Don’t criticise what you don’t understand!

I was pleasantly surprised by the level of positive support my latest anti-Ada polemic received on Twitter, I had expected much more negative reaction to be honest. But I did receive two attacks that I would like to comment on more fully here. The first came from a certain Yael Moussaieff (@sachaieff) and reads as follows:


It still blows my mind how convinced mediocre men are that they’re not mediocre and that their opinions are in fact urgent and needed.

I’m not really sure in what sense here I am supposedly mediocre: my intelligence, my expertise, my abilities, all three, in all aspects of my existence? And how does Ms Moussaieff (I assume she is a she) know this, never having met me, on the basis of one, what I consider to be a fairly reasonably argued, blog post on the evaluation of the contributions of one Victorian woman to computer science. If she had brought some counter arguments to demonstrate the mediocrity of my thought processes or the mediocrity of my understanding of the historical period or the mediocrity of my abilities as a historian of computing (and I am one, see the reply to the next comment) then perhaps I could understand the intension or meaning of her criticism but for the moment I remain perplexed. Maybe my inability to comprehend is, in itself, a sign of my mediocrity.

Peter Robinson (@PeterRobinson76) chose a different line of attack:

We also love to put down anyone that dares to have popularity. Even long dead women.

To which I spontaneously responded:

There is a difference between a put down and a reasoned argument based on facts. I formally studied and researched both Babbage and Lovelace long before the current Lovelace hagiography started, as a professional historian of logic and computing. What are your qualifications?

For his benefit I would like to elucidate and explain my claim to professionalism in this matter. Some or even most of what I am now going to relate ought to be already known to those who have been reading this blog for a number of years for newer readers it might prove instructive.

Throughout the 1980s and the early 1990s I studied as a mature student at the Friedrich-Alexander University of Erlangen & Nürnberg. The first two and a half years I studied mathematics with philosophy as my subsidiary. I then changed to philosophy with English philology and history as my subsidiaries. The emphasis of my studies was always on the history and philosophy of science. During this time I worked for ten years as a paid research assistant in a major research project into the history of formal/symbolic/mathematical logic under the supervision of one of the world’s leading logic historians. This means that somebody, who is considered knowledgeable in these things, thought me competent enough to appoint me to this position. The fact that I was still there ten years later shows that he still believed in my competence. Possibly because I was the only English native speaker in the research team, my main area of research was nineteenth century British algebraic logics, which means I was researching Boole, Jevons, De Morgan, Venn, Cayley, McColl and others including the Americans working together with Peirce. Because algebraic logic was just a small part of the much wider field of abstract algebras emerging in the nineteenth century, I also researched Peacock, John Herschel, Babbage, Cayley, Sylvester, William Rowan Hamilton and various others. Calculating machines was also a part of our remit so Babbage and his computers along with the good Countess Lovelace came in for extensive study on my part.

Now ten plus years might seem a rather long time to study as a student but as I said I was a mature student without grant or parental support, which meant I had to earn money to do silly things like pay the rent or even on occasions eat and the pittance paid to research assistants in those days did not cover my daily living costs, so I also worked outside of the university. I had virtually finished my studies with just my master thesis to complete and my final exams to write–not a very big deal, as there was in those days a strong emphasis on continual assessment–when I crashed out with serious mental health problems. You can only burn the candle at both ends for a limited period of time until the two flames meet in the middle. Coming out of the loony bin I chucked my studies because being a qualified historian of science was never going to pay those pesky bills.

When I quit I had completed the entire research for both my master’s thesis and my doctoral thesis. I had written about 50–70% of my master’s thesis and a complete, highly detailed outline for my doctoral thesis. Now it might seem strange that I was writing both theses at the same time but my original master’s thesis, a wide-ranging study of the entire English speaking nineteenth century algebraic logic community, had grown far too big to be a master’s thesis, so I had cut out one section, on the life and work of Hugh McColl, to be my master’s thesis and turned the main project into a potential doctoral thesis. I recently, whilst clearing out some old cartons, came across all the material for that doctoral thesis. I was stunned at how far I had got with it, having in the intervening years forgotten most of the work I had invested. I sat and stared at it for three days then threw it all away.

So you see, if I say that I have researched and studied Babbage and Lovelace in a professional capacity it is simply the truth. I should point out that if I write about either of them now, I don’t rely on my memory of work done long ago but go back and read the original sources that I sorted out and studied then, modifying if necessary my views, as my knowledge has grown over the intervening years. In more recent years I have been paid by reputable, educational institutions to hold public lectures on Mr Babbage and his computing engines, so yes through preparing those lectures my knowledge has grown.

Let us return to my critics. Over the years battling the Ada hagiography I have come to the conclusion that the majority of her acolytes don’t actually bother to look at the sources at all. It seems some of them have read a blog post or an article in a non-academic Internet magazine, highly biased and based on dubious secondary sources rather than primary ones (and yes I am aware of the irony of writing that on a blog post). The rest have only ever read a short précis of those blog posts/articles posted on one or other of the Internet’s social media, which parrot the inaccurate accounts of their sources. This majority continue to parrot this ‘fake news’ without bothering to check whether it is historical accurate. The result is that we now have a major Ada myth industry.

If I had the chance to discuss with Yael, Peter or any of the acolytes who have criticised and attacked me over the years I would ask them the following questions:

Which Ada biography have you read?

 I have read five of which I have what I regard as the two best ones standing on my bookshelf.

What about Babbage? Have you read his autobiography?

It’s actually a fascinating piece of literature covering much more than the computing engines for which Babbage is famous.

Maybe you have instead read the more modern and objective biography contained in Laura Snyder’s “The Philosophical Breakfast Club”?

A wonderful book, as I wrote in my review of it for the journal Endeavour

Have you read his 9thBridgewater Treatise, in which Babbage discusses religion and expands on his theory that one could explain miracles by unexpected changes in computer programmes?

An interesting if slightly bizarre  argument.

Or perhaps, you have read his On the Economy of Machinery Manufactures, the result of his extensive research into automation?

Babbage’s interest in automation drove much of his studies including his work on computing and computers. His On the Economy was a highly influential book in the nineteenth century.

Maybe you have read his unpublished writings on abstract algebra, now in the British Library, that are thought to have inspired George Peacock’s “Treatise on Algebra”?

 I will admit that I haven’t but it’s on my bucket list. I have however read Peacock’s book, fascinating and an important milestone in the history of mathematics,

Maybe you’ve read up on the Analytical Society, the student group Babbage and Herschel created in Cambridge to convince the university to introduce continental methods of analysis to replace Newton?

I stumbled across this intriguing piece of maths history during my research; it shows the dynamic that drove Babbage even from an early age.

This might seem like an intellectual pissing contest but if you wish to criticise me and maybe show me that I have erred, that I am mistaken or that I’m just plain wrong then I expect you to at least do the leg work. I actually like being shown that I am wrong because it means that I have learnt something new and I love to learn, to improve and to expand my knowledge of a subject. It is what I live for. I am a historian of science with a good international reputation that I have worked very hard to earn. I also work very hard to get my facts right. If you criticise me and hold a different opinion on some topic that I have written about but treat me with respect then I will treat you with respect even if I know that you are wrong. If, however, you just gratuitously insult me, as, in my opinion, Yael and Peter have done then I will treat you with disdain and if the mood suits me with a generous portion of sarcasm.






Filed under Autobiographical, History of Computing, Uncategorized


I realise that in writing this blog post I am banging my head against a reinforced concrete wall, pissing against a hurricane, crying into the void and definitely not going to do my reputation any good with a certain class of feminist historians of science, but I cannot stay silent.

The Bank of England has announced that there is going to be a new British £50 banknote and that it will be graced with the portrait of a notable British scientist. To this end they have invited the great British public, renowned for their forethought and wisdom, see for example Brexit, to nominate potential candidates for this great honour. The only rules are that the nominated scientist must be British and dead! Upon this announcement going public Internet social media became an instant hotbed of wishes, suggestions, claims, counterclaims and sure-fire certs.

Unfortunately, the acolytes of Augusta Ada King, Countess of Lovelacewere immediately out in force shouting their, in their minds indisputable, claims from the rooftops and proclaiming their, in their minds unchallengeable, right to this honour for their saintly heroine in the highways and byways of the Internet. Unfortunately, the only criterion by which she qualifies is that she is dead. She was in no way by any meaningful definition of the term a scientist. Some have, however, pled that the honour should in fact not be awarded to a scientist at all but to a mathematician and that she would thus be an eminently suitable candidate. However, she was in no way by any meaningful definition of the term a mathematician and none of the recent published research on the topic does anything whatsoever to change this fact.

Although I have addressed this subject on a number of occasions on this blog let us briefly recap the largely mythical claims made on behalf of the good Countess. Indisputable is the fact that she translated, from the original French, at the suggestion of Charles Wheatstone, a memoir on Charles Babbage’s planned Analytical Engine written by Luigi Menabrea and based on a series of talks that Babbage had given on his planned computer in Turin in 1840. She was also asked by Babbage to expand on Menabrea’s original essay with an appended series of long notes. Indisputable is also the fact that these note were not compiled by Lovelace alone but in extensive cooperation with Babbage.

Note G of these appended notes contains the outline of a programme for the Analytical Engine to calculate the so-called Bernoulli numbers. On the basis of this note Lovelace has been incorrectly dubbed the first computer programmer. I say incorrectly, as Babbage had already demonstrated several programs for the Analytical Engine during his talks in Turin, some of which are outlined by Menabrea in his published memoir that Lovelace translated. If this were not enough Babbage actually states very clearly in his autobiography that although Countess Lovelace suggested the topic for Note G, he actually wrote the programme. In order to maintain their dubious claim on behalf of the Countess her acolytes either simply ignore this statement by Babbage or accuse him of lying. One interesting variant is to claim that the actual real first computer programme is the tabular presentation of the Bernoulli number programme that is appended to Note G and that this is alone the work of Lovelace. There are no such tabular representations of the programmes in Menabrea’s memoir. Again, unfortunately, in her correspondence Lovelace remarks on this subject that her table is an improvement on Babbage’s version. In what sense she improved it–simplified, made more readable, attractive, clearer–is not known, but this correspondence clearly shows that the tabular presentation also was originated by Babbage.

Not content with declaring her to be the first computer programmer, her acolytes moved on to making the, quite frankly ludicrous, claim that the appended notes show that she clearly understood the potential of the computer and computing much better than its inventor, Charles Babbage. Whilst anybody who can read must freely acknowledge that Lovelace can write considerable better than Babbage, whose prose tends to be rather turgid, whereas she has a poetic turn of phrase, such a claim can only be made by someone who simply ignores Babbage’s own extensive writings on the topic of the Analytical Engine. There is not a single idea or concept on the computer or computing in the Notes that cannot be found either in Babbage’s published writings, his masses of unpublished notes or his correspondence before Lovelace even became involved in the promotion of his project. At best she is a tech journalist and at worst Babbage’s sock puppet used by him to popularise his project and try to get financial backing for it.

Let us be generous and take the first option, this would make Ada Lovelace a female nineteenth century science writer, of which there were quite a few notable examples. It is not unusual that an intelligent, literate science writer can express the ideas of a scientist or inventor better for the lay reader than the originator of those ideas. That does not make the science writer a scientist or co-inventor, merely a communicator of concepts and ideas. If I, as a non-physicist, wish to acquire an understanding of the current state of quantum physics then I stand a better chance of doing so if I read Philip Ball’s Beyond Weird, than if I try to plough through the original papers published by the physicists who created the discipline. Ada Lovelace was perhaps a talented science writer but she was definitely neither a scientist nor a mathematician and thus although dead does not qualify as a potential candidate to adorn the new British £50 banknote.

I am personally totally in favour of a female scientist being chosen to adorn the new piece of British currency and a host of eminently good suggestions have already been made on social media from Dorothy Hodgkin, Britain’s only female Nobel Laureate, and inevitably Rosalind Franklin for her contributions to the discovery of the structure of DNA, to Jonathan Healey’s charming suggestion of Margaret Cavendish, as well as a whole host more of highly deserving and often neglected female scientists. So let us all nominate one of these genuine female scientists and not Ada Lovelace.



Filed under History of Computing, Uncategorized

Apples & Pears – comparing print technologies


On Facebook I recently stumbled across a link to a piece on 3 Quarks Daily, which in turn was only a lede for a short essay on the London Review of Books entitled, The Oldest Printed Book in the World. This is an article about the Chinese Dunhuang Diamond Sūtra


Frontispiece of the Chinese Diamond Sūtra, the oldest known dated printed book in the world. The colophon, at the inner end, reads: Reverently [caused to be] made for universal free distribution by Wang Jie on behalf of his two parents on the 13th of the 4th moon of the 9th year of Xiantong [i.e. 11th May, CE 868 ] Source: British Library via Wikimedia Commons

 from the ninth century explaining its origin and how it came to be housed in the British Library. The article contains the following sentence:

A colophon at the end of the Dunhuang Diamond Sūtra scroll dates it to 868, nearly six centuries before the first Gutenberg Bible.

Although not stated explicitly the intention of this sentence seems to be, the Chinese invented book printing six hundred years before the Europeans. Although on a very superficial level this is true it is actually a case of comparing apples with pears, as the two books in question are printed with very different reproduction technologies. The Dunhuang Diamond Sūtra is a woodblock print, whereas the Gutenberg Bible is printed with movable type.


First page of the first volume: The Epistle of St. Jerome from the University of Texas copy. Source: Ransom Center of the University of Texas at Austin via Wikimedia Commons

For woodblock printing the image to be printed is carved into a woodblock or rather the parts that are not to be printed are cut away with a knife or chisel. This is then inked and pressed onto the sheet of material, cloth or paper, to be printed. The used block produced by this difficult process can only be used to print this one page. With moveable type the individual pieces of type, or sorts, are composed into the image to be printed, inked and pressed into the sheet of material to be printed. When finished the sorts can be reused to compose a new page and so on. Once cut a set of woodblocks can only be used to print the same book over and over again. A full set of type can be continually reconfigured to print literally thousand of different books. This difference is important and the six hundred year gap throws up some very important and intriguing historical questions.


A case of cast metal type pieces and typeset matter in a composing stick Source: Wikimedia Commons

Central to these is the question of technological transfer. Woodblock printing was developed in East Asia sometime before the third century CE. The oldest fragments of printed cloth date to 220 CE. The oldest woodblock prints on paper date to the late seventh century CE. And as stated above to oldest extant woodblock printed book the Dunhuang Diamond Sūtra dates to 868 CE. Although the Chinese invention of paper arrived in Spain via the Islamic Empire in the late eleventh century CE and crossed the Alps into Northern Europe in the late fourteenth century CE, woodblock printing does not appear to have accompanied it. Strangely European books printed with woodblocks, block books, apparently only appeared after Gutenberg had introduced printing with movable type in the second half of the fifteenth century. There are a very limited number of such books mostly dating from the 1460s and 1470s and printed in the Netherlands of Southern Germany.


Block book – Biblia Pauperum (“Bible of the Poor”) Netherlands 1460s/70s Source: Wikimedia Commons

Gutenberg was by no means the first to use moveable type. Around 1040 CE a Chinese inventor, Bi Sheng (990–1051) invented a form of moveable type with the pieces of type made of ceramics. Beyond a short description of his invention nothing more is known about it and nothing he might have printed has survived. This was followed in East Asia by various other forms of moveable type carved from wood or made of various metals. The oldest book printed with wooden movable type was Records of Jingde County printed by Wang Zhen in 1298. In 1313 he published an account of his invention A method of making moveable wooden types for printing books.


A revolving typecase for wooden type in China, from Wang Zhen’s book published in 1313 Source: Wikimedia Commons

The oldest known book printed with metal moveable type is the two volume Jikji, a collection of excerpts from the analects of revered Buddhist monks, printed with metal type in Korea in 1377; that is at least seventy years before Gutenberg’s famous Bible. However, whereas 49 copies of Gutenberg’s Bible still exist, of which 21 are complete, only one copy of the second volume of the Jikji is still extant.


Korean movable type from 1377 used for the Jikji Source: Wikimedia Commons


Jikji or “Selected Teachings of Buddhist Sages and Seon Masters”, published in 1377, Korea during the Goryeo Dynasty. Source: Wikimedia Commons

Even within Europe Gutenberg was not the first to use moveable type, with several people experimenting with varying system. However Gutenberg was the first to produce anything functional and in reality his greatest inventions were not so much moveable type as the printing press (he converted a wine press) and printing ink or to put it another way he didn’t just invent moveable type but the whole printing process.


Replica of the Gutenberg press at the International Printing Museum in Carson, California Source: Wikimedia Commons

Although extensive effort has been invested into the research on the topic, no evidence has been found of a technology transfer from East Asia to Europe and it is thought that Gutenberg’s was an independent (re)invention.

Although my account is itself only a sketch of the development of printing, both woodblock and moveable type ( I don’t even touch upon book (re)production before woodblock printing or after moveable type), my main argument is that the London Review of Books article in just making its invalid comparison between the Dunhuang Diamond Sūtra and Gutenberg’s Bible creates an inadequate and distorted impression of a long and complex historical process; an impression that uninformed readers will take away with them. A mythical historical meme has been created “the first printed book is the Dunhuang Diamond Sūtra and not the Gutenberg Bible” to replace the Eurocentric myth that Gutenberg invented movable type printing and his Bible is the earliest printed book. If writing short popular historical pieces for the general public we should avoid simplistic descriptions and thereby the risk of creating myths rather than transmitting real knowledge.



Filed under Early Scientific Publishing, History of Technology, Uncategorized

A Newtonian Refugee

Erlangen, the Franconian university town, where I (almost) live and where I went to university is known in German as ‘Die Hugenottenstadt’, in English the Huguenot town. This name reflects the religious conflicts within Europe in the 17thcentury. The Huguenots were Calvinists living in a strongly and predominantly Catholic France. Much persecuted their suffering reached a low point in 1572 with the St Bartholomew’s Day massacre, which started in the night of 23-24 August. It is not know how many Huguenots were murdered, estimates vary between five and thirty thousand. Amongst the more prominent victims was Pierre de la Ramée the highly influential Humanist logician and educationalist. The ascent of Henry IV to the French Throne saw an easing of the situation for the Huguenots, when he issued the Edict of Nantes confirming Catholicism as the state religion but giving Protestants equal rights with the Catholics. However the seventeenth century saw much tension and conflict between the two communities. In 1643 Louis XIV gained the throne and began systematic persecution of the Huguenots. In 1685 he issued the Edict of Fontainebleau revoking the Edict of Nantes and declaring Protestantism illegal. This led to a mass exodus of Huguenots out of France into other European countries.

Franconia had suffered intensely like the rest of Middle Europe during the Thirty Years War (1618-1648) in which somewhere between one third and two thirds of the population of this area died, most of them through famine and disease. The Margrave of Brandenburg-Bayreuth, Christian Ernst invited Huguenot refugees to come to Erlangen to replace the depleted inhabitants. The first six Huguenots reached Erlangen on 17 May 1686 and about fifteen hundred more followed in waves. Due to the comparatively large numbers the Margrave decided to establish a new town south of the old town of Erlangen and so “Die Hugenottenstadt” came into being.


The earliest known plan of New Erlangen (1686) Attributed to Johann Moritz Richter Source: Wikimedia Commons

In 1698 one thousand Huguenots and three hundred and seventeen Germans lived in Erlangen. Many of the Huguenot refugees also fled to Protestant England establish settlements in many towns such as Canterbury, Norwich and London.


Town plan of Erlangen 1721 Johann Christoph Homann Source: Wikimedia Commons

In the early eighteenth century Isaac Newton, now well established in London at the Royal Mint, would hold court in the London coffee houses surrounded by a group of enthusiastic mathematical scholars, the first Newtonian, eager to absorb the wisdom of Europe’s most famous mathematician and to read the unpublished mathematical manuscripts than he passed around for their enlightenment. One of those coffee house acolytes was the Huguenot refugee, Abraham de Moivre (1667–1754).


Abraham de Moivre artist unknown

Abraham de Moivre the son of a surgeon was born in Vitry-le-François on 26 May 1667. Although a Huguenot, he was initially educated at the Christian Brothers’ Catholic school. At the age of eleven he moved to Protestant Academy at Sedan, where he studied Greek. As a result of the increasing religious tension the Protestant Academy was suppressed in 1682 and de Moivre moved to Saumur to study logic. By this time he was teaching himself mathematics using amongst others Jean Prestet’s Elémens desmathématiquesand Christiaan Huygens’ De Rationciniis in Ludo Aleae, a small book on games of chance. In 1684 he moved to Paris to study physics and received for the first time formal teaching in mathematics from Jacques Ozanam a respected and successful journeyman mathematician.

Although it is not known for sure why de Moivre left France it is a reasonable assumption that it was Edict of Fontainebleau that motivated this move. Accounts vary as to when he arrived in London with some saying he was already there in 1686, others that he first arrived a year later, whilst a different account has him imprisoned in France in 1688. Suffering the fate of many a refugee de Moivre was unable to find employment and was forced to learn his living as a private maths tutor and through holding lectures on mathematics in the London coffee houses, the so-called Penny Universities.

Shortly after his arrival in England, de Moivre first encountered Newton’s Principia, which impressed him greatly. Due to the pressure of having to earn a living he had very little time to study, so according to his own account he tore pages out of the book and studied them whilst walking between his tutoring appointments. In the 1690s he had already become friends with Edmund Halley and acquainted with Newton himself. In 1695 Halley communicated de Moivre’s first paper Methods of Fluxions to the Royal Society of which he was elected a member in 1697.


Edmund Halley portrait by Thomas Murray Source: Wikipedia Commons

In 1710 de Moivre, now an established member of Newton’s inner circle, was appointed to the Royal Society Commission set up to determine whether Newton or Leibniz should be considered the inventor of the calculus. Not surprisingly this Commission found in favour of Newton, the Society’s President.

De Moivre produced papers in many areas of mathematics but he is best remembered for his contributions to probability theory. He published the first edition of The Doctrine of Chances: A method of calculating the probabilities of events in playin 1718 (175 pages).


Title page of he Doctrine of Chances: A method of calculating the probabilities of events in playin 1718

An earlier Latin version of his thesis was published in the Philosophical Transactionsof the Royal Society in 1711. Although there were earlier works on probability, most notably Cardano’s Liber de ludo aleae(published posthumously 1663), Huygens’De Rationciniis in Ludo Aleaeand the correspondence on the subject between Pascal and Fermat, De Moivre’s book along with Jacob Bernoulli’s Ars Conjectandi(published posthumously in 1713) laid the foundations of modern mathematical probability theory. There were new expanded editions of The Doctrine of Chance sin 1738 (258 pages) and posthumously in 1756 (348 pages).

De Moivre is most well known for the so-called De Moivre’s formula, which he first

(cos θ + i sin θ)n = cos n θ + i sin n θ

published in a paper in 1722 but which follows from a formula he published in 1707. In his Miscellanea Analytica from 1730 he published what is now falsely known as Stirling’s formula, although de Moivre credits James Stirling (1692–1770) with having improved his original version.

Although a well known mathematician, with a Europa wide reputation, producing much original mathematics de Moivre, the refugee (he became a naturalised British citizen in 1705), never succeeded in obtaining a university appointment and remained a private tutor all of his life, dying in poverty on 27 November 1754. It is claimed that he accurately predicted the date of his own death.








Filed under Autobiographical, History of Mathematics, Newton, Uncategorized

Two Greek scholars butting heads in the Renaissance and the consequences for astronomy

The adversaries of the title were Georg of Trebizond (1395–1472) and Basilios Bessarion (1403–1472). There is an ironic twist to their names. George of Trebizond derived his name from his ancestors, who originated in the Empire of Trebizond but he was born in Crete. His later antagonist Basilios Bessarion, however, was born in Trebizond.

At sometime unknown point, whilst he was still relatively young, George of Trebizond moved to Italy, where he learnt Latin and acted as amanuensis to the politician Francesco Barbaro (1390–1454) in Venice. A brilliant Aristotelian scholar he entered the entourage of Pope Nicholas V (1397–1455) a convinced Aristotelian.


George of Trebizond Source: Wikimedia commons

Basilios Bessarion was educated in Constantinople then went in 1423 to study Plato under Georgius Gemistus (c.1355–c. 1452), known as Plethon, a highly influential revivalist and teacher of Neo-Platonism. He became an orthodox monk, advancing to abbot in 1436 and metropolitan of Nicaea in 1437. In 1439 he travelled with the Orthodox delegation to Italy to try to persuade the Catholic Church to join the Orthodox Church in a crusade against the Ottoman Turks. Bessarion’s political position led to him being heavily criticised in Byzantium and so he stayed in Italy where Pope Eugene IV (1383–1447) appointed him a cardinal of the Catholic Church. A convinced humanist he devoted his life to spreading support for humanism and to amassing a large private library, containing an extensive collection of Greek manuscripts. He presented his library to the Senate of Venice in 1468 and the 482 Greek manuscripts and 264 Latin manuscripts today still form the core of the St. Mark’s Biblioteca Marciana.


Basilios Bessarion Justus van Gent and Pedro Berruguete Source: Wikimedia Commons

Initially Bessarion and George of Trebizond were friends and Bessarion did much to support his colleague. However in the early 1450s their friendship began to unravel. In that year George undertook a translation from Greek into Latin of Ptolemaeus’ Mathēmatikē Syntaxis or as it is better known the Almagest, as a replacement for Gerard of Cremona’s twelfth-century translation from Arabic.  Bessarion lent him his best Greek manuscript for the purpose and suggested that he used Theon of Alexandria’s Commentary, as a guide. He duly produced his translation and an extensive commentary in nine months finishing in December 1451. His work was hurried, sloppy and strewn with errors and the Pope’s evaluator Jacopo di San Cassiano (ca.1400–ca.1454) judged the work deficient and the Pope, Nicholas V, rejected the dedication. Bessarion took issue with George’s treatment of Theon. The incident ruined George’s reputation and he was forced to flee from Rome.

The situation between the two Greek immigrants escalated when in 1458 George published a vicious attack on Plato in his Comparatio Aristotelis et Platonis, which historian James Hankins has described as “one of the most remarkable mixtures of learning and lunacy ever penned.” In this work he accused Plato of being a traitor to Athens, a besmircher of rhetoric, an advocate of paedophilia, and a pagan who lent aid and comfort to Greek Christians. Bessarion, a Platonist, could not let this stand and issued a powerful response, In calumnatorem Platonis, which was printed in 1469. The situation became even more heated when George offered to dedicate his Commentary on the Almagest to Mehmet II, the Ottoman Turk Sultan, who had conquered Constantinople and ended the Byzantine Empire. George entreated Mehmet to convert to Christianity, to conquer Rome and thus to unite Islam and Christianity under his sovereignty. Bessarion got hold of George’s correspondence with Mehmet and appealled to the Pope, Pius II (for whom George might have been working as an agent!), accusing George of treachery and George was imprisoned for four months in 1466-67. Released from prison, George now offered to dedicate both translation and commentary to Matthias Corvinus (1443–1490), the king of Hungary.

We now need to back peddle to 1460. In that year, Bessarion, who was a Papal legate, visited Vienna to negotiate with Frederick III and made the acquaintance of Georg von Peuerbach (1423–1461), who was at the time the leading astronomical scholar in Europe. Bessarion, still deeply upset by George’s abortive Almagest efforts, asked Peuerbach to produce a new commentary on Ptolemaeus’ work. Peuerbach acquiesced and began immediately to produce an epitome or digest of the Almagest. This was an updated, modernised, shortened, mathematically improved version of the Almagest. Peuerbach died in 1461, having only completed the first six of thirteen book of his epitome. He did, however, extract the deathbed promise from his star pupil, Regiomontanus, to finish the work. In the same year Regiomontanus left Vienna for Italy as a member Bessarion’s entourage, where he spent the next four years learning Greek, finishing the epitome and acting as Bessarion’s manuscript collector and librarian. The Epitome of the Almagestis a masterpiece:

The Epitome is neither a translation (an oft repeated error) nor a commentary but a detailed sometimes updated, overview of the Almagest. Swerdlow once called it “the finest textbook of Ptolemaic astronomy ever written.”[1]

I’ve already written an earlier blog post on Regiomontanus so we don’t need to outline the rest of his life but Shank does have an interesting hypothesis. He suggests that Regiomontanus went to Hungary at Bessarion’s behest in order to counter any influence that George might win at the Court of Corvinus through his second attempt to rededicate his Almagest and Commentary.


Johannes Regiomontanus, Woodcut Source: Wikimedia Commons

When he set up his printing business in Nürnberg, Regiomontanus published Peuerbach’s lectures on astronomy, Theoricae Novae Planetarum, as his first book.


Georg von Peuerbach: Theoricarum novarum planetarum testus, Paris 1515 Source: Wikimedia Commons


Peuerbach Theoricae novae planetarum 1473 Source: Wikimedia Commons

Although he included the Epitome in his publisher’s prospect he didn’t succeed in publishing it before his untimely death in 1476. The Epitoma in Almagestum Ptolemae was first published in 1496 in Venice by Johannes Hamman. Together with Peuerbach’s lectures the Epitome became the standard textbooks for teaching astronomy at the European universities for much of the next century. The influence of the Epitome goes much deeper than this in the history of astronomy.


Title page Epitoma in Almagestum Ptolemae Source: Wikimedia Commons

It is well known that Copernicus modelled his De revolutionibus on Ptolemaeus’ Almagest. In fact text analysis has shown that he actually modelled his magnum opus on the Peuerbach-Regiomontanus Epitome, for example taking most of his knowledge of Arabic astronomy from Regiomontanus’ work. This is, however, rather minor compared to what several expert think is the most important influence that Regiomontanus had on Copernicus.


Nicolaus Copernicus portrait from Town Hall in Toruń – 1580 Source: Wikimedia Commons

According to ancient Greek cosmology the planets orbit the earth with uniform circular motion. Any extended observation of the planets show that this is not the case and it was the job of the astronomers to construct geometrical model, which corrected the visible deviation from the cosmological norm; these deviations are known as the anomalies. Ptolemaeus had basically two geometrical tools to describe planetary orbits. With the eccentric deferent the centre of the circle that describes the orbit, the deferent, is not in the same position as the earth, i.e. the earth is not at the centre of the planets orbit. The alternative is the epicycle-deferent model in which the planet is carried around an epicycle, which is itself carried around the deferent. The mathematician Apollonius (late 3rdcentury–early 2ndcentury BCE) had shown that the two models were in fact mathematically equivalent; meaning any motion that could be described with the one model could equally well be described with the other.

Ptolemaeus, however, argued in the Almagest that whereas the retrograde motion (the so-called second anomaly, when the planet appears to reverse its orbital direction for a period of time) of the outer planets could be described with either model that of the inner planets (Venus and Mercury) could only be described with the epicycle-deferent model. In Book XII of the Epitome, Regiomontanus proved that the second anomaly of the inner planets could also be described with the eccentric deferent model. Without going into detail this seems to have led Copernicus directly to his heliocentric system for the inner planets, which he then extended to the outer ones.

Thinking hypothetically, if George had not written his translation of and commentary on the Almagest, then Bessarion would not has asked Peuerbach to write the Epitomeand Regiomontanus might never have provided Copernicus with that vital clue.

Regiomontanus wrote a second book inspired by George’s work. His Defensio Theonis contra Georgium Trapezuntium is a vast rambling mathematical work centred on a defence of Theon of Alexandria against what he saw as George’s unfair treatment of him. He accused George as having both misrepresenting Theon and plagiarising him. This work has never been published but Regiomontanus’ antagonism against George was known at the time. The Defensio was announced in Regiomontanus’ prospect and also in works published by Erhard Ratdolt. This situation led to a rather strange claim made by Pierre Gassendi. In the 1650s Gassendi published a collective biography of the great astronomers Brahe, Copernicus, Regiomontanus etc. in which he claimed that Regiomontanus was murdered in Rome by two of George’s sons in 1476. George had many vocal critics, none of whom were murdered and sensible historians think that Regiomontanus died in one of the epidemics that regularly swept Rome.


[1]Michael H. Shank, Regiomontanus and Astronomical Controversy in the Background of Copernicus, pp. 79-109 in Rivka Feldhay and F. Jamil Ragep eds., Before Copernicus: The Cultures and Contexts of Scientific Learning in the Fifteenth Century, McGill-Queen’s University Press, Montreal& Kingston, London, Chicago, 2017, p. 90

This blog post owes much to the above paper and to Michael H. Shank, The Almagest, Politics, and Apocalypticism in the Conflict between George of Trebizond and Cardinal Bessarion, in Almagest International Journal for the History of Scientific Ideas, Volume 8, Issue 2, 2017, pp. 49-83


Filed under Early Scientific Publishing, History of Astronomy, History of science, Renaissance Science, Uncategorized

Monsieur Joseph Jérôme Lefrançois de Lalande et Les Dames

The cliché concept of a Frenchman is of the prime example of a chauvinist and the eighteenth century is not renowned as a period of equality for women, so it might come as somewhat of a surprise that an eighteenth century Frenchman very much championed the positive role of women in astronomy; that man was Joseph Jérôme Lefrançois de Lalande (1732–1807).


Jérôme Lalande after Joseph Ducreux Source: Wikimedia Commons

Jérôme Lalande illustrates rather well something that is fundamentally wrong with the way that much history of science is conceived and presented. I have a moderately large collection of general reference works on the history of science and the history of astronomy, encyclopaedia, dictionaries, and lexica. In this works Jérôme Lalande almost never appears and if at all usually just as a minor footnote to somebody or something else. However, although he never made a major astronomical discovery, and thus his absence from the reference works, he was in the second half of the eighteenth century a leading figure in the astronomical community, not just in France but throughout the whole of Europe, as a organiser, coordinator, communicator, educator and populariser, all activities very necessary to the evolution of any scientific discipline.

He was born 11 July 1832 in Bourge-en-Bresse and was educated at a Jesuit academy. He went to Paris to study law but having got to know Joseph-Nicolas Delisle (1644­–1720) he became an ardent astronomer and a pupil of both Delisle and Charles Le Monnier (1715–1799).


Joseph Nicolas Delisle by Konrad Westermayr Source: Wikipedia Commons

Despite this passion, he completed his law degree and was about to return to Bourge-en-Bresse to become a lawyer when Lemonnier sent him to Berlin to measure lunar parallax together with Nicolas-Louis de Lacaille (1732–1762) in South Africa. The success of this operation led to his election to the Academy of Berlin, as well as the French Academy of Science. He now devoted his life to astronomy. Over the years he was successively elected to the Royal Swedish Academy of Science and The American Academy of Arts and Sciences. In 1762 he was appointed Delisle’s successor as professor of astronomy at the Collège de France. Amongst his most famous students were Jean-Baptiste Joseph Delambre (1749–1822), Giuseppe Piazzi (1746–1826), Pierre Méchain (1744–1804) and his nephew Michel Lefrançois de Lalande (1766–1839). In 1773 he edited more that 250 articles on astronomy for the supplement to Diderot’s and d’Alembert’s legendary encyclopaedia. From 1760 to 1776 he was editor of the Connaissance des tempsthe official French astronomical year book. From 1795 he also became the director of the Paris observatory in which role he issued a star catalogue of 30,000 stars later expanded to 41,000. As an astronomer his principle activity of the years consisted of carrying out the mathematical calculation of orbits, the paths of comets, solar eclipses and the astronomical unit based on the observations of the Transit of Venus in 1761 and 69, as well as the orbit of Venus.  It was here that the lady astronomers entered his life and his work.

As a young man he assisted Alexis-Claude Clairaut in the recalculation of the orbit of Comet Halley. Lalande was ably assisted in this tedious but complex mathematical work by Nicole-Reine Lepaute (1723–1788). In his publication Clairaut did not acknowledge Lepaute’s contribution, which angered Lalande, who honoured her work so:

We calculated from morning to night for six months…Mme. Lépaute’s help was such that I would not have been able to tackle the enormous task without her.


Taken from Winterburn The Quite Revolution of Caroline Herschel see footnote 1

Nicole-Reine Étable de la Briere was born 5 January 1723 in Paris began to take an interest in mathematics and astronomy in around the time she married her husband Jean-André Lepaute the royal clock maker. Together with her husband she designed and constructed an astronomical clock, which was presented to the French Academy of Science in 1753. She, her husband and Lalande worked on a book entitled Traite d’horologerie(Treatise on Clockmaking) that was published under her husbands name in 1755. Although she was not mentioned as author Lalande honoured her contribution as follows:

“Madame Lepaute computed for this book a table of numbers of oscillations for pendulums of different lengths, or the lengths for each given number of vibrations, from that of 18 lignes, that does 18000 vibrations per hour, up to that of 3000 leagues.”

Following her work with Lalande on Comet Halley, she again collaborated with him on the ephemeris for the 1761 Transit of Venus.  She also collaborated with Lalande for fifteen years on the calculations for the Connaissance des temps. In 1762 she calculated the exact time for a solar eclipse that occurred on 1 April 1764. She also wrote an article on the eclipse with an eclipse map. She produced star catalogues and calculated an ephemeris of the sun, moon and the planets from 1774 to 1784. Although childless she adopted and trained he husband nephew, Joseph Lepaute Dagelet (175116788) in astronomy and mathematics. He went on to become professor of mathematics at the French Military School and later deputy astronomer at the French Academy of Science, where he had a distinguished career. A comet and a crater on the moon are named in her honour.

Lalande’s second lady ‘computer’ (the term used for the people, usually women, employed to do the often complex but tedious and repetitious astronomical calculations was Elisabeth Louise Félicité du Pierry, née Pourra de la Madeleine, who was born 1746 but who’s date of death is unknown/disputed, possibly 1807. She met Lalande in 1779 and began to study astronomy under him after the death of her husband. Her main work was on eclipses of the sun and moon based on historical data that she collected. Lalande based his own lunar orbit work on her research. She is said to have been the first woman to have offered lecture courses at a French university when she lectured at the Sorbonne on astronomy for women­–Cours d´astronomie ouvert pour les dames et mis à leur portée. Lalande dedicated his book, Astronomie des Dames(of which more later) to her stating: “She represents a model for all women through her high intellectual qualities.” She later dropped out of astronomy and took up chemistry instead.

Lalande’s third lady computer was his own illegitimate daughter Marie-Jeanne-Amélie Harley (1768–1832), who married his nephew Michel Lefrançois de Lalande. The young couple studied astronomy together under Lalande and were his assistants at the Paris Observatory helping to calculate and complete the star catalogues. Marie-Jeanne-Amélie work very closely with her father contributing to many of his publications. Gauss is reputed to have said that he knew only one French women working in science, Madame Lefrançois de Lalande. She had two children, a daughter named Caroline after Caroline Herschel and a son named Isaac after Newton. The De Lalande crater on the moon is named after her.

In the naming of his grand daughter we get a strong clue that Lalande’s respect for female astronomers was not restricted to his own assistants and family. In fact Lalande was one of the strongest male supporters of Caroline Herschel, who he respected immensely, which is reflected by her writing directly to him rather than communicating through her brother William, although William was a close colleague and friend of Lalande’s.


Caroline Herschel Source: Wikimedia Commons

Without a doubt Lalande’s greatest contribution to the support of women in astronomy was his Astronomie des Dames published in 1785 with two further updated and expanded editions in 1795 and 1806,which explains various aspects of astronomy for the female reader and praises the work of famous female astronomers beginning with Hypatia, including his own co-workers and going up to Caroline Herschel, who was added in the second edition. Lalande was a renowned and successful author of popular books on astronomy so his decision to write about female astronomers in a laudatory manner had quite a lot of impact. The second editions from 1795 covers the following women:

Hypatia (the ancient Greek philosopher)

Maria Cunitz

Maria-Claire Eimart Muller

Jeanne Dumée

Hevelius’s wife (this is how he describes her, not by name but by association)

Manfredi’s sisters (as above)

Kirch’s thre sisters and his wife, née Winkelmann

La Marquise de Châtelet

Madame Lapute

Mrs Edwards (from the Nautical Almanacin England)

Madam du Piery

His niece Lefrançois de Lalande

Miss Caroline Herschel[1]

 (you can read about Maria Cunitz, Maria Kirch née Winkelmann, Elisabeth Koopman Hevelius and Maria Clara Eimart here)

As Emily Winterburn explains (see footnote 1) Lalande’s book follows in a tradition of popular science books written specifically for ladies. This starts with Bernard Le Bovier de Fontenelle’s Entretiens sur la pluralité des mondes(Conversations on the Plurality of Worlds) (1686) and includes John Harris’ Astronomical Dialogues Between a Gentleman and a Lady(1719), Benjamin Martin’s Gentlemen and Ladies Philosophy(1759) and Francesco Algarotti’s Il newtonianismo per le dame(1737) (Sir Isaac Newton’s Philosophy Explained for the use of Ladies, in six dialogues on Light and Colour(1739)). Lalande acknowledges Fontenelle’s influence on his own work.

Although with Lalande we still have a man employing women in a subservient position and then writing about them rather than women working for and writing about themselves, we have in the way that he supported, acknowledged and praised women in his work a major advance on nearly everything that had gone before.







[1]This list is taken from Emily Winterburn’s excellent The Quite Revolution of Caroline Herschel:The Lost Heroine of Astronomy, The History Press, Stroud, 2017 pp. 221-222, which I reviewed here. Winterburn’s book together with a tweet from RAS Women in STEM @RAS_Women about Marie-Jeanne-AmélieLefrançois de Lalande inspired this blog post.

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Filed under History of Astronomy, Ladies of Science

Science, War and Pestilence

In my recent blog post about the Renaissance polymath Wilhelm Schickard I wrote the following paragraph about the demise of him and his family, killed by plague brought into his home by invading soldiers in the Thirty Years War.


Wilhelm Schickard, artist unknown Source: Wikimedia Commons

The last years of Schickard’s life were filled with tragedy. Following the death of Gustav Adolf in the Thirty Years War in 1632, the Protestant land of Württemberg was invaded by Catholic troops. Along with chaos and destruction, the invading army also brought the plague. Schickard’s wife had born nine children of which four, three girls and a boy, were still living in 1634. Within a sort time the plague claimed his wife and his three daughters leaving just Schickard and his son alive. The invading troops treated Schickard with respect because they wished to exploit his cartographical knowledge and abilities. In 1635 his sister became homeless and she and her three daughters moved into his home. Shortly thereafter they too became ill and one after another died. Initially Schickard fled with his son to escape the plague but unable to abandon his work he soon returned home and he also died on 23 October 1635, just 43 years old, followed one day later by his son.

The fate of Schickard and his family made me, as a historian of science, once again brutally aware that the people that I, and other STEM historians, research and write about are not just producers of theories, theorems, hypotheses and discoveries living in some sort of Platonic space of Ideals but real people living working and often suffering in in a very real and frequently hostile world. Many of the scholars that form the subject of my own main interests in the history of science and mathematics suffered disruption, displacement and even death during the turmoil that engulfed Europe during the religious wars of the seventeenth century. In the following I’ll sketch some of those life-disturbing incidents suffered by those scholars, without any pretention to being exhaustive.

Johannes Kepler (1571–1630) spent large parts of his life coping with the disruptions caused by the reformation and counter-reformation.


Portrait of Johannes Kepler. Source: Wikimedia Commons

In his youth he came to Graz as a Lutheran Protestant teacher in a prominently Catholic district. During the counter-reformation this couldn’t last and it didn’t; the Protestants were ordered to convert or to leave. Initially Kepler, the district mathematicus, was granted an exception due to his successful astrological prognostica but in the end he too was forced to leave losing much of his wealth in the process. In Prague he was in a similar situation as Protestant Imperial Mathematicus to a Catholic Emperor. This time it was civil strive, as Rudolf II was deposed by his brother Matthias, which caused Kepler to leave Prague to become district mathematicus in Linz. Here once again he was a Lutheran in a predominantly Catholic district, which caused Kepler much stress. In 1625 Linz was besieged for two months by a peasants uprising. The printing press that Kepler had founded to print and published his own works was burnt to the ground with much of his work. The last years of Kepler’s life were spent wandering from town to town in Southern Germany and Austria never again finding a truly safe haven. Ironically he spent much of this time serving as court astronomer to Wallenstein the deposed Catholic commander in chief.

Even Galileo (1564–1642) can be considered to have suffered under the religious conflicts, although in Northern Italy he was outside of the immediate war zone. His problems in 1616 were certainly exacerbated by the fact that the conflicts between the Protestants and Catholics were reaching a highpoint just two years before the start of the Thirty Years War. In the 1630s Galileo’s situation was certainly worsened by the fact that he was perceived, as a Medici courtier, to be on the wrong side in the political struggle between the two great Catholic powers, France and Spain, to control the Papacy.


Galileo Galilei portrait by Domenico Tintoretto Source: Wikimedia Commons

Perhaps the most obvious victim of the religious conflicts of the times was Pierre de la Ramée (Petrus Ramus) (1515–1572), who had a much bigger influence of the evolution of modern science than is usually acknowledged.


Source: Wikimedia Commons

A convert to Calvinism in 1562 he was initially forced to flee Paris, where he was Regius Professor at the Collège de France, and his house was pillaged and his library burnt in his absence. He spent two years wandering around Europe before returning to Paris. In 1572 he was murdered, one of the most famous victims, during the St. Bartholomew’s Day massacre, when a Catholic mob rose up against the Huguenots. It is not known how many Huguenots died during this slaughter but estimates range between five and thirty thousand.

The Calvinists in Geneva were responsible in 1553 for the immolation of the Spanish mathematicus and physicus Michael Servetus (1509 or 1511–1553)  (Span. Miguel Serveto) for his heterodox religious views. Although the Catholics and Lutherans would probably all have done the job if the Calvinists hadn’t.


Miguel Servet, (Villanueva de Sigena 1511- Genevra 1553) Spanish theologian & physicus Source: Wikimedia Commons

In England, the Keplerian astronomer William Gascoigne (1612–1642) died fighting on the royalist side at the Battle of Marston Moor during the English Civil War, which can also be viewed to a large extent as one of the European religious wars.


The Battle of Marston Moor 1644, by J. Barker Source: Wikimedia Commons

On the royalist side, which lost the battle, William and Charles Cavendish, both actively engaged supporters of the new sciences evolving at the time, were forced to flee to France, where they met up with natural philosopher Kenelm Digby (1603–1685) and Margaret Lucas (1623–1673), the future Lady William Cavendish and notorious female natural philosopher, two further Civil War refugees. In this later case these English refugees, although displaced by war, became part of an exhilarating philosophical scene in Paris, which featured Descartes, Mersenne, Gassendi and another English exile, Thomas Hobbes.


Margaret Cavendish: Segment from Frontispiece for several of her books in the 1650s and 1660s. Source: Wikimedia Commons

Do not misinterpret the above as in anyway supporting the unsubstantiated hypothesis of a conflict between religion and science. In each case, those I have listed suffered because of their religious affiliations or political views not because of their science. In fact it is interesting that during these times of intense religious strife, scientific scholars very often reached across religious and political boundaries to cooperate with each other, to share data, discuss discoveries and generally aid each other in their work.

Following the death of the Italian astronomer, Giovanni Antonio Magini (1555–1617) the Jesuits offered his chair for mathematics in Bologna to the Lutheran Johannes Kepler, with the assurance that he would not have to convert. When the Lutheran Protestant Georg Joachim Rheticus (1514–1574), professor for mathematics in Wittenberg, centre of the Reformation, visited the Catholic cathedral cannon Nicolaus Copernicus (1473–1543) in Warmia, Dantiscus (1485–1548), the Bishop of Warmia and a counter-reformation hardliner, greeted him with warmth and honour as a scholar. Christoph Clavius (1538–1612), Jesuit professor of mathematics at the Collegio Romano, corresponded with scientific scholars from all religious persuasions exchanging scientific news. One of his successors, Athanasius Kircher (1602–1680), collected astronomical data from other Jesuits from all over the world and then redistributed it to astronomers throughout Europe, both Catholic and Protestant.

In all of our #histSTM studies we should never lose sight of the fact that those we are researching are first and foremost human beings, who, to quote Shakespeare, suffer the slings and arrows of outrageous fortune, whilst trying to complete their own scientific investigations.








Filed under History of science