The Hindu-Arabic Numerals Part 5

The genuineness of the arithmetic and the treatise on music is generally recognized, but the geometry, which contains the Hindu numerals with the zero, is under suspicion.[337] There are plenty of supporters of the idea that Boethius knew the numerals and included them in this book,[338] and on the other hand there are as many who {85} feel that the geometry, or at least the part mentioning the numerals, is spurious.[339] The argument of those who deny the authenticity of the particular pa.s.sage in question may briefly be stated thus:

1. The falsification of texts has always been the subject of complaint. It was so with the Romans,[340] it was common in the Middle Ages,[341] and it is much more prevalent {86} to-day than we commonly think. We have but to see how every hymn-book compiler feels himself authorized to change at will the cla.s.sics of our language, and how unknown editors have mutilated Shakespeare, to see how much more easy it was for medieval scribes to insert or eliminate paragraphs without any protest from critics.[342]

2. If Boethius had known these numerals he would have mentioned them in his arithmetic, but he does not do so.[343]

3. If he had known them, and had mentioned them in any of his works, his contemporaries, disciples, and successors would have known and mentioned them. But neither Capella (c. 475)[344] nor any of the numerous medieval writers who knew the works of Boethius makes any reference to the system.[345]

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4. The pa.s.sage in question has all the appearance of an interpolation by some scribe. Boethius is speaking of angles, in his work on geometry, when the text suddenly changes to a discussion of cla.s.ses of numbers.[346] This is followed by a chapter in explanation of the abacus,[347] in which are described those numeral forms which are called _apices_ or _caracteres_.[348] The forms[349] of these characters vary in different ma.n.u.scripts, but in general are about as shown on page 88. They are commonly written with the 9 at the left, decreasing to the unit at the right, numerous writers stating that this was because they were derived from Semitic sources in which the direction of writing is the opposite of our own. This practice continued until the sixteenth century.[350] The writer then leaves the subject entirely, using the Roman numerals for the rest of his discussion, a proceeding so foreign to the method of Boethius as to be inexplicable on the hypothesis of authenticity. Why should such a scholarly writer have given them with no mention of their origin or use?

Either he would have mentioned some historical interest attaching to them, or he would have used them in some discussion; he certainly would not have left the pa.s.sage as it is.

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FORMS OF THE NUMERALS, LARGELY FROM WORKS ON THE ABACUS[351]

a[352] [Ill.u.s.tration]

b[353] [Ill.u.s.tration]

c[354] [Ill.u.s.tration]

d[355] [Ill.u.s.tration]

e[356] [Ill.u.s.tration]

f[357] [Ill.u.s.tration]

g[358] [Ill.u.s.tration]

h[359] [Ill.u.s.tration]

i[360] [Ill.u.s.tration]

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Sir E. Clive Bayley has added[361] a further reason for believing them spurious, namely that the 4 is not of the N[=a]n[=a] Gh[=a]t type, but of the Kabul form which the Arabs did not receive until 776;[362] so that it is not likely, even if the characters were known in Europe in the time of Boethius, that this particular form was recognized. It is worthy of mention, also, that in the six abacus forms from the chief ma.n.u.scripts as given by Friedlein,[363] each contains some form of zero, which symbol probably originated in India about this time or later. It could hardly have reached Europe so soon.

As to the fourth question, Did Boethius probably know the numerals? It seems to be a fair conclusion, according to our present evidence, that (1) Boethius might very easily have known these numerals without the zero, but, (2) there is no reliable evidence that he did know them. And just as Boethius might have come in contact with them, so any other inquiring mind might have done so either in his time or at any time before they definitely appeared in the tenth century. These centuries, five in number, represented the darkest of the Dark Ages, and even if these numerals were occasionally met and studied, no trace of them would be likely to show itself in the {90} literature of the period, unless by chance it should get into the writings of some man like Alcuin. As a matter of fact, it was not until the ninth or tenth century that there is any tangible evidence of their presence in Christendom. They were probably known to merchants here and there, but in their incomplete state they were not of sufficient importance to attract any considerable attention.

As a result of this brief survey of the evidence several conclusions seem reasonable: (1) commerce, and travel for travel's sake, never died out between the East and the West; (2) merchants had every opportunity of knowing, and would have been unreasonably stupid if they had not known, the elementary number systems of the peoples with whom they were trading, but they would not have put this knowledge in permanent written form; (3) wandering scholars would have known many and strange things about the peoples they met, but they too were not, as a cla.s.s, writers; (4) there is every reason a priori for believing that the [.g]ob[=a]r numerals would have been known to merchants, and probably to some of the wandering scholars, long before the Arabs conquered northern Africa; (5) the wonder is not that the Hindu-Arabic numerals were known about 1000 A.D., and that they were the subject of an elaborate work in 1202 by Fibonacci, but rather that more extended ma.n.u.script evidence of their appearance before that time has not been found. That they were more or less known early in the Middle Ages, certainly to many merchants of Christian Europe, and probably to several scholars, but without the zero, is hardly to be doubted. The lack of doc.u.mentary evidence is not at all strange, in view of all of the circ.u.mstances.

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CHAPTER VI

THE DEVELOPMENT OF THE NUMERALS AMONG THE ARABS

If the numerals had their origin in India, as seems most probable, when did the Arabs come to know of them? It is customary to say that it was due to the influence of Mohammedanism that learning spread through Persia and Arabia; and so it was, in part. But learning was already respected in these countries long before Mohammed appeared, and commerce flourished all through this region. In Persia, for example, the reign of Khosr[=u]

Nu['s][=i]rw[=a]n,[364] the great contemporary of Justinian the law-maker, was characterized not only by an improvement in social and economic conditions, but by the cultivation of letters. Khosr[=u] fostered learning, inviting to his court scholars from Greece, and encouraging the introduction of culture from the West as well as from the East. At this time Aristotle and Plato were translated, and portions of the _Hito-pad[=e]['s]a_, or Fables of Pilpay, were rendered from the Sanskrit into Persian. All this means that some three centuries before the great intellectual ascendancy of Bagdad a similar fostering of learning was taking place in Persia, and under pre-Mohammedan influences.

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The first definite trace that we have of the introduction of the Hindu system into Arabia dates from 773 A.D.,[365] when an Indian astronomer visited the court of the caliph, bringing with him astronomical tables which at the caliph's command were translated into Arabic by Al-Faz[=a]r[=i].[366] Al-Khow[=a]razm[=i] and [H.]abash (A[h.]med ibn 'Abdall[=a]h, died c. 870) based their well-known tables upon the work of Al-F[=a]zar[=i]. It may be a.s.serted as highly probable that the numerals came at the same time as the tables. They were certainly known a few decades later, and before 825 A.D., about which time the original of the _Algoritmi de numero Indorum_ was written, as that work makes no pretense of being the first work to treat of the Hindu numerals.

The three writers mentioned cover the period from the end of the eighth to the end of the ninth century. While the historians Al-Ma['s]'[=u]d[=i] and Al-B[=i]r[=u]n[=i] follow quite closely upon the men mentioned, it is well to note again the Arab writers on Hindu arithmetic, contemporary with Al-Khow[=a]razm[=i], who were mentioned in chapter I, viz. Al-Kind[=i], Sened ibn 'Al[=i], and Al-[S.][=u]f[=i].

For over five hundred years Arabic writers and others continued to apply to works on arithmetic the name "Indian." In the tenth century such writers are 'Abdall[=a]h ibn al-[H.]asan, Ab[=u] 'l-Q[=a]sim[367] (died 987 A.D.) of Antioch, and Mo[h.]ammed ibn 'Abdall[=a]h, Ab[=u] Na[s.]r[368] (c. 982), of Kalw[=a]d[=a] near Bagdad. Others of the same period or {93} earlier (since they are mentioned in the _Fihrist_,[369] 987 A.D.), who explicitly use the word "Hindu" or "Indian," are Sin[=a]n ibn al-Fat[h.][370] of [H.]arr[=a]n, and Ahmed ibn 'Omar, al-Kar[=a]b[=i]s[=i].[371] In the eleventh century come Al-B[=i]r[=u]n[=i][372] (973-1048) and 'Ali ibn A[h.]med, Ab[=u] 'l-[H.]asan, Al-Nasaw[=i][373] (c. 1030). The following century brings similar works by Ish[=a]q ibn Y[=u]suf al-[S.]ardaf[=i][374]

and Sam[=u]'[=i]l ibn Ya[h.]y[=a] ibn 'Abb[=a]s al-Ma[.g]reb[=i]

al-Andalus[=i][375] (c. 1174), and in the thirteenth century are 'Abdallat[=i]f ibn Y[=u]suf ibn Mo[h.]ammed, Muwaffaq al-D[=i]n Ab[=u]

Mo[h.]ammed al-Ba[.g]d[=a]d[=i][376] (c. 1231), and Ibn al-Bann[=a].[377]

The Greek monk Maximus Planudes, writing in the first half of the fourteenth century, followed the Arabic usage in calling his work _Indian Arithmetic_.[378] There were numerous other Arabic writers upon arithmetic, as that subject occupied one of the high places among the sciences, but most of them did not feel it necessary to refer to the origin of the symbols, the knowledge of which might well have been taken for granted.

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One doc.u.ment, cited by Woepcke,[379] is of special interest since it shows at an early period, 970 A.D., the use of the ordinary Arabic forms alongside the [.g]ob[=a]r. The t.i.tle of the work is _Interesting and Beautiful Problems on Numbers_ copied by A[h.]med ibn Mo[h.]ammed ibn 'Abdaljal[=i]l, Ab[=u] Sa'[=i]d, al-Sijz[=i],[380] (951-1024) from a work by a priest and physician, Na[z.][=i]f ibn Yumn,[381] al-Qa.s.s (died c.

990). Suter does not mention this work of Na[z.][=i]f.

The second reason for not ascribing too much credit to the purely Arab influence is that the Arab by himself never showed any intellectual strength. What took place after Mo[h.]ammed had lighted the fire in the hearts of his people was just what always takes place when different types of strong races blend,--a great renaissance in divers lines. It was seen in the blending of such types at Miletus in the time of Thales, at Rome in the days of the early invaders, at Alexandria when the Greek set firm foot on Egyptian soil, and we see it now when all the nations mingle their vitality in the New World. So when the Arab culture joined with the Persian, a new civilization rose and flourished.[382] The Arab influence came not from its purity, but from its intermingling with an influence more cultured if less virile.

As a result of this interactivity among peoples of diverse interests and powers, Mohammedanism was to the world from the eighth to the thirteenth century what Rome and Athens and the Italo-h.e.l.lenic influence generally had {95} been to the ancient civilization. "If they did not possess the spirit of invention which distinguished the Greeks and the Hindus, if they did not show the perseverance in their observations that characterized the Chinese astronomers, they at least possessed the virility of a new and victorious people, with a desire to understand what others had accomplished, and a taste which led them with equal ardor to the study of algebra and of poetry, of philosophy and of language."[383]

It was in 622 A.D. that Mo[h.]ammed fled from Mecca, and within a century from that time the crescent had replaced the cross in Christian Asia, in Northern Africa, and in a goodly portion of Spain. The Arab empire was an ellipse of learning with its foci at Bagdad and Cordova, and its rulers not infrequently took pride in demanding intellectual rather than commercial treasure as the result of conquest.[384]

It was under these influences, either pre-Mohammedan or later, that the Hindu numerals found their way to the North. If they were known before Mo[h.]ammed's time, the proof of this fact is now lost. This much, however, is known, that in the eighth century they were taken to Bagdad. It was early in that century that the Mohammedans obtained their first foothold in northern India, thus foreshadowing an epoch of supremacy that endured with varied fortunes until after the golden age of Akbar the Great (1542-1605) and Shah Jehan. They also conquered Khora.s.san and Afghanistan, so that the learning and the commercial customs of India at once found easy {96} access to the newly-established schools and the bazaars of Mesopotamia and western Asia. The particular paths of conquest and of commerce were either by way of the Khyber Pa.s.s and through Kabul, Herat and Khora.s.san, or by sea through the strait of Ormuz to Basra (Busra) at the head of the Persian Gulf, and thence to Bagdad. As a matter of fact, one form of Arabic numerals, the one now in use by the Arabs, is attributed to the influence of Kabul, while the other, which eventually became our numerals, may very likely have reached Arabia by the other route. It is in Bagdad,[385] D[=a]r al-Sal[=a]m--"the Abode of Peace," that our special interest in the introduction of the numerals centers. Built upon the ruins of an ancient town by Al-Man[s.][=u]r[386] in the second half of the eighth century, it lies in one of those regions where the converging routes of trade give rise to large cities.[387] Quite as well of Bagdad as of Athens might Cardinal Newman have said:[388]

"What it lost in conveniences of approach, it gained in its neighborhood to the traditions of the mysterious East, and in the loveliness of the region in which it lay. Hither, then, as to a sort of ideal land, where all archetypes of the great and the fair were found in substantial being, and all departments of truth explored, and all diversities of intellectual power exhibited, where taste and philosophy were majestically enthroned as in a royal court, where there was no sovereignty but that of mind, and no n.o.bility but that of genius, where professors were {97} rulers, and princes did homage, thither flocked continually from the very corners of the _orbis terrarum_ the many-tongued generation, just rising, or just risen into manhood, in order to gain wisdom." For here it was that Al-Man[s.][=u]r and Al-M[=a]m[=u]n and H[=a]r[=u]n al-Rash[=i]d (Aaron the Just) made for a time the world's center of intellectual activity in general and in the domain of mathematics in particular.[389] It was just after the _Sindhind_ was brought to Bagdad that Mo[h.]ammed ibn M[=u]s[=a] al-Khow[=a]razm[=i], whose name has already been mentioned,[390] was called to that city. He was the most celebrated mathematician of his time, either in the East or West, writing treatises on arithmetic, the sundial, the astrolabe, chronology, geometry, and algebra, and giving through the Latin transliteration of his name, _algoritmi_, the name of algorism to the early arithmetics using the new Hindu numerals.[391] Appreciating at once the value of the position system so recently brought from India, he wrote an arithmetic based upon these numerals, and this was translated into Latin in the time of Adelhard of Bath (c. 1180), although possibly by his contemporary countryman Robert Cestrensis.[392] This translation was found in Cambridge and was published by Boncompagni in 1857.[393]

Contemporary with Al-Khow[=a]razm[=i], and working also under Al-M[=a]m[=u]n, was a Jewish astronomer, Ab[=u] 'l-[T.]eiyib, {98} Sened ibn 'Al[=i], who is said to have adopted the Mohammedan religion at the caliph's request. He also wrote a work on Hindu arithmetic,[394] so that the subject must have been attracting considerable attention at that time.

Indeed, the struggle to have the Hindu numerals replace the Arabic did not cease for a long time thereafter. 'Al[=i] ibn A[h.]med al-Nasaw[=i], in his arithmetic of c. 1025, tells us that the symbolism of number was still unsettled in his day, although most people preferred the strictly Arabic forms.[395]

We thus have the numerals in Arabia, in two forms: one the form now used there, and the other the one used by Al-Khow[=a]razm[=i]. The question then remains, how did this second form find its way into Europe? and this question will be considered in the next chapter.

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CHAPTER VII

THE DEFINITE INTRODUCTION OF THE NUMERALS INTO EUROPE

It being doubtful whether Boethius ever knew the Hindu numeral forms, certainly without the zero in any case, it becomes necessary now to consider the question of their definite introduction into Europe. From what has been said of the trade relations between the East and the West, and of the probability that it was the trader rather than the scholar who carried these numerals from their original habitat to various commercial centers, it is evident that we shall never know when they first made their inconspicuous entrance into Europe. Curious customs from the East and from the tropics,--concerning games, social peculiarities, oddities of dress, and the like,--are continually being related by sailors and traders in their resorts in New York, London, Hamburg, and Rotterdam to-day, customs that no scholar has yet described in print and that may not become known for many years, if ever. And if this be so now, how much more would it have been true a thousand years before the invention of printing, when learning was at its lowest ebb. It was at this period of low esteem of culture that the Hindu numerals undoubtedly made their first appearance in Europe.

There were many opportunities for such knowledge to reach Spain and Italy.

In the first place the Moors went into Spain as helpers of a claimant of the throne, and {100} remained as conquerors. The power of the Goths, who had held Spain for three centuries, was shattered at the battle of Jerez de la Frontera in 711, and almost immediately the Moors became masters of Spain and so remained for five hundred years, and masters of Granada for a much longer period. Until 850 the Christians were absolutely free as to religion and as to holding political office, so that priests and monks were not infrequently skilled both in Latin and Arabic, acting as official translators, and naturally reporting directly or indirectly to Rome. There was indeed at this time a complaint that Christian youths cultivated too a.s.siduously a love for the literature of the Saracen, and married too frequently the daughters of the infidel.[396] It is true that this happy state of affairs was not permanent, but while it lasted the learning and the customs of the East must have become more or less the property of Christian Spain. At this time the [.g]ob[=a]r numerals were probably in that country, and these may well have made their way into Europe from the schools of Cordova, Granada, and Toledo.

Furthermore, there was abundant opportunity for the numerals of the East to reach Europe through the journeys of travelers and amba.s.sadors. It was from the records of Suleim[=a]n the Merchant, a well-known Arab trader of the ninth century, that part of the story of Sindb[=a]d the Sailor was taken.[397] Such a merchant would have been particularly likely to know the numerals of the people whom he met, and he is a type of man that may well have taken such symbols to European markets. A little later, {101} Ab[=u]

'l-[H.]asan 'Al[=i] al-Mas'[=u]d[=i] (d. 956) of Bagdad traveled to the China Sea on the east, at least as far south as Zanzibar, and to the Atlantic on the west,[398] and he speaks of the nine figures with which the Hindus reckoned.[399]

There was also a Bagdad merchant, one Ab[=u] 'l-Q[=a]sim 'Obeidall[=a]h ibn A[h.]med, better known by his Persian name Ibn Khord[=a][d.]beh,[400] who wrote about 850 A.D. a work ent.i.tled _Book of Roads and Provinces_[401] in which the following graphic account appears:[402] "The Jewish merchants speak Persian, Roman (Greek and Latin), Arabic, French, Spanish, and Slavic. They travel from the West to the East, and from the East to the West, sometimes by land, sometimes by sea. They take ship from France on the Western Sea, and they voyage to Farama (near the ruins of the ancient Pelusium); there they transfer their goods to caravans and go by land to Colzom (on the Red Sea). They there reembark on the Oriental (Red) Sea and go to Hejaz and to Jiddah, and thence to the Sind, India, and China.

Returning, they bring back the products of the oriental lands.... These journeys are also made by land. The merchants, leaving France and Spain, cross to Tangier and thence pa.s.s through the African provinces and Egypt.

They then go to Ramleh, visit Damascus, Kufa, Bagdad, and Basra, penetrate into Ahwaz, Fars, Kerman, Sind, and thus reach India and China." Such travelers, about 900 A.D., must necessarily have spread abroad a knowledge of all number {102} systems used in recording prices or in the computations of the market. There is an interesting witness to this movement, a cruciform brooch now in the British Museum. It is English, certainly as early as the eleventh century, but it is inlaid with a piece of paste on which is the Mohammedan inscription, in Kufic characters, "There is no G.o.d but G.o.d." How did such an inscription find its way, perhaps in the time of Alcuin of York, to England? And if these Kufic characters reached there, then why not the numeral forms as well?