Marco Cimarosti wrote:
> Eliotte Rusty Harold wrote (on unicode@...):
> > Today's European digits like 0, 1, 2, and 3 are actually closer to
> > the original Hindu glyphs from 1000 years ago than to true Arabic
> > numerals.

About 0, that is for sure. About 2, I believe the contrary, see below.

> > Both Arabic and European digits derive from the original
> > sources in India.

There are two different schools here. One claims for a direct heritage
from India to some place in Mediteranean Europa, while the other claims
for a (or more precisely, some, maybe more than one) Arabic step(s).

I am not sure (to say the least) the issue is clearly resolved.
But it looks like scholars are still hotly debating the issue. And as
it often happens in similar cases, political issues that have nothing
to do with the problem do complexify the issue (such as, "we discovered
the Xxxx heritage independently..." hope you see the picture).

> > however, the Arabic numerals had to shift a lot
> > more to make for convenient writing in the right-to-left script
> > system employed in Arabic than in the left-to-right printed system
> > used in the West in the Middle Ages.

Others explain that the forms used in (Latin) Europe were derived from
the rotated forms of the Arabs, with a further rotation... This is
particularly valid for digit 2.

> I think that the early (Italian? Spanish?) mathematicians who adopted the
> "Arabic" digits actually used the Arabic glyphs (which, BTW, at that timer
> were probably more similar to Hindi glyphs that they are today). I assume
> that those mathematicians had a working knowledge of written Arabic because
> they needed to use Arabic ("Moresque") math manuals.

I think this is worse than that: I think that the early mathematicians,
particularly the Spanish ones, who adopted the Arab glyphs, were actually
writing in Arabic! ;-)

By the way: this happened around the XIth century. As far as I remember (my
source is obviously Georges Ifrah's /Histoire universelle des chiffres/),
there are two different (identified) "discoveries" of the Arab digits in
European manuscripts, the latter (XIIIth century IIRC) being much more
probably the source for our present system.
Typography matters only later (in fact, the invention of typography is
one of the limit that departs Middle Ages from Modern Times).

> I think that the great differentiation came when typographers engraved the
> types to print math books, trying to "harmonize" the digits to the Latin
> Letters.

Same process did apply for Arabic as well, obviously with a very different
result, since the evolution were not comparable ;-).

> However, looking at the shape of some digits (e.g., "2" and "3") I wondered
> too whether these glyph had undergone 45 degree rotations during their
> travel from LTR Indic scripts through RTL Arabic script to LTR European
> scripts.

I would say, two 90 degree rotations, first clockwise, then contrary clockwise.
For 2, there are a lot of material to elaborate on this hypothesis (a number of
variations appear in the so-called "apices" numbers, including mirroring forms,
that give credits to this hypothesis). I have no good explanations for the
figure 90, however, even if I know the relative position of the hand vs. the
support is quite different between LTR and RTL (look after a left-hand writer
to understand what I mean).