Category Archives: Uncategorized

Der Erdapfel

Erdapfel is the word for potato in my local Franconia dialect, in fact in most of Southern Germany and Austria. In High Germany a potato is ein Kartoffel. Don’t worry this is not a post about root vegetables or variations in German regional dialects. Der Erdapfel is also the name given to the so-called Behaim Globe, the oldest known surviving terrestrial globe, Nürnberg’s most famous historical artefact. The name, which literally translates as Earth Apple, is thought to be derived from the medieval term Reichsapfel (Empire Apple), which was the name of the Globus Cruciger, or orb, as in orb and sceptre, the symbols of power of the Holy Roman Emperor; the orb symbolising the earth. The Behaim globe, which was conceived but not constructed by Martin Behaim, is together with Behaim, the subject of many historical myths.


Martin Behaim was born in Nürnberg in 1459 and lived with his parent on the market place next door to the businessman Bernhard Walther (1430–1504) who was the partner to Regiomontanus in his printing and astronomical activities during the last five years of his life living in Nürnberg. Martin’s father was one of the rich traders, who dominated Nürnberg culture. In 1576 he was sent away to Flanders to apprentice as a cloth trader. In 1484 he journeyed to Portugal, which is where to mythological part of his life begins. According to the traditional version of his life story he took part in two sea voyages down the west coast of Africa with Diogo Cão. He was knighted by the Portuguese king and appointed to the Portuguese Board of Navigation. All of this took place because he was supposedly a student of Regiomontanus, whose ephemerides, the first ever printed ones and highly accurate, were well known and respected on the Iberian Peninsula. All of this information comes from Behaim himself and some of it can be read in the texts on the Behaim Globe.


Artist's impression of Martin Behaim with his globe. Artist unknown

Artist’s impression of Martin Behaim with his globe. Artist unknown

Between 1490 and 1493 Behaim returned to Nürnberg to sort out his mother’s testament and it was during this period that he persuaded to city council to commission him to produce a globe and a large-scale wall map of the world. It is not certain if the wall map was ever produced and if it was it has not survived but the globe certainly was and it is now, as already said, the oldest known surviving terrestrial globe. It is not however, as is often falsely claimed the oldest or first terrestrial globe. The earliest recorded terrestrial globe was constructed by Crates of Mallus in the second century BCE. Also Ptolemaeus in his Geographia, in his discussion of different methods of cartographical projection, acknowledges that a globe in the only way to accurately represent to earth. The Behaim Globe is not even the earliest European medieval globe as the Pope in known to have commissioned earlier terrestrial globes, which have not survived. Given their method of construction and the materials out of which they are made the survival rate of globes is relatively low.

The globe remained the property of the city council of Nürnberg until the middle of the sixteenth century when it was returned to the Behaim family who basically threw it into the corner of an attic and forgot about it. In the nineteenth century it was rediscovered and studied by various historians of cartography and a copy was made for a museum in Paris. Unfortunately it was also ‘restored’ several times through processes that did far more damage than good. In the early twentieth century it was lent to the Germanische Nationalmuseum in Nürnberg. In the 1930s the Behaim family considered selling the globe, most probably in America, and to prevent this Adolf Hitler bought the globe with his own private money and presented it to the German nations. It still resides in the Germanische Nationalmuseum.

I said that the globe is veiled in myths and we will start to sort them out. Firstly Behaim only conceived the globe he didn’t construct it as many people believe. The globe was made by pasting strips of linen onto a fired clay ball. The ball produced by Hans Glockengiesser (a family name that translates as bell founder) and the globe constructed by Ruprecht Kolberger. After the paste had set the globe was cut free from the clay form by a single cut around its equator and the two halves we then pasted together on a wooded frame. The actually map was painted onto the linen ball by the painter and woodblock cutter Georg Glockendon and the lettering was carried out by Petrus Gegenhart. Behaim only seems to have directed and coordinated these activities.


Another popular myth is that because of Behaim’s activities in Portugal the cartography of the globe is cutting edge up to the minute modern; nothing could be further from the truth. The basis of the cartography is Ptolemaeus with obvious additions from other ancient Greek sources as well as The Travels of Sir John Mandeville and The Travels of Marco Polo. Much of the cartographical work is inaccurate even by the standards of the time, including surprisingly the west coast of Africa that Behaim supposedly had explored himself, which brings us to Behaim’s personal claims.


His claim to have sailed with Diogo Cão is almost certainly a lie. At the time of Cão’s first voyage along the African coast Behaim is known to have been in Antwerp. On his second voyage Cão erected pillars at all of his landing places naming all of the important members of the crew, who were on the voyage, Martin Behaim is not amongst them. They is no confirmatory evidence that Behaim was actually a member of Portuguese Board of Navigation and if he was his membership almost certainly owed nothing to Regiomontanus, as there is absolutely no evidence that he ever studied under him. The historian of navigation, David Waters, suggests that if Behaim was actually a member of this august body then it was because the Portuguese hoped to persuade the rich Nürnberger traders to invest money in their expeditionary endeavours, Behaim thus functioning as a sort of informal ambassador for the Republic of Nürnberg.

The picture that emerges is that Martin Behaim was con artist probably deceiving both the Portuguese court and the Nürnberg city council. The Behaim Globe is an interesting artefact but its historical or scientific significance is minimal. If you are in Nürnberg, I can recommend going to the Germanische Nationalmuseum to see it but when you are there also take a look at the Schöner 1520 terrestrial manuscript globe in the neighbouring room. It’s cartographically much more interesting and Schöner, as opposed to Behaim, plays a very important role in the history of globe making.


Johannes Söner's 1520 terrestrial Globe. Germanische Nationalmuseum

Johannes Söner’s 1520 terrestrial Globe.
Germanische Nationalmuseum




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

Teaching the Revolution.

Anthony Millevolte is professor for chemistry at the University of Wisconsin Colleges where he also teaches the history of science courses. When he was teaching an introductory course on the so-called Copernican or Astronomical Revolution he realised that there was no suitable modern textbook available for such a course so he decided to write one: The Copernican Revolution: Putting the Earth into Motion.[1] His resolve to do so was strengthened when he realised that some people wee still teaching such courses using Thomas Kuhn’s The Copernican Revolution from 1957. He writes, “As well written as it is, the obviously unavoidable weakness of Kuhn’s text is that it doesn’t reflect over a half century of active scholarship in this field”[2]. Being somewhat less diplomatic than Millevolte I would add that Kuhn’s book was flawed in some aspects in 1957 and those flaws haven’t improved in the almost sixty years since.


Millevolte’s book is exactly what he set out to write an introductory textbook for college students on the developments in European astronomy in the sixteenth and early seventeenth centuries centred on the period between Copernicus and Galileo. Having above referred to the so-called Copernican Revolution I should point out that Millevolte doesn’t believe in a revolution either, as he explains in the final chapter of the book, An Epilogue, but uses the term in his title because it “reflects a long-standing historical convention – not because it accurately summarizes a series of events that unfolded over many centuries”[3].

The first three chapters could be summarized as setting the scene, giving a quick survey of European astronomy prior to the Renaissance. Consisting of only eight-two pages they don’t offer much depth but however cover all of the salient points clearly and accurately. All the chapters of the book have excellent endnotes and these contain references to the extensive bibliography helping any reader who wishes to pursue any given topic further.

The fourth chapter is devoted to Renaissance astronomy and Copernicus and contains one of the few minor criticisms that I have of the book. In his biographical sketch of Copernicus Millevolte makes some errors only significant to a pedant like me, which however could profitably corrected in a second edition. Otherwise this like all the other chapters in the book is clearly presented and the history of science is as far as it goes correct.

In his introduction Millevolte says that in the process of writing he realised why nobody had written such an up to date textbook. He writes, “It turns out that the experts disagree on a good many of the central elements of the story – so much so that it is sometimes challenging to identify an acceptable narrative”[4]. On this point I agree with him so one should bear this in mind when considering any criticism that I might make here. Despite this problem throughout the book Millevolte had managed to produce a clear, coherent narrative suitable for beginners. On those points that are contentious he includes clearly written, extensive endnotes, which list alternative viewpoints, thus managing very successfully to have his cake and eat it, too.

Having set the astronomical revolution in motion Millevolte produces one chapter each on Tycho Brahe and Kepler and three on Galileo. Here I would complain that the balance is false as Kepler contributed far more to the astronomical revolution than Galileo. However the traditional narrative always favours Galileo over Kepler and as this is a college textbook Millevolte stays within the tradition. He does however redress the balance somewhat in the final chapter where he attributes equal weight to Kepler and Galileo in establishing heliocentricity. I still think this gives too much credit to Galileo but it is it is better than the standard mythology that gives almost all the credit to Galileo and almost none to Kepler.

In his chapters on Galileo Millevolte also tend to emphasise positive aspects of Galileo’s activities oft by simply omitting the negative. For example whilst discussing the dispute between Galileo and Orazio Grassi concerning comets, that led to Galileo writing Il Saggiatore, whilst conceding that Galileo’s attacks on Grassi were, to say the least, immoderate Millevolte neglects to mention that on the question of whether the comets were sub- or supralunar Grassi was in the right and Galileo very much in the wrong.

The same subject turns up in the discussion of the third day in the Dialogo, which is devoted amongst other things to the novas and that they were supralunar. Millevolte claims that Galileo devoted space to this theme because “there remained many Aristotelians who refused to believe the novas were located beyond the sphere of the moon”[5]. This may well have been but the Jesuit, who were without doubt the leading geocentric astronomers, had already accepted the supralunar status of the novas in the sixteenth century. Galileo is here flogging the proverbial dead horse. Again not mentioned by Millevolte, who in general fails to make the important distinction between Aristotelian cosmology and Ptolemaic and/or Tychonic astronomy; a distinction that played a central and significant role in the gradual acceptance of heliocentricity. Geocentric astronomers were prepared to abandon Aristotelian cosmology when the evidence showed it to be wrong but not to give up geocentric astronomy without clear evidence against it and for heliocentricity.

Concerning day four of the Dialogo, Millevolte fails to mention that Galileo’s much favoured theory of the tides was in fact refuted by the empirical facts.

All of the above points whilst, in my opinion important, are for an introductory text not absolutely essential and should not be thought to lead to a negative assessment of Millevolte’s book.

The closing chapter of the book delivers a brief but very clear assessment of the further progress towards heliocentricity up to and including Isaac Newton. As already mentioned the book has an extensive bibliography and the endnotes to each chapter deal skilfully with many of the historically contentious points in the story. I personally would have welcomed an index. The book is attractively illustrated with black and white pictures and diagrams.

Taken as a whole Millevolte has fulfilled his original resolve extremely well and what we have here is a first class up to date textbook on one of the most important episodes in the history of astronomy. I would heartily recommend this book to anyone who wishes to read an introductory text on the subject to inform and educate themselves and especially to anyone wishing to teach an introductory course on the subject to college students or even to the upper classes/grades of grammar schools, high schools etc. Currently priced at circa $17 US on most students should be able to afford a copy.


[1] Anthony Millevolte, The Copernican Revolution: Putting the Earth into Motion, Tuscobia Press, 2014.

[2] Millevolte, p. iv

[3] Millevolte, p. 294

[4] Millevolte, p. v

[5] Millevolte, p. 270


Filed under Book Reviews, History of Astronomy, Uncategorized

History or political propaganda?

Quite a stir has been caused in the Internet by an article written by David Abulafia and published in History Today entitled Britain: apart from or a part of Europe, which to put it quite simply argues for a British exit from the EU based on the concept that Britain has a unique history that separates it from its European neighbours. Possibly the worst part of this blatant piece of political propaganda, masquerading as history, is that it is presented as a sort of manifesto for a group of historians calling themselves Historians for Britain, thereby implicitly implying that they represent the British community of historians. As a convinced European who has lived more than half his life in Germany, I hardly need to say that they don’t represent this British historian.

The last couple of days has seen some informed criticisms of this piece by Charles West at Sheffield University’s History Matters, England: Apart From or a Part of Europe? An Early Medieval Perspective, by Fiona Whelan and Kieran Hazzard at The History Vault, Historians for Britain: The Betrayal of History and Historical Practice, and by Neil Gregor at The Huffington Post, Historians, Britain and Europe. Chiming in on behalf of the historians of science my #histsci soul sister Rebekah “Becky” Higgitt has written an excellent piece on her H-Word Blog at The Guardian, Beware Eurosceptic versions of history and science.


16 May: Sean Lang at The Conversation, There is no dastardly EU plot to hijack the history curriculum

17 May: Historian for History Statement May 2015

18 May: A very large number of historians at History Today: Historians Isolated, Fog in Channel

All of these save me the trouble of writing something myself, but in her article Becky reminded me that Brian Cox had written an essay for the BBC a couple of years ago claiming the same sort of exceptionalism for the history of British science entitled, The Wonder of British Science. At the time I wrote a demolition of Cox’s arguments, Rule Britannia: Britannia rules the science, which I humbly offer up as my contribution to the current debate.


Filed under Uncategorized

Why The Imitation Game is a disaster for historians.

I made the mistake, as a former professional historian of logic and meta-mathematics and, as a consequence, an amateur historian of the computer, of going to the cinema to watch the Alan Turing biopic The Imitation Game. I knew that it wouldn’t be historically accurate but that it would be a total historical disaster and, as I said on leaving the cinema, an insult to the memory of both Alan Turing and the others who worked in Bletchley Park surprised even me, a dyed in the wool, life-long cynic.

As I ventilated my disgust over the next few days on Twitter some, quite correctly, took me to task, informing me that it is a film and not a history book and therefore one shouldn’t criticise it for any inaccuracies that it contains. This attitude is of course perfectly correct and I would accept it,m if only the people who watch the film, who unlike myself are not knowledgeable historians, would view the film in this way; unfortunately they don’t.

The pre-release publicity for the film emphasised very intensely that the film tells a “true” story. This is screwed back somewhat in the film itself which opens with the claim that it is “based on a true story”. Unfortunately people simply ignore the “based on” and as I left a full cinema, at the end of the film, people all around me were saying to each other, “Wow, I didn’t know that. It’s a true story, you know?” and other similar expressions. This was compounded by both the Golden Globes and the Oscars, as the film won the awards of the respective organisations for best-adapted script! The film is supposedly based on Andrew Hodges’ Alan Turing biography, The Enigma. This book, which I read when it was first published, is one of the best biographies of a scientist that I’ve ever read, superbly researched, meticulously detailed and a real pleasure to read. Hodges is apparently prohibited by a gag clause in his contract for the film rights to his book from commenting on the film. “Take this large sum of money son and shut your mouth whilst we destroy your book!” It is not much of an exaggeration to say that the adaption consists of dumping the factual content of the book, plus several of the central characters, and writing a piece of third rate fiction using the names of some of the figures in Hodges’ biography. If that’s the film industries definition of ‘best adapted’ I don’t won’t to know what they consider to be the ‘worst adapted’.

I’m not going to go into great detail about everything that is wrong with the film because to a certain extent others have already done the work for me. The film almost completely ignores the contributions of the Poles in breaking the Enigma Codes (note the plural, there was more than one, another thing that doesn’t get mentioned in the film). They only get mentioned in a passing half sentence, which I strongly suspect almost all viewers failed to notice. You can read about the Polish contribution here, here and here. A short, general but largely accurate account of Turing’s involvement can be read here. There is a biting general criticism of the film on Ursula Writes, and another slightly less acerbic by L. V. Anderson on the Slate website. Another demolition job both of the Imitation Game and the Hawking biopic The Theory of Everything is on the Nature website by Colin Macilwain.

In case anybody doubts that the lay public think that the film is a ‘true’ story I have extracted part of a fairly typical critique of the film from the website of G. B. Hatch

I wanted to see this film the minute I heard about it. The plot sounded very intriguing. I had never learned about Alan Turing, and I now believe every History teacher should be showing this film while teaching WWII. Alan Turing and his team are some of the heroes of WWII that didn’t need to fire a single shot. This film, like “Argo”, is a great historical thriller based on a story that had remained confidential for several decades. This film is “The Imitation Game”.

“The Imitation Game” tells the true story of Alan Turing (played by Benedict Cumberbatch), a brilliant yet socially awkward British mathematician who is hired as a German code-breaker during WWII. He sets out to create a machine that will crack the Enigma Code, a German code that many claim as unbreakable. With the help of fellow code-breaker Joan Clarke (played by Keira Knightley), Turing invents this machine, which he calls ‘Christopher’, while also trying to hide his homosexuality which was illegal at the time. The film perfectly blends intensity and humor, while also transitioning between the past, present, and future.

As can be clearly seen Mr (or is that Ms?) Hatch is convinced that the film tells a true story and even goes so far as to suggest that the film should be used in school history lessons!

The historian is clearly presented by a dilemma when the film industry decides to make a film about a well-researched and well-documented historical episode. Almost without exception the scriptwriters decide that history is too complex, too boring, not sexy enough or whatever. They throw out ninety per cent of the historical facts and write there own ‘better than reality’ version usually retaining not much more that the names of the historical characters. They then add a bucket full of false historical touches, such as horns on Viking helmets, that everybody knows are “true”. The whole thing is then packaged up by the advertising department as the “amazing unknown true story of”! If the historian complains he gets firmly put in his place by people telling him “it’s only a film”. If he doesn’t complain he can listen to all those film goers sitting around in bars and cafés saying, “Did you know Alan Turing won the Second World War almost single handed!”

What ever else you have no hope of winning if you are a historian.


Filed under Myths of Science, Uncategorized

A Swiss Clockmaker

We all have clichéd images in our heads when we hear the names of countries other than our own. For many people the name Switzerland evokes a muddled collection of snow-covered mountains, delicious superior chocolates and high precision clocks and watches. Jost Bürgi who was born in the small town of Lichtensteig, in the  Toggenburg region of the canton of St. Gallen on 28 February 1552 fills this cliché as the most expert clockmaker in the sixteenth century. However Bürgi was much more that just a Swiss clockmaker, he was also an instrument maker, an astronomer, a mathematician and in his private life a successful property owner and private banker, the last of course serving yet another Swiss cliché.

As we all too many figures, who made significant contributions to science and technology in the Renaissance we know next to nothing about Bürgi’s origins or background. There is no known registration of his birth or his baptism; his date of birth is known from the engraving shown below from 1592, in which the portrait was added in 1619 but which was first published in 1648. That the included date is his birthday was confirmed by Bürgi’s brother in law.


His father was probably the locksmith Lienz Bürgi but that is not known for certain. About his education or lack of it nothing is known at all and just as little is known about where he learnt his trade as clockmaker. Various speculations have been made by historians over the years but they remain just speculations. The earliest documentary proof that we have of Bürgi’s existence is his employment contract when he entered the service of the Landgrave Wilhelm IV of Hessen-Kassel as court clockmaker, already twenty-seven years old, on 25 July 1579. Wilhelm was unique amongst the German rulers of the Renaissance in that he was not only a fan or supporter of astronomy but was himself an active practicing astronomer. In his castle in Kassel he constructed, what is recognised as, the first observatory in Early Modern Europe.

Wilhelm IV. von Hessen-Kassel Source: Wikimedia Commons

Wilhelm IV. von Hessen-Kassel
Source: Wikimedia Commons

He also played a major role in persuading the Danish King Frederick II, a cousin, to supply Tycho Brahe with the necessary land and money to establish an observatory in Denmark. In the 1560s Wilhelm was supported in his astronomical activities by Andreas Schöner, the son of the famous Nürnberger cartographer, globe and instrument maker, astronomer, astrologer and mathematician Johannes Schöner. He also commissioned the clockmaker Eberhard Baldewein (1525-1593) to construct two planet clocks and a mechanical globe.


Eberhart Baldewein Planet clock 1661 Source: Wikimedia Commons

Eberhart Baldewein Planet clock 1661
Source: Wikimedia Commons

The planet clock shows the positions of the sun, moon and the planets, based on Peter Apian’s Astronomicom Caessareum, on its various dials.


Eberhard Baldewein Mechanical Celestial Globe circa 1573

Eberhard Baldewein Mechanical Celestial Globe circa 1573 The globe, finished by Heinrich Lennep in 1693, was used to record the position of the stars mapped by Wilhelm and his team in their observations.

These mechanical objects were serviced and maintained by Baldewein’s ex-apprentice, Hans Bucher, who had helped to build them and who had been employed by Wilhelm, for this purpose, since 1560. When Bucher died in 1578-1579 Bürgi was employed to replace him, charged with the maintenance of the existing objects on a fixed, but very generous salary, and commissioned to produce new mechanical instruments for which he would be paid extra. Over the next fifty years Bürgi produced many beautiful and highly efficient clocks and mechanical globes both for Wilhelm and for others.

Bürgi Quartz Clock 1622-27 Source: Swiss Physical Society

Bürgi Quartz Clock 1622-27
Source: Swiss Physical Society






Bürgi Mechanical Celestial Globe 1594 Source: Wikimedia Commons

Bürgi Mechanical Celestial Globe 1594
Source: Wikimedia Commons



Jost Bürgi and Antonius Eisenhoit: Armillary sphere with astronomical clock made 1585 in Kassel, now at Nordiska Museet in Stockholm. Source Wikimedia Commons

Jost Bürgi and Antonius Eisenhoit: Armillary sphere with astronomical clock made 1585 in Kassel, now at Nordiska Museet in Stockholm.
Source Wikimedia Commons

Bürgi was also a highly inventive clockmaker, who is credited with the invention of both the cross-beat escapement and the remontoire, two highly important improvements in clock mechanics. In the late sixteenth century the average clocks were accurate to about thirty minutes a day, Bürgi’s clock were said to be accurate to less than one minute a day. This amazing increase in accuracy allowed mechanical clocks to be used, for the first time ever, for timing astronomical observations. Bürgi also supplied clocks for this purpose for Tycho’s observatory on Hven. In 1592 Wilhelm presented his nephew Rudolph II, the German Emperor, with one of Bürgi’s mechanical globes and Bürgi was sent to Prague with the globe to demonstrate it to Rudolph. This was his first contact with what would later become his workplace. Whilst away from Kassel Bürgi’s employer, Wilhelm died. Before continuing the story we need to go back and look at some of Bürgi’s other activities.

As stated at the beginning Bürgi was not just a clockmaker. In 1584 Wilhelm appointed the Wittenberg University graduate Christoph Rothmann as court astronomer. From this point on the three, Wilhelm, Rothmann and Bürgi, were engaged in a major programme to map the heavens, similar to and just as accurate, as that of Tycho on Hven. The two observatories exchanged much information on instruments, observations and astronomical and cosmological theories. However all was not harmonious in this three-man team. Although Wilhelm treated Bürgi, whom he held in high regard, with great respect Rothmann, who appears to have been a bit of a snob, treated Bürgi with contempt because he was uneducated and couldn’t read or write Latin, that Bürgi was the better mathematician of the two might have been one reason for Rothmann’s attitude.

In the 1580s the itinerant mathematician and astronomer Paul Wittich came to Kassel from Hven and taught Bürgi prosthaphaeresis, a method using trigonometric formulas, of turning multiplication into addition, thus simplifying complex astronomical calculations. The method was first discovered by Johannes Werner in Nürnberg at the beginning of the sixteenth century but he never published it and so his discovery remained unknown. It is not known whether Wittich rediscovered the method or learnt of it from Werner’s manuscripts whilst visiting Nürnberg. The method was first published by Nicolaus Reimers Baer, who was then accused by Tycho of having plagiarised the method, Tycho claiming falsely that he had discovered it. In fact Tycho had also learnt it from Wittich. Bürgi had expanded and improved the method and when Baer also came to Kassel in 1588, Bürgi taught him the method and how to use it, in exchange for which Baer translated Copernicus’ De revolutionibus into German for Bürgi. This was the first such translation and a copy of Baer’s manuscript is still in existence in Graz. Whilst Baer was in Kassel Bürgi created a brass model of the Tychonic geocentric-heliocentric model of the cosmos, which Baer claimed to have discovered himself. When Tycho got wind of this he was apoplectic with rage.

In 1590 Rothmann disappeared off the face of the earth following a visit to Hven and for the last two years of Wilhelm’s life Bürgi took over as chief astronomical observer in Kassel, proving to be just as good in this work as in his clock making.

Following Wilhelm’s death his son Maurice who inherited the title renewed Bürgi’s contract with the court.


Kupferstich mit dem Porträt Moritz von Hessen-Kassel aus dem Werk Theatrum Europaeum von 1662 Source: Wikimedia Commons

Kupferstich mit dem Porträt Moritz von Hessen-Kassel aus dem Werk Theatrum Europaeum von 1662
Source: Wikimedia Commons

However Maurice did not share his father’s love of astronomy investing his spare time instead in the study of alchemy. Bürgi however continued to serve the court as clock and instrument maker. Over the next eight years Bürgi made several visits to the Emperor’s court in Prague and in 1604 Rudolph requested Maurice to allow him to retain Bürgi’s services on a permanent basis. Maurice acquiesced and Bürgi moved permanently to Prague although still remaining formally in service to Maurice in Kassel. Rudolph gave Bürgi a very generous contract paying him 60 gulden a month as well as full board and lodging. As in Kassel all clocks and globes were paid extra. To put that into perspective 60 gulden was a yearly wage for a young academic starting out on his career!

In Prague Bürgi worked closely with the Imperial Mathematicus, Johannes Kepler. Kepler, unlike Rothmann, respected Bürgi immensely and encouraged him to publish his mathematical works. Bürgi was the author of an original Cos, an algebra textbook, from which Kepler says he learnt much and which only saw the light of day through Kepler’s efforts. Kepler was also responsible for the publication of Bürgi’s logarithmic tables in 1620.


Bürgi's Logarithmic Tables Source: University of Graz

Bürgi’s Logarithmic Tables
Source: University of Graz

This is probably Bürgi’s greatest mathematical achievement and he is considered along side of John Napier as the inventor of logarithms. In many earlier historical works Bürgi is credited with having invented logarithms before Napier. Napier published his tables in 1614 six years before Bürgi and is known to have been working on them for twenty years, that is since 1594. Bürgi’s fan club claim that he had invented his logarithms in 1588 that is six years earlier than Napier. However modern experts on the history of logarithms think that references to 1588 are to Bürgi’s use of prosthaphaeresis and that he didn’t start work on his logarithms before 1604. However it is clear that the two men developed the concept independently of each other and both deserve the laurels for their invention. It should however be pointed out that the concept on which logarithms are based was known to Archimedes and had already been investigated by Michael Stifel earlier in the sixteenth century in a work that was probably known to Bürgi.

Through his work as clock maker Bürgi became a very wealthy man and invested his wealth with profit in property deals and as a private banker lending quite substantial sums to his customers. In 1631 Bürgi, now 80 years old, retired and returned ‘home’ to Kassel where he died in January of the following year shortly before his 81st birthday. His death was registered in the Church of St Martin’s on the 31 January 1632. Although now only known to historians of science and horology, in his own time Bürgi was a well-known and highly respected, astronomer, mathematician and clock maker who made significant and important contributions to all three disciplines.




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

Christmas Trilogy Part 3: Choosing a wife.

Johannes Kepler was an incredibly prolific writer. He wrote and published more that eighty books and pamphlets on a very wide range of topics from astronomy to optics, from astrology to Bible chronology, from stereometry (that’s 3-D geometry) to the determination of the volumes of wine barrels and much, much more. A well as all of these publications he was also a very prolific letter writer. Many of his letters were in effect scientific papers, the exchange of letters between researchers taking the place of scientific journals in the Early Modern Period. For example his extensive correspondence with the Frisian astronomer David Fabricius gives us an important historical view of his struggles to derive and establish his second law of planetary motion. However not all of his letters were of a scientific nature. A letter he wrote on 23rd October 1613 to an unknown recipient goes into great detail concerning his attempts over the preceding two years to find a wife.

Kepler had married for the first time in 1595, at the age of 24, a wealthy young widow with daughter, Barbara Müller then aged 23, whilst he was serving as schoolteacher and district mathematicus in Graz. It seems to have been a love match and should have been a happy marriage, however Barbara, who suffered many trials and tribulations with Kepler’s expulsion from Catholic Austria and his subsequent more than rocky time as first assistant to Tycho and then Imperial Mathematicus in Prague, appears to have suffered from clinical depression making their marriage to a time of great stress to Johannes. Worse was to come. In 1611 Kepler’s three children contracted small pox and his son Felix died at the age of six. Barbara fell ill shortly after and passed away on July 3rd. All of this took place whilst Rudolph the German Emperor, and Kepler’s employer, was being deposed by his brother and Kepler was desperately trying to find a new position anywhere but Prague.

In those times it was perfectly normal for a widow with small children to look for and marry a new wife to run his household and look after his children. It was also perfectly normal for marriages, at least at Kepler’s social level, not to be love matches but rather arranged or brokered. Suitable partners being brought together in what more resembled a business deal than a personal relationship. Kepler was no exception to these norms and immediately following Barbara’s death he set about looking for a new wife to care for his children. In the end the whole process would take more than two years and involve negotiations with a total of eleven different women. In the letter mention above, and which I’m going to précis in the following, Kepler himself provides us with all the gory details.

Potential wife number one was a widow in Prague who was a mutual friend of Kepler and his wife. Barbara had recommended her, as her successor on her deathbed. Kepler opened negotiations and the widow seemed to be interested at the beginning but then withdrew, turning down the offer. Kepler was now offered a young maiden by her mother, as Kepler expressed it from widow to virgin. Kepler described to girl as having a pretty face and beening well educated but too young to bear the responsibilities of a household. In the end the mother withdrew the offer on the grounds that her daughter was too young.

At the commencement of this second negotiation Kepler had stated that he would either marry or leave Prague. The marriage having fallen through he now left the city on his way to Linz. In Moravia he met a girl who warmed his soul; a well brought up girl who took over his children with enthusiasm. Leaving his children in the care of their future mother he continued his journey. However when he returned the girl was engaged to another. Onward to Linz.

In Linz Kepler turned his attention to number four, apparently a bit of a stunner, tall, beautiful and athletic. Kepler was proceeding to tying the knot when his attention was distracted by number five, and here we get the longest description. She impressed through her love, her humble fidelity, her economy, her zeal and her affection for his children. It also appealed to Kepler that she was a solitary orphan.

Having almost accepted number five Kepler was urged by the wife of Helmhard Jörger (?) to decide on number four. Caught in a quandary, Kepler’s stepdaughter and her husband recommended a sixth candidate, an attractive, wealthy, but rather too young aristocrat. Kepler who suffered from a serious inferiority complex was worried she would look down on him. Lack of money being a permanent problem in his life he also feared the high costs of an eventual wedding so she too was rejected.

His thoughts returning to number five he now ran into number seven. His friends praised her nobility and her economy. As Kepler pressed his suit with her relatives he was warned off and in the end he was rejected. Enter number eight, by Kepler’s own account not attractive but with an honest mother. Kepler’s nervous and uncertain approach was met with an equally uncertain and nervous response, the whole project collapsed. Kepler now turned his attention to a ninth who simply turned him down. Kepler regarded number ten as unsuitable, describing himself as thin as a stick and his potential partner as short and fat, on to number eleven.

This time everything seemed to be in order the new potential Mrs Kepler was noble, wealthy, and economic, if somewhat young. However after four months of serious negotiations Kepler’s suit was once again rejected on the grounds that the lady was too young.

Kepler finally did the sensible thing, returned to number five, asked her to marry him and was accepted. The lady in question was Susanna Reuttinger twenty-four years old at the time to Kepler’s forty-one. They were married in Eferding on 30 October 1613. Despite Kepler’s vacillations in the two years leading up to the marriage it was a happy and loving union blessed by the birth of six children although, as was not unusual in the seventeenth century, three of them died in childbirth. Kepler took a long time and travelled a circuitous route to find his Susanna but in the end find her he did and she proved a good catch.


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Christmas Trilogy Part 2: Computing mathematical miracles.

In modern perception Charles Babbage has become reduced to narrow minded Victorian number cruncher whose only interest in life was producing mechanical computing machines to crunch ever more numbers. He has even been accused by the acolytes of St Ada of Lovelace of not understanding the real future purpose of those machines, knowledge of which had to be supplied by her saintliness. This rather dismal one-sided portrait of Babbage is very far from the truth Babbage being in reality a multi-talented man whose knowledge of the potentials embodied in the newly emerging machines of the nineteenth century was both very broad and deep. He even, within the context of a religious debate, conceived of the possibility of pre-programmed miracles a concept that he would demonstrate like a mechanical conjuror on early prototypes of his difference engine.

In the first half of the nineteenth century intellectual discourse in Victorian England was dominated by the concept of natural theology, particularly as presented by William Paley in his Natural Theology, or Evidences of the Existence and Attributes of the Deity collected from the Appearances of Nature published in 1802; Paley being today much loved by creationists and much derided by their opponents. The central argument of natural theology is very simple, stating that one can deduce the existence of God through the (scientific) study of the natural world. Paley is famous for having used the watchmaker analogy, the natural world resembles a watch in its complexity and design therefore there must be a watchmaker. (I have a sneaking feeling that I’m going to get hammered by my philosophical friends for this very simplified presentation of natural theology).

Paley was by no means the only believer in natural philosopher in that age and Francis Egerton, 8th Earl of Bridgewater, left a bequest of £8 000, a lot of money in those days, to pay one or more authors to write one or more treatises defending the principle of natural theology against the then modern scientific discoveries; the money to be administered by the Royal Society. The Royal Society decide to divide the money into eight portions of £1 000 and to commission eight treatises covering the full range of the then natural and moral sciences.

John Herschel was originally approached to write the treatise on astronomy but he declined on the grounds that it was wrong for a scholar to write for money! This volume was then offered to William Whewell, who having neither Herschel’s wealth nor his scruples eagerly accepted the task. Whewell duly wrote and published the Third Bridgewater Treatise, Astronomy and General Physics considered with reference to Natural Theology, which became the most successful and widely read of all of them, running to nine editions in his own lifetime. Whewell produced all of the argument brought earlier by Isaac Newton, who can be considered natural theological, for a God designed cosmos but adding all of the newer astronomical discoveries made since Newton’s times even including Herschel’s very recent work on double stars, showing how they too obeyed the law of gravity. Whewell’s cosmos was one governed by the laws of science as laid out by a scientific God; having established that God’s cosmos is governed by scientific laws Whewell then goes on to expound his philosophy of science. As he was soon to declare in his legendary three volume History of the Inductive Sciences (1st ed. 1837) and two volume The Philosophy of the Inductive Sciences Founded upon their History (1st ed. 1840) Whewell was a Baconian through and through who argued that the laws of science are obtained through induction. Not content to leave it at that he then went on to deny the ability of mathematics and deductions to discover new laws of nature.

Whewell, Herschel and Babbage had been close friends as students at Cambridge[1] and although all three of them were excellent mathematicians, who together as students had fought for the introduction of the continental analysis into Cambridge, it was Babbage who most considered himself to be a mathematician and who took umbrage at what he saw as a personal slight in Whewell’s dismissal of mathematicians in the process of scientific discovery. Never one to take insults lying down Babbage rose to the challenge and wrote and published his own Bridgewater Treatise, although he was not one of the eight chosen authors. Entitled The Ninth Bridgewater Treatise A Fragment by Charles Babbage, Esq. it contained Whewell’s offending passage on its title page:

“We may thus, with the greatest propriety, deny to the mechanical philosophers and mathematicians of recent times any authority with regard to their views of the administration of the universe; we have no reason whatever to expect from their speculations any help, when we ascend to the first cause and supreme ruler of the universe. But we might perhaps go farther, and assert that they.are in some respects less likely than men employed in other pursuits, to make any clear advance towards such a subject of speculation.”—Bridgewater Treatise, by the REV. WM. WHEWELL, p. 334.

This small book contains much of interest but what concerns us here is Chapter II, Argument in Favour of Design from the changing of Laws in Natural Events, which is a clever move by Babbage the computing expert to score points over Whewell.

Not in his Bridgewater Treatise, but in his reviews of the two volumes Charles Lyell’s Principles of Geology from 1831and 1832 Whewell addressed a problem that was central to the problems of natural philosophy caused by the recent scientific developments, evolution. Although Darwin’s own theory of evolution still lay some decades in the future evolution as a scientific fact was becoming more and more established as the geologists and palaeontologists found and examined more and more fossils of extinct species. If God had created the world and all that was in it, how come the geological record clearly displayed the disappearance and appearance of different species over the ages. Whewell’s solution was to invoke a caretaker God who popped in from time to time introducing new species to replace those that had died out these interventions being in the form of miracles. It is here that Babbage set out to demonstrate the superiority of a mathematical computing God.

Babbage argued by analogy, he describes the possibility of a computer programme (not the terminology that Babbage uses by the way) that generates the natural numbers 1, 2, 3, 4, … up to and including 100,000,001 but then instead of producing the number 100,000,002 as expected jumps to 100,010,002, continuing the series 100,030,003; 100,060,004; 100,100,005; 100,150,006; 100,210,007 … and so forth. Babbage states that the law generating the series has changed at the jump. The expected numbers being exceeded by the series 10,000, 30,000, 60,000, 100,000, 150,000 … and so on this being the series of triangular numbers 1, 3, 6, 10, 15, … multiplied by 10,000.

Babbage goes on to explain that the operator does not need to interfere with the calculating engine (he is of course thinking of his own Difference Engine) at this point but can pre-programme it from the beginning to make the change at the given juncture.

Unlike Whewell’s God who has to intervene in his own laws of nature with miracles to explain the presence of new species in the geological record Babbage’s mathematical God can pre-programme his laws of nature to change at the required point in time thus pre-programming his miracles at the point of creation.

Babbage actually programmed one of the calculating units of his Difference Engine to perform a miracle of the type described here, which he then demonstrated to guests at the soirees he held at his home in London. It was one of these demonstrations that so impressed the seventeen year old Ada Byron in 1833 and drew her into Babbage’s sphere of influence.

Babbage was so pleased with his mathematical miracles that he included another account of them in his autobiography, Passages from the Life of a Philosopher originally published in London in 1864.

Some readers might note a strong similarity between Babbage’s argument, sketched here, for a divine pre-programmed replacement of species and the arguments of those modern Christians who accept the theory of evolution but state that this is God’s method of creating the world.





[1] Laura J. Snyder’s The Philosophical Breakfast Club, Broadway Books New York, 2011 is an excellent account of that friendship that I strongly recommend.


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