Underweysung der Messung mit dem Zirckel und Richtscheyt (Instructions for Measuring with Compass and Straightedge). It is a basic introduction to geometry and its applications, which Dürer wrote when he realised that his Vier Bücher von Menschlicher Proportion was too advanced for the artist apprentices that he thought should read it. The idea was first read and digest the Underweysung then read the Vier Bücher von Menschlicher Proportion.

Luecking tells us that:

As a trained metalsmith, Dürer possessed the expertise to craft this complex tool. Precision calibration and adjustable arms allowed its user to plot an endless number of curves by setting the length of each telescoping arm and determining the rate at which the arms turned. This, in effect, constituted manual programming by setting the parameters of each curve plotted.

As a teenager Dürer did indeed serve an apprenticeship under his father as a goldsmith, but immediately on completing that apprenticeship he undertook a second apprenticeship as a painter with Michael Wolgemut from 1486 to 1490 and dedicated his life to painting and fine art printing. Luecking has already correctly stated that Nürnberg was the major European centre for scientific instrument making and Dürer almost certainly got one of those instrument makers to produce his multi-armed compass. Luecking describes the use to which Dürer put this instrument in drawing complex geometrical curves. He then goes on to claim that Dürer might actually have constructed it to draw the looping planetary orbits produced by the epicycle-deferent model. There is absolutely no evidence for this in the Underweysung and Luecking’s speculation is simple pulled out of thin air.

To summarise for those at the back who haven’t been paying attention. Dürer did not absorb scientific methods in Italy. He did not abandon astrology for astronomy. He didn’t publish Masha’Allah’s De scientia motus orbis, Johannes Stabius did. Dürer only bought ten of Regiomontanus’ manuscripts and not his entire library. The Stabius-Dürer world map was not “the first map of the world portraying the earth as a sphere”. The Stabius–Dürer–Heinfogel star charts were the first star-charts printed in Europe but by no means the first ones published. Star charts are as much astrological, as they are astronomical. Astrology did not slip into astronomy in the 16th century, which was rather the golden age of astrology. There is absolutely no evidence that Dürer’s multi-arm compass, as illustrated in his geometry book the Underweysung, was ever conceived for drawing the looping orbits of epicycle-deferent planetary models, let alone used for this purpose.

It comes as no surprise that Stephen Luecking is not a historian of mathematics or art for that matter. He is the aged (83), retired chairman of the art department of DePaul University in Chicago.

Whenever I come across an article as terrible as this one published by a leading scientific publisher in a journal from a major mathematical organisation such as the MAA I cringe. I ask myself if the commissioning editor even bothered to read the article; it was certainly not put out to peer review, as any knowledgeable Dürer expert would have projected it in an elegant geometrical curve into his trashcan. Above all I worry about the innocent undergraduates who are subjected to this absolute crap.



















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

Conversations in a sixteenth century prison cell

Science writer Michael Brooks has thought up a delightful conceit for his latest book.* The narrative takes place in a sixteenth century prison cell in Bologna in the form of a conversation between a twenty-first century quantum physicist (the author) and a Renaissance polymath. What makes this conversation particularly spicy is that the Renaissance polymath is physician, biologist, chemist, mathematician, astronomer, astrologer, philosopher, inventor, writer, auto-biographer, gambler and scoundrel Girolamo Cardano, although Brooks calls him by the English translation of his name Jerome. In case anybody is wondering why I listed autobiographer separately after writer, it is because Jerome was a pioneer in the field writing what is probably the first autobiography by a mathematician/astronomer/etc. in the Early Modern Period.


Portrait of Cardano on display at the School of Mathematics and Statistics, University of St Andrews. Source: Wikimedia Commons

So what do our unlikely pair talk about? We gets fragments of conversation about Jerome’s current situation; a broken old man rotting away the end of his more than extraordinary life in a prison cell with very little chance of reprieve. This leads to the visitor from the future, relating episodes out of that extraordinary life. The visitor also picks up some of Jerome’s seemingly more strange beliefs and relates them to some of the equally, seemingly strange phenomena of quantum mechanics. But why should anyone link the misadventures of an, albeit brilliant, Renaissance miscreant to quantum mechanics. Because our author sees Jerome the mathematician, and he was a brilliant one, as the great-great-great-great-great-great-great-great-great-great-great-great-great grandfather of quantum mechanics!


As most people know quantum mechanics is largely non-deterministic in the conventional sense and relies heavily on probability theory for its results. Jerome wrote the first mathematical tome on probability theory, a field he entered because of his professional gambling activities. He even included a section about how to cheat at cards. I said he was a scoundrel. The other thing turns up in his Ars Magna (printed and published by Johannes Petreius the publisher of Copernicus’ De revolutionibus in Nürnberg and often called, by maths historians, the first modern maths book); he was the first person to calculate with so-called imaginary numbers. That’s numbers using ‘i’ the square root of minus one. Jerome didn’t call it ‘i’ or the numbers imaginary, in fact he didn’t like them very much but realised one could use them when determining the roots of cubic equation, so, holding his nose, that is exactly what he did. Like probability theory ‘i’ plays a very major role in quantum mechanics.

What Michael Brooks offers up for his readers is a mixture of history of Renaissance science together with an explanation of many of the weird phenomena and explanations of those phenomena in quantum mechanics. A heady brew but it works; in fact it works wonderfully.

This is not really a history of science book or a modern physics science communications volume but it’s a bit of both served up as science entertainment for the science interested reader, lay or professional. Michael Brooks has a light touch, spiced with some irony and a twinkle in his eyes and he has produced a fine piece of science writing in a pocket-sized book just right for that long train journey, that boring intercontinental flight or for the week in hospital that this reviewer used to read it. If this was a five star reviewing system I would be tempted to give it six.

*  Michael Brooks, The Quantum Astrologer’s Handbook, Scribe, Melbourne & London, 2017


Filed under Book Reviews, Early Scientific Publishing, History of Astrology, History of Astronomy, History of Physics, Renaissance Science, Uncategorized

Galileo & Roberto

One of the books that I am currently reading is Rob Iliffe’s Priest of Nature: The Religious Worlds of Isaac Newton (a full review will follow when I finish it but I can already say it will be very positive). I stumbled more than somewhat when I read the following:

…and Lucas Trelcatius’s list of some of the most significant places in Scripture, which was composed as a response to the Catholic interpretations of various texts offered by the great scholar (and scourge of Galileo [my emphasis]) Cardinal Robert Bellarmine.

Four words that caused me to draw in my breath, why? Let as first take a look at the meaning of the word scourge:

A scourge was originally a particularly nasty and extremely cruel multi-thong whip. Transferred to describe a person it means: a person that causes great trouble of suffering. Can Robert Bellarmine really be described as “scourge of Galileo”?

Robert Bellarmine (actually Roberto Bellarmino) (1542-1621) was a Jesuit scholar who was specialist for post Tridentine theology, that is the theological teachings of the Catholic Church as laid down as official church doctrine at the Council of Trent (1545-1563. He rose through the ranks to arch-bishop and then cardinal, was professor for theology at the Collegio Romano, the Jesuit University in Rome, and later the universities rector. In the early seventeenth century he was regarded as the leading Catholic authority on theology and as such he was a powerful and highly influential figure in Rome.


Robert Bellarmine artist unknown Source: Wikimedia Commons

How did Bellarmine’s life interact with that of Galileo? The first contact was very indirect and occurred after Galileo had published his Sidereus Nuncius, making public his telescopic discoveries. Bellarmine inquired of the mathematician astronomers under Clavius’ leadership at the Collegio Romano, whether the discoveries claimed by Galileo were real. Being the first astronomers to confirm those discoveries, Clavius was able to report in the positive.

In 1615 Galileo wrote his Letter to Castelli in which he argued that those Bible passages that contradicted Copernican heliocentricity should be re-interpreted to solve the contradiction. He was stepping into dangerous territory, a mere mathematicus—the lowest of the low in the academic hierarchy—telling the theologians how to interpret the Bible. This was particularly risky, as it was in the middle of the Counter-Reformation given that the Reformation was about who is allowed to interpret the Bible. The Protestants said that everyman should be able to interpret it for themselves and the Catholic Church said that only the Church should be allowed to do so. Remember we are only three years away from the Thirty Years War the high point, or should that be the low point, of the conflict between the two religions, which led to the destruction of most of central Europe and the death of between one and two thirds of its population.


Justus Sustermans – Portrait of Galileo Galilei, 1636 Source: Wikimedia Commons

Galileo’s suggestion in his letter came to the attention of his opponents in the Church and led the Pope, Paul V, to set up a commission of eleven theologians, known as the Qualifiers, to investigate the propositions of heliocentricity.

In the meantime Paolo Antonio Foscarini (c. 1565–June 1616), a Carmelite father, attempted to publish his Epistle concerning the Pythagorean and Copernican opinion of the Mobility of the Earth and stability of the sun and the new system or constitution of the WORLD, which basically contained the same arguments for reinterpreting the Bible as Galileo’s Letter to Castelli. The censor of Foscarini’s order rejected his tract, as too contentious. I should point out at this point something that most people ignore that is all powers both civil and religious in Europe exercised censorship; there was no such thing as free thought or freedom of speech in seventeenth century Europe. Foscarini wrote a defence of his Epistle and sent the two pieces to Bellarmine, as the leading theologian, for his considered opinion. Bellarmine’s answers the so-called Foscarini Letter is legendary and I reproduce it in full below.

My Reverend Father,

I have read with interest the letter in Italian and the essay in Latin which your Paternity sent to me; I thank you for one and for the other and confess that they are all full of intelligence and erudition. You ask for my opinion, and so I shall give it to you, but very briefly, since now you have little time for reading and I for writing.

First I say that it seems to me that your Paternity and Mr. Galileo are proceeding prudently by limiting yourselves to speaking suppositionally and not absolutely, as I have always believed that Copernicus spoke. For there is no danger in saying that, by assuming the Earth moves and the sun stands still, one saves all of the appearances better than by postulating eccentrics and epicycles; and that is sufficient for the mathematician. However, it is different to want to affirm that in reality the sun is at the center of the world and only turns on itself, without moving from east to west, and the earth is in the third heaven and revolves with great speed around the sun; this is a very dangerous thing, likely not only to irritate all scholastic philosophers and theologians, but also to harm the Holy Faith by rendering Holy Scripture false. For Your Paternity has well shown many ways of interpreting Holy Scripture, but has not applied them to particular cases; without a doubt you would have encountered very great difficulties if you had wanted to interpret all those passages you yourself cited.

Second, I say that, as you know, the Council [of Trent] prohibits interpreting Scripture against the common consensus of the Holy Fathers; and if Your Paternity wants to read not only the Holy Fathers, but also the modern commentaries on Genesis, the Psalms, Ecclesiastes, and Joshua, you will find all agreeing in the literal interpretation that the sun is in heaven and turns around the earth with great speed, and that the earth is very far from heaven and sits motionless at the center of the world. Consider now, with your sense of prudence, whether the church can tolerate giving Scripture a meaning contrary to the Holy Fathers and to all the Greek and Latin commentators. Nor can one answer that this is not a matter of faith, since it is not a matter of faith “as regards the topic”, it is a matter of faith “as regards the speaker”; and so it would be heretical to say that Abraham did not have two children and Jacob twelve, as well as to say that Christ was not born of a virgin, because both are said by the Holy Spirit through the mouth of the prophets and the apostles.


Third, I say that if there were a true demonstration that the sun is at the center of the world and the earth in the third heaven, and that the sun does not circle the earth but the earth circles the sun, then one would have to proceed with great care in explaining the Scriptures that appear contrary; and say rather that we do not understand them than that what is demonstrated is false. But I will not believe that there is such a demonstration, until it is shown me. Nor is it the same to demonstrate that by supposing the sun to be at the center and the earth in heaven one can save the appearances, and to demonstrate that in truth the sun is at the center and the earth in the heaven; for I believe the first demonstration may be available, but I have very great doubts about the second, and in case of doubt one must not abandon the Holy Scripture as interpreted by the Holy Fathers. I add that the one who wrote, “The sun also riseth, and the sun goeth down, and hasteth to his place where he arose,” was Solomon, who not only spoke inspired by God, but was a man above all others wise and learned in the human sciences and in the knowledge of created things; he received all this wisdom from God; therefore it is not likely that he was affirming something that was contrary to truth already demonstrated or capable of being demonstrated. Now, suppose you say that Solomon speaks in accordance with appearances, since it seems to us that the sun moves (while the earth does so), just as to someone who moves away from the seashore on a ship it looks like the shore is moving, I shall answer that when someone moves away from the shore, although it appears to him that the shore is moving away from him, nevertheless he knows that it is an error and corrects it, seeing clearly that the ship moves and not the shore; but in regard to the sun and the earth, no wise man has any need to correct the error, since he clearly experiences that the earth stands still and that the eye is not in error when it judges that the it also is not in error when it judges that the stars move. And this is enough for now.

With this I greet dearly Your Paternity, and I pray to God to grant you all your wishes.

At home, 12 April 1615.

To Your Very Reverend Paternity.

As a Brother,

Cardinal Bellarmine


(Source for the English transl.: M. Finocchiaro, The Galileo Affair. A Documentary History (Berkeley, CA: University of California Press, 1989), pp. 67-69.Original Italian text, G. Galilei, Opere, edited by A. Favaro (Firenze: Giunti Barbera, 1968), vol. XII, pp. 171-172.)

A, in my opinion, brilliant piece of measured, diplomatic writing. Bellarmine tactfully suggests that one should only talk of heliocentricity hypothetically, its correct scientific status in 1615, the first empirical proof for the movement of the Earth was found in 1725, when Bradley discovered stellar aberration. He, as the great Tridentine theologian, then reiterates the Church’s position on the interpretation of Holy Scripture. Finally he brings, what is without doubt, the most interesting statement in the letter.

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

What he says is bring proof and we’ll reinterpret the Bible but until then…

On 24 February the Qualifiers delivered the results of their deliberations on the heliocentricity hypothesis:

( i ) The sun is the centre of the universe (“mundi”) and absolutely

immobile in local motion.

( ii ) The earth is not the centre of the universe (“mundi”); it is not

immobile but turns on itself with a diurnal movement.

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

It should be pointed out that although the Qualifiers called the first statement heretical, only the Pope could formally declare something heretical and no pope ever did, so heliocentricity was never officially heretical.

Pope Paul V now ordered Bellarmine to covey the judgement of the Qualifiers to Galileo and to inform him that he may not hold or teach the heliocentric theory. This he did on 26 February 1616. Bellarmine was not one of the Qualifiers and here functioned only as the messenger. By all accounts the meetings between Bellarmine and Galileo were cordial and friendly.

When Galileo returned to Florence rumours started spreading that he had been forced to recant and do penance, which was of course not true. Galileo wrote to Bellarmine requesting a letter explaining that this was not true. Bellarmine gladly supplied said letter, defending Galileo’s honour. However Galileo made the mistake in 1633 of thinking that Bellarmine’s letter was a get out of jail free card.

Bellarmine died in 1621 and between 1616 and his death there was no further contact between the Cardinal and the mathematicus. Personally I can see nothing in the three interactions, indirect and direct, between Bellarmine and Galileo that would in anyway justify labelling Bellarmine as the “scourge of Galileo”. This accusation is historically highly inaccurate and paints a wholly false picture of the relationship between the two men. I expect better of Rob Iliffe, who is without doubt one on Britain’s best historians of seventeenth century science.

NB Before somebody pops up in the comments claiming that Robert Bellarmine was one of the three Inquisition judges, who confirmed the death sentence on Giordano Bruno. He was but that has no relevance to his interactions with Galileo, so save yourself time and energy and don’t bother.

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

Exposing Galileo’s strawmanning

There is a widespread, highly erroneous, popular perception in the world, much loved by gnu atheists and supporters of scientism, that as soon as Petreius published Copernicus’s De Revolutionibus in 1543 the question as to which was the correct astronomical/cosmological system for the cosmos was as good as settled and that when Galileo published his Dialogo[1] everything was finally done and dusted and anybody who still persisted in opposing the acceptance of the heliocentric world view, did so purely on grounds of ignorant, anti-science, religious prejudice. Readers of this blog will know that I have expended a certain amount of energy and several thousand words over the years countering this totally mistaken interpretation of the history of astronomy in the early modern period and today I’m going to add even more words to the struggle.

Galileo is held up by his numerous acolytes as a man of great scientific virtue, who preached a gospel of empirical scientific truth in the face of the superstitious, faith based errors of his numerous detractors; he was a true martyr for science. The fact that Galileo was capable of scientific skulduggery does not occur to them, but not only was he capable of such, his work is littered with examples of it. One of his favourite tactics was not to present his opponents true views when criticising them but to create a strawman, claiming that this represents the views of his opponent and then to burn it down with his always-red-hot rhetorical flamethrower.

Towards the end of The First Day in the Dialogo, Galileo has Simplicio, the fall guy for geocentricity, introduce a “booklet of theses, which is full of novelties.” Salviati, who is the champion of heliocentricity and at the same time Galileo’s mouthpiece, ridicules this booklet as producing arguments full of “falsehoods and fallacies and contradictions” and as “thinking up, one by one, things that would be required to serve his purposes, instead of adjusting his purposes step by step to things as they are.” Galileo goes on to do a polemical hatchet job on what he claims are the main arguments in said “booklet of theses.” Amongst others he accuses the author of “setting himself up to refute another’s doctrine while remaining ignorant of the basic foundations upon which the whole structure are supported.”

The “booklet of theses”, which Galileo doesn’t name, is in fact the splendidly titled:


English translation of the Latin title page Source: Notre Dame Press

Now most of the acolytes who fervently praise Galileo as the great defender of science against superstition probably have no idea who Johann Georg Locher was but they might well have heard of Christoph Scheiner, who was famously embroiled in a dispute with Galileo over the nature of sunspots and who first observed them with a telescope. In fact the authorship of the Mathematical Disquisitions has often falsely attributed to Scheiner and Galileo’s demolition of it seen as an extension of that dispute and it’s sequel in the pages of his Il Saggiatore.

Whereas Galileo’s Dialogo has been available to the general reader in a good English translation by Stillman Drake since 1953, anybody who wished to consult Locher’s Mathematical Disquisitions in order to check the veracity or lack thereof of Galileo’s account would have had to hunt down a 17th century Latin original in the rare books room of a specialist library. The playing field has now been levelled with the publication of an excellent modern English translation of Locher’s booklet by Renaissance Mathematicus friend, commentator and occasional guest contributor Chris Graney[2].


Graney’s translation (Christopher M. Graney, Mathematical Disquisitions: The Booklet of Theses Immortalised by Galileo, University of Notre Dame Press, Notre Dame, Indiana, 2017)  presents a more than somewhat different picture of Locher’s views on astronomy to that served up by Galileo in the Dialogo and in fact gives us a very clear picture of the definitely rational arguments presented by the opponents to heliocentricity in the early part of the seventeenth century. The translation contains an excellent explanatory introduction by Graney, extensive endnotes explaining various technical aspects of Locher’s text and also some of the specific translation decisions of difficult terms. (I should point out that another Renaissance Mathematicus friend, Darin Hayton acted as translation consultant on this volume). There is an extensive bibliography of the works consulted for the explanatory notes and an excellent index.

The book is very nicely presented by Notre Dame Press, with fine reproductions of Locher’s wonderful original illustrations.


Locher’s illustration to his discussion of diurnal rotation p. 32

Graney’s translation provides a great addition to his previous Setting Aside All Authority, which I reviewed here. Graney is doing sterling work in adjusting the very distorted view of the astronomical system discussion in the first half of the seventeenth century and anybody, who is seriously interested in learning the true facts of that discussion, should definitely read his latest contribution.




[1] By a strange cosmic coincidence the first printed copy of the Dialogo was presented to the dedicatee Ferdinando II d’Medici, Grand Duke of Tuscany 386 years ago today on 22 February 1632.

[2] At the end of my review of Setting Aside All Authority I wrote the following, which applies equally to this review; in this case I provided one of the cover blurbs for Chris’ latest book.

Disclosure; Chris Graney is not only a colleague, but he and his wife, Christina, are also personal friends of mine. Beyond that, Chris has written, at my request, several guest blogs here at the Renaissance Mathematicus, all of which were based on his research for the book. Even more relevant I was, purely by accident I hasten to add, one of those responsible for sending Chris off on the historical trail that led to him writing this book; a fact that is acknowledged on page xiv of the introduction. All of this, of course, disqualifies me as an impartial reviewer of this book but I’m going to review it anyway. Anybody who knows me, knows that I don’t pull punches and when the subject is history of science I don’t do favours for friends. If I thought Chris’ book was not up to par I might refrain from reviewing it and explain to him privately why. If I thought the book was truly bad I would warn him privately and still write a negative review to keep people from wasting their time with it. However, thankfully, none of this is the case, so I could with a clear conscience write the positive review you are reading. If you don’t trust my impartiality, fair enough, read somebody else’s review.

Addendum: The orthography of the neologism in the title was change—23,02,18— following a straw pole on Twitter


Filed under Book Reviews, Early Scientific Publishing, History of Astronomy, History of Mathematics, Myths of Science, Renaissance Science

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

Andromeda – From nebula to galaxy

The word galaxy derives from the Greek word galaxias meaning milky one, which was the ancient Greek term for the Milky Way that indistinct band of stars visible across the night sky in areas that don’t suffer from too much light pollution. Today galaxy is used as the general term for the very large groups of stars scattered around the universe. Current estimates of the total number of galaxies range from 2×1011 to 2×1012 or even more. Confronted by these vast numbers it is oft easy to forget that less than one hundred years ago we still thought that our galaxy, the Milky Way Galaxy, was the entire universe. This changed on 1 January 1925 when H.N. Russell read a paper by Edwin Hubble to the American Association for the Advancement of Science, which established that spiral nebulae were in fact separate galaxies. The path through the history of astronomy leading up to that epoch defining paper in 1925 goes back almost one thousand years and in what follows I shall briefly outline some of the important stations, nearly all of which concern our nearest galactic neighbour Andromeda, along that path.

The word nebula comes from the Latin and means a cloud, mist, fog, smoke, vapour, exhalation, as you can see the definition is fairly nebulous. In astronomy it can be traced back to Ptolemaeus’ Mathēmatikē Syntaxis or as it is more commonly known The Almagest. In this founding work of Western astronomy Ptolemaeus lists a total of six astronomical nebulae without giving them any great attention. All of Ptolemaeus’ nebulae were in fact indistinct star clusters too far away to be resolved with the naked eye. The first so-to-speak true nebula, the Andromeda nebula, was recorded by the Persian astronomer Abd al-Rahman al-Sufi, usually just referred to as Al Sufi, in his Book of Fixed Stars (Arabic: kitab suwar al-kawakib) around 964 CE. He describes and illustrated the Andromeda nebula as a little cloud before the mouth of the Arabic constellation Fish.


Al Sufi’s drawing of the constellation Fish with the Andromeda nebula in fount of it mouth

Amongst his other early telescopic observations Galileo showed that the Ptolemaic nebulae resolved into many unseen stars when viewed through the telescope. In 1612, it was, however, Galileo’s telescopic rival, Simon Marius who first turned his telescope on the Andromeda nebula and saw that it didn’t resolve into stars when viewed through his telescopic lenses. In his Mundus Iovialis (1614) Marius described what he saw as follows:

Among them the first is that with the spy-glass, from 15 December 1612 I discovered and observed a fixed star with a certain wonderful shape that I cannot find in the entire heavens. It is near the third and northernmost [star] in the belt of Andromeda. Without the instrument the same is seen as some sort of little cloud; and with the instrument no distinct stars are seen as in the nebular star in Cancer and other nebular stars, but rather only white rays, which the closer to the centre the brighter they come out; in the centre there is a dull and pale light; and its diameter is about a quarter of a degree. About the same brilliance appears when a bright candle is observed through a clear lantern from a long distance.


Simon Marius from the frontispiece of the Mundus Iovialis Source: Wikimedia Commons

The research into nebulae came of age first in the eighteenth century with the work of the French comet hunter Charles Messier (1730–1817). In order to make it easier for comet hunters to distinguish potential comet sightings from other indistinct and nebulous object in the night sky, Messier began to compile a catalogue of the positions and appearance of all such objects that he detected during his nightly vigils. His work, the final version of which was published in 1781 and is now known as the Messier Catalogue, contains a list of 110 Messier objects, in his time nebulae and star clusters. The Messier objects are now known to be 39 galaxies, 5 planetary nebulae, 7 other types of nebulae and 55 star clusters. The Andromeda nebula, the discovery of which Messier, ignorant of Al Sufi’s book, falsely attributes to Marius, is Messier object M31.


Charles Messier, French astronomer, at the age of 40 Source: Wikimedia Commons

Although Messier’s catalogue was compiled to assist comet hunters in differentiating potential comets from other faint celestial objects it is usually regarded as an early example of so-called deep sky astronomy; that is the study of objects well outside the solar system. The man who first practiced deep sky astronomy systematically was William Herschel, who together with his sister Caroline, methodically map the heavens quadrant for quadrant recording with his 20 foot reflecting telescope all of the non-stellar objects he could find. Caroline and he recorded 2400 nebulae in three catalogues.


William and Caroline Herschel polishing a telescope lens, 1896 Lithograph. Source: Wellcome Collection via Wikimedia Commons

They categorised the objects that they recorded into eight classes: (I) bright nebulae, (II) faint nebulae, (III) very faint nebulae, (IV) planetary nebulae, (V) very large nebulae, (VI) very compressed and rich clusters of stars, (VII) compressed clusters of small and large [faint and bright] stars and (VIII) coarsely scattered clusters of stars. Extended by his son and later John Dreyer, Herschel’s catalogue became the New General Catalogue (NGC) of 7840 deep sky objects in 1888. The NGC numbering is still used for most of the objects recorded therein. In 1785 Herschel observed a faint reddish hue in the core region of Andromeda. He believed Andromeda to be the nearest of all the great nebula.

In 1750 the English astronomer Thomas Wright (1711–1786) published his An Original Theory on New Hypothesis of the Universe in which he was the first to correctly describe the shape of the Milky Way Galaxy. He also speculated that the faint nebulae where in fact distant galaxies. However, his very perceptive thoughts remained speculations that he was unable to verify.


Thomas Wright in 1737 Source: Wikimedia Commons


Illustration of groups of stars, from An original theory or new hypothesis of the Universe, plate XVII Source: Wikimedia Commons

Interestingly his speculations were taken up by the German philosopher Immanuel Kant (1724–1804) and further developed in his anonymously published Allgemeine Naturgeschichte und Theorie des Himmels (Universal Natural History and Theory of Heaven) (1755). At the time neither Wright’s nor Kant’s theories received much credence but with hindsight both have been praised for their perceptiveness.


Title page of Kant’s Allgemeine Naturgeschichte und Theorie des Himmels Source: Wikimedia Commons

In 1850, William Parsons, using the largest reflecting telescope constructed in the nineteenth century the Leviathan of Parsonstown, was able to identify the spiral structure of the Andromeda nebula for the first time. This was just one of a series of spiral nebula, in reality galaxies, that he was able to identify.


The largest telescope of the 19th century, the Leviathan of Parsonstown. Source: Wikimedia Commons

In 1864 William Huggins, a pioneer in stellar spectroscopy, noted that the spectrum of Andromeda differs from that of a gaseous nebula. The spectrum, as observed by Huggins, had the same characteristics as the spectrum of individual stars leading he to conclude that Andromeda was in fact stellar in nature.


Sir William Huggins, by John Collier Source: Wikimedia Commons

We have already come a long way from Al Sufi’s first record of a small cloud. In 1887, Isaac Roberts, who thought that spiral nebula were solar systems in the process of forming, took the first-ever photograph of Andromeda.


Isaac Roberts’ picture of the Great Nebula in Andromeda Source: Wikimedia Commons

In 1912 the American astronomer, Vesto Slipher, measured the rotational velocity of Andromeda using spectroscopy at 300kilometres per second the highest yet measured velocity.


V.M. Slipher, astronomer at Lowell Observatory from 1901 to 1954. Source: Wikimedia Commons

In 1917 Heber Curtis observed a nova in Andromeda and discovered eleven more in the photographic record. These were on average ten magnitudes weaker that others observed in the heavens. Based in this data he estimated that Andromeda was 500,000 light-years distant. Curtis now proposed the island universes hypothesis i.e. spiral nebulae are actually independent galaxies.


Heber Doust Curtis poses before the Crossley telescope. Source: Wikimedia Commons

On 26 April 1920 Heber Curtis and Harlow Shapley held the so-called great debate at the Smithsonian Museum of Natural History on the nature of spiral nebulae. Curtis argued that they were distant independent galaxies, Shapley that they were much smaller and much nearly and thus within the Milky Way galaxy, which was the entire universe. This debate raised the question to the priority question in astronomy.


Portrait of Harlow Shapely Source: Wikimedia Commons

In 1922 Ernst Öpik measured the distance of Andromeda using the velocity of stars. His estimate was 1,500,00 light-years.


Ernst Julius Öpik Source: Wikimedia Commons

As I said in the opening paragraph Edwin Hubble finally settled the mater when he measured the distance of Andromeda using Cepheid variable stars and proved conclusively that Andromeda was not a nebula inside the Milky Way but a separate galaxy. With this result the age of galactic astronomy was born.


Studio Portrait of Edwin Powell Hubble. Photographer: Johan Hagemeyer Source: Wikimedia Commons

Of interest the method of determining distances using Cepheids was developed by Henrietta Swan Leavitt, one of the Harvard computers, investigating thousands of variable stars in the Magellanic Clouds in 1908; she published her results in 1912.


Henrietta Swan Leavitt working at her desk in the Harvard College Observatory Source: Wikimedia Commons


Early photograph of ‘Pickering’s Harem’, as the group of women assembled by Harvard astronomer Edward Charles Pickering, who were dubbed as his “computers”. The group included Leavitt, Annie Jump Cannon, Williamina Fleming, and Antonia Maury. Source: Wikimedia Commons

The story of Andromeda’s historical journey from Al Sufi’s nebula to Curtis’ galaxy illustrates very nicely how scientific knowledge grows over time with generations of researchers with differing interests and motivations contributing directly and indirectly to that growth.

Post amended 11 January 2018



Filed under astrophysics, History of Astronomy, History of science, Uncategorized

Christmas Trilogy 2017: Bonus!

Yesterday was Johannes Kepler’s nominal birthday (as he was born before the calendar reform in a Protestant state his birthday on the Gregorian calendar would be 6 January!) and as in my wont, I posted a birthday post for the good Johannes. Of course I was far from being the only person to acknowledge his birthday and amongst many others somebody linked to the 2016 article on the website of the popular science magazine, Physics Today. Upon reading this brief tribute to my favourite seventeenth century polymath I cringed inwardly and didn’t know whether to let out a prolonged #histsigh or to turn loose the HistSci_Hulk; I have decided on the latter. Below the complete text of the offending document:

Born on 27 December 1571 in Weil der Stadt in the Holy Roman Empire, Johannes Kepler was an astronomer whose careful measurements led him to develop his three laws of planetary motion. He received a Lutheran education at the University of Tübingen and originally planned to be a theologian. Then one of his teachers gave him a copy of a book by Nicolaus Copernicus, sparking Kepler’s interest in astronomy. In 1600 Danish astronomer Tycho Brahe invited Kepler to Prague to help amass a precise set of astronomical measurements. Brahe died the following year, and Kepler inherited his mentor’s data and position as imperial mathematician to the Holy Roman emperor. In 1609 Kepler published Astronomia Nova, which included his first two laws of planetary motion; his third law was published in 1619. Kepler observed a supernova (though he called it a “new star”) and completed the detailed astronomical tables Brahe had been so determined to produce. Kepler also contributed research in optics and vision. Later in the century Isaac Newton would prove his law of universal gravitation by showing that it could produce Kepler’s orbits.

Born … in Weil der Stadt in the Holy Roman Empire… This contains something about which I have had bitter disputes on Wikipedia. There is a famous quip that the Holy Roman Empire was neither holy nor Roman nor an empire, it was also neither a country nor a state. The Holy Roman Empire was a loose feudal conglomeration of autonomous and semi-autonomous states. Weil der Stadt, Kepler’s birthplace was at the time of his birth in the autonomous Duchy of Württemberg.


Map of the Duchy of Württemberg 1619 by Pieter van den Keere. You can see Weyl (Weil der Stadt) roughly in the middle. Source: Wikimedia Commons

…Johannes Kepler was an astronomer whose careful measurements led him to develop his three laws of planetary motion. Kepler was a theorist, who didn’t on the whole take measurements careful or otherwise. The measurements that he used to derive his three laws were, of course, made very carefully by Tycho Brahe.

Kepler did not originally plan to be a theologian. He was on an educational tack designed to produce Lutheran Protestant pastors and schoolteachers. He would have become a pastor but was appointed to a position as a maths teacher instead.


Then one of his teachers gave him a copy of a book by Nicolaus Copernicus, sparking Kepler’s interest in astronomy. One of Kepler’s professors in Tübingen was Michael Maestlin, who in his courses taught Copernican heliocentric astronomy alongside the then dominant geocentric astronomy. Kepler took this course and developed an interest in heliocentrism. It was Maestlin who recognised Kepler’s aptitude for mathematics and recommended that he be appointed to a teaching post rather than a village church.

In 1600 Danish astronomer Tycho Brahe invited Kepler to Prague to help amass a precise set of astronomical measurements. Tycho Brahe invited Kepler to Prague not to help amass a precise set of astronomical measurements but to use his mathematical skills to turn the already amassed measurements into calculated orbits, ephemerides etc.

Brahe died the following year, and Kepler inherited his mentor’s data and position as imperial mathematician to the Holy Roman emperor. Kepler didn’t inherit his mentor’s data, Tycho’s daughter Elizabeth and her husband Frans Gansned Genaamd Tengnagel van de Camp did. This caused Kepler no end of problems, as he needed that data to realise his vision of a heliocentric astronomy. After tough negotiations, Tengnagel allowed Kepler to use the data but only if his name was included as co-author on any books that Kepler published based on it; a condition that Kepler duly fulfilled. Given my own inabilities to spell or write grammatically I’m not usually a grammar fetishist but, as I’m putting the boot in, Imperial Mathematician is a title and should be written with capital letters as in the emperor in Holy Roman Emperor.

Kepler observed a supernova (though he called it a “new star”). Well yes, as the term supernova was only coined in 1931 Kepler could hardly have used it. However, the nova part of the name, which simple means new, comes from Kepler’s term Stellar Nova, his being the most recent supernova observed with the naked eye.

…and completed the detailed astronomical tables Brahe had been so determined to produce. Kepler didn’t just complete them he produced them single-handedly, calculating, writing, typesetting, printing, publishing and selling them. This was the task assigned to him by Tycho and to which he was official appointed by the Emperor Rudolph II.

Physics Today is a fairly major popular science magazine but it would appear that they don’t really care enough about the history of science to indulge in a modicum of fact checking.





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