Normal service will be resumed as soon as possible


I am currently engaged in copyediting the English translations of a collected volume of history of science papers. The translations are mostly crappy and the English more than somewhat dubious. The result is that it is difficult, irritating, exasperating and at time down right shitty. The official deadline was 30 September but I am not to blame, as I had not even received the majority of the typescripts by then!

Add to this the fact that I am trying to cope with three different moderately serious physical health problems. The end result of all this is that my mental health is starting to deteriorate. I am currently even more of an aggressive, obnoxious arsehole than usual.

Conserving my mental health has been the number one priority in my life for a number of years now, so I have decided that I need to reduce the stress in my life. This means that I will not be blogging for the next couple of weeks. I am planning on being back for my usual Christmas trilogy if all goes well.

To keep you occupied in my absence you can offer your opinions on the following thoughts. The man who more than anyone else in responsible for the existence of this blog the Albino Aussie Anthropoid,TM John Wilkins, has once again tackled the problem of those that say , evolution is ‘just’ a theory.

I personally think that scientists and science communicators are themselves partially to blame. A theory is actually what the denialists think it is, a point of view, an idea, a standpoint, as in, “I don’t know why she left him but I have a theory.” The theory of evolution and all other scientific theories are just that they are scientific theories and not just theories; a scientific theory being a tested hypothesis that explains the given scientific facts. Scientist and science communicators need to stop being lazy and start saying scientific theory and not just sloppily saying theory.



Filed under Autobiographical

Observing for the long haul

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

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


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

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

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

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

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


William IV of Hessen Kassel
Source: Wikimedia Commons

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

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

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

Giovanni Domenico Cassini
Source: Wikimedia Commons

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

Johannes Hevelius by Daniel Schultz
Source: Wikimedia Commons

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

John Flamsteed by Godfrey Kneller, 1702
Source: Wikimedia Commons

Flamsteed House in 1824
Royal Observatory Greenwich
Source: Wikimedia Commons

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

Lithograph of Caroline Herschel, 1847
Source: Wikimedia Commons

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

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

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


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

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

Christoph Schiene
Source: Wikimedia Commons

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

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

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Filed under History of Astronomy, History of science

History of the little things

This is going to be one of those blog posts where I indulge in thinking out loud. I will ramble and meander over and through some aspects of something that has been occupying my thoughts for quite sometime without necessarily reaching any very definite conclusions.

As I said the topic I’m about to discuss has occupied my thoughts for quite sometime but this post was triggered by an interesting blog post by Rachel Laudan, one time historian of science, currently food historian and most recently the author of the excellent Cuisine and Empire: Cooking in World History. In her blog post Rachel discusses the uses to which gourds have been put in the history of cooking. Depending on how you cut it the same gourd can become a spoon or a bowl or a flask (and much, much more. Read the article!). Although this is an article about the history of food and cooking it is at the same time an article about the history of technology. All of the things that Rachel describes are tools and the history of technology is the history of human beings as toolmakers and the tools that they have made.

Here, from Senegal on the west bulge of Africa, is a gourd cut in half to make a spoon, holding millet porridge with raisins. The tablespoon gives the scale.


The thought that Rachel’s post triggered is my answer to the oft stated question, what is the greatest, most important, most significant or whatever human invention? Most people answer the wheel, or the light bulb or the steam engine or the motorcar or the airplane or something else along those lines. Some sort of, for its time, high tech development that they think changed the course of history. My, I’ll admit deliberately provocative answer, is the sewing needle; a, for most people, insignificant everyday object produced in factories by the millions. An object that most people normally don’t really give any thought to, unless they are desperately searching for one to sew on that button that fell off their best jacket an hour before that all important interview.

So, how would I justify my chose of the sewing needle as the most important human invention? The sewing needle made it possible for humanity to make clothes way back in the depths of prehistory. The oldest known needles go back at least 50,000 years but they are arguably much older. Making clothes was a necessary prerequisite of early humans moving out of tropical Africa into less clement climes. Naturally before the invention of the needle humans could simply wrap themselves in animal skins or furs joined together by primitive buttons or toggles. However a tailored and sewn set of clothes allows the wearer to move easily, to hunt or to run when threatened, things that are difficult when simply wrapped in a heap of skins or furs.

Sewing is just one of the technologies that people don’t automatically thing of when the term history of technology is mentioned. Others from the same domestic area are weaving, crochet and knitting and yes crochet and knitting are technologies. I have a suspicion that such domestic technologies get ignored in the popular conception of the history of technology is because they are women’s activities. In the popular imagination technology is masculine; man is the toolmaker, woman is the carer. The strange thing about this essentially sexist view of the history of technology is that the domestic technologies, clothes making, cooking etc. play a very central role in human survival and human progress. Humans can survive without cars but a naked human being without cooked food in a hostile environment is on a fast track to the grave. These small, everyday aspects of human existence need to receive a much greater prominence in the popular history of technology.

It is not just in the history of technology that the small and everyday gets ignored in #histSTM accounts. A recent discussion on an Internet mailing list complained about the fact that the discussion of the 100th anniversary of the Mount Wilson Observatory Hooker telescope spent a lot of time discussing Edwin Hubble’s discoveries made with it but wasted not a single word on the technicians who built and installed it or those who operated it. Without the work of these people Hubble wouldn’t have discovered anything. In general in the popular accounts of #histSTM the instrument makers and technicians rarely if ever get mentioned, just the big name scientists. Most of those big name scientists would never have become big name without the services of the instrument makers and technicians but throughout history most of them don’t just remain in the background they remain nameless. We need to do more to emphasise the fact that developments in science and technology are not just made by big names but by whole teams of people many of whom remain, in our fame obsessed society, anonymous.

Another area where popular #histSTM falls down is in the dissemination and teaching of science and technology. People tend not to consider the teachers and the textbook authors when discussing the history of science. These people, however, play an important and very central role in the propagation of new developments and discoveries. Students of a scientific discipline tend on the whole to gain their knowledge of the latest developments in their discipline from their teachers and the textbooks and not from reading the original books and papers of the discoverers. Science is propagated down the generation by these background workers far more than by the “great” men or women who hog the headlines in #histSTM. A good example for such an important teacher and textbook author is Christoph Clavius, about whom I wrote my first actual #histSTM post here on the Renaissance Mathematicus. Another good example is Philipp Melanchthon, who as a teacher and textbook author introduced the mathematical sciences into the newly founded Lutheran Protestant education system; Clavius did the same for the Catholic education system.

Christopher Clavius (1538–1612)
Source: Wikimedia Common



Portrait of Philip Melanchthon, 1537, by Lucas Cranach the Elder
Source: Wikimedia Commons

Napoleon, a major fan and supporter of the sciences, recognised the importance of good textbooks in the propagation of science. When he established new universities in Paris he insisted that the leading French scientists and mathematicians, whose very active patron he was, write the new textbooks for his new institutions. A model we could well copy.

If we are to progress beyond the big names, big event, hagiographic presentations of #histSTM, and we seriously need to do so, then we should not just look towards the minor, less well-known or completely unknown, scientists in the second row, as I have endeavoured to do over the years here, but even further down the fame tree to the instrument makers, technicians, teachers, textbook writers and others who assists the scientists and propagate and disseminate their discoveries, the facilitators. There are already scholars who have and do research and publish about these facilitators and the reviewers and science communicators need to do more to bring this work to the fore and into the public gaze and not just promote the umpteenth Newton biography.




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

Juggling information

One of the parlour games played by intellectuals and academic, as well as those who like to think of themselves as such, is which famous historical figures would you invite to a cocktail or dinner party and why. One premise for the game being, which historical figure or figures would you most like to meet and converse with. As a historian of mostly Early Modern science I am a bit wary of this question, as many of the people I study or have studied in depth have very unpleasant sides to their characters, as I have commented in the past in more than one blog post. However in my other guise, as a historian of formal or mathematical logic and the history of the computer there is actually one figure, who I would have been more than pleased to have met and that is the mathematician and engineer, Claude Shannon.

A young Claude Shannon
Source: Wikimedia Commons

For those who might not know who Claude Shannon was, he was a man who made two very major contributions to the development of the computers on which I am typing this post and on which you are reading it. The first was when he at the age of twenty-one, in what has been described as the most important master’s thesis written in the twentieth century, combined Boolean algebra with electric circuit design thus rationalising the whole process and simplifying the design of complex circuitry beyond measure. The second was sixteen years later when he in his A Mathematical Theory of Communication, building, it should be added, on the work of others, basically laid the foundations of our so-called information age. His work laid out how to transmit digital signals through circuitry without loss of information. He is regarded as the über-guru of information theory, to quote Wikipedia:

 Information theory studies the quantification, storage, and communication of information. It was originally proposed by Claude E. Shannon in 1948 to find fundamental limits on signal processing and communication operations such as data compression, in a landmark paper entitled “A Mathematical Theory of Communication”.

Given that the period we live in is called both the computer age and the information age, it is somewhat surprising that the first full-length biography of Shannon, A Mind at Play,[1] only appeared this year. Having somewhat foolishly said that I would hold a public lecture in November on Vannevar Bush, who was Shannon’s master’s thesis supervisor, and Shannon, I have been reading Soni’s and Goodman’s Shannon biography, which I have to say I enjoyed immensely.


This is a full length, full width biography that covers both the live of the human being as well as the intellectual achievements of the engineer-mathematician. Shannon couldn’t decide which to study as an undergraduate so he did a double BSc in both engineering and mathematics. This dual course of studies is what led to that extraordinary master’s thesis. Having studied Boolean algebra in his maths courses Shannon realised that he could apply it to rationalise and simplify electrical switching when working, as a postgrad, on the switching circuits for Bush’s analogue computer, the differential analyser. It’s one of those things that seems obvious with hindsight but required the right ‘prepared mind’, Shannon’s, to realise it in the first place. It is a mark of his character that he shrugged off any genius on his part in conceiving the idea, claiming that he had just been lucky.

Shannon’s other great contribution, his treatise on communication and information transmission, came out of his work at Bell Labs as a cryptanalyst during World War II. The analysis of language that he developed in order to break down codes led him to a more general consideration of the transmission of information with languages out of which he then laid down the foundations of his theories on communication and information.

Soni’s and Goodman’s and volume deals well with the algebraic calculus for circuit design and I came away with a much clearer picture of a subject about which I already knew quite a lot. However I found myself working really hard on their explanation of Shannon’s information theory but this is largely because it is not the easiest subject in the world to understand.

The rest of the book contains much of interest about the man and his work and I came away with the impression of a fascinating, very deep thinking, modest man who also possessed a, for me, very personable sense of humour. One aspect that appealed to me was that Shannon was a unicyclist and a juggler, who also loved toys, hence the title of my review. As I said at the beginning Claude Shannon is a man I would have liked to have met for a long chat over a cup of tea.

An elder Claude Shannon
Source: Wikimedia Commons

On the whole I found the biography well written and light to read, except for the technical details of Shannon information theory, and it contains a fairly large collection of black and white photos detailing all of Shannon’s life. As far as the notes are concerned we have the worst of all possible solutions, hanging endnotes; that is endnotes, with page numbers, to which there is no link or reference in the text. There is an extensive and comprehensive bibliography as well as a good index. This is a biography that I would whole-heartedly recommend to anybody who might be interested in the man or his area of work or both.



[1] Jimmy Soni & Rob Goodman, A Mind at Play: How Claude Shannon Invented the Information Age, Simon & Shuster, New York etc., 2017


Filed under Book Reviews, History of Computing, History of Logic, History of Technology

An hour forwards, an hour back

In my last post I talked about the Albrecht Dürer House that is at the end of my history of astronomy tour of Nürnberg. My tour starts under the rather spectacular sundial painted on the south side of the church of St Lorenz.

I start my tour by talking about the way the day was divided up in the past; the observing, quantifying and recording of the passage of time down the ages being a particular interest of mine. I mention that it was the ancient Egyptians who initially introduced the 24 hour day, first dividing the night into twelve segments based on the rising of stars and the by analogy the day was divided into twelve segments. Adopted by the rest of the ancient world this became the European norm.

However during the Middle Ages our equinoctial system in which all twenty-four hours are equally long was not used but one in which the day starts at dawn and ends at dusk meaning that the twelve daylight hours and the twelve night time hours vary continually in length throughout the year. Nürnberg had its own special system, the great Nürnberg clock, which I explained earlier in an extra post. The sundial on the church displays various system of calculating the hours including Nürnberg’s special system making it one of the most complex sundials in Europe.

Moving around the corner we come to two more sundials, one south facing and one fairly rare east facing one that only shows the afternoon hours. Here on my tour I explain that a sundial usually displays local time i.e. time measured from a midday that is marked by the sun being directly overhead. This was the way that time was recorded, almost universally, down to the end of the nineteenth century. This means that every settlement has its own time. One-degree difference in longitude means a difference of four minutes in time. Prague is 3° 20’ east of Nürnberg so on local time when it’s twelve noon in Nürnberg it’s already 13’ 20’’ past twelve in Prague.

It was the invention of the railways and the telegraph that required and made possible the standardisation of time. A train timetable between two towns some distance apart requires that both towns are on the same clock, so to speak. This necessity led to the introduction of our system of standardised time zones, which are in reality purely convenient fictions, although based around some point, whose twelve-midday is actually local solar time such as Greenwich for the UK’s time zone. This system was discussed at the 1884 Washington longitude conference and finally accepted in the early twentieth century. When the clocks change, as was the case a couple of weeks ago in the EU and last week in North America it is purely an arbitrary redefining of the twelve-midday point within that particular time zone, largely divorced from local solar time. Some countries actually operate outside of the time zone system. Spain, which geographically is in the GMT time zone, is in the CET time zone one hour to the east.

Having set the scene, what I’m now about to say will probably convince many of my readers that I lack a sense of humour but when I see cartoons of the following type during the clock change period I don’t find them funny I just think of them as being horribly wrong. The prejudices of the expert.

Repositioning the Stones at Stonehenge today ready for the end of British Summer Time this weekend.

This is how they change the clocks for summertime at the prehistoric Avebury Stone Circle in England

What’s the problem? Firstly the Neolithic stone circles such as Stonehenge and Avebury are not and never have been clocks. They probably are constructed along solar alignments. I say probably because although they almost certainly are, because the builders are long dead and we possess no construction plans we can never be one hundred per cent certain. Stonehenge appears to have been constructed to align not with the summer solstice but with the winter solstice. These alignments are based not on time zones but on local solar time.

Stonehenge Winter

This is actually a major problem for archeoastronomers searching for possible alignments in Neolithic and other ancient monuments because due to the precession of the equinox local solar time changes over time. From year to year the effect is almost undetectable but is noticeable over a period of several thousand years. What might have been well aligned in 3000 BCE is now 5000 years later a bit off.

All of this, means that the alignments of Neolithic monuments such as Stonehenge and Avebury, being based on local solar time, don’t actually change in anyway what so ever when we change our clocks arbitrarily in our artificial time zones. The so-called jokes display a fundamental misconception of the conventions that we apply to keep track of time.

One thing I did learn this year during the European time change is that The Maritime Museum in Greenwich has a modern sundial, the Dolphin Sundial that has changeable plates for GMT and BST. Cool! You can watch a video of somebody changing the plates here.







Filed under Uncategorized

The Albrecht Dürer or should that be the Bernhard Walther House?

On Saturday I did my history of astronomy tour of Nürnberg for some readers of this blog who were visiting the city[1]. As usually it ended at Nürnberg’s biggest tourist attraction the Albrecht Dürer House. There are of course good reasons for including Nürnberg’s most famous artist in such a tour, as readers of this blog should know. He wrote and published the very first printed maths book in German and was the artist involved in creating the first every printed European star maps. However this is another reason for including this building in a history of astronomy tour. Before it became the Albrecht Dürer House it had been the Bernhard Walther House and this was one of the reasons that motivated Dürer to purchase it. But who, I hear you say, was Bernhard Walther?

Bernhard Walther (Albrecht Dürer) House on Tiergärtentor Nürnberg
Photo: Monica Weidemann
Source: Wikipedia Commons

Bernhard Walther was born in Memmingen in Bavaria in 1430. The first really reliable fact we have about his life is when he became a citizen of Nürnberg in 1467; remember Nürnberg was an independent city-state in the fifteenth century. He was the general manager of the Nürnberg trading post of the Memmingen merchant traders the Vöhlin-Welser-Company. When Regiomontanus came to Nürnberg in 1471, he and Walther became friends and Walther became his astronomical assistant and companion. The accounts that claim that Walther was Regiomontanus’ patron are false, as are also the claims that the two of them built an observatory financed by Walther. They carried out their astronomical observations with portable instruments out in the streets. As well as astronomy Walther apparently learnt Greek from Regiomontanus, who had learnt the language whilst a member of Cardinal Bessarion’s household in Italy. We know of Walther’s abilities in the ancient language because they are mentioned in an ode that Conrad Celtis, the so-called arch humanist, wrote in his honour.

Regiomontanus had come to Nürnberg, according to his own account, to reform astronomy in two ways; firstly by starting a new programme of astronomical observations to replace those of Ptolemaeus corrupted by centuries of copying and recopying in manuscripts and secondly by printing and publishing new editions of the astronomical literature cleared of their errors through careful philological editing. Regiomontanus had chosen Nürnberg for his programme because the city made the best scientific instruments and because of its extensive communications network being aware of the fact that his programme was only achievable with the active assistance of other European astronomers. In an age without postal services, Nürnberg, as a major European trading city, had a private communications system second only to that of Venice.

Walther assisted Regiomontanus in both of his reform endeavours but they had only succeeded in publishing nine items, including the publishing house’s ambitious publication programme, when Regiomontanus again left Nürnberg in the direction of Rome to answer the Pope’s call to work on a calendar reform in 1475. Regiomontanus never returned from that journey, dying in Rome in 1476, presumable during some sort of epidemic. Walther did not continue the publishing endeavour, although he bought up Regiomontanus extensive collection of manuscripts, but he did carry on making a series of basic simple astronomical observations for the next almost thirty years. This was the first such series of astronomical observations carried out in Early Modern Europe, making Walther to an important if minor figure in the history of astronomy.

As the general manager of the trading company Walther occupied a house on the West side of the market place in Nürnberg, today Market Place No. 11. The original hose was destroyed in the Second World War.

Walther’s trading depot was on the west side of the Nürnberg market place, next door to the right of where the Körn & Berg bookshop now stands.

When he finally retired, seventy years old, he sold the house on the market place and bought the house on Tiergärtentor (The Zoo Gate) in 1501, which is now known as the Albrecht Dürer House. Walther substantially rebuilt the house adding the whole of what is now the top floor. He also had a small window let into the south gable with a stone window ledge; he used this window to make his astronomical observations resting his observing instruments on that stone ledge, this was his observatory. We know that Walther had this window constructed because in the document with which the city council gave permission for its construction, Walther had to give a guarantee that he wouldn’t empty his chamber pot out on to the roof of the neighbouring building.

Walther House with Observatory Window in the south gable
Photo: Nora Reim
Source: Astronomie in Nürnberg

Walther’s observation programme was comparatively simple and consisted largely of regularly determining the altitude of the Sun, observing eclipses and determining the positions of the planets during conjunctions etc. The latter set of observations leads to the assumption that the observations were principally for use by astrologers. This is not surprising as Regiomontanus was a practicing astrologer, with a very good reputation, whose stated intention in reforming astronomy was in order to improve astrological predictions. He claimed that such predictions were often wrong because the astronomical data on which they were based was inaccurate. Three of Walther’s observations found their way into Copernicus’ De revolutionibus, although we don’t know how they got there. Copernicus falsely attributes part of the used data to Johannes Schöner. In 1544 Schöner did publish Regiomontanus’ and Walther’s observations in his Scripta clarissimi Mathematici M. Joannis Regiomontani. Walther’s observation were, for their time, highly accurate only to be first superceded by those of Tycho Brahe at the end of the century.

Another little known Nürnberg astronomer, Conrad Heinfogel, referred to himself as a pupil of Bernard Walther and it was Heinfogel who provided the astronomical knowledge for Dürer’s star maps.

Largely forgotten today Walther was well known and highly regarded by his contemporaries and the astronomical community down to Tycho and Kepler, Tycho using Walther’s observations to check against his own. Walther died in 1504 and in 1509 Albrecht Dürer bought the house on the Tiergärtentor, partially because being himself a big fan of the mathematical sciences he desired to own Walther’s house. At the same time he also acquired ten manuscripts out of the Regiomontanus/Walther collection including an Elements of Euclid.

If you are ever in Nürnberg go round to the back of the Dürer house and you can see Walther’s observatory for yourself. However please be quite when doing so as the people who live next door get really pissed off with the tourists and the noise that they make.

[1] Any readers of the blog who visit Nürnberg are welcome to the same tour, you just need to arrange it in advance; all you have to do is buy me lunch at the end of it. A low price of a highly entertaining and educational tour that lasts between three and four hours!


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

Men of Mathematics

This is something that I wrote this morning as a response on the History of Astronomy mailing list; having written it I have decided to cross post it here.

John Briggs is the second person in two days, who has recommended Eric Temple Bell’s “Men of Mathematics”. I can’t remember who the first one was, as I only registered it in passing, and it might not even have been on this particular mailing list. Immediately after John Briggs recommended it Rudi Lindner endorsed that recommendation. This series of recommendations has led me to say something about the role that book played in my own life and my view of it now.

“Men of Mathematics” was the first book on the history of science and/or mathematics that I ever read. I was deeply passionate fan of maths at school and my father gave me Bell’s book to read when I was sixteen years old. My other great passion was history and I had been reading history books since I taught myself to read at the age of three. Here was a book that magically combined my two great passions. I devoured it. Bell has a fluid narrative style and the book is easy to read and very stimulating.

Bell showed me that the calculus, that I had recently fallen in love with, had been invented/discovered (choose the verb that best fits your philosophy of maths), something I had never even considered before. Not only that but it was done independently by two of the greatest names in the history of science, Newton and Leibniz, and that this led to one of the most embittered priority and plagiarism disputes in intellectual history. He introduced me to George Boole, whom I had never heard of before and whose work and its reception in the 19th century I would seriously study many years later in a long-year research project into the history of formal or mathematical logic, my apprenticeship as a historian of science.

Bell’s tome ignited a burning passion for the history of mathematics in my soul, which rapidly developed into a passion for the whole of the history of science; a passion that is still burning brightly fifty years later. So would I join the chorus of those warmly recommending “Men of Mathematics”? No, actually I wouldn’t.

Why, if as I say Bell’s book played such a decisive role in my own development as a historian of mathematics/science, do I reject it now? Bell’s florid narrative writing style is very seductive but it is unfortunately also very misleading. Bell is always more than prepared to sacrifice truth and historical accuracy for a good story. The result is that his potted biographies are hagiographic, mythologizing and historically inaccurate, often to a painful degree. I spent a lot of time and effort unlearning a lot of what I had learnt from Bell. His is exactly the type of sloppy historiography against which I have taken up my crusade on my blog and in my public lectures in my later life. Sorry but, although it inspired me in my youth, I think Bell’s book should be laid to rest and not recommended to new generations.



Filed under Book Reviews, History of Logic, History of Mathematics, History of science, Myths of Science