Category Archives: History of Astrology

The Arch-Humanist

The name Conrad Celtis is not one that you’ll find in most standard books on the history of mathematics, which is not surprising as he was a Renaissance humanist scholar best known in his lifetime as a poet. However, Celtis played an important role in the history of mathematics and is a good example of the fact that if you really wish to study the evolution of the mathematical sciences it is necessary to leave the narrow confines of the mathematics books.

Conrad Celtis: Gedächtnisbild von Hans Burgkmair dem Älteren, 1507 Source: Wikimedia Commons

Conrad Celtis: Gedächtnisbild von Hans Burgkmair dem Älteren, 1507
Source: Wikimedia Commons

Born Konrad Bickel or Pyckell, (Conrad Celtis was his humanist pseudonym) the son of a winemaker, in Franconian Wipfield am Main near Schweinfurt on 1 February 1459, he obtained his BA at the University of Cologne in 1497. Unsatisfied with the quality of tuition in Cologne he undertook the first of many study journeys, which typified his life, to Buda in 1482, where he came into contact with the humanist circle on the court of Matthias Corvinus, the earlier patron of Regiomontanus. 1484 he continued his studies at the University of Heidelberg specialising in poetics and rhetoric, learning Greek and Hebrew and humanism as a student of Rudolf Agricola, a leading Dutch early humanist scholar. Celtis obtained his MA in 1485. 1486 found him underway in Italy, where he continued his humanist studies at the leading Italian universities and in conversation with many leading humanist scholars. Returning to Germany he taught poetics at the universities of Erfurt, Rostock and Leipzig and on 18 April 1487 he was crowned Poet Laureate by Emperor Friedrich III in Nürnberg during the Reichstag. In Nürnberg he became part of the circle of humanists that produced the Nürnberger Chronicle to which he contributed the section on the history and geography of Nürnberg. It is here that we see the central occupation of Celtis’ life that brought him into contact with the Renaissance mathematical sciences.

During his time in Italy he suffered under the jibes of his Italian colleges who said that whilst Italy had perfect humanist credentials being the inheritors of the ancient Roman culture, Germany was historically a land of uncultured barbarians. This spurred Celtis on to prove them wrong. He set himself the task of researching and writing a history of Germany to show that its culture was the equal of Italy’s. Celtis’ concept of history, like that of his Renaissance contemporaries, was more a mixture of our history and geography the two disciplines being regarded as two sides of the same coin. Geography being based on Ptolemaeus’ Geographia (Geographike Hyphegesis), which of course meant cartography, a branch of the mathematical sciences.

Continuing his travels in 1489 Celtis matriculated at the University of Kraków specifically to study the mathematical sciences for which Kraków had an excellent reputation. A couple of years later Nicolaus Copernicus would learn the fundamentals of mathematics and astronomy there. Wandering back to Germany via Prague and Nürnberg Celtis was appointed professor of poetics and rhetoric at the University of Ingolstadt in 1491/92. Ingolstadt was the first German university to have a dedicated chair for mathematics, established around 1470 to teach medical students astrology and the necessary mathematics and astronomy to cast a horoscope. When Celtis came to Ingolstadt there were the professor of mathematics was Andreas Stiborius (born Stöberl 1464–1515) who was followed by his best student Johannes Stabius (born Stöberer before 1468­–1522) both of whom Celtis convinced to support him in his cartographic endeavours.

In 1497 Celtis received a call to the University of Vienna where he established a Collegium poetarum et mathematicorum, that is a college for poetry and mathematics, with Stiborius, whom he had brought with him from Ingolstadt, as the professor for mathematics. In 1502 he also brought Stabius, who had succeeded Stiborius as professor in Ingolstadt, and his star student Georg Tanstetter to Vienna. Stiborius, Stabius and Tanstetter became what is known, to historians of mathematics, as the Second Viennese School of Mathematics, the First Viennese School being Johannes von Gmunden, Peuerbach and Regiomontanus, in the middle of the fifteenth century. Under these three Vienna became a major European centre for the mathematical sciences producing many important mathematicians the most notable being Peter Apian.

Although not a mathematician himself Conrad Celtis, the humanist poet, was the driving force behind one of the most important German language centres for Renaissance mathematics and as such earns a place in the history of mathematics. A dedicated humanist, wherever he went on his travels Celtis would establish humanist societies to propagate humanist studies and it was this activity that earned him the German title of Der Erzhumanist, in English the Arch Humanist. Celtis died in 1508 but his Collegium poetarum et mathematicorum survived him by twenty-two years, closing first in 1530

 

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

Hans Holbein and the Nürnberg–Ingolstadt–Vienna Renaissance mathematical nexus.

There is a strong tendency, particularly in the popular history of science, to write about or present scientists as individuals. This leads to a serious distortion of the way that science develops and in particular propagates the lone genius myth. In reality science has always been a collective endeavour with its practitioners interacting in many different ways and on many different levels. In the Renaissance, when travelling from one end of Europe to the other would take weeks and letters often even longer, one might be excused for thinking that such cooperation was very low level but in fact the opposite was the truth, with scholars in the mathematical sciences exchanging information and ideas throughout Europe. A particularly strong mathematical nexus existed in the Southern German speaking area between the cities of Nürnberg, Ingolstadt and Vienna in the century between 1450 and 1550. Interestingly two of the paintings of the Northern Renaissance artist Hans Holbein the Younger open a door into this nexus.

Holbein (c. 1497–1543) was born in Augsburg the son of the painter and draughtsman Hans Holbein the Elder. As a young artist he lived and worked for a time in Basel where he became acquainted with Erasmus and worked for the printer publisher Johann Froben amongst others. Between 1526 and 1528 he spent some time in England in the household of Thomas More and it is here that he painted the second portrait I shall be discussing. The next four years find him living in Basel again before he returned to England in 1532 where he became associated with the court of Henry VIII, More having fallen out of favour. It was at the court that he painted, what is probably his most well know portrait, The Ambassadors in 1533.

Hans Holbein The Ambassadors Source: Wikimedia Commons

Hans Holbein The Ambassadors
Source: Wikimedia Commons

The painting shows two courtiers, usually identified as the French Ambassador Jean de Dinteville and Georges de Selve, Bishop of Lavaur standing on either side of a set of shelves laden with various books and instruments. There is much discussion was to what the instruments are supposed to represent but it is certain that, whatever else they stand for, they represent the quadrivium, arithmetic, geometry music and astronomy, the four mathematical sciences taught at European medieval universities. There are two globes, on the lower shelf a terrestrial and on the upper a celestial one. The celestial globe has been positively identified, as a Schöner globe and the terrestrial globe also displays characteristics of Schöner’s handwork.

Terrestrial Globe The Ambassadors Source Wikimedia Commons

Terrestrial Globe The Ambassadors
Source Wikimedia Commons

Celestial Globe The Ambassadors Source Wikimedia Commons

Celestial Globe The Ambassadors
Source Wikimedia Commons

Johannes Schöner (1477–1547) was professor for mathematics at the Egidienöberschule in Nürnberg, the addressee of Rheticus’ Narratio Prima, the founder of the tradition of printed globe pairs, an editor of mathematical texts for publication (especially for Johannes Petreius the sixteenth centuries most important scientific publisher) and one of the most influential astrologers in Europe. Schöner is a central and highly influential figure in Renaissance mathematics.

On the left hand side of the lower shelf is a copy of Peter Apian’s Ein newe und wolgegründete underweisung aller Kauffmanns Rechnung in dreyen Büchern, mit schönen Regeln und fragstücken begriffen (published in Ingolstadt in 1527) held open by a ruler. This is a popular book of commercial arithmetic, written in German, typical of the period. Peter Apian (1495–1552) professor of mathematics at the University of Ingolstadt, cartographer, printer-publisher and astronomer was a third generation representative of the so-called Second Viennese School of Mathematics. A pupil of Georg Tannstetter (1482–1535) a graduate of the University of Ingolstadt who had followed his teachers Johannes Stabius and Andreas Stiborious to teach at Conrad Celtis’ Collegium poetarum et mathematicorum, of which more later. Together Apian and Tannstetter produced the first printed edition of the Optic of Witelo, one of the most important medieval optic texts, which was printed by Petreius in Nürnberg in 1535. The Tannstetter/Apian/Petreius Witelo was one of the books that Rheticus took with him as a present for Copernicus when he visited him in 1539. Already, a brief description of the activities of Schöner and Apian is beginning to illustrate the connection between our three cities.

Apian's Arithmetic Book The Ambassadors Source: Wikimedia Commons

Apian’s Arithmetic Book The Ambassadors
Source: Wikimedia Commons

When Sebastian Münster (1488–1552), the cosmographer, sent out a circular requesting the cartographers of Germany to supply him with data and maps for his Cosmographia, he specifically addressed both Schöner and Apian by name as the leading cartographers of the age. Münster’s Cosmographia, which became the biggest selling book of the sixteenth century, was first published by Heinrich Petri in Basel in 1544. Münster was Petri’s stepfather and Petri was the cousin of Johannes Petreius, who learnt his trade as printer publisher in Heinrich’s printing shop in Basel. The Petri publishing house was also part of a consortium with Johann Amerbach and Johann Froben who had employed Hans Holbein in his time in Basel. Wheels within wheels.

The, mostly astronomical, instruments on the upper shelf are almost certainly the property of the German mathematician Nicolaus Kratzer (1487–1550), who is the subject of the second Holbein portrait who will be looking at.

Nicolas Kratzer by Hans Holbein Source: Wikimedia Commona

Nicolas Kratzer by Hans Holbein
Source: Wikimedia Commona

Born in Munich and educated at the universities of Cologne and Wittenberg Kratzer, originally came to England, like Holbein, to become part of the Thomas More household, where he was employed as a tutor for More’s children. Also like Holbein, Kratzer moved over to Henry VIII’s court as court horologist or clock maker, although the clocks he was responsible for making were more probably sundials than mechanical ones. During his time as a courtier Kratzer also lectured at Oxford and is said to have erected a monumental stone sundial in the grounds of Corpus Christi College. One polyhedral sundial attributed to Kratzer is in the Oxford Museum for the History of Science.

Polyhedral Sundial attributed to Nicolas Kratzer Source: MHS Oxford

Polyhedral Sundial attributed to Nicolas Kratzer
Source: MHS Oxford

In 1520 Kratzer travelled to Antwerp to visit Erasmus and here he met up with Nürnberg’s most famous painter Albrecht Dürer, who regular readers of this blog will know was also the author of a book on mathematics. Dürer’s book contains the first printed instructions, in German, on how to design, construct and install sundials, so the two men will have had a common topic of interest to liven there conversations. Kratzer witnessed Dürer, who was in Antwerp to negotiate with the German Emperor, painting Erasmus’ portrait and Dürer is said to have also drawn a portrait of Kratzer that is now missing. After Kratzer returned to England and Dürer to Nürnberg the two of them exchanged, at least once, letters and it is Kratzer’s letter that reveals some new connections in out nexus.

Albrecht Dürer selfportrait Source: Wikimedia Commons

Albrecht Dürer selfportrait
Source: Wikimedia Commons

In his letter, from 1524, Kratzer makes inquires about Willibald Pirckheimer and also asks if Dürer knows what has happened to the mathematical papers of Johannes Werner and Johannes Stabius who had both died two years earlier.

Willibald Pirckheimer (1470–1530) a close friend and patron of Dürer’s was a rich merchant, a politician, a soldier and a humanist scholar. In the last capacity he was the hub of a group of largely mathematical humanist scholars now known as the Pirckheimer circle. Although not a mathematician himself Pirckheimer was a fervent supporter of the mathematical sciences and produced a Latin translation from the Greek of Ptolemaeus’ Geōgraphikḕ or Geographia, Pirckheimer’s translation provided the basis for Sebastian Münster’s edition, which was regarded as the definitive text in the sixteenth century. Stabius and Werner were both prominent members of the Pirckheimer circle.

Willibald Pirckheimer by Albrecht Dürer Source: Wikimedia Commons

Willibald Pirckheimer by Albrecht Dürer
Source: Wikimedia Commons

The two Johanneses, Stabius (1450–1522) and Werner (1468–1522), had become friends at the University of Ingolstadt where the both studied mathematics. Ingolstadt was the first German university to have a dedicated chair for mathematics. Werner returned to his hometown of Nürnberg where he became a priest but the Austrian Stabius remained in Ingolstadt, where he became professor of mathematics. The two of them continued to correspond and work together and Werner is said to have instigated the highly complex sundial on the wall of the Saint Lorenz Church in Nürnberg, which was designed by Stabius and constructed in 1502.

St Lorenz Church Nürnberg Sundial 1502 Source: Astronomie in Nürnberg

St Lorenz Church Nürnberg Sundial 1502
Source: Astronomie in Nürnberg

It was also Werner who first published Stabius’ heart shaped or cordiform map projection leading to it being labelled the Werner-Stabius Projection. This projection was used for world maps by Peter Apian as well as Oronce Fine, France’s leading mathematicus of the sixteenth century and Gerard Mercator, of whom more, later. The network expands.

Mercator cordiform world map 1538 Source: American Geographical Society Library

Mercator cordiform world map 1538
Source: American Geographical Society Library

In his own right Werner produced a partial Latin translation from the Greek of Ptolemaeus’ Geographia, was the first to write about prosthaphaeresis (a trigonometrical method of simplifying calculation prior to the invention of logarithms), was the first to suggest the lunar distance method of determining longitude and was in all probability Albrecht Dürer’s maths teacher. He also was the subject of an astronomical dispute with Copernicus.

Johannes Werner Source: Wikimedia Commons

Johannes Werner
Source: Wikimedia Commons

Regular readers of this blog will know that Stabius co-operated with Albrecht Dürer on a series of projects, including his famous star maps, which you can read about in an earlier post here.

Johannes Statius Portrait by Albrecht Dürer Source: Wikimedia Commons

Johannes Statius Portrait by Albrecht Dürer
Source: Wikimedia Commons

An important non-Nürnberger member of the Pirckheimer Circle was Conrad Celtis (1459–1508), who is known in Germany as the arch-humanist. Like his friend Pirckheimer, Celtis was not a mathematician but believed in the importance of the mathematical sciences. Although already graduated he spent time in 1489 on the University of Kraków in order to get the education in mathematics and astronomy that he couldn’t get at a German university. Celtis had spent time at the humanist universities of Northern Italy and his mission in life was to demonstrate that Germany was just as civilised and educated as Italy and not a land of barbarians as the Italians claimed. His contributions to the Nuremberg Chronicle can be viewed as part of this demonstration. He believed he could achieve his aim by writing a comprehensive history of Germany including, as was common at the time its geography. In 1491/92 he received a teaching post in Ingolstadt, where he seduced the professors of mathematics Johannes Stabius and Andreas Stiborius (1464–1515) into turning their attention from astrology for medicine student, their official assignment, to mathematical cartography in order to help him with his historical geography.

Conrad Celtis Source: Wikimedia Commons

Conrad Celtis
Source: Wikimedia Commons

Unable to achieve his ends in Ingolstadt Celtis decamped to Vienna, taking Stabius and Stiborius with him, to found his Collegium poetarum et mathematicorum as mentioned above and with it the so-called Second Viennese School of Mathematics; the first had been Peuerbach and Regiomontanus in the middle of the fifteenth century. Regiomontanus spent the last five years of his life living in Nürnberg, where he set up the world’s first scientific publishing house. Stiborius’ pupil Georg Tannstetter proved to be a gifted teacher and Peter Apian was by no means his only famous pupil.

The influence of the Nürnberg–Ingolstadt–Vienna mathematicians reached far beyond their own relatively small Southern German corridor. As already stated Münster in Basel stood in contact with both Apian and Schöner and Stabius’ cordiform projection found favour with cartographers throughout Northern Europe. Both Apian and Schöner exercised a major influence on Gemma Frisius in Louvain and through him on his pupils Gerard Mercator and John Dee. As outlined in my blog post on Frisius, he took over editing the second and all subsequent editions of Apian’s Cosmographia, one of the most important textbooks for all things astronomical, cartographical and to do with surveying in the sixteenth century. Frisius also learnt his globe making, a skill he passed on to Mercator, through the works of Schöner. Dee and Mercator also had connections to Pedro Nunes (1502–1578) the most important mathematicus on the Iberian peninsular. Frisius had several other important pupils who spread the skills in cosmography, and globe and instrument making that he had acquired from Apian and Schöner all over Europe.

Famously Rheticus came to Nürnberg to study astrology at the feet of Johannes Schöner, who maintained close contacts to Philipp Melanchthon Rheticus patron. Schöner was the first professor of mathematics at a school designed by Melanchthon. Melanchthon had learnt his mathematics and astrology at the University of Tübingen from Johannes Stöffler (1452–1531) another mathematical graduate from Ingolstadt.

Kupferstich aus der Werkstatt Theodor de Brys, erschienen 1598 im 2. Bd. der Bibliotheca chalcographica Source: Wikimedia Commons

Kupferstich aus der Werkstatt Theodor de Brys, erschienen 1598 im 2. Bd. der Bibliotheca chalcographica
Source: Wikimedia Commons

Another of Stöffler’s pupils was Sebastian Münster. During his time in Nürnberg Rheticus became acquainted with the other Nürnberger mathematicians and above all with the printer-publisher Johannes Petreius and it was famously Rheticus who brought the manuscript of Copernicus’ De revolutionibus to Nürnberg for Petreius to publish. Rheticus says that he first learnt of Copernicus’s existence during his travels on his sabbatical and historians think that it was probably in Nürnberg that he acquired this knowledge. One of the few pieces of astronomical writing from Copernicus that we have is the so-called Letter to Werner. In this manuscript Copernicus criticises Werner’s theory of trepidation. Trepidation was a mistaken belief based on faulty data that the rate of the precession of the equinoxes is not constant but varies with time. Because of this highly technical dispute amongst astronomers Copernicus would have been known in Nürnberg and thus the assumption that Rheticus first heard of him there. Interestingly Copernicus includes observations of Mercury made by Bernhard Walther (1430–1504), Regiomontanus partner, in Nürnberg; falsely attributing some of them to Schöner, so a connection between Copernicus and Nürnberg seems to have existed.

In this brief outline we have covered a lot of ground but I hope I have made clear just how interconnected the mathematical practitioners of Germany and indeed Europe were in the second half of the fifteenth century and the first half of the sixteenth. Science is very much a collective endeavour and historians of science should not just concentrate on individuals but look at the networks within which those individual operate bringing to light the influences and exchanges that take place within those networks.

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

Asterisms and Constellations and how not to confuse them with Tropical Signs.

If you are going to write about something, especially if you intend to lay bare somebody else’s ignorance, it pays to actually know what you are talking about otherwise you could well end up looking like a total idiot, as does Anna Culaba in her article on the RYOT website, The Stars and Your Astrological Signs Have Been Lying to You This Whole Time. I should point out that Ms Culaba is by no means the first person to publically embarrass themselves pontificating on this subject, in fact it’s a reoccurring theme much loved by scientists and science fans who want to take a cheap shot at astrology. Indeed, as we will see later Ms Culaba, in her article, is in fact just regurgitating the content of a BBC website. So what exactly does our intrepid science fan say in her blog post?

My horoscope for today (I’m a Virgo) according to Astrology.com reads, “Today, explore an aspect of an unfamiliar religion or culture. Today is a day to make plans and aim high.” There are only two things that are keeping me from leaving work right now: one, I don’t really believe that the stars can determine what will happen in my life and two, I wasn’t really born under the star sign that the world told me I was born into. According to the BBC, about 86 percent of people are actually born under a different sign than the one they think. This is because 2,000 years ago, when the Ancient Greeks first created the zodiacs, the star signs corresponded to the position of the sun relative to the constellations that appeared in the sky the day people were born. Unfortunately, during that time people didn’t know of the phenomenon known as the precession. Live Sciences reports that the precession is when the Earth continually wobbles around its axis in an almost 26,000-year cycle thanks to the gravitational attraction of the moon. Thanks to this phenomenon, the constellations some people live and die by have actually drifted away from us. This means that constellations are now actually off by a month. So if you were born between August 11 to September 16 you’re not the picky and critical Virgo that you thought you were — you’re really an ambitious Leo whose strength of purpose allows you to accomplish many, many things. And if you’re astrological world hasn’t been rocked enough, if you thought you had your star sign wrong, wait until some of you realize that there’s actually a 13th zodiac sign known as the Ophiuchus. According to the BBC, the Ancient Greeks deliberately left out the original zodiac so that ancient astrologers would be able to divide the sun’s 360 degree path into 12 equal parts. Where does Ophiuchus fit into the zodiac calendar? It goes between Scorpio and Sagittarius, so if you were born between November 30 and December 18 consider yourself an Ophiuchus. You’re probably very secretive and good at hide and seek.

I have reproduced the whole of Ms Culaba’s screed here to save me having to quote it in little bits, merely removing the links from the original. If you read it through you what will discover is the central claim that astrologers were too stupid to realise the astronomical phenomenon of precession and so you were not actually born under the star sign that they claim you were. There are two general points to be made here, firstly astrologers were well aware of precession and secondly Ms Culaba and the source she is quoting don’t know the fundamental difference between constellations and tropical signs. So for the benefit of Ms Culaba and all others who are confused by the topic we will have a Renaissance Mathematicus guide to asterisms, constellations, the zodiac and tropical signs.

If you go out on a dark night with a clear sky in an area with little or no light pollution (and if you have never done so you should, it’s awesome) and look up in the heavens you will see a myriad of stars looking down on you in a vast blue black vault. If you are not a trained astronomer you will probably find no means of orienting your gaze in this confusion of twinkling lights. This problem was confronted by all human cultures since the dawn of human existence. The human brain seems to be programmed for pattern recognition and so, like children with a join up the dots picture book, all cultures started to create pictures by imagining lines joining up or outlining eye-catching groups of stars and giving these pictures names. These pictures, and they exist in all human cultures, are known technically as asterisms. These asterisms help the observing eye gain orientation when traversing the vast dome of the night sky and early astronomers started compiling lists of the most prominent such join-up-the-dots-pictures or asterisms in order to use them as a scaffolding for mapping the heavens. Those asterisms contained in such formal lists are called constellations. Our modern, western list of constellations has its origins in ancient Babylonian astrology/astronomy and comes down to us via the ancient Greeks and the medieval Islamic astronomers. In his Syntaxis Mathematiké, Ptolemaeus lists 48 constellations by name. Currently, the International Astronomical Union (IAU) recognises 88 named constellations. We now need to turn our attention to the origins of the zodiac.

Viewed from the earth, and before the beginning of the so-called space age that was the only way possible to view the heavens, the sun appears to orbit the earth once every year. In fact the year is defined as the time it takes for the sun to orbit the earth. The path the sun follows on its way around the earth is called the ecliptic and is tilted at approximately 23 degrees to the earth’s equator. This tilt, known as the obliquity of the ecliptic, is the reason why we have seasons on the earth. The six planets visible to the naked eye and know in antiquity – Moon, Mercury, Venus, Mars, Jupiter and Saturn – all appear to orbit the earth in the plane of the ecliptic making this imaginary belt around the heavens very important for the study of astronomy. The earliest known mapping of the ecliptic is contained in a set of Babylonian clay tablets known as the MUL.APIN, which date from around 1000 BCE. Here the path of the moon’s orbit is described or mapped with 17 or 18 (the text is somewhat ambiguous) constellations and stars. The moon’s orbit is tilted at about five degrees to the ecliptic. This mapping was still in use around 700 BCE. By around 500 BCE the 17/18 constellations/stars had be replaced by twelve constellations of varying sizes. Circa 420 BCE the Babylonians had replaced those twelve constellations with twelve equal divisions of the ecliptic comprising 30° segments. These segments were named after the constellations they replaced and form the zodiac that was taken over by the Greeks and made its way down to us. Those segments are known technically as tropical or sun signs, form the basis of zodiacal astrology and are abstract geometrical segment of the ecliptic and not constellations. The constellations slowly circle the heavens due to precession, the tropical signs do not! If an astrologer says you were born under the sign Virgo it means that the sun was in the 30° segment of the ecliptic that bears the name Virgo at the moment of your birth. This has nothing apart from the name in common with the constellation Virgo.

It is not the astrologers who display ignorance of the precession of the equinox, to give the phenomenon its full name, but Ms Culaba who displays total ignorance of both astronomy and astrology. This is not a very good situation to be in if you are going to write about the history of science and yes we are talking about the history of science here, the zodiac with its tropical signs was originally conceived for astronomical purposes. Ms Culaba might be excused because she did not originate this particular piece of history of science rubbish but is merely regurgitating false information from what she obviously thought was a reliable source, the BBC.

Here we have the presenter of Stargazing Live, a high prestige BBC science programme, Dara O Brian presenting the world with high-grade bullshit under the BBC’s banner. O Brian and his co-presenter Brian Cox should know better and I find it a total disgrace that the fee payers money is being wasted on such rubbish under the guise of educational television, both the presenters and the Beeb should be thoroughly ashamed of themselves.

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

Do you believe in magic?

I’m in a bit of a quandary about this post for two different reasons. Firstly I didn’t really want to write yet another negative post at the moment and was considering various positive options when somebody drew my attention to the article that is going to be the subject of this one. However having once read through it I just couldn’t let it go. On the other hand having always been a powerful advocate of seriously investigating the so-called occult science activities of the scholars in the Early Modern period I find it slightly bizarre to now be giving the Hist-Sci Hulk treatment to an article that appears to do just that. The article in question is posted on the Vox website and is entitled, These 5 men were scientific geniuses. They also thought magic is real.

Before dealing with the ‘5 men’ there are a couple of general points of criticism that have to be levelled at this article. To begin with the whole thing is written in a supercilious tone of superiority. Despite the authors disclaimer, “We have the benefit of hindsight today, which gives us an unfair advantage over these geniuses” he creates the impression the whole time of ‘I’m just a simple Joe’ but I’m way more enlightened than these ‘geniuses’. Not a good way to approach any historical topic. The other major failure that weaves its way through the whole article is the equating of astrology, alchemy and magic, as one and the same thing. This is of course historically a serious mistake and disqualifies the entire article from the start. The grounds for justification, academic status and the levels of acceptance of the three disciplines differ from each other, as well as over time and place. Each one of them has to be dealt with separately within the given context and they cannot and should not be lumped together. This of course relates to the authors supercilious tone of superiority and is typical of the woolly thinking of all too many gnu atheists and adherents of scientism. Anything that doesn’t conform with their, often badly articulated, concept of science is dismissed as ‘magical thinking’ and as worthless. Let us now turn to the ‘5 men’.

First up we have Tuscany’s favourite son, Galileo Galilei who apparently believed “astrology changed everything”:

Today, Galileo (1564-1642) is held up as a paragon of rationality. He advocated heliocentrism — the idea that the sun, not the Earth, was at the center of the solar system — fought an anti-heliocentric church at great risk, and greatly advanced astronomy throughout Europe.

He also was something like a fortune teller.

Galileo didn’t just believe in astrology: he practiced it, conducted it for wealthy clients, and taught it to medical school students. If students at the University of Padua had taken MCATs, Galileo would have included a question about whether a Leo should date a Gemini.

Galileo wasn’t alone in keeping up on his signs. His contemporary, Johannes Kepler conducted his own astrological studies, though more reluctantly (he called people who believed in astrology “fatheads”).

Ignoring the opening paragraph and cutting to the chase a Renaissance astrologer, particularly an academic one, would object intensely to being referred to as ‘a fortune teller’. In the Renaissance astrology was generally accepted as a reputable academic disciple, a science i.e. a system of knowledge, whereas most other forms of divination i.e. fortune telling were frowned on as charlatanry. Here we have historical context, blithely ignored by our author, poking its nose in. Medical astrology, or iatro-mathematics, was a mainstream academic discipline taught at all Renaissance universities in the medical faculty, usually by the professor of mathematics. So if Galileo did indeed teach iatro-mathematics he would have been merely fulfilling the terms of his contract. I say if because it is to be assumed that Galileo did indeed teach such courses, however the proof that he did so doesn’t exists. The comment about ‘whether a Leo should date a Gemini’ is just plain stupid, as iatro-mathematics has nothing to do with judicial astrology, that is the everyday horoscope astrology, a completely different branch of the discipline.

Of course Galileo, who really did accept the truth of astrology, did practice judicial astrology famously casting and interpreting his own horoscope and those of his daughters. He also cast and interpreted the horoscopes not of ‘rich clients’ but wealthy patrons; there is a substantial difference. Rich clients would imply that Galileo’s services as an astrologer were for hire like any other street vendor, this was not the case. Rich patrons sought out Galileo’s company to share in his intellectual talents. Here his abilities to cast and interpret horoscopes became instruments of credit. Galileo entertained his patrons by supplying witty and stimulating after dinner discourses or debates or by providing the required horoscope. In exchange Galileo received favours from his patrons, a case of good wine, help with the cost of publishing his books or introductions to important and influential people such as the Pope.

On the good Johannes Kepler our author walks right into one of the most persistent myths of all in the history of science based on a classic case of quote mining, the claim that he was reluctant about astrology. Kepler was much more concerned about astrology, which he definitely believed in, than Galileo and wrote several books about it. However he totally rejected conventional horoscope astrology believing that the stars signs were artificial constructs with no significance whatsoever. He developed his own system based on planetary alignments, astrological aspects, and directio (directions, which I’m not going to explain!). Not unsurprisingly he didn’t find any takers for his reformed astrology. However his vitriolic diatribes against the conventional horoscope astrology and its practitioners, when quote mined, leads many people to the mistaken belief that he was in some way anti-astrology.

Our author next reveals, oh my god, that Newton was an alchemist. This is probably the most often ‘revealed secret’ about Grantham’s most famous son. This is titled “Isaac Newton thought alchemy was the future”, as we will see Newton was actually much more interested in alchemy’s past.

John Maynard Keynes called Isaac Newton (1642-1726) “the last of the magicians” with good reason. Newton spent half his life obsessed with alchemy, the transformative magic most frequently associated with turning different metals into gold. To make things even more complicated, in 1696, Newton became Warden of the Mint, and he became master of the Mint in 1700. The Royal Mint, of course, makes the coins for the entire United Kingdom. To be clear: an alchemist was the person in charge of making all the money.

Newton wasn’t the only respected mind who had visions of diving into gold coins. Robert Boyle is considered the father of chemistry, but he dabbled in alchemy as well. In fact, he was so committed to the alchemical cause that he fought to make alchemy legal, since Henry IV had banned it (because alchemy wasn’t good for the monetary supply). Needless to say, the repeal wasn’t necessary.

The philosopher’s stone Newton chased after wasn’t only able to “cure” metals that weren’t gold. It also had medical powers that fascinated Newton and his peers. Unfortunately, today you can only find the philosopher’s stone in the British subtitle of the first Harry Potter book.

Alchemy is not magic and any medieval or renaissance alchemist would have been deeply insulted if anybody had accused him of practicing magic. Alchemy as practiced by Newton or Boyle considered itself to be a well-founded knowledge system and it was this that attracted Newton. Newton certainly never had vision of diving into gold coins and neither did Boyle. Newton’s beliefs were in fact even weirder than our author thinks. Newton was an adherent of a widespread Renaissance philosophy known as prisca sapientia.

This theory thought that humanity had been in possession of perfect knowledge of the world shortly after the creation. This knowledge had become lost over time and Newton believed that his scientific discoveries were not discoveries but rediscoveries. He also believed that alchemy was the oldest form of knowledge and that if he could discover the secrets of alchemy he could tap into that ancient source of all knowledge. Pretty bizarre, I know, but it all formed a coherent whole in Newton’s worldview. On a scientific level the Newton experts are now convinced that his belief in alchemy enabled him to develop his theory of universal gravity, which, with its action at a distance, heavily contradicted the prevailing mechanical philosophy. The Cartesian and Leibnizian mechanical philosophers criticised his theory of gravity for exactly this reason.

Our author seems to think that there is something wrong with an alchemist becoming Warden or Master of the Mint. In fact Newton’s extensive chemical knowledge, won through his alchemical experimentation over many years, enabled him to develop and to put into practice new much improved methods of assaying metals to test the purity of coins. A major win for the Royal Mint.

The closing comment about alchemy and Harry Potter is a perfect example of the author’s childish attitude, supercilious superiority. This attitude is displayed to the full in his paragraphs about Tycho Brahe, entitled “Tycho Brahe made everyone believe he was a sorcerer”.

Tycho Brahe (1546-1601) created his own model of the universe and, though he didn’t get things quite right, helped advance astronomy and catalogued more than 1,000 stars. He also convinced everyone he was a sorcerer.

He did so from the unique perch of his private sorcerer’s island, Hveen (today known in English as Ven). Fantastically wealthy, Brahe built multiple observatories there, had a squad of astronomical assistants, and he used tiny automata (robots) to convince the locals he had magic powers. It didn’t hurt that he partied hard, had his nose partly sliced off in a duel and got his pet moose drunk at parties.

But Tycho didn’t just hoodwink the public into believing he was magical — he believed it too. He publically lectured against anyone who believed astrology was fake, and he also believed alchemy was the future for mystical discoveries. Brahe even became so synonymous with magic that an entire calendar of magical days was made in his honor (and his name was slapped on to give it magical credibility).

This is a bizarre mixture of half true facts and fairy stories. Tycho only catalogued 700 stars but added 300 more from the Ptolemaic star catalogue to bring his own up to 1000. He did nothing at all to convince anyone that he was a sorcerer. The island of Hven was his fief, awarded to him by the Danish King as his birth right as a highborn aristocrat and to call it a sorcerer’s island is not only wrong but also childish. He only built two observatories, one in his mansion house Uraniborg and the other a sunken observatory in the grounds called Stjerneborg. The story about the automata is a myth created by Pierre Gassendi in his biography of Tycho. The nose and moose stories are actually irrelevancies to the subject under discussion along the lines of, if I show that Tycho was weird then people are more likely to believe the rest of the shit that I’m dishing up.

Once again we have a very fundamental category error. Tycho was a practicing astrologer and a Paracelsian pharmacist neither of which activities is magic. Tycho held an oration at the beginning of a guest lecture course on astronomy that he held at the University of Copenhagen defending the validity of astrology, a not unusual presentation in that age. Rheticus’ public oration on being appointed professor for mathematics in Wittenberg was on the same subject. Tycho an adherent of the Renaissance microcosmos/macrocosmos philosophy, as above so below, also believed that alchemy served the same function on earth as astrology in the heavens but both were in his opinion ‘scientific’ and not mystical. Tycho’s interest in alchemy centred on his belief in and practice of Paracelsian medicine, a leading medical theory in some circles in Europe at the time and consisted mainly of research into and production of medicines.

The Magical Calendar is an engraving not a book and the author, Adam McLean, of the modern book on this object that our author links to writes the following:

“Although his name appears at the bottom right hand corner of the plate, the Magical Calendar probably has no direct connection with Tycho Brahe […] It seems most likely that the well known name of Tycho Brahe was associated with the Magical Calendar in order to gain a degree of publicity and supposed authority for the work. Certainly there is nothing in Brahe’s accepted corpus of writings of a similar nature.” [my emphasis]

Doesn’t quite say what our author wants it to say, does it?

Our author’s next selection is a truly bad example of low fruit. He presents us with Carl Linnaeus with the title “Carl Linnaeus classified magical animals like the hydra and believed in mermaids”.

Carl Linnaeus (1707-1778) imposed taxonomical order on animal and plant life. In his era, scientists were discovering all sorts of new species at a rapid clip (Linnaeus himself thought that pelicans might be a myth). That rapid pace of discovery led Linnaeus to believe, perhaps reasonably enough, that humans would soon find a host of mythological animals.

Linnaeus devoted a whole section of his landmark Systema Naturae to these strange beasts. It was called Animalia Paradoxa and included:

  • the hydra
  • the satyrus (a monkey-like man, similar to Pan in Greek mythology)
  • the phoenix (the bird that rose from the ashes)

Did Linnaeus believe in these animals? It’s hard to know, and some of Linnaeus’s defenders say he only included the animals to point out how absurd they were. In the 1730s, he became famous for debunking a hydra in Hamburg. However, we can reasonably claim that Linnaeus believed he’d found a troglodyte, was pretty confident he’d seen a unicorn horn, and was very excited at the chance to find a mermaid.

Whatever the motivation, Linnaeus wasn’t alone in believing in bizarre, vaguely magical animals. Gottfried Leibniz managed to help found calculus, yet he still wanted to fill a museum with weird (and imaginary) animals like the myrmecoleon (some sort of ant-lion).

The tone of this whole section is concerned with how superior our author is in comparison with the poor benighted Linnaeus; the heavy sent of mockery cannot be overlooked. He gives no consideration to the time in which Linnaeus was working and writing. He also appears to have left his own theme, as there is nothing ‘magical’ about the things he lists Linnaeus as having done.

Linnaeus lived and worked in the eighteenth century there was no Internet, no telephones, no telegraph, not even a reliable let alone universal postal system; a letter to South America, for example, would probably take months to arrive at its destination and quite possibly might not arrive at all. Linnaeus lived all of his life in Northern Europe and was dependent on the reports of others for descriptions of non-European species of plants and animals. If he got no chance to view one personally then a tiger was just as much a mythical animal as a manticore and he had no chance of proving the real existence of the one or the other. What we have here is an eighteenth century natural historian carefully classifying all the plants and animals that are known to him through multiple written sources. It’s worth noting that Linnaeus places those mythical creatures that he classifies into a separate category that he names Paradoxa the Greek pardoxon meaning contrary to accepted opinion, i.e. dodgy. Systema Naturae went through many editions and in the later ones this category was left out. Only one real animal was included in Paradoxa, the pelican, which given the fact that travellers tales described the pelican as cutting its own breast to feed its children was not an irrational decision. None of the mythical animals was included in a category with real animals. What we have here is careful rational scientific behaviour not magical thinking.

Linnaeus included humans as primates, which of course caused a controversy in the eighteenth century. He also included two other species in the genus homo, Homo troglodytes based on the accounts of Jacob Bontius and Homo lar based on other reports. He asked the Swedish East India Company to look for confirming evidence of the existence of Homo troglodytes, which they couldn’t deliver and Homo lar was later categorised as a gibbon, again a good natural historian doing his work. Belief in unicorns, some form of single horned horse, based on the existence of narwhal tusks was still very widespread in the eighteenth century, so to try and ridicule Linnaeus or this is pathetic. The same applies to mermaids.

The author’s attempt to besmirch Leibniz is really clutching at straws. What the hell is ‘managed to help invent calculus’ supposed to mean? That’s not exactly the usual way of talking about one of the greatest mathematical achievements of the seventeenth century. Curiosity cabinets and natural history collections played a central role in scientific activities throughout the sixteenth, seventeenth and eighteenth centuries, one of the largest, that of Hans Sloane, forming the basis of the British museum after Sloane’s death. Leibniz’ Drôle de Pensée, amusing thought, was to extend the curiosity cabinet into a much larger public exhibition space with active displays and machines alongside the passive objects displaying the full spectrum of science, technology and medicine, Science Museum anyone? That his long list of potential exhibits contains one mythical animal hardly makes this something to deride.

Our author’s fifth genius is, as would be expected, Paracelsus who apparently “loved natural magic and himself”.

Paracelsus (1493-1541) did a lot when he was alive, including basically inventing toxicology and naming zinc. But when he wasn’t revolutionizing scientific methods and naming metals, he was a big fan of magical things.

Born as Philippus Aureolus Theophrastus Bombastus von Hohenheim, he renamed himself Paracelsus, both because it was shorter and it literally meant he was “better than Celsus,” a first century Roman medical researcher (in Paracelsus’s defense, he may have been renamed by his biggest fans). Paracelsus wrote that from an early age the “transmutation of metals” was his obsession, and he pursued it with vigor as an adult.

When he wasn’t traveling the world performing surgeries, he tried to utilize “natural magic” to help patients. He was quoted as saying “magic is a great secret wisdom,” and while his understanding of natural magic occasionally lent itself to scientific inquiry, he also believed that “the soul strongly desires sulphur.” As the scientist on this list closest in time to Aristotle, it makes sense that Paracelsus would indulge in magic and the occult.

In his defense, that belief in magic was grounded in a commitment to inquiry: Paracelsus thought magic was just science that wasn’t understood yet. In a way, that unites all the scientists on this list, who pursued new knowledge even when it meant looking in some very unusual places.

The claim that Paracelsus basically invented toxicology, although not original to our author (who I doubt has any original thoughts), is historically highly dubious as poisons have been studied extensively since antiquity and it is rather strangely based on the legendary Paracelsus quote Dosis sola venenum facit, the dose makes the poison. Paracelsus was not born Philippus Aureolus Theophrastus Bombastus von Hohenheim, I refer the reader to my earlier post on the subject of his name.

The rest of the paragraphs on Paracelsus are a confused mess of unrelated claims picked at random from other peoples writings and doesn’t earn the right to be analysed so I won’t. I would ask the author why, having suddenly introduced the term, he doesn’t actually explain what natural magic is or was. Possibly the worst single sentence in the whole sorry mess that is this article is, As the scientist on this list closest in time to Aristotle, it makes sense that Paracelsus would indulge in magic and the occult. Anybody who actually knew anything about either Paracelsus or Aristotle could not conceive of writing this sentence, even as a parody.

Returning to my initial criticism of this apology for a historical article, astrology and alchemy are not magic if dealing academically and historically with these disciplines and because he introduces it at the end ‘natural magic’ is not magic as it is generally understood either. As often the case I find it fascinating that people who quite literally don’t know what they’re talking about think that it’s OK to write an article about the history of science on a widely read popular website. If they were to write about something popular, such as football or cars, on the same level no editor in the world would allow them to publish it, so why do they treat the history of science with such disrespect?

 

 

 

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Filed under History of Alchemy, History of Astrology, Myths of Science, Renaissance Science

The weather and the stars

My attention was recently drawn to the MacTutor history of maths website article on The History of Weather Forecasting. The article is largely concerned with the mathematics of weather forecasting from the nineteenth century onwards but has some short introductory paragraphs covering the prehistory of meteorology, which unfortunately displays a woeful ignorance of the subject. Under the heading Early Attempts we get served up the following:

It is not known when people first started to observe the skies, but at around 650 BC, the Babylonians produced the first short-range weather forecasts, based on their observations of the stars and clouds. The Chinese also recognised weather patterns, and by 300 BC astronomers had developed a calendar which divided the year into 24 festivals, each associated with a different weather phenomenon. Generally, weather was attributed to the vagaries of the gods, as the wide range of weather gods in various cultures, for example the Egyptian sun god Ra and Thor, the Norse god of thunder and lightning, proves. Many ancient civilisations developed rites such as rain dances and animal sacrifices in order to propitiate the weather gods.

The ancient Greeks were the first to develop a more scientific approach to explaining the weather. The work of the philosopher and scientist Aristotle (384-322 BC) is especially noteworthy, as it dominated people’s views on and their knowledge of the weather for the next 2000 years. In 340 BC, Aristotle wrote his book Meteorologica, where he tried to explain the formation of rain, clouds, wind and storms. In addition, he also described celestial phenomena such as comets and haloes. Many of his observations were — in retrospect — surprisingly accurate. For example, he believed that heat could cause water to evaporate. But he also jumped to quite a few wrong conclusions, such as that winds form “as the Earth exhales“, which were rectified from the Renaissance onwards.

Throughout the Middle Ages and beyond, the Church was the only official institution that was allowed to explain the causes of weather, and Aristotle’s Meteorologica was established as Christian dogma. Besides, weather observations were passed on in the form of rhymes, which are now known as weather lore. Many of these proverbs are based on very good observations and are accurate, as contemporary meteorologists have discovered.

This brief synopsis, which covers approximately one thousand years actually almost completely ignores the main form of weather forecasting practiced throughout the period covered astrometeorology. As any astute reader will have already deduce astrometeorology is a branch of astrology and is in fact astrological weather forecasting. This is one of the more rational forms of astrology; weather comes from the heavens, be it sunshine, fog, wind, or one of the many forms of precipitation (rain, snow, sleet, hail), so it would seem fairly logical to assume that the heaven cause or control the weather. This is exactly what people in antiquity did in many different cultures and actually what the article above is referring to in both of the first two quoted sentences although the author doesn’t seem to or doesn’t want to know it. It was not Aristotle’s views as expressed in the Meteorologica that “dominated people’s views on and knowledge of the weather for the next 2000 years” but astrometeorology. There is a slight irony here as a quote from Aristotle’s Meteorologica delivered one of main justifications for astrology in Western thought up to the Early Modern period. Astrometeorology is along with astro-medicine one of the branches of natural astrology and as such was even accepted throughout the Middle Ages and the Renaissance by people who rejected other forms of astrology, for example judicial or horoscope astrology.

This very widespread acceptance meant that it was astrometeorology that was the dominant form of weather forecasting in the Middle Ages accepted even by the Church at a time when judicial astrology was, at least official, heavily frowned upon. One might well say, so what? What does it matter what people believed before the emergence of scientific meteorology in the seventeenth century, when this superstitious twaddle got drop anyway? The answer is quit simple; astrometeorology played a significant role in the emergence of that scientific meteorology.

During the Renaissance astrology reached its highest level of popularity in the history of Western culture. Almost all mathematicians and astronomers (mostly one and the same) were also practicing astrologers and they were not just doing it for the money as is often falsely claimed by those who try to deny the significance of astrology in the Early Modern period; they really believed in it. However these were the people who also laid the foundations of the modern empirical approach to the sciences and they were often painfully aware of the lack of empirical justification for the science of astrology that they practiced. To counter this weakness they set about developing various projects to give astrology a solid empirical base, one of the principle projects involving astrometeorology. This project consisted of keeping accurate and continuous weather diaries. They thought that by recording the weather over long periods of time on a daily basis they could then distinguish the correlation, that they were sure existed, between the weather and the movement of the celestial bodies. The oldest known such weather diary was kept by Roger Bacon in the thirteenth century. Bacon was of course not only a fervent believer in astrology but also an early proponent of empirical methods in science. There are other scattered medieval weather diaries but the process first really kicked off at the end of the fifteenth century. The keeping of weather diaries was greatly furthered by the introduction of printed ephemerides, which provided the potential meteorologist with a convenient place to record his observations directly next to the astronomical/astrological information for the day.

A notable writer of weather diaries was Johannes Stöfler (1452-1531), who taught and influenced Philipp Melanchthon (a powerful advocate of Renaissance astrology), Sebastian Münster and others. Another was the Nürnberger mathematicus Johannes Werner (1462-1522), who first suggested the chronometer method of determining longitude. Probably most well-known as weather diary keeper was Tycho Brahe (1546-1601), without doubt the important observational astronomer in the pre-telescope era. Tycho is possibly also responsible for David Fabricius (1564-1617), discoverer, amongst other things, of the first variable star, Mira, keeping a weather diary. Fabricius help Johannes Kepler (1571-1630) to formulate his theory of elliptical planetary orbits in an extended correspondence; systematically criticising Kepler various formulations. Kepler a passionate astrologer also kept a weather diary. He famously established his reputation as an astrologer by correctly predicting an especially hard winter in his first prognostications as district mathematicus in Graz in 1594. Weather diaries were also kept by many other less well-known figures. It is significant that Pico della Mirandola (1463-1494) the most strident Renaissance critic of astrology also kept a weather diary and used the results as one of his arguments for rejecting astrology.

Pico della Mirandola was of course right the systematic keeping of weather diaries did not, as hoped, provide an empirical basis for the science of astrology but did exactly the opposite showing that astrometeorology, at least, was a refuted theory. However the results were not all negative. The systematic empirical weather observations contained in the diaries laid the foundations for scientific meteorology in the seventeenth century. The data collected by those Renaissance astrologers is still used by modern meteorologists to help establish long-term weather patterns.

 

 

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

The horror, the horror!

For those readers who might have wondered what The Renaissance Mathematicus looks and sounds like, you need wonder no more. There is now a video on Youtube in which I stumble and stutter my way through a very impromptu, not quite fifteen minute, lecture on the relationship between astronomy, astrology and medicine in the Early Modern Period. During which I indulge in a lot of arm waving and from time to time scratch my fleas. This video was filmed in the kitchen of the Remeis Observatory in Bamberg during a coffee break at the Astronomy in Franconia Conference last Monday, complete with the sounds of somebody loading the dishwasher.

The cameraman, who also puts some questions during this solo performance, was Chris Graney who requested my golden words for his students back in Louisville, the poor sods.

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Filed under Autobiographical, History of Astrology, History of Astronomy, History of medicine

Planetary Tables and Heliocentricity: A Rough Guide

Since it emerged sometime in the middle of the first millennium BCE the principal function of mathematical astronomy was to provide the most accurate possible predictions of the future positions of the main celestial bodies. This information was contained in the form of tables calculated with the help of the mathematical models, which had been derived by the astronomers from the observed behaviour of those bodies, the planets. The earliest Babylonian models were algebraic but were soon replaced by the Greeks with geometrical models based on spheres and circles. To a large extent it did not matter if those models were depictions of reality, what mattered was the accuracy of the prediction that they produced; that is the reliability of the associated tables. The models of mathematical astronomy were judge on the quality of the data they produced and not on whether they were a true reproduction of what was going on in the heavens. This data was used principally for astrology but also for cartography and navigation. Mathematical astronomy was a handmaiden to other disciplines.

Before I outline the history of such tables, a brief comment on terminology. Data on the movement of celestial bodies is published under the titles planetary tables and ephemerides (singular ephemeris). I know of no formal distinction between the two names but as far as I can determine planetary tables is generally used for tables calculated for quantitatively larger intervals, ten days for example, and these are normally calculated directly from the mathematical models for the planetary movement. Ephemeris is generally used for tables calculated for smaller interval, daily positions for example, and are often not calculated directly from the mathematical models but are interpolated from the values given in the planetary tables. Maybe one of my super intelligent and incredibly well read readers knows better and will correct me in the comments.

The Babylonians produced individual planetary tables, in particular of Venus, but we find the first extensive set in the work of Ptolemaeus. He included tables calculated from his geometrical models in his Syntaxis Mathematiké (The Almagest), published around 150 CE, and to make life easier for those who wished to use them he extracted the tables and published them separately, in extended form with directions of their use, in what is known as his Handy Tables. This publication provided both a source and an archetype for all future planetary tables.

The important role played by planetary tables in mathematical astronomy is illustrated by the fact that the first astronomical works produced by Islamic astronomers in Arabic in the eighth-century CE were planetary tables known in Arabic as zījes (singular zīj). These initial zījes were based on Indian sources and earlier Sassanid Persian models. These were quickly followed by those based on Ptolemaeus’ Handy Tables. Later sets of tables included material drawn from Islamic Arabic sources. Over 200 zījes are known from the period between the eighth and the fifteenth centuries. Because planetary tables are dependent on the observers geographical position most of these are only recalculation of existing tables for new locations. New zījes continued to be produced in India well into the eighteenth-century.

With the coming of the European translators in the twelfth and thirteenth centuries and the first mathematical Renaissance the pattern repeated itself with zījes being amongst the first astronomical documents translated from Arabic into Latin. Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī was originally better known in Europe for his zīj than for The Compendious Book on Calculation by Completion and Balancing” (al-Kitab al-mukhtasar fi hisab al-jabr wa’l-muqabala), the book that introduced algebra into the West. The Toledan Tables were created in Toledo in the eleventh-century partially based on the work of Abū Isḥāq Ibrāhīm ibn Yaḥyā al-Naqqāsh al-Zarqālī, known in Latin as Arzachel. In the twelfth-century they were translated in Latin by Gerard of Cremona, the most prolific of the translators, and became the benchmark for European planetary tables.

In the thirteenth- century the Toledan Tables were superseded by the Alfonsine Tables, which were produced by the so-called Toledo School of Translators from Islamic sources under the sponsorship of Alfonso X of Castile. The Alfonsine Tables remained the primary source of planetary tables and ephemerides in Europe down to the Renaissance where they were used by Peuerbach, Regiomontanus and Copernicus. Having set up the world’s first scientific press Regiomontanus produced the first ever printed ephemerides, which were distinguished by the accuracies of their calculations and low level of printing errors. Regiomontanus’ ephemerides were very popular and enjoyed many editions, many of them pirated. Columbus took a pirate edition of them on his first voyage to America and used them to impress some natives by accurately predicting an eclipse of the moon.

By the fifteenth-century astronomers and other users of astronomical data were very much aware of the numerous inaccuracies in that data, many of them having crept in over the centuries through frequent translation and copying errors. Regiomontanus was aware that the problem could only be solved by collecting new basic observational data from which to calculate the tables. He started on such an observational programme in Nürnberg in 1470 but his early death in 1475 put an end to his endeavours.

When Copernicus published his De revolutionibus in 1543 many astronomers hoped that his mathematical models for the planetary orbits would lead to more accurate planetary tables and this pragmatic attitude to his work was the principle positive reception that it received. Copernicus’ fellow professor of mathematic in Wittenberg Erasmus Reinhold calculated the first set of planetary tables based on De revolutionibus. The Prutenic Tables, sponsored by Duke Albrecht of Brandenburg Prussia (Prutenic is Latin for Prussian), were printed and published in 1551. Ephemerides based on Copernicus were produced by Johannes Stadius, a student of Gemma Frisius, in 1554 and by John Feild (sic), with a forward by John Dee, in 1557. Unfortunately they didn’t live up to expectations. The problem was that Copernicus’ work and the tables were based on the same corrupted data as the Alfonsine Tables. In his unpublished manuscript on navigation Thomas Harriot complained about the inaccuracies in the Alfonsine Tables and then goes on to say that the Prutenic Tables are not any better. However he follows this complaint up with the information that Wilhelm IV of Hessen-Kassel and Tycho Brahe on Hven are gathering new observational data that should improve the situation.

As a young astronomer the Danish aristocrat, Tycho Brahe, was indignant that the times given in both the Alfonsine and the Prutenic tables for a specific astronomical event that he wished to observe were highly inaccurate. Like Regiomontanus, a hundred years earlier, he realised that the problem lay in the inaccurate and corrupted data on which both sets of tables were based. Like Regiomontanus he started an extensive programme of astronomical observations to solve the problem, initially at his purpose built observatory financed by the Danish Crown on the island of Hven and then later, through force of circumstances, under the auspices of Rudolph II, the Holy Roman German Emperor, in Prague. Tycho devoted almost thirty years to accruing a vast collection of astronomical data. Although he was using the same observational instruments available to Ptolemaeus fifteen hundred years earlier, he devoted an incredible amount of time and effort to improving those instruments and the methods of using them, meaning that his observations were more accurate by several factors than those of his predecessors. What was now needed was somebody to turn this data into planetary tables, enter Johannes Kepler. Kepler joined Tycho in Prague in 1600 and was specifically appointed to the task of producing planetary tables from Tycho’s data. Contrary to popular belief he was not employed by Tycho but directly by Rudolph.

Following Tycho’s death, a short time later, a major problem ensued. Kepler was official appointed Imperial Mathematicus, as Tycho’s successor, and still had his original commission to produce the planetary tables for the Emperor, however, legally, he no longer had the data; this was Tycho’s private property and on his death passed into the possession of his heirs. Kepler was in physical possession of the data, however, and hung on to it during the protracted, complicated and at times vitriolic negotiations with Tycho’s son in law, Frans Gansneb Genaamd Tengnagel van de Camp, over their future use. In the end the heirs granted Kepler permission to use the data with the proviso that any publications based on them must carry Tengnagel’s name as co-author. Kepler then proceeded to calculate the tables.

Put like this, it sounds like a fairly straightforward task, however it was difficult and tedious work that Kepler loathed intensely. It was not made any easier by the personal and political circumstances surrounding Kepler over the years he took to complete the task. Wars, famine, usurpation of the Emperor’s throne (don’t forget the Emperor was his employer) and family disasters all served to make his life more difficult.

Finally in 1626, twenty-six years after he started Kepler had finally reduced Tycho’s thirty years of observations into planetary tables for general use, now he only had to get them printed. Drumming up the financial resources for the task was the first hurdle that Kepler successfully cleared. He then purchased the necessary paper and settled in Linz to complete the task of turning his calculations into a book. As the printing was progressing all the Protestants in Linz were ordered to leave the city, Kepler, being Imperial Mathematicus, and his printer were granted an exemption to finish printing the tables but then Wallenstein laid siege to the city to supress a peasants uprising. In the ensuing chaos the printing shop and the partially finished tables went up in flames.

Leaving Linz Kepler now moved to Ulm where, starting from the beginning again, he was finally able to complete the printing of the Rudophine Tables, named after the Emperor who had originally commissioned them but dedicated to the current Emperor, Ferdinand II. Although technically not his property, because he had paid the costs of having them printed Kepler took the finished volumes to the book fair in Frankfurt to sell in September 1627.

Due to the accuracy of Tycho’s observational data and the diligence of Kepler’s mathematical calculations the new tables were of a level of accuracy never seen before in the history of astronomy and fairly quickly became the benchmark for all astronomical work. Perceived to have been calculated on the basis of Kepler’s own elliptical heliocentric astronomy they became the most important artefact in the general acceptance of heliocentricity in the seventeenth century. As already stated above systems of mathematical astronomy were judged on the data that they produced for use by astrologers, cartographers, navigators et al. Using the Rudolphine Tables Gassendi was able to predict and observe a transit of Mercury in 1631, as Jeremiah Horrocks succeeded in predicting and observing a transit of Venus for the first time in human history based on his own calculations of an ephemeris for Venus using Kepler’s tables, it served as a confirming instance of the superiority of both the tables and Kepler’s elliptical astronomy, which was the system that came to be accepted by most working astronomers in Europe around 1660. The principle battle in the war of the astronomical systems had been won by a rather boring set of mathematical tables, Johannes Kepler’s Tabulae Rudolphinae.

Rudolphine Tables Frontispiece

Rudolphine Tables Frontispiece

 

 

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