Читать книгу The Hindu-Arabic Numerals - Louis Charles Karpinski - Страница 9

Table of Contents

Numerals
Aśoka[80]
Śaka[81]
Aśoka[82]
Nāgarī[83]
Nasik[84]
Kṣatrapa[85]
Kuṣana[86]
Gupta[87]
Valhabī[88]
Nepal[89]
Kaliṅga[90]
Vākāṭaka[91]

[Most of these numerals are given by Bühler, loc. cit., Tafel IX.]

With respect to these numerals it should first be noted that no zero appears in the table, and as a matter of fact none existed in any of the cases cited. It was therefore impossible to have any place value, and the numbers like twenty, thirty, and other multiples of ten, one hundred, and so on, required separate symbols except where they were written out in words. The ancient Hindus had no less than twenty of these symbols,^[92] a number that was afterward greatly increased. The following are examples of their method of indicating certain numbers between one hundred and one thousand:

^[93] for 174

^[94] for 191

^[95] for 269

^[96] for 252

^[97] for 400

^[98] for 356

To these may be added the following numerals below one hundred, similar to those in the table:

^[99] for 90

^[100] for 70

We have thus far spoken of the Kharoṣṭhī and Brāhmī numerals, and it remains to mention the third type, the word and letter forms. These are, however, so closely connected with the perfecting of the system by the invention of the zero that they are more appropriately considered in the next chapter, particularly as they have little relation to the problem of the origin of the forms known as the Arabic.

Having now examined types of the early forms it is appropriate to turn our attention to the question of their origin. As to the first three there is no question. The or is simply one stroke, or one stick laid down by the computer. The or represents two strokes or two sticks, and so for the and . From some primitive came the two of Egypt, of Rome, of early Greece, and of various other civilizations. It appears in the three Egyptian numeral systems in the following forms:

Hieroglyphic

Hieratic

Demotic

The last of these is merely a cursive form as in the Arabic , which becomes our 2 if tipped through a right angle. From some primitive came the Chinese symbol, which is practically identical with the symbols found commonly in India from 150 B.C. to 700 A.D. In the cursive form it becomes , and this was frequently used for two in Germany until the 18th century. It finally went into the modern form 2, and the in the same way became our 3.

There is, however, considerable ground for interesting speculation with respect to these first three numerals. The earliest Hindu forms were perpendicular. In the Nānā Ghāt inscriptions they are vertical. But long before either the Aśoka or the Nānā Ghāt inscriptions the Chinese were using the horizontal forms for the first three numerals, but a vertical arrangement for four.^[101] Now where did China get these forms? Surely not from India, for she had them, as her monuments and literature^[102] show, long before the Hindus knew them. The tradition is that China brought her civilization around the north of Tibet, from Mongolia, the primitive habitat being Mesopotamia, or possibly the oases of Turkestan. Now what numerals did Mesopotamia use? The Babylonian system, simple in its general principles but very complicated in many of its details, is now well known.^[103] In particular, one, two, and three were represented by vertical arrow-heads. Why, then, did the Chinese write theirs horizontally? The problem now takes a new interest when we find that these Babylonian forms were not the primitive ones of this region, but that the early Sumerian forms were horizontal.^[104]

What interpretation shall be given to these facts? Shall we say that it was mere accident that one people wrote "one" vertically and that another wrote it horizontally? This may be the case; but it may also be the case that the tribal migrations that ended in the Mongol invasion of China started from the Euphrates while yet the Sumerian civilization was prominent, or from some common source in Turkestan, and that they carried to the East the primitive numerals of their ancient home, the first three, these being all that the people as a whole knew or needed. It is equally possible that these three horizontal forms represent primitive stick-laying, the most natural position of a stick placed in front of a calculator being the horizontal one. When, however, the cuneiform writing developed more fully, the vertical form may have been proved the easier to make, so that by the time the migrations to the West began these were in use, and from them came the upright forms of Egypt, Greece, Rome, and other Mediterranean lands, and those of Aśoka's time in India. After Aśoka, and perhaps among the merchants of earlier centuries, the horizontal forms may have come down into India from China, thus giving those of the Nānā Ghāt cave and of later inscriptions. This is in the realm of speculation, but it is not improbable that further epigraphical studies may confirm the hypothesis.

As to the numerals above three there have been very many conjectures. The figure one of the Demotic looks like the one of the Sanskrit, the two (reversed) like that of the Arabic, the four has some resemblance to that in the Nasik caves, the five (reversed) to that on the Kṣatrapa coins, the nine to that of the Kuṣana inscriptions, and other points of similarity have been imagined. Some have traced resemblance between the Hieratic five and seven and those of the Indian inscriptions. There have not, therefore, been wanting those who asserted an Egyptian origin for these numerals.^[105] There has already been mentioned the fact that the Kharoṣṭhī numerals were formerly known as Bactrian, Indo-Bactrian, and Aryan. Cunningham^[106] was the first to suggest that these numerals were derived from the alphabet of the Bactrian civilization of Eastern Persia, perhaps a thousand years before our era, and in this he was supported by the scholarly work of Sir E. Clive Bayley,^[107] who in turn was followed by Canon Taylor.^[108] The resemblance has not proved convincing, however, and Bayley's drawings have been criticized as being affected by his theory. The following is part of the hypothesis:^[109]

Numeral	Hindu	Bactrian	Sanskrit
4		= ch	chatur, Lat. quattuor
5		= p	pancha, Gk. πέντε
6		= s	ṣaṣ
7		= ṣ	sapta
(the s and ṣ are interchanged as occasionally in N. W. India)

Bühler^[110] rejects this hypothesis, stating that in four cases (four, six, seven, and ten) the facts are absolutely against it.

While the relation to ancient Bactrian forms has been generally doubted, it is agreed that most of the numerals resemble Brāhmī letters, and we would naturally expect them to be initials.^[111] But, knowing the ancient pronunciation of most of the number names,^[112] we find this not to be the case. We next fall back upon the hypothesis that they represent the order of letters^[113] in the ancient alphabet. From what we know of this order, however, there seems also no basis for this assumption. We have, therefore, to confess that we are not certain that the numerals were alphabetic at all, and if they were alphabetic we have no evidence at present as to the basis of selection. The later forms may possibly have been alphabetical expressions of certain syllables called akṣaras, which possessed in Sanskrit fixed numerical values,^[114] but this is equally uncertain with the rest. Bayley also thought^[115] that some of the forms were Phœnician, as notably the use of a circle for twenty, but the resemblance is in general too remote to be convincing.

There is also some slight possibility that Chinese influence is to be seen in certain of the early forms of Hindu numerals.^[116]

More absurd is the hypothesis of a Greek origin, supposedly supported by derivation of the current symbols from the first nine letters of the Greek alphabet.^[117] This difficult feat is accomplished by twisting some of the letters, cutting off, adding on, and effecting other changes to make the letters fit the theory. This peculiar theory was first set up by Dasypodius^[118] (Conrad Rauhfuss), and was later elaborated by Huet.^[119]

A bizarre derivation based upon early Arabic (c. 1040 A.D.) sources is given by Kircher in his work^[120] on number mysticism. He quotes from Abenragel,^[121] giving the Arabic and a Latin translation^[122] and stating that the ordinary Arabic forms are derived from sectors of a circle, .

Out of all these conflicting theories, and from all the resemblances seen or imagined between the numerals of the West and those of the East, what conclusions are we prepared to draw as the evidence now stands? Probably none that is satisfactory. Indeed, upon the evidence at hand we might properly feel that everything points to the numerals as being substantially indigenous to India. And why should this not be the case? If the king Srong-tsan-Gampo (639 A.D.), the founder of Lhāsa,^[123] could have set about to devise a new alphabet for Tibet, and if the Siamese, and the Singhalese, and the Burmese, and other peoples in the East, could have created alphabets of their own, why should not the numerals also have been fashioned by some temple school, or some king, or some merchant guild? By way of illustration, there are shown in the table on page 36 certain systems of the East, and while a few resemblances are evident, it is also evident that the creators of each system endeavored to find original forms that should not be found in other systems. This, then, would seem to be a fair interpretation of the evidence. A human mind cannot readily create simple forms that are absolutely new; what it fashions will naturally resemble what other minds have fashioned, or what it has known through hearsay or through sight. A circle is one of the world's common stock of figures, and that it should mean twenty in Phœnicia and in India is hardly more surprising than that it signified ten at one time in Babylon.^[124] It is therefore quite probable that an extraneous origin cannot be found for the very sufficient reason that none exists.

Of absolute nonsense about the origin of the symbols which we use much has been written. Conjectures, however, without any historical evidence for support, have no place in a serious discussion of the gradual evolution of the present numeral forms.^[125]