Category Archives: Uncategorized

Why The Imitation Game is a disaster for historians.

I made the mistake, as a former professional historian of logic and meta-mathematics and, as a consequence, an amateur historian of the computer, of going to the cinema to watch the Alan Turing biopic The Imitation Game. I knew that it wouldn’t be historically accurate but that it would be a total historical disaster and, as I said on leaving the cinema, an insult to the memory of both Alan Turing and the others who worked in Bletchley Park surprised even me, a dyed in the wool, life-long cynic.

As I ventilated my disgust over the next few days on Twitter some, quite correctly, took me to task, informing me that it is a film and not a history book and therefore one shouldn’t criticise it for any inaccuracies that it contains. This attitude is of course perfectly correct and I would accept it,m if only the people who watch the film, who unlike myself are not knowledgeable historians, would view the film in this way; unfortunately they don’t.

The pre-release publicity for the film emphasised very intensely that the film tells a “true” story. This is screwed back somewhat in the film itself which opens with the claim that it is “based on a true story”. Unfortunately people simply ignore the “based on” and as I left a full cinema, at the end of the film, people all around me were saying to each other, “Wow, I didn’t know that. It’s a true story, you know?” and other similar expressions. This was compounded by both the Golden Globes and the Oscars, as the film won the awards of the respective organisations for best-adapted script! The film is supposedly based on Andrew Hodges’ Alan Turing biography, The Enigma. This book, which I read when it was first published, is one of the best biographies of a scientist that I’ve ever read, superbly researched, meticulously detailed and a real pleasure to read. Hodges is apparently prohibited by a gag clause in his contract for the film rights to his book from commenting on the film. “Take this large sum of money son and shut your mouth whilst we destroy your book!” It is not much of an exaggeration to say that the adaption consists of dumping the factual content of the book, plus several of the central characters, and writing a piece of third rate fiction using the names of some of the figures in Hodges’ biography. If that’s the film industries definition of ‘best adapted’ I don’t won’t to know what they consider to be the ‘worst adapted’.

I’m not going to go into great detail about everything that is wrong with the film because to a certain extent others have already done the work for me. The film almost completely ignores the contributions of the Poles in breaking the Enigma Codes (note the plural, there was more than one, another thing that doesn’t get mentioned in the film). They only get mentioned in a passing half sentence, which I strongly suspect almost all viewers failed to notice. You can read about the Polish contribution here, here and here. A short, general but largely accurate account of Turing’s involvement can be read here. There is a biting general criticism of the film on Ursula Writes, and another slightly less acerbic by L. V. Anderson on the Slate website. Another demolition job both of the Imitation Game and the Hawking biopic The Theory of Everything is on the Nature website by Colin Macilwain.

In case anybody doubts that the lay public think that the film is a ‘true’ story I have extracted part of a fairly typical critique of the film from the website of G. B. Hatch

I wanted to see this film the minute I heard about it. The plot sounded very intriguing. I had never learned about Alan Turing, and I now believe every History teacher should be showing this film while teaching WWII. Alan Turing and his team are some of the heroes of WWII that didn’t need to fire a single shot. This film, like “Argo”, is a great historical thriller based on a story that had remained confidential for several decades. This film is “The Imitation Game”.

“The Imitation Game” tells the true story of Alan Turing (played by Benedict Cumberbatch), a brilliant yet socially awkward British mathematician who is hired as a German code-breaker during WWII. He sets out to create a machine that will crack the Enigma Code, a German code that many claim as unbreakable. With the help of fellow code-breaker Joan Clarke (played by Keira Knightley), Turing invents this machine, which he calls ‘Christopher’, while also trying to hide his homosexuality which was illegal at the time. The film perfectly blends intensity and humor, while also transitioning between the past, present, and future.

As can be clearly seen Mr (or is that Ms?) Hatch is convinced that the film tells a true story and even goes so far as to suggest that the film should be used in school history lessons!

The historian is clearly presented by a dilemma when the film industry decides to make a film about a well-researched and well-documented historical episode. Almost without exception the scriptwriters decide that history is too complex, too boring, not sexy enough or whatever. They throw out ninety per cent of the historical facts and write there own ‘better than reality’ version usually retaining not much more that the names of the historical characters. They then add a bucket full of false historical touches, such as horns on Viking helmets, that everybody knows are “true”. The whole thing is then packaged up by the advertising department as the “amazing unknown true story of”! If the historian complains he gets firmly put in his place by people telling him “it’s only a film”. If he doesn’t complain he can listen to all those film goers sitting around in bars and cafés saying, “Did you know Alan Turing won the Second World War almost single handed!”

What ever else you have no hope of winning if you are a historian.


Filed under Myths of Science, Uncategorized

A Swiss Clockmaker

We all have clichéd images in our heads when we hear the names of countries other than our own. For many people the name Switzerland evokes a muddled collection of snow-covered mountains, delicious superior chocolates and high precision clocks and watches. Jost Bürgi who was born in the small town of Lichtensteig, in the  Toggenburg region of the canton of St. Gallen on 28 February 1552 fills this cliché as the most expert clockmaker in the sixteenth century. However Bürgi was much more that just a Swiss clockmaker, he was also an instrument maker, an astronomer, a mathematician and in his private life a successful property owner and private banker, the last of course serving yet another Swiss cliché.

As we all too many figures, who made significant contributions to science and technology in the Renaissance we know next to nothing about Bürgi’s origins or background. There is no known registration of his birth or his baptism; his date of birth is known from the engraving shown below from 1592, in which the portrait was added in 1619 but which was first published in 1648. That the included date is his birthday was confirmed by Bürgi’s brother in law.


His father was probably the locksmith Lienz Bürgi but that is not known for certain. About his education or lack of it nothing is known at all and just as little is known about where he learnt his trade as clockmaker. Various speculations have been made by historians over the years but they remain just speculations. The earliest documentary proof that we have of Bürgi’s existence is his employment contract when he entered the service of the Landgrave Wilhelm IV of Hessen-Kassel as court clockmaker, already twenty-seven years old, on 25 July 1579. Wilhelm was unique amongst the German rulers of the Renaissance in that he was not only a fan or supporter of astronomy but was himself an active practicing astronomer. In his castle in Kassel he constructed, what is recognised as, the first observatory in Early Modern Europe.

Wilhelm IV. von Hessen-Kassel Source: Wikimedia Commons

Wilhelm IV. von Hessen-Kassel
Source: Wikimedia Commons

He also played a major role in persuading the Danish King Frederick II, a cousin, to supply Tycho Brahe with the necessary land and money to establish an observatory in Denmark. In the 1560s Wilhelm was supported in his astronomical activities by Andreas Schöner, the son of the famous Nürnberger cartographer, globe and instrument maker, astronomer, astrologer and mathematician Johannes Schöner. He also commissioned the clockmaker Eberhard Baldewein (1525-1593) to construct two planet clocks and a mechanical globe.


Eberhart Baldewein Planet clock 1661 Source: Wikimedia Commons

Eberhart Baldewein Planet clock 1661
Source: Wikimedia Commons

The planet clock shows the positions of the sun, moon and the planets, based on Peter Apian’s Astronomicom Caessareum, on its various dials.


Eberhard Baldewein Mechanical Celestial Globe circa 1573

Eberhard Baldewein Mechanical Celestial Globe circa 1573 The globe, finished by Heinrich Lennep in 1693, was used to record the position of the stars mapped by Wilhelm and his team in their observations.

These mechanical objects were serviced and maintained by Baldewein’s ex-apprentice, Hans Bucher, who had helped to build them and who had been employed by Wilhelm, for this purpose, since 1560. When Bucher died in 1578-1579 Bürgi was employed to replace him, charged with the maintenance of the existing objects on a fixed, but very generous salary, and commissioned to produce new mechanical instruments for which he would be paid extra. Over the next fifty years Bürgi produced many beautiful and highly efficient clocks and mechanical globes both for Wilhelm and for others.

Bürgi Quartz Clock 1622-27 Source: Swiss Physical Society

Bürgi Quartz Clock 1622-27
Source: Swiss Physical Society






Bürgi Mechanical Celestial Globe 1594 Source: Wikimedia Commons

Bürgi Mechanical Celestial Globe 1594
Source: Wikimedia Commons



Jost Bürgi and Antonius Eisenhoit: Armillary sphere with astronomical clock made 1585 in Kassel, now at Nordiska Museet in Stockholm. Source Wikimedia Commons

Jost Bürgi and Antonius Eisenhoit: Armillary sphere with astronomical clock made 1585 in Kassel, now at Nordiska Museet in Stockholm.
Source Wikimedia Commons

Bürgi was also a highly inventive clockmaker, who is credited with the invention of both the cross-beat escapement and the remontoire, two highly important improvements in clock mechanics. In the late sixteenth century the average clocks were accurate to about thirty minutes a day, Bürgi’s clock were said to be accurate to less than one minute a day. This amazing increase in accuracy allowed mechanical clocks to be used, for the first time ever, for timing astronomical observations. Bürgi also supplied clocks for this purpose for Tycho’s observatory on Hven. In 1592 Wilhelm presented his nephew Rudolph II, the German Emperor, with one of Bürgi’s mechanical globes and Bürgi was sent to Prague with the globe to demonstrate it to Rudolph. This was his first contact with what would later become his workplace. Whilst away from Kassel Bürgi’s employer, Wilhelm died. Before continuing the story we need to go back and look at some of Bürgi’s other activities.

As stated at the beginning Bürgi was not just a clockmaker. In 1584 Wilhelm appointed the Wittenberg University graduate Christoph Rothmann as court astronomer. From this point on the three, Wilhelm, Rothmann and Bürgi, were engaged in a major programme to map the heavens, similar to and just as accurate, as that of Tycho on Hven. The two observatories exchanged much information on instruments, observations and astronomical and cosmological theories. However all was not harmonious in this three-man team. Although Wilhelm treated Bürgi, whom he held in high regard, with great respect Rothmann, who appears to have been a bit of a snob, treated Bürgi with contempt because he was uneducated and couldn’t read or write Latin, that Bürgi was the better mathematician of the two might have been one reason for Rothmann’s attitude.

In the 1580s the itinerant mathematician and astronomer Paul Wittich came to Kassel from Hven and taught Bürgi prosthaphaeresis, a method using trigonometric formulas, of turning multiplication into addition, thus simplifying complex astronomical calculations. The method was first discovered by Johannes Werner in Nürnberg at the beginning of the sixteenth century but he never published it and so his discovery remained unknown. It is not known whether Wittich rediscovered the method or learnt of it from Werner’s manuscripts whilst visiting Nürnberg. The method was first published by Nicolaus Reimers Baer, who was then accused by Tycho of having plagiarised the method, Tycho claiming falsely that he had discovered it. In fact Tycho had also learnt it from Wittich. Bürgi had expanded and improved the method and when Baer also came to Kassel in 1588, Bürgi taught him the method and how to use it, in exchange for which Baer translated Copernicus’ De revolutionibus into German for Bürgi. This was the first such translation and a copy of Baer’s manuscript is still in existence in Graz. Whilst Baer was in Kassel Bürgi created a brass model of the Tychonic geocentric-heliocentric model of the cosmos, which Baer claimed to have discovered himself. When Tycho got wind of this he was apoplectic with rage.

In 1590 Rothmann disappeared off the face of the earth following a visit to Hven and for the last two years of Wilhelm’s life Bürgi took over as chief astronomical observer in Kassel, proving to be just as good in this work as in his clock making.

Following Wilhelm’s death his son Maurice who inherited the title renewed Bürgi’s contract with the court.


Kupferstich mit dem Porträt Moritz von Hessen-Kassel aus dem Werk Theatrum Europaeum von 1662 Source: Wikimedia Commons

Kupferstich mit dem Porträt Moritz von Hessen-Kassel aus dem Werk Theatrum Europaeum von 1662
Source: Wikimedia Commons

However Maurice did not share his father’s love of astronomy investing his spare time instead in the study of alchemy. Bürgi however continued to serve the court as clock and instrument maker. Over the next eight years Bürgi made several visits to the Emperor’s court in Prague and in 1604 Rudolph requested Maurice to allow him to retain Bürgi’s services on a permanent basis. Maurice acquiesced and Bürgi moved permanently to Prague although still remaining formally in service to Maurice in Kassel. Rudolph gave Bürgi a very generous contract paying him 60 gulden a month as well as full board and lodging. As in Kassel all clocks and globes were paid extra. To put that into perspective 60 gulden was a yearly wage for a young academic starting out on his career!

In Prague Bürgi worked closely with the Imperial Mathematicus, Johannes Kepler. Kepler, unlike Rothmann, respected Bürgi immensely and encouraged him to publish his mathematical works. Bürgi was the author of an original Cos, an algebra textbook, from which Kepler says he learnt much and which only saw the light of day through Kepler’s efforts. Kepler was also responsible for the publication of Bürgi’s logarithmic tables in 1620.


Bürgi's Logarithmic Tables Source: University of Graz

Bürgi’s Logarithmic Tables
Source: University of Graz

This is probably Bürgi’s greatest mathematical achievement and he is considered along side of John Napier as the inventor of logarithms. In many earlier historical works Bürgi is credited with having invented logarithms before Napier. Napier published his tables in 1614 six years before Bürgi and is known to have been working on them for twenty years, that is since 1594. Bürgi’s fan club claim that he had invented his logarithms in 1588 that is six years earlier than Napier. However modern experts on the history of logarithms think that references to 1588 are to Bürgi’s use of prosthaphaeresis and that he didn’t start work on his logarithms before 1604. However it is clear that the two men developed the concept independently of each other and both deserve the laurels for their invention. It should however be pointed out that the concept on which logarithms are based was known to Archimedes and had already been investigated by Michael Stifel earlier in the sixteenth century in a work that was probably known to Bürgi.

Through his work as clock maker Bürgi became a very wealthy man and invested his wealth with profit in property deals and as a private banker lending quite substantial sums to his customers. In 1631 Bürgi, now 80 years old, retired and returned ‘home’ to Kassel where he died in January of the following year shortly before his 81st birthday. His death was registered in the Church of St Martin’s on the 31 January 1632. Although now only known to historians of science and horology, in his own time Bürgi was a well-known and highly respected, astronomer, mathematician and clock maker who made significant and important contributions to all three disciplines.




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

Christmas Trilogy Part 3: Choosing a wife.

Johannes Kepler was an incredibly prolific writer. He wrote and published more that eighty books and pamphlets on a very wide range of topics from astronomy to optics, from astrology to Bible chronology, from stereometry (that’s 3-D geometry) to the determination of the volumes of wine barrels and much, much more. A well as all of these publications he was also a very prolific letter writer. Many of his letters were in effect scientific papers, the exchange of letters between researchers taking the place of scientific journals in the Early Modern Period. For example his extensive correspondence with the Frisian astronomer David Fabricius gives us an important historical view of his struggles to derive and establish his second law of planetary motion. However not all of his letters were of a scientific nature. A letter he wrote on 23rd October 1613 to an unknown recipient goes into great detail concerning his attempts over the preceding two years to find a wife.

Kepler had married for the first time in 1595, at the age of 24, a wealthy young widow with daughter, Barbara Müller then aged 23, whilst he was serving as schoolteacher and district mathematicus in Graz. It seems to have been a love match and should have been a happy marriage, however Barbara, who suffered many trials and tribulations with Kepler’s expulsion from Catholic Austria and his subsequent more than rocky time as first assistant to Tycho and then Imperial Mathematicus in Prague, appears to have suffered from clinical depression making their marriage to a time of great stress to Johannes. Worse was to come. In 1611 Kepler’s three children contracted small pox and his son Felix died at the age of six. Barbara fell ill shortly after and passed away on July 3rd. All of this took place whilst Rudolph the German Emperor, and Kepler’s employer, was being deposed by his brother and Kepler was desperately trying to find a new position anywhere but Prague.

In those times it was perfectly normal for a widow with small children to look for and marry a new wife to run his household and look after his children. It was also perfectly normal for marriages, at least at Kepler’s social level, not to be love matches but rather arranged or brokered. Suitable partners being brought together in what more resembled a business deal than a personal relationship. Kepler was no exception to these norms and immediately following Barbara’s death he set about looking for a new wife to care for his children. In the end the whole process would take more than two years and involve negotiations with a total of eleven different women. In the letter mention above, and which I’m going to précis in the following, Kepler himself provides us with all the gory details.

Potential wife number one was a widow in Prague who was a mutual friend of Kepler and his wife. Barbara had recommended her, as her successor on her deathbed. Kepler opened negotiations and the widow seemed to be interested at the beginning but then withdrew, turning down the offer. Kepler was now offered a young maiden by her mother, as Kepler expressed it from widow to virgin. Kepler described to girl as having a pretty face and beening well educated but too young to bear the responsibilities of a household. In the end the mother withdrew the offer on the grounds that her daughter was too young.

At the commencement of this second negotiation Kepler had stated that he would either marry or leave Prague. The marriage having fallen through he now left the city on his way to Linz. In Moravia he met a girl who warmed his soul; a well brought up girl who took over his children with enthusiasm. Leaving his children in the care of their future mother he continued his journey. However when he returned the girl was engaged to another. Onward to Linz.

In Linz Kepler turned his attention to number four, apparently a bit of a stunner, tall, beautiful and athletic. Kepler was proceeding to tying the knot when his attention was distracted by number five, and here we get the longest description. She impressed through her love, her humble fidelity, her economy, her zeal and her affection for his children. It also appealed to Kepler that she was a solitary orphan.

Having almost accepted number five Kepler was urged by the wife of Helmhard Jörger (?) to decide on number four. Caught in a quandary, Kepler’s stepdaughter and her husband recommended a sixth candidate, an attractive, wealthy, but rather too young aristocrat. Kepler who suffered from a serious inferiority complex was worried she would look down on him. Lack of money being a permanent problem in his life he also feared the high costs of an eventual wedding so she too was rejected.

His thoughts returning to number five he now ran into number seven. His friends praised her nobility and her economy. As Kepler pressed his suit with her relatives he was warned off and in the end he was rejected. Enter number eight, by Kepler’s own account not attractive but with an honest mother. Kepler’s nervous and uncertain approach was met with an equally uncertain and nervous response, the whole project collapsed. Kepler now turned his attention to a ninth who simply turned him down. Kepler regarded number ten as unsuitable, describing himself as thin as a stick and his potential partner as short and fat, on to number eleven.

This time everything seemed to be in order the new potential Mrs Kepler was noble, wealthy, and economic, if somewhat young. However after four months of serious negotiations Kepler’s suit was once again rejected on the grounds that the lady was too young.

Kepler finally did the sensible thing, returned to number five, asked her to marry him and was accepted. The lady in question was Susanna Reuttinger twenty-four years old at the time to Kepler’s forty-one. They were married in Eferding on 30 October 1613. Despite Kepler’s vacillations in the two years leading up to the marriage it was a happy and loving union blessed by the birth of six children although, as was not unusual in the seventeenth century, three of them died in childbirth. Kepler took a long time and travelled a circuitous route to find his Susanna but in the end find her he did and she proved a good catch.


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Christmas Trilogy Part 2: Computing mathematical miracles.

In modern perception Charles Babbage has become reduced to narrow minded Victorian number cruncher whose only interest in life was producing mechanical computing machines to crunch ever more numbers. He has even been accused by the acolytes of St Ada of Lovelace of not understanding the real future purpose of those machines, knowledge of which had to be supplied by her saintliness. This rather dismal one-sided portrait of Babbage is very far from the truth Babbage being in reality a multi-talented man whose knowledge of the potentials embodied in the newly emerging machines of the nineteenth century was both very broad and deep. He even, within the context of a religious debate, conceived of the possibility of pre-programmed miracles a concept that he would demonstrate like a mechanical conjuror on early prototypes of his difference engine.

In the first half of the nineteenth century intellectual discourse in Victorian England was dominated by the concept of natural theology, particularly as presented by William Paley in his Natural Theology, or Evidences of the Existence and Attributes of the Deity collected from the Appearances of Nature published in 1802; Paley being today much loved by creationists and much derided by their opponents. The central argument of natural theology is very simple, stating that one can deduce the existence of God through the (scientific) study of the natural world. Paley is famous for having used the watchmaker analogy, the natural world resembles a watch in its complexity and design therefore there must be a watchmaker. (I have a sneaking feeling that I’m going to get hammered by my philosophical friends for this very simplified presentation of natural theology).

Paley was by no means the only believer in natural philosopher in that age and Francis Egerton, 8th Earl of Bridgewater, left a bequest of £8 000, a lot of money in those days, to pay one or more authors to write one or more treatises defending the principle of natural theology against the then modern scientific discoveries; the money to be administered by the Royal Society. The Royal Society decide to divide the money into eight portions of £1 000 and to commission eight treatises covering the full range of the then natural and moral sciences.

John Herschel was originally approached to write the treatise on astronomy but he declined on the grounds that it was wrong for a scholar to write for money! This volume was then offered to William Whewell, who having neither Herschel’s wealth nor his scruples eagerly accepted the task. Whewell duly wrote and published the Third Bridgewater Treatise, Astronomy and General Physics considered with reference to Natural Theology, which became the most successful and widely read of all of them, running to nine editions in his own lifetime. Whewell produced all of the argument brought earlier by Isaac Newton, who can be considered natural theological, for a God designed cosmos but adding all of the newer astronomical discoveries made since Newton’s times even including Herschel’s very recent work on double stars, showing how they too obeyed the law of gravity. Whewell’s cosmos was one governed by the laws of science as laid out by a scientific God; having established that God’s cosmos is governed by scientific laws Whewell then goes on to expound his philosophy of science. As he was soon to declare in his legendary three volume History of the Inductive Sciences (1st ed. 1837) and two volume The Philosophy of the Inductive Sciences Founded upon their History (1st ed. 1840) Whewell was a Baconian through and through who argued that the laws of science are obtained through induction. Not content to leave it at that he then went on to deny the ability of mathematics and deductions to discover new laws of nature.

Whewell, Herschel and Babbage had been close friends as students at Cambridge[1] and although all three of them were excellent mathematicians, who together as students had fought for the introduction of the continental analysis into Cambridge, it was Babbage who most considered himself to be a mathematician and who took umbrage at what he saw as a personal slight in Whewell’s dismissal of mathematicians in the process of scientific discovery. Never one to take insults lying down Babbage rose to the challenge and wrote and published his own Bridgewater Treatise, although he was not one of the eight chosen authors. Entitled The Ninth Bridgewater Treatise A Fragment by Charles Babbage, Esq. it contained Whewell’s offending passage on its title page:

“We may thus, with the greatest propriety, deny to the mechanical philosophers and mathematicians of recent times any authority with regard to their views of the administration of the universe; we have no reason whatever to expect from their speculations any help, when we ascend to the first cause and supreme ruler of the universe. But we might perhaps go farther, and assert that they.are in some respects less likely than men employed in other pursuits, to make any clear advance towards such a subject of speculation.”—Bridgewater Treatise, by the REV. WM. WHEWELL, p. 334.

This small book contains much of interest but what concerns us here is Chapter II, Argument in Favour of Design from the changing of Laws in Natural Events, which is a clever move by Babbage the computing expert to score points over Whewell.

Not in his Bridgewater Treatise, but in his reviews of the two volumes Charles Lyell’s Principles of Geology from 1831and 1832 Whewell addressed a problem that was central to the problems of natural philosophy caused by the recent scientific developments, evolution. Although Darwin’s own theory of evolution still lay some decades in the future evolution as a scientific fact was becoming more and more established as the geologists and palaeontologists found and examined more and more fossils of extinct species. If God had created the world and all that was in it, how come the geological record clearly displayed the disappearance and appearance of different species over the ages. Whewell’s solution was to invoke a caretaker God who popped in from time to time introducing new species to replace those that had died out these interventions being in the form of miracles. It is here that Babbage set out to demonstrate the superiority of a mathematical computing God.

Babbage argued by analogy, he describes the possibility of a computer programme (not the terminology that Babbage uses by the way) that generates the natural numbers 1, 2, 3, 4, … up to and including 100,000,001 but then instead of producing the number 100,000,002 as expected jumps to 100,010,002, continuing the series 100,030,003; 100,060,004; 100,100,005; 100,150,006; 100,210,007 … and so forth. Babbage states that the law generating the series has changed at the jump. The expected numbers being exceeded by the series 10,000, 30,000, 60,000, 100,000, 150,000 … and so on this being the series of triangular numbers 1, 3, 6, 10, 15, … multiplied by 10,000.

Babbage goes on to explain that the operator does not need to interfere with the calculating engine (he is of course thinking of his own Difference Engine) at this point but can pre-programme it from the beginning to make the change at the given juncture.

Unlike Whewell’s God who has to intervene in his own laws of nature with miracles to explain the presence of new species in the geological record Babbage’s mathematical God can pre-programme his laws of nature to change at the required point in time thus pre-programming his miracles at the point of creation.

Babbage actually programmed one of the calculating units of his Difference Engine to perform a miracle of the type described here, which he then demonstrated to guests at the soirees he held at his home in London. It was one of these demonstrations that so impressed the seventeen year old Ada Byron in 1833 and drew her into Babbage’s sphere of influence.

Babbage was so pleased with his mathematical miracles that he included another account of them in his autobiography, Passages from the Life of a Philosopher originally published in London in 1864.

Some readers might note a strong similarity between Babbage’s argument, sketched here, for a divine pre-programmed replacement of species and the arguments of those modern Christians who accept the theory of evolution but state that this is God’s method of creating the world.





[1] Laura J. Snyder’s The Philosophical Breakfast Club, Broadway Books New York, 2011 is an excellent account of that friendship that I strongly recommend.


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Christmas Trilogy, what’s that?

I have had another year with a comparatively large number of new readers many of whom are possible wondering why todays post is titled, Christmas Trilogy Part 1. I wrote a brief post explaining the Renaissance Mathematicus Christmas Trilogy last year, which also contains links to the Christmas Trilogy Posts from 2009, 2010, 2011 and 2012.

The Christmas Trilogy posts for 2013 were Part I: The Other Isaac, Part II: On Her Majesty’s Secret Service and Part III: A New Years Offering.

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Christmas Trilogy 2014 Part I: Was he or wasn’t he and does it matter?

Isaac Newton supposedly boasted on his deathbed that he had never known a woman. That’s known in the Biblical sense meaning to have sexual intercourse. Most people interpret this to mean that Newton died a virgin but is this true? Had he perhaps known a man?

Anybody setting out to write a biography of Isaac Newton has a problem, what can you do to make your biography stand out from all the ones that have already been written and there are a lot of them out there. Even Richard Westfall, whose Never at Rest[1] is without doubt king of the pack, has written three different Newton biographies! Michael White who could be described as a profession writer of intellectual biographies decided to go the shock, horror, did you know?, route with his biography from 1997, Isaac Newton: The Last Sorcerer[2], in which he reveals “the extraordinary influence of alchemy on the greatest mind of the modern world”. Unfortunately for White this is very much stale news as was pointed out four years ago by my #histsci soul sister Rebekah “Becky Higgitt in a blog post entitled Newton and alchemy: a constant surprise? To quote the good Dr Higgitt:

However, the thing that bugs me most is the fact that Newton has been ‘revealed’ as an alchemist, or as a magician, over and over again. In recent years the major popular interest in Newton has related to alchemy and prophecy, and such presentations tend to be accompanied by the suggestion that this is a surprising and novel revelation. This process goes back at least as far as John Maynard Keynes and his 1946 essay ‘Newton the Man’, which presented Newton as ‘the last of the magicians’. Keynes had acquired a significant portion of the ‘non-scientific’ part of Newton’s archive (as judged by the scientists who catalogued and divided them in the late 19th century), and he was undoubtedly struck by what he found. But, as I have said in my book, he shouldn’t have been as surprised as he evidently was.

White was of course aiming for the general lay public with his popular biography so he might have surprised some of his readers with his alchemical revelations, however he definitely did cause quite a stir with another revelation in his book, the claim that Newton was homosexual. In this post I want to examine the evidence that White puts forward for this claim and give my views on the question, was Isaac Newton a homosexual? Equally important in my opinion is the question; does it matter?

There is no actual solid evidence that Newton was homosexual that is, he never outed himself, as we would say today, and none of friend acquaintances or enemies ever outed or denounced him as being so. Newton acquired enough enemies throughout his long and cantankerous life, several of whom would happily have wished him to the devil so I think if there had been even a hint that he was homosexual one of them would have made the information public with malicious glee. This being the actually situation as far as our biographical knowledge of Newton goes White is reduced to circumstantial evidence and plausible assumption. He thinks he has found two separate pieces of evidence that point to Newton’s homosexuality and as they are unrelated I shall deal with them independently.

White’s first scenario concerns John Wickins, a fellow Cambridge student and later fellow of Trinity College who shared a chamber with Newton for twenty years from 1663 to 1683. We know next to nothing about Wickins one of the few sources being a brief note written by his son Nicolas Wickins to Robert Smith in 1728.

My Father’s intimacy with him came by mere accident. My Father’s first Chamber-fellow being very disagreeable to him he retired one day into the walks where he found Mr Newton solitary & dejected; Upon entering into discourse they found their cause of Retirement the same &thereupon agreed to shake off their present disorderly Companions & Chum together, which they did as soon as conveniently they could &and so continued as long as my Father stayed at College.[3]

During their time together Wickins functioned as Newton’s amanuensis copying up notes for him and acting as his assistant during alchemical experiments. White can offer no evidence that their relationship was anything other than just roommates but believes there is a smoking gun. He writes:

There is no hard evidence of their relationship being sexual in nature, only speculation surrounding the intensity of their bond as indicated by the absolute and clinical manner of its breaking.[4]

He and Newton separated in 1683 under a cloud and, despite Wickins living for another thirty-six years, the two men never met again.[5]

This is the full extent of White’s evidence and even as it stands it is mighty thin. There is nothing unusual in people who have been friends for long periods of time after they part, for whatever reasons, completely losing contact with each other. Having moved around quite a bit in my life I could quote quite a few examples out of my own life. However White’s argument is further weakened if we turn to Westfall’s account of their relationship.

With John Wickins, the young pensioner he met on a solitary walk in the college, he continued to share a chamber until Wickins resigned his fellowship in 1683 for the vicarage of Stoke Edith. Wickins was frequently absent for extended periods, and during the final five years he was hardly there at all.[6]

This added information doesn’t quite tie in with White’s “intensity of their bond” and “absolute and clinical manner of its breaking”. It appears more likely that their friendship simply drifted apart as many similar friendships do.

Interestingly White doesn’t try to conjure up a homosexual relationship between Newton and Humphrey Newton (a young man from Grantham who was no relation) who following Wickins’ final departure lived in Newton’s chambers for five years functioning as his amanuensis.

With his second piece of evidence White is on much firmer ground and describes a friendship of Newton’s that does appear to have been a love relationship with another man, the young Swiss mathematician Nicolas Fatio de Duillier (1664-1753).

Fatio c. 1700 Artist unknown Source: Wikimedia commons

Fatio c. 1700 Artist unknown
Source: Wikimedia commons

Fatio, as he is known, having previously studied with Cassini in Paris and becoming friends with Huygens and Jakob Bernoulli, travelled to London in 1687, where he met many of the leading scholars including John Wallis and was elected a member of the Royal Society. It was probably at a meeting of the Royal Society in 1689, where “Huygens discoursed on light and gravity” that he first met Isaac Newton. “The attraction between the two was instantaneous”[7] There then followed very close intellectual and personal relationship between the two men, well documented in a series of very intimate letters that can, without a very great stretch of the imagination, be described as love letters. This relationship lasted about four years with Newton offering to lend his young friend money and at times entreating him to come and share his chambers with him so that he can care for the health and wellbeing of the young scholar. There is no evidence that their relationship was ever physical but there is little doubt of the affection that it entailed. Was it a homosexual love affair? It seems very likely on the evidence of the correspondence however it could also be explained with a father son relationship; Newton having perhaps seen something of himself in the young Fatio and having adopted him like a mother hen. The tone of some of Newton’s letters would certainly support such an interpretation.

I personally think there was at least a non-physical love relationship between Newton and Fatio and one could be justified in including Newton in the very small number of known homosexual scientists. This of course raises the question included in my title, does it matter? In an ideal world, at least in my vision of one, a scientist’s gender, nationality, religion, sexual orientation, political opinions or any other personal traits should not play any role whatsoever in how we view their scientific work; however we a very far from living in such an ideal world. People are discriminated because of their gender, their skin colour, their sexual orientation, their religion etc. etc. We even recently had the unappetising spectacle of a self-proclaimed champion of free thought ridiculing Islam because of the lack of Islamic Nobel Prize laureates.

Since a number of years many people, including myself, have been pushing to raise the general awareness of female scientists, both in the history of science and in the current world, as role models to encourage young women to consider science as a possible career and to try to reduce the prejudice against those that do make this their career choice. Whilst female scientists are thin on the ground in the history of science before the twentieth century, homosexual scientists are almost non-existent. In several recent articles in the Internet provoked by the Alan Turing biopic, The Imitation, young homosexual scientists have emphasised the importance of Turing as a role model for them when choosing their careers. I feel it would be good if young homosexuals could also point to Newton, often presented as the greatest of all scientists, as a role model when contemplating a career in science.

[1] Richard S. Westfall, Never at Rest: A Biography of Isaac Newton, Cambridge University Press, Cambridge etc., 1980

[2] Michael White, Isaac Newton: The Last Sorcerer, Fourth Estate, London, 1998.

[3] Westfall, p. 74

[4] White, p. 235

[5] White, p. 52

[6] Westfall, p. 194

[7] Westfall, p. 493


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Galileo, Foscarini, The Catholic Church, and heliocentricity in 1615 Part 1 – the occurrences: A Rough Guide.

I have been criticised for claiming, in a recent post, that given time the Catholic Church would have come to accept heliocentricity in the seventeenth-century and in fact because Galileo acted unadvisedly he drove the Church to reject and condemn heliocentricity and thus to substantially delaying its acceptance by that organisation. The criticism was that this claim is speculative and thus not history and one critic even said not scientific. Point one, history is not science and is considerably more speculative than science, although, contrary to popular opinion, science is by no means free of speculation. In this case I think a certain amount of speculation is justified and by looking at the available facts on the attitudes of Catholic astronomers, and in particular the Jesuits, during the seventeenth-century both before and after the events of 1615, which will be discussed, it is possible to argue for a Catholic acceptance of heliocentricity, if Galileo and Foscarini had not driven the theologians into a corner causing them to reject it.

In the first seven decades following the publication of Copernicus’ De revolutionibus there was almost no rejection of heliocentricity on religious grounds but also very little acceptance by astronomers because of the substantial scientific problems that the theory entailed; problems associated with the physics of a moving earth. In a notorious footnote Copernican expert, Robert Westman, pointed out that there were only ten Copernican in the whole world between the publication of De revolutionibus in 1543 and 1600 and not all of those were astronomers, although it did include both Kepler and Galileo. After an initial period of excitement following the books publication Copernicanism was slowly drifting into obscurity due to its failure to deliver the goods, accurate astronomical tables. This situation changed dramatically in 1609.

In 1609 Kepler published his Astronomia Nova containing his first two laws of planetary motion based on solid empirical evidence supplied by Tycho Brahe and providing the best evidence for a heliocentric system by that time. The same year also saw the advent of telescopic astronomy, the telescope having been invented in the previous year, and the beginning of a series of astronomical discoveries by Thomas Harriot, Simon Marius, Galileo Galilei, and the Jesuit astronomers Odo van Maelcote, Giovanni Paolo Lembo and Christoph Grienberger that brought about the biggest changes in astronomy since human being first turned their gaze to the heavens; most notably Galileo published his initial discoveries in his Sidereus Nuncius in 1610. None of these discoveries proved heliocentricity but they did refute significant aspects of the accepted Aristotelian cosmology and the Ptolemaic geocentric astronomy forcing a serious and deep re-alignment of both disciplines. It was the Church’s own astronomers from the Jesuit Collegio Romano, who had quietly been making their own observations and discoveries before the publication of Sidereus Nuncius, who provided the much needed scientific confirmation of Galileo’s discoveries; passing this information on to the Church’s theologians. The Jesuit astronomers fully aware that Ptolemaic geocentricity was no longer tenable, following the discovery of the phases of Venus, like most other European astronomers, adopted the Tychonic helio-geocentric system; an intermediate solution that combined the best technical aspects of heliocentricity, for example the explanation of retrograde motion, without moving the earth. This was an important step down the road to heliocentricity, especially if, as it often was, combined with diurnal rotation. However Galileo could not accept this rational compromise, his ambition drove him on, because he wanted to go down in history as the man who established heliocentricity, ignoring in his egotism the work of Kepler who was much more advanced in his heliocentric astronomy than Galileo himself. To understand what happened next we need to briefly examine the position of the Church in this situation.

Religions are by their very nature conservative and opposed to sudden or significant change. They claim to be purveyors not just of truth but ‘the’ truth. This being the case all change is in one way or another an admission of failure; we got it wrong! This does not mean that religions are never changing, frozen in time, but it does mean that all change should be gradual, controlled and fully explainable within the religion’s own model of reality. A religion cannot allow itself to be seen to be forced to change by outside forces, otherwise believers might begin to question their monopoly on the truth. Since the thirteenth-century the Catholic Church had integrated an uneasy synthesis of Aristotelian cosmology and Ptolemaic astronomy, largely created by Albertus Magnus and his pupil Thomas Aquinas, into their model of reality, one that seemed to fit the known empirical facts. Now at the end of the first decade of the seventeenth-century this synthesis was crumbling away very fast and the Church was in a very dodgy situation, over which they had very little control, a potential nightmare for the theologians, the official purveyors of the truth. The central problem in this situation was that various passages in the Bible, supposedly the indisputable word of God, contradicted a heliocentric model with a stationary sun and a mobile earth, most notably Joshua 10:12 “…and he said in the sight of Israel, Sun, stand thou still upon Gibeon; and, Moon, in the valley of Ajalon”. If the sun wasn’t moving how could the Lord command it to stand still? The Church’s theologians were not stupid and it was very clear to them that if they accepted heliocentricity then they would have to abandon a literal interpretation of this and some other passages in the Bible; a change that they were only prepared to make if there was solid empirical evidence available to make it inevitable, as we will see.

By 1613 Galileo was chomping at the bit and was very egger eager to persuade the whole world, including the Church, to accept Copernican heliocentricity. His influential friends within the Church, who included Cardinal Maffeo Barberini the future Pope Urban VIII, were very much aware of the situation sketched above and warned Galileo that he should proceed with caution and not stir up trouble with the Church’s theologians. Galileo ignored this very sensible advice. The matter first came to a head with the so-called Letter to Castelli that in a modified form is better known as the Letter to Christina. How this came about we need to look at Galileo’s official function at the Medici Court in Florence.

Galileo had used the Sidereus Nuncius to acquire a position at the Medici Court dedicating the pamphlet to Cosimo II, his former mathematics pupil, and naming the Moons of Jupiter, his greatest discovery, the Medicean Stars in his honour. This followed lengthy correspondence with court officials as to which name would be most acceptable to the Grand Duke. Galileo’s efforts were rewarded with a position as court philosophicus and mathematicus and an appointment as professor of mathematics at the University of Pisa without teaching obligations, all for a very generous salary. What exactly was Galileo’s role as court philosophicus? The position sounds very impressive but in reality, within the structure of a Renaissance absolutist court, Galileo was a sort of intellectual court jester. In an age without Internet, radio, television or any of the other modern invention with which we waste our time, after dinner entertainment at a Renaissance court took various forms; one of these took the form of intellectual debates. Galileo was expected to entertain the dinner guests by disputing given philosophical or scientific themes with others, especially invited for the purpose. Cosimo and his guest were not particularly concerned who won a given debate or who was right, they were more interested in being entertained by clever and witty repartee, Galileo a brilliant polemicist was naturally a master at this game and more than earned his keep. The situation that led to Galileo writing the Letter to Christina actually took place in Galileo’s absence.

Late in 1613 the newly appointed professor of mathematics at the University of Pisa, Benedetto Castelli, a pupil of Galileo’s, attended a lunch hosted by the Grand Duchess Christina, Galileo’s earlier patron who had employed him to teach mathematics to Cosimo. Also present on this occasion was the Pisan professor for philosophy, Cosimo Boscaglia. Christina expressed doubts about the existence of the Moons of Jupiter and about their possible connection with the, in her eyes, heretical Copernican astronomy. Boscaglia assured her that the moons were indeed real and expressed similar doubts about their astronomical implications. After the meal Christina summoned Castelli to her chamber and in the presence of Boscaglia and other guests challenged him on the mobility of the earth. Castelli was in the hot spot, but according to his own account, in a letter to Galileo, he acquitted himself skilfully. Galileo now set in motion a chain of events that probably constitute the biggest error in his life. He wrote a long letter to Castelli supplying him with arguments to use against those quoting Bible passages against heliocentricity. He set about playing the theologian, reinterpreting those passages to make them conform to Copernican thought. He suggested for example that when the Lord commanded the sun to stand still he stopped its rotation about its axis, a rotation that Galileo had recently proved with his study of sunspots. The whole letter was, to put it mildly, a blunder.

Some of Galileo’s enemies, disgruntled Aristotelians who had been subjected publically to the scorn of Galileo’s sharp tongue, got hold of a copy of the letter and presented it to the Church authorities. Surprisingly the Church found most of the letter unobjectionable except for a handful of passages. Galileo tried to bluff his way out of the matter by claiming that those passages were not in the original but had been added to the copy by his enemies, whether you believe him or not is left entirely up to you. The Church demanded the original. In the meantime Galileo instead of backing down was working on an expanded version of the letter, which would go down in history as the Letter to Christina, to whom it was directly addressed. Galileo really did not know when to leave things alone. Why one might ask was it so terrible for Galileo to suggest new interpretations of the Bible?

The Catholic Church was founded on the premise that they, and they alone, were privileged to interpret the word of God. In the early sixteenth century various thinkers, who became known collectively as the Protestants, challenged the Church on this very issue, claiming that every individual had the right to read and interpret the word of God for himself. A universal claim that was later modified as the various branches of this protest movement solidified into established churches themselves. But I digress. This led to the greatest schism in Church history now known as the Reformation. From the middle of the century following the Council of Trent the Catholic Church hit back with its own movement, which became known as the Counter-Reformation, leading storm-troopers being the Jesuits, although they were not initially founded for this purpose. Galileo, a mere mathematicus and thus the lowest of the low in the intellectual hierarchy, was claiming the right to re-interpret the Bible just five years before the outbreak of the Thirty Years War the devastating and extremely bloody highpoint of this struggle between the forces of Reformation and Counter-Reformation. Not a clever move from a man who many regard as a genius.

To pour even more oil into the fire, as if Galileo’s own efforts were not enough, a Carmelite theologian, Paolo Antonio Foscarini, submitted a book he had written to the Church censors in 1615, which contained very similar reinterpretations of the Bible to bring it into line with the Copernican heliocentric hypothesis. Not surprisingly the anonymous censor thought the book to “excessively favour the rash opinion” of Copernicus. Like Galileo, Foscarini was not prepared to let matter lie and submitted both the text of his book and the censor’s judgement to the Jesuit Cardinal Roberto Bellarmino, who was considered one of the greatest living theologians. Bellarmino considered Foscarini’s book and Galileo’s letter and came to a famous conclusion that he sent to Foscarini in the form of a letter the relevant passages of which I have reproduced below.

My Very Reverend Father,

It has been a pleasure for me to read the Italian letter and the Latin paper you sent me. I thank you for both the one and the other, and I may tell you that I found them replete with skill and learning. As you ask for m y opinion, I will give it as briefly as possible because, at the moment I have very little time for writing.

First, I say it seems to me that your Reverence and Signor Galileo act prudently when you content yourselves with speaking hypothetically and no absolutely, as I have always understood that Copernicus spoke. For to say that the assumptions that the Earth moves and the Sun stands still saves all the celestial appearances better than do eccentrics and epicycles is to speak with excellent good sense and to run the risk whatever. Such a manner of speaking suffices for a mathematician. But to want to affirm that the Sun, in very truth, is at the centre of the universe and only rotates on its axis without traveling from east to west, and that the Earth is situated in the third sphere and revolves very swiftly around the Sun, is a very dangerous attitude and one calculated not only to arouse all Scholastic philosophers and theologians but also to injure our hold faith by contradicting the Scriptures….

Second, I say that, as you know, the Council of Trent forbids the interpretation of the Scriptures in a way contrary to the common agreement of the holy Fathers. Now if your Reverence will read, not merely the Fathers, but modern commentators on Genesis, the Psalms, Ecclesiastes, and Joshua, you will discover that all agree in interpreting them literally as teaching that the Sun is in the heavens and revolves round the Earth with immense speed and that the Earth is very distant from the heavens, at the centre of the universe, and motionless. Consider, then in your prudence, whether the Church can support that the Scriptures should be interpreted in a manner contrary to that of the holy Fathers and of all modern commentators, both Latin and Greek….

Third, I say that, if there were a real proof that the Sun is in the centre of the universe, that the Earth is in the third sphere, and that the Sun does not go round the Earth but the Earth round the Sun, then we should have to proceed with great circumspection in explaining passages of Scripture which appear to teach the contrary, and we should rather have to say that we did not understand them than declare an opinion to be false which is proved to be true. But I do not think there is any such proof since none has been shown to me. To demonstrate that the appearances are saved by assuming the sun at the centre and the earth in the heavens is not the same thing as to demonstrate that in fact the sun is in the centre and the earth is in the heavens. I believe that the first demonstration may exist, but I have very grave doubts about the second; and in case of doubt one may not abandon the Holy Scriptures as expounded by the hold Fathers…

Having very firmly pointed out that neither Galileo nor Foscarini had the right to interpret or reinterpret Holy Scripture, Bellarmino adds a very important comment in the final paragraph. He states very clearly that if there were proof of the heliocentric system then the Church would have to very carefully reinterpret the Bible, but he says, quite correctly, such proof does not exist at the moment so no deal. He then goes on the say that he personally doesn’t think that such proof would ever be found, proving that even Saint Roberto Bellarmino S. J. was not infallible. This final passage clearly illustrates something that the modern Galileo fan club love to ignore; in 1615 there was no empirical proof for the heliocentric hypothesis. It has been suggested that some Jesuit astronomers interpreted Bellarmino’s concession that if such a proof were to be found, as an instruction to go out and find one, but more of that in Part 2 – the consequences.

Things were now approaching the denouement. It was very clear to Galileo and all the other interested parties that the whole episode had been submitted to the Roman Inquisition. Instead of doing the sensible thing and keeping his head below the parapet, as advised by all of his influential friends including Cesi the head of the Academia dei LIncei and Cardinal Barberini, Galileo decided to go on the offensive. Obtaining permission from his employer, Cosimo, Galileo set off to Rome to canvas for the acceptance of heliocentricity. Knowing full well that he lacked empirical proof of heliocentricity, Galileo wrote up for the first time his infamous theory of the tides, thought out by him and Paolo Sarpi in the 1590s and which would go on to become Day Four, the crowning glory as he saw it, of his Dialogo. This theory posited that the tides were the result of the oceans swapping about like water in a moving bowl, as a result of the motion of the earth. It suffered from one major failure, and lots of minor ones, it only allowed for one tide a day, whereas there are in reality two.

Galileo arrived in Rome and began badgering anybody and everybody of influence that he could get hold off pressing copies of his theory of the tides into their hands and trying to persuade them to support his cause. He might as well have stayed at home, nobody in Rome, least of all influential public figures, was going to stick his neck out and help a mere mathematicus who was under investigation by the Inquisition.

It came as it had to come, the eleven members of the commission set up to adjudicate on the affair found that the idea that the Sun is stationary is “foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture…”; while the Earth’s movement “receives the same judgement in philosophy and … in regard to theological truth it is at least erroneous in faith.” Put into simple terms heliocentricity, as a theory of fact was both scientifically and theologically wrong. Galileo and Foscarini had forced the Church into making, what was to all intents and purposes, a disastrous judgement. As everybody knows the Pope instructed Bellarmino to inform Galileo of the commission’s judgement and to formally forbid him from holding or teaching the heliocentric theory. It is important to note that the theory, heliocentricity as a statement of fact, was forbidden and not the hypothesis, a distinction that was to play a very central role in the following decades.

Personally, this judgement had very little influence on Galileo life or status in Northern Italian society. Initially there were some rumours that he had been punished in some way by the Church, but at Galileo’s request Bellarmino wrote a letter stating that they had merely had a friendly chat and that Galileo was free of all suspicion. Unfortunately Galileo would later view this letter as a get out of gaol free card but that is the subject of another story. Galileo continued to be a highly feted figure in Northern Italian intellectual circles and to have easy access to the highest circles of the Church. He was not some sort of outcast battling the ignorant Curia, as he is often falsely depicted.

The direct consequences for the heliocentric hypothesis were that Foscarini’s book together with the books of the Protestant Copernicans, Michael Maestlin and Johannes Kepler were placed on the Index of Forbidden Books. Interestingly De revolutionibus was only placed on the Index until corrected. What this meant and the effect that all of this on the future development of heliocentricity will be dealt with in Part 2 – the consequences, which should, all thing being well appear here next week.

For those reading one of my The Transition to Heliocentricity: The Rough Guides posts for the first time you can find a list of links at the top of the website.


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