The West’s intellectual birthright!

The American cultural magazine, The Atlantic recently published an article by Daniel Foster entitled, In Defense of ‘The West’. This was a political article questioning the speech that Donald Trump had made in Warsaw and what the author sees, as what The Trump White means when they talk of ‘The West’. Amongst many other things the article contains the following paragraph encapsulating the authors view of what he sees as The West’s intellectual birthright in the history of science:

Likewise, Egypt hosted the first great repository of Western knowledge—the library at Alexandria—and for a millennium or so following that library’s destruction, it was Muslim metaphysicians who kept lit the flame of Greek ideas. The West’s intellectual birthright, then, was reborn in Latin and French and German and English because it was vouchsafed in Arabic, in the dark interregnum between Charlemagne and the Renaissance.

These sixty-six words made my hair stand on end, or would have done if I had any, for several different reasons that I shall attempt to explicate in what follows.

We will start off with the expression The West’s intellectual birthright. What is meant here is of course Greek science, which doesn’t actually exist and never did. However, how is Greek science The West’s intellectual birthright? The article’s author is trying to argue against a view of the West as being white and bordering the North Atlantic and he could start right here. Even the Greek’s were quite happy to admit that their scientific endeavours were based on those of their predecessors in Egyptian and Babylon, whereby Babylon is shorthand for the various cultures that occupied the so-called fertile crescent in antiquity. So why is Greek science not the intellectual birthright of North Africa or the Middle East, the areas that laid its foundations? Greek science is nobody’s intellectual birthright; the various schools of intellectual thought who developed scientific and proto-scientific ideas within Greek culture in the period between roughly 600 BCE and 600 CE sowed seeds in various cultures throughout the world some of which blossomed and some of which withered and the cumulative developments out of those seeds belong to the whole of humanity.

The author tries to argue against a white North Atlantic West by pointing out that it is geographically and culturally intertwined with much outside of this narrow concept viewed historically and so the opening sentence of the paragraph is supposed to imply a non European source for that intellectual birthright. This ignores the fact that although Alexandria lies in Egypt it was a Greek city and the library was a Greek institution and not an Egyptian one. The next problem is that the library in Alexandria was not the first, and by no means the only, great repository of Western knowledge and was not in any meaningful sense destroyed but declined over several centuries probably disappearing from the world stage around 300 CE. For full details of this story I direct you to Tim O’Neill’s recent excellent essay on the subject.

We now stumble over the next problem; Muhammad first fled from Mecca to Medina in 622 CE, this being the formal date of the establishment of Islam. The establishment of Islam as an intellectual culture begins first in the 8th century CE, so more than 400 years after the final collapse of the library of Alexandria. The Muslims, Christians, Jews and Zoroastrians who established the intellectual culture within the Islamic Empire collected their science and philosophy not only from various Greek sources but also from Persian, Indian and Chinese ones, so they are not just keeping the flame of Greek ideas lit but a melange of ideas from numerous sources. Even more important, they didn’t just keep a flame lit but analysed, criticised, commented upon and improved and expanded the knowledge that they had collected from those other cultures. They were not simply guardians of the flame but added fuel of their own to make it burn brighter.

This knowledge came back into Europe through the boundaries between the Islamic Empire and Christian Europe in Spain and Sicily in the 12th and 13th centuries through the efforts of the so-called translators. These were Christian scholars who worked together with Arabs and Jews to translate the Greek, Latin and Arabic works from Arabic into Latin. This means that the Islamic Empire had only had ‘exclusive’ access to this conglomeration of knowledge for five hundred years and not a millennium as claimed above. Note that this knowledge returned to Europe only in Latin and not also in French German and English as claimed. The introduction of the use of the vernacular for scientific texts only really began in the seventeenth century long after this knowledge had become established in Europe.

We now turn to the final and by far and away the worst piece of shoddy history in this strange paragraph, its final clause: in the dark interregnum between Charlemagne and the Renaissance. When I read this the first time I did more than a double take. I seriously couldn’t believe what I had just read. Let us be clear. We are not talking here about the Early Middle Ages, long known as The Dark Ages, a term that historians now shun but about the period that represents the emergence from the Early Middle Ages into what is generally known as the High Middle Ages and this is according to our author a ‘dark interregnum’. Sorry but this is just simple wrong.

There was a definable intellectual decline within the Roman Empire that begins gradually in the middle of the 2nd century CE and can be regarded as complete by around 400 CE with the collapse of the Western Empire. Over the next approximately 400 years there is little of no intellectual activity in Europe and it is first with Karl der Große (that’s Charlemagne) and the so-called Carolinian Renaissance that this situation begins to change. Far from being the start of a dark interregnum Charlemagne marks the end of one and the gradual climb out of the intellectual darkness into the sunshine of knowledge. Starting with Charlemagne’s own intellectual reformer, Alcuin of York, there is a long chain of medieval scholars including the translators mentioned above, the Oxford Calculatores, the Paris Physicists and many others who laid the foundations for the Renaissance and the so-called Scientific Revolution.

The rich world of medieval science and technology has been well documented beginning with the work of Pierre Duhem in the 19th and early 20th centuries over the substantial contributions of Alistair Crombie, Marshall Clagett, Edward Grant, John Murdoch, Toby Huff and David Lindberg amongst others. With the work of James Hannam and John Freely there are even two good popular books on the subject available for those who don’t want to plough through heavy academic texts, so there is really no excuse for the piece of arrant bullshit presented by Daniel Foster.

The scant paragraph that I have eviscerated above is unfortunately typical for the type of history of science, although to even call it history is a misnomer, that gets presented all too often by journalists, a collection of random myths, legends, clichés and ignorance that they have picked up somewhere down the line. Checking their facts or even consulting an expert on the subject seems to be too much trouble for these people, what does it matter, it’s just history of science seems to be their creed and that really pisses me off.


Filed under Myths of Science

A very innovative early scientific printer/publisher

It is a commonplace amongst historians that the invention of movable type, and through it the advent of the printed book, in the middle of the fifteenth century, was one of the principal driving forces behind the emergence of modern science in the Early Modern Period. However, although historians of science pay lip service to this supposedly established fact very few of them give any consideration to the printer/publishers who produced those apparently so important early books on science, medicine and technology. Like the technicians and instrument makers, the printer/publishers, not being scientist, are pushed to the margins of the historical accounts, left to the book historians.

Here at the Renaissance Mathematicus I have in the past featured Regiomontanus, considered to be the very first printer/publisher of science, Johannes Petreius the publisher of Copernicus’ De revolutionibus amongst numerous other scientific works and Anton Koberger around 1500 the world’s biggest printer/publisher and the man who produced the first printed encyclopaedia, The Nuremberg Chronicle. Today I want to turn my attention to a less well-known but equally important printer/publisher of scientific texts, who was responsible for several significant innovations in book production, Erhard Ratdolt.

Erhard Ratdolt was born in Aichach in Bavaria in 1459 or 60 the son of the carpenter Erhard Ratdolt and wife Anna. Erhard apprenticed as a carpenter and a maker of plaster figures. At the age of fifteen, according to his own account, he travelled to Venice, where he set up a printer/publisher office together with Bernhart Pictor a painter from Augsburg and Peter Loslein from Langenzenn, a small town near Nürnberg, in 1476.[1] The printing house was one of the earliest in Venice, where Johannes de Spira had set up the first one in 1469. By 1480 Venice had become to main centre for book production in Europe It seems that Ratdolt ran the business, whilst Pictor was responsible for the book decoration and Loslein for the text and copyediting. Both Pictor and Loslein had left the publishing house by 1478 leaving Ratdolt as the sole proprietor. Ratdolt’s two partners were probably victims of the plague, which wiped out eleven of the twenty-two printer/publishing establisments existing in Venice in 1478.

Their first publication was Regiomontanus’ Calendar, published in Latin and Italian in 1476 and in German in 1478. This book already contained several innovations. Ratdolt and his partners introduced the concept of printed ornamental borders for the pages of their books, a style that became typical for Renaissance books. They also introduced the first modern title page! It almost certainly seems strange to the modern book reader but the volumes printed in the first twenty or so years of book printing didn’t have title pages, as we know them. Ratdolt’s Regiomontanus Calendar was the first book to have a separate page at the beginning of the volume giving place, date and name of the printer. It was also the first book to have its publication date printed in Hindu-Arabic numerals and not in Roman ones. It would be some time before title pages of the type introduced by Ratdolt became common.

Calendarius by Regiomontanus, printed by Erhard Ratdolt, Venice 1478, title page with printers’ names
Source: Wikimedia Commons

In terms of the sciences Ratdolt’s most important work was the first printed edition of Euclid’s Elements, which he published in 1482. Here the innovation, a very major one was the inclusion of illustrations in the text. I say within the text but in fact the book was printed with very wide margins and the geometrical diagrams were printed next to the relevant text passage in these margins.

A page with marginalia from the first printed edition of Euclid’s Elements, printed by Erhard Ratdolt in 1482
Folger Shakespeare Library Digital Image Collection
Source: Wikimedia Commons

Another of Ratdolt’s innovations was the introduction of first two-coloured printing and then over time building up to books printed in as many as five colours and also printing with gold leaf.

Diagram, showing eclipse of the moon; woodcut, printed in three colours, from Sphaericum opusculum by Johannes de Sacro Bosco, printed by Erhard Ratdolt, Venice 1485
Source: Wikimedia Commons

In 1486 Ratdolt returned to Bavaria and set up a new publishing house in Augsburg at the invitation of the bishop and it was here that he introduced his next innovation. He is the earliest known printer/publisher to issue a printer’s type specimen book, in his case a broadsheet, displaying the fonts that he had available to print his wares. Upon his return to Augsburg Ratdolt was the first to introduce the Italian Rotunda font into Germany. He was also one of the earliest printers to offer Greek fonts for printing. Another of his innovations was the dust jacket. Like most other printer/publishers in the first half-century of book printing Ratdolt’s output in Augsburg was mostly religious works, although he did print some astrological/astronomical volumes. Ratdolt’s output declined from 1500 onwards but between 1487 and his death in 1522 his publishing house issued some 220 volumes.

Wappen des Bischofs Johann von Werdenberg, in der Widmung des Augsburger Breviers, 1485
Source: Wikimedia Commons

Given his youth when he left Bavaria for Venice Ratdolt’s contributions to the development of early book printing were truly remarkable. Even if his original partners were older and had started this chain of innovation, Ratdolt was still a teenager when they both disappeared from the business (died?) and the innovations continued when he was running the business alone.

Two interesting historical questions remain open concerning Ratdolt’s activities as a printer/publisher. We actually have no idea when, where or how he learnt the black art, as printing was known in that early period. The second problem concerns another early printer of scientific texts, Regiomontanus, and his connection to Ratdolt. The first book that Ratdolt published was Regiomontanus’ Calendar an important astrological/astronomical text that was something of a fifteenth-century best seller. The manuscript of the Euclid that Ratdolt published was one of the ones that Regiomontanus had discovered in Northern Italy when he was in the service of Cardinal Bessarion, as his book collector between 1461 and 1467. This raises the question, how did Ratdolt come into possession of Regiomontanus’ manuscripts?

Some earlier writers solved both questions by making Ratdolt into Regiomontanus’ apprentice in his publishing house in Nürnberg. The theory is not so far fetched, as Aichach is not so far away from Nürnberg and Ratdolt moved to Venice at about the same time as Regiomontanus disappeared and is presumed to have died. Unfortunately there is absolutely no evidence whatsoever to support this theory. Also given Regiomontanus’s renown at the time of his death, not just as a mathematical scholar but also as a printer/publisher, if Ratdolt had been his apprentice he would surely have advertised the fact in his own printing endeavours. I suspect that we will never know the answers to these questions.






[1] On a personal note I spent my first four years in Germany living just down the road from Langenzenn, where I spent most of my free time.

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Filed under Early Scientific Publishing, Uncategorized

All at sea

As I’ve said more than once in the past, mathematics as a discipline as we know it today didn’t exist in the Early Modern Period. Mathematics, astronomy, astrology, geography, cartography, navigation, hydrography, surveying, instrument design and construction, and horology were all facets or sub-disciplines of a sort of mega-discipline that was the stomping ground of the working mathematicus, whether inside or outside the university. The making of sea charts – or to give it its technical name, hydrography – combines mathematics, geography, cartography, astronomy, surveying, and the use of instruments so I am always happy to add a new volume on the history of sea charts to my collection of books on cartography and hydrography.

I recently acquired the “revised and updated” reissue of Peter Whitfield’s Charting the Oceans, a British Library publication.

The original edition from 1996 carried the subtitle Ten Centuries of Maritime Maps (missing from the new edition) and this is what Whitfield delivers in his superb tome. The book has four sections: Navigation before Charts, The Sea-Chart and the Age of Exploration, Sea-Charts in Europe’s Maritime Age and War, Empire and Technology: The Last 200 years. As can be seen from these section titles Whitfield not only deals with the details of the hydrography and the charts produced but defines the driving forces behind the cartographic developments: explorations, trade, war and colonisation. This makes the book to a valuable all round introduction of the subject highly recommended to anybody looking for a general overview of the topic.

However, what really makes this book very special is the illustrations.

The Nile Delta, c. 1540, from Piri Re’is Kitab-i Bahriye
Charting the Oceans page 90

A large format volume, more than fifty per cent of the pages are adorned with amazing reproductions of the historical charts that Whitfield describes in his text.

Willem van de Velde II, Dutch Ships in a Calm, c. 1665
Charting the Oceans page 132

Beautifully photographed and expertly printed the illustrations make this a book to treasure. Although not an academic text, in the strict sense, there is a short bibliography for those, whose appetites wetted, wish to delve deeper into the subject and an excellent index. Given the quality of the presentation the official British Library shop price of £14.99 is ridiculously low and a real bargain. If you love maps all I can say is buy this book.

Title page to the English edition of Lucas Janszoon Waghenaer’s Spiegheel der Zeevaert, 1588
Charting the Oceans page 109

The A Very Short Introduction series of books published by the Oxford University Press is a really excellent undertaking. Very small format 11×17 and a bit cm, they are somewhere between 100 and 150 pages long and provide a concise introduction to a single topic. One thing that distinguishes them is the quality of the authors that OUP commissions to write them; they really are experts in their field. The Galileo volume, for example, is authored by Stillman Drake, one of the great Galileo experts, and The Periodic Table: A Very Short Introduction was written by Mr Periodic Table himself, Eric Scerri. So when Navigation: A Very Short Introduction appeared recently I couldn’t resist. Especially, as it is authored by Jim Bennett a man who probably knows more about the topic then almost anybody else on the surface of the planet.

Mr Bennett does not disappoint, in a scant 135-small-format-pages he delivers a very comprehensive introduction to the history of navigation. He carefully explains all of the principal developments down the centuries and does not shy away from explaining the intricate mathematical and astronomical details of various forms of navigation.

Navigation: A Very Short Introduction page 50

The book contains a very useful seven page Glossary of Terms, a short but very useful annotated bibliography, which includes the first edition of Whitfield’s excellent tome, and a comprehensive index. One aspect of the annotated bibliography that particularly appealed to me was his comments on Dava Sobel’s Longitude; he writes:

“[It] …has the disadvantage of being very one-sided despite the more scrupulous work found in in earlier books such as Rupert T. Gould, The Marine Chronometer: Its History and Development (London, Holland Press, 1960); and Humphrey Quill, John Harrison: The Man Who Found Longitude (London, John Baker, 1966)”

I have read both of these books earlier and can warmly recommend them. He then recommends Derek Howse, Greenwich Time and the Discovery of Longitude (Oxford, Oxford University Press, 1980), which sits on my bookshelf, and Derek Howse, Nevil Maskelyne: The Seaman’s Astronomer, (Cambridge, Cambridge University Press, 1989), which I haven’t read. However it was his closing comment that I found most interesting:

“A welcome recent corrective is Richard Dunn and Rebekah Higgitt, Ships, Clocks, and Stars: The Quest for Longitude (Collins: Glasgow, 2014)”. A judgement with which, regular readers of this blog will already know, I heartily concur.

The flyleaf of the Navigation volume contains the following quote:

‘a thoroughly good idea. Snappy, small-format…stylish design…perfect to pop into your pocket for spare moments’ – Lisa Jardine, The Times

Another judgement with which I heartily concur. Although square centimetre for square centimetre considerably more expensive than Whitfield’s book the Bennett navigation volume is still cheap enough (official OUP price £7.99) not to break the household budget. For those wishing to learn more about the history of navigation and the closely related mapping of the seas I can only recommend that they acquire both of these excellent publications.




Filed under History of Cartography, History of Mathematics, History of Navigation

Did Eratosthenes really measure the size of the earth?

Last Thursday was Summer Solstice in the Northern Hemisphere and The Guardian chose to mark the occasion with an article by astrophysicist turned journalist and novelist, Stuart Clark, who chose to regale his readers with a bit of history of science. The big question was would he get it right? He has form for not doing so and in fact, he succeeded in living up to that form. His article entitled Summer solstice: the perfect day to bask in a dazzling scientific feat, recounted the well know history of geodesy tale of how Eratosthenes used the summer solstice to determine the size of the earth.

Eratosthenes of Cyrene was the chief librarian at the great library of Alexandria in the third century BC. So the story goes, he read in one of the library’s many manuscripts an account of the sun being directly overhead on the summer solstice as seen from Syene (now Aswan, Egypt). This was known because the shadows disappeared at noon, when the sun was directly overhead. This sparked his curiosity and he set out to make the same observation in Alexandria. On the next solstice, he watched as the shadows grew small – but did not disappear, even at noon.

The length of the shadows in Alexandria indicated that the sun was seven degrees away from being directly overhead. Eratosthenes realised that the only way for the shadow to disappear at Syene but not at Alexandria was if the Earth’s surface was curved. Since a full circle contains 360 degrees, it meant that Syene and Alexandria were roughly one fiftieth of the Earth’s circumference away from each other.

Knowing that Syene is roughly 5000 stadia away from Alexandria, Eratosthenes calculated that the circumference of the Earth was about 250,000 stadia. In modern distance measurements, that’s about 44,000km – which is remarkably close to today’s measurement of 40,075km.

Eratosthenes also calculated that the tilt of the Earth’s polar axis (23.5 degrees) is why we have the solstice in the first place.

Illustration showing a portion of the globe showing a part of the African continent. The sunbeams shown as two rays hitting the ground at Syene and Alexandria. Angle of sunbeam and the gnomons (vertical pole) is shown at Alexandria, which allowed Eratosthenes’ estimates of radius and circumference of Earth.
Source: Wikimedia Commons

Whilst it is correct that Eratosthenes was chief librarian of the Alexandrian library one should be aware that the Mouseion (Shrine of the Muses, the origin of the modern word, museum), which housed the library was more akin to a modern academic research institute than what one envisages under the word library. Eratosthenes was according to the legends a polymath, astronomer, cartographer, geographer, mathematician, poet and music theorist.

From the information that during the summer solstice the sun was directly overhead in Syene at noon, and cast no shadows and that a gnomon in Alexandria 5000 stadia north of Syene did cast a shadow, Eratosthenes did not, and I repeat did not, realise that the Earth’s surface was curved. Eratosthenes knew that the Earth’s surface was curved, as did every educated Greek scholar in the third century BCE. Sometimes I get tired of repeating this but the first to realise that the Earth was a sphere were the Pythagoreans in the sixth century BCE. Aristotle had summarised the empirical evidence that showed that the Earth is a sphere in the fourth century BCE, in writings that Eratosthenes, as chief librarian in Alexandria, would have been well acquainted with. Put simply, Eratosthenes knew that he could, using trigonometry, calculate the diameter of the Earth’s sphere with the data he had accumulated, because he already knew that it was a sphere.

The next problem with the account given here is one that almost always turns up in popular version of the Eratosthenes story; there wasn’t just one measure of length in the ancient Greek world known as a stadium but quite a collection of different ones, all differing in length, and we have absolutely no idea which one is meant here. It is in the end not so important as all of them give a final figure with 17% or less error compared to the true value, which is for the method used quite a reasonable ball park figure for the size of the Earth. However this point is one that should be mentioned when recounting the Eratosthenes story. Eratosthenes may or may not have calculated the tilt of the Earth’s axis but this is of no real historical significance, as the obliquity of the ecliptic, as it is also known, was, like the spherical shape of the Earth, known well before his times.

An astute reader might have noticed that above I used the expression, according to the legends, when describing Eratosthenes’ supposed talents. The problem is that everything we know about Eratosthenes is hearsay. None of his alleged many writings have survived. We only have second hand reports of his supposed achievements, most of them centuries after he lived. This raises the question, how reliable are these reports? A comparable situation is the so-called theorem of Pythagoras, well known to other cultures well before Pythagoras lived and only attributed to him long after he had died.

The most extreme stance is elucidated by historian of astronomy, John North, in his one volume history of astronomy, Cosmos:

None of Eratosthenes’ writings survive, however, and some have questioned whether he ever found either the circumference of the Earth, or – as is often stated – the obliquity of the ecliptic, on the basis of measurements.

So what is our source for this story? The only account of Eratosthenes’ measurement comes from the book On the Circular Motions of the Celestial Bodies by the Greek astronomer Cleomedes and with that the next problems start. It is not actually known when Cleomodes lived. On the basis of his writings Thomas Heath, the historian of Greek mathematics, thought that text was written in the middle of the first century BCE. However, Otto Neugebauer, historian of ancient science, thought that On the Circular Motions of the Celestial Bodies was written around 370 CE. Amongst historians of science the debate rumbles on. North favours the Neugebauer date, placing the account six centuries after Eratosthenes’ death. What exactly did Cleomodes say?

The method of Eratosthenes depends on a geometrical argument and gives the impression of being slightly more difficult to follow. But his statement will be made clear if we premise the following. Let us suppose, in this case too, first, that Syene and Alexandria he under the same meridian circle, secondly, that the distance between the two cities is 5,000 stades; 1 and thirdly, that the rays sent down from different parts of the sun on different parts of the earth are parallel; for this is the hypothesis on which geometers proceed Fourthly, let us assume that, as proved by the geometers, straight lines falling on parallel straight lines make the alternate angles equal, and fifthly, that the arcs standing on (i e., subtended by) equal angles are similar, that is, have the same proportion and the same ratio to their proper circles—this, too, being a fact proved by the geometers. Whenever, therefore, arcs of circles stand on equal angles, if any one of these is (say) one-tenth of its proper circle, all the other arcs will be tenth parts of their proper circles.

Any one who has grasped these facts will have no difficulty in understanding the method of Eratosthenes, which is this Syene and Alexandria lie, he says, under the same mendian circle. Since meridian circles are great circles in the universe, the circles of the earth which lie under them are necessarily also great circles. Thus, of whatever size this method shows the circle on the earth passing through Syene and Alexandria to be, this will be the size of the great circle of the earth Now Eratosthenes asserts, and it is the fact, that Syene lies under the summer tropic. Whenever, therefore, the sun, beingin the Crab at the summer solstice, is exactly in the middle of the heaven, the gnomons (pointers) of sundials necessarily throw no shadows, the position of the sun above them being exactly vertical; and it is said that this is true throughout a space three hundred stades in diameter. But in Alexandria, at the same hour, the pointers of sundials throw shadows, because Alexandria lies further to the north than Syene. The two cities lying under the same meridian great circle, if we draw an arc from the extremity of the shadow to the base of the pointer of the sundial in Alexandria, the arc will be a segment of a great circle in the (hemispherical) bowl of the sundial, since the bowl of the sundial lies under the great circle (of the meridian). If now we conceive straight lines produced from each of the pointers through the earth, they will meet at the centre of the earth. Since then the sundial at Syene is vertically under the sun, if we conceive a straight line coming from the sun to the top of the pointer of the sundial, the line reaching from the sun to the centre of the earth will be one straight line. If now we conceive another straight line drawn upwards from the extremity of the shadow of the pointer of the sundial in Alexandria, through the top of the pointer to the sun, this straight line and the aforesaid straight line will be parallel, since they are straight lines coming through from different parts of the sun to different parts of the earth. On these straight lines, therefore, which are parallel, there falls the straight line drawn from the centre of the earth to the pointer at Alexandria, so that the alternate angles which it makes arc equal. One of these angles is that formed at the centre of the earth, at the intersection of the straight lines which were drawn from the sundials to the centre of the earth; the other is at the point of intersection of the top of the pointer at Alexandria and the straight line drawn from the extremity of its shadow to the sun through the point (the top) where it meets the pointer. Now on this latter angle stands the arc carried round from the extremity of the shadow of the pointer to its base, while on the angle at the centre of the earth stands the arc reaching from Syene to Alexandria. But the arcs are similar, since they stand on equal angles. Whatever ratio, therefore, the arc in the bowl of the sundial has to its proper circle, the arc reaching from Syene to Alexandria has that ratio to its proper circle. But the arc in the bowl is found to be one-fiftieth of its proper circle.’ Therefore the distance from Syene to Alexandria must necessarily be one-fiftieth part of the great circle of the earth. And the said distance is 5,000 stades; therefore the complete great circle measures 250,000 stades. Such is Eratosthenes’ method. (This is Thomas Heath’s translation) 

You will note that Cleomedes makes no mention of Eratosthenes determining the spherical shape of the Earth through his observations but writes very clearly of great circles on the globe, an assumption of spherical form. So where does Stuart Clark get this part of his story? In his article he tells us his source:

I first heard the story when it was told by Carl Sagan in his masterpiece TV series, Cosmos.

The article has a video of the relevant section of Sagan’s Cosmos and he does indeed devote a large part of his version of the story to explaining how Eratosthenes used his observations to determine that the Earth is curved. In other words Stuart Clark is just repeating verbatim a story, which Carl Sagan, and or his scriptwriters, made up in 1980 without taken the trouble to verify the accuracies or even the truth of what he saw more than thirty years ago. Carl Sagan said it, so it must be true. I have got into trouble on numerous occasions by pointing out to Carl Sagan acolytes that whatever his talents as a science communicator/populariser, his history of science was to put it mildly totally crap. Every week he pumped his souped-up versions of crappy history of science myths into millions of homes throughout the world. In one sense it is only right that Neil deGasse Tyson presented the modern remake of Cosmos, as he does exactly the same.



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

The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time

The title of this post is the subtitle of Dava Sobel’s Longitude, her mega bestselling account of the life and work of the eighteenth-century clock maker John Harrison; probably the biggest selling popular #histSTM book of all time.

I’m quite happy to admit that when I first read it I was very impressed by her account of a man I didn’t know from a period of history with which I was not particularly well acquainted. However, because I was very impressed, I went looking for more information about the history of John Harrison and the marine chronometer. I found and read quite a lot of academic literature on both topics and came to the realisation that Sobel’s account was not really the true story and that she had twisted the facts to make for a more exciting story but quite far removed from the true narrative.

P.L. Tassaert’s half-tone print of Thomas King’s original 1767 portrait of John Harrison, located at the Science and Society Picture Library, London
Source: Wikimedia Commons

The next segment of the subtitle is also not true. Harrison was supported and encouraged in his endeavours by George Graham, possibly the greatest eighteenth-century English clockmaker, and James Short, almost certainly the greatest telescope maker in the world in the eighteenth century. Both men were important and highly influential figures in the scientific and technological communities of the period. Their support of Harrison rather gives the lie to the claim that Harrison was a lone genius.

George Graham
Source: Wikimedia Commons

The final segment of the subtitle is also highly inaccurate. The problem that Harrison and others were working on in the eighteenth century was a reliable method of determining longitude at sea. They were trying to solve a technological problem not a scientific one. The scientific problem had already been solved in antiquity. Scholars in ancient Greece already knew that to determine the difference in longitude between two locations, one ‘merely’ had to determine the local time difference between them; knowing this the problem was how to determine that time difference, as I said a technological problem.

In antiquity and up to the early modern period cartographers and astronomers (usually the same person) used astronomical phenomena such as solar or lunar eclipses. Observers determined the local time of the occurrence of a given astronomical phenomenon at two different locations and it was then possible to determine their longitudinal difference. Unfortunately eclipses are not very frequent occurrences and so this method has rather limited usefulness. Something else had to be developed.

In the early seventeenth century both Galileo Galilei and Simon Marius discovered the four largest moons of Jupiter and Galileo realised that the orbits of these moons and their appearances and disappearances as the circled Jupiter could, if tabulated accurately enough, be used as a clock to determine longitude. Towards the end of the seventeenth century Giovanni Domenico Cassini and Ole Rømer succeeded in producing the necessary tables and Galileo’s idea could be put into practice. Whilst this method was very successful for cartographers on land, on a rolling ship it was not possible to observe the Jupiter moons accurately enough with a telescope to be able to apply this method; something else had to be used.

The two solutions that came to be developed in the eighteenth century and form the backbone of Sobel’s book, the lunar distance method (lunars) and the marine chronometer, were both first suggested in the sixteenth century, the former by Johannes Werner and the latter by Gemma Frisius. Other methods were suggested but proved either impractical or downright impossible. For lunars you need accurate lunar orbit tables and an accurate instrument to determine the position of the moon. Tobias Mayer provided the necessary tables and John Hadley the instrument with his sextant. For the clock method you require a clock that has a high level of accuracy over a long period of time and which retains that accuracy under the often very adverse conditions of a sea voyage; this is the technological problem that Harrison solved. Sobel presents the two methods as in competition but for navigators they are in fact complimentary and they were both used. As my #histsci soul sister Rebekah ‘Becky’ Higgitt constantly repeats, with the marine chronometer you can carry longitude with you, but if you chronometer breaks down you can’t find it, whereas with lunars you can find longitude, as James Cook did in fact do on one of his voyages.

As I said above, I began to seriously doubt the veracity of Sobel’s account through my own study of the academic accounts of the story, these doubts were then confirmed as I began to follow the blog of the Longitude Board research project set up by Cambridge University and the Maritime Museum in Greenwich, of which Becky Higgitt was one of the lead researchers. For a more balanced and accurate account of the story I recommend Finding Longitude the book written by Becky and Richard Dunn to accompany the longitude exhibition at the Maritime Museum, one of the products of the research project.

Recently I have become fully aware of another aspect of the Harrison story that Sobel does not cover. I say fully aware because I already knew something of it before reading David S. Landes’ excellent Revolution in Time: Clocks and the making of the Modern World (Harvard University Press, 1983). Landes covers the whole history of the mechanical clock from the Middle Ages through to the quartz wristwatch. One of his central themes is the increasing accuracy of clocks down the ages in which the invention of the marine chronometer played a central role, so he devotes a whole chapter to Harrison’s endeavours.

Landes quite correctly points out that after a lifetime of experimentation and ingenious invention John Harrison did indeed produce a solution to the technological problem of determining longitude with a clock. An astute reader with a feel for language might have noticed that in the previous sentence I wrote ‘a solution’ and not ‘the solution’ and therein lies the rub. Over the years that he worked on the problem Harrison produced many ingenious innovations in clock making in order to achieve his aim, an accurate, reliable, highly durable timepiece, however the timepiece that he finally produced was too complex and too expensive to be practicable for widespread everyday service at sea. Harrison had, so to speak, priced himself out of the market.

Harrison’s “Sea Watch” No.1 (H4), with winding crank
Source: Wikimedia Commons

Harrison was by no means the only clock maker working on a viable marine chronometer in the eighteenth century and it is actually his competitors who in the end carried away the laurels and not Harrison. Two clockmakers who made important contributions to the eventual development of a mechanically and financially viable marine chronometer were the Frenchman Pierre Le Roy and Swiss Ferdinand Berthoud, who were bitter rivals.

Pierre Le Roy (1717–1785)
Source: Wikimedia Commons

Plans of Le Roy chronometer
Source: Wikimedia Commons

Ferdinand Berthoud (1727–1807)
Source: Wikimedia Commons

Berthoud marine clock no.2, with motor spring and double pendulum wheel, 1763
Source: Wikimedia Commons

Neither of them can be said to have solved the problem but the work of both of them in different ways led in the right direction. Another contributor was George Graham’s one time apprentice, Thomas Mudge, his highly praised marine chronometer suffered from the same problem as Harrison’s too complex and thus too expensive to manufacture.

The two English clock makers, who actually first solved the problem of a viable marine chronometer were John Arnold and Thomas Earnshaw, who also became bitter rivals. This rivalry involved accusations of theft of innovations and disputes over patents. In the end it was John Arnold and Thomas Earnshaw, who became the most successful of the early clock makers, who worked on the development of the marine chronometer.

Chronometer-maker John Arnold (1736–1799) (attributed to Mason Chamberlin, ca. 1767)
Source: Wikimedia Commons

Thomas Earnshaw (!749–1829)
Source: Wikimedia Commons

Earnshaw chronometer No. 506
Source: Wikimedia Commons

I don’t intend to go into the details of which innovations in clock manufacture each of the man listed above contributed to the development of the marine chronometer that would go on to become an essential navigation tool in the nineteenth century. What I wish to make clear is exactly the same point as my essay on the history of the reflecting telescope for AEON made. From its first conception by Gemma Frisius in the sixteenth century, through the failure of Christiaan Huygens to realise it with his pendulum clock in the late seventeenth century (not discussed here), over its first successful realisation by John Harrison and on to the creation of a viable model by a succession of eighteenth-century clock makers, the marine chronometer was not the product of a single man’s (John Harrison’s) genius but a tool that evolved through the endeavours of a succession of dedicated inventors and innovators. Scientific and technological progress is teamwork.


Filed under History of Navigation, History of Technology, Myths of Science

Why doesn’t he just shut up?

Neil deGrasse Tyson (NdGT), probably the most influential science communicator in the world, spends a lot of time spouting out the message that learning science allows you to better detect bullshit, charlatans, fake news etc. etc. However it apparently doesn’t enable you to detect bullshit in the history of science, at least judging by NdGT’s own record on the subject. Not for the first time, I was tempted recently to throw my computer through the window upon witnessing NdGT pontificating on the history of science.

On a recent video recorded for Big Think, and also available on Youtube and already viewed by 2.6 million sycophants, he answers the question “Who’s the greatest physicist in history?” His answer appears under the title My Man, Sir Isaac Newton. Thoughtfully, Big Think have provided a transcription of NdGT’s blathering that I reproduce below for your delectation before I perform a Hist_Sci Hulk autopsy upon it.

Question: Who’s the greatest physicist in history?DeGrasse Tyson:    Isaac Newton.  I mean, just look… You read his writings.  Hair stands up… I don’t have hair there but if I did, it would stand up on the back of my neck.  You read his writings, the man was connected to the universe in ways that I never seen another human being connected.  It’s kind of spooky actually.  He discovers the laws of optics, figured out that white light is composed of colors.  That’s kind of freaky right there.  You take your colors of the rainbow, put them back together, you have white light again.  That freaked out the artist of the day.  How does that work?  Red, orange, yellow, green, blue, violet gives you white.  The laws of optics.  He discovers the laws of motion and the universal law of gravitation.  Then, a friend of his says, “Well, why do these orbits of the planets… Why are they in a shape of an ellipse, sort of flattened circle?  Why aren’t… some other shape?”  He said, you know, “I can’t… I don’t know.  I’ll get back to you.”  So he goes… goes home, comes back couple of months later, “Here’s why.  They’re actually conic sections, sections of a cone that you cut.”  And… And he said, “Well, how did find this out?  How did you determine this?”  “Well, I had to invent integral and differential calculus to determine this.”  Then, he turned 26.  Then, he turned 26.  We got people slogging through calculus in college just to learn what it is that Isaac Newtown invented on a dare, practically.  So that’s my man, Isaac Newton. 


Let us examine the actual history of science content of this stream of consciousness bullshit. We get told, “He discovers the laws of optic…!” Now Isaac Newton is indeed a very important figure in the history of physical optics but he by no means discovered the laws of optics. By the time he started doing his work in optics he stood at the end of a two thousand year long chain of researchers, starting with Euclid in the fourth century BCE, all of whom had been uncovering the laws of optics. This chain includes Ptolemaeus, Hero of Alexandria, al-Kindi, Ibn al-Haytham, Ibn Sahl, Robert Grosseteste, Roger Bacon, John Pecham, Witelo, Kamal al-Din al-Farisi, Theodoric of Freiberg, Francesco Maurolico, Giovanni Battista Della Porta, Friedrich Risner, Johannes Kepler, Thomas Harriot, Marco Antonio de Dominis, Willebrord Snellius, René Descartes, Christiaan Huygens, Francesco Maria Grimaldi, Robert Hooke, James Gregory and quite a few lesser known figures, much of whose work Newton was well acquainted with. Here we have an example of a generalisation that is so wrong it borders on the moronic.

What comes next is on safer ground, “…figured out that white light is composed of colors…” Newton did in fact, in a series of groundbreaking experiment, do exactly that. However NdGT, like almost everybody else is apparently not aware that Newton was by no means the first to make this discovery. The Bohemian Jesuit scholar Jan Marek (or Marcus) Marci (1595–1667) actually made this discovery earlier than Newton but firstly his explanation of the phenomenon was confused and largely wrong and secondly almost nobody knew of his work so the laurels go, probably correctly, to Newton.

NdGT’s next statement is for a physicist quite simply mindboggling he says, “That freaked out the artist of the day.  How does that work?  Red, orange, yellow, green, blue, violet gives you white.” Apparently NdGT is not aware of the fact that the rules for mixing coloured light and those for mixing pigments are different. I got taught this in primary school; NdGT appears never to have learnt it.

Up next are Newton’s contributions to mechanics, “He discovers the laws of motion and the universal law of gravitation.  Then, a friend of his says, “Well, why do these orbits of the planets… Why are they in a shape of an ellipse, sort of flattened circle?  Why aren’t… some other shape?”  He said, you know, “I can’t… I don’t know.  I’ll get back to you.”  So he goes… goes home, comes back couple of months later, “Here’s why.  They’re actually conic sections, sections of a cone that you cut.””

Where to begin? First off Newton did not discover either the laws of motion or the law of gravity. He borrowed all of them from others; his crowing achievement lay not in discovering them but in the way that he combined them. The questioning friend was of course Edmond Halley in what is one of the most famous and well document episodes in the history of physics, so why can’t NdGT get it right? What Halley actually asked was, assuming an inverse squared law of attraction what would be the shape of aa planetary orbit? This goes back to a question posed earlier by Christopher Wren in a discussion with Halley and Robert Hooke, “would an inverse squared law of attraction lead to Kepler’s laws of planetary motion?” Halley could not solve the problem so took the opportunity to ask Newton, at that time an acquaintance rather than a friend, who supposedly answered Halley’s question spontaneously with, “an ellipse.” Halley then asked how he knew it and Newton supposedly answered, “I have calculated it.” Newton being unable to find his claimed calculation sent Halley away and after some time supplied him with the nine-page manuscript De motu corporum in gyrum, which in massively expanded form would become Newton’s Principia.

NdGT blithely ignoring the, as I’ve said, well documented historical facts now continues his #histsigh fairy story, “And he said, “Well, how did find this out?  How did you determine this?”  “Well, I had to invent integral and differential calculus to determine this.”” This is complete an utter bullshit! This is in no way what Newton did and as such he also never claimed to have done it. In fact one of the most perplexing facts in Newton’s biography is that although he was a co-discoverer/co-inventor of the calculus (we’ll ignore for the moment the fact that even this is not strictly true, read the story here) there is no evidence that he used calculus to write Principia.

NdGT now drops his biggest historical clangour! He says, “Then, he turned 26.  Then, he turned 26.  We got people slogging through calculus in college just to learn what it is that Isaac Newtown invented on a dare, practically.  So that’s my man, Isaac Newton.” Newton was twenty-six going on twenty seven when he carried out the optics research that led to his theory of colours in 1666-67 but the episode with Halley concerning the shape of planetary orbits took place in 1682 when he was forty years old and he first delivered up De motu corporum in gyrum two years later in 1684. NdGT might, as an astro-physicist, be an expert on a telescope but he shouldn’t telescope time when talking about historical events.


Filed under History of Optics, History of science, Myths of Science, Newton

“One man takes the credit, one man takes the blame…”

Er war einst groß in Spiel mit den Symbolen,

War viele Künste, viele Sprachen Meister,

War ein weltkundiger, ein weit gereister,

Berühmter Mann, gekannt bis zu den Polen,

Umgeben stets von Schülern und Kollegen.

Ein Fragment von den Gedichten des jungen Josef K.[1]


In my blog anniversary post yesterday I explained how I came to live in Germany; today in what is a sort of continuation of that post, I will explain how I came to evolve from a rank amateur deeply interested in the histories of mathematics and science into a full blown quasi-professional historian of science. This post is a tribute to the man who is responsible for that evolution, my friend, mentor and teacher Christian Thiel, who celebrates his eightieth birthday today.


I tell a joke that when I first came to Germany I could only speak six words of German: ja, nein, bitte, danke, Bier and Scheiße. In reality this was almost the truth, so the first task I set myself, when I decided to stay, was to learn the language. As well as buying teach-yourself books, I also started attending German courses at the adult education evening classes in Nürnberg. These were actually very good but were, as far as I was concerned, far too slow and so I began to look around for alternatives. Somebody told me that the local university in Erlangen ran courses in German as a foreign language, so I trundled off to investigate. It turned out that to register for these courses I needed to apply for a place as a normal student at the university. Now I had dropped out of university in Cardiff ten years earlier, with the intention of returning to higher education when I had sorted out what it was that I really wanted to study, so I thought why not. I registered to become a maths student and was thus admitted to the German as a foreign language course.

I now spent a year learning German at the university in the mornings and working as an industrial cleaner in the afternoons. The course was very intensive, as the students are expected to be capable of taking a degree course in any academic subject in German at the end of it. To my own surprise I passed the course with flying colours and was now qualified to start my studies as a student of mathematics.

In those days the first degree in mathematics at the university of Erlangen was a diploma, equivalent of a master’s degree at an English university. Alongside the main subject students had to choose a subsidiary subject. In the 1970s I had become very interested in the philosophy of science and so I thought I would take a shot at that. One chair in the philosophy department was also offering a seminar in constructive geometry for the coming semester. I had no idea what constructive geometry was but it was an added incentive to choose philosophy as my subsidiary. The chair in question was one specialising in history and philosophy of science; I decided to go take a look see.

I found out when the professor held his office hours and went along at the appointed time. He wasn’t there. Knocking on his secretary’s door I asked when the professor would be there. She very kindly rang the professor and said that if I could wait, he would be along soon. I had waited maybe a quarter of an hour when I then met Christian Thiel for the first time. What I didn’t know was that it was not only my first semester as a student at the university but it was also Christian Thiel’s first semester as occupant of that chair. He, an Erlanger, had studied in Erlangen, taken his doctorate and his habilitation there but had then gone away to a chair elsewhere, as was normal in the German academic system. He was now returning to Erlangen to occupy the chair of his own mentor, Paul Lorenzen. What I also didn’t know at the time was that the department secretary had warned Christian Thiel that there was a ‘dangerous looking man’ waiting to see him. I was wearing a complete set of black motorcycle leathers, had my long hair tied back in a ponytail and sported three very prominent silver earrings, dangerous?

Christian Thiel wasn’t at all fazed by my dangerous appearance. We got on from the very first moment and were soon deep in a conversation about maths and the philosophy of science. In the time (ten years!) that I spent studying at Erlangen University more than fifty per cent of the courses that I took were with Christian Thiel. I think I learnt more from him than all of the other teachers that I have had in my life put together. He formed me, any abilities that I might possess as a historian of science I owe largely to Christian Thiel.

The maths department in Erlangen, when I studied, was not interested in the history of mathematics, my main motivation for studying the subject, Christian Thiel, however, was a historian of mathematics and mathematical logic, so after a time I dropped maths and became a student of philosophy with English philology and history as my subsidiaries. This move was also motivated by the fact that very early in my studies Christian Thiel, who obviously saw something in me that I couldn’t see in myself, offered me, to my surprise, a position in a major research project into the social history (read external history) of formal logic. I learnt so much in that research project, probably more than in my official studies and it is here that I really became a genuine historian of science. I can’t say how much being offered that chance, as a student, to do real cutting edge historical research meant to me. Without it I would not be sitting here now writing this blog post.

As the title of this blog post says, ‘one man takes the credit, one man takes the blame’ and that man is Christian Thiel and I am very pleased to be able to write this brief tribute to him on my blog on the occasion of his eightieth birthday.

I should point out that this is not the first tribute that I have written to Christian Thiel. The German quote that opens this post is taken from my essay in the Festschrift[2] published in honour of his retirement twelve years ago. This in turn is loosely based on the speech I held at the conference in his honour in Altdorf in 2005. Nearly all of the lectures at the conference related to Christian Thiel as an academic researcher, I had the privilege of honouring Christian Thiel the teacher. There is not a little irony in this. Over the years Christian Thiel has taught many, many successful students, postgraduates and postdocs, I, however, am, so to speak, one of his failures, falling at the final fence and failing to graduate. I closed my speech and my essay with a simple phrase, which I’m going to repeat once again here.


“Thanks Chris, you have been a bloody good teacher.”


[1] A couple of words about the title and the opening quote to this post. The title is a line from Tom Lehrer’s song Lobachevsky. I would like to point out that whilst the title hero of the song has inspired the narrator to plagiarise, Christian Thiel actually taught me and all of his students the exact opposite. I chose the quote because a love of Tom Lehrer and of Hermann Hesse the source of the opening quote are two of the many things that I and Christian Thiel have in common. Das Glasperlenspiel, the source of the opening quote, is my favourite novel and when I set out to learn German, one of my aims was  to be able to read it in German one day. In Germany to become a professor a scholar has to do a sort of second doctorate called a habilitation. When the habilitation thesis has been graded and accepted the potential habilitant then has to hold a habilitation lecture in front of an audience of all of the habilitanten of his faculty. Thiel’s habilitation lecture was on Das Glasperlenspiel.

[2] Thony Christie, The Teacher in G. Löffladt (Hrsg), Mathematik – Logik – Philosophie: Ideen und ihre historischen Wechselwirkungen, Verlag Harri Deutsch, Frankfurt am Main, 2012

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Filed under Autobiographical