Category Archives: Myths of Science

Perpetuating the myths addendum – ‘The Copernican Shock

Frequent Renaissance Mathematicus commentator (comment-writer, commenter, commentor), Phillip Helbig, sent me an interesting email in response to my previous blog post. In skewering the Nadlers’ comic book I didn’t actually comment on every single detail of everything that was wrong with it, one of the things I left out was Galileo saying:

It is not the center of the cosmos it is a planet just like the others and they all orbit the sun.

As Phillip correctly pointed out in the Ptolemaic-Aristotelian geocentric model of the cosmos the Earth was not viewed as the centre of the cosmos but rather as the bottom. I wrote a brief post long ago quoting a wonderful passage by Otto von Guericke, the inventor of the vacuum pump on exactly this topic:

Since, however, almost everyone has been of the conviction that the earth is immobile since it is a heavy body, the dregs, as it were, of the universe and for this reason situated in the middle or the lowest region of the heaven

Otto von Guericke; The New (So-Called) Magdeburg Experiments of Otto von Guericke, trans. with pref. by Margaret Glover Foley Ames. Kluwer Academic Publishers, Dordrecht/Boston/London, 1994, pp. 15 – 16. (my emphasis)

Phillip then asks, “So what was the “shock” of the Copernican Revolution (how many even get that pun?)?  Was it demoting humanity from the centre of the universe, or promoting the Earth to be on par with the other heavenly bodies?”

Before I answer his question I would point out that the idea that Copernicus had demoted the Earth from the centre of the cosmos first emerged much later, sometime in the late eighteenth or early nineteenth century, as an explanation for the supposed irrational rejection of the heliocentric hypothesis. Of course as is now well known, or at least should be, the initial rejection of the heliocentric hypothesis was not irrational but was based on solid common sense and the available empirical scientific evidence nearly all of which spoke against it. For a lot, but by no means all, of the astronomical arguments read Chris Graney’s excellent Setting Aside All Authority.

So back to Phillip’s question, what was the real Copernican shock? The answer is as simple as it is surprising, there wasn’t one. The acknowledgement and acceptance of the heliocentric hypothesis was so gradual and spread out over such a long period of time that it caused almost no waves at all.

First up, there was nothing very new in Copernicus suggesting a heliocentric cosmos. As should be well known it had already been proposed by Aristarchus of Samos in the third century BCE and Ptolemaeus’ Syntaxis Mathematiké (Almagest) contains a long section detailing the counter arguments to it, which were well known to all renaissance and medieval astronomers. Also in the centuries prior to Copernicus various scholars such as Nicholas of Cusa had extensively discussed both geocentric models with diurnal rotation and full heliocentric ones. All that was new with Copernicus was an extensive mathematical model for a heliocentric cosmos.

At first this was greeted with some enthusiasm as a purely hypothetical model with the hope that it would deliver better predictions of the heavenly movements than the geocentric models for use in astrology, cartography, navigation etc. However it soon became apparent that Copernicus was not really any better than the older models, as it was based on the same inaccurate and oft corrupted data as Ptolemaeus, so the interest waned, although it was these inaccuracies in both model that inspired Tycho Brahe to undertake his very extensive programme of new astronomical observations on which Kepler would base his models.

As Robert Westman pointed out, in a now legendary footnote, between the publication of De revolutionibus in 1543 and 1600 there were only ten people in the whole world, who accepted Copernicus’ heliocentric cosmology, not exactly earth shattering. Even after 1600 the acceptance of a heliocentric worldview only increased very slowly and in gradual increments as the evidence for it accumulated.

The first two factors are the work of Kepler and the early telescopic discoveries. Because Kepler couldn’t or rather didn’t deal with the physical problems of a moving earth his work initially fell on deaf ears. The early telescopic discoveries only refuted a pure Ptolemaic geocentric model but were consistent with a Tychonic geo-heliocentric one and as this had a stationary earth, it became the model of choice. Of interest, and I think up till now not adequately explained, a Tychonic model with diurnal rotation, i.e. a spinning earth, became the preferred variation. A partial step in the right direction. Kepler’s publication of the Rudolphine Tables in 1627 led to an acceptance of his elliptical astronomy at least for calculations if not cosmologically. Then Cassini, with the help of Riccioli, demonstrated with a heliometer in the San Petronio Basilica in Bologna that the sun’s orbit around the earth or the earth’s orbit around the sun was indeed a Keplerian ellipse, but couldn’t determine which of the two possibilities was the right one. Another partial step in the right direction.

Both Kepler’s first and third laws, solidly empirical, were now accepted but his second law still caused problems. Around 1670 Nicholas Mercator provided a new solid proof of Kepler’s second law and it is about then that the majority of European astronomers finally accepted heliocentricity, although it was Kepler’s elliptical astronomy and not Copernicus’ model; the two models were regarded as competitors; also there was still a distinct lack of empirical proof for a heliocentric cosmos.

The developments in physics over the seventeenth century combined with the discovery of the physical reality of the atmosphere and Newton’s gravitation law finally solved the problems of why, if the earth is moving various disasters don’t occur: high winds, atmosphere blowing away etc., all of those arguments already listed by Ptolemaeus. The final empirical proofs of the annual orbit, Bradley and stellar aberration in 1727, and diurnal rotation, measuring the shape of the earth, around 1750, were delivered in the eighteenth century.

As can been seen by this very brief outline of the acceptance and confirmation of heliocentrism it was a process that took nearly two hundred years and proceeded in small increments so there was never anything that could possibly be described as a shock. As already stated above the concept that the ‘Copernican Revolution’ caused consternation or was a shock is a myth created sometime in the late eighteenth or early nineteenth century to explain something that never took place. One might even call it fake news!

Addendum: A lot of the themes touched on here are dealt with in greater detail in my The transition to heliocentricity: The Rough Guides series of blog posts

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

Perpetuating the myths

Since the re-emergence of science in Europe in the High Middle Ages down to the present the relationship between science and religion has been a very complex and multifaceted one that cannot be reduced to a simple formula or a handful of clichés. Many of the practitioners, who produced that science, were themselves active servants of their respective churches and many of their colleagues, whilst not clerics, were devoted believers and deeply religious. On they other had there were those within the various church communities, who were deeply suspicious of or even openly hostile to the newly won scientific knowledge that they saw as a threat to their beliefs. Over the centuries positions changed constantly and oft radically and any historian, who wishes to investigate and understand that relationship at any particular time or in any given period needs to tread very carefully and above all not to approach their research with any preconceived conclusions or laden down with personal prejudices in one direction or another.

In the nineteenth century just such preconceived conclusions based on prejudice became dominant in the study of the history of science propagated by the publications of the English-American chemist John William Draper and his colleague the American historian and educator Andrew Dickson White. These two scholar propagated what is now know as the Conflict or Draper-White Thesis, which claims that throughout history the forces of science and religion have been in permanent conflict or even war with each other. Draper wrote in his provocatively titled, History of the Conflict between Religion and Science (1874)

The history of Science is not a mere record of isolated discoveries; it is a narrative of the conflict of two contending powers, the expansive force of the human intellect on one side, and the compression arising from traditionary faith and human interests on the other.

In 1876 in his equally provocative The Warfare of Science, White wrote:

In all modern history, interference with science in the supposed interest of religion, no matter how conscientious such interference may have been, has resulted in the direst evils both to religion and to science—and invariably. And, on the other hand, all untrammeled scientific investigation, no matter how dangerous to religion some of its stages may have seemed, for the time, to be, has invariably resulted in the highest good of religion and of science.

Twenty years later White ramped up the heat in his A History of the Warfare of Science with Theology in Christendom.

Draper’s and White’s polemics became widely accepted and Galileo, Darwin and other figures out of the history of science came to be regarded as martyrs of science, persecuted by the bigoted forces of religion.

Throughout the twentieth century historians of science have striven to undo the damage done by the Draper-White thesis and return the history of the relationship between science and religion to the complex and multifaceted reality with which I introduced this post. They were not helped in recent decades by the emergence of the so-called New Atheists and the ill considered and unfortunately often historically ignorant anti-religious polemics spewed out by the likes of Richard Dawkins and Sam Harris, supposedly in the name of freedom of thought. I have, although a life-long atheist myself, on more than one occasion taken up arms, on this blog, against the sweeping anti-religious generalisations with respect to the history of science spouted by the new atheist hordes.

So it was with more than slight sense of despair that I read the preview in The Atlantic of

A Graphic Novel About 17th-Century Philosophy with the title Heretics!

This is described by its publishers the Princeton University Press as follows:

An entertaining, enlightening, and humorous graphic narrative of the dangerous thinkers who laid the foundation of modern thought

The Atlantic’s review/preview confirmed my darkest suspicions. We get informed:

Dark spots across the sun, men burned at the stake, an all-powerful church that brooks no idea outside its dogma—there is no subject so imbued with drama, intrigue, and fast-paced action as 17th-century Western philosophy. And thus no medium does it justice like the graphic novel.

No, really.

Heretics!, a graphic novel by Steven and Ben Nadler, introduces readers to what is arguably the most interesting, important, and consequential period in the history of Western philosophy. While respecting recent scholarship on 17th-century thought, [my emphasis] the Nadlers sought to make these stories and ideas as accessible and engaging to as broad an audience as possible without condescension. At times, this called for some historical liberties and anachronism. (Full disclosure: there were no laptop computers or iPods in the 17th century.)

We are back in Draper-White territory with a vengeance! The last thing that the Nadlers do is to respect recent scholarship, in fact they turn the clock back a long way, deliberately avoiding all the work done by modern historians of science.

The sample chapter provided by The Atlantic starts with Giordano Bruno, who else, much loved as a martyr for science by the new atheist hordes.

Source: The Atlantic

We see here that, as usual, Bruno’s cosmology is featured large, whilst his theological views are tucked away in the corner. Just two comments, Bruno was by no stretch of the imagination a scientist, read this wonderful essay by Tim O’Neill if you don’t believe me, and his “highly unorthodox” theological views included denial of the trinity, denial of Jesus’ divinity and denial of the virgin birth any one of which would have got him a free roasting courtesy of the Catholic Church if he had never written a single word about cosmology.

Up next, prime witness for the prosecution, who else but our old friend Galileo Galilei. We get the hoary old cliché of him throwing rocks off the Leaning Tower of Pisa, which he almost certainly never did.

We now move on to Galileo the astronomer,

Source: The Atlantic

who having made his telescopic discoveries claims that, “Copernicus was right.”

Source: The Atlantic

Know what, in 1615 Galileo was very careful not to claim that because he knew that it was a claim that he couldn’t back up. What he did do, which brought him into conflict with the Church was to suggest that the Church should change its interpretations of the Bible, definitely not on for a mere mathematician in the middle of the Counter Reformation and for which he got, not unsurprisingly, rapped over the knuckles. In 1616 Pope Paul V did not condemn Copernicus’s theory as heresy, in fact no pope ever did.

We then have Galileo sulking in his room and he isgoing to show them! In fact Galileo courted the Catholic Church and was a favourite of the papal court in Rome; he received official permission from Pope Urban VIII to write his Diologo. I’m not going to go into the very complex detail as to why this backfired but a couple of short comments are necessary here. At that time the heliocentric theory did not do a much better job of explain the phenomena in the heavens and on earth. Galileo’s book is strong on polemic and weak on actual proofs. Also, and I get tired of pointing this out, Galileo was not condemned as a heretic but found guilty of grave suspicion of heresy. There is a massive legal difference between the two charges. Paying attention to the fine detail is what makes for a good historian. We close, of course with the classic cliché, “And yet the earth moves.” No, he didn’t say that!

Source: The Atlantic

We then get a comic book description of the differences between the philosophies of Aristotle and Descartes that unsurprisingly doesn’t do either of them justice. All of this is of course only a lead up to the fact that Descartes decided not to publish his early work explicating his philosophy including his belief in heliocentricity, Traité du monde et de la lumière, on hearing of Galileo’s trial and punishment. This is dealt with by the Nadlers with a piece of slapstick humour, “Zut alors! I don’t want to get into trouble too!” Has anybody ever actually heard a Frenchman say “Zut alors!”?

Source: The Atlantic

This episode in intellectual history is actually of great interest because as far as is known Descartes is the only author in the seventeenth century who withdrew a book from publication because of the Pope’s edict against teaching heliocentricity. He appears to have done so not out of fear for his own safety but out of respect for his Jesuit teachers, whom he did not wish to embarrass. This was rather strange as other Jesuits and students of Jesuit academies wrote and published books on heliocentrism merely prefacing them with the disclaimer that the Holy Mother Church in its wisdom has correctly condemned this theory but it’s still quite fun to play with it hypothetically. The Church rarely complained and appearances were maintained.

This very superficial and historically highly inaccurate comic book in no way does justice to its subject but will do a lot of damage to the efforts of historians of science to present an accurate and balanced picture of the complex historical relationship between science and religion.

For anybody who is interested in the real story I recommend John Hadley Brooke’s classic Science and Religion: Some Historical Perspectives (1991) and Peter Harrison’s, soon to be equally classic, The Territories of Science and Religion (2015). On reading The Atlantic review/preview Peter Harrison tweeted the following:

Oh dear…. Not the optimal format for communicating the complexities of history – Peter Harrison (@uqharri)

James Ungureanu another expert on the relations between science, religion and culture also tweeted his despair on reading The Atlantic review/preview:

When I saw this earlier, I died a little. It must be right because it’s funny! – James C Ungureanu (@JamesCUngureanu)

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Filed under Book Reviews, History of science, Myths of Science

The problem with superlatives

I have on several occasions in the past written about the problems of the use of certain superlative terms in presentations of the history of science, in particular in popular ones, such as first, father of, founder of and the greatest, as they only lead to a distortion of what really happens in the historical evolution of the scientific disciplines.

The term the greatest reared its ugly head again last week in the form of a tweet by Professor Frank McDonough (@FXMC1957) (historian).

18 April 1955. Albert Einstein (aged 76) died. He was arguably the greatest scientist who ever lived.

If Einstein is arguably the greatest scientist who ever lived, it raises the question, who his competitors might possibly be for this obviously coveted accolade. A typical discussion would almost certainly immediately throw up the names Isaac Newton, Galileo Galilei and Archimedes, going backwards in time. This almost canonical list, including of course Einstein, throws up a whole series of problems.

For me personally the first problem is that the list almost never includes Johannes Kepler, although any serious and unbiased comparison of their achievements, and they were contemporaries, would show quite clearly that Kepler actually contributed significantly more to the evolution of the sciences than Galileo. However for various reasons Kepler lacks the historical nimbus that Galileo has acquired down the centuries.

The second problem is that one is not actually comparing like with like. The mathematician and maths historian Eric Temple bell, whose book Men of Mathematics ignited my interest in the history of mathematics as a teenager, asked the question, “who was the greatest mathematician of all times?” He came up with a list of three names Archimedes, Isaac Newton and Johann Carl Friedrich Gauss (Gauss was also an extraordinary polymath who made important and significant contributions to astronomy, geodesy, cartography, optics, mechanics and, and…, so why isn’t he ever on the greatest scientist lists?). Bell then argued that it was impossible to say, which of the three was the greatest in terms of their mathematical achievements but Archimedes was operating on a much smaller basis of pre-existing knowledge so his achievements should be judged as greater.

Bell’s argument has a certain historical validity and makes us very much aware of the problems and dangers of trying to compare the achievements of practitioners of science across the depths of time. Galileo’s achievements can only be judged against the background of the late sixteenth century and early seventeenth, Newton’s against the background of the late seventeenth, when the situation in physics and astronomy was very different to that at the beginning of the century. Both of them are separated by a vast gulf in time from Archimedes and although the gap between Newton and Einstein is smaller the difference in background situations is immense. In the end we can only really compare a given scientist with his contemporaries.

Another problem that the canonical list immediately calls to attention is that all four of our candidates are basically mathematical physicists, which displays a strong bias against all the other scientific disciplines. This bias has existed for a very long time and is one of the things that current historians of science try to combat. For a very long time the history of science was seen principally as the history of the exact sciences i.e. mathematics, astronomy and physics. All other disciplines tended to be treaded as somehow secondary. Also the philosophy of science tended to be defined as the philosophy of physics. Returning to our list and its built in bias, not a few life scientists on reading it would say, quite correctly, what about Charles Darwin? Is not the discovery of the principle of evolution equal or even superior to anything discovered by the physicists or the astronomers? Having opened that can of worms somebody might put in a vote for Watson and Crick, after all Matthew Cobb’s excellent book on the discovery of the structure of DNA is titled, Life’s Greatest Secret! Oh dear that nasty superlative has crept in again.

At this point the chemists, who always get left out of such discussions, could well chime in with claims for Joseph Priestley, Antoine Lavoisier, Humphry Davy, Justus von Liebig and of course Marie Curie (after all she got two Nobels whereas Albert only got one!). Having brought up Humphry Davy a self taught, brilliant scientist, one should immediately think of his famous assistant and successor, the equally self taught, Michael Faraday; now there is a serious candidate for the greatest.

Another problem with this form of historical deification of scientists, the greatest, is that it fosters and perpetuates the myth of the lone genius. Returning to Einstein, undoubtedly an incredibly productive physicist, who contributed substantially to two of the biggest fields in twentieth century physics, his work built on the work of many, many others and contributions were made to the development of his own major discoveries, Relativity and Quantum Theory, by a fairly large group of other mathematicians, physicists and astronomers. No scientist exists in a vacuum but is part of a collective endeavour pushing forward the boundaries of their discipline. Historians of science should not concern themselves with the irrelevant and uninformative question, who’s the greatest, but should rather try to embed individuals into the context in which they did their work and the nexus of others who contributed to that work and those effected by it in their own efforts. Context is everything could well be the motto of this blog.

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Has The Renaissance Mathematicus gone over to the dark side?

As the ultimate anti-establishment, indie rock band, The Grateful Dead, was inducted into the Rock and Roll Hall of fame, lead guitarist, Jerry Garcia, commented something along the lines of, it’s like the neighbourhood whore, if she stands on the corner long enough then eventually she becomes part of the establishment. And so it has came to pass than your friendly neighbourhood indie, anti-establishment, arse kicking, history of science blogger, The Renaissance Mathematicus, got asked, no, not asked, invited to submit an article to the latest edition[1] of the British Society for the History of Science online journal Viewpoints! He, being the publicity whore that he is, putting aside all thoughts of tarnishing his brand or weakening his reputation accepted with alacrity. And so it is that you, dear readers, can peruse his words of wisdom in the latest edition of that honourable establishment publication. For those that brave of vicissitudes of this dubious blog at regular intervals there is nothing in the latest outpourings of the #histsci hooligan that will be new to you but there are, with certainty, many other good and worthy things to read in this excellent journal, so why don’t you just stroll on over and indulge in some first class history of science story telling.

[1] When I originally wrote this post it was the latest edition of Viewpoint but I couldn’t find a link so I never posted this. Now that I have found a link it’s still the latest issue but no longer dew fresh.

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Filed under Autobiographical, History of science, Myths of Science

The poetic astronomer

 

Regular readers of this blog will know that I can on occasion be a stroppy, belligerent, pedant, who gets rather riled up over people who spread myths of science and who has a tendency to give such people a public kicking on this blog. This tendency earned me the nickname, the HistSci_Hulk in earlier years. The subtitle to a podcast that I stumbled across yesterday on the BBC website provoked my inner Hist_Sci Hulk and has generated this post.

The podcast is a BBC Radio 4 “Radio 4 in Four” four minute documentary on the work of the Indian mathematician and astronomer, Aryabhata: Maths expressed as poetry. The subtitle was: In 5th century India, clever man Aryabhata wrote his definitive mathematical work entirely in verse and long before Galileo, argued the world was round [my emphasis]. It was that final clause that provoked my HistSci_Hulk moment.

I’ve lost count of how many times over the years I have explained patiently and oft not so patiently that educated society in European culture have known and accepted that the world is a sphere since at least the sixth century BCE. This is the most recent account here on the blog. Bizarrely in the podcast no mention is made of Aryabhata’s cosmological or astronomical views, so it is real puzzle as to why it’s mentioned in the subtitle. What is interesting is the fact that as a cosmologist Aryabhata held a fairly rare position, although he was a geocentrist he believed that the earth revolved around its own axis, i.e. geocentrism with diurnal rotation. You can read about the history of this theory here in an earlier blog post.

Statue of Aryabhata on the grounds of IUCAA, Pune. As there is no known information regarding his appearance, any image of Aryabhata originates from an artist’s conception.
Source: Wikimedia Commons

More interesting is the correct fact that Aryabhata wrote his astronomical/mathematical thesis in verse form. As the podcast points out this is because the culture in which he was writing was an oral one and complex facts are easier to remember in verse rather than in prose. What the podcast doesn’t say is that Aryabhata was not the only astronomer/mathematician to express his results in verse and was in this sense by no means unique. In fact he is part of a solid tradition of mathematical Sanskrit poetry.

India was not the only culture to use poetry to express scientific content. Probably the most famous example is the Latin poem De rerum natura by the first century BCE Roman poet Lucretius, which is the most extensive description of the physics of the ancient Greek atomists. The poem played a central role in the revival of atomism in the early modern period; a revival that several historians of science, such as David Lindberg, consider to be a key element in the so-called scientific revolution of the seventeenth century.

In astronomy/ astrology there is a poem from antiquity that played a significant role in the Renaissance. This is the Astronomica probably written by the poet Marcus Manilius in the first century CE; the first printed edition of this was published by Regiomontanus in Nürnberg in 1473.

Many people are not aware of some highly significant scientific poems from the eighteenth century written and published by Charles Darwin’s grandfather, Erasmus.

Joseph Wright of Derby, Erasmus Darwin (1770; Birmingham Museum and Art Gallery).
Source: Wikimedia Commons

Darwin’s The Loves of the Plants was the first work in English to popularise the botanical works of Linnaeus in English. The poem caused something of a scandal because it emphasised the explicit sexual nature of Linnaeus’ system of botanical nomenclature and was thus considered unsuitable for polite society. The Loves of the Plants was published together with another poem, The Economy of Vegetation, a more general poem on scientific progress and technological innovation, of which Darwin as a prominent member of the Lunar Society of Birmingham was very much aware. The Economy of Vegetation expresses an evolutionary view of progress. A footnote to The Loves of the Plants contains the first outlines of Darwin’s theory of biological evolution, which he would then expand upon in his prose work Zoonomia. Erasmus Darwin’s is an adaptive theory of evolution and is thus oft referred to as Lamarckian, although as Erasmus preceded Lamarck, maybe his theory should be referred to as Darwinian! A posthumous poem of Darwin’s, The Temple of Nature, contains a full description of his theory of evolution in verse.

Writing this led me to the thought that maybe editors of modern scientific journals should require their authors to submit their papers in iambic pentameters or in Shakespearean blank verse, with the abstracts written as sonnets. It would certainly make reading scientific papers more interesting.

 

 

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Sorry Caroline but you were not the first, Maria was

Today is the birthday of Caroline Herschel, important member of the Herschel astronomical clan and significant astronomer in her own right, who was born 16 March 1750.

Caroline Herschel
Source: Wikimedia Commons

Throughout the Internet this anniversary is being acknowledged and celebrated, and quite rightly so, but all of those doing so that I have stumbled across, including such august organisations as the BBC, the Royal Society, NASA and ESA amongst other, have all being perpetuating a history of astronomy myth, namely that Caroline Herschel was the first woman to discover a comet. She wasn’t Maria Kirch was!

Caroline Herschel made her first cometary discovery, having been trained to sweep for comets by her brother William and being provided by him with her own comet sweeping telescope, on 1 August 1786, almost sixty-six years after the death of her fellow German female astronomer and the real first woman to discover a comet, Maria Kirch.

Maria Kirch, who I’ve written about briefly in the past, was the wife and working partner of Gottfried Kirch, who was a pupil of Erhard Weigel and who became the first Prussian state astronomer in Berlin in 1700. Maria and Gottfried had married in 1692. On 21 April 1702 Maria discovered the so-called comet of 1702 (C/1702 H1). You will note this is eighty-four years before Caroline Herschel discovered her first comet. Unfortunately for Maria, the sexist eighteenth century attributed the discovery to her husband Gottfried and not to her. Although Gottfried publically attributed the discovery to Maria in 1710 the official attribution has not been changed to this day.

Not only was Maria Kirch robbed of recognition of her discovery in the sexist eighteenth century but people too lazy to check their facts deny her achievement every time they falsely claim that Caroline Herschel was the first woman to discovery a comet.

 

 

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Christmas Trilogy 2016 Part 2: What a difference an engine makes

Charles Babbage is credited with having devised the first ever special-purpose mechanical computer as well as the first ever general-purpose mechanical computer. The first claim seems rather dubious in an age where there is general agreement that the Antikythera mechanism is some sort of analogue computer. However, Babbage did indeed conceive and design the Difference Engine, a special purpose mechanical computer, in the first half of the nineteenth century. But what is a Difference Engine and why “Difference”?

Both Babbage and John Herschel were deeply interested in mathematical tables – trigonometrical tables, logarithmic tables – when they were still students and Babbage started collecting as many different editions of such tables as he could find. His main object was to check them for mistakes. Such mathematical tables were essential for navigation and errors in the figures could lead to serious navigation error for the users. Today if I want to know the natural logarithm of a number, let’s take 23.483 for example, I just tip it into my pocket calculator, which cost me all of €18, and I instantly get an answer to nine decimal places, 3.156276755. In Babbage’s day one would have to look the answer up in a table each value of which had been arduously calculated by hand. The risk that those calculations contained errors was very high indeed.

Babbage reasoned that it should be possible to devise a machine that could carryout those arduous calculations free of error and if it included a printer, to print out the calculated answer avoiding printing errors as well. The result of this stream of thought was his Difference Engine but why Difference?

The London Science Museum's reconstruction of Difference Engine No. 2 Source: Wikimedia Commons

The London Science Museum’s reconstruction of Difference Engine No. 2
Source: Wikimedia Commons

Babbage needed to keep his machine as simple as possible, which meant that the simplest solution would be a machine that could calculate all the necessary tables with variations on one algorithm, where an algorithm is just a step-by-step recipe to solve a mathematical problem. However, he needed to calculate logarithms, sines, cosines and tangents, did such an algorithm exist. Yes it did and it had been discovered by Isaac Newton and known as the method of finite differences.

The method of finite differences describes a property shared by all polynomials. If it has been a while since you did any mathematics, polynomials are mathematical expressions of the type x2+5x-3 or 7x5-3x3+2x2-3x+6 or x2-2 etc, etc. If you tabulate the values of a given polynomial for x=0, x=1, x=2, x=3 and so on then subtract the first value from the second, the second from the third and so on you get a new column of numbers. Repeating the process with this column produces yet another column and so on. At some point in the process you end up with a column that is filled with a numerical constant. Confused? OK look at the table below!

 

x x3-3x2+6 xn+1-xn diff(1)n+1 –diff(1)n diff(2)n+1 – diff(2)n
0 6 -2 0 6
1 4 -2 6 6
2 2 4 12 6
3 6 16 18
4 22 34
5 56
6

 

As you can see this particular polynomial bottoms out, so to speak, with as constant of 6. If we now go back into the right hand column and enter a new 6 in the first free line then add this to its immediate left hand neighbour repeating this process across the table we arrive at the polynomial column with the next value for the polynomial. See below:

 

x x3-3x2+6 xn+1-xn diff(1)n+1 –diff(1)n diff(2)n+1 – diff(2)n
0 6 -2 0 6
1 4 -2 6 6
2 2 4 12 6
3 6 16 18 6
4 22 34
5 56
6

 

x x3-3x2+6 xn+1-xn diff(1)n+1 –diff(1)n diff(2)n+1 – diff(2)n
0 6 -2 0 6
1 4 -2 6 6
2 2 4 12 6
3 6 16 18 6
4 22 34 24
5 56
6

 

x x3-3x2+6 xn+1-xn diff(1)n+1 –diff(1)n diff(2)n+1 – diff(2)n
0 6 -2 0 6
1 4 -2 6 6
2 2 4 12 6
3 6 16 18 6
4 22 34 24
5 56 58
6

 

x x3-3x2+6 xn+1-xn diff(1)n+1 –diff(1)n diff(2)n+1 – diff(2)n
0 6 -2 0 6
1 4 -2 6 6
2 2 4 12 6
3 6 16 18 6
4 22 34 24
5 56 58
6 114

This means that if we set up our table and calculate enough values to determine the difference constant then we can by a process of simple addition calculate all further values of the polynomial. This is exactly what Babbage designed his difference engine to do.

If you’ve been paying attention you might notice that the method of finite differences applies to polynomials and Babbage wished to calculate were logarithmic and trigonometrical functions. This is however not a serious problem, through the use of other bits of higher mathematics, which we don’t need to go into here, it is possible to represent both logarithmic and trigonometrical functions as polynomials. There are some problems involved with using the method of finite differences with these polynomials but these are surmountable and Babbage was a good enough mathematician to cope with these difficulties.

Babbage now had a concept and a plan to realise it, all he now needed was the finances to put his plan into action. This was not a problem. Great Britain was a world power with a large empire and the British Government was more than ready to cough up the readies for a scheme to provide reliable mathematical tables for navigation for the Royal Navy and Merchant Marine that serviced, controlled and defended that empire. In total over a period of about ten years the Government provided Babbage with about £17, 000, literally a fortune in the early nineteen hundreds. What did they get for their money, in the end nothing!

Why didn’t Babbage deliver the Difference Engine? There is a widespread myth that Babbage’s computer couldn’t be built with the technology available in the first half of the nineteenth century. This is simply not true, as I said a myth. Several modules of the Difference Engine were built and functioned perfectly. Babbage himself had one, which he would demonstrate at his scientific soirées, amongst other things to demonstrate his theory of miracles.

The Difference Engine model used by Babbage for his demonstrations of his miracle theory Source: Wikimedia Commons

The Difference Engine model used by Babbage for his demonstrations of his miracle theory
Source: Wikimedia Commons

Other Difference Engines modules were exhibited and demonstrated at the Great Exhibition in Crystal Palace. So why didn’t Babbage finish building the Difference Engine and deliver it up to the British Government? Babbage was not an easy man, argumentative and prone to bitter disputes. He became embroiled in one such dispute with Joseph Clement, the engineer who was actually building the Difference Engine, about ownership of and rights to the tools developed to construct the engine and various already constructed elements. Joseph Clement won the dispute and decamped together with said tools and elements. By now Babbage was consumed with a passion for his new computing vision, the general purpose Analytical Engine. He now abandoned the Difference Engine and tried to convince the government to instead finance the, in his opinion, far superior Analytical Engine. Having sunk a fortune into the Difference Engine and receiving nothing in return, the government, not surprisingly, demurred. The much hyped Ada Lovelace Memoire on the Analytical Engine was just one of Babbage’s attempts to advertise his scheme and attract financing.

However, the story of the Difference Engine didn’t end there. Using knowledge that he had won through his work on the Analytical Engine, Babbage produced plans for an improved, simplified Difference Engine 2 at the beginning of the 1850s.

Per Georg Schutz Source: Wikimedia Commons

Per Georg Schutz
Source: Wikimedia Commons

The Swedish engineer Per Georg Scheutz, who had already been designing and building mechanical calculators, began to manufacture difference engines based on Babbage’s plans for the Difference Engine 2 in 1855. He even sold one to the British Government.

Scheutz Difference Engine No. 2. (1859) Maschine im Science Museum, London Source: Wikimedia Commons

Scheutz Difference Engine No. 2. (1859) Maschine im Science Museum, London
Source: Wikimedia Commons

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Filed under History of Computing, History of Mathematics, History of Technology, Myths of Science