November 17, 1916] 



SCIENCE 



715 



all dated monuments had their origin within 

 400 years of each other. The Maya had an 

 accurate system of chronology, but the diffi- 

 culty lies in establishing a correlation between 

 their chronology and our own. Authorities 

 differ on this point. Take one of the monu- 

 ments, called Stela 9, in the ancient town of 

 Copan in Honduras. Mr. Morley summarizes 

 the various conclusions regarding the date for 

 Stela 9 thus : 2 



Professor Seler's date of 1255 B.C. for this is by 

 far the oldest; Mr. Bowditch's date, a.d. 34, comes 

 next. My own correlation assigns a date to this 

 monument somewhere between the years 284 to 

 304 A.D., which an assumption made by both Mr. 

 Bowditch and Professor Seler in their correlations 

 would narrow to A.D. 294. Finally, the passage 

 from The Book of Chilan Balam of Mani, as I 

 have amended it, gives the date of this monument 

 as a.d. 282. 



The Ethnologist-in-Charge, F. W. Hodge, in 

 his " Letter of Transmittal " of Morley's book 

 expresses himself thus: 



The earliest inscriptions now extant probably 

 date from about the beginning of the Christian 

 era, but such is the complexity of the glyphs and 

 subject-matter even at this early period, that in 

 order to estimate the age of the system it is neces- 

 sary to postulate a far greater antiquity for its 

 origin. 



For purposes of comparison, let us recall the 

 dates of the number systems of the Baby- 

 lonians and Hindus. The early Babylonians 

 possessed the principle of local value, but, so 

 far as now known, did not possess a zero. 

 About two centuries B.C. they did have a zero- 

 symbol, which was " not used in calculation, 

 nor does it always occur when units of any 

 order are lacking." 3 They did not employ it 

 systematically in writing numbers and not at 

 all in performing computations. The Hindus 

 certainly did not use their zero-symbol sys- 

 tematically in their decimal number-system 

 before probably the sixth century a.d.; the 

 earliest undoubted occurrence of our zero in 



2 S. G. Morley, ' ' The Correlation of Maya and 

 Christian Chronology," American Journal of 

 ArcluBology, Vol. 14, 1910, p. 204. 



3 D. E. Smith and L. C. Karpinski, ' ' Hindu- 

 Arabic Numerals," 1911, p. 51. 



India is a.d. 876. Mr. G. E. Kaye 4 mentions 

 a.d. 595 and a.d. 662 as dates when, as claimed 

 by some, Indian figures were known ; " on the 

 other hand it is held that there is no sound 

 evidence of the employment in India of a 

 place-value system earlier than about the ninth 

 century." 



In view of this, special interest attaches to 

 the occurrence of zero-symbols and the prin- 

 ciple of local value among the inhabitants of 

 the flat lands of Central America, at a period 

 as early as the beginning of the Christian era, 

 if not much earlier. It would seem that in 

 this invention, the Maya in Central America 

 possessed priority over the Asiatic peoples by 

 a margin of five or six centuries. 



The Maya number system is remarkable for 

 the extent of its early development. Records 

 of Maya calendars and chronology are numer- 

 ous and have been successfully deciphered. 

 In fact, " it must be admitted that very little 

 progress has been made in deciphering the 

 Maya glyphs except those relating to the 

 calendar and chronology; that is, the signs for 

 the various time periods (days and months), 

 the numerals, and a few name-glyphs; how- 

 ever, as these known signs comprise possibly 

 two fifths of all the glyphs, it is clear that 

 the general tenor of the Maya inscriptions is 

 no longer concealed from us." 5 As far as 

 known, the Maya used their numeral systems 

 only in the counting of time, as it arose in 

 their calendar, ritual and astronomy. Many 

 numbers that are found in inscriptions and 

 codices occur in connection with signs, the 

 meanings of which have not yet been ascer- 

 tained. Hence, after the meanings of more 

 glyphs are deciphered, it may be found that 

 the numeral system had much wider applica- 

 tion than is evident at present. 



Of the several Maya numeral notations we 

 briefly describe the one which is of greatest 

 interest to mathematicians on account of its 

 embodying the principle of local value and the 

 use of symbols for zero. It is found in Maya 

 codices, but not in their inscriptions. The 



* G. R. Kaye, ' ' Indian Mathematics, ' ' Calcutta 

 and Simla, 1915, p. 31. 



5 S. G. Morley, op. cit., p. iv. 



