It’s elementary dear readers

The legendary soul singer, James Brown, was often referred to as “the Hardest Working Man in Show Business.” In analogy, one could refer to Philip Ball as “the Hardest Working Man in Science Communication.” He churns out books at a higher rate than most other science writers articles, as well as a constant stream of articles for a range of journals. On top of the flood of print on paper he also writes, produces, and presents an excellent radio broadcast for BBC Radio 4, called Science Stories; it’s well worth a listen if you don’t already. I have a running gag on Twitter that the work is actually done by a team of gnomes chained to their desks in the cellars of Ball mansions. As we follow each other on Twitter I finally managed to con him into sending me one of his books to be reviewed here at the Renaissance Mathematicus.[1]

The book in question is The ElementsA Visual History of Their Discovery[2], it’s actually from 2021, as the publishers kept on ignoring Phil’s request that they should send me a review copy, but I kept reminding Phil and he kept prodding the publishers and persistence won out in the end. 

The visual history is to be taken literally, it is a large format book chock full of incredible colour and sepia illustration with accompanying text. It is what is also sometimes, somewhat deprecatingly, referred to as a coffee table book, but despite the format and the visual emphasis this is a high value, easy access volume of absolutely first class, popular history of science. 

The money quote in Ball’s introduction is:

All this implies that charting the history of the discovery of the chemical elements is more than an account of the development of chemistry as a science. It also offers us a view of how we have come to understand the natural world, including our own constitution. Furthermore, it shows how this knowledge has accompanied the evolution of our technologies and crafts – and ‘accompany’ is the right word to use, because this narrative challenges the common but inaccurate view that science always moves from discovery to application. Often it the reverse: practical concerns (such as mining or manufacture) generate questions and challenges that lead to fresh discoveries.

The book wonderfully illustrates all that is stated and implied in these few sentences. 

Before I look at the book in more detail, one last general comment. The book consists of a large number of short, compact, stand-alone essays. Each one of these covers a single topic in at most a few pages. A lot of them are only two or three pages long and I think the longest only run to five pages. It should be noted that a large percentage of those pages are also taken up by the lavish illustrations. However, Ball is an absolute master of the short essay form. He manages, in each case, to include all of the relevant, cultural, historical, and scientific information necessary for a clear understanding of the topic at hand in a style that is easy to read and comprehend, even for the previously, completely uninformed reader. Believe me, as the author of a blog, I know how difficult that is. 

As one might expect, given the subject, the book opens with a multi-coloured double page spread, periodic table. Each article on an element or group of elements has a small schematic periodic table at the top of a sidebar that shows their position in the periodic table. This sidebar also, to quote the author:

…show their atomic number, atomic symbol, atomic weight, periodic group name and number, and in some cases their phase at standard temperature and pressure (solid, liquid or gas)

Although the book opens with the periodic table, we don’t jump straight in with the modern chemical elements, it is constructed chronologically, and the first chapter starts with a general essay on the four classical elements, earth, water, fire, air. This is followed by one on the various ancient Greek philosophical matter theories before we plunge into individual essays on those four elements. This is followed by an excellent introduction to the Chinese five element system. We now go in search of the atom and having found it investigate the aether, the fifth element or quintessence, which closes out the first chapter. 

Chapter Two introduces us to the metal of antiquity. After an introductory essay, we have the precious metals, gold, silver, and copper, followed by an essay on tin and lead and the chapter closes with a comparatively long one on iron, in many senses one of the most important materials discovered and exploited by humanity. 

Chapter Three takes us into the world of the alchemist with the same schema, first an introduction then essays on sulphur, phosphorus, and antimony. Up next is a discourse on a substance that never existed but proved incredibly productive in the history of chemistry, phlogiston. The chapter closes with the question, “What exactly is an element?” answered with a presentation of the thoughts of Robert Boyle, a practicing alchemist, who is considered to have given the first halfway modern answer to the question. 

Chapter Four delivers up the new metals, nine in total, leading us into Chapter Five and chemistry’s golden age. We have the gasses, hydrogen, oxygen, and nitrogen, followed by carbon. Once again, we have a substance that never existed but formed the basis for much experimentation, caloric. Just as phlogiston was considered to be substance given off by burning, so calorific was thought to be the elemental form of heat. The elements now come thick and fast, the halogens, chromium and cadmium, the sixteen rare earth elements. The chapter closes with John Dalton and the beginnings of the modern atomic theory.

Silver mining in Kutná Hora, Bohemia (now the Czech Republic). From an illuminated choirbook, 1490, Sotheby’s London.

Electricity enters the scene in Chapter Six and with it the elements discovered using it by chemists such as Humphry Davy: potassium, sodium, calcium, magnesium, barium, strontium, boron, aluminium, silicon, and zirconium. The book opens with the periodic table known. I think, to all of us from the classroom wall, now we get introduced to the man, who is credited with having discovered it, Dmitri Mendeleev, although Ball also credits those who laid the trail to its discovery before Mendeleev. 

I’ve already described the sidebars on the element essays, on the introductory essays the sidebars have a continuous chronic of the histories of science and technology interspersed with general historical events. In Chapter Seven, The Radiant Age, this chronic starts with the first transatlantic telegraph communication in 1858 and ends with the Russian Revolution in 1917. We have entered the realm of modern physics, electromagnetism, radiation, James Clerk Maxwell, Wilhelm Röntgen, Henri Becquerel, Marie and Pierre Curie, and many more. Following the introductory essay, we have caesium and rubidium with an introduction to spectroscopy, thallium and indium, helium, the inert gases, and to close radium and polonium.

The final chapter takes us into the nuclear age the chronic running from Albert Einstein in 1905 to the dissolution of the USSR in 1991. We fill a gap with technetium and extend the table with neptunium and plutonium, the accelerator elements–americium, curium, berkelium, californium–with claims and counter claims as to who created them first and thus won the right to name them. The bomb-test deliver up einsteinium and fermium. We have eight early trans-fermium elements, from atomic number 101 to 108, and the proofs of their existence gets harder. We enter the realm of less than a teaspoon full, and does it really exist with elements 109 to 118. 

The book closes with a ‘sources for quotes’, or as they are known hanging endnotes to which there are no references in the text, as it is not an academic book, not so bad. There is then a very brief but very good list for further reading, followed by a very extensive picture credits list. It ends with a usable index.

All in all, Philip Ball is to be congratulated on an excellent, accessible, entertaining, and educational tome and I wish I could say that it is as near perfect as a commercial history of science book can be, but I can’t. The book has a serious blemish, a lacuna that I simply can’t ignore. I will introduce it with a couple of quotes from the book:

Paracelsus broadened this ‘unified theory of metals’ to include all substances, by adding a third principle, salt. He argued that mercury was the principle that made things fluid, salt gave them ‘body’ and made them solid. While sulphur was the principle of flammability: it made things burn. (page, 56) 

The ‘alchemist’s trinity’ of sulphur, mercury and salt. An allegorical image from Zoroaster’s Clauvis Artis, Ms-2-27, Vol. 3, 1858, Attilio Hortis Civic Library, Trieste

First the German alchemist Johann Joachim Becher modified the Paracelsian scheme in claiming that there were three types of ‘earth’: a fluid sort (like mercury), a solid sort (like salt), and a fatty and combustible sort (like sulphur). (page, 66)

In ancient times, philosophers and craftspeople recognised seven different metals: gold, silver, mercury, copper, iron, tin and lead. This was a neat scheme, because each of the metals could be assigned a heavenly body: the Sun, Moon, and the five known planets Mercury, Venus, Mars, Jupiter and Saturn. Why do that, though? Because many natural philosophers believed that nature was governed by ‘correspondences’ like this between different classes of things. (page, 78)

Remember Chapter Two, The Antique Metals? We had gold, silver, and copper, followed by tin and lead, and then came iron, where was mercury? When I first realised that there was no entry for mercury, I couldn’t believe it and searched the book from beginning to end thinking I must have somehow overlooked it, but no, there is no entry for mercury. Still not believing my eyes I contacted Phil Ball and discretely inquired whether it was really so that he had forgotten, left out, mercury. His reply was an expletive, that I won’t repeat here. This has got to be the biggest copyediting error that I’ve ever encountered in a book. Phil says he will correct it in the paperback edition. At least he didn’t blame the gnomes.

Despite the absence of mercury, I whole heartedly recommend this wonderful book to just about everybody. In particular I think every home with children should own a copy, not stowed away on a bookshelf but laying around, on a coffee table for example, where inquiring minds could from time-to-time dip in and out of its beautifully illustrated and informative pages. It is a book that lends itself perfectly to dipping. 

One small improvement that I would recommend, apart from an essay on mercury, is that each copy should come with a CD with Tom Lehrer’s The Elements.

[1] Actually, he was quite happy to do so, even the threat of a mauling by the HISTSCI_HULK didn’t stop him from doing so.

[2] Philip Ball, The ElementsA Visual History of Their Discovery, Thames and Hudson, London, 2021


Filed under Book Reviews, History of Chemistry

Renaissance garbage ­– I

In case you hadn’t noticed there is a four-weekly cycle of blog posts here at the Renaissance Mathematicus. Week one is a new series post, week two a fairly random #histSTM post, week three the next new series post, and week four a book review. Sometimes I throw in a random HISTSCI_HULK post just because. Today should be the next series post but I posted the last episode of my Renaissance Science series two weeks ago. You might be pleased or dismayed to learn that I have a new series lined up, at least in my head, but I want to take a little breathing space before I start in on it. To bridge the gap, I shall be posting a series of posts, which are sort of related to the Renaissance Science series, on a book by Paul Strathern, The Other RenaissanceFrom Copernicus to Shakespeare, (Atlantic Books, 2023). The Other Renaissance is, of course, what is normally referred to as the Northern Renaissance.

I must admit that I had never heard of Paul Strathern, but a friend, who shall remain nameless, received a review copy of this book, and thought it was so bad that he decided not to review it at all. My historical garbage antenna went up and I made further inquiries, whereupon said friend was kind enough to send me a pdf of said book. And yes folks, it is truly a stinker. I don’t intend to review the whole thing, but I thought I would post a series of HISTSCI_HULK typical put downs of selected elements of the text.

However, before we get down to the nitty-gritty a few words about our author. According to his Wikipedia page, Paul Strathern (born 1940!!) is a Scots Irish writer and academic, and an incredibly prolific writer he is too. To date, he has published five novels, fifteen “academic” books, nineteen titles in his Philosophers in 90 Minutesseries, eleven titles in his Great Writers in 90 Minutes series, twelve titles in his The Big Idea: Scientists Who Changed the World series, and finally three travel guides. I wonder what he does in his spare time? Also, if his The Big Idea: Scientists Who Changed the World are as bad as his The Other RenaissanceFrom Copernicus to Shakespeare, then I’m glad that the HISTSCI_HULK hasn’t read any of them.

As I will be only commenting on selected bits of the book here is the full contents list:

Map viii–ix Timeline of Significant Events during the Northern Renaissance x-xi 

Prologue: Lifting the Lid 1 

1 Gutenberg 13 

2 Jan van Eyck 21 

3 Nicholas of Cusa 33 

4 Francis I and the French Renaissance 47 

5 A New Literature: Rabelais 63 

6 Martin Luther and the Protestant Reformation 73 

7 The Rise of England 89 

8 The Rise and Rise of the Fuggers 105 

9 Copernicus 125 

10 Erasmus 141 

11 Dürer 157

12 Straddling Two Ages: Paracelsus and Bruegel the Elder 175 

13 Versions of the True: Mercator and Viète 193 

14 Vesalius 211 

15 Catherine de’ Medici 229 

16 Montaigne 249 

17 Elizabethan England 265 

18 Brahe and Kepler 281 

19 Europe Expands 301 

Conclusion: A Last Legacy 317 

And the timeline: (The formatting is a bit weird, result of my cut and paste)


1415 Jan Hus, founder of the Hussites, burned at the stake
1432 Van Eyck completes the Ghent Altarpiece
1460s Regiomontanus oversees the building of the first observatory in Europe (Rubbish!)
1464 Death of Nicholas of Cusa
1474 Technique of painting in oils spreads from the Netherlands to Italy
1494 Signing of the Treaty of Tordesillas: Pope Alexander VI draws a line down the Atlantic Ocean, dividing the globe between Spain and Portugal
1497 John Cabot sails from Bristol and reaches North America 

1509 Erasmus writes In Praise of Folly
1512 Torrigiano is commissioned by Henry VIII to create a Renaissance tomb for Henry VII

1514  Dürer produces Melencolia I 

1515  Francis I ascends to the throne of France

1517 Martin Luther nails his Ninety-Five Theses to the door of Wittenberg Castle Church
1519 The death of Leonardo da Vinci in France
1519 Charles V is crowned Holy Roman Emperor
1525 Death of Jacob Fugger the Rich
1529 The Colloquy of Marburg fails to unite Protestants 

1533 Henry VIII breaks with Rome 

1536 John Calvin arrives in Geneva; Calvinist missionaries soon begin to spread over northern Europe 

1536 French explorer Jacques Cartier brings Chief Donnacona from the New World to see Francis I 

1541 Death of Paracelsus
1543 Copernicus is shown the first published edition of his De Revolutionibus Orbium Coelestium, describing the solar system, while on his deathbed
1543 Vesalius publishes De Fabrica, describing human anatomy
1547 The completion of the Château de Chambord in the Loire Valley 

1547 The death of Francis I of France
1553 The death of Rabelais
1553 English explorer Richard Chancellor visits the court of Ivan the Terrible
1558 The death of Holy Roman Emperor Charles V
1569 Mercator publishes his Atlas, containing his cylindrical projection map of the world
1572 The St Bartholomew’s Day massacre of Huguenots in France 

1588  The Spanish Armada fails to invade Elizabethan England 

1589  The death of Catherine de’ Medici, mother of French kings and ruler of France 

1596 Johannes Kepler publishes his laws describing the elliptical orbit of plants (Love this typo!)

1600  The founding of the East India Company in London 

1601  Tycho Brahe dies in Prague 

1608 Invention of the perspicillium in Holland, which inspires Galileo to create the telescope (Rubbish!)
1616 The death of Shakespeare
1642 Cardinal Richelieu dies in France
1648 The Peace of Westphalia ends the Thirty Years’ War 

I decided to start this week with Strathern’s chapter on Albrecht Dürer, as I have a local connection to the man. 

After a conventional biographical introduction from birth to marriage, Strathern tells us:

Dürer did not travel on his own. He is thought to have been accompanied by an ebullient rugged-faced companion named Willibald Pirckheimer, [my emphasis] whose appearance belied his acute intelligence and thirst for learning. Pirckheimer came from a distinguished family in Nuremberg, was a year older than Dürer, and was filled with patrician self-confidence. He was studying law at Padua, and during the course of their friendship Pirckheimer would fill the huge gaps in Dürer’s education, introducing him to the humanist ideas he had picked up at university and amongst his father’s intellectual circle in Nuremberg. 

When I read that Dürer, on his first journey to Italy, was accompanied by Willibald Pirckheimer, I did a double take. Having read quite a lot about Dürer and Pirckheimer and I’ve never come across any such claim. So back to the literature. My first stop was German Wikipedia, where to my surprise I read the following:

In der Folgezeit bis 1500 schuf er eine Serie von kleinen Landschaftsaquarellen mit Nürnberger Motiven bzw. mit Motiven von Stationen seiner ersten Italienreise, die er in der ersten Hälfte des Oktobers 1494, bereits drei Monate nach seiner Hochzeit, antrat. Diese Reise verstärkte sein Interesse an der Kunst des Quattrocento. Im Mai 1495 kehrte er zurück nach Nürnberg.

Von der jüngeren Forschung wird angezweifelt, dass Dürer im Rahmen dieser Reise jemals die Grenzen des deutschen Sprachgebiets überschritt, und die Indizien, die gegen einen Aufenthalt in Venedig sprechen, häufen sich: Dürer selbst erwähnte in seiner Familienchronik 1494/95 keine Reise nach Venedig. Die italienischen Züge in seinen Werken ab 1497 interpretieren manche als direkten Einfluss des paduanischen Malers Andrea Mantegna, der 1494/95 zwar nicht in Padua war, dessen Werke Dürer aber dort gesehen haben könnte. Beweisbar ist nur, dass Dürer in Innsbruck, Trient und Arco beim Gardasee war. Von Orten südlich von Arco gibt es bei Dürers Aquarellen keine Spur, also auch nicht von Venedig. Auch die Route spricht gegen die Venedig-Theorie: Für Dürer hätte es näher gelegen, den für Nürnberger (Kaufleute) üblichen Weg nach Venedig zu nehmen, der über Cortina und Treviso verlief und „Via Norimbergi“ genannt wurde. Die Bilder aus seiner späteren, nachweisbar venezianischen Zeit ab 1505 haben deutlich stärker venezianische Charakteristika.

For those who don’t read German, it basically says that recent research doubts that Dürer ever left the German language area in 1494 and thus was never in Italy on this journey. This was new to me as I have always read about and accepted that Dürer made two journeys to Italy, the first in 1494. Happily, in 2021, the National Gallery in London put on a major expedition Dürer’s JourneysTravels of a Renaissance Artist for which there is an amazing book[1], which thanks to my very generous stepmother I own a copy. Turning to this wonderful tome I discovered that it is really so that historians now believe that Dürer did not reach Italy in 1494. Apparently, the whole story of the first Italian journey is based on two very short ambiguous quotes and the rest has been built up over the years based on reading the tealeaves in Dürer’s work. 

I actually began to question these two paragraphs of Strathern because of his claim that Pirckheimer had accompanied Dürer on this journey. No journey so no Pirckheimer but there is more. Strathern correctly states that Pirckheimer was studying in law in Padua, which he did for seven years from 1488, first returning to Nürnberg on 1495. This was when Willibald and Albrecht first met!

Later Strathern turns to the “second” Italian journey, the one that really did take place and dishing up a myth that has been long debunked, he tells us:

Between 1507 and 1509 Dürer paid a second visit to Italy, passing beyond Venice to Padua and maybe even Mantua. He certainly visited Bologna, for it was here that he met Luca Pacioli, the friar mathematician and friend of Leonardo da Vinci. It was Pacioli who had taught Leonardo mathematics, and it seems that Dürer too studied with him. Dürer’s meticulous and exact art inclined him to mathematics, and it would play an increasing role in both his painting and his other intellectual interests. Pacioli is known to have taught Dürer linear perspective, which was by now widely developed amongst Italian Renaissance artists. But Pacioli probably taught Dürer much more than this useful mathematical–artistic device, for Dürer would continue to study mathematics over the coming years. 

It is simply not known from whom Dürer learnt the basics of, the then still comparatively new, linear perspective. The question has a certain historical importance, as he is credited with having introduced linear perspective into Northern European art. I have no idea who first introduced the theory that he learnt it from Luca Pacioli during his time in Bologna but that is absolutely no evidence to support it. The theory was finally totally debunked, when somebody pointed out that when Dürer was in Bologna, Pacioli was in Milano! Maybe Pacioli taught him telepathically? As for the implication that Pacioli also taught Dürer mathematics, we know from fairly solid evidence that Dürer didn’t need to go to Italy for his maths lessons, he got them at home in Nürnberg from Johannes Werner. (1468–1522)

Source: Wikimedia Commons

Next up we get a strange twist in the Dürer timeline from Strathern:

By the time Dürer returned home from his second visit to Italy, he was known by reputation throughout Europe. In 1512, the Holy Roman Emperor Maximilian I became one of his patrons. Despite this, Dürer found that he was making insufficient income from his paintings, and even abandoned this art form for several years in favour of making woodcuts and engravings – which could be reproduced and thus sold many times over. He may not have been the best painter in Europe, but his engravings were unsurpassed. 

Dürer served his apprenticeship in the studio of Michael Wolgemut between 1486 and 1490. Wolgemut specialised in producing woodblock prints as book illustrations. For example, his studio produced the illustrations for the famous  Liber Chronicarum, better known as the Nuremberg Chronicle in English and Die Schedel’sche Weltchronik in German. There are even speculations by art historians as to whether the young apprentice was responsible for some of those illustrations. From the very beginning when he set up his own workshop in 1495, Dürer specialised in woodblock printing. He also developed his skill in engraving, almost certainly learnt in his original apprenticeship under his father, a goldsmith. To illustrate a couple of quotes from Wikipedia:

Arguably his best works in the first years of the workshop were his woodcut prints, mostly religious, but including secular scenes such as The Men’s Bath House (ca. 1496). These were larger and more finely cut than the great majority of German woodcuts hitherto, and far more complex and balanced in composition.

His series of sixteen designs for the Apocalypse] is dated 1498, as is his engraving of St Michael Fighting the Dragon. He made the first seven scenes of the Great Passion in the same year, and a little later, a series of eleven on the Holy Family and saints. The Seven Sorrows Polyptych, commissioned by Frederick III of Saxony in 1496, was executed by Dürer and his assistants c. 1500. In 1502, Dürer’s father died. Around 1503–1505 Dürer produced the first 17 of a set illustrating the Life of the Virgin which he did not finish for some years. Neither these nor the Great Passion were published as sets until several years later, but prints were sold individually in considerable numbers.

In 1496 he executed the Prodigal Son, which the Italian Renaissance art historian Giorgio Vasari singled out for praise some decades later, noting its Germanic quality. He was soon producing some spectacular and original images, notably Nemesis (1502), The Sea Monster (1498), and Saint Eustace (c. 1501), with a highly detailed landscape background and animals.

Prints are highly portable and these works made Dürer famous throughout the main artistic centres of Europe within a very few years.

As you can see this is not post 1512 but we have just reached 1505 and Dürer is a highly prolific and famous producer of fine art prints. In fact, rather than being a painter, who turned to fine art printing for financial reasons, as Strathern would have us believe, Dürer was a highly successful fine art printer, who painted on the side.

We get the standard discussions of The Rhinoceros, Dürer’s most famous print, and Melencolia I, his most enigmatic and most interpreted print. I have only one question about Strathern’s waffle here, he writes about Melencolia I:

Though mathematics, especially geometry (Plato’s favourite), underlies much of the scene. 

There is no other reference to Plato anywhere in his convoluted discussion of Melencolia I, so why shove him in here? Earlier he makes the equally strange comment:

Set into the wall above the angel’s head is a four-by-four magic square, indisputable evidence of Dürer’s continuing mathematical interest. 

There was nothing to say that Dürer had ever stopped being interested in mathematics.

Having dealt with The Rhinoceros and before Melencolia I, Strathern enlightens us with the following paragraph:

As we have seen, the year 1500 marked one and a half millennia since the birth of Christ, and there was a widespread belief around this time that it heralded the Second Coming of Christ, which is mentioned in the Bible: ‘This same Jesus, which is taken up from you into heaven, shall so come in like manner as ye have seen him go into heaven.’ Such an event would precede the Last Judgement, after which our souls would be despatched to Purgatory, Hell or Heaven.

Various dates were considered by various people to signify the second coming but I personally have never come across a reference to 1500 as one of them.

Strathern also turns his spotlight on the Ehrenpforte Maximilians I, known in English as The Triumphal Arch or the Arch of Maximillian I, he writes:

Dürer created a number of works for his most important patron, Maximilian I. Amongst these is a large, highly complex woodcut of a triumphal arch, which measures almost ten feet by ten feet. Dürer spent over two years – on and off – busying himself with this work, which includes 195 separate woodcuts printed on 36 sheets of paper. The intention was that it should be hung in princely palaces and city halls throughout the Holy Roman Empire. Indeed, Maximilian I made a habit of giving away copies of this work with this intention. 

The work itself is a suitably grandiose hotchpotch of styles – resembling, if anything, an example of Indian architecture rather than any classical triumphal arch (such as Marble Arch in London, or the Washington Square Arch in New York). It stands more as a monument to Dürer’s indefatigable technical expertise than any aesthetic achievement. Such a work made him rich, allowing him independence – even if it contributed nothing to his artistic attainment and was otherwise a complete waste of his time. [my emphasis]

Ehrenpforte Maximilians I, Source: Wikimedia Commons

As is, unfortunately, all to common Strathern attributes this work to Dürer alone but it was the work of a group of people, quoting, yet again, Wikipedia:

The design program and explanations were devised by Johannes Stabius, the architectural design by the master builder and court-painter Jörg Kölderer and the woodcutting itself by Hieronymous Andreae, with Dürer as designer-in-chief. […] the flanking round towers are attributed to Albrecht Altdorfer.

The closing clause from Strathern, that I have emphasised, displays, in my opinion, his ignorance of the professional life of an artist and in particular that of his subject Albrecht Dürer. Dürer ran a highly professional, commercial fine art print studio, with which he not only earned the money on which he and his family lived but also the money with which he paid his employees. The Ehrenpforte was anything but a complete waste of time, as the commission raised the status of his studio and did in fact contribute to his artistic attainment, as it displayed his mastership in woodblock printing to the world. 

Here we have the name of the mathematician, Johannes Stabius 1450–1522), who was the Imperial Court historian, was the director of the project, as he would employ Dürer on two further commissions, neither of which Strathern considers worth mentioning, despite his continued references to Dürer’s interest in mathematics.

Johannes Stabius portrait by Albrecht Dürer Source: Wikimedia Commons

The first was the Stabius-Dürer World Map

Stabius-Dürer World Map published in 1515, a perspective representation of the earth as a globe. Source: Wikimedia Commons

and the second, and historically much more important the Stabius-Dürer-Heinfogel planispheres of the southern and northern hemispheres, the first European, printed celestial maps, which I wrote about here.

The Dürer Star Maps in a hand coloured edition Source: Ian Ridpath Star Tales

 We get accounts of Dürer’s journey to the Netherlands to get his Imperial pension renewed following the death of Maximillian, including an account of his portrait of Erasmus and Strathern’s rather bizarre interpretation of its Greek inscription. 

Almost at the end of his chapter, Strathern turns to Dürer the mathematician:

With Dürer’s eyesight fading, he devoted less of his energies to his art. Instead he concentrated on writing treatises on such subjects as ‘human proportions’ and ‘fortifications’. However, his most important work was his Four Books on Measurement. These contain the wealth of mathematical knowledge he accumulated during his life – including the geometrical construction of shadows in prints (projective geometry), as well as several ideas by the Tuscan artist Piero della Francesca which had not yet been published. (These Dürer had almost certainly learned from Luca Pacioli.) Very little of this vast compendium of work is original, but it was written in the vernacular German rather than in Latin. This established Dürer as the first figure of the northern Renaissance to outline in German Euclidean geometry and demonstrate the construction of the five Platonic solids, other Archimedean semi-regular truncated solids, and a number of constructed figures which are thought to have been of his own invention. His treatises were the first printed north of the Alps to view art in a scientific fashion, exposing the mathematical bones upon which much artistic flesh is based. 

I’m sure Dürer would be delighted to know that his Four Books on Measurement was his most important work, whereas his ‘human proportions’ was just a treatise on “such subjects”! 

About the time of his “second” journey to Italy, Dürer became obsessed with the idea that the secret of beauty lies in the mathematical theory of proportions. He began working on his Vier Bücher von menschlicher Proportion (Four Books on Human Proportion) in 1512 and the four books, written at different time over the years, deal with various aspects of exactly that, human proportion. An appendix to the book explains Dürer’s theories on ideal beauty.

Title page of Vier Bücher von menschlicher Proportion Source: Wikimedia Commons

The book was written for apprentice artists and in the middle of the 1520s, Dürer realised that the geometry of the book was too advanced for the intended readers, so he sat down and wrote his Four Books on Measurement (Underweysung der Messung mit dem Zirckel und Richtscheyt or Instructions for Measuring with Compass and Ruler), (which I wrote about here) an introductory textbook on geometry for apprentice artists. It is the book on human proportions that is his most important work, the Four Books on Measurement merely developed the mathematical tools needed to understand it. 

Underweysung der Messung mit dem Zirkel und Richtscheyt Title Page

I have no idea which not yet published ideas from Piero della Francesca Dürer’s book supposedly contains. It goes without saying that Dürer didn’t learn anything from Luca Pacioli, whom he never met and with whom, as far as we know, he didn’t correspond. However, he might have accessed della Francesca work via Pacioli, who had plagiarised it in his Divina proportione, published in 1509, which was possibly owned by one of the Nürnberg mathematicians, Werner or Stabius, but that’s just speculation. 

Far from being a vast compendium of work, Underweysung der Messung is 27cm X 18cm and probably less than 200 pages long, it’s not paginated so I had to guess. Dürer’s Underweysung der Messung is actually the very first mathematics book printed in German and like most textbooks it is of course derivative. However, it does contain one important geometrical innovation. Dürer introduced the geometry net, which is the two-dimensional figure that arises when you open a three-dimensional figure along edges.

Underweysung der Messung geometrical net

In one sense Underweysung der Messung did become more important than Vier Bücher von menschlicher Proportion both were into Latin and Underweysung der Messung was translated into several different European languages. Vier Bücher von menschlicher Proportion appealed to a very limited readership but Underweysung der Messung became a very widely read geometry textbook throughout Europe for most of the next hundred years. 

Strathern has obviously not bothered to do serious research for his book but has just thrown it together from the first sources that crossed his path without bothering to check whether they were factually correct or not. As we will see in later chapters this sloppy approach is not confined to Dürer but is characteristic of the whole book. 

[1] Susan Foister and Peter van den Brink eds., Dürer’s JourneysTravels of a Renaissance Artist, National Gallery, London, distributed by Yale University Press, 2021. 


Filed under Book Reviews, Renaissance Science, Uncategorized

Artificial Bullshit!

There has been much hot air expended in recent days over the supposed artificially intelligent program Chat-GPT, which is, in reality, a more sophisticated Internet search engine. James Maynard on his website The Cosmic Companion proudly announced that he had used it “to construct a pictorial journey exploring the story of Hypatia!” Having spent some time using my biological intelligence to survey the modern historical literature on the lady and used the information gained to write a blog post, I have decided to don my pedagogical persona and evaluate the results produced by this new program. The full text is below with my comments in italics.

Reconstructing Hypatia of Alexandria Using Artificial Intelligence

Using Chat-GPT and MidJourney to construct a pictorial journey exploring the story of Hypatia – The last great scientist of the ancient age of the western world.

We’ve used generative artificial intelligence to learn about the last great scientist of the ancient age in the western world.

Sorry but Hypatia was not a great scientist and as for being last of the ancient age in the western world, I think Proclus, Boethius, Simplicius, John Philoponus, and a couple of others might like a word. This is a variant on the, “they murdered science when they murdered Hypatia,” myth, more of which gets spewed out in the closing paragraphs.

Hypatia of Alexandria was an accomplished astronomer, mathematician, and philosopher who lived in the final days of the ancient age of science. Born sometime around 360 CE, Hypatia was raised in the cultural and intellectual center of the Mediterranean, Alexandria, by her mathematician father Theon.

We don’t have any direct proof as to how accomplished Hypatia actually was, as none of her writings have survived.

Hypatia dedicated her life to advancing science and reason in an age when dark forces were closing in on her society.

Once again, a statement with no basis in known facts, as we have no evidence to support it and what are these ominous dark forces?

The Great Library of Alexandria, founded just after 300BCE, was once the greatest storehouse of information in the ancient world. The Library was one part of a larger institution of learning, the Musaeum of Alexandria, which also included a grand university.

Hyperbole, the Great Library of Alexandria was one of the great libraries of antiquity. It was part of the Mouseion, why use Musaeum, the Latin name, for a Greek institution in a Greek city?  The Mouseion was a research institute, or one might call it an institute of advanced learning. However, there was no university, grand or otherwise.

The root of our English word museum, the term Musaeum originally referred to temples honoring the Muses. Over time, this word came to represent centers of learning. 

Nothing to criticize here, but I wonder why articles about Hypatia almost always include sections on the Library and the Mouseion, as both had ceased to exist long before Hypatia was even born?

At the start of the Fifth Century, in the final years of the Alexandrian University, Theon raised his budding scientist in the manner usually reserved for boys — in the father’s trade — in this case, math and science. History leaves us no knowledge about Hypatia’s mother.

What Alexandrian University? Anachronical use of the term scientist is here especially unnecessary as mathematician and astronomer would be more accurate.

Living her life in the cultural and intellectual center of the Mediterranean, Alexandria, Hypatia attended classes and later taught on the ancient grounds of learning, delivering understandable lessons on complex scientific subjects.

Notes based on her teachings are said to cover astronomy, geometry, the use of astrolabes, and more. Hypatia taught classes, some of them to large audiences. Ancient accounts are nearly unanimous in noting her intellectual prowess.

In the normal meaning of the term there are no surviving “notes based on her teachings.” What we have are a handful of general comments on the areas that she taught.

She was a gifted science educator and her works were reported to contain insights on astronomy, geometry, the use of astrolabes, and more.

Very general and rather vague reports, with almost no specifics.

Even her rivals often admired her talents, including John of Nikiu, who stated, “The breadth of her interests is most impressive. Within mathematics, she wrote or lectured on astronomy, geometry, and algebra, and made an advance in computational technique — all this as well as engaging in religious philosophy and aspiring to a good writing style.”

Not a bad review from someone who really doesn’t like you.

What John of Nikiû, who lived more than two hundred years after Hypatia died, actually wrote about her:

In those days a female philosopher appeared in Alexandria, a pagan named Hypatia, and she was completely devoted to magic, astrolabes and music instruments, and she deceived many people through (her) Satanic wiles.

There appears to be something of a discrepancy here between the two accounts!

As violence between Christians, Jewish residents, and Pagans grew, Hypatia assigned herself the task of updating, recording, and safeguarding the mathematical and astronomical knowledge of her age.

This is pure fantasy and has no basis in the known historical facts.

Her fate was sealed in 391 CE, when Emperor Theodosius I issued a decree directing the burning of all Pagan temples. 

Let us see what Wikipedia has to say about Theodosius and pagans: 

Although Theodosius interfered little in the functioning of traditional pagan cults and appointed non-Christians to high offices, he failed to prevent or punish the damaging of several Hellenistic temples of classical antiquity, such as the Serapeum of Alexandria, by Christian zealots. 

We appear to have a contradiction and I know which version I think is correct.

Armed with this acquiescence, Theophilus, bishop of Alexandria, ordered that the center of learning be destroyed. He and his followers carried out the decree, dealing massive destruction to the grounds. Theophilus then ordered a church to be built on the site.

More than 20 years later, in the year 412, he ordered the pillaging of the Serapeum or Temple to Serapis, the Pagan protector of Alexandria. This would prove prophetic. 

We have accounts of Theophilius destroying a hidden pagan temple and his followers mocking the pagan artifacts, which led to a riot during which the pagans withdrew to the Serapeum, which Theophilius then destroyed. I know of no center of learning that he supposedly destroyed. The Serapeum had probably earlier been a smaller daughter library to the Library of Alexandria but no longer fulfilled this function when it was destroyed by order of Theophilius, not in 412 but in 391. 

There is no center of learning involved. The Serapeum was a center for the Neoplatonism of Iamblichus a rival group to the Neoplatonism of Plotinus to which Hypatia adhered. Theophilius actually tolerated Hypatia’s school, so hardly prophetic.

Cyril, Theophilus’s nephew, was named bishop of the region, and he launched a campaign against Pagan temples and set about expelling the Jewish population from Alexandria. Civil unrest between Pagans, Christians, and the Jewish population broke out into years of violence in the city.

In March 415, followers of Cyril ransacked the remaining classrooms and study rooms, destroying what remained of the greatest institution of learning in the ancient world.

This paragraph is pure fantasy. The Mouseion, which I assume is being referenced here, had ceased to exist a couple of hundred years earlier.

The crowds ambushed Hypatia as she rode through the city. The last great scientist and science educator of the ancient western world was flailed, dismembered, and her remains were paraded through the city and burned in a mockery of Pagan funerary rites.

Hypatia was not “the last great scientist and science educator of the ancient western world.” She wasn’t even a great scientist. 

Hypatia’s brutal murder marked the end of science in the west for a thousand years. Europe soon fell into ten centuries of intellectual stagnation that would not lift until the Scientific Renaissance in the middle of the 15th Century. 

Remember that myth at the beginning? This whole paragraph is totally and utter hogwash! We have the classic myth about a thousand-year gap in the history of science from 500 CE to 1500 CE. To counter this rubbish, I could recommend several books e.g. Stephen C. McCluskey, “Astronomies and Cultures in Early Medieval Europe (CUP, 1998), Seb Falk, The Light Ages: The Surprising Story of Medieval Science, (W.W. Norton, 2020), or Edward Grant, Science & Religion 400 BC –AD 1550: From Aristotle to Copernicus (Johns Hopkins University Press, 2004).

Today, Hypatia stands as an example to all science educators to connect with their audience and with those around us. She also broke the gender barrier for science in ancient Europe, an accomplishment for feminism and women that would not be matched until the 18th Century.

We have entered the realm of Hypatia hagiography and mythology.

Hypatia of Alexandria dedicated her life to exploring the mysteries of the Cosmos, and relating her knowledge so that everyone could understand and learn. As darkness closed in on Alexandria, Hypatia spread the light of science for all humanity, and all time.

We are still in the realm of Hypatia hagiography and mythology.

She remains an inspiration to us all.

Does she?

How this was done:

We do not know exactly what Hypatia of Alexandria or the institution looked like, but there are descriptions in ancient texts, as well as modern insights based on contemporary technologies and insights into history and genetics.

The Cosmic Companion used Chat-GPT to merge information from both ancient and modern sources into the most accurate description of her we could produce.

Facts were checked and cross-referenced with accounts from reliable sources, including Encyclopedia Brittanica, The Smithsonian Institution, and National Geographic. The resulting text was translated, as closely as possible, into a prompt for the artificial intelligence graphics engine MidJourney.

Text was created by a similar AI/human process.

Given the explanation above, what this demonstrates is that you get the results based on the quality of the sources you use, a truism for all historical research, and it is painfully clear that the sources used in this case were totally crap. According to the computer programming rule GIGO­–garbage in, garbage out–here Chat-GPT has used garbage sources and produced a garbage text.

If I was grading this apology for an essay as a piece of work handed in by a student, it would of course garner a big fat for fail.Not only is it factually a total disaster area but it is from style a bizarre collection of fragmentary paragraphs that don’t even add up to a coherent whole. If this is the best that Chat-GPT can do even with human editing, then historians have nothing to fear from this AB i.e., Artificial Bullshit


Filed under History of science, Myths of Science, Uncategorized

Horrocks Bollocks!

The HISTSCI_HULK was gently easing his way into Monday morning, occasionally glancing over my shoulder at my Twitter stream, when a link posted in my notifications by the Aussie AnthropoidTM, John Wilkins, caught his eye. Before I could stop him, I knew no good could come of it, he had clicked on the link and as he read the linked article from The Observer, the steam started coming out of his ears. 

Romanticised Victorian painting of Horrocks making the first observation of the transit of Venus in 1639. No contemporary portraits of Horrocks survive Source: Wikimedia Commons

The article is titled The forgotten maths genius who laid the foundations for Isaac Newton and is about the early seventeenth-century, English astronomer Jeremiah Horrocks, whom I honoured with a blog post back in 2009. The article is occasioned by the fact that somebody has written a stage play about him entitled simply, Horrox, presented as part of the Cambridge Festival 2023.

The lede to the article is:

A new play explores the short life of Jeremiah Horrocks, whose astonishing discoveries ‘changed the way we see the universe’

This is total hyper-bollocks as old Hulky is fond of screaming, when he gets really worked up. Horrocks made some important contributions to the development of astronomy in the early seventeenth century but none of them ‘changed the way we see the universe’.

The opening paragraph is OK…

On a cloudy afternoon in England in 1639, 20-year-old Jeremiah Horrocks became the first person to accurately predict the transit of Venus and measure the distance from the Earth to the sun.

But in the next paragraph the whole think develops into a major trainwreck of astronomical proportions:

His work proved, for the first time, that Earth is not at the centre of the universe, but revolves around the sun, refuting contemporary religious beliefs and laying the foundations for Isaac Newton’s groundbreaking work on gravity.

His work did nothing of the sort, but the claim gets repeated as a direct quote from the author of the play David Sears, a couple of paragraphs further on:

Now, a new play, Horrox, will attempt to reassert Horrocks’s rightful place in history as a British genius who, according to the playwright David Sear, “changed the way we see the universe”.

“We had no idea of the scale of the universe until Jeremiah Horrocks,” said Sear. “He was the first person to prove that the Earth was not the centre of creation, destroying key precepts of Christian teachings and the primacy of a literal interpretation of the Bible in the process.”

By the time poor old Hulky got this far in the article he was incandescent.

Sears is obviously under the mistaken impression that Horrocks’ observation of the transit of Venus was the first proof that Venus orbits the Sun and that this is a proof of the heliocentric model of the cosmos. Neither of these statements are true, as regular readers of the Renaissance Mathematicus will already know. 

Telescopic observations of the phases of Venus by Thomas Harriot, Simon Marius, Galileo, and the Jesuit astronomers of the Collegio Romano, all made around 1611, so twenty-eight years before Horrocks observed the transit, had proven that Venus orbits the Sun and not the Earth. This is, however, totally consistent not only with a heliocentric model, but also with a geoheliocentric model, in which several or all the other planets orbit the Sun, which in turn orbits the Earth. 

Sears also gets Horrocks’ determination of the astronomical unit (AU), distance between the Earth and the Sun, wrong. He says:

“The only way you could measure the distance to the sun at the time was by getting an object to fix on, between the Earth and the sun, and then triangulating through,” said Sear.

I’m not going to go through the method in detail that Horrocks used, it occupies several pages of Albert van Helden’s excellent Measuring the UniverseCosmic Dimensions from Aristarchus to Halley (University of Chicago Press, 1985), which I recommend if you want all the grisly details, but Horrocks did not use triangulation as claimed here by Sears but a highly speculative method based on the diameters of the planets (he had measured the diameter of Venus during the transit) and a theory of Kepler’s that the diameters of the planets was proportional to their distance from the Sun. Using this highly dubious calculation he arrived at a figure of 59 million miles, much bigger than previous determinations but still well short of the actual value of 93 million miles.

We now get some more hyper-bollocks from Sears:

In 1687, Newton acknowledged the importance of Horrocks’s observations in his Principia: “Newton wouldn’t have been able to complete his work on gravity, if Horrocks hadn’t done these observations at the time he did,” said Sear. “Newton relied on this earlier work.”

Neither Horrocks’ observations of the transit of Venus nor his determination of the AU appear anywhere in Newton’s Principia. There are a couple of very brief references to the solar parallax value of Flamsteed and Horrocks, which Newton originally rejected but then latter adopted. Beyond this Horrocks’ main contribution to Newton’s work was his model for the Moon’s orbit around the Earth, which Sears nowhere mentions. Kepler, perhaps wisely, had not included the Moon’s orbit in his elliptical model of heliocentricity. Horrocks was the first to adopt an elliptical orbit for the Moon, which Newton briefly acknowledges in passing. Newton, in his failed attempts to make the Moon fit his model of universal gravity, used Flamsteed’s values for the lunar apogees, which he states are, “adapted to the hypothesis of Horrocks.”  These are literally the only references to Horrocks in the whole of the Principia. This doesn’t quite seem to fit Sears’ grandiose claims. 

Sears really piles on the pathos when it comes to the posthumous publication of Horrocks’ Venus in sole visa (Venus seen on the Sun).

Despite this, Horrocks’s great treatise on the transit of Venus was nearly lost for ever. Only a Latin manuscript survived the ravages of the civil war and the Great Fire of London. Passed from one astronomer to another for 20 years after Horrocks’s death, it would not be published until 1662, in an appendage to a Polish astronomer’s work.

Firstly, I strongly suspect that there were several copies of Horrocks manuscript made by Nos Kepleri the group of English supporters of the Keplerian model of the cosmos founded by Horrocks. It was John Wallis, who was a contemporary of Horrocks’ at university, who sent a copy of the manuscript to that Polish astronomer, who was none other than Johannes Hevelius, Europe’s most prominent astronomer, meaning Horrocks’ text got maximum exposure. Those who have been paying attention and remember their school history lessons will have noticed that Hevelius published Venus in sole visa in 1662, whereas the Great Fire of London was first four years later in 1666. It should also be noted that the Royal Society published Horrocks’ Opera Posthuma edited by William Crabtree and John Flamsteed in 1673.

Sears now tries his hand at a bit of biography:

Horrox, which will run in Cambridge’s ADC theatre from 28 March to 1 April as part of the   Cambridge Festival, begins in 1632 as Horrocks makes his way to university in the city on foot. Sear said: “At the age of 14 or 15 – no one’s quite sure – he walked to Cambridge from Lancashire, to study the stars.”

The son of a watchmaker, who was largely self-taught, Horrocks worked as a sizar while studying at Cambridge, serving his fellow students and even emptying their bedpans to pay his way. “He begged and borrowed books from the various Cambridge colleges, and left without a degree, probably because he’d run out of things to read,” said Sear. 

The Aspinwalls, Horrocks maternal grandparent, with whom his father worked, were very successful and wealthy watchmakers, so it is very unlikely that Jeremiah walked from his home in Toxteth Park to Cambridge. Both the Aspinwalls and the Horrocks were highly educated and not self-taught. They were also very strict Puritans, which would have explained why he was a sizar at Cambridge. Puritan ethics dictating that if you wanted a university education you worked for it and didn’t get it served up on a plate. Horrocks is known to have enquired about the latest and best book on astronomy, which would explain Sears’ “begged and borrowed books.” It is not known why he left university without a degree.

Sears makes a last attempt in this article for the most hyper-bollocking statement possible:

At his age, understanding the maths he did, making these amazing observations on rudimentary telescopes and then drawing conclusions that overturned established religious and scientific beliefs about the nature of the universe – he was a genius and 400 years ahead of his time.”

Jeremiah Horrocks was an intelligent and astute astronomer, but he did not overturn any “established religious and scientific beliefs about the nature of the universe,” and I fail to see how he was in anyway “400 years ahead of his time.”

The pain continues. On the webpage for the play Horrox. Here Sears writes:

The arc of his life is shown in parallel with that of his main inspiration, Johannes Kepler, the Copernican astronomer- mathematician who measured the movement of the planets. Kepler, called a heretic by the world, served three Holy Roman Emperors and a Duke (and wasn’t paid for his labours by any of them).

Kepler had his religious differences with the Lutheran Church because of his liberal ecumenical views but he wasn’t called a heretic by anybody. Whilst Kepler, at times, had difficulties getting the monies due to him from the Imperial treasury, to say that “wasn’t paid for his labours by any of them” is a crass exaggeration. 

Sears delivers up a splendid example of how not to do the history of science. He appears to have gathered a small collection of half facts that he doesn’t really understand and woven a third-rate fairy story out of them. Apparently, the Observer doesn’t believe in fact checking and appears to believe that its readers will swallow any old garbage.  


Filed under History of Astronomy

Ptolemy the pagan

The descriptive panel below, from the Museum of the Bible in Washington DC was posted on Twitter by the historian of Chinese astrology, Jeffrey Kotyk, who posed the question, “I wonder whether Ptolemy would have considered himself “pagan”?”

Reading through the text I have several other comments and queries, but first I will address Jeffrey’s question. Ptolemy lived in the second century CE and was an Alexandrian Greek. At that point in time the Latin word pagan from pāgānus meant “villager, rustic; civilian, non-combatant”. Only in the fourth century did early Christians begin to refer to people who practiced polytheism, or ethic religions other than Judaism as pagans. The word pagan meaning “person of non-Christian or non-Jewish faith” first entered the English language around 1400 CE, so Ptolemy would definitely not have considered himself pagan.

Also referring to Ptolemy, one of the greatest mathematical polymaths of antiquity, as “scholar of the stars” is somewhat limited, not to say strange. The text then attributes a “passion for mathematics, geography, and astronomy” to him but leaves out optics, music theory, and, of course, astrology.  Strangely the opening paragraph seems to attribute those things that developed out of astronomy all to Ptolemy alone. What about all the other astronomers, geographers, mathematicians, who existed before Ptolemy, contemporaneously with him, and after him, didn’t they contribute anything?

Of the things listed, “the ability to navigate the earth, determine agricultural seasons, and organise time into days, months, and years,” only the first, navigation, can really be said to have grown out of astronomy. Systematic agriculture and with it, knowledge of the agricultural seasons predates mathematical astronomy by about six thousand years. Days are a natural phenomenon of which homo sapiens would have been aware since they first evolved, although I assume that animals are also aware of days. 

The same of course applies to the year of which every sentient creature that lives long enough becomes aware without any help from astronomers. Astronomers, of course, determined how many days there are in a solar year, but they took long enough to get it right.

Months are a completely different problem. If we are referring to lunar months, and after all the word month derives from the word for moon, then the same applies, as to days and years. Although the astronomers had the problem of how to align lunar months with solar years, they don’t fit at all, as became obvious fairly early on and you don’t really want to know about the history of early calendrics. Trust me you don’t, that way lies madness! If, however, we are referring to our current system of twelve irregular months fitted into the solar year, then, although the astronomers played a role, they are largely the result of political decisions.

As a result, the Church was able to use scripture and science to identify and commemorate holy days such as Easter.

Knowing something about the history of the determination of the so-called movable Christian holy days, I cringed when I read this very short paragraph. I will pass over it with the simple comment that these holy days are determined not identified and that determination was a very complex religio-political process stretching over several centuries and astronomers had very little to do with it, other than providing the date of the vernal equinox, which in early days was falsely considered to be the 25 March and providing lunar tables. 

I developed the most advanced geocentric model of the universe, at which I believed Earth was the center. 

This sentence is, of course, wonderfully tautological, geocentric meaning the earth is at the centre. The sentence is also, as Blake Stacey pointed out on Mastodon after I posted this, “not only redundant, it’s not even grammatical.”

My geocentric model of the universe was accepted until Copernicus, Galileo, and others introduced a heliocentric model.

Ptolemy’s model was extensively modified by a succession of Arabic astronomers and “the most advanced geocentric model of the universe” before Copernicus was that of the Austrian, Renaissance astronomer, Georg von Peuerbach (1423–1461), whose system Copernicus studied as a student. 

Galileo, who in reality contributed very little to the heliocentric model or to its acceptance, in fact by rejecting supralunar comets, which orbited the sun, and ignoring Kepler’s laws of planetary motions, he explicitly hindered that acceptance, gets a name check with Copernicus, whereas, Kepler, whose heliocentric model was the one that actually became accepted gets dumped under others!

This is a more than questionable piece of museum signage and I wish I could blame it on the religious nature of the museum but such ill researched signage is unfortunately too common. 


Filed under History of Astronomy, Uncategorized

Renaissance Science – LII

Another Renaissance Mathematicus series comes to an end a little more than two years after it began with the questions Renaissance Science? Which Renaissance? and eight weeks later, is there any such thing as Renaissance science and if so, what is it? Having established that we were talking about the Humanist Renaissance, which began in Northern Italy in the fourteenth century, as a literary movement, and expanded into other areas in the fifteenth and sixteenth centuries. I took the middle of the seventeenth century as its culmination. However, already in that early episode I ended thus:

A important closing comment is that there is actually a very high level of continuity rather than disruption from the High Middle Ages through the Renaissance and one can regard the Renaissance both as a phase of the Middle Ages but also of the Early Modern Period; all historical periodisations are of course artificial and also to some extent arbitrary.

Raphael’s School of Athens an idealisation of the Humanist Renaissance by one of it’s greatest artists

The School of Athens is a fresco by Raphael. The fresco was painted between 1509 and 1511 as a part of Raphael’s commission to decorate the rooms now known as the Stanze di Raffaello , in the Apostolic Palace in the Vatican. It depicts a congregation of philosophers, mathematicians, and scientists from Ancient Greece, including Plato, Aristotle, Pythagoras, Archimedes, and Heraclitus. The Italian artists Leonardo da Vinci and Michelangelo are also featured in the painting, shown as Plato and Heraclitus respectively.

The painting notably features accurate perspective projection, a defining characteristic of the Renaissance era. Raphael learned perspective from Leonardo, whose role as Plato is central in the painting. The themes of the painting, such as the rebirth of Ancient Greek philosophy and culture in Europe (along with Raphael’s work) were inspired by Leonardo’s individual pursuits in theatre, engineering, optics, geometry, physiology, anatomy, history, architecture and art.

Description and picture both taken from Wikipedia

I then posed the all-important question, is there such a thing as Renaissance science, and if so, what is it? If I wished to write a series of episodes about it, then I should first establish what it is I’m writing about. To give a brief summary of that episode I stated that in my defined period of Renaissance science, from c. 1400 to c. 1650, a crossover took place between academic book knowledge and the empirical and practical knowledge of the artisan, areas that had previously been separated from each other. This crossover was driven by external forces drawn from political, social, cultural, and economic developments. Added to this was the literary Humanist drive to recover the knowledge of classical antiquity, which didn’t restrict itself to works of literature but revived interest in many half-forgotten scientific texts. These two developments blended together to produce a new wave of empirical, practice orientated knowledge, which when theorised in a further evolution, which began in the sixteenth century following into the seventeenth led to the so-called scientific revolution. 

Having delineated an area that, I was happy to label Renaissance science, I then over the next forty-five episodes tried to expand on this theoretical definition by displaying how these changes developed in various areas of knowledge production. In the last two episodes I gave first a brief outline of the philosophical revivals that contributed to the downfall of the all-embracing Aristotelian philosophy of the medieval scholastics and then explained why I believe that the much-quoted Francis Bacon actually presented a summation of Renaissance science rather than pointing to the future and modern science as he is all too oft presented

Having defined a general development in the sciences that took place in the historical period I defined as the scientific Renaissance i.e., a period defined by the scientific development that took place during it, we now have to apply the same caution that we applied above to the time period itself. Expressed very simply, there is no point in time were people stopped doing medieval science and started doing Renaissance science. Equally there is no point in time were people stopped doing Renaissance science and started doing modern science. These developments were both gradual and included much takeover of thoughts and practices from one era into the other. A key concept here is continuity, although we must be careful not to evoke a Whig historical concept of progress. I will now look back at a couple of the topics we have discussed over the last two years and point out the threads of continuity that they contain.

I will start with the botanical gardens, in themselves part of the much wider complex of natural history, materia medica, medical education, and botany. As I pointed out the concept of the specialist, medicinal herb garden had already existed in antiquity, and had also been fostered in the medieval monasteries, whose gardens also served as a role model for the university botanical gardens that emerged in the Renaissance. Here, there was a change of emphasis, as well as serving as a practical resource for medicinal herbs, to save having to scavenge them from nature, the university botanical gardens served as a centre for teaching and research. Also, botanical gardens did not cease to exist with the advent of modern science but are still going strong, to quote Wikipedia:

Worldwide, there are now about 1800 botanical gardens and arboreta in about 150 countries (mostly in temperate regions) of which about 550 are in Europe (150 of which are in Russia), 200 in North America, and an increasing number in East Asia. These gardens attract about 300 million visitors a year.

The last sentence shows that botanical gardens now function as tourist attractions, the entrance fees helping to finance their upkeep. Although, the Renaissance botanical gardens also attracted a steady flow of visitors from all over Europe. The modern botanical gardens, many of which a government sponsored, are major scientific research centres and are networked worldwide to increase their effectivity, exchanging plants, seeds, and knowledge. This networking and scientific exchange was already developing during the Renaissance, albeit on a much smaller scale. 

As you can see there is a strong continuity in the concept and existence of botanical gardens from some point deep in antiquity down to the present day. However, that continuity is not a smooth curve but has suffered breaks and seen changes in the people operating them and the functions that they have fulfilled. 

I don’t intend to deal with all the topics that I have covered in the episodes of this series in the same way here, but I will bring one more example from a completely different area, mathematics and in particular algebra.

Although the word algebra is a comparatively modern coinage, stemming as it does from the title of a ninth-century book, al-Kitāb al-Mukhtaṣar fī Ḥisāb al-Jabr wal-Muqābalah (The Compendious Book on Calculation by Completion and Balancing) by the Persian mathematician, Muḥammad ibn Mūsā al-Khwārizmī (c. 780–c. 850), the commonly used definition for elementary algebra is to quote Wikipedia:

Historically, and in current teaching, the study of algebra starts with the solving of equations, such as the quadratic equation above. Then more general questions, such as “does an equation have a solution?”, “how many solutions does an equation have?”, “what can be said about the nature of the solutions?” are considered.

A definition that covers all of the algebra under discussion here.

Both the ancient Egyptians and Babylonians wrote about the solution of equations in their mathematical texts. The Babylonian’s even had a version of the general solution for quadratic equations as early as 1700 BCE. It is in a different form to that taught in schools today and of course only accepts positive solutions. Babylonian algebra grew out of the commercial arithmetic that they developed for their central, state-controlled economy.

We find our form of the general solution for quadratic equations with both positive and negative solutions in the Brāhma-sphuṭa-siddhānta (Correctly Established Doctrine of Brahma) of the Indian mathematician and astronomer Brahmagupta (c. 598­–c. 668) a text that did much to inform the work of al-Khwārizmī. 

Al-Khwārizmī’ s book was first translated into Latin by Robert of Chester in 1145 but initially had little impact in Europe. Algebra first became truly establish in Europe with the publication of the Liber Abbaci (The Book of Calculation) by Leonardo Pisano (c. 1170–c. 1245) in 1201. This established algebra as commercial arithmetic, which was then taught throughout Europe in so-called Abbacus schools to apprentice traders, in order to be able to calculate interest rates on loans, exchange rates of currencies when crossing borders, and profit shares in joint trading ventures, amongst other things. This had also been the primary use of algebra in Islamicate culture from whom Leonardo had directly taken his knowledge of the discipline. 

It was first in the sixteenth century, also within my defined timeframe for Renaissance science, that algebra first became recognised as a proper branch of mathematics during the disputes over the discovery of the general solutions of the cubic, and quartic equations. Some even refer to Cardano’s Ars Magna (Nürnberg 1543), a central text in those disputes, as the first modern mathematics book. Algebra only became truly establish as the core of analytical mathematics in the seventeenth century as part of the so-called scientific revolution. The sixteenth and seventeenth centuries also saw a gradual development from rhetorical algebra, written entirely in words, over syncopated algebra, with some symbolism, to our symbolic algebra.

Algebra, as the doctrine of the solution of equations, is of course a central element of the modern school mathematics curriculum. In German the general solution for quadratic equations is called the Mitternachtsformel (Midnight formula), because school children are expected to be able to rattle it off if woken up by their maths teacher at midnight. 

As I have outlined above algebra winds its way through history from at least 2000 BCE down to the present, changing in presentation, and function over the centuries. It is by no means a continuous evolution but continuity over time in its history is just as important, if not more so, that the developments in any given, artificially defined period such as the Humanist Renaissance.

What I hope I have made clear in this blog post is that, although historically useful, the concepts, of a time period that we call the Humanist Renaissance, and the developments in the sciences within that period, that I, following others, have chosen the define as Renaissance science, are artificial constructs and when we use them, we should be very much aware of the continuity that exists with the periods and the science within them, that exists both before and after our defined period. 


Filed under Renaissance Science

A masterclass in wide-ranging narrative history

 Long ago in another life, when I first became interested in, involved in, began learning, the history of science, the classic texts one was supposed to have read where all big books. Big theme books, big in scope and big in message. They covered deep periods of time and extensive areas of the evolution of a branch of science. All the big names had at least one big book and often more than one. Over time the big book went out of fashion, too general, too concentrated on big names and big events. They became replaced with close, detailed studies of one aspect of one corner of one discipline. 

Over the years, the Welsh historian of science, Iwan Rhys Morus has written a series of detailed studies of various aspects of nineteenth-century British science, in particular detailing the history of electricity. 2005 saw When Physics Became King (University of Chicago Press), 2011, Shocking Bodies: Life, Death & Electricity in Victorian England (The history Press), 2017, Michael Faraday and the Electrical Century (Icon Books), also 2017, Willian Robert Grove: Victorian Gentleman of Science (University of Wales press, and most recently, 2019, Nikola Tesla and the Electric Future (Icon Books) (reviewed here), with a raft of papers to similar topics both in journals and collected volumes in between. Now he has written and published as big book and what a book it is, How the Victorians Took Us to the MoonThe Story of the 19th-Centuiry Innovators Who Forged Our Future[1], covering as it does a very wide range of science and technology throughout the nineteenth century, it is an absolute master class in how to write wide-ranging, big theme, narrative history. 

Morus weaves internal history of science and technology together with the political, social, and cultural histories of science and technology into a single multidimensional, narrative strand that in not quite three hundred pages gives a densely packed, comprehensive overview of the development of the two disciplines in the nineteenth-century United Kingdom. A narrative that pulls the reader into that century and lets them breathe in the excitement and expectation that sparkles and crackles in the air generated by the future visionaries of Victorian Britain. 

The book is structured chronologically on two different but interrelated levels.  Each of the chapters, which are perhaps better described as sections, deals with a different aspect of the developments in the nineteenth century but taken together they describe an arc beginning in the late eighteenth and early nineteenth centuries science wars between the old guard Baconian naturalists gathered around Sir Joseph Banks, a gentleman’s club that dominated the Royal Society, Britain’s leading scientific institution, on the one side and the younger generation of Cambridge University mathematical scientists led by Charles Babbage and John Herschel, who believed that science should be carried out by those with expertise and not those with social privilege. Travelling topic by topic through the century the arc closes with the advent of powered, heavier than air flight at the end of the nineteenth century, beginning of the twentieth century. However, within each topic there is a second chronological arc tracing the development of that topic from its early gleam in the eyes of its initial innovators through to its final fruition as a successful trendsetting, future defining technology. 

The book opens with a science fiction vignette, describing the launch of the first British moon-landing mission in 1909 and closes with its successful return. Here Morus displays a quality of narrative writing that he maintains throughout the main text of the book, making it a pleasure to read, as well as both an entertaining and highly informative discourse. 

Following the opening chapter with its description of the war between the Banksian gentlemen of science and the Cambridge mathematical men of science, Morus takes to another arena of conflict between the much-heralded engineers such as the Stephensons and Brunels, who shaped the infrastructure of the Victorian future with their railways, ships, bridges and tunnels, and the craftsmen who actually constructed those railway lines, tunnels, and bridges. Morus delivers here a fine demolition of the big names, big events style of historiography. 

The third chapter illustrates the efforts to tame the new technology of electricity by fitting it with a solid quantified scientific corset. Defining the standards for the units of electrical potential, force and resistance and the laboratories and their researchers that grew out of those endeavours. Chapter four takes us into the wonderful world of the Victorian scientific and technological exhibitions in which innovators and inventors competed in their endeavours to persuade the general public and those in power to back their latest concepts designed to shape the future. Here we have everything from shop style exhibition spaces on the high street to the legendary spectacle that was the 1851 Great Exhibition of the Works of Industry of All Nations held in the specially constructed Crystal Palace.  

Chapter five is an object lesson in how quickly times change. It leads off with the euphoria that followed the introduction of the railways and how steam power was going to shape and revolutionise the future. A euphoria that was quickly pushed out of the way and replaced with exaltations for a future powered by the newest trend in energy, electricity. Both this and the previous chapter, on exhibitions, bring one of the book’s central themes to the fore, how the Victorians shaped their visions of the future based on emerging technology. 

Chapter six deals with one of the great technological leaps of the nineteenth century, long distance communication. Electrical signals, first through wires, the telegraph and then the telephone and finally through the air with the wireless telegraph. Here another central theme of the book is emphasised the role played by the British Empire, in nineteenth-century Britain, in the production of new technologies, and in the marketing and exploitation. The Empire provided much of the raw materials needed to produce new technologies and a world-wide market where the inventors and innovators could maximise their profits. Technologies such as the telegraph and wireless telegraphy were, of course, useful tools to control and govern the Empire.

Another useful tool for those in control and governance that came into general use in the nineteenth century were the mechanical and later electro-mechanical calculators. Chapter seven, which deals with those development, features one of my personal favourite Victorians, Charles Babbage, who had major vision for his computing machines, vision that would only be truly realised in our own computer age. However, the slightly simpler calculating machines provided the politicians with a tool to develop the realm of social statistics and plan for the future. 

As, stated earlier, the closing chapter deals with the history of manned flight. It was only in 1783 that the world saw the advent of unmanned and manned flights with both hot air and hydrogen balloons. The nineteenth century saw attempts to first power and steer balloons, rather than just letting them drift on the whims of the wind and then latter the development of the heavier than air aeroplane, including early plans to build steam powered flying machines. 

The book closes with an epilogue that opens with the account of the return of the successful British moon landing expedition that opened the book. Morus then poses the question, whether the Victorians really could have staged a Moon landing? The answer is of course no, but is it? As Morus tells us:

In that sense, at least, the Victorians really did take us to the Moon. When Apollo 11 took off from the Kennedy Space Center on 16 July 1969 – just 60 years after the scene imagined after the scene imagined at the beginning of this book – and when the Eagle landed on the lunar surface on 20 July, it really was the culmination of a technological fantasy that began with the Victorians. What this book has tried to describe is the emergence during the course of the nineteenth century of new ways of thinking of thinking about and organising science that were directed at the future in a wholly new and unprecedented way, and some of the consequences of that reorientation. It is, by and large, the way we think about and organise science now, and the book is also an invitation to think what it means that we still do things the Victorian.

Page 287

This paragraph summarises Morus’ book far better than I ever could in fact the entire epilogue is a better review of the book than the one that I’ve written. Maybe I should just have scanned and posted it instead.

The book is well illustrated with the now ubiquitous grayscale picture, which Victorian media delivers lots of. There are extensive end notes listing the sources used but, as has become quite common in recent years, there is no separate bibliography. The book closes with an excellent index. 

The title of this blog post reveals quite clearly what I think about this book but I’m now going to double down on it. Morus is a truly excellent writer and he has obviously invested much effort and thought in producing this jewel of a book. I have grown old and now read very slowly but I have had my nose stuck in a book since I was three years old and have over the decades read literally hundred of tomes. From time to time in my perusal of the world’s literature I have stumbled across a book that has left the deepest of impression on me. Such volumes are rare and with Iwan Morus’ latest publication I have added a new one to that brief list. If you study nineteenth century British history this book should be obligatory. As a case study for historians of science and/or technology it should probably also be obligatory. If you just like reading accessible, good quality, well written history books then you will love this one, so just acquire a copy and enjoy. 

[1] Iwan Rhys Morus, How the Victorians Took Us to the MoonThe Story of the 19th-Centuiry Innovators Who Forged Our Future, Icon Books, London, 2022

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Filed under Book Reviews, History of science, History of Technology

Renaissance Science – LI

One of the most ubiquitous figures in the history of science in the first half of the seventeenth century was Francis Bacon, 1st Viscount St Alban (1561–1626), jurist, and politician, who rose to become Lord High Chancellor of England.

Portrait of Francis Bacon by Paul van Somer 1617 Source: Wikimedia Commons

A prolific author of polemical text, he gets labelled the father of empiricism, the father of the scientific method, and even the father of modern science. Regular readers of this blog will know, without asking, that I reject all three labels. In fact, I go much further, rejecting the deification of Francis Bacon in the hierarchy of modern science. First, and it gets said far too little, Bacon was not a scientist and secondly, he didn’t even understand science or, if it comes to that the scientific method. In my opinion, Bacon is not the signpost to the future of science that his fans claim him to be, but someone, who looks back at the development in science that had taken place in the recent past and collated, idealised, and systemised them, whilst projecting them into an imaginary future.  

Bacon’s record on the leading scientific developments in the early seventeenth century is so abysmal that it is difficult to understand how anybody ever took him seriously as a philosopher of science. 

His attitude to the already advancing mathematisation of the sciences was to say the least retrograde or even reactionary. In his writings he, like Aristotle, says that pure mathematics has no place in natural philosophy, because its objects are not material. At one point he specifically rejects the developments that had been made in algebra, as it had not been well perfected. He, also like Aristotle, allows mixed mathematics, even acknowledging an increasing list of areas where this applies listing, perspective, music, astronomy, cosmography, architecture, engineering, and diverse others. This list encapsulates many of the developments during the Renaissance that we have examined in various episodes of this series. However, he only allows mathematics a measuring role in the, for him all important, empirical investigations, but not a determining or philosophical one. It should, however, be noted that in his own examples of empirical investigations there are no quantitative tables of measurement. His attitude to the role of mathematics is best illustrated by his rejection of Copernican astronomy. Bacon feared abstract reasoning not based upon experience, and rejected purely theoretical science such as Copernican astronomy, a purely mathematical model. A model for which there was no empirical, observational evidence. One must admit, a fairly reasonable argument at the time.

Bacon rejected another important milestone in the history of science, William Gilbert’s De Magnete, which had been published in 1600. This was a work solidly based on experience, experiments, and empirical observations, so one would have thought that it would be acceptable to Bacon, but this was not the case. He criticised Gilbert heavily because although based on a wealth of experiments, he had made a philosophy out of the loadstone, indulging in extravagant speculation.

Perhaps surprisingly, Bacon also raised serious doubts about both the telescope and the microscope, empirical research instruments. He found Galileo’s initial telescopic discoveries admirable, but then there was nothing more and he thus found the handful of discoveries suspicious because they were so few and had then petered out. As I’ve noted elsewhere there was indeed a lull after 1613 in telescopic discoveries, which lasted until astronomers adopted the astronomical telescope, which had a much greater magnification than the original Dutch or Galilean telescope. Bacon, who was not an optician or astronomer, had no real understanding of that which he was criticising. His doubts concerning the microscope can possibly be excused as he died much to early to see any real results of microscopic investigations, although I wonder if he attended any of Cornelis Drebble’s public demonstrations of his Keplerian microscopes in the early 1620s.

There are three major publications outlining Bacon’s views on education, which include his views on natural philosophy and his thoughts on how it should be practiced i.e., his much-praised methodology. The first of these is his The Advancement of Learning from 1605. This is a polemic advocating for a general state sponsored education. The emphasis in this polemic is very much on religion and civics. There is very little in this work that in anyway relates to the developing sciences of the period and his highly abstract discussion of natural philosophy is, for a man who supposedly dethroned Aristotle, highly Aristotelian. 

Title page Source: Wikimedia Commons

It is in fact first in his Novum Organum from 1620 that he seeks to dethrone Aristotle replacing, as the title states Aristotle’s Organon, his six books on logical analysis, which underly his physics, that is the description of nature, with Bacon’s own new empirical inductive logic, which is so often falsely claimed to be “the” modern scientific methodology.

Title page Source: Wikimedia Commons

There of course being no singular scientific method and also those who believe there is one describe something very different to Bacon’s model. Bacon rejects Aristotle’s top-down methodology, which starts with supposedly obvious first principle or axioms to which deductive logic is systematically applied until one arrives at empirically observed facts. He wishes to replace it with a bottom-up system, which starts with empirically observed facts and then uses inductive logic to arrive at general statements derived from those facts. 

Bacon’s system is very naïve and primitive and consists of creating lists of empirical observations. For a given phenomenon, the example Bacon uses is heat, he collects in a list all the empirical instances where heat occurs. He then complies a second list of all the instances where heat doesn’t occur. This is of course a major problem as, whilst not infinite, such a list would be impossibly long, so he makes some arbitrary decisions to reduce the list. He then compares the properties of the lists to eliminate any that appear in both lists. Finally in the parred down list of heat occurrences he removes those properties that are not in all instances, for example light, which is in fire but not in hot water. In the list that is left over the form (cause) of heat should naturally emerge. He explicitly warns against speculating too far from the acquired evidence. 

This is of course not how science works. Is it argued that Bacon plays an important role in the development of the scientific method because he suggests experimentation as a method to produce more empirical instances. Of course, Bacon is not the first to introduce experimentation into scientific research, alchemy, which Bacon disdained, had been using experimentation for centuries and experimental laboratories were a feature of Renaissance science. Bacon’s insistence on empirical observation and induction appears to me to be a very similar, but formalised, approach to that of the work of the Renaissance researchers, who developed the materia medica and botany. 

I think the best comment on Bacon’s approach was supposedly made by William Harvey, in his Brief Lives, John Aubrey tells us that Harvey:

“had been physitian to the Lord Chancellour Bacon, whom he esteemed much for his witt and style, but would not allow him to be a great Philosopher. Said he to me, ‘He writes Philosophy like a Lord Chancellour,’ speaking in derision, ‘I have cured him.'”

One of the most often referenced of Bacon’s texts in his utopia, The New Atlantis, the House of Salomon in which supposedly inspired the foundation of the Royal Society. It was never completed and first published posthumously.

Title page Source: Wikimedia Commons

In the modern English version that I own, it is forty-nine pages long and the first thirty-six pages tell the story of a ship blown of course arriving at the Island of Bensalem, apparently Bacon’s concept of an ideal society. I’m not going to describe the culture of Bensalem, which appears to me to be basically a form of theocracy but will briefly sketch his account of the House of Salomon. The official of the House of Salomon, who gives a verbal guided tour to the book’s narrator, a member of the ship’s crew, who is not more closely identified, just rattles of long lists of all the wonderful things that each section or division of the house contains. There is no real attempt to describe the science that produced these wonders or explain the methodology behind them. In general, large parts of this pean to the scientific achievements of the Bensalemites read like an idealised cross between the Renaissance botanical gardens of Northern Italy and the curiosity cabinets of the German aristocrats. In fact, elsewhere Bacon suggests that systemised curiosity cabinets could be used for his type of inductive scientific research. Some of them, such as that of Rudolf II, were already used for scientific research but not using Baconian methodology.

Returning to my original position, I contend that Bacon is not the father of modern science shining a methodological beacon into the future of scientific research but rather a man with very little real understanding of how science works, who held up a mirror, which reflected various aspects of the Renaissance science that had preceded him.


Filed under Early Scientific Publishing, Renaissance Science

The Renaissance Mathematicus has lost a good friend.

Today, I learnt the sad news of the death of Renaissance Mathematicus friend Tom McLeish. This didn’t come as a surprise, as I have known for several months that Tom was suffering from terminal cancer and was in palliative care. 

The official University of York photo announcing Tom’s appointment as Professor of Natural Philosophy in the Department of Physics

They say that opposites attract and you can’t get much more opposite than Tom and I. Tom was a highly successful Professor of physics with a worldwide reputation, the founder and co-director of a prestigious history of science research project at Durham University, and a world class science communicator, who was appointed Professor of Natural Philosophy at York University, as an academic you can’t get much further up the greasy pole than Tom did. I am a two-time university drop out with virtually no formal qualifications, who presents himself to the world as a history of science rebel and mischief-maker. Tom was always socially correct and conservatively dressed in public, often in blazer, with collar and tie. I haven’t owned, let alone worn, a tie for more than fifty years. I’m an earring wearing, aging hippie, nearly always clothed in hoody and jeans, who will put on a collarless, grandad shirt, and waistcoat for a public lecture. Tom loved classical music. I’m a Deadhead and free jazz fan. Tom was openly and deeply religious. I’m the life-long atheist son of an atheist father and agnostic mother. But, and it’s a big but, we were good even close Internet friends.

The meeting point was of course history of science and science communication to which we both devoted a lot of time and effort. I first came across Tom through his Ordered Universe Project, an in-depth study of the work of the thirteenth century cleric, theologian, and philosopher Robert Grosseteste, who made important contributions to the evolution of medieval science. At first, I thought Tom’s work was presentist, but soon came to realise that it was anything but and became a fan of the project’s output. At the same time Tom became a fan of this blog, which I found more than somewhat flattering. 

The mutual admiration grew over the years and developed into a strong Internet friendship, which reached a highpoint, when I invited Tom to write a guest post here at the Renaissance Mathematicus criticising an essay in the BBC Proms guide in 2019, on the historical relationship between astronomy and music, an apt topic for this blog.

Now Tom has gone the way of all flesh and I know that I am not the only member of the Internet history of science and science communication community who will sorely miss him. If the God that he so ardently believed in does exist, then I know that Tom will have truly gone to meet his maker. Tom was one of a kind and the world is a little poorer following his departure. 


Filed under Autobiographical

Mathematicall Lecturer to the Citie of London 

The so-called European Age of Discovery is usually considered to have begun as adventurers from the Iberian Peninsular began to venture out into the Atlantic Ocean in the fifteenth century, reaching a high point when Bartolomeu Dias (c. 1450–1500) first rounded the southern tip of Africa in 1488 and Christopher Columbus (1441–1506) accidentally ran into the Americas trying to reach the Indies by sailing west. Those who made successful voyages, basically meaning returned alive, passed on any useful information they had garnered to future adventurers. It would be first at the end of the sixteenth century that the governments of the sea faring nations first began to establish central, national schools of navigation that accumulated such navigational and cartographical knowledge, processed it, and then taught it to new generations of navigators. Through out the sixteenth century individual experts were hired to teach these skills to individual groups setting out on new voyages of discovery. 

In England this function was filled by Thomas Harriot (c. 1560–1621), who not alone taught navigation and cartography to Walter Raleigh’s sailors but also sailed with them to North America, making him that continent’s first scientist. John Dee (1527–c. 1608) supplied the same service to the seamen of the Muscovy Trading Company, although, unlike Harriot, he did not sail with them. Richard Hakluyt (1553–1616), a promotor of voyages of discovery, collected, collated, and published much information on all the foreign voyages but only passed this information on in manuscript to Raleigh. 

In the 1580s Dee disappeared off to the continent, Harriot after returning from the Americas disappeared into the private service of Henry Percy, 9th Earl of Northumberland (1564–1632) and Hakluyt, a clergyman, after returning from government service in Paris, investigating the voyages of the continental nations, went into private service. In Paris, in 1584, Hakluyt noted that there was a lectureship for mathematics at the Collège Royal and wrote a letter to Sir Francis Walsingham (c. 1532–1590), the Queen’s principal secretary, the most powerful politician in England and a major supporter of voyages of discovery. In his letter, Hakluyt, urged Walsingham to establish a lectureship for mathematics at Oxford University for scholars to study the theory of navigation and the application of mathematics to its problem, and a public lectureship of navigation in London to educate seamen. 

Walsingham undertook nothing and the demand grew loud for some form of public lectureship in mathematics to supply the necessary mathematics-based information in navigation and cartography to English seamen. In 1588, a private initiative was launched by Sir Thomas Smith (c. 1558–1625), Sir John Wolstenholme (1562–1639), and John Lumley, 1st Baron Lumley and Thomas Hood (1556–1620) was appointed Mathematicall Lecturer to the Citie of London. 

Thomas Hood, baptised 23 June 1556, was the son of Thomas Hood a merchant tailor of London. He entered Merchant Taylors’ School in 1567 and matriculated at Trinity College Cambridge in 1573.  He graduated BA c. 1578, was elected a fellow of Trinity and graduated MA in 1581. He was granted a licence to practice medicine by Cambridge University in 1585 and, as already mentioned, lecturer for mathematics in London in 1588. This appointment and his subsequent publications indicate that he was a competent mathematical practitioner but from whom he learnt his mathematics is not known.

Before turning to Hood’s lectureship and the associated publications, it is interesting to look at those who sponsored the lectureship. Thomas Smith was the son and grandson of haberdashers and like Hood attended Merchant Taylors School, entering in 1571.

Source: Wikimedia Commons

He entered the Worshipful Company of Haberdashers and the Worshipful Company of Skinners in 1580 and went on to have an impressive political career in the City of London, occupying a series of influential posts over the years. His father had founded the Levant Trading Company and Thomas was the first governor of the East India Company, when it was founded in 1600, but only held the post for four months having fallen into suspicion of being involved in the Essex Rebellion. He was reappointed governor in 1603 and with one break in 1606-7 remained in the post until 1621. Later, he was a subscriber to the Virginia Company, as was Hood, and obtained its royal charter in 1609 and became the new colony’s treasurer making him de facto non-resident governor until his resignation in 1620. His grandfather had founded the Muscovy Company and Smith also became involved in that. It’s easy to see why Smith was motivated to promote a lectureship in practical mathematics.

John Wolstenholme was cut from a very similar cloth to Smythe, son of another John Wolstenholme a customs’ official in London, he became a rich successful merchant at an early age.

An effigy of Sir John Wolstenholme (1562 – 1639), carved by master stone mason to Charles I, Nicholas Stone, for the old St John the Evangelist Church, Great Stanmore Source: Wikimedia Commons

Like Smythe a founding member of both the East India and Virginia Companies, he was also a strong supporter of the attempts to find the North-West Passage. He fitted out several of the expeditions, Henry Hudson (c. 1556–disappeared 1611) named Cape Wolstenholme, the extreme northern most point of the province of Quebec after him. William Baffin (c. 1584–1622) named Wolstenholme Island in Baffin Bay after him.

John Lumley was slightly different to the two powerful merchants, a member of the landed gentry, he was an art collector and bibliophile.

John Lumley 1st Baron Lumley portrait attributed to Steven van de Meulen Source: Wikipedia Commons

In the same year 1582, that the three founded Hood’s mathematical lectureship, Lumley founded with Richard Caldwell (1505?–1584), a physician, the Lumleian Lectures. Initially intended to be a weekly lecture course on anatomy and surgery they had been reduced to three lectures a year by 1616. They still exist as a yearly lecture on general medicine organised by the Royal College of Physicians.

The mathematical lectures finally came into being in 1588, following the threat of the Spanish Armada in that year. The original intended audience consisted of the captains of the city’s train bands or armed militia but also open to the ship’s captains, who rapidly became the main audience. The lectures were on geometry, astronomy, geography, hydrography, and the art of navigation. The lectures were originally held in the Staplers’ Chapel in Leadenhall Street but later moved to Smith’s private residence in Gracechurch Street, where he had held the inaugural lecture. In total Hood lectured for four years and later he attempted to obtain license to practice medicine in London from the Royal College of Physicians. This was denied him due to his inadequate knowledge of Galen. He was finally granted a conditional licence in 1597 and sometime after that he moved to Worcester, where he practiced medicine until his death in 1620. 

His first publication was his inaugural lecture under the title, A COPIE OF THE SPEACHE: MADE by the Mathematicall Lecturer, unto the Worshipful Companye present. At the house of the Worshipfull M. Thomas Smithdwelling in Gracious Street: the 4. of November, 1588. T. Hood. Imprinted at London by Edward Allde.

In this lecture he set out the reasons for the establishment of the lectureship and emphasised the importance of mathematics to people in all walks of life. He also sketched a history of mathematics from Adam down to his own times. The lectures were obviously successful, and he was urged to publish them, which he did to some extent.

His next major publication was The VSE OF THE CELESTIAL GLOBE IN PLANO; SET FOORTH IN TWO HEMISPHERES: WHEREIN ARE PLACED ALL THE MOST NOTa[ble] Starres of the heauen according to their longitude, latitude, magnitude, and constellation: Whereunto are annexed their names, both Latin Greeke, and Arabian or Chaldee; … (1590) They don’t write title like that anymore.


There is also an advert explaining that one can buy the hemispheres from the author at his address. He explains that he has presented the celestial spheres in plano in order to make it easier for seamen to read off the longitude and latitude of stars than it would be from a small globe. His beautifully coloured planispheres are the first printed planispheres in England. A seaman who bought Hood’s planispheres no longer needed to buy a celestial globe or planispheric astrolabe. 

Thomas Hood celestial sphere in plano northern hemisphere Source
Thomas Hood celestial sphere in plano southern hemisphere Source

Before he published The Use of the Celestial Globe, he published a pamphlet on the use of a novel cross-staff that he had devised. Hood’s cross staff was a significant step towards the back staff, which eliminated the necessity of looking directly into the sun to take readings. This was so successful that he was urged to produce a similar pamphlet for the Jacobs Staff, and he obliged publishing two pamphlets in 1590, The vse of the two Mathematicall instrumentes, the crosse Staffe … and the Iacobes Staffe in two parts with separate titles. The pamphlets attracted the attention of the Lord Admiral, Lord Howard (1536–1624), who became his patron. Hood dedicated a second edition of the double pamphlet to Howard in 1596. 

Thomas Hood cross staff Source: Wikimeia Commons

Hood’s finally publication of 1590 was a translation of The Geometry of Petrus Ramus, THE ELEMENTES OF GEOMETRIE: Written in Latin by that excellent Scholler, P. RamusProfessor of the Mathematical Sciences in the Vuniverstie of ParisAnd faithfully translated by Tho. Hood, Mathematicall Lecturer in the Citie of London. Knowledge hath no enemie but the ignorant

Like many others in this period, Hood’s books were written in the form of dialogues between a master and a student, and he continued in this form with his next book on the use of globes in 1592. Serial production printed celestial and terrestrial globes had been in existence on the continent since Johannes Schöner (1477–1547) had produced the first pair in the second decade of the sixteenth century but none had been produced in England. Probably at the suggestion of John Davis (c. 1550–1605), a leading Elizabethan navigator, the London merchant William Sanderson (c. 1548–1638) commissioned and sponsored the instrument maker Emery Molyneux (died 1598) to produce the first English printed pair of globes, in the early 1590s. The globe gores were printed by the Flemish engraver Jodocus Hondius (1563–1612), at the time living in exile in London, who would go on to found one of the two largest publishing houses for maps and globes in Europe in the seventeenth century

Sanderson request Hood to write a guide to the use of such globes and Hood complied publishing his THE VSE of both the Globes, Celestiall, and Terrestriall, most plainely deliuered in forme of a Dialogue. Containing most pleasant, and profitable conclusions for the Marinerand generally for all those, that are addicted to these kinde of mathematicall instrumentes in 1592. 

In the same year Hood edited a new edition of the popular navigation manual A Regiment for the Sea by William Bourne (c. 1535–1582) which was originally published in 1574. Hood edition would be printed in two further editions.

In 1598 Hood published his The Making and Use of the Geometricall Instrument called a sector, the first printed account of this versatile instrument, which almost certainly informed the much more extensive account of the sector by Edmund Gunter (1581–1626) published in 1624. 

Astronomical sector, 16th-century artwork. This device was used to make accurate observations of the position of an object in the sky, such as a star or the Sun. The sight (lower left) would be used to line up the hinged rulers (right) with the object being observed. The position of the star was recorded as an angle from the vertical or horizontal, as read from the curved area (left). Artwork from ‘The making and use of the geometricall instrument, called a sector’ (1598) by Thomas Hood.

Hood’s most peculiar publication was an English translation of the Elementa arithmeticae, logicis legibus deducta in usum Academiae Basiliensis. Opera et studio Christiani Urstisii originally published in 1579. Christiani Urstisii was the relatively obscure Swiss mathematician, theologian, and historian Christian Wurstisen (1544–1588).

Why Hood stopped his lectures after four years in nor clear, he seems to have been both popular and successful and later Smith and Wolstenholme would later employ Edward Wright (1561–1615), who we will meet again in the next post in this series, through the East India Company in the same role. However, after he ceased lecturing Hood continued to sell instruments and his hemisphere charts. Hood’s lectureship was an important step towards the professional teaching of navigation to mariners in England at the end of the sixteenth century. 


Filed under Early Scientific Publishing, History of Astronomy, History of Cartography, History of Navigation