4. The passage 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 classes 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 manuscripts, 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 passage as it is.
Forms of the Numerals, Largely from Works on the Abacus[[351]]
| a [[352]] | |
| b [[353]] | |
| c [[354]] | |
| d [[355]] | |
| e [[356]] | |
| f [[357]] | |
| g [[358]] | |
| h [[359]] | |
| i [[360]] |
Sir E. Clive Bayley has added[[361]] a further reason for believing them spurious, namely that the 4 is not of the Nānā Ghāt 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 manuscripts 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
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 class, writers; (4) there is every reason a priori for believing that the ġobār 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 manuscript 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 documentary evidence is not at all strange, in view of all of the circumstances.