Christmas Trilogy 2015 Part 2: Understanding the Analytical Engine.

The Acolytes of the Holy Church of Saint Ada still persist in calling her a brilliant mathematician and the ‘first computer programmer’ despite the fact that both are provably wrong. In fact they have now moved into the realm of denialists, similar to evolution or climate denialists, in that they accuse people like myself who point to the historical facts of being male chauvinists who are trying to deny women their rights in the history of science! However the acolytes have gone a step further in the adulation of Lady King in that they now claim that she understood the Analytical Engine better than Babbage! Confronted by this patently ridiculous claim I’m not sure whether to laugh or cry. Babbage conceived, designed and attempted to construct parts of the Analytical Engine whereas Ada Lovelace merely wrote an essay about it based on her exchanges with Babbage on the subject, to suggest that she understood the machine better than its sole creator borders on the insane. I cannot be certain who first set this bizarre claim in the world as nearly all of those who repeat it give neither justification or source for their utterances but the most often quoted in this context is James Essinger and his biography of Ada, which appears to enjoy several different titles[1].

Trial model of a part of the Analytical Engine, built by Babbage, as displayed at the Science Museum (London). Source: Wikimedia Commons

Trial model of a part of the Analytical Engine, built by Babbage, as displayed at the Science Museum (London).
Source: Wikimedia Commons

Before going into detail it should be pointed out the Essinger’s book, which is popular rather then academic and thus lacks sources for many of his claims, suffers from two fundamental flaws. Like much pro Ada writing it doesn’t delve deep enough into the live and work of Charles Babbage. This type of writing tends to treat Babbage as an extra in the film of Ada’s life, whereas in reality in relation to the Analytical Engine it is Ada who is a minor character in Babbage’s life. Also Essinger writes about the translation of the Menabrea essay on the Analytical engine as if the appended notes were exclusively the product of Ada’s brain, whereas it is an established fact from the correspondence that they were very much a co-production between Babbage and Lovelace based on many exchanges both in personal conversations and in that correspondence. This means that in basing any argument on any idea contained in those notes the writer has the job of determining, which of the two would be the more probable source of that idea and not simply blindly attribute it to Ada. As we shall see Essinger’s failure to do this leads to a major flaw in his central argument that Ada understood the Analytical Engine better than Babbage.

Essinger’s approach is two pronged. On the one side he claims that Babbage didn’t understand the future potential of the machine that he, and he alone, conceived and created (on paper at least) and on the other he proposes on the basis of his interpretation of Note A of the essay that Ada, whom he assumes to be the originator of the thoughts this not contains, had a vision of the Analytical engine equivalent to modern computer science. As we shall see Essinger is mistaken on both counts.

Whilst offering absolutely no source for his claim, Essinger states time and again throughout his book that Babbage only every conceived of the Analytical Engine as a device for doing mathematics, a super number cruncher so to speak. If Essinger had taken the trouble to elucidate the origins of Babbage’s inspiration for the Analytical Engine he would know that he is seriously mistaken in his view, although in one sense he was right in thinking that Babbage concentrated on the mathematical aspects of the Engine but for reasons that Essinger doesn’t consider anywhere in his book.

Babbage lived in the middle of the Industrial Revolution and was fascinated by mechanisation and automation throughout his entire life. During the 1820s Babbage travelled throughout the British Isles visiting all sorts of industrial plant to study and analyse their uses of mechanisation and automation. In 1827 his wife, Georgiana, died and Babbage who had married against the opposition of his father out of love was grief stricken. Leaving Britain to escape the scene of his sorrow Babbage, by now having inherited his fathers fortune a rich man, spent many months touring the continent carrying out the same survey of the industrial advances in mechanisation and automation wherever his wanderings took him. It was on this journey that he first learnt of the automated Jacquard loom that would supply him with the idea of programming the Analytical Engine with punch cards. Returning to Britain Babbage now turned all those years of research into a book, On the Economy of Machinery and Manufactures published in 1832, that is a year before he met Ada Lovelace for the first time and ten years before Menabrea essay was written. The book was a massive success going through six editions in quick succession and influencing the work of Karl Marx and John Stuart Mill amongst others. It would be safe to say that in 1832 Babbage knew more about mechanisation and automation that almost anybody else on the entire planet and what it was capable of doing and which activities could be mechanised and/or automated. It was in this situation that Babbage decided to transfer his main interest from the Difference Engine to developing the concept of the Analytical Engine conceived from the very beginning as a general-purpose computer capable of carrying out everything that could be accomplished by such a machine, far more than just a super number cruncher.

analytical_engine

What is true, however, is that Babbage did concentrate in his plans and drafts, and the Analytical Engine never got past the plans and drafts phase, on the mathematical aspects of the machine. This however does not mean that Babbage considered it purely as a mathematical machine. I am writing this post on a modern state of the art computer. I also use the same device to exchange views with my history of sciences peers on Twitter and Facebook, to post my outpourings, such as this one, on my Internet blog. I can telephone, with visual contact if I choose, with people all over the world using Skype. At the touch, or two, of a keyboard key I have access to dictionaries, encyclopaedias and all sorts of other reference tools and through various means I can exchange documents, photographs, sound files and videos with anybody who owns a similar device. I can listen to and watch all sorts of music recordings and videos and with easily accessible software even turn my computer into an unbelievably flexible musical instrument. Finally when I’m done for the day I can settle back and watch television on my large, high-resolution monitor screen. This is only a fraction of the tasks that my computer is capable of carrying out but they all have one thing in common, they can all only be accomplished if they are capable of being coded into an astoundingly banal logical language consisting only of ‘0s’ and ‘1s’. Of course between the activities I carry out on my monitor screen and the electrical circuits that are only capable of reading those ‘0s’ and ‘1s’ there are layer upon layer of so-called sub-routines and sub-sub-routines and sub-sub-sub…, you get the idea, translating an upper layer into a simpler logical form until we get all the way down to those ubiquitous ‘0s’ and ‘1s’. The language in which those ‘0s’ and ‘1s’ exist is a mathematical language, known as Boolean Algebra, and so in the final analysis my super smart ultra modern computer is nothing but a super number cruncher and only two numbers at that.

Babbage, a brilliant mathematician, was well aware that he could only programme his Engine to carry out tasks that could be reduced over a series of steps to a mathematical language and this is the reason he concentrated on the mathematical aspects of his machine but this by no means meant that he only conceived of it only carrying out mathematical tasks, as we will see when addressing Essinger’s second prong.

Essinger quotes the following passage from Note A of the Malebrea translation:

In studying the action of the Analytical Engine, we find that the peculiar and independent nature of the considerations which in all mathematical analysis belong to operations, as distinguished from the objects operated upon and from the results of the operations performed upon those objects, is very strikingly defined and separated.

It is well to draw attention to this point, not only because its full appreciation is essential to the attainment of any very just and adequate general comprehension of the powers and mode of action of the Analytical Engine, but also because it is one which is perhaps too little kept in view in the study of mathematical science in general. It is, however, impossible to confound it with other considerations, either when we trace the manner in which that engine attains its results, or when we prepare the data for its attainment of those results. It were much to be desired, that when mathematical processes pass through the human brain instead of through the medium of inanimate mechanism, it were equally a necessity of things that the reasonings connected with operations should hold the same just place as a clear and well-defined branch of the subject of analysis, a fundamental but yet independent ingredient in the science, which they must do in studying the engine. The confusion, the difficulties, the contradictions which, in consequence of a want of accurate distinctions in this particular, have up to even a recent period encumbered mathematics in all those branches involving the consideration of negative and impossible quantities, will at once occur to the reader who is at all versed in this science, and would alone suffice to justify dwelling somewhat on the point, in connexion with any subject so peculiarly fitted to give forcible illustration of it as the Analytical Engine.

Attributing its contents to Ada he makes the following comment, “What Ada is emphasising here is the clear distinction between data and data processing: a distinction we tend to take for granted today, but which – like so much of her thinking about computers –was in her own day not only revolutionary but truly visionary”. What is being described here is indeed new in Ada’s day but is a well known development in mathematics know at the time as the Calculus of Operations, a branch of mathematics developed in the first half of the nineteenth century, which differentiates between operators and operations, and in which Babbage worked and to which he made contributions. If the ideas contained in this passage are indeed visionary then the vision is Babbage’s being channelled by Ada and not originating with her. The words might be Ada’s but the thoughts they express are clearly Babbage’s.

Essinger now quotes the next part of the Note:

It may be desirable to explain, that by the word operation, we mean any process which alters the mutual relation of two or more things, be this relation of what kind it may. This is the most general definition, and would include all subjects in the universe. In abstract mathematics, of course operations alter those particular relations which are involved in the considerations of number and space, and the results of operations are those peculiar results which correspond to the nature of the subjects of operation. But the science of operations, as derived from mathematics more especially, is a science of itself, and has its own abstract truth and value; just as logic has its own peculiar truth and value, independently of the subjects to which we may apply its reasonings and processes.

Essinger now reaches maximum bullshit level, “Ada is seeking to do nothing less than invent the science of computing and separate it from the science of mathematics. What she calls ‘the science of operations’ is indeed in effect computing”. As I have already explained what she calls the ‘science of operations’ is in fact the calculus of operation a new but well developed branch of mathematics of which Babbage was fully cognisant. If anybody is inventing the science of computing it is once again Babbage and not Ada.

Essinger now takes up the case further along in Note A:

The distinctive characteristic of the Analytical Engine, […]is the introduction into it of the principle which Jacquard devised for regulating, by means of punched cards, the most complicated patterns in the fabrication of brocaded stuffs… […]The bounds of arithmetic [emphasis in original] were however outstepped the moment the idea of applying the cards had occurred; and the Analytical Engine does not occupy common ground with mere “calculating machines.” It holds a position wholly its own; and the considerations it suggests are most interesting in their nature. In enabling mechanism to combine together general [emphasis in original] symbols in successions of unlimited variety and extent, a uniting link is established between the operations of matter and the abstract mental processes of the most abstract [emphasis in original] branch of mathematical science. [Ellipsis in quote by Essinger]

Essinger introduces this quote with the following: “In a terse passage she explains (perhaps better than Babbage ever could, who as designer saw many trees but perhaps no longer the forest itself) the essential relationship between the Analytical Engine and the Jacquard loom and how it is different from the earlier invention”. After the quote he then writes: “In perhaps one of the most visionary sentences written during the nineteenth century [he sure doesn’t hold back on the hyperbole], she lays out what these cards shall be capable of doing by way of programming the machine”

First off, if you put back the bits Essinger removed from this passage it is anything but terse, in fact it’s rather verbose. Is Essinger really trying to tell us that Babbage was not aware of what he was doing when he conceived of programming his Engine with punch cards? Unfortunately for Essinger Babbage himself tells us that this is not the case, writing in his notebook on 10 July 1836, that is 8 years before the original French version of the Malebrea essay was published, he has the following to say:

This day I had for the first time a general but very indistinct conception of the possibility of making the engine work out algebraic developments – I mean without any reference to the value of the letters. My notion is that as the cards (Jacquards) of the calc. engine direct a series of operations and the recommence with the first…[2]

Here we have in Babbage’s own words the germ of the idea contained in the Ada quote, an idea that would naturally mature over the intervening nine years before Ada wrote her piece, so I have problems whatsoever in again attributing the thoughts contained here to Babbage.

I’m not going to go on analysing Essinger’s Ada hagiography for almost all of the things that he attributes to Ada it is not difficult to find its origins in Babbage’s work thus reinforcing the claim in an earlier post that Ada is being used here as Babbage’s mouth piece. Not so much the originator as the parrot. I will however close with one last quote from Note A and Essinger’s comment to demonstrate that his grasp of the history of science in the nineteenth century is apparently almost non-existent. Without really introducing it Essinger quotes the following sentence:

Those who view mathematical science, not merely as a vast body of abstract and immutable truths, whose intrinsic beauty, symmetry and logical completeness, when regarded in their connexion together as a whole, entitle them to a prominent place in the interest of all profound and logical minds, but as possessing a yet deeper interest for the human race, when it is remembered that this science constitutes the language through which alone we can adequately express the great facts of the natural world, and those unceasing changes of mutual relationship which, visibly or invisibly, consciously or unconsciously to our immediate physical perceptions, are interminably going on in the agencies of the creation we live amidst: those who thus think on mathematical truth as the instrument through which the weak mind of man can most effectually read his Creator’s works, will regard with especial interest all that can tend to facilitate the translation of its principles into explicit practical forms.

Essinger wonderingly comments on this sentence, “This 158-word sentence is very likely one of the longest sentences in the history of science, but it is also one of the most intriguing. Ada succeeds in this one sentence in linking mathematics, science, religion and philosophy.” Any competent historian of science would immediately recognise this as a rather flowery expression of the basic tenets of natural theology, a philosophy that flourished in the first half of the nineteenth century. This statement could have been made by a very large number of natural philosophers starting with Isaac Newton and going up to and beyond William Whewell and Charles Babbage, for example in the dispute that I outlined on this day last year. What this example clearly illustrates is that Essinger is in no way a real historian who researches and understands his sources but one who thinks he can read the text of Note A and interpret it on the basis of his lack of knowledge rather than on his procession of it.

[1] The copy I read was James Essinger, A Female Genius: how Ada Lovelace, Lord Byron’s daughter started the computer age, London 2015

[2] Babbage notebook quote taken from Dorothy Stein, Ada: A Life and a Legacy, MIT Press, Cambridge Massachusetts &London, 1985 p.102

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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

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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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The greatest villain in the history of science?

In the popular version of the so-called astronomical revolution Andreas Osiander, who was born on the 19th December 1496 or 1498, is very often presented as the greatest villain in the history of science because he dared to suggest in the ad lectorum (to the reader) that he added to the front of Copernicus’ De revolutionibus that one could regard the heliocentric hypothesis as a mere mathematical model and not necessarily a true representation of the cosmos. Is the judgement of history just and who was Andreas Osiander anyway?

Andreas Osiander portrait by Georg Pencz Source: Wikimedia Commons

Andreas Osiander portrait by Georg Pencz
Source: Wikimedia Commons

Andreas Osiander was born in Gunzenhausen, a small town to the south of Nürnberg, the son of Endres Osannder a smith and Anna Herzog. His father was also a local councillor, who later became mayor. He entered the University of Ingolstadt in 1515 where he, amongst other things, studied Hebrew under Johannes Reuchlin one of the greatest humanist scholars in Germany at that time, the great uncle from Philipp Melanchthon and the leading Hebrew scholar of the age. In 1520 Osiander was ordained a priest and called to Nürnberg to teach Hebrew at the Augustinian Cloister. This had been a major centre for reformatory debate for a number of years and it is here that Osiander became a religious reformer. In 1522 he was appointed preacher at the Saint Lorenz church in Nürnberg and became the leading voice for religious reform in the city. In 1525 Nürnberg, a city-state, became the first state to officially adopt the Lutheran Protestant religion, and Osiander became a highly influential and powerful figure. He was largely responsible for converting Albrecht of Prussia to Protestantism and also had a major influence on Thomas Cranmer, later Archbishop of Canterbury and author of the Common Book of Prayer. A trivial pursuits fact is that Cranmer married one of Osiander’s nieces.

Osiander’s first links with the printer/publisher Johannes Petreius was as the author of polemical religious tracts, which Petreius published. How he became an editor for Petreius is not know. It is also not known when and where Osiander developed his interest in and knowledge of the mathematical sciences. What is certain is that it was Osiander who, after Petreius had discovered Cardano’s books at the book fair in Frankfurt, who wrote to the Italian mathematician/physician/philosopher on Petreius’ behalf offering to publish his books in Germany; an offer that Cardano was more than willing to accept. Osiander then became the editor of those books of Cardano’s that Petreius published over the years; a service for which Cardano thanks him very warmly in the preface to one of his books, praising him highly for his abilities as an editor.

When Rheticus published his account of Copernicus’ heliocentric astronomy in his Narratio Prima, in the form of an open letter addressed to Johannes Schöner, another of Petreius’ editors, it was Osiander who wrote to Rheticus on behalf of the publishing house showing great interest in the cyclical astrological theory of history outlined by Rheticus in his little book.

After Rheticus had brought the manuscript of De revolutionibus to Nürnberg, Philipp Melanchthon pressured him to take up the professorship for mathematics in Leipzig and Osiander took over the task of seeing the text through the press. It is here that Osiander added the ad lectorum to the finished book, which has, over the centuries, pulled down so much odium on his head. Is this harsh judgement of his actions justified or have we, as I believe, been blaming the wrong man for the last four and a half centuries.

In the early days of printing there was no such thing as authors rights. The rights to a book lay with the printer/publisher, who was also the first port of call should the authorities decide that a book or pamphlet was seditious, blasphemous or in any other way unacceptable. And please remember our concepts of freedom of speech simply did not exist in sixteenth-century Europe. The ad lectorum was added to De revolutionibus certainly with Petreius’ knowledge and almost certainly at his instigation. This is confirmed by his reaction as Copernicus’ friend Bishop Tiedemann Giese complained to the city council of Nürnberg about the inclusion of the ad lectorum in his dead friend’s magnum opus. Consulted by the council on the subject Petreius basically flew off the handle and told them to get stuffed, it was his book and he’d put what the hell he liked in it.

Osiander continued to edit the books of Cardano for Petreius but in 1548 the city of Nürnberg accepted the Augsburg Interim an edict issued by Charles V, Holy Roman Emperor, who had just won a decisive victory against the Protestant forces, forcing the Protestant states within the Empire to revert to Catholicism. In a moonlight flit Osiander fled the city of Nürnberg and made his way north to Königsberg, where Albrecht appointed him professor of theology at the newly established university. This caused much bad blood, as Osiander was not a qualified theologian. In this position Osiander became embroiled in a major theological dispute with the supporters of Melanchthon in Wittenberg over the doctrine of justification. This dispute is known in German church history as the Osiander Dispute and led to a schism between the two parties, with Osiander basically forming his own branch of Protestantism.

Osiander died in 1552 a controversial figure both in the history of religion and the history of science. However as I have sketched above I think his bad reputation in the history of science is not really justified and the real villain of the piece, if there is one, is Johannes Petreius. I say if there is one, because many historians are of the opinion that the ad lectorum saved the De revolutionibus from being condemned straight away, when it was published, and allowed the heliocentric hypothesis it contained to spread relatively unhindered and become established.

 

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Mensis or menstruation?

I recently stumbled upon this rather charming rant by Anglo-Danish comedian, writer, broadcaster and feminist Sandi Toksvig.

Women's Calendar

 

Now I’m a very big fan of Ms Toksvig and was very sad when she retired as presenter of BBC Radio 4’s excellent News Quiz, so I don’t want to give the impression that I’m trying to put her down, but if she had know a little bit more about the early history of the calendar then she might not have jumped to the conclusion that this supposed bone calendar must have been made by a woman.

Before I start to explain why Ms Toksvig might be mistaken in her assumption that this purported primitive calendar came from the hands of a woman I would like to waste a few words on all such artefacts. There are a number of bone and stone objects of great antiquity bearing some number of scratches, incisions, notches, indentations or other forms of apparent marking and someone almost always comes along and declares them to be purposely created mathematical artefacts with one or other function. I must say that being highly sceptical by nature I treat all such claims with more than a modicum of wariness. Even assuming that the markings were made by a human hand might they not have been made in an idle moment by a Neolithic teenager trying out his newly acquired flint knife or in the case of our incised bone by an early musician making himself scraper to accompany the evening camp fire sing-a-long? What I’m am saying is that there are often multiple possible explanations for the existence of such marked artefacts and regarding them as signs of some sort of mathematical activity is only one of those possibilities.

However, back to Ms Toksvig and her revelation. She is of course assuming that the twenty-eight incisions are the result of a women counting off the days between her periods, the menstrual cycle being roughly twenty-eight days for most women. Now if Ms Toksvig had taken her thoughts a little further she might have realised that the word menstruation derives from the Latin word for month, which is mensis: a month being originally a lunar month which, depending on how you measure it, has approximately twenty-eight days. In fact much human thought has been expended over the centuries over the fact that a lunar month and the menstrual circle have the same length.

What we have here with this incised bone could well be not a menstrual record, as Ms Toksvig seems to assume, but a mensis record or part of a lunar calendar. This supposition is lent credence by the fact that, with the very notable exception of the ancient Egyptian calendar, all early cultures and civilisations had lunar and not solar calendars including the ancient Romans before Gaius Julius Caesar borrowed the Egyptian solar calendar, the forerunner of our own Gregorian one.

Assuming that the archaeologist or anthropologist who decided that said bone was a primitive calendar was right and it is not the idle whittling of some bored stone-age teenager, we of course still have no idea whether it was the work of a man or a woman.

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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

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