I spent much of this morning browsing in The Cornell Library of Mathematics Monographs, following cues from Dr. Renfro on the Math Forum, one of our more scholarly filers. I found myself reading The Hindu-Arabic Numerals (1911) by Smith and Karpinski, wondering to what extent I might find corroboration for Bucky Fuller's curious telling in his Everything I Know, of the introduction of ciphers to Europe at the end of the dark ages:I'm quite certain that the Arabic numerals represented a symbol for the content of the columns; and when they moved over and left an empty column, they had to have the cipher, so the Arabic numerals had the cipher. [1]Our authors above do a fine job of describing how a mercantile class would have had calculating proficiency far in advance of what school men would have needed, but with only the latter having the time, training (and inclination) to write scholarly treatises. So the formal teaching of algorithms within the curriculum lagged practical applications by some centuries (a well known pattern, especially before the printing press). Bagdad (spelled with no h) was indeed a cultural center for both the formal and informal teaching of such technologies.
However, despite a lengthy discussion of numerals inheriting from sand-drawn abacus characters (so-called gobar numbers), the need for an actual symbol to mark an empty abacus column, versus simply a blank space, gets bleeped over, which seems to me a blind spot, as Fuller's hypothesis is highly credible.
