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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 Kitchener
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
(1847–1930)
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.

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The Great Man paradox

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

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

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

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

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

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

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

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

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

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

Galileo Galilei. Portrait by Leoni
Source: Wikimedia Commons

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

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

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

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

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

 

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

 

Hello JSTOR my old friend[1]

I’ve come to search in you again[2]

Because a reference softly creeping

Left its seeds while I was reading[3]

And the paper that was gnawing at my brain

Still remains[4]

Within the stress of research[5]

 

Through restless links I searched alone

Papers from journals I do not own

Neath the halo from my desk-lamp

I turn my collar to the research lab[6]

 

When my eyes were stabbed by the pain

Of a sleepless night

As I tried to write

Through the stress of research[7]

 

And in the flickering light I saw

Ten thousand deadlines maybe more[8]

Within the stress of research

 

Post-doc said, ah you do not know

Research like a cancer grows

Hear my words that I might teach you

Read my diss’ and it might reach you

But my sources like undergrads they failed

Adding to the stress of research[9]

 

Then the faculty bowed and prayed

To bureaucratic gods they made

And the REF flashed out its warnings

Low impact scores were alarming[10]

 

And the graphs and words from students

Were projected on the classroom walls and lecture halls

Folks breaking under the stress from research[11]

 

Composed 31 August 2017

Extended 5 September 2017

[1] Clare @mcclare95

[2] JSTOR @JSTOR

[3] Thony Christie @rmathematicus

[4] Vivek Santayana @viveksantayana

[5] Thony Christie @rmathematicus

[6] Eric Keeton @w0wkeeton

[7] Vivek Santayana @viveksantayana

[8] Vivek Santayana @viveksantayana

[9] Eric Keeton @w0wkeeton

[10] Vivek Santayana @viveksantayana

[11] Eric Keeton @w0wkeeton

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Journalists getting the facts wrong in the 19th century

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

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

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

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

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

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

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

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

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

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

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

Per Georg Schutz
Source: Wikimedia Commons

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

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

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

 

 

 

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

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A very special book

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

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

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

Hieronymo Schr[ei]ber Petreus dedit 1543

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

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

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

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

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

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

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

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A very innovative early scientific printer/publisher

It is a commonplace amongst historians that the invention of movable type, and through it the advent of the printed book, in the middle of the fifteenth century, was one of the principal driving forces behind the emergence of modern science in the Early Modern Period. However, although historians of science pay lip service to this supposedly established fact very few of them give any consideration to the printer/publishers who produced those apparently so important early books on science, medicine and technology. Like the technicians and instrument makers, the printer/publishers, not being scientist, are pushed to the margins of the historical accounts, left to the book historians.

Here at the Renaissance Mathematicus I have in the past featured Regiomontanus, considered to be the very first printer/publisher of science, Johannes Petreius the publisher of Copernicus’ De revolutionibus amongst numerous other scientific works and Anton Koberger around 1500 the world’s biggest printer/publisher and the man who produced the first printed encyclopaedia, The Nuremberg Chronicle. Today I want to turn my attention to a less well-known but equally important printer/publisher of scientific texts, who was responsible for several significant innovations in book production, Erhard Ratdolt.

Erhard Ratdolt was born in Aichach in Bavaria in 1459 or 60 the son of the carpenter Erhard Ratdolt and wife Anna. Erhard apprenticed as a carpenter and a maker of plaster figures. At the age of fifteen, according to his own account, he travelled to Venice, where he set up a printer/publisher office together with Bernhart Pictor a painter from Augsburg and Peter Loslein from Langenzenn, a small town near Nürnberg, in 1476.[1] The printing house was one of the earliest in Venice, where Johannes de Spira had set up the first one in 1469. By 1480 Venice had become to main centre for book production in Europe It seems that Ratdolt ran the business, whilst Pictor was responsible for the book decoration and Loslein for the text and copyediting. Both Pictor and Loslein had left the publishing house by 1478 leaving Ratdolt as the sole proprietor. Ratdolt’s two partners were probably victims of the plague, which wiped out eleven of the twenty-two printer/publishing establisments existing in Venice in 1478.

Their first publication was Regiomontanus’ Calendar, published in Latin and Italian in 1476 and in German in 1478. This book already contained several innovations. Ratdolt and his partners introduced the concept of printed ornamental borders for the pages of their books, a style that became typical for Renaissance books. They also introduced the first modern title page! It almost certainly seems strange to the modern book reader but the volumes printed in the first twenty or so years of book printing didn’t have title pages, as we know them. Ratdolt’s Regiomontanus Calendar was the first book to have a separate page at the beginning of the volume giving place, date and name of the printer. It was also the first book to have its publication date printed in Hindu-Arabic numerals and not in Roman ones. It would be some time before title pages of the type introduced by Ratdolt became common.

Calendarius by Regiomontanus, printed by Erhard Ratdolt, Venice 1478, title page with printers’ names
Source: Wikimedia Commons

In terms of the sciences Ratdolt’s most important work was the first printed edition of Euclid’s Elements, which he published in 1482. Here the innovation, a very major one was the inclusion of illustrations in the text. I say within the text but in fact the book was printed with very wide margins and the geometrical diagrams were printed next to the relevant text passage in these margins.

A page with marginalia from the first printed edition of Euclid’s Elements, printed by Erhard Ratdolt in 1482
Folger Shakespeare Library Digital Image Collection
Source: Wikimedia Commons

Another of Ratdolt’s innovations was the introduction of first two-coloured printing and then over time building up to books printed in as many as five colours and also printing with gold leaf.

Diagram, showing eclipse of the moon; woodcut, printed in three colours, from Sphaericum opusculum by Johannes de Sacro Bosco, printed by Erhard Ratdolt, Venice 1485
Source: Wikimedia Commons

In 1486 Ratdolt returned to Bavaria and set up a new publishing house in Augsburg at the invitation of the bishop and it was here that he introduced his next innovation. He is the earliest known printer/publisher to issue a printer’s type specimen book, in his case a broadsheet, displaying the fonts that he had available to print his wares. Upon his return to Augsburg Ratdolt was the first to introduce the Italian Rotunda font into Germany. He was also one of the earliest printers to offer Greek fonts for printing. Another of his innovations was the dust jacket. Like most other printer/publishers in the first half-century of book printing Ratdolt’s output in Augsburg was mostly religious works, although he did print some astrological/astronomical volumes. Ratdolt’s output declined from 1500 onwards but between 1487 and his death in 1522 his publishing house issued some 220 volumes.

Wappen des Bischofs Johann von Werdenberg, in der Widmung des Augsburger Breviers, 1485
Source: Wikimedia Commons

Given his youth when he left Bavaria for Venice Ratdolt’s contributions to the development of early book printing were truly remarkable. Even if his original partners were older and had started this chain of innovation, Ratdolt was still a teenager when they both disappeared from the business (died?) and the innovations continued when he was running the business alone.

Two interesting historical questions remain open concerning Ratdolt’s activities as a printer/publisher. We actually have no idea when, where or how he learnt the black art, as printing was known in that early period. The second problem concerns another early printer of scientific texts, Regiomontanus, and his connection to Ratdolt. The first book that Ratdolt published was Regiomontanus’ Calendar an important astrological/astronomical text that was something of a fifteenth-century best seller. The manuscript of the Euclid that Ratdolt published was one of the ones that Regiomontanus had discovered in Northern Italy when he was in the service of Cardinal Bessarion, as his book collector between 1461 and 1467. This raises the question, how did Ratdolt come into possession of Regiomontanus’ manuscripts?

Some earlier writers solved both questions by making Ratdolt into Regiomontanus’ apprentice in his publishing house in Nürnberg. The theory is not so far fetched, as Aichach is not so far away from Nürnberg and Ratdolt moved to Venice at about the same time as Regiomontanus disappeared and is presumed to have died. Unfortunately there is absolutely no evidence whatsoever to support this theory. Also given Regiomontanus’s renown at the time of his death, not just as a mathematical scholar but also as a printer/publisher, if Ratdolt had been his apprentice he would surely have advertised the fact in his own printing endeavours. I suspect that we will never know the answers to these questions.

 

 

 

 

 

[1] On a personal note I spent my first four years in Germany living just down the road from Langenzenn, where I spent most of my free time.

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“I went on holiday and I haven’t gone back home yet”

Today is the eighth anniversary of the founding of The Renaissance Mathematicus and, as on a couple of similar occasions in the past, I have decided to regale you with something biographical[1]. This is quite literally a tale of sex and drugs and rock’n’roll, so if you have any objections, moral or otherwise, to reading about such things or to the people who indulge or have indulged in them then I suggest you stop reading now.

In what follows I intend to tell the tale of how I came to live in Germany, where I have substantially now spent more than half of my life and where, all things being equal, I shall probably die. You might ask what my coming to live in Germany has to do with my blogging about the history of science but the connection is really quite direct. If I hadn’t come to Germany in 1980, I wouldn’t have ended up studying the history and philosophy of science, as a mature student, at Erlangen University and although I never completed my master’s degree, due to mental health problems, going on to become a sort of semi-professional historian of science and then a history of science blogger. But back to the beginning.

It all started in the summer 1977 when I moved back to Cardiff from Malmö in Sweden (that’s another story!). D (all the other people in this story will only be identified by their initials) had started constructing a yurt or ger, the round tents used as dwellings by the nomads of Central Asia, most notably the Mongolians.

A ger sits on the Steppes near Mandalgovi
Source: Wikimedia Commons

Why D had decided to construct a yurt I never quite fathomed but it was a typical D project. D had a good degree in biology but had decided instead of becoming a biologist, to smoke dope and indulge in moderately crazy projects. The projects were financed by the collective’s dope dealing activities. The collective consisted of those who lived in number 24, where D was at home, a rotating group of about twelve and various friends and acquaintances, of which I was one, bringing the total to somewhere around thirty. Many members of the collective were musicians. One member of the collective would buy dope in wholesale quantities and then others would distribute it at low profit margins to a relatively large network throughout the city. The professional dealers didn’t like us because we seriously undercut their prices but we had the protection of the big guys, who found our ‘socialist’ dealing somehow charming. I was a distributer, my only profit being my own not inconsiderable consumption. I got to smoke for free and my ‘customers’ enjoyed low priced dope. Everybody was happy. The central profits were used to finance projects like the yurt or the collective’s long wheel based Land Rover.

In the evenings members of the collective would come together in the large ground flour living room in number 24, get totally wasted and then indulge in long musical jam sessions, playing blues, folk, rock and often long open-ended snake dance instrumental jams. K & C were a couple who were both excellent guitarists who also sang and C, an American medical student, who had a beautiful voice like Joanie Mitchell also played flute. A, who had a degree in philosophy but who had gone off the rails and now ran a whole food shop, played saxophone and clarinet. Both B and JC were professional base players and were also excellent guitarists. B had a double music degree in classical guitar and composition. I played blues harp and jaw harp and almost everyone played percussion. Those sessions often ran for hours. There was also a formal house band built around K & C, which would occasionally play public gigs.

Various members of the collective, including me, were involved in constructing the wooden frame of the yurt and N, who worked as a theatre company seamstress sewed the roof and wall coverings out of lorry tarpaulins on an industrial sewing machine. We road tested the yurt on a very stoned, long weekend in Mid Wales in autumn during the magic mushroom season. It proved to be very reliable.

Mongolian Ger: starting to place roof poles
Source: Wikimedia Commons

In 1979 we decided to take yurt, house band and whoever wanted to come to the summer solstice free festival at Stonehenge. We loaded the yurt onto the Land Rover together with a lot of serious camping equipment, saws, axes, cooking pots etc. and set off for the full tens days of sex and drugs and rock’n’roll on Salisbury Plain. All together we were about thirty people, the yurt was big enough to sleep up to twenty and several people, myself included, took their own tents.

Surprisingly several of this bunch of dope smoking hippies had been boy scouts in their youth, including me, and we set a very professional camp site with a large fire pit on which we not only cooked food for all of our own group, funded from a communal kitty, but cooked and sold food to other attendees. A lot of drugs were consumed and a lot of music was played. On the afternoon before the solstice A and I took off across the festival site selling some first class acid that we had acquired. In the evening A, B and I dropped some acid and taking our respective instruments went off to a tepee with a generator to take part in an amplified jam session. We played raga rock, flying on acid for several hours until the generator ran out of petrol.

I wound my way back to our campsite in the early hours of the solstice dawn to join a fairly large gathering that had assembled around our fire pit to greet the solstice. One of those sitting around the glowing embers was a young German lady, AZ. We got into conversation and as the party wound down we retired to my tent. The following day AZ moved on in her Interrail trip around Britain but not before we had exchanged addresses. Over the next year we exchanged occasional letters and postcards.

Your author at Stonehenge Free Festival 1979 sawing firewood courtesy of AZ
I have no idea who the young lady on the right is!

In the summer of 1980 I was at something of a lose end in my personal life that didn’t seem to be going anywhere in particular. I was busy rewiring the photo and graphics studio of a friend one afternoon when I decided that what I needed was a holiday. Due to the work I was doing I knew that I would have some funds and fell to thinking where I could possibly go. The first two thoughts I had were that I could visit AZ in Germany or I could take a trip to Morocco, the destination of choice of various of my traveller friends at the time. Travellers were people who would work for six months or a year saving as much of their earnings as possible and then set off with a rucksack and sleeping bag to parts exotic for as long as they could make the money last. I had several such friends in those days but I wasn’t a traveller. When I got home to my flat on that evening there was a postcard from AZ who was on holiday in Morocco! I kid you not this really did happen.

Never one to ignore a wink of fate, in particular not one that obvious, I set off in September to hitch to Morocco via Southern Germany. I took a ferry to Hoek van Holland because I wanted to visit a friend who had moved there. Nobody had his address but I was assured by his brother that he was in the local telephone book. If he was, I couldn’t find him and so I set out to hitch down to Nürnberg in the vicinity of which AZ was living. It took two days including a night spent sleeping on the periphery of Frankfurt Airport. Not a quiet night. I had intended to stay just a couple of days in Franconia but ended up staying two weeks and getting to know a great crowd of people. When I started out again I hitched down through Austria to Florence in Northern Italy. From here I moved across Italy into Southern France winding my way across the south into Spain. Here I got picked up by a group of French Canadians with whom I spent a couple of crazy days. Working my way further south at snails pace, Spain was not a good country for hitch hiking in those days, I finally arrived in Algeciras and took the ferry to Ceuta, where I met a Swiss hippy who offered a sort of unofficial taxi service down to Marrakesh, which I took.

Having spent several days in Marrakesh I moved on to Meknes, which at that time had the only functioning mosque that one could visit as a non-Muslim. Here I had two very nice experiences. In order to visit the mosque you have to be shown round by a guide. I got shown round, together with two German tourists, by a young Moroccan student. The student only spoke French and the Germans only spoke English so I ended up acting as translator, because of this a got my guided tour for free, the student being thankful for my services. The student then took me to a student café where I spent the evening in the company of about twenty young Moroccans, mostly students, dinking mint tea and smoking kief. The young students made me feel very much at home and those were the happiest hours that I spent in Morocco.

In classic style my money began to run out and I got sick, some sort of flu like virus, so I began to head back to Europe. I was feeling shit and was very, very low on funds by the time I reached Madrid and was wondering how I could get back home when I met a German who had been deported from Morocco and had a one-way train ticket to Munich paid for by the German Embassy in Morocco. He sold me his train ticket for most of the cash that I had left and I rode the train back to Germany getting off in Nürnberg and going back to AZ’s.

My plan was to get well, find some casual work and earn enough money to get back to the UK. Having recovered my health, speaking no German I went down the honoured George Orwell route and got a job as a dishwasher in a local hotel. Here I had the best name-dropping experience of my entire life. The hotel manager was rather chuffed at having a genuine white British dishwasher, all of my colleagues where Indians, and would come and practice his English on me. One day I came into work at 7 am and he rushed to meet me asking if I knew who had slept in his hotel that night? I of course had no idea and playing the required role of straight man responded, no who? He burst out excitedly, “Roy Jenkins, President of the European Commission!” I, without thinking at all about what I was saying, “Oh, I went to school with his children”. His face dropped a mile, trumped by a mere dishwasher. He turned and walked away without saying a word.

In December I decided that I was going to stay in Germany and I’m still here thirty-seven years later. If people ask how I came to live in Germany I always answer, as I said above, “I went on holiday and I haven’t gone back home yet”, which is the simple truth.

 

 

[1] This also fulfils a request made by some commentators on my 2016 Winter Solstice post.

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