board gave rise to the great discovery of the principle of 
position in the early centuries of our era. By simply putting 3 
and 4 and 2 in position on the board, one after another, it was 
possible to step up the speed and potential of calculation 
fantastically. The discovery of calculation by positional 
numbers rather than by merely additive numbers led, also, to 
the discovery of zero . Mere positions for 3 and 2 on the board 
created ambiguities about whether the number was 32 or 302. 
The need was to have a sign for the gaps between numbers. It 
was not till the thirteenth century that sifr , the Arab word for 
“gap” or “empty,” was Latinized and added to our culture as 
“cipher” (ziphirum ) and finally became the Italian zero . Zero 
really meant a positional gap. It did not acquire the 
indispensable quality of “infinity” until the rise of perspective 
and “vanishing point” in Renaissance painting. The new visual 
space of Renaissance painting affected number as much as