Category Archives: Renaissance Science

A Renaissance artist-engineer icon – Vitruvian Man

Leonardo da Vinci’s drawing of Vitruvian Man is one of the most well known graphic images in the world. Many people don’t even know the title I have used for the image and of those that do, many have no idea why it’s so called. Even less people are aware that the image is not unique or original to Leonardo, although his rendition is probably the most beautiful and most powerful, but is in fact an iconic concept in the work of Renaissance artist-engineers.

The origin of the Vitruvian Man is to be found in Vitruvius, De architectura (Ten Books of Architecture).[1] Vitruvius lived in ancient Rome in the first century BCE and his Ten Books of Architecture is the only known full treatise on architecture that we have from classical antiquity. Almost nothing is known about Vitruvius himself and even the full name that tradition has accredited him with, Marcus Vitruvius Pollio, is questionable the name Vitruvius being the only part that is certain. Although the book is nominally about architecture more than half of the text is about things we would not normally associate with a textbook on architecture such as astronomy, geography and natural philosophy to quote Tomas Noble Howe, himself quoting Frank Brown, “…the mission of Vitruvius is to present architecture as a liberal art, based on a Hellenistic belief of the unity of knowledge.”

It is against this background that we find the passages referencing the dimensions of the human body, the origins of the iconic diagram, in Book 3: Temples Chapter 1: First Principles of Symmetry.

  1. The composition of a temple is based on symmetry, whose principles architects should take the greatest care to master Symmetry derives from proportion, which is called analogia in Greek. Proportion is the mutual calibration of each element of the work and of the whole, from which the proportional system is achieved. No temple can have any compositional system without symmetry and proportion, unless, as it were, it has an exact system of correspondence to the likeness of a well-formed human being.

 

  1. For Nature composed the human body in such a way that the face, from the chin to the top of the forehead and the lowest roots of the hairline should be one-tenth [of the total height of the body]; the palm of the hand from the wrist to the tip of the middle finger should measure likewise; the head from the chin to the crown, one-eighth; from the top of the chest to the hairline including the base of the neck, one-sixth; from the centre of the chest to the crown of the had, one-fourth. Of the height of the face itself, one-third goes from the base of the chin to the lowermost part of the nostrils, another third from the base of the nostrils to the point between the eyebrows, from that point to the hairline, the forehead also measures one-third. The foot should be one-sixth the height, the cubit, one-fourth, the chest also one-fourth. The other limbs, as well, have their own commensurate proportions, which the famous ancient painters and sculptors employed to attain great and unending praise.

 

I have quoted theses passages in full to make it very clear that for Vitruvius the form of the human body is quite literally the mass of all things. Symmetry and proportion is everything and the human body is the model for this claim. In his next paragraph Vitruvius delivers up the construction plan for Vitruvian Man.

  1. Similarly, indeed, the elements of holy temples should have dimensions for each individual part that agree with the magnitude of the work. So, too, for example, the centre and midpoint of the human body is the navel. For if a person is imagined lying back with outstretched arms and feet within a circle whose centre is at the navel, the fingers and toes will trace the circumference of this circle as they move about. But to whatever extent a circular scheme may be present in the body, a square design may also be discerned there. For if we measure from the soles of the feet to the crown of the head, and this measurement is compared with that of the outstretched hands, one discovers that this breadth equals the height, just as in areas which have been squared off by use of the set square.

 

The illustrations are Thomas Noble Howe’s modern reconstructions but we have good reason to believe that manuscripts of Vitruvius’ work in antiquity would have had illustration.[2]

Given his unified approach to art, science, design, engineering and metaphysics it comes as no surprise that Vitruvius served as a major role model for the Renaissance artist-engineers and that his Ten Books of Architecture served them as a bible. We already find the Florentine artist Lorenzo Ghiberti (1378–1455), an acknowledged forerunner to the artist-engineers, quoting Vitruvius in his potted history of linear perspective; the humanist scholar Poggio Bracciolini having ‘rediscovered’ Vitruvius in 1406.

Vitruvian man emerged in the works of the so-called Sienese engineers. The first of these was Mariano di Jacopo (1382–1543) known as Taccola. Taccola an engineer produced two annotated manuscripts of drawings of machines De ingeneis (Concerning engines)

Machines, by Taccola, De ingeneis

and De machinis (Concerning machines).

Paddle boat system, by Taccola, De machinis (1449)

In his notes we find his rendition of Vitruvian Man, not an artistic one like Leonardo’s but the simple diagrammatic version of an engineer.

Taccola Vitruvian Man

Taccola was the major influence on a second Sienese engineer Francesco di Giorgio Martini (1493–1501), whose studies of machines are almost all based on those of Taccola.

Extract from a notebook of Francesco di Giorgio Martini, 1470

 

However unlike Taccola he was also a painter, a sculptor and a leading architect. His rendition of the Vitruvian Man is very simplistic

Trattato di architettura di Francesco di Giorgio Martini

He, however, went one stage further incorporating inscribed human bodies into the architectural drawings of his ‘temples’, the churches he designed.

Trattato di architettura di Francesco di Giorgio Martini

Trattato di architettura di Francesco di Giorgio Martini

Both Taccola and Francesco di Giorgio influenced Leonardo who processed manuscripts of the work of both men; his manuscript of di Giorgio being particularly heavily annotated.

Although Luca Pacioli (1445–1517) doesn’t include a version of the Vitruvian Man in his De divina proportioni (Venice, 1509), famously illustrated by Leonardo, the second part of the book Trattato dell’architettura (Treatise on Architecture) is a twenty chapter discussion of the theories of Vitruvius comparing the proportions of the human body to those of artificial structures.

Having considered the right arrangement of the human body, the ancients proportionedall their work, particularly the temples, in accordance with it. In the human body the discovered the two main figures without which it is impossible to achieve anything, namely the perfect circle and the square.

Luca Pacioli De divina proportione

Naturally the early printed editions of De architectura contain illustrations of the Vitruvian Man. The first printed and illustrated edition of De architecture edited by Italian architect and scholar, Fra. Giovanni Giocondo, in 1511 contained images for both square and circle:

The first Italian edition by Cesare Cesariano in 1521 also contains two images

cesariano_2

Another edition from 1525 edited by Francesco Giorgi contains only one image of the circle.

 

The artist who spread the Italian concepts of linear perspective north of the Alps, Albrecht Dürer, was also obsessed with the idea of the perfect mathematical proportions of the human body and devoted a large part of his life to writing his magnum opus Vier Bücher von Menschlicher Proportion (Four Books on Human Proportion), published posthumously in 1528. Followed in 1532 by a Latin edition. Of interest is the fact that as he had almost completed his book he realised that the mathematics it contained was too difficult for the apprentice painters for whom he was writing so he wrote an introductory geometry book, Underweysung der Messung mit dem Zirkel und Richtscheyt (Instruction in Measurement with Compass and Straightedge). Dürer’s book does not contain a Vitruvian Man but contains many diagrams demonstrating the mathematical proportions of the human body.

Dürer Vier bücher von menschlicher Proportion

In the middle of the sixteenth century another Renaissance polymath, physician, astronomer, astrologer, mathematician and philosopher, Girolamo Cardano, wrote in his De subtilitate rerum (1552) that Vitruvius was one of the twelve persons who he supposes to have excelled all men in the force of genius and invention; and would not have scrupled to have given him the first place, if it could be imagined that he had delivered nothing but his own discoveries.

Since the ‘rediscovery’ of Leonardo in the eighteenth century his version of Vitruvian Man has been used, modified and parodied in a thousand different images, diagrams, adverts, poster and whatever. By a strange coincidence as I was preparing this post Monica Azzolini, Renaissance historian and Leonardo expert, posted two modern parodies of Leonardo’s Vitruvian Man on Facebook, which caught my fancy and I offer them for your amusement.

 

From the Uncyclopedia

 And of course a Ninja Turtle Leonardo Vitruvian Man

[1] All references to Vitruvius, Ten Books of Architecture are taken from the English translation edited by Ingrid D. Rowland (translator) and Thomas Noble Howe (illustrator), CUP, pb 2001

[2] On the subject of illustrations in scientific works in antiquity see: Alfred Stückelberger, Bild und Work: Das illustrierte Fachbuch in der antiken Naturwissenschaft, Medizin und Technik

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Conrad Gesner Day 2017

Anyone who pokes around long enough here at the Renaissance Mathematicus will realise that I have a fondness for polymaths. It is in fact interesting how many of the leading researcher in history were in fact polymaths. One of my favourites is the Swiss Renaissance physician, classicist, Hebraist, natural historian, bibliographer and mountaineer, Conrad Gesner.

Conrad Gessner memorial at the Old Botanical Garden, Zürich Source: Wikimedia Commons

Conrad Gessner memorial at the Old Botanical Garden, Zürich
Source: Wikimedia Commons

Last year on the five hundredth anniversary of his birth I duly recycled my old Conrad Gesner post and discovered to my delight that I had a small but distinguished Gesner fan club on my Twitter stream. We spent a happy 24 plus hours tweeting and retweeting each other’s tributes to and admirations of the Swiss polymath. At some point in a flippant mood I suggested that we should celebrate an annual Conrad Gesner Day on, 26 March his birthday. The suggestion was taken up with enthusiasm by the others and so we parted.

A couple of months ago Gesner’s name came up again and I said I was serious about celebrating Conrad Gesner Day and all the others immediately responded that they were very much still up for it so it’s on. At the moment Biodiversity Heritage Library (BHL @BioDivLIbrary), Michelle Marshall (Historical SciArt (@HistSciArt), New York Academy of Medicine Center for History (@NYAMHistory), the rare book librarian at Smithsonian Libraries and I are committed to celebrating Conrad Gesner Day. What about you?

What is going to happen? That’s up to all those involved. You can post blog posts, post illustrations from Gesner’s works on Twitter, Facebook, Instagram, whatever, where ever. Post links to sites about Gesner. If you want to write something on Gesner but don’t have your own blog, contact me and I’ll post it here at the Renaissance Mathematicus. I will collect all the contributions and post a Whewell’s Gazette style links list here at RM on the Monday.

The aim is not to glorify Conrad Gesner but to raise peoples’ awareness of a fascinating and important figure in the history of Renaissance science. Join us! Make a contribution! We already have a hash tag .

 

 

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Not German but also not Polish

I recently wrote a post concerning the problems historians can and do face assigning a nationality to figures from the past that they are studying. In the history of science one of the most contentious figures in this sense was and apparently still is the Renaissance astronomer Nicolas Copernicus. The question of his nationality produced a massive war of words between Poland and Germany, both of whom claim him as their own, which started in the late eighteenth century and unfortunately still rumbles on today.

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

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

Today is Copernicus’ birthday (19 February 1473) and all over the Internet British and American posters are being, what they see as, scrupulously, politically correct and announcing today as the birthday of the Polish astronomer… All very well but it isn’t factually right.

Nicolas Copernicus was born in the city of Toruń, which is today in Poland but wasn’t at the time of his birth. The whole area in which Copernicus was born and in which he lived for all of his life, except when he was away studying at university, was highly dispute territory over which several wars were fought. Between 1454 and 1466 the Thirteen Years’ War was fought between the Prussian Confederation allied with the Crown of the Kingdom of Poland and the State of the Teutonic Knights. This war ended with the Second Peace of Toruń under which Toruń remained a free city now under the patronage of the Polish King.

As I pointed out in an earlier post Copernicus spent all of his adult life, after graduating from university, as a citizen of Ermland (Warmia), which was then an autonomous Prince Bishopric ruled by the Bishop of Frombork and the canons of the cathedral chapter, of which Copernicus was one.

All of this means that Copernicus was neither German nor Polish but was born a citizen of Toruń and died a citizen of Ermland. I realise that this doesn’t fit our neat modern concept of national states but that is the historical reality that people should learn to live with and to accept.

 

 

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The problem with Jonathan Jones and #histSTM

It cannot be said that I am a fan of Jonathan Jones The Guardian’s wanna be art critic but although I find most of his attempts at art criticism questionable at best, as a historian of science I am normal content to simply ignore him. However when he strays into the area of #histSTM I occasionally feel the desire to give him a good kicking if only a metaphorical one. In recent times he has twice committed the sin of publicly displaying his ignorance of #histSTM thereby provoking this post. In both cases Leonard da Vinci plays a central role in his transgressions, so I feel the need to make a general comment first. Many people are fascinated by Leonardo and some of them feel the need to express that fascination in public. These can be roughly divided into two categories, the first are experts who have seriously studied Leonardo and whose utterances are based on knowledge and informed analysis, examples of this first group are Matin Kemp the art historian and Monica Azzolini the Renaissance historian. The second category could be grouped together under the title Leonardo groupies and their utterances are mostly distinguished by lack of knowledge and often mind boggling stupidity. Jonathan Jones is definitely a Leonardo groupie.

Jones’ first foray into the world of #histSTM on 28 January with a piece entitled, The charisma droids: today’s robots and the artists who foresaw them, which is a review of the new major robot exhibition at the Science Museum. What he has to say about the exhibition doesn’t really interest me here but in the middle of his article we stumble across the following paragraph:

So it is oddly inevitable that one of the first recorded inventors of robots was Leonardo da Vinci, consummate artist and pioneering engineer [my emphasis]. Leonardo apparently made, or at least designed, a robot knight to amuse the court of Milan. It worked with pulleys and was capable of simple movements. Documents of this invention are frustratingly sparse, but there is a reliable eyewitness account of another of Leonardo’s automata. In 1515 he delighted Francois I, king of France, with a robot lion that walked forward towards the monarch, then released a bunch of lilies, the royal flower, from a panel that opened in its back.

Now I have no doubts that amongst his many other accomplishments Leonardo turned his amazingly fertile thoughts to the subject of automata, after all he, like his fellow Renaissance engineers, was a fan of Hero of Alexandria who wrote extensively about automata and also constructed them. Here we have the crux of the problem. Leonardo was not “one of the first recorded inventors of robots”. In fact by the time Leonardo came on the scene automata as a topic of discussion, speculation, legend and myth had already enjoyed a couple of thousand years of history. If Jones had taken the trouble to read Ellie Truitt’s (@MedievalRobots) excellent Medieval Robots: Mechanism, Magic, Nature and Art (University of Pennsylvania Press, 2015) he would have known just how wrong his claim was. However Jones is one of those who wish to perpetuate the myth that Leonardo is the source of everything. Actually one doesn’t even need to read Ms. Truitt’s wonderful tome, you can listen to her sketching the early history of automata on the first episode of Adam Rutherford’s documentary The Rise of the Robots on BBC Radio 4, also inspired by the Science Museums exhibition. The whole series is well worth a listen.

On 6 February Jones took his Leonardo fantasies to new heights in a piece, entitled Did the Mona Lisa have syphilis? Yes, seriously that is the title of his article. Retro-diagnosis in historical studies is a best a dodgy business and should, I think, be avoided. We have whole libraries of literature diagnosing Joan of Arc’s voices, Van Gough’s mental disorders and the causes of death of numerous historical figures. There are whole lists of figures from the history of science, including such notables as Newton and Einstein, who are considered by some, usually self declared, experts to have suffered from Asperger’s syndrome. All of these theories are at best half way founded speculations and all too oft wild ones. So why does Jonathan Jones think that the Mona Lisa had syphilis? He reveals his evidence already in the sub-title to his piece:

Lisa del Giocondo, the model for Leonardo’s painting, was recorded buying snail water – then considered a cur for the STD: It could be the secret to a painting haunted by the spectre of death.

That’s it folks don’t buy any snail water or Jonathan Jones will think that you have syphilis.

Let’s look at the detail of Jones’ amazingly revelatory discovery:

Yet, as it happens, a handful of documents have survived that give glimpses of Del Giocondo’s life. For instance, she is recorded in the ledger of a Florentine convent as buying snail water (acqua di chiocciole) from its apothecary.

Snail water? I remember finding it comical when I first read this. Beyond that, I accepted a bland suggestion that it was used as a cosmetic or for indigestion. In fact, this is nonsense. The main use of snail water in pre-modern medicine was, I have recently discovered, to combat sexually transmitted diseases, including syphilis.

So she bought some snail water from an apothecary, she was the female head of the household and there is absolutely no evidence that she acquired the snail water for herself. This is something that Jones admits but then casually brushes aside. Can’t let ugly doubts get in the way of such a wonderful theory. More importantly is the claim that “the main use of snail water snail water in pre-modern medicine was […] to combat sexually transmitted diseases, including syphilis” actually correct? Those in the know disagree. I reproduce for your entertainment the following exchange concerning the subject from Twitter.

Greg Jenner (@greg_jenner)

Hello, you may have read that the Mona Lisa had syphilis. This thread points out that is probably bollocks

 Dubious theory – the key evidence is her buying “snail water”, but this was used as a remedy for rashes, earaches, wounds, bad eyes, etc…

Greg Jenner added,

Seen this ‪@DrAlun ‪@DrJaninaRamirez ? What say you? I’ve seen snail water used in so many different Early Modern remedies

Alun Withey (@DrAlun)

I think it’s an ENORMOUS leap to that conclusion. Most commonly I’ve seen it for eye complaints.

Greg Jenner

‪@DrAlun @DrJaninaRamirez yeah, as I thought – and syphilis expert @monaob1 agrees

 Alun Withey

‪@greg_jenner @DrJaninaRamirez @monaob1 So, the burning question then, did the real Mona Lisa have sore eyes? It’s a game-changer!

Mona O’Brian (@monaob1)

‪@DrAlun @greg_jenner @DrJaninaRamirez interested to hear the art historical interpretation on the ‘unhealthy’ eyes comment!

Alun Withey

‪@monaob1 @greg_jenner @DrJaninaRamirez doesn’t JJ say in the article there’s a shadow around her eyes? Mystery solved. *mic drop*

Greg Jenner

‪@DrAlun @monaob1 @DrJaninaRamirez speaking as a man who recently had to buy eye moisturiser, eyes get tired with age? No disease needed

 Mona O’Brian

@greg_jenner Agreed! Also against the pinning of the disease on the New World, considering debates about the disease’s origin are ongoing

Jen Roberts (@jshermanroberts)

‪@greg_jenner I just wrote a blog post about snail water for @historecipes –common household cure for phlegmy complaints like consumption.

Tim Kimber (@Tim_Kimber)

‪@greg_jenner Doesn’t the definite article imply the painting, rather than the person? So they’re saying the painting had syphilis… right?

Minister for Moths (@GrahamMoonieD)

‪@greg_jenner but useless against enigmatic smiles

Interestingly around the same time an advert was doing the rounds on the Internet concerning the use of snail slime as a skin beauty treatment. You can read Jen Roberts highly informative blog post on the history of snail water on The Recipes Project, which includes a closing paragraph on modern snail facials!

 

 

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Why Mathematicus?

“The Renaissance Mathematiwot?”

“Mathematicus, it’s the Latin root of the word mathematician.”

“Then why can’t you just write The Renaissance Mathematician instead of showing off and confusing people?”

“Because a mathematicus is not the same as a mathematician.”

“But you just said…”

“Words evolve over time and change their meanings, what we now understand as the occupational profile of a mathematician has some things in common with the occupational profile of a Renaissance mathematicus but an awful lot more that isn’t. I will attempt to explain.”

The word mathematician actually has its origins in the Greek word mathema, which literally meant ‘that which is learnt’, and came to mean knowledge in general or more specifically scientific knowledge or mathematical knowledge. In the Hellenistic period, when Latin became the lingua franca, so to speak, the knowledge most associated with the word mathematica was astrological knowledge. In fact the terms for the professors[1] of such knowledge, mathematicus and astrologus, were synonymous. This led to the famous historical error that St. Augustine rejected mathematics, whereas his notorious attack on the mathematici[2] was launched not against mathematicians, as we understand the term, but against astrologers.

The earliest known portrait of Saint Augustine in a 6th-century fresco, Lateran, Rome Source: Wikimedia Commons

The earliest known portrait of Saint Augustine in a 6th-century fresco, Lateran, Rome
Source: Wikimedia Commons

However St. Augustine lived in North Africa in the fourth century CE and we are concerned with the European Renaissance, which, for the purposes of this post we will define as being from roughly 1400 to 1650 CE.

The Renaissance was a period of strong revival for Greek astrology and the two hundred and fifty years that I have bracketed have been called the golden age of astrology and the principle occupation of our mathematicus is still very much the casting and interpretation of horoscopes. Mathematics had played a very minor role at the medieval universities but the Renaissance humanist universities of Northern Italy and Krakow in Poland introduced dedicated chairs for mathematics in the early fifteenth century, which were in fact chairs for astrology, whose occupants were expected to teach astrology to the medical students for their astro-medicine or as it was known iatro-mathematics. All Renaissance professors of mathematics down to and including Galileo were expected to and did teach astrology.

A Renaissance Horoscope Kepler's Horoskop für Wallenstein Source: Wikimedia Commons

A Renaissance Horoscope
Kepler’s Horoskop für Wallenstein
Source: Wikimedia Commons

Of course, to teach astrology they also had to practice and teach astronomy, which in turn required the basics of mathematics – arithmetic, geometry and trigonometry – which is what our mathematicus has in common with the modern mathematician. Throughout this period the terms Astrologus, astronomus and mathematicus – astrologer, astronomer and mathematician ­– were synonymous.

A Renaissance mathematicus was not just required to be an astronomer but to quantify and describe the entire cosmos making him a cosmographer i.e. a geographer and cartographer as well as astronomer. A Renaissance geographer/cartographer also covered much that we would now consider to be history, rather than geography.

The Renaissance mathematicus was also in general expected to produce the tools of his trade meaning conceiving, designing and manufacturing or having manufactured the mathematical instruments needed for astronomer, surveying and cartography. Many were not just cartographers but also globe makers.

Many Renaissance mathematici earned their living outside of the universities. Most of these worked at courts both secular and clerical. Here once again their primary function was usually court astrologer but they were expected to fulfil any functions considered to fall within the scope of the mathematical science much of which we would see as assignments for architects and/or engineers rather than mathematicians. Like their university colleagues they were also instrument makers a principle function being horologist, i.e. clock maker, which mostly meant the design and construction of sundials.

If we pull all of this together our Renaissance mathematicus is an astrologer, astronomer, mathematician, geographer, cartographer, surveyor, architect, engineer, instrument designer and maker, and globe maker. This long list of functions with its strong emphasis on practical applications of knowledge means that it is common historical practice to refer to Renaissance mathematici as mathematical practitioners rather than mathematicians.

This very wide range of functions fulfilled by a Renaissance mathematicus leads to a common historiographical problem in the history of Renaissance mathematics, which I will explain with reference to one of my favourite Renaissance mathematici, Johannes Schöner.

Joan Schonerus Mathematicus Source: Wikimedia Commons

Joan Schonerus Mathematicus
Source: Wikimedia Commons

Schöner who was a school professor of mathematics for twenty years was an astrologer, astronomer, geographer, cartographer, instrument maker, globe maker, textbook author, and mathematical editor and like many other mathematici such as Peter Apian, Gemma Frisius, Oronce Fine and Gerard Mercator, he regarded all of his activities as different aspects or facets of one single discipline, mathematica. From the modern standpoint almost all of activities represent a separate discipline each of which has its own discipline historians, this means that our historical picture of Schöner is a very fragmented one.

Because he produced no original mathematics historians of mathematics tend to ignore him and although they should really be looking at how the discipline evolved in this period, many just spring over it. Historians of astronomy treat him as a minor figure, whilst ignoring his astrology although it was this that played the major role in his relationship to Rheticus and thus to the publication of Copernicus’ De revolutionibus. For historians of astrology, Schöner is a major figure in Renaissance astrology although a major study of his role and influence in the discipline still has to be written. Historians of geography tend to leave him to the historians of cartography, these whilst using the maps on his globes for their studies ignore his role in the history of globe making whilst doing so. For the historians of globe making, and yes it really is a separate discipline, Schöner is a central and highly significant figure as the founder of the long tradition of printed globe pairs but they don’t tend to look outside of their own discipline to see how his globe making fits together with his other activities. I’m still looking for a serious study of his activities as an instrument maker. There is also, as far as I know no real comprehensive study of his role as textbook author and editor, areas that tend to be the neglected stepchildren of the histories of science and technology. What is glaringly missing is a historiographical approach that treats the work of Schöner or of the Renaissance mathematici as an integrated coherent whole.

Western hemisphere of the Schöner globe from 1520. Source: Wikimedia Commons

Western hemisphere of the Schöner globe from 1520.
Source: Wikimedia Commons

The world of this blog is at its core the world of the Renaissance mathematici and thus we are the Renaissance Mathematicus and not the Renaissance Mathematician.

[1] That is professor in its original meaning donated somebody who claims to possessing a particular area of knowledge.

[2] Augustinus De Genesi ad Litteram,

Quapropter bono christiano, sive mathematici, sive quilibet impie divinantium, maxime dicentes vera, cavendi sunt, ne consortio daemoniorum animam deceptam, pacto quodam societatis irretiant. II, xvii, 37

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He fought for his mother

There are not many books about the Renaissance mathematician and astronomer Johannes Kepler in which he only plays a supporting role but this is the case in Ulinka Rublack’s The Astronomer and the Witch: Johannes Kepler’s Fight for His Mother[1]. In fact in Rublack’s excellent book even Kepler’s mother, Katherina, the nominal subject of the book only really takes a supporting role; the lead role being taken by the context within which the whole tragic story unfolds and it is exactly this that makes this book so excellent.

book-cover

Regular readers of this blog will know that I champion the claims of Johannes Kepler to being the most significant natural philosopher of the Early Modern Period against the rival claims of Copernicus, Galileo, Descartes, Newton et al. So I am naturally interested in any new books that appear with Kepler as their subject. Having looked closely at one of the strangest events in Kepler’s unbelievably bizarre life, the arrest and trial of his mother, Katherina, on a charge of witchcraft – and having blogged about it twice – my interest was particularly piqued by an announcement of a new book on this topic. A decent, well-researched book in English devoted exclusively to the subject would be a very positive addition to the Kepler literature. Rublack’s book is just the bill.

Nearly all accounts of Katherina Kepler’s ordeal are merely chapters or sections in more general books about Kepler’s life and work and mostly deal chronologically with the original accusations of witchcraft, counter accusations, the attempted violent intimidation of Katherina, the frustrated strivings to bring charges against her tormentors, her arrest and finally the trial with its famous defence by Johannes. Except for thumbnail sketches of those involved very little attempt is ever made to place the occurrences into a wider or more general context and this is, as already said above, exactly the strength of Rublack’s book.

Rublack in having devoted an entire book to the whole affair draws back from the accusations, charges, counter charges and the trial itself to flesh out the story with the social, cultural, political and economic circumstances in which the whole sorry story took place. In doing so Rublack has created minor masterpiece of social history. Her research has obviously been deep and thorough and she displays a fine eye for detail, whilst maintaining a stirring narrative style that pulls the reader along at a steady pace.

One point in particular intrigued me having read all the prepublication advertising for the book, including several illuminating interviews on the subject with the author, as well as short essays by her. Rublack takes what might be seen as a strong feminist stand against the previous, exclusively male, characterisations of Katherina Kepler, all of which painted her as a mean spirited, crabby, old hag, who was, so to speak, largely to blame for the situation in which she found herself. Having over the years read almost all of these accounts I was curious how Rublack would justify her rejection of these portrayals of Katherina, which I knew were based on Kepler’s own accounts of his mother. Rublack does not disappoint. She points out quite correctly that Kepler’s description of his mother was written when he was still very young and is part of an almost psychopathic put down of himself and all those related or connected to him and calls rather his own mental state into question. Interestingly we have virtually no other accounts of Katherina from Johannes’ pen and to judge her purely on this one piece of strange juvenilia is probably, as Rublack makes very clear, a bridge too far. Piecing together all of the, admittedly scant, evidence Rublack paints a much more sympathetic picture of Katherina, a hard working, illiterate, sixteenth/seventeenth-century peasant woman, who had never had it easy in life but still managed to raise her children well and give them chances that she never had.

This book is not perfect, as Rublack relies in her accounts of Johannes on older standard biographies, whilst apparently not consulting some of the more recent scholarly studies of his life and work, and thus repeats several false claims concerning him. However I’m prepared to cut her some slack on this as none of the errors that she (unknowingly?) repeats have any direct bearing on the story of Katherina that she tells so skilfully.

The book is beautifully presented by the OUP. Printed in a pleasant, easy on the eyes typeface and charmingly illustrated with a large number of black and white pictures. The text is excellently annotated, but as always I would have preferred footnotes to endnotes, and there is an adequate index. I personally would have liked a separate bibliography but this might have been sacrificed on cost grounds, the hardback being available at a very civilised price for a serious academic volume. Although having called it that I should point out that the book is very accessible and readable for the non-expert or general reader.

I heartily recommend this book to anybody interested in seventeenth-century history, Johannes Kepler, the history of witchcraft or who just likes reading good informative, entertaining books, if one is allowed to call a book about the sufferings of an innocent woman entertaining. Put simply, it’s an excellent read that deserves to, and probably will, become the standard English text on the subject.

[1] Ulinka Rublack, The Astronomer and the Witch: Johannes Kepler’s Fight for His Mother. OUP, 2015

 

 

 

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Christmas Trilogy 2016 Part 3: The English Keplerians

For any scientific theory to succeed, no matter how good or true it is; it needs people who support and propagate it. Disciples, so to speak, who are prepared to spread the gospel. Kepler’s astronomical theories, his three laws of planetary motion and everything that went with them, were no different from every other theory in this aspect; they needed a fan club. On the continent of Europe the reception of Kepler’s theories was initially lukewarm to say the least and it was not only Galileo, who did his best to ignore them. Therefore it is somewhat surprising that they found a group of enthusiastic supporters right from the beginning in England. Surprising because in general in the first half of the seventeenth century England lagged well behind the continent in astronomy, as in all things mathematical.

The first Englishmen to pick up on Kepler’s theories was the small group around Thomas Harriot, who did so immediately after the publication of the Astronomia nova in 1609.

Portrait often claimed to be Thomas Harriot (1602), which hangs in Oriel College, Oxford. Source: Wikimedia Commons

Portrait often claimed to be Thomas Harriot (1602), which hangs in Oriel College, Oxford. Source: Wikimedia Commons

The group included not only Harriot but also his lens grinder Christopher Tooke, the Cornish MP Sir William Lower (c.1570–1615) and his Welsh neighbour John Prydderch (or Protheroe). Lower had long been an astronomical pupil of Harriot’s and had in turn introduced his neighbour Prydderch to the science.

The cartoon of Lower and Prydderch on page 265 of Seryddiaeth a Seryddwyr By J.S. Evans. Lower looks through a telescope while Prydderch holds a cross-staff. The cartoon had been used earlier by Arthur Mee in his book The Story of the Telescope in 1909. The artist was J. M. Staniforth, the artist-in-chief of the Western Mail newspaper.

The cartoon of Lower and Prydderch on page 265 of Seryddiaeth a Seryddwyr By J.S. Evans. Lower looks through a telescope while Prydderch holds a cross-staff. The cartoon had been used earlier by Arthur Mee in his book The Story of the Telescope in 1909. The artist was J. M. Staniforth, the artist-in-chief of the Western Mail newspaper.

This group was one of the very earliest astronomical telescopic observing teams, exchanging information and comparing observations already in 1609/10. In 1610 they were enthusiastically reading Astronomia nova and discussing the new elliptical astronomy. It was Lower, who had carefully observed Halley’s comet in 1607 (pre-telescope) together with Harriot, who first suggested that the orbits of comets would also be ellipses. Kepler still thought that comets move in straight lines. The Harriot group did not publish their active support of the Keplerian elliptical astronomy but Harriot was well networked within the mathematical communities of both England and the Continent. He had even earlier had a fairly substantial correspondence with Kepler on the topic of atmospheric refraction. It is a fairly safe assumption that Harriot’s and Lower’s support of Kepler’s theories was known to other contemporary English mathematical practitioners.

Our next group of English Keplerians is that initiated by the astronomical prodigy Jeremiah Horrocks (1618–1641). Horrocks was a self-taught astronomer who stumbled across Kepler’s theories, whilst on the search for reliable astronomical tables. He quickly established that Kepler’s Rudolphine Tables were superior to other available tables and soon became a disciple of Kepler’s elliptical astronomy. Horrocks passed on his enthusiasm for Kepler’s theories to his astronomical helpmate William Crabtree (1610–1644). In turn Crabtree seems to have been responsible for converting another young autodidactic astronomer William Gascoigne (1612–1644) to the Keplerian astronomical gospel. Crabtree referred to this little group as Nos Keplari. Horrocks contributed to the development of Keplerian astronomy with an elliptical model of the Moon’s orbit, something that Kepler had not achieved. This model was the one that would eventually make its way into Newton’s Principia. He also corrected and extended the Rudolphine Tables enabling Horrocks and Crabtree to become, famously, the first people ever to observe a transit of Venus.

opera_posthuma

Like Harriot’s group, Nos Keplari published little but they were collectively even better networked than Harriot. Horrocks had been at Oxford Emmanual College Cambridge with John Wallis and it was Wallis, a convinced nationalist, who propagated Horrocks’ posthumous astronomical reputation against foreign rivals, as he also did in the question of algebra for Harriot. Both Gascoigne and Crabtree had connections to the Towneley family, landed gentry who took a strong interest in the emerging modern science of the period. Later the Towneley’s who had connections to the Royal Society ensured that the work of Nos Keplari was not lost and forgotten, bringing it, amongst other things, to the attention of a young John Flamsteed, who would later become the first Astronomer Royal. . Gascoigne had connections to William Cavendish, the later Duke of Newcastle, under whose command he served at the battle of Marston Moor, where he died. William, his brother Charles and his wife Margaret were all enthusiastic supporters of the new sciences and important members of the English scientific and philosophical community. Gascoigne also corresponded with William Oughtred who served as private mathematics tutor to many leading members of the burgeoning English mathematical community. It is to two of Oughtred’s students that we now turn

William Oughtred by Wenceslas Hollar 1646

William Oughtred
by Wenceslas Hollar 1646

Seth Ward (1617–1689) studied at Oxford Cambridge University from 1636 to 1640 when he became a fellow of Sidney Sussex College.

Greenhill, John; Seth Ward (1617-1689), Savilian Professor of Astronomy, Oxford (1649-1660) Source: Wikimedia Commons

Greenhill, John; Seth Ward (1617-1689), Savilian Professor of Astronomy, Oxford (1649-1660)
Source: Wikimedia Commons

In the same year he took instruction in mathematics from William Oughtred. In 1649 he became Savilian Professor of Astronomy at Oxford University the same year that John Wallis was appointed Savilian Professor of Mathematics. Whilst serving as Savilian Professor, Ward became embroiled in a dispute about Keplerian astronomy with the French astronomer and mathematician Ismaël Boulliau.

Ismaël Boulliau  Source: Wikimedia Commons

Ismaël Boulliau
Source: Wikimedia Commons

Boulliau was an early and strong defender of Keplerian elliptical astronomy, who however rejected Kepler’s attempts to create a physical explanation of planetary orbits. Boulliau published his Keplerian theories in his Astronomia philoaïca in 1645. Ward attacked Boulliau’s model in his In Ismaelis Bullialdi astro-nomiae philolaicae fundamenta inquisitio brevis from 1653, presenting his own model for Kepler’s planetary laws. Boulliau responded to Ward’s attack in his De lineis spiralibus from 1657. Ward had amplified his own views in his Astronomia geometrica from 1656. This public exchange between two heavyweight champions of the elliptical astronomy did much to raise the general awareness of Kepler’s work in England. It has been suggested that the dispute was instrumental in bringing Newton’s attention to Kepler’s ideas, a claim that is however disputed by historians.

Ward went on to make a successful career in the Church of England, eventually becoming Bishop of Salisbury his successor, as Savilian Professor of Astronomy was another one of Oughtred’s student, Christopher Wren (1632–1723).

Christopher Wren by Godfrey Keller 1711  Source: Wikimedia Commons

Christopher Wren by Godfrey Keller 1711
Source: Wikimedia Commons

Wren is of course much better known as the foremost English architect of the seventeenth-century but started out as mathematician and astronomer. Wren studied at Wadham College Oxford from 1650 to 1653, where he was part of the circle of scientifically interested scholars centred on John Wilkins (1614–1672), the highly influential early supporter of heliocentric astronomy. The Wilkins group included at various times Seth Ward, John Wallis, Robert Boyle, William Petty and Robert Hooke amongst others and would go on to become one of the groups that founded the Royal Society. Wren was a protégé of Sir Charles Scarborough, a student of William Harvey who later became a famous physician in his own right; Scarborough had been a fellow student of Ward’s and was another student of Oughtred’s. Wren was appointed Gresham Professor of Astronomy and it was following his lectures at Gresham College that the meetings took place that would develop into the Royal Society. As already noted Wren then went on to succeed Ward as Savilian Professor for astronomy in 1661, a post that he resigned in 1673 when his work as Surveyor of the King’s Works (a post he took on in 1669), rebuilding London following the Great Fire of 1666, became too demanding. Wren enjoyed a good reputation as a mathematician and astronomer and like Ward was a convinced Keplerian.

Our final English Keplerian is Nicolaus Mercator (1620–1687), who was not English at all but German, but who lived in London from 1658 to 1682 teaching mathematics.

Nicolaus Mercator © 1996-2007 Eric W. Weisstein

Nicolaus Mercator
© 1996-2007 Eric W. Weisstein

In his first years in England Mercator corresponded with Boulliau on the subject of Horrock’s Transit of Venus observations. Mercator stood in contact with the leading English mathematicians, including Oughtred, John Pell and John Collins and in 1664 he published a defence of Keplerian astronomy Hypothesis astronomica nova. Mercator’s work contained an acceptable mathematical proof of Kepler’s second law, the area law, which had been a bone of contention ever since Kepler published it in 1609; Kepler’s own proof being highly debateable, to put it mildly. Mercator continued his defence of Kepler in his Institutiones astronomicae in 1676. It was probably through Mercator’s works, rather than Ward’s, that Newton became acquainted with Kepler’s astronomy. We still have Newton’s annotated copy of the latter work. Newton and Mercator were acquainted and corresponded with each other.

As I hope to have shown there was a strong continuing interest in England in Keplerian astronomy from its very beginnings in 1609 through to the 1660s when it had become de facto the astronomical model of choice in English scientific circles. As I stated at the outset, to become accepted a new scientific theory has to find supporters who are prepared to champion it against its critics. Kepler’s elliptical astronomy certainly found those supporters in England’s green and pleasant lands.

 

 

 

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