History of the Intellectual Development of Europe, Volume II (of 2)

Their great improvements in arithmetic. From the Hindus the Arabs learned arithmetic, especially that valuable invention termed by us the Arabic numerals, but honourably ascribed by them to its proper source, under the designation of "Indian numerals." They also entitled their treatises on the subject "Systems of Indian Arithmetic." This admirable notation by nine digits and cipher occasioned a complete revolution in arithmetical computations. As in the case of so many other things, the Arab impress is upon it; our word cipher, and its derivatives, ciphering, etc., recall the Arabic word tsaphara or ciphra, the name for the 0, and meaning that which is blank or void. Mohammed Ben Musa, said to be the earliest of the Saracen authors on algebra, and who made the great improvement of substituting sines for chords in trigonometry, wrote also on this Indian system. He lived at the end of the ninth century; before the end of the tenth it was in common use among the African and Spanish mathematicians. Ebn Junis, A.D. 1008, used it in his astronomical works. From Spain it passed into Italy, its singular advantage in commercial computation causing it to be eagerly adopted in the great trading cities. We still use the word algorithm in reference to calculations. The study of algebra was intently cultivated among the Arabs, who gave it the name it bears. Ben Musa, just referred to, was the inventor of the common method of solving quadratic equations. Their astronomical discoveries. In the application of mathematics to astronomy and physics they had been long distinguished. Almaimon had determined with considerable accuracy the obliquity of the ecliptic. His result, with those of some other Saracen astronomers, is as follows:

Almaimon had also ascertained the size of the earth from the measurement of a degree on the shore of the Red Sea – an operation implying true ideas of its form, and in singular contrast with the doctrine of Constantinople and Rome. While the latter was asserting, in all its absurdity, the flatness of the earth, the Spanish Moors were teaching geography in their common schools from globes. In Africa, there was still preserved, with almost religious reverence, in the library at Cairo, one of brass, reputed to have belonged to the great astronomer Ptolemy. Al Idrisi made one of silver for Roger II., of Sicily; and Gerbert used one which he had brought from Cordova in the school he established at Rheims. It cost a struggle of several centuries, illustrated by some martyrdoms, before the dictum of Lactantius and Augustine could be overthrown. Among problems of interest that were solved may be mentioned the determination of the length of the year by Albategnius and Thebit Ben Corrah; and increased accuracy was given to the correction of astronomical observations by Alhazen's great discovery of atmospheric refraction. Among the astronomers, some composed tables; some wrote on the measure of time; some on the improvement of clocks, for which purpose they were the first to apply the pendulum; some on instruments, as the astrolabe. The introduction of astronomy into Christian Europe has been attributed to the translation of the works of Mohammed Fargani. In Europe, also, the Arabs were the first to build observatories; the Giralda, or tower of Seville, was erected under the superintendence of Geber, the mathematician, A.D. 1196, for that purpose. Its fate was not a little characteristic. After the expulsion of the Moors it was turned into a belfry, the Spaniards not knowing what else to do with it.

Europe tries to hide its obligations to them. I have to deplore the systematic manner in which the literature of Europe has contrived to put out of sight our scientific obligations to the Mohammedans. Surely they cannot be much longer hidden. Injustice founded on religious rancour and national conceit cannot be perpetuated for ever. What should the modern astronomer say when, remembering the contemporary barbarism of Europe, he finds the Arab Abul Hassan speaking of tubes, to the extremities of which ocular and object diopters, perhaps sights, were attached, as used at Meragha? what when he reads of the attempts of Abderrahman Sufi at improving the photometry of the stars? Are the astronomical tables of Ebn Junis (A.D. 1008), called the Hakemite tables, or the Ilkanic tables of Nasser Eddin Tasi, constructed at the great observatory just mentioned, Meragha, near Tauris, A.D. 1259, or the measurement of time by pendulum oscillations, and the methods of correcting astronomical tables by systematic observations – are such things worthless indications of the mental state? The Arab has left his intellectual impress on Europe, as, before long, Christendom will have to confess; he has indelibly written it on the heavens, as any one may see who reads the names of the stars on a common celestial globe.

Improvements in the arts of life. Our obligations to the Spanish Moors in the arts of life are even more marked than in the higher branches of science, perhaps only because our ancestors were better prepared to take advantage of things connected with daily affairs. They set an example of skilful agriculture, the practice of which was regulated by a code of laws. Not only did they attend to the cultivation of plants, introducing very many new ones, they likewise paid great attention to the breeding of cattle, especially the sheep and horse. To them we owe the introduction of the great products, rice, sugar, cotton, and also, as we have previously observed, nearly all the fine garden and orchard fruits, together with many less important plants, as spinach and saffron. To them Spain owes the culture of silk; they gave to Xeres and Malaga their celebrity for wine. They introduced the Egyptian system of irrigation by flood-gates, wheels, and pumps. They also promoted many important branches of industry; improved the manufacture of textile fabrics, earthenware, iron, steel; the Toledo sword-blades were everywhere prized for their temper. The Arabs, on their expulsion from Spain, carried the manufacture of a kind of leather, in which they were acknowledged to excel, to Morocco, from which country the leather itself has now taken its name. They also introduced inventions of a more ominous kind – gunpowder and artillery. The cannon they used appeared to have been made of wrought iron. But perhaps they more than compensated for these evil contrivances by the introduction of the mariner's compass.

Their commerce. The mention of the mariner's compass might lead us correctly to infer that the Spanish Arabs were interested in commercial pursuits, a conclusion to which we should also come when we consider the revenues of some of their khalifs. That of Abderrahman III. is stated at five and a half million sterling – a vast sum if considered by its modern equivalent, and far more than could possibly be raised by taxes on the produce of the soil. It probably exceeded the entire revenue of all the sovereigns of Christendom taken together. From Barcelona and other ports an immense trade with the Levant was maintained, but it was mainly in the hands of the Jews, who, from the first invasion of Spain by Musa, had ever been the firm allies and collaborators of the Arabs. Together they had participated in the dangers of the invasion; together they had shared its boundless success; together they had held in irreverent derision, nay, even in contempt, the woman-worshippers and polytheistic savages beyond the Pyrenees – as they mirthfully called those whose long-delayed vengeance they were in the end to feel; together they were expelled. Against such Jews as lingered behind the hideous persecutions of the Inquisition were directed. But in the days of their prosperity they maintained a merchant marine of more than a thousand ships. They had factories and consuls on the Tanaïs. With Constantinople alone they maintained a great trade; it ramified from the Black Sea and East Mediterranean into the interior of Asia; it reached the ports of India and China, and extended along the African coast as far as Madagascar. Even in these commercial affairs the singular genius of the Jew and Arabs shines forth. In the midst of the tenth century, when Europe was about in the same condition that Caffraria is now, enlightened Moors, like Abul Cassem, were writing treatises on the principles of trade and commerce. As on so many other occasions, on these affairs they have left their traces. The smallest weight they used in trade was the grain of barley, four of which were equal to one sweet pea, called in Arabic carat. We still use the grain as our unit of weight, and still speak of gold as being so many carats fine.

Obligations to the Khalifs of the West. Such were the Khalifs of the West; such their splendour, their luxury, their knowledge; such some of the obligations we are under to them – obligations which Christian Europe, with singular insincerity, has ever been fain to hide. The cry against the misbeliever has long outlived the Crusades. Considering the enchanting country over which they ruled, it was not without reason that they caused to be engraven on the public seal, "The servant of the Merciful rests contented in the decrees of God." What more, indeed, could Paradise give them? But, considering also the evil end of all this happiness and pomp, this learning, liberality, and wealth, we may well appreciate the solemn truth which these monarchs, in their day of pride and power, grandly wrote in the beautiful mosaics on their palace walls, an ever-recurring warning to him who owes dominion to the sword, "There is no conqueror but God."

Examination of Mohammedan science. The value of a philosophical or political system may be determined by its fruits. On this principle I examined in Vol. I., Chapter XII., the Italian system, estimating its religious merit from the biographies of the popes, which afford the proper criterion. In like manner, the intellectual state of the Mohammedan nations at successive epochs may be ascertained from what is its proper criterion, the contemporaneous scientific manifestation.

At the time when the Moorish influences in Spain began to exert a pressure on the Italian system, there were several scientific writers, fragments of whose works have descended to us. As an architect may judge of the skill of the ancient Egyptians in his art from a study of the Pyramids, so from these relics of Saracenic learning we may demonstrate the intellectual state of the Mohammedan people, though much of their work has been lost and more has been purposely destroyed.

Review of the works of Alhazen. Among such writers is Alhazen; his date was about A.D. 1100. It appears that he resided both in Spain and Egypt, but the details of his biography are very confused. Through his optical works, which have been translated into Latin, he is best known to Europe. He corrects the theory of vision. He was the first to correct the Greek misconception as to the nature of vision, showing that the rays of light come from external objects to the eye, and do not issue forth from the eye, and impinge on external things, as, up to his time, had been supposed. His explanation does not depend upon mere hypothesis or supposition, but is plainly based upon anatomical investigation as well as on geometrical discussion. Determines the function of the retina. He determines that the retina is the seat of vision, and that impressions made by light upon it are conveyed along the optic nerve to the brain. Though it might not be convenient, at the time when Alhazen lived, to make such an acknowledgment, no one could come to these conclusions, nor, indeed, know anything about these facts, unless he had been engaged in the forbidden practice of dissection. Explains single vision. With felicity he explains that we see single when we use both eyes, because of the formation of the visual images on symmetrical portions of the two retinas. To the modern physiologist the mere mention of such things is as significant as the occurrence of an arch in the interior of the pyramid is to the architect. But Alhazen shows that our sense of sight is by no means a trustworthy guide, and that there are illusions arising from the course which the rays of light may take when they suffer refraction or reflexion. It is in the discussion of one of these physical problems that his scientific greatness truly shines forth. Traces the course of a ray of light through the air. He is perfectly aware that the atmosphere decreases in density with increase of height; and from that consideration he shows that a ray of light, entering it obliquely, follows a curvilinear path which is concave toward the earth; and that, since the mind refers the position of an object to the direction in which the ray of light from it enters the eye, the result must be an illusion as respects the starry bodies; they appear to us, to use the Arabic term, nearer to the zenith than they actually are, and not in their true place. Astronomical refraction. We see them in the direction of the tangent to the curve of refraction as it reaches the eye. Hence also he shows that we actually see the stars, and the sun, and the moon before they have risen and after they have set – a wonderful illusion. He shows that in its passage through the air the curvature of a ray increases with the increasing density, and that its path does not depend on vapours that chance to be present, but on the variation of density in the medium. The horizontal sun and moon. To this refraction he truly refers the shortening, in their vertical diameter, of the horizontal sun and moon; to its variations he imputes the twinkling of the fixed stars. The apparent increase of size of the former bodies when they are in the horizon he refers to a mental deception, arising from the presence of intervening terrestrial objects. Explains the twilight. He shows that the effect of refraction is to shorten the duration of night and darkness by prolonging the visibility of the sun, and considering the reflecting action of the air, he deduces that beautiful explanation of the nature of twilight – the light that we perceive before the rising and after the setting of the sun – which we accept at the present time as true. Determines the height of the atmosphere. With extraordinary acuteness, he applies the principles with which he is dealing to the determination of the height of the atmosphere, deciding that its limit is nearly 58 ½ miles.

All this is very grand. Shall we compare it with the contemporaneous monk miracles and monkish philosophy of Europe? It would make a profound impression if communicated for the first time to a scientific society in our own age. Nor perhaps does his merit end here. If the Book of the Balance of Wisdom, for a translation of which we are indebted to M. Khanikoff, the Russian consul-general at Tabriz, be the production of Alhazen, of which there seems to be internal proof, it offers us evidence of a singular clearness in mechanical conception for which we should scarcely have been prepared, and, if it be not his, at all events it indisputably shows the scientific acquirements of his age. The weight of the air. In that book is plainly set forth the connexion between the weight of the atmosphere and its increasing density. The weight of the atmosphere was therefore understood before Torricelli. This author shows that a body will weigh differently in a rare and in a dense atmosphere; that its loss of weight will be greater in proportion as the air is more dense. Principles of hydrostatics. He considers the force with which plunged bodies will rise through heavier media in which they are immersed, and discusses the submergence of floating bodies, as ships upon the sea. He understands the doctrine of the centre of gravity. Theory of the balance. He applies it to the investigation of balances and steelyards, showing the relations between the centre of gravity and the centre of suspension – when those instruments will set and when they will vibrate. He recognizes gravity as a force; asserts that it diminishes with the distance; but falls into the mistake that the diminution is as the distance, and not as its square. Gravity; capillary attraction; the hydrometer. He considers gravity as terrestrial, and fails to perceive that it is universal – that was reserved for Newton. He knows correctly the relation between the velocities, spaces, and times of falling bodies, and has very distinct ideas of capillary attraction. He improves the construction of that old Alexandrian invention, the hydrometer – the instrument which, in a letter to his fair but pagan friend Hypatia, the good Bishop of Ptolemais, Synesius, six hundred years previously, requests her to have made for him in Alexandria, as he wishes to try the wines he is using, his health being a little delicate. Tables of specific gravities. The determinations of the densities of bodies, as given by Alhazen, approach very closely to our own; in the case of mercury they are even more exact than some of those of the last century. I join, as, doubtless, all natural philosophers will do, in the pious prayer of Alhazen, that, in the day of judgment, the All-Merciful will take pity on the soul of Abur-Raihân, because he was the first of the race of men to construct a table of specific gravities; and I will ask the same for Alhazen himself, since he was the first to trace the curvilinear path of a ray of light through the air. Though more than seven centuries part him from our times, the physiologists of this age may accept him as their compeer, since he received and defended the doctrine now forcing its way, of the progressive development of animal forms. The theory of development of organisms. He upheld the affirmation of those who said that man, in his progress, passes through a definite succession of states; not, however, "that he was once a bull, and was then changed to an ass, and afterwards into a horse, and after that into an ape, and finally became a man." This, he says, is only a misrepresentation by "common people" of what is really meant. The "common people" who withstood Alhazen have representatives among us, themselves the only example in the Fauna of the world of that non-development which they so loudly affirm. At the best they are only passing through some of the earlier forms of that series of transmutations to which the devout Mohammedan in the above quotation alludes.

The Arabians, with all this physical knowledge, do not appear to have been in possession of the thermometer, though they knew the great importance of temperature measures, employing the areometer for that purpose. They had detected the variation in density of liquids by heat, but not the variation in volume. In their measures of time they were more successful; they had several kinds of clepsydras. A balance clepsydra is described in the work from which I am quoting. The pendulum clock. But it was their great astronomer, Ebn Junis, who accomplished the most valuable of all chronometric improvements. He first applied the pendulum to the measure of time. Laplace, in the fifth note to his Systeme du Monde, avails himself of the observations of this philosopher, with those of Albategnius and other Arabians, as incontestable proof of the diminution of the eccentricity of the earth's orbit. Astronomical works of Ebn Junis. He states, moreover, that the observation of Ebn Junis of the obliquity of the ecliptic, properly corrected for parallax and refraction, gives for the year A.D. 1000 a result closely approaching to the theoretical. He also mentions another observation of Ebn Junis, October 31, A.D. 1007, as of much importance in reference to the great inequalities of Jupiter and Saturn. The Arabic numerals. I have already remarked that, in the writings of this great Arabian, the Arabic numerals and our common arithmetical processes are currently used. From Africa and Spain they passed into Italy, finding ready acceptance among commercial men, who recognised at once their value, and, as William of Malmesbury says, being a wonderful relief to the "sweating calculators;" an epithet of which the correctness will soon appear to any one who will try to do a common multiplication or division problem by the aid of the old Roman numerals. It is said that Gerbert – Pope Sylvester – was the first to introduce a knowledge of them into Europe; he had learned them at the Mohammedan university of Cordova. It is in allusion to the cipher, which follows the 9, but which, added to any of the other digits, increases by tenfold its power, that, in a letter to his patron, the Emperor Otho III., with humility he playfully but truly says, "I am like the last of all the numbers."

Arabian philosophy. The overthrow of the Roman by the Arabic numerals foreshadowed the result of a far more important – a political – contest between those rival names. But, before showing how the Arabian intellect pressed upon Rome, and the convulsive struggles of desperation which Rome made to resist it, I must for a moment consider the former under another point of view, and speak of Saracen philosophy. The writings of Algazzali. And here Algazzali shall be my guide. He was born A.D. 1058.

Let us hear him speak for himself. He is relating his attempt to detach himself from the opinions which he had imbibed in his childhood: "I said to myself, 'My aim is simply to know the truth of things; consequently, it is indispensable for me to ascertain what is knowledge.' Now it was evident to me that certain knowledge must be that which explains the object to be known in such a manner that no doubt can remain, so that in future all error and conjecture respecting it must be impossible. The certitude of knowledge. Not only would the understanding then need no efforts to be convinced of certitude, but security against error is in such close connexion with knowledge, that, even were an apparent proof of falsehood to be brought forward, it would cause no doubt, because no suspicion of error would be possible. Thus, when I have acknowledged ten to be more than three, if any one were to say, 'On the contrary, three is more than ten, and to prove the truth of my assertion, I will change this rod into a serpent,' and if he were to change it, my conviction of his error would remain unshaken. His manœuvre would only produce in me admiration for his ability. I should not doubt my own knowledge.

"Then was I convinced that knowledge which I did not possess in this manner, and respecting which I had not this certainty, could inspire me with neither confidence nor assurance; and no knowledge without assurance deserves the name of knowledge.

"Having examined the state of my own knowledge, I found it divested of all that could be said to have these qualities, unless perceptions of the senses and irrefragable principles were to be considered such. Fallibility of the senses. I then said to myself, 'Now, having fallen into this despair, the only hope of acquiring incontestable convictions is by the perceptions of the senses and by necessary truths.' Their evidence seemed to me to be indubitable. I began, however, to examine the objects of sensation and speculation, to see if they possibly could admit of doubt. Then doubts crowded upon me in such numbers that my incertitude became complete. Whence results the confidence I have in sensible things? The strongest of all our senses is sight; and yet, looking at a shadow, and perceiving it to be fixed and immovable, we judge it to be deprived of movement; nevertheless, experience teaches us that, when we return to the same place an hour after, the shadow is displaced, for it does not vanish suddenly, but gradually, little by little, so as never to be at rest. If we look at the stars, they seem to be as small as money-pieces; but mathematical proofs convince us that they are larger than the earth. These and other things are judged by the senses, but rejected by reason as false. I abandoned the senses, therefore, having seen all my confidence in their truth shaken.

"'Perhaps,' said I, 'there is no assurance but in the notions of reason, that is to say, first principles, as that ten is more than three; the same thing cannot have been created and yet have existed from all eternity; to exist and not to exist at the same time is impossible.'

Fallibility of reason. "Upon this the senses replied, 'What assurance have you that your confidence in reason is not of the same nature as your confidence in us? When you relied on us, reason stepped in and gave us the lie; had not reason been there, you would have continued to rely on us. Well, may there not exist some other judge superior to reason, who, if he appeared, would refute the judgments of reason in the same way that reason refuted us? The non-appearance of such a judge is no proof of his non-existence.'

The nature of dreams. "I strove in vain to answer the objection, and my difficulties increased when I came to reflect on sleep. I said to myself, 'During sleep, you give to visions a reality and consistence, and you have no suspicion of their untruth. On awakening, you are made aware that they were nothing but visions. What assurance have you that all you feel and know when you are awake does actually exist? It is all true as respects your condition at that moment; but it is nevertheless possible that another condition should present itself which should be to your awakened state that which to your awakened state is now to you sleep; so that, as respects this higher condition, your waking is but sleep.'"

It would not be possible to find in any European work a clearer statement of the scepticism to which philosophy leads than what is thus given by this Arabian. Indeed, it is not possible to put the argument in a more effective way. His perspicuity is in singular contrast with the obscurity of many metaphysical writers.

Intellectual despair. "Reflecting on my situation, I found myself bound to this world by a thousand ties, temptations assailing me on all sides. I then examined my actions. The best were those relating to instruction and education, and even there I saw myself given up to unimportant sciences, all useless in another world. Reflecting on the aim of my teaching, I found it was not pure in the sight of the Lord. I saw that all my efforts were directed toward the acquisition of glory to myself. Having, therefore, distributed my wealth, I left Bagdad and retired into Syria, where I remained two years in solitary struggle with my soul, combating my passions, and exercising myself, in the purification of my heart and in preparation for the other world."

This is a very beautiful picture of the mental struggles and the actions of a truthful and earnest man. In all this the Christian philosopher can sympathize with the devout Mohammedan. After all, they are not very far apart. Algazzali is not the only one to whom such thoughts have occurred, but he has found words to tell his experience better than any other man. And what is the conclusion at which he arrives? Algazzali's ages of man. The life of man, he says, is marked by three stages: "the first, or infantile stage, is that of pure sensation; the second, which begins at the age of seven, is that of understanding; the third is that of reason, by means of which the intellect perceives the necessary, the possible, the absolute, and all those higher objects which transcend the understanding. But after this there is a fourth stage, when another eye is opened, by which man perceives things hidden from others – perceives all that will be – perceives the things that escape the perceptions of reason, as the objects of reason escape the understanding, and as the objects of the understanding escape the sensitive faculty. This is prophetism." Algazzali thus finds a philosophical basis for the rule of life, and reconciles religion and philosophy.

And now I have to turn from Arabian civilized life, its science, its philosophy, to another, a repulsive state of things. With reluctance I come back to the Italian system, defiling the holy name of religion with its intrigues, its bloodshed, its oppression of human thought, its hatred of intellectual advancement. Renewal of the operation of Mohammedan influences. Especially I have now to direct attention to two countries, the scenes of important events – countries in which the Mohammedan influences began to take effect and to press upon Rome. These are the South of France and Sicily.

Innocent III. had been elected pope at the early age of thirty-seven years, A.D. 1198. The papal power had reached its culminating point. The weapons of the Church had attained their utmost force. In Italy, in Germany, in France and England, interdicts and excommunications vindicated the pontifical authority, as in the cases of the Duke of Ravenna, the Emperor Otho, Philip Augustus of France, King John of England. Interference of Innocent III. in France. In each of these cases it was not for the sake of sustaining great moral principles or the rights of humanity that the thunder was launched – it was in behalf of temporary political interests; interests that, in Germany, were sustained at the cost of a long war, and cemented by assassination; in France, strengthened by the well-tried device of an intervention in a matrimonial broil – the domestic quarrel of the king and queen about Agnes of Meran. "Ah! happy Saladin!" said the insulted Philip, when his kingdom was put under interdict; "he has no pope above him. I too will turn Mohammedan."

In Spain and Portugal. So, likewise, in Spain, Innocent interfered in the matrimonial life of the King of Leon. The remorseless venality of the papal government was felt in every direction. Portugal had already been advanced to the dignity of a kingdom on payment of an annual tribute to Rome. The King of Aragon held his kingdom as feudatory to the pope.