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A misleading illustration.



The difference between an easy model and a complicated one.

The gif above, from Malin Christersson’s  Website, has been making the rounds of the Internet to much acclamation but it is in my opinion severely misleading in what it claims to represent. Some people have pointed out that the heliocentric model is false because the orbits should be elliptical. This is my opinion an irrelevance because the eccentricity of the planetary orbits, that is the degree by which the ellipses differ from a circle, is so small that in a diagram of this sizel it wouldn’t be really detectable. In fact illustrations of the heliocentric system tend to exaggerate the eccentricity to make it clear that the orbits are in fact ellipses. My problem is another. The two models are presented side by side as if they were directly comparable but in fact they are two radically different representations.

The heliocentric system is displayed from a bird’s eye, or perhaps a god’s eye, view from a position directly above the sun perpendicular to the plane of the planetary orbits somewhere a couple of billion kilometres out in space. One should point out the sizes of the orbits are not to scale. Opposed to this the presentation of the geocentric system is not something one could actually view in reality. It is a fictitious birds eye view of the system as reconstructed by the astronomers in antiquity based on the activities they saw in the heavens and herein lies the crux of the problem.

Viewed from the earth the moments of the celestial bodies is not the lovely regular circles depicted in the heliocentric model above but a bizarre dance of confusing movements. The sun appears to go around the earth once a year and the moon once every approximately twenty-nine days. The so-called inner planets mercury and venus both also appeared to take a year to orbit the earth never wandering far from the sun, at times to one side and at other times on the other. Often both disappeared for periods of time. This behaviour led some people in antiquity to speculate that they orbit the sun and not the earth, the so-called Egyptian or Heracleidian model. It is however the so-called outer planets mars, jupiter and saturn that display the most puzzling behaviour. They role along in one direction for a lengthy period of time and then appear to stand still for a short period before turning tail and heading back in the opposite direction after a short time remaining stationary again before resuming in the original direction. These apparent loops in the planets progress are known technically as retrograde motion. We now know that this is an illusion created within the heliocentric system as the earth moving faster overtakes one or other of the outer planets. Given the seemingly stationary condition of the earth this was a difficult conception leap for astronomical observers to make. In fact in two thousand or more years of astronomy only two people appear to have made that leap, Aristarchus of Samos in the third century BCE and Copernicus in the fifteenth century CE. Both of these visionaries still had to cope with the very obvious empirical evidence that the earth doesn’t move.

The gif above creates a false impression because it seems to imply that the simplicity of the heliocentric system makes its an obvious choice over the geocentric model but as should be obvious from my description of what you actually see as an observer on the earth, and all observers in the past were on the earth, making that choice is anything but simple or obvious. The creator of the gif includes a short history of the journey from geocentricity to heliocentricity, which unfortunately contains various errors and misconceptions, which I will now highlight.

≈ 350 BC, Aristotle 

Aristotle a pupil of Plato, becomes the tutor of Alexander the Great. Aristotle’s views of the world shape science for centuries. His influence lasts until the enlightenment. In his book On the Heavens (part 14), Aristotle asserts that:

From these considerations then it is clear that the earth does not move and does not lie elsewhere than at the centre.

Aristotle is just one of many scholars from antiquity whose views influenced the future views of the world. He in fact inherited and modified the homocentric geocentric views and models of Eudoxus and Callippus. These models could explain retrograde motion fairly well but not the observable variation in brightness of the planets. This was not the system that medieval Europe inherited from antiquity. See below Ptolemy.

 ≈ 250 BC, Aristarchus

Aristarchus estimates the size of the sun to be much larger than the size of the earth. Based on this observation he then presents the heliocentric model.

The geometrical text, which is attributed to Aristarchus, is for determining both the distance of the sun from the earth and its size relative to the moon. It is a purely geocentric text and has nothing to do with his speculation about a heliocentric cosmos. There are no direct accounts of Aristarchus’ heliocentric model so we don’t actually know what caused him to adopt it.

 ≈ 250 BC, Archimedes

In The Sand-Reckoner, Archimedes estimates the number of sand corns in the universe using the heliocentric model of Aristarchus.

In the Sand Reckoner Archimedes wishes to demonstrate his system for recorded extremely large numbers. He uses Aristarchus’ heliocentric model, which he sketches, because Aristarchus argued that the stars were much further away than hypothesised in the normal geocentric model in order to explain why there was no observable stellar parallax. Archimedes used this model because it would require many more grains of sand to fill thus giving him a much greater number to express with his system. It is only one of two accounts of Aristarchus’ heliocentric system both of which are uninformative.

≈ 150 AD, Ptolemy

In his book Almagest, Ptolemy introduces so called epicycles to explain planetary motions, based on the assumption that the earth is at the centre and does not move. Almagest is considered to be one of the most influential scientific works in history.

The epicycle system of planetary motion, used extensively by Ptolemy in the Almagest in the second century CE, was first introduced by Apollonius of Perga in the third century BCE and used extensively by Hipparchus of Rhodes in the second century BCE.

1543, Nicholaus Copernicus

Just before his death, Copernicus publishes the book De Revolutionibus Orbium Coelestium (On the Revolutions of the Heavenly Spheres) in which he places the sun rather than the earth at the centre of the universe. This book is the beginning of the Copernican Revolution.

In English it’s Nicolaus (no ‘h’) Copernicus and in De revolutionibus the sun is not at the centre of the universe but somewhat off centre. Viewed strictly Copernicus’s system is heliostatic but not heliocentric.

1572, Tycho Brahe

Tyco Brahe observes a star being born and publishes his observation in De nova stella. Brahe’s observation refutes the commonly held view at the time, a view which dates back to Aristotle, that the stars are fix and never changing at the outskirts of the universe. Since Brahe couldn’t observe a stellar parallax, he concluded that the earth did not move. He proposed a model where the planets move around the sun, and the sun moves around the earth. (It was later shown that it wasn’t a star being born Brahe had observed, but the supernova SN 1572, i.e. a star exploding.)

In the first half of this paragraph we have an oft-repeated semi-myth. Although Tycho did indeed observe the nova of 1572 and it did contradict Aristotle’s cosmological theory of an immutable heaven this story is a myth for three different reasons. Firstly Aristotle’s concept of a an immutable heaven had already been seriously challenged in the sixteenth century by several leading astronomers based on their observations of several comets in the 1530s, so the nova of 1572 was not the first problem for Aristotle’s cosmology. Secondly Tycho was by no means the only astronomer to observe and comment on the 1572 nova and Michael Maestlin’s and Christoph Clavius’ acceptance that the nova was supralunar had more impact than Tycho’s. The attribution of this impact to Tycho alone is a version of the lone genius myth and historically false. Thirdly the refutation of Aristotle’s theory of the immutability of heaven actually has no real relevance for the geocentricity/heliocentricity discussion.

1609, Johannes Kepler

Using the observational data collected by Tycho Brahe, Johannes Kepler introduces his first two laws of planetary motion in Astronomia nova. The first law: the planets move in elliptical orbits with the sun at one focus.

Given that it was actually Kepler’s work that led to the acceptance of heliocentricity our author gives him rather short shrift in his chronology. What about the other two laws of planetary motion or the Rudolphine Tables?

 1616, Roman Inquisition

On 24 February 1616 a team of eleven consultants for the Roman Inquisition condemns the Copernican System, stating that the heliocentric system is “foolish and absurd in philosophy and “formally heretical”.

It should be pointed out that the Pope never confirmed the heretical status of heliocentricity thus it never was heretical.

 1633, Galileo Galilei

Galileo Galilei stands trial on suspicion of heresy “ for holding as true the false doctrine taught by some that the sun is the centre of the world”. At the trial he is found guilty and sentenced to formal imprisonment. Galileo spends the rest of his life under house arrest.

 1687, Isaac Newton

Sir Isaac Newton publishes Philosophiæ Naturalis Principia Mathematica (Principia). In Principia, Newton explains Kepler’s laws of planetary motion in terms of universal gravitation. Newton doesn’t consider the sun to be at rest, instead he uses the center of gravity of the solar system.

A small point, but one that irritates me. The man who published the Principia in 1687 was not ‘Sir’ Isaac Newton but just plain Isaac Newton who didn’t get knighted until 1705.

1838, Friedrich Bessel

Friedrich Bessel is the first to accurately measure a stellar parallax. In 1838 he announces that the star 61 Cygni has a parallax of 0.314 arcseconds.

Friedrich Bessel was not the first to accurately measure stellar parallax that honour goes to the Scottish astronomer Thomas Henderson, who measured the parallax of Alpha Centauri. Friedrich Bessel, however, was the first to publish.

1992, Roman Catholic Church

Pope John Paul II closes a 13-year investigation into the church’s condemnation of Galileo in 1633 by declaring that Galileo was right:

 Thanks to his intuition as a brilliant physicist and by relying on different arguments, Galileo, who practically invented the experimental method, understood why only the sun could function as the centre of the world, as it was then known, that is to say, as a planetary system. The error of the theologians of the time, when they maintained the centrality of the earth, was to think that our understanding of the physical world’s structure was, in some way, imposed by the literal sense of Sacred Scripture.

This final paragraph is just a horrible mess. Galileo did not practically invent the experiment method. Also the claim that he “understood why only the sun could function as the centre of the world” is simply bizarre. As I have pointed out in a number of different posts, in Galileo’s time the scientific evidence actually favoured a geocentric system. This also applies to the comment about the theologians, whose belief in a geocentric system was strongly supported by the available scientific evidence and was not just based on Sacred Scripture. It is also interesting to note how a chronology of the geocentric/heliocentric astronomical systems suddenly veers off into an account of Galileo’s troubles with the Catholic Church, which in real terms in the history of astronomy and cosmology is just a small side show.



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Just another day

A very large number of my Internet acquaintances along with both the English and German language media that I have access to are indulging in their yearly hysteria because today is New Year’s Eve and tomorrow is New Year’s Day, what they all seem to have forgotten is that it’s actually just another day.

A part, but by no means all, of human kind has arbitrarily decided to designate today as the day that they stop counting the days of the sun’s annual journey around the ecliptic and tomorrow start again from one. I say a part but by no means all because tomorrow is only New Year’s Day on the Gregorian calendar but not on many, many other calendars currently in use throughout the world, for example the Jewish, Muslim, Persian, Chinese, Vietnamese and numerous others.


The analemma traces the position of the sun in the sky throughout the solar year Source: KBCC Meteorology

The Gregorian New Year’s celebration doesn’t even coincide with a significant day in the annual solar journey, either of the equinoxes when the day and night are equally long or either of the solstices in summer with the longest day or in winter with the shortest day. My favoured candidate for New Year’s would be the winter solstice with, for me in the northern hemisphere, the start of the slow climb to spring and then on to summer, a genuine reason to celebrate and not an arbitrary and artificial one.

January the first wasn’t always the beginning of the calendrical year. Originally the Romans, from whom we inherit our calendar, celebrated the start of the year, as did and do other culture, at the spring equinox around the twenty-fifth of March, also in my opinion a good choice for a calendrical celebration.

When Julius Caesar introduced the solar calendar, that would go on to bear his name, in 46 BCE he moved the start of the year from 25 March to 1 January, the feast of Janus, the Roman god of beginnings and endings. In the Middle Ages some countries, not keen to celebrate a pagan festival, moved New Year’s Day back to 25 March the Christian Feast of the Annunciation, that is the day that Mary supposedly became pregnant with Jesus. This led to two different ways of numbering the days of the year, Circumcision Style starting from 1 January, Circumcision of Our Lord in the Church calendar and Annunciation Style from 25 March. For a time in the Middle Ages the start of the year was counted by some from the 25 December, Nativity Style, or from the Easter Feast, Easter Style. The latter was considered somewhat inconvenient because Easter is a moveable feast.

When Pope Gregory introduced his calendar reform in 1582 his reform committee has settled on 1 January as the unified start of the year. Some countries, most notably Great Britain and its colonies, which initially rejected the Catholic calendar reform retained the Annunciation Style of counting leading to the strange anomaly of Newton’s date of death. On the Gregorian calendar, new style, he not only died eleven days but a whole year later than on the Julian calendar, old style.

So when you set out, to do what ever it is that you plan to do, to celebrate this evening just remember that in reality today is just another day in the sun’s seemingly endless journey along the ecliptic and any other day would do just as well and has done so throughout human history and continues to do so in many other cultures.

However what ever your beliefs and no mater which calendar you follow and on which day you celebrate the start of another round of the loop, I wish you all the best for the next 366 days of your life, as 2016 is a leap year on the Gregorian calendar.


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Christmas Trilogies!

For those who started following this blog within the last twelve months and there are quite a lot of you, I write three posts every year as my Christmas Trilogy, although they didn’t acquire this name until 2012. The First on the Christmas Day is for Isaac Newton who was born 25 December 1642 (os). The second on St. Stephen’s or Boxing Day is for Charles Babbage who was born on 26 December 1791. The Trilogy is rounded out by Johannes Kepler who was born on 27 December 1571. If you want to read the earlier posts you can find them here:

Christmas Trilogy 2009 Post 1

Christmas Trilogy 2009 Post 2

Christmas Trilogy 2009 Post 3

Christmas Trilogy 2010 Post 1

Christmas Trilogy 2010 Post 2

Christmas Trilogy 2010 Post 3

Christmas Trilogy 2011 Post 1

Christmas Trilogy 2011 Post 2

Christmas Trilogy 2011 Post 3

Christmas Trilogy 2012 Post 1

Christmas Trilogy 2012 Post 2

Christmas Trilogy 2012 Post 3

Christmas Trilogy 2013 Post 1

Christmas Trilogy 2013 Post 2

Christmas Trilogy 2013 Post 3

Christmas Trilogy 2014 Post 1

Christmas Trilogy 2014 Post 2

Christmas Trilogy 2014 Post 3

Reading that lot should keep you occupied for a couple of hours.







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Christmas Trilogy 2015 Part 1: The famous witty Mrs Barton


Younger readers might be excused if they thought that the IT Girl phenomenon, as illustrated by the likes of Paris Hilton and Kim Kardashian, was a product of the computer social media age but those of us who are somewhat more mature can remember such as Jacqueline Lee “Jackie” Kennedy Onassis (née Bouvier) and Bianca Jagger (born Bianca Pérez-Mora Macias), who were IT Girls of their respective generations. In fact I assume there have been IT Girls as long as there has been human society. That is young attractive women, who became famous or even infamous purely on the strength of their appearances and social behaviour.

In the Augustan age of London at the beginning of the eighteenth century one such IT Girl was Catherine Barton who’s beauty was celebrated at the Kit-Kat Club, drinking den of the Whig Party grandees, in the following verse[1]:

At Barton’s feet the God of Love

His Arrows and his Quiver lays,

Forgets he has a Throne above,

And with this lovely Creature stays.

Not Venus’ Beauties are more bright,

But each appear so like the other,

That Cupid has mistook the Right,

And takes the Nymph to be his Mother.

Apparently the only image of the young Catherine Barton Source: Wikimedia Commons

Apparently the only image of the young Catherine Barton
Source: Wikimedia Commons

Now those not already in the know are probably wondering why I’m wittering on about an eighteenth-century It Girl instead of the history of science, especially in the first part of my traditional Christmas Trilogy, which is normally dedicated to Isaac Newton who was born 25 December 1642 (os). The answer is very simple, because the charming Catherine Barton was Newton’s niece, the daughter of his half sister Hannah Baton née Smith, and his housekeeper for part of the thirty years that he lived in London.

It is not know for certain when Newton brought his niece, who was born in 1679, from her native Lincolnshire to look after his house in London but not before 1696 when he first moved there himself and probably not later than 1700, however she stayed with her uncle until she married John Conduitt in 1717.

As well as being the toast of London’s high society Catherine Barton played an important part in Newton’s London life. For example she was closely acquainted with the satirist Jonathan Swift and it was through his friendship with Barton that the Tory Swift approached the Whig Newton in 1713 to try to persuade him to relinquish the Mastership of the Mint, an important political sinecure that the Tories wished to bestow on one of their own, in exchange for a state pension of £2,000 per annum, a very large sum of money. An offer than Newton simply refused remaining Master of the Mint until his death.

Catherine’s fame or maybe notoriety extended beyond London to the continent. Rémond de Monmort, a member of the French Regency Council, who met her in 1716 whilst visiting Newton later wrote of her, “I have retained the most magnificent idea in the world of her wit and her beauty”. More famously Voltaire wrote of her:

I thought in my youth that Newton made his fortune by his merit. I supposed that the Court and the city of London named him Master of the Mint by acclamation. No such thing. Isaac Newton had a very charming niece, Madame Conduitt, who made a conquest of the minister Halifax. Fluxions and gravitation would have been of no use without a pretty niece.

Voltaire was wrong. It was indeed Charles Montagu, Lord Halifax, who appointed Newton initially to the Wardenship of the Mint in 1696, the two had been friends when Montagu was a student at Cambridge in the 1680s, but this was before Newton had brought Catherine to London so Montagu could not have known her then. However Voltaire’s quip was almost certainly based on knowledge of a real scandal involving Lord Halifax and Catherine Barton.

Charles Montagu, 1st Earl of Halifax by Sir Godfrey Kneller (NPG) Source: Wikimedia Commons

Charles Montagu, 1st Earl of Halifax by Sir Godfrey Kneller (NPG)
Source: Wikimedia Commons

Halifax had become acquainted with Catherine by 1703 at the latest when he engraved a toasting glass at the Kit-Kat Club with her name and composed the following verse to her:

Stampt with her reigning Charms, this Standard Glass

Shall current through the Realms of Bacchus pass;

Full fraught with beauty shall new Flames impart,

And mint her shining Image on the Heart.


Montagu may have been a successful politician and a great economics expert but he was no poet. Toasting a beauty at the Kit-Kat Club does not constitute a scandal but Halifax’s will, originally drafted in 1706, did. In a codicil he bequeathed Catherine £3,000 and all his jewels, “as a small Token of the great Love and Affection I have long had for her”. Faced with this anything but small token, and there was worse to come, Newton’s nineteenth-century biographers were left snapping for air in their attempts to find a not scandalous explanation for this act. Later in the year he even purchased a £200 per annum annuity for her. Was she his lover, his mistress? This explanation seems to offer itself. In 1710 Mrs Mary de la Rivière Manly a Tory satirist published a satire on the Whig’s, which featured a mistress called Bartica for the Halifax figure.

As I said above, the situation got worse in 1713 when Halifax revoked the first codicil and drew up a new one bequeathing £5,000 to Mrs Barton with the grant during her life of the rangership and lodge of Bushey Park and all its furnishings, to enable her to maintain the house and garden, the manor of Apscourt in Surrey. “These Gifts and Legacies, I leave to her as a Token of the sincere Love, Affection, and Esteem I have long had for her Person, and as a small Recompence for the Pleasure and Happiness I have had in her Conversation”.

Flamsteed, always eager to to get in a jibe against Newton, writing to Abraham Sharp on hearing of the bequest after Halifax’s death said sarcastically that it was given to Mrs Barton “for her excellent conversation”. In his desperate attempt to avoid the obvious implications for the morality of the Newton household, Augustus De Morgan, in his Newton biography, constructed a secrete marriage between Catherine and Halifax to explain the level of the bequest, which now, including the worth of the house, stood at about £25,000, a very large sum indeed. However when Catherine married John Conduitt, a retired soldier, following a whirlwind romance in 1717, she gave her status as spinster and not widow. Newton appeared to have no problems with the bequest, ever a shrewd businessman rather than a moralist, as he assisted Catherine with negotiations with Halifax’s heirs to settle the bequest.

Catherine is also one of two sources for the infamous apple story, the other being William Stukeley, Newton’s personal physician in his later life. Her version of the story appears in her husbands never finished or published memoir of Newton’s life and more importantly, it was she who told the story to Voltaire, who published it and thus started the legend.

Newton spent his last days living with the Conduitts and it fell to Catherine’s husband John to divide up the spoils amongst the various half brothers and sisters and their offspring. These eager to screw as much as possible out of Uncle Isaac’s estate forced Conduitt to sell off Newton’s extensive library of almost 2,000 volumes and wanted him to also sell off Newton’s papers convinced that anything connected with the great man would fetch a good price. Conduitt persuaded them to let the papers be sorted and evaluated for publication and in the end only Newton’s Chronology, an original draft of Principia and his Observations upon the Prophecies were printed and published the rest of his papers becoming the property of Catherine and her husband. After their deaths the papers passed to their daughter Catherine, who married the Hon. John Wallop, Viscount Lymington. Their son became the second Earl of Portsmouth and thus Newton’s papers were passed down through the years by the Portsmouth family who eventually disposed of them in the 1930s, but what became of them then is another story.

Female beauty and glamour are not things that one would normally think of if somebody mentions the name of Isaac Newton, but through the famous witty Mrs Barton these things did indeed play a role in Newton’s later life.








[1] This and all other quotes, as indeed the meat of the story, are all taken from Richard Westfall’s excellent Newton biography Never at Rest


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Aristotle Killer of Science!

Recent times have seen a plague of Aristotle bashing basically accusing him of having held up the progress of science. I’m not sure if this started with Steven Weinberg’s book To Explain the World: The Discovery of Science but its publication and the interviews he gave, in which he forcibly expressed one or other version of this idea, certainly increased the occurrence of this accusation. Recently I stumble across a particular concise and trenchant version and I thought it might be instructive, as a historian of science, to analyse its core claim. As I hope to demonstrate only somebody totally ignorant of Western history could possible claim as, the splendidly named, Fuck Em Up Squanto (@Bro_Pair) did, on Twitter, that:

Aristotle was so smart it took world civilization 2000 years to recover from his disastrous physics ideas

First we need to get his time frame turned into concrete dates. According to Wikipedia, Aristotle lived from 384 to 322 BCE so following his death 2000 years would bring us to 1678 CE. Now most people who believe in a Scientific Revolution would date its commencement, and thus the overthrow of Aristotle’s stranglehold, somewhat earlier. Conventional wisdom dates its start to 1543 and the publication of Copernicus’ De Revolutionibus and Vesalius’ De fabrica. More recently David Wootton was touting the nova of 1572 as kick off point. Let us agree on a compromise date of 1600 CE so we have a claim that Aristotle singlehandedly prevented the invention or discovery (take you pick according to your personal philosophy of science) of physics from 322 BCE until 1600 CE.

The first problem is what exactly Fuck Em Up Squanto means by physics. For Aristotle physics was the study of nature and included much that we would now file under natural history but I assume our intrepid tweeter means something approximating to our modern definition of physics and I shall proceed on this assumption. Aristotle contributed thoughts to three major areas that could today be considered parts of physics, astronomy, optics and dynamics. We will briefly look at each of these and its acceptance in antiquity before marching forward through history to the seventeenth century.

In astronomy Aristotle took over and modified the homocentric theories of Eudoxus. Basically a geocentric model using nested spheres to try and reproduce the real movements of the planets and this was already superceded in antiquity, in the second century CE, by the epicycle and deferent models of Ptolemaeus, although much of Aristotle’s cosmology was, at least nominally, retained, of which more later. This means that any (as we will see, misplaced) blame for Greek astronomy should be addressed to Ptolemaeus and not Aristotle.

In optics we actually have a very interesting situation. Amongst the Greeks there are several competing models to explain sight of which one is Aristotle’s. What is interesting here is that Aristotle’s model is a so-called mediumistic one, that is a connection is built up between the eye and the seen object through the medium of the light and the air and the information that constitutes seeing is transmitted to the eye by vibration. This bears a strong resemblance to the wave theory of light developed by Hooke and Huygens in the seventeenth century. In fact some historians of optics go so far as to see Aristotle as a precursor of his seventeenth century colleges. I personally think this is a step too far but at least one cannot accuse Aristotle of stopping the development of modern physics in the field of optics, rather he was ahead of his times. Actually in the optics competition in antiquity Aristotle’s theory didn’t find many takers, the geometric intromission theories of Euclid, Heron and Ptolemy mostly making the running. Again, nothing to blame Aristotle with here.

It is of course in the field of dynamics, the theory of motion, that we will find to true cause of complaint because it is exactly here that Galileo, Newton et al made the great strides that people hail as the scientific revolution, Galileo’s laws of fall and Newton’s laws of motion. So let us examine Aristotle’s theories and their progress through the two thousand years that separate him from the good old Isaac.

Aristotle’s theories of motion seem rather strange when viewed from a modern standpoint. Firstly he regarded motion as just one form of change, change of place. Other forms of change were growth and decay for example. Considering change just for itself he thought it could be divided into natural motion and violent motion. Natural motion was fall on the earth and the motion of the celestial bodies. Celestial bodies moved naturally in circles, a theory he took over from Empedocles, as did most Greek philosophers. Aristotle’s homocentric astronomy of nested spheres functioned like a giant friction drive system with each sphere driving the sphere inside it. Only the outer most sphere needed a driver, Aristotle’s unmoved mover. On the earth, things dropped fell to the earth because they were returning to their natural place. Implying some sort of low-level animism.

All forms of violent, that is non-natural, motion require a mover, which is where Aristotle’s problems start. Why does something that is thrown continue to move once it has left the throwing hand? Aristotle came up with an explanation of the air opening up in front of the thrown object and closing behind it continue to push the object. He was never very happy with his own solution.

On fall modern commentators tend to mock Aristotle because he said heavy objects fall faster than light ones. Because of Galileo we know better! But we don’t. Galileo’s laws of fall are valid for objects falling in a vacuum. Aristotle’s claims are based on observation in the real world. In fact if you formalise Aristotle’s thoughts on fall, what comes out is very close to Stokes’ laws for fall in a viscous fluid. Air is a viscous fluid.

Aristotle’s theories of motion were not all dominant in antiquity but where just the views of one school of philosophy amongst several. In fact in later antiquity the physics of the Stoics was far more prevalent that that of Aristotle. Around the end of the second century CE Romano-Hellenistic society and culture went into decline and eventually total collapse and with it all forms of intellectual endeavour in Europe. Talk of 2000 years of Aristotelian blockage of science becomes simply ridiculous.

A revival of Greek knowledge began in the Islamic Empire in the eighth century CE. Aristotle’s works were known to the Islamic scholars and highly respected but one cannot speak of any form of total dominance or hindrance of the development of science. The Islamic Empire saw advances in mathematics, medicine, engineering, optics and astronomy.

Around one thousand CE Europe started to again develop an urban civilisation and a thirst for knowledge. In the eleventh and twelfth centuries the so-called translators brought translations into Latin of both the ancient Greek and the more recent Arabic knowledge. At first the Catholic Church, the main centre of learning, was wary of what they saw as heathen knowledge and it was first in the latter part of the thirteenth century that Albertus Magnus and Thomas Aquinas created an acceptable melange of Christian theology and Aristotelian philosophy. Particularly appealing was Aristotle’s unmoved mover whom the equated with the Christian God. It is this that people like Fuck Em Up Squanto are referencing with their objections to Aristotle. However we are now talking about the period thirteen hundred to sixteen hundred that is three hundred not two thousand years! But even here we have to be very careful of our criticism of Aristotle.

As Edward Grant, expert historian of medieval science and religion, quipped (medieval) Aristotelian philosophy was not Aristotle’s philosophy. That is the compromise that Albertus Magnus and Thomas Aquinas created between Christian theology and what the considered to be Aristotelian philosophy differed considerably from the philosophy that Aristotle presented in the fourth century BCE. Another point that Grant makes is that it’s very difficult to actually say what Aristotelian philosophy was as it changes constantly throughout the High Middle Ages. That Aristotelian Philosophy was some sort of unchanging, unchangeable monster cast in concrete by the Catholic Church with an injunction against all forms of inquiry is a myth perpetuated by people who believe in the Draper-White hypothesis of an eternal war between science and religion.

Let us look at a specific example of that process of change; in fact an area that would play a central role in the creation of modern science in the Early modern period, the laws of motion. Already in the sixth century CE John Philoponus criticised Aristotle theory of motion and introduced the concept of impetus. This stated that the thrower imparted a motive force to the thrown object, impetus, which decreases over time till the object stops moving. Via the Islamic thinker Nur ad-Din al-Bitruji in the twelfth century the theory was taken up and elaborated by Jean Buridan in the fourteenth century and through him entered mainstream Medieval thought. The theory of impetus played a central role in the early considerations of both Giambattista Benedetti and Galileo who developed the modern laws of fall. The seventeenth-century theory of inertia, Newton’s first law of motion is in reality a consequent development of the theory of impetus.

Also in the fourteenth century the so-called Oxford Calculatores developed mathematical quantified version of Aristotle’s theories, in particular deriving the mean speed theorem, which lies at the heart of the laws of fall. The Paris physicists took up this work and produced graphical representations of the mean speed theorem identical to the ones presented later by Galileo. To quote historian of mathematics, Clifford Truesdall:

The now published sources prove to us, beyond contention, that the main kinematical properties of uniform accelerated motion, still attributed to Galileo by the physics texts, were discovered and proved by scholars of Merton college…. In principle, the qualities of Greek physics were replaced, at least for motions, by the numerical quantities that have ruled Western science ever since. The work was quickly diffused into France, Italy, and other parts of Europe. Almost immediately, Giovanni di Casale and Nicole Oresme found how to represent the results by geometrical graphs, introducing the connection between geometry and the physical world that became a second characteristic habit of Western thought …

These are medieval scholars working within the Aristotelian tradition not blocking science but furthering it.

The optics that the scholastics inherited from the Islamic Empire was that of Ibn al-Haytham, introduced into Europe in the thirteenth century by Roger Bacon, John Peckham and Witelo, and not that of Aristotle. This European version of al-Haytham’s optics laid the basis on which Kepler and others developed modern optics in the seventeenth century. This optics formed a central part of the medieval university science curriculum, no obstruction from Aristotle here.

As already stated above the geocentric astronomy inherited by the medieval universities was that of Ptolemaeus and not Aristotle’s. On the whole during the period leading up to Copernicus whenever Ptolemaic astronomy clashed with Aristotelian cosmology, the astronomers had little problem abandoning Aristotle’s thought in favour of mathematical observation. The period between fourteen hundred and sixteenth hundred saw a steady modification and improvement in Ptolemaic astronomy. Copernicus’ work was part of a general programme of improvement and not some sort of rebellion against an unchanging or unchangeable orthodoxy. That Copernicus’ ideas were not accepted immediately lies in their inherent scientific problems and not some sort of rejection for being heterodox.

Although the above is fairly superficial I hope that I have made clear that the claim that Aristotle’s ideas were detrimental for the development of science for two thousand years in quite simply historical rubbish.










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A misleading book title that creates the wrong impression

A new biography of Johannes Kepler has just appeared and although I haven’t even seen it yet, let alone read it, it brings out the HistSci Hulk side of my personality. What really annoys me on David Love’s book, Kepler and the Universe[1], is the title or rather the subtitle, How One Man Revolutionised Astronomy. Now, I for one have for many years conducted a private campaign to persuade people not to claim that we live in a Copernican Cosmos, a standard cliché, but that we live in a Keplerian Cosmos, because it was the very different elliptical system of Kepler that helped heliocentricity to its breakthrough and not the system of Copernicus. However Love’s subtitle immediately evokes the spectre of the lone genius and for all his undoubted brilliance Kepler was not a lone genius and especially not in terms of his cosmology/astronomy.

A 1610 portrait of Johannes Kepler by an unknown artist Source: Wikipedia Commons

A 1610 portrait of Johannes Kepler by an unknown artist
Source: Wikipedia Commons

Even a cursory examination of Kepler’s road to his system will immediately reveal his intellectual debts and his co-conspirators, both willing and unwilling. First off is naturally Copernicus himself. Kepler did not conceive a heliocentric system from scratch but was, on his own admission a glowing admirer or even acolyte of the Ermländer scholar. This admiration is one of the principle reasons that we don’t truly acknowledge Kepler’s achievement but tend to dismiss it as having just dotted the ‘Is’ and crossed the ‘Ts’ in Copernicus’ system, a demonstrably false judgement. Kepler, of course, didn’t help the situation when he titled the most simple and readable version of his system, and the one that together with the Rudolphine Tables had the most influence, the Epitome Astronomiae Copernicanae. Not a smart move! Whatever, we are already at two men who revolutionised astronomy.

Nicolaus Copernicus 1580 portrait (artist unknown) in the Old Town City Hall, Toruń Source: Wikimedia Commons

Nicolaus Copernicus 1580 portrait (artist unknown) in the Old Town City Hall, Toruń
Source: Wikimedia Commons

Kepler did not discover Copernicus himself but was introduced to him by his teacher Michael Maestlin at the University of Tübingen. Usually Maestlin gets mentioned in passing as Kepler’s teacher and then forgotten but he played a very important role in Kepler’s early development. In reality Maestlin was himself one of the leading European astronomers and mathematicians in the latter part of the sixteenth century, as well as being by all accounts an excellent teacher. He was also one of the very few supporters of both Copernican astronomy and cosmology. This meant that he gave Kepler probably the best foundation in the mathematical sciences that he could have found anywhere at the time, as well as awakening his interest in Copernican thought. It was also Maestlin who decided Kepler would be better off becoming a teacher of mathematics and district mathematician rather than training for the priesthood; a decision that Kepler only accepted very, very reluctantly. Even after he had left Tübingen Maestlin continued to support the young Kepler, although he would withdraw from him in later years. Maestlin edited, corrected and polished Kepler’s, so important, first publication, the Mysterium Cosmographicum. In fact Maestlin’s contributions to the finished book were so great he might even be considered a co-author. Some people think that in later life Kepler abandoned the, for us, rather bizarre Renaissance hypothesis of the Cosmographicum, but he remained true to his initial flash of inspiration till the very end, regarding all of his later work as just refinements of that first big idea. Maestlin’s contribution to the Keplerian system was very substantial. And then there were three.

Michael Maestlin Source: Wikimedia Commons

Michael Maestlin
Source: Wikimedia Commons

Tycho! Without Tycho Brahe there would be no Keplerian System. Tycho and Kepler are the Siamese twins of elliptical astronomy joined at the astronomical data. Without Tycho’s data Kepler could never have built his system. This duality is recognised in many history of astronomy texts with the two, so different, giants of Renaissance astronomy being handled together. The popular history of science writer, Kitty Ferguson even wrote a dual biography, Tycho and Kepler, The Unlikely Partnership that Forever Changed our Understanding of the Heavens[2], a title that of course contradicts Love’s One Man. Her original title was The Nobleman and His Housedog, with the rest as a subtitle, but it seems to have been dropped in later editions of the book. The ‘housedog’ is a reference to Kepler characterising himself as such in the horoscope he wrote when he was twenty-five years old.

Portrait of Tycho Brahe (1596) Skokloster Castle Source: Wikimedia Commons

Portrait of Tycho Brahe (1596) Skokloster Castle
Source: Wikimedia Commons

Tycho invited Kepler to come and work with him in Prague when the Counter Reformation made him jobless and homeless. Tycho welcomed him back when Kepler went off in a huff at their first meeting. It was Tycho who assigned him the task of calculating the orbit of Mars that would lead him to discover his first two laws of planetary motion. It has been said that Tycho’s data had just the right level of accuracy to enable Kepler to determine his elliptical orbits. Any less accurate and the slight eccentricities would not have been discernable. Any more accurate and the irregularities in the orbits, thus made visible, would have made the discovery of the elliptical form almost impossible. It has also been said that of all the planets for which Tycho had observation data Mars was the one with the most easily discernable elliptical orbit. Serendipity seems to have also played a role in the discovery of Kepler’s system. The high quality of Tycho’s data also led Kepler to reject an earlier non-elliptical solution for the orbit of Mars, which another astronomer would probably have accepted, with the argument that it was not mathematically accurate enough to do honour to Tycho’s so carefully acquired observational data.

Tycho was anything but a one-man show and his observatory on the island of Hven has quite correctly been described as a research institute. A substantial number of astronomer, mathematicians and instrument maker came and went both on Hven and later in Prague over the almost thirty years that Tycho took to accumulate his data. The number of people who deserve a share in the cake that was Kepler’s system now reaches a point where it become silly to count them individually.

Our list even includes royalty. Rudolph II, Holly Roman Emperor, was the man, who, at Tycho’s request, gave Kepler a position at court, even if he was more than somewhat lax at paying his salary, official to calculate the Rudolphine Tables, a task that would plague Kepler for almost thirty years but would in the end lead to the acceptance of his system by other astronomers. Rudolph also appointed Kepler as Tycho’s successor, as Imperial Mathematicus, after the latter’s untimely death, thus giving him the chance to continue his analysis of Tycho’s data. Rudolph could just as easily have sacked him and sent him on his way. Tycho’s heirs did not assist Kepler in his struggle to maintain access to that all important data, which belonged to them and not the Emperor, causing him much heartache before they finally allowed him to use Tycho’s inheritance. After he had usurped his brother, Rudolph, in 1612, Matthias allowed Kepler to keep his official position and title as Imperial Mathematicus, although sending him away from court, a fact that certainly assisted Kepler in his work. Being Imperial Mathematicus gave him social status and clout.

Rudolph II portrait by Joseph Heinz the Elder Source: Wikimedia Commons

Rudolph II portrait by Joseph Heinz the Elder
Source: Wikimedia Commons

Kepler described his long and weary struggles with the orbit of Mars as a battle, but he did not fight this battle alone. In a long and fascinating correspondence with the astronomer, David Fabricius, Kepler tried out his ideas and results with a convinced supporter of Tycho’s system. Kepler would present his ideas and David Fabricius subjected them to high level and very knowledgeable criticism. Through this procedure Kepler honed, refined and polished his theories to perfection before he submitted them to public gaze in his Astronomia Nova, Knowing that they would now withstand high-level professional criticism. David Fabricius, who never met Kepler, nevertheless took a highly active role in the shaping of the Keplerian system[3].

Monument for David and Johann Fabricius in the Graveyard of Osteel

Monument for David and Johann Fabricius in the Graveyard of Osteel

Even after Kepler’s death the active participation of others in shaping his astronomical system did not cease. Jeremiah Horrocks corrected and extended the calculations of the Rudolphine Tables, enabling him to predict and observe a transit of Venus, an important stepping-stone in the acceptance of the elliptical astronomy. Horrocks also determined that the moon’s orbit was a Keplerian ellipse, something that Kepler had not done.


Stained glass roundel memorial in Much Hoole Church to Jeremiah Horrocks making the first observation and recording of a transit of Venus in 1639. The Latin reads "Ecce gratissimum spectaculum et tot votorum materiem": "oh, most grateful spectacle, the realization of so many ardent desires". It is taken from Horrocks's report of the transit

Stained glass roundel memorial in Much Hoole Church to Jeremiah Horrocks making the first observation and recording of a transit of Venus in 1639. The Latin reads “Ecce gratissimum spectaculum et tot votorum materiem”: “oh, most grateful spectacle, the realization of so many ardent desires”. It is taken from Horrocks’s report of the transit

Cassini, together with Riccioli and Grimaldi, using a heliometer determined that either the orbit of the sun around the earth or the earth around the sun, the method can’t determine which is true, is an ellipse another important empirical stepping-stone on the road to final acceptance for the system.

Giovanni Cassini Source: Wikimedia Commons

Giovanni Cassini
Source: Wikimedia Commons

Nicholas Mercator produced a new mathematical derivation of Kepler’s second law around 1670. Kepler’s own derivation was, as he himself admitted, more than a little suspect, viewed mathematically. The first and third laws had been accepted by the astronomical community fairly easily but the second law was a major bone of contention. Mercator’s new derivation basically laid the dispute to rest.

Cassini in his new role as director of the Paris observatory showed empirically that the satellite systems of both Jupiter and Saturn also obeyed Kepler’s third law extending it effectively to all orbitary systems and not just the planets of the solar system.

Lastly Newton derived Kepler’s first and second laws from his axiomatic system of dynamics giving them the true status of laws of physics. This led Newton to claim that the third law was Kepler’s but the first two were his because he, as opposed to Kepler, had really proved them

As we can see the list of people involved in revolutionising astronomy in the seventeenth century in that they replaced all the geocentric systems with a Keplerian elliptical system is by no means restricted to ‘one man’ as claimed in the subtitle to David Love’s book but is quite extensive and very diverse. There are no lone geniuses; science is a collective, collaborative enterprise.





[1] David Love, Kepler and the Universe: How One Man Revolutionized Astronomy, Prometheus Books, 2015

[2] Kitty Ferguson, Tycho and Kepler, The Unlikely Partnership that Forever Changed our Understanding of the Heavens, Walker Books, 2002

[3] For a wonderful description of this correspondence and how it contributed to the genesis of Astronmia Nova see James Voelkel’s excellent, The Composition of Kepler’s Astronomia nova, Princeton University Press, 2001


Filed under History of Astronomy, Myths of Science, Uncategorized

Let the debate begin!

David Wootton, whose new book The Invention of Science I featured recently on my list of books I have to, and want to, find time to read, was on the BBC’s flagship news magazine, Today, this morning talking about his book (starts at about 49.20 mins). Wootton started off his short slot by denying the ancient Greeks any form of scientific status and joining the, in the mean time fashionable, chorus of those slagging off Aristotle. Another notable member of this particular chorus being Steven Weinberg in his recent To Explain the World: The Discovery of Modern Science. He then went on to claim that the medieval scholars only discussed problems without end but didn’t achieve any resolution or progress; a claim that certainly had Pierre Duhem, Alistair Crombie and David C. Lindberg all rotating violently in their graves. Wootton thinks that science only starts after Columbus discovered America, thereby introducing the concept of discovery into intellectual discourse and according to the flyleaf of his book, the first discovery or change introducing the scientific age was Tycho’s observation of the nova in 1572.

Wootton’s book is a highly explosive grenade lobbed into the middle of the revolution contra gradualism debate at a time when the gradualists are very much in ascendance, within the history of science community. Those on the revolution side will eagerly clutch his good points, and I’m sure they are there in abundance, in order to shore up their sagging positions, whilst the gradualists will be forced to sharpen up their arguments to refute Wootton’s thesis of a reinstated Scientific Revolution.

I for one, a declared gradualist, welcome the conflict as it can only serve to bolster the history of science as a discipline. As I quoted Frank McDonough in a recent edition of Whewell’s Gazette, “The role of the historian is to move the debate forward, no more, no less”. So, let the debate begin.


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