MCGEE] SIGNIFICANCE OF VESTIGES 851 
concept.1. The most conspicuous and persistent graphic vestiges are 
those of the barbaric Roman notation, which barred arithmetical prog- 
ress for ages, and even to-day saps vitality by its crude extravagance 
in form and function. In certain aspects this notation may be consid- 
ered binary, or rather dichotomous, and a reciprocal of the bifurcate 
classification of Aristotle with the Tree of Porphyry,’ although, as has 
been well shown by Cushing, the integers of the ystem stand for 
fingers and represent in their combinations the ordinary inger-counts 
employed throughout the lower medial strata of cultural development. 
In reality the system is neither perfectly binary nor fully quinary, 
and still less is it susceptible (by reason of the indefiniteness® as well 
as the inelasticity of the notation) of development into a complete 
decimal system; yet its survival as a mere enumerative system opens 
a vista through the millenniums to a thought-plane in which men man- 
aged to exist without arithmetic, without number systems save of the 
crudest, without numerical bases of ratiocination, without traceable 
germs of ideas now fundamental in daily thought. The Chinese 
number symbols also show traces of genesis and development from the 
lowly plane of finger-counting; but to the Aryan mind the most strik-| 
ing vestiges of essentially prescriptorial thought relating to numbers 
are those conserved in the Roman notation. 
The various vestiges, verbal, proverbial, and graphic (vestiges far 
too many for full enumeration), at once illumine prerational numera- 
tion and seem to establish that course of development of number- 
concepts suggested by the customs of people still living in the lower 
culture-stages. Conversely, the definition of almacabala serves to 
explain certain 2urious vestiges of primitive thought prevailing even 
today and in the highest culture; and the vestiges and developmental 
outlines combine to form a useful means of tracing the general course 
of intellectual progress from the obscure beginnings in lower savagery 
toward the present culmination in modern enlightenment. 


1Manual Concepts, American Anthropologist, vol. v, 1892, pp. 289-317. [t is to be observed that 
throughout this luminous discussion, than in which his genius never shone more brightly, Cushing 
confined himself to the middle strata of development in which numerical concepts are quinary, and 
in which counting is habitually manual, and made no reference to the lower strata of numerical 
conceptuality represesented by peoples less advanced than the Zufi. 
2The Foundation of Science, The Forum, vol. xxv, 1899, p. 177. 
8Thus a prodigal publisher may burden his title-page with the cabala mpcccci; if a shade less 
prodigal of ink, he may substitute the sign mpcp1; orif still more economical of ink and no less 
inconsiderate of the convenience of readers, he may recast the formula as McMI. 
