674 AMERICAN ANTHROPOLOGIST [n. s., i, 1899
Suggestive vestiges of the mystical number-groups persist widely in the form of irrational and functionless supernumeraries, such as the thirteenth loaf in the baker's dozen, the twenty-first skerret in the coster's score, the thousand-and-first night of Arabian tale, and the conventional overplus in the legal " year and a day." It is possible that the supernumerary habit was crystallized in some cases by simple object-counting so con- ducted as to include an additional object as a tally ; but there are many indications that the habit originally sprang from alma- cabalic augmentation, in which the sum is always one more than the multiple. Moreover, the supernumerary habit is especially characteristic of countries and culture-stages in which mystical number-jumbles are rife.
The various vestiges (which are far too many for full enumera- tion) at once illumine pre-rational numeration, and establish the course of development of number concepts suggested by the customs of peoples still living in the lower culture stages ; while conversely the definition of almacabala serves to explain certain curious vestiges of primitive thought prevailing even today and in the highest culture.
VI
The way from alchemy to chemistry was long and devious, as shown by a voluminous literature worth scanning only as a means of tracing the growth of knowledge ; the way from astrology to astronomy was still longer and more devious, as shown by loose straws of both literature and lore ; and the way from almacabala through algorism to the rational science of quantities must have been longest and most devious of all. Yet it is worth while to gather and arrange the shreds of record and tradition which alone remain to mark the original way, and to compare them with the more abundant remnants of similar lines now followed by lower races — for these shreds, scanty though they be, define the birth of science.
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