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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