Category Archives: History of Optics

If you are going to blazon out history of science ‘facts’ at least get them right

Today’s Torygraph has a short video entitled 10 Remarkable Facts about rainbows, at 57 seconds it displays the following text:

Until the 17th Century, no one had

the faintest idea what a rainbow

was, how it got there or what it was

made of…

This is, of course, simply not true. In the 14th century the Persian scholar Kamal al-Din Hasan ibn Ali ibn Hasan al-Farisi (1267–1319) gave the correct scientific explanation of the rainbow in his Tanqih al-Manazir (The Revision of the Optics). Almost contemporaneously the German scholar Theodoric of Freiberg (c. 1250–c. 1310) gave the same correct explanation in his De iride et radialibus impressionibus (On the Rainbow and the impressions created by irradiance). The two scholars arrived at their conclusion independently of each other but both of them did experiments involving the study of light rays passing through glass spheres full of water and both scholars were influenced by the optical theories of Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham. Unfortunately both explanations disappeared and it was in fact first in the 17th Century that the Croatian scholar Marco de Antonio Dominis (1560–1624) once again gave an almost correct explanation of the rainbow in his Tractatus de radiis visus et lucis in vitris, perspectivis et iride.

De Dominis' explanation of the rainbow Source: Wikimedia Commons

De Dominis’ explanation of the rainbow
Source: Wikimedia Commons


Filed under History of Optics, History of Physics, History of science, Myths of Science

Isaac and the apple – the story and the myth

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

The Woolsthorpe Manor apple tree Source:Wikimedia Commons

The Woolsthorpe Manor apple tree
Source:Wikimedia Commons

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

Tim Peake's Mission Logo

Tim Peake’s Mission Logo

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

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

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


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


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

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

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

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

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

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

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

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

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

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

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

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

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

The Newtonian Reflector Source: Wikimedia Commons

The Newtonian Reflector
Source: Wikimedia Commons

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

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

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

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

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


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

The Huygens Enigma

The seventeenth century produced a large number of excellent scientific researches and mathematicians in Europe, several of whom have been elevated to the status of giants of science or even gods of science by the writers of the popular history of science. Regular readers of this blog should be aware that I don’t believe in the gods of science, but even I am well aware that not all researches are equal and the contributions of some of them are much greater and more important than those of others, although the progress of science is dependent on the contributions of all the players in the science game. Keeping to the game analogy, one could describe them as playing in different leagues. One thing that has puzzled me for a number of years is what I regard as the Huygens enigma. There is no doubt in my mind whatsoever that the Dutch polymath Christiaan Huygens, who was born on the 14 April 1629, was a top premier league player but when those pop history of science writers list their gods they never include him, why not?

Christiaan Huygens by Caspar Netscher, Museum Hofwijck, Voorburg Source: Wikimedia Commons

Christiaan Huygens by Caspar Netscher, Museum Hofwijck, Voorburg
Source: Wikimedia Commons

Christiaan was the second son of Constantijn Huygens poet, composer, civil servant and diplomat and was thus born into the highest echelons of Dutch society. Sent to university to study law by his father Christiaan received a solid mathematical education from Frans van Schooten, one of the leading mathematicians in Europe and an expert on the new analytical mathematics of Descartes and Fermat. Already as a student Christiaan had contacts to top European intellectuals, including corresponding with Marine Mersenne, who confirmed his mathematical talent to his father. Later in his student life he also studied under the English mathematician John Pell.

Already at the age of twenty-five Christiaan dedicated himself to the scientific life, the family wealth sparing him the problem of having to earn a living. Whilst still a student he established himself as a respected mathematician with an international reputation and would later serve as one of Leibniz’s mathematics teachers. In his first publication at the age of twenty-two Huygens made an important contribution to the then relatively new discipline of probability. In physics Huygens originated what would become Newton’s second law of motion and in a century that saw the development of the concept of force it was Huygens’ work on centripetal force that led Christopher Wren and Isaac Newton to the derivation of the inverse square law of gravity. In fact in Book I of Principia, where Newton develops the physics that he goes on to use for his planetary theory in Book III, he only refers to centripetal force and never to the force of gravity. Huygens contribution to the Newtonian revolution in physics and astronomy was substantial and essential.

In astronomy Christiaan with his brother Constantijn ground their own lenses and constructed their own telescopes. He developed one of the early multiple lens eyepieces that improved astronomical observation immensely and which is still known as a Huygens eyepiece. He established his own reputation as an observational astronomer by discovering Titan the largest moon of Saturn. He also demonstrated that all the peculiar observations made over the years of Saturn since Galileo’s first observations in 1610 could be explained by assuming that Saturn had a system of rings, their appearance varying depending on where Saturn and the Earth were in their respective solar orbits at the time of observations. This discovery was made by theoretical analysis and not, as is often wrongly claimed, because he had a more powerful telescope.

In optics Huygens was, along with Robert Hooke, the co-creator of a wave theory of light, which he used to explain the phenomenon of double refraction in calcite crystals. Unfortunately Newton’s corpuscular theory of light initially won out over Huygens’ wave theory until Young and others confirmed Huygens’ theory in the nineteenth century.

Many people know Huygens best for his contributions to the history of clocks. He developed the first accurate pendulum clocks and was again along with Robert Hooke, who accused him of plagiarism, the developer of the balance spring watch. There were attempts to use his pendulum clocks to determine longitude but they proved not to be reliable enough under open sea conditions.

Huygens’ last book published posthumously, Cosmotheoros, is a speculation about the possibility of alien life in the cosmos.

Huygens made important contributions to many fields of science during the second half of the seventeenth century of which the above is but a brief and inadequate sketch and is the intellectual equal of any other seventeenth century researcher with the possible exceptions of Newton and Kepler but does not enjoy the historical reputation that he so obviously deserve, so why?

I personally think it is because there exists no philosophical system or magnum opus associated with his contributions to the development of science. He work is scattered over a series of relatively low-key publications and he offers no grand philosophical concept to pull his work together. Galileo had his Dialogo and his Discorsi, Descartes his Cartesian philosophy, Newton his Principia and his Opticks. It seems to be regarded as one of the gods of science it is not enough to be a top class premier league player who makes vital contributions across a wide spectrum of disciplines, one also has to have a literary symbol or philosophical methodology attached to ones name to be elevated into the history of science Olympus.

P.S. If you like most English speakers think that his name is pronounced something like Hoi-gens then you are wrong, it being Dutch is nothing like that as you can hear in this splendid Youtube video!


Filed under History of Astronomy, History of Optics, History of Physics, History of science, Newton

The unfortunate backlash in the historiography of Islamic science

Anybody with a basic knowledge of the history of Western science will know that there is a standard narrative of its development that goes something like this. Its roots are firmly planted in the cultures of ancient Egypt and Babylon and it bloomed for the first time in ancient Greece, reaching a peak in the work of Ptolemaeus in astronomy and Galen in medicine in the second-century CE. It then goes into decline along with the Roman Empire effectively disappearing from Europe by the fifth-century CE. It began to re-emerge in the Islamic Empire[1] in the eight-century CE from whence it was brought back into Europe beginning in the twelfth-century CE. In Europe it began to bloom again in the Renaissance transforming into modern science in the so-called Scientific Revolution in the seventeenth-century. There is much that is questionable in this broad narrative but that is not the subject of this post.

In earlier versions of this narrative, its European propagators claimed that the Islamic scholars who appropriated Greek knowledge in the eighth-century and then passed it back to their European successors, beginning in the twelfth-century, only conserved that knowledge, effectively doing nothing with it and not increasing it. For these narrators their heroes of science were either ancient Greeks or Early Modern Europeans; Islamic scholars definitely did not belong to the pantheon. However, a later generation of historians of science began to research the work of those Islamic scholars, reading, transcribing, translating and analysing their work and showing that they had in fact made substantial contributions to many areas of science and mathematics, contributions that had flowed into modern European science along with the earlier Greek, Babylonian and Egyptian contributions. Also Islamic scholars such as al-Biruni, al-Kindi, al-Haytham, Ibn Sina, al-Khwarizmi and many others were on a level with such heroes of science as Archimedes, Ptolemaeus, Galen or Kepler, Galileo and Newton. Although this work redressed the balance there is still much work to be done on the breadth and deep of Islamic science.

Unfortunately the hagiographic, amateur, wannabe pop historians of science now entered the field keen to atone for the sins of the earlier Eurocentric historical narrative and began to exaggerate the achievements of the Islamic scholars to show how superior they were to the puny Europeans who stole their ideas, like the colonial bullies who stole their lands. There came into being a type of hagiographical popular history of Islamic science that owes more to the Thousand and One Nights than it does to any form of serious historical scholarship. I came across an example of this last week during the Gravity Fields Festival, an annual shindig put on in Grantham to celebrate the life and work of one Isaac Newton, late of that parish.

On Twitter Ammār ibn Aziz Ahmed (@Ammar_Ibn_AA) tweeted the following:

I’m sorry to let you know that Isaac Newton learned about gravity from the books of Ibn al-Haytham

I naturally responded in my usual graceless style that this statement was total rubbish to which Ammār ibn Aziz Ahmed responded with a link to his ‘source

I answered this time somewhat more moderately that a very large part of that article is quite simply wrong. One of my Internet friends, a maths librarian (@MathsBooks) told me I was being unfair and that I should explain what was wrong with his source, so here I am.

The article in question is one of many potted biographies of al-Haytham that you can find dotted all other the Internet and which are mostly virtual clones of each other. They all contain the same collection of legends, half-truths, myths and straightforward lies usually without sources, or, as in this case, quoting bad popular books written by a non-historian as their source. It is fairly obvious that they all plagiarise each other without bothering to consult original sources or the work done by real historian of science on the life and work of al-Haytham.

The biography of al-Haytham is, like that of most medieval Islamic scholars, badly documented and very patchy at best. Like most popular accounts this article starts with the legend of al-Haytham’s feigned madness and ten-year incarceration. This legend is not mentioned in all the biographical sources and should be viewed with extreme scepticism by anybody seriously interested in the man and his work. The article then moves on to the most pernicious modern myth concerning al-Haytham that he was the ‘first real scientist’.

This claim is based on a misrepresentation of what al-Haytham did. He did not as the article claims introduce the scientific method, whatever that might be. For a limited part of his work al-Haytham used experiments to prove points, for the majority of it he reasoned in exactly the same way as the Greek philosophers whose heir he was. Even where he used the experimental method he was doing nothing that could not be found in the work of Archimedes or Ptolemaeus. There is also an interesting discussion outlined in Peter Dear’s Discipline and Experience (1995) as to whether al-Haytham used or understood experiments in the same ways as researchers in the seventeenth-century; Dear concludes that he doesn’t. (pp. 51-53) It is, however, interesting to sketch how this ‘misunderstanding’ came about.

The original narrative of the development of Western science not only denied the contribution of the Islamic Empire but also claimed that the Middle Ages totally rejected science, modern science only emerging after the Renaissance had reclaimed the Greek scientific inheritance. The nineteenth-century French physicist and historian of science, Pierre Duhem, was the first to challenge this fairy tale claiming instead, based on his own researches, that the Scientific Revolution didn’t take place in the seventeenth–century but in the High Middle Ages, “the mechanics and physics of which modern times are justifiably proud to proceed, by an uninterrupted series of scarcely perceptible improvements, from doctrines professed in the heart of the medieval schools.” After the Second World War Duhem’s thesis was modernised by the Australian historian of science, Alistair C. Crombie, whose studies on medieval science in general and Robert Grosseteste in particular set a new high water mark in the history of science. Crombie attributed the origins of modern science and the scientific method to Grosseteste and Roger Bacon in the twelfth and thirteenth-centuries. A view that has been somewhat modified and watered down by more recent historians, such as David Lindberg. Enter Matthias Schramm.

Matthias Schramm was a German historian of science who wrote his doctoral thesis on al-Haytham. A fan of Crombie’s work Schramm argued that the principle scientific work of Grosseteste and Bacon in physical optics was based on the work of al-Haytham, correct for Bacon not so for Grosseteste, and so he should be viewed as the originator of the scientific method and not they. He makes this claim in the introduction to his Ibn al-Haythams Weg zur Physik (1964), but doesn’t really substantiate it in the book itself. (And yes, I have read it!) Al-Haytham’s use of experiment is very limited and to credit him with being the inventor of the scientific method is a step too far. However since Schramm made his claims they have been expanded, exaggerated and repeated ad nauseam by the al-Haytham hagiographers.

We now move on to what is without doubt al-Haytham’s greatest achievement his Book of Optics, the most important work on physical optics written between Ptolemaeus in the second-century CE and Kepler in the seventeenth-century. Our author writes:

In his book, The Book of Optics, he was the first to disprove the ancient Greek idea that light comes out of the eye, bounces off objects, and comes back to the eye. He delved further into the way the eye itself works. Using dissections and the knowledge of previous scholars, he was able to begin to explain how light enters the eye, is focused, and is projected to the back of the eye.

Here our author demonstrates very clearly that he really has no idea what he is talking about. It should be very easy to write a clear and correct synopsis of al-Haytham’s achievements, as there is a considerable amount of very good literature on his Book of Optics, but our author gets it wrong[2].

Al-Haytham didn’t prove or disprove anything he rationally argued for a plausible hypothesis concerning light and vision, which was later proved to be, to a large extent, correct by others. The idea that vision consists of rays (not light) coming out of the eyes (extramission) is only one of several ideas used to explain vision by Greek thinkers. That vision is the product of light entering the eyes (intromission) also originates with the Greeks. The idea that light bounces off every point of an object in every direction comes from al-Haytham’s Islamic predecessor al-Kindi. Al-Haytham’s great achievement was to combine an intromission theory of vision with the geometrical optics of Euclid, Heron and Ptolemaeus (who had supported an extramission theory) integrating al-Kindi’s punctiform theory of light reflection. In its essence, this theory is fundamentally correct. The second part of the paragraph quoted above, on the structure and function of the eye, is pure fantasy and bears no relation to al-Haytham’s work. His views on the subject were largely borrowed from Galen and were substantially wrong.

Next up we have the pinhole camera or better camera obscura, although al-Haytham was probably the first to systematically investigate the camera obscura its basic principle was already known to the Chinese philosopher Mo-Ti in the fifth-century BCE and Aristotle in the fourth-century BCE. The claims for al-Haytham’s studies of atmospheric refraction are also hopelessly exaggerated.

We the have an interesting statement on the impact of al-Haytham’s optics, the author writes:

The translation of The Book of Optics had a huge impact on Europe. From it, later European scholars were able to build the same devices as he did, and understand the way light works. From this, such important things as eyeglasses, magnifying glasses, telescopes, and cameras were developed.

The Book of Optics did indeed have a massive impact on European optics in Latin translation from the work of Bacon in the thirteenth-century up to Kepler in the seventeenth-century and this is the principle reason why he counts as one of the very important figures in the history of science, however I wonder what devices the author is referring to here, I know of none. Interesting in this context is that The Book of Optics appears to have had very little impact on the development of physical optics in the Islamic Empire. One of the anomalies in the history of science and technology is the fact that as far was we know the developments in optical physics made by al-Haytham, Bacon, Witelo, Kepler et al had no influence on the invention of optical instruments, glasses, magnifying glasses, the telescope, which were developed along a parallel but totally separate path.

Moving out of optics we get told about al-Haytham’s work in astronomy. It is true that he like many other Islamic astronomers criticised Ptolemaeus and suggested changes in his system but his influence was small in comparison to other Islamic astronomers. What follows is a collection of total rubbish.

He had a great influence on Isaac Newton, who was aware of Ibn al-Haytham’s works.

He was not an influence on Newton. Newton would have been aware of al-Haytham’s work in optics but by the time Newton did his own work in this field al-Haytham’s work had been superseded by that of Kepler, Scheiner, Descartes and Gregory amongst others.

He studied the basis of calculus, which would later lead to the engineering formulas and methods used today.

Al-Haytham did not study the basis of calculus!

He also wrote about the laws governing the movement of bodies (later known as Newton’s 3 laws of motion)

Like many others before and after him al-Haytham did discuss motion but he did not come anywhere near formulating Newton’s laws of motion, this claim is just pure bullshit.

and the attraction between two bodies – gravity. It was not, in fact, the apple that fell from the tree that told Newton about gravity, but the books of Ibn al-Haytham.

We’re back in bullshit territory again!

If anybody thinks I should give a more detailed refutation of these claims and not just dismiss them as bullshit, I can’t because al-Haytham never ever did the things being claimed. If you think he did then please show me where he did so then I will be prepared to discuss the matter, till then I’ll stick to my bullshit!

I shall examine one more claim from this ghastly piece of hagiography. Our author writes the following:

When his books were translated into Latin as the Spanish conquered Muslim lands in the Iberian Peninsula, he was not referred to by his name, but rather as “Alhazen”. The practice of changing the names of great Muslim scholars to more European sounding names was common in the European Renaissance, as a means to discredit Muslims and erase their contributions to Christian Europe.

Alhazen is merely the attempt by the unknown Latin translator of The Book of Optics to transliterate the Arabic name al-Haytham there was no discrimination intended or attempted.

Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham is without any doubt an important figure in the history of science whose contribution, particularly those in physical optics, should be known to anybody taking a serious interest in the subject, but he is not well served by inaccurate, factually false, hagiographic crap like that presented in the article I have briefly discussed here.






[1] Throughout this post I will refer to Islamic science an inadequate but conventional term. An alternative would be Arabic science, which is equally problematic. Both terms refer to the science produced within the Islamic Empire, which was mostly written in Arabic, as European science in the Middle Ages was mostly written in Latin. The terms do not intend to imply that all of the authors were Muslims, many of them were not, or Arabs, again many of them were not.

[2] For a good account of the history of optics including a detailed analysis of al-Haytham’s contributions read David C. Lindberg’s Theories of Vision: From al-Kindi to Kepler, University of Chicago Press, 1976.


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

Luca, Leonardo, Albrecht and the search for the third dimension.

Many of my more recent readers will not be aware that I lost a good Internet friend last year with the unexpected demise of the history of art blogger, Hasan Niyazi. If you want to know more about my relationship with Hasan then read the elegy I wrote for him when I first heard the news. Hasan was passionate about Renaissance art and his true love was reserved for the painter Raffaello Sanzio da Urbino, better known as Raphael. Today, 6th April is Raphael’s birthday and Hasan’s partner Shazza (Sharon) Bishop has asked Hasan’s friends in the Internet blogging community to write and post something today to celebrate his life, this is my post for Hasan.


I’m not an art historian but there were a couple of themes that Hasan and I had in common, one of these was, for example, the problem of historical dating given differing calendars. Another shared interest was the history of linear perspective, which is of course absolutely central to the history of Renaissance art but was also at the same time an important theme in Renaissance mathematics and optics. I have decided therefore to write a post for Hasan about the Renaissance mathematicus Luca Pacioli who played an important role in the history of linear perspective.


Luca Pacioli artist unknown

Luca Pacioli
artist unknown

Luca Pacioli was born in Sansepolcro in the Duchy of Urbino in 1445.

Duchy of Urbino  Henricus Hondius 1635

Duchy of Urbino
Henricus Hondius 1635

Almost nothing is known of his background or upbringing but it can be assumed that he received at least part of his education in the studio of painter and mathematician Piero della Francesca (1415 – 1492), who like Pacioli was born in Sansepolcro.

Piero della Francesca Self Portrait

Piero della Francesca
Self Portrait

Pacioli and della Francesca were members of what is now known as the Urbino school of mathematics, as was Galileo’s patron Guidobaldo del Monte (1545 – 1607). These three Urbino mathematicians together with, Renaissance polymath, Leone Battista Alberti (1404 – 1472) all played an important role in the history of linear perspective.


Leon Battista Alberti  Artist unknown

Leon Battista Alberti
Artist unknown

Whilst still young Pacioli left Sansepolcro for Venice where he work as a mathematics tutor. Here he wrote his first book, an arithmetic textbook, around 1470. Around this time he left Venice for Rome where he lived for several months in the house of Alberti, from whom he not only learnt mathematics but also gained good connections within the Catholic hierarchy. Alberti was a Papal secretary.

In Rome Pacioli studied theology and became a Franciscan friar. From 1477 Pacioli became a peripatetic mathematics teacher moving around the courts and universities of Northern Italy, writing two more arithmetic textbooks, which like his first one were never published.

Ludovico Sforza became the most powerful man in Milan in 1476, at first as regent for his nephew Gian Galeazzo, and then, after his death in 1494, Duke of Milan.

Ludovico Sforza Zanetto Bugatto

Ludovico Sforza
Zanetto Bugatto

Ludovico was a great patron of the arts and he enticed Leonardo to come and serve him in Milan in 1482. In 1496 Pacioli became Ludivico’s court mathematicus. Leonardo and Pacioli became colleges and close friends stimulating each other over a wide range of topics.


Leonardo Francesco Melzi

Francesco Melzi

Before he went to Milan Pacioli wrote his most famous and influential book his Summa de arithmetica, geometria, proportioni et proportionalità, which he published in Venice in 1494. The Summa, as it is generally known, is a six hundred-page textbook that covers the whole range of practical mathematics, as it was known in the fifteenth-century. Pacioli was not an original mathematician and the Summa is a collection of other peoples work, however it became the most influential mathematics textbook in Europe and remained so for almost the whole of the sixteenth-century. As well as the basics of arithmetic and geometry the Summa contains the first printed accounts of double entry bookkeeping and probability, although Pacioli’s account of determining odds is wrong. From our point of view the most important aspect of the Summa is that it also contains the first extensive printed account of the mathematics of linear perspective.


Pacioli Summa Title Page

Pacioli Summa
Title Page

According to legend linear perspective in painting was first demonstrated by Fillipo Brunelleschi (1377 – 1446) in Florence early in the fifteenth-century. Brunelleschi never published an account of his discovery and this task was taken up by Alberti, who first described the construction of linear perspective in his book De pictura in 1435. Piero della Francesca wrote three mathematical treatises one on arithmetic, one on linear perspective and one on the five regular Euclidian solids. However della Francesca never published his books, which seem to have been written as textbooks for the Court of Urbino where they existed in the court library only in manuscript. Della Francesca treatment of perspective was much more comprehensive than Alberti’s.

During his time in Milan, Pacioli wrote his second major work his Divina proportione, which contains an extensive study of the regular geometrical solids with the illustrations famously drawn by his friend Leonardo.


Leonardo Polyhedra


These two books earned Pacioli a certain amount of notoriety as the Summa contains della Francesca’s book on linear perspective and the Divina proportione his book on the five regular solids both without proper attribution. In his Lives of the Most Excellent Italian Painters, Sculptors, and Architects, from Cimabue to Our Timesthe Italianartist and art historian, Giorgio Vasari (1511 – 1574)


Giorgio Vasari Self Portrait

Giorgio Vasari
Self Portrait

accused Pacioli of having plagiarised della Francesca, a not entirely fair accusation, as Pacioli does acknowledge that the entire contents of his works are taken from other authors. However whether he should have given della Francesca more credit or not Pacioli’s two works laid the foundations for all future mathematical works on linear perspective, which remained an important topic in practical mathematics throughout the sixteenth and seventeenth centuries and even into the eighteenth with many of the leading European mathematicians contributing to the genre.

With the fall of Ludovico in 1499 Pacioli fled Milan together with Leonardo travelling to Florence, by way of Mantua and Venice, where they shared a house. Although both undertook journeys to work in other cities they remained together in Florence until 1506. From 1506 until his death in his hometown in 1517 Pacioli went back to his peripatetic life as a teacher of mathematics. At his death he left behind the unfinished manuscript of a book on recreational mathematics, De viribus quantitatis, which he had compiled together with Leonardo.

Before his death Pacioli possibly played a last bit part in the history of linear perspective. This mathematical technique for providing a third dimensional to two dimensional paintings was discovered and developed by the Renaissance painters of Northern Italy in the fifteenth century, one of the artists who played a very central role in bringing this revolution in fine art to Northern art was Albrecht Dürer, who coincidentally died 6 April 1528, and who undertook two journeys to Northern Italy explicitly to learn the new methods of his Italian colleagues.

Albrecht Dürer Self Portrait

Albrecht Dürer
Self Portrait

On the second of these journey’s in 1506-7, legend has it, that Dürer met a man in Bologna who taught him the secrets of linear perspective.  It has been much speculated as to who this mysterious teacher might have been and one of the favoured candidates is Luca Pacioli but this is highly unlikely. Dürer was however well acquainted with the work of his Italian colleagues including Leonardo and he became friends with and exchanged gifts with Hasan’s favourite painter Raphael.


Filed under History of Mathematics, History of Optics, Renaissance Science, Uncategorized

Indian spectacles?

With out any doubt the most well known Indian of the last century was Mahatma Gandhi who led India to independence. In fact he is one of the most well known figures of the twentieth century from any country. The iconic pictures of Gandhi depict him as an older man wrapped in cotton sheets and wearing round nickel spectacles.

Mahatma Gandhi

Mahatma Gandhi

Gandhi always wore hand woven Indian cotton, as an act of political protest and principle against the cheap machine woven cotton imported into India by the British colonial powers, from the cotton mills of Lancashire. However were his spectacles also Indian? By this I don’t mean were they manufactured in India but were spectacles invented in India? An article that next months host of Giants’ Shoulders, Fade Singh (@fadesingh), drew to my attention makes exactly this claim, thereby disputing the usual opinion that spectacles originated in medieval Italy. Although this article is somewhat dated, and in my opinion wrong, it does provide some interesting points for discussion that I now intend to do. The article by Rishi Kumar Agarwal first appeared in the British Journal of Ophthamology in 1971 and can be read here in original with its bibliography. This is according to Wikipedia a peer-reviewed journal but I have serious doubts as to whether this short article was ever peer reviewed.

The European records of the origin of spectacles are very controversial. The suggestion that spectacles were first invented during the I3th century in Italy by an unknown layman of Pisa is not convincing, because there are also references to spectacles in Hindu literature at about the same time.

In the life of Vyasaraya (1446-1539), written in Sanskrit by his contemporary, the poet Somnath, the 74-year-old Vyasaraya is described as using a pair of “spectacles”* to read a book in I520 A.D. at the Court of King Krishna Deva Raya, one of the rulers of the Vijaynagar Empire (1336-I646). The Portuguese traders, well known to Vyasaraya, arrived in India in I498 and were established in Goa in I5I0. Gode (1947) referred to by Pendse (1954) assumed that the Portuguese presented spectacles amongst other gifts to Vyasaraya, but this does not necessarily mean that the Portuguese introduced spectacles into India.

It is claimed that in Ceylon, during the reign of Bhuvanaikabahu IV (1344-1353), lenses and spectacles were made by Devanarayan, an Indian architect, who was originally commissioned from India to build a Buddhist monument at Gadaladeniya. Since this monument is in the Vijaynagar style of architecture, it would confirm that Devanarayan came to Ceylon from the Hindu Empire of Vijaynagar. He must have known the art of spectacle-making in India before he went to Ceylon, and this means that the Vijaynagar courtiers must have known the use of spectacles before the arrival of the Portuguese at the end of the I5th century.

Quartz crystals were used for manufacturing spectacle lenses in a South Indian town near Tanjore, which was taken by the British in I77I. It is interesting that Oppert  (I907) also mentioned a South Indian Hindu caste which possessed polished crystal lenses. It is significant that in the South Indian languages the terms for spectacles are very different from those of North India. In the Kannada language of Mysore, South India, the term “Kannadak” is used for spectacles, and two other South Indian languages, i.e. Malayalam and Tamil, use similar words to describe spectacles.

The widespread use of spectacles for presbyopia can be inferred from the popular terminology for spectacles in certain parts of India: e.g. “Chaleesi” and “Chalesa” meaning “forty” in Maharashtra and Orissa, “Chatwar” meaning “fourth decade” in Andhra, and “Betalan” meaning” forty-two” in Gujarat. Ramdasa (I608-82) used the word” Chalasi” to describe spectacles, and requested contemporary scribes to use middle-sized letters to write their manuscripts. This would imply that the use of spectacles was perhaps confined to certain classes, e.g. the Brahmins.

The term used is “upa-lochana” (substitute or secondary eyes), “upa” being a Sanskrit prefix losely meaning substitute or secondary which was widely used in Sanskrit, e.g. the “Vedas” and the “upa-Vedas”. A Marathi poet Vamanpandita (I636-95) used the term “upa-netra” (netra meaning eyes) for spectacles. It would, therefore, be incorrect to assume that the term “upa-lochana” was specially coined to describe foreign spectacles.

The agents of the British East India Company (which received the Royal charter in I6oo A.D.) have been incorrectly credited by some writers with introducing spectacles into India. There is a reference (in a letter dated September 22, 1616, from an English firm “Kerridge, Barker, and Mittford”) to the slow sale of English spectacles in Rajputana, the  modern state of Rajsthan in North India. There are references to spectacles in the Hindu literature much earlier than this, and spectacles are also depicted in some of the Mughal miniatures. The ancient Indian spectacles generally had carvings of a deity, and perhaps Indians at that period did not want to use non-Indian spectacles, which may account for the slow sale of the English importations.


The account of Devanarayan (between I344-I353), the use of spectacles by Vyasaraya (I520 A. D.), the indigenous manufacture of spectacle lenses in South India, the different terms used for spectacles in the North and South Indian languages, and other historical facts all indicate that spectacles were invented in India, in all probability by the Kannada- speaking Hindus. It is therefore most likely that the use of lenses reached Europe via the Arabs, as did Hindu mathematics and the ophthalmological works of the ancient Hindu surgeon Susruta.

Our author starts with a very provocative claim:

The European records of the origin of spectacles are very controversial. The suggestion that spectacles were first invented during the I3th century in Italy by an unknown layman of Pisa is not convincing, because there are also references to spectacles in Hindu literature at about the same time.

Not only does he claim that spectacles had their origins in India he appears to be casting serious doubts on the claim that spectacles first appeared in Pisa in the late 13th century so let us first examine the evidence for this claim.

There are two independent written accounts that place the first appearance of spectacles in Europe in Northern Italy in the last quarter of the thirteenth century, both of them are considered reliable. One of them from 1306 actually states that spectacles were first produced by a monk in Pisa some twenty years earlier giving the now accepted date of 1286 for the invention of spectacles. These accounts are backed up by the fact that the glass making guilds of Venice were already issuing written regulations concerning the manufacture of glass spectacle lenses in 1300 showing that the manufacture of spectacles had already become industrialised by this date. If our author wishes to shift the invention of spectacles to the Indian subcontinent then he must produce solid evidence for their manufacture in India before 1280. It might be claimed that because this article is more than forty years old our author may not have known just how certain the evidence for the appearance of spectacles in Europe at this time is. He could have done as the research on this is contained in Edward Rosen’s legendary paper The invention of Eyeglasses from 1956[1]. This paper actually established Rosen’s reputation as a first class historian of science, even if somewhat of a cranky one.

Before we examine his evidence, the appearance of spectacles in around 1280 in Europe throws up two very interesting questions for historians of optics that I would like to sketch first. The first of these is what connection, if any, is there between the appearance of spectacles and the renaissance of geometrical optics slightly earlier in the same century? The main Greek and Arabic text on geometrical optics, including the most important Book of Optics of Ibn al-Haytham, became available in Europe around the beginning of the thirteenth century and Robert Grosseteste, Roger Bacon, John Peckham and Witelo all wrote their highly influential works on the science of perspective, as it was then known, around the middle of the thirteenth century.  Is it just coincidence that spectacles first appeared immediately after this almost explosive rebirth of geometrical optics in Europe? The simple answer appears to be yes, it was a coincidence. Thorough examination of the sources have found absolutely no connection between the theoretical study of geometrical optics and the manufacture of spectacle lenses earlier than the work of Franciscus Maurolycus and Johannes Kepler at the beginning of the seventeenth century. This being the case how were spectacle lenses invented?

The simple answer is we don’t know but we can speculate. The Swiss mathematical astronomer and historian of optics Rolph Willach[2] has produced an interesting and plausible hypothesis based on his researches. As part of his investigations into the origins of the telescope, of which more shortly, he examined, measured and analysed the optical properties all the pre-seventeenth century lenses in Europe to which he could gain access, making him the world’s leading expert on medieval and early modern lenses. During the High Middle Ages the monks in monasteries began to construct elaborate decorated cases to house the saints finger bones, pieces of the true cross and other holy relics that the Catholic Church was busy collecting. These cases, known technically as reliquaries were often decorated with semi-precious and precious stones cut and polished in the shape of plano-convex lenses (flat on one side, spherical on the other).

Byzantine Icon of the Crucifixion

Byzantine Icon of the Crucifixion

Willach applied the same analysis to some of these stones that he had applied to his lenses and was able to establish that some of them had the same optical properties as the lenses used in early spectacles to cure presbyopia, the need for reading glasses in old age. Willach assumes, I think correctly, that one of the stone polishers realised that the stone he had just polished enabled him to read the text that he couldn’t see clearly before because of his presbyopia, common amongst elder monks, and then developed this discovery through a process of trial and error into the first spectacles. Till now nobody has come up with a more plausible explanation for the invention of spectacles.

The second optical problem thrown up by the invention of glasses is that if lenses for glasses were invented in the late thirteenth century why was the telescope, which was invented by a spectacle maker, first discovered only three hundred years later at the beginning of the seventeenth century? Now one reason is that the early Dutch or Galilean telescope requires both a plano-convex and a plano-concave lens and the first spectacles only had plano-convex lenses. However we know that glasses with plano-concave lenses were being manufacture on an industrial scale by 1450 at the very latest, which still leaves a one hundred and fifty year gap before the emergence of the telescope. Why? The old theory was that the quality of lens making didn’t reach a high enough standard until the beginning of the seventeenth century, because of their closeness to the eye spectacle lenses don’t have to be very high quality to be effective. Willach’s research on the optical quality of lenses in the early modern period effectively disproved this theory because there was no measurable improvement in the lenses between the fifteenth and the seventeenth centuries and the spectacle lenses at the beginning of the seventeenth century were still too poor in quality to function as a telescope as they were. According to Willach the solution is a diaphragm placed before the lens covering the outer edges. The middle of the lenses is usually good enough for telescopes, if the distortions caused by the badly formed outer area of the lens are bended out by the diaphragm. Because of the proximity the eye only uses the well-formed middle of the lens in spectacles. It is known that Galileo employed diaphragms on his telescope for just this reason. Because of the demand for telescope lenses there was a rapid improvement in lens grinding and polishing techniques in the seventeenth century.

But back to spectacles and India. There is no doubt what so ever that spectacles were available in Europe in the late thirteenth century but were they, as our author claims, available earlier than this in India? To back up his claim one would expect him to bring some fairly solid evidence but if you read through his article you will find that this is not the case. The only statement in his article that comes anywhere near his claim is in the third paragraph:

It is claimed that in Ceylon, during the reign of Bhuvanaikabahu IV (1344-1353), lenses and spectacles were made by Devanarayan, an Indian architect,…

Now this is three quarters of a century later than the confirmed date for the appearance of spectacles in Europe and whereas Rosen in his article produces reams of exacting research and documentation to back up the European claim our author just provides an unsubstantiated statement for his Indian case, not exactly convincing. He then goes on to compound the shakiness of his argument a couple of lines further on:

He must have known the art of spectacle-making in India before he went to Ceylon,…

Why and what proof do you have for this speculation? Not exactly the stuff of solid historical argument. In the whole article the author provides no further arguments what so ever to support, let alone to prove, his claim. What he does do is to put in question earlier claims for the introduction of spectacles into Southern India by the Portuguese and North India by the British at least making his article useful in this sense. However all this means is one must look for other means of transmission not that spectacles were invented in India. Given the extensive North Italian trade along the Spice Road and Arabic trade across the Indian Ocean much more plausible explanations than an independent Indian invention of spectacles are available.

I fail completely to understand why differing regional names within India for spectacles should be an indicator for Indian invention. We know that within Europe spectacles emerged in Northern Italy but every European language has its own name for them. In the early phase there were even several differing terms for the new invention in Northern Italy. The situation is no different to the naming of the telescope when it was first invented and even today we have two different names in English glasses and spectacles as well as two for the telescope counting the still used spyglass. I did find the Southern Indian use quartz crystal for spectacle lenses interesting, as this practice was also widespread in Europe. The German word for spectacles is Brille, which is a corruption of the word berille Old German for Beryll, English Beryl, a naturally occurring crystal.

The author’s conclusion, It is therefore most likely that the use of lenses reached Europe via the Arabs… is quite extraordinary because this would indicated an Arabic use of lenses and spectacles before their appearance in Europe and no evidence for such a usage exists. Or does are author think that the Arabs passed on Indian glasses to Europe without trying them out themselves?



[1] Edward Rosen, The Invention of Eyeglasses, Journal of the History of Medicine and Allied Sciences 11, 1956, pp. 13-46, 183-218

Also very useful in this context is Vincent Ilardi, Renaissance Vision From Spectacles to Telescopes, American Philosophical Society, Philadelphia, 2007. The definitive account!

[2] Rolf Willach, Der lange Weg zur Erfindung des Fernrohres, in Jürgen Hamel and Inge Keil ed., Der Meister und die Fernrohre: Das Wechselspiel zwischen Astronomie und Optik in der Geschichte, Acta Historica AStronomiae Vol. 33, Verlag Harri Deutsch, Frankfurt am Main, 2007.

English: Rolf Willach, The Long Route to the Invention of the Telescope, Transactions of the American Philosophical Society, Philadelphia, 2008.


Filed under History of Optics

Christmas Trilogy 2013 Part I: The Other Isaac [1].

In a recent post on John Wallis I commented on seventeenth century English mathematicians who have been largely lost to history, obscured by the vast shadow cast by Isaac Newton. One person, who has suffered this fate, possibly more than any other, was the first Lucasian Professor of Mathematics at Cambridge, and thus Newton’s predecessor on that chair, Isaac Barrow (1630 – 1677), who in popular history has been reduced to a mere footnote in the Newton mythology.

Statue of Isaac Barrow in the Chapel of Trinity College

Statue of Isaac Barrow in the Chapel of Trinity College

He was born in London in 1630 the son of John Barrow a draper. The Barrow’s were a Cambridge family notable for its many prominent scholars and theologians. Isaac father was the exception in that he had gone into trade but he was keen that his son should follow the family tradition and become a scholar.  With this aim in view the young Isaac was originally sent to Charterhouse School where he unfortunately more renowned as the school ruffian than for his learning. His father thus placed him in Felsted School in Essex, where John Wallis was also prepared for university, and where he soon turned his hand to more scholarly pursuits. Barrow’s success at school can be judged by the fact that when his father got into financial difficulties, and could no longer pay his school fees, the headmaster of the school took him out of the boarding house and lodged him in his own private dwelling free of charge and also arranged for him to earn money as tutor to William Fairfax.

In 1643 he was due to go up to Peterhouse Cambridge, where his uncle Isaac was a fellow. However his uncle was ejected from the college by the puritans and so the plan came to nought. Cut loose in society young Barrow ended up in Norfolk at the house of Edward Walpole a former schoolfellow who on going up to Cambridge decided to take Barrow with him and pay his keep. So it was that Barrow was admitted to Trinity College in 1646. Following further trials and tribulations he graduated BA in 1649 and was elected fellow shortly after. He went on to graduate MA in 1652 displaying thereby a mastery of the new philosophy. Barrow’s scholarly success was all the more remarkable, as throughout his studies he remained an outspoken Anglican High Church man and a devout royalist, things not likely to endear him to his puritan tutors.

In the 1650s Barrow devoted much of his time and efforts to the study of mathematics and the natural sciences together with a group of young scholars dedicated to these pursuits that included John Ray and Ray’s future patron Francis Willughby who had both shared the same Trinity tutor as Barrow, James Duport. Barrow embraced the mathematical and natural science of Descartes, whilst rejecting his metaphysics, as leading to atheism. He also believed students should continue to study Aristotle and the other ancients for the refinement of their language.  During this period Barrow began to study medicine, a common choice for those interested in the natural sciences, but remembering a promise made to himself whilst still at school to devote his life to the study of divinity he dropped his medical studies.

It was during this period that Barrow produced his first mathematical studies producing epitomes of both Euclid’s Elements and his Data, as well as of the known works of Archimedes, the first four books of Apollonius’ Conics and The Sphaerics of Theodosius. Barrow used the compact symbolism of William Oughtred to produce the abridged editions of these classical works of Greek mathematics. His Elements was published in 1656 and then again together with the Data in 1657. The other works were first published in the 1670s.

In 1654 a new wave of puritanism hit the English university and to avoid conflict Barrow applied for and obtained a travel scholarship leaving Cambridge in the direction of Paris in 1655. He spent eight months in Paris, which he described as, “devoid of its former renown and inferior to Cambridge!” From Paris he travelled to Florence where he was forced to extend his stay because an outbreak of the plague prevented him continuing on to Rome. In November 1656 he embarked on a ship to Smyrna, which on route was attacked by Barbary pirates, Barrow joining the crew in defending the ship acquitted himself honourably. He stayed in Smyrna for seven months before continuing to Constantinople. Although a skilled linguist fluent in eight languages Barrow made no attempt to learn Arabic, probably because of his religious prejudices against Islam, instead deepening his knowledge of Greek in order to study the church fathers.  Barrow left Constantinople in December 1658 arriving back in Cambridge, via Venice, Germany and the Netherlands, in September 1659.  It should be noted that the Interregnum was over and the Restoration of the monarchy would take place in the very near future. Unfortunately all of Barrow’s possessions including his paper from his travels were lost on the return journey, as his ship went up in flames shortly after docking in Venice

Barrow’s career, strongly supported by John Wilkins, now took off. In 1660 he was appointed Regius Professor of Greek at Cambridge followed in 1662 by his appointment as Gresham Professor of Geometry at Gresham College in London. His Gresham lectures were unfortunately lost without being published so we know little of what he taught there.  On the creation of the Lucasian Chair for Mathematics in 1663 Barrow was, at the suggestion of Wilkins, appointed as it first occupant. In 1664 he resigned both the Regius and the Gresham professorships. Meanwhile Barrow had started on the divinity trail being granted a BD in 1661 and beginning his career as a preacher.

Barrow only retained the Lucasian Chair for six years and in this time he lectured on mathematics, geometry and optics. His attitude to mathematics was strange and rather unique at the time. He was immensely knowledgeable of the new analytical mathematics possessing and having studied intently the works of Galileo, Cavalieri, Oughtred, Fermat, Descartes and many others however he did not follow them in reducing mathematics to algebra and analysis but went in the opposite directions reducing arithmetic to geometry and rejecting algebra completely. As a result his mathematical work was at one and the same time totally modern and up to date in its content whilst being totally old fashioned in its execution. Whereas his earlier Euclid remained a popular university textbook well into the eighteenth century his mathematical work as Lucasian professor fell by the wayside superseded by those who developed the new analysis. His optics lectures were a different matter. Although they were the last to be held they were the first to be published after he resigned the Lucasian chair. Pushed by that irrepressible mathematics communicator, John Collins, to publish his Lucasian Lectures Barrow prepared his optics lectures for publication assisted by his successor as Lucasian Professor, Isaac Newton, who was at the time delivering his own optics lectures, and who proof read and corrected the older Isaac’s manuscript. Building on the work of Kepler, Scheiner and Descartes Barrow’s Optics Lectures is the first work to deal mathematically with the position of the image in geometrical optics and as such remained highly influential well into the next century.

As he had once given up the study of medicine in his youth Barrow resigned the Lucasian Professorship in 1669 to devote his life to the study of divinity. His supporters, who now included an impressive list of influential bishops, were prepared to have him appointed to a bishopric but Barrow was a Cambridge man through and through and did not want to leave the college life. To solve the problem his friends had him appointed Master of Trinity instead, an appointment he retained until his tragically early death in 1677, just forty-seven years old. Following his death his collected sermons were published and it is they, rather than his mathematical work, that remain his intellectual legacy. Throughout his life all who came into contact with him acknowledge Barrow as a great scholar.

Near the beginning of this post I described Barrow as, having “been reduced to a mere footnote in the Newton mythology”. What did I mean by this statement and what exactly was the connection between the two Isaacs, apart from Barrow’s Optics Lectures? Older biographies of Newton and unfortunately much modern popular work state that Barrow was Newton’s teacher at Cambridge and that the older Isaac in realising the younger Isaac’s vast superiority as a mathematician resigned the Lucasian Chair in his favour. Both statements are myths. We don’t actually know who Newton’s tutor was but we can say with certainty that it was not Barrow. As far as can be ascertained the older Isaac first became aware of his younger colleague after Newton had graduated MA and been elected a fellow of Trinity. The two mathematicians enjoyed cordial relations with the older doing his best to support and further the career of the younger. As we have already seen above Barrow resigned the Lucasian Professorship in order to devote his live to the study and practice of divinity, however he did recommend his young colleague as his successor and Newton was duly elected to the post in 1669. Barrow also actively helped Newton in obtaining a special dispensation from King Charles, whose royal chaplain he had become, permitting him not to have to be ordained in order to hold the post of Lucasian Professor[2].

[1] On Monday I wrote that I might not be blogging for a while following Sascha untimely death. However I spent some time and effort preparing this years usual Christmas Trilogy of post and I find that writing helps to divert my attention from thoughts of him and to stop me staring at the wall. Also it’s what Sascha as general manager of this blog would have wanted.

[2] Should anyone feel a desire to learn more about Isaac Barrow I can highly recommend Before Newton: The Life and Times of Isaac Barrow, ed. Mordechai Feingold, CUP, Cambridge, 1990 from which most of the content of this post was distilled.


Filed under History of Mathematics, History of Optics, History of science, Newton