Category Archives: History of Optics

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

Apelles hiding behind the painting

Todays post combines two oft-repeated themes here at the Renaissance Mathematicus. We have another highly significant researcher who, however, does not belong to the pantheon of seventeenth century scientific gods and therefore tends to remain unknown to the non-experts. Our subject is also one more refutation of the widely held belief that in the seventeenth century Catholics in general and the Jesuits in particular were anti-science. Today we will take a look at the first man to be involved in a major scientific dispute with Galileo following the invention of the telescope the Jesuit mathematician, astronomer and optical physicist Christoph Scheiner, who was born in the town of Markt Wald in Bavarian Swabia on 25th July (NS) in either 1573 or 1575.

Christoph Scheinet (artist unknown)

Christoph Scheinet (artist unknown)

Scheiner attended a Jesuit Latin school in Augsburg from 1591 to 1595 before entering the Jesuit Order in Landsberg am Lech in 1595. He was educated in Landsberg am Lech, Augsburg and Ingolstadt obtaining his doctorate in theology, the normal higher degree for a Jesuit, in Ingolstadt in 1609. Over the years he had held various teaching post in Bavaria and in 1610 he was appointed professor of mathematics in Ingolstadt. The chair for mathematics in Ingolstadt was the oldest in Germany and Scheiner had several illustrious predecessors including Peter Apian. Scheiner is notorious amongst historians of astronomy for his more than somewhat heated dispute with Galileo on the nature of the sunspots and who had the honour of having discovered them first. However this was not his only scientific achievement.

One thing that I personally find fascinating is that Scheiner invented the pantograph in 1603 whilst still a student a fact that illustrates his ingenuity as an instrument maker. Although he first published his invention, which he had however already displayed publically on numerous occasions, in 1631. Now, if I had been writing this in the nineteen sixties or seventies I could be fairly certain that all of my readers would know what a pantograph is, however in this age of computer graphics where the most amazing graphical transformations can be accomplished by the most ham-fisted of us with the simple click of a mouse the pantograph like many other drawing instruments has almost disappeared from public awareness.

Scheiner's Pantograph

Scheiner’s Pantograph

A pantograph is an instrument for copying pictures and diagrams either one to one or scaled up or down. On the apparatus pictured above the three points at the bottom are the operative parts of the instrument. The instrument is anchored with the point on the left (XN) whilst the original drawing is traced out with the other hand with the middle point (MH) steering (OZ). The point on the right (PT) thus draws the required copy. By adjusting the length of the arms one can determine whether the copy is one to one, enlarged or reduced.

The thing for which Scheiner should be most well known, but he isn’t, is his work on the optical function of the eye Oculus hoc est: Fundamentum opticum, which he published in 1609 1619. Although there were many competing theories of vision in antiquity the majority opinion was that the image was formed in the crystal lens at the front of the eye. Even Ibn al-Haytham who laid the foundation of modern optics in the eleventh century CE with his synthesis of ancient Greek optical theory believed that the image was formed in the lens. In 1604 in his Astronomiae Pars Optica Johannes Kepler made a radical change in that he claimed that the lens is just that, a lens, and the image in formed, as in a camera obscura (a name he coined), on the retina at the back of the eye. This is, as we now know, the correct solution. However Kepler’s suggestion did not go down particularly well as any such image would of course be inverted; we would see everything upside down! Kepler’s ingenious and correct solution to this problem was to suggest that the brain copes with this situation telling the viewer which side in up. Now Kepler did not offer any form of empirical evidence for his theories and so they remained more than somewhat disputed; enter Scheiner who delivered the empirical proof that Kepler was right and quite a bit more.

Scheiner took bull’s eyes, the real things and not the middle of archery targets or darts boards. And pared them down so that he could see through the retina from outside of the eye. He then projected an image through the lens and could observe its inverted formation on the retina, Kepler vindicated. Unfortunately for Scheiner in most popular presentations of the history of optics this achievement is almost always wrongly attributed to Descartes. Scheiner’s work on vision contains many other important discoveries on the physiology of the eye making him alongside Kepler, Descartes, Gregory and Huygens to one of the important optical researchers of the seventeenth century.

Scheiner's Optics

Scheiner’s Optics

As already stated above Scheiner is most well know for his sunspots dispute with Galileo, which rumbled on for more than twenty years after its initial very heated phase between 1611 and 1613. Scheiner and Galileo both began observing sunspots with a telescope around the same time at the beginning of 1611, although Galileo would later claim he had begun earlier in order to claim priority, whereas unknown to both of them the priority in observation went to Thomas Harriot in England and the priority in publication to Johannes Fabricius in Frisia. The Augsburger businessman and astronomy enthusiast Marcus Welser published two sets of three letters from Scheiner on his sunspot observations under the pseudonym Apelles latenspost tabulam a reference to the fourth century Greek painter Apelles who is said to have displayed his paintings in his shop window whilst hiding behind them to listen to any criticism that might fall from the viewers, hence the title of this post. Scheiner hypothesised that the sunspots were actually small satellites orbiting the sun and casting their shadows on its surface, a theory that preserved the Aristotelian perfection of the heavens. Galileo countered with three letters of his own written in Tuscan and published by the Accademia dei Lincei in which he proved by careful observation and mathematical analysis that the sunspots must be on the surface of the sun, something that Scheiner then came to accept. Welser had declined to publish Galileo’s letters partially because of the gratuitous insults against Scheiner that they contained, some of which even the Lincei removed.

Later in his dispute with another Jesuit Orazio Grassi over the nature of comets, which would eventually lead to the publication of his Il Saggiatore (The Assayer), Galileo even went as far as to falsely accuse Scheiner of plagiarism. Unlike Galileo who basically abandoned his telescopic astronomy in 1613 Scheiner went on to make an extensive telescopic study of the sun, which he published as Rosa Ursina in 1630.

Scheiner Observing the Sun

Scheiner Observing the Sun

In the first of the four books of his masterwork Scheiner very carefully detailed the sunspot observations made by Galileo and himself correctly attributing to each his discoveries, something that did not please Galileo at all. Galileo’s supporters rubbished the Rosa Ursina upon publication and the book being a rather turgid scientific study was a flop although it is without doubt one of the most important astronomical works published in the seventeenth century; it just wasn’t very readable!

Scheiner's Sunspot Observations

Scheiner’s Sunspot Observations

In his infamous Dialogo Galileo compounded his sins again gratuitously insulting Scheiner whilst knowingly claiming several of Scheiner’s discoveries as his own. Galileo was not a nice man.

Initially Scheiner had built his own thirty power Dutch telescope and had, like Harriot, observed the sun at dawn through low clouds. Later at the suggestion of his assistant Johann Baptist Cysat, another Jesuit astronomer of some importance, he began to use filters of coloured glass so as not to damage his eyes. Scheiner was the first astronomer to construct and use Keplerian telescopes, two convex lenses, rather than Dutch or Galilean ones, one convex and one concave lens, for his observations, something that Galileo also criticised him for. The Keplerian or astronomical telescope is in fact superior but more susceptible to spherical aberration. It would be another twenty years before other astronomers, largely influenced by Galileo, followed Scheiner’s lead. For his solar observations Scheiner developed his helioscope a Keplerian telescope mounted on a sophisticated stand, which projected the image of the sun on to a screen.

Scheiner's Helioscope

Scheiner’s Helioscope

Scheiner was a first class astronomer and optician who suffered much under the arrogance and spitefulness of Galileo and who deserves to be much better known than he is.


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

He didn’t publish and so he perished (historically).

On 2nd July 1621 Thomas Harriot died of cancer of the nose in London. As he had learnt to smoke from the Indians, in what would later become Virginia, he is possibly the first recorded death caused by smoking. This would naturally give him a small footnote in the history of science but he deserves much, much more than a footnote.

Readers of this blog should by now be well aware that I think that expressions such as ‘the greatest’ should be banned forever out of the history of science. If people, as they do, ponder who was the greatest scientist in the seventeenth century (ignoring the anachronistic use of the term scientist for the moment) they invariably discuss the respective merits of Kepler, Galileo, Descartes and Newton just possibly adding Huygens to the mix. I personally think that Thomas Harriot is a serious candidate for such a discussion. Now I can already hear one or the other of my readers thinking, if Harriot is so important for the history of seventeenth century science how come I’ve never even heard of him? The answer is quite simple; although the good Thomas made starting contributions to many branches of knowledge in the early years of the seventeenth century he published almost nothing, thus depriving himself of the fame and historical recognition that went to others. As the title of this post says, he didn’t publish and so he perished.

Little is known about Harriot’s origins other than the fact that he was born in Oxfordshire around 1560 and entered Oxford University in 1577; graduating in 1580 whence he is thought to have moved to London. In 1583 he entered the service of Sir Walter Raleigh, who had been his contemporary at Oxford. He seems to have been a promising mathematician at university as is confirmed by his friendship there with Thomas Allen (1542 – 1632) and Richard Hakluyt (c.1552 – 1616) both acknowledged as leading mathematical practitioners of the age. Harriot served as house mathematicus to Raleigh, teaching his master mariners the then comparatively knew arts of mathematical navigation and cartography for their expeditions, as well as helping to design his ships and serving as his accountant. During his instruction Harriot wrote a manual on mathematical navigation, which included the correct mathematical method for the construction of the Mercator projection but this manual like nearly all of his scientific work was to remain unpublished. However Harriot’s work was not just theoretical he possibly sailed on Raleigh’s 1584 exploratory voyage to Roanoke Island fore the coast of North America and definitely took part in the 1585 – 1586 attempt to establish a colony on Roanoke. This second voyage gives Harriot the distinction of being the first natural philosopher/natural historian/mathematician of North America. During his time in the failed colony Harriot carried out cartographical surveys, studied the flora and fauna and made an anthropological study of the natives even starting to learn the Algonquian language; inventing a phonetic alphabet to record it and writing a grammar of the language.

The attempt to establish a colony ended in disaster and the colonists, including Harriot had to be rescued by Francis Drake, on his way back from harassing the Spanish in Middle America, Raleigh having sailed back to England to fetch more supplies and settlers. This adventure was to provide Harriot’s one and only publication during his lifetime entitled A Brief and True Report of the New Found Land of Virginia; an advertising pamphlet published in 1588 designed to help Raleigh find new sponsors for a renewed attempt at establishing a colony. This pamphlet, the first English language publication on North America, was reprinted in Latin in a collection of literature about the America’s published in Frankfurt and became known throughout Europe.

Back in England Harriot became involved in another scheme of Raleigh’s to establish a colony in Ireland, serving for a number of years as his surveyor and general factotum. In the 1590s he left Raleigh’s service and became a pensioner of Henry Percy, Duke of Northumberland. Percy gave Harriot a very generous pension as well as title to some land in the North of England and a house on his estate of Syon House near London. It appears that Percy required nothing in return from Harriot and had given him what amounted to an extremely generous research grant for life, allowing him to become what we would now call a research scientist. Quite why Percy should choose to take this course of action with Harriot is not known, other than his own interest in the sciences. It was during his time in Percy’s service that Harriot did most of the scientific work that should by rights have made him famous.

Harriot was already, by necessity, a working astronomer during his time as Raleigh’s mathematicus but that his knowledge was wider and deeper than that required for cartography and navigation is obvious from a comment in one of his manuscripts. He complains about the inaccuracies of the Alfonsine Tables based on Ptolemaeus’ Syntaxis Mathematiké and then goes on to state that the Prutenic Tables based on Copernicus’ De revolutionibus are, in the specific case under consideration, even worse. However he’s sure the situation will improve in the future because of the work being carried out by Wilhelm IV and his astronomers in Kassel and Tycho Brahe in Hven. Harriot was obviously well connected and well informed as this before either group had published any of their results.

Now freed of obligations by Percy’s generosity Harriot took up serious astronomical research. In 1607 he and his pupil Sir William Lower (1570 – 1615) made accurate observations of Comet Halley. This led Lower to become the first to suggest in 1610 after they had both read Kepler’s Astronomia Nova that the paths of comets orbits, a hot topic of discussion in the astronomical community of the times, were Keplerian ellipses. Harriot and Lower are considered to be the earliest Keplerian astronomers, accepting Kepler’s theories almost immediately on publication. In 1609 Harriot became probably the first practicing astronomer to make systematic observations of the heavens with the new Dutch instrument invented in the previous year, the telescope. On 26 July 1609 he made a sketch of the moon using a telescope with a magnification of 6. This was several weeks before Galileo first turned a telescope towards the heavens. It should in fairness be pointed out that, unlike Galileo, Harriot did not recognise the three dimensionality of the moons surface. However after seeing a copy of Sidereus Nuncius he drew maps of the moon that were much more complete and accurate than those of his Tuscan rival. He also made the first systematic telescopic study of sunspots, which had he published would have spared Scheiner and Galileo their dispute over which of them had first observed sunspots. Harriot constructed very good telescopes and together with Lower, using one of Harriot’s instruments, continued a programme of observation. Harriot observing in London and Lower in Wales; the two of them comparing there their results in a correspondence parts of which still exist. Harriot also observed the phases of Venus independently of Galileo. Had he published his astronomical work his impact would have been at least as great as that of the Tuscan mathematicus.

It should not be thought that being set up as he was by a rich benefactor that life was just plain sailing for Harriot. In 1603 Raleigh, with whom he was still in close contact, was imprisoned in the Tower of London for treason. He was tried, found guilty and sentenced to death. The sentence was commuted to imprisonment and he remained in the Tower until 1616. In 1605 he was joined in the Tower by Harriot’s new patron, Henry Percy, together with Harriot himself. Percy had been arrested on suspicion because his second cousin, Thomas Percy, who was also the manager of his Syon estate, was one of the principals in the Gunpowder Plot. Harriot it seems was arrested simply because of his connections to Henry Percy and was released without charge within a couple of months. Percy was also never charged, although he was fined a fortune for his cousin’s involvement and remained imprisoned in the Tower until 1621. Percy was an immensely rich man and rented Martin Tower where he set up home even installing a bowling alley. Over the years Harriot regularly visited his two patrons in their stately prison where the three of them discussed scientific problems even conducting some experiments. This was certainly one of the most peculiar scientific societies ever.

Like most astronomers of the time Harriot was also very interested in physical optics because of the role that atmospheric refraction plays in astronomical observations. Harriot discovered the sine law of refraction twenty years before Willebrord Snel after whom the law is usually named. Although Harriot corresponded with Kepler on this very subject, after he had discovered the law, he never revealed his discovery again missing the chance to enter the history of science hall of fame.

Like his contemporaries Galileo and Stevin Harriot was very interested in dynamics and although he failed to abandon the Aristotelian concept that heavier bodies fall faster than lighter ones, his analysis of projectiles in flight is more advanced than Galileo’s. Harriot separately analysed the vertical and horizontal components of the projectiles’ flight and came very close to inventing vector analysis. One historian of science places Harriot’s achievements in dynamics between those of Galileo and Newton but once again he failed to publish.

Harriot’s greatest achievement was probably his algebra book, which was without doubt the most advanced work on the subject produced in the first half of the sixteenth century. It was superior to Viète’s work on the subject although there are some questions as to how much exchange took place between the two men’s efforts, as Nathaniel Torporley an associate of Harriot’s who would become one of his mathematical executors had earlier been Viète’s amanuensis. Harriot gave a complete analysis of the solution of simple algebraic equations that was well in advance of anything previously published. His algebra book was the only one of his works other than his Virginia pamphlet that was actually published if only posthumously. Unfortunately his mathematical executors Torporley and Walter Warner did not understand his innovations and removed them before publication. Even in its castrated form the book was very impressive. The real nature of his work in algebra was obviously known to his near contemporaries leading to John Wallis accusing Descartes of having plagiarised Harriot in his Géométrie. An accusation that probably had more to do with Wallis’ dislike of the French than any real intellectual theft, although Harriot’s work is certainly on a level with the Frenchman’s.

Mathematician, cartographer, navigator, anthropologist, linguist, astronomer, optical physicist, natural philosopher Thomas Harriot was a polymath of astounding breadth and in almost all that he attempted of significant depth. However, for reasons that are still not clear today he chose to publish next to nothing of a life’s work devoted to science. Had he published he would without doubt now be considered a member of the pantheon of gods of the so-called scientific revolution but because he chose not to he suffered the fate of all academics who don’t publish, he perished.


Filed under History of Astronomy, History of Cartography, History of Mathematics, History of Optics, History of Physics, History of science, Renaissance Science

5 Brilliant Mathematicians – 4 Crappy Commentaries

I still tend to call myself a historian of mathematics although my historical interests have long since expanded to include a much wider field of science and technology, in fact I have recently been considering just calling myself a historian to avoid being pushed into a ghetto by those who don’t take the history of science seriously. Whatever, I have never lost my initial love for the history of mathematics and will automatically follow any link offering some of the same. So it was that I arrived on the Mother Nature Network and a blog post titled 5 brilliant mathematicians and their impact on the modern world. The author, Shea Gunther, had actually chosen 5 brilliant mathematicians with Isaac Newton, Carl Gauss, John von Neumann, Alan Turing and Benoit Mandelbrot and had even managed to avoid the temptation of calling them ‘the greatest’ or something similar. However a closer examination of his commentaries on his chosen subjects reveals some pretty dodgy not to say down right crappy claims, which I shall now correct in my usual restrained style.

He starts of fairly well on Newton with the following:

There aren’t many subjects that Newton didn’t have a huge impact in — he was one of the inventors of calculus, built the first reflecting telescope and helped establish the field of classical mechanics with his seminal work, “Philosophiæ Naturalis Principia Mathematica.” He was the first to decompose white light into its constituent colors and gave us, the three laws of motion, now known as Newton’s laws.

But then blows it completely with his closing paragraph:

We would live in a very different world had Sir Isaac Newton not been born. Other scientists would probably have worked out most of his ideas eventually, but there is no telling how long it would have taken and how far behind we might have fallen from our current technological trajectory.

This is the type of hagiographical claim that fans of great scientists tend to make who have no real idea of the context in which their hero worked. Let’s examine step by step each of the achievements of Newton listed here and see if the claim made in this final paragraph actually holds up.

Ignoring the problems inherent in the claim that Newton invented calculus, which I’ve discussed here, the author acknowledges that Newton was only co-inventor together with Leibniz and although Newton almost certainly developed his system first it was Leibniz who published first and it was his system that spread throughout Europe and eventually the world so no changes here if Isaac had not been born.

Newton did indeed construct the first functioning reflecting telescope but as I explained here it was by no means the first. It would also be fifty years before John Hadley succeeded in repeating Newton’s feat and finally making the commercial production of reflecting telescopes viable. However Hadley also succeeded in making working models of James Gregory’s reflecting telescope, which actually predated Newton’s and it was the Gregorian that, principally in the hands of James Short, became the dominant model in the eighteenth century. Although to be fair one should mention that William Herschel made his discoveries with Newtonians. Once again our author’s claim fails to hold water.

Sticking with optics for the moment it is a little know and even less acknowledge fact that the Bohemian physicus and mathematician Jan Marek Marci (1595 – 1667) actually decomposed white light into its constituent colours before Newton. Remaining for a time with optics, James Gregory, Francesco Maria Grimaldi, Christian Huygens and Robert Hooke were all on a level with Newton although none of them wrote such an influential book as Newton’s Optics on the subject. Now this was not all positive. Due to the influence won through the Principia, The Optics became all dominant preventing the introduction of the wave theory of light developed by Huygens and Hooke and even slowing down its acceptance in the nineteenth century when proposed by Fresnel and Young. If Newton hadn’t been born optics might even have developed and advance more quickly than it did.

This just leaves the field of classical mechanics Newton real scientific monument. Now, as I’ve pointed out several times before the three laws of motion were all borrowed by Newton from others and the inverse square law of gravity was general public property in the second half of the seventeenth century. Newton’s true genius lay in his mathematical combination of the various elements to create a whole. Now the question is how quickly might this synthesis come about had Newton never lived. Both Huygens and Leibniz had made substantial contribution to mechanics contemporaneously with Newton and the succeeding generation of French and Swiss-German mathematicians created a synthesis of Newton’s, Leibniz’s and Huygens’ work and it is this that is what we know as the field of classical mechanics. Without Newton’s undoubtedly massive contribution this synthesis might have taken a little longer to come into being but I don’t think the delay would have radically changed the world in which we live.

Like almost all great scientists Newton’s discoveries were of their time and he was only a fraction ahead of and sometimes even behind his rivals. His non-existence would probably not have had that much impact on the development of history.

Moving on to Gauss we will have other problems. Our author again makes a good start:

Isaac Newton is a hard act to follow, but if anyone can pull it off, it’s Carl Gauss. If Newton is considered the greatest scientist of all time, Gauss could easily be called the greatest mathematician ever.

Very hyperbolic and hagiographic but if anybody could be called the greatest mathematician ever then Gauss would be a serious candidate. However in the next paragraph we go off the rails. The paragraph starts OK:

Carl Friedrich Gauss was born to a poor family in Germany in 1777 and quickly showed himself to be a brilliant mathematician. He published “Arithmetical Investigations,” a foundational textbook that laid out the tenets of number theory (the study of whole numbers).

So far so good but then our author demonstrates his lack of knowledge of the subject on a grand scale:

Without number theory, you could kiss computers goodbye. Computers operate, on a the most basic level, using just two digits — 1 and 0

Here we have gone over to the binary number system, with which Gauss book on number theory has nothing to do, what so ever. In modern European mathematics the binary number system was first investigated in depth by Gottfried Leibniz in 1679 more than one hundred years before Gauss wrote his Disquisitiones Arithmeticae, which as already stated has nothing on the subject. The use of the binary number system in computing is an application of the two valued symbolic logic of George Boole the 1 and 0 standing for true and false in programing and on and off in circuit design. All of which has nothing to do with Gauss. Gauss made so many epochal contributions to mathematics, physics, cartography, surveying and god knows what else so why credit him with something he didn’t do?

Moving on to John von Neumann we again have a case of credit being given where credit is not due but to be fair to our author, this time he is probably not to blame for this misattribution.  Our author ends his von Neumann description as follows:

Before his death in 1957, von Neumann made important discoveries in set theory, geometry, quantum mechanics, game theory, statistics, computer science and was a vital member of the Manhattan Project.

This paragraph is fine and if Shea Gunther had chosen to feature von Neumann’s invention of game theory or three valued quantum logic I would have said fine, praised the writer for his knowledge and moved on without comment. However instead our author dishes up one of the biggest myths in the history of the computer.

he went on to design the architecture underlying nearly every single computer built on the planet today. Right now, whatever device or computer that you are reading this on, be it phone or computer, is cycling through a series of basic steps billions of times over each second; steps that allow it to do things like render Internet articles and play videos and music, steps that were first thought up by John von Neumann.

Now any standard computer is called a von Neumann machine in terms of its architecture because of a paper that von Neumann published in 1945, First Draft of a Report on the EDVAC. This paper described the architecture of the EDVAC one of the earliest stored memory computers but von Neumann was not responsible for the design, the team led by Eckert and Mauchly were. Von Neumann had merely described and analysed the architecture. His publication caused massive problems for the design team because the information now being in the public realm it meant that they were no longer able to patent their innovations. Also von Neumann’s name as author on the report meant that people, including our author, falsely believed that he had designed the EDVAC. Of historical interest is the fact that Charles Babbage’s Analytical Engine in the nineteenth century already possessed von Neumann architecture!

Unsurprisingly we walk straight into another couple of history of the computer myths when we turn to Alan Turing.  We start with the Enigma story:

During World War II, Turing bent his brain to the problem of breaking Nazi crypto-code and was the one to finally unravel messages protected by the infamous Enigma machine.

There were various versions of the Enigma machine and various codes used by different branches of the German armed forces. The Polish Cipher Bureau were the first to break an Enigma code in 1932. Various other forms of the Enigma codes were broken by various teams at Bletchley Park without Turing. Turing was responsible for cracking the German Naval Enigma. The statement above denies credit to the Polish Cipher Bureau and the other 9000 workers in Bletchley Park for their contributions to encoding Enigma.

Besides helping to stop Nazi Germany from achieving world domination, Alan Turing was instrumental in the development of the modern day computer. His design for a so-called “Turing machine” remains central to how computers operate today.

I’ve lost count of how many times that I’ve seen variations on the claim in the above paragraph in the last eighteen months or so, all equally incorrect. What such comments demonstrate is that their authors actually have no idea what a Turing machine is or how it relates to computer design.

In 1936 Alan Turing, a mathematician, published a paper entitled On Computable Numbers, with an Application to the Entscheidungsproblem. This was in fact one of four contemporaneous solutions offered to a problem in meta-mathematics first broached by David Hilbert, the Entscheidungsproblem. The other solutions, which needn’t concern us here, apart from the fact that Post’s solution is strongly similar to Turing’s, were from Kurt Gödel, Alonso Church and Emil Post. Entscheidung is the German for decision and the Entscheidungsproblem asks if for a given axiomatic system whether it is also possible with the help of an algorithm to decide if a given statement in that axiom system is true or false. The straightforward answer that all four men arrived at by different strategies is that it isn’t. There will always be undecidable statements within any sufficiently complex axiomatic system.

Turing’s solution to the Entscheidungsproblem is simple, elegant and ingenious. He hypothesised a very simple machine that was capable of reading a potentially infinite tape and following instruction encoded on that tape. Instruction that moved the tape either right or left or simply stopped the whole process. Through this analogy Turing was able to show that within an axiomatic system some problems would never be Entscheidbar or in English decidable. What Turing’s work does is, on a very abstract level, to delineate the maximum computability of any automated calculating system. Only much later, in the 1950s, after the invention of electronic computers a process in which Turing also played a role did it occur to people to describe the computational abilities of real computers with the expression ‘Turing machine’.  A Turing machine is not a design for a computer it is term used to described the capabilities of a computer.

To be quite open and honest I don’t know enough about Benoit Mandelbrot and fractals to be able to say whether our author at least got that one right, so I’m going to cut him some slack and assume that he did. If he didn’t I hope somebody who knows more about the subject that I will provide the necessary corrections in the comments.

All of the errors listed above are errors that could have been easily avoided if the author of the article had cared in anyway about historical accuracy and truth. However as is all to often the case in the history of science or in this case mathematics people are prepared to dish up a collection of half baked myths, misconceptions and not to put too fine a point on it crap and think they are performing some sort of public service in doing so. Sometimes I despair.



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