304 On the Systems of Numerical Signs 



a certain awkwardness in the numerical command of language 

 and writing is a very false standard of what is called the state 

 of cultivation of mankind. Here the same complicated and 

 contrasted relations to each other take place, as with nations, 

 of which some possess an alphabet, or mere ideographical signs, 

 some have the most luxuriant abundance of grammatical forms 

 and flexions, rising out of the root in systematical progressidrt^ 

 whilst others use languages destitute of forms and flexions, as 

 if benumbed in their very birth ; and all this in the most dif- 

 ferent gradations of intellectual culture and political institu- 

 tions. So the one race of mankind finds itself driven in the 

 most opposite directions by the alternate action of the internal 

 and external world, (an alternate action whose first decisive 

 eflbrts are wrapped up in the mythological darkness of the 

 remotest antiquity) ; keeping most stedfastly to its old nature, 

 even when great revolutions of the world bring geographi- 

 cally near to each other races the most heterogeneous in 

 language : whilst the similarity of the sounds which re-echo 

 from the remotest zones, in grammatical forms of language, and 

 graphic attempts to express large numbers, proves the unity of 

 the old stock — the ascendancy of that which springs out of 

 the internal intelligence, out of the common organization of 

 mankind. 



Travellers observing that some nations formed heaps of five 

 or twenty pebbles or grains of seed, when they were about to 

 make a computation, asserted that these nations were fiot 

 capable to count farther than till five or twenty^, ^ b'i^.r?iSo 



As^ well may it be asserted that the Europeans are hot 

 capable of counting farther than ten, because seventeen is com- 

 pounded of seven and ten. In the language of the most cul- 

 tivated nations of the west, for instance in those of the Greeks 

 and Romans, some expressions are yet preserved, which refer 

 evidently to such heaps or groups, ■^£(pl^siv, ponere calculani^ 

 calculum detrahere. Groups of unities prociire resting-place^ 

 in countinjr; and as in the different nations the members of 

 the body are similarly formed (the four extremities are divided 

 fivefoldly) they stop either after having counted the fip^^b of 



ill .ji 



* Pauw, Reclierchcs Philos. sur les Am6ricains, ft.fA,l»f/*ig^8»iri(H«iiiboldt; 

 Monuraeus Ainericain8;t.B.j;p.^32— -237.) .sVo\«m°>5\ o«\W ) ?;>v^.u.v. 



