PATHFINDERS

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Pathfinders : The Golden Age of Arabic Science by Jim al-Khalili
335 pages PB 2010 USA 

( published in HB as HOUSE OF WISDOM ) 

Was Adam Smith really the father of modern economics?

The twentieth-century economist and political scientist Joseph Schumpeter has carefully studied the history of economic theory as far back as Aristotle and argues that Ibn Khaldūn is without doubt the true father of economic science. In fact, it is worth comparing him with the man whom many economists might regard as the father of modern economic theory, Adam Smith. For when one considers the sheer number of original ideas and contributions across so many areas of economic thought that Ibn Khaldūn invented we are left in absolutely no doubt that he is more worthy of the title. Ibn Khaldūn discovered a number of key economic notions several hundred years before their ‘official’ births, such as the virtues and necessity of a division of labour (before Smith), the principle of labour value (before David Ricardo), a theory of population (before Thomas Malthus) and the role of the state in the economy (before John Maynard Keynes). He then used these concepts to build a coherent dynamic system of economic theory.

Not only was he the forerunner of European economists, such was his intellect that he is also considered to be the undisputed founder and father of the field of sociology. His best-known work is the Muqaddima , which literally means ‘Introduction’ or ‘Prologue’. But neither word really does it justice, and it is more correctly translated as The Prolegomenon . The book is a treatise on human civilization in which Ibn Khaldūn discusses at length the nature of the state and society. It is essentially the first volume of a larger treatise dedicated to the history of the Arabs and those states and peoples that had played, in Ibn Khaldūn’s view, a historically significant role. The historian Arnold Toynbee said of the Muqaddima that it is ‘undoubtedly the greatest work of its kind that has ever yet been created by any mind in any time or place’.


Where is coffee really from?

I shall mention in passing just one example of a gift from the Arabs that I for one am rather grateful for: coffee – especially as it was originally banned in Europe as a ‘Muslim drink’. Its use can be traced back to ninth- century Ethiopia where, according to legend, an Arab goatherd named Khalid observed that his goats became livelier after eating the berries of the coffee plant. Intrigued, he boiled the berries in water to produce the first cup of coffee. From Ethiopia, the drink spread to Egypt and Yemen, but it was in Arabia that coffee beans were first roasted and brewed as is done today. By the fifteenth century coffee had reached the rest of the Middle East, Persia, Turkey and North Africa.

In 1583, Leonhard Rauwolf, a German physician, gave this description of coffee after returning from a ten-year trip to the Near East:

A beverage as black as ink, useful against numerous illnesses, particularly those of the stomach. Its consumers take it in the morning, quite frankly, in a porcelain cup that is passed around and from which each one drinks a cupful. It is composed of water and the fruit from a bush called bunnu.

From the Muslim world, coffee first spread to Italy via Venice and quickly to the rest of Europe. The first European coffee house opened in Italy in the mid-seventeenth century. The colonial Dutch then began to grow it in Indonesia and, by the early eighteenth century, thanks to the efforts of the British East India Company, coffee finally became popular in England.

The story of coffee finally comes full-circle when, in 2007, an agreement was reached after a high-profile court battle between the government of Ethiopia, the home of coffee, and the coffee giants Starbucks over copyright of trademark names of certain Ethiopian coffee beans.


Where does the mathematical ‘sine’ come from?

Among the most important Arabic texts to be studied early on was al-Khwārizmi’s al-Jebr , which was first translated into Latin in 1145 by Robert of Chester (a few years before Gerard of Cremona’s version). Robert was thus the first person to introduce the word ‘algebra’ into Europe. He also gave us the word ‘sine’, for the trigonometric quantity defined as the ratio of two sides of a right-angled triangle. But the way we arrived at this word from its Hindu origins also deserves mention, not least because most historians have got it slightly wrong.

Etymologically, we must begin with the Sanskrit word jya-ardha, which means ‘half the bowstring’ (or, geometrically, half the chord of a circle – see diagram opposite). The word jya-ardha was abbreviated by Hindu mathematicians to jiva , and this was transliterated in Arabic as jiba (since there is no ‘v’-sounding letter in the Arabic alphabet). This was in turn written with just the two letters j ( jīm ) and b ( bā’ ). It is not clear to me whether this was a deliberate abbreviation or because the two vowels in the word were short sounds, and are therefore not written in Arabic. When Robert of Chester came to translate this word, he misread it as jayb, which in Arabic means ‘pocket’ (and not, as so many scholars have claimed ‘fold’, ‘bosom’, ‘bundle’ or ‘bay’). So he simply used the Latin word for pocket: sinus. Finally, English usage converted this word to ‘sine’. The first published use of the abbreviation ‘sin’, along with ‘cos’, and ‘tan’, was by the sixteenth century French mathematician Albert Girard. Interestingly, in Arabic today the word for sine is in fact pronounced jayb.


Who was the first real scientist?

For Ibn al-Haytham, the supremacy of the scientific method, valuing meticulous and painstaking experimentation and the careful recording of results, became central to his research. It is for this reason that a number of historians have referred to him as the first real scientist. Ibn al-Haytham makes his views clear in the following extract:

We should distinguish the properties of particulars, and gather by induction what pertains to the eye and what is found in the manner of sensation to be uniform, unchanging, manifest and not subject to doubt. After which we should ascend in our enquiry and reasoning, gradually and orderly, criticizing premises and exercising caution in regard to conclusions – our aim in all that we make subject to inspection and review being to employ justice, not to follow prejudice, and to take care in all that we judge and criticize that we seek the truth and not be swayed by opinion.

In unpicking Ibn al-Haytham’s contributions to science we find that his greatness is thus not so much a consequence of any single revolutionary discovery, such as Newton’s inverse square law of gravity or Einstein’s theory of relativity, or even al-Khwārizmi’s algebra. Rather, it is the way he taught us how to ‘do’ science. I would therefore argue that he has a stronger claim to the title of ‘father of the scientific method’ than either Francis Bacon or Descartes. Ultimately what Ibn al-Haytham did was to turn experimentation from a general practice of investigation into the standard means of proof of scientific theories.

We have no evidence to suggest that Ibn al-Haytham was not a devout Muslim, but his rational mind meant that he would accept nothing about the world that could not be verified experimentally. He always trusted and relied upon his observational skills and powers of deduction, for he believed that through logic and induction one can reduce all phenomena in nature to mathematical axioms and laws. In this way, he is every bit a modern physicist.


Is Isaac Newton really the father of optics? Or did he stand on the shoulders of giants of Islamic science?

To most people in the West, and indeed in the Muslim world, Isaac Newton is the undisputed father of modern optics; at least, that is what we are told at school, where our textbooks abound with his famous experiments with lenses and prisms, his study of the nature of light and its reflection, refraction and decomposition into the colours of the rainbow. Even historians of science who acknowledge that work on optics predates Newton often do not go back any earlier than other notables from the European scientific revolution of the seventeenth century such as René Descartes, Willebrord Snell and Johannes Kepler. But studies of the properties of light, particularly catoptrics (reflection of light by mirrors) and dioptrics (refraction of light through lenses) go back all the way to the Greeks.

An interest in optics began in antiquity, with the Babylonians, Egyptians and Assyrians all making use of polished quartz to make rudimentary lenses. The basic principles of geometric optics were laid down by Plato and Euclid and included ideas such as the propagation of light in straight lines and the simple laws of reflection from plane mirrors, while the earliest serious contribution to the field in the Islamic world came from al-Kindi.

Far less well known than these men was a scholar who flourished in Baghdad in the late tenth century, a few years before Ibn al-Haytham, who would advance the subject of optics in a way that has until recently been almost completely ignored. His name was Ibn Sahl and he wrote a treatise around 984 called On the Burning Instruments (by which is meant lenses and mirrors that can be used to focus sunlight to create a hot spot). Although such burning methods had been known in antiquity – there is a story that Archimedes used concave bronze mirrors to focus sunlight on Roman warships and set them on fire – the work of Ibn Sahl is regarded as the first serious mathematical study of lenses for focusing light. The manuscript’s pages were recently discovered in two different locations, one part in Damascus and the other in Tehran. The historian Roshdi Rashed was able to fit the two pieces together and reconstruct the full original text, earning himself worldwide acclaim in the early 1990s. The most incredible insight in this work is something that everyone learns about at school: what we call Snell’s law of refraction.

To appreciate what Ibn Sahl did, we must again return to the Greeks and the writings of Ptolemy, who had described the refraction of light in his Optics. He presented tables of angles of incidence and refraction from different materials, and is credited with proposing an approximate version of the law of refraction by suggesting that the ratio of the angles made by a beam of light on either side of a surface boundary, as it travels between two transparent media, is a constant. We know today that the constancy of this ratio of angles only holds when the rays of light travel between the two media at almost right angles to their surface boundary. This is because what is really constant is not the ratio of the angles themselves but that of their trigonometric sines, and this correct ratio only approximates to that of the angles when they are small: when the rays enter almost vertically. This correct trigonometric ratio was stated by Snell and confirmed independently by Descartes. It is these two men who are therefore usually credited with the law of refraction. However, the now incontrovertible fact is that Ibn Sahl arrived at the same result 650 years earlier. He correctly stated the law geometrically, as the ratio of the sides of triangles of light rays, which is exactly equivalent to the ratio of the sines. Thus, while Europeans have argued over whether it should be referred to as Snell’s law or Descartes’ law, there is no doubt that the real credit should go to Ibn Sahl. And while much of the work on refraction that was used by the Europeans in the seventeenth century came from Ibn al-Haytham’s Optics, it is to Ibn Sahl that equal debt is owed.



Hanging rotten meat in medieval Baghdad to choose hospital sites? Jim Al-Khalili explains

In the Islamic world, al-Rāzi’s name will always be associated with some of the earliest hospitals. In Abbāsid times, these were not known by their current Arabic name of mustashfa, but rather by the Persian word bīmāristān (from Pahlavi vīmār or vemār , meaning ‘sick’ and - stan , the suffix for ‘place’). These institutions were initially modelled on Nestorian Christian establishments, particularly when it came to their administration and reliance on charitable funding. Indeed, one finds that most physicians of ninth- and tenth-century Baghdad were Christian or Jewish.

Charitable endowments within Islamic law, called waqf, began to be set up around this time and some of the funds from these trusts went into building hospitals. These multiplied throughout the empire with large cities such as Cairo and Córdoba also boasting dozens of hospitals.

Soon after the turn of the tenth century, al-Rāzi was called upon by the Caliph al-Muktafi to help in selecting the site of a new hospital. He had pieces of fresh meat hung up in various districts of Baghdad. A few days later, he checked the pieces, and he selected the area where the least rotten one was found, stating that the ‘air’ was cleaner and healthier there. Following the death of the caliph in 907, al-Rāzi returned to his home town of Rayy and took charge of the hospital there.

Later, under the Caliph al-Muqtadir (r. 908–32) several more new hospitals were built in Baghdad. The largest of these, al-Bīmāristān al Muqtadirī, was built by the vizier Ali ibn Īsa in a part of Baghdad known as Sūq Yehya on the east bank of the Tigris. Al-Rāzi, still head of the hospital in Rayy at this time, was recruited again to take over as director of this new establishment.

The renowned Arab traveller Ibn Jubayr describes visiting Baghdad and the then two-hundred-year-old al-Muqtadirī hospital:

This great establishment is a beautiful structure stretching along the banks of the Tigris. Its physicians make their rounds every Monday and Thursday to examine patients and prescribe for their needs. At the physicians’ disposal are attendants who fill drug prescriptions and prepare food. The hospital is split up into various wards, each containing a number of rooms, giving the impression that the place is as a royal palace in which every convenience is provided.

Among the features in medieval Muslim hospitals that distinguished them from their contemporaries elsewhere were their higher standards of medical ethics. Physicians there treated patients of all religions or ethnicities. They were expected to have obligations towards their patients, regardless of their wealth or background. These ethical standards were first laid down in the ninth century by Ishāq bin Ali al-Rahawi, who wrote The Conduct of a Physician (Adab al-Tabīb), the earliest known Arabic treatise dedicated to medical ethics.



Algebra

Suppose that a man, in his illness, emancipates two slaves, the
price of one being three hundred dirhems and that of the other
five hundred dirhems; the one for three hundred dirhems dies,
leaving a daughter; then the master dies, leaving a daughter
likewise; and the slave leaves property to the amount of four
hundred dirhems. With how much must everyone ransom himself?
Al-Khwārizmi

The above quotation comes from al-Kitab al-Mukhtasar fi Hisāb al-Jebr wal- Muqābala. That’s easy for you to say, you might be thinking. The full translation of this title is: The Compendium on Calculation by Restoration and Balancing , and for reasons that will soon become clear, it is admissible to abbreviate this mouthful to just al-Jebr. Its author is that stalwart of al-Ma’mūn’s House of Wisdom, Ibn Mūsa al- Khwārizmi, and in it he sets out for the first time the subject of algebra as a mathematical discipline in its own right rather than a branch of arithmetic or geometry. Indeed, the word ‘algebra’ originates from the al-jebr in the title. Al-Khwārizmi came to Baghdad in the early ninth century from a region of Central Asia just south of the Aral Sea. He was originally a Zoroastrian who we think converted to Islam. On the very first page of al-Jeb , he begins with the line Bism-Illāh al-Rahmān al-Rahīm (‘In the name of God, the most Gracious and Compassionate’), with which all books written by Muslims begin, even to this day. But it could of course be that al-Khwārizmi was simply following tradition and did not wish to offend the caliph whose patronage he enjoyed. In producing his famous Picture of the Earth treatise, in which he tabulated the coordinates of hundreds of cities in the known world and gave instructions for drawing a new map of the world, he secured his legacy as the first geographer of Islam. And by overseeing the astronomical work at the Shammāsiyya observatory in Baghdad and then producing a highly influential zīj , he marked himself out as one of its great astronomers. But he is primarily known as a mathematician, and his treatise on Hindu numerals introduced the Muslim world to the decimal number system. Yet all these achievements pale alongside his greatest claim to fame, which is without doubt his book on algebra. Interestingly, and unlike his famous contemporary, al-Kindi, he never ventured into philosophy; nor was he involved in translations, and had no knowledge of the Greek language.

It is not known in what year al-Khwārizmi completed his al-Jebr, but on the very first page he wrote a dedication to his patron, al-Ma’mūn. It is from these early passages that we learn of his motivation for writing it: ‘That fondness for science, by which God has distinguished the Imam al-Ma’mūn, the Commander of the Faithful . . .has encouraged me to compose a short work on calculating by (the rules of) completion and reduction.’ And here lies part of the real value of his work, for what al-Khwārizmi did was to bring together obscure mathematical rules, known only to the few, and turn them into an instruction manual for solving mathematical problems that crop up in a wide range of everyday situations. Before delving into the details of his book, it might be useful to explore exactly what is meant by algebra.

We all learn at school how to solve problems involving ‘unknown’ quantities, usually labelled as x and y. It is quite straightforward to demonstrate why algebra is so useful in solving many different kinds of problems in mathematics, science, engineering, finance and so on. As a quick refresher, let us begin with a trivial example. Writing the equation x − 4 = 2 means that there is a number, currently designated by the letter x, that has a value such that if we subtract 4 from it the answer will be 2. It is obvious then that x must be 6, and I could have dispensed with the trouble of writing a mathematical equation involving the symbol x and simply stated in words: what is the number that, if we subtract 2 from it, leaves 4? But how about another problem, where a knowledge of algebra and its rules can come in useful (even though the problem itself is no more than a simple brainteaser)? Here it is. You and I each have a basket of eggs, but we do not know how many eggs either basket contains. We are informed that if I give you one of my eggs then we shall both have the same number. If, on the other hand, you were to give me one of your eggs then I would have twice as many as you. How many eggs does this mean we each had originally? 

Try thinking through this puzzle before reading on. The standard response from most people when set this problem is to resort to ‘trial and error’, testing out pairs of numbers to see if they satisfy the two criteria. First, you should quickly surmise that I must have two more eggs than you, so that by giving you one, we end up with the same number (I lose one but you gain one). But this does not give us a unique answer, for I could have twelve and you ten, or I could have 150 and you 148. The second piece of information now needs to be taken into account, but without algebra you would just be trying pairs of numbers until you hit upon the correct combination. In fact, the answer is that I have seven eggs and you have five – giving you one of mine means we both end up with six, but you giving me one of yours results in you being left with four while I have eight – twice as many as you. To set up the problem algebraically, we would begin by saying: let the larger number of eggs be x and the smaller number y. We can now generate two equations: x − 1 = y + 1 and x + 1 = 2 ( y − 1). We would then have to know the rules of algebraic manipulation (rearranging and reorganizing the letters and numbers in the equations) in order to arrive at the answer: x = 7, y = 5. It was this set of rules that al-Khwārizmi describes in his al-Jebr, and he is therefore widely hailed as the ‘father of algebra’. But the matter turns out to be rather more complicated than this. We should be careful not to credit al-Khwārizmi with inventing a discipline just because the name we use for it today originated from the title of his book. Such a distinction as the founder of a discipline will need to be backed up with a more careful investigation into the mathematical legacy he inherited.

This issue was highlighted for me several years ago when I gave a public lecture at the Royal Society in London on the contributions to science from the golden age of Islam. I glibly, and without really backing up my claim, credited al-Khwārizmi with the invention of algebra. At the end of the lecture, a member of the audience approached me and argued indignantly that in fact algebra went back long before al-Khwārizmi and that if anyone deserved the title of ‘the father of algebra’ then it was a Greek mathematician by the name of Diophantus. Not being an expert on this matter at that time, I had no strong counter-argument. Had I been too hasty in my praise of al-Khwārizmi? Worse still, had I been guilty of intellectually lazy bias towards the scholars of Islam by downplaying some of the great achievements of the ancient Greeks – something I unfortunately encounter regularly and which I was determined to avoid?




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