Category Archives: Mediaeval Science

Counting the hours

My #histsci-soul-sisterTM, Rebekah “Becky” Higgitt, wrote a charming post on her H-Word Blog to mark the end of European summer time describing the mad scheme of a certain William Willett to introduce the time change in twenty minute increments over several weeks. This reminded me of a local time phenomenon that I’ve not yet blogged about, Der Große Nürnberger Uhr

The time taken for the earth to rotate once upon its axis or for the sun to appear to circle the earth (its irrelevant how you view it) is a given but how one then chooses to divide up this period into smaller, easier to handle units is purely arbitrary. We owe our twenty-four hour day to the ancient Egyptians. They marked the passing of time in the night by the raising of stars; twelve stars being allotted for any given night, thus dividing the night into twelve units. They being normally decimal in their thinking divided the day into ten units. Allotting one unit for twilight at each junction between day and night brought the total to twenty-four.

The ancient Greek astronomers took over the Egyptian solar calendar and their twenty-four hour day dividing the diurnal revolution into twenty-four equally long, or equinoctial, hours as we do now. However most cultures who adopted the twenty-four system before the early modern period divided the night and day each into twelve units producing hours that varied in length depending on the time of year. This variation got larger the further away from the equator the culture was. In the middle of summer daytime hours were very long and night-time ones very short and vice versa in the middle of winter.

Beginning in the fourteenth century the city state of Nürnberg introduced a system of dividing up the day that is a sort of halfway station between the unequal hours of the middle ages and equinoctial hours, the so called ‘Große Uhr’, in English ‘Large Clock’. In this system the number of hours allotted to the day and night changed approximately every three weeks, the number of daytime hours increasing from midwinter (8) to midsummer (16) and then decreasing from midsummer to midwinter. The number of night-time hours doing the opposite.

Date of change 1st half of year Daylight hours Night-time hours Date of change 2nd half of year

8

16

7 January

9

15

16 November

28 January

10

14

26 October

14 February

11

13

8 October

3 March

12

12

22 September

19 March

13

11

5 September

5 April

14

10

20 August

23 April

15

9

2 August

15 May

16

8

11 June

In 1506 the Nürnberger humanists created one of the most complicated sundials in the whole of Europe on the wall of the St Lorenz church in the city.

Sundial on the St Lorenz Church Nürnberg

Sundial on the St Lorenz Church Nürnberg

This sundial shows the time of day in various different variations of hours including of course the Large Nürnberg Clock

The definition on this picture is not good enough to say which lines are which.

The good citizens of Nürnberg continued to use their own unique way of counting the hours right down to the year 1811.

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

Nicolaus was not a priest.

Erik Kwakkei (@erik_kwakkei) drew my attention to a rather nice short video from Prager University by Anthony Esolen of Providence College explaining that the Middle Ages were anything but Dark and should actually be called the bright ages. This is a very well done little piece managing to correct a whole series of myths in a very short time span. However I can’t resist taking a pot shot at his completely inaccurate description of Nicolaus Copernicus.

Esolen says:

Nicolaus Copernicus was, “a priest astronomer at a Polish university”.

The only part of this brief statement that is correct is that Copernicus was an astronomer.  However, it is important to point out that he was only ever an amateur astronomer; astronomy was his hobby so to speak. He never taught it at a university.

Copernicus started his undergraduate studies at the University of Kraków in Poland but left without taking a degree. He continued his studies a various universities in Northern Italy, where he studied law and medicine, not astronomy, completing his studies in 1503 with a doctorate in canon law from the University of Ferrara.

Already as a teenager Copernicus had been appointed a cannon canon of the Chapter of Frauenburg Cathedral in Warmia, where his Uncle Lucas Watzenrode was Prince Bishop. The cannons canons of the cathedral were the administration or government of Warmia.

After graduation Copernicus became private physician and secretary to his Uncle. Later he served the chapter in numerous administrative positions until his death in 1543, this being his profession and not astronomy.

Although attached to the cathedral all of his life Copernicus never took holy orders and was thus never a priest. The false claim that he was appears to have been put into the world by Galileo.

As always I find it disappointing that in an otherwise good video disposing of myths about the Middle Ages the one sentence about Copernicus should consist of false facts. A little bit of research, about five minute, could have avoided this piece of stupidity.

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Oh dear! More crap than you can shake a stick at.

One of the websites that I usually enjoy reading is Wonders & Marvels a collective of historians[1] who post mostly short reports on historical things, oft medical, that they have found fascinating. However, as I recently visited this delightful oasis of historical frivolity I groaned inwardly upon reading the post on Abū Alī al-Hasan ibn al-Hasan ibn al-Haytham (known simply as Ibn al Haytham or in mediaeval Europe as Alhacen or Alhazen) the mediaeval Islamic scholar by Pamela Toler that I found there. I hasten to add that Ms Toler is not solely to blame for the heap of excrement posing as history of science that she has posted there, as she was just regurgitating, probably inaccurately, what she had read in a popular book on Islamic science, about which more later.

After an opening paragraph that gives a somewhat mangled version of a part of Ibn al-Haytham’s biography Ms Toler presents us with the following paragraph:

While confined in his home, Alhazen revolutionized the study of optics and laid the foundation for the scientific method. (Move over, Sir Isaac Newton.) Before Alhazen, vision and light were questions of philosophy. Alhazen considered vision and light in terms of mathematics, physics, physiology, and even psychology. In his Book of Optics, he discussed the nature of light and color. He accurately described the mechanism of sight and the anatomy of the eye. He was concerned with reflection and refraction. He experimented with mirrors and lenses. He discovered that rainbows are caused by refraction and calculated the height of earth’s atmosphere. In his spare time, he built the first camera obscura.

Nearly every single claim in this brief paragraph is wrong and I shall now try, at least in outline, to correct some of the worst errors.

Whilst it is true that Ibn al-Haytham made a major advance in the study of optics I personally, as a gradualist, object strongly to any use of the word revolution in any of its forms when writing about the history of science. Ibn al-Haytham made an important step forward building on the work of others, his work in turn being pushed forward by others. He did not in anyway what so ever invent the scientific method. Put quite simply nobody did. (see next post!)

Before Alhazen, vision and light were questions of philosophy.

Here we start in on the real rubbish. The Islamic scholars inherited their knowledge of optics from the Greeks and to state simply that Greek optics consisted of questions of philosophy is to display a deep ignorance of the history of the subject. The Greek study of optics can be divided into three main areas: philosophical, medical and mathematical. The opinions on vision can be further categorised according to whether the rays that enable vision extrude from the eyes to the object viewed, extramission, from the object viewed to the eyes, intromission, or in both directions mixed.

Philosophical theories of vision were propagated by the Atomists, intromission, Plato, mixed, Aristotle, intromission mediumistic, and the Stoics also mixed. The mathematical theories laid the basis of geometrical optics, and were propagated by Euclid, Hero of Alexandria and Ptolemaeus, all three supporting an intromission extramission theory although it is not clear if this is purely instrumental in order to facilitate simpler calculations. The principle medical theory transmitted to the Islamic scientists was that of Galen who combined a surprisingly accurate physiological knowledge of the eye with a Stoic philosophy of vision. It is not necessary for our purposes to go into greater details. It should be pointed out that all the theories except that of the atomists involved the presence and active involvement of light although the visual rays were not simply light rays.

Ibn al-Haytham argued philosophically very strongly against extramission and for intromission whilst at the same time demonstrating that an intromission theory could successfully be combined with the geometric optics of Euclid. At the same time he integrated the theory of al-Kindi that light reflects in all directions from all points of a viewed object arguing that only light rays are involved in vision. His theory of vision was thus a clever synthesis of several different theories into a coherent whole and thus a major advance in the understanding of optics.

He accurately described the mechanism of sight and the anatomy of the eye.

Ibn al-Haytham adopted Galen’s description of the anatomy of the eye and added nothing to it. His theory of vision was defective in that he like Galen believed that vision takes place in the lens of the eye and not as Kepler correctly surmised on the retina. Because of this major defect in his theory Ibn al-Haytham was forced to develop an erroneous theory that only rays falling perpendicularly onto the lens of the eye were perceived. Otherwise the eye would perceive multiple images of the object. In reality the lens focusing all the rays no matter from which angle creates just one image on the retina.

He experimented with mirrors and lenses

Ibn al-Haytham describes a limited number of experiments to demonstrate that light in propgated in straight lines, something that nobody had doubted since Euclid at the latest. To what extent these were actual experiments or just thought experiments is disputed amongst the experts.

In his spare time, he built the first camera obscura.

The principle of the camera obscura was already known to Aristotle and even earlier to the Chinese scholar Mo-Ti in the fifth century BCE who referred to it as the locked treasure room.

Ms Toler discovered her enthusiasm for Ibn al-Haytham as she tells us through reading a popular book on Islamic science.

Modern physicist Jim al-Khalili, in his excellent The House of Wisdom: How Arabic Science Saved Ancient Knowledge and Gave Us the Renaissance, calls Alhazen the greatest physicist of the medieval world, and possibly the greatest in the 2000 years between Archimedes and Sir Isaac Newton. His Book of Optics was first translated into Latin in the late twelfth or early thirteen century. It had an enormous impact on the work of western scientists from Roger Bacon (c. 1214-1292) to Isaac Newton (1642-1727).

By pure chance I stumbled across a video of a public lecture that Jim al-Khalili gave earlier this year on the subject of his book. I’m not going to give a detailed analysis of this lecture as it contains enough errors to keep me in blog posts for at least a year. He seems to be of the opinion that because he is a physicist and was born in Baghdad that this qualifies him to write a book about the history of Islamic science. In the lecture he proudly tells us that he devoted all of eighteen months of his research time to researching this book. A. Mark Smith took fourteen years to research and write his annotated translation of the first three books of the Latin edition of Ibn al-Haytham’s Book of Optics but he is a mere historian and not a physicist. In his lecture al-Khahili gives a clear and explicit commitment to a Whig interpretation of the history of science and strong implied commitment to the great man theory; both of these have been rejected by real historians of science long ago.

A typical example of al-Khalili’s arrogant ignorance occurs in his lecture when he talks about the first use of place value decimal fractions in Arabic mathematics. First of all he apparently doesn’t know the difference between the decimal point and decimal fractions. He also doesn’t appear to know that the Babylonians were using place value fractions, albeit sexagesimal not decimal, a thousand years earlier. He then goes on to say that The Chinese developed decimal fractions about the same time as Arabic mathematicians “but we don’t know as much about them”! I hope he doesn’t make this statement within reach of the Needham Research Insitute. Al-Khalili appears to confuse his own ignorance of the history of science with the general state of the art.

Returning to the blog post we have the following statement:

Jim al-Khalili […] calls Alhazen the greatest physicist of the medieval world, and possibly the greatest in the 2000 years between Archimedes and Sir Isaac Newton.

None of the three scholars named above was a physicist in the modern sense of the word and as I’ve said in the past there is no such thing as “the greatest”.  Even if we ignore these criticisms al-Khalili’s statement would be a hopeless exaggeration. A much more sensible assessment of Ibn al-Haytham’s achievements is given by somebody who knows what he is talking about, historian of optics David C. Lindberg[2]:

Alhazen was undoubtedly the most significant figure in the history of optics between antiquity and the seventeenth century.

There is a substantial difference between the two claims most important, historically, Ibn al-Haytham’s influence stops with the new model of optics developed by Kepler.

As far as I can see without having read his book al-Khalili is a typical example of a scientist thinking because I’m an expert in my subject I can also write about its history without doing the groundwork. Writing history requires a different form of expertise to doing modern science and writing about the history of science requires a wide range of expertise that cannot be thrown together in ones spare time in eighteenth months if one is trying to write a survey of the scientific activity of a major culture over a period of something approaching a thousand years. To do so without first acquiring the necessary expertise results not in history but in a collection of anecdotes and clichés most of them inaccurate and many simply false.


[1] What is the collective noun for historians? A heap? A huddle? A hysteria? I somehow feel it should be alliterative.

[2] This quote is taken from David C. Lindberg, Theories of Vision from al-Kindi to Kepler, which is a good source for anybody wishing to fill in on the history of optics that I only sketch above.

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A mathematician who became Pope.

A standard question amongst historians of art and historians of science is Renaissance or renaissances? Was there just one large event in European history, The Renaissance, during which the whole of the lost knowledge of antiquity was recovered or were there a series of such periods throughout the Middle Ages in which this knowledge gradually trickled back into European culture bit by bit? The first version is the myth created by the scholars in the fifteenth century who first coined the terms Renaissance and Middle Ages. The second is much closer to what really happened in history.

One of these renaissances is the so-called first scientific or mathematical renaissance beginning in the twelfth century in which the so-called translators travelled to Spain and Sicily to translate both classical and Islamic scientific manuscripts from Arabic into Latin, reintroducing such classics as Euclid’s Elements or Ptolemaeus’ Syntaxis Mathematiké into Europe. However there had already been a steady trickle of Islamic scientific knowledge into Europe through Spain since the ninth century conveyed by individual scholars who had studied in Spain and then taught others in Northern Europe their freshly acquired treasures. One of the most well known of these was the French monk Gerbert d’Aurillac who died 12th May 1003.

Gerbert, a peasant, was born about 945 and as a youth entered the Monastery of Aurillac as a menial but his intelligence was recognised and instead of being assigned kitchen duties he was given an education. From 967 to 970 he studied under Bishop Atto of Vich in Catalonia in the Spanish March, i.e. that part of Spain not under the rule of the Islamic Empire. In these three years Gerbert absorbed as much of the Islamic science and mathematics as he could. From Spain he went to Rome where he was introduced to the Pope and the German Emperor, Otto I, who was so impressed with the young scholar that he sent him to Rheims to complete his education.  He also served as tutor to Otto’s son the future Otto II. Under Otto II patronage he was appointed Abbott of Bobbio. He later succeeded to the Archbishopric of Rheims. After the death of Otto II he became tutor to the teenage Otto III and his cousin Pope Gregory V who appointed him Archbishop of Ravenna in 998. After Gregory’s death in 999 Gerbert was elevated to Pope with the support of Otto III, taking the name Sylvester II, although he only held the office for less than four years until his death in 1003.

Throughout his career at court and in the Church Gerbert was a passionate teacher of the mathematical sciences that he had learnt in his time in Spain. He wrote books on arithmetic, geometry and astronomy and was particularly interested in the astronomical methods of measuring time. He corresponded widely on mathematical topics and avidly collected manuscripts to extend his knowledge. He introduced the armillary sphere from Spain into Northern Europe and almost certainly played a roll in the introduction of the astrolabe. He might also have played a role in introducing the Hindu-Arabic numbers into Northern Europe.

His achievements cannot be compared to some of the twelfth century translators such as Gerard of Cremona or Adelard of Bath but he was almost certainly the leading European scholar of the mathematical sciences outside of Muslim Spain in the tenth century and he and his student did much to make the Islamic knowledge of mathematics and astronomy known to a wider audience.

Next time a Gnu atheist tries to tell you that the Catholic Church was irreconcilably opposed to science in the Middle Ages tell them about Gerbert the mathematician who became Pope.

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It’s only been about 100 years!

There has been a lot of nonsense spouted in the last couple of days about the BBC’s decision to use the CE/BCE dating system instead of the AD/BC one, as usual the various commentators have trampled with both feet on the historical facts preferring brainless rhetoric to historical reality. So we have M. J. Robins on his Guardian blog claiming that the system has been in use for two thousand years in his tirade against the Daily Fail and Boris Johnson claiming 1500 years in his equally ridiculous tirade in the Daily Telegraph.

Let us look at the historical facts. The principle of counting years from the supposed birth of Christ was first introduced in 525 CE by Dionysius Exiguus in his efforts to determine the correct date for Easter. At the time it wasn’t used by anybody else. In the 8th century CE the English monk Bede used it in his work to determine the date of Easter. His pupil Alcuin of York introduced into the Court of Karl der Große (that’s Charlemagne for the English) From here its use spread slowly throughout Europe. Even the Vatican didn’t use it preferring to date years in terms of the reigns of popes. You will notice we are only talking about AD. The use of BC was first introduced in the 17th century as history within Europe started to become a real academic discipline. The use of the AD/BC dating system was first adopted by the Orthodox churches in the 18th century. The usage of this dating system was restricted to Europe and its colonies and was ignored by the majority of the world, until at the very earliest the late 19th century and in most cases the 20th century.

Through international trade and industry in the 20th century there was a need for a unified dating system and because of the economic dominance of the USA and Europe for such purposes the Gregorian calendar was adopted as the world’s norm. Why the rest of the world should also adopt a Christian system of referring to dates when less than 30% of the world’s population is Christian, even by the wildly inflated methods used by the churches to claim adherence, in this at best 100 year old universal dating system is something that those doing the screaming need to explain. As an explanation, to claim that the system has been in use for 2000 or 1500 years is a straight forward historical lie and wont wash.

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Pissing on a Holy Cow

I have become somewhat notorious in the limited circles of those denizens of the intertubes who interest themselves for science and its history for being nasty to Tuscany’s second most famous son Galileo Galilei, today, just for a change, I thought I would raise my leg and piss on its most famous son, Leonardo da Vinci, who was born on 15th April 1452.

Now as should be obvious from the title of this blog I specialise, as a historian of science, in that period of European history known as the Renaissance, which I date for my purposes as stretching approximately from the beginning of the 15th century to the middle of the 17th century. A period that because of the vagaries of historical dating also includes parts of the periods known as the High Middle Ages and the Early Modern Period. When each of the three periods named here begins or ends if a matter of conjecture, dispute and personal opinion, as always I keep my own council. Leonardo who lived from 1452 to 1519 and who is regarded, quite correctly, as one of the greatest Renaissance artists falls of course into the period I study.

Over the years I have in the pursuit of my interests read an incredible number of books, articles and essays on the history of science and or technology or one or other of the sub-divisions thereof in the Middle Ages, the Renaissance and the Early Modern Period and an incredibly high percentage of these writings have a section, a chapter or a whole series of chapters on the science and or technology of Leonardo and that is very bad.

Now you may ask yourself why I am making what seems to be a highly provocative statement when after all it is well known that Leonardo wrote and drew an incredible amount of material about scientific and technological subjects. The answer is very, very simple Leonardo played absolutely no role what so ever in the history of science and or technology because none of his voluminous writings on those subjects saw the light of day before the 19th century when they were nothing more than a historic curiosity, admittedly a fascinating curiosity but nothing more than that.

By all means write learned or popular books about this strangely visionary and ingenious Tuscan painter who filled up sheet after sheet of drawing paper with his speculations on all sorts of topics but who never deemed it necessary to share his thoughts with the rest of the world. By all means reconstruct his fantasies in wood and canvas and demonstrate to the world that his idea for a parachute or whatever actually functions. However if you are going to write books about the history of Renaissance science or technology please do not include Leonardo because he doesn’t belong, as he made no actual contribution to that history.

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When did the (Scientific) Renaissance take place?

Whilst I have been inactive two of my commentators have been conducting a discussion on their respective takes on the history of alchemy, magic and other related activities. In the course of their skirmishes one of them had the following to say:

…the name of the Blog is RENAISSANCE Mathematicus, not RESTORATION Mathematicus.
The Renaissance started in the 1430s and may be considered complete by 1560, and was driven by the sponsorship of the nobility, perhaps the last flowering of the feudal system.

Now his dating of the Renaissance is interesting and this and the dating of historical periods in general is what I wish to talk about here but before I do, I will just say that although I mainly write about the early modern period (and what exactly that is I say explain later), as this is one area in which I could possibly claim a modicum of knowledge or even expertise, I retain the right to write about any and all aspects of the history and philosophy of science beginning with the big bang and going up to tea time last Thursday afternoon. Just because I’m a Renaissance Mathematicus doesn’t mean that I confine myself to the fifteenth century, as any attentive regular reader will have already noticed.

Periodisation in human history is an artifice. We the historians impose periods onto history in order to try to tame it and make it easier to handle and in doing so we run the very real risk of falsifying it. There are no sign posts rammed into the real roadmap of time saying you are now leaving the Early Middle Ages please conduct your self in future in a manner suitable for the High Middle Ages. In fact as the peasant farmer in Middle Europe turned over the page of his calendar from the 25th to the 26th of March (or on which ever day in his part of the woods the new year happened to start) in 1199 and thus entered the thirteenth century nothing changed in his life at all. Time is a constantly flowing river and change is incremental and on the ground mostly imperceptible as societies, cultures and ways of live evolve within the general flow. It is only with hindsight and selective interpretation of the facts that we can perceive the major changes that we then use to identify the periods that we stamp out of the riverbed.

One of the major problems that this post hoc imposition of periods is that we begin to ignore or filter facts in order to make people and events better fit our arbitrary definitions of the period in question. Newton was a product and the crowning glory of the Scientific Revolution (an arbitrarily imposed historical period) so Newton is and must be a modern scientist. That he was nothing of the sort is casually swept under the carpet by all but a handful of Newton specialists buried somewhere deep in the bowels of dusty archives. I have been told on more than one occasion that to claim that Newton was a woo master, even if true, is to undermine peoples faith in the effectiveness of science, so please be so kind and shut up.

In terms of artificial historical periods the Renaissance is a particularly difficult beast to pin down (as is for very similar reasons the Scientific Revolution) because it has less to do with any socio-cultural attributes, such as the introduction of the deep blade plough, as with a philosophical mindset that was held by an elitist minority of the population. The problem is made even more complex by the fact that there was not one set of intellectual values that define the Renaissance but sets of varying and even contradictory ones that existed side by side over the period in question. This is wonderfully illustrated in the protracted mudslinging match between Johannes Kepler and Robert Fludd. Fludd is a Renaissance magus in all his glory revelling in alchemy in its most arcane form and totally rejecting the encroaching wave of mathematical science, one of whose staunchest exponents was Kepler. For the historian the answer in surely simple, Fludd is a representative of the dying Renaissance and Kepler an early personification of modern science. Wrong! Kepler is just as much part of the Renaissance as Fludd (who, by the way, also made sensible contribution to the progress of science) but with a different set of Renaissance philosophical beliefs.

Interesting in this context is the fact that it was the Renaissance humanists who first developed the periodisation scheme that we continue, with modifications, to use today. The humanist scholars of the Renaissance saw themselves as the natural successors to the glories of antiquity or the classical period (i.e. the Greeks and Romans) and regarded the period that had elapsed between the collapse of Rome and classical learning and its rebirth in their hands as the Middle Ages in which everything had been decidedly inferior. Through this rhetorical trick they sort to place themselves on a level with those authors of antiquity whose work they took as a model for their own.

So when does the Renaissance start and end? In my title I have included the word scientific in brackets to indicate that we are in fact dealing with two different but related concepts on the one side the Renaissance and on the other the Scientific Renaissance; the title of my blog of course references the later. The Renaissance proper was initially a literary movement and is said to start with Petrarca (1304 – 1374) gaining momentum over the next two centuries expanding into art and reaching a climax some time around 1500 or slightly later. Originally a return to the style of the classical or golden Latin in literature as exemplified by Cicero in its later phase it came to include the great Greek authors and in the 16th century the humanist became identified with the tri lingua scholar fluent in Latin Greek and Hebrew. This movement in the humanities (from which this branch of academia takes its name) continues to flourish into the 17th century and pinning down exactly where it ends is very difficult. Francis Yates sees its demise somewhere in the Thirty Years War with humanism still a dominant intellectual force before the start of this bloody altercation but very much in decline after the smoke had cleared on the battle fields of Middle Europe. On the whole I tend to agree with her but I would note that when I attended an English grammar school in the 1960s the model of pedagogic excellence to which I was exposed was a modified version of the Renaissance humanist ideals with A-Levels in Latin, Greek and Ancient History being the most exalted educational goal.

The Scientific Renaissance, which is in itself a fairly recent concept, in of course embedded in the wider Humanist Renaissance. Originally conceived by Maria Boas in her book in her book “The scientific Renaissance” from 1962 it has received its most recent treatment from Peter Dear in his “Revolutionizing the Sciences” from 2001. Whereas Boas saw it as an early phase of the scientific revolution, Dear sees the two as separate identifiable periods with differing characteristics. On the whole, as a gradualist, I side with Boas although I also reject the concept of ‘a’ or ‘the’ scientific revolution preferring a gradualist model of scientific evolution, which I wont however discuss here. The popular version of the Scientific Renaissance has it beginning with the fall of Constantinople in 1453 and a supposed influx of Greek scientific text into Western Europe brought by the refugees. Its end is signalled, 90 years later, by the publication in 1543 of Copernicus’ De revolutionibus. Both of these dates are problematic. Starting with the supposed end of the Scientific Renaissance, Copernicus was a Renaissance humanist scholar and apart from his heliocentricity his book is very much in the tradition of the Epytoma Almagesti from Peuerbach and Regiomontanus (the founders of Renaissance astronomy), which served as one of his major sources, an astronomical tradition that remained dominant in Europe until it was finally replaced by Kepler’s elliptical astronomy around 1660. This continuity is nicely illustrated by Kepler himself in the frontispiece of his Tabulae Rudolphinae from 1609. This displays astronomy as a somewhat ramshackle pavilion with its various pillars each constructed and contributed by different figure in the history of astronomy. One of the lesser figures included in the wonderful graphic is Bernhard Walther the colleague and pupil of Regiomontanus in Nürnberg who continued his astronomical observation programme after his untimely death in 1476 and whose observation where used by Copernicus in the De revolutionibus. However saying that the Scientific Renaissance comes to an end around 1660 is not without problems. I said earlier that Newton is presented as a modern scientist but even his work is steeped in the mindset of the Renaissance scholar with his alchemical studies and his prisca theology.

The supposed start of the Scientific Renaissance is also very problematic, as the Italian scholars had been collecting Greek scientific manuscripts in large quantities long before the fall of Constantinople as is well documented in Paul Rose’s “The Italian Renaissance in Mathematics”. The City of Florence was already importing teachers to teach its intellectuals Greek in the 1390s. I personally take the appearance of the manuscript of the first Latin translation of Ptolemaeus’ Geographia in Florence in 1409, as a convenient starting point of the Scientific Renaissance, as this led to new developments in the sciences that increased and accelerated throughout the 15th century.

As I have already indicated above I personally reject both the Scientific Renaissance and the Scientific Revolution. I’m prepared to discuss both of them when discussing or criticising the work of others but in my own work I talk about the evolution of the (mathematical) sciences in the early modern period. Of course to use the concept early modern period is just as artificial as any other periodisation but it doesn’t contain any terms loaded with preconceptions such as renaissance and revolution. For me the early modern period starts around 1400 and ends around 1750 but always with the awareness that the processes that I’m investigating actually start before this period and continue on after it.

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Bruno was not scientific

Jason Rosenhouse at EvolutionBlog has been reading Ronald Number’s Galileo Goes to Jail and Other Myths About Science and Religion and is unhappy about the following statement made by Numbers

No scientist, to our knowledge, ever lost his life because of his scientific views, though, … the Italian Inquisition did incinerate the sixteenth century Copernican Giordano Bruno for his heretical theological notions. (Emphasis in original)

Jason thinks that this claim is evasive because as he says:

It is absurd to pretend that Bruno’s theological views can be treated as completely separate from his scientific views. That the stated reasons for Bruno’s execution involved his heretical theology does not mean that he was not also killed because of his scientific views. One suspects that for Bruno, as for so many modern thinkers, his science and theology complemented each other, to the point where it is difficult to say which aspect of his thinking was scientific and which part was theological.

Now this is an interesting standpoint that Jason is defending because by his own standards Bruno didn’t have any scientific** views! A strong statement on my part but one that I think is fully justified when one actually examines Bruno’s work. Before doing so, let us first see how Jason defines science and scientific views. In his comments column in a direct answer on his understanding as to what constitutes science Jason writes:

I’m viewing science as an approach to inquiry. It’s (sic) main tenet is that assertions of fact about the natural world should be based on experimentation, evidence gathering, hypothesis testing, and all the other sorts of things scientists do.

You can look long and hard at Bruno’s writings but you will never find anything remotely similar to this. Having claimed this, how come Bruno came to be regarded as a scientific martyr at all? The reason is very simple Bruno was one of only ten people to subscribe to astronomical Copernican heliocentrism in the 16th century. But doesn’t this make him scientific? No, because Bruno’s defence of heliocentrism is purely philosophical he makes no attempt to provide any form of empirical, experimental or in any other way scientific justification for his adoption of this theory. Holding a theory to be true does not make the holder the possessor of a scientific viewpoint. Bruno also excites modern commentators because of his cosmological ideas of an infinite universe uniformly filled with an infinite number of inhabited worlds, interesting speculations but in no way scientific. Bruno’s cosmological speculations are just that, speculations without basis, the only way that one can bring them in connection with the word science is when one calls them science fiction but even this would be stretching a point as they are nearer to science fantasy than science fiction.

This however is not the worst. If one examines Bruno’s world of thought in the context of the emerging science of his age he reveals himself as a woo master. Between 1400 and 1750 the nature of science and scientific enquiry went through a major shift of emphasis from the scholastic Aristotelian* science, which is largely a priori, descriptive, and qualitative to the modern concept of science empirical, quantitative and a posteriori. The quantitative element of this new understanding is provided by mathematics. It is not a coincidence that the same period has been called the golden age of mathematics with the development of logarithms, trigonometry as a discipline in its own right and not part of astronomy, symbolic algebra, analytical geometry and the infinitesimal calculus. These developments have led to the so-called scientific revolution being described as the mathematisation of nature. Where did Bruno stand with regard to this absolutely central aspect of modern science, he categorically rejected it. For Bruno modern mathematics and the attempts to describe nature with it were anathema. Instead he proposed a system of multi-coloured mystical geometrical diagrams to describe nature that bear a strong resemblance to Vedic mandalas.

Jason is right when he describes Bruno as a modern thinker, he was indeed such with regard to theology where his views were way ahead of his time and the Catholic Church’s persecution and murder of Bruno for holding those views can only be condemned in the strongest terms. However to ascribe scientific views to Bruno is misuse of the term scientific as he was not a scientist or a scientific thinker and didn’t have a scientific view.

*Mediaeval Aristotelian science is, as Edward Grant always emphasises, not Aristotle’s science.

**I am well aware that the use of the term science when talking about the early modern period is anachronistic but using it is a useful form of shorthand and save complex explanations. If anyone objects please feel free to vent your spleen in the comments

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Filed under Mediaeval Science, Myths of Science, Renaissance Science

The Book of Curiosities

Regular commentator Jeb, both here and at the Aussie Anthropoids Pad (he who has lost his underpants), has drawn my attention in the comments to Mapping Africa to the online exhibition at the Bodlian Library of the Arabic “Book of Curiosities”. This is truly a wonderful presentation of a fascinating document and so I have promoted the tip up front with thanks to Jeb.

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Filed under History of Astronomy, Mediaeval Science

Christians are not Christians!

Jim Harrison from ‘inanis et vacua’ posted the following comment on my post Two Quote for Christians,

Since Christianity permeated the culture of Europe during the emergence of modern science, the question isn’t whether it played a role in the advent of science but what that role was. If you look at everything polemically, of course, you may cavil at this rather obvious observation, which is offered in defense of objective historical understanding and not in praise (or criticism) of religion.

As far as it goes the first sentence of his comment is very sensible and would seem to justify an answer but unfortunately it suffers from a subtle flaw that is reflected in the title of this post, in the context of the emergence of science in the Early Modern Period the term Christian is virtually meaningless. When one talks about Christians and Christianity it implies that there is something that is common to and binds together all of those individuals who are indicated by the terms used, however in the context of academic intellectual activity, and science in particular, this is far from being the case. Even before the Reformation in Europe when all Christians were at least nominally members of the Holy Roman Catholic Church the unity implied by the use of the concept Christian did not exist in the pursuit of, what we would now term, scientific knowledge.

As I wrote in my very first internet blog post on the ideas of Rodney Stark when every single member of society in supposedly a Christian to talk in terms of a Christian role in the advent of science is meaningless, one must instead examine the proponents of natural philosophy according to the various schools of philosophy that they adhered to. Here, we don’t have a unified Christian thought propelling advances in science but various groups, Thomists, Ockhamists, Realists, Nominalists, Averroeists and a whole artist’s pallete of all shades to all sides and in-between, as well individualist loose cannons some of whom despite being outside of all cliques and group exercised a lot of influence. The very fact that there were so many shades of opinion and open conflicts produced an atmosphere of intense discussion that almost certainly played a significant role in the furtherance of scientific inquiry.

To understand the evolution of science in the early modern period the concept ‘Christian’ is useless; the historian has to dig deeper and examine the philosophical concepts of each group and each individual in order to see how those concepts contributed to or hindered the advance of science.

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Filed under Mediaeval Science, Renaissance Science