Category Archives: 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

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

Did Isaac leap or was he pushed?

In 2016 2017 it would not be too much to expect a professor of philosophy at an American university to have a working knowledge of the evolution of science in the seventeenth century, particularly given that said evolution had a massive impact on the historical evolution of philosophy. One might excuse a freshly baked adjunct professor at a small liberal arts college, in his first year, if they were not au fait with the minutiae of the history of seventeenth-century astronomy but one would expect better from an established and acknowledged expert. Andrew Janiak is just that, an established and acknowledged expert. Creed C. Black Professor of Philosophy and Chair of Department at Duke University; according to Wikipedia, “Duke is consistently included among the best universities in the world by numerous university rankings”. Janiak is also an acknowledge expert on Isaac Newton and author of Isaac Newton in the Blackwell Great Minds series, so one is all the more dumbfounded to read the following in his article entitled Newton’s Leap on the Institute of Arts and Ideas: Philosophy for our times website:


Isaac Newton 1677 after Peter Lely Source: Wikimedia Commons Comment from CJ Schilt (a Newton expert) on Facebook: On another note, that picture is probably not Newton, despite what Finegold thinks.


But wait a minute: what could be more amazing than a young man discovering a fundamental force of nature while sitting under a tree? For starters, we have to recognize how foreign Newton’s ultimate idea about gravity was to philosophers, astronomers and mathematicians in the era of the Scientific Revolution. Newton provided an answer to a question that hadn’t even been asked yet. The problem with understanding the distant past is that we take our twenty-first century ideas and attitudes for granted. We think, for example, that the following is obvious: if the planets, like the Earth and Jupiter, regularly orbit the Sun, there must be something that causes them to follow their orbits. After all, if nothing caused them to orbit the Sun, they would fly off into deep space. [my emphasis]That seems so obvious to us, it’s hard to imagine that for centuries, the world’s leading thinkers, from Aristotle to Ptolemy and onwards, did not have that idea at all. Instead, for many generations, leading philosophers and mathematicians thought this: the circle is a perfect mathematical form, and the planetary orbits are circular, so they are ever-lasting aspects of the natural world. To them, the orbits were so perfect that nothing caused them to occur. They simply were. [my emphasis] The question of what caused the planetary orbits was not even on the table for astronomers in those days. [my emphasis] Down on earth, apples fell from trees throughout history just as they do now. But philosophers and mathematicians didn’t have any reason to think that whatever causes apples to fall to the ground might somehow be connected to anything going on in the heavens. After all, the heavens were thought to be the home of everlasting motions, of perfect circles, and were therefore nothing like the constantly changing, messy world down below, where worms eat through apples as they rot on the ground.

So what is wrong with this piece of #histSTM prose? Let us start with the second of my bold emphasised segments:

Instead, for many generations, leading philosophers and mathematicians thought this: the circle is a perfect mathematical form, and the planetary orbits are circular, so they are ever-lasting aspects of the natural world. To them, the orbits were so perfect that nothing caused them to occur. They simply were.

Whilst it is true that, following Empedocles, Western culture adopted the so-called Platonic axioms, which stated that celestial motion was uniform and circular, it is not true that they claimed this motion to be without cause. Aristotle, whose system became dominant for a time in the Middle Ages, hypothesised a system of nested crystalline spheres, which working from the outside to the centre drove each other through direct contact; a system that probably would not have worked due to friction. His outer-most sphere was moved by the unmoved mover, who remained unnamed, making the theory very attractive for Christian theologians in the High Middle Ages, who simple called the unmoved mover God. Interestingly the expression love makes the world go round originates in the Aristotelian belief that that driving force was love. In the Middle Ages we also find the beliefs that each of the heavenly bodies has a soul, which propels it through space or alternatively an angel pushing it around its orbit.

All of this is all well and good but of course doesn’t have any real relevance for Newton because by the time he came on the scene the Platonic axioms were well and truly dead, killed off by one Johannes Kepler. You might have heard of him? Kepler published the first two of his planetary laws, number one: that the planetary orbits are ellipses and that the sun is at one focus of the ellipse and number two: that a line connecting the sun to the planet sweeps out equal areas in equal time periods in 1609, that’s thirty-three years before Newton was born. Somewhat later Cassini proved with the support of his teachers, Riccioli and Grimaldi, using a heliometer they had constructed in the San Petronio Basilica in Bologna, that the earth’s orbit around the sun or the sun’s around the earth, (the method couldn’t decide which) was definitely elliptical.

Part of the San Petronio Basilica heliometer.
The meridian line sundial inscribed on the floor at the San Petronio Basilica in Bologna, Emilia Romagna, northern Italy. An image of the Sun produced by a pinhole gnomon in the churches vaults 66.8 meters (219 ft) away fills this 168×64 cm oval at noon on the winter solstice.
Source Wikimedia Commons

By the time Newton became interested in astronomy it was accepted by all that the planetary orbits were Keplerian ellipses and not circles. Kepler’s first and third laws were accepted almost immediately being based on observation and solid mathematics but law two remained contentious until about 1670, when it was newly derived by Nicholas Mercator. The dispute over alternatives to Kepler’s second law between Ismaël Boulliau and Seth Ward was almost certainly Newton’s introduction to Kepler’s theories.

Turning to the other two bold emphasised claims we have:

 Newton provided an answer to a question that hadn’t even been asked yet. The problem with understanding the distant past is that we take our twenty-first century ideas and attitudes for granted. We think, for example, that the following is obvious: if the planets, like the Earth and Jupiter, regularly orbit the Sun, there must be something that causes them to follow their orbits. After all, if nothing caused them to orbit the Sun, they would fly off into deep space.


The question of what caused the planetary orbits was not even on the table for astronomers in those days.

I’m afraid that Herr Kepler would disagree rather strongly with these claims. Not only had he asked this question he had also supplied a fairly ingenious and complex answer to it. Also quite famously his teacher Michael Maestlin rebuked him quite strongly for having done so. Kepler is usually credited with being the first to reject vitalist explanations of planetary motion by souls, spirits or angels (anima) and suggest instead a non-vitalist force (vir). His theory, based on the magnetic theories of Gilbert, was some sort of magnetic attraction emanating from the sun that weakened the further out it got. Kepler’s work started a debate that wound its way through the seventeenth century.

Ismaël Boulliau, a Keplerian, in his Astronomia philolaica from 1645 discussed Kepler’s theory of planetary force, which he rejected but added that if it did exist it would be an inverse-square law in analogy to Kepler’s law of the propagation of light. Newton was well aware of Boulliau’s suggestion of an inverse-square law. In 1666 Giovanni Alfonso Borelli, a disciple of Galileo, published his Theoricae Mediceorum planetarum ex causis physicis deductae in which he suggested that planetary motion was the result of three forces.

Famously in 1684 in a London coffee house Christopher Wren posed the question to Robert Hooke and Edmond Halley, if the force driving the planets was an inverse-square force would the orbits be Keplerian ellipses, offering a book token as prize to the first one to solve the problem. This, as is well known, led to Halley asking Newton who answered in the positive and wrote his Principia to prove it; in the Principia Newton shows that he is fully aware of both Kepler’s and Borelli’s work on the subject. What Newton deliberately left out of the Principia is that in an earlier exchange it had in fact been Hooke who first posited a universal force of gravity.

As this all too brief survey of the history shows, far from Newton providing an answer to a question that hadn’t been asked yet, he was, so to speak, a Johnny-come-lately to a debate that when he added his contribution was already eighty years old.

The Institute of Arts and Ideas advertises itself as follows:

So the IAI seeks to challenge the notion that our present accepted wisdom is the truth. It aims to uncover the flaws and limitations in our current thinking in search of alternative and better ways to hold the world.

Personally I don’t see how having a leading philosopher of science propagating the lone genius myth by spouting crap about the history of science fulfils that aim.







Filed under History of Astronomy, History of science, Myths of Science, Newton

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

Galileo, The Church and that ban

Quite Interesting @qikipedia is the Twitter account of the highly successful British television comedy panel game QI (Quite Interesting). For those who are not aficionados of this piece of modern television culture it is described on Wikipedia thus:

The format of the show focuses on Davies and three other guest panelists answering questions that are extremely obscure, making it unlikely that the correct answer will be given. To compensate, the panelists are awarded points not only for the right answer, but also for interesting ones, regardless of whether they are right or even relate to the original question, while points are deducted for “answers which are not only wrong, but pathetically obvious”– typically answers that are generally believed to be true but in fact are misconceptions. These answers, referred to as “forfeits”, are usually indicated by a loud klaxon and alarm bell, flashing lights, and the incorrect answer being flashed on the video screens behind the panelists. [my emphasis]

Given the section that I have highlighted above the Twitter account should have points deducted to the sounds of a loud klaxon and an alarm bell accompanied by flashing lights for having tweeted the following on 12 September

It wasn’t until 1992 that the Catholic Church finally admitted that Galileo’s views on the solar system were correct – @qikipedia

Portrait of Galileo that accompanied the @qikipedia tweet


This is of course complete rubbish. In what follows I will give a brief summary of the Catholic Church’s ban on heliocentrism, as propagated by Galileo amongst others.

The initial ban on propagating heliocentrism as a proven theory, one could still present it as a hypothetical one, was issued by the Inquisition in 1616. Interestingly whilst the books of Kepler and Maestlin, for example, were placed on the Index of Forbidden Books, Copernicus’ De revolutionibus was not but merely banned temporarily until corrected, which took place surprisingly rapidly; correction meaning the removal of the very few passages where heliocentricity is presented as a fact. By 1621 De revolutionibus was back in circulation for Catholic astronomers. Galileo’s Dialogo was placed on the Index following his trial in 1632.

A title page of the Index of Forbidden Books 1758
Source: Linda Hall Library

Books openly espousing heliocentricity as a true fact, which was more that the science of the time could deliver, were placed on the Index by the Catholic Church, so all good Catholics immediately dropped the subject? Well no actually. The ban had surprising little effect outside of Italy. Within Italy, astronomers kept their heads below the parapet for a couple of decades but outside of Italy things were very different. Protestant countries, naturally, totally ignored the ban and even astronomers in Catholic countries on the whole took very little notice of it. The one notable exception was René Descartes who dropped plans to publish his book Le Monde, ou Traite de la lumiere in 1633, which contained his views supporting heliocentricity, the full text only appearing posthumously in 1677. Quite why he did so was not very clear but it is thought that he did it out of respect to his Jesuit teachers. However, Descartes remained the exception. Galileo’s offending Dialogo quickly appeared in a ‘pirate’ edition, translated into Latin in the Netherlands, where later his Discorsi, would also be published. I say pirate but Galileo was well aware of the publication, which had his blessing, but officially knew nothing about it.

Title page of the 1635 ‘pirate’ Latin edition of Dialogo
Source: The History of Science Collections of the University of Oklahoma Libraries

Within Italy once the dust had settled Catholic astronomers began to publish books on heliocentricity that opened with some sort of nod in the direction of the Church along the lines of, “The Holy Mother Church has in its wisdom condemned heliocentricity as contrary to Holy Scripture…” but then continued something like this “…however it is an interesting hypothetical mathematical model, which we will now discuss.” This face saving trick was accepted by the Church and everybody was happy. By the early eighteenth century almost all astronomers in Italy, with the exception of some Jesuits, were following this course.

In 1758 the ball game changed again as the then Pope basically dropped the ban on heliocentricity, although this was done informally and the formal prohibition stayed in place. The publication of a complete works of Galileo was even permitted with a suitable preface to the Dialogo pointing out its faults. From this time on Catholic astronomers were quite free to propagate a factual heliocentricity in their publications.

This was the situation up till 1820 when an over zealous Master of the Sacred Palace (the Church’s chief censor), Fillipo Anfossi, refused to licence a book containing a factual account of heliocentricity by Giuseppe Settele. Settele appealed directly to the Pope and after deliberations the ban on heliocentricity was formally lifted by the Church in 1821. The next edition of the Index, which didn’t appear until 1835, no longer contained books on heliocentricity. Anfossi and Settele only feature in the history of science because of this incidence.

So to summarise, the Church only banned factual claims for the heliocentric system but not hypothetical statements about it, so this is how Catholic astronomer got around the ban. In 1758 the Pope informally lifted the ban clearing the way for Catholic astronomers to write freely about it. In 1821 the ban was formally lifted and in 1835 books on heliocentricity were removed from the Index, so where did QI get their date of 1992 from?

In 1981 the Church constituted the Pontifical Interdisciplinary Study Commission to re-examine the Galileo trial, which came to rather wishy-washy conclusions. In 1992 the Pope held a speech formally closing the commission and saying that the whole affair had been rather unfortunate and that the Church had been probably wrong to prosecute Galileo.






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

Hyping the history of mathematics

A while back the Internet was full of reports about a sensational discovery in the history of mathematics. Two researchers had apparently proved that a well know Babylonian cuneiform clay tablet (Plimpton 322), which contains a list of Pythagorean triples, is in fact a proof that the Babylonians had developed trigonometry one thousand years before the Greeks and it was even a superior and more accurate system than that of the Greeks. My first reaction was that the reports contained considerably more hype than substance, a reaction that was largely confirmed by an excellent blog post on the topic by Evelyn Lamb.

Plimpton 322, Babylonian tablet listing pythagorean triples
Source: Wikimedia Commons

This was followed by an equally excellent and equally deflating essay by Eduardo A Escobar an expert on cuneiform tablets. And so another hyped sensation is brought crashing down into the real world. Both put downs were endorsed by Eleanor Robson author of Mathematics in Ancient Iraq: A Social History and a leading expert on Babylonian mathematics.

Last week saw the next history of mathematics press feeding frenzy with the announcement by the Bodleian Library in Oxford that an Indian manuscript containing a symbol for zero had been re-dated using radio carbon dating and was now considered to be from the third to fourth centuries CE rather than the eight century CE, making it the earliest known Indian symbol for zero. This is of course an interesting and significant discovery in the history of mathematics but it doesn’t actually change our knowledge of that history in any really significant way. I will explain later, but first the hype in the various Internet reports.

A leaf from the Bakhshali Manuscript, showing off Indian mathematical genius. A zero symbol has been highlighted in the image.
Courtesy of the Bodleian Library


We start off with Richard Ovenden from Bodleian Libraries who announced, “The finding is of “vital importance” to the history of mathematics.”

Bodleian Library Carbon dating finds Bakhshali manuscript contains oldest recorded origins of the symbol ‘zero’

The Guardian leads off with an article by Marcus Du Sautoy: Much ado about nothing: ancient Indian text contains earliest zero symbol. Who in a video film and in the text of his article tells us, “This becomes the birth of the concept of zero in it’s own right and this is a total revolution that happens out of India.”

The Science Museum’s article Illuminating India: starring the oldest recorded origins of ‘zero’, the Bakhshali manuscript, basically repeats the Du Sautoy doctrine, makes the fundamental mistake of entitling their contribution, The First Zero, although in the text they return to the wording, “the world’s oldest recorded origin of the zero that we use today.”

The BBC joins the party with another clone of the basic article, Carbon dating reveals earliest origins of zero symbol.

Entrepreneur Cecile G Tamura summed up the implicit and sometimes explicit message of all these reports with the following tweet, One of the greatest conceptual breakthroughs in mathematics has been traced to the Bakhshali manuscript dating from the 3rd or 4th century at a period even earlier than we thought. To which I can only reply, has it?

All of the articles, which are all basically clones of the original announcement state quite clearly that this is a placeholder zero and not the number concept zero[1] and that there are earlier recorded symbols for placeholder zeros in both Babylonian and Mayan mathematics. Of course it was only in Indian mathematics that the place-holder zero developed into the number concept zero of which the earliest evidence can be found in Brahmagupta’s Brahmasphuṭasiddhanta from the seven century CE. However, this re-dating of the Bakhshali manuscript doesn’t actually bring us any closer to knowing when, why or how that conceptual shift, so important in the history of mathematics, took place. Does it in anyway actually change the history of the zero concept within the history of mathematics? No not really.

Historians of mathematics have known for a long time that the history of the zero concept within Indian culture doesn’t begin with Brahmagupta and that it was certainly preceded by a long complex prehistory. They are well aware of zero concepts in Sanskrit linguistics and in Hindu philosophy that stretch back well before the turn of the millennium. In fact it is exactly this linguistic and philosophical acceptance of ‘nothing’ that the historian assume enabled the Indian mathematicians to make the leap to the concept of a number signifying nothing, whereas the Greeks with their philosophical rejection of the void were unable to spring the gap. Having a new earliest symbol in Indian mathematics for zero as a placeholder, as opposed to the earlier recorded words for the concept of nothingness doesn’t actually change anything fundamental in our historical knowledge of the number concept of zero.

There is a small technical problem that should be mentioned in this context. Due to the fact that early Indian culture tended to write on perishable organic material, such as the bark used here, means that the chances of our ever discovering manuscripts documenting that oh so important conceptual leap are relatively low.

I’m afraid I must also take umbrage with another of Richard Ovenden’s claims in the original Bodleian report:

 Richard Ovenden, head of the Bodleian Library, said the results highlight a Western bias that has often seen the contributions of South Asian scholars being overlooked. “These surprising research results testify to the subcontinent’s rich and longstanding scientific tradition,” he said.

Whilst this claim might be true in other areas of #histSTM, as far as the history of the so-called Hindu-Arabic numbers system and the number concept zero are concerned it is totally bosh. Pierre-Simon, marquis de Laplace (1749-1827) wrote the following:

“It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.”

I started buying general books on the history of mathematics more than 45 years ago and now have nine such volumes all of which deal explicitly with the Indian development of the decimal place value number system and the invention of the number concept zero. I own two monographs dedicated solely to the history of the number concept zero. I have four volumes dedicated to the history of number systems all of which deal extensively with the immensely important Indian contributions. I also own two books that are entirely devoted to the history of Indian mathematics. Somehow I can’t see in the case of the massive Indian contribution to the development of number systems that a Western bias has here overseen the contributions of South Asian scholars.

This of course opens the question as to why this discovery was made public at this time and in this overblown manner? Maybe I’m being cynical but could it have something to do with the fact that this manuscript is going on display in a major Science Museum exhibition starting in October?

The hype that I have outlined here in the recent history of mathematics has unfortunately become the norm in all genres of history and in the historical sciences such as archaeology or palaeontology. New discoveries are not presented in a reasonable manner putting them correctly into the context of the state of the art research in the given field but are trumpeted out at a metaphorical 140 decibel claiming that this is a sensation, a discipline re-defining, an unbelievable, a unique, a choose your own hyperbolic superlative discovery. The context is, as above, very often misrepresented to make the new discovery seem more important, more significant, whatever. Everybody is struggling to make themselves heard above the clamour of all the other discovery announcements being made by the competition thereby creating a totally false impression of how academia works and how it progresses. Can we please turn down the volume, cut out the hype and present the results of academic research in history in a manner appropriate to it and not to the marketing of the latest Hollywood mega-bucks, blockbuster?

[1] For those who are not to sure about these terms, a placeholder zero just indicates an empty space in a place value number system, so you can distinguish between 11 and 101, where here the zero is a placeholder. A number concept zero also fulfils the same function but beyond this is a number in its own right. You can perform the arithmetical operations of addition, subtraction and multiplication with it. However, as we all learnt at school (didn’t we!) you can’t divide by zero; division by zero is not defined.


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