Abraham Ortelius and the 16th century information age.

The sixteenth century saw the evolution of modern cartography emerge out of a renaissance in Ptolemaic cartography. In the second half of the century the Netherlands played a leading role in this process. I have already blogged twice about Gerard Mercator the man most closely associated with the modern cartography, here and here, and also about his teacher Gemma Frisius, so today I want to turn my attention to Mercator’s friend and rival Abraham Ortelius.

 

Abraham Ortelius by Peter Paul Rubens Source: Wikimedia Commons

Abraham Ortelius by Peter Paul Rubens
Source: Wikimedia Commons

He was born Abraham Ortel (as we most Renaissance scholars there are numerous variant spellings of the family name) in Antwerp on 14 April 1527, to where his grandfather William had moved the family from Augsburg in Southern Germany in 1460, supposedly because of religious persecution. The son of a merchant who died whilst he was still young, in about 1535. Ortelius studied mathematics, Latin and Greek as a youth and apprenticed as an engraver of maps and entered the Antwerp guild of map illuminators in 1547. He set a shop trading in books, prints and maps with his sister and became an engraver for the highly influential Plantin publishing house. Through his various activities as a trader Ortelius came to travel extensively throughout Europe, visiting all the regions of Germany, Italy, France, England and Ireland.

He met and became friends with Gerard Mercator at the Frankfurt book Fair in 1554. In 1559-1560 he accompanied Mercator on his cartographical expedition through Trier, Lorraine and Poitiers. It was during this trip that Mercator is supposed to have persuaded his friend to not just engrave and colour other people’s maps but to become a cartographer in his own right.

Following the example of his mentor, Ortelius started out producing single maps sold as prints. His first effort was an eight-sheet world map produced in 1564. This was followed by a two-sheet map of Egypt (1565), a single-sheet map of the Holy Land in 1566, a two-sheet map of Asia (1567) and a six-sheet map of Spain (1570). Ortelius’ entry into the map business was a success. Gemma Frisius, Mercator and Ortelius were all cartographers and businessmen. However, whereas it is safe to say that Gemma Frisius and Mercator were cartographers first and businessmen second in the case of Ortelius it was the other way round; he was very much a businessman first and a cartographer second.

 

Ortelius' World Map 1564 Source: Wikimedia Commons

Ortelius’ World Map 1564
Source: Wikimedia Commons

Given the massive increase in international trade and the travel involved in it, there was a strong increase in the demand for good maps. To save themselves the trouble of carrying around large bundles of loose maps various people had started collecting together maps from various sources and binding them together in a book. However, the maps in such collections were of different styles, varying qualities and highly varying usefulness. Ortelius and his business partners came up with the idea of printing and publishing a comprehensive collection of maps of uniform size all in the same style and containing the most up to date geographical data available. Published by Ortelius and printed by Egidius Coppens van Diest the first edition of Ortelius’ Theatrum orbis terrum (the first modern atlas!?) containing fifty-three maps appeared in 1570.

 

Theatrum Orbis Terrarum Title Page Source: Wikimedia Commons

Theatrum Orbis Terrarum Title Page
Source: Wikimedia Commons

Ortelius didn’t produced the maps from scratch himself but relied on the maps of other cartographers, modifying and improving them as he reproduced them in his uniform style oft incorporating elements of several maps into his finished product. This method of working was not new but had been employed by the leading cartographers throughout the sixteenth century, where Ortelius differed was in that he included a Catlogus cartographorum, a list of eighty-seven cartographers whose work he had used to compose his Theatrum. The Theatrum was a major success going through forty editions between 1570 and 1624. As well as numerous Latin editions there were also several editions each in German, French, Italian, Spanish and English. The Theatrum was very definitely a sixteenth-century bestseller.

 

Map of the Persian Empire from the Theatrum Orbis Terrarum Source: Wikimedia Commons

Map of the Persian Empire from the Theatrum Orbis Terrarum
Source: Wikimedia Commons

One of the most important features of the Theatrum was its evolution. Each new edition would be modified and updated with as much new information as Ortelius could obtain.

Starting with 53 maps in 1570, it grew to 70 maps in 1573, 93 maps in 1579, 122 maps in 1584 and in the final edition prepared by Ortelius and published in 1590, one year after his death, 134 maps. Plantin had been involved in marketing and selling the Theatrum from the very beginning and took over printing it in 1579 uptil his own death in 1589.

Of interest is a pocket sized version, or epitome, of the Theatrum that was published by Philips Galle and printed by Plantin beginning in 1577. Like the original this too went through many editions in several different languages, the first edition having been in Dutch.

The evolution of the Theatrum between its birth in 1570 and Ortelius’ death in 1589 is a wonderful example of the so-called Republic of Letters in operation in the Early Modern Period. Ortelius had connections all over Europe and even further afield amongst the scholars of his day. Through correspondence they supplied him with the information he needed to update and modernise his maps. Also supplying the geographical and historical information with which he annotated later editions of his magnum opus. This information network worked in both directions with Ortelius passing on information he had received from one member of the network to others he thought might be interested. This correspondence did not only deal in matters geographical and cartographical but also included much information from all the various branches of natural history. An impression of Ortelius’ correspondence network can be gained from his Album Amicorum (friendship book), which he maintained from 1574 to 1596. It has 130 entries that read like a who’s who of the European intellectual elite of the period.

 

Maris Pacifici, 1589, the first dedicated map of the Pacific to be printed Source: Wikimedia Commons

Maris Pacifici, 1589, the first dedicated map of the Pacific to be printed
Source: Wikimedia Commons

Ortelius’ second major geographical work was his Synonymia Geographica sive Popularum, Regionum, Insularum, Urbium… Appelationes et Nomina, originally an appendix in the Theatrum but then published in expanded form as a separate volume beginning in 1578. This is a list of classical place names identifying their modern locations based on Ortelius’ own historical research, an important research tool for anybody studying classical works.

Another minor claim to fame possessed by Ortelius is that he appears to be the first person to have suggested a theory of continental drift based on his recognition that the continents surrounding the Atlantic basin seemed to fit together. He suggested that the Americas had been torn away from Europe and Africa by earthquakes and floods. His theory fell on deaf ears in his own times.

We still have one rather important linguistic question to clear up. If the ‘first modern atlas’, was entitled the Theatrum orbis terrum by Ortelius, its creator, then why do we call a collection of maps an atlas?

Almost at the same time as Ortelius, his friend Mercator embarked on a very similar project if his motivation was somewhat different. I have blogged about Mercator’s map collection, which he called an atlas already here so I won’t repeat the story now. Mercator’s book only appeared in full, bearing for the first time the title Atlas, posthumously in 1595, twenty-five years after the first appearance of the Theatrum. Although Mercator’s work was without doubt superior to Ortelius’, the later was already a well-established best seller and the larger more complex work of Mercator failed to seriously challenge the market leader. Had the situation remained as it was, we would probably still refer to a bound collection of maps as a theatre. In case you are wondering Ortelius’ original title translates as something like view of the earthly globe. However at the end of the 1590s things changed. Ortelius died and although his Theatrum continued to appear until 1624 nobody took the trouble to update it. On the other hand Mercator’s son died in 1599 and Jodocus Hondius a cartographical publisher and globe maker from Amsterdam bought up the rights to Mercator’s Atlas. Hondius did update and modify Mercator’s work and so took over dominance in the market. In 1624 Hondius’ biggest rival Willem Janszoon Blaeu bought the rights to Ortelius’ Theatrum incorporating it into his own map book that he titled an atlas in imitation of Hondius. And so it is that we now call a bound collection of maps an atlas and not a theatre.

 

 

 

 

 

 

 

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Asterisms and Constellations and how not to confuse them with Tropical Signs.

If you are going to write about something, especially if you intend to lay bare somebody else’s ignorance, it pays to actually know what you are talking about otherwise you could well end up looking like a total idiot, as does Anna Culaba in her article on the RYOT website, The Stars and Your Astrological Signs Have Been Lying to You This Whole Time. I should point out that Ms Culaba is by no means the first person to publically embarrass themselves pontificating on this subject, in fact it’s a reoccurring theme much loved by scientists and science fans who want to take a cheap shot at astrology. Indeed, as we will see later Ms Culaba, in her article, is in fact just regurgitating the content of a BBC website. So what exactly does our intrepid science fan say in her blog post?

My horoscope for today (I’m a Virgo) according to Astrology.com reads, “Today, explore an aspect of an unfamiliar religion or culture. Today is a day to make plans and aim high.” There are only two things that are keeping me from leaving work right now: one, I don’t really believe that the stars can determine what will happen in my life and two, I wasn’t really born under the star sign that the world told me I was born into. According to the BBC, about 86 percent of people are actually born under a different sign than the one they think. This is because 2,000 years ago, when the Ancient Greeks first created the zodiacs, the star signs corresponded to the position of the sun relative to the constellations that appeared in the sky the day people were born. Unfortunately, during that time people didn’t know of the phenomenon known as the precession. Live Sciences reports that the precession is when the Earth continually wobbles around its axis in an almost 26,000-year cycle thanks to the gravitational attraction of the moon. Thanks to this phenomenon, the constellations some people live and die by have actually drifted away from us. This means that constellations are now actually off by a month. So if you were born between August 11 to September 16 you’re not the picky and critical Virgo that you thought you were — you’re really an ambitious Leo whose strength of purpose allows you to accomplish many, many things. And if you’re astrological world hasn’t been rocked enough, if you thought you had your star sign wrong, wait until some of you realize that there’s actually a 13th zodiac sign known as the Ophiuchus. According to the BBC, the Ancient Greeks deliberately left out the original zodiac so that ancient astrologers would be able to divide the sun’s 360 degree path into 12 equal parts. Where does Ophiuchus fit into the zodiac calendar? It goes between Scorpio and Sagittarius, so if you were born between November 30 and December 18 consider yourself an Ophiuchus. You’re probably very secretive and good at hide and seek.

I have reproduced the whole of Ms Culaba’s screed here to save me having to quote it in little bits, merely removing the links from the original. If you read it through you what will discover is the central claim that astrologers were too stupid to realise the astronomical phenomenon of precession and so you were not actually born under the star sign that they claim you were. There are two general points to be made here, firstly astrologers were well aware of precession and secondly Ms Culaba and the source she is quoting don’t know the fundamental difference between constellations and tropical signs. So for the benefit of Ms Culaba and all others who are confused by the topic we will have a Renaissance Mathematicus guide to asterisms, constellations, the zodiac and tropical signs.

If you go out on a dark night with a clear sky in an area with little or no light pollution (and if you have never done so you should, it’s awesome) and look up in the heavens you will see a myriad of stars looking down on you in a vast blue black vault. If you are not a trained astronomer you will probably find no means of orienting your gaze in this confusion of twinkling lights. This problem was confronted by all human cultures since the dawn of human existence. The human brain seems to be programmed for pattern recognition and so, like children with a join up the dots picture book, all cultures started to create pictures by imagining lines joining up or outlining eye-catching groups of stars and giving these pictures names. These pictures, and they exist in all human cultures, are known technically as asterisms. These asterisms help the observing eye gain orientation when traversing the vast dome of the night sky and early astronomers started compiling lists of the most prominent such join-up-the-dots-pictures or asterisms in order to use them as a scaffolding for mapping the heavens. Those asterisms contained in such formal lists are called constellations. Our modern, western list of constellations has its origins in ancient Babylonian astrology/astronomy and comes down to us via the ancient Greeks and the medieval Islamic astronomers. In his Syntaxis Mathematiké, Ptolemaeus lists 48 constellations by name. Currently, the International Astronomical Union (IAU) recognises 88 named constellations. We now need to turn our attention to the origins of the zodiac.

Viewed from the earth, and before the beginning of the so-called space age that was the only way possible to view the heavens, the sun appears to orbit the earth once every year. In fact the year is defined as the time it takes for the sun to orbit the earth. The path the sun follows on its way around the earth is called the ecliptic and is tilted at approximately 23 degrees to the earth’s equator. This tilt, known as the obliquity of the ecliptic, is the reason why we have seasons on the earth. The six planets visible to the naked eye and know in antiquity – Moon, Mercury, Venus, Mars, Jupiter and Saturn – all appear to orbit the earth in the plane of the ecliptic making this imaginary belt around the heavens very important for the study of astronomy. The earliest known mapping of the ecliptic is contained in a set of Babylonian clay tablets known as the MUL.APIN, which date from around 1000 BCE. Here the path of the moon’s orbit is described or mapped with 17 or 18 (the text is somewhat ambiguous) constellations and stars. The moon’s orbit is tilted at about five degrees to the ecliptic. This mapping was still in use around 700 BCE. By around 500 BCE the 17/18 constellations/stars had be replaced by twelve constellations of varying sizes. Circa 420 BCE the Babylonians had replaced those twelve constellations with twelve equal divisions of the ecliptic comprising 30° segments. These segments were named after the constellations they replaced and form the zodiac that was taken over by the Greeks and made its way down to us. Those segments are known technically as tropical or sun signs, form the basis of zodiacal astrology and are abstract geometrical segment of the ecliptic and not constellations. The constellations slowly circle the heavens due to precession, the tropical signs do not! If an astrologer says you were born under the sign Virgo it means that the sun was in the 30° segment of the ecliptic that bears the name Virgo at the moment of your birth. This has nothing apart from the name in common with the constellation Virgo.

It is not the astrologers who display ignorance of the precession of the equinox, to give the phenomenon its full name, but Ms Culaba who displays total ignorance of both astronomy and astrology. This is not a very good situation to be in if you are going to write about the history of science and yes we are talking about the history of science here, the zodiac with its tropical signs was originally conceived for astronomical purposes. Ms Culaba might be excused because she did not originate this particular piece of history of science rubbish but is merely regurgitating false information from what she obviously thought was a reliable source, the BBC.

Here we have the presenter of Stargazing Live, a high prestige BBC science programme, Dara O Brian presenting the world with high-grade bullshit under the BBC’s banner. O Brian and his co-presenter Brian Cox should know better and I find it a total disgrace that the fee payers money is being wasted on such rubbish under the guise of educational television, both the presenters and the Beeb should be thoroughly ashamed of themselves.

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

The worst history of technology headline of the year?

The Guardian website produced a couple of articles to announce the publication of Sydney Padua’s graphic novel, The Thrilling Adventures of Lovelace and Babbage: The (Mostly) True Story of the First Computer. I strongly suspect that despite Padua’s qualifying ‘mostly’ in her subtitle what we will be presented with here bears very little relation to the historical facts. However, not actually having read the book, it is not the subject of this brief post but rather the Guardian article. This article is crowned with the following headline:

Ada Lovelace and Charles Babbage designed a computer in the 1840s.

A cartoonist finishes the project.

 Can you spot the major howler in the very brief first sentence? Who designed a computer? Charles Babbage designed a computer. Ada Lovelace wrote a puff piece about that computer, which was in all probability largely ghost-written by Babbage. Just in case you should think that this was an inadvertent slip of a subeditor’s thumb on his computer keyboard the claim is repeated even more emphatically in the title of an illustration to the article.

200 years after Ada Lovelace’s birth, the Analytical Engine she designed with Charles Babbage is finally built, thanks to the imagination of Sydney Padua. Illustration: The Observer

In case you should still think that the writer of the piece could or should be excused of all blame, embarrassed by the hyperbolic flights of fancy of that technology history ignorant subeditor, we find the following in the main body of the article.

Brought up to shun the lure of poetry and revel instead in numbers, Lovelace teamed up with mathematician Charles Babbage who had grand plans for an adding machine, named the Difference Engine, and a computer called the Analytical Engine, for which Lovelace wrote the programs.

Where to begin? First off both the Difference Engine and the Analytical Engine are computers. The former a special purpose computer and the latter a general purpose one. Babbage would have been deeply offended having his mighty Difference Engine denigrated to a mere adding machine, although all computers are by name adding machines; computer coming, as it does, from the Latin computare which means to reckon/compute/calculate, sum/count (up). As a brief aside, when the word computer was coined in the 17th century it referred to a person employed to do calculations. Second, and in this context most important, Lovelace did not write the programs for the Analytical Engine. The afore mentioned puff piece from her pen contained one, note the singular, specimen program for the Analytical Engine, which she might possibly have written, although it seems more probable that Babbage wrote it. All the other programs for the Analytical Engine, and there were others were written by, you’ve guessed it, Charles Babbage.

The deification of Ada Lovelace marches on a pace with the honest historian of the computer barely able to keep pace with the waves of mythology that pour out of the unsavvy media almost every day it seems.

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There is no such thing as Greek science.

I’m pretty certain that a fair number of people reading the title of this post will be going, ‘what the hell is he talking about? We heard all about Greek science at primary (grade) school, secondary school, high school, college, university” or “I’ve read about Greek science in that popular history of science book, popular science journal, that website, on Wikipedia, in that magazine at the hairdressers!” “Of course there is such a thing as Greek science you can hear/read about it all over the place. Has he gone barmy or something?” Others are probably thinking he’s about to go on about how the word science when used for the ancient Greeks is anachronistic and we shouldn’t call it science but … This chain of thought is in fact correct but is not the topic of this post. In fact for the moment I’m quite happy to use the word science in this context as a shorthand way of describing all of the intellectual disciplines practiced by the ancient Greeks that are related to the disciplines that we call the sciences today, even if this usage is more than somewhat anachronistic. What I’m objecting to, in fact rejecting is the whole term ‘Greek science’ it doesn’t exist has never existed and its usage leads to a series of dangerous misconceptions; dangerous that is for our understanding of the history of western science. Why do I say this and what misconceptions?

The usage of the term Greek science implies that there is a coherent, albeit, abstract object that can be indicated by this term, no such object has ever existed. This becomes very obvious if one takes the time to look closely at what is usually labelled Greek science.

If we look at the time dimension we are talking about a set of activities that begins some what earlier than six hundred BCE with the earliest of the so-called pre-Socratic philosophers i.e. Thales and co. It carries on in the western world until the death of the last of the so-called encyclopaedists Isidore of Seville in 632 C. That is a time span of more than twelve hundred years. Just to put that in perspective, if we go back twelve hundred and fifty years from today Pippin the Short, the first of the Carolingians to become King of the Franks, was on the throne. His son Karl der Große, or Charlemagne, as the English call him, might be better known to you. Twelve hundred years is a lot of human history and a lot can happen in a time span that long.

A geographical examination yields a similar result. The pre-Socratics lived in what became known as Asia Minor and is now part of Turkey. It stretches over the Greek island and mainland in its development to Southern Italy. It took in the whole of the Hellenistic Empire of Alexander the Great and later the whole of the Roman Empire. Our last representative Isidore, as his name tells us, lived in Seville in Spain. Up till now I’ve not mentioned the final Greek Empire, Byzantium, which begins when the Roman Emperor Constantine moved his capital from Rome to Constantinople and ended with the fall of that noble city to the Turks in 1453. It occupied a large part of what is now Turkey. Geo-politically over our twelve hundred plus years we progress from ancient Greek culture through Hellenistic culture, on to Romano-Hellenistic culture and finishing up in post-classical Roman late antiquity or the Early Medieval period. It should be clear by now that to refer to Greek science is a fairly pointless exercise from the point of view of time, geography, and politics and culture. It’s about as meaningless as referring to European science and using the term to designate some sort of coherent whole beginning with Charlemagne and going up to the present and encompassing the whole of the continent of Europe. That coherent whole simply doesn’t exist.

Of course the time, special and politico-cultural dimensions are only part of the problem and not even the most important part. Despite the vast diversity that we have just sketched people still insist in talking about a single coherent science and it is here that the real damage caused by misconception takes place. Let us start with one typical example to illustrate what I mean. In popular presentations of the study of the theory of optics I constantly stumble across statement of the type, ‘the Greeks believed that we see by beams projected from the eyes to the objects perceived’. Such standpoint is know technically as an extramission theory of vision and is indeed one of the theories of vision proposed and discussed by the ancient Greeks. The important phrase here is ‘one of the theories’; the various groups in ancient Greece proposed at least five different contrasting, conflicting and contradictory theories of vision over a number of centuries that they investigated and discussed. These theories were then taken up and debated further by both the Islamic and the European scholars in the Middle Ages. We don’t have a case of ‘the Greeks thought/believed this’ but rather the Atomists believed this, the Platonists believed this, the Aristotelians believed this, the Stoics believe this and the mathematical optical theorists believed this. In other words we have conflicting competing theories presented by different schools of thought each of which was different at different times and often in different areas during those twelve hundred years that Greek culture existed. Those who just present the extramission theory as being what the Greeks thought seem to be motivated by presenting the Greeks in a bad light. Look how stupid the Greeks were, they actually believed that the eyes send out rays of fire enabling people to see.

One could of course argue that this is one example and doesn’t necessarily represent the whole of Greek science but it does. The list of groups that I named as holding differing theories of vision is basically the list of principle schools of thought within ancient Greek culture who developed and presented views on a multitude of scientific topics throughout the Greek cultural period. They are others who didn’t necessarily have views on optics, such as the Pythagoreans, but did develop theories in other areas. Each of the named schools came into being and enjoyed a period of prominence as their ideas were shiny new and stimulating then falling somewhat into the background as new schools emerged with other shiny new ideas.

A second example is provided by the disciplines of astronomy and cosmology. It is a commonplace that the Greeks believed the heavens to be divided into two spheres, the sublunar and the supralunar, the latter being perfect and the former corruptible. They, the Greeks, also believed that comets being corruptible inhabit the sublunar sphere. These views are not the views of the Greeks but of Aristotle and the Aristotelians. Another school of thought the Stoics regarded the entire heavens to be of one nature with no division and comets to be phenomena of the supralunar region. The Stoics and there cosmology were in general more dominant in later antiquity than the Aristotelians.

The opinion that the views of the Aristotle were those of the Greeks comes from adoption of those views by Europeans in the High Middle Ages and the misconception that they and they alone dominated European thought until deposed by the ‘modern’ astronomy in the Early Modern Period. In fact modern research into the history of astronomy has revealed that a renaissance of the Stoic cosmology in Europe in the fifteenth and sixteenth centuries played a significant role in the so-called astronomical revolution.

I could go on producing examples from every branch of Greek knowledge that display the diversity of Greek thought across the centuries. Even the much-quoted Greek mathematics was in reality a varying range of diverse and oft conflicting schools. The two most famous Greek mathematicians Euclid and Archimedes represent two conflicting approaches to the subject, Euclid synthetic, Archimedes analytical. These two fundamentally different approaches resurfaced in conflict with each other during the seventeenth century following the renaissances of synthetic Euclidian mathematics in the fifteenth century and analytic Archimedean mathematics in the sixteenth century.

Any extensive in depth survey of science carried out in the Greek language in the Mediterranean region in antiquity should convince anybody that there never was anything that could reasonably be called Greek science and we should all endeavour to stop using the term and instead talk about the Platonic theory of vision, Aristotelian cosmology, Euclidian geometry or whatever label correctly identifies the topic under discussion. By pure chance Mary Beard, a leading British classicist, tweeted the following statement during the week that perfectly sums up the message of this post in 140 characters:

 

Afraid I bridle at generalising “did THE GREEKS think?” M Finley always said “which Greeks? when?” Not unitary culture – @wmarybeard

 

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Emmy the student and Emmy the communist!

Emmy Noether’s birthday on 23 March saw her honoured with a Google Doodle, which of course led to various people posting brief biographies of Erlangen’s most famous science personality or drawing attention to existing posts in the Internet.

Emmy Google Doodle

Almost all of these posts contain two significant errors concerning Emmy’s career that I would like to correct here. For those interested I have written earlier posts on Emmy’s family home in Erlangen and the problems she went through trying to get her habilitation, the German qualification required to be able to teach at university.

The first oft repeated error concerns Emmy’s education and I quote a typical example below:

Today she is celebrated for her contributions to abstract algebra and theoretical physics, but in 20th-century Bavaria, Noether had to fight for every bit of education and academic achievement. Women were not allowed to enrol at the University of Erlangen, so Noether had to petition each professor to attend classes.

As a teenager Emmy displayed neither an interest nor a special aptitude for mathematics but rather more for music and dance. She attended the Städtische Höhere Töchterschule (the town secondary girls’ school), now the Marie-Therese-Gymnasium, and in 1900 graduated as a teacher for English and French at the girls’ school in Ansbach. In 1903 she took her Abitur exam externally at the Königlichen Realgymnasium in Nürnberg. The Abitur is the diploma from German secondary school qualifying for university admission or matriculation. Previous to this she had been auditing some mathematics courses in Göttingen as a guest student with the personal permission of the professors whose courses she visited, hence the claim above. However she had become ill and had returned home to Erlangen. In 1903 the laws were changed in Bavaria allowing women to register at university for the first time. Emmy registered as a regular student at the University of Erlangen in 1903 and graduated with a PhD in mathematics in 1907, under the supervision of Paul Gordon, in invariant theory. She was only the second woman in Germany to obtain a PhD in mathematics. In 1908 she became a member of the Circolo Matematico di Palermo and in 1909 a member of the Deutschen Mathematiker-Vereinigung. In 1909 Hilbert and Klein invited her to come to the University of Göttingen, as a post-doc researcher. It was here in 1915 that Hilbert suggested that she should habilitate with the well know consequences.

Emmy remained in Göttingen until the Nazis came to power in 1933. She held guest professorships in Moscow in 1928/29 and in Frankfort am Main in 1930. She was awarded the Ackermann-Teubner Memorial Prize for her complete scientific work in 1932 and held the plenary lecture at the International Mathematical Congress in Zurich also in 1932. In 1933 when the Nazis came to power she was expelled from her teaching position in Göttingen and it is here that the second oft repeated error turns up.

On coming to power the Nazis introduced the so-called Gesetz zur Wiederherstellung des Berufsbeamtentums, (The Law for the Restoration of the Professional Civil Service). This was a law introduced by the Nazis to remove all undesirables from state employment, this of course meant the Jews but also, socialists, communists and anybody else deemed undesirable by the Nazi Party. Like many of her colleges in the mathematics department at Göttingen Emmy was removed from her teaching position under this law. In fact the culling in the mathematics department was so extreme that it led to a famous, possibly apocryphal, exchange between Bernhard Rust (and not Hermann Göring, see comments) and David Hilbert.

Rust: “I hear you have some problems in the mathematics department at Göttingen Herr Professor”.

Hilbert: “No, there are no problems; there is no mathematics department in Göttingen”.

The Wikipedia article on the history of the University Göttingen gives the story as follows (in German)

Ein Jahr später erkundigte sich der Reichserziehungsminister Bernhard Rust anlässlich eines Banketts bei dem neben ihm platzierten Mathematiker David Hilbert ob das mathematische Institut in Göttingen durch die Entfernung der jüdischen, demokratischen und sozialistischen Mathematiker gelitten habe. Hilbert soll in seiner ostpreußischen Mundart (laut Abraham Fraenkel, Lebenskreise, 1967, S. 159) erwidert haben: „Jelitten? Dat hat nich jelitten, Herr Minister. Dat jibt es doch janich mehr.“

The source here is given as Abraham Fraenkel in his autobiography Lebenkreise published in 1967.

This translates as follows:

One year later [that is after the expulsions in 1933] the Imperial Education Minister Bernhard Rust, who was seated next to the mathematician David Hilbert at a banquet, inquired, whether the Mathematics Institute at Göttingen had suffered through the removal of the Jewish, democratic and socialist mathematicians. Hilbert is said to have replied in his East Prussian dialect” Suffered? It hasn’t suffered, Herr Minister. It doesn’t exist anymore”

It is usually claimed that Emmy lost her position because she was Jewish, a reasonable assumption but not true. Emmy lost her position, like many other in Göttingen, because the Nazis thought she was a communist. Like many European universities in the 1920s and 30s Göttingen was a hot bed of radical intellectual socialism. Emmy had been a member of a radical socialist party in the early twenties but changed later to the more moderate SPD, who were also banned by the Nazis. However it was her guest professorship in Moscow that proved her undoing. Because she reported positively on her year in Russia the Nazis considered her to be a communist and this was the reason for her expulsion from the university in 1933.

Initially Emmy, after her expulsion, actually applied for a position at the University of Moscow but the attempts by the Russian topologist Pavel Alexandrov to get her a position got bogged down in the Russian bureaucracy and so when, through the good offices of Hermann Weyl, she received the offer of a guest professorship in America at Bryn Mawr College she accepted. In America she taught at Bryn Mawr and the Institute of Advanced Studies in Princeton but tragically died of cancer of the uterus in 1935.

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Calendrical confusion or just when did Newton die?

Today there is general agreement throughout the world that for commercial and international political purposes everybody uses the Gregorian calendar, first introduced into the Catholic countries of Europe in 1582. However Europeans should never forget that for other purposes other cultures have their own calendars often wildly at odds with the Gregorian one. Tomorrow is for example the Persian New Year’s a festival, which marks the first day of spring. The Persian calendar is not only used in Iran but in many other countries that were historically under Persian influence. Tomorrow also marks the first day of the year 1394 for Persians. Earlier all cultures used their own calendars a bewildering array of lunar calendars, lunar-solar calendars and pure solar calendars making life very difficult for both astronomers and historians. Trying to find out what a given date in an original document is, or better would have been, on our ‘universal’ Gregorian calendar is often a complex and tortuous problem. Astronomers whose observations of the heavens need to span long periods of time solved the problem for themselves by introducing a standard calendrical scale into which they then converted all historical astronomical data from diverse cultures. Throughout late antiquity, the Islamic Empire and well into the European Early Modern Period astronomers used the Egyptian solar calendar for this purpose. You can still find astronomical dates given according to this system in Copernicus’ De revolutionibus. In modern times they introduced the Julian day count for this purpose.

Within Europe the most famous calendrical confusion occurred in the early centuries following the introduction in Catholic countries of the Gregorian calendar. Exactly because it was Catholic most Protestant states refused, at first, to introduce it, meaning that Europe was running on two different time scales making life difficult for anybody having to do outside of their own national borders, in particular for traders. This problem was particularly acute in The Holy Roman Empire of German States that patchwork of small, medium and large states, principalities and independent cities that occupied most of middle Europe. Neighbouring states were often of conflicting religious affiliation meaning that people living in the border regions only needed to go a couple of kilometres down the road to go ten days backwards or forwards in time. The only people who were happy with this system were the calendar makers who could sell two sets of calendars Gregorian, so-called new style or ‘ns’ and Julian, so-called old-style or ‘os’. Some enterprising printer publishers even printed both calendars in one pamphlet, for a higher price of course.

Within Germany the problem was finally solved at the end of the seventeenth century, largely due to the efforts of Erhard Weigel who campaigned tirelessly to get the Protestant states to adopt the Gregorian calendar, which they finally did on 1 January 1700. England as usual had to go its own way.

Although John Dee, the court advisor on all things mathematical, recommended the adoption of the Gregorian calendar in the sixteenth century the Anglican Bishops blocked its adoption because it came from the Pope and the Anglican Church couldn’t be seen cowing down to the Vatican. Even when the Protestant German states finally accepted that adopting the Gregorian calendar was more rational than any religious prejudices the English still remained obdurate, not prepared to have anything to do with Catholicism. England final came into line in 1752. So what about Isaac Newton?

Many Internet sources are saying that Isaac Newton died on 20 March almost none of them say whether this is new-style or old-style. Most of the sources give 1727 as the year of death a few 1726. Most sources give Newton’s life span as 1642–1727, others 1642–1726 and yet others 1643–1727, what is going on here?

Isaac Newton was born 25 December 1642 according to the Julian calendar that is old-style. If converted to the Georgian calendar, we have to add ten days, and so his date of birth was 4 January 1643 new-style. Things become slightly more complicated with his date of death. Newton died 20 March 1726 according to the Julian calendar that is old-style. Converting to the Georgian calendar we now have to add eleven days because the Julian calendar has slipped another day behind the Gregorian one so his date of death is 31 March 1727 new-style. Wait a minute we just jumped a year what happened here? When Julius Caesar introduced the solar calendar in Rome he moved the New Year from the traditional Roman spring equinox, 25 March, to the first of January. During the Middle Ages the Church moved the New Year back to 25 March. With the adoption of the Gregorian calendar New Year’s Day moved back to 1 January. However England still retaining the medieval version of the Julian calendar kept 25 March as New Year’s Day. Thus at the time of Newton’s death 1727 started on 25 March in England meaning that Newton died 20 March 1726 (os).

Just to summarise if you wish to correctly quote Newton’s dates of birth and death then they are 25 December 1642 – 20 March 1726 (os) or 4 January 1643 – 31 March 1727 (ns).

 

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Filed under History of Astronomy, Newton

The continuing saga of io9’s history of science inanities.

I made a sort of deal with myself to, if possible, avoid io9 and above all the inane utterances of Esther Inglis-Arkell. Unfortunately I fell for a bit of history of science click bait on Twitter and stumbled into her attempt to retell the story of the degenerating relations between Isaac Newton and John Flamsteed, the Astronomer Royal. I say attempt but that is actual a misuse of the word because it somehow implies making an effort, something that Ms Inglis-Arkell is not willed to do. Her post resembles something half read, half understood and then half forgotten spewed out onto the page in a semblance of English sentences. It in no way approaches being something that one could honestly label history of science story telling even if one were to stretch this concept to its outer most limits.

I have blogged on the relations between Newton and Flamsteed on a number of occasion but let us look at Ms Inglis-Arkell miserable attempt at telling the story and in so doing bring the correct story out into the open. Our storyteller opens her tale thus:

Isaac Newton reached the level of genius in two different disciplines: physics and making people miserable. This is a tale of his accomplishments in the latter discipline. The object of his scorn, this time, is a poor astronomer named John Flamsteed, who made the mistake of not being agreeable enough.

I tend to dislike the term genius but if one is going to apply it to Newton’s various activities then one should acknowledge that as an academic he also reached the level of genius as a mathematician, as a theoretical astronomer and as an instrument maker and not just as a physicist. Credit where credit is due. On the subject of his making people miserable, John Flamsteed was anything but a saint and as I pointed out in an earlier post, Grumpy old astronomers behaving badly or don’t just blame Isaac!, in the dispute in question both of them gave as good as he got.

We now get to the factual part of the story where our storyteller displays her grasp of the facts or rather her lack of one:

Flamsteed and Newton started their acquaintance on good terms. They spent the 1680s happily corresponding about two lights in the sky, seen in 1680, which were either two comets or one comet that made two trips by Earth. This got Flamsteed interested in cataloguing [sic] the heavens. If enough information was compiled about the lay of the night sky, astronomers would be able to understand all kinds of things about the shape of the universe and how its various pieces worked. By the mid-1690s, Flamsteed was the Astronomer Royal and was making a star catalogue which he would publish when it was completed.

Remember that bit about half read and half forgotten? John Flamsteed had been installed by Charles II as Astronomer Royal for the newly commissioned Royal Observatory at Greenwich on 22 June 1675 “forthwith to apply himself with the most exact care and diligence to the rectifying the tables of the motions of the heavens, and the places of the fixed stars, so as to find out the so-much desired longitude of places, for the perfecting the art of navigation.” Not by the mid-1690s as Ms Inglis-Arkell would have us believe. I love the bit about how, astronomers would be able to understand all kinds of things about the shape of the universe and how its various pieces worked”, Which basically just says that she doesn’t have a clue what she’s talking about so she’ll just waffle for a bit and hope nobody notices. The Observatory itself wasn’t finished till 1685 but by the beginning of the 1680 Flamsteed was already busily fulfilling his obligations as official state astronomical observer.

The early 1680s saw a series of spectacular comets observable from Europe, and Flamsteed along with all the other European astronomers devoted himself to observing their trajectories and it was a conjecture based on his observations that led to his correspondence with Newton. He observed two comets in 1680, one in November and the second in mid December. Flamsteed became convinced that they were one and the same comet, which had orbited the sun. He communicated his thoughts by letter to Isaac Newton (1642–1727) in Cambridge, the two hadn’t fallen out with each other yet, and Newton initially rejected Flamsteed’s findings. However on consideration he came to the conclusion that Flamsteed was probably right and drawing also on the observations of Edmund Halley began to calculate possible orbits for the comet. He and Halley began to pay particular attention to observing comets, in particular the comet of 1682. By the time Newton published his Principia, his study of cometary orbits took up one third of the third volume, the volume that actually deals with the cosmos and the laws of motion and the law of gravity. By showing that not only the planets and their satellite systems obeyed the law of gravity but that also comets did so, Newton was able to demonstrate that his laws were truly universal. Note that Flamsteed two-in-one comet was orbiting the sun and not “one comet that made two trips by Earth”; this will come up again in the next paragraph:

Newton, meanwhile, believed that returning comets might be drawn to the Earth by some mysterious force. They might circle the Earth, in fact, the way the Moon circled the Earth. Perhaps, the force that drew the Moon and the comets might be the same. Newton wanted to study his “Moon’s Theory,” and to do so he needed the information in Flamsteed’s catalogue, incomplete though it was. Newton had risen to the rank President of the Royal Society of London for Improving Natural Knowledge; the titles might leave one in doubt as to who had the power, but Newton’s fame and connections far outstripped Flamsteed’s. When Isaac Newton wanted information from the catalogue, he wanted it immediately, whether it was published or not.

The opening sentences of this paragraph are a confession of complete incompetence for somebody, who, if I remember correctly, has a degree in physics. We are of course talking about the force of gravity, so why not call it that? Anyone who has studied physics at school knows that according to the law of gravity any two bodies “attract each other” something that Newton had spelled out very clearly in his Principia, which was published in 1687 before the dispute that Inglis-Arkell is attempting to describe took place. So the comets are not being “drawn to the Earth by some mysterious force”. In fact they are not being drawn to the Earth at all and there are certainly not circling it. Flamsteed’s careful observations and astute deduction had correctly led Newton to the conclusion that the force of gravity causes some comets to orbit the sun. As we shall see shortly when Newton and Flamsteed got in each others hair about Newton’s need for fresh observational date on the moon he was still Lucasian Professor of Mathematics in Cambridge and still ten years away from becoming President of the Royal Society. However before I go into detail let us look at Inglis-Arkell’s account of the affair.

You can get a lot done when you’re friends with the Queen, but it still took a lot of time for Isaac Newton to get what he wanted from John Flamsteed. First Flamsteed sent assistants’ work instead of his own. Newton was exasperated with the mistakes they had made. Newton wrote nasty letters. Flamsteed wrote nasty diary entries. Newton turned to the royal Prince George, asking him to order Flamsteed to write a book that would include all his current data. Flamsteed just couldn’t get it together to produce the book, much as he must have wished to comply with his Prince’s order.

Newton inspected the Royal Observatory. Flamsteed guarded the equipment so jealously that the two physically fought over it. Flamsteed ended that day with a very smug diary entry declaring that the “instruments… were my own.”

Now the Astronomer Royal was not only disobeying Isaac Newton but the actual Royals, and so it’s impressive that Flamsteed managed to keep his prestigious appointment. He didn’t lose his position or his data for over a decade. It wasn’t until 1712 that Newton was able to influence Queen Anne and Prince George enough to force Flamsteed to publish his data in a small volume. Still, Flamsteed was bitter at the defeat.

Our intrepid wanna-be historian of science has conflated and confused three separate struggles between the two protagonists into one, getting her facts wrong along the way and even making thinks up, not a very good advertisement for a website that wishes to inform its readers or maybe this is one of their sci-fi contributions.

Let us take a look at what really happened. In an incredible tour de force Newton wrote and published his Principia in the three years between 1684 and 1687 and as I noted above Flamsteed’s recognition that some comets orbit the sun went on to play a central role in this ground-breaking work. In his magnum opus Newton was able to demonstrate that the whole of the then known cosmos lay under the rule of the law of gravity. It determined the elliptical orbits of the planets around the sun as well as the orbits of the then known satellites of Jupiter and Saturn. It converted the comets from irregular prophets of doom into celestial objects with regular but extremely long orbits. Everything seemed to fit neatly into place in a clockwork cosmos. Well almost everything! The earth’s closest neighbour appeared not to want to obey the dictates of gravity. Although Newton managed to get a fairly good approximation of a gravity-determined orbit for the moon it wasn’t anywhere near as good as he would have liked.

The problem lies on the size of the moon. Having an unusually large mass for a satellite the moon is involved in a gravitational system with both the earth and the sun, the classical three-body problem. As a result its orbit is not a smooth ellipse but being pulled hither and thither by both the earth and the sun its orbit contains many substantial irregularities making it very difficult to calculate. There is in fact no general analytical solution to the three-body problem, as was finally proved in the nineteenth century by Henri Poincaré. The physicist or astronomer is forced to calculate each irregularity step by step, the situation that Newton found himself in whilst writing the Principia.

In 1693 Newton was contemplating a second edition of the Principia and decided to tackle the moon’s orbit anew. This required new observational data and the person who was in procession of that data was Flamsteed. Newton never the most diplomatic of men at the best of times was even more grumpy than usual in the early 1690s. He was recovering from what appears to have been some sort of major mental breakdown, he was tackling one of the few mathematical problem that would always defeat him (the moon’s orbit, which was finally solved by Laplace in his Exposition du système du monde at the end of the eighteenth century), and he was frustrated by his situation in Cambridge and was looking for a suitable position in recognition of his, in the meantime, considerable status in London. The latter would be solved by Charles Montagu appointing him Warden of the Mint in 1696. His approach to Flamsteed to obtain the data that he required was high handed to say the least. Flamsteed, also an irritable man, who was overworked, underpaid and underfinanced in his efforts to map the entire heavens, was less than pleased by Newton’s imperious demands but delivered the requested data none the less. Newton failed to solve his problem and blaming Flamsteed and his data demanded more. Flamsteed feeling put upon grumbled but delivered; and so the pair of grumpy old men continued, each developing an intense dislike of the other. In the end Newton’s demands became so impossible that Flamsteed started sending Newton raw observational data letting him calculate the lunar positions for himself. It is difficult to say where this vicious circle would have led if Newton had not lost interest in the problem and shelved it, and the plans for a second edition of Principia, in 1695. By now the two men were totally at loggerheads but would have nothing more to do with each other for the next nine years.

In 1704 Newton, by now Master of the Mint and resident in London, was elected President of the Royal Society. On 12 April 1704 Newton took a boat down the river from the Tower of London, home of the Mint, to Greenwich, home of the Royal Observatory, to visit Flamsteed. Surprisingly amicable Newton suggested to Flamsteed that he should speak to Prince George of Denmark, Queen Anne’s consort, on Flamsteed’s behalf about obtaining funds to have Flamsteed’s life work published. Flamsteed was agreeable to having his work published especially as his critics, most notably Edmond Halley and David Gregory, were pointing out that he had nothing to show for almost thirty years of endeavour. However he would have preferred to deal with the matter himself rather than have Newton as his broker. Newton spoke to Prince George and obtained the promise of the necessary funds. Meanwhile Flamsteed drew up a publication plan for his work. He wanted three volumes with his star catalogue the high point of his work in the third and final volume. Newton had other plans. He set up an editorial board at the Royal Society consisting of himself, David Gregory, Christopher Wren, Francis Robartes and John Arbuthnot to oversee the publication. Flamsteed, the author and also a member of the Royal Society, was not included. Newton ignored Flamsteed’s wishes and declared that the star catalogue would be printed in volume one. Newton commissioned a printer to print sample sheets, however Flamsteed found them to be of poor quality and wished to find a new printer. Newton ignored him and gave the printer the commission to print the work ordering Flamsteed to supply the introductory material for the first volume.

One major problem was that the star catalogue was at this time not complete. Flamsteed kept stalling declining to supply with Newton with the catalogue until he could complete it. He needed to calculate the stellar positions from the raw observational data. Newton promised him the money to pay the computers and actually obtained the money from Prince George. Flamsteed employed the computers to do the work and paid them out of his own pocket requesting restitution from Newton. Newton refused to pay up. So the whole sorry affair dragged on until Prince George died in 1708 with which the project ground to an end. If Flamsteed had grown to dislike Newton in the 1690s he truly hated him now.

Things remained quiet for two years then at the end of 1710 John Arbuthnot, who was physician to Queen Anne, suddenly announced that Anne had issued a warrant that appointed the president and others as the council of the Royal Society saw fit to be ‘constant Visitors’ of the Royal Society. As used here visitor means supervisor and it effectively meant that Newton was now Flamsteed’s boss. With their newly won authority Newton and his cronies did everything in their power to make life uncomfortable for Flamsteed over the next few years. On 26 October 1711 Newton summoned Flamsteed to a meeting in Crane Court, the home of the Royal Society, to inform him of the state of the observatory instruments. Here we meet a classic of institutional funding. The Crown had paid to have the Royal Observatory built and having appointed Flamsteed to run it the Crown paid his wages, on a very miserly level, however no money was ever supplied for instruments and so Flamsteed had bought his instruments with his own money. When Newton demanded account of the state of the instruments Flamsteed could prove that they were all his own private property and thus no concern of Newton’s. Newton was far from pleased by this defeat. He now ordered the Royal Ordnance to service, repair and upgrade the instruments and thus to win official control over them. Unfortunately the Ordnance, which, like the Mint, occupied the Tower of London didn’t like Newton so taking sides with Flamsteed informed Newton that there were no funds available for this work. A minor victory for Flamsteed but he had already suffered a major defeat. Before discussing this I should point out that contrary to Ms Inglis-Arkell’s claims, at no time did the elderly combatants resort to any form of physical contact.

On 14 March 1711 Arbuthnot had informed Flamsteed that the Queen had commanded the complete publication of his work; the brief reprieve brought about by the death of Prince George was over. Although the star catalogue, which was all that Newton was interested in publishing, was now finished Flamsteed at first prevaricated again. Arbuthnot wrote to Flamsteed requesting him to deliver up the catalogue, Flamsteed declined with further excuses. Newton exploded and shot off a letter ripping a strip of Flamsteed for defying a Royal command and the fight was now effectively over. Flamsteed met with Arbuthnot and handed over the manuscript requesting conditions concerning the printing and editing to which Arbuthnot acquiesced and promptly ignored. Flamsteed went ballistic, as he discovered that printing was going ahead without his knowledge and even worse his manuscript was being edited by Edmond Halley! Flamsteed by now hated Newton but he reserved his greatest loathing for Halley. It has been much speculated why Flamsteed had such an extreme aversion to Halley but it went so far that he refused to use his name and only referred to him as Reimers after Nicolaus Reimers Bär, whom Flamsteed believed had plagiarised his hero Tycho and was thus the most despicable person in the history of astronomy. Flamsteed had lost all down the line and in 1712 his star catalogue appeared in a large folio volume (not the small volume claimed by Inglis-Arkell). Deeply bitter Flamsteed now swore to publish his life’s work in three volumes, as he had originally planned in 1704, at his own expense and began with the preparation. It should be noted that far from ‘Newton being able to influence Queen Anne and Prince George enough to force Flamsteed to publish his data’, Prince George had by now been dead for four years!

However Newton might have won a victory but he hadn’t yet won the war and the tide began finally to turn in Flamsteed’s favour. In 1714 Queen Anne died and was succeeded on the throne by George I, Elector of Hanover. The succession also brought with it a change of government. Now Inglius-Arkell claims that George didn’t like Newton but this is not true. He greatly respected Newton who had long been regarded as the greatest natural philosopher in Europe; he even forced his librarian, Gottfried Wilhelm von Leibniz, who would have loved to have moved to London to escape his Hanoverian backwater (no offense intended to Hannover or the Hanoverians), to stay at home so as not to offend Newton, who was at war with Leibniz when he wasn’t battling Flamsteed. However the succession and the change of government did mean a loss of influence for Newton. In early 1715 Charles Montagu, Lord Halifax, one of the most powerful politicians in England during the previous twenty years and Newton’s political patron, died. Charles Paulet, 2nd Duke of Boulton, the Lord Chamberlin, was a friend of Flamsteed’s and on 30 November 1715 he signed a warrant ordering Newton to return the three hundred remaining copies of the printed star catalogue to Flamsteed. He “made a Sacrifice of them to Heavenly Truth”; i.e. he burnt them.

Flamsteed continued with his project to publish his life’s work at his own expense but died in 1719 before he could finish the project. His widow with the willing help of his two assistants Joseph Crosthwait and Abraham Sharp finished the job and his three-volume Historia coelestis britannica was finally published in 1725, followed by his charts of the constellations the Atlas coelestis, edited by his widow and James Hodgson in 1727. Together they form a fitting monument to one of history’s greatest observational astronomers. Flamsteed had written a long preface for the Historia describing, from his standpoint, in great detail his twenty year long war with Newton but this did not make it into the final printed edition, probably because Newton, by now a living legend, was still very much alive. It only resurfaced a hundred years later. Flamsteed got his revenge, from beyond the grave, on Halley, who followed him as Astronomer Royal. As already explained above, Flamsteed’s observational instruments were his own personal property so when he died his widow stripped the observatory bare leaving Halley an empty building in which to pursue his new office.

The whole, more than twenty year long, farce is one of the more unsavoury episodes in the history of science and certainly not how one would expect two senior officers of state to behave. It is clear that Newton caries most of the blame although Flamsteed was not exactly a model of virtue deliberately fanning the flames through renitent and provocative behaviour. In particular his behaviour towards Halley, who was more than qualified and very capable of editing the star catalogue, was extremely childish and inexcusable.

You might think that I am being very unfair to Ms Inglis-Arkell having turned her very brief account into an overlong post but that is actually the point and her central failure, ignoring all of the factual errors in her version of the story. What I have laid out here are only the bare bones of the whole story, if I were to go into real detail this post would be ten times longer than it already is. Ms Inglis-Arkell attempt to reduce a highly complex series of episodes out of the history of science to a couple of hundred words in a throwaway post could only end in a level of distortion that makes the whole exercise a complete waste of time, effort (not that she seems to expended much of that) and cyberspace.

 

 

 

 

 

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Filed under Early Scientific Publishing, History of Astronomy, History of science, Newton