TIME INNUMERABLE




"Experience and long time -- which may always display and promote what does not exist, as well as throw into oblivion and hide what happened as if it never existed ("long and innumerable time unearths the hidden and hides the uncovered", said a certain sage ) -- revealed to us a most handy and safe method, which was always known to the thoroughly learned and most scholarly Persians, yet never reached us, but remained obscure in the lands west of us and only recently became known to certain Latins in Italy; a method that we learned thanks to our association with Latins who visited us frequently for the sake of commerce. And I think that this method has not been available and known to certain people in Italy for more than one hundred years, and this undertaking was not known to us Greek speakers. And now time has revealed that to us, too. And in order not to allow time to throw again into oblivion -- which it can always achieve, as stated above -- a method not yet spread and established, but rather unknown to many, we think that it is fair and even necessary to describe it here, so that it will become familiar to those who do not know and are willing to master it."

These words come (in my translation) from the introduction to an anonymous Greek manuscript (Codex phil. gr. 65 of Austrian National Library) dated 1555-1562, as published by J. L. Heiberg in "Abhandlungen zur Geschichte der Mathematik" (Byzantinische Analekten 9, 1899, pp. 161-174) and quoted in Nikos Kastanis' dissertation on "The introduction of Mathematics into Neohellenic Education" (Aristotle University, 2001). And the 'new method' is the Hindu-Arabic number notation, already described by Maximos Planoudes in his "Psifoforia kat' Indous" ... close to two hundred, rather than just one hundred, years before the manuscript in question. Putting everything together, we see that what we today know as Arabic numeral system reached the Greek world through the West and took at least two centuries to become prevalent there (with the printing of "Logariastiki" (BIBLION PROCHEIRON TOIS PASI...) in Venice in 1569). What I would like to know concerns reactions against the new system in the Christian World, western and eastern alike: reactions natural under the circumstances and even implied by the facts, but not necessarily documented. [Notice that even "Logariastiki" contains a method for the finding of the date of Easter that employs the Greek numeral system (in contrast to the rest of the book).]

[posted on BYZANS-L on May 3, 2001]

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