7. G. Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer (Wiley, 2000).
8. G. Sarton, Introduction to the History of Science (Carnegie Institution of Washington, 1927), vol. 1, p. 585.
9. G. Sarton, ‘Decimal Systems Early and Late’, Osiris, 9 (1950), pp. 581–601.
10. Here is the technique the Romans used (which actually goes back to much earlier times and is similar to the method used by the ancient Egyptians). They would put the two numbers to be multiplied alongside each other and then underneath they would halve one number and double the other. This they learnt to do very well. They would keep doing this, ignoring the remainder when halving an odd number, until the number being halved got down to 1. Then they would cross out all those numbers on the doubling column that corresponded to an even number on the halving column and added up what was left on the doubled column. They could add their Roman numerals quite quickly.
To try this with our example I have written the Roman numerals with Hindu-Arabic numerals in brackets for you to follow:
Step 1 (double and halve):
XI (11) CXXIII (123)
V (5) CCXLVI (246)
II (2) CDXCII (492)
I (1) CMLXXXIV (984)
Step 2 (remove number adjacent to only even number on left):
XI (11) CXXIII (123)
V (5) CCXLVI (246)
II (2)
I (1) CMLXXXIV (984)
Step 3 (add):
MCCCLIII (1,353)
11. Roshdi Rashed, The Development of Arabic Mathematics: Between Arithmetic and Algebra (Kluwer Academic Publishers, 1994), p. 55.
12. Heinrich Hermelink, ‘A Commentary upon Bīrūni’s Kitab Taḥdīd al-Amākin, an 11th Century Treatise on Mathematical Geography by E. S. Kennedy’, Isis, 67/4 (1976), pp. 634–6.
13. A good discussion on the Babylonian use of zero can be found in Neugebauer, The Exact Sciences in Antiquity, pp. 14–20.
14. C. B. Boyer, ‘An Early Reference to Division by Zero’, American Mathematical Monthly, 50/8 (1943), pp. 487–91.
15. Bibhutibhusan Datta, ‘Early Literary Evidence of the Use of the Zero in India’, American Mathematical Monthly, 38 (1931), pp. 566–72.
16. C. B. Boyer, ‘Zero: The Symbol, the Concept, the Number’, National Mathematics Magazine, 18/8 (1944), pp. 323–30.
17. A. S. Sa’īdān, ‘The Earliest Extant Arabic Arithmetic: Kitab al-Fusūl fī al-Hisāb al-Hindī of Abū al-Hasan Ahmed ibn Ibrāhīm al-Uqlīdisī’, Isis, 57/4 (1966), pp. 475–90.
18. J. L. Berggren, Episodes in the Mathematics of Medieval Islam (Springer-Verlag, 2000), p. 36.
19. The three examples of al-Uqlīdisi’s use of decimals in specific problems are (a) halving an odd number a certain number of times, (b) increasing or decreasing a number by a tenth of its value a certain number of times, and (c) the extraction of square and cube roots of numbers.
20. Rashed, The Development of Arabic Mathematics, p. 124.
21. There is still some debate over the title of this great book. The problem is in the second word hussāb, which means ‘calculators’ (those who calculate). But because of the absence of the first, shorter, vowel in the Arabic word it could also be read as hisāb, meaning ‘arithmetic’. This is why two highly acclaimed historians of mathematics, Berggren and Rashed, refer to the book as The Calculators’ Key and The Key to Arithmetic, respectively.
22. The only other mathematician who seems to have picked up on the subject properly was Abū Mansūr al-Baghdādī (d. 1037) in his book Al-Takmila fi ’Ilm al-Hisāb (MS 2708, Lala-Li Library, Istanbul).
23. J. Needham, Science and Civilisation in China (Cambridge University Press, 1959), vol. 3, pp. 33–91.
24. Of course, while in English we use a decimal ‘point’ (e.g. 1.5 to mean one and a half), in French, as well as in Arabic, a comma is used to separate the units from the fractions (e.g. 1,5).
25. A. S. Sa’īdān, ‘The Earliest Extant Arabic Arithmetic’, p. 487.
CHAPTER 8. ALGEBRA
1. Muhammad b. Mūsa al-Khwārizmi (trans. F. Rosen), The Algebra of Muhammad ibn Mūsa (Oriental Translation Fund, London, 1831).
2. Fermat’s copy of Arithmetica was the version published in 1621 and translated from Greek into Latin by Claude Gaspard Bachet de Méziriac.
3. e.g. Roshdi Rashed, The Development of Arabic Mathematics: Between Arithmetic and Algebra (Kluwer Academic Publishers, 1994), p. 13.
4. S. Gandz, ‘The Sources of al-Khwārizmi Algebra’, Osiris, 1 (1936), pp. 263–77.
5. G. Sarfatti, Mathematical Terminology in Hebrew Scientific Literature of the Middle Ages (Magnus Press, Jerusalem, 1969).
6. Al-Khwārizmi, The Algebra of Muhammad ibn Mūsa, p. 3.
7. A calendar is any table or register that marks the passage of time by organizing days into constant time units of weeks, months and years following the naturally repeating cycles of the seasons and the motion of the sun and moon across the sky.
8. A. Youschkevitch and B. A. Rosenfeld, ‘Al-Khayyāmī’, in Charles Coulston Gillispie (ed.), Dictionary of Scientific Biography (Charles Scribner’s Sons, 1973), vol. 7, pp. 323–34.
CHAPTER 9. THE PHILOSOPHER
1. John A. Nawas, ‘A Reexamination of Three Current Explanations for Al-Ma’mun’s Introduction of the Miḥna’, International Journal of Middle East Studies, 26/4 (1994), pp. 615–29.
2. Peter Adamson, Al-Kindi, Great Medieval Thinkers (Oxford University Press, 2006), p. 4.
3. Socrates did not himself leave any philosophical writings. His ideas reach us only through the writings of his contemporaries and students, most notably Plato.
4. Quoted in Richard Walzer, ‘The Rise of Islamic Philosophy’, Oriens, 3/1 (1950), p. 9.
5. Simon Singh, The Code Book (Fourth Estate, 2000), pp. 14–20.
6. Lynn Thorndike, Arabic Occult Science of the Ninth Century (Kessinger Publishing, 2005), p. 649.
7. Alfred L. Ivry, ‘Al-Kindi and the Mu’tazila: A Philosophical and Political Reevaluation’, Oriens, 25 (1976), p. 82.
8. Adamson, Al-Kindi, p. 5.
9. Seyyed Hossein Nasr and Oliver Leaman (eds.), History of Islamic Philosophy (Routledge, 1996), p. 166.
CHAPTER 10. THE MEDIC
1. The author of this treatise should not be confused with the philosopher Ya’qūb ibn Ishāq al-Kindi; he is an Egyptian-Jewish physician who wrote these words following a visit to Damascus in 1202.
2. I do not mention Chinese medicine here only because it had less of an influence on the Muslim world than Indian and Greek medicine and so is not a part of my story, which is not of course to downplay its importance or impact on the world to this day.
3. Bayard Dodge (ed. and trans.), The Fihrist of al-Nadīm (Columbia University Press, 1970), vol. 2, p. 702.
4. P. E. Pormann and E. Savage-Smith, Medieval Islamic Medicine (American University in Cairo Press, 2007), p. 96.
5. Later, much larger hospitals would be built, such as the Adudi hospital in 982, the Nūri hospital in Damascus in the mid-twelfth century and the massive Mansūri hospital in Cairo in 1284.
6. Ibn Jubayr, Travels of Ibn Jubayr, trans. J. C. Broadhurst (Goodword Books, New Delhi, 2004), p. 234.
7. Pormann and Savage-Smith, Medieval Islamic Medicine, p. 117.
8. Described in detail by Albert Zaki Iskandar, ‘Al-Rāzi, the Clinical Physician’, in P. E. Pormann (ed.), Islamic Medical and Scientific Tradition (Routledge, 2010).
9. P. E. Pormann, ‘Medical Methodology and Hospital Practice: The Case of Tenth-Century Baghdad’, in P. Adamson (ed.), In the Age of al-Farabi: Arabic Philosophy in the 4th/10th Century, Warburg Institute Colloquia, 12 (Warburg Institute, 2008), pp. 95–118.
10. M. Dunlop, Arab Civilisation, to AD 1500 (Longman/Librairie du Liban, 1971), p. 235, an extract from the Treatise on Smallpox and Measles.
11. G. Wiet, V. Elisseeff, P. Wolff and J. Naudu, History of Mankind, vol. 3: The Great Medieval Civilizations, trans. from the Fr
ench (George Allen & Unwin/Unesco, 1975), p. 654.
12. Quoted in Jennifer Michael Hecht, Doubt: A History. The Great Doubters and their Legacy of Innovation from Socrates and Jesus to Thomas Jefferson and Emily Dickinson (HarperOne, 2006), p. 227.
13. L. E. Goodman, ‘Al-Razi’, in C. E. Bosworth et al. (eds.), The Encyclopedia of Islam (Brill, 1995), pp. 474–7.
14. Quoted in Hecht, Doubt, p. 31.
15. It is interesting that ‘zenith’ actually derives from the Arabic word samt (meaning ‘path’ and coming from samt al-ra’s, or ‘path over the head’), but the word was transcribed incorrectly into medieval Latin as senit. Likewise, the word ‘nadir’, the opposite of ‘zenith’, comes from the Arabic nadir al-samt.
CHAPTER 11. THE PHYSICIST
1. I do not make this claim lightly, for Newton followed some truly great scientists, such as Descartes, Galileo and Kepler.
2. Like some of the other best-known Islamic scholars in the West, such as al-Rāzi (Rhazes), Ibn Sīna (Avicenna) and Ibn Rushd (Averroës), Ibn al-Haytham is probably still far better known as Alhazen, as I found when researching for this book and having to look his work up in library catalogues under ‘A’ rather than ‘I’ or ‘H’.
3. Some have argued that Dar al-Hikma translates as ‘Hall of Wisdom’ – as in ‘Hall of Fame’.
4. Roshdi Rashed, ‘A Pioneer of Anaclastics: Ibn Sahl on Burning Mirrors and Lenses’, Isis, 81/3 (September 1990), p. 465.
5. Kurt Bernardo Wolf and Guillermo Krötzsch, ‘Geometry and Dynamics in Refracting Systems’, European Journal of Physics, 16 (1995), pp. 14–20.
6. D. C. Lindberg, Theories of Vision from al-Kindi to Kepler (University of Chicago Press, 1976), p. 209.
7. David Lindberg, ‘Alhazen’s Theory of Vision and its Reception in the West’, Isis, 58/3 (1967), p. 331.
8. Nader El-Bizri, ‘A Philosophical Perspective on Alhazen’s Optics’, Arabic Sciences and Philosophy, 15/2 (2005), pp. 189–218.
9. G. J. Holton and S. G. Brush, Physics, the Human Adventure: From Copernicus to Einstein and Beyond (Rutgers University Press, 2001), p. 32.
10. Opticae Thesaurus, vol. 1, sect. 1, p. 1, quoted in Lindberg, ‘Alhazen’s Theory of Vision and its Reception in the West’, p. 322.
11. Ibid.
12. Contrary to popular myth, Ibn al-Haytham did not invent the camera obscura, nor is his writing the first mention of it, for its actions were crudely understood by the ancient Chinese before 300 BCE (found in a passage of the Mo Ching). But Ibn al-Haytham was the first to describe mathematically how it worked.
13. W. H. Lehn and S. van der Werf, ‘Atmospheric Refraction: A History’, Applied Optics, 44 (2005), pp. 5624–36.
14. H. J. J. Winter, ‘The Optical Researches of Ibn al-Haitham’, Centaurus, 3 (1954), p. 196.
15. Nader El-Bizri, ‘In Defence of the Sovereignty of Philosophy: Al-Baghdādī’s Critique of Ibn al-Haytham’s Geometrisation of Place’, Arabic Sciences and Philosophy, 17/1 (2007), pp. 57–80.
16. A. I. Sabri, ‘The authorship of Liber de crepusculis, an Eleventh-century Work on Atmospheric Refraction’, Isis, 58 (1967), pp. 77–85.
17. Books I–IV survive in the original Greek while Books V–VII reach us only from their Arabic translation made in the ninth century by the Banū Mūsa brothers.
18. Peter M. Neumann, ‘Reflections on Reflection in a Spherical Mirror’, American Mathematical Monthly, 105 (1998), pp. 523–8.
19. Roshdi Rashed, ‘The Celestial Kinematics of Ibn al-Haytham’, Arabic Sciences and Philosophy, 17 (2007), p. 8.
20. Quoted in ibid., p. 11.
21. Gerhard Endress, in J. P. Hogendijk and A. I. Sabra (eds.), The Enterprise of Science in Islam (MIT Press, 2003), p. 148.
22. Bradley Steffens, Ibn al-Haytham: First Scientist (Morgan Reynolds Publishing, 2005), p. 62.
23. Robert Briffault, The Making of Humanity (The Macmillan Co., 1930), p. 141, quoted in Mohaini Mohamed, Great Muslim Mathematicians (Penerbit UTM, 2000), p. 52.
CHAPTER 12. THE PRINCE AND THE PAUPER
1. The Greek Leucippus, who flourished in the fifth century BCE, is regarded as the father of atomic theory. His ideas were extended and developed by his student and disciple Democritus (c. 460–370 BCE). According to them, all matter – indeed the whole universe – consists of fundamental building blocks (atoms) and the void. Aristotle criticized this view.
2. H. M. Said and A. Z. Khan, Al-Bīrūni: His Times, Life and Works (Renaissance Publishing House, Delhi, 1990), p. 105.
3. The full correspondence, known as Al-As’ila wal-Ajwiba (The Questions and Answers) is reproduced in a series of eight journal articles by Rafik Berjak and Muzaffar Iqbal in Islam & Science, 1/1 (2003), p. 91; 1/2 (2003), p. 253; 2/1 (2004), p. 57; 2/2 (2004), p. 181; 3/1 (2005), p. 57; 3/2 (2005), p. 166; 4/2 (2006), p. 165; 5/1 (2007), p. 53.
4. This is known today as the Amu Darya river and flows down from the Pamir Mountains to the west of the Himalayas, winding its way west and north through the region of Khwārizm until it finally spills into the southern tip of the Aral Sea.
5. Aisha Khan, Avicenna (The Rosen Publishing Group, New York, 2006), p. 39.
6. Because of the different spelling of the two cities Gorgan (Jurjān) and Gurgānj (Old Urganch, Kunya Urgench or Jurjāniah), the two are often confused with each other. The former is today a thriving city in northern Iran; the latter, in its heyday one of the greatest cities in Central Asia, was razed to the ground by Genghis Khan in 1221.
7. i.e. those who study the languages, literature, history and cultures of the Indian subcontinent.
8. Lenn E. Goodman, Avicenna (Cornell University Press, 2006), p. 155.
9. Not forgetting of course Tycho Brahe’s careful observations and Johannes Kepler’s brilliant deductions.
10. Jamil Ali, The Determination of the Coordinates of the Cities: Al-Bīrūni’s Tahdīd al-Amākin (Centennial Publications, The American University of Beirut, 1967), p. 188.
11. Ibid., p. 183.
12. I should point out though that the ancient Greeks also had some understanding of how land is recovered from the sea from their discovery of marine fossils high above ground (see the beginning of Plato’s Timaeus).
13. Abdus Salam, ‘Islam and Science’, in C. H. Lai and Azim Kidwai (eds.), Ideals and Realities: Selected Essays of Abdus Salam (World Scientific, Singapore, 1987), pp. 179–213.
14. Ali, The Determination of the Coordinates of the Cities, p. 2.
CHAPTER 13. ANDALUSIA
1. Ivan Van Sertima, Golden Age of the Moor (Transaction Publishers, 1991), p. 17.
2. It is a coincidence that the three most famous Andalusian rulers are all called Abd al-Rahmān, for there were others who ruled in between, and there would be five caliphs in total with this name.
3. George F. Hourani, ‘The Early Growth of the Secular Sciences in Andalusia’, Studia Islamica, 32 (1970), p. 149.
4. However, it is most likely that the present name originates from the pre-Islamic toponym, Sumrā in Syriac, and that the popular name of Surra man Ra’a itself derived from Sāmarra.
5. Hugh Kennedy, in D. Luscombe and J. Riley-Smith (eds.), The New Cambridge Medieval History (Cambridge University Press, 2004), vol. 4, p. 601.
6. M. S. Spink and G. L. Lewis, Albucasis on Surgery and Instruments (Wellcome Institute of the History of Medicine, 1973), p. 8.
7. Ibid., p. 406.
8. G. Sarton, Introduction to the History of Science (Carnegie Institution of Washington, 1927), vol. 1, p. 694.
9. Alexander Broadie, in Seyyed Hossein Nasr and Oliver Leaman (eds.), History of Islamic Philosophy (Routledge, 1996), p. 725.
10. Hourani, ‘The Early Growth of the Secular Sciences in Andalusia’, p. 153.
11. R. W. Southern, The Making of the Middle Ages (Yale University Press, 1953), p. 121.
12. David C. Lindberg (ed), Science in the Middle Ages (University of Chicago Press, 1976), p. 60.
13. He is also known by the misspelt
‘Albucasis’.
14. S. P. Scott, History of the Moorish Empire in Europe (Lippincott, 1904), vol. 3, pp. 461–2.
CHAPTER 14. THE MARĀGHA REVOLUTION
1. F. Jamil Ragep, ‘Freeing Astronomy from Philosophy: An Aspect of Islamic Influence on Science’, Osiris, 16 (2001), p. 51.
2. Ibid., p. 50.
3. In the Ptolemaic model, the sun revolves around in a circular orbit that is not centred on the earth. So there is a point in its orbit when it is at its furthest point from the earth: the apogee. Imagine two almost completely overlapping circles of the same size, with the earth at the centre of one and the sun revolving around the other. The measurement made by the Greeks and corrected by Islamic astronomers is that of the longitudinal angle of the sun in the sky at this point in its cycle.
4. Rudolf von Erhardt and Erika von Erhardt-Siebold, ‘Archimedes’ Sand-Reckoner: Aristarchos and Copernicus’, Isis, 33/5 (1942), pp. 578–602; O. Neugebauer, ‘Archimedes and Aristarchus’, Isis, 34/1 (1942), pp. 4–6.
5. William Harris Stahl, ‘The Greek Heliocentric Theory and Its Abandonment’, Transactions and Proceedings of the American Philological Association, 76 (1945), pp. 321–32.
6. Noel Swerdlow, ‘A Lost Monument of Indian Astronomy’, Isis, 64/2 (1973), pp. 239–43.
7. Jose Wudka, Space-Time, Relativity and Cosmology (Cambridge University Press, 2006), p. 46.
8. Hugh Thurston, Early Astronomy (Springer, 1994), p. 178.
9. Aydin Sayili, The Observatory in Islam and its Place in the General History of the Observatory, Publications of the Turkish Historical Society, 7/38 (Ayer Co. Pub., Ankara, 1988).
10. The term was coined by historian Edward Kennedy in his paper ‘Late Medieval Planetary Theory’, Isis, 57 (1966), pp. 365–78.
11. Noel Swerdlow, ‘The Derivation and First Draft of Copernicus’ Planetary Theory: A Translation of the Commentariolus with Commentary’, Proceedings of the American Philosophical Society, 117 (1973), p. 426.
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