From τὰ φυσικά (ta physika) to physics – XIX

Although Islamic scholars made substantial contributions to mechanics, astronomy, and especially optics along the road from the Greek ta physika to modern physics, it was in the realm of mathematics that they made what was probably their greatest contribution to the development of that discipline. 

Greek science was to a great extent dominated by geometry, first and foremost the work of Euclid but also that of Apollonius and Archimedes. This continued to be the case during the Middle Ages and Greek geometry also loomed large in Islamic scientific culture. However, one characteristic of the new science developed in the seventeenth century in Europe was the rejection of the synthetic mathematics of Euclidian geometry for the newly emerging analytical mathematics that would become known as calculus. The roots of this change are to be found in the new streams of mathematics inherited from Islamic sources.

Islamic mathematicians developed three new streams of mathematics, arithmetic, algebra, and trigonometry all three of which they had in turn acquired from their predecessors in India. Of course, all three streams existed in one form or another in Ancient Greece but what the Islamic scholars acquired from India was of an entirely different calibre to what had gone before in Ancient Greece.

The arithmetic that Islamic science acquired from India was, of course, the place value decimal number system of which the eighteenth-century French mathematician, physicist, astronomer Pierre-Simon Laplace once wrote:

It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.

The place value decimal number system evolved over a period of several centuries finally reaching a semi-complete form with the introduction of zero as a number in the Brāhmasphuṭasiddhānta of the mathematician and astronomer Brahmagupta (c. 598–c. 668 CE).

Brahmagupta?

In this work Brahmagupta presents the place value decimal number system including positive, negative numbers and zero, the rules of the four fundamental operations (addition, subtraction, multiplication, and division) in a form that would be at home in a modern elementary arithmetic textbook. The one exception being his attempt to define division by zero, which as we all know ids a no,no. 

Verse from chapter XVIII of the Brāhmasphuṭasiddhānta describing the rules for zero as a number

Brahmagupta’s texts were translated into Arabic in about 750 by Abū ʿAbdallāh Muḥammad bin Ibrāhīm bin Ḥabīb al-Fazārī (died early ninth century) together with Yaʿqūb ibn Ṭāriq  (died c. 796) as ‘Az-Zīj ‛alā Sinī al-‛Arab or the Sindhind. 

The earliest Arabic text on the Hindu numerals was written by Muḥammad ibn Musá al-Khwārizmī (c. 780–c. 850) The kitab al-jam’ wa’l-tafriq al-ḥisāb al-hindī (Addition and subtraction According to the Hindu Calculation) probably written about 800 CE. It didn’t survive in Arabic but there is a Latin translation made in the twelfth century.

First page of the Latin translation Source: Wikimedia Commons

 Abū Yūsuf Yaʻqūb ibn ʼIsḥāq aṣ-Ṣabbāḥ al-Kindī (c. 801–873) wrote his kitāb fī isti’māl al-‘adād al-hindī (On the Use of the Hindu Numerals) around the same time, which also didn’t survive.

Al-Kindi on an Iraqi stamp from 1962 Source: Wilimedia Commons

The earliest surviving works are Kitāb al-uṣūl fī l-ḥisāb al-hindī (“Book of the Principles of Hindu reckoning”) by Abul-Hasan Kūshyār ibn Labbān (971–1029), and Kitāb al‑takmila fī l-ḥisāb (“The completion of arithmetic”) by Ibn Ṭāhir al-Baghdādī (d. 1037). The Kitāb al-fuṣūl fī l-ḥisāb al-hindī (“The book of chapters on Hindu arithmetic”) by Abū l‑Ḥasan al-Uqlīdisī (fl. c. 950) is the first text to describe decimal fractions, which the Indian mathematicians had not developed. 

However, Islamic scholars used a variety of number systems. They used the place value decimal number system written with number symbols but also written with Arabic letters as in an alpha-numerical number system. Beyond that they used a pure sexagesimal system, inherited from the Babylonians. They also followed Ptolemaeus with a so-called astronomical number system that used a decimal system for the whole numbers combined with sexagesimal fractions for the fraction part. One area in which the place value decimal number system was widely used was in what we would now term commercial arithmetic. Special applications that drifted towards algebra were the determination of profit or loss shares in trade deals and in the determination of  inheritance shares under the complex Islamic inheritance rules.

Algebra and arithmetic are closely linked and this was very much the case in the medieval Islamic adoption and development of algebra. In its origins algebra was restricted to what we would now term the theory of equations. We find aspects of this in virtually all pre-Islamic mathematical cultures, Egyptian, Babylonia, China, Indian and Greece. Whereas the first four all practiced a largely arithmetical approach to the solution of equations, the Greeks developed a geometrical algebra for such solutions. We still  retain elements of this when we talk about quadratic and cubic equations; for the Ancient Greek mathematicians such equations describing geometrical figures. 

The early Islamic mathematicians borrowed heavily from all of the earlier sources. Once again very influential was the Brāhmasphuṭasiddhānta of Brahmagupta. J. L. Berggren attributes the  creation of algebra to al-Khwārizmī:

Out of this dual heritage of solutions to problems asking for the discovery of numerical and geometrical unknowns Islamic civilisation created and named a science–algebra.^[1]

A Soviet postage stamp issued 6 September 1983, commemorating al-Khwārizmī’s (approximate) 1200th birthday Source: Wikimedia Commons

It is well-known that the term algebra is derived from the title of al- Khwārizmī’s book al-Kitāb al-Mukhtaṣar fī Ḥisāb al-Jabr wal-Muqābalah (The Compendious Book on Calculation by Completion and Balancing), whereal-Jabr means “setting back in its place” or “restoration.” Al- Khwārizmī “uses the term to denote the operation of restoring a quantity subtracted from one side of the equation to the other side to make it positive.”^[2] The Latinised version of his name also provided us with the term algorithm. Although, Algorisme was originally the term for calculating with the Hindu-Arabic numer system. 

A page from al-Kitāb al-Mukhtaṣar fī Ḥisāb al-Jabr wal-Muqābalah Source: Wikimedia Commons

Although al- Khwārizmī is the best known Islamic algebra author he is by no means the only one. The Mesopotamian polymath Thābit ibn Qurra (c. 830–901) gave a more general demonstration of the solution of quadratic equations than al- Khwārizmī. 

The prominent Egyptian mathematician Abū Kāmil Shujāʿ ibn Aslam ibn Muḥammad Ibn Shujāʿ (c. 850–c. 930) was known as Al-ḥāsib al-miṣrī (The Egyptian Calculator). His most influential work was his Kitāb fī al-jabr wa al-muqābala (Book of Algebra), which superseded and expanded on al- Khwārizmī work. 

He wrote about al_Khwārizmī:

I have studied with great attention the writings of the mathematicians, examined their assertions, and scrutinized what they explain in their works; I thus observed that the book by Muḥammad ibn Mūsā al-Khwārizmī known as Algebra is superior in the accuracy of its principle and the exactness of its argumentation. It thus behooves us, the community of mathematicians, to recognize his priority and to admit his knowledge and his superiority, as in writing his book on algebra he was an initiator and the discoverer of its principles, …(Wikipedia)

Kitāb fī al-jabr wa al-muqābala 

The first chapter teaches algebra by solving problems of application to geometry, often involving an unknown variable and square roots. The second chapter deals with the six types of problems found in Al-Khwarizmi’s book, but some of which, especially those of x², were now worked out directly instead of first solving for x and accompanied with geometrical illustrations and proofs. The third chapter contains examples of quadratic irrationals as solutions and coefficients. The fourth chapter shows how these irrationalities are used to solve problems involving polygons. The rest of the book contains solutions for sets of indeterminate equations, problems of application in realistic situations, and problems involving unrealistic situations intended forrecreational mathematics. (Wikipedia)

Like that of al- Khwārizmī, Abū Kāmil’s work would filter through to Europe in the later Middle Ages, as did the work of the Persian mathematician and engineer Abū Bakr Muḥammad ibn al Ḥasan al-Karajī (c. 935–c. 1029). His three principal surviving works are mathematical: Al-Badi’ fi’l-hisab (Wonderful on calculation), Al-Fakhri fi’l-jabr wa’l-muqabala (Glorious on algebra), and Al-Kafi fi’l-hisab (Sufficient on calculation). Whereas the work of al- Khwārizmī and , Abū Kāmil were still anchored in the algebraic geometry of the Greeks, al-Karajī went as long way to making it a numerical discipline. 

Although Brahmagupta had dealt with negative numbers and the rules for calculating with negative quantities, they were largely ignored  by the early Islamic algebraists. Al-Samawʾal ibn Yaḥyā al-Maghribī (c. 1130–c. 1180), who was born in Baghdad into a Jewish family of North African origin he converted to Islam, introduced the rule of signs in his al-Bahir fi’l-jabr, (The brilliant in algebra), written when he was nineteen years old. He also dealt with the law of exponents and polynomial division. 

Binomial coefficients from Al-Samawal al-Maghribi al-Bahir fi’l-jabr,

Our final Islamic algebraist is Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm Nīsābūrī (1048–1131) better known in English as Omar Khayyam (‘Umar al-Khayyāmī) as a poet but he was polymath, who did important work in mathematics and astronomy. His most important development in algebra was a geometrical general theory of cubic equations. 

‘Umar al-Khayyāmī) “Cubic equation and intersection of conic sections” the first page of a two-chaptered manuscript kept in Tehran University. Source: Wikimedua Commons

The third major innovative area of Islamic mathematics was trigonometry. Trigonometry had its origins in Greek astronomy, with Hipparchus (c. 190–c. 120 BCE) providing a table of chords of a circle to designate the size of angles.

Being astronomy, the application is, of course only to spherical triangles. His table did not survive but Ptolemaeus took it over in his Mathēmatikē Syntaxis know in Arabic as the Almagest. 

When the Indians took over many aspects of Ancient Greek astronomy they also acquired the cord measure of angles, which they halved to create the sine, a table of sines is presented in the Surya Siddhanta from the 4^thor fifth centuries.

English translation of the Surya Siddhanta by Rev. Ebenezer Burgess 1935 Source

This work also defines the cosine, versine and inverse sine. Early Islamic astronomers acquired their astronomy from both Ancient Greece and India but went on to use the Indian sine rather than the Greek cord measure for angles. 

The tangent function was known to various ancient cultures, outside of astronomy, as a means for determining the hight of structures. Because the shadow of a tall object creates a right angle triangle from which the tangent and cotangent can be used to determine the height of the object, the tangent became known as the shadow function. 

Once again the Persian mathematician al- Khwārizmī was a pioneer in this branch of mathematics producing sine, cosine, and tangent tables. Another Persian astronomer, mathematician and geographer, Habash al-Hasib al-Marwazi (766 – d. after 869) described and produced tables of the tangent and cotangent. 

The Syrian astronomer Abū ʿAbd Allāh Muḥammad ibn Jābir ibn Sinān al-Raqqī al-Ḥarrānī aṣ-Ṣābiʾ al-Battānī (before 858–929) defined and produced tables for the secant and cosecant. He was also the first to apply the trigonometric functions to plane triangles. In general, Islamic mathematicians introduced the use of trigonometrical functions into surveying and cartography. 

al-Battānī Source: Wikimedia Commons

Abū al-Wafāʾ Muḥammad ibn Muḥammad ibn Yaḥyā ibn Ismāʿīl ibn al-ʿAbbās al-Būzjānī (940–998), born in Khorasan (in today’s Iran), was the first to present all six of the trigonometrical functions in his Kitab al‐Majisṭī . 

 Page of the manuscript of Kitab al-majisti by Abu al-Wafa. (Source)

Abū ʿAbd Allāh Muḥammad ibn Muʿādh al-Jayyānī (989–1079), an Arabic mathematician from al-Andalus produced his Kitab madschhulat qisiyy al-kura (The book of unknown arcs of the sphere) a treatise on spherical trigonometry. Al-Jayyānī’s work on spherical trigonometry contains formulae for right-handed triangles, the general law of sines, and the solution of a spherical triangle by means of the polar triangle.

A page from Al-Jayyānī’s work on spherical trigonometry

The Persian polymath, Nasīr al-Dīn al-Tusī (1201–1274), in his work asch-Schakl al-Qattāʿ (Treatise on the Quadrilateral) was the first to handle trigonometry as a mathematical disciple independent of astronomy. He dealt both with the cordal trigonometry of the Greeks as well as the six modern functions, introducing the law of tangents for spherical triangles and providing proofs of it and the law of sines. 

Throughout the medieval Islamic period from al- Khwārizmī in the eighth century to Ulugh Beg in the fifteenth, Islamic astronomers and mathematicians continually worked on developing new mathematical methods to calculate ever more accurate tables of trigonometrical functions. In general, they took the simple method developed by Hipparchus to determine the size of angles in astronomy and over many generations developed an entire branch of mathematics, which would continue to increase in importance after re-entering Europe.

It is difficult to overemphasise to contributions that Islamic mathematicians made in various areas of mathematics that they had inherited from their predecessors, developments that would play a significant role in the general development of science and physics in particular in later centuries.

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^[1] J. L. Berggren, Episodes in the Mathematics of Medieval Islam, Springer, New York, 2003, p. 102 

^[2] Berggren, p. 102

Little things that made a big impact.

It is quite common that people get asked what they think is the most import development in technology or the most significant technological invention in human history. Apart from the ubiquitous wheel, which is almost certainly the most common answer, unless they are historians, they will almost always name something comparatively modern and usually big and impressive–the steam engine, the automobile, the airplane, the computer or whatever. However, having been at one time in my life, for a number of years, an archaeologist, I am very much aware of the massive impact that seemingly everyday things had on the development of human society–the most obvious is cooking with fire, but also making, ceramics, bricks, glass, simple tools, and many other things many of them seemingly small and insignificant. In response to a fascinating blog post by Rachel Laudan on the uses to which gourds were put in the history of cooking, I once wrote a blog post on the significance of the invention of the sewing needle. 

This being the case, I couldn’t resist when I came across reviews of Roma Agrawal’s book Nuts & Bolts and bought a copy, which I read with growing enthusiasm and delight. I couldn’t resist because the full title is Nuts & Bolts: Seven Small Inventions That Changed the World (in a Big Way).^[1]

Roma Agrawal is not a historian but a structural engineer, a graduate of Oxford University, BA physics, and Imperial college, MA Structural engineering, who has worked on major engineering project, including  the Shard in London. In her book she brings an engineer’s eyes to a popular historical view of the nail, the wheel, the spring, the magnet, the lens, string, and the pump. Outlining not only their origins, their evolution, the multiple forms they have taken and the multiple uses to which they have been put but also giving a soft scientific and engineering explanation of how they work in terms of forces and resistance. 

From the outset this book is wonderfully written and a delight to read. The world’s textbook writers could learn a lesson or two from Agrawal on how to hold a reader’s interest and entertain them whilst at the same time educating them. She makes it seem very easy. 

She starts with the nail, a very simple, small, seemingly insignificant everyday object that most people wouldn’t even think of when asked to list important historical invention. However, the nail is and has been a very important element in building projects of all sizes throughout the world for millennia. She traces its origins, its developments, and its very important transition from being hand forged to machine made.  She explains how the force of friction enables nails to hold things together. However, she doesn’t just deal with nails in this chapter but with screws, rivets, and nuts and bolts, which as she explains are all basically evolved forms of the humble nail. In this direction the mental leap that most surprised me is that the piles–wood, metal, concrete–driven into the ground to support building are in reality just very big nails.

After the nail, Agrawal turns to that perennial favourite greatest invention, the wheel. We of course get the wheel enabling transport but more significantly she takes her readers on a whirlwind tour of many of the other places where wheel can be found fulfilling an important function. We have the potter’s wheel,  cog wheels and gear wheels, the invention of the bicycle and the invention of the gyroscope. She includes a fascinating section on Josephine Cochran’s invention of the dishwasher. One facet of Agrawal’s narratives is that where possible she draws attention to the contributions made by women to the history of technology.  She takes us through the evolution of better wheels from the simple solid plank wheel down to the sophisticated spoked wheels of modern bicycles and closes by stating, “Human progress and the reincarnations of the wheel and axel are intricately intertwined. And that’s why we should absolutely continue to reinvent the wheel.”

Our next small invention is the humble spring, which doesn’t immediately spring to mind when asked about the greatest inventions. (I’ll let myself out!) One revelation that totally blew my mind when I first read it, is that the bow, as in bow and arrow, is a spring! If you want to know why the elaborately curved Mongolian bow is superior to the European longbow this is the place to go. Moving on via springs in guns Agrawal land at a device that lives from its springs the mechanical clock. Here we meet another aspect of Agrawal’s approach, hands on. The opening paragraphs of the nail section found her hand forging nails in a smithy, we now find in the workshop of Dr Rebecca Struthers, independent watchmaker and horologist. Struthers put out her own book Hands of Time: A Watchmaker’s History of Time (Hodder & Stoughton) in 2023. The lady engineer and the lady watchmaker take the reader through the history of the clock and the central role that springs came to play in their construction. John Harrison, of course, gets a nod on route. Fascinatingly the structural engineer introduces her readers to building, suspended on springs to protect them from earthquakes or to shield them from external vibrations. 

Our interest is now directed to the magnet, where it is not long before we get briefly introduced Dr William Gilbert and his De Magnete but we don’t linger, quickly progressing to the development in magnets and their materials now that magnetism had been established as a science. Having sketched the developed the modern magnet we get introduced to the electric telegraph, a massive communications revolution, that depended on magnets. The electric telegraph was superceded by the telephone another communications device dependent on the magnet. This capital argues for the magnet as the driver of modernity with the television following on the heels of the telegraph and telephone. Here Agrawal pulls another rabbit out of her hat, ignoring the western developers in favour of the story Takayanagi Kenjiro the independent Japanese inventor of the television. The section closes with the story of LEDs.

Up till now, whilst reading, I was really enjoying Agrawal’s fascinating and stimulating book and then I ran into her section on the lens, and soon wished I hadn’t. Readers of this blog will know that the history of optics is one of my special areas of study and I’m sorry but Agrawal’s story of the lens is a trainwreck! I’ll move on for now but return to the lens later.

As opposed to the chapter on the lens, the chapter on string is a delight. Agrawal opens with the steel cables that hold up suspension bridges, which is not what one normally thinks about when somebody uses the word string. However, as she points out the cables on smaller suspensions bridges, such as the one that was one of he first engineering projects, are twisted together out of steel fibres in exactly the same way as string is made by twisting together plant fibres. The heavier ones are made with a slightly different process but are also basically string. She then moves on to sewing and the sawing needle, sewing thread being, of course another form of string. Moving on we have cloth which is usually woven or knitted string. String has truly played a major roll in human history. The chapter closes with a discourse on music made with string instruments and instead of the violins or guitars, one might expect we get a fascinating detailed description on the tanpura, the drone instrument in Indian music, and how the strings are manipulated to produce the vibrating, droning sound. 

The final chapter is devoted to the pump, which Agrawal defines as a way of raising water to a higher level. After a brief sketch of the history of the water lifting devices, she turns to a description of the most fascinating of all pumps, the human heart. The heart is a small pump with an incredible performance. However, Agrawal is not deviating from engineering to biology but the description of the heart is used as an introduction to the story of the development of the heart-lung machine, a truly fascinating story of a piece of medical engineering history. After this excurse into the medical discipline we follow Agrawal into the equally fascinating story of the development of the breast milk pump, which Agrawal was led to through her own problems with breast feeding. 

We  return to the lens. This starts, as much of the book, with a personal anecdote about the conception of Agrawal’s daughter, which was by artificial insemination and a description of the microscope developed to study the insemination of ova. This is one of several personal stories in the book that illustrates Agrawal’s interest in the topic under discussion. Having introduced the lens through the microscope, we now move back to the origins and history of the lens, here she goes off the rails. She accepts that the so-called Nimrud  lenses (7^thcentury BCE) are lenses and not simply ground and polished pieces of lens shaped crystal, for which there is simply no proof whatsoever. I think they are more probably decorative stones.

She now moves on to the Greeks and writes the following:

The Greeks laid down some basic rules of how light reflects off mirrors and even bends through lenses.

The Greeks did indeed study the basics of refraction but those studies had almost nothing to do with lenses. The most extensive study of refraction was by Ptolemaeus, who was concerned with atmospheric refraction in astronomy and most important failed to determine the sine law of refraction. She continues:

Having quickly rubbished Greek theories of optics without going into detail we arrive at Ibn al-Haytham (b. 965 BCE). After a biographical sketch she makes the claim that “he finally explained correctly how sight works.” Although Ibn al-Haytham made great progress towards a correct explanation of how sight works, it is by no means completely correct and above all most of the elements he uses in his model are taken from the Greek sources that she doesn’t present. She then presents one of al-Haytham’s experiments claiming that it proves his theories, which it doesn’t. We then get the extraordinary statement:

Ibn al-Haytham’s work related to optics was groundbreaking for many reasons. For the first time, someone suggested correctly, that light exists independently of vision.

Sorry, but this is pure and utter garbage!

He also said that light travels in rays along straight lines, and these rays are not modified by other rays that cross their path.

This was already known to the Greeks.

For the first time, he conducted a scientific study of images formed by lenses.

Ibn al-Haytham did not conduct a scientific study of images formed by lenses. He made some minor comments on the images formed by spherical lenses. 

We then get the classic:

In another interesting link, physicist  Jim Al-Khalili writes that Ibn al-Haytham’s discussion on perspective-which was translated into Italian in the fourteenth century-enabled Renaissance artists to create the illusion of three-dimensional depth in their work. 

This illustrates a major problem in her work on al-Haytham, she uses the highly hagiographic and historically inaccurate work of Al-Khalili as her source, rather than the historically accurate, in depth studies of David C. Lindberg, A. Mark Smith, and A. I. Sabre. 

As far as the development of linear perspective during the Renaissance is concerned, the geometry of linear perspective is the optical geometry of Euclid, which is in no way dependent on anything al-Haytham wrote. Of the early developers of linear perspective Lorenzo Ghiberti (1378–1455) indeed quotes al-Haytham. However, we know nothing about the sources which inspired Filippo Brunelleschi (1377–1446) to carry out his famous demonstration of linear perspective. Finally, Mark Smith thinks that Leon Battista Alberti (1404–1472), who wrote and published the first explanation of linear perspective in his Della Pittura (1435)/De Pictura (1436) did not reference optical literature to write his book but that it was based on his work recording the architectural ruins in Rome using a plane table. More importantly, Alberti states clearly in his book that for linear perspective it is irrelevant whether one holds an extramission theory of optics, Euclid, or an intromission one, al-Haytham.  

We then get the claim that that Ibn al-Haytham “laid the foundation of what we now describe as scientific method.” As al-Haytham’s experimental programme is an extended copy of that of Ptolemaeus’ programme this claim is simply refuted. 

Following an explanation of how lenses work, we get a horrible piece of ahistorical garbage:

The science of optics advanced significantly in the Islamic empires, but the practical applications of lenses remained largely limited to burning glasses and simple magnification. Centuries later, when the Islamic Golden Age of science [my emphasis] began to dim in the Middle East, and as light began to break through the Dark Ages in the West, [my emphasis] Europe’s Renaissance thinkers built on the work of their medieval counterparts to truly harness the superpower of lenses.

The concept of the Islamic Golden Age of science is, today, increasingly viewed with scepticism by historians as it is particularly difficult to define just when it was supposed to have ended. The term Dark Ages, however, is not just viewed with scepticism but has been totally banned from the vocabulary of serious historical discussion. 

Having written this paragraph, Agrawal then dives straight into the invention of the microscope, strangely making here no mention of either the invention of eyeglasses (spectacles) or the telescope. This is particularly bizarre as a couple of pages earlier she had written, “ He [Ibn al-Haytham] laid the foundations for scientists after him – including Newton, who published his work 700 years later – to not only study and explain light even further, but also to engineer spectacles, microscopes, telescopes, cameras, and more.” Note Newton gets a name check but a whole list of other significant contributors to the history of optics, Kepler for example, don’t. Without the invention of spectacles, no industry of lens making would have developed, and without spectacles no telescope, and without the telescope no microscope! 

Interestingly, the earliest date for the end of the so-called Islamic Golden Age of science is the fall of Baghdad at the hand of the Mongols in 1258, which almost coincides with the invention of spectacles in Northern Italy, which by the way, was in no way connected to the optical theories of Ibn al-Haytham. 

We get a few lines on Robert Hooke and his Micrographia before she writes the following:

No doubt inspired by Hooke’s work, a Dutch shopkeeper with little formal education decided to look closer, leading him to seeing many things that humans had never seen before.

The Dutch shopkeeper is, of course Antony Leeuwenhoek, who was actually quite a bit more than just a shop keeper. There is actually no evidence that Leeuwenhoek was inspired by Hooke. This is a purely speculative theory proposed by Brian J. Ford, who is the source that Agrawal uses for he comments on Leeuwenhoek.     

There follows an account of Leeuwenhoek’s single lens microscopes which ends with the following:

Holding the microscope up to his eye, he could peer through his handmade lenses, some of which could magnify objects by an astonishing 266 times. To put this in perspective, the microscopes with two lenses invented in the late sixteenth century by the Dutch father and son team, Hans and Zacharias Janssen[my emphasis], could only magnify up to a maximum of ten times, because of the limited quality of the lenses and blurring effects first studied by Ibn al-Haytham. 

The claim that Hans and Zacharias Janssen invented the microscope in the sixteenth century was very dubious at the best when it was first presented, apart from anything else Zacharias Janssen would have been only four-years-old at the time given in the story. However, modern research by Huib Zuidervaaart, has shown that Zacharias Janssen, who is also credited with the invention of the telescope, had nothing whatsoever to do with optics before 1616. 

We don’t actually know who invented the microscope but it is assumed that several early telescope makers and user, such as Galileo, looked through their Dutch or Galilean telescopes the wrong way round and realised that it functioned as a microscope. Several people in Galileo’s circle in the Accademia dei Lincei used such Galilean microscopes and it was Giovanni Faber of the Lincei, who gave the instrument its name. The first use of a Keplerian telescope, with two convex lenses, is credited to Cornelis Drebbel in 1619. 

We then get an account of Leeuwenhoek’s discoveries culminating in his discovery of sperm. Agrawal writes:

Combined with the theory that all female animals have eggs, which also made its appearance in the mid-1670s…

This theory originated with William Harvey in his De Generatione, Ex ovo omnia – All things come from an egg, in 1651.

The rest of the chapter deals with the development of the microscope and its use in artificial insemination followed by a long section on the history of the history of the camera, both more or less acceptable. 

Of course, the series of historical errors in this chapters leads on to speculate if the history in the other chapters is accurate. Unlike this chapter the others are not my speciality but as far as I could ascertain they are historically acceptable. 

The book has neither foot nor endnotes. There are lists of the experts consulted for each chapter and also a separate extensive bibliography of sources for each. There is also a useful index. The book has occasional black and white illustrations many of which are had drawn, one assumes by the author. Despite my complaints about the chapter on the lens, I recommend Roma Agrawal’s book, which is despite the flaws mentioned above an excellent read. 

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^[1] Roma Agrawal, Nuts & Bolts: Seven Small Inventions That Changed the World (in a Big Way), Hodder & Stoughton, London, 2023.

Origins of the astrolabe

In a recent excellent video on Hypatia – Myths and History, Tim O’Neill  correctly pointed out that the claim that Hypatia created the astrolabe was rubbish, going on to claim that it had existed for at least five centuries before she lived. Tim’s second claim is in fact wrong but is just one of many commons claims about the ancient origins of the astrolabe. I have decided to give a brief sketch of what we actually know about the origins of this multipurpose astronomical instrument. 

NATIONAL MARITIME MUSEUM, GREENWICH
In 694 ah (1294–95 ce), Mahmud ibn Shawka al-Baghdadi produced this astrolabe.

It would surprise most people to discover that the earliest known treatise on the astrolabe was written by Theon of Alexandria (c. 335–c. 405 CE), Hypatia’s father. This work is no longer extant but the Suda, the tenth-century Byzantine encyclopaedia, mentions it. Both the treatise on the astrolabe by the Greek, Christian scholar John Philoponus (c.490–c. 570) and that of the Syriac scholar Severus Sebokht (575–667) draw heavily on the treatise of Theon. It is not known and cannot be ascertained whether Theon invented the plane astrolabe or was merely writing about an already existing instrument.

The earliest surviving reference to the plane astrolabe is in a letter from Synesius of Cyrene (c. 373–c. 414), the Greek bishop of Ptolemais describing how Hypatia taught him how to construct a silver plane astrolabe as a gift for an official. This is the origin of the myth that she invented the astrolabe.

The invention of the astrolabe has been variously attributed to Ptolemaeus (c. 100–c. 170), Hipparchus (c. 190–c. 120 BCE) and Apollonius of Perga (c. 240–c. 190 BCE) but there is absolutely no evidence to support any of these attributions. Hipparchus and Apollonius both probably used a dioptra attached to a protractor to measure angles, which can be regarded as a precursor to the astrolabe.

A dioptra (Greek: διόπτρα) is a classical astronomical and surveying instrument, dating from the 3rd century BC. The dioptra was a sighting tube or, alternatively, a rod with a sight at both ends, attached to a stand. If fitted with protractors, it could be used to measure angles. (Wikipedia) 

The reverse face of a plane astrolabe is basically a dioptra mounted on a protractor

Reverse face of an astrolabe with alidade (dioptra) North African, 9th century AD, Planispheric Astrolabe Khalili Collection Source: Wikimedia Commons

but it is the front of the instrument that is the key element of the instrument.

This is a stereographic projection of the celestial hemisphere known as a planisphere.

The planisphere face of an astrolabe

The earliest known reference to the planisphere is a text by Ptolemaeus:

The Planisphaeium (Greek: Ἅπλωσις ἐπιφανείας σφαίρας, lit. ’Flattening of the sphere’) contains 16 propositions dealing with the projection of the celestial circles onto a plane. The text is lost in Greek (except for a fragment) and survives in Arabic and Latin only. (Wikipedia)

Once again people try to attribute the origin of the planisphere to Hipparchus but as with the astrolabe, there is absolutely no evidence to support this attribution. 

Based on his authorship of the Planisphaeium, some try to attribute the invention of the astrolabe to Ptolemaeus but in his Mathēmatikē Syntaxis (Greek: Μαθηματικὴ Σύνταξις, lit. ’Mathematical Systematic Treatise’), better known as the Almagest, he describes the instrument that he used for his observations and it was an armillary sphere, not an astrolabe.

Even those who know history are doomed to repeat it!

On Thursday 15 November 2023, I checked into a clinic in Bad Kissingen, Lower Franconia to start twenty-one days of orthopaedic rehabilitation for my fucked back. On the following Monday, the fifth day, I was feeling totally shitty and on the Tuesday morning I tested positive for Covid. I broke off my rehabilitation and on the Wednesday I was sent home.

Having waited for the Christmas’ and New Years’ holiday period to pass I reapplied to my health insurance  and was granted a new rehabilitation.

On Monday 25 March 2024, I checked into a clinic in Bad Kissingen, Lower Franconia to start twenty-one days of orthopaedic rehabilitation for my fucked back. On Monday 8 march, the fifteenth day, I was feeling totally shitty and on the Tuesday morning I tested positive for Covid. I broke off my rehabilitation and on the Wednesday I was sent home.

Normal service will be resumed as soon as I stop coughing my soul out!

Hiatus replay!

Some of you will remember that back in November I announced that I would be taking a break from writing my blog in order  to get some medical rehabilitation for my fucked spine (official medical terminology). You might also remember that this turned into a farce when on entering the clinic I almost immediately acquired a dose of the dreaded Covid. Having successfully jumped over all the bureaucratic hurdles, I’m now due to restart my medical rehabilitation on next Monday, 25 March, meaning there will be no new blog posts during the next three weeks.

Here’s hoping that I don’t develop typhoid or something this time. As Phillip Helbig suggested I should have signed off my hiatus post last time:

I’LL BE BACK!

From τὰ φυσικά (ta physika) to physics – XVIII

During the Middle ages Islamicate scholars analysed, studies, criticised and developed a wide range of academic disciples that they had adopted from their Greek, Persian, Chinese, and India predecessors before passing them back into Europe during the twelfth-century Scientific Renaissance. One of the disciples where their endeavours had the biggest impact was in the science of optics. 

As we saw in an earlier episode, as opposed to the popular cliché, the Ancient Greeks propagated a wide range of theories of vision ranging from the Atomist intromission theory, over the Platonist combined extramission/intromission theory, the pure extramission theory in the geometric optics of Euclid, Heron, and Ptolemaeus, to the Aristotelian intromission theory and finally the Stoic pneuma based theory shared by Galen. All of these reached the medieval Islamic society in translation and each of them found their critics, supporters, and propagators.  

Already in the ninth century Abū Yūsuf Yaʻqūb ibn ʼIsḥāq aṣ-Ṣabbāḥ al-Kindī (c. 801–873), an Arabic Muslim polymath, who was born in Kufa, in what is now south-central Iraq, the son and grandson of the governor. Originally educated in his home town he moved at some point to Baghdad to complete his education and where he would go on to serve three ‘Abbāsid Caliphs.

An Iraqi postage stamp issued in 1962 on the occasion of the millennium anniversary of the founding of the city of Baghdad and in memory of the philosopher Yacoub bin Ishaq Al-Kindi. Source: Wikimedia Commons

His interests were wide-ranging and he is said to have written at least two hundred and sixty books, which, as is often the case, have mostly been lost. Of major interest for his contributions to optics is his De radiis stellarum, a work that only exists in Latin translation, the Arabic original being lost. Here al-Kindī presents a central element of his general philosophy:

It is manifest that everything in this world, whether it be substance or accident, produces rays in its own manner like a star … Everything that has actual existence in the world of the elements emits rays in every direction, which fill the whole world.^[1]

De radiis, manuscript, 17th century. Cambridge, Trinity College Library, Medieval manuscripts, MS R.15.17 (937). Source: Wikimedia Commons

Of course, given this general statement optics with its light rays and visual rays is a central area for al-Kindī. He wrote several works on optics of which On the Causes of Differences in Perspective or De aspectibus, to give it its Latin title, is the most important but like De radiis stellarum, the Arabic original is lost. In this work al-Kindī comes down in favour of the Euclidian theory of geometrical optics with its pure extramission theory of vision but not without criticism. To start he summarises the various alternative theories he has inherited from antiquity:

Therefore I say that it is impossible that the eye should perceive its sensibles except [1] by their forms travelling to the eye, as many of the ancients have judged, and being impressed in it, or [2] by power proceeding from the eye to sensible things, by which it perceives them, or [3] by these two things occurring simultaneously, or [4] by their forms being stamped and impressed in the air and the air stamping and impressing them in the eye, which [forms] the eye comprehends by its power of perceiving that which air, which light mediates, impresses in it.^[2]

One is obviously the atomists, two is Euclid and Ptolemaeus, three is clearly Plato, and four is the mediumistic theory of Aristotle. Through argument al-Kindī eliminates all but Euclid by attacking the basic principle of intromission. He argues that a circle viewed edgewise, should in an intromission theory still appear as a circle but in reality it appears as a straight line:

Therefore it remains that the power proceeds from the observer to the visible objects, by which they are perceived . this power proceeds from the eye in straight lines and falls only on the edges of the circles, perceiving them as straight lines.^[3]

Having established that Euclid is the only valid model of perception he now takes him to task. He presents six propositions at the beginning of his work that demonstrate that luminous rays are rectilinear, although he is not intending to replace Euclid’s visual rays with luminous rays. He also differs from Euclid on the constitution of the visual cone. Whereas Euclid conceives it to consist of single rectilinear rays, al-Kindī sees it as a continuous whole. He goes further and argues that rays issue in all directions from every point on the surface of the eye. He bases this claim on the analogous behaviour of external light. al-Kindī argued that light reflects from every point on an object in every direction. He appears to have been the first to explicitly  state this simple concept which would go on to be an important element in theories of vision and optics in general. Although Euclid’s extramission theory of vision would prove to be wrong in the long run al-Kindī’s De aspectibusremained popular amongst Islamic scholars and together with his De radiis stellarum would have a major impact in Europe following the twelfth-century Scientific Renaissance. 

al-Kindī’s Arabic, Nestorian Christian, contemporary Ḥunayn ibn ʾIsḥāq al-ʿIbādī  (808–873), who was born in al–Hirah, near Kufa in what is now south-central Iraq, but moved to Baghdad where he worked as a translator and physician. Ḥunayn ibn ʾIsḥāq had studied medicine under Yuhanna ibn Masawaih (c. 777–857), a Persian or Assyrian, East Syriac Christian physician, the first to write in Arabic over ophthalmology  and the student would come to outperform his teacher in this area of medicine. His medicine is principally Galenic, who was for the Arabic physicians the “Prince of Physicians”, so it comes as no surprise that his ophthalmology is basically Galenic and his theory of vision Galenic and Stoic. He wrote two works on ophthalmology, Ten Treatises on theEye and the Book of the Questions on the Eye.

Hunayn ibn Ishaq 9th century CE description of the eye diagram in a copy of his book, Kitab al-Ashr Maqalat fil-Ayn (“Ten Treatises on the Eye”), in a 12th century CE edition Source: Wikimedia Commons

In his Ten Treatises on the Eye, Ḥunayn ibn ʾIsḥāq gives a detailed description of the structure and function of the eye that closely parallels that of Galen.

The eye according to Hunain ibn Ishaq. From a “Book of the Ten Treatises of the Eye” manuscript dated c. 1200.

Lindberg p. 35

His theory of vision is also that of Galen, which he specifically choses over alternatives, he writes: 

We say: the object of vision can be seen only in one of the following three ways: [i] by sending out something from itself to us by which it indicates its presence so that we know what it is; [ii] by not sending anything out but remaining steady and unchanged in its place; then the faculty of perception goes out from us to it, and we recognise what it is through this medium; [iii] by there being another thing  … intermediate between us and it; it is this which gives us information about it, so that we learn what it is. And we shall now see which of these three [theories] is the right one.^[4]

Alternative one covers both the intromission theories of the atomist and Aristotle, which Ḥunayn rejects with the old argument, how can a perceived mountain enter the eye? The second alternative covers the extramission theories of Euclid and Ptolemaeus, which Ḥunayn also dismisses thus:

It is not possible that the visual spirit extends over all this space [between the eye and a distant visible object] until it spreads round the seen body and encircles it entirely.^[5]

The third alternative turns out to be that of Galen and the Stoic in which pneuma coming out of the eye triggers the air that already exists between the object and the eye creating a connection along which the visual perception takes place. This is according to Ḥunayn the right one.

Ḥunayn’s Ten Treatises on the Eye was very widely read both in Islamicate culture and later in Latin translation in medieval Europe. It was in the latter case for many people their introduction to the theories of Galen, whose own work was first translated into Latin much later.

The work of both al-Kindī and Ḥunayn ibn ʾIsḥāq were widely read and highly influential and both of them dismissed the intromission theory of vision of Aristotle. However, Aristotle had two heavyweight champions, who defended and propagated his theory in Ibn  Sīnā (980–1073), Latin Avicenna, and Ibn Rushd (1126–1198), Latin Averroes, probably the two must influential medieval, Islamic philosophers. I have included brief biographical sketches of both in the episode on Islamic theories of motion so I won’t repeat myself here.

Ibn  Sīnā, who was incredibly prolific, wrote about the theory of vision is a number of still extant works including the Kitab al-Shifa (The Book of Healing, also known as Sufficientia), Kitab al-Najat (The Book of Deliverance), Maqala fi ’l-Nafs (Epistle or Compendium of the Soul), Danishnama (Book of Knowledge), and Kitab al-Qanum fi ‘l-Tibb (Liber canonis of Canon of Medicine). 

Portrait of Avicenna on a Iranian postage stamp Source: Wikipedia Commons

Ibn  Sīnā doesn’t so much defend Aristotle’s intromission theory of vision as demolish the extramission theory in its various forms. I’m not going to go into detail, just say that his arguments are convincing. His main argument is that the rays going out to the object do not perceive the object but the object is perceived by something returning to the eye. This being the case we perceive by something entering the eye so we don’t need the rays going out from the eye. Against the Galenic theory he basically argues convincingly that either air as a medium can convey perception or it can’t and if it can it doesn’t need to be activated by pneuma. This naturally leaves him with just Aristotle’s theory as acceptable. Both Ibn  Sīnā and Ibn Rushd take over the basic Galenic  structure and function of the eye from Ḥunayn. 

Ibn Rushd is, of course the most avid Aristotelian during the Islamic Middle Ages, which earned him the title of “The Commentator” when his works were translated into Latin. He refutes the theories of visual perception of Euclid, Ptolemaeus, Galen, and al-Kindi arguing that they would all imply the ability to see in the dark. He also says that an extramission theory would imply that the eye produces enough rays to fill a hemisphere of the world every time somebody opened their eyes which was just absurd. In general, Ibn Rushd is more concerned with what happens to the image once it enters the eye, which is physiology and/or psychology and not physics, so doesn’t concern us here. 

Detail of Averroes in a 14th-century painting by Andrea di Bonaiuto Source: Wikimedia Commons

We now turn our attention to Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham, Latin Alhazen or Alhacen, (c. 965–c. 1040), a Persian or Arabic mathematician, astronomer, and physicist, who was born in Basra and spent a large part of his life in Cairo. Ibn al-Haytham is one of the most important figures in the history of optics before the seventeenth century and he worked a revolution in the discipline. In his From Sight to Light: The Passage from Ancient to Modern Optics (University of Chicago Press, 2015) Mark Smith titles his chapter on Ibn al-Haytham Alhacen and the Grand Synthesis, which is a pretty good summary in five words. 

Cropped version of the frontispiece of Johannes Hevelius, Selenographia, depicting Ibn al-Haytham (Alhacen) Source: Wikimedia Commons

Amongst Ibn al-Haytham’s extant works eleven deal wholly or partially with aspects of optics. Amongst the no longer extant works another six deal with the topic in one way or another. However, there is one work that is in the history of optics dominant and that we will look at briefly here, that is his Kitab al-Manazir (Book of Optics) which was translated into Latin by an unknown translator in the twelfth century as De aspectibus or Perspectiva. 

Ibn al-Haytham rejects the extramission theories basically taking over the arguments of Ibn  Sīnā. He also notes that strong light entering the eyes causes pain and prolonged staring at strong light sources produced after images when the eyes are returned to the dark, so the eyes are sensible to light, which comes in, not goes out. Interestingly and also very important to the future development of optics, although he dismisses the extramission theory he doesn’t dismiss the geometric optics of Euclid and Ptolemaeus. He accepts their cone of vision, and as we will see even utilises it himself, but on the condition that their rectilinear rays are merely geometrical constructs and not real visual rays. Thus, making Euclid’s and Ptolemaeus’ geometrical optics independent of the extramission theory. A seemingly trivial but highly significant redefining. 

Having followed Ibn  Sīnā in dismissing the extramission theory he doesn’t follow him in adopting Aristotle’s intromission theory but develops an entirely new one. Adopting al-Kindī’s theory that every point on an illuminated object reflects light rays in every direction, Ibn al-Haytham states that it is these reflected light rays that transmit the colour and luminosity of the object to and into the eye. This is truly a radically new concept. The theories of Plato, Aristotle, and the Stoic all required the presence of light to facilitate visual perception but Ibn al-Haytham says quite simply that all it requires is light, anything else is superfluous. 

Ibn al-Haytham sees a problem with his intromission theory, if light rays are meeting the eye from every possible direction how does the eye form a distinct image of the viewed object? He offers up a fairly refined solution to this problem. Firstly, although the structure of the eye that he adopts is that of Galen/ Ḥunayn for Ibn al-Haytham the surface of the cornea, in his model, is a perfect sphere. He then hypothesises that only those rays that meet the surface of the eye perpendicularly can actually enter the eye. All the other light rays slide or veer off. 

He justifies this with an analogy. He says, consider an iron ball thrown at a wooden plank. If it hits the plank perpendicularly it rebounds or if thrown hard enough breaks the plank, If the ball hits the plank at an angle it slides or veers off. Ibn al-Haytham argues perpendicular rays are strong and penetrate the eye, whereas rays that meet to eye at an angle are weak and veer off. 

Because his cornea is perfectly spherical this means that all the perpendicular rays meet at the centre of this sphere and this is where the image of the object is formed. The rays coming from the viewed object to the centre of the sphere form a visual cone like that of Euclid and Ptolemaeus but with the rays going from object to eye and not from the eye to the object. This explains or justifies his retention of their geometric optics. Alongside making vision purely based on light this justification of a geometric optics within an intromission theory is Ibn al-Haytham’s second major contribution to the evolution of optics.

Lindberg p. 72

Ibn al-Haytham’s visual cone from object to eye

You will often come across the claim that Ibn al-Haytham established his theory of vision experimentally and empirically, this is simply not true. The theory of vision is argued entirely philosophically without any experimentation involved. The experiments appear first in the later chapters of his Kitab al-Manazir where he deals with the mathematics of reflection and refraction, in both cases building on and extending the work of Ptolemaeus in his Optics.

The structure of the human eye according to Ibn al-Haytham showing optic nerve transmitting image to brain —Manuscript copy of his Kitāb al-Manāẓir (MS Fatih 3212, vol. 1, fol. 81b, Süleymaniye Mosque Library, Istanbul) Source: Wikimedia Commons

Because of these false claims, Ibn al-Haytham, like Galileo, is often credited with being the inventor of modern science, or the inventor of empirical experimental science, or the inventor of the scientific method, or the inventor of mathematics based science, all of which claims are total rubbish. It is in particular rubbish because almost everything he did was a copy and extension of the empirical, experimental work done by Ptolemaeus. There are even people who make these claims for both Ibn al-Haytham and Galileo! Are they really one and the same scientist cursed to travel through time inventing modern science  over and over again?

In the section on reflection Ibn al-Haytham describes a very complex and sophisticated experimental set up to investigate reflection in plane, concave, and convex mirrors. As already noted these experiments are more complex version of the ones that can be found in Ptolemaeus’ work, so not as ground-breaking as they are very often painted. However, having  described in great detail the set up and how it supposedly worked Mark Smith has the following to say:

Indeed, given its obvious unfeasibility as actually described–with all the planes perfectly aligned and all measurements perfectly reproduced–the test appears to have been an elaborate thought experiment designed to confirm what Alhacen already took for granted, that is, that light reflects at equal angles. The experiment is therefore intellectually but not physically replicable.^[6]

Ibn al-Haytham does, however, go on to subject the topic of reflection to a detailed, very accurate, high level mathematical analysis. 

As already mentioned following on to his analysis of reflection Ibn al-Haytham now handles the topic of refraction, once again taking Ptolemaeus as his inspiration and role model. Once again we get a complex experimental set up and once again, this time for different reasons, Mark Smith doubts whether they were ever carried out:

We are therefore led to raise the same doubt about feasibility that we did with the reflection experiment, and in this case the doubt is deepened by Alhacen’s failure to acknowledge the problem posed by critical angle for the tests for refraction from glass to air and glass to water. In short, there is good reason to believe that he did not carry out the experiment as described, which helps explain his failure to provide any values. That in turn raises serious doubt about the experiment’s replicability and, therefore, its “modernity.” Furthermore, its originality is questionable in that it is clearly based on Ptolemy’s experimental derivation of the angles of refraction.^[7]

As with the section on reflection there is extensive mathematical analysis.

Although Ibn al-Haytham building on the work of others very clearly laid the foundations of modern optics, it would be a mistake to think that his work immediately established itself as the go to theory of the discipline. The rival theories of al-Kindī, Ibn  Sīnā, and Ibn Rushd continues to have their supporters almost all the way down to the seventeenth century.

I have now sketched the full spectrum of theories of vision presented by scholars during the Islamic Middle Ages. All of these theories would be translated into Latin during the twelfth century and as we will see in a later episode would have a major impact. 

---

^[1] David C. Lindberg, Theories of Vision: From Al-Kindi to Kepler, University of Chicago Press, 1976, p. 19

^[2] Lindberg, pp. 21-22

^[3] Lindberg, p. 23

^[4] Lindberg, p. 38

^[5] Lindberg, pp. 38-39

^[6]A. Mark Smith, From Sight to Light: The Passage from Ancient to Modern Optics, University of Chicago Press, 2015, p. 199

^[7] Smith, p. 218

Magnetic Variations – VII One author, two authors, three authors, more

William Gilbert’s De Magnete is a book that covers a wide range of information on all aspects of magnetism, loadstones, magnets, and the magnetic compasses. He was a high ranking physician living in London and doesn’t appear to have travelled anywhere else let along sailed anywhere on a ship. This raises the justified question; how did he acquire much of the knowledge that he presents to his readers? Did he write the book alone, or were there others involved in its production? 

We know that he borrowed liberally from the works of Petrus Peregrinus de Maricourt (fl. 1269), Robert Norman (dates unknown), and William Barlow (1544–1625) without really acknowledging those borrowings. We would say he plagiarised them, but what he did was common practice amongst scientific authors during the Renaissance. There were, however, other parts of the book that relied on mariner’s knowledge to which Gilbert almost certainly did not have access. He boasts of having acquired knowledge of the behaviour of the mariner’s compass over all on the globe from conversations with the circumnavigators, Francis Drake (c. 1540–1596) and Thomas Cavendish (1560–1592) but were there others? 

We know according to the reports that at least one and possibly two others actually contributed text to De Magnete. Following Gilberts death, two other magnetists claimed the right to be considered his true disciple, William Barlow (1544–1625), who I dealt with in an earlier episode, and Mark Ridley (1560–c. 1624), who as I noted in an earlier episode lived in Wingfield House with Gilbert and whom I will deal with in the next post. Their rivalry developed into a mudslinging match in various publications, which I will also deal with in the next post. In one of his ripostes to Barlow,  Mark Ridley wrote:

[Edward Wright] was a verie skilful and painefull man in the Mathematickes, a worthy reader of that Lecture of Navigation for the East-India Company … [T]his man took great paines in the correcting the printing of Doctor Gilberts booke, and was very conversant with him, and considering of that sixt booke [of De Magnete] which you [Barlow] no way beleeve, I asked him whether it was any way of his making or assistance, for that I knew him to be most perfect in Copernicus from his youth, and he denied that he gave any aide thereunto, I replied that the 12 chapter of the 4 Booke must needs be his, because of the table of the fixed Starres, so he confessed that he was the author of that chapter, and inquiring further whether he observed the Author [Gilbert] skillfull in Copernicus, he answered that he did not, then it was found that one Doctor Gissope [Joseph Jessop] was much esteemed by him, and lodged in his house whom he knew alwaies to be a great Scholler in the Mathematick, who was a long time entertained by Sir Charles Chandish, he was a great assistance in that matter as we judged, and I have seen whole sheetes of this mans own hand writing of Demonstrations to this purpose out of Copernicus, in a book of Philosophie copied out in another hand[.] 

All that I can find about Joseph Jessop, who, according to Ridley, instructed Gilbert in Copernican cosmology is that he was apparently a fellow London physician and an erstwhile fellow of King’s. 

In contrast to the elusive Dr Jessop, Edward Wright (1561–1615) is one of the most prominent figures in relevant circles in the last quarter of the sixteenth century and the first quarter of the seventeenth. A leading mathematical practitioner, not just in England but in the whole of Europe, particularly in the areas of cartography and navigation. He had solved the mathematical problem of how to construct the Mercator projection and published it in one of the most important English books on navigation, his Certaine Errors in Navigation in 1599. He had made Simon Stevin’s equally important De Havenvinding (1599) available to English mariners by translating it into English and publishing it as The Hauen-finding Art, or The VVay to Find any Hauen or Place at Sea, by the Latitude and Variation also in 1599. He was the designer of important mathematical instruments, an advisor on and teacher of navigation and cartography.

Cover of Wright’s Certaine Errors Source: Wikimedia Commons

Source

As well as this supposed anonymous contribution to Gilbert’s masterpiece he is also a named contributor as the author of a so-called laudatory address at the beginning of the book or to give it its full title:

To the most learned Mr. William Gilbert, the distinguished London physician and father of the magnetic philosophy : a laudatory address concerning these books on magnetism, by Edward Wright. 

Wright lays it on thick in his opening paragraph:

Should there be any one, most worthy sir, who shall disparage these books and researchers of yours, and who shall deem these studies trifling and in no wise sufficiently worthy of a man consecrated to the graver study of medicine, of a surety he will be esteemed no common simpleton. For that the uses of the loadstone are very considerable, yea admirable, is too well known even among men of the lowest class to call for many words from me at this time or for any commendation. In truth in my opinion, there is no subject-matter of higher importance or of greater utility to the human race upon which you could have brought your philosophical talents to bear. 

Having in a long passage of purple prose emphasised the importance of the invention of the compass for mariners, Wright initially concentrates on the topic of magnetic variation, seeming to believe in opposition to Gilbert that the use of variation to determine longitude is a real possibility. He then moves on to the topic of magnetic dip and the possibility that this seems to offer to determine latitude by inclement and overcast weather. Here his praise goes into overdrive:

Thus then, to bring our discourse back again to you, most  worthy and learned Mr. Gilbert (whom I gladly acknowledge as my master in this magnetic philosophy [my emphasis]), if these books of yours on the Loadstone contained nought save this one method of finding latitude from the magnetic dip, now first published by you, even so our British mariners as well as the French, the Dutch, the Dames, whenever they have to enter the British sea or the strait of Gibraltar from the Atlantic Ocean, will justly hold them worth no small sum of gold. 

With reference to the sentence in brackets that I have emphasised, it should be remembered that Wright is no humble mariner but a graduate of Cambridge University, who is a leading authority on all aspects of navigation and the magnetic compass, as well as a published author and translator, so high praise indeed. It should however be noted that the plan to determine latitude by magnetic dip propagated by Gilbert in his book and so highly praised here, by Wright, was never actually realised.

Wright goes on to address Gilbert’s theory of diurnal rotation and rehashes the standard physical argument in its favour, that it is more plausible to believe that the comparatively small sphere of the Earth rotates once every twenty-four hours than that the vastly larger sphere of the fixed stars does so. He considers the religious objection but finally comes down in favour of a geocentric model with diurnal rotation.

Towards the end of his laudatory address Wright references two other European experts:

Nor is there any doubt that those most learned men, Petrus Plantius (a most diligent student not so much of geography as of magnetic observations) and Simon Stevinius, a most eminent mathematician will be not a little rejoiced when first they set eyes on these your books and therein see their own 𝜆𝜄𝜇𝜈𝜀𝜐-𝜌𝜀𝜏𝜄𝜅ή𝜈 or method of finding ports so greatly and unexpectedly enlarged and developed; and of course they will, as far as the may be able, induce all navigators among their own countrymen to note the dip no less than the variation of the needle.

Petrus Plancius (1552–1622) was a Flemish astronomer, cartographer, and clergyman, who was an expert on safe maritime routes to India and the Spice Islands. He would go on to become one of the founders of the Dutch East India Company in 1602. He is famous for his celestial globes and in particular for training the navigator Pieter Dirkszoon Keyser (c. 1540–1596)to be one of the first to map the stars in the southern hemisphere. Simon Stevin is already known to us and Gilbert endorsed the scheme of Simon Stevin (1548–1620), put forward in his The Hauen-finding Art to provide tables of the correctly measured variation to compare with measured observations as an aid to navigation. It can be assumed that Wright as the translator of The Hauen-finding Art introduced Gilbert to Stevin’s work. 

Of interest is the following allusion:

Let your magnetic Philosophy, most learned Mr. Gilbert, go forth then under the best auspices­–that work held back not for nine years only, according to Horace’s Council, but for almost another nine…

Copernicus alludes to the same advice from Horace’s The Art of Poetry on the opening page of the preface to De Revolutionibus:

For he [Tiedemann Giese] repeatedly encouraged me and, sometimes adding reproaches, urgently requested me to publish this volume and finally permit it to appear after being buried among my papers and lying concealed not merely until the ninth year but by now the fourth period of nine years. 

Turning now to Book 4 Chapter 12 of De Magnete, which Ridley relates was authored by Wright we find a detailed technical section on the best way to determine magnetic variation, which I described in my post in this series on De Magnete so, The twelfth chapter of book four provides the best and most detailed description of how to determine variation published up till that time.

The chapter describes in great technical details the various ways of determining magnetic variation at sea and on land. It includes detailed instruction for the design and construction of special instruments for this task and  outlines the mathematics necessary to carry out the calculations. It includes Tycho Brahe’s value for the deviation of the Arctic pole-star from true north, 2 deg. 55 min. but gives 3 degrees as a good approximation. It also includes a list of the right ascension and declination of bright, brilliant stars not far from the equator for determining variation at night and the construction of an instrument to do so. It closes with instructions on how to construct an instrument for finding the ortive amplitude on the horizon. For those who don’t know, the ortive amplitude is defined thus:

The arc of the horizon between the true east or west point and the centre of the sun, or a star, at its rising or setting. At the rising, the amplitude is eastern or ortive. (Wiktionary)

Instrument for determining variation on land

Instrument for determining variation at sea at night

an instrument for finding the ortive amplitude on the horizon.

All the above is very much in Wright’s area of expertise rather than Gilbert’s, so the claim that he wrote this chapter is very plausible. This of course raises the question as to whether Wright was the author,  or co-author of, or advisor on other sections of the book of a similar technical nature. This question could probably only be answered if we could find Gilberts working notes, draft manuscript(s), or correspondence from when he was working on the book. Unfortunately, when he died he donated his library and one assumes his papers to the College of Physicians of which he was President. I say, unfortunately, because the College of Physicians and its entire library was lost in the Great Fire of London, so we will never know if Wright contributed more to De Magnete or not.

From τὰ φυσικά (ta physika) to physics – XVII

As I explained in episode XII of this series where I introduced the work of the ancient Greek engineers and their machines, the discipline mechanics derives its name from the study of machines.

Greek μηχανική mēkhanikḗ, lit. “of machines” and in antiquity it is literally the discipline of the so-called simple machines: lever, wheel and axel, pulley, balance, inclined plane, wedge, and screw. 

Just as some scholars during the ‘Abbāsid  Caliphate studies, absorbed, criticised, and developed the works of Aristotle and John Philoponus on motion, and those of Aristotle and Ptolemaeus on astronomy, so there were others who took up the translated works of the Greek engineers such as Hero of Alexandria and Philo of Byzantium, extending and improving their work on machines. The Islamic texts on machines have an emphasis on timekeeping and hydrostatics.

For the earliest Islamic book on machines, we turn once again to the translation power house, the Persian Banū Mūsā brothers  Abū Jaʿfar, Muḥammad ibn Mūsā ibn Shākir (before 803 – February 873); Abū al‐Qāsim, Aḥmad ibn Mūsā ibn Shākir (d. 9th century) and Al-Ḥasan ibn Mūsā ibn Shākir (d. 9th century), the sons of the astronomer and astrologer on the court of the ‘Abbāsid caliph al-Maʾmūn, Mūsā ibn Shākir. Amongst their approximately twenty books, of which only three survived, the most famous is Kitab al-Hiyal al Naficah (Book of Ingenious Devices), which draw on knowledge of the works of Hero and Philo but also on Persian, Chinese, and Indian sources but which goes well beyond anything achieved by their Greek predecessors.  

It contains designs for almost a hundred trick vessels and automata the effects of which, “were produces by a sophisticated, if empirical, use of the principles of hydrostatics, aerostatics, and mechanics. The components used included tanks, pipes, floats siphons, lever arms balanced on axles, taps with multiple borings, cone-valves , rack-and-pinion gears, and screw-and-pinion gears.”^[1]

A thirsty bull gets to drink. Courtesy of Library of Topkapi Palace Museum, Istanbul, manuscript A.3474, model 6.

How a thirsty bull gets to drink. From D. Hill, The Book of Ingenious Devices, model 6.

(Right) Lamp with a perpetual wick. Courtesy of Staatsbibliothek zu Berlin, Preußischer Kulturbesitz, arabischen Handschriften, manuscript 5562, model 96. (Left) Inner workings of a lamp with a perpetual wick. From D. Hill, The Book of Ingenious Devices, model 96.

In the ninth century the ‘Abbāsid caliph al-Mustaʿīn (c. 836 – 17 October 866) commissioned the philosopher, physician, mathematician, and astronomer Qusta ibn Luqa al-Ba’albakki (820–912) to translate Hero’s Mechanica, a text in which Hero explored the parallelograms of velocities, determined certain simple centres of gravity, analysed the intricate mechanical powers by which small forces are used to move large weights, discussed the problems of the two mean proportions, and estimated the forces of motion on an inclined plane, which has only survived in the Arabic translation. 

Ibn Khalaf al-Murādī

In al-Andalus in the eleventh century, the engineer Ibn Khalaf al-Murādī about whom we know almost nothing authored Kitāb al-asrār fī natā’ij al-afkār (The Book of Secrets in the Results of Ideas), which describes 31 models consisting of 15 clocks, 5 large mechanical toys (automata), 4 war machines, 2 machines for raising water from wells and one portable universal sundial.

When I looked at the science of engineering and saw that it had disappeared after its ancient heritage, that its masters have perished, and that their memories are now forgotten, I worked my wits and thoughts in secrecy about philosophical shapes and figures, which could move the mind, with effort, from nothingness to being and from idleness to motion. And I arranged these shapes one by one in drawings and explained them.

Al-Muradi, The Book of Secrets in the Results of Ideas

Page from The Book of Secrets in the Results of Ideas

Page from The Book of Secrets in the Results of Ideas

Page from The Book of Secrets in the Results of Ideas

The most spectacular of all the Islamicate text on machines and mechanics is the Kitab fi ma’rifat al-hiyal al-handasiya, (The Book of Knowledge of Ingenious Mechanical Devices) commissioned in Amid (modern day Diyarbakir in Turkey) in 1206 by the Artuqid ruler Nāṣir al-Dīn Maḥmūd (ruled 1201–1222) and created by the artisan, engineer artist and mathematician Badīʿ az-Zaman Abu l-ʿIzz ibn Ismāʿīl ibn ar-Razāz al-Jazarī (1136–after 1206).

All that we know about al-Jazarī comes from his book. He was born in 1136 in Upper Mesopotamia the son of the chief engineer at the Artuklu Palace, the residence of the Mardin branch of the Artuqids the vassal rulers of Upper Mesopotamia, a position he inherited from his father. Al-Jazarī was an artisan rather than a scholar, an engineer rather than an inventor. 

The book, which al-Jazarī wrote at the command of Nāsir al-Dīn, is divided into fifty chapters, grouped into six categories; I, water clocks and candle clocks (ten chapters); II, vessels and figures suitable for drinking sessions (ten chapters); III, pitchers and basins for phlebotomy and ritual washing (ten chapters); IV, fountains that change their shape and machines for the perpetual flute (ten chapters); V, machines for raising water (five chapters); and VI, miscellaneous (five chapters): a large ornamental door cast in brass and copper, a protractor, combination locks, a lock with bolts, and a small water clock. Donald R. Hill, DSB

A Candle Clock from a copy of al-Jazaris treatise on automata

Al-Jazari’s “peacock fountain” was a sophisticated hand washing device featuring humanoid automata which offer soap and towels.

His work was clearly derivative and he cites the  Banū Mūsā, the mathematician, astronomer, and astrolabe maker Abū Ḥāmid Aḥmad ibn Muḥammad al‐Ṣāghānī al‐Asṭurlābī (died, 990), Hibatullah ibn al-Husayn (d. 1139), and a Pseudo-Archimedes as sources. Many of his devices are improved models of ones described by Hero of Alexandria and Philo of Byzantium. He probably also drew on Indian and Chinese sources. 

The book is clearly written in straightforward Arabic; and the text is accompanied by 173 drawings, ranging from rudimentary sketches to full page paintings. On these drawings the individual parts are in many cases marked with the letters of the Arabic alphabet, to which al-Jazarī refers in his descriptions. The drawings are usually in partial perspective; but despite considerable artistic merit, they seem rather crude to modern eyes. They are, however, effective aids to understanding the text. Donald R. Hill, DSB

Diagram of a hydropowered perpetual flute from The Book of Knowledge of Ingenious Mechanical Devices by Al-Jazari in 1206.

The elephant clock was one of the most famous inventions of al-Jazari

The book was obviously fairly widespread in Islamicate culture judging by the number of surviving manuscripts but unlike the work of the Banū Mūsā it was first translated from the Arabic into a European language in modern times. 

Our last Islamic engineer is the Ottoman Turk polymath Taqi ad-Din Muhammad ibn Ma’ruf ash-Shami al-Asadi (1526–1585), who as we saw in the last episode designed, built, and managed the observatory in Istanbul for Sultan Murad III (1546–1595). Taqī al-Dīn is famous for his mechanical clocks about which he wrote two books. 

1. The Brightest Stars for the Construction of Mechanical Clocks (al–Kawākib al–durriyya fī waḍ ^ҁ al–bankāmāt al–dawriyya) was written by Taqī al-Dīn in 1559 and addressed mechanical-automatic clocks. This work is considered the first written work on mechanical-automatic clocks in the Islamic and Ottoman world. Taqī al-Dīn mentions that he benefited from using Samiz ‘Alī Pasha’s private library and his collection of European mechanical clocks.
2. al–Ṭuruq al–saniyya fī al–ālāt al–rūḥāniyya is a second book on mechanics by Taqī al-Dīn that emphasizes the geometrical-mechanical structure of clocks, which was a topic previously observed and studied by the Banū Mūsā and al-Jazarī.

Mechanical clock of Taqī al-Dīn. Image taken from Sifat ālāt rasadiya bi-naw’in ākhar.

He also wrote The Sublime Methods in Spiritual Devices (al-Turuq al-saniyya fi’1-alat al-ruhaniyya) a treatise in six chapters 1) clepsydras, 2) devices for lifting weights, 3) devices for raising water, 4) fountains and continually playing flutes and kettle-drums, 5) irrigation devices, 6) self-moving spit. 

Sixteenth-century Ottoman scientist and engineer Taqi al-Din harnessed surging river water in his designs for an advanced six-cylinder pump, publishing his ideas in a book called ‘The Sublime Methods of Spiritual Machine’. 
The pistons of the pump were similar to drop hammers, and they could have been used to either create wood pulp for paper or to beat long strips of metal in a single pass.

The self-moving spit in part six uses an early steam turbine as motive power:

“Part Six: Making a spit which carries meat over fire so that it will rotate by itself without the power of an animal. This was made by people in several ways, and one of these is to have at the end of the spit a wheel with vanes, and opposite the wheel place a hollow pitcher made of copper with a closed head and full of water. Let the nozzle of the pitcher be opposite the vanes of the wheel. Kindle fire under the pitcher and steam will issue from its nozzle in a restricted form and it will turn the vane wheel. When the pitcher becomes empty of water bring close to it cold water in a basin and let the nozzle of the pitcher dip into the cold water. The heat will cause all the water in the basin to be attracted into the pitcher and the [the steam] will start rotating the vane wheel again.” 

Naturally by Taqī al-Dīn’s time the Renaissance was in full swing in Europe and European artist-engineers were already writing their own books on machines and mechanics. 

As can be seen Islamic engineers knew of and built on the work of their Greek predecessors and the work of the Banū Mūsā and Ibn Khalaf al-Murādī became known in Europe exercising an influence on the European developments in machines and mechanics. There was also an information flow in the 16^th century between the observatory in Istanbul and Europe.

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^[1] E. R. Truitt, Medieval Robots: Mechanisms, Magic, Nature, and Art, University of Pennsylvania Press, 2015 p. 20 quoting Donald Hill, “Medieval Arabic Mechanical Technology,” in Proceedings of the First International Symposium for the History of Arabic Science, Aleppo, April 5–12 1976, Aleppo: Institute forb the History of Arabic Science, 1979.

Politicians (not) taking advice from experts in 19th-century Britain.

Roland Jackson is a historian of nineteenth-century science in Great Britain, who is the author of a highly praised biography of John Tyndall, The Ascent of John Tyndall: Victorian Scientist, Mountaineer, and Public Intellectual (OUP, 2018), which given the nature of some of Tyndall’s research work established Jackson as an expert on the early history of the very actual climate debate. He has, also, in this capacity published some very sensible work on the, somewhat heated, “did Tyndall steal from Eunice Newton Foote” discussion. Tyndall also features in Jackson’s newest book, albeit as just one of a cast of a multitude of expert voices, Scientific Advice to the Nineteenth-Century British State (University of Pittsburgh Press, 2023)^[1].

Jackson’s book is a vast repository of information, detailing the interactions between experts­–scientists, engineers, medical advisers­–and politicians over an extraordinary wide range of topic, seemingly from every aspect of human activity, in Great Britain throughout the nineteenth century, cooked down to a bare minimum to fit it into its slightly more than three-hundred pages. If expanded to its fullest extent, the information packed into those pages would, with certainty, fill a multi-volume encyclopaedia. However, despite its compactness, Jackson’s tome is not dry and indigestible, but well written, highly readable, informative, lucid, at times almost lyrical and it left this reader, at least, with a strong desire to discover more in greater depth about, what seems like, a thousand different topics. 

In the nineteenth century expert advisors interacted with and were consulted on a myriad of different topic by politicians, including health and safety in mines, factories, and explosive stores, public heath, the building of railways and the prevention of rail accidents, the prevention of marine disasters, the design of weapons, taxation, and much more. To handle all of these diverse topics in one continuous, chronological narrative would, I think, produce a highly complex and probably unreadable text, but Jackson approaches the task with a different strategy. 

His book is divided into seven section, six of which, excluding the first, deals with an area of public political policy and in which Jackson then deals with separate and interrelated topics chronological, showing how the handling of them by politicians and their expert advisors developed throughout the century, the main divisions are–(II) Empire and War, (III) Food, (IV) Infrastructure and Transport, (V) Industry, (VI) Social Condition and Public Health, (VII) Revenue and Standards.

As already pointed out his opening section (I) is different and deals with the Rise of Science. The books opening sentences state: 

Any starting point for a history of scientific advice to the British state will be arbitrary. The founding in 1660 of the Royal Society of London for the Improvement of Natural Knowledge, generally known as the Royal Society, is as good a place as any to begin. That is because this organization, surviving today as Britain’s elite scientific institution, had strong links to the state from the outset. 

This is followed by a brief sketch of the evolution of science in general and the Royal Society in particular during the eighteenth century leading up to the major sea change that the Royal Society underwent in the early part of the nineteenth century and the emergence of new scientific bodies such as the British Association, the Geological Society, the Astronomical society, the Institute of Civil Engineers, and others. The medical profession had professional societies with much older roots. Jackson goes deeper into both the Royal Society and the British Association. 

Having established the sources of many of the expert advisors, in particular the Royal Society, Jackson now takes us, topic for topic, through those areas where politicians called upon those advisors to dispense their wisdom to the political decision making machine, the British Parliament in Westminster. On each topic the reader gets introduced to a seemingly endless flood of committees and Royal commissions that were formed and in which selected advisors were called upon to add their opinions to the weight of the decision making process. 

What is made very obvious, particular in the first half of the century in how little influence those selected advisors had on any given issue in comparison to other political factors and how often inquiries petered out without any substantial legislation making it onto the books. It becomes very clear the parliamentarians, who themselves come almost exclusively to the upper echelons, practiced what would now be labelled a libertarian attitude to reform, propagating the view that problems such as health and safety or pollution would be regulated by the owners of the factories, railways, or whatever because it was in their own interest and didn’t need the interference of the state in their private affairs. This attitude being oft contrary to the advice given by the experts. Whilst reading, the term that kept popping up in my head was laissez faire but as Jackson did not use the term in his main text, I began to wonder if I was misinterpreting his narrative. However, in his excellent twenty-seven page Conclusion, of which more later, he uses laissez faire to describe exactly those attitudes where it had occurred to me.

It is interesting to follow how as the century advanced this laissez faire approach was gradually eroded, as it became more and more obvious that the various areas were anything but self-controlling and/or self-improving and that legislation based on the advice proffered by the experts in those committees and commissions was actually necessary. Sometimes, this recognition and the necessary implementation took a look time to finally come to fruition. Jackson drops the example of air pollution, a constant theme throughout the nineteenth century was only finally, really tackled with the Clean Air Act of 1956! Decimalisation of the British currency was discussed and recommended by the experts for much of the century, but was rejected by the politicians on the grounds that it would not be understood and thus rejected by the great unwashed, probably leading to public disturbances, it was finally introduced on 15 February 1971! Metrication was on the table from early on in the century when the need for a unified national system of weights and measures was under discussion but was initially rejected in favour of the Imperial System as being too French and too revolutionary. It continued to be discussed and recommended by the experts throughout the century but despite the 1897 Weights and Measures Act, which finally legalised the use of metric units for trade, it was first 1965 before Britain began metrication, although as Jackson points out they still have miles and the pint!

Some random thoughts on the political side from the vast convolute that Jackson presents. The major influence on policies by members of both the House of Commons and the House of Lords was due to personal vested interests; these launching, disrupting, blocking, or even killing of policy initiatives on a regular basis. The number of times that proposed legislations was stymied by a change of government. The constant back and forth between the government and local authorities over responsibility for areas such as sewage disposal and public health before late in the century central bodies with responsibility for the area were finally established. The highly active role of the Privy Council in the nineteenth century, then still a powerful political force, unlike today. 

On the other side, within a long list of expert advisors who served on committees, gave evidence to Royal commissions, gave advice on specific problems, and were consulted on a bewildering range of topics, a small number of names, some of them well known from the history of science keep cropping up again and again asked to apply their expertise to the latest problem under discussion. One gets the feeling that figures such as Michael Faraday, George Airy, John Tyndall and Lyon Playfair must have spent their entire time rushing from one advisory meeting to another, in between doing extensive scientific research into some relevant political question or another. One aspect that I personally found fascinating was the battles between medical experts who supported the different theories of the hypothesised general causes of ill health, this being a period when the real answers were not yet know, a strong reminder how recent the discovery of the real scientific causes of disease is. 

The aspect of the book that most impressed me whilst reading is how Jackson manages to juggle the streams of information that he delivers to his readers without sending their brains into overload, truly a master class in succinct formulation and delivery. I mentioned earlier that the information that he delivers is very compact and if expanded to its fullest extent, the information packed into those pages would, with certainty, fill a multi-volume encyclopaedia. Jackson did, in his original manuscript unpack and expand some examples of how the problems were approached and handled in a series of case studies. The publishers decided the book was too long and the case studies were sacrificed in the service of comparative brevity. However, these have been published separately under the title Case Studies in Scientific Advice to the Nineteenth-Century British State: A companion to Scientific Advice to the Nineteenth-Century British State (University of Pittsburgh Press, 2023), two-hundred pages of absolutely fascinating reading available in hardback and paperback at very reasonable prices (the main book is not cheap) and almost given away as a Kindle.  

The book closes with a twenty-eight page Conclusion: Constraints on Influence, which summarises the entire contents of the book brilliantly and in its entirety would make for a much better review than my feeble efforts. 

There are sadly no illustrations, but there are very extensive endnotes that largely refer to the impressive bibliography but also contain occasional supplementary information to specific points. As already stated the bibliography is very long and very impressive, in particular the very, very long list of Parliamentary Papers that Jackson consulted during his research. There is also a very comprehensive index.

This book is, in my opinion, destined to become a classic and an obligatory read for scholars of virtually all aspects of nineteenth-century British science, engineering, and medicine, as well as scholars of nineteenth-century British politics. It is a serious academic tome and not really designed for the casual reader, although the case studies could definitely appeal to a wider audience. However, I suspect that those scholars who do take up Jackson’s excellent tome will, like myself, find themselves going, now that is fascinating or really!, I must find out more about it. 

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^[1] Roland Jackson, Scientific Advice to the Nineteenth-Century British State, University of Pittsburgh Press, Pittsburgh Pa., 2023

From τὰ φυσικά (ta physika) to physics – XVI

As astrology was one of the very first scientific disciplines to be adopted by the ‘Abbāsid in their assimilation of Persian cultural it followed automatically that that they also adopted astronomy; you need astronomy in order to do astrology. Also, the practice of Islam itself required both the determination of the times for the five daily prayers as well as the qibla the geographical direction of the Kaaba in the Sacred Mosque in Mecca both astronomical problems. 

Pre-Islamic Arabic society already possessed a fairly simple astronomy based on observation but not an advanced mathematical astronomy as had been developed by the Babylonians, Greeks, and Indians. Their first appropriations were from Persian and Indian astronomy. Indian astronomy had been strongly influenced by Greek astronomy since the time of Alexander the Great. 

Ptolemaeus’ Mathēmatikē Syntaxis contained many astronomical tables along with the vast amount of theoretical geometrical information on how to determine that data from the orbits of the celestial bodies. Astrologers and other practical users of astronomy wanted the data without the theoretical content, so Ptolemaeus also published his Handy Tables containing the tables and instructions on how to use them. These proved to be very popular and the first astronomical texts produced in the Islamic Empire were translations of similar astronomical tables from India, the most notable being Zīj as-Sindhind (Great astronomical tables of the Sindhind) translated from Sanskrit by Muhammad ibn Ibrāhīm al-Fazārī (died 796 or 806) and Yaʿqūb ibn Ṭāriq (died 796). The historian of science Ṣāʿid al-Andalusī (1029–1170) claimed that Ibn Sa’d (784/5–845) and Muhammad ibn Musa al-Khwārizmī (c. 780–c. 850) were also involved in the translation but in fact al-Khwārizmī’s Zīj as-Sindhind, whilst very similar is different. Also translated during the same period Zij al-Shah a Persian set of astronomical tables also based on Indian data. 

Zīj (plural Azyāj, modern English plural zījes) is derived from a Middle Persian word, zih or zīg “cord”. The term is believed to refer to the arrangement of threads in weaving, which was transferred to the arrangement of rows and columns in tabulated data. These early translations set a standard for astronomical texts, zīj, astronomical books that tabulates parameters used for astronomical calculations of the position of the sun, moon, stars, and planets being produced by many leading Islamic astronomers and being the first Islamic astronomical texts that were translated into Latin during the twelfth century Scientific Renaissance. Such tables were of course of practical use for astrologers, but also combined with instruments for determining prayer times and the qibla. 

Sanjufini Zij by Samarkandi astronomer Khwaja Ghazi al-Sanjufini. Compiled in 1363.

From these simple beginning medieval Islamic astronomy expanded into a massive field of study over several centuries and I can only offer a sketch here, highlighting some of the major participants and developments. Its influence can be measured on the number of Arabic star names that are still in use today. 

Islamic astronomy was based on Ptolemaic astronomy and there are reports of at least five translations of his Mathēmatikē Syntaxis during the ‘Abbāsid  Caliphate of which only two survive, the earliest (829-830) is that of Al-Ḥajjāj ibn Yūsuf ibn Maṭar (786–833) done during the reign of al-Ma’mun (786–833), who reigned from 813. The second surviving translation was by Hunayn ibn Ishaq al-Ibadi (808–873), a Nestorian Christian, who was a very prolific translator. His translation was corrected by Thābit ibn Qurra (826 or 836­–901), a Sabian of Harran, who was also a prolific translator. The Arabic influence can also be seen in the fact that Ptolemaeus master work is today mostly known was the Almagest, a version of its Arabic title al-majisṭī, with al meaning the  and magesti being a corruption of Greek μεγίστη megístē ‘greatest, translated into Almagestum in Latin in the twelfth century. The Greek title Mathēmatikē Syntaxis later became Hē Megalē Syntaxis (Ἡ Μεγάλη Σύνταξις, “The Great Treatise”; Latin: Magna Syntaxis) not because it was considered the “greatest” work on astronomy, as is often falsely claimed but because Ptolemaeus produced two collected works on astronomy a small one and a big one, the Mathēmatikē Syntaxis being the big one, hence Hē Megalē Syntaxis. 

Pages from the Almagest in Arabic translation showing astronomical tables Bodleian Library via Wikimedia Commons

Although the Almagest provided the back bone of medieval Islamic astronomy the Islamic astronomers did not in any way venerate it but as we will see challenged, criticised, and corrected it, some even rejected it. 

Habash al-Hasib al-Marwazi (766 – d. after 869) is typical of the early medieval Islamic astronomers, a Persian astronomer, mathematician, and geographer who worked under the caliphs al-Maʾmūn (786–833) and al-Muʿtaṣim biʾllāh (796–842) making observations at the al-Shammisisyyah observatory in Baghdad. His zījes are in the Indian style and show no Ptolemaic influence.

The Banū Mūsā, or sons of Mūsā, were the three sons– Abū Jaʿfar, Muḥammad ibn Mūsā ibn Shākir (before 803 – February 873), Abū al‐Qāsim, Aḥmad ibn Mūsā ibn Shākir (d. 9th century), Al-Ḥasan ibn Mūsā ibn Shākir (d. 9th century)–of the Persian, astronomer, astrologer Mūsā ibn Shākir employed by the caliph al-Maʾmūn, who following their father’s death educated the three and provided them with employment in Baghdad. They are best known as prolific translators of Greek works from Byzantium although they also produced around twenty original works on astronomy, astrology, mathematics, and technology of which only three have survived. Their work on astronomy was Ptolemaic and concentrated on theoretical aspects rather than being based on their own observations. Of greatest interest they challenged the real feasibility of the Aristotelian–Ptolemaic cosmological model arguing that friction between the crystalline sphere would hinder the orbits. They treated the cosmological model presented by Ptolemaeus as real and not just as a theoretical mathematical model designed to save the phenomena.

Cover of the Kitāb al-Daraj (Book of Degrees) astronomical/astrological book by the Bana Musa (Princeton University Library)

Born in Basra, Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham (c. 965–c. 1040)–known in Latin as Alhazen–is best known for his work in optics but he also wrote on astronomy following the line started by the Banū Mūsā. In his  Epitome of Astronomy, he argued against a philosophical and for a physical astronomy. In his Al-Shukuk ala Batlamyus (“Doubts on Ptolemy”), whilst accepting a Ptolemaic geocentric cosmos he strongly criticised various element of Ptolemaeus’ astronomy.

One of the most influential ‘Abbāsid astronomers was Abū al-ʿAbbās Aḥmad ibn Muḥammad ibn Kathīr al-Farghānī (c.800–870)–known in Latin as Alfraganus–who  wrote an astronomical textbook Kitāb fī Jawāmiʿ ʿIlm al-Nujūm (A Compendium of the Science of the Stars) sometime between 833 and 857. This is a descriptive summary of the Almagest, which is however corrected using the findings and calculations of earlier Islamic astronomers. An easy to understand, highly accessible presentation of Ptolemaic astronomy it was widely in read in both the Islamic Middle Ages and also in Latin translation in Europe.

Portrait of Alfraganus in the Compilatio astronomica, 1493 Source: Wikimedia Commons

As already noted in the previous episode of this series the Neoplatonist Abu Nasr Muhammad al-Farabi (c.870–950) played a major role in making the works of both Plato and Aristotle known in medieval Islamicate culture. He viewed astronomy as descriptive and in his comprehensive Arabic classification of the sciences in his Kitab al-ibsa al ‘Ulum (Catalogue of Sciences), he separated mathematical astronomy from science thus adhering to a Platonic saving of the phenomena rather that a realistic, physical astronomy as propagated by the Banū Mūsā and al-Haytham.

Iranian stamp with al-Farabi’s imagined face Source: Wikimedia Commons

Abū ʿAbd Allāh Muḥammad ibn Jābir ibn Sinān al-Raqqī al-Ḥarrānī aṣ-Ṣābiʾ al-Battānī (before 858 – 929)–known in Latin as Albategnius–was  born in Harran in Bilād al-Shām (Islamic Syria) the son of Jabir ibn Sinan al-Harrani, an astronomical instrument maker. There is circumstantial evidence that father was a Sabian but al-Battānī was a Muslim.  He established  his own observatory in Raqqa, now in Syria. He used large astronomical instruments which enabled him to make very accurate observations and he became one of the most important medieval, Islamic observational astronomers.  He was a convinced Ptolemaic astronomer and his Kitāb az-Zīj aṣ-Ṣābi’, written around 900, a very major set of astronomical tables shows almost no Hindu or Sassanian influence. The book was highly influential in Latin transition as De motu stellarum (On stellar Motion) in medieval and Renaissance Europe, even being printed in Nürnberg from a manuscript owned by Regiomontanus in 1537, with a second printed edition appearing in Bologna in 1645. 

A folio from a Latin translation of Kitāb az-Zīj aṣ-Ṣābi’ (c. 900), Latin 7266, Bibliothèque nationale de France Via Wikimedia Commons

One of the most well known books of medieval, Islamic astronomy is the Kitāb suwar al-kawākib (The Book of the Fixed Stars) by Abd-al-Raḥmān ibn ʿOmar Ṣūfī, Abu’l-Ḥosayn,  (903– 986), written in 964. Abd al-Rahman al-Sufi was a Persian astronomer living and working in the court of the emir of the Buyid dynasty ʿAḍud al-Dawla (936–983) in Isfahan south of Tehran. He was an avid translator into Arabic of Hellenistic astronomy that had been centred on Alexandria. The Kitāb suwar al-kawākib compares Greek constellations and stars as described by Ptolemaeus in the Almagest with Arabic ones linking those that are the same. The book contains two pictures of each of the forty eight Ptolemaic constellation one as seen from the Earth and the other, the so-called god’s eye view, as seen from outside the celestial globe. The  book contains the first depiction of the Andromeda nebula as a small cloud in front of the mouth of the constellation Fish. 

Kitab suwar al-kawakib al-thabita (Book of The Images of The Fixed Stars) of al-Sufi 

The constellation Andromeda and the Andromeda nebula (M 31) as depicted in Ismael Boulliauʼs Ad astronomos monita duo (Paris, 1667)

Abu al-Hasan ‘Ali ibn ‘Abd al-Rahman ibn Ahmad ibn Yunus al-Sadafi al-Misri  (c. 950–1009) usually known simply as Ibn Yunus was an Egyptian Arabic astronomer renowned for the quality and accuracy of his observations. He worked from his observatory near Fustat, now part of Cairo, that was built for him by the then new Fatimid dynasty. Once again his most famous astronomical work was a zīj his al-Zij al-Kabir al-Hakimi written by order of Fatimid Caliph Al-Aziz in the year 380 AH/990 and completed in 1007. The historian of astronomy, Noel. Swerdlow (1941–2021) described it as  “a work of outstanding originality of which just over half survives.” 

Ibn Yunus’ records of the solar eclipses of 993 and 1004 as well as the lunar eclipses of 1001 and 1002. Source: Wikimedia Commons

The major Islamic polymath Abu Rayhan Muhammad ibn Ahmad al-Biruni (973–after 1050), a Khwarazmian scholar, who wrote on everything also wrote about astronomy. Famous for his description of India and its culture, his Taḥqīq mā li-l-Hind is an extensive commentary on Indian astronomy consisting mostly of translation of the work of Aryabhatta (476–550). He discussed Aryabhatta’s acceptance of a geocentric system with diurnal rotation of the Earth, a theory originally proposed by Heraclides Ponticus (c. 390–c. 310 BCE), in his Miftah-ilm-alhai’a (“Key to Astronomy“), which is no longer extant, but in the end rejected it Al-Biruni rejected the theory. In a heated debate with Ibn Sina, al-Biruni rejected the physics of Aristotle. 

Abu Sa’id Ahmed ibn Mohammed ibn Abd al-Jalil al-Sijzi (c. 945 – c. 1020) a Persian mathematician, astrologer, and astronomer, who corresponded with al-Biruni, defended the theory of diurnal rotation in his al-Qānūn al-Masʿūdī.

A page from Al Sijzi’s geometrical treatise. Source: Wikimedia Commons

Abū Ḥāmid Muḥammad ibn Muḥammad aṭ-Ṭūsiyy al-Ġazzālīy (c. 1058–1111), known as  al-Ghazālī, famously launched a philosophical attack on the work of Ibn Sina and al-Farabi Tahāfut al-Falāsifa (The Incoherence of the Philosophers) in which he rejected the Greek astronomy of Ptolemaeus arguing that the motion of the celestial bodies was the direct result of God’s will. However, rather than leading to a decline in astronomy as is often claimed, the presence of science and philosophy in religious texts  increased after Ghazālī’s attacks.

Name of Imam al-Ghazali with title “Hujjat ul-Islam” Source: Wikimedia Commons

Most of the astronomers discussed up till now used comparatively small local observatories to carry out their astronomical work but there were a series of major observatories built during the Islamic period beginning with the observatory built in Maragheh, in the East Azerbaijan Province of Iran, by the Mongol ruler Hulegu Kahn (c. 1217–1265) notorious for having sacked the ‘Abbāsid capital Baghdad in 1258.

Depiction of Hulegu’s army besieging the city, in 1258 Source: Wikimedia Commons

Central Tower of the Maragheh Observatory Source: Wikimedia Commons

The director of the Maragheh observatory was the Persian polymath Muhammad ibn Muhammad ibn al-Hasan al-Tusi (1201 – 1274). As others before him  al-Tusi produced a zīj based on his new very accurate observation, Zīj-i Īlkhānī (Ilkhanic Tables).

al-Tusi Zīj-i Īlkhānī

Painting of Al-Tusi and colleagues working on the Zij-i Ilkhani at the observatory Source: Wikimedia Commons

He heavily criticised Ptolemaeus’ planetary models and in particular his use of the equant point, a bone of contention for many astronomers over the centuries, and developed new models utilising his own invention the geometrical construction, now known as the Tusi-couple. 

Tusi couple from Vat. Arabic ms 319 via Wikimedia Commons

Other notable astronomers working at the Maragheh observatory including the Arabic astronomer Al-Urdi (full name: Moayad Al-Din Al-Urdi Al-Amiri Al-Dimashqi) (died 1266) born in Syria, who had previously worked in Damascus. His most notable works were Risālat al-Raṣd, a treatise on observational instruments, and Kitāb al-Hayʾa a work on theoretical astronomy. 

Manuscrit Arabe BNF 2544 al-Urdi f78 Source: Wikimedia Commons

Also, the Persian astronomer Qotb al-Din Mahmoud b. Zia al-Din Mas’ud b. Mosleh Shirazi (1236–1311), who was born into a Sufi family in Karezun. After a short stay in Maragheh he moved on to Qazvin, Isfahan, Baghdad, and Konya in Anatolia. He wrote several astronomical texts most notably Nehāyat al-edrāk fi dirayat al-aflak (The Limit of Accomplishment concerning Knowledge of the Heavens)  1281, and Al-Tuhfat al-Shahiya (The Royal Present)  1284. Both presented his models for planetary motion, improving on Ptolemaic principles. In his The Limit of Accomplishment concerning Knowledge of the Heavens, he also discussed the possibility of heliocentricity.

Epicyclic planetary model in a medieval manuscript by Qutb al-Din al-Shirazi. Source: Wikimedia Commons

Shams al-Din Muhammad b. Ahmad al-Khafri al-Kashi (died 1550),known as al-Din Khafri a Persian theologian and astronomer wrote al-Takmila fi sharh al-tadhkira (The complement to the explanation of the memento) This commentary by al-Khafri is a technical commentary on a work written by al-Sharif al-Jurjani on the astronomical critique by Nasir al-Din al-Tusi’s of Ptolemaic astronomy, al-Tadhkira fi ‘ilm al-Hay’a (Memento in astronomy). 

Al-Sharif al-Jurjani, a revision of Nasir al-Din Tusi’s Tazkirah, a treatise on astronomy with extensive annotations and corrections by Shams al-Din Khafri. Created in Iran, probably Shiraz, the manuscript was created in the early 15th century; Khafri’s commentaries were added to it in the 16th century Source: Wikimedia Commons

Also influenced by the Maragheh astronomers was the Arabic astronomer Abu al-Ḥasan Alāʾ al‐Dīn bin Alī bin Ibrāhīm bin Muhammad bin al-Matam al-Ansari (1304–1375) known as Ibn al-Shatir, who was born in Damascus and studied astronomy in Cairo and Alexandria. He returned to Damascus where he was appointed time keeper of the Umayyad Mosque. Ibn al-Shatir presented a radical reform of the Ptolemaic planetary models in his kitab nihayat al-sul fi tashih al-usul (The Final Quest Concerning the Rectification of Principles) in which he incorporated the so-called Urdi lemma, which allowed  an equant in an astronomic model to be replaced with an equivalent epicycle (the Tusi-couple) that moved around a deferent centred at half the distance to the equant point. Like Ibn a-Haytham, Ibn al-Shatir rejected philosophical astronomy and Aristotelian cosmology. Promoting instead an astronomy of models based on empirical observations. Perhaps his most notable achievement was his new, highly accurate, double epicycle lunar model, the first lunar model which matched physical observations.

Ibn al-Shatir’s lunar model Source: Wikimedia Commons

The Timurid sultan Mīrzā Muhammad Tāraghay bin Shāhrukh (1394–1449), better known as Ulugh Beg, a moniker meaning Great  Ruler, was not just a patron of astronomy like other rulers but was himself a passionate mathematician and astronomer and a notable linguist.

Ulugh Beg, Timurid painting 1425-50 Source: Wikimedia Commons

During his reign, he turned his capital Samarkand into an international centre for learning. Inspired by a visit to the Maragheh observatory in his youth he constructed an enormous observatory in Samarkand in 1428 and brought some of the leading Islamic astronomers of the fifteenth century to work with him there. 

Ulugh Beg Observatory Source: Wikimedia Commons

Ophiuchus – miniature from the manuscript of The Book of Fixed Stars commissioned by Ulugh Beg. Probably Samarkand, c. 1430-1440. Bibliothèque nationale de France vis Wikimedia Commons

The Timurid astronomer Ala al-Dīn Ali ibn Muhammed (1403–1474), known as Ali Qushji, was born in Samarkand the son of one of Ulugh Beg’s falconers.

Portrait of Ali Qushji Source: Wikimedia Commons

After studying in Samarkand, he moved to Kerman in Persia the on to Herat before returning to Samarkand where he presented his work on the Moon to Ulugh Beg, who appointed him to the observatory, where he worked until Ulugh Beg was assassinated. Following Ulugh Beg’s death he again travelled around to Herat, Tashkent, Tabriz and finally Constantinople where he worked under the Ottoman Sultan Mehmed II.

Portrait of Mehmet II by Gentile Bellini, dated 1480 Source: Wikimedia Commons

He wrote nine works on astronomy, two in Persian and seven in Arabic but his most important work was his Concerning the Supposed Dependence of Astronomy upon Philosophy in which he totally rejected Aristotelian physics and natural philosophy from astronomy, developing a purely empirical and mathematical astronomy. He was another Islamic astronomer after al-Biruni and al-Sijzi, who investigated the possibility of diurnal rotation. 

A page from Ali al-Qushji’s al-Risala al-Fathiyya Source: Wikimedia Commons

The Persian astronomer Ghiyāth al-Dīn Jamshīd Masʿūd al-Kāshī  (c. 1380–1429) was born in Kashan in Iran part of the Timurid Empire and he like many others was drawn to Samarkand and Ulugh Beg and his observatory. Al-Kāshī produced the Khaqani Zīj which was an updated improved version of al-Tusi’s Zīj-i Īlkhānī. He also wrote Sullam al-sama’ (The Ladder of the Sky) an astronomical treatise on the determination of the size and distance of celestial bodies and a treatise on astronomical observational instruments.

JAMSHID BIN MAS’UD BIN MAHMUD KNOWN AS GHIYATH (D. 1429 AD): AL-RISALA AL-KAMALIYA SAFAVID IRAN, DATED SATURDAY 25 RAJAB AH 1029/26 JUNE 1520 AD Also known as Sullam al-sama (The Stairway of Heaven) Source: Wikimedia Commons

The Maragheh observatory also served as inspiration and model for the observatory built by Turkish astronomer Taqi ad-Din Muhammad ibn Ma’ruf ash-Shami al-Asadi (1526–1585) for his patron Sultan Murad III (1546–1595) in Constantinople in 1574.

Work in the observatorium of Taqi ad-Din Source: Wikimedia Commons

and the observatories built by Sawai Jai Singh II (1688–1743) in Delhi, Mathura, Benares, Ujjain and more famously in his capital Jaipur in India.

Jantar Mantar Observatory in Jaipur Source: Wikimedia Commons

Up till now all of the astronomers we have briefly sketched lived and worked in the Islamic East, early under the ‘Abbāsid  Caliphate but then later on under the Fatimid Caliphate and still later under the Timurid Sultanate. Another astronomical scene developed in the Islamic West in al-Andalus, the Iberian Peninsula, under a Umayyad Caliphate and its successors. 

The first astronomer of note was  Abū Bakr Muḥammad ibn Yaḥyà ibn aṣ-Ṣā’igh at-Tūjībī ibn Bājja (c. 1085 – 1138), known in Latin as Avempace.

ibn Bājja (Avempace)

An Arab born in Zaragoza he was an important philosopher but also a polymath, who wrote about astronomy. The Jewish philosopher Maimonides (1138–1204) wrote:

I have heard that Abu Bakr [Ibn Bajja] discovered a system in which no epicycles occur, but eccentric spheres are not excluded by him. I have not heard it from his pupils; and even if it be correct that he discovered such a system, he has not gained much by it, for eccentricity is likewise contrary to the principles laid down by Aristotle…. I have explained to you that these difficulties do not concern the astronomer, for he does not profess to tell us the existing properties of the spheres, but to suggest, whether correctly or not, a theory in which the motion of the stars and planets is uniform and circular, and in agreement with observation.

Abū Bakr Muḥammad bin ʿAbd al-Malik bin Muḥammad bin Ṭufayl al-Qaysiyy al-ʾAndalusiyy (c. 1105 – 1185), Ibn Tufail, known in Latin as Abubacer Aben Tofail, was an Arab born near Granada,  who was a student of Ibn Bājja and is said to have completely rejected the astronomical models of Ptolemaeus, reverting to the homocentric spheres of Aristotle. He held important political posts and was the vizier and physician to Abu Ya`qub Yusuf (1135–1184) the first Almohad Caliph to whom he recommended Abū l-Walīd Muḥammad Ibn ʾAḥmad Ibn Rušd (1126–1198), known in Latin as Averroes, as his successor.  

Ibn Ṭufayl

Ibn Rušd was one of the most important Islamic philosophers and a mainstream Aristotelian, rejecting the Neoplatonism of the  ‘Abbāsid  philosopher, particularly that of Ibn Sina. Because of his work promoting Aristotle he became known as the Commentator in medieval Europe. Rejecting Ptolemaeus, he strongly propagated the Aristotelian homocentric spheres model of astronomy.

Detail of Averroes in a 14th-century painting by Andrea di Bonaiuto Source: Wikimedia Commons

Nur ad-Din al-Bitruji (died 1204), known in Latin as Alpetragius an Arabic astronomer born in al-Andalus was a disciple of Ibn Tufail and a contemporary Ibn Rušd, who also presented a homocentric spheres model of astronomy, a development of the concept of Ibn Bājja and Ibn Tufail. He applies the impetus theory of John Philoponus to planetary motion. His  Kitāb al-Hayʾah (The book of theoretical astronomy/cosmology) presented criticism of Ptolemaeus’ Almagest from a physical point of view.

Al-Bitruji wrote Kitāb al-Hayʾah ( كتاب الهيئة), It was well known in Europe between the 13th and the 16th CE’s, and was regarded as a valid alternative to Ptolemy’s Almagest in scholastic circles.

Abu Jafar Ahmad ibn Yusuf ibn al‐Kammad  (died 1195) was an Arabic astronomer born in Seville, whose works such as al Kawr ala al dawr, al Amad ala al abad, and al Muqtabas, which is a compilation of the two previous zijes were read throughout the Iberian Peninsula, and North Africa.

Abu Muhammad Abd al-Haqq al‐Ghafiqi al‐Ishbili, also known as Ibn al‐Hāʾim (fl. c. 1213) was another Arabic astronomer born in Seville, who wrote al‐Zīj al‐kāmil fī al‐talim (The Perfect Handbook on Mathematical Astronomy) a complete and accurate description of astronomy in al-Andalus. 

It should be clear from the sketches above that medieval Islamicate culture presented a wide ranging and diverse dialogue on astronomy over a period of several centuries much of which as we shall see entered medieval Europe during the twelfth century Scientific Renaissance.