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Tycho’s last bastion

In the history of science, scholars who end up on the wrong side of history tend to get either forgotten and/or vilified. What do I mean by ‘end up on the wrong side of history’? This refers to scholars who defend a theory that in the end turns out to be wrong against one that in the end turns out to be right. My very first history of science post on this blog was about just such a figure, Christoph Clavius, who gets mocked by many as the last Ptolemaic dinosaur in the astronomy/cosmology debate at the beginning of the seventeenth century. In fact there is much to praise about Clavius, as I tried to make clear in my post and he made many positive contributions to the evolution of the mathematical sciences. Another man, who ended up on the wrong side of history in the same period is the Danish astronomer, Christen Sørensen, better known, if at all, by the name Longomontanus, the Latinised toponym based on Lomborg, the Jutland village where he was born on 4 October 1562 the son of a poor labourer, who died when he was only eight years old.


Longomontanus Source: Wikimedia Commons

Tycho Brahe backed the wrong astronomical theory in this period, a theory that is generally named after him although several people seem to have devised it independently of each other in the closing quarter of the sixteenth century. However, Tycho has not been forgotten because he delivered the new data with which Johannes Kepler created his elliptical model of the solar system. However, what people tend to ignore is that Tycho did not produce that data single-handedly, far from it.

The island of Hven, Tycho’s fiefdom, was a large-scale research institute with two observatories, an alchemy laboratory, a paper mill and a printing workshop.


Map of Hven from the Blaeu Atlas 1663, based on maps drawn by Tycho Brahe in the previous century Source: Wikimedia Commons

This enterprise was staffed by a veritable army of servants, technicians and research assistant with Tycho as the managing director and head of research.


Engraving of the mural quadrant from Brahe’s book Astronomiae instauratae mechanica (1598) Showing Tyco direction observations Source: Wikimedia Commons

Over the years the data that would prove so crucial to Kepler’s endeavours was collected, recorded and analysed by a long list of astronomical research assistants; by far and away the most important of those astronomical research assistants was Christen Sørensen called Longomontanus, who also inherited Tycho’s intellectual mantle and continued to defend his system into the seventeenth century until his death in 1647.

Christen Sørensen came from a very poor background so acquiring an education proved more than somewhat difficult. After the death of his father he was taken into care by an uncle who sent him to the village school in Lemvig. However, after three years his mother took him back to work on the farm; she only allowed him to study with the village pastor during the winter months. In 1577 he ran away to Viborg, where he studied at the cathedral school, supporting himself by working as a labourer. This arrangement meant that he only entered the university in Copenhagen in 1588, but with a good academic reputation. It was here at the university that he acquired his toponym, Longomontanus. In 1589 his professor recommended him to Tycho Brahe and he entered into service on the island of Hven.


Tycho Brahe’s Uraniborg main building from the 1663 Blaeu’s Atlas Major Centre of operations Source: Wikimedia Commons

He was probably instructed in Tycho’s methods by Elias Olsen Morsing, who served Tycho from 1583 to 1590, and Peter Jacobsen Flemløse, who served from 1577-1588 but stayed in working contact for several years more and became a good friend of Longomontanus. Longomontanus proved to be an excellent observer and spent his first three years working on Tycho’s star catalogue.


Stjerneborg Tycho Brahe’s second observatory on Hven: Johan Blaeu, Atlas Major, Amsterdam Source: Wikimedia Commons

Later he took on a wider range of responsibilities. In 1597, Tycho having clashed with the new king, the entire research institute prepared to leave Hven. Longomontanus was put in charge of the attempt to bring Tycho’s star catalogue up from 777 stars to 1,000. When Tycho left Copenhagen, destination unknown, Longomontanus asked for and received his discharge from Tycho’s service.

While Tycho wandered around Europe trying to find a new home for his observatory, Longomontanus also wandered around Europe attending various universities–Breslau, Leipzig and Rostock–and trying to find a new patron. He graduated MA in Rostock. During their respective wanderings, Tycho’s and Longomontanus’ paths crossed several times and the corresponded frequently, Tycho always urging Longomontanus to re-enter his service. In January 1600 Longomontanus finally succumbed and joined Tycho in his new quarters in Prague, where Johannes Kepler would soon join the party.

When Kepler became part of Tycho’s astronomical circus in Prague, Longomontanus the senior assistant was working on the reduction of the orbit of Mars. Tycho took him off this project putting him instead onto the orbit of the Moon and giving Mars to Kepler, a move that would prove history making. As should be well known, Kepler battled many years with the orbit of Mars finally determining that it was an ellipse thereby laying the foundation stone for his elliptical astronomy. The results of his battle were published in 1609, together with his first two laws of planetary motion, in his Astronomia nova.


Portrait of Johannes Kepler. Source: Wikimedia Commons

Meanwhile, Longomontanus having finished Tycho’s lunar theory and corrected his solar theory took his final departure from Tycho’s service, with letters of recommendation, on 4 August 1600.  When Tycho died 24 October 1601 it was thus Kepler, who became his successor as Imperial Mathematicus and inherited his data, if only after a long dispute with Tycho’s relatives, and not Longomontanus, which Tycho would certainly have preferred.

Longomontanus again wandered around Northern Europe finally becoming rector of his alma mater the cathedral school in Viborg in 1603. In 1605, supported by the Royal Chancellor, Christian Friis, he became extraordinary professor for mathematics at the University of Copenhagen, moving on to become professor for Latin literature in the same year. In 1607 he became professor for mathematics, and in 1621 his chair was transformed into an extraordinary chair for astronomy a post he held until his death.

As a professor in Copenhagen he was a member of an influential group of Hven alumni: Cort Aslakssøn (Hven 159-93) professor for theology, Christian Hansen Riber (Hven 1586-90) professor for Greek, as well as Johannes Stephanius (Hven 1582-84) professor for dialectic and Gellius Sascerides (Hven 1585-86) professor for medicine.

Kepler and Longomontanus corresponded for a time in the first decade of the seventeenth century but the exchange between the convinced supporter of heliocentricity and Tycho’s most loyal lieutenant was not a friendly one as can be seen from the following exchange:

Longomontanus wrote to Kepler 6th May 1604:

These and perhaps all other things that were discovered and worked out by Tycho during his restoration of astronomy for our eternal benefit, you, my dear Kepler, although submerged in shit in the Augean stable of old, do not scruple to equal. And you promise your labor in cleansing them anew and even triumph, as if we should recognise you as Hercules reborn. But certainly no one does, and prefers you to such a man, unless when all of it has been cleaned away, he understands that you have substituted more appropriate things in the heaven and in the celestial appearances. For in this is victory for the astronomer to be seen, in this, triumph. On the other hand, I seriously doubt that such things can ever be presented by you. However, I am concerned lest this sordid insolence of yours defile the excellent opinion of all good and intelligent men about the late Tycho, and become offensive.

Kepler responded early in 1605:

The tone of your reference to my Augean stable sticks in my mind. I entreat you to avoid chicanery, which is wont to be used frequently with regard to unpopular things. So that you might see that I have in mind how the Augean stable provided me with the certain conviction that I have not discredited astronomy – although you can gather from the present letter – I will use it with the greatest possible justification. But it is to be used as an analogy, not for those things that you or Tycho were responsible for constructing – which either blinded by rage or perverted by malice you quite wrongfully attributed to me – but rather in the comparison of the ancient hypotheses with my oval path2. You discredit my oval path. I hold up to you the hundred-times-more-absurd spirals of the ancients (which Tycho imitated by not setting up anything new but letting the old things remain). If you are angry that I cannot eliminate the oval path, how much more ought you to be angry with the spirals, which I abolished. It is as though I have sinned with the oval I have left, even though to you all the rest of the ancients do not sin with so many spirals. This is like being punished for leaving behind one barrow full of shit although I have cleaned the rest of the Augean stables. Or in your sense, you repudiate my oval as one wagon of manure while you tolerate the spirals which are the whole stable, to the extent that my oval is one wagon. But it is unpleasant to tarry in rebutting this most manifest slander.

 Whereas, as already mentioned above, Kepler presented his heliocentric theory to the world in 1609, Longomontanus first honoured Tycho’s memory with his Astronomia Danica in 1622. Using Tycho’s data Longomontanus provided planetary models and planetary tables for Tycho’s geo-heliocentric system. Longomontanus, however, differed from Tycho in that he adopted the diurnal rotation of Helisaeus Roeslin, Nicolaus Raimarus and David Origanus.


The Astronomia Danica saw two new editions in 1640 and 1663. For the five decades between 1620 and 1670 Kepler’s elliptical astronomy and the Tychonic geo-heliocentric system with diurnal rotation competed for supremacy in the European astronomical community with Kepler’s elliptical system finally triumphing.

 In 1625 Longomontanus suggested to the King, Christian IV, that he should build an observatory to replace Tycho’s Stjerneborg, which had been demolished in 1601. The observatory, the Rundetaarn (Round Tower), was conceived as part of the Trinitatis Complex: a university church, a library and the observatory. The foundation stone was laid on 7 July 1637 and the tower was finished in 1642. Longomontanus was appointed the first director of the observatory, after Leiden 1632 only the second national observatory in Europe.


Copenhagen – Rundetårn Source: Wikimedia Commons

Both Kepler and Longomontanus, who lost their fathers early, started life as paupers Both of them worked they way up to become leading European astronomers. Kepler has entered the pantheon of scientific gods, whereas Longomontanus has largely been assigned to the dustbin of history. Although Longomontanus cannot be considered Kepler’s equal, I think he deserves better, even if he did back the wrong theory.








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

Spicing up the evolution of the mathematical sciences

When we talk about the history of mathematics one thing that often gets forgotten is that from its beginnings right up to the latter part of the Early Modern Period almost all mathematics was developed to serve a particular practical function. For example, according to Greek legend geometry was first developed by the ancient Egyptians to measure (…metry) plots of land (geo…) following the annual Nile floods. Trade has always played a very central role in the development of mathematics, the weights and measures used to quantify the goods traded, the conversion rates of different currencies used by long distance traders, the calculation of final prices, taxes, surcharges etc. etc. A good historical example of this is the Islamic adoption of the Hindu place value decimal number system together with the associated arithmetic and algebra for use in trade, mirrored by the same adoption some time later by the Europeans through the trader Leonardo Pisano. In what follows I want to sketch the indirect impact that the spice trade had on the evolution of the mathematical sciences in Europe during the Renaissance.

The spice trade does not begin in the Renaissance and in fact had a long prehistory going back into antiquity. Both the ancient Egyptians and the Romans had extensive trade in spices from India and the Spice Islands, as indeed the ancient Chinese also did coming from the other direction.


The spice trade from India attracted the attention of the Ptolemaic dynasty, and subsequently the Roman empire. Source: Wikimedia Commons

Throughout history spice meant a much wider range of edible, medicinal, ritual and cosmetic products than our current usage and this trade was high volume and financially very rewarding. The Romans brought spices from India across the Indian Ocean themselves but by the Middle Ages that trade was dominated by the Arabs who brought the spices to the east coast of Africa and to the lands at the eastern end of the Mediterranean, known as the Levant; a second trade route existed overland from China to the Levant, the much fabled Silk Road. The Republic of Venice dominated the transfer of spices from the Levant into Europe, shipping them along the Mediterranean.


The economically important Silk Road (red) and spice trade routes (blue) blocked by the Ottoman Empire c. 1453 with the fall of the Byzantine Empire, spurring exploration motivated initially by the finding of a sea route around Africa and triggering the Age of Discovery. Source: Wikimedia Commons

Here I go local because it was Nürnberg, almost literally at the centre of Europe, whose traders collected the spices in Venice and distributed them throughout Europe. As Europe’s premier spice traders the Nürnberger Patrizier (from the Latin patrician), as they called themselves, grew very rich and looking for other investment possibilities bought up the metal ore mines in central Europe. In a short period of time they went from selling metal ore, to smelting the ore themselves and selling the metal, to working the metal and selling the finished products; each step producing more profit. They quite literally produced anything that could be made of metal from sewing needles to suits of armour. Scientific and mathematical instruments are also largely made of metal and so Nürnberg became Europe’s main centre for the manufacture of mathematical instruments in the Renaissance. The line from spice to mathematical instruments in Nürnberg is a straight one.


Torquetum designed by Johannes Praetorius and made in Nürnberg

By the middle of the fifteenth century the Levant had become a part of the Ottoman Empire, which now effectively controlled the flow of spices into Europe and put the screws on the prices. The Europeans needed to find an alternative way to acquire the much-desired products of India and the Spice Islands, cutting out the middlemen. This need led to the so-called age of discovery, which might more appropriately be called the age of international sea trade. The most desirable and profitable trade goods being those spices.

The Portuguese set out navigating their way down the west coast of Africa and in 1488 Bartolomeu Dias succeeded in rounding the southern most tip of Africa and entering the Indian Ocean.


Statue of Bartolomeu Dias at the High Commission of South Africa in London. Source: Wikimedia Commons

This showed that contrary to the Ptolemaic world maps the Indian Ocean was not an inland sea but that it could be entered from the south opening up a direct sea route to India and the Spice Islands.


A printed map from the 15th century depicting Ptolemy’s description of the Ecumene, (1482, Johannes Schnitzer, engraver). Showing the Indian Ocean bordered by land from the south Source: Wikimedia Commons

In 1497 Vasco da Gama took that advantage of this new knowledge and sailed around the Cape, up the east coast of Africa and then crossing the Indian Ocean to Goa; the final part of the journey only being made possible with the assistance of an Arab navigator.


The route followed in Vasco da Gama’s first voyage (1497–1499) Source: Wikimedia Commons

Famously, Christopher Columbus mistakenly believed that it would be simpler to sail west across, what he thought was, an open ocean to Japan and from there to the Spice Islands. So, as we all learn in school, he set out to do just that in 1492.

In fourteen hundred and ninety two

Columbus sailed the ocean blue.

The distance was of course much greater than he had calculated and when, what is now called, America had not been in the way he and his crews would almost certainly have all died of hunger somewhere out on the open seas.


Columbus’ voyage. Modern place names in black, Columbus’s place names in blue Source: Wikimedia Commons

The Portuguese would go on over the next two decades to conquer the Spice Islands setting up a period of extreme wealth for themselves. Meanwhile, the Spanish after the initial disappointment of realising that they had after all not reached Asia and the source of the spices began to exploit the gold and silver of South America, as well as the new, previously unknown spices, most famously chilli, that they found there. In the following centuries, eager also to cash in on the spice wealth, the English and French pushed out the Portuguese in India and the Dutch did the same in the Spice Islands themselves. The efforts to establish sea borne trading routes to Asia did not stop there. Much time, effort and money was expended by the Europeans in attempts to find the North West and North East Passages around the north of Canada and the north of Russia respectively; these efforts often failed spectacularly.

So, you might by now be asking, what does all this have to do with the evolution of the mathematical science as announced in the title? When those first Portuguese and Spanish expedition set out their knowledge of navigation and cartography was to say the least very rudimentary. These various attempts to reach Asia and the subsequent exploration of the Americas led to an increased effort to improve just those two areas of knowledge both of which are heavily based on mathematics. This had the knock on effect of attempts to improve astronomy on which both navigation and cartography depend. It is not chance or coincidence that the so-called age of discovery is also the period in which modern astronomy, navigation and cartography came of age. Long distance sea trading drove the developments in those mathematically based disciplines.

This is not something that happened overnight but there is a steady curve of improvement in this disciplines that can be observed over the two plus centuries that followed Dias’ first rounding of the Cape. New instruments to help determine latitude and later longitude such as mariners’ astrolabe (which is not really an astrolabe, around 1500) the backstaff (John Davis, 1594) and the Hadley quadrant (later sextant, 1731) were developed. The Gunter Scale or Gunter Rule, a straight edge with various logarithmic and trigonometrical scales, which together with a pair of compasses was used for cartographical calculations (Edmund Gunter, early seventeenth century). William Oughtred would go on to lay two Gunter Scales on each other and invent the slide rule, also used by navigators and cartographers to make calculations.

New surveying instruments such as the surveyor’s chain (also Edmund Gunter), the theodolite (Gregorius Reisch and Martin Waldseemüller independently of each other but both in 1512) and the plane table (various possible inventors, middle of the sixteenth century). Perhaps the most important development in both surveying and cartography being triangulation, first described in print by Gemma Frisius in 1533.

Cartography developed steadily throughout the sixteenth century with cartographers adding the new discoveries and new knowledge to their world maps (for example the legendary Waldseemüller world map naming America) and searching for new ways to project the three-dimensional earth globe onto two-dimensional maps. An early example being the Stabius-Werner cordiform projection used by Peter Apian, Oronce Fine and Mercator.


Cordiform projection in a map of the world by Apianus 1524 which is one of the earliest maps that shows America Source: Wikimedia Commons

This development eventually leading to the Mercator-Wright projection, a projection specifically designed for marine navigators based on Pedro Nunes discovery that a path of constant bearing is not a great circle but a spiral, known as a loxodrome or rhumb line. Nunes is just one example of a mathematical practitioner, who was appointed to an official position to develop and teach new methods of navigation and cartography to mariners, others were John Dee and Thomas Harriot.


Pedro Nunes was professor of mathematics at the University of Coimbra and Royal Cosmographer to the Portuguese Crown. Source: Wikimedia Commons

To outline all of the developments in astronomy, navigation and cartography that were driven by the demands the so-called age of discovery, itself triggered by the European demand for Asian spices would turn this blog post into a book but I will just mention one last thing. In his one volume history of mathematics, Ivor Grattan-Guinness calls this period the age of trigonometry. The period saw a strong development in the use of trigonometry because this is the mathematical discipline most necessary for astronomy, navigation and cartography. One could say a demand for spices led to a demand for geometrical angles.



Filed under History of Astronomy, History of Cartography, History of Navigation, Renaissance Science, Uncategorized

Does the world really need another Galileo hagiography?

When it was first advertised several people drew my attention to Michael E. Hobart’s The Great Rift: Literacy, Numeracy, and the Religion-Science Divide[1]and it had hardly appeared when others began to ask what I thought about it and whether one should read it? I find it kind of flattering but also kind of scary that people want to know my opinion of a book before committing but even I can’t read a more than 500 page, intellectually dense book at the drop of the proverbial hat. Curiosity peaked piqued I acquired a copy, for a thick bound volume it’s actually quite reasonably priced, and took it with me to America, as my travel book. I will now give my considered opinion of Hobart’s tome and I’m afraid that it’s largely negative.


Hobart’s title says nearly everything about his book and to make sure you know where he is going he spells it out in detail in an 18-page introductory chapter The Rift between Religion and Science, which he attributes to the fact that in the seventeenth century science ceased to be verbal and became numerical. If this should awaken any suspicions in your mind, yes his whole thesis is centred round Galileo’s infamous two books diatribe in Il Saggiatore. As far as I can see the only new thing that Hobart introduces in his book is that he clothes his central thesis in the jargon of information technology, something that I found irritating.

The next 34 pages are devoted to explaining that in antiquity the world was described both philosophically and theologically in words. Moving on, we get a 124-page section dealing with numbers and mathematics entitled, From the “Imagination Mathematical” to the Threshold of Analysis. Here Hobart argues that in antiquity and the Middle Ages numbers were thing numbers, i.e. they were only used in connection with concrete objects and never in an abstract sense simply as numbers for themselves. His presentation suffers from selective confirmation bias of his theory, when talking about the use of numbers in the Middle ages he only examines and quotes the philosophers, ignoring the mathematicians, who very obviously used numbers differently.

He moves on to the High Middle Ages and the Renaissance and outlines what he sees as the liberation of numbers from their thing status through the introduction of the Hindu-Arabic numbers through Leonardo Pisano, the invention of music notation, the introduction of linear perspective in art and the introduction of both Scaliger’s chronology and the Gregorian calendar. Here once again his presentation definitely suffers from selective confirmation bias. He sees both Scaliger and the Gregorian calendar as the first uses of a universal time measuring system for years. Nowhere in his accounts of using numbers or the recording of time in years does he deal with astronomy in antiquity and down to the Early Modern Period. Astronomers used the Babylonian number system, just as abstract as the Hindu-Arabic system, and the Egyptian solar calendar in exactly the same way as Scaliger’s chronology. He also ignores, except somewhere in a brief not much later, the earlier use of the Hindu-Arabic number system in computos.

Here it is worth mentioning a criticism of others that Hobart brings later. In a chapter entitled, Towards the Mathematization of Matter, he briefly discusses Peter Harrison on science and religion and David Wootton on the introduction of a new terminology in the seventeenth century. He goes on to say, “…both of these fine scholars overlook just how the mathematical abstractions born of the new information technology and modern numeracy supplied an alternative to literacy as a means for discerning patterns in nature.” Two things occur to me here, firstly the mathematization of science as the principle driving force behind the so-called scientific revolution is one of the oldest and most discussed explanation of the emergence of modern science, so Hobart is only really offering old wine in new bottles and not the great revolutionary idea that he thinks he has discovered. The second is that in his book, The Invention of Science, David Wootton has a 47-page section entitled The Mathematization of the World, dealing with the changes in the use and perception of mathematics in the Renaissance that is, in my opinion, superior to Hobart’s account.

The third and final part of Hobart’s book is titled Galileo and the Analytical Temper and is a straight up hagiography. This starts with a gushing account of Galileo’s proportional compass or sector, prominent on the book’s cover. In all of his account of how fantastic and significant this instrument is Hobart neglects an important part of its history. He lets the reader assume that this is a Galileo invention, which is far from true. Although in other places Hobart mentions Galileo’s patron and mentor Guidobaldo del Monte he makes no mention of the fact that Galileo’s instrument was a modification and development of any earlier instrument of del Monte’s, which in turn was a modification of an instrument designed and constructed by Fabrizio Mordente.

This sets the tone for Hobart’s Galileo. He invents the scientific method, really? Then we get told, “Then in a dazzling stroke he pointed it [the telescope] skyward. He was not the first to do so, but he was certainly the first to exploit the new telescope, using it to expand beyond normal eyesight and peer into the vastness of space.” No he wasn’t!  Hobart gives us a long discourse on Galileo’s atomism explaining in detail his theory of floating bodies but neglects to point out that Galileo was simply wrong. He is even more crass when discussing Galileo’s theory of the tides in his Dialogo. After a long discourse on how brilliantly-scientific Galileo’s analysis leading to his theory is Hobart calmly informs us, “Galileo’s theory, of course was subsequently proved wrong by Newton…”! Yes, he really did write that! Galileo’s theory of the tides was contradicted by the empirical facts before he even published it and is the biggest example of blind hubris in all of Galileo’s works.

Hobart’s Galileo bias is also displayed in his treatment of Galileo’s conflicts with the Catholic Church and Catholic scientists. After a very good presentation of Galileo’s excellent proof, in his dispute with Scheiner, that the sunspots are on the surface of the sun and not satellites orbiting it. Hobart writes in an endnote, “A committed Aristotelian, Scheiner continued to advance fierce polemics against Galileo, but even he eventually accepted Galileo’s analysis.” In fact Scheiner accepted Galileo’s analysis fairly rapidly and went on to write the definitive work on sunspots. Hobart somehow neglects to mention that Galileo falsely accused Scheiner of plagiarism in his Il Saggiatore and then presented some of Scheiner’s results as his own in his Dialogo. Describing the dispute in 1615/16 Hobart quoting Bellarmino’s Foscarini letter, “I say that if there were a true demonstration that the sun is at the centre of the world and the earth in the third heaven, and that the sun does not circle the earth but the earth circles the sun, then one would have to proceed with great care in explaining the Scriptures that appear contrary, and say rather that we do not understand them, than that what is demonstrated is false”, goes on to say without justification that Bellarmino would not have accepted a scientific proof but only an Aristotelian one. This is, to put it mildly, pure crap. The behaviour of the Jesuit astronomers throughout the seventeenth century proves Hobart clearly wrong.

I’m not even going to bother with Hobart’s presentation of the circumstances surrounding the trial, it suffices to say that it doesn’t really confirm with the known facts.

I also have problems with Hobart’s central thesis, “The Great Rift.” At times he talks about it as if it was some sort of explosive event, as his title would suggest then admits on more than one occasion that it was a very long drawn out gradual process. Although he mentions it in asides he never really addresses the fact that long after Galileo many leading scientists were deeply religious and saw their scientific work as revealing God’s handy work; scientists such as Kepler and Newton who were just as analytical and even more mathematical than Galileo.

Throughout the book I kept getting the feeling that Hobart is simply out of touch with much of the more recent research in the history of science although he has obviously invested an incredible amount of work in his book, which boasts 144-pages of very extensive endnotes quoting a library full of literature. Yes, the mathematization of science played a significant role in the evolution of science. Yes, science and religion have been drifting slowly apart since the Early Modern Period but I don’t think that the mathematization of science is the all-encompassing reason for that separation that Hobart is trying to sell here. No, Galileo did not singlehandedly create modern science as Hobart seem to want us to believe, he was, as I pointed out in a somewhat notorious post several years ago, merely one amongst a crowd of researchers and scholars involved in that process at the end of the sixteenth and the beginning of the seventeenth centuries. Does Hobart’s book bring anything new to the table? No, I don’t think it does. Should one read it? That is up to the individual but if I had known what was in it before I read it, I wouldn’t have bothered.




[1]Michael E. Hobart, The Great Rift: Literacy, Numeracy, and the Religion-Science Divide, Harvard University Press, Cambridge & London, 2018


Filed under Book Reviews, History of Astronomy, History of Mathematics, Uncategorized

A seventeenth century picture from Nürnberg

During my daily rounds on Facebook I stumbled across this wonderful seventeenth century frontispiece from a book published in Nürnberg and thought it was so nice that I would share it here. I don’t really know who all the gentlemen sitting at the table are but that is the city of Nürnberg in the background.


I really dig the table leg.

This is the title page of the book: Jacobi Bartschii … Planisphærium stellatum; seu, Vice-globus coelestis in piano delineatus (Nuremberg 1661)


You can read it or even download it here

H/T Gudrun Wolfschmidt

Leave a comment

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Hold on it’s coming

The English translation of our Simon Marius book is becoming a reality. Should become available to purchase early next year or possibly late in this one.


Engraved image of Simon Marius (1573-1624), from his book Mundus Iovialis, 1614 Source: Houghton Library via Wikimedia Commons


  • Simon Marius and his Research
  • Hans Gaab and Pierre Leich (Eds.)
  • In the series Historical & Cultural Astronomy, Springer International Publishing, Cham 2019
  • Translation with additional material of the German conference report “Simon Marius und seine Forschung”
  • Authors: Thony Christie, Wolfgang R. Dick, Hans Gaab, Christopher M. Graney, Jürgen Hamel, Albert van Helden, Dieter Kempkens, Richard L. Kremer, Pierre Leich, Klaus Matthäus, Thomas Müller, Dagmar L. und Ralph Neuhäuser, Jay M. Pasachoff, Rudolf Pausenberger, Joachim Schlör, Norman Schmidt, Olga Sinzev und Huib J. Zuidervaart. With a bibliography of Simon Marius’s publications and a word of welcome from Joachim Wambsganß.
  • 20 Essays (Content). 481 pages, 144 illustrations, trim size: 155 mm x 235 mm, weight 640 g.
  • ISBN 978-3-319-92620-9 (Hardcover), Price ca. €149,79; 978-3-319-92621-6 (eBook)
  • Acquisition:
  • Springer International Publishing, Cham/CH

P.S. I’m only first in the list of authors because it’s done alphabetically!



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Some good Copernican mythbusting

For those who haven’t already seen it Tim O’Neill, Renaissance Mathematicus friend and guest blogger, has posted a superb essay on his excellent blog, History for Atheists, on the myths surrounding the dissemination, publication and reception of Copernicus’ heliocentric theory, The Great Myths 6: Copernicus’ Deathbed Publication. Regular readers of the Renaissance Mathematicus won’t learn anything new but it is an excellent summary of the known historical facts and well worth a read. As with this blog the comments are also well worth reading.

The earliest mention of Copernicus’ theory – Matthew of Miechów’s 1514 catalogue

Go on over and give Tim a boost!


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

Michael Mästlin: not just Kepler’s teacher

A large number of significant but minor figures in the history of science tend to get lost in the shadows of those, whom we have raised to god like status within that history; whole hordes have been swallowed up by the shadows cast by Galileo and Newton. Lesley Murdin even wrote an excellent book, Under Newton’s Shadow[1], in acknowledgement of the latter. One figure who suffers from this phenomenon is the German astronomer Michael Mästlin (1550–1631), who if he gets mentioned at all, it is only with reference to his most famous student, Johannes Kepler. Although his substantial influence on Kepler is probably his most important role in the history of astronomy, Mästlin (or Maestlin, as he is usually written in English) deserves to be much better known in his own right.


Michael Mästlin portrait 1619 artist unknown

Michael Mästlin was born 30 September 1550 in Göppingen into a strict Lutheran Protestant family. He was schooled in the convent schools of Königsbronn and Herrenalb. He matriculated at the University of Tübingen in 1658 where he graduated BA in 1569. In the same year he entered the Tübingen Stift (the Lutheran Church hall of residence) with a stipend from the Duke of Württemberg. He graduated MA in in 1571 and completed his theology studies in 1573.

As a student he studied astronomy and mathematics under Philipp Apian (1531–1589) the son of the astronomer, mathematician and cartographer Peter Apian.


Philipp Apian, artist unknown Source: Wikimedia Commons

Philipp had already succeeded his father as professor for mathematics and astronomy in Ingolstadt at the age of twenty-one. Like many others he studied medicine alongside his teaching duties finishing his medical studies later in the Northern Italian universities. In 1569 he was forced by the Jesuits to quit his post in Ingolstadt because of his membership of the Lutheran Church. In the same year he received the professorship in Tübingen. Apian was professor in Tübingen for fourteen years until he was, ironically, forced to resign because he refused to sign the Formula of Concord a document setting out the Lutheran statement of faith and condemning Calvinists.

Apian inspired and guided Mästlin’s interest in astronomy and mathematics. Already in 1570 Mästlin acquired a copy of Copernicus’ De revolutionibus and he would go on to become one of the first university teachers to teach Copernican heliocentricity. From 1573 until he first left Tübingen in 1576 he was Repetens mathematicus (teacher for revision in the mathematical sciences) at the Stift. In 1570 he published the second edition of Erasmus Reinhold’s Prutenicae Tabulae. In 1572 he observed the Supernova, publishing his observations in his Demonstratio Astronomica Loci Stellae Novae the following year. In 1575 he represented the absent Apian as mathematics professor.

In 1576 Mästlin was appointed Diaconus (2nd pastor) in the parish of Backnang, a small town near Stuttgart. His clerical appointment didn’t stop his astronomical activities. He observed the comet of 1577 publishing his Observatio et Demostratio Cometae Aetherei, qui anno … 1577 in 1578. Much is made, in the secondary literature, of Tycho Brahe’s observations of the 1572 supernova and the 1577 comet and how the determination of the supralunar occurrence of both phenomena led to the refutation of the Aristotelian principle of an unchanging heavens. However, at the time Tycho’s were not the only observations and Mästlin’s reports had at least as much if not more influence on the debate as those of Tycho. In fact Tycho named Mästlin as his prime witness confirming his own observations.

In the years between 1578 and 1580 Mästlin constructed his own observing instruments, a quadrant and a Jacob’s staff. In 1580 he published his Ephemerides Novae … for the years 1577 to 1590. His highly visible astronomical activities led to Mästlin being appointed professor for astronomy and mathematics at the University of Heidelberg in 1580, which had become Protestant in 1556. In Heidelberg he published the first edition of his astronomy textbook, Epitome Astronominae, a standard Ptolemaic geocentric work 1582, which over the years would see six further editions.


In 1584 he was called back to Tübingen his alma mater to succeed his own teacher Philipp Apian as professor for the mathematical sciences, a post that he would hold for more than 47 years until his death in 1631.

Whilst still at Heidelberg Mästlin, as a leading Protestant mathematicus was consulted by the rulers of the German Protestant states on whether to adopt the new Gregorian calendar. In his Gründtlicher Bericht von der allgemeinen und nunmehr bei 1600 Jahren von dem ersten Kaiser Julio bis jetzt gebrauchten jarrechnung oder kalender (Rigorous report on the general and up till now for 1600 years used calculation of years or calendar from the first Caesar Julio), published in 1583, he rejected the new calendar on mathematical and astronomical grounds, noting it was not clear how it was calculated, (this information didn’t become available until much later) and also on religious grounds. In his anti-Catholic polemic he referred to the Pope as “seiner Heilosigkeyt”, that is “his Awfulness”, a pun in German on Heiligkeit meaning holiness and Heillos meaning awful. Mästlin played a central role in the rejection of the calendar reform in the Protestant states, who only adopted the Gregorian calendar in 1700.

It is in his role as professor in Tübingen that is best known and in particular his relationship with his most famous student Johannes Kepler. Kepler studied in Tübingen from 1589 till 1594, like Mästlin as a stipendiary in the Tübinger Stift. From Mästlin’s lectures Kepler learnt about the heliocentric system of Copernicus and not through some sort of secret instruction as is often falsely claimed. It was almost certainly Mästlin who recommended Kepler for the post of mathematics teacher in Graz and it was definitely Mästlin who convinced Kepler to accept the post. The two stayed close after Kepler’s move to Graz and exchanged many long letters on a range of subject. In 1596 Mästlin assisted Kepler in getting his Mysterium Cosmographicum published, adding Rheticus’ Narratio Prima, as an appendix to the work thereby demonstrating his strong support for the Copernican hypothesis.


Strangely after 1600 Mästlin began to distance himself from his most famous pupil, no longer answering all of his letters and declining to help when Kepler was desperately looking for a new position. This cooling of their relationship from the side of the mentor has never been satisfactorily explained but two things probably played a role. On the scientific side Mästlin strongly disapproved of Kepler’s attempts to explain the physical cause of planetary motion, admonishing him to stick to the astronomer’s role of providing mathematical models of that motion and to leave the explanations to the philosophers. Also a thorn in Mästlin’s highly devout Lutheran eyes was Kepler’s sympathy for other religious viewpoints, which led to his being excluded from communion.

Kepler’s was by no means Mästlin’s only renowned student. His most notorious student is certainly Johann Valentin Andreae (1586–1654)


Johann Valentin Andreae Source: Wikimedia Commons

author of the Rosicrucian Chymische Hochzeit Christiani Rosencreutz anno 1459 (Chymical Wedding of Christian Rosenkreutz) published in 1616

valentin_hochzeit_1616_0005_800pxand the Christian utopia Reipublicae Christianopolitanae descriptio (Description of the Republic of Christianopolis) published in 1619. Andreae initially studied theology and mathematics in Tübingen from 1602 till 1605. Mästlin as his mathematics teacher had a major influence on him also introducing him to Kepler with whom he corresponded until the latters death. He was also responsible for Andeae coming into contact with Kepler’s close friend Christoph Besold, who introduced Andreae to the esoteric studies that would lead to his Rosicrucian activities. Andeae’s utopia is, like that from Bacon, one that is endowed with natural philosophy and the mathematical science.


Less notorious but more scientific than Andeae was the polymath Wilhelm Schickard (1592–1635), who as well as being one of Mästlin’s students was also part of the circle of scholars around Besold and Andeae.


Wilhelm Schickard, artist unknown Source: Wikimedia Commons

Like Mästlin and Kepler, a student on the Tübinger Stift he graduated MA in 1611 and went on to study theology. 1613 he received the first of various clerical posts. In 1617 he meet and got to know Kepler, in Württemberg for his mother’s witch trial. He provided engravings and woodcuts for Kepler’s magnum opus the Harmonice Mundi. In 1619 he was appointed professor for Hebrew in Tübingen and here first displayed his talent for logical analysis and leaning. He invented the Rota Hebræa two rotating discs to help his students learn Hebraic conjugations. He also wrote a Horologium Hebræum a Hebrew textbook in 24 capitals, each of which was learnable in one hour. During his time as professor for Hebrew he was also an active astronomer amongst other things producing highly accurate ephemerides. Schickard was a skilled instrument maker and in 1623 he designed and built the earliest known calculating machine, his Rechenuhr (calculating clock) with the intension of helping Kepler with his astronomical calculations. His calculating machine could only add and subtract but included a set of Napier’s Bones in the form of cylinders to aid multiplication and division. He started to build one for Kepler but it got destroyed in a fire. Knowledge of Schickard’s calculating machine got lost in the seventeenth century but was rediscovered in the twentieth century amongst Kepler’s letters by Max Casper. Bruno von Freytag-Löringhoff reconstructed the machine in the 1960s.


In 1631 Schickard succeeded Mästlin as professor of the mathematical sciences at Tübingen. Like Mästlin, Mästlin’s teacher Apian as well as Kepler, Schickard also worked as a surveyor and cartographer.

Schickards Rechenmaschine

Schickard’s Rechenuhr. Reconstruction by Bruno Baron von Freytag-Löringhoff

Throughout his career as an astronomer Mästlin stood in contact and corresponded with nearly all the leading astronomers in Europe. During his later years as professor Mästlin continued working as an active astronomer. Like Kepler he observed the nova of 1604 and the comet of 1618. In 1628 he is known to have observed a lunar eclipse and a second one together with Schickard in 1630. Mästlin was the first person to publish an account of earthshine, the illumination of the moon by sunlight reflected from the earth.


Earthshine reflected from the Moon during conjunction with Venus (left) Source: Wikimedia Commons

Largely forgotten today, except in his role as Kepler’s teacher and an early Copernican, Mästlin was viewed in his own lifetime as one of Europe’s leading astronomers and that with justification.




[1] Lesley Murdin, Under Newton’s Shadow, Astronomical Practices in the Seventeenth Century, Adam Hilger Ltd., Bristol and Boston, 1985


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