Category Archives: History of science

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 vexed problem of nationality in the history of science

People seem to like/want/need heroes in sport, culture, politics, in fact in almost every area of life including the history of science. In particular for many people this desire for heroes is closely tied to feelings of national pride – a great Argentinian footballer, a great German composer, a great American boxer, a great English physicist and so on and so forth. This identification of people, whatever their field of activity, with their nationality is problematic for historians of science both geographically and historically

The earth did not come into existence about four and a half billion years ago with the borders of the national states stamped into its surface. In fact even within the one hundred to two hundred thousand years that Homo sapiens have occupied the earth the concept of a nation state is, in historical terms, a very recent one. Also within the time since nation states have existed their borders have not been static but have ebbed and flowed like the tide; states coming into and going out of existence down the centuries.

Brabant and Savoy, two important European states that existed in the High Middle Ages and Early Modern Period have long since disappeared into the mists of history. Looking at the modern map of Europe, The Netherlands only came into existence in the late sixteenth century, whilst its neighbour Belgium was created in 1815. Germany only really became a nation state following the fall of Hitler and the Nazis in 1945 and was for several decades two nation states, East and West, which only became finally united on 3 October 1990.

Duchy of Brabant 1477 Source Wikimedia Commons

Duchy of Brabant 1477
Source Wikimedia Commons

The early years of Wikipedia saw several epic battles over the nationality of scientific heroes, the most notorious being over Nicolaus Copernicus, which became so vitriolic that it was a news item on BBC Radio 4’s flagship news magazine, The Today Programme. The Poles and Germans carrying on a dispute that dates back to the late eighteenth century; a dispute that is totally barmy, as he was actually neither Polish nor German, as I explained in an earlier post. The nationality of the Islamic mathematician Muḥammad ibn Mūsā al-Khwārizmī, who gave algebra and the algorithm their names, is also disputed between Persia and Uzbekistan. The astronomer Johannes Hevelius, a native of Danzig, or should that be Gdańsk, is like Copernicus claimed by both Germany and Poland. The Jesuit mathematician, astronomer and physicist Ruđer Josip Bošković (English: Roger Joseph Boscovich) is claimed by Croatia, Serbia and Italy, although it should be noted he became a naturalised French citizen and the end of his life. Anther astronomer with dual nationality is the Italian Giovanni Domenico Cassini who ended his life as the Frenchman Jean-Dominique Cassini. Although it is debateable whether it is correct to call Cassini an Italian, as Italy only became a united national state in 1861, about one hundred and fifty years after his death

The latest case of, potentially, disputed nationality that caught my eye and generated this post occurred in an article on the BBC News website, The Irish novel that seduced the USSR, the story of the novel The Gadfly by Ethel Voynich. Don’t Panic! The Renaissance Mathematicus has not metamorphosed overnight into a blog for literature criticism, you might understand when I say that Ethel Voynich was born Ethel Lilian Boole the youngest of the five daughters of the mathematician and logician George Boole and his wife the proto-feminist and educationalist Mary Everest-Boole. What provoked this post was that the article describes Ethel Voynich as an Irish writer.

Ethel Lilian Voynich née Boole

Ethel Lilian Voynich née Boole

Ethel Lilian Boole was born 11 May 1864 in the city of Cork in the Irish province of Munster, so she is Irish, right? Well, maybe not. My eldest sister was born in Rangoon in Burma, so she is Burmese, right? Actually she isn’t, she was born British and has remained British all of her life. Likewise, my brother was born in Lahore, so he’s Pakistani, right. Once again no, he was born British and remained British up to his death two years ago. Both of them were born in what was then British India of British parents, although my mother like my sister was born in Rangoon, and so both of them were automatically British citizens. My bother’s potential nationality is made even more complex by the fact that when he was born Lahore was in India but is now in Pakistan.

Let’s take a closer look at Ethel Lilian. At the time of her birth Ireland was part of the United Kingdom of Britain and Ireland, a country ruled by a single government in Westminster, London. Her father, George Boole, was born in Lincoln and was thus English.

Georg Boole Source: Wikimedia Commons

Georg Boole
Source: Wikimedia Commons

Her mother Mary Everest, the niece of Georg Everest for whom the mountain is named, was born in Wickwar in Gloucestershire and so was also English, although her family is Welsh. The family name, by the way, is pronounced Eve-rest and not Ever-est.

Mary Everest Boole Source: Wikimedia Commons

Mary Everest Boole
Source: Wikimedia Commons

To complicate matters, George Boole died 8 December 1864 just seven months after Ethel Lilian’s birth and Mary immediately returned to England with her five daughters. Ethel Lilian grew up in England and never returned to Ireland and identified as English not Irish. Given her parentage it is doubtful whether she should be referred to as Irish at all, despite having been born in Cork.

It is even more of a stretch to call The Gadfly an Irish novel. Ethel Lilian travelled extensively throughout Europe, as an adult and the novel, which is set in Italy and features an English hero, was first published in New York and then London before being translated into Russian, whereupon it became a mega best seller in Russia. To call it an Irish novel purely because of Ethel Lilian’s birth and seven-month residency in Cork is in my opinion a bridge too far.

Cover of the first publication of E. L. Vojnich's novel «The Gadfly» Source: Wikimedia Commons

Cover of the first publication of E. L. Vojnich’s novel «The Gadfly»
Source: Wikimedia Commons

All five of Boole’s daughters led fascinating and historically significant lives. You can read a short account of Those Amazing Boole Girls on my friend Pat’s Blog or for a fuller account I heartily recommend Desmond MacHale’s excellent biography, The Life and Work of George Boole: A Prelude to the Digital Age. The family history is dealt with even more fully in Gerry Kennedy’s The Booles and the Hintons: Two Dynasties That Helped Shape the Modern World, which I haven’t read yet (it’s on the infinite reading list) but which has received excellent reviews.

 

 

 

 

 

 

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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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Two views of the celestial spheres

When the Bishop of Salisbury scanned the heavens in the 1670s it was difficult to know if he was contemplating the wonders of his God, or those of Kepler’s planetary laws. Seth Ward, the incumbent of the Salisbury bishopric, was both a successful Anglican churchman and an acknowledge astronomer, who did much to boost Kepler’s theories in the middle of the seventeenth century.

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

Born in Aspenden in Hertfordshire on an unknown day in 1617, Seth Ward was the son of John Ward, an attorney, and his wife Mary Dalton. Having received a basic schooling he was admitted to Sidney-Sussex College, Cambridge on 1 December 1632, where he graduated B.A. in 1637 and M.A. on 27 July 1640, following which he was elected a fellow of the college. Ward was a keen mathematician, who, like many others in the Early Modern Period, was largely self-taught, studying William Oughtred’s Clavis Mathematicae together with fellow maths enthusiast Charles Scarburgh, a future physician to Charles II. Finding some passages difficult the two of them travelled to Albury in Surrey where Oughtred was rector. Here they took instruction from Oughtred and it was the start of a relationship between Ward and Oughtred that lasted until Oughtred’s death in 1660.

Sir Charles Scarborough Jean Demetrius (attributed to) Royal College of Physicians, London Source: Wikimedia Commons

Sir Charles Scarborough Jean Demetrius (attributed to)
Royal College of Physicians, London
Source: Wikimedia Commons

In 1643 Ward was appointed lecture for mathematics for the university but he did not exercise this post for very long. Some of the Cambridge colleges, and in particular Sidney-Sussex, Cromwell’s alma mater, became centres for the Puritan uprising and in 1644 Seth Ward, a devote Anglican, was expelled from his fellowship for refusing to sign the covenant. At first he took refuge with friends in and around London but then he went back to Albury where he received tuition in mathematics from Oughtred for several months. Afterwards he became private tutor in mathematics to the children of a friend, where he remained until 1649. Having used the Clavis Mathematicae, as a textbook whilst teaching at he university he made several suggestions for improving the book and persuaded Oughtred to publish a third edition in 1652

William Oughtred by Wenceslas Hollar 1646 Source: Wikimedia Commons

William Oughtred
by Wenceslas Hollar 1646
Source: Wikimedia Commons

In 1648 John Greaves, one of the first English translators of Arabic and Persian scientific texts into Latin, also became a victim of a Puritan purge and was evicted from the Savilian Chair for Astronomy at Oxford. Greaves recommended Ward as his successor and in 1649, having overcame his scruples, Ward took the oath to the English Commonwealth and was appointed Savilian Professor.

yooniqimages_102046418

These episodes, Wards expulsion from Sidney-Sussex and Greave’s from Oxford, serve to remind us that much of the scientific investigations that took place in the Early Modern Period, and which led to the creation of modern science, did so in the midst of the many bitter and very destructive religious wars that raged throughout Europe during this period. The scholars who carried out those investigations did not remain unscathed by these disturbances and careers were often deeply affected by them. The most notable example being, of course Johannes Kepler, who was tossed around by the Reformation and Counter-Reformation like a leaf in a storm. Anyone attempting to write a history of the science of this period has to, in my opinion, take these external vicissitudes into account; a history that does not do so is only a half history.

It was in his role as Savilian Professor that Ward made his greatest contribution to the development of the new heliocentric astronomy in an academic dispute with the French astronomer and mathematician Ismaël Boulliau (1605–1694).

Ismaël Boulliau  Source: Wikimedia Commons

Ismaël Boulliau
Source: Wikimedia Commons

Boulliau was an early supporter of the elliptical astronomy of Johannes Kepler, who however rejected much of Kepler’s ideas. In 1645 he published his own theories based on Kepler’s work in his Astronomia philolaïca. This was the first major work by another astronomer that incorporated Kepler’s elliptical astronomy. Ward another Keplerian wrote his own work In Ismaelis Bullialdi Astronomiæ Philolaicæ Fundamenta Inquisitio Brevis, which heavily criticised Boulliau’s theories and present his own, in his opinion superior, interpretations of Kepler’s ideas. He followed this with another more extensive presentation of his theories in 1656, Astronomia Geometrica; ubi Methodus proponitur qua Primariorum Planetarum Astronomia sive Elliptica sive Circularis possit Geometrice absolve. Boulliau responded in 1657 in his Ismaelis Bullialdi Astronomiæ Philolaicæ Fundamenta clarius explicata et asserta, printed in his Exercitationes Geometricæ tres in which he acknowledged errors in his own work but also pointing out inaccuracies in Ward’s. In final analysis both Boulliau and Ward were wrong, and we don’t need to go into detail her, but their dispute drew the attention of other mathematicians and astronomers to Kepler’s work and thus played a major role in its final acceptance as the preferred model for astronomy in the latter part of the seventeenth century.

The worst popular model of the emergence of modern astronomy in the Early Modern Period sees the inspiring creation of heliocentric astronomy by Copernicus in his De revolutionibus in the sixteenth century, the doting of a few ‘I’s and crossing of a few ‘T’s by Galileo and Kepler in the early seventeenth century followed by the triumphant completion of the whole by Newton in his Principia in 1687. Even those who acknowledge that Kepler created something new with his elliptical astronomy still spring directly to Newton and the Principia. In fact many scholars contributed to the development of the ideas of Kepler and Galileo in the decades between them and Isaac Newton and if we are going to correctly understand how science evolves it is important to give weight to the work of those supposedly minor figures. The scientific debate between Boulliau and Ward is a good example of an episode in the history of astronomy that we ignore at the peril of falsifying the evolution of a disciple that we are trying to understand.

Ward continued to make career as an astronomer mathematician. He was awarded an Oxford M.A. on 23 October 1649 and became a fellow of Wadham College in 1650. The mathematician John Wilkins was warden of Wadham and the centre of a group of likeminded enthusiasts for the emerging new sciences that at times included Robert Boyle, Robert Hooke, Christopher Wren, John Wallis and many others. This became known as the Philosophical Society of Oxford, and they would go on to become one of the founding groups of the Royal Society in the early 1660s.

During his time at Oxford Ward together with his friend John Wallis, the Savilian Professor of Geometry, became involved in a bitter dispute with the philosopher Thomas Hobbes on the teaching of geometry at Oxford and the latter’s claim to have squared the circle; he hadn’t it’s impossible but the proof of that impossibility came first a couple of hundred years later.

Thomas Hobbes Artist unknown

Thomas Hobbes Artist unknown

Ward however was able to expose the errors in Hobbes’ geometrical deductions. In some circles Ward is better known for this dispute than for his contributions to astronomy.

John Wallis by Godfrey Kneller Source: Wikimedia Commons

John Wallis by Godfrey Kneller
Source: Wikimedia Commons

When the alchemist and cleric John Webster launched an attack on the curriculum of the English universities in his Academiarum Examen (1654) Ward joined forces with John Wilkins to write a defence refuting Webster’s arguments, Viniciae Acadmiarum, which also included refutations of other prominent critics of Oxford and Cambridge.

Greenhill, John; John Wilkins (1614-1672), Warden (1648-1659); Wadham College, University of Oxford;

Greenhill, John; John Wilkins (1614-1672), Warden (1648-1659); Wadham College, University of Oxford;

Ward’s career as an astronomer and mathematician was very successful and his work was known and respected throughout Europe, where he stood in contact with many of the leading exponents of his discipline. However, his career in academic politics was not so successful. He received a doctorate in theology (D.D.) from Oxford in 1654 and one from Cambridge in 1659. He was elected principle of Jesus College, Oxford in 1657 but Cromwell appointed somebody else promising Ward compensation, which he never delivered. In 1659 he was appointed president of Trinity College, Oxford but because he was not qualified for the office he was compelled to resign in 1660. This appears to have been the final straw and in 1660 he left academia, resigning his professorship to take up a career in the Church of England, with the active support of the recently restored Charles II.

He proceeded through a series of clerical positions culminating in the bishopric in Salisbury in 1667. He was appointed chancellor of the Order of the Garter in 1671. Ward turned down the offer of the bishopric of Durham remaining in Salisbury until his death 6 January 1689. He was a very active churchman, just as he had been a very active university professor, and enjoyed as good a reputation as a bishop as he had enjoyed as an astronomer.

 

 

 

 

 

 

 

 

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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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Filed under History of Astronomy, History of Mathematics, History of science, Renaissance Science

Christmas Trilogy 2016 Part 1: Is Newtonian physics Newton’s physics?

Nature and nature’s laws lay hid in night;

God said “Let Newton be” and all was light.

Isaac Newton's Tomb in Westminster Abbey Photo: Klaus-Dieter Keller Source: Wikimedia Commons

Isaac Newton’s Tomb in Westminster Abbey
Photo: Klaus-Dieter Keller
Source: Wikimedia Commons

Alexander Pope’s epitaph sets the capstone on the myth of Newton’s achievements that had been under construction since the publication of the Principia in 1687. Newton had single-handedly delivered up the core of modern science – mechanics, astronomy/cosmology, optics with a side order of mathematics – all packed up and ready to go, just pay at the cash desk on your way out. We, of course, know (you do know don’t you?) that Pope’s claim is more than somewhat hyperbolic and that Newton’s achievements have, over the centuries since his death, been greatly exaggerated. But what about the mechanics? Surely that is something that Newton delivered up as a finished package in the Principia? We all learnt Newtonian physics at school, didn’t we, and that – the three laws of motion, the definition of force and the rest – is all straight out of the Principia, isn’t it? Newtonian physics is Newton’s physics, isn’t it? There is a rule in journalism/blogging that if the title of an article/post is in the form of a question then the answer is no. So Newtonian physics is not Newton’s physics, or is it? The answer is actually a qualified yes, Newtonian physics is Newton’s physics, but it’s very qualified.

Newton's own copy of his Principia, with hand-written corrections for the second edition Source: Wikimedia Commons

Newton’s own copy of his Principia, with hand-written corrections for the second edition
Source: Wikimedia Commons

The differences begin with the mathematics and this is important, after all Newton’s masterwork is The Mathematical Principles of Natural Philosophy with the emphasis very much on the mathematical. Newton wanted to differentiate his work, which he considered to be rigorously mathematical, from other versions of natural philosophy, in particular that of Descartes, which he saw as more speculatively philosophical. In this sense the Principia is a real change from much that went before and was rejected by some of a more philosophical and literary bent for exactly that reason. However Newton’s mathematics would prove a problem for any modern student learning Newtonian mechanics.

Our student would use calculus in his study of the mechanics writing his work either in Leibniz’s dx/dy notation or the more modern F’(x) = f(x) notation of the French mathematician, Lagrange (1736–1813). He won’t be using the dot notation developed by Newton and against which Babbage, Peacock, Herschel and the Analytical Society campaigned so hard at the beginning of the nineteenth century. In fact if our student turns to the Principia, he won’t find Newton’s dot notation calculus there either, as I explained in an earlier post Newton didn’t use calculus when writing the Principia, but did all of his mathematics with Euclidian geometry. This makes the Principia difficult to read for the modern reader and at times impenetrable. It should also be noted that although both Leibniz and Newton, independently of each other, codified a system of calculus – they didn’t invent it – at the end of the seventeenth century, they didn’t produce a completed system. A lot of the calculus that our student will be using was developed in the eighteenth century by such mathematicians as Pierre Varignon (1654–1722) in France and various Bernoullis as well as Leonard Euler (1707­1783) in Switzerland. The concept of limits that are so important to our modern student’s calculus proofs was first introduced by Bernard Bolzano (1781–1848), Augustin-Louis Cauchy (1789–1857) and above all Karl Theodor Wilhelm Weierstrass (1815–1897) in the nineteenth century.

Turning from the mathematics to the physics itself, although the core of what we now know as Newtonian mechanics can be found in the Principia, what we actually use/ teach today is actually an eighteenth-century synthesis of Newton’s work with elements taken from the works of Descartes and Leibniz; something our Isaac would definitely not have been very happy about, as he nursed a strong aversion to both of them.

A notable example of this synthesis concerns the relationship between mass, velocity and energy and was brought about one of the very few women to be involved in these developments in the eighteenth century, Gabrielle-Émilie Le Tonnelier de Breteuil, Marquise du Châtelet, the French aristocrat, lover of Voltaire and translator of the first French edition of the Principia.

In the frontispiece to Voltaire's book on Newton's philosophy, du Châtelet appears as Voltaire's muse, reflecting Newton's heavenly insights down to Voltaire. Source: Wikimedia Commons

In the frontispiece to Voltaire’s book on Newton’s philosophy, du Châtelet appears as Voltaire’s muse, reflecting Newton’s heavenly insights down to Voltaire.
Source: Wikimedia Commons

One should remember that mechanics doesn’t begin with Newton; Simon Stevin, Galileo Galilei, Giovanni Alfonso Borelli, René Descartes, Christiaan Huygens and others all produced works on mechanics before Newton and a lot of their work flowed into the Principia. One of the problems of mechanics discussed in the seventeenth century was the physics of elastic and inelastic collisions, sounds horribly technical but it’s the physics of billiard and snooker for example, which Descartes famously got wrong. Part of the problem is the value of the energy[1] imparted upon impact by an object of mass m travelling at a velocity v upon impact.

Newton believed that the solution was simply mass times velocity, mv and belief is the right term his explanation being surprisingly non-mathematical and rather religious. Leibniz, however, thought that the solution was mass times velocity squared, again with very little scientific justification. The support for the two theories was divided largely along nationalist line, the Germans siding with Leibniz and the British with Newton and it was the French Newtonian Émilie du Châtelet who settled the dispute in favour of Leibniz. Drawing on experimental results produced by the Dutch Newtonian, Willem Jacob ‘s Gravesande (1688–1742), she was able to demonstrate the impact energy is indeed mv2.

Willem Jacob 's Gravesande (1688-1745) Portrait by Hendrik van Limborch (1681-1759) Source: Wikimedia Commons

Willem Jacob ‘s Gravesande (1688-1745) Portrait by Hendrik van Limborch (1681-1759)
Source: Wikimedia Commons

The purpose of this brief excurse into eighteenth-century physics is intended to show that contrary to Pope’s epitaph not even the great Isaac Newton can illuminate a whole branch of science in one sweep. He added a strong beam of light to many beacons already ignited by others throughout the seventeenth century but even he left many corners in the shadows for other researchers to find and illuminate in their turn.

 

 

 

 

[1] The use of the term energy here is of course anachronistic

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Filed under History of Physics, History of science, Myths of Science, Newton, Uncategorized