The Earth was definitely not flat in the Middle Ages

Gossuin de Metz L'image du monde

Gossuin de Metz L’image du monde

 

One of my most recent posts concerned the myth that people in the Middle Ages believed the world to be flat. Tim O’Neill, friend of the Renaissance Mathematicus, guest poster and frequent commentator, also added interesting comments to that post. Now he has gone one better and written an extensive blog post of his own on the subject on his History for Atheists website, The New Atheists Bad History Guide 1: The Medieval Flat Earth. Much more wide ranging and informative than my own brief rant it is definitely worth reading, so get on over there and do just that.

 

 

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Galileo Super Star – Galileo Galilei to get Hollywood biopic

My attention was drawn recently to a Hollywood gossip website that announced that a movie is to be made of a play by Richard Goodwin about Galileo, The Hinge of the World. I must admit that my curiosity was piqued, not least because I had never heard of either Mr Goodwin or his play and I naturally wondered what his line on the Tuscan mathematicus would be. It turns out that Richard Goodwin is a former high power Washington political advisor and speechwriter who served Presidents Kennedy and Johnson as well as JFK’s brother Robert, not exactly the best qualifications for the author of a play about the history of science. My doubts about this particular production were only heightened upon reading the full original title of the play, The Hinge of the World: In Which Professor Galileo Galilei, Chief Mathematician and Philosopher to His Serene Highness the Grand Duke of Tuscany, and His Holiness Urban VIII, Bishop of Rome, Battle for the Soul of the World. This title does not bode well for a historically accurate account of Galileo’s clash with the Catholic Church. However I will reserve judgement, because as I say, I do not know the play. I have however ordered a second hand copy that is at this very moment wending its way from some distant land to my humble abode and when it arrives and I have perused it with due diligence, I will report back with a critical assessment.

A scene from the stage production of The Hinge of the World

A scene from the stage production of The Hinge of the World

The website report does however offer a précis of the contents of the soon to be film and this is possibly the most confused and inaccurate presentation of the affair and the events leading up to it that I have read in a very long time:

The film will stay true to the spirit of the play in that it will revolve around the one-time friends whose vehement disagreements led to the Church calling Galileo out for heresy when science started to challenge long-held beliefs.

Science had been challenging long held beliefs long before Galileo came along. Apart from anything else Galileo was tried for defending the truth of Copernicus’ heliocentric hypothesis and Copernicus had died twenty-one years before Galileo was born. Just for the record Copernicus was also by no means the first person to present science that challenged the Church’s long-held beliefs.

Just to be a little bit pedantic, the one-time friends, Galileo and Maffeo Barberini (Pope Urban VIII) only had one vehement disagreement.

During that time, around 1610, the Church was never questioned,…

Somebody really ought to have consulted a historian of the Catholic Church. People both inside and outside of the Church questioned it continuous, some with impunity, for example Galileo’s friend Paolo Sarpi, and some with dire consequences, such as Giordano Bruno.

…yet Galileo who had a passion, curiosity and a telescope started to question everything after logging what he was learning through his scientific research. He published much of his findings in a book that were disavowed by Pope Urban VIII and the Catholic Church. Despite delving into dangerous territory, Galileo continued his research into comets, tide movements until he was ultimately ordered by the Church to stop teaching his ideas.

 The above is just a historical train wreck. The book of Galileo’s disavowed by Urban VII and the Church was the Dialogue Concerning the Two Chief World Systems, published in 1632, which led directly to his trail and imprisonment in 1633. However, he was told to stop teaching the truth of the heliocentric hypothesis and only that, the rest of his ideas were not the subject of Church condemnation, in 1616 following the semi-public distribution of the so-called Letter to Castelli, much later published in expanded form, as the Letter to the Grand Duchess Christina. Also in 1616 Paul V was Pope and Maffeo Barberini was a mere Cardinal and still a good friend of Galileo’s.

 The brilliant scientist, engineer, physicist and mathematician who helped discover the law of the pendulum (which became the basis for modern-day clocks), who pushed scientists to conduct experiments to prove theorems, who continued the work of Nicolaus Copernicus to help understand our own universe and laid the groundwork for modern astronomy eventually lost his battle with the powerful Roman Catholic Church.

Again being somewhat pedantic, Galileo got the law of the pendulum wrong and modern day clocks stopped being pendulum driven some time ago. Also, and this is not so pedantic, it was Kepler, and not Galileo, who laid the groundwork for modern astronomy.

 He was tried for heresy and sentenced to imprisonment at the age of 68 where he would remain until his death nine years later at age 77.

A final point, that people love to forget because it rather spoils the image of Galileo the martyr, his sentence of imprisonment imposed for vehement suspicion of heresy, not heresy, was instantly commuted to house arrest, which whilst somewhat restrictive was by no means harsh.

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All of this ties in rather nicely with an exchange that I took part in yesterday evening on twitter. Tim Skellet (@Gurdur) asked me and others, “what’s the very best, most comprehensive bio of Galileo, please?” My answer was, “I don’t think it exists. Read several: Wootton, Heilbron, Biagioli, Shea/Artigas.” I was not trying to be clever or awkward. I genuinely believe that if you wish to study any major figure out of the history of science then you should consult multiple sources, as all sources have their advantages and disadvantages. History is, to a large extent, a game of interpretation. There are facts but they only give a partial picture and it is the role or responsibility of the historian to complete that picture to the best of their ability. All historians have agendas and biases and to obtain a rounded picture it is always advisable to view the facts through the eyes of more than one historian.

Turning to the special case of Galileo, the two most recent complete biographies are J. L. Heilbron’s Galileo (OUP, 2010) and David Wootton’s Galileo: Watcher of the Skies (Yale University Press, 2010). Both are very good but differ in their interpretations and emphases. I wouldn’t recommend one over the other, so if you only want to read one then toss a coin or something. If you really want to get to grips with Galileo then read both. One important aspect of Wootton’s book is that he systematically dismantles the myth that Galileo was a good devout Catholic. This myth is trotted out regularly to make the Church look even worse for having persecuted him. Wootton demonstrates, I think convincingly, that Galileo was at best an indifferent Catholic and in no way the devout son of the Church that historical myth has made him out to be.

Although not a complete biography in the traditional sense I would also strongly recommend Mario Biagioli’s Galileo Courtier: The Practice of Science in the Culture of Absolutism (University of Chicago Press, 1993) Biagioli examines Galileo the social climber who uses his scientific discoveries to further his social status rather than for any idealistic belief in truth. Biagioli’s work is a useful complement to the more conventional scientific style of biography; what did Galileo discover and when. In what is effectively a second volume to his first book, Galileo’s Instruments of Credit: Telescopes, Images, Secrecy (University of Chicago Press, 2006), Biagioli explains how Galileo used the telescopes that he manufactured and the images that he produced to broker social advantages.

William R. Shea’s and Mariano Artigas’ Galileo in Rome: The Rise and Fall of a Troublesome Genius (OUP; 2003) just deals with the six extended visits that Galileo made to Rome, the home-base of the Church and the centre of political and social power in the period, during his lifetime. These include, his triumphal visit in 1611, as the author of his sensational Sidereus Nuncius, his visit in 1615-1616 and his failed attempt to prevent the Church condemning heliocentricity and finally his summons to his trial in 1633. By concentrating only on Galileo’s interactions with the Roman culture of the period the authors succeed in shedding light from a different angle on Galileo’s fateful path to his condemnation and fall.

At some point David Wootton joined the Twitter discussion and he recommended Pietro Redondi’s Galileo Heretic (Princeton University Press, 1992), a recommendation that I would one hundred pro cent endorse. Although Redondi’s central thesis, that Galileo was actually attacked by the Church for his atomism has, in the meantime, been largely refuted this is a superb book and still very much worth reading by anyone who wishes to learn about Galileo and the culture in which he lived and worked.

If you read all of the books that I have recommended above you should, by the time you have finished, have a fairly good all round picture of the life and work of Galileo Galilei and the footnotes and bibliographies will have given you lots of information for further reading. I will however close with a warning, do not read Michael White’s Galileo Antichrist: a Biography (Weidenfeld & Nicolson, 2007). I can deliver a comprehensive and profound review of White’s book in three words, “It is crap!”

 

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Repeat after me! – They knew it was round, damn it!

Last week saw various reports about a rare stolen copy of a Columbus letter that had turned up in the Library of Congress and has now been restored to its Italian owners; a comparatively happy end to one of a series of recent stories about the theft of precious books and documents from archives and libraries. Unfortunately the report on the website of NPR (that’s National Public Radio a non-commercial public American educational radio network) opened with the following paragraph:

The heist of a major historical document apparently went undiscovered for more than 20 years. Now, a stolen letter from Christopher Columbus spreading the news that the world isn’t flat has been returned from the U.S. to Italy.

As some readers might already have guessed the second sentence, specifically the phrase spreading the news that the world isn’t flat, had me screaming and banging my head against the wall to relieve the pain. This is just horrendously wrong in several different ways.

Posthumous portrait of Christopher Columbus by Sebastiano del Piombo, 1519. There are no known authentic portraits of Columbus. Source: Wikimedia Commons

Posthumous portrait of Christopher Columbus by Sebastiano del Piombo, 1519. There are no known authentic portraits of Columbus.
Source: Wikimedia Commons

On his first voyage Columbus set sail from Spain in September 1492 and after approximately a month of sailing westward he landed on a set of previous unknown islands, unknown to the Europeans that is. This voyage proves or disproves absolutely nothing about the shape of the earth. To even contemplate a voyage proving the earth to be spherical and not flat we would have to fast forward thirty years to the return to Spain of the one ship and eighteen men from Ferdinand Magellan’s disastrous circumnavigation in 1522; just for the record Magellan was not one of the eighteen survivors, so to call him the first man to circumnavigate the world, as many people do, is simply false. Some flat-earthers could, and probably do/did, argue that Magellan’s fleet just sailed round in a circle on a flat disc and not around a spherical earth so even that is not a totally convincing proof (even if the objection is somewhat iffy).

Let us return to the good Cristoforo. One could argue that he set sail westward to reach the Spice Islands, instead of heading to the east, as was normal because he believed the earth to be a sphere and also believed that that sphere was small enough that the route west to the Spice Islands was shorter and thus quicker than the route east (A belief, as it turns out, that was based on faulty calculation, of which more later). Having reached what he erroneously believed to be the Spice Islands, leading to the equally erroneous name, the West Indies, he believed that he had proved the world to be spherical. There is however a fundamental flaw in this argument. Columbus did not sail westward because he believed the earth to be a sphere; he did so because he, like almost every other educated European, knew that it was a sphere, knowledge that had been part of the European cultural heritage for the best part of two thousand years.

This should in the meantime be well known, but for those, like the NPR reporter(s), who have been sitting at the back and not paying attention let us pass review over those two thousand years.

We have no direct records but latter authors tell us that the Pythagoreans in the sixth century BCE already accepted that the earth was spherical. Their reasons for doing so are unknown but it was possible in analogy to the celestial sphere of the so-called fixed stars. If you look up into the heavens on a clear dark night the sky appears to take the form of an inverted bowl or hemisphere. By the latest in the fourth century BCE, Aristotle, who would go on to have a massive influence on European intellectual history, knew that the earth was spherical and he offers up a series of empirical proofs for this claim. For example he wrote, “there are stars seen in Egypt and […] Cyprus which are not seen in the northerly regions.” Since this could only happen on a curved surface, he too believed Earth was a sphere “of no great size, for otherwise the effect of so slight a change of place would not be quickly apparent.” (De caelo, 298a2–10). He also pointed out that the shadow of the earth on the moon during a lunar eclipse is circular. Following Aristotle all Greek schools of philosophy accepted that the earth was spherical and following them the Romans. There was no doubt in the classical world that the earth was a sphere. Ptolemaeus, the most influential Greek astronomer, brought a series of arguments and proofs for the spherical form of the earth in his Syntaxis Mathematiké (Almagest) in the second century CE. Most notably that as ships approach over the horizon one sees the top of the mast before one sees the hull.

A lot of this specific knowledge got temporarily lost within Europe in the Early Middle Ages but still almost nobody who was educated doubted that the earth was a sphere. With the rise of the Islamic empire the astronomers writing in Arabic adopted the views of Aristotle and Ptolemaeus including the spherical form of the earth.

Back in the third century BCE the astronomer mathematician Eratosthenes from Alexandria determined the size of the sphere using the angle of the sun’s shadow and a bit of basic trigonometry. He achieved a fairly accurate result, its accuracy depends on which Stadia (an ancient measure of length) you think he used; we don’t know for certain. Other geographers and astronomers also determined the size of the earth’s sphere; all arriving at reasonable ball park figures. Ptolemaeus, in his Geōgraphikḕ (Geography) also determined that the known land area the oikoumenè, Europe, Africa and Asia, stretched over 180° of the earth’s surface from east to west.

In the High Middle Ages, Europe regained this knowledge, largely via the Islamic Empire through Spain and Sicily. The standard European university astronomy text Johannes de Sacrobosco’s De sphaera mundi, written in the twelfth century CE, contained all the standard Greek arguments for a spherical earth including the lunar eclipse shadow, ship breasting the horizon and the change in visible asterism travelling from south to north. There existed no doubt amongst the educated in the Middle Ages that the earth was a sphere.

Picture from a 1550 edition of De sphaera, showing the earth to be a sphere. Source: Wikimedia Commons

Picture from a 1550 edition of De sphaera, showing the earth to be a sphere.
Source: Wikimedia Commons

When Columbus started making his plans at the end of the fifteenth century he knew that the world was a sphere, as did all of the people he tried to get to back his scheme. The only disputed point was how big the earth’s sphere was, how long the central landmass, Europe, Africa and Asia, was and thus how far the Spice Islands were if one sailed west from Europe. It was here that Columbus made some fundamental calculating errors. The Arabic astronomer al-Farghānī gave 5623 Arabic miles (being 111.8 km) as the length of one degree of longitude, whereas Ptolemaeus gave 6023 Roman miles (being 89.7 km). Columbus took al-Farghānī’s figure but multiplied it with the length of a Italian mile (much shorter than the Arabic one) to determine the circumference of the earth thus arriving at a figure that was far too small: approx. 25,255 km instead of al-Farghānī’s very accurate figure of 40,248 km. Ptolemaeus’ estimate of the spread of the main landmass was 180°, whereas it is in fact only about 130°. Columbus however took the even more inaccurate estimate of Marius from Tyre of 225°. The sum of these error meant that Columbus thought he only had about 3,700 km from the Canary Islands to Japan instead of the real 19,600 km! Having convinced his sponsors of the correctness of his calculations he set sail. If America had not been in the way Columbus and his entire crew would have stared starved to death on the open ocean.

So where does the myth of the flat earth come from? There were a few European scholars in antiquity and the early Middle Ages who, against the evidence, still argued that the earth was flat. However none of them enjoyed much support. One of the ironies of history is that Copernicus probably drew attention to the most famous of them, the third century cleric Lucius Caecilius Firmianus Lactantius, by mentioning him in his De revolutionibus. The real myth of the medieval flat earth begins first in the eighteenth and nineteenth centuries and has two principal sources. Probably the most influential of these was the American author Washington Irving who in his fictional biography of Columbus claimed that Columbus had to fight against the Church’s belief that the world was flat in order to get permission and backing for his voyage, a complete fabrication. This falsehood was supported by the nineteenth centuries false interpretation of the medieval T and O Mappa Mundi.

The Hereford Mappa Mundi, about 1300, Hereford Cathedral, England. Source: Wikimedia Commons

The Hereford Mappa Mundi, about 1300, Hereford Cathedral, England.
Source: Wikimedia Commons

These medieval world maps were in the form of a circle, the O, with the three known continents, Europe, Africa and Asia, displayed in the form of a T with east at the top. These maps were interpreted in the nineteenth century as indicating that the medieval cartographers believed the earth to be a flat disc. This is not without irony as they were circular in order to indicate that the world in a sphere. The myth of the flat medieval world was taken up by two figures well known to readers of this blog John William Draper (1811–1882) and Andrew Dickson White (1832–1918) in their widespread myth of the eternal war between religion and science. Science believing in a spherical earth whereas the reactionary Church believed in a flat one.

That Europe in the Middle Ages believed in a flat earth is a total myth that just doesn’t seem to want to die. The next time somebody tells you that the medieval Church thought the world was flat, or that Columbus was a revolutionary for believing in a spherical earth or any other version of this nonsense, do me a favour, take a large, heavy, flat, round, metal object, such as a frying pan, and beat them around the head with it.

 

 

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Bertrand Russell did not write Principia Mathematica

Yesterday would have been Bertrand Russell’s 144th birthday and numerous people on the Internet took notice of the occasion. Unfortunately several of them, including some who should know better, included in their brief descriptions of his life and work the fact that he was the author of Principia Mathematica, he wasn’t. At this point some readers will probably be thinking that I have gone mad. Anybody who has an interest in the history of modern mathematics and logic knows that Bertrand Russell wrote Principia Mathematica. Sorry, he didn’t! The three volumes of Principia Mathematica were co-authored by Alfred North Whitehead and Bertrand Russell.

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Now you might think that I’m just splitting hairs but I’m not. If you note the order in which the authors are named you will observe that they are not listed alphabetically but that Whitehead is listed first, ahead of Russell. This is because Whitehead being senior to Russell, in both years and status within the Cambridge academic hierarchy, was considered to be the lead author. In fact Whitehead had been both Russell’s teacher, as an undergraduate, and his examiner in his viva voce, where he in his own account gave Russell a hard time because he knew that it was the last time that he would be his mathematical superior.

Alfred North Whitehead

Alfred North Whitehead

Both of them were interested in metamathematics and had published books on the subject: Whitehead’s A Treatise on Universal Algebra (1898) and Russell’s The Principles of Mathematics (1903). Both of them were working on second volumes of their respective works when they decided to combine forces on a joint work the result of the decision being the monumental three volumes of Principia Mathematica (Vol. I, 1910, Vol. II, 1912, Vol. III, 1913). According to Russell’s own account the first two volumes where a true collaborative effort, whilst volume three was almost entirely written by Whitehead.

Bertrand Russell 1907 Source: Wikimedia Commons

Bertrand Russell 1907
Source: Wikimedia Commons

People referring to Russell’s Principia Mathematica instead of Whitehead’s and Russell’s Principia Mathematica is not new but I have the feeling that it is becoming more common as the years progress. This is not a good thing because it is a gradual blending out, at least on a semi-popular level, of Alfred Whitehead’s important contributions to the history of logic and metamathematics. I think this is partially due to the paths that their lives took after the publication of Principia Mathematica.

The title page of the shortened version of the Principia Mathematica to *56 Source: Wikimedia Commons

The title page of the shortened version of the Principia Mathematica to *56
Source: Wikimedia Commons

Whilst Russell, amongst his many other activities, remained very active at the centre of the European logic and metamathematics community, Whitehead turned, after the First World War, comparatively late in life, to philosophy and in particular metaphysics going on to found what has become known as process philosophy and which became particularly influential in the USA.

In history, as in academia in general, getting your facts right is one of the basics, so if you have occasion to refer to Principia Mathematica then please remember that it was written by Whitehead and Russell and not just by Russell and if you are talking about Bertrand Russell then he was co-author of Principia Mathematica and not its author.

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Isaac and the apple – the story and the myth

The tale of Isaac Newton and the apple is, along with Archimedes’ bath time Eureka-ejaculation and Galileo defiantly mumbling ‘but it moves’ whilst capitulating before the Inquisition, is one of the most widely spread and well known stories in the history of science. Visitors to his place of birth in Woolsthorpe get to see a tree from which the infamous apple is said to have fallen, inspiring the youthful Isaac to discover the law of gravity.

The Woolsthorpe Manor apple tree Source:Wikimedia Commons

The Woolsthorpe Manor apple tree
Source:Wikimedia Commons

Reputed descendants of the tree exist in various places, including Trinity College Cambridge, and apple pips from the Woolsthorpe tree was taken up to the International Space Station for an experiment by the ‘first’ British ISS crew member, Tim Peake. Peake’s overalls also feature a Principia patch displaying the apple in fall.

Tim Peake's Mission Logo

Tim Peake’s Mission Logo

All of this is well and good but it leads automatically to the question, is the tale of Isaac and the apple a real story or is it just a myth? The answer is that it is both.

Modern historians of Early Modern science tend to contemptuously dismiss the whole story as a myth. One who vehemently rejects it is Patricia Fara, who is an expert on Newtonian mythology and legend building having researched and written the excellent book, Newton: The Making of Genius[1]. In her Science: A Four Thousand Year History she has the following to say about the apple story[2]:

More than any other scientific myth, Newton’s falling apple promotes the romantic notion that great geniuses make momentous discoveries suddenly and in isolation […] According to simplistic accounts of its [Principia’s] impact, Newton founded modern physics by introducing gravity and simultaneously implementing two major transformations in methodology: unification and mathematization. By drawing a parallel between an apple and the Moon, he linked an everyday event on Earth with the motion of the planets through the heavens, thus eliminating the older, Aristotelian division between the terrestrial and celestial realms.

[…]

Although Newton was undoubtedly a brilliant man, eulogies of a lone genius fail to match events. Like all innovators, he depended on the earlier work of Kepler, Galileo, Descartes and countless others […]

[…]

The apple story was virtually unknown before Byron’s time. [Fara opens the chapter with a Byron poem hailing Newton’s discovery of gravity by watching the apple fall].

Whilst I would agree with almost everything that Fara says, here I think she is, to quote Kepler, guilty of throwing out the baby with the bath water. But before I explain why I think this let us pass review of the myth that she is, in my opinion, quite rightly rejecting.

The standard simplistic version of the apple story has Newton sitting under the Woolsthorpe Manor apple tree on a balmy summer’s day meditation on mechanics when he observes an apple falling. Usually in this version the apple actually hits him on the head and in an instantaneous flash of genius he discovers the law of gravity.

This is of course, as Fara correctly points out, a complete load of rubbish. We know from Newton’s notebooks and from the draughts of Principia that the path from his first studies of mechanics, both terrestrial and celestial, to the finished published version of his masterpiece was a very long and winding one, with many cul-de-sacs, false turnings and diversions. It involved a long and very steep learning curve and an awful lot of very long, very tedious and very difficult mathematical calculations. To modify a famous cliché the genius of Principia and the theories that it contains was one pro cent inspiration and ninety-nine pro cent perspiration.

If all of this is true why do I accuse Fara of throwing out the baby with the bath water? I do so because although the simplistic story of the apple is a complete myth there really was a story of an apple told by Newton himself and in the real versions, which differ substantially from the myth, there is a core of truth about one step along that long and winding path.

Having quoted Fara I will now turn to, perhaps Newton’s greatest biographer, Richard Westfall. In his Never at Rest, Westfall of course addresses the apple story:

What then is one to make of the story of the apple? It is too well attested to be thrown out of court. In Conduitt’s version one of four independent ones, …

Westfall tells us that the story is in fact from Newton and he told to on at least four different occasions to four different people. The one Westfall quotes is from John Conduitt, who was Newton’s successor at the Royal Mint, married his niece and house keeper Catherine Barton and together with her provided Newton with care in his last years. The other versions are from the physician and antiquarian William Stukeley, who like Newton was from Lincolnshire and became his friend in the last decade of Newton’s life, the Huguenot mathematician Abraham DeMoivre, a convinced Newtonian and Robert Greene who had the story from Martin Folkes, vice-president of the Royal Society whilst Newton was president. There is also an account from Newton’s successor as Lucasian professor, William Whiston, that may or may not be independent. The account published by Newton’s first published biographer, Henry Pemberton, is definitely dependent on the accounts of DeMoivre and Whiston. The most well known account is that of Voltaire, which he published in his Letters Concerning the English Nation, London 1733 (Lettres philosophiques sur les Anglais, Rouen, 1734), and which he says he heard from Catherine Conduitt née Barton. As you can see there are a substantial number of sources for the story although DeMoivre’s account, which is very similar to Conduitt’s doesn’t actually mention the apple, so as Westfall says to dismiss it out of hand is being somewhat cavalier, as a historian.

To be fair to Fara she does quote Stukeley’s version before the dismissal that I quoted above, so why does she still dismiss the story. She doesn’t, she dismisses the myth, which has little in common with the story as related by the witnesses listed above. Before repeating the Conduitt version as quoted by Westfall we need a bit of background.

In 1666 Isaac, still an undergraduate, had, together with all his fellow students, been sent down from Cambridge because of an outbreak of the plague. He spent the time living in his mother’s house, the manor house in Woolsthorpe, teaching himself the basics of the modern terrestrial mechanics from the works of Descartes, Huygens and the Salisbury English translation of Galileo’s Dialogo. Although he came nowhere near the edifice that was the Principia, he did make quite remarkable progress for a self-taught twenty-four year old. It was at this point in his life that the incident with the apple took place. We can now consider Conduitt’s account:

In the year 1666 he retired again from Cambridge … to his mother in Lincolnshire & whilst he was musing in a garden it came to his thought that the power of gravity (wch brought an apple from the tree to the ground) was not limited to a certain distance from the earth but that this power must extend much further than was normally thought. Why not as high as the moon said he to himself & if so that must influence her motion & and perhaps retain her in her orbit, where-upon he fell to calculating what would be the effect of this supposition but being absent from books & taking common estimate in use among Geographers & our seamen before Norwood had measured the earth, that 60 English miles were contained in one degree latitude on the surface of the Earth his computation did not agree with his theory & inclined him to entertain a notion that together with the force of gravity there might be a mixture of that force wch the moon would have if it was carried along in a vortex…[3]

As you can see the account presented here by Conduitt differs quite substantially from the myth. No tree, no apple on the head, no instantaneous discovery of the theory of gravity. What we have here is a young man who had been intensely studying the theory of forces, in particular forces acting on a body moving in a circle, applying what he had learnt to an everyday situation the falling apple and asking himself if those forces would also be applicable to the moon. What is of note here is the fact that his supposition didn’t work out. Based on the data he was using, which was inaccurate, his calculations showed that the forces acting on the apple and those acting on the moon where not the same! An interesting thought but it didn’t work out. Oh well, back to the drawing board. Also of note here is the reference to a vortex, revealing Newton to be a convinced Cartesian. By the time he finally wrote the Principia twenty years later he had turned against Descartes and in fact Book II of Principia is devoted to demolishing Descartes’ vortex theory.

In 1666 Newton dropped his study of mechanics for the meantime and moved onto optics, where his endeavours would prove more fruitful, leading to his discoveries on the nature of light and eventually to his first publication in 1672, as well as the construction of his reflecting telescope.

The Newtonian Reflector Source: Wikimedia Commons

The Newtonian Reflector
Source: Wikimedia Commons

Over the next two decades Newton developed and extended his knowledge of mechanics, whilst also developing his mathematical skills so that when Halley came calling in 1684 to ask what form a planetary orbit would take under an inverse squared law of gravity, Newton was now in a position to give the correct answer. At Halley’s instigation Newton now turned that knowledge into a book, his Principia, which only took him the best part of three years to write! As can be seen even with this briefest of outlines there was definitely nothing instantaneous or miraculous about the creation of Newton’ masterpiece.

So have we said all that needs to be said about Newton and his apple, both the story and the myth? Well no. There still remains another objection that has been raised by historians, who would definitely like to chuck the baby out with the bath water. Although there are, as noted above, multiple sources for the apple-story all of them date from the last decade of Newton’s life, fifty years after the event. There is a strong suspicion that Newton, who was know to be intensely jealous of his priorities in all of his inventions and discoveries, made up the apple story to establish beyond all doubt that he and he alone deserved the credit for the discovery of universal gravitation. This suspicion cannot be simply dismissed as Newton has form in such falsification of his own history. As I have blogged on an earlier occasion, he definitely lied about having created Principia using the, from himself newly invented, calculus translating it back into conventional Euclidian geometry for publication. We will probably never know the final truth about the apple-story but I for one find it totally plausible and am prepared to give Isaac the benefit of the doubt and to say he really did take a step along the road to his theory of universal gravitation one summer afternoon in Woolsthorpe in the Year of Our Lord 1666.

[1] Patricia Fara, Newton: The Making of Genius, Columbia University Press, 2002

[2] Patricia Fara, Science: A Four Thousand Year History, ppb. OUP, 2010, pp. 164-165

[3] Richard S. Westfall, Never at Rest: A Biography of Isaac Newton, ppb. CUP, 1980 p. 154

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Filed under History of Astronomy, History of Mathematics, History of Optics, History of Physics, History of science, Myths of Science, Newton

Tracking the Messenger of the Gods

On 9 May the astronomers of Europe, and other regions, having screwed their sun filters onto their telescopes, will settle down to observe a transit of Mercury. For any not familiar with astronomical jargon that is when the planet Mercury crosses the face of the sun.

Astronomy Picture of the Day: A Mercury Transit Sequence: Image Credit & Copyright Dominique Dierick

Astronomy Picture of the Day: A Mercury Transit Sequence: Image Credit & Copyright Dominique Dierick

Neither as rare nor as spectacular as the similar transits of Venus, it will still be regarded as a major event in the astronomical calendar. Transits of Venus occur in pairs separated by eight years approximately once every one hundred and twenty years. The last pair was in 2004 and 2012. The cycle of occurrences of transits of Mercury is much more complex but there will be a total of fourteen in the twenty-first century with next Monday’s being the third. Because Mercury is much smaller than Venus and much further from the Earth, unlike a transit of Venus which can be observed with the naked-eye (taking the necessary precautions against the sunlight of course), a transit of Mercury can only be observed with a telescope. The French astronomer, Pierre Gassendi, was the first person to observe a transit of Mercury in 1631 but this historic event was preceded by a couple of thousand years of speculation about the orbital path of the Messenger of the Gods.

Pierre Gassendi after Louis-Édouard Rioult. Source: Wikimedia Common

Pierre Gassendi
after Louis-Édouard Rioult.
Source: Wikimedia Common

Both Mercury and Venus when viewed from the Earth never appear to move very far away from the sun leading some astronomers in antiquity to suggest the so-called Heracleidian of Egyptian system in which the two planets orbited the sun whilst the sun orbited the earth in a geocentric system. Thanks to the De nuptiis of Martianus Cappella (fl. 410-420 CE) this partial helio-geocentric model was well known and moderately popular in the Middle Ages, so the idea that Mercury and Venus orbit the sun was not new when Tycho Brahe suggested it in his full helio-geocentric system, in which all the planets, except the moon, orbit the sun which in turn orbits the earth.

Naboth's representation of Martianus Capella's geo-heliocentric astronomical model (1573) Source: Wikimedia Commons

Naboth’s representation of Martianus Capella’s geo-heliocentric astronomical model (1573)
Source: Wikimedia Commons

In 1608 Hans Lipperhey invented the telescope and within a very short time various astronomers began to use it to observe the heavens. In November 1610 Benedetto Castelli (1578–1643) wrote to Galileo reminding him that Copernicus had predicted that Venus would have phases like the moon in a heliocentric system[1].

Benedetto Castelli

Benedetto Castelli Source: Wikimedia Commons

On 11 December Galileo wrote to Kepler informing him that he had discovered those phases, famously putting the information into an anagram, which Kepler failed to decode properly. Galileo was not alone in making these observations, Thomas Harriot in England, Simon Marius in Germany and Giovanni Paolo Lembo in Rome all independently discovered the phases proving that Venus did indeed orbit the sun and by analogy Mercury probably did as well. The telescopes in the early seventeenth century were not powerful enough to resolve the phases of Mercury.

That Venus and Mercury had been shown to orbit the sun was not a proof of heliocentricity, as this was also the case in the Heracleidian as well as various Tychonic and semi-Tychonic systems but it did mean that theoretically it should be possible to observe a transit of one or the other of them. Due to the fact that the orbits of the earth, Venus and Mercury do not all lie in the same plane but are all slightly tilted with respect to each other a visible transit does not occur by every orbit but as mentioned above at semi regular irregular intervals and in order to observe such a transit someone first had to calculate when they would take place. This task was carried out by Johannes Kepler in his Rudolphine Tables based on Tycho Brahe’s observations and published in 1627.

Frontispiece Rudolphine Table 1627 Source: Wikimedia Commons

Frontispiece Rudolphine Table 1627
Source: Wikimedia Commons

Using the information supplied by Kepler’s tables Gassendi tried to observe a transit of Venus in 1631 unaware that it would take place at nighttime for an observer in Europe. Kepler’s table lacked this level of accuracy. However earlier in the same year, on 7 November, Gassendi had become the first person to observe a transit of Mercury. The first observation of a transit of Venus was made by Jeremiah Horrocks in 1639. Gassendi was very initially cautious in going public with his discovery because his measurements of the size of the planet showed it to be much smaller than previous estimates. However three further transit observations in the seventeenth century, Jeremy Shakerly 1651, Christiaan Huygens 1661 and Edmund Halley 1677, confirmed Gassendi’s first observations and measurements.

Observation of transits of Mercury have long since become routine but that won’t stop the amateur and professional astronomers on next Monday putting up their telescopes to follow the tracks of the Messenger of the Gods as he plods his way across the sun.

[1] For a fuller description of the discovery of the phases of Venus and its significance for the history of heliocentricity see my post The Phases of Venus and Heliocentricity: A Rough Guide.

 

 

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Boole, Shannon and the Electronic Computer

Photo of George Boole by Samuel Prout Newcombe  Source: Wikimedia Commons

Photo of George Boole by Samuel Prout Newcombe
Source: Wikimedia Commons

In 1847, the self-taught English Mathematician George Boole (1815–1864), whose two hundredth birthday we celebrated last year, published a very small book, little more than a pamphlet, entitled Mathematical Analysis of Logic. This was the first modern book on symbolic or mathematical logic and contained Boole’s first efforts towards an algebraic logic of classes.

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Although very ingenious and only the second published non-standard algebra, Hamilton’s Quaternions was the first, Boole’s work attracted very little attention outside of his close circle of friends. His friend, Augustus De Morgan, would falsely claim that his own Formal Logic Boole’s work were published on the same day, they were actually published several days apart, but their almost simultaneous appearance does signal a growing interest in formal logic in the early nineteenth century. Boole went on to publish a much improved and expanded version of his algebraic logic in his An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities in 1854.

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The title contains an interesting aspect of Boole’s work in that it is an early example of structural mathematics. In structural mathematics, mathematicians set up formal axiomatic systems, which are capable of various interpretations and investigate the properties of the structure rather than any one specific interpretation, anything proved of the structure being valid for all interpretations. Structural mathematics lies at the heart of modern mathematics and its introduction is usually attributed to David Hilbert, but in his Laws of Thought, Boole anticipated Hilbert by half a century. The title of the book already mentions two interpretations of the axiomatic system contained within, logic and probability and the book actually contains more, in the first instance Boole’s system is a two valued logic of classes or as we would probably now call it a naïve set theory. Again despite its ingenuity the work was initially largely ignored till after Boole’s death ten years later.

As the nineteenth century progressed the interest in Boole’s algebraic logic grew and his system was modified and improved. Most importantly, Boole’s original logic contained no method of quantification, i.e. there was no simple way of expressing simply in symbols the statements, “there exists an X” or “for all X”, fundamental statements necessary for mathematical proofs. The first symbolic logic with quantification was Gottlob Frege’s, which first appeared in 1879. In the following years both Charles Saunders Peirce in America and Ernst Schröder in German introduced quantification into Boole’s algebraic logic. Both Peirce’s group at Johns Hopkins, which included Christine Ladd-Franklin or rather simply Christine Ladd as she was then, and Schröder produced substantial works of formal logic using Boole’s system. There is a popular misconception that Boole’s logic disappeared without major impact, to be replaced by the supposedly superior mathematical logic of Whitehead and Russell’s Principia Mathematica. This is not true. In fact Whitehead’s earlier pre-Principia work was carried out in Boolean algebra, as were the very important meta-logical works or both Löwenheim and Skolem. Alfred Tarski’s early work was also done in Bool’s algebra and not the logic of PM. PM first supplanted Boole with the publication of Hilbert’s and Ackermann’s Grundzüge der theoretischen Logik published in 1928.

It now seemed that Boole’s logic was destined for the rubbish bin of history, a short-lived curiosity, which was no longer relevant but that was to change radically in the next decade in the hands of an American mathematical prodigy, Claude Shannon who was born 30 April 1916.

Claude Shannon Photo by Konrad Jacobs Source: Wikimedia Commons (Konrad Jacobs was one of my maths teachers and a personal friend)

Claude Shannon
Photo by Konrad Jacobs
Source: Wikimedia Commons
(Konrad Jacobs was one of my maths teachers and a personal friend)

Shannon entered the University of Michigan in 1932 and graduated with a double bachelor’s degree in engineering and mathematics in 1936. Whilst at Michigan University he took a course in Boolean logic. He went on to MIT where under the supervision of Vannevar Bush he worked on Bush’s differential analyser, a mechanical analogue computer designed to solve differential equations. It was whilst he as working on the electrical circuitry for the differential analyser that Shannon realised that he could apply Boole’s algebraic logic to electrical circuit design, using the simple two valued logical functions as switching gates in the circuitry. This simple but brilliant insight became Shannon’s master’s thesis in 1937, when Shannon was just twenty-one years old. It was published as a paper, A Symbolic Analysis of Relay and Switching Circuits, in the Transactions of the American Institute of Electrical Engineers in 1938. Described by psychologist Howard Gardner as, “possibly the most important, and also most famous, master’s thesis of the century” this paper formed the basis of all future computer hardware design. Shannon had delivered the blueprint for what are now known as logic circuits and provided a new lease of life for Boole’s logical algebra.

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Later Shannon would go on to become on of the founders of information theory, which lies at the heart of the computer age and the Internet but it was that first insight combining Boolean logic with electrical circuit design that first made the computer age a viable prospect. Shannon would later play down the brilliance of his insight claiming that it was merely the product of his having access to both areas of knowledge, Boolean algebra and electrical engineering, and thus nothing special but it was seeing that the one could be interpreted as the other, which is anything but an obvious step that makes the young Shannon’s insight one of the greatest intellectual breakthroughs of the twentieth century.

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Filed under History of Computing, History of Logic