Renaissance Science – I

To paraphrase what is possibly the most infamous opening sentence in a history of science book[1], there was no such thing as Renaissance science, and this is the is the start of a blog post series about it. Put another way there are all sorts of problems with the term or concept Renaissance Science, several of which should entail abandoning the use of the term and in a later post I will attempt to sketch the problems that exist with the term Renaissance itself and whether there is such a thing as Renaissance science? Nevertheless, I intend to write a blog post series about Renaissance science starting today.

We could and should of course start with the question, which Renaissance? When they hear the term Renaissance, most non-historians tend to think of what is often referred to as the Humanist Renaissance, but historians now use the term for a whole series of period in European history or even for historical periods in other cultures outside of Europe.

Renaissance means rebirth and is generally used to refer to the rediscovery or re-emergence of the predominantly Greek, intellectual culture of antiquity following a period when it didn’t entirely disappear in Europe but was definitely on the backburner for several centuries following the decline and collapse of the Western Roman Empire. The first point to note is that this predominantly Greek, intellectual culture didn’t disappear in the Eastern Roman Empire centred round its capitol Constantinople. An empire that later became known as the Byzantine Empire. The standard myth is that the Humanist Renaissance began with the fall of Byzantium to the Muslims in 1453 but it is just that, a myth.


Raphael’s ‘School of Athens’ (1509–1511) symbolises the recovery of Greek knowledge in the Renaissance Source: Wikimedia Commons

As soon as one mentions the Muslims, one is confronted with a much earlier rebirth of predominantly Greek, intellectual culture, when the, then comparatively young, Islamic Empire began to revive and adopt it in the eight century CE through a massive translation movement of original Greek works covering almost every subject. Writing in Arabic, Arab, Persian, Jewish and other scholars, actively translated the complete spectrum of Greek science into Arabic, analysed it, commented on it, and expanded and developed it, over a period of at least eight centuries.  It is also important to note that the Islamic scholars also collected and translated works from China and India, passing much of the last on to Europe together with the Greek works later during the European renaissances.


The city of Baghdad 150–300 AH (767 and 912 CE) centre of the Islamic recovery and revival of Greek scientific culture Source: Wikimedia Commons

Note the plural at the end of the sentence. Many historians recognise three renaissances during the European Middle Ages. The first of these is the Carolingian Renaissance, which dates to the eighth and ninth century CE and the reigns of Karl der Große (742–814) (known as Charlemagne in English) and Louis the Pious (778–840).


Charlemagne (left) and Pepin the Hunchback (10th-century copy of 9th-century original) Source: Wikimedia Commons

This largely consisted of the setting up of an education system for the clergy throughout Europe and increasing the spread of Latin as the language of learning. Basically, not scientific it had, however, an element of the mathematical sciences, some mathematics, computus (calendrical calculations to determine the date of Easter), astrology and simple astronomy due to the presence of Alcuin of York (c. 735–804) as the leading scholar at Karl’s court in Aachen.


Rabanus Maurus Magnentius (left) another important teacher in the Carolignian Renaissance with Alcuin (middle) presenting his work to Otgar Archbishop of Mainz a supporter of Louis the Pious Source: Wikimedia Commons

Through Alcuin the mathematical work of the Venerable Bede (c. 673–735), (who wrote extensively on mathematical topics and who was also the teacher of Alcuin’s teacher, Ecgbert, Archbishop of York) flowed onto the European continent and became widely disseminated.


The Venerable Bede writing the Ecclesiastical History of the English People, from a codex at Engelberg Abbey in Switzerland. Source: Wikimedia Commons

Karl’s Court had trade and diplomatic relations with the Islamic Empire and there was almost certainly some mathematical influence there in the astrology and astronomy practiced in the Carolingian Empire. It should also be noted that Alcuin and associates didn’t start from scratch as some knowledge of the scholars from late antiquity, such as Boethius (477–524), Macrobius (fl. c. 400), Martianus Capella (fl. c. 410–420) and Isidore of Seville (c. 560–636) had survived. For example, Bede quotes from Isidore’s encyclopaedia the Etymologiae.

The second medieval renaissance was the Ottonian Renaissance in the eleventh century CE during the reigns of Otto I (912–973), Otto II (955–983), and Otto III (980–1002). The start of the Ottonian Renaissance is usually dated to Otto I’s second marriage to Adelheid of Burgundy (931–999), the widowed Queen of Italy in 951, uniting the thrones of Germany (East Francia) and Italy, which led to Otto being crowned Holy Roman Emperor by the Pope in 962.


Statues of Otto I, right, and Adelaide in Meissen Cathedral. Otto and Adelaide were married after his annexation of Italy. Source: Wikimedia Commons

This renaissance was largely confined to the Imperial court and monasteries and cathedral schools. The major influences came from closer contacts with Byzantium with an emphasis on art and architecture.

There was, however, a strong mathematical influence brought about through Otto’s patronage of Gerbert of Aurillac (c. 946–1003). A patronage that would eventually lead to Gerbert becoming Pope Sylvester II.


Sylvester, in blue, as depicted in the Evangelistary of Otto III Source: Wikimedia Commons

A monk in the Monastery of St. Gerald of Aurillac, Gerbert was taken by Count Borrell II of Barcelona to Spain, where he came into direct contact with Islamic culture and studied and learnt some astronomy and mathematics from the available Arabic sources. In 969, Borrell II took Gerbert with him to Rome, where he met both Otto I and Pope John XIII, the latter persuaded Otto to employ Gerbert as tutor for his son the future Otto II. Later Gerbert would exercise the same function for Otto II’s son the future Otto III. The close connection with the Imperial family promoted Gerbert’s ecclesiastical career and led to him eventually being appointed pope but more importantly in our context it promoted his career as an educator.

Gerbert taught the whole of the seven liberal arts, as handed down by Boethius but placed special emphasis on teaching the quadrivium–arithmetic, geometry, music and astronomy–bringing in the knowledge that he had acquired from Arabic sources during his years in Spain. He was responsible for reintroducing the armillary sphere and the abacus into Europe and was one of the first to use Hindu-Arabic numerals, although his usage of them had little effect. He is also reported to have used sighting tubes to aid naked-eye astronomical observations.

Gerbert was not a practicing scientist but rather a teacher who wrote a series of textbook on the then mathematical sciences: Libellus de numerorum divisione, De geometria, Regula de abaco computi, Liber abaci, and Libellus de rationali et ratione uti.


12th century copy of De geometria Source: Wikimedia Commons

His own influence through his manuscripts and his letters was fairly substantial and this was extended by various of his colleagues and students. Abbo of Fleury (c. 945–1004), a colleague, wrote extensively on computus and astronomy, Fulbert of Chartres (c. 960–1028), a direct student, also introduced the use of the Hindu-Arabic numerals. Hermann of Reichenau (1013–1054 continued the tradition writing on the astrolabe, mathematics and astronomy.

Gerbert and his low level, partial reintroduction into Europe of the mathematical science from out of the Islamic cultural sphere can be viewed as a precursor to the third medieval renaissance the so-called Scientific Renaissance with began a century later at the beginning of the twelfth century. This was the mass translation of scientific works, across a wide spectrum, from Arabic into Latin by European scholars, who had become aware of their own relative ignorance compared to their Islamic neighbours and travelled to the border areas between Europe and the Islamic cultural sphere of influence in Southern Italy and Spain. Some of them even travelling in Islamic lands. This Scientific Renaissance took place over a couple of centuries and was concurrent with the founding of the European universities and played a major role in the later Humanist Renaissance to which it was viewed by the humanists as a counterpart. We shall look at it in some detail in the next post.

[1] For any readers, who might not already know, the original quote is, “There was no such thing as the Scientific Revolution, and this is a book about it”, which is the opening sentence of Stevin Shapin’s The Scientific Revolution, The University of Chicago Press, Chicago and London, 1996


Filed under History of science, Mediaeval Science, Renaissance Science, Uncategorized

Reading Euclid

This is an addendum to yesterday review of Reading Mathematics in Early Modern Europe. As I noted there the book was an outcome of two workshops held, as part of the research project Reading Euclid that ran from 2016 to 2018. The project, which was based at Oxford University was led by Benjamin Wardhaugh, Yelda Nasifoglu (@YeldaNasif) and Philip Beeley.

The research project has its own website and Twitter account @ReadingEuclid. As well as Benjamin Wardhaugh’s The Book of Wonders: The Many Lives of Euclid’s Elements, which I reviewed here:


And Reading Mathematics in Early Modern EuropeStudies in the Production, Collection, and Use of Mathematical Books, which I reviewed yesterday.

Reading Maths01

There is also a third online publication Euclid in print, 1482–1703: A catalogue of the editions of the Elements and other Euclidian Works, which is open access and can be downloaded as a pdf for free.

All of this is essential reading for anybody interested in the history of the most often published mathematics textbook of all times.

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Filed under Book Reviews, History of Mathematics

There’s more to reading than just looking at the words

When I first became interested in the history of mathematics, now literally a lifetime ago, it was dominated by a big events, big names approach to the discipline. It was also largely presentist, only interested in those aspects of the history that are still relevant in the present. As well as this, it was internalist history only interested in results and not really interested in any aspects of the context in which those results were created. This began to change as some historians began to research the external circumstances in which the mathematics itself was created and also the context, which was often different to the context in which the mathematics is used today. This led to the internalist-externalist debate in which the generation of strictly internalist historians questioned the sense of doing external history with many of them rejecting the approach completely.

As I have said on several occasions, in the 1980s, I served my own apprenticeship, as a mature student, as a historian of science in a major research project into the external history of formal or mathematical logic. As far as I know it was the first such research project in this area. In the intervening years things have evolved substantially and every aspect of the history of mathematics is open to the historian. During my lifetime the history of the book has undergone a similar trajectory, moving from the big names, big events modus to a much more open and diverse approach.

The two streams converged some time back and there are now interesting approaches to examining in depth mathematical publications in the contexts of their genesis, their continuing history and their use over the years. I recently reviewed a fascinating volume in this genre, Benjamin Wardhaugh’s The Book of Wonder: The Many Lives of Euclid’s Elements. Wardhaugh was a central figure in the Oxford-based Reading Euclid research project (2016–2018) and I now have a second volume that has grown out of two workshops, which took place within that project, Reading Mathematics in Early Modern Europe: Studies in the Production, Collection, and Use of Mathematical Books[1]. As the subtitle implies this is a wide-ranging and stimulating collection of papers covering many different aspects of how writers, researchers, and readers dealt with the mathematical written word in the Early Modern Period.

Reading Maths01

In general, the academic standard of all the papers presented here is at the highest level.  The authors of the individual papers are all very obviously experts on the themes that they write about and display a high-level of knowledge on them. However, all of the papers are well written, easily accessible and easy to understand for the non-expert. The book opens with a ten-page introduction that explains what is being presented here is clear, simple terms for those new to the field of study, which, I suspect, will probably the majority of the readers.

The first paper deals with Euclid, which is not surprising given the origin of the volume. Vincenzo De Risi takes use through the discussion in the 16th and 17th centuries by mathematical readers of the Elements of Book 1, Proposition 1 and whether Euclid makes a hidden assumption in his construction. Risi points out that this discussion is normally attributed to Pasch and Hilbert in the 19th century but that the Early Modern mathematicians were very much on the ball three hundred years earlier.

We stay with Euclid and his Elements in the second paper by Robert Goulding, who takes us through Henry Savile’s attempts to understand and maybe improve on the Euclidean theory of proportions. Savile, best known for giving his name and his money to establish the first chairs for mathematics and astronomy at the University of Oxford, is an important figure in Early Modern mathematics, who largely gets ignored in the big names, big events history of the subject, but quite rightly turns up a couple of times here. Goulding guides the reader skilfully through Savile’s struggles with the Euclidean theory, an interesting insight into the thought processes of an undeniably, brilliant polymath.

In the third paper, Yelda Nasifoglu stays with Euclid and geometry but takes the reader into a completely different aspect of reading, namely how did Early Modern mathematicians read, that is interpret and present geometrical drawings? Thereby, she demonstrates very clearly how this process changed over time, with the readings of the diagrams evolving and changing with successive generations.

We stick with the reading of a diagram, but leave Euclid, with the fourth paper from Renée Raphael, who goes through the various reactions of readers to a problematic diagram that Tycho Brahe used to argue that the comet of 1577 was supralunar. It is interesting and very informative, how Tycho’s opponents and supporters used different reading strategies to justify their standpoints on the question. It illuminates very clearly that one brings a preformed opinion to a given text when reading, there is no tabula rasa.

Reading Maths02

We change direction completely with Mordechai Feingold, who takes us through the reading of mathematics in the English collegiate-humanist universities. This is a far from trivial topic, as the Early Modern humanist scholars were, at least superficially, not really interested in the mathematical sciences. Feingold elucidates the ambivalent attitude of the humanists to mathematical topics in detail. This paper was of particular interest to me, as I am currently trying to deepen and expand my knowledge of Renaissance science.

Richard Oosterhoff, in his paper, takes us into the mathematical world of the relatively obscure Oxford fellow and tutor Brian Twyne (1581–1644). Twyne’s manuscript mathematical notes, complied from various sources open a window on the actual level and style of mathematics’ teaching at the university in the Early Modern Period, which is somewhat removed from what one might have expected.

Librarian William Poole takes us back to Henry Savile. As well as giving his name and his money to the Savilian mathematical chairs, Savile also donated his library of books and manuscripts to be used by the Savilian professors in their work. Poole takes us on a highly informative tour of that library from its foundations by Savile and on through the usage, additions and occasional subtractions made by the Savilian professors down to the end of the 17th century.

Philip Beeley reintroduced me to a recently acquired 17th century mathematical friend, Edward Bernard and his doomed attempt to produce and publish an annotated, Greek/Latin, definitive editions of the Elements. I first became aware of Bernard in Wardhaugh’s The Book of Wonder. Whereas Wardhaugh, in his account, concentrated on the extraordinary one off, trilingual, annotated, Euclid (Greek, Latin, Arabic) that Bernard put together to aid his research and which is currently housed in the Bodleian, Beeley examines Bernard’s increasing desperate attempts to find sponsors to promote the subscription scheme that is intended to finance his planned volume. This is discussed within the context of the problems involved in the late 17th and early 18th century in getting publishers to finance serious academic publications at all. The paper closes with an account of the history behind the editing and publishing of David Gregory’s Euclid, which also failed to find financial backers and was in the end paid for by the university.

Following highbrow publications, Wardhaugh’s own contribution to this volume goes down market to the world of Georgian mathematical textbooks and their readers annotations. Wardhaugh devotes a large part of his paper to the methodology he uses to sort and categorise the annotations in the 366 copies of the books that he examined. He acknowledges that any conclusions that he draws from his investigations are tentative, but his paper definitely indicates a direction for more research of this type.

Boris Jardine takes us back to the 16th century and the Pantometria co-authored by father and son Leonard and Thomas Digges. This was a popular book of practical mathematics in its time and well into the 17th century. Jardine examines how such a practical mathematics text was read and then utilised by its readers.

Kevin Tracey closes out the volume with a final contribution on lowbrow mathematical literature and its readers with an examination of John Seller’s A Pocket Book, a compendium of a wide range of elementary mathematical topics written for the layman. Following a brief description of Seller’s career as an instrument maker, cartographer and mathematical book author, Tracey examines marginalia in copies of the book and shows that it was also actually used by university undergraduates.

Reading Maths03

The book is nicely presented and in the relevant papers illustrated with the now ubiquitous grey in grey prints. Each paper has its own collection of detailed, informative, largely bibliographical endnotes. The books referenced in those endnotes are collected in an extensive bibliography at the end of the book and there is also a comprehensive index.

As a whole, this volume meets the highest standards for an academic publication, whilst remaining very accessible for the general reader. This book should definitely be read by all those interested in the history of mathematics in the Early Modern Period and in fact by anybody interested in the history of mathematics. It is also a book for those interested in the history of the book and in the comparatively new discipline, the history of reading. I would go further and recommend it for general historians of the Early Modern Period, as well as interested non experts.

[1] Reading Mathematics in Early Modern Europe: Studies in the Production, Collection, and Use of Mathematical Books, eds. Philip Beeley, Yelda Nasifoglu and Benjamin Wardhaugh, Material Readings in Early Modern Culture, Routledge, New York and London, 2021

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Charles not Ada, Charles not Charles and Ada, just Charles…

The is an old saying in English, “if you’ve got an itch scratch it!” A medically more correct piece of advice is offered, usually by mothers in a loud stern voice, “Don’t scratch!”  I have had an itch since the start of December and have been manfully trying to heed the wise words of mother but have finally cracked and am going to have a bloody good scratch.

I actually don’t wish to dump on Lady Science, which I regard as a usually excellent website promoting the role of women in science, particularly in the history of science but the essay, Before Lovelace, that they posted 3 December 2020 is so full of errors concerning Ada Lovelace and Charles Babbage that I simply cannot ignore it. In and of itself the main point that the concept of the algorithm exists in many fields and did so long before the invention of the computer is interesting and of course correct. In fact, it is a trivial point, that is trivial in the sense of simple and obvious. An algorithm is just a finite, step by step procedure to complete a task or solve a problem, a recipe!

My objections concern the wildly inaccurate claims about the respective roles of Charles Babbage and Ada Lovelace in the story of the Analytical Engine. Let us examine those claims, the essay opens at follows:

Charles Babbage and Ada Lovelace loom large in the history of computing. These famous 19th-century figures are consistently cited as the origin points for the modern day computer: Babbage hailed as the “father of computing” and Lovelace as the “first computer programmer” Babbage was a mathematician, inventor, and engineer, famous for his lavish parties and his curmudgeonly attitude. Lady Augusta Ada King, Countess of Lovelace was a mathematician and scientist, introduced to Babbage when she was a teenager. The two developed a long professional relationship, which included their collaborative work on a machine called the Analytical Engine, a design for the first mechanical, programmable computer.

They might be cited as the origin points of the modern-day computer, but such claims are historically wrong. For all of Babbage’s ingenuity in the design and conception of his mechanical, programmable calculating machines they played absolutely no role in and had no influence on the later development of the computer in the twentieth century. They were and remain an interesting historical anomaly. Regular readers of this blog will know that I reject the use of the expression “the father of” for anything in #histSTM and that for very good reasons. They will also know that I reject Ada Lovelace being called the “first computer programmer” for the very simple reason that she wasn’t. (See addendum below) I am of the opinion that Ada Lovelace was not a mathematician in any meaningful sense of the word, and she was in absolutely no way a scientist. Ada Lovelace and Charles Babbage did not have a long professional relationship and did not collaborate on the design of the Analytical Engine, which was entirely the work of Charles Babbage alone, and in which Ada Lovelace played absolutely no part. Assigning co-authorship and co-development to Ada Lovelace for Babbage’s work is no different to saying that a journalist, who interviews a scientist about his research work and then write a puff piece about it, is the scientist’s co-researcher! The train-wreck continues:

Much of what we know about the Analytical Engine comes from Lovelace’s paper on the machine. In 1842, she published” A Sketch of the Analytical Engine, with notes by the Translator”,” a translation of an earlier article by mathematician Luigi Menabrea. Lovelace’s English translation of Menabrea’s article included her own extended appendix in which she elaborated on the machine’s design and proposed several early computer programs. Her notes were instrumental for Alan Turing’s work on the first modern computer in the 1930s. His work would later provide the basis for the Colossus computer, the world’s first large-scale programmable, electronic, digital computer, developed to assist with cryptography work during World War II. Machines like the Colossus were the precursors to the computers we carry around today in our pockets and our backpacks.

We actually know far more about the Analytical Engine from Babbage’s biography (see footnote 1) and his own extensive papers on it, which were collected and published by his son Henry, Babbage’s Calculating Engines: Being a Collection of Papers Relating to Them; Their History and Construction, Charles Babbage, Edited by Henry P. Babbage, CUP, 1889. The notes to the translation, which the author calls an appendix, we know to have been co-authored by Babbage and Lovelace and not as here stated written by Lovelace alone. There is only one computer program in the notes and that we know to have been written by Babbage and not Lovelace. (See addendum below) Her notes played absolutely no role whatsoever in Turing’s work in the 1930s, which was not on the first modern computer but on a problem in metamathematics, known as the Entscheidungsproblem (English: decision problem). Turing discussed one part of the notes in his paper on artificial intelligence, Computing Machinery and Intelligence, (Mind, October 1950). Turing’s 1930s work had nothing to do with the design of the Colossus, although his work on the use of probability in cryptoanalysis did. Colossus was designed and built by Tommy Flowers, who generally gets far too little credit for his pioneering work in computers. The Colossus played no role in the future development of computers because the British government dismantled or hid all of the Colossus computers from Bletchley Park after the war and closed access to the information on the Colossus for thirty years under the official secret act. We are not done yet:

With Babbage and Lovelace’s work as the foundation and the Turing Machine as the next step toward what we now think of as computers…

Babbage’s work, not Babbage’s and Lovelace’s, was not, as already stated above, the foundation and the Turing Machine was very definitely not the next step towards what we now think of as the computer. I really do wish that people would take the trouble to find out what a Turing Machine really is. It’s an abstract metamathematical concept that is useful for describing, on an abstract level, how a computer works and for defining the computing power or capabilities of a given computer. It played no role in the development of real computers in the 1940s and wasn’t even referenced in the computer industry before the 1950s at the very earliest. Small tip for future authors, if you are going to write about the history of the computer, it pays to learn something about that history before you start. We are approaching the finish line:

One part of the history of computing that is much less familiar is the role the textile industry played in Babbage and Lovelace’s plans for the Analytical Engine. In a key line from Lovelace’s publication, she observes, “we may say most aptly that the Analytical Engine weaves algebraical patterns just as the Jacquard loom weaves flowers and leaves.” The Jacquard Loom was a mechanical weaving system controlled by a chain of punched cards. The punched cards were fed into the weaving loom and dictated which threads were activated as the machine wove each row. The result was an intricate textile pattern that had been “programmed” by the punch cards.

Impressed by the ingenuity of this automation system, Babbage and Lovelace used punched cards as the processing input for the Analytical Engine. The punched cards, Lovelace explains in her notes, contain “the impress of whatever special function we may desire to develop or to tabulate” using the machine.

Why is it that so many authors use ‘less familiar’ or ‘less well known’ about things that are very well known to those, who take an interest in the given topic? For those, who take an interest in Babbage and his computers, the fact that he borrowed the punch card concept from Jacquard’s mechanical, silk weaving loom is very well known. Once again, I must emphasise, Babbage and not Babbage and Lovelace. He adopted the idea of using punch cards to program the Analytical Engine entirely alone, Ada Lovelace was not in anyway involved in this decision.

Itch now successfully scratched! As, I said at the beginning the rest of the essay makes some interesting points and is well worth a read, but I really do wish she had done some real research before writing the totally crap introduction.


I have pointed out on numerous occasions that it was Babbage, who wrote the program for the Analytical Engine to calculate the Bernoulli numbers, as presented in Note G of the Lovelace memoir. He tells us this himself in his autobiography[1]. I have been called a liar for stating this and also challenged to provide evidence by people to lazy to check for themselves, so here are his own words in black and white (16-bit grayscale actually)

Babbage 01

[1] Charles Babbage, Passages from the Life of a Philosopher, Longman, Green, Longman, Roberts, Green, London, 1864, p. 136


Filed under History of Computing, History of Logic

The emergence of modern astronomy – a complex mosaic: Part LII

This is a concluding summary to my The emergence of modern astronomy – a complex mosaic blog post series. It is an attempt to produce an outline sketch of the path that we have followed over the last two years. There are, at the appropriate points, links to the original posts for those, who wish to examine a given point in more detail. I thank all the readers, who have made the journey with me and in particular all those who have posted helpful comments and corrections. Constructive comments and especially corrections are always very welcome. For those who have developed a taste for a continuous history of science narrative served up in easily digestible slices at regular intervals, a new series will start today in two weeks if all goes according to plan!

There is a sort of standard popular description of the so-called astronomical revolution that took place in the Early Modern period that goes something liker this. The Ptolemaic geocentric model of the cosmos ruled unchallenged for 1400 years until Nicolas Copernicus published his trailblazing De revolutionibus in 1453, introducing the concept of the heliocentric cosmos. Following some initial resistance, Kepler with his three laws of planetary motion and Galileo with his revelatory telescopic discoveries proved the existence of heliocentricity. Isaac Newton with his law of gravity in his Principia in 1687 provided the physical mechanism for a heliocentric cosmos and astronomy became modern. What I have tried to do in this series is to show that this version of the story is almost totally mythical and that in fact the transition from a geocentric to a heliocentric model of the cosmos was a long drawn out, complex process that took many stages and involved many people and their ideas, some right, some only half right and some even totally false, but all of which contributed in some way to that transition.

The whole process started at least one hundred and fifty years before Copernicus published his magnum opus, when at the beginning of the fifteenth century it was generally acknowledged that astronomy needed to be improved, renewed and reformed. Copernicus’ heliocentric hypothesis was just one contribution, albeit a highly significant one, to that reform process. This reform process was largely triggered by the reintroduction of mathematical cartography into Europe with the translation into Latin of Ptolemaeus’ Geōgraphikḕ Hyphḗgēsis by Jacopo d’Angelo (c. 1360 – 1411) in 1406. A reliable and accurate astronomy was needed to determine longitude and latitude. Other driving forces behind the need for renewal and reform were astrology, principally in the form of astro-medicine, a widened interest in surveying driven by changes in land ownership and navigation as the Europeans began to widen and expand their trading routes and to explore the world outside of Europe.


The Ptolemaic Cosmos: Andreas Cellarius, Harmonia Macrocosmica 1660 Source: Wikimedia Commons

At the beginning of the fifteenth century the predominant system was an uneasy marriage of Aristotelian cosmology and Ptolemaic astronomy, uneasy because they contradicted each other to a large extent. Given the need for renewal and reform there were lively debates about almost all aspects of the cosmology and astronomy throughout the fifteenth and sixteenth centuries, many aspects of the discussions had their roots deep in the European and Islamic Middle Ages, which shows that the 1400 years of unchallenged Ptolemaic geocentricity is a myth, although an underlying general acceptance of geocentricity was the norm.

A major influence on this programme of renewal was the invention of moving type book printing in the middle of the fifteenth century, which made important texts in accurate editions more readily available to interested scholars. The programme for renewal also drove a change in the teaching of mathematics and astronomy on the fifteenth century European universities. 

One debate that was new was on the nature and status of comets, a debate that starts with Toscanelli in the early fifteenth century, was taken up by Peuerbach and Regiomontanus in the middle of the century, was revived in the early sixteenth century in a Europe wide debate between Apian, Schöner, Fine, Cardano, Fracastoro and Copernicus, leading to the decisive claims in the 1570s by Tycho Brahe, Michael Mästlin, and Thaddaeus Hagecius ab Hayek that comets were celestial object above the Moon’s orbit and thus Aristotle’s claim that they were a sub-lunar meteorological phenomenon was false. Supralunar comets also demolished the Aristotelian celestial, crystalline spheres. These claims were acknowledged and accepted by the leading European Ptolemaic astronomer, Christoph Clavius, as were the claims that the 1572 nova was supralunar. Both occurrences shredded the Aristotelian cosmological concept that the heaven were immutable and unchanging.

The comet debate continued with significant impact in 1618, the 1660s, the 1680s and especially in the combined efforts of Isaac Newton and Edmund Halley, reaching a culmination in the latter’s correct prediction that the comet of 1682 would return in 1758. A major confirmation of the law of gravity.

During those early debates it was not just single objects, such as comets, that were discussed but whole astronomical systems were touted as alternatives to the Ptolemaic model. There was an active revival of the Eudoxian-Aristotelian homocentric astronomy, already proposed in the Middle Ages, because the Ptolemaic system, of deferents, epicycles and equant points, was seen to violate the so-called Platonic axioms of circular orbits and uniform circular motion. Another much discussed proposal was the possibility of diurnal rotation, a discussion that had its roots in antiquity. Also, on the table as a possibility was the Capellan system with Mercury and Venus orbiting the Sun in a geocentric system rather than the Earth.


The Copernican Cosmos: Andreas Cellarius, Harmonia Macrocosmica 1660 Source: Wikimedia Commons

Early in the sixteenth century, Copernicus entered these debates, as one who questioned the Ptolemaic system because of its breaches of the Platonic axioms, in particular the equant point, which he wished to ban. Quite how he arrived at his radical solution, replace geocentricity with heliocentricity we don’t know but it certainly stirred up those debates, without actually dominating them. The reception of Copernicus’ heliocentric hypothesis was complex. Some simply rejected it, as he offered no real proof for it. A small number had embraced and accepted it by the turn of the century. A larger number treated it as an instrumentalist theory and hoped that his models would deliver more accurate planetary tables and ephemerides, which they duly created. Their hopes were dashed, as the Copernican tables, based on the same ancient and corrupt data, proved just as inaccurate as the already existing Ptolemaic ones. Of interests is the fact that it generated a serious competitor, as various astronomers produced geo-heliocentric systems, extensions of the Capellan model, in which the planets orbit the Sun, which together with the Moon orbits the Earth. Such so-called Tychonic or semi-Tychonic systems, named after their most well-known propagator, incorporated all the acknowledged advantages of the Copernican model, without the problem of a moving Earth, although some of the proposed models did have diurnal rotation.


The Tychonic Cosmos: Andreas Cellarius, Harmonia Macrocosmica 1660 Source: Wikimedia Commons

The problem of inaccurate planetary tables and ephemerides was already well known in the Middle Ages and regarded as a major problem. The production of such tables was seen as the primary function of astronomy since antiquity and they were essential to all the applied areas mentioned earlier that were the driving forces behind the need for renewal and reform. Already in the fifteenth century, Regiomontanus had set out an ambitious programme of astronomical observation to provide a new data base for such tables. Unfortunately, he died before he even really got started. In the second half of the sixteenth century both Wilhelm IV Landgrave of Hessen-Kassel and Tycho Brahe took up the challenge and set up ambitious observation programmes that would eventually deliver the desired new, more accurate astronomical data.

At the end of the first decade of the seventeenth century, Kepler’s Astronomia Nova, with his first two planetary laws (derived from Tycho’s new accurate data), and the invention of the telescope and Galileo’s Sidereus Nuncius with his telescopic discoveries are, in the standard mythology, presented as significant game changing events in favour of heliocentricity. They were indeed significant but did not have the impact on the system debate that is usually attributed them. Kepler’s initial publication fell largely on deaf ears and only later became relevant. On Galileo’s telescopic observations, firstly he was only one of a group of astronomers, who in the period 1610 to 1613 each independently made those discoveries, (Thomas Harriot and William Lower, Simon Marius, Johannes Fabricius, Odo van Maelcote and Giovanni Paolo Lembo, and Christoph Scheiner) but what did they show or prove? The lunar features were another nail in the coffin of the Aristotelian concept of celestial perfection, as were the sunspots. The moons of Jupiter disproved the homocentric hypothesis. Most significant discovery was the of the phases of Venus, which showed that a pure geocentric model was impossible, but they were conform with various geo-heliocentric models.

1613 did not show any clarity on the way to finding the true model of the cosmos but rather saw a plethora of models competing for attention. There were still convinced supporters of a Ptolemaic model, both with and without diurnal rotation, despite the phases of Venus. Various Tychonic and semi-Tychonic models, once again both with and without diurnal rotation. Copernicus’ heliocentric model with its Ptolemaic deferents and epicycles and lastly Kepler’s heliocentric system with its elliptical orbits, which was regarded as a competitor to Copernicus’ system. Over the next twenty years the fog cleared substantially and following Kepler’s publication of his third law, his Epitome Astronomiae Copernicanae, which despite its title is a textbook on his elliptical system and the Rudolphine Tables, again based on Tycho’s data, which delivered the much desired accurate tables for the astrologers, navigators, surveyors and cartographers, and also of Longomontanus’ Astronomia Danica (1622) with his own tables derived from Tycho’s data presenting an updated Tychonic system with diurnal rotation, there were only two systems left in contention.

Around 1630, we now have two major world systems but not the already refuted geocentric system of Ptolemaeus and the largely forgotten Copernican system as presented in Galileo’s Dialogo but Kepler’s elliptical heliocentricity and a Tychonic system, usually with diurnal rotation. It is interesting that diurnal rotation became accepted well before full heliocentricity, although there was no actually empirical evidence for it. In terms of acceptance the Tychonic system had its nose well ahead of Kepler because of the lack of any empirical evidence for movement of the Earth.

Although there was still not a general acceptance of the heliocentric hypothesis during the seventeenth century the widespread discussion of it in continued in the published astronomical literature, which helped to spread knowledge of it and to some extent popularise it. This discussion also spread into and even dominated the newly emerging field of proto-sciencefiction.

Galileo’s Dialogo was hopelessly outdated and contributed little to nothing to the real debate on the astronomical system. However, his Discorsi made a very significant and important contribution to a closely related topic that of the evolution of modern physics. The mainstream medieval Aristotelian-Ptolemaic cosmological- astronomical model came as a complete package together with Aristotle’s theories of celestial and terrestrial motion. His cosmological model also contained a sort of friction drive rotating the spheres from the outer celestial sphere, driven by the unmoved mover (for Christians their God), down to the lunar sphere. With the gradual demolition of Aristotelian cosmology, a new physics must be developed to replace the Aristotelian theories.

Once again challenges to the Aristotelian physics had already begun in the Middle Ages, in the sixth century CE with the work of John Philoponus and the impetus theory, was extended by Islamic astronomers and then European ones in the High Middle Ages. In the fourteenth century the so-called Oxford Calculatores derived the mean speed theorem, the core of the laws of fall and this work was developed and disseminated by the so-called Paris Physicists. In the sixteenth century various mathematicians, most notably Tartaglia and Benedetti developed the theories of motion and fall further. As did in the early seventeenth century the work of Simon Stevin and Isaac Beeckman. These developments reached a temporary high point in Galileo’s Discorsi. Not only was a new terrestrial physics necessary but also importantly for astronomy a new celestial physics had to be developed. The first person to attempt this was Kepler, who replaced the early concept of animation for the planets with the concept of a force, hypothesising some sort of magnetic force emanating from the Sun driving the planets around their orbits. Giovanni Alfonso Borelli also proposed a system of forces as the source of planetary motion.

Throughout the seventeenth century various natural philosophers worked on and made contributions to defining and clarifying the basic terms that make up the science of dynamics: force, speed, velocity, acceleration, etc. as well as developing other areas of physics, Amongst them were Simon Stevin, Isaac Beeckman, Borelli, Descartes, Pascal, Riccioli and Christiaan Huygens. Their efforts were brought together and synthesised by Isaac Newton in his Principia with its three laws of motion, the law of gravity and Kepler’s three laws of planetary motion, which laid the foundations of modern physics.

In astronomy telescopic observations continued to add new details to the knowledge of the solar system. It was discovered that the planets have diurnal rotation, and the periods of their diurnal rotations were determined. This was a strong indication the Earth would also have diurnal rotation. Huygens figured out the rings of Saturn and discovered Titan its largest moon. Cassini discovered four further moons of Saturn. It was already known that the four moons of Jupiter obeyed Kepler’s third law and it would later be determined that the then known five moons of Saturn also did so. Strong confirming evidence for a Keplerian model.

Cassini showed by use of a heliometer that either the orbit of the Sun around the Earth or the Earth around the Sun was definitively an ellipse but could not determine which orbited which. There was still no real empirical evidence to distinguish between Kepler’s elliptical heliocentric model and a Tychonic geo-heliocentric one, but a new proof of Kepler’s disputed second law and an Occam’s razor argument led to the general acceptance of the Keplerian model around 1660-1670, although there was still no empirical evidence for either the Earth’s orbit around the Sun or for diurnal rotation. Newton’s Principia, with its inverse square law of gravity provided the physical mechanism for what should now best be called the Keplerian-Newtonian heliocentric cosmos.

Even at this juncture with a very widespread general acceptance of this Keplerian-Newtonian heliocentric cosmos there were still a number of open questions that needed to be answered. There were challenges to Newton’s work, which, for example, couldn’t at that point fully explain the erratic orbit of the Moon around the Earth. This problem had been solved by the middle of the eighteenth century. The mechanical philosophers on the European continent were anything but happy with Newton’s gravity, an attractive force that operates at a distance. What exactly is it and how does it function? Questions that even Newton couldn’t really answer. Leibniz also questioned Newton’s insistence that time and space were absolute, that there exists a nil point in the system from which all measurement of these parameters are taken. Leibniz preferred a relative model.

There was of course also the very major problem of the lack of any form of empirical evidence for the Earth’s movement. Going back to Copernicus nobody had in the intervening one hundred and fifty years succeeded in detecting a stellar parallax that would confirm that the Earth does indeed orbit the Sun. This proof was finally delivered in 1725 by Samuel Molyneux and James Bradley, who first observed, not stellar parallax but stellar aberration. An indirect proof of diurnal rotation was provided in the middle of the eighteenth century, when the natural philosophers of the French Scientific Academy correctly determined the shape of the Earth, as an oblate spheroid, flattened at the pols and with an equatorial bulge, confirming the hypothetical model proposed by Newton and Huygens based on the assumption of a rotating Earth.

Another outstanding problem that had existed since antiquity was determining the dimensions of the known cosmos. The first obvious method to fulfil this task was the use of parallax, but whilst it was already possible in antiquity to determine the distance of the Moon reasonably accurately using parallax, down to the eighteenth century it proved totally impossible to detect the parallax of any other celestial body and thus its distance from the Earth. Ptolemaeus’ geocentric model had dimensions cobbled together from its data on the crystalline spheres. One of the advantages of the heliocentric model is that it gives automatically relative distances for the planets from the sun and each other. This means that one only needs to determine a single actually distance correctly and all the others are automatically given. Efforts concentrated on determining the distance between the Earth and the Sun, the astronomical unit, without any real success; most efforts producing figures that were much too small.

Developing a suggestion of James Gregory, Edmond Halley explained how a transit of Venus could be used to determine solar parallax and thus the true size of the astronomical unit. In the 1760s two transits of Venus gave the world the opportunity to put Halley’s theory into practice and whilst various problems reduced the accuracy of the measurements, a reasonable approximation for the Sun’s distance from the Earth was obtained for the very first time and with it the actually dimensions of the planetary part of the then known solar system. What still remained completely in the dark was the distance of the stars from the Earth. In the 1830s, three astronomers–Thomas Henderson, Friedrich Wilhelm Bessel and Friedrich Georg Wilhelm von Struve–all independently succeeded in detecting and measuring a stellar parallax thus completing the search for the dimensions of the known cosmos and supplying a second confirmation, after stellar aberration, for the Earth’s orbiting the Sun.

In 1851, Léon Foucault, exploiting the Coriolis effect first hypothesised by Riccioli in the seventeenth century, finally gave a direct empirical demonstration of diurnal rotation using a simple pendulum, three centuries after Copernicus published his heliocentric hypothesis. Ironically this demonstration was within the grasp of Galileo, who experiment with pendulums and who so desperately wanted to be the man who proved the reality of the heliocentric model, but he never realised the possibility. His last student, Vincenzo Viviani, actually recorded the Coriolis effect on a pendulum but didn’t realise what it was and dismissed it as an experimental error.

From the middle of the eighteenth century, at the latest, the Keplerian-Newtonian heliocentric model had become accepted as the real description of the known cosmos. Newton was thought not just to have produced a real description of the cosmos but the have uncovered the final scientific truth. This was confirmed on several occasions. Firstly, Herschel’s freshly discovered new planet Uranus in 1781 fitted Newton’s theories without problem, as did the series of asteroids discovered in the early nineteenth century. Even more spectacular was the discovery of Neptune in 1846 based on observed perturbations from the path of Uranus calculated with Newton’s theory, a clear confirmation of the theory of gravity. Philosophers, such as Immanuel Kant, no longer questioned whether Newton had discovered the true picture of the cosmos but how it had been possible for him to do so.


However, appearances were deceptive, and cracks were perceptible in the Keplerian-Newtonian heliocentric model. Firstly, Leibniz’s criticism of Newton’s insistence on absolute time and space rather than a relative model would turn out to have been very perceptive. Secondly, Newton’s theory of gravity couldn’t account for the observed perihelion precession of the planet Mercury. Thirdly in the 1860s, based on the experimental work of Michael Faraday, James Maxwell produced a theory of electromagnetism, which was not compatible with Newtonian physics. Throughout the rest of the century various scientists including Hendrik Lorentz, Georg Fitzgerald, Oliver Heaviside, Henri Poincaré, Albert Michelson and Edward Morley tried to find a resolution to the disparities between the Newton’s and Maxwell’s theories. Their efforts finally lead to Albert Einstein’s Special Theory of Relativity and then on to his General theory of Relativity, which could explain the perihelion precession of the planet Mercury. The completion of the one model, the Keplerian-Newtonian heliocentric one marked the beginnings of the route to a new system that would come to replace it.


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

Christmas Trilogy 2020 Part 3: The peregrinations of Johannes K

We know that human beings have been traversing vast distances on the surface of the globe since Homo sapiens first emerged from Africa. However, in medieval Europe it would not have been uncommon for somebody born into a poor family never in their life to have journeyed more than perhaps thirty kilometres from their place of birth. Maybe a journey into the next larger settlement on market day or perhaps once a year to an even larger town for a fair on a public holiday. This might well have been Johannes Kepler’s fate, born as he was into an impoverished family, had it not been for his extraordinary intellectual abilities. Although he never left the Southern German speaking area of Europe (today, Southern Germany, Austria and the Czech Republic), he managed to clock up a large number of journey kilometres over the fifty-eight years of his life. In those days there was, of course, no public transport and in general we don’t know how he travelled. We can assume that for some of his longer journeys that he joined trader caravans. Traders often travelled in large wagon trains with hired guards to protect them from thieves and marauding bands and travellers could, for a fee, join them for protection. We do know that as an adult Kepler travelled on horseback but was often forced to go by foot due to the pain caused by his piles.[1]

It is estimated that in the Middle ages someone travelling on foot with luggage would probably only manage 15 km per day going up to perhaps 22 km with minimal luggage. A horse rider without a spare mount maybe as much as 40 km per day, with a second horse up to 60 km per day. I leave it to the reader to work out how long each of Kepler’s journeys might have taken him.


Johannes Kepler Source: Wikimedia Commons

Johannes’ first journey from home took place, when he attended the convent-school in Adelberg at the age of thirteen, which lies about 70 km due west of his birthplace, Weil der Stadt, and about 90 km, also due west of Ellmendigen, where his family were living at the time.


Adelberg Convent Source: Wikimedia Commons

His next journey took place a couple of years later when he transferred to the Cistercian monastery in Maulbronn about 50 km north of Weil der Stadt and 30 west of Ellmendingen.


Maulbronn Monastery Source: Wikimedia Commons

Finished with the lower schools in 1589, he undertook the journey to the University of Tübingen, where he was enrolled in the Tübinger Stift, about 40 km south of Weil der Stadt.


The Evangelical Tübinger Stift on the banks of the Neckar Source: WIkimedia Commons

Johannes’ first really long journey took place in 1594, when on 11 April he set out for Graz the capital city of Styria in Austria to take up the posts of mathematics teacher in the Lutheran academy, as well as district mathematicus, a distance of about 650 km. The young scholar would have been on the road for quite a few days.


Graz, Mur und Schloßberg, Georg Matthäus Vischer (1670) Source: Wikimedia Commons

Although he only spent a few years in Graz, Kepler manged at first to stabilise his life even marrying, Barbara Müller, and starting a family. However, the religious conflicts of the period intervened and Kepler, a Lutheran Protestant living in a heavily Catholic area became a victim of those conflicts. First, the Protestants of the area were forced to convert or leave, which led to the closing of the school where Kepler was teaching and his losing his job. Because of his success as astrologer, part of his duties as district mathematicus, Kepler was granted an exception to the anti-Protestant order, but it was obvious that he would have to leave. He appealed to Tübingen to give him employment, but his request fell on deaf ears. The most promising alternative seemed to be to go and work for Tycho Brahe, the Imperial Mathematicus, currently ensconced in the imperial capital, Prague, a mere 450 km distant.


Prague in the Nuremberg Chronicle 1493 Source: Wikimedia Commons

At first Kepler didn’t know how he would manage the journey to Prague to negotiate about possible employment with Tycho. However, an aristocratic friend was undertaking the journey and took Johannes along as a favour. After, several weeks of fraught and at times downright nasty negotiations with the imperious Dane, Kepler was finally offered employment and with this promise in his pocket he returned to Graz to settle his affairs, pack up his household and move his family to Prague. He made the journey between Graz and Prague three times in less than a year.

Not long after his arrival in Prague, with his family, Tycho died and Kepler was appointed his successor, as Imperial Mathematicus, the start of a ten year relatively stable period in his life. That is, if you can call being an imperial servant at the court of Rudolf II, stable. Being on call 24/7 to answer the emperor’s astrological queries, battling permanently with the imperial treasury to get your promised salary paid, fighting with Tycho’s heirs over the rights to his data. Kepler’s life in Prague was not exactly stress free.

1608 saw Johannes back on the road. First to Heidelberg to see his first major and possibly most important contribution to modern astronomy, his Astronomia Nova (1609), through the press and then onto the book fair in Frankfurt to sell the finished work, that had cost him several years of his life. Finally, back home to Prague from Frankfurt. A total round-trip of 1100 km, plus he almost certainly took a detour to visit his mother somewhere along his route.

Back in Prague things began to look rather dodgy again for Kepler and his family, as Rudolf became more and more unstable and Johannes began to look for a new appointment and a new place to live. His appeals to Tübingen for a professorship, not an unreasonable request, as he was by now widely acknowledged as Europe’s leading theoretical astronomer, once again fell on deaf ears. His search for new employment eventually led him to Linz the capital city of Upper Austria and the post of district mathematicus. 1612, found Johannes and his children once again on the move, his wife, Barbara, had died shortly before, this time transferring their household over the comparatively short distance of 250 km.


Linz anno 1594 Source: Wikimedia Commons

Settled in Linz, Kepler married his second wife, Susanna Reuttinger, after having weighed up the odds on various potential marriage candidates and the beginning of a comparative settled fourteen-year period in his life. That is, if you can call becoming embroiled in the Thirty Years War and having your mother arrested and charged with witchcraft settled. His mother’s witchcraft trial saw Johannes undertaking the journey from Linz to Tübingen and home again, to organise and conduct her defence, from October to December in 1617 and again from September 1620 to November 1621, a round trip each time of about 1,000 km, not to forget the detours to Leonberg, his mother’s home, 50 km from Tübingen, from where he took his mother, a feeble woman of 70, back to Linz on the first journey.

In 1624, Johannes set out once again, this time to Vienna, now the imperial capital, to try and obtain the money necessary to print the Rudolphine Tables from Ferdinand II the ruling emperor, just 200 km in one direction. Ferdinand refused to give Kepler the money he required, although the production of the Rudolphine Tables had been an imperial assignment. Instead, he ordered the imperial treasury to issues Kepler promissory notes on debts owed to the emperor by the imperial cities of Kempten, Augsburg and Nürnberg, instructing him to go and collect on the debts himself. Kepler returned to Linz more than somewhat disgruntled and it is not an exaggeration that his life went downhill from here.

Kepler set out from Linz to Augsburg, approximately 300 km, but the Augsburg city council wasn’t playing ball and he left empty handed for Kempten, a relatively short 100 km. In Kempten the authorities agreed to purchase and pay for the paper that he needed to print the Rudolphine Tables. From Kempten he travelled on to Nürnberg, another 250 km, which he left again empty handed, returning the 300 km to Linz, completing a nearly 1,000 km frustrating round trip that took four months.

In 1626, the War forced him once again to pack up his home and to leave Linz forever with his family. He first travelled to Regensburg where he found accommodation for his family before travelling on to Ulm where he had had the paper from Kempten delivered so that he could begin printing, a combined journey of about 500 km. When the printing was completed in 1627, having paid the majority of the printing costs out of his own pocket, Kepler took the entire print run to the bookfair in Frankfurt and sold it in balk to a book dealer to recoup his money, another journey of 300 km. He first travelled back to Ulm and then home to his family in Regensburg, adding another 550 km to his life’s total. Regensburg was visited by the emperor and Wallenstein, commander in chief of the Catholic forces, and Kepler presented the Tables to the Emperor, who received them with much praise for the author.

In 1628, he entered the service of Wallenstein, as his astrologer, moving from Regensburg to Wallenstein’s estates in the Dutchy of Sagan, yet another 500 km. In 1630, the emperor called a Reichstag in Regensburg and on 8 October Kepler set out on the last journey of his life to attend. Why he chose to attend is not very clear, but he did. He journeyed from Zagan to Leipzig and from there to Nürnberg before going on to Regensburg a total of 700 km. He fell ill on his arrival in Regensburg and died 15 November 1630.


Regensburg Nuremberg Chronicle 1493 Source: Wikimedia Commons

The mathematical abilities of the young boy born to an impoverish family in Weil der Stadt fifty-eight-years earlier had taken him on a long intellectual journey but also as we have seen on a long physical one, down many a road.


[1] I almost certainly haven’t included all of the journeys that Kepler made in his lifetime, but I think I’ve got most of the important ones. The distances are rounded up or down and are based on the modern distances by road connecting the places travelled to and from. The roads might have run differently in Kepler’s day.

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Filed under History of Astrology, History of Astronomy, Renaissance Science

Christmas Trilogy 2020 Part 2: Charles brightens up the theatre

There is a strong tendency in the present to view Charles Babbage as a one trick pony i.e., Babbage the computer pioneer. In reality he was a true polymath whose intellectual activities covered a very wide spectrum.

Already as a student at Cambridge, he agitated for major curriculum reform in the mathematics taught and practiced in Britain. He also produced some first class cutting edge mathematics, much of which for some reason he never published. His interest in automation stretched way beyond his computing engines and after extensive research on automations in industry, both throughout Europe and in Britain, he wrote and published a book on the organisation of industrial production, On the Economy of Machinery and Manufactures (1832), which became a highly influential bestseller, influencing the work of both John Stuart Mill and Karl Marx. He was a leader in a campaign to improve the standard of science research in Britain, largely aimed at what he saw as the moribund Royal society, which resulted in his Reflections on the Decline of Science and some of its Causes (1830). As part of this campaign, he was a leading figure in the establishment of the British Association for the Advancement of Science (BAAS).


Engraving of Charles Babbage dated 1833 Source: Wikimedia Commons 

His achievements were not confined to purely intellectual activities, he was also an assiduous inventor of mechanical devices and improvement, well outside of his proto computers. For example, he designed and had constructed a four wheeled light carriage for one of his extensive tours of Europe. It was so designed that he could sleep on board and had drawers large enough to stow frock coats and technical plans without folding, as well as a small on board kitchen. However, it is his activities in practical optics that interest me here, in particular his foray into early theatre lighting, which I found fascinating, having, for several years in my youth, been a lighting technician both in theatre and live music.  

An ophthalmoscope is a medical instrument designed to make it possible to observe the interior of the eye by means of a beam of light. The invention of the ophthalmoscope is traditionally attributed to Hermann von Helmholtz in 1851. However, it would appear that Babbage preceded him by four years.

Charles Babbage, the mathematic genius and inventor of what many consider to be the forerunner of today’s computer, his analytical machine, was the first to construct an instrument for looking into the eye. He did this in 1847 but when showing it to the eminent ophthalmologist Thomas Wharton Jones he was unable to obtain an image with it and, thus discouraged, did not proceed further. Little did he know that his instrument would have worked if a minus lens of about 4 or 5 dioptres had been inserted between the observer’s eye and the back of the plano mirror from which two or three holes had been scraped. Some seven years later it was his design and not that of Helmholtz which had been adopted.


The image shows a reconstruction of Babbage’s ophthalmoscope, c. 1847. No actual example survives but this replica was made for the Science Museum in 2003, based upon Wharton Jones’ written description.

Dr. Helmholtz, of Konigsberg, has the merit of specially inventing the ophthalmoscope. It is but justice that I should here state, however, that seven years ago Mr. Babbage showed me the model of an instrument which he had contrived for the purpose of looking into the interior of the eye. It consisted of a bit of plain mirror, with the silvering scraped off at two or three small spots in the middle, fixed within a tube at such an angle that the rays of light falling on it through an opening in the side of the tube, were reflected into the eye to be observed, and to which the one end of the tube was directed. The observer looked through the clear spots of the mirror from the other end. This ophthalmoscope of Mr Babbage, we shall see, is in principle essentially the same as those of Epkens and Donders, of Coccius and of Meyerstein, which themselves are modifications of Helmhotlz’s.

         Wharton-Jones, T., 1854, ‘Report on the Ophthalmoscope’, Chronicle of Medical Science (October 1854).

Around the same time as he built his ophthalmoscope, Babbage designed and built a mechanical, clockwork, programmable, self-occulting, signalling lamp to aid ship to ship and ship to shore communications. He was disappointed that the British marine fleets showed no interest in his invention, but the Russian navy used it against the British during the Crimean War. During the Great Exhibition of 1851, in which Babbage played a central role, he set his signal lamp in the window of his house in the evenings and people passing by would drop in their visiting card with the signalled number written on them. Babbage’s occulting lights were later used in lighthouses in various parts of the world starting in the USA.


Babbage’s mechanical, clockwork, programmable, self-occulting, signalling lamp mechanism

Babbage was a theatre goer and during his phase of light experiments and invention he undertook an interesting project in theatre lighting. During the Renaissance, theatres, such as Shakespeare’s Globe, were open air arenas and performances took place in daylight. Later closed theatre and opera house were lit with chandeliers with the cut glass or crystal prisms dispersing the candlelight in all directions. Of course, the large number of candles needed caused much smoke and the dripping wax was a real problem. By the early nineteenth century theatres were illuminated with gas lamps.

One day during a theatre visit, Babbage noticed that during a moonlit scene the white bonnet of his companion had a pink taint and wondered about the possibility of using coloured light in theatre. He began a serious of interesting experiments with the then comparatively new limelight.

Limelight is an intense illumination created when an oxyhydrogen flame is directed at a cylinder of quicklime (calcium oxide). Quicklime can be heated to 2,572°C before melting and the light is produced by a combination of incandescence (the emission of electromagnetic radiation such as visible light e.g., red hot steel) and candoluminescence a form of radiation first observed and investigated in the early nineteenth century.


Diagram of a limelight burner Source: Wikimedia Commons

As with many inventions the oxyhydrogen blowpipe has many fathers and was first developed in the late eighteenth and early nineteenth centuries by Jean-Baptiste-Gaspard Bochart de Saron (1730–1794), Edward Daniel Clarke (1769–1822) and Robert Hare (1781–1858) all of whose work followed out of the pneumatic discoveries of Carl Wilhelm Scheele (1742–1786), Joseph Priestly (1733–1804), who both discovered oxygen, and Henry Cavendish (1731–1810), who discovered hydrogen.


Nineteenth century bellows-operated oxy-hydrogen blowpipe, including two different types of flashback arrestor John Griffen – A Practical Treatise on the Use of the Blowpipe, 1827 Source: Wikimedia Commons

The first to discover and experiment with limelight was the English chemist Goldsworthy Gurney (1792–1875)


Goldsworthy Gurney Source: Wikimedia Commons

but it was the Scottish engineer Thomas Drummond (1797–1840) who, having seen it demonstrated by Michael Faraday (1791–1867),  first exploited its potential as a light source. Drummond built a practical working light in 1826, which he then used as a signal lamp in trigonometrical surveying. The light was bright enough to be seen at a distance of 68 miles by sunlight. Drummond’s application was so successful that limelight was also known as Drummond light and he was falsely credited with its discovery, instead of Gurney.


Thomas Drummond by Henry William Pickersgill. The original picture is in the National gallery of Ireland Source: Wikimedia Commons

The earliest know public performance illuminated with limelight was an outdoor juggling performance by the magician Ching Lau Lauro (real name unknown) Herne Bay Pier in Kent in 1836. It was first used in theatre lighting in Covent Garden Theatre in 1837. By the 1860s and 1870s limelight was used worldwide in theatres and operas, used to highlight solo performers in the same way as modern spotlights, hence the expression, standing in the limelight. By the end of the nineteenth century, it had been largely replaced by electrical, carbon arc lighting.

 Babbage wanted to take the process one step further and use limelight not just as a very bright white light, but to introduce colour into theatre lighting. Babbage began to experiment with glass cells constructed out of two parallel sheets of glass and filled with solutions of various metal salts, such as chrome and copper. His experiment proved very successful and he developed coloured, limelight spots. Babbage now developed a dance scenario to display his new invention. He proposed replacing the stage footlights with four limelight projectors in the colours red, blue, yellow and purple. His imagined piece had four groups of dancers dressed in white, each of which entered the stage dancing in one of the four pools of light. Dancers springing from one pool of light into another would change colour. Gradually the apertures would widen with the lights crossing each other producing a rainbow of colours through which the dancers would circle. Babbage went on to develop a dramaturgy with dioramas telling an allegorical story.

Babbage discussed his project with Benjamin Lumley, the manager of the Italian Opera House (now Her Majesty’s Theatre) and arranged a demonstration of his new lights. The demonstration took place in the theatre with a smaller group of dancers, and it was apparently a great success. However, because of the fire risk he had two fire engines and their crews on standby during his demonstration and although impressed, Lumley declined a real performance with an audience because of the fire risk. Babbage didn’t develop the idea further.


Portrait of Benjamin Lumley by D’Orsay Source: Wikimedia Commons

As a onetime theatre lighting technician and a historian of science, I would would quite like the idea of staging a modern version of Babbage’s little dance fantasy. I would also like to draw this episode in his life to the attention of all the Ada Lovelace acolytes, who are firmly of the opinion that Babbage was only capable of thinking about mathematics and therefore the imaginative flights of fancy in the Analytical Engine memoir notes must be entirely the work of Lady King.

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Filed under History of Optics, History of Technology

Christmas Trilogy 2020 Part 1: Where did all that money come from Isaac?

If you have read my review of Thomas Levenson’s excellent Money for Nothing, then you know that when the South Sea Bubble burst in 1621 Isaac Newton lost £25,000 and despite these loses, when he died eight years later his estate was estimated to be worth about the same sum. By today’s standards £25,000, whilst a tidy sum, is not actually a lot of money. However, in the early seventeenth century £25,000 was the equivalent of as much as £3 million pounds today. This, of course, raises the question as to how a poor farm boy from Lincolnshire, who had to work his way through college, who then became a professor of mathematics, not the best paid job at the end of the seventeenth century, succeeded in becoming, by anybody’s standards, a very wealthy man.


Portrait of Newton at 46 by Godfrey Kneller, 1689 Source: Wikimedia Commons

Starting at the beginning, Isaac wasn’t actually a poor farm boy. It is true that when he went up to Cambridge in 1661, he entered Trinity College as a subsizar, which meant he had to pay his way by working as a valet for other students, but the facts deceive. His father, also called Isaac, was a wealthy yeoman farmer and the owner of Woolsthorpe Manor in Woolsthorpe-by-Colsterworth.


Woolsthorpe Manor Source: Wikimedia Commons

Isaac senior died before his only son was born leaving Isaac’s mother, Hannah Ayscough a wealthy woman. Hannah could have paid for her son’s tuition with ease and there is some discussion, as to why she chose not to do so. The standard account is that she was simple mean and miserly. However, I personally think, that there is another reason. The Newtons were of puritan stock and I think that the decision to make Isaac earn his tuition was a moral one. At the beginning of the seventeenth century Jeremiah Horrocks, who also came from a well-off puritan family, also had to pay his university tuition by working as a servant. In 1664, Isaac won a scholarship and in 1667 he was appointed a minor fellow of Trinity and a year later a major fellow, which meant that he was now financially independent but by no means well-off. However, the fact that as fellow he received free board and lodging meant that he could afford to live comfortably.


Trinity College Cambridge: David Loggan’s print of 1690 showing Nevile’s Great Court (foreground) and Nevile’s Court with the then-new Wren Library (background) – New Court had yet to be built. Source: Wikimedia Commons

The minor fellowship received a stipend of £2 p.a. with a livery allowance of £1 6s 8d per annum. In the Oxbridge college system, the fellows are the share holders of the college and receive a yearly dividend, as a minor fellow Newton received a dividend of £10 p.a. As a major fellow his stipend was £2 13s 4d p.a. plus £1 13s 4d for livery and a yearly dividend of £25. As a major fellow his total income was about £60 a year of which about £20 t0 £25 was his board and lodging. By modern standards this might not seem a lot, but it is approximately double the yearly income of a skilled craftsman at the time, with a fellow free to do whatever he liked with his time.

In 1669, Newton’s financial situation improved once again when Isaac Barrow resigned the Lucasian chair of mathematics to take on the study of divinity and was appointed Master of Trinity College and Newton was appointed as his successor to the Lucasian chair. This position carried with it a salary of £100 p.a., which is equivalent to £10,000 p.a. at todays prices. He also retained the income from his fellowship. I love the fact that on the National Archive historical converter I’m using, they point out that £100 was worth 24 cows. I have visions of Newton grazing his herd of milk cows on the lawns of Trinity College.

Newton’s steadily increasing wealth received a very major boost ten years later in 1679, when his mother, Hannah, died and he inherited the Newton family estates. These generated an income of about £600 p.a. Newton was by any standards now a wealthy man, although this income would not have enabled him to generate saving of £50,000 by the 1720s. In fact, Newton did not hoard his money but spent freely, stocking up his extensive library and equipping the alchemy laboratory that he set up in the gardens of Trinity College.


Hannah Newton-Smith born Ayscough Source

Contrary to the popular myths that Newton living in isolation, totally immersed in his studies was completely unworldly, Newton, although an absentee manager of the family estate mastered the task skilfully and also took good care of the needs of his extended family.

It was normal practice for fellows to increase their incomes through preferment in the Anglican Church, stipends often being awarded in absentia, with a minor cleric undertaking the actuall duties. Although all fellows were required to take holy orders, Newton, because of his unorthodox beliefs, had received a special dispensation from the King upon his appointment to the Lucasian Chair, so this route was not open to him.

Towards the end of the century, Newton tired of Cambridge and now, following the publication of his Principia, universally acknowledge as Europe’s leading natural philosopher, he began looking for some form of public post with a sinecure or pension to match his social status. In 1696, he achieved his aim, when his one-time student and mentor in the Whig Party, Charles Montagu, offered him the post of Warden of the Royal Mint in London. Newton accepted the post without hesitation. The warden’s income was £400 p.a. a large step up from the Lucasian £100, which, however, together with his fellowship he initially retained.


Portrait of Charles Montagu by Godfrey Kneller

The job of warden was a sinecure and Newton could have simply played the man about town and left the actually work to assistants. However, that was not Newton’s style and he took over the day-to-day management of the mint. One anomaly, that Newton became aware of straight away, was that although the warden was the boss, the master, who was actually responsible for minting the coinage, received a salary of £500 p.a., so more than the warden, plus a payment for every pound weight of copper, silver or gold that he minted. Newton immediately petitioned for equal pay with the master, but this was denied. However, when the incumbent master died in 1699, Newton had himself appointed as his successor. This was the only time in the history of the Royal Mint that a warden became the master.


In 1701, Newton finally resigned from the Lucasian chair and his Trinity fellowship. In that year his income from the mint was £3,500, we have now arrived at the source of that vast later wealth. Although it tended to go up and down like a yo-yo, Newton’s average income over the twenty-six years that he was master was about £1,650 p.a. One should not forget that he also had the £600 p.a. from his estates in Lincolnshire.

Newton was a good financial manager and through his work as advisor to the treasury he also had close contacts to all the leading finance experts in London. By nature, a cautious man, he usually invested his wealth wisely in the flourishing joint stock companies operating in London. He owed sizable stocks in both the Bank of England, set up by his mentor Charles Montagu, and the highly profitable East India Company both of which generated further income for him. However, even Newton couldn’t resist the allure of the spectacularly rising value of the South Sea Company and he invested heavily. Interestingly, he sold out once, making a tidy profit but as the value continued to rise and rise, he couldn’t resist and reinvested heavily taking that famous £25,000 hit.

There was however one occasion when Newton actually turned down the chance to improve his financially situation. Around 1713, during a period of Tory rule, the party wanted to secure the various political sinecures for their own supporters but knew that due to his, in the meantime, massive social status to remove Newton from the Royal Mint would be a political disaster, so the sent Jonathan Swift to offer him a bribe. If he would freely resign, as master of the mint, the government would bestow a lifetime pension of £2,000 p.a. upon him. Newton must have loved his work, or maybe he just wanted to annoy the Tories, he was after all a Whig, because he declined this incredibly generous offer.


Filed under Newton

Wot no new blog post, but it’s Wednesday

Where’s the new blog post?

There isn’t one.

But it’s Wednesday.

I know.

There’s always, well almost always, a new blog post on Wednesdays

Yes, but not today

Why not?

Because Friday is Christmas Day

Oh, do you have a break over Christmas?

No, exactly the opposite. Over Christmas I always post the Renaissance Mathematicus Christmas Trilogy celebrating the birthdays of Isaac Newton, 25th, Charles Babbage, 26th, and Johannes Kepler, 27th. To learn a little more and for links to all the Christmas Trilogies going back to 2009 follow this link here.

See you on Friday!


Filed under Uncategorized

The solar year ends and starts with a great conjunction

Today is the winter solstice, which as I have explained on various occasions, in the past, is for me the natural New Year’s Eve/New Year’s Day rather than the arbitrary 31 December/1 January.


Obligatory Stonehenge winter solstice image

Today in also the occurrence of a so-called great conjunction in astronomy/astrology, which is when, viewed from the Earth, Jupiter and Saturn appear closest together in the night sky. Great conjunctions occur every twenty years but this one is one in which the two planets appear particularly close to each other.


Great conjunctions played a decisive role in the life of Johannes Kepler. As a youth Kepler received a state grant to study at the University of Tübingen. The course was a general-studies one to prepare the students to become Lutheran schoolteachers or village pastors in the newly converted Protestant state. Kepler, who was deeply religious, hoped to get an appointment as a pastor but when a vacancy came up for Protestant mathematics teacher in Graz, Michael Mästlin recommended Kepler and so his dream of becoming a pastor collapsed. He could have turned down the appointment but then he would have had to pay back his grant, which he was in no position to do so.

In 1594, Kepler thus began to teach the Protestant youths of Graz mathematics. He accepted his fate reluctantly, as he still yearned for the chance to serve his God as a pastor. Always interested in astronomy and converted to heliocentricity by Michael Mästlin, whilst still a student, he had long pondered the question as to why there were exactly six planets. Kepler’s God didn’t do anything by chance, so there had to be a rational reason for this. According to his own account, one day in class whilst explaining the cyclical nature of the great conjunctions in astronomy/astrology, which is when, viewed from the Earth, Jupiter and Saturn appear closest together in the night sky, he had a revelation.  Looking at the diagram that he had drawn on the board he asked himself, “What if his God’s cosmos was a geometrical construction and this was the determining factor in the number of planets?”


Kepler’s geometrical diagram of the cyclical nature of the great conjunctions in his Mysterium Cosmographicum Source: Linda Hall Library

Kepler determined from that point on in his life to serve his God as an astronomer by revealing the geometric structure of God’s cosmos. He first experimented with various regular polygons, inspired by the great conjunction diagram, but couldn’t find anything that fit, so he moved into three dimensions and polyhedra. Here he struck gold and decided that there were exactly six planets because their orbital spheres were separated by the five regular Platonic solids.


Source: Wikimedia Commons


He published this theory in his first academic book, Mysterium Cosmographicum (lit. The Cosmographic Mystery, alternately translated as Cosmic MysteryThe Secret of the World) 1597. The book also contains his account of the revelation inspired by the great conjunction diagram. This was the start of his whole life’s work as a theoretical astronomer, which basically consisted of trying to fine tune this model.

In the early seventeenth century, Kepler was still deeply religious, a brilliant mathematician and theoretical astronomer, and a practicing astrologer. As an astrologer Kepler rejected the standard Ptolemaic sun sign i.e., Aquarius, Virgo, Gemini, etc., astrology. Normal horoscope astrology. Sun signs, or as most people call them star signs, are 30° segments of the circular ecliptic, the apparent path of the Sun around the Earth and not the asterisms or stellar constellations with the same names. Kepler developed his own astrology based entirely on planetary aspects, that is the angles subtended by the planets with each other on the ecliptic. (see the Wikipedia article Astrological aspect). Of course, in Kepler’s own astrology conjunctions play a major role.

Turning to the so-called Star of Bethlehem, the men from the east (no number is mentioned), who according to Matthew 2:2, followed the star were, in the original Greek, Magoi (Latin/English Magi) and this means they were astrologers and not the sanitised wise men or kings of the modern story telling. Kepler would have been very well aware of this. This led Kepler to speculate that what the Magoi followed was an important astrological occurrence and not a star in the normal meaning of the word. One should note that in antiquity all visible celestial objects were stars. Stars simple Asteres, planets (asteres) planētai wandering (stars) and a comet (aster) komētēs, literally long-haired (star), so interpreting the Star of Bethlehem as an astrological occurrence was not a great sketch.

His revelation in 1603 was that this astrological occurrence was a great conjunction and in fact a very special one, a so-called fiery trigon, one that links the three fire signs, Aries, Leo, Sagittarius.


Calculating backwards, Kepler the astronomer, determined that one such had occurred in 7 BCE and this was the star that the Magoi followed.

Whether Kepler’s theory was historically correct or an accepted view in antiquity is completely impossible to determine, is the Bible story of Jesus’ birth even true? In Kepler’s own time, nobody accepted his deviant astrology, so I very much doubt that many people accepted his Star of Bethlehem story, which he published in his De Stella Nova in Pede Serpentarii (On the New Star in the Foot of the Serpent Handler) in 1606.

I’m sure that a great conjunction on the date of the winter solstice has a very deep astrological significance but whether astrologers will look back and say, “Ah, that triggered this or that historical occurrence” only the future will tell.

I thank all of those who have read, digested and even commented upon my outpourings over the last twelve months and fully intend to do my best to keep you entertained over the next twelve. No matter which days you choose to celebrate during the next couple of weeks, in which way whatsoever and for what reasons, I wish all of my readers all the best and brace yourselves for another Renaissance Mathematicus Christmas Trilogy starting on 25 December.



Filed under History of Astrology, History of Astronomy, Renaissance Science