Category Archives: History of Astronomy

The emergence of modern astronomy – a complex mosaic: Part XXX

As stated earlier the predominant medieval view of the cosmos was an uneasy bundle of Aristotle’s cosmology, Ptolemaic astronomy, Aristotelian terrestrial mechanics, which was not Aristotle’s but had evolved out of it, and Aristotle’s celestial mechanics, which we will look at in a moment. As also pointed out earlier this was not a static view but one that was constantly being challenged from various other models. In the early seventeenth century the central problem was, having demolished nearly all of Aristotle’s cosmology and shown Ptolemaic astronomy to be defective, without however yet having found a totally convincing successor, to now find replacements for the terrestrial and celestial mechanics. We have looked at the development of the foundations for a new terrestrial mechanics and it is now time to turn to the problem of a new celestial mechanics. The first question we need to answer is what did Aristotle’s celestial mechanics look like and why was it no longer viable?

The homocentric astronomy in which everything in the heavens revolve around a single central point, the earth, in spheres was created by the mathematician and astronomer Eudoxus of Cnidus (c. 390–c. 337 BCE), a contemporary and student of Plato (c. 428/27–348/47 BCE), who assigned a total of twenty-seven spheres to his system. Callippus (c. 370–c. 300 BCE) a student of Eudoxus added another seven spheres. Aristotle (384–322 BCE) took this model and added another twenty-two spheres. Whereas Eudoxus and Callippus both probably viewed this model as a purely mathematical construction to help determine planetary position, Aristotle seems to have viewed it as reality. To explain the movement of the planets Aristotle thought of his system being driven by friction. The outermost sphere, that of the fixed stars drove the outer most sphere of Saturn, which in turn drove the next sphere down in the system and so on all the way down to the Moon. According to Aristotle the outermost sphere was set in motion by the unmoved mover. This last aspect was what most appealed to the churchmen of the medieval universities, who identified the unmoved mover with the Christian God.


During the Middle Ages an aspect of vitalism was added to this model, with some believing that the planets had souls, which animated them. Another theory claimed that each planet had its own angel, who pushed it round its orbit. Not exactly my idea of heaven, pushing a planet around its orbit for all of eternity. Aristotelian cosmology said that the spheres were real and made of crystal. When, in the sixteenth century astronomers came to accept that comets were supralunar celestial phenomena, and not as Aristotle had thought sublunar meteorological ones, it effectively killed off Aristotle’s crystalline spheres, as a supralunar comet would crash right through them. If fact, the existence or non-existence of the crystalline spheres was a major cosmological debate in the sixteenth century. By the early seventeenth century almost nobody still believed in them.

An alternative theory that had its origins in the Middle Ages but, which was revived in the sixteenth century was that the heavens were fluid and the planets swam through them like a fish or flew threw them like a bird. This theory, of course, has again a strong element of vitalism. However, with the definitive collapse of the crystalline spheres it became quite popular and was subscribed to be some important and influential thinkers at the end of the sixteenth beginning of the seventeenth centuries, for example Roberto Bellarmino (1542–1621) the most important Jesuit theologian, who had lectured on astronomy at the University of Leuven in his younger days.


Robert Bellarmine artist unknown Source: Wikimedia Commons

It should come as no surprise that the first astronomer to suggest a halfway scientific explanation for the motion of the planets was Johannes Kepler. In fact he devoted quite a lot of space to his theories in his Astronomia nova (1609).


Astronomia Nova title page Source: Wikimedia Commons

That the periods between the equinoxes and the solstices were of unequal length had been known to astronomers since at least the time of Hipparchus in the second century BCE. This seemed to imply that the speed of either the Sun orbiting the Earth, in a geocentric model, or the Earth orbiting the Sun, in a heliocentric model, varied through out the year. Kepler calculated a table for his elliptical, heliocentric model of the distances of the Sun from the Earth and deduced from this that the Earth moved fastest when it was closest to the Sun and slowest when it was furthest away. From this he deduced or rather speculated that the Sun controlled the motion of the Earth and by analogy of all the planets. The thirty-third chapter of Astronomia nova is headed, The power that moves the planets resides in the body of the sun.

His next question is, of course, what is this power and how does it operate? He found his answer in William Gilbert’s (1544–1603) De Magnete, which had been published in 1600.


William Gilbert Source: Wikimedia Commons

Kepler speculated that the Sun was in fact a magnet, as Gilbert had demonstrated the Earth to be, and that it rotated on its axis in the same way that Gilbert believed, falsely, that a freely suspended terrella (a globe shaped magnet) did. Gilbert had used this false belief to explain the Earth’s diurnal rotation.


It should be pointed out that Kepler was hypothesising a diurnal rotation for the Sun in 1609 that is a couple of years before Galileo had demonstrated the Sun’s rotation in his dispute over the nature of sunspots with Christoph Scheiner (c. 1574–1650). He then argues that there is power that goes out from the rotating Sun that drives the planets around there orbits. This power diminishes with its distance from the Sun, which explains why the speed of the planetary orbits also diminishes the further the respective planets are from the Sun. In different sections of the Astronomia nova Kepler argues both for and against this power being magnetic in nature. It should also be noted that although Kepler is moving in the right direction with his convoluted and at times opaque ideas on planetary motion there is still an element of vitalism present in his thoughts.

Kepler conceived the relationship between his planetary motive force and distance as a simple inverse ratio but it inspired the idea of an inverse squared force. The French mathematician and astronomer Ismaël Boulliau (1605–1694) was a convinced Keplerian and played a central roll in spreading Kepler’s ideas throughout Europe.


Ismaël Boulliau portrait by Pieter van Schuppen Source: Wikimedia Commons

His most important and influential work was his Astronomia philolaica (1645). In this work Boulliau hypothesised by analogy to Kepler’s own law on the propagation of light that if a force existed going out from the Sun driving the planets then it would decrease in inverse squared ratio and not a simple one as hypothesised by Kepler. Interestingly Boulliau himself did not believe that such a motive force for the planet existed.


Another mathematician and astronomer, who looked for a scientific explanation of planetary motion was the Italian, Giovanni Alfonso Borelli (1608–1697) a student of Benedetto Castelli (1578–1643) and thus a second-generation student of Galileo.


Giovanni Alfonso Borelli Source: Wikimedia Commons

Borelli developed a force-based theory of planetary motion in his Theoricae Mediceorum Planatarum ex Causius Physicis Deductae (Theory [of the motion] of the Medicean planets [i.e. moons of Jupiter] deduced from physical causes) published in 1666. He hypothesised three forces that acted on a planet. Firstly a natural attraction of the planet towards the sun, secondly a force emanating from the rotating Sun that swept the planet sideway and kept it in its orbit and thirdly the same force emanating from the sun pushed the planet outwards balancing the inwards attraction.

The ideas of both Kepler and Borelli laid the foundations for a celestial mechanics that would eventually in the work of Isaac Newton, who knew of both theories, produced a purely force-based mathematical explanation of planetary motion.







Filed under History of Astronomy, History of Mathematics, History of Physics, History of science, Mediaeval Science

It’s all a question of angles.

Thomas Paine (1736–1809) was an eighteenth-century political radical famous, or perhaps that should be infamous, for two political pamphlets, Common Sense (1776) and Rights of Man (1791) (he also wrote many others) and for being hounded out of England for his political views and taking part in both the French and American Revolutions.


Thomas Paine portrait of Laurent Dabos c. 1792 Source: Wikimedia Commons

So I was more than somewhat surprised when Michael Brooks, author of the excellent The Quantum Astrologer’s Handbook, posted the following excerpt from Paine’s The Age of Reason, praising trigonometry as the soul of science:


My first reaction to this beautiful quote was that he could be describing this blog, as the activities he names, astronomy, navigation, geometry, land surveying make up the core of the writings on here. This is not surprising as Ivor Grattan-Guinness in his single volume survey of the history of maths, The Rainbow of Mathematics: A History of the Mathematical Sciences, called the period from 1540 to 1660 (which is basically the second half of the European Renaissance) The Age of Trigonometry. This being the case I thought it might be time for a sketch of the history of trigonometry.

Trigonometry is the branch of mathematics that studies the relationships between the side lengths and the angles of triangles. Possibly the oldest trigonometrical function, although not regarded as part of the trigonometrical cannon till much later, was the tangent. The relationship between a gnomon (a fancy word for a stick stuck upright in the ground or anything similar) and the shadow it casts defines the angle of inclination of the sun in the heavens. This knowledge existed in all ancient cultures with a certain level of mathematical development and is reflected in the shadow box found on the reverse of many astrolabes.


Shadow box in the middle of a drawing of the reverse of Astrolabium Masha’Allah Public Library Bruges [nl] Ms. 522. Basically the tangent and cotangent functions when combined with the alidade

Trigonometry as we know it begins with ancient Greek astronomers, in order to determine the relative distance between celestial objects. These distances were determined by the angle subtended between the two objects as observed from the earth. As the heavens were thought to be a sphere this was spherical trigonometry[1], as opposed to the trigonometry that we all learnt at school that is plane trigonometry. The earliest known trigonometrical tables were said to have been constructed by Hipparchus of Nicaea (c. 190–c. 120 BCE) and the angles were defined by chords of circles. Hipparchus’ table of chords no longer exist but those of Ptolemaeus (fl. 150 CE) in his Mathēmatikē Syntaxis (Almagest) still do.


The chord of an angle subtends the arc of the angle. Source: Wikimedia Commons

With Greek astronomy, trigonometry moved from Greece to India, where the Hindu mathematicians halved the Greek chords and thus created the sine and also defined the cosine. The first recoded uses of theses function can be found in the Surya Siddhanta (late 4th or early 5th century CE) an astronomical text and the Aryabhatiya of Aryabhata (476–550 CE).


Statue depicting Aryabhata on the grounds of IUCAA, Pune (although there is no historical record of his appearance). Source: Wikimedia Commons

Medieval Islam in its general acquisition of mathematical knowledge took over trigonometry from both Greek and Indian sources and it was here that trigonometry in the modern sense first took shape.  Muḥammad ibn Mūsā al-Khwārizmī (c. 780–c. 850), famous for having introduced algebra into Europe, produced accurate sine and cosine tables and the first table of tangents.


Statue of al-Khwarizmi in front of the Faculty of Mathematics of Amirkabir University of Technology in Tehran Source: Wikimedia Commons

In 830 CE Ahmad ibn ‘Abdallah Habash Hasib Marwazi (766–died after 869) produced the first table of cotangents. Abū ʿAbd Allāh Muḥammad ibn Jābir ibn Sinān al-Raqqī al-Ḥarrānī aṣ-Ṣābiʾ al-Battānī (c. 858–929) discovered the secant and cosecant and produced the first cosecant tables.

Abū al-Wafāʾ, Muḥammad ibn Muḥammad ibn Yaḥyā ibn Ismāʿīl ibn al-ʿAbbās al-Būzjānī (940–998) was the first mathematician to use all six trigonometrical functions.


Abū al-Wafā Source: Wikimedia Commons

Islamic mathematicians extended the use of trigonometry from astronomy to cartography and surveying. Muhammad ibn Muhammad ibn al-Hasan al-Tūsī (1201–1274) is regarded as the first mathematician to present trigonometry as a mathematical discipline and not just a sub-discipline of astronomy.


Iranian stamp for the 700th anniversary of Nasir al-Din Tusi’s death Source: Wikimedia Commons

Trigonometry came into Europe along with astronomy and mathematics as part the translation movement during the 11th and 12th centuries. Levi ben Gershon (1288–1344), a French Jewish mathematician/astronomer produced a trigonometrical text On Sines, Chords and Arcs in 1342. Trigonometry first really took off in Renaissance Europe with the translation of Ptolemaeus’ Geōgraphikḕ Hyphḗgēsis (Geographia) into Latin by Jacopo d’Angelo (before 1360–c. 1410) in 1406, which triggered a renaissance in cartography and astronomy.

The so-called first Viennese School of Mathematics made substantial contributions to the development of trigonometry in the sixteenth century. John of Gmunden (c. 1380–1442) produced a Tractatus de sinibus, chodis et arcubus. His successor, Georg von Peuerbach (1423–1461), published an abridgement of Gmunden’s work, Tractatus super propositiones Ptolemaei de sinibus et chordis together with a sine table produced by his pupil Regiomontanus (1436–1476) in 1541. He also calculated a monumental table of sines. Regiomontanus produced the first complete European account of all six trigonometrical functions as a separate mathematical discipline with his De Triangulis omnimodis (On Triangles) in 1464. To what extent his work borrowed from Arabic sources is the subject of discussion. Although Regiomontanus set up the first scientific publishing house in Nürnberg in 1471 he died before he could print De Triangulis. It was first edited by Johannes Schöner (1477–1547) and printed and published by Johannes Petreius (1497–1550) in Nürnberg in 1533.

At the request of Cardinal Bessarion, Peuerbach began the Epitoma in Almagestum Ptolomei in 1461 but died before he could complete it. It was completed by Regiomontanus and is a condensed and modernised version of Ptolemaeus’ Almagest. Peuerbach and Regiomontanus replaced the table of chords with trigonometrical tables and modernised many of the proofs with trigonometry. The Epitoma was published in Venice in 1496 and became the standard textbook for Ptolemaic geocentric astronomy throughout Europe for the next hundred years, spreading knowledge of trigonometry and its uses.

In 1533 in the third edition of the Apian/Frisius Cosmographia, Gemma Frisius (1508–1555) published as an appendix the first account of triangulationin his Libellus de locorum describendum ratione. This laid the trigonometry-based methodology of both surveying and cartography, which still exists today. Even GPS is based on triangulation.


With the beginnings of deep-sea exploration in the fifteenth century first in Portugal and then in Spain the need for trigonometry in navigation started. Over the next centuries that need grew for determining latitude, for charting ships courses and for creating sea charts. This led to a rise in teaching trigonometry to seamen, as excellently described by Margaret Schotte in her Sailing School: Navigating Science and Skill, 1550–1800.

One of those students, who learnt their astronomy from the Epitoma was Nicolaus Copernicus (1473–1543). Modelled on the Almagest or more accurately the Epitoma, Copernicus’ De revolutionibus, published by Petreius in Nürnberg in 1543, also contained trigonometrical tables. WhenGeorg Joachim Rheticus (1514–1574) took Copernicus’ manuscript to Nürnberg to be printed, he also took the trigonometrical section home to Wittenberg, where he extended and improved it and published it under the title De lateribus et angulis triangulorum (On the Sides and Angles of Triangles) in 1542, a year before De revolutionibus was published. He would dedicate a large part of his future life to the science of trigonometry. In 1551 he published Canon doctrinae triangvlorvm in Leipzig. He then worked on what was intended to be the definitive work on trigonometry his Opus palatinum de triangulis, which he failed to finish before his death. It was completed by his student Valentin Otho (c. 1548–1603) and published in Neustadt an der Haardt in 1596.


Source: Wikimedia Commons

In the meantime Bartholomäus Pitiscus (1561–1613) had published his own extensive work on both spherical and plane trigonometry, which coined the term trigonometry, Trigonometria: sive de solutione triangulorum tractatus brevis et perspicuous in 1595.


Source: Wikimedia Commons

This work was republished in expanded editions in 1600, 1608 and 1612. The tables contained in Pitiscus’ Trigonometria were calculated to five or six places, where as those of Rheticus were calculated up to more than twenty places for large angles and fifteenth for small ones. However, on inspection, despite the years of effort that Rheticus and Otho had invested in the work, some of the calculations were found to be defective. Pitiscus recalculated them and republished the work as Magnus canon doctrinae triangulorum in 1607. He published a second further improved version under the title Thesaurus mathematicus in 1613. These tables remained the definitive trigonometrical tables for three centuries only being replaced by Henri Andoyer’s tables in 1915–18.

We have come a long way from ancient Greece in the second century BCE to Germany at the turn of the seventeenth century CE by way of Early Medieval India and the Medieval Islamic Empire. During the seventeenth century the trigonometrical relationships, which I have up till now somewhat anachronistically referred to as functions became functions in the true meaning of the term and through analytical geometry received graphical presentations completely divorced from the triangle. However, I’m not going to follow these developments here. The above is merely a superficial sketch that does not cover the problems involved in actually calculating trigonometrical tables or the discovery and development of the various relationships between the trigonometrical functions such as the sine and cosine laws. For a detailed description of these developments from the beginnings up to Pitiscus I highly recommend Glen van Brummelen’s The Mathematics of the Heavens and the Earth: The Early History of Trigonometry, Princeton University Press, Princeton and Oxford, 2009.


[1] For a wonderful detailed description of spherical trigonometry and its history see Glen van Brummelen, Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry, Princeton University Press, Princeton and Oxford, 2013


Filed under History of Astronomy, History of Cartography, History of Mathematics, History of Navigation, History of science, Mediaeval Science, Renaissance Science

Mathematics at the Meridian

Historically Greenwich was a village, home to a royal palace from the fifteenth to the seventeenth centuries, that lay to the southeast of the city of London on the banks of the river Thames, about six miles from Charing Cross. Since the beginning of the twentieth century it has been part of London. With the Cutty Sark, a late nineteenth century clipper built for the Chinese tea trade, the Queen’s House, a seventeenth-century royal residence designed and built by Inigo Jones for Anne of Denmark, wife of James I & VI, and now an art gallery, the National Maritime Museum, Christopher Wren’s Royal Observatory building and of course the Zero Meridian line Greenwich is a much visited, international tourist attraction.

Naturally, given that it is/was the home of the Royal Observatory, the Zero Meridian, the Greenwich Royal Hospital School, the Royal Naval College (of both of which more later), and most recently Greenwich University, Greenwich has been the site of a lot mathematical activity over the last four hundred plus years and now a collection of essays has been published outlining in detail that history: Mathematics at the Meridian: The History of Mathematics at Greenwich[1]


This collection of essays gives a fairly comprehensive description of the mathematical activity that took place at the various Greenwich institutions. As a result it also function as an institutional history, an often-neglected aspect of the histories of science and mathematics with their concentration on big names and significant theories and theorems. Institutions play an important role in the histories of mathematic and science and should receive much more attention than they usually do.

The first four essays in the collection cover the history of the Royal Observatory from its foundation down to when it was finally closed down in 1998 following several moves from its original home in Greenwich. They also contain biographies of all the Astronomers Royal and how they interpreted their role as the nation’s official state astronomer.

This is followed by an essay on the mathematical education at the Greenwich Royal Hospital School. The Greenwich Royal Hospital was established at the end of the seventeenth century as an institution for aged and injured seamen. The institution included a school for the sons of deceased or disabled sailors. The teaching was centred round seamanship and so included mathematics, astronomy and navigation.

When the Greenwich Royal Hospital closed at the end of the nineteenth century the buildings were occupied by the Royal Naval College, which was moved from Portsmouth to Greenwich. The next three chapters deal with the Royal Naval College and two of the significant mathematicians, who had been employed there as teachers and their contributions to mathematics.


Another institute that was originally housed at Greenwich was The Nautical Almanac office, founded in 1832. The chapter dealing with this institute concentrates on the life and work of Leslie John Comrie (1893–1950), who modernised the production of mathematical tables introducing mechanisation to the process.

Today, apart from the Observatory itself and the Meridian line, the biggest attraction in Greenwich is the National Maritime Museum, one of the world’s leading science museums and there is a chapter dedicated to the scientific instruments on display there.


Also today, the buildings that once housed the Greenwich Royal Hospital and then the Royal Naval College now house the University of Greenwich and the last substantial chapter of the book brings the reader up to the present outlining the mathematics that has been and is being taught there.

The book closes with a two-page afterword, The Mathematical Tourist in Greenwich.

Each essay in the book is written by an expert on the topic and they are all well researched and maintain a high standard throughout the entire book. The essays covers a wide and diverse range of topics and will most probably not all appeal equally to all readers. Some might be more interested in the history of the Royal Observatory, whilst the chapters on the mathematical education at the Greenwich Royal Hospital School and on its successor the Royal Naval College should definitely be of interest to the readers of Margaret Schotte’s Sailing School, which I reviewed in an earlier post.

Being the hopelessly non-specialist that I am, I read, enjoyed and learnt something from all of the essays. If I had to select the four chapters that most stimulated me I would chose the opening chapter on the foundation and early history of the Royal Observatory, the chapter on George Biddel Airy and his dispute with Charles Babbage over the financing of the Difference Engine, which I blogged about in December, the chapter on Leslie John Comrie, as I’ve always had a bit of a thing about mathematical tables and finally, one could say of course, the chapter on the scientific instruments in the National Maritime Museum.

The book is nicely illustrated with, what appears to have become the standard for modern academic books, grey in grey prints. There are extensive endnotes for each chapter, which include all of the bibliographical references, there being no general bibliography, which I view as the books only defect. There is however a good, comprehensive general index.

I can thoroughly recommend this book for anybody interested in any of the diverse topic covered however, despite what at first glance, might appear as a somewhat specialised book, I can also recommend it for the more general reader interested in the histories of mathematics, astronomy and navigation or those perhaps interested in the cultural history of one of London’s most fascinating district. After all mathematics, astronomy and navigation are all parts of human culture.

[1] Mathematics at the Meridian: The History of Mathematics at Greenwich, eds. Raymond Flood, Tony Mann, Mary Croarken, CRC Press, Taylor & Francis Group, Bacon Raton, London, New York, 2020.


Filed under Book Reviews, History of Astronomy, History of Mathematics, History of Navigation

Stylish writing is not necessarily good science

I have become somewhat infamous for writing #histSTM blog posts that are a predominately negative take on the scientific achievements of Galileo Galilei. In fact I think I probably made my breakthrough as a #histsci blogger with my notorious Extracting the Stopper post, deflating Galileo’s popular reputation. I actually got commissioned to write a toned down version of that post for AEON several years later. In my opinion Galileo was an important figure in the evolution of science during the early seventeenth century but his reputation has been blown up out of all proportion, well beyond his actual contributions. To make a simple comparison, in the same period of time the contributions of Johannes Kepler were immensely greater and more significant than those made by Galileo but whereas Galileo is regarded as one of the giants of modern science and is probably one of the three most well known historical practitioners of the mathematical sciences, alongside Newton and Einstein, Kepler is at best an also ran, whose popular image is not even a fraction of that of Galileo’s. This of course raises the question, why? What does/did Galileo have that Kepler didn’t? I think the answer lies in Galileo’s undeniable talents as a writer.

Galileo was a master stylist, a brilliant polemicist and science communicator, whose major works are still a stimulating pleasure to read. If you ask people about Galileo they will more often than not quote one of his well-known turns of phrase rather than his scientific achievements. The two books trope with its ‘mathematics is the language of nature’, which in the original actually reads: Philosophy is written in this grand book, which stands continually open before our eyes (I say the ‘Universe’), but can not be understood without first learning to comprehend the language and know the characters as it is written. It is written in mathematical language, and its characters are triangles, circles and other geometric figures, without which it is impossible to humanly understand a word; without these one is wandering in a dark labyrinth. Or the much-loved, the Bible shows the way to go to heaven, not the way the heavens go, which again in the original reads: The intention of the Holy Ghost is to teach us how one goes to heaven, not how heaven goes. It is a trivial truth that Galileo had a way with words.

This cannot be said of Johannes Kepler. I shall probably bring the wrath of a horde of Kepler scholars on my head for saying this but even in translation, Johannes Kepler is anything but an easy read. Galileo even commented on this. When confronted with Kepler’s Dioptrice (1611), one of the most important books on optics ever written, Galileo complained that it was turgid and unreadable. Having ploughed my way through it in German translation, I sympathise with Galileo’s negative judgement. However, in his rejection Galileo failed to realise just how scientifically important the Dioptrice actually was. Nobody in their right mind would describe Kepler as a master stylist or a brilliant polemicist.

I think this contrast in literary abilities goes a long way to explaining the very different popular conceptions of the two men. People read Galileo’s major works or selections from them and are stimulated and impressed by his literary mastery, whereas Kepler’s major works are not even presented, as something to be read by anyone, who is not a historian of science. One just gets his three laws of planetary motion served up in modern guise, as a horribly mathematical side product of heliocentricity.

Of course, a serious factor in their respective notorieties is Galileo’s infamous trial by the Roman Inquisition. This was used to style him as a martyr for science, a process that only really began at the end of the eighteenth and beginning of the nineteenth centuries. Kepler’s life, which in many ways was far more spectacular and far more tragic than Galileo’s doesn’t have such a singular defining moment in it.

Returning to the literary theme I think that what has happened is that non-scientists and non-historians of science have read Galileo and impressed by his literary abilities, his skill at turning a phrase, his adroit, and oft deceitful, presentation of pro and contra arguments often fail to notice that they are being sold a pup. As I tried to make clear in the last episode of my continuing ‘the emergence of modern astronomy’ series although Galileo’s Dialogo has an awesome reputation in Early Modern history, its scientific value is, to put it mildly, negligible. To say this appears to most people as some form of sacrilege, “but the Dialogo is an important defence of science against the forces of religious ignorance” or some such they would splutter. But in reality it isn’t, as I hope I made clear the work contributed nothing new to the on going debate and all that Galileo succeeded in doing was getting up the Pope’s nose.

The same can be said of Il Saggiatore, another highly praised work of literature. As I commented in another post the, oft quoted line on mathematics, which had led to Galileo being praised as the man, who, apparently single handed, mathematized the physical science was actually, when he wrote it, old hat and others had been writing the book of nature in the language of mathematics for at least one hundred years before Galileo put pen to paper but none of them had taken the time to express what they were doing poetically. In fact it took historians of science a long time to correct this mistaken perception, as they also tended to suffer from a serious dose of Galileo adoration. The core of Il Saggiatore is as I have explained elsewhere is total rubbish, as Galileo is arguing against the scientific knowledge of his time with very spurious assertions merely so that he doesn’t have to acknowledge that Grassi is right and he is wrong. An admission that very few Galileo scholars are prepared to make in public, it might tarnish his reputation.

Interestingly one work that deserves its historical reputation Galileo’s Sidereus Nuncius, also suffers from serious scientific deficits that tend to get overlooked. Written and published in haste to avoid getting beaten to the punch by a potential, unknown rival the book actually reads more like an extended press release that a work of science. It might well be that Galileo intended to write a more scientific evaluation of his telescopic observations and discoveries once he had established his priority but somehow, having become something of a scientific superstar overnight, he never quite got round to it. This is once again a failing that most readers tend to overlook, over awed by the very impressive literary presentation.

Much of Galileo’s written work is actually more appearance than substance, or as the Germans say Mehr Schein als Sein, but ironically, there is one major work of Galileo’s that is both literarily brilliant and scientifically solid but which tends to get mostly overlooked, his Discorsi. The experiments on which part of it is based get described by the book itself remains for most people largely unknown. I shall be taking a closer look at it in a later post.







Filed under History of Astronomy, History of Optics, History of Physics, Myths of Science, Renaissance Science

The emergence of modern astronomy – a complex mosaic: Part XXVII

Without a doubt the most well-known, in fact notorious, episode in the transition from a geocentric to a heliocentric cosmology/astronomy in the seventeenth century was the publication of Galileo Galilei’s Dialogo sopra i due massimi sistemi del mondo (Dialogue Concerning the Two Chief World Systems) in 1632 and his subsequent trial and conviction by the Supreme Sacred Congregation of the Roman and Universal Inquisition or simply Roman Inquisition; an episode that has been blown up out of all proportions over the centuries. It would require a whole book of its own to really do this subject justice but I shall deal with it here in two sketches. The first to outline how and why the publication of this book led to Galileo’s trial and the second to assess the impact of the book on the seventeenth century astronomical/cosmological debate, which was much less than is often claimed.


Frontispiece and title page of the Dialogo, 1632 Source: Wikimedia Commons

The first salient point is Galileo’s social status in the early seventeenth century. Nowadays we place ‘great scientists’ on a pedestal and accord them a very high social status but this was not always the case. In the Renaissance, within society in general, natural philosophers and mathematicians had a comparatively low status and within the ruling political and religious hierarchies Galileo was effectively a nobody. Yes, he was famous for his telescopic discoveries but this did not change the fact that he was a mere mathematicus. As court mathematicus and philosophicus to the Medici in Florence he was little more than a high-level court jester, he should reflect positively on his masters. His role was to entertain the grand duke and his guests at banquets and other social occasions with his sparkling wit, either in the form of a discourse or if a suitable opponent was at hand, in a staged dispute. Points were awarded not for truth content but for verbal brilliance. Galileo was a master at such games. However, his real status as a courtier was very low and should he bring negative attention to the court, they would drop him without a thought, as they did when the Inquisition moved against him.


Galileo Portrait by Ottavio Leoni Source: Wikimedia Commons

As a cardinal, Maffeo Barberini (1568–1644) had befriended Galileo when his first came to prominence in 1611 and he was also an admirer of the Accademia dei Lincei. When he was elected Pope in 1623 the Accademia celebrated his election and amongst other things presented him with a copy of Galileo’s Il Saggiatore, which he read and apparently very much enjoyed. As a result he granted Galileo several private audiences, a great honour. Through his actions Barberini had raised Galileo to the status of papal favourite, a situation not without its dangers.


C. 1598 painting of Maffeo Barberini at age 30 by Caravaggio Source: Wikimedia Commons

Mario Biagioli presents the, I think correct, hypothesis that having raised Galileo up as a court favourite Barberini then destroyed him. Such behaviour was quite common under absolutist rulers, as a power demonstration to intimidate potential rebels. Galileo was a perfect victim for such a demonstration highly prominent and popular but with no real political or religious significance. Would Barberini have staged such a demonstration at the time? There is evidence that he was growing more and more paranoid during this period. Barberini, who believed deeply in astrology, heard rumours that an astrologer had foreseen his death in the stars. His death was to coincide with a solar eclipse in 1630. Barberini with the help of his court astrologer, Tommaso Campanella (1568–1639) took extreme evasive action and survived the cosmic threat but he had Orazio Morandi (c. 1570–1630), a close friend and supporter of Galileo’s, arrested and thrown in the papal dungeons, where he died, for having cast the offending horoscope.

Turning to the Dialogo, the official bone of contention, Galileo succeeded in his egotism in alienating Barberini with its publication. Apparently during the phase when he was very much in Barberini’s good books, Galileo had told the Pope that the Protestants were laughing at the Catholics because they didn’t understand the heliocentric hypothesis. Of course, during the Thirty Years War any such mockery was totally unacceptable. Barberini gave Galileo permission to write a book presenting and contrasting the heliocentric and geocentric systems but with certain conditions. Both systems were to be presented as equals with no attempts to prove the superiority or truth of either and Galileo was to include the philosophical and theological opinion of the Pope that whatever the empirical evidence might suggest, God in his infinite wisdom could create the cosmos in what ever way he chose.

The book that Galileo wrote in no way fulfilled the condition stated by Barberini. Presented as a discussion over four days between on the one side a Copernican, Salviati named after Filippo Salviati (1682–1614) a close friend of Galileo’s and Sagredo, supposedly neutral but leaning strongly to heliocentricity, named after Giovanni Francesco Sagredo (1571–1620) another close friend of Galileo’s. Opposing these learned gentlemen is Simplicio, an Aristotelian, named after Simplicius of Cilicia a sixth-century commentator on Aristotle. This name is with relative certainty a play on the Italian word “semplice”, which means simple as in simple minded. Galileo stacked the deck from the beginning.

The first three days of discussion are a rehash of the previous decades of discoveries and developments in astronomy and cosmology with the arguments for heliocentricity, or rather against geocentricity in its Ptolemaic/Aristotelian form, presented in their best light and the counter arguments presented decidedly less well. Galileo was leaving nothing to chance, he knew who was going to win this discussion. The whole thing is crowned with Galileo’s theory of the tides on day four, which he falsely believed, despite its very obvious flaws, to be a solid empirical proof of the Earth’s movements in a heliocentric model. This was in no way an unbiased presentation of two equal systems but an obvious propaganda text for heliocentricity. Worse than this, he placed the Pope’s words on the subject in the mouth of Simplicio, the simpleton, not a smart move. When it was published the shit hit the fan.

However, before considering the events leading up to the trial and the trial itself there are a couple of other factors that prejudiced the case against Galileo. In order to get published at all, the book, as with every other book, had to be given publication permission by the censor. To repeat something that people tend to forget, censorship was practiced by all secular and all religious authorities throughout the whole of Europe and was not peculiar to the Catholic Church. Freedom of speech and freedom of thought were alien concepts in the world of seventeenth century religion and politics. Galileo wanted initially to title the book, Dialogue on the Ebb and Flow of the Seas, referring of course to his theory of the tides, and include a preface to this effect. He was told to remove both by the censor, as they, of course, implied a proof of heliocentricity. Because of an outbreak of the plague, Galileo retired to Florence to write his book and preceded to play the censor in Florence and the censor in Rome off against each other, which meant that the book was published without being properly controlled by a censor. This, of course, all came out after publication and did not help Galileo’s case at all; he had been far too clever for his own good.

Another major problem had specifically nothing to do with Galileo in the first instance but rebounded on him at the worst time.  On 8 March 1632 Cardinal Borgia castigated the Pope for not supporting King Philipp IV of Spain against the German Protestants. The situation almost degenerated into a punch up with the Swiss Guard being called in to separate the adversaries. As a result Barberini decided to purge the Vatican of pro-Spanish elements. One of the most prominent men to be banished was Giovanni Ciampoli (1589–1643) Barberini’s chamberlain. Ciampoli was an old friend and supporter of Galileo and a member of the Accademia dei Lincei. He was highly active in helping Galileo trick the censors and had read the manuscript of the Dialogo, telling Barberini that it fulfilled his conditions. His banishment was a major disaster for Galileo.


Giovanni Ciampoli Source: Wikimedia Commons

One should of course also not forget that Galileo had effectively destroyed any hope of support from the Jesuits, the leading astronomers and mathematicians of the age, who had very actively supported him in 1611, with his unwarranted and libellous attacks on Grazi and Scheiner in his Il Saggiatore. He repeated the attacks on Scheiner in the Dialogo, whilst at the same time plagiarising him, claiming some of Scheiner’s sunspot discoveries as his own. There is even some evidence that the Jesuits worked behind the scenes urging the Pope to put Galileo on trial.

When the Dialogo was published it immediately caused a major stir. Barberini appointed officials to read and assess it. Their judgement was conclusive, the Dialogo obviously breached the judgement of 1616 forbidding the teaching of heliocentricity as a factual theory. Anybody reading the Dialogo today would confirm that judgement. The consequence was that Galileo was summoned to Rome to answer to the Inquisition. Galileo stalled claiming bad health but was informed either he comes or he would be fetched. The Medici’s refused to support him; they did no consider him worth going into confrontation with the Pope for.


Ferdinando II de’ Medici Grand Duke of Tuscany in Coronation Robes (school of Justus Sustermans). Source: Wikimedia Commons

We don’t need to go into details of the trial. Like all authoritarian courts the Inquisition didn’t wish to try their accused but preferred them to confess, this was the case with Galileo. During his interviews with the Inquisition Galileo was treated with care and consideration because of his age and bad health. He was provided with an apartment in the Inquisition building with servants to care for him. At first he denied the charges but when he realised that this wouldn’t work he said that he had got carried away whilst writing and he offered to rewrite the book. This also didn’t work, the book was already on the market and was a comparative best seller, there was no going back. Galileo thought he possessed a get out of jail free card. In 1616, after he had been interviewed by Bellarmino, rumours circulated that he had been formally censured by the Inquisition. Galileo wrote to Bellarmino complaining and the Cardinal provided him with a letter stating categorically that this was not the case. Galileo now produced this letter thinking it would absolve him of the charges. The Inquisition now produced the written version of the statement that had been read to Galileo by an official of the Inquisition immediately following his interview with Bellarmino expressly forbidding the teaching of the heliocentric theory as fact. This document still exists and there have been discussions as to its genuineness but the general consensus is that it is genuine and not a forgery. Galileo was finished, guilty as charged. Some opponents of the Church make a lot of noise about Galileo being shown the instruments of torture but this was a mere formality in a heresy trial and at no point was Galileo threatened with torture.

The rest is history. Galileo confessed and formally adjured to the charge of grave suspicion of heresy, compared to heresy a comparatively minor charge. He was sentenced to prison, which was immediately commuted to house arrest. He spent the first months of his house arrest as the guest of Ascanio II Piccolomini (1590–1671), Archbishop of Siena,


Ascanio II Piccolomini Source: Wikimedia Commons

until Barberini intervened and sent him home to his villa in Arcetri. Here he lived out his last decade in comparative comfort, cared for by loyal servants, receiving visitor and writing his most important book, Discorsi e dimostrazioni matematiche intorno a due nuove scienze (Discourses and Mathematical Demonstrations Relating to Two New Sciences).

Galileo’s real crime was hubris, trying to play an absolutist ruler, the Pope, for a fool. Others were executed for less in the seventeenth century and not just by the Catholic Church. Galileo got off comparatively lightly.

What role did the Dialogo actually play in the ongoing cosmological/astronomical debate in the seventeenth century? The real answer is, given its reputation, surprisingly little. In reality Galileo was totally out of step with the actual debate that was taking place around 1630. Driven by his egotistical desire to be the man, who proved the truth of heliocentricity, he deliberately turned a blind eye to the most important developments and so side lined himself.

We saw earlier that around 1613 there were more that a half a dozen systems vying for a place in the debate, however by 1630 nearly all of the systems had been eliminated leaving just two in serious consideration. Galileo called his book Dialogue Concerning the Two Chief World Systems, but the two systems that he chose to discuss, the Ptolemaic/Aristotelian geocentric system and the Copernican heliocentric system, were ones that had already been rejected by almost all participants in the debate by 1630 . The choice of the pure geocentric system of Ptolemaeus was particularly disingenuous, as Galileo had helped to show that it was no longer viable twenty years earlier. The first system actually under discussion when Galileo published his book was a Tychonic geo-heliocentric system with diurnal rotation, Christen Longomontanus (1562–1647), Tycho’s chief assistant, had published an updated version based on Tycho’s data in his Astronomia Danica in 1622. This was the system that had been formally adopted by the Jesuits.


The second was the elliptical heliocentric system of Johannes Kepler, of which I dealt with the relevant publications in the last post.

Galileo completely ignores Tycho, whose system could explain all of the available evidence for heliocentricity, because he didn’t want to admit that this was the case, arguing instead that the evidence must imply a heliocentric system. He also, against all the available empirical evidence, maintained his belief that comets were sublunar meteorological phenomena, because the supporters of a Tychonic system used their perceived solar orbit as an argument for their system.  He is even intensely disrespectful to Tycho in the Dialogo, for which Kepler severely castigated him. He also completely ignores Kepler, which is even more crass, as the best available arguments for heliocentricity were to be found clearly in Kepler published works. Galileo could not adopt Kepler’s system because it would mean that Kepler and not he would be the man, who proved the truth of the heliocentric system.

Although the first three days of the Dialogo provide a good polemic presentation for all of the evidence up till that point for a refutation of the Ptolemaic/Aristotelian system, with the very notable exception of the comets, Galileo’s book was out dated when it was written and had very little impact on the subsequent astronomical/cosmological debate in the seventeenth century. I will indulge in a little bit of hypothetical historical speculation here. If Galileo had actually written a balanced and neutral account of the positive and negative points of the Tychonic geo-heliocentric system with diurnal rotation and Kepler’s elliptical heliocentric system, it might have had the following consequences. Firstly, given his preeminent skills as a science communicator, his book would have been a valuable contribution to the ongoing debate and secondly he probably wouldn’t have been persecuted by the Catholic Church. However, one can’t turn back the clock and undo what has already been done.

I will close this overlong post with a few brief comments on the impact of the Church’s ban on the heliocentric theory, the heliocentric hypothesis was still permitted, and the trial and sentencing of Galileo, after all he was the most famous astronomer in Europe. Basically the impact was much more minimal than is usually implied in all the popular presentations of the subject. Outside of Italy these actions of the Church had almost no impact whatsoever, even in other Catholic countries. In fact a Latin edition of the Dialogo was published openly in Lyon in 1641, by the bookseller Jean-Antoine Huguetan (1567–1650), and dedicated to the French diplomat Balthasar de Monconys (1611–1665), who was educated by the Jesuits.


Within Italy well-behaved Catholics censored their copies of Copernicus’ De revolutionibus according to the Church’s instructions but continued to read and use them. Censored copies of the book are virtually unknown outside of Italy. Also within Italy, astronomers would begin their discussions of heliocentricity by stating in the preface that the Holy Mother Church in its wisdom had declared this system to be false, but it is an interesting mathematical hypothesis and then go on in their books to discuss it fully. On the whole the Inquisition left them in peace.


***A brief footnote to the above: this is a historical sketch of what took place around 1630 in Northern Italy written from the viewpoint of the politics, laws and customs that ruled there at that time. It is not a moral judgement on the behaviour of either the Catholic Church or Galileo Galilei and I would be grateful if any commentators on this post would confine themselves to the contextual historical facts and not go off on wild moral polemics based on hindsight. Comments on and criticism of the historical context and/or content are, as always, welcome.











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

Christmas Trilogy Part 3: The emergence of modern astronomy – a complex mosaic: Part XXVI


In popular presentations of the so-called scientific or astronomical revolutions Galileo Galilei is almost always presented as the great champion of heliocentricity in the first third of the seventeenth century. In fact, as we shall see, his contribution was considerably smaller than is usually claimed and mostly had a negative rather than a positive influence. The real champion of heliocentricity in this period was Johannes Kepler, who in the decade between 1617 and 1627 published four major works that laid the foundations for the eventual triumph of heliocentricity over its rivals. I have already dealt with one of these in the previous post in this series, the De cometis libelli tres I. astronomicus, theoremata continens de motu cometarum … II. physicus, continens physiologiam cometarum novam … III. astrologicus, de significationibus cometarum annorum 1607 et 1618 / autore Iohanne Keplero …, which was published in 1619 and as I’ve already said became the most important reference text on comets in the 1680’s during a period of high comet activity that we will deal with in a later post.


Source: ETH Library Zurich

Chronologically the first of Kepler’s influential books from this decade was Volume I (books I–III) of his Epitome Astronomiae Copernicanae published in 1617, Volume II (book IV) followed in 1620 and Volume III (books V–VII) in 1621. This was a text book on heliocentric astronomy written in question and answer dialogue form between a teacher and a student spelling out the whole of heliocentric astronomy and cosmology in comparatively straight forward and simple terms, the first such textbook. There was a second edition containing all three volumes in 1635.


Second edition 1635 Source

This book was highly influential in the decades following its publication and although it claims to be a digest of Copernican astronomy, it in fact presents Kepler’s own elliptical astronomy. For the first time his, now legendary, three laws of planetary motion are presented as such together. As we saw earlier the first two laws–I. The orbit of a planet is an ellipse and the Sun is at one of the focal points of that ellipse II: A line connecting the Sun and the planet sweeps out equal areas in equal times–were published in his Astronomia Nova in 1609. The third law was new first appearing in, what he considered to be his opus magnum, Ioannis Keppleri Harmonices mundi libri V (The Five Books of Johannes Kepler’s The Harmony of the World) published in 1619 and to which we now turn our attention.


Source: Wikimedia Commons

Kepler’s first book was his Mysterium Cosmographicum published in 1597 with its, to our way of thinking, somewhat bizarre hypothesis that there are only six planets because the spaces between their orbits are defined by the five regular Platonic solids.


Kepler’s Platonic solid model of the Solar System from Mysterium Cosmographicum Source: Wikimedia Commons

Although his calculation in 1597 showed a fairly good geometrical fit for his theory, it was to Kepler’s mind not good enough and this was his motivation for acquiring Tycho Brahe’s newly won more accurate data for the planetary orbits. He believed he could quite literally fine tune his model using the Pythagorean theory of the harmony of the spheres, that is that the ratio of the planetary orbits build a musical scale that is only discernable to the enlightened Pythagorean astronomer. The Harmonices Mundi was that fine tuning.

The first two books of the Harmonices Mundi layout Kepler’s geometrical theory of music, which geometrical constructions produced harmonious musical intervals and which disharmonious ones, based on which are constructible with straight edge and compass, harmonious, and which are not, disharmonious. The third book is Kepler’s contribution to the contemporary debate on the correct division of the intervals of the musical scale, in which Vincenzo Galilei (1520–1591), Galileo’s father, had played a leading role. The fourth book is the application of the whole to astrology and the fifth its application to astronomy and it is here that we find the third law.

In the fifth Kepler compare all possible ratios of planetary speeds and distances constructing musical scales for planets and musical intervals for the relationship between planets. It is here that he, one could say, stumbles upon his third law, which is known as the harmony law. Kepler was very much aware of the importance of his discovery as he tells us in his own words:

“After I had discovered true intervals of the orbits by ceaseless labour over a very long time and with the help of Brahe’s observations, finally the true proportion of the orbits showed itself to me. On the 8th of March of this year 1618, if exact information about the time is desired, it appeared in my head. But I was unlucky when I inserted it into the calculation, and rejected it as false. Finally, on May 15, it came again and with a new onset conquered the darkness of my mind, whereat there followed such an excellent agreement between my seventeen years of work at the Tychonic observations and my present deliberation that I at first believed that I had dreamed and assumed the sought for in the supporting proofs. But it is entirely certain and exact that the proportion between the periodic times of any two planets is precisely one and a half times the proportion of the mean distances.”

Translated into modern notation the third law is P12/P22=R13/R23, where P is the period of a planet and R is the mean radius of its orbit. It can be argues that this was Kepler’s greatest contribution to the history of the emergence of heliocentricity but rather strangely nobody really noticed its true significance until Newton came along at the end of the seventeenth century.

However they should have done because the third law gives us is a direct mathematical relationship between the size of the orbits of the planets and their duration, which only works in a heliocentric system. There is nothing comparable for either a full geocentric system or for a geo-heliocentric Tychonic or semi-Tychonic system. It should have hit the early seventeenth-century astronomical community like a bomb but it didn’t, which raises the question why it didn’t. The answer is because it is buried in an enormous pile of irrelevance in the Harmonices Mundi and when Kepler repeated it in the Epitome he gave it no real emphasis, so it remained relatively ignored.

On a side note, it is often thought that Kepler had abandoned his comparatively baroque Platonic solids concepts from the Mysterium Cosmographicum but now that he had, in his opinion, ratified it in the Harmonices Mundi he published a second edition of the book in 1621.


Second Edition 1621 Source

Ironically the book of Kepler’s that really carried the day for heliocentricity against the geocentric and geo-heliocentric systems was his book of planetary tables based on Tycho Brahe’s data the Tabulae Rudolphinae (Rudolphine Tables) published in 1627, twenty-eight years after he first began working on them. Kepler had in fact been appointed directly by Rudolph II in Prague to produce these tables at the suggestion of Tycho in 1601. Turning Tycho’s vast collection of data into accurately calculated tables was a horrendous and tedious task and over the years Kepler complained often and bitterly about this burden.


Tabulae Rudolphinae The frontispiece presents in graphic form a potted history of Western astronomy Source

However, he persevered and towards the end of the 1620s he was so far. Because he was the Imperial Mathematicus and had prepared the tables under the orders of the Emperor he tried to get the funds to cover the printing costs from the imperial treasury. This proved to be very difficult and after major struggles he managed to acquire 2000 florins of the more than 6000 that the Emperor owed him, enough to pay for the paper. He began printing in Linz but in the turmoil of the Thirty Years War the printing workshop got burnt down and he lost the already printed pages. Kepler decamped to Ulm, where with more difficulties he succeeded in finishing the first edition of 1000 copies. Although these were theoretically the property of the Emperor, Kepler took them to the Frankfurt book fair where he sold the entire edition to recoup his costs.

The Tabulae Rudolphinae were pretty much an instant hit. The principle function of astronomy since its beginnings in Babylon had always been to produce accurate tables and ephemerides for use initially by astrologers and then with time also cartographers, navigators etc. Astronomical systems and the astronomers, who created them, were judged on the quality and accuracy of their tables. Kepler’s Tabulae Rudolphinae based on Tycho’s data were of a level of accuracy previous unknown and thus immediately won many supporters. Those who used the tables assumed that their accuracies was due to Kepler’s elliptical planetary models leading to a gradually increasing acceptance of heliocentricity but this was Kepler’s system and not Copernicus’. Supported by the Epitome with the three laws of planetary motion Kepler’s version of heliocentricity became the dominant astronomical/cosmological system over the next decades but it would be another thirty to forty years, long after Kepler’s death, before it became the fully accepted system amongst astronomers.









Filed under History of Astrology, History of Astronomy, History of science, Renaissance Science

Christmas Trilogy 2019 Part 2: Babbage, Airy and financing the Difference Engine.

Charles Babbage first announced his concept for his first computer, the Difference Engine, in a Royal Astronomical Society paper, Note on the application of machinery to the computation of astronomical and mathematical tables in 1822.


Engraving of Charles Babbage dated 1833 Source: Wikimedia Commons

He managed to convince the British Government that a mechanical calculator would be useful for producing numerical tables faster, cheaper and more accurately and in 1823 they advance Babbage £1700 to begin construction of a full scale machine. It took Babbage and his engineer, Joseph Clements, nine years to produce a small working model but costs had spiralled out of control and the government suspended payment at around £17,000, in those days a small fortune, in 1833.


A portion of the difference engine. Woodcut after a drawing by Benjamin Herschel Babbage Source: Wikimedia Commons

Babbage and Clement had parted in dispute by this time. The next nine years saw Babbage negotiating with various government officials to try and get payment reinstated. Enter George Biddel Airy (1801–1892).


George Biddell Airy caricatured by Ape in Vanity Fair Nov 1875 Source: Wikimedia Commons

Airy entered Trinity College Cambridge in 1819, graduating Senior Wrangler and Smith Prize man in 1823. He was elected a fellow of Trinity in 1824 and Lucasian Professor of mathematics beating Babbage for the position in 1826. In 1828 he was elected Plumian Professor of astronomy and director of the new Cambridge Observatory. Babbage succeeded him as Lucasian Professor. Airy proved very competent and very efficient as the director of the observatory, which led to him being appointed Astronomer Royal at the Greenwich Observatory in 1835 and thus the leading state scientist and effectively the government scientific advisor. It was in this capacity that the paths of the two Cambridge mathematicians crossed once again[1].

In 1842 Henry Goulburn (1784–1856), Chancellor of the Exchequer in the cabinet of Sir Robert Peel (1788–1850) was asked by Peel to gather information on Babbage’s Difference Engine project, which he would have liked to ditch, preferable yesterday rather than tomorrow. Goulburn turned to Airy as the countries leading scientific civil servant and also because the Royal Observatory was responsible for producing many of the mathematical tables, the productions of which the Difference Engine was supposed to facilitate. Could Airy offer an opinion on the utility of the proposed mechanical calculator? Airy could and it was anything but positive:

Mr Babbage made the approval of the machine a personal question. In consequence of this, I, and I believe other persons, have carefully abstained for several years from alluding to it in his presence. I think he lives in a sort of dream as to its utility.

An absurd notion has been spread abroad, that the machine was intended for all calculations of every kind. This is quite wrong. The machine is intended solely for calculations which can be made by addition and subtraction in a particular way. This excludes all ordinary calculation.

Scarcely a figure of the Nautical Almanac could be computed by it. Not a single figure of the Geenwich Observations or the great human Computations now going on could be computed by it. Indeed it was proposed only for the computation of new Tables (as Tables of Logarithms and the like), and even for these, the difficult part must be done by human computers. The necessity for such new tables does not occur, as I really believe, once in fifty years. I can therefore state without the least hesitation that I believe the machine to be useless, and that the sooner it is abandoned, the better it will be for all parties[2].

Airy’s opinion was devastating Peel acting on Goulburn’s advice abandoned the financing of the Difference Engine once and for all. Even the personal appeals of Babbage directly to Peel were unable to change this decision. Airy’s judgement was actually based on common sense and solid economic arguments. The tables computed by human computers were comparatively free of errors and nothing could be gained here by replacing their labour with a machine that would probably prove more expensive. Also setting up the machine to compute any particular set of tables would first require human computers to determine the initially values for the algorithms and to determine that the approximations delivered by the difference series remained within an acceptable tolerance range. Airy could really see no advantages in employing Babbage’s machine rather than his highly trained human computers. Also any human computers employed to work with the Difference Engine would, by necessity, also need first to be trained for the task.

Airy’s views on the utility or rather lack thereof of mechanical calculators was shared by the Swedish astronomer Nils Seelander (1804–1870) also used the same arguments against the use of mechanical calculators in 1844 as did Urbain Le Verrier (1811–1877) at the Paris Observatory.

Babbage was never one to take criticism or defeat lying down and in 1851 when the working model of the Difference Engine No. 1 was on display at the Great Exhibition he launched a vicious attack on Airy in his book The Exposition of 1851: Views of The Industry, The Science and The Government of England.


Babbage was not a happy man. By 1851 Airy was firmly established as a leading European scientist and an exemplary public servant and could and did publically ignore Babbage’s diatribe. Privately he wrote a parody of the rhyme This is the House that Jack Built mocking Babbage’s efforts to realise his Difference Engine. Verse seven of This is the Engine that Charles Built reads as follows:

There are Treasury lords, slightly furnished with sense,

Who the wealth of the nation unfairly dispense:

They know but one man, in the Queen’s vast dominion,

Who in things scientific can give an opinion:

And when Babbage for funds for the Engine applied,

The called upon Airy, no doubt, to decide:

And doubtless adopted, in apathy slavish,

The hostile suggestions of enmity knavish:

The powers of official position abused,

And flatly all further advances refused.

For completing the Engine that Charles built.[3]

Today Charles Babbage is seen as a visionary in the history of computers and computing, George Airy very clearly did not share that vision but he was no Luddite opposing the progress of technology out of principle. His opposition to the financing of Babbage’s Difference Engine was based on sound mathematical and financial principles and delivered with well-considered arguments.

[1] The following account is based almost entirely on Doran D. Swade’s excellent paper, George Biddell Airy, Greenwich and the Utility of Calculating Engines in Mathematics at the Meridian: The History of Mathematics at Greenwich, de. Raymond Flood, Tony Mann & Mary Croarken, CRC Press, Boca Raton, London New York, 2019 pp. 63–81. A review of the entire, excellent volume will follow some time next year.

[2] All three quotes are from Airy’s letter to Goulburn 16 September 1842 RGO6–427, f. 65. Emphasis original. Quoted by Swade p. 69.

[3] Swade p. 74 The whole poem can be read in Appendix I of Doran David Swade, Calculation and Tabulation in the Nineteenth Century: Airy versus Babbage, Thesis submitted for the degree of PhD, University College London, 2003, which of course deals with the whole story in great depth and detail and is available here on the Internet.

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Filed under History of Astronomy, History of Computing, History of Mathematics, History of science