Pathfinders

by Jim Al-Khalili

  The problem is difficult because even a very tiny shift in the position that the billiard ball or light ray strikes the reflecting surface would lead to it bouncing off at a different angle altogether. Ibn al-Haytham provided the first (partial) solution to the problem using the technique of conic sections described by Apollonius of Perga (c. 262–190 BCE). Apollonius’ Conics is regarded as one of the most important books on mathematics ever written. In it he showed how different types of mathematical curves (circles, ellipses, parabolas, hyperbolas) can be produced when a cone is sliced through at different angles. Ibn al-Haytham knew this work well and even devoted a substantial effort to reconstructing the lost eighth book of the Conics.17 He solved the quartic equation by splitting it into equations for two intersecting curves, a circle and a hyperbola. The points of intersection are the solutions of the problem, but his solution was long and complicated. Amazingly, an exact algebraic solution had to wait until 1997, when Oxford mathematician Peter Neumann showed that the problem could be solved using a theory developed by the French mathematical prodigy Évariste Galois (1811–32).18

  Conic sections. By slicing through a cone at different angles, a variety of different geometric curves are found, which can be used to solve certain types of algebraic problems.

  In astronomy, it is only now that historians of science are beginning to see Ibn al-Haytham’s true contribution. In the past, this has been confined to acknowledging that he was one of the first scholars seriously to challenge Ptolemy. His challenge, however, was not to the geocentric idea itself, but rather to Ptolemy’s mathematical models. Those historians of science prepared to dig a little deeper into the subject have found some hidden gems in Ibn al-Haytham’s texts. He wrote twenty-five works on astronomy, which is twice as many as he wrote on optics.19 These include treatises on cosmology, astronomical observation and calculation, and technical applications such as the determination of meridians, the direction of Mecca and the design of sundials. But it is his work on what might be called astronomical theory that is most important. For it is on this subject that we find his criticisms of Ptolemy and many corrections to the Almagest. All this body of work was written during the last decade of his life, when he was almost exclusively engaged in astronomy.

  Just as al-Rāzi took it upon himself to highlight the deficiencies and errors in the medical writings of Galen, so Ibn al-Haytham did the same with Ptolemy. Both men pioneered the spirit of shukūk (‘doubts’), which is so crucial in science. Here is a wonderful example of Ibn al-Haytham’s damning response to an anonymous scholar who disapproved of his disparaging remarks about the Almagest in his Doubts on Ptolemy (al-Shukūk ala Batlamyūs):

  From the statements made by the noble Sheikh, it is clear that he believes in Ptolemy’s words in everything he says, without relying on a demonstration or calling on a proof, but by pure imitation; that is how experts in the prophetic tradition have faith in Prophets, may the blessing of God be upon them. But it is not the way that mathematicians have faith in specialists in the demonstrative sciences. And I have taken note that it gives him [i.e. the Sheikh] pain that I have contradicted Ptolemy, and that he finds it distasteful; his statements suggest that error is foreign to Ptolemy. Now there are many errors in Ptolemy, in many passages of his books … If he wishes me to specify them and point them out, I shall do so.20

  Ibn al-Haytham then really lets the noble Sheikh have it with both barrels, for he does indeed go on to list the errors and mistakes in several of Ptolemy’s works: the Almagest, the Book of Optics and the Book of Hypotheses.

  Not all scholars agreed with or even understood Ibn al-Haytham’s approach. Philosophers in particular resisted his mathematical theories of astronomy. An Andalusian scholar by the name of Ibn Bājja (Avempace) a century after Ibn al-Haytham even argued that he was not ‘one of the true experts of his science’ and that his criticisms of Ptolemy were based on only a superficial understanding of the Greek’s works, having read them only ‘in the most simple of ways’.21

  It is always easier to find mistakes in the work of others than to come up with original ideas of one’s own. But Ibn al-Haytham’s work in astronomy is still remarkable. For instance, one of his texts, The Model of Motions of Each of the Seven Planets, came in three books and outlined a new theory of planetary motion far in advance of anything Ptolemy had written. Modern historians of science now regard it as a monumental achievement and at the cutting edge of science at the time. We must not forget that Ibn al-Haytham still believed in a geocentric model of the universe, but what he wanted above all was to ‘mathematize’ astronomy as he had done with optics. He wanted to be able to describe the observed motion of the planets in terms of pure geometry and was not particularly interested in the physical mechanism or reason behind their motion. Nor was he interested in the way the planets move in an absolute sense, but only as they are seen to move from the vantage point of the observer on earth. This ‘phenomenological’ approach is therefore independent of any notion of the earth going round the sun or the sun going round the earth; it was a theory of planetary dynamics from the earth’s frame of reference. To help with this, he introduced a new concept – what he called ‘required time’: the time needed for a planet to trace an arc in the sky. But he treated time in a way that a modern theoretical physicist would recognize, as a parameter in his mathematics; in fact, as a purely geometrical quantity.

  A good scientist should never be so arrogant as to be certain about anything. Never, that is, apart from on one point: that what we refer to as the modern scientific method is non-negotiable in its all-encompassing importance as a world-view. Many would argue it is the only world-view that a rational, thinking person can have in explaining how and why the world is the way it is.

  I shall expand briefly here on what I mean by the scientific method. While it is true that there are no certainties in science, when scientists say they ‘believe’ a particular theory to be correct, they mean that it is in all probability a correct description of some aspect of nature. For instance, our current best picture of the subatomic world comes from the predictions of quantum theory developed in the early twentieth century. I believe quantum theory gives us a correct and true description of atoms. However, my belief is not based on the blind faith of religion but is instead based on the way that the theory’s incredible predictive power has been tested time and time again over the past century. Similarly, I believe that Darwin’s theory of natural selection is the true description of the way that life on earth has evolved. This does not mean that my mind is closed to the possibility of something better coming along in the future to replace it; it is just that I think it highly unlikely that natural selection is wrong given the overwhelming evidence in its favour, both logical and empirical.

  As commonly defined, the scientific method is the approach to investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge, based on the gathering of data through observation and measurement, followed by the formulation and testing of hypotheses to explain the data. It is often still claimed that the modern scientific method was not established until the Renaissance by Francis Bacon in his work Novum Organum (1620) and by Descartes in his treatise Discours de la Méthode (1637). But there is no doubt that Ibn al-Haytham, along with al-Rāzi and al-Bīrūni, whom we shall meet in the next chapter, arrived there much earlier.

  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 exercisin
g 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.22

  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.

  Unlike his two equally famous Persian contemporaries Ibn Sīna and al-Bīrūni, Ibn al-Haytham was not particularly philosophically minded; he was more of an Archimedes than an Aristotle. Like al-Rāzi before him, Ibn al-Haytham embodied the spirit of the experimental method in science. In many ways, even the cynic who refuses to acknowledge that medieval Islam made any great paradigm-shifting discoveries such as those seen in Europe by Copernicus, Galileo, Kepler or Newton must nevertheless acknowledge the great debt we owe to these tenth- and eleventh-century scientists. Robert Briffault, in his book The Making of Humanity, puts it thus:

  The Greeks systematised, generalised and theorised, but the patient ways of investigation, the accumulation of positive knowledge, the minute methods of science, detailed and prolonged observation and experimental enquiry, were altogether alien to the Greeks’ temperament … What we call science arose in Europe as a result of a new spirit of inquiry … of the methods of experiment, observation and measurement, of the development of mathematics in a form unknown to the Greeks. That spirit and those methods were introduced into the European world by the Arabs.23

  12

  The Prince and the Pauper

  The stubborn critic would say: ‘What is the benefit of these sciences?’ He does not know the virtue that distinguishes mankind from all the animals: it is knowledge, in general, which is pursued solely by man, and which is pursued for the sake of knowledge itself, because its acquisition is truly delightful, and is unlike the pleasures desirable from other pursuits. For the good cannot be brought forth, and evil cannot be avoided, except by knowledge. What benefit then is more vivid? What use is more abundant?

  Al-Bīrūni

  In a famous correspondence around the year 1000 CE, two Persian geniuses argued about the nature of reality in a way that would not sound out of place in any modern university physics department. Of all the great thinkers and polymaths of the Islamic golden age, these two men were giants, for they were in every way the equals of the very best that the golden age of Greece had produced. The younger of the two had been a privileged child prodigy who grew up to become the brash superstar of his age, a celebrity polymath whose philosophy would influence the world’s greatest minds, and whose Canon of Medicine (al-Qānūn fi al-Tibb) would become the world’s most important medical textbook for over half a millennium. His name was Ibn Sīna, better known in the West as Avicenna. The other man, seven years older, quieter, less flamboyant, from a family of modest means, but with an encyclopedic mind and razor-sharp intellect, is less well known today. In fact, remarkably, and unlike many of the great scholars of Islam, there does not exist a Latinized version of his name: Abū Rayhān al-Bīrūni.

  Where did these two men come from? Where and when did they meet? And what were the sorts of issues they debated? It is not clear exactly when their famous correspondence took place but it was certainly early on in their careers, when both men were still in their twenties and may have even both been working under the same roof in the royal courts of Gurgānj, the capital of Khwārizm in Central Asia. Al-Bīrūni rightly regarded himself as the superior intellect in matters of mathematics, physics and astronomy, but was genuinely interested in what the younger Ibn Sīna, the more able philosopher, had to say on more abstract metaphysical matters, and so posed for him a list of eighteen questions. Here are just a few of the more philosophical ones:

  1. What was the justification for insisting that the heavenly bodies had neither levity nor gravity and that their orbits were perfectly circular around the earth? In other words, why do they not fall towards the earth or float away from it?

  2. Why did he (Ibn Sīna) support Aristotle’s rejection of the theory of atomism,1 since the notion of continuous and infinitely divisible matter that Aristotle and Ibn Sīna subscribed to was equally speculative?

  3. Do the sun’s rays have material substance? If not, how do they transmit its warmth to us?

  4. How would he defend the Aristotelian view that rejected the possibility of the existence of parallel universes?2

  I shall mention here Ibn Sīna’s response to just one of these questions: the issue of how the sun’s heat reaches us. For here it was not a case of al-Bīrūni challenging Ibn Sīna’s philosophical views but an honest desire to see if he could provide a satisfactory answer. Ibn Sīna gives the following explanation:

  You must also know that the heat of the sun does not come to us by descending down from the sun for the following reasons: firstly, heat does not move by itself; secondly, there is no hot body that descends from above and heats what is down below; third, the sun is not even hot because heat that is being created here is not descending from above for the three reasons already mentioned. Rather, heat occurs here from the reflection of light and air is heated by this process, as can be observed in the experiment of burning mirrors. And you must know that the rays are not bodies – for if they were bodies there would be two bodies in one place: the air and the rays.3

  Of course, we know now that the sun is indeed very hot and this heat is radiated to us as electromagnetic waves in the same way that its light reaches us, but it would be nearly nine hundred years before James Clerk Maxwell would explain this correctly.

  Ibn Sīna dealt with each of al-Bīrūni’s eighteen questions carefully, strongly defending his (and Aristotle’s) views. But many of his clever, slippery and often evasive answers were unsatisfactory to al-Bīrūni, who challenged them with his own impeccable logic. It would appear that the tone of the correspondence from both men grew increasingly confrontational, even acrimonious. Al-Bīrūni sounds as though he is throwing down the gauntlet to his younger adversary, while Ibn Sīna’s famous arrogance is clearly in evidence.

  And the questions were not all of such an abstract nature, for it seems that al-Bīrūni was also keen to see if he could get some long-standing mysteries solved, such as why ice floats on water (Ibn Sīna thought this was due to tiny air pockets trapped inside the ice making it lighter than water – of course we know now that ice floats because it is less dense than liquid water).

  Eventually, Ibn Sīna left the correspondence to his most able student, al-Ma’sūmi, an act that must have been a painful snub to al-Bīrūni; in particular, al-Ma’sūmi’s tone is somewhat impatient, as though he is exasperated by al-Bīrūni’s rejection of earlier answers from his master, whom he refers to as ‘the Wise One’. The following is an example of al-Ma’sūmi’s correspondence: ‘As for your response to the Wise One … I do not think it was correct, and it would have been better had you worded your comment more appropriately. Further, had you perceived what the Wise One meant by his noble words on this issue, you would not have allowed yourself to make this objection.’

  Just as fascinating as the ideas being discussed by the
se two men is the world they inhabited. Both were born in the land of Khwārizm (modern Uzbekistan) that had already produced the father of algebra, al-Khwārizmi, two centuries earlier. But they came from contrasting backgrounds.

  That Abū Rayhan Muhammad al-Bīrūni (973–1048) ranks as one of the greatest scientists of all time makes it all the more puzzling that his name is so little known in the West. He was a polymath with a free-ranging and formidable intellect; not only did he make significant breakthroughs as a brilliant mathematician and astronomer, he also left his mark as a philosopher, theologian, encyclopedist, linguist, historian, geographer, geologist, anthropologist, pharmacist and physician. He was also, alongside al-Rāzi and Ibn al-Haytham, one of the earliest and leading exponents of the modern scientific method of experimentation and observation.

  Little is known about his early life, as he left no autobiographical details. We know that he was born near the city of Kath in Khwārizm in a family of modest means that, while Persian in every way, had originally come from Tajikistan to the east. His distinctive name is thought to come from the Persian word for ‘outsider’ and could refer either to his family’s Tajik origins or to the fact that he came to Kath as a boy from an outlying suburb, or it may have been a name given him later in life. What is unusual is that the name is not given to any other scholars of the period, many of whom would have travelled far and wide. So it could simply be that he was born in a place called Bīrūn, near Kath.

  As a young man, he worked in the courts of the Banū Irāq princes of Kath, who ruled over that region of Khwārizm on behalf of the Samanid dynasty. But peace was shattered when a rival dynasty from across the river Oxus4 overran the city in 995, and al-Bīrūni had to flee. He travelled first to the Samanid capital, Bukhara, where he came under the protection of the Samanid ruler, Prince Nūh ibn Mansūr, and befriended another deposed ruler, Prince Qābūs of Gorgan (a city in northern Persia near the Caspian Sea). But making influential friends was not enough for al-Bīrūni; he needed to go where he could continue his research, particularly in astronomy. He considered going west to Baghdad, but decided against it as it was too far to travel, and so made his way instead to Rayy, where he spent a miserable few years living in poverty, unable to gain royal patronage to support his work.