Category Archives: 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

History of science that had this (pedantic) historian grinding his teeth in the last week.

On 11 October, The American Astronomical Society had an article on its website by Teresa Wilson (Michigan Technological University) title, This Month in Astronomical History: The Invention of the Telescope that is liberally strewn with easily avoidable errors.

We start off with:

The inventor of the refracting telescope is unknown, but the accomplishment is often attributed to the man who first filed a patent for it: Hans Lippershey (or Lipperhey), a 16th century Dutch eyeglass maker and inventor from Middelburg.

Pierre Borel – De vero telescopii inventore
Source: Wikimedia Commons

Although both variations turn up in the literature, historians of the telescope are clear that the man’s name was Lipperhey and not Lippershey, however he was German, born in Wessel, and not Dutch although he lived in Middelburg in the Dutch province of Zeeland. We continue:

Incidentally, the stories of his inspiration for building the instrument vary and tend to discredit his originality. In one scenario, two children were playing with optical lenses in his shop and he overheard them remark that a distant weather vane appeared closer when they looked through a pair of different lenses. In others, he took credit for the work of his assistant, or stole the idea from a third party altogether.

All of the above are fairy stories, which have no basis in history so why bother to mention them at all? And further:

Regardless of how events transpired, Lippershey filed for a 30-year patent from the States General of the Netherlands on 2 October 1608, creating the first written record for an instrument “for seeing things far away as if they were near.”

The first written record of the telescope is in the letter of introduction written for Lipperhey by the Council of Zeeland to Zeeland’s delegates at the States General, dated 25 September 1608. The quoted description of his telescope is actually from this letter.

Only weeks later, a lens maker from Alkmaar in North Holland, Jacob Metius, applied for a patent on a similar design. Zacharias Jansen, another eyeglass maker from Middelburg and purported inventor of the compound microscope, is also claimed to have invented the telescope.

Since the work of Huib Zuidervaart made public in 2008 and published in The Origins of the Telescope (2010) we know that Zacharias Jansen was not a potential inventor of the telescope.

Accounts disagree on whether Lippershey’s original instrument was made with a convex and a concave lens providing an upright image, or two concave [sic] lenses  providing an inverted image, but they agree that the instrument provided three-times magnification of distant objects.

This is no disagreement whatsoever; Lipperhey’s telescope had one convex (objective) and one concave (eyepiece) lens. One couldn’t construct a telescope with two concave lenses, which is obviously a fatal, given the context, typo for two convex lenses.

 Word reached Italy in 1609 and Galileo created his own modified version. By the end of the year, he had built a telescope that could magnify 20 times. He was the first to turn it skyward for a concerted series of astronomical observations. With his new instrument, Galileo discovered Jupiter’s four largest moons, observed a supernova, verified the phases of Venus, and observed sunspots.

The only difference between Lipperhey’s telescope and Galileo’s was the focal length of the lenses; I’m not really sure that qualifies as modified. Galileo was not the first to turn it skywards for a concerted series of astronomical observations; this honour definitely goes to Thomas Harriot and it is possible that Simon Marius also preceded Galileo in telescopic astronomical observations. Galileo did not observe a supernova with his telescope. The last supernova observable in Europe was in 1604 that is four years before the telescope was invented.

What makes all these errors even more embarrassing is that if the author had actually read the literature that she lists at the end of her article then she could have written a factually accurate article.

Inspired by this years 250th anniversary of the Mason-Dixon line I took down my tsundoku*** copy of Edwin Danson’s Drawing the Line: How Mason and Dixon Surveyed the Most Famous Border in America from the geodesy and surveying section of my humble home library.

From the beginning, whilst reading I was irritated by minor historical errors and an aggressive promotion of the Dava Sobel warped version of the longitude story. However my irritation boiled over when I read the following:

In 1753, Johann Tobias Mayer (1723–1762), the Swiss astronomer and professor of geography at Göttingen published a table of lunar distances…

The man who made the lunars method of determining longitude viable was Tobias Mayer; Johann Tobias Mayer (1752–1830) was his son, who after studying in Göttingen became professor of mathematics in Altdorf in 1780. Tobias Mayer was born in Marbach and grew up in Esslingen, which makes him thoroughly German and not Swiss. Lastly he was professor of economics in Göttingen not geography. I those days there was a department of economics and mathematics at the university and it was the latter, which Mayer actually taught.

Slightly earlier in the text a statement that almost set me off was:

The clarity of Auzout lenses, mirrors and telescopes enabled Huygens to improve the observing accuracy of Jovian eclipses and to discover the rings of Saturn.

The observing accuracy of Jovian eclipses was due to Giovanni Domenico Cassini, here falsely called Gian Domenico, and not to Huygens. Huygens did not use the lenses and telescopes of Adrian Auzout but famously constructed his own together with his older brother Constantijn. Huygens also did not discover the rings of Saturn but correctly hypothesised their existence by analysing all of the earlier records of the observations of this particular phenomenon.

Earlier than this Danson, a surveyor, makes the standard error of attributing the invention of triangulation to Willebrord Snel van Royen instead of Gemma Frisius. All of this would normally have had this mild mannered historian of science hurling this volume at the wall but on this occasion I persevered.

As I said above Danson aggressively promotes Sobel’s warped version of the longitude story including the myth that the Board of Longitude discriminated in favour of Maskelyne against Harrison because the latter was working class, whereas Maskelyne was a gentleman scholar. This is patent rubbish, as almost all of the eighteenth-century British instrument makers, regarded as the best in the world, were working class and were highly respected and honoured by the scientific community. Danson, when introducing Maskelyne, sets up this supposed class rivalry as follows:

With the start of the Michaelmas term [1755], Maskelyne returned to his college [Trinity] to take Holly Orders, a prerequisite for a Cambridge fellowship in the eighteenth century. In the tower above Trinity College, the inventor of the chronometer, John Harrison, was busy installing one of his famous turret clocks, oblivious of Maskelyne, his future adversary, strolling around the quad bellow.

I must admit that I was mildly excited when I read that, what a fascinating historical coincidence, if it’s true, but is it true? I had never come across this claim before, maybe it’s in Sobel’s book, but I don’t remember it, I read it many years ago. Stimulated by the claim I did what I always do in such circumstances, I went looking for evidence.

The Trinity College Tower Clock is quite famous so I was reasonably certain that I could dig up something on its history fairly easily and I was right. On the Trinity website we have a webpage titled, The College Clock. This tells us that the clock was constructed by one Richard Holdfield in 1610. A new clock and dial-plate was put in place under the Mastership of Richard Bentley in 1726-27. No clock maker in named but Harrison was still in Yorkshire at the time and it’s also not 1755. The clock was renewed once more in 1910 long after Harrison was deceased. Had Danson completely invented this episode, he had proved to be a bad historian, but falsifying a whole story? I dug deeper.

Tower or turret clocks need regular maintenance and repair and on the Cambridge University Digital Library website we find a drawing of a turret clock escapement, which was designed by John Harrison for a turret clock at Trinity College, Cambridge, dated 1755. Not a whole clock but at least part of one. Danson’s honour as an author is restored or is it?

The entry goes on:

Though designed by Harrison, the escapement was actually made by another clockmaker, William Smith, something which was far from unusual in the extensive sub-contracting system which was fundamental to the production of time-keeping devices in the eighteenth century.

Made and one can reasonably assume installed by William Smith, so no close encounter of Maskelyne and Harrison in Trinity College in 1755.

Later in the text we are in America surveying with Mason and Dixon when Danson informs us that:

For their mathematical and trigonometric calculations, the surveyors used seven-figure logarithmic tables. John Napier invented logarithms, a tabular method for multiplication and division, in 1614; in 1624 his colleague, Henry Briggs, published a set of natural logarithms (log tables), and later developed tables of trigonometrical logarithmic functions (trig tables). The slide rule had also been invented and perfected between 1654 and 1683 by Seth Partridge and Henry Coggeswall.

Where to begin? Napier did invent logarithms in 1614 and published the first log tables, which are often falsely called natural logarithms (i.e. logarithms base e), although they are closely related to natural logarithms. In 1624 Henry Briggs published the first tables of common or base 10 logarithms and not natural logarithms. John Speidell had published the first table of what were effectively naturel logarithms based on Napier’s work in 1619. The first description of natural logarithms was by Nicholas Mercator in 1668. Tables of trigonometrical logarithmic functions are not trig tables. Surprisingly, trig tables are tables of trigonometrical functions. The slide rule was invented by William Oughtred in 1630. Seth Partridge developed the moving slide/fixed stock principle in 1657. Henry Coggeshall developed the so-called carpenter’s slide rule for measuring the dimensions of timber in 1677.

All of this leads me to ask in John Wiley & Sons Inc., a large and successful academic publishing company, the publishers of Danson’s tome, have actually heard of fact checking or if they just don’t care. The mistakes that I have picked up on here are all fairly elementary history of science errors and make me as a reader of the book wonder how much of the other information in the book is trust worthy. If I was doing anything formal on Mason and Dixon I would be very wary of quoting anything from Danson’s book before checking it thoroughly against other sources.

The sloppiness of both Wilson’s article on the telescope and Danson’s book on the Mason-Dixon line make me angry because with a small modicum of effort on the part of the respective authors the mistakes they have made could easily have been avoided.





Filed under Uncategorized

A Lady Logician

Today George Boole is regarded as one of the founders of the computer age that now dominates our culture.

George Boole
Source: Wikimedia Commons

His algebra lies at the base of computer circuit design and of most computer programming languages and Booleans power the algorithms of the ubiquitous search engines. As a result two years ago the bicentenary of his birth was celebrated extensively and very publically. All of this would have been very hard to predict when his work on the algebra of logic first saw the light of day in the nineteenth century. His first publication Mathematical Analysis of Logic (1847) was largely ignored by the wider world of mathematics and his definitive presentation of his logic An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities fared little better, initially attracting very little attention. It was only some time after his death that Boole’s logical works began to attract deeper interest, most notably in Germany by Ernst Schröder and in America by Charles Sanders Peirce.

Charles Sanders Peirce
Source: Wikimedia Commons

In 1883 Peirce published Studies in Logic: by Members of the Johns Hopkins University, edited by himself it contained seven papers written largely by his students. Of central interest is the fact that it contains a doctoral thesis, On the Algebra of Logic, written by a women, Christine Ladd.

Christine Ladd’s life story is a casebook study of the prejudices that women, who wished to enter academia suffered in the nineteenth and early twentieth centuries. Born 1 December 1847 (the year Boole published his first logic book) in Windsor, Connecticut the daughter of Eliphalet and Augusta Ladd, she grew up in New York and Windsor. Her mother and her aunt Julie Niles brought her up to believe in education for women and women’s rights. Her mother died in 1860 but her father initially supported her wish for advanced education and enrolled her at Welshing academy in a two year course for preparing students for college; she graduated as valedictorian in 1865 but now her father opposed her wish to go on to college. Only by arguing that she was too ugly to get a husband was she able to persuade her father and grandmother to allow her to study at the women’s college Vassar. She entered Vassar in 1866 but was forced by financial difficulties to leave before completing her first year. She now became a schoolteacher until her aunt helped her to finance her studies and she returned to Vassar.

At Vassar the pioneering female astronomer Maria Mitchell took her under her wing and fostered her developing interest in physics and mathematics.

Due to the fact that women could not do experiment work in laboratories she was forced to choose mathematics[1] over physics, a decision that she regretted all of her life. She graduated from Vassar in 1869 and became a secondary school teacher of mathematics and science in Washington, Pennsylvania. Over the next nine years she published six items in The Analyst: A Journal of Pure and Applied Mathematics and three in the American Journal of Mathematics. More importantly she took a very active part in the mathematical questions column of the Educational Times, the journal of the College of Preceptors in London, a profession body for schoolteachers. This mathematical questions column was a very popular forum for nineteenth century mathematicians and logicians with many leading practitioners contribution both question and solutions. For example the nineteenth-century Scottish logician Hugh McColl published his first logical essays here and Bertrand Russell’s first mathematical publication can also be found here[2]. Ladd contributed a total of seventy-seven problem and solution to the Education Times, which would prove highly significant for her future career.

In 1878 she applied for and won a fellowship to study mathematics at the Johns Hopkins University. Her fellowship application was simply signed C. Ladd and the university had assumed that she was male. When they realised that she was in fact a woman, they withdrew their offer of a fellowship. However the English professor of mathematics at Johns Hopkins, James J. Sylvester, who knew of Ladd’s abilities from those Educational Times contribution insisted on the university honouring the fellowship offer.

James Joseph Sylvester
Source: Wikimedia Commons

At the time Johns Hopkins did not have a very good reputation but Sylvester did, in fact he was a mathematical star, not wishing to lose him the university conceded and allowed Ladd to take up her three-year scholarship. However her name was not allowed to be printed in circulars and basically the university denied her existence. At the beginning she was only allowed to attend Sylvester’s classes but as it became clear that she was an exceptional student she was allowed to attend classes by other professors.

In the year 1879 to 1880 she studied mathematics, logic and psychology under Charles Sanders Peirce becoming the first American women to be involved in psychology. Under Peirce’s supervision she wrote her doctoral thesis On the Algebra of Logic, which was then, as mentioned above, published in 1883. Although she had completed all the requirements of a doctoral degree Johns Hopkins University refused to award her a doctorate because she was a woman. They only finally did so forty-four years later in 1927, when she was already seventy-eight years old.

In 1882 she married fellow Johns Hopkins mathematician Fabian Franklin and became Christine Ladd-Franklin, the name by which she is universally known today. As a married woman she was barred from holding a paid position at an American university but she would lecture unpaid for five years on logic and psychology at Johns Hopkins and later at Columbia University for thirty years.

In the 1880s she developed an interest in vision and theories of colour perception publishing her first paper on the subject in 1887. She accompanied her husband on a research trip to Germany 1891-92 and used the opportunity to study with the psychologist Georg Elias Müller (1850–1934) in Göttingen

George Elias Muller
Source: Wikimedia Commons

and with the physiologist and physicist Hermann von Helmholtz (1821-1894) in Berlin.

Hermannvon Helmholtz in 1848
Source: Wikimedia Commons

In 1894 she returned alone to Germany to work with physicist Arthur König (1856–1901), with whom she did not get on and whom she accused of having stolen her ideas, and again in 1901 to work with Müller.

Portrait of Arthur Konig from Pokorny, J.
Source: Wikimedia Commons

As a result of her researches she developed and published her own theories of colour vision and the causes of colour blindness that were highly influential.

Ladd-Franklin was a tireless campaigner for women’s rights and even persuaded the inventor of the record player, Emile Berliner, to establish a fellowship for female professors, the Sarah Berliner postdoctoral endowment, in 1909, which she administered for the first ten years and which is still awarded annually.

Emile Berliner
Source: Wikimedia Commons

She herself continued to suffer rejection and humiliation as a female academic. In 1904 the British psychologist Edward Titchener (1867–1927) founded a society for experimental psychologists, “The Experimentalists”, and although he knew Ladd-Franklin well her barred her, as a woman, from membership. A decision, which she fought against in vain for many years. Women were only permitted to attend following Titchener’s death.

Edward Bradford Titchener
Source: Wikimedia Commons

Despite the discrimination that she suffered Christine Ladd-Franklin published many papers in the leading journals and her work was held in high regard. She died of pneumonia, aged 82, in 1930. Today the American Association for women in Psychology have an annual Christine-Ladd Franklin Award, awarded for significant and substantial contributions to the Association.

Christine Ladd-Franklin
Source: Wikimedia Commons

Although she struggled against prejudice and discrimination all of her life and never received the formal recognition that should have been her due, Christine Ladd-Franklin made significant contributions to the fields of Boolean algebra and colour vision for which she is highly regarded today. Through her fighting spirit and unbending will she helped open the doors of scientific research and academia for later generations of women.



[1] It is interesting to note that barred from access to academia and its institutions a small but significant number of women managed to some extent to break through the glass ceiling in logic and the mathematics in the nineteenth century, because these are subjects in which one can make an impression with nothing more than a pencil and a piece of paper.

[2] In my days as a logic historian I spent a not very pleasant two weeks in the British Newspaper Library in Colindale (the tenth circle of hell), amongst other things, going through the Educational Times looking for contributions on the algebra of logic. During this search I came across the Bertrand Russell contribution, which I showed, some time later, to a leading Russell scholar of my acquaintance, who shall remain here nameless. Imagine my surprise when shortly afterwards an article was published by said Russell expert explaining how he had discovered Russell’s first ever mathematical publication in the Mathematical Questions column of The Educational Times. He made no mention of the fact that it was actually I who had made the discovery.


Filed under History of Logic, History of Mathematics, History of science, Ladies of Science, Uncategorized

The Great Man paradox

Over the years a fair number of the blog posts here have been fairly speculative, basically me thinking out loud about something that has recently crossed my mind or my path. What follows is one of those posts and as I begin writing I have a germ of an idea what I think I want to say but I can’t guarantee that what will come out is what I initial intended or that it will be particularly illuminating or informative. At the end of last week I had the following very brief exchange with zoologist and historian, Matthew the Mancunian Maggot Man (@matthewcobb)

MC: What would have happened if Einstein fell under a tram in 1900? What difference would it have made, for how long?

Me: Not a lot, Poincaré was almost there and others were working on the various problems. I’d guess at most a ten-year delay

MC: So are there any true examples of ‘great men’ or is science all over-determined?

My instantaneous response to Mathew’s last comment was yes there are great men in the history of science and Einstein was certainly one of them but not in the sense that people usually mean when they use the term. It is this response that I will try to unpack and elucidate here.

When people describe Einstein as a great man of science what they usually mean is that if he hadn’t lived, see Matthew’s original question, we ‘wouldn’t have the theories of relativity’ or ‘physics would have been held back for decades or even longer’. Both of the expression in scare quote are ones that occur regularly following statements along the lines of if X hadn’t existed we wouldn’t have Y and both are expressions that I think should be banned from #histSTM. They should be banned because they are simply not true.

Let’s take a brief look at the three papers Einstein published in 1905 that made his initial reputation. The paper on quantum theory, for which he would eventually get his Nobel Prize, was, of course, in response to Planck’s work in this field and was a topic on which many would work in the first half of the twentieth century. The so-called black body problem, which sparked off the whole thing, was regarded as one of the most important unsolved problems in physics at the turn of the century. Brownian motion, the subject of the second paper, was another hot topic with various people producing mathematically formulations of it in the nineteenth century. In fact Marian Smoluchowski produced a solution very similar to Einstein’s independently, which was published in 1906. This just leaves Special Relativity. The problem solved here had been debated ever since it had been known that the Clerk Maxwell equations did not agree with Newtonian physics. We have both Lorentz and FitzGerald producing the alternative to the Newtonian Galilean transformations that lie at the heart of Einstein’s Special Relativity theory. The Michelson-Morley experiment also demanded a solution. Poincaré had almost reached that solution when Einstein pipped him at the post. The four dimensional space-time continuum now considered so central to the whole concept was delivered, not by Einstein, but by his one time teacher Minkowski. Minkowski’s formulation was, of course, also central for the General Theory of Relativity; the solution for the field equations of which were found independently by Einstein and Hilbert, although Hilbert clearly acknowledged Einstein’s priority.

Albert Einstein in 1904 (age 25)
Lucien Chavan [1] (1868 – 1942), a friend of Einstein’s when he was living in Berne. – Cropped from original at the Historical Museum of Berne.
Source: Wikimedia Commons

Without going into a lot of detail it should be clear that Einstein is solving problems on which a number of other people are working and making important contributions. He is not pulling new physics out of a hat but solving problems over-determined by the field of physics itself.

What about other ‘great men’? The two most obvious examples are also physicists, Galileo and Newton. I’ve already done a major demolition job on Galileo several years ago, in which I show that everything he worked on was being worked on parallel by other highly competent scholars that you can read here. And a more recent version here.

Galileo Galilei. Portrait by Leoni
Source: Wikimedia Commons

So what about Newton?As should be well known Leibnitz and Newton both developed calculus roughly contemporaneously, even more important, as I explained here, they were both building on foundations laid down by other leading seventeenth-century mathematicians. Newton was anticipated in his colour theory of white light by the Bohemian scholar Jan Marek Marci. As I’ve explained here and here Newton was only one of three people who developed a reflecting telescope in the 1660s. Robert Hooke anticipated and probably motivated Newton on the theory of universal gravity and Newton’s work on dynamics built on the work of many others beginning with Tartaglia and Benedetti in the sixteenth century. His first law of motion was from Isaac Beeckman via Descartes and the second from Christiaan Huygens from whose work he also derived the law of gravity. Once again we have a physicist working on problem of his time that were being worked actively on by other competent scholars.

Copy of a portrait of Newton at 46 in 1689 by Godfrey Kneller
Source: Wikimedia Commons

I think this brief analysis that the work of these ‘great men’, Einstein, Galileo and Newton, was to a large extent over-determined that is dictated by the scientific evolution of their respective times and their finding solutions to those problems, solutions that others also found contemporaneously, does not qualify them as special, as ‘great men’.

Having said all of that I would be insane to deny that all three of these physicists are, with right, regarded as special, as great men, so what is the solution to this seeming paradox?

I think the answer lies not in the fact that they solved the problems that they solved but in the breadth and quality of their work. Each of them did not just solve one major problem but a whole series of them and their solutions were of a quality and depth unequalled by others also offering solutions. This can be illustrated by looking at Hooke and Newton on gravity. Hooke got there first and there are good grounds for believing that his work laid the foundations for Newton’s. However whereas Hooke’s contribution consist of a brief series of well founded speculations, Newton built with his Principia a vast mathematical edifice that went on to dominate physics for two hundred years. Put simply it is not the originality or uniqueness of their work but the quality and depth of it that makes these researchers great men.



Filed under Uncategorized

“Within the stress of Research” – A collaborative composition with apologies to Paul Simon


Hello JSTOR my old friend[1]

I’ve come to search in you again[2]

Because a reference softly creeping

Left its seeds while I was reading[3]

And the paper that was gnawing at my brain

Still remains[4]

Within the stress of research[5]


Through restless links I searched alone

Papers from journals I do not own

Neath the halo from my desk-lamp

I turn my collar to the research lab[6]


When my eyes were stabbed by the pain

Of a sleepless night

As I tried to write

Through the stress of research[7]


And in the flickering light I saw

Ten thousand deadlines maybe more[8]

Within the stress of research


Post-doc said, ah you do not know

Research like a cancer grows

Hear my words that I might teach you

Read my diss’ and it might reach you

But my sources like undergrads they failed

Adding to the stress of research[9]


Then the faculty bowed and prayed

To bureaucratic gods they made

And the REF flashed out its warnings

Low impact scores were alarming[10]


And the graphs and words from students

Were projected on the classroom walls and lecture halls

Folks breaking under the stress from research[11]


Composed 31 August 2017

Extended 5 September 2017

[1] Clare @mcclare95


[3] Thony Christie @rmathematicus

[4] Vivek Santayana @viveksantayana

[5] Thony Christie @rmathematicus

[6] Eric Keeton @w0wkeeton

[7] Vivek Santayana @viveksantayana

[8] Vivek Santayana @viveksantayana

[9] Eric Keeton @w0wkeeton

[10] Vivek Santayana @viveksantayana

[11] Eric Keeton @w0wkeeton


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Journalists getting the facts wrong in the 19th century

One of the joys of having an extensive twitter stream is the unexpected titbits that it throws up from time to time. Recently Lee Jackson[1] (@VictorianLondon) posted this small newspaper cutting from The Times for the 2nd May 1862.

This is an excerpt from an account of the 1862 Great London Exposition not to be confused with the more famous Crystal Palace Exhibition of 1851. This Exposition was held in a building especially constructed for the purpose in South Kensington, where the Natural History Museum now stands.

Panoramic view of the International Exhibition of 1862 in South Kensington, London
Source: Wikimedia Commons

A twenty-one acre construction designed by Captain Francis Fowke (1823–1865) of the Royal Engineers, it was supposed to be a permanent structure but when parliament refused to buy the building after the Exposition closed it was demolished and the materials used to build Alexandra Palace. The building cost £300,000 paid for out the profits of the 1851 Exhibition. Fowke also produced the original plans for the Natural History Museum but died before they could be realised. His plans were modified by Alfred Waterhouse, the new architect, when the museum was finally constructed in 1870.

Francis Fowke (1823-1865)
Source: Victoria & Albert Museum

The main aim of the Exposition, which ran from 1 May to 15 November attracting over six million visitors, was to present the latest technological advances of the industrial revolution, hence the presence an engine of Charles Babbage as described in the cutting. However the author of the piece has got his facts wonderfully mixed up.

The author introduces Charles Babbage by way of his notorious disputes with the street musicians of London for which he was better known than for his mathematical and technical achievements and which I blogged about several years ago. We then get told that the Exposition is displaying “Mr Babbage’s great calculating machine, which will work quadrations and calculate logarithms up to seven places of decimals.” All well and good so far but then he goes on, “It was the account of this invention written by the late Lady Lovelace – Lord Byron’s daughter –…” Anybody cognisant with the calculating engines designed by Charles Babbage will have immediately realised that the reporter can’t tell his Difference Engines from his Analytical Engines.

The calculating machine capable of calculating logarithms to seven places of decimals, of which a demonstration module was indeed displayed at the 1862 Exposition, was Babbage’s Difference Engine. The computer described by Lady Lovelace in her notorious memoire from 1842 was Babbage’s Analytical Engine of which he only constructed a model in 1871, nine years after the Exposition. This brings us to Messrs Scheutz of Stockholm.

Difference Engine No. 1, portion,1832
Source: Science Museum London

Analytical Engine, experimental model, 1871
Source: Science Museum London

Per Georg Scheutz (1785-1873) was a Swedish lawyer and inventor, who invented the Scheutzian calculation engine in 1837 based on the design of Babbage’s Difference Engine.

Per Georg Schutz
Source: Wikimedia Commons

This was constructed by his son Edvard and finished in 1843. An improved model was created in 1853 and displayed at the World Fair in Paris in 1855. This machine was bought by the British Government in 1859 and was in fact displayed at the 1862 Exposition but had apparently been removed by the time the Time’s reporter paid his visit to South Kensington. Scheutz’s machine gives a lie to those who claim that Babbage’s Difference Engine was never realised. Scheutz constructed a third machine in 1860, which was sold to the American Government.

The third Difference engine (Scheutz No. 2) built by Per Georg Scheutz, Edvard Scheutz and Bryan Donkin
Source: Science Museum London

It would seem that journalist screwing up their accounts of scientific and technological advances has a long history.




[1] You should read his excellent Dirty Old London: The Victorian Fight Against Filth, Yale University Press, Reprint 2015


Filed under History of Computing, Uncategorized

A very special book

In 1543 the printer/publisher Johannes Petreius published Nicolaus Copernicus’ De revolutionibus orbium coelestium, the first mathematical description of a heliocentric system for the then known cosmos, in Nürnberg. Initially appearing with little resonance, more than two hundred years later the great, German, enlightenment philosopher Immanuel Kant thought that its publication signalled the greatest ever change in humanities perception of its own place in the cosmos. Today many historians of science regard it as the most important scientific publication ever. Although I object to the use of superlatives in the history of science, I do think that it is one of the most significant scientific publication of the Early Modern Period.

Title page of the first edition of De revolutionibus
Source: Wikimedia Commons

It is not actually known how many copies Petreius printed of that first edition but Owen Gingerich[1], the greatest authority on the subject, estimates that the first edition was probably about five hundred copies of which about three hundred still exist. A small number of the surviving copies of the first edition were given by Petreius to selected people as presents with a hand written dedication from himself. One of these resides in the University of Leipzig library. The Leipzig De revolutionibus has the following dedication:

Hieronymo Schr[ei]ber Petreus dedit 1543

Hieronymus Schreiber was born in Nürnberg; his date of birth is unknown. He is thought to have attended the Egidien Gymnasium in Nürnberg, where he would have been taught mathematics by Johannes Schöner. Schöner later dedicated an edition of Peuerbach’s Tractatus super propositiones Ptolemaei, that he edited and Petreius published in 1541, to him. In 1532 Schreiber matriculated at the University of Wittenberg, in the same year as Georg Joachim Rheticus. When Rheticus took his sabbatical in 1539, which lead him to go off to Frombork and bring back the manuscript of De revolutionibus to Nürnberg, it was Schreiber who took over his teaching duties in Wittenberg, teaching mathematics to the undergraduates there. It was almost certainly for this work that Petreius rewarded him with a personally dedicated copy of De revolutionibus.

When Rheticus left Wittenberg in 1542, to take up the post of mathematics professor in Leipzig, his chair was not awarded to Schreiber but to the Nürnberger mathematician Erasmus Flock (1514–1568), another of Schöner’s pupils. Schreiber left Wittenberg for Italy and died in 1547 during a period of study in Paris.

In 1598 Schreiber’s copy of De revolutionibus came into the possession of the young Johannes Kepler, together with two other astronomy books that had belonged to Schreiber. Quite how Kepler acquired these books is not known.

The book nowadays known as the Kepler De revolutionibus contains some very interesting marginalia. Schreiber added one of the most complete collections of corrections to the text, not only the errata contained on the official errata sheet but also many others. Schreiber’s most interesting annotation is the addition of the name Andreas Osiander above the Ad lectorum, which prefaces the book. Kepler draws attention to this on the back of the flyleaf and it was Kepler who first made Osiander’s authorship of the Ad lectorum general knowledge, thereby sealing his fate as ‘the greatest villain in the history of science.’ Kepler added comparatively few comments in the margins after he acquired the book but those that he did add show his progress as he worked his way through Copernicus’ opus.

The value of collectable works from the history of science depends not only on the works themselves but also on their provenances, who were the owners and what did they write in the margins? First editions of De revolutionibus rarely appear for sale but when one that had belonged to John Greaves (1602–1652) the Savilian Professor of Astronomy at Oxford was auctioned some years back it sold for almost 2.5 million dollars. Should Kepler’s De revolutionibus, with its rare handwritten Petreius dedication, ever come on to the open market, which I doubt it will, I suspect the sky’s the limit, as they say.

Last Sunday I took a trip to Nürnberg to the Germanisches National Museum to see their new exhibition celebrating The Luther Year (it’s five hundred years since Luther made his 95 Theses public), Luther, Kolumbus und die Folgen: Welt im Wandle 1500 – 1600. This exhibition had lots of very nice stuff from the histories of astronomy, cartography and exploration and is highly recommended if you are in the area before the beginning of November when it ends. I was happily trundling round the exhibition giving detailed background information to my companion, as is my wont, when I rounded a corner and espied a glass cabinet with copies of De revolutionibus. One of the ironies of history is that although the book was printed in the city, Nürnberg does not possess a first edition of De revolutionibus, so imagine my surprise and delight when I realised that the first edition sitting in the cabinet, next to the museum’s own second edition (Basel 1561), was in fact the Kepler De revolutionibus, on loan from the University of Leipzig library – a very special book indeed.

[1] Much of the information in this post is taken from Owen Gingerich’s excellent An Annotated Census of Copernicus’ De Revolutionibus (Nuremberg, 1543 en Basel, 1566), Brill, Leiden-Boston-Koln, 2002

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